R<x>:=PolynomialRing(Rationals());
S<a> := PolynomialRing(Rationals());
T<q> := PowerSeriesRing(S);

J := [rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> : 
         i in [1..500]];

J[1] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.141 seconds




J[2] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.18 seconds




J[3] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.16 seconds




J[5] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.16 seconds




J[6] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.181 seconds




J[7] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.149 seconds




J[10] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.169 seconds




J[11] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 11 ], new_dimensions := [ 1 ], dimensions := [ 1 ], intersection_graph := [ 0 ], ap_traces := [
[ -2, -1, 1, -2, 1, 4, -2, 0, -1, 0, 7, 3 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 5 ]
], tamagawa_numbers := [
[ 5 ]
], torsion_upper_bounds := [ 5 ], torsion_lower_bounds := [ 5 ], l_ratios := [ 1/5 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ -2, -1, 1, -2, 1, 4, -2, 0, -1, 0, 7, 3 ]
*], q_expansions := [*
q - 2*q^2 - q^3 + 2*q^4 + q^5 + 2*q^6 - 2*q^7 - 2*q^9 - 2*q^10 + q^11 - 2*q^12 + 4*q^13 + 4*q^14 - q^15 - 4*q^16 - 2*q^17 + 4*q^18 + 2*q^20 + 2*q^21 - 2*q^22 - q^23 - 4*q^25 - 8*q^26 + 5*q^27 - 4*q^28 + 2*q^30 + 7*q^31 + 8*q^32 - q^33 + 4*q^34 - 2*q^35 - 4*q^36 + 3*q^37 + O(q^38)
*]> ;  // time = 0.52 seconds




J[13] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.16 seconds




J[14] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 14 ], new_dimensions := [ 1 ], dimensions := [ 1 ], intersection_graph := [ 0 ], ap_traces := [
[ -1, -2, 0, 1, 0, -4, 6, 2, 0, -6, -4, 2 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ 1, -1 ]
], component_group_orders := [
[ 3, 3 ]
], tamagawa_numbers := [
[ 1, 3 ]
], torsion_upper_bounds := [ 3 ], torsion_lower_bounds := [ 3 ], l_ratios := [ 1/3 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ -1, -2, 0, 1, 0, -4, 6, 2, 0, -6, -4, 2 ]
*], q_expansions := [*
q - q^2 - 2*q^3 + q^4 + 2*q^6 + q^7 - q^8 + q^9 - 2*q^12 - 4*q^13 - q^14 + q^16 + 6*q^17 - q^18 + 2*q^19 - 2*q^21 + 2*q^24 - 5*q^25 + 4*q^26 + 4*q^27 + q^28 - 6*q^29 - 4*q^31 - q^32 - 6*q^34 + q^36 + 2*q^37 + O(q^38)
*]> ;  // time = 2.601 seconds




J[15] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 15 ], new_dimensions := [ 1 ], dimensions := [ 1 ], intersection_graph := [ 0 ], ap_traces := [
[ -1, -1, 1, 0, -4, -2, 2, 4, 0, -2, 0, -10 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ]
], torsion_upper_bounds := [ 1 ], torsion_lower_bounds := [ 1 ], l_ratios := [ 1 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ -1, -1, 1, 0, -4, -2, 2, 4, 0, -2, 0, -10 ]
*], q_expansions := [*
q - q^2 - q^3 - q^4 + q^5 + q^6 + 3*q^8 + q^9 - q^10 - 4*q^11 + q^12 - 2*q^13 - q^15 - q^16 + 2*q^17 - q^18 + 4*q^19 - q^20 + 4*q^22 - 3*q^24 + q^25 + 2*q^26 - q^27 - 2*q^29 + q^30 - 5*q^32 + 4*q^33 - 2*q^34 - q^36 - 10*q^37 + O(q^38)
*]> ;  // time = 1.81 seconds




J[17] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 17 ], new_dimensions := [ 1 ], dimensions := [ 1 ], intersection_graph := [ 0 ], ap_traces := [
[ -1, 0, -2, 4, 0, -2, 1, -4, 4, 6, 4, -2 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 1 ]
], tamagawa_numbers := [
[ 1 ]
], torsion_upper_bounds := [ 1 ], torsion_lower_bounds := [ 1 ], l_ratios := [ 1 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ -1, 0, -2, 4, 0, -2, 1, -4, 4, 6, 4, -2 ]
*], q_expansions := [*
q - q^2 - q^4 - 2*q^5 + 4*q^7 + 3*q^8 - 3*q^9 + 2*q^10 - 2*q^13 - 4*q^14 - q^16 + q^17 + 3*q^18 - 4*q^19 + 2*q^20 + 4*q^23 - q^25 + 2*q^26 - 4*q^28 + 6*q^29 + 4*q^31 - 5*q^32 - q^34 - 8*q^35 + 3*q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 0.509 seconds




J[19] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 19 ], new_dimensions := [ 1 ], dimensions := [ 1 ], intersection_graph := [ 0 ], ap_traces := [
[ 0, -2, 3, -1, 3, -4, -3, 1, 0, 6, -4, 2 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 3 ]
], tamagawa_numbers := [
[ 3 ]
], torsion_upper_bounds := [ 3 ], torsion_lower_bounds := [ 3 ], l_ratios := [ 1/3 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ 0, -2, 3, -1, 3, -4, -3, 1, 0, 6, -4, 2 ]
*], q_expansions := [*
q - 2*q^3 - 2*q^4 + 3*q^5 - q^7 + q^9 + 3*q^11 + 4*q^12 - 4*q^13 - 6*q^15 + 4*q^16 - 3*q^17 + q^19 - 6*q^20 + 2*q^21 + 4*q^25 + 4*q^27 + 2*q^28 + 6*q^29 - 4*q^31 - 6*q^33 - 3*q^35 - 2*q^36 + 2*q^37 + O(q^38)
*]> ;  // time = 0.52 seconds




J[21] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 21 ], new_dimensions := [ 1 ], dimensions := [ 1 ], intersection_graph := [ 0 ], ap_traces := [
[ -1, 1, -2, -1, 4, -2, -6, 4, 0, -2, 0, 6 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ]
], torsion_upper_bounds := [ 1 ], torsion_lower_bounds := [ 1 ], l_ratios := [ 1 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ -1, 1, -2, -1, 4, -2, -6, 4, 0, -2, 0, 6 ]
*], q_expansions := [*
q - q^2 + q^3 - q^4 - 2*q^5 - q^6 - q^7 + 3*q^8 + q^9 + 2*q^10 + 4*q^11 - q^12 - 2*q^13 + q^14 - 2*q^15 - q^16 - 6*q^17 - q^18 + 4*q^19 + 2*q^20 - q^21 - 4*q^22 + 3*q^24 - q^25 + 2*q^26 + q^27 + q^28 - 2*q^29 + 2*q^30 - 5*q^32 + 4*q^33 + 6*q^34 + 2*q^35 - q^36 + 6*q^37 + O(q^38)
*]> ;  // time = 1.821 seconds




J[22] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 11 ], new_dimensions := [ 1 ], dimensions := [ 2 ], intersection_graph := [ 0 ], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.66 seconds




J[23] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 23 ], new_dimensions := [ 2 ], dimensions := [ 2 ], intersection_graph := [ 0 ], ap_traces := [
[ -1, 0, -2, 2, -6, 6, 6, -4, 2, -6, 0, 2 ]
], hecke_fields := [
x^2 + x - 1
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 11 ]
], tamagawa_numbers := [
[ 11 ]
], torsion_upper_bounds := [ 11 ], torsion_lower_bounds := [ 11 ], l_ratios := [ 1/11 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[
a,
-2*a - 1,
2*a,
2*a + 2,
-2*a - 4,
3,
-2*a + 2,
-2,
1,
-3,
6*a + 3,
-2*a
]
*], q_expansions := [*
q + a*q^2 + (-2*a - 1)*q^3 + (-a - 1)*q^4 + 2*a*q^5 + (a - 2)*q^6 + (2*a + 2)*q^7 + (-2*a - 1)*q^8 + 2*q^9 + (-2*a + 2)*q^10 + (-2*a - 4)*q^11 + (a + 3)*q^12 + 3*q^13 + 2*q^14 + (2*a - 4)*q^15 + 3*a*q^16 + (-2*a + 2)*q^17 + 2*a*q^18 - 2*q^19 - 2*q^20 + (-2*a - 6)*q^21 + (-2*a - 2)*q^22 + q^23 + 5*q^24 + (-4*a - 1)*q^25 + 3*a*q^26 + (2*a + 1)*q^27 + (-2*a - 4)*q^28 - 3*q^29 + (-6*a + 2)*q^30 + (6*a + 3)*q^31 + (a + 5)*q^32 + (6*a + 8)*q^33 + (4*a - 2)*q^34 + 4*q^35 + (-2*a - 2)*q^36 - 2*a*q^37 + O(q^38)
*]> ;  // time = 0.56 seconds




J[26] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 26, 26 ], new_dimensions := [ 1, 1 ], dimensions := [ 1, 1 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, 1, -3, -1, 6, 1, -3, 2, 0, 6, -4, -7 ],
[ 1, -3, -1, 1, -2, -1, -3, 6, -4, 2, 4, 3 ]
], hecke_fields := [
x - 1,
x - 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 3 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 7, 1 ]
], torsion_upper_bounds := [ 3, 7 ], torsion_lower_bounds := [ 3, 7 ], l_ratios := [ 1/3, 1/7 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ -1, 1, -3, -1, 6, 1, -3, 2, 0, 6, -4, -7 ],
[ 1, -3, -1, 1, -2, -1, -3, 6, -4, 2, 4, 3 ]
*], q_expansions := [*
q - q^2 + q^3 + q^4 - 3*q^5 - q^6 - q^7 - q^8 - 2*q^9 + 3*q^10 + 6*q^11 + q^12 + q^13 + q^14 - 3*q^15 + q^16 - 3*q^17 + 2*q^18 + 2*q^19 - 3*q^20 - q^21 - 6*q^22 - q^24 + 4*q^25 - q^26 - 5*q^27 - q^28 + 6*q^29 + 3*q^30 - 4*q^31 - q^32 + 6*q^33 + 3*q^34 + 3*q^35 - 2*q^36 - 7*q^37 + O(q^38),
q + q^2 - 3*q^3 + q^4 - q^5 - 3*q^6 + q^7 + q^8 + 6*q^9 - q^10 - 2*q^11 - 3*q^12 - q^13 + q^14 + 3*q^15 + q^16 - 3*q^17 + 6*q^18 + 6*q^19 - q^20 - 3*q^21 - 2*q^22 - 4*q^23 - 3*q^24 - 4*q^25 - q^26 - 9*q^27 + q^28 + 2*q^29 + 3*q^30 + 4*q^31 + q^32 + 6*q^33 - 3*q^34 - q^35 + 6*q^36 + 3*q^37 + O(q^38)
*]> ;  // time = 3.819 seconds




J[29] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 29 ], new_dimensions := [ 2 ], dimensions := [ 2 ], intersection_graph := [ 0 ], ap_traces := [
[ -2, 2, -2, 0, 2, -2, -4, 12, -4, 2, 6, -8 ]
], hecke_fields := [
x^2 + 2*x - 1
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 7 ]
], tamagawa_numbers := [
[ 7 ]
], torsion_upper_bounds := [ 7 ], torsion_lower_bounds := [ 7 ], l_ratios := [ 1/7 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[
a,
-a,
-1,
2*a + 2,
a + 2,
2*a + 1,
-2*a - 4,
6,
-4*a - 6,
1,
-5*a - 2,
-4
]
*], q_expansions := [*
q + a*q^2 - a*q^3 + (-2*a - 1)*q^4 - q^5 + (2*a - 1)*q^6 + (2*a + 2)*q^7 + (a - 2)*q^8 + (-2*a - 2)*q^9 - a*q^10 + (a + 2)*q^11 + (-3*a + 2)*q^12 + (2*a + 1)*q^13 + (-2*a + 2)*q^14 + a*q^15 + 3*q^16 + (-2*a - 4)*q^17 + (2*a - 2)*q^18 + 6*q^19 + (2*a + 1)*q^20 + (2*a - 2)*q^21 + q^22 + (-4*a - 6)*q^23 + (4*a - 1)*q^24 - 4*q^25 + (-3*a + 2)*q^26 + (a + 2)*q^27 + (2*a - 6)*q^28 + q^29 + (-2*a + 1)*q^30 + (-5*a - 2)*q^31 + (a + 4)*q^32 - q^33 - 2*q^34 + (-2*a - 2)*q^35 + (-2*a + 6)*q^36 - 4*q^37 + O(q^38)
*]> ;  // time = 0.58 seconds




J[30] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 30, 15 ], new_dimensions := [ 1, 1 ], dimensions := [ 1, 2 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, 1, -1, -4, 0, 2, 6, -4, 0, -6, 8, 2 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ 1, -1, 1 ]
], component_group_orders := [
[ 1, 3, 1 ]
], tamagawa_numbers := [
[ 1, 3, 1 ]
], torsion_upper_bounds := [ 3 ], torsion_lower_bounds := [ 3 ], l_ratios := [ 1/3 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ -1, 1, -1, -4, 0, 2, 6, -4, 0, -6, 8, 2 ]
*], q_expansions := [*
q - q^2 + q^3 + q^4 - q^5 - q^6 - 4*q^7 - q^8 + q^9 + q^10 + q^12 + 2*q^13 + 4*q^14 - q^15 + q^16 + 6*q^17 - q^18 - 4*q^19 - q^20 - 4*q^21 - q^24 + q^25 - 2*q^26 + q^27 - 4*q^28 - 6*q^29 + q^30 + 8*q^31 - q^32 - 6*q^34 + 4*q^35 + q^36 + 2*q^37 + O(q^38)
*]> ;  // time = 10.479 seconds




J[31] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 31 ], new_dimensions := [ 2 ], dimensions := [ 2 ], intersection_graph := [ 0 ], ap_traces := [
[ 1, -2, 2, -4, 4, -2, 6, 0, -2, 10, 2, -4 ]
], hecke_fields := [
x^2 - x - 1
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 5 ]
], tamagawa_numbers := [
[ 5 ]
], torsion_upper_bounds := [ 5 ], torsion_lower_bounds := [ 5 ], l_ratios := [ 1/5 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[
a,
-2*a,
1,
2*a - 3,
2,
-2*a,
-2*a + 4,
-2*a + 1,
6*a - 4,
-2*a + 6,
1,
-2
]
*], q_expansions := [*
q + a*q^2 - 2*a*q^3 + (a - 1)*q^4 + q^5 + (-2*a - 2)*q^6 + (2*a - 3)*q^7 + (-2*a + 1)*q^8 + (4*a + 1)*q^9 + a*q^10 + 2*q^11 - 2*q^12 - 2*a*q^13 + (-a + 2)*q^14 - 2*a*q^15 - 3*a*q^16 + (-2*a + 4)*q^17 + (5*a + 4)*q^18 + (-2*a + 1)*q^19 + (a - 1)*q^20 + (2*a - 4)*q^21 + 2*a*q^22 + (6*a - 4)*q^23 + (2*a + 4)*q^24 - 4*q^25 + (-2*a - 2)*q^26 + (-4*a - 8)*q^27 + (-3*a + 5)*q^28 + (-2*a + 6)*q^29 + (-2*a - 2)*q^30 + q^31 + (a - 5)*q^32 - 4*a*q^33 + (2*a - 2)*q^34 + (2*a - 3)*q^35 + (a + 3)*q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 0.56 seconds




J[33] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 33, 11 ], new_dimensions := [ 1, 1 ], dimensions := [ 1, 2 ], intersection_graph := [ 0, 3, 3, 0 ], ap_traces := [
[ 1, -1, -2, 4, 1, -2, -2, 0, 8, -6, -8, 6 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ 1, -1 ]
], component_group_orders := [
[ 3, 1 ]
], tamagawa_numbers := [
[ 1, 1 ]
], torsion_upper_bounds := [ 1 ], torsion_lower_bounds := [ 1 ], l_ratios := [ 1 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ 1, -1, -2, 4, 1, -2, -2, 0, 8, -6, -8, 6 ]
*], q_expansions := [*
q + q^2 - q^3 - q^4 - 2*q^5 - q^6 + 4*q^7 - 3*q^8 + q^9 - 2*q^10 + q^11 + q^12 - 2*q^13 + 4*q^14 + 2*q^15 - q^16 - 2*q^17 + q^18 + 2*q^20 - 4*q^21 + q^22 + 8*q^23 + 3*q^24 - q^25 - 2*q^26 - q^27 - 4*q^28 - 6*q^29 + 2*q^30 - 8*q^31 + 5*q^32 - q^33 - 2*q^34 - 8*q^35 - q^36 + 6*q^37 + O(q^38)
*]> ;  // time = 2.76 seconds




J[34] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 34, 17 ], new_dimensions := [ 1, 1 ], dimensions := [ 1, 2 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ 1, -2, 0, -4, 6, 2, -1, -4, 0, 0, -4, -4 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ -1, 1 ]
], component_group_orders := [
[ 3, 1 ]
], tamagawa_numbers := [
[ 3, 1 ]
], torsion_upper_bounds := [ 3 ], torsion_lower_bounds := [ 3 ], l_ratios := [ 1/3 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ 1, -2, 0, -4, 6, 2, -1, -4, 0, 0, -4, -4 ]
*], q_expansions := [*
q + q^2 - 2*q^3 + q^4 - 2*q^6 - 4*q^7 + q^8 + q^9 + 6*q^11 - 2*q^12 + 2*q^13 - 4*q^14 + q^16 - q^17 + q^18 - 4*q^19 + 8*q^21 + 6*q^22 - 2*q^24 - 5*q^25 + 2*q^26 + 4*q^27 - 4*q^28 - 4*q^31 + q^32 - 12*q^33 - q^34 + q^36 - 4*q^37 + O(q^38)
*]> ;  // time = 3.571 seconds




J[35] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 35, 35 ], new_dimensions := [ 1, 2 ], dimensions := [ 1, 2 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ 0, 1, -1, 1, -3, 5, 3, 2, -6, 3, -4, 2 ],
[ -1, -1, 2, -2, 1, 5, -5, -6, -2, 1, 0, 12 ]
], hecke_fields := [
x - 1,
x^2 + x - 4
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 3 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 3, 1 ], torsion_lower_bounds := [ 3, 1 ], l_ratios := [ 1/3, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ 0, 1, -1, 1, -3, 5, 3, 2, -6, 3, -4, 2 ],
[
a,
-a - 1,
1,
-1,
a + 1,
a + 3,
-a - 3,
2*a - 2,
-2*a - 2,
-3*a - 1,
0,
6
]
*], q_expansions := [*
q + q^3 - 2*q^4 - q^5 + q^7 - 2*q^9 - 3*q^11 - 2*q^12 + 5*q^13 - q^15 + 4*q^16 + 3*q^17 + 2*q^19 + 2*q^20 + q^21 - 6*q^23 + q^25 - 5*q^27 - 2*q^28 + 3*q^29 - 4*q^31 - 3*q^33 - q^35 + 4*q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (-a + 2)*q^4 + q^5 - 4*q^6 - q^7 + (a - 4)*q^8 + (a + 2)*q^9 + a*q^10 + (a + 1)*q^11 + (-2*a + 2)*q^12 + (a + 3)*q^13 - a*q^14 + (-a - 1)*q^15 - 3*a*q^16 + (-a - 3)*q^17 + (a + 4)*q^18 + (2*a - 2)*q^19 + (-a + 2)*q^20 + (a + 1)*q^21 + 4*q^22 + (-2*a - 2)*q^23 + 4*a*q^24 + q^25 + (2*a + 4)*q^26 + (a - 3)*q^27 + (a - 2)*q^28 + (-3*a - 1)*q^29 - 4*q^30 + (a - 4)*q^32 + (-a - 5)*q^33 + (-2*a - 4)*q^34 - q^35 + a*q^36 + 6*q^37 + O(q^38)
*]> ;  // time = 3.46 seconds




J[37] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 37, 37 ], new_dimensions := [ 1, 1 ], dimensions := [ 1, 1 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -2, -3, -2, -1, -5, -2, 0, 0, 2, 6, -4, -1 ],
[ 0, 1, 0, -1, 3, -4, 6, 2, 6, -6, -4, 1 ]
], hecke_fields := [
x - 1,
x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 3 ]
], tamagawa_numbers := [
[ 1 ],
[ 3 ]
], torsion_upper_bounds := [ 1, 3 ], torsion_lower_bounds := [ 1, 3 ], l_ratios := [ 0, 1/3 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ -2, -3, -2, -1, -5, -2, 0, 0, 2, 6, -4, -1 ],
[ 0, 1, 0, -1, 3, -4, 6, 2, 6, -6, -4, 1 ]
*], q_expansions := [*
q - 2*q^2 - 3*q^3 + 2*q^4 - 2*q^5 + 6*q^6 - q^7 + 6*q^9 + 4*q^10 - 5*q^11 - 6*q^12 - 2*q^13 + 2*q^14 + 6*q^15 - 4*q^16 - 12*q^18 - 4*q^20 + 3*q^21 + 10*q^22 + 2*q^23 - q^25 + 4*q^26 - 9*q^27 - 2*q^28 + 6*q^29 - 12*q^30 - 4*q^31 + 8*q^32 + 15*q^33 + 2*q^35 + 12*q^36 - q^37 + O(q^38),
q + q^3 - 2*q^4 - q^7 - 2*q^9 + 3*q^11 - 2*q^12 - 4*q^13 + 4*q^16 + 6*q^17 + 2*q^19 - q^21 + 6*q^23 - 5*q^25 - 5*q^27 + 2*q^28 - 6*q^29 - 4*q^31 + 3*q^33 + 4*q^36 + q^37 + O(q^38)
*]> ;  // time = 0.64 seconds




J[38] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 38, 38, 19 ], new_dimensions := [ 1, 1, 1 ], dimensions := [ 1, 1, 2 ], intersection_graph := [ 0, 1, 3, 1, 0, 1, 3, 1, 0 ], ap_traces := [
[ -1, 1, 0, -1, -6, 5, 3, 1, 3, 9, -4, 2 ],
[ 1, -1, -4, 3, 2, -1, 3, -1, -1, -5, -8, -2 ]
], hecke_fields := [
x - 1,
x - 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 9, 3 ],
[ 5, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 5, 1 ]
], torsion_upper_bounds := [ 3, 5 ], torsion_lower_bounds := [ 3, 5 ], l_ratios := [ 1/3, 1/5 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ -1, 1, 0, -1, -6, 5, 3, 1, 3, 9, -4, 2 ],
[ 1, -1, -4, 3, 2, -1, 3, -1, -1, -5, -8, -2 ]
*], q_expansions := [*
q - q^2 + q^3 + q^4 - q^6 - q^7 - q^8 - 2*q^9 - 6*q^11 + q^12 + 5*q^13 + q^14 + q^16 + 3*q^17 + 2*q^18 + q^19 - q^21 + 6*q^22 + 3*q^23 - q^24 - 5*q^25 - 5*q^26 - 5*q^27 - q^28 + 9*q^29 - 4*q^31 - q^32 - 6*q^33 - 3*q^34 - 2*q^36 + 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 4*q^5 - q^6 + 3*q^7 + q^8 - 2*q^9 - 4*q^10 + 2*q^11 - q^12 - q^13 + 3*q^14 + 4*q^15 + q^16 + 3*q^17 - 2*q^18 - q^19 - 4*q^20 - 3*q^21 + 2*q^22 - q^23 - q^24 + 11*q^25 - q^26 + 5*q^27 + 3*q^28 - 5*q^29 + 4*q^30 - 8*q^31 + q^32 - 2*q^33 + 3*q^34 - 12*q^35 - 2*q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 4.451 seconds




J[39] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 39, 39 ], new_dimensions := [ 1, 2 ], dimensions := [ 1, 2 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ 1, -1, 2, -4, 4, 1, 2, 0, 0, -10, 4, -2 ],
[ -2, 2, 0, 0, -4, -2, 4, 0, -8, 4, -8, -4 ]
], hecke_fields := [
x - 1,
x^2 + 2*x - 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 7, 1 ]
], torsion_upper_bounds := [ 1, 7 ], torsion_lower_bounds := [ 1, 7 ], l_ratios := [ 1, 1/7 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ 1, -1, 2, -4, 4, 1, 2, 0, 0, -10, 4, -2 ],
[
a,
1,
-2*a - 2,
2*a + 2,
-2,
-1,
4*a + 6,
-2*a - 2,
-4,
2,
2*a - 2,
-4*a - 6
]
*], q_expansions := [*
q + q^2 - q^3 - q^4 + 2*q^5 - q^6 - 4*q^7 - 3*q^8 + q^9 + 2*q^10 + 4*q^11 + q^12 + q^13 - 4*q^14 - 2*q^15 - q^16 + 2*q^17 + q^18 - 2*q^20 + 4*q^21 + 4*q^22 + 3*q^24 - q^25 + q^26 - q^27 + 4*q^28 - 10*q^29 - 2*q^30 + 4*q^31 + 5*q^32 - 4*q^33 + 2*q^34 - 8*q^35 - q^36 - 2*q^37 + O(q^38),
q + a*q^2 + q^3 + (-2*a - 1)*q^4 + (-2*a - 2)*q^5 + a*q^6 + (2*a + 2)*q^7 + (a - 2)*q^8 + q^9 + (2*a - 2)*q^10 - 2*q^11 + (-2*a - 1)*q^12 - q^13 + (-2*a + 2)*q^14 + (-2*a - 2)*q^15 + 3*q^16 + (4*a + 6)*q^17 + a*q^18 + (-2*a - 2)*q^19 + (-2*a + 6)*q^20 + (2*a + 2)*q^21 - 2*a*q^22 - 4*q^23 + (a - 2)*q^24 + 3*q^25 - a*q^26 + q^27 + (2*a - 6)*q^28 + 2*q^29 + (2*a - 2)*q^30 + (2*a - 2)*q^31 + (a + 4)*q^32 - 2*q^33 + (-2*a + 4)*q^34 - 8*q^35 + (-2*a - 1)*q^36 + (-4*a - 6)*q^37 + O(q^38)
*]> ;  // time = 3.229 seconds




J[41] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 41 ], new_dimensions := [ 3 ], dimensions := [ 3 ], intersection_graph := [ 0 ], ap_traces := [
[ -1, 0, -2, 6, 2, -2, -6, 4, 4, -6, 16, -6 ]
], hecke_fields := [
x^3 + x^2 - 5*x - 1
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 5 ]
], tamagawa_numbers := [
[ 5 ]
], torsion_upper_bounds := [ 5 ], torsion_lower_bounds := [ 5 ], l_ratios := [ 1/5 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[
a,
-1/2*a^2 - a + 3/2,
-a - 1,
1/2*a^2 + a + 1/2,
3/2*a^2 + a - 9/2,
-a^2 + 3,
-2,
-3/2*a^2 - a + 13/2,
-2*a^2 - 2*a + 8,
a^2 + 2*a - 5,
2*a + 6,
-3*a - 3
]
*], q_expansions := [*
q + a*q^2 + (-1/2*a^2 - a + 3/2)*q^3 + (a^2 - 2)*q^4 + (-a - 1)*q^5 + (-1/2*a^2 - a - 1/2)*q^6 + (1/2*a^2 + a + 1/2)*q^7 + (-a^2 + a + 1)*q^8 + a*q^9 + (-a^2 - a)*q^10 + (3/2*a^2 + a - 9/2)*q^11 + (1/2*a^2 - a - 7/2)*q^12 + (-a^2 + 3)*q^13 + (1/2*a^2 + 3*a + 1/2)*q^14 + (a^2 + 2*a - 1)*q^15 + (-4*a + 3)*q^16 - 2*q^17 + a^2*q^18 + (-3/2*a^2 - a + 13/2)*q^19 + (-3*a + 1)*q^20 + (-a^2 - 3*a)*q^21 + (-1/2*a^2 + 3*a + 3/2)*q^22 + (-2*a^2 - 2*a + 8)*q^23 + (-1/2*a^2 + a + 3/2)*q^24 + (a^2 + 2*a - 4)*q^25 + (a^2 - 2*a - 1)*q^26 + (a^2 + 2*a - 5)*q^27 + (3/2*a^2 + a - 1/2)*q^28 + (a^2 + 2*a - 5)*q^29 + (a^2 + 4*a + 1)*q^30 + (2*a + 6)*q^31 + (-2*a^2 + a - 2)*q^32 + (a^2 - a - 8)*q^33 - 2*a*q^34 + (-a^2 - 4*a - 1)*q^35 + (-a^2 + 3*a + 1)*q^36 + (-3*a - 3)*q^37 + O(q^38)
*]> ;  // time = 0.649 seconds




J[42] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 42, 21, 14 ], new_dimensions := [ 1, 1, 1 ], dimensions := [ 1, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 0, 1, 1, 1, 0 ], ap_traces := [
[ 1, -1, -2, -1, -4, 6, 2, -4, 8, -2, 0, -10 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ -1, 1, 1 ]
], component_group_orders := [
[ 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1 ], torsion_lower_bounds := [ 1 ], l_ratios := [ 1 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ 1, -1, -2, -1, -4, 6, 2, -4, 8, -2, 0, -10 ]
*], q_expansions := [*
q + q^2 - q^3 + q^4 - 2*q^5 - q^6 - q^7 + q^8 + q^9 - 2*q^10 - 4*q^11 - q^12 + 6*q^13 - q^14 + 2*q^15 + q^16 + 2*q^17 + q^18 - 4*q^19 - 2*q^20 + q^21 - 4*q^22 + 8*q^23 - q^24 - q^25 + 6*q^26 - q^27 - q^28 - 2*q^29 + 2*q^30 + q^32 + 4*q^33 + 2*q^34 + 2*q^35 + q^36 - 10*q^37 + O(q^38)
*]> ;  // time = 11.65 seconds




J[43] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 43, 43 ], new_dimensions := [ 1, 2 ], dimensions := [ 1, 2 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -2, -2, -4, 0, 3, -5, -3, -2, -1, -6, -1, 0 ],
[ 0, 0, 4, -4, -2, 2, 10, -4, 2, 0, -6, 0 ]
], hecke_fields := [
x - 1,
x^2 - 2
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 7 ]
], tamagawa_numbers := [
[ 1 ],
[ 7 ]
], torsion_upper_bounds := [ 1, 7 ], torsion_lower_bounds := [ 1, 7 ], l_ratios := [ 0, 1/7 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ -2, -2, -4, 0, 3, -5, -3, -2, -1, -6, -1, 0 ],
[
a,
-a,
-a + 2,
a - 2,
2*a - 1,
2*a + 1,
2*a + 5,
-2*a - 2,
-4*a + 1,
3*a,
-3,
-6*a
]
*], q_expansions := [*
q - 2*q^2 - 2*q^3 + 2*q^4 - 4*q^5 + 4*q^6 + q^9 + 8*q^10 + 3*q^11 - 4*q^12 - 5*q^13 + 8*q^15 - 4*q^16 - 3*q^17 - 2*q^18 - 2*q^19 - 8*q^20 - 6*q^22 - q^23 + 11*q^25 + 10*q^26 + 4*q^27 - 6*q^29 - 16*q^30 - q^31 + 8*q^32 - 6*q^33 + 6*q^34 + 2*q^36 + O(q^38),
q + a*q^2 - a*q^3 + (-a + 2)*q^5 - 2*q^6 + (a - 2)*q^7 - 2*a*q^8 - q^9 + (2*a - 2)*q^10 + (2*a - 1)*q^11 + (2*a + 1)*q^13 + (-2*a + 2)*q^14 + (-2*a + 2)*q^15 - 4*q^16 + (2*a + 5)*q^17 - a*q^18 + (-2*a - 2)*q^19 + (2*a - 2)*q^21 + (-a + 4)*q^22 + (-4*a + 1)*q^23 + 4*q^24 + (-4*a + 1)*q^25 + (a + 4)*q^26 + 4*a*q^27 + 3*a*q^29 + (2*a - 4)*q^30 - 3*q^31 + (a - 4)*q^33 + (5*a + 4)*q^34 + (4*a - 6)*q^35 - 6*a*q^37 + O(q^38)
*]> ;  // time = 0.699 seconds




J[46] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 46, 23 ], new_dimensions := [ 1, 2 ], dimensions := [ 1, 4 ], intersection_graph := [ 0, 5, 5, 0 ], ap_traces := [
[ -1, 0, 4, -4, 2, -2, -2, -2, 1, 2, 0, -4 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ 1, -1 ]
], component_group_orders := [
[ 5, 1 ]
], tamagawa_numbers := [
[ 1, 1 ]
], torsion_upper_bounds := [ 1 ], torsion_lower_bounds := [ 1 ], l_ratios := [ 1 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ -1, 0, 4, -4, 2, -2, -2, -2, 1, 2, 0, -4 ]
*], q_expansions := [*
q - q^2 + q^4 + 4*q^5 - 4*q^7 - q^8 - 3*q^9 - 4*q^10 + 2*q^11 - 2*q^13 + 4*q^14 + q^16 - 2*q^17 + 3*q^18 - 2*q^19 + 4*q^20 - 2*q^22 + q^23 + 11*q^25 + 2*q^26 - 4*q^28 + 2*q^29 - q^32 + 2*q^34 - 16*q^35 - 3*q^36 - 4*q^37 + O(q^38)
*]> ;  // time = 4.579 seconds




J[47] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 47 ], new_dimensions := [ 4 ], dimensions := [ 4 ], intersection_graph := [ 0 ], ap_traces := [
[ 1, 0, -2, 4, -6, 8, 6, 0, -6, -10, -8, 10 ]
], hecke_fields := [
x^4 - x^3 - 5*x^2 + 5*x - 1
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 23 ]
], tamagawa_numbers := [
[ 23 ]
], torsion_upper_bounds := [ 23 ], torsion_lower_bounds := [ 23 ], l_ratios := [ 1/23 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[
a,
a^3 - a^2 - 6*a + 4,
-4*a^3 + 2*a^2 + 20*a - 10,
3*a^3 - a^2 - 16*a + 7,
2*a^3 - 2*a^2 - 10*a + 6,
-4*a^3 + 2*a^2 + 22*a - 8,
a^3 + a^2 - 6*a,
-2*a^3 + 10*a - 2,
-2*a^3 + 12*a - 4,
-2*a^3 + 2*a^2 + 10*a - 10,
4*a^3 - 2*a^2 - 22*a + 8,
3*a^3 - a^2 - 14*a + 8
]
*], q_expansions := [*
q + a*q^2 + (a^3 - a^2 - 6*a + 4)*q^3 + (a^2 - 2)*q^4 + (-4*a^3 + 2*a^2 + 20*a - 10)*q^5 + (-a^2 - a + 1)*q^6 + (3*a^3 - a^2 - 16*a + 7)*q^7 + (a^3 - 4*a)*q^8 + (3*a^3 - a^2 - 14*a + 6)*q^9 + (-2*a^3 + 10*a - 4)*q^10 + (2*a^3 - 2*a^2 - 10*a + 6)*q^11 + (-3*a^3 + a^2 + 13*a - 8)*q^12 + (-4*a^3 + 2*a^2 + 22*a - 8)*q^13 + (2*a^3 - a^2 - 8*a + 3)*q^14 + (-4*a^3 + 4*a^2 + 22*a - 16)*q^15 + (a^3 - a^2 - 5*a + 5)*q^16 + (a^3 + a^2 - 6*a)*q^17 + (2*a^3 + a^2 - 9*a + 3)*q^18 + (-2*a^3 + 10*a - 2)*q^19 + (6*a^3 - 4*a^2 - 34*a + 18)*q^20 + (2*a^3 - 2*a^2 - 12*a + 9)*q^21 + (-4*a + 2)*q^22 + (-2*a^3 + 12*a - 4)*q^23 + (-2*a^3 + 9*a - 5)*q^24 + (4*a^3 - 4*a^2 - 20*a + 19)*q^25 + (-2*a^3 + 2*a^2 + 12*a - 4)*q^26 + (-2*a^3 + 10*a - 5)*q^27 + (-5*a^3 + 4*a^2 + 25*a - 12)*q^28 + (-2*a^3 + 2*a^2 + 10*a - 10)*q^29 + (2*a^2 + 4*a - 4)*q^30 + (4*a^3 - 2*a^2 - 22*a + 8)*q^31 + (-2*a^3 + 8*a + 1)*q^32 + (4*a^3 - 2*a^2 - 18*a + 12)*q^33 + (2*a^3 - a^2 - 5*a + 1)*q^34 + (2*a^2 - 2*a - 10)*q^35 + (-3*a^3 + 3*a^2 + 21*a - 10)*q^36 + (3*a^3 - a^2 - 14*a + 8)*q^37 + O(q^38)
*]> ;  // time = 0.701 seconds




J[51] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 51, 51, 17 ], new_dimensions := [ 1, 2, 1 ], dimensions := [ 1, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 0, 1, 1, 1, 0 ], ap_traces := [
[ 0, 1, 3, -4, -3, -1, -1, -1, 9, 6, 2, -4 ],
[ -1, -2, 3, 0, -1, 5, 2, 3, -9, 0, -2, -2 ]
], hecke_fields := [
x - 1,
x^2 + x - 4
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 3, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 3, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 3, 1 ], torsion_lower_bounds := [ 3, 1 ], l_ratios := [ 1/3, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ 0, 1, 3, -4, -3, -1, -1, -1, 9, 6, 2, -4 ],
[
a,
-1,
-a + 1,
0,
-a - 1,
a + 3,
1,
3*a + 3,
-a - 5,
4*a + 2,
-2*a - 2,
2*a
]
*], q_expansions := [*
q + q^3 - 2*q^4 + 3*q^5 - 4*q^7 + q^9 - 3*q^11 - 2*q^12 - q^13 + 3*q^15 + 4*q^16 - q^17 - q^19 - 6*q^20 - 4*q^21 + 9*q^23 + 4*q^25 + q^27 + 8*q^28 + 6*q^29 + 2*q^31 - 3*q^33 - 12*q^35 - 2*q^36 - 4*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a + 2)*q^4 + (-a + 1)*q^5 - a*q^6 + (a - 4)*q^8 + q^9 + (2*a - 4)*q^10 + (-a - 1)*q^11 + (a - 2)*q^12 + (a + 3)*q^13 + (a - 1)*q^15 - 3*a*q^16 + q^17 + a*q^18 + (3*a + 3)*q^19 + (-4*a + 6)*q^20 - 4*q^22 + (-a - 5)*q^23 + (-a + 4)*q^24 - 3*a*q^25 + (2*a + 4)*q^26 - q^27 + (4*a + 2)*q^29 + (-2*a + 4)*q^30 + (-2*a - 2)*q^31 + (a - 4)*q^32 + (a + 1)*q^33 + a*q^34 + (-a + 2)*q^36 + 2*a*q^37 + O(q^38)
*]> ;  // time = 4.25 seconds




J[53] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 53, 53 ], new_dimensions := [ 1, 3 ], dimensions := [ 1, 3 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -3, 0, -4, 0, -3, -3, -5, 7, -7, 4, 5 ],
[ -1, 3, -2, 4, -4, 3, -5, 11, 3, -5, -2, -5 ]
], hecke_fields := [
x - 1,
x^3 + x^2 - 3*x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 13 ]
], tamagawa_numbers := [
[ 1 ],
[ 13 ]
], torsion_upper_bounds := [ 1, 13 ], torsion_lower_bounds := [ 1, 13 ], l_ratios := [ 0, 1/13 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ -1, -3, 0, -4, 0, -3, -3, -5, 7, -7, 4, 5 ],
[
a,
-a^2 - a + 3,
a^2 - 3,
a^2 - 1,
a^2 + 2*a - 3,
1,
2*a - 1,
a + 4,
2*a^2 - a - 4,
-3*a^2 - 4*a + 4,
-a^2 + 4*a + 3,
a^2 + 6*a - 2
]
*], q_expansions := [*
q - q^2 - 3*q^3 - q^4 + 3*q^6 - 4*q^7 + 3*q^8 + 6*q^9 + 3*q^12 - 3*q^13 + 4*q^14 - q^16 - 3*q^17 - 6*q^18 - 5*q^19 + 12*q^21 + 7*q^23 - 9*q^24 - 5*q^25 + 3*q^26 - 9*q^27 + 4*q^28 - 7*q^29 + 4*q^31 - 5*q^32 + 3*q^34 - 6*q^36 + 5*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 3)*q^3 + (a^2 - 2)*q^4 + (a^2 - 3)*q^5 - q^6 + (a^2 - 1)*q^7 + (-a^2 - a + 1)*q^8 + (-3*a^2 - 2*a + 7)*q^9 + (-a^2 + 1)*q^10 + (a^2 + 2*a - 3)*q^11 + (2*a^2 + a - 6)*q^12 + q^13 + (-a^2 + 2*a + 1)*q^14 + (3*a^2 + 2*a - 9)*q^15 + (-2*a^2 - 2*a + 3)*q^16 + (2*a - 1)*q^17 + (a^2 - 2*a - 3)*q^18 + (a + 4)*q^19 + (-a^2 - 2*a + 5)*q^20 + (a^2 - 3)*q^21 + (a^2 + 1)*q^22 + (2*a^2 - a - 4)*q^23 + (-a^2 + 4)*q^24 + (-2*a^2 - 2*a + 3)*q^25 + a*q^26 + (-4*a^2 - a + 14)*q^27 + (a^2 - 2*a + 1)*q^28 + (-3*a^2 - 4*a + 4)*q^29 + (-a^2 + 3)*q^30 + (-a^2 + 4*a + 3)*q^31 + (2*a^2 - a - 4)*q^32 + (3*a^2 + 2*a - 11)*q^33 + (2*a^2 - a)*q^34 + (-2*a + 2)*q^35 + (3*a^2 + 4*a - 13)*q^36 + (a^2 + 6*a - 2)*q^37 + O(q^38)
*]> ;  // time = 0.79 seconds




J[55] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 55, 55, 11 ], new_dimensions := [ 1, 2, 1 ], dimensions := [ 1, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 0, 7, 1, 7, 0 ], ap_traces := [
[ 1, 0, 1, 0, -1, 2, 6, -4, 4, 6, -8, -2 ],
[ 2, 0, -2, -4, 2, -8, 8, 0, 0, 4, 0, -4 ]
], hecke_fields := [
x - 1,
x^2 - 2*x - 1
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1 ], torsion_lower_bounds := [ 1, 1 ], l_ratios := [ 1, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ 1, 0, 1, 0, -1, 2, 6, -4, 4, 6, -8, -2 ],
[
a,
-2*a + 2,
-1,
-2,
1,
2*a - 6,
2*a + 2,
0,
-2*a + 2,
-4*a + 6,
0,
-4*a + 2
]
*], q_expansions := [*
q + q^2 - q^4 + q^5 - 3*q^8 - 3*q^9 + q^10 - q^11 + 2*q^13 - q^16 + 6*q^17 - 3*q^18 - 4*q^19 - q^20 - q^22 + 4*q^23 + q^25 + 2*q^26 + 6*q^29 - 8*q^31 + 5*q^32 + 6*q^34 + 3*q^36 - 2*q^37 + O(q^38),
q + a*q^2 + (-2*a + 2)*q^3 + (2*a - 1)*q^4 - q^5 + (-2*a - 2)*q^6 - 2*q^7 + (a + 2)*q^8 + 5*q^9 - a*q^10 + q^11 + (-2*a - 6)*q^12 + (2*a - 6)*q^13 - 2*a*q^14 + (2*a - 2)*q^15 + 3*q^16 + (2*a + 2)*q^17 + 5*a*q^18 + (-2*a + 1)*q^20 + (4*a - 4)*q^21 + a*q^22 + (-2*a + 2)*q^23 + (-6*a + 2)*q^24 + q^25 + (-2*a + 2)*q^26 + (-4*a + 4)*q^27 + (-4*a + 2)*q^28 + (-4*a + 6)*q^29 + (2*a + 2)*q^30 + (a - 4)*q^32 + (-2*a + 2)*q^33 + (6*a + 2)*q^34 + 2*q^35 + (10*a - 5)*q^36 + (-4*a + 2)*q^37 + O(q^38)
*]> ;  // time = 4.151 seconds




J[57] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 57, 57, 57, 19 ], new_dimensions := [ 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 0, 3, 1, 1, 3, 0, 1, 1, 1, 1, 0 ], ap_traces := [
[ -2, -1, -3, -5, 1, 2, -1, -1, -4, -2, -6, 0 ],
[ 1, 1, -2, 0, 0, 6, -6, -1, 4, 2, 8, -10 ],
[ -2, 1, 1, 3, -3, -6, 3, -1, 4, -10, 2, 8 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 5, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 5, 1 ]
], torsion_upper_bounds := [ 1, 1, 5 ], torsion_lower_bounds := [ 1, 1, 5 ], l_ratios := [ 0, 1, 1/5 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ -2, -1, -3, -5, 1, 2, -1, -1, -4, -2, -6, 0 ],
[ 1, 1, -2, 0, 0, 6, -6, -1, 4, 2, 8, -10 ],
[ -2, 1, 1, 3, -3, -6, 3, -1, 4, -10, 2, 8 ]
*], q_expansions := [*
q - 2*q^2 - q^3 + 2*q^4 - 3*q^5 + 2*q^6 - 5*q^7 + q^9 + 6*q^10 + q^11 - 2*q^12 + 2*q^13 + 10*q^14 + 3*q^15 - 4*q^16 - q^17 - 2*q^18 - q^19 - 6*q^20 + 5*q^21 - 2*q^22 - 4*q^23 + 4*q^25 - 4*q^26 - q^27 - 10*q^28 - 2*q^29 - 6*q^30 - 6*q^31 + 8*q^32 - q^33 + 2*q^34 + 15*q^35 + 2*q^36 + O(q^38),
q + q^2 + q^3 - q^4 - 2*q^5 + q^6 - 3*q^8 + q^9 - 2*q^10 - q^12 + 6*q^13 - 2*q^15 - q^16 - 6*q^17 + q^18 - q^19 + 2*q^20 + 4*q^23 - 3*q^24 - q^25 + 6*q^26 + q^27 + 2*q^29 - 2*q^30 + 8*q^31 + 5*q^32 - 6*q^34 - q^36 - 10*q^37 + O(q^38),
q - 2*q^2 + q^3 + 2*q^4 + q^5 - 2*q^6 + 3*q^7 + q^9 - 2*q^10 - 3*q^11 + 2*q^12 - 6*q^13 - 6*q^14 + q^15 - 4*q^16 + 3*q^17 - 2*q^18 - q^19 + 2*q^20 + 3*q^21 + 6*q^22 + 4*q^23 - 4*q^25 + 12*q^26 + q^27 + 6*q^28 - 10*q^29 - 2*q^30 + 2*q^31 + 8*q^32 - 3*q^33 - 6*q^34 + 3*q^35 + 2*q^36 + 8*q^37 + O(q^38)
*]> ;  // time = 4.781 seconds




J[58] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 58, 58, 29 ], new_dimensions := [ 1, 1, 2 ], dimensions := [ 1, 1, 4 ], intersection_graph := [ 0, 1, 1, 1, 0, 1, 1, 1, 0 ], ap_traces := [
[ -1, -3, -3, -2, -1, 3, -4, -8, 0, -1, 3, -8 ],
[ 1, -1, 1, -2, -3, -1, 8, 0, 4, -1, -3, 8 ]
], hecke_fields := [
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 5, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 5, 1 ]
], torsion_upper_bounds := [ 1, 5 ], torsion_lower_bounds := [ 1, 5 ], l_ratios := [ 0, 1/5 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ -1, -3, -3, -2, -1, 3, -4, -8, 0, -1, 3, -8 ],
[ 1, -1, 1, -2, -3, -1, 8, 0, 4, -1, -3, 8 ]
*], q_expansions := [*
q - q^2 - 3*q^3 + q^4 - 3*q^5 + 3*q^6 - 2*q^7 - q^8 + 6*q^9 + 3*q^10 - q^11 - 3*q^12 + 3*q^13 + 2*q^14 + 9*q^15 + q^16 - 4*q^17 - 6*q^18 - 8*q^19 - 3*q^20 + 6*q^21 + q^22 + 3*q^24 + 4*q^25 - 3*q^26 - 9*q^27 - 2*q^28 - q^29 - 9*q^30 + 3*q^31 - q^32 + 3*q^33 + 4*q^34 + 6*q^35 + 6*q^36 - 8*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 - 2*q^7 + q^8 - 2*q^9 + q^10 - 3*q^11 - q^12 - q^13 - 2*q^14 - q^15 + q^16 + 8*q^17 - 2*q^18 + q^20 + 2*q^21 - 3*q^22 + 4*q^23 - q^24 - 4*q^25 - q^26 + 5*q^27 - 2*q^28 - q^29 - q^30 - 3*q^31 + q^32 + 3*q^33 + 8*q^34 - 2*q^35 - 2*q^36 + 8*q^37 + O(q^38)
*]> ;  // time = 6.101 seconds




J[59] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 59 ], new_dimensions := [ 5 ], dimensions := [ 5 ], intersection_graph := [ 0 ], ap_traces := [
[ 0, -2, 2, 2, -2, 8, -1, 6, -8, 14, 0, 18 ]
], hecke_fields := [
x^5 - 9*x^3 + 2*x^2 + 16*x - 8
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 29 ]
], tamagawa_numbers := [
[ 29 ]
], torsion_upper_bounds := [ 29 ], torsion_lower_bounds := [ 29 ], l_ratios := [ 1/29 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[
a,
-1/4*a^4 + 5/4*a^2 - 1/2*a,
3/4*a^4 + 1/2*a^3 - 23/4*a^2 - 3*a + 7,
-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 3/2*a - 3,
-1/2*a^4 - a^3 + 9/2*a^2 + 6*a - 8,
-1/2*a^4 - a^3 + 9/2*a^2 + 6*a - 6,
a^4 - 8*a^2 + 9,
3/4*a^4 + 3/2*a^3 - 23/4*a^2 - 8*a + 9,
-1/2*a^4 + 9/2*a^2 + a - 8,
-a^4 - 1/2*a^3 + 8*a^2 + 1/2*a - 7,
a^4 + a^3 - 9*a^2 - 3*a + 14,
-a^4 + 7*a^2 - 2
]
*], q_expansions := [*
q + a*q^2 + (-1/4*a^4 + 5/4*a^2 - 1/2*a)*q^3 + (a^2 - 2)*q^4 + (3/4*a^4 + 1/2*a^3 - 23/4*a^2 - 3*a + 7)*q^5 + (-a^3 + 4*a - 2)*q^6 + (-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 3/2*a - 3)*q^7 + (a^3 - 4*a)*q^8 + (1/2*a^3 + a^2 - 5/2*a - 2)*q^9 + (1/2*a^4 + a^3 - 9/2*a^2 - 5*a + 6)*q^10 + (-1/2*a^4 - a^3 + 9/2*a^2 + 6*a - 8)*q^11 + (-1/2*a^4 + 3/2*a^2 - a)*q^12 + (-1/2*a^4 - a^3 + 9/2*a^2 + 6*a - 6)*q^13 + (-1/2*a^4 - a^3 + 5/2*a^2 + 5*a - 4)*q^14 + (1/4*a^4 + 1/2*a^3 - 9/4*a^2 - 2*a + 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 - 8*a^2 + 9)*q^17 + (1/2*a^4 + a^3 - 5/2*a^2 - 2*a)*q^18 + (3/4*a^4 + 3/2*a^3 - 23/4*a^2 - 8*a + 9)*q^19 + (-1/2*a^4 - a^3 + 11/2*a^2 + 4*a - 10)*q^20 + (-1/4*a^4 + a^3 + 9/4*a^2 - 7/2*a + 1)*q^21 + (-a^4 + 7*a^2 - 4)*q^22 + (-1/2*a^4 + 9/2*a^2 + a - 8)*q^23 - a^3*q^24 + (1/4*a^4 - a^3 - 13/4*a^2 + 11/2*a + 7)*q^25 + (-a^4 + 7*a^2 + 2*a - 4)*q^26 + (1/4*a^4 - 9/4*a^2 - 3/2*a + 1)*q^27 + (-a^3 - a^2 + a + 2)*q^28 + (-a^4 - 1/2*a^3 + 8*a^2 + 1/2*a - 7)*q^29 + (1/2*a^4 - 5/2*a^2 - 2*a + 2)*q^30 + (a^4 + a^3 - 9*a^2 - 3*a + 14)*q^31 + (a^3 - 2*a^2 - 4*a + 8)*q^32 + (-a^3 + 7*a - 4)*q^33 + (a^3 - 2*a^2 - 7*a + 8)*q^34 + (1/2*a^4 + 1/2*a^3 - 5/2*a^2 - 7/2*a - 2)*q^35 + (a^4 + a^3 - 5*a^2 - 3*a + 8)*q^36 + (-a^4 + 7*a^2 - 2)*q^37 + O(q^38)
*]> ;  // time = 0.759 seconds




J[61] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 61, 61 ], new_dimensions := [ 1, 3 ], dimensions := [ 1, 3 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -2, -3, 1, -5, 1, 4, -4, -9, -6, 0, 8 ],
[ 1, 2, -1, -3, 13, -9, -2, 0, 5, 4, -2, -6 ]
], hecke_fields := [
x - 1,
x^3 - x^2 - 3*x + 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 5 ]
], tamagawa_numbers := [
[ 1 ],
[ 5 ]
], torsion_upper_bounds := [ 1, 5 ], torsion_lower_bounds := [ 1, 5 ], l_ratios := [ 0, 1/5 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ -1, -2, -3, 1, -5, 1, 4, -4, -9, -6, 0, 8 ],
[
a,
-a^2 + 3,
a^2 - 2*a - 2,
a^2 - a - 3,
a + 4,
-2*a^2 + 2*a + 1,
-a^2 + 2*a + 1,
3*a^2 - 7,
-a + 2,
-a^2 + 2*a + 3,
-a^2 - 4*a + 3,
3*a^2 - 9
]
*], q_expansions := [*
q - q^2 - 2*q^3 - q^4 - 3*q^5 + 2*q^6 + q^7 + 3*q^8 + q^9 + 3*q^10 - 5*q^11 + 2*q^12 + q^13 - q^14 + 6*q^15 - q^16 + 4*q^17 - q^18 - 4*q^19 + 3*q^20 - 2*q^21 + 5*q^22 - 9*q^23 - 6*q^24 + 4*q^25 - q^26 + 4*q^27 - q^28 - 6*q^29 - 6*q^30 - 5*q^32 + 10*q^33 - 4*q^34 - 3*q^35 - q^36 + 8*q^37 + O(q^38),
q + a*q^2 + (-a^2 + 3)*q^3 + (a^2 - 2)*q^4 + (a^2 - 2*a - 2)*q^5 + (-a^2 + 1)*q^6 + (a^2 - a - 3)*q^7 + (a^2 - a - 1)*q^8 + (-2*a^2 + 2*a + 5)*q^9 + (-a^2 + a - 1)*q^10 + (a + 4)*q^11 + (a^2 - 2*a - 5)*q^12 + (-2*a^2 + 2*a + 1)*q^13 - q^14 + (3*a^2 - 2*a - 7)*q^15 + (-2*a^2 + 2*a + 3)*q^16 + (-a^2 + 2*a + 1)*q^17 + (-a + 2)*q^18 + (3*a^2 - 7)*q^19 + (-2*a^2 + 5)*q^20 + (3*a^2 - 2*a - 9)*q^21 + (a^2 + 4*a)*q^22 + (-a + 2)*q^23 + (a^2 - 2*a - 3)*q^24 + (-2*a + 2)*q^25 + (-5*a + 2)*q^26 + (-2*a^2 + 4*a + 6)*q^27 + (-2*a^2 + a + 6)*q^28 + (-a^2 + 2*a + 3)*q^29 + (a^2 + 2*a - 3)*q^30 + (-a^2 - 4*a + 3)*q^31 + (-2*a^2 - a + 4)*q^32 + (-5*a^2 + 13)*q^33 + (a^2 - 2*a + 1)*q^34 + (-2*a^2 + a + 8)*q^35 + (3*a^2 - 2*a - 10)*q^36 + (3*a^2 - 9)*q^37 + O(q^38)
*]> ;  // time = 0.81 seconds




J[62] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 62, 62, 31 ], new_dimensions := [ 1, 2, 2 ], dimensions := [ 1, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 0, 11, 1, 11, 0 ], ap_traces := [
[ 1, 0, -2, 0, 0, 2, -6, 4, 8, 2, -1, 10 ],
[ -2, 2, 0, 4, -6, -2, 0, -8, 0, -6, 2, 10 ]
], hecke_fields := [
x - 1,
x^2 - 2*x - 2
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 33, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 1, 3 ], torsion_lower_bounds := [ 1, 3 ], l_ratios := [ 1, 1/3 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ 1, 0, -2, 0, 0, 2, -6, 4, 8, 2, -1, 10 ],
[
-1,
a,
-2*a + 2,
2,
a - 4,
-3*a + 2,
2*a - 2,
-4,
0,
3*a - 6,
1,
3*a + 2
]
*], q_expansions := [*
q + q^2 + q^4 - 2*q^5 + q^8 - 3*q^9 - 2*q^10 + 2*q^13 + q^16 - 6*q^17 - 3*q^18 + 4*q^19 - 2*q^20 + 8*q^23 - q^25 + 2*q^26 + 2*q^29 - q^31 + q^32 - 6*q^34 - 3*q^36 + 10*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-2*a + 2)*q^5 - a*q^6 + 2*q^7 - q^8 + (2*a - 1)*q^9 + (2*a - 2)*q^10 + (a - 4)*q^11 + a*q^12 + (-3*a + 2)*q^13 - 2*q^14 + (-2*a - 4)*q^15 + q^16 + (2*a - 2)*q^17 + (-2*a + 1)*q^18 - 4*q^19 + (-2*a + 2)*q^20 + 2*a*q^21 + (-a + 4)*q^22 - a*q^24 + 7*q^25 + (3*a - 2)*q^26 + 4*q^27 + 2*q^28 + (3*a - 6)*q^29 + (2*a + 4)*q^30 + q^31 - q^32 + (-2*a + 2)*q^33 + (-2*a + 2)*q^34 + (-4*a + 4)*q^35 + (2*a - 1)*q^36 + (3*a + 2)*q^37 + O(q^38)
*]> ;  // time = 6.84 seconds




J[65] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 65, 65, 65 ], new_dimensions := [ 1, 2, 2 ], dimensions := [ 1, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 0, 1, 1, 1, 0 ], ap_traces := [
[ -1, -2, -1, -4, 2, -1, 2, -6, -6, 2, -10, -2 ],
[ 0, 2, -2, 4, -6, 2, 0, -2, 6, -12, 10, -8 ],
[ -2, 0, 2, 4, 4, -2, -4, 4, 0, 0, 12, 0 ]
], hecke_fields := [
x - 1,
x^2 - 3,
x^2 + 2*x - 1
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 3 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 3 ],
[ 7, 1 ]
], torsion_upper_bounds := [ 1, 3, 7 ], torsion_lower_bounds := [ 1, 3, 7 ], l_ratios := [ 0, 1/3, 1/7 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ -1, -2, -1, -4, 2, -1, 2, -6, -6, 2, -10, -2 ],
[
a,
-a + 1,
-1,
2,
a - 3,
1,
2*a,
3*a - 1,
a + 3,
-2*a - 6,
-3*a + 5,
-4
],
[
a,
a + 1,
1,
-2*a,
-a + 1,
-1,
-2*a - 4,
a + 3,
-a - 1,
4*a + 4,
3*a + 9,
6*a + 6
]
*], q_expansions := [*
q - q^2 - 2*q^3 - q^4 - q^5 + 2*q^6 - 4*q^7 + 3*q^8 + q^9 + q^10 + 2*q^11 + 2*q^12 - q^13 + 4*q^14 + 2*q^15 - q^16 + 2*q^17 - q^18 - 6*q^19 + q^20 + 8*q^21 - 2*q^22 - 6*q^23 - 6*q^24 + q^25 + q^26 + 4*q^27 + 4*q^28 + 2*q^29 - 2*q^30 - 10*q^31 - 5*q^32 - 4*q^33 - 2*q^34 + 4*q^35 - q^36 - 2*q^37 + O(q^38),
q + a*q^2 + (-a + 1)*q^3 + q^4 - q^5 + (a - 3)*q^6 + 2*q^7 - a*q^8 + (-2*a + 1)*q^9 - a*q^10 + (a - 3)*q^11 + (-a + 1)*q^12 + q^13 + 2*a*q^14 + (a - 1)*q^15 - 5*q^16 + 2*a*q^17 + (a - 6)*q^18 + (3*a - 1)*q^19 - q^20 + (-2*a + 2)*q^21 + (-3*a + 3)*q^22 + (a + 3)*q^23 + (-a + 3)*q^24 + q^25 + a*q^26 + 4*q^27 + 2*q^28 + (-2*a - 6)*q^29 + (-a + 3)*q^30 + (-3*a + 5)*q^31 - 3*a*q^32 + (4*a - 6)*q^33 + 6*q^34 - 2*q^35 + (-2*a + 1)*q^36 - 4*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + (-2*a - 1)*q^4 + q^5 + (-a + 1)*q^6 - 2*a*q^7 + (a - 2)*q^8 - q^9 + a*q^10 + (-a + 1)*q^11 + (a - 3)*q^12 - q^13 + (4*a - 2)*q^14 + (a + 1)*q^15 + 3*q^16 + (-2*a - 4)*q^17 - a*q^18 + (a + 3)*q^19 + (-2*a - 1)*q^20 + (2*a - 2)*q^21 + (3*a - 1)*q^22 + (-a - 1)*q^23 + (-3*a - 1)*q^24 + q^25 - a*q^26 + (-4*a - 4)*q^27 + (-6*a + 4)*q^28 + (4*a + 4)*q^29 + (-a + 1)*q^30 + (3*a + 9)*q^31 + (a + 4)*q^32 + 2*a*q^33 - 2*q^34 - 2*a*q^35 + (2*a + 1)*q^36 + (6*a + 6)*q^37 + O(q^38)
*]> ;  // time = 5.169 seconds




J[66] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 66, 66, 66, 33, 11 ], new_dimensions := [ 1, 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 5, 1, 1, 1, 0, 9, 1, 1, 5, 9, 0 ], ap_traces := [
[ -1, 1, 0, 2, -1, -4, -6, -4, 6, 6, 8, -10 ],
[ 1, -1, 2, -4, -1, -6, 2, 4, 4, 6, 0, 6 ],
[ 1, 1, -4, -2, 1, 4, -2, 0, -6, 10, -8, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 5, 5, 1 ]
], tamagawa_numbers := [
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 5, 5, 1 ]
], torsion_upper_bounds := [ 3, 1, 5 ], torsion_lower_bounds := [ 3, 1, 1 ], l_ratios := [ 1/3, 1, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1/25 ], eigenvalues := [*
[ -1, 1, 0, 2, -1, -4, -6, -4, 6, 6, 8, -10 ],
[ 1, -1, 2, -4, -1, -6, 2, 4, 4, 6, 0, 6 ],
[ 1, 1, -4, -2, 1, 4, -2, 0, -6, 10, -8, -2 ]
*], q_expansions := [*
q - q^2 + q^3 + q^4 - q^6 + 2*q^7 - q^8 + q^9 - q^11 + q^12 - 4*q^13 - 2*q^14 + q^16 - 6*q^17 - q^18 - 4*q^19 + 2*q^21 + q^22 + 6*q^23 - q^24 - 5*q^25 + 4*q^26 + q^27 + 2*q^28 + 6*q^29 + 8*q^31 - q^32 - q^33 + 6*q^34 + q^36 - 10*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + 2*q^5 - q^6 - 4*q^7 + q^8 + q^9 + 2*q^10 - q^11 - q^12 - 6*q^13 - 4*q^14 - 2*q^15 + q^16 + 2*q^17 + q^18 + 4*q^19 + 2*q^20 + 4*q^21 - q^22 + 4*q^23 - q^24 - q^25 - 6*q^26 - q^27 - 4*q^28 + 6*q^29 - 2*q^30 + q^32 + q^33 + 2*q^34 - 8*q^35 + q^36 + 6*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - 4*q^5 + q^6 - 2*q^7 + q^8 + q^9 - 4*q^10 + q^11 + q^12 + 4*q^13 - 2*q^14 - 4*q^15 + q^16 - 2*q^17 + q^18 - 4*q^20 - 2*q^21 + q^22 - 6*q^23 + q^24 + 11*q^25 + 4*q^26 + q^27 - 2*q^28 + 10*q^29 - 4*q^30 - 8*q^31 + q^32 + q^33 - 2*q^34 + 8*q^35 + q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 19.689 seconds




J[67] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 67, 67, 67 ], new_dimensions := [ 1, 2, 2 ], dimensions := [ 1, 2, 2 ], intersection_graph := [ 0, 1, 5, 1, 0, 1, 5, 1, 0 ], ap_traces := [
[ 2, -2, 2, -2, -4, 2, 3, 7, 9, -5, -10, -1 ],
[ -3, -3, -6, -1, 0, -7, -6, 1, 6, -6, -2, -1 ],
[ -1, 1, 4, 1, 2, -1, 6, -11, -2, 10, 0, 3 ]
], hecke_fields := [
x - 1,
x^2 + 3*x + 1,
x^2 + x - 1
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 11 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 11 ]
], torsion_upper_bounds := [ 1, 1, 11 ], torsion_lower_bounds := [ 1, 1, 11 ], l_ratios := [ 1, 0, 1/11 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ 2, -2, 2, -2, -4, 2, 3, 7, 9, -5, -10, -1 ],
[
a,
-a - 3,
-3,
3*a + 4,
-2*a - 3,
-3*a - 8,
-2*a - 6,
3*a + 5,
-4*a - 3,
4*a + 3,
-1,
3*a + 4
],
[
a,
a + 1,
-2*a + 1,
-a,
1,
a,
-2*a + 2,
a - 5,
4*a + 1,
4*a + 7,
6*a + 3,
a + 2
]
*], q_expansions := [*
q + 2*q^2 - 2*q^3 + 2*q^4 + 2*q^5 - 4*q^6 - 2*q^7 + q^9 + 4*q^10 - 4*q^11 - 4*q^12 + 2*q^13 - 4*q^14 - 4*q^15 - 4*q^16 + 3*q^17 + 2*q^18 + 7*q^19 + 4*q^20 + 4*q^21 - 8*q^22 + 9*q^23 - q^25 + 4*q^26 + 4*q^27 - 4*q^28 - 5*q^29 - 8*q^30 - 10*q^31 - 8*q^32 + 8*q^33 + 6*q^34 - 4*q^35 + 2*q^36 - q^37 + O(q^38),
q + a*q^2 + (-a - 3)*q^3 + (-3*a - 3)*q^4 - 3*q^5 + q^6 + (3*a + 4)*q^7 + (4*a + 3)*q^8 + (3*a + 5)*q^9 - 3*a*q^10 + (-2*a - 3)*q^11 + (3*a + 6)*q^12 + (-3*a - 8)*q^13 + (-5*a - 3)*q^14 + (3*a + 9)*q^15 + (-3*a + 2)*q^16 + (-2*a - 6)*q^17 + (-4*a - 3)*q^18 + (3*a + 5)*q^19 + (9*a + 9)*q^20 + (-4*a - 9)*q^21 + (3*a + 2)*q^22 + (-4*a - 3)*q^23 + (-3*a - 5)*q^24 + 4*q^25 + (a + 3)*q^26 + (-2*a - 3)*q^27 + (6*a - 3)*q^28 + (4*a + 3)*q^29 - 3*q^30 - q^31 + (3*a - 3)*q^32 + (3*a + 7)*q^33 + 2*q^34 + (-9*a - 12)*q^35 + (3*a - 6)*q^36 + (3*a + 4)*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + (-a - 1)*q^4 + (-2*a + 1)*q^5 + q^6 - a*q^7 + (-2*a - 1)*q^8 + (a - 1)*q^9 + (3*a - 2)*q^10 + q^11 + (-a - 2)*q^12 + a*q^13 + (a - 1)*q^14 + (a - 1)*q^15 + 3*a*q^16 + (-2*a + 2)*q^17 + (-2*a + 1)*q^18 + (a - 5)*q^19 + (-a + 1)*q^20 - q^21 + a*q^22 + (4*a + 1)*q^23 + (-a - 3)*q^24 - 8*a*q^25 + (-a + 1)*q^26 + (-4*a - 3)*q^27 + q^28 + (4*a + 7)*q^29 + (-2*a + 1)*q^30 + (6*a + 3)*q^31 + (a + 5)*q^32 + (a + 1)*q^33 + (4*a - 2)*q^34 + (-3*a + 2)*q^35 + a*q^36 + (a + 2)*q^37 + O(q^38)
*]> ;  // time = 0.94 seconds




J[69] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 69, 69, 23 ], new_dimensions := [ 1, 2, 2 ], dimensions := [ 1, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 0, 11, 1, 11, 0 ], ap_traces := [
[ 1, 1, 0, -2, 4, -6, 4, 2, -1, 2, 4, 2 ],
[ 0, -2, -2, 2, 8, 0, -10, 10, 2, 0, -4, 0 ]
], hecke_fields := [
x - 1,
x^2 - 5
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 11, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1 ], torsion_lower_bounds := [ 1, 1 ], l_ratios := [ 1, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ 1, 1, 0, -2, 4, -6, 4, 2, -1, 2, 4, 2 ],
[
a,
-1,
-a - 1,
-a + 1,
4,
2*a,
-a - 5,
-a + 5,
1,
-2*a,
2*a - 2,
-2*a
]
*], q_expansions := [*
q + q^2 + q^3 - q^4 + q^6 - 2*q^7 - 3*q^8 + q^9 + 4*q^11 - q^12 - 6*q^13 - 2*q^14 - q^16 + 4*q^17 + q^18 + 2*q^19 - 2*q^21 + 4*q^22 - q^23 - 3*q^24 - 5*q^25 - 6*q^26 + q^27 + 2*q^28 + 2*q^29 + 4*q^31 + 5*q^32 + 4*q^33 + 4*q^34 - q^36 + 2*q^37 + O(q^38),
q + a*q^2 - q^3 + 3*q^4 + (-a - 1)*q^5 - a*q^6 + (-a + 1)*q^7 + a*q^8 + q^9 + (-a - 5)*q^10 + 4*q^11 - 3*q^12 + 2*a*q^13 + (a - 5)*q^14 + (a + 1)*q^15 - q^16 + (-a - 5)*q^17 + a*q^18 + (-a + 5)*q^19 + (-3*a - 3)*q^20 + (a - 1)*q^21 + 4*a*q^22 + q^23 - a*q^24 + (2*a + 1)*q^25 + 10*q^26 - q^27 + (-3*a + 3)*q^28 - 2*a*q^29 + (a + 5)*q^30 + (2*a - 2)*q^31 - 3*a*q^32 - 4*q^33 + (-5*a - 5)*q^34 + 4*q^35 + 3*q^36 - 2*a*q^37 + O(q^38)
*]> ;  // time = 5.06 seconds




J[70] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 70, 35, 35, 14 ], new_dimensions := [ 1, 1, 2, 1 ], dimensions := [ 1, 2, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 0, 1, 3, 1, 1, 0, 1, 1, 3, 1, 0 ], ap_traces := [
[ 1, 0, -1, -1, 4, -6, 2, 0, 0, 6, 8, -10 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ -1, 1, 1 ]
], component_group_orders := [
[ 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1 ], torsion_lower_bounds := [ 1 ], l_ratios := [ 1 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ 1, 0, -1, -1, 4, -6, 2, 0, 0, 6, 8, -10 ]
*], q_expansions := [*
q + q^2 + q^4 - q^5 - q^7 + q^8 - 3*q^9 - q^10 + 4*q^11 - 6*q^13 - q^14 + q^16 + 2*q^17 - 3*q^18 - q^20 + 4*q^22 + q^25 - 6*q^26 - q^28 + 6*q^29 + 8*q^31 + q^32 + 2*q^34 + q^35 - 3*q^36 - 10*q^37 + O(q^38)
*]> ;  // time = 14.431 seconds




J[71] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 71, 71 ], new_dimensions := [ 3, 3 ], dimensions := [ 3, 3 ], intersection_graph := [ 0, 9, 9, 0 ], ap_traces := [
[ 0, -1, -3, 2, -2, 12, 2, 11, 8, -5, -6, 9 ],
[ -1, 1, 5, 2, 0, -6, -2, 1, -12, 11, 12, -15 ]
], hecke_fields := [
x^3 - 5*x + 3,
x^3 + x^2 - 4*x - 3
], atkin_lehners := [
[ -1 ],
[ -1 ]
], component_group_orders := [
[ 5 ],
[ 7 ]
], tamagawa_numbers := [
[ 5 ],
[ 7 ]
], torsion_upper_bounds := [ 5, 7 ], torsion_lower_bounds := [ 5, 7 ], l_ratios := [ 1/5, 1/7 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
a,
-a^2 + 3,
-a - 1,
2*a^2 + 2*a - 6,
-2*a^2 - 2*a + 6,
4,
2*a^2 + 2*a - 6,
-a^2 - a + 7,
2*a^2 - 4,
a^2 + 2*a - 5,
-2*a - 2,
-3*a^2 - a + 13
],
[
a,
-a,
-a^2 + a + 5,
-2*a,
2*a^2 - 6,
-2*a^2 + 4,
2*a^2 + 2*a - 6,
a^2 + 2*a - 2,
-4,
-2*a^2 + a + 10,
4,
-a^2 - 2
]
*], q_expansions := [*
q + a*q^2 + (-a^2 + 3)*q^3 + (a^2 - 2)*q^4 + (-a - 1)*q^5 + (-2*a + 3)*q^6 + (2*a^2 + 2*a - 6)*q^7 + (a - 3)*q^8 + (-a^2 - 3*a + 6)*q^9 + (-a^2 - a)*q^10 + (-2*a^2 - 2*a + 6)*q^11 + (3*a - 6)*q^12 + 4*q^13 + (2*a^2 + 4*a - 6)*q^14 + (a^2 + 2*a - 6)*q^15 + (-a^2 - 3*a + 4)*q^16 + (2*a^2 + 2*a - 6)*q^17 + (-3*a^2 + a + 3)*q^18 + (-a^2 - a + 7)*q^19 + (-a^2 - 3*a + 5)*q^20 + (2*a^2 + 2*a - 12)*q^21 + (-2*a^2 - 4*a + 6)*q^22 + (2*a^2 - 4)*q^23 + (3*a^2 - 2*a - 6)*q^24 + (a^2 + 2*a - 4)*q^25 + 4*a*q^26 + (-a^2 + 3*a)*q^27 + 6*q^28 + (a^2 + 2*a - 5)*q^29 + (2*a^2 - a - 3)*q^30 + (-2*a - 2)*q^31 + (-3*a^2 - 3*a + 9)*q^32 + (-2*a^2 - 2*a + 12)*q^33 + (2*a^2 + 4*a - 6)*q^34 + (-4*a^2 - 6*a + 12)*q^35 + (3*a^2 - 6*a - 3)*q^36 + (-3*a^2 - a + 13)*q^37 + O(q^38),
q + a*q^2 - a*q^3 + (a^2 - 2)*q^4 + (-a^2 + a + 5)*q^5 - a^2*q^6 - 2*a*q^7 + (-a^2 + 3)*q^8 + (a^2 - 3)*q^9 + (2*a^2 + a - 3)*q^10 + (2*a^2 - 6)*q^11 + (a^2 - 2*a - 3)*q^12 + (-2*a^2 + 4)*q^13 - 2*a^2*q^14 + (-2*a^2 - a + 3)*q^15 + (-a^2 - a + 1)*q^16 + (2*a^2 + 2*a - 6)*q^17 + (-a^2 + a + 3)*q^18 + (a^2 + 2*a - 2)*q^19 + (a^2 + 3*a - 4)*q^20 + 2*a^2*q^21 + (-2*a^2 + 2*a + 6)*q^22 - 4*q^23 + (-a^2 + a + 3)*q^24 + (-2*a^2 + a + 11)*q^25 + (2*a^2 - 4*a - 6)*q^26 + (a^2 + 2*a - 3)*q^27 + (2*a^2 - 4*a - 6)*q^28 + (-2*a^2 + a + 10)*q^29 + (a^2 - 5*a - 6)*q^30 + 4*q^31 + (2*a^2 - 3*a - 9)*q^32 + (2*a^2 - 2*a - 6)*q^33 + (2*a + 6)*q^34 + (-4*a^2 - 2*a + 6)*q^35 + (-a + 3)*q^36 + (-a^2 - 2)*q^37 + O(q^38)
*]> ;  // time = 0.941 seconds




J[73] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 73, 73, 73 ], new_dimensions := [ 1, 2, 2 ], dimensions := [ 1, 2, 2 ], intersection_graph := [ 0, 1, 3, 1, 0, 1, 3, 1, 0 ], ap_traces := [
[ 1, 0, 2, 2, -2, -6, 2, 8, 4, 2, -2, -6 ],
[ -3, -3, -3, -6, -3, 1, 0, 2, -15, 6, 2, -4 ],
[ 1, 1, -1, -2, 7, -1, -4, -14, 13, 2, 6, 8 ]
], hecke_fields := [
x - 1,
x^2 + 3*x + 1,
x^2 - x - 3
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 3 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 3 ]
], torsion_upper_bounds := [ 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 3 ], l_ratios := [ 1, 0, 1/3 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ 1, 0, 2, 2, -2, -6, 2, 8, 4, 2, -2, -6 ],
[
a,
-a - 3,
a,
-3,
-a - 3,
3*a + 5,
-6*a - 9,
1,
a - 6,
-4*a - 3,
6*a + 10,
-6*a - 11
],
[
a,
-a + 1,
-a,
-1,
a + 3,
a - 1,
2*a - 3,
-7,
a + 6,
-4*a + 3,
2*a + 2,
-2*a + 5
]
*], q_expansions := [*
q + q^2 - q^4 + 2*q^5 + 2*q^7 - 3*q^8 - 3*q^9 + 2*q^10 - 2*q^11 - 6*q^13 + 2*q^14 - q^16 + 2*q^17 - 3*q^18 + 8*q^19 - 2*q^20 - 2*q^22 + 4*q^23 - q^25 - 6*q^26 - 2*q^28 + 2*q^29 - 2*q^31 + 5*q^32 + 2*q^34 + 4*q^35 + 3*q^36 - 6*q^37 + O(q^38),
q + a*q^2 + (-a - 3)*q^3 + (-3*a - 3)*q^4 + a*q^5 + q^6 - 3*q^7 + (4*a + 3)*q^8 + (3*a + 5)*q^9 + (-3*a - 1)*q^10 + (-a - 3)*q^11 + (3*a + 6)*q^12 + (3*a + 5)*q^13 - 3*a*q^14 + q^15 + (-3*a + 2)*q^16 + (-6*a - 9)*q^17 + (-4*a - 3)*q^18 + q^19 + (6*a + 3)*q^20 + (3*a + 9)*q^21 + q^22 + (a - 6)*q^23 + (-3*a - 5)*q^24 + (-3*a - 6)*q^25 + (-4*a - 3)*q^26 + (-2*a - 3)*q^27 + (9*a + 9)*q^28 + (-4*a - 3)*q^29 + a*q^30 + (6*a + 10)*q^31 + (3*a - 3)*q^32 + (3*a + 8)*q^33 + (9*a + 6)*q^34 - 3*a*q^35 + (3*a - 6)*q^36 + (-6*a - 11)*q^37 + O(q^38),
q + a*q^2 + (-a + 1)*q^3 + (a + 1)*q^4 - a*q^5 - 3*q^6 - q^7 + 3*q^8 + (-a + 1)*q^9 + (-a - 3)*q^10 + (a + 3)*q^11 + (-a - 2)*q^12 + (a - 1)*q^13 - a*q^14 + 3*q^15 + (a - 2)*q^16 + (2*a - 3)*q^17 - 3*q^18 - 7*q^19 + (-2*a - 3)*q^20 + (a - 1)*q^21 + (4*a + 3)*q^22 + (a + 6)*q^23 + (-3*a + 3)*q^24 + (a - 2)*q^25 + 3*q^26 + (2*a + 1)*q^27 + (-a - 1)*q^28 + (-4*a + 3)*q^29 + 3*a*q^30 + (2*a + 2)*q^31 + (-a - 3)*q^32 - 3*a*q^33 + (-a + 6)*q^34 + a*q^35 + (-a - 2)*q^36 + (-2*a + 5)*q^37 + O(q^38)
*]> ;  // time = 0.96 seconds




J[74] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 74, 74, 37, 37 ], new_dimensions := [ 2, 2, 1, 1 ], dimensions := [ 2, 2, 2, 2 ], intersection_graph := [ 0, 1, 1, 3, 1, 0, 5, 1, 1, 5, 0, 1, 3, 1, 1, 0 ], ap_traces := [
[ -2, 3, -1, 2, -1, -1, -12, 4, -3, 3, 3, 2 ],
[ 2, -1, 1, -2, -5, 1, 0, 0, -1, -3, 17, -2 ]
], hecke_fields := [
x^2 - 3*x - 1,
x^2 + x - 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 9, 3 ],
[ 95, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 95, 1 ]
], torsion_upper_bounds := [ 3, 19 ], torsion_lower_bounds := [ 3, 19 ], l_ratios := [ 1/3, 5/19 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
-1,
a,
-a + 1,
-2*a + 4,
-a + 1,
a - 2,
-6,
2,
3*a - 6,
-3*a + 6,
-a + 3,
1
],
[
1,
a,
-3*a - 1,
2*a,
-a - 3,
3*a + 2,
4*a + 2,
-4*a - 2,
-3*a - 2,
7*a + 2,
a + 9,
-1
]
*], q_expansions := [*
q - q^2 + a*q^3 + q^4 + (-a + 1)*q^5 - a*q^6 + (-2*a + 4)*q^7 - q^8 + (3*a - 2)*q^9 + (a - 1)*q^10 + (-a + 1)*q^11 + a*q^12 + (a - 2)*q^13 + (2*a - 4)*q^14 + (-2*a - 1)*q^15 + q^16 - 6*q^17 + (-3*a + 2)*q^18 + 2*q^19 + (-a + 1)*q^20 + (-2*a - 2)*q^21 + (a - 1)*q^22 + (3*a - 6)*q^23 - a*q^24 + (a - 3)*q^25 + (-a + 2)*q^26 + (4*a + 3)*q^27 + (-2*a + 4)*q^28 + (-3*a + 6)*q^29 + (2*a + 1)*q^30 + (-a + 3)*q^31 - q^32 + (-2*a - 1)*q^33 + 6*q^34 + 6*q^35 + (3*a - 2)*q^36 + q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-3*a - 1)*q^5 + a*q^6 + 2*a*q^7 + q^8 + (-a - 2)*q^9 + (-3*a - 1)*q^10 + (-a - 3)*q^11 + a*q^12 + (3*a + 2)*q^13 + 2*a*q^14 + (2*a - 3)*q^15 + q^16 + (4*a + 2)*q^17 + (-a - 2)*q^18 + (-4*a - 2)*q^19 + (-3*a - 1)*q^20 + (-2*a + 2)*q^21 + (-a - 3)*q^22 + (-3*a - 2)*q^23 + a*q^24 + (-3*a + 5)*q^25 + (3*a + 2)*q^26 + (-4*a - 1)*q^27 + 2*a*q^28 + (7*a + 2)*q^29 + (2*a - 3)*q^30 + (a + 9)*q^31 + q^32 + (-2*a - 1)*q^33 + (4*a + 2)*q^34 + (4*a - 6)*q^35 + (-a - 2)*q^36 - q^37 + O(q^38)
*]> ;  // time = 9.699 seconds




J[77] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 77, 77, 77, 77, 11 ], new_dimensions := [ 1, 1, 1, 2, 1 ], dimensions := [ 1, 1, 1, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 0, 5, 1, 1, 1, 5, 0, 1, 1, 3, 1, 1, 0 ], ap_traces := [
[ 0, -3, -1, -1, -1, -4, 2, -6, -5, 10, 1, -5 ],
[ 1, 2, -2, -1, 1, 4, 4, 0, -4, -6, 10, -6 ],
[ 0, 1, 3, 1, -1, -4, -6, 2, 3, -6, 5, 11 ],
[ 0, 2, -4, 2, -2, 2, -2, 4, -4, 8, -10, -8 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 - 5
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 1 ],
[ 3, 3 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1 ], torsion_lower_bounds := [ 1, 1, 3, 1 ], l_ratios := [ 0, 1, 1/3, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1 ], eigenvalues := [*
[ 0, -3, -1, -1, -1, -4, 2, -6, -5, 10, 1, -5 ],
[ 1, 2, -2, -1, 1, 4, 4, 0, -4, -6, 10, -6 ],
[ 0, 1, 3, 1, -1, -4, -6, 2, 3, -6, 5, 11 ],
[
a,
-a + 1,
-2,
1,
-1,
a + 1,
-a - 1,
2*a + 2,
2*a - 2,
2*a + 4,
a - 5,
-2*a - 4
]
*], q_expansions := [*
q - 3*q^3 - 2*q^4 - q^5 - q^7 + 6*q^9 - q^11 + 6*q^12 - 4*q^13 + 3*q^15 + 4*q^16 + 2*q^17 - 6*q^19 + 2*q^20 + 3*q^21 - 5*q^23 - 4*q^25 - 9*q^27 + 2*q^28 + 10*q^29 + q^31 + 3*q^33 + q^35 - 12*q^36 - 5*q^37 + O(q^38),
q + q^2 + 2*q^3 - q^4 - 2*q^5 + 2*q^6 - q^7 - 3*q^8 + q^9 - 2*q^10 + q^11 - 2*q^12 + 4*q^13 - q^14 - 4*q^15 - q^16 + 4*q^17 + q^18 + 2*q^20 - 2*q^21 + q^22 - 4*q^23 - 6*q^24 - q^25 + 4*q^26 - 4*q^27 + q^28 - 6*q^29 - 4*q^30 + 10*q^31 + 5*q^32 + 2*q^33 + 4*q^34 + 2*q^35 - q^36 - 6*q^37 + O(q^38),
q + q^3 - 2*q^4 + 3*q^5 + q^7 - 2*q^9 - q^11 - 2*q^12 - 4*q^13 + 3*q^15 + 4*q^16 - 6*q^17 + 2*q^19 - 6*q^20 + q^21 + 3*q^23 + 4*q^25 - 5*q^27 - 2*q^28 - 6*q^29 + 5*q^31 - q^33 + 3*q^35 + 4*q^36 + 11*q^37 + O(q^38),
q + a*q^2 + (-a + 1)*q^3 + 3*q^4 - 2*q^5 + (a - 5)*q^6 + q^7 + a*q^8 + (-2*a + 3)*q^9 - 2*a*q^10 - q^11 + (-3*a + 3)*q^12 + (a + 1)*q^13 + a*q^14 + (2*a - 2)*q^15 - q^16 + (-a - 1)*q^17 + (3*a - 10)*q^18 + (2*a + 2)*q^19 - 6*q^20 + (-a + 1)*q^21 - a*q^22 + (2*a - 2)*q^23 + (a - 5)*q^24 - q^25 + (a + 5)*q^26 + (-2*a + 10)*q^27 + 3*q^28 + (2*a + 4)*q^29 + (-2*a + 10)*q^30 + (a - 5)*q^31 - 3*a*q^32 + (a - 1)*q^33 + (-a - 5)*q^34 - 2*q^35 + (-6*a + 9)*q^36 + (-2*a - 4)*q^37 + O(q^38)
*]> ;  // time = 6.4 seconds




J[78] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 78, 39, 39, 26, 26 ], new_dimensions := [ 1, 1, 2, 1, 1 ], dimensions := [ 1, 2, 4, 2, 2 ], intersection_graph := [ 0, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 7, 5, 1, 1, 0, 1, 1, 1, 7, 1, 0 ], ap_traces := [
[ -1, -1, 2, 4, -4, 1, 2, -8, 0, 6, -4, -2 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ 1, 1, -1 ]
], component_group_orders := [
[ 1, 5, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1 ], torsion_lower_bounds := [ 1 ], l_ratios := [ 1 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ -1, -1, 2, 4, -4, 1, 2, -8, 0, 6, -4, -2 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + 2*q^5 + q^6 + 4*q^7 - q^8 + q^9 - 2*q^10 - 4*q^11 - q^12 + q^13 - 4*q^14 - 2*q^15 + q^16 + 2*q^17 - q^18 - 8*q^19 + 2*q^20 - 4*q^21 + 4*q^22 + q^24 - q^25 - q^26 - q^27 + 4*q^28 + 6*q^29 + 2*q^30 - 4*q^31 - q^32 + 4*q^33 - 2*q^34 + 8*q^35 + q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 25.54 seconds




J[79] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 79, 79 ], new_dimensions := [ 1, 5 ], dimensions := [ 1, 5 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -1, -3, -1, -2, 3, -6, 4, 2, -6, -10, -2 ],
[ 0, 1, 7, -5, 2, -3, 10, -4, 2, 6, 2, 0 ]
], hecke_fields := [
x - 1,
x^5 - 6*x^3 + 8*x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 13 ]
], tamagawa_numbers := [
[ 1 ],
[ 13 ]
], torsion_upper_bounds := [ 1, 13 ], torsion_lower_bounds := [ 1, 13 ], l_ratios := [ 0, 1/13 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ -1, -1, -3, -1, -2, 3, -6, 4, 2, -6, -10, -2 ],
[
a,
-a^4 + a^3 + 3*a^2 - 3*a + 1,
a^4 - 4*a^2 - a + 3,
a^4 - a^3 - 5*a^2 + 3*a + 3,
-a^4 - 2*a^3 + 6*a^2 + 7*a - 6,
a^3 + a^2 - 2*a - 3,
-2*a^3 + 6*a + 2,
-3*a^3 + 3*a^2 + 10*a - 8,
2*a^4 + a^3 - 9*a^2 - 4*a + 6,
2*a^3 - 2*a^2 - 4*a + 6,
-a^4 + 2*a^3 + 6*a^2 - 5*a - 6,
2*a^4 - 2*a^3 - 10*a^2 + 4*a + 8
]
*], q_expansions := [*
q - q^2 - q^3 - q^4 - 3*q^5 + q^6 - q^7 + 3*q^8 - 2*q^9 + 3*q^10 - 2*q^11 + q^12 + 3*q^13 + q^14 + 3*q^15 - q^16 - 6*q^17 + 2*q^18 + 4*q^19 + 3*q^20 + q^21 + 2*q^22 + 2*q^23 - 3*q^24 + 4*q^25 - 3*q^26 + 5*q^27 + q^28 - 6*q^29 - 3*q^30 - 10*q^31 - 5*q^32 + 2*q^33 + 6*q^34 + 3*q^35 + 2*q^36 - 2*q^37 + O(q^38),
q + a*q^2 + (-a^4 + a^3 + 3*a^2 - 3*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^4 - 4*a^2 - a + 3)*q^5 + (a^4 - 3*a^3 - 3*a^2 + 9*a - 1)*q^6 + (a^4 - a^3 - 5*a^2 + 3*a + 3)*q^7 + (a^3 - 4*a)*q^8 + (-a^4 + a^3 + 5*a^2 - 5*a - 2)*q^9 + (2*a^3 - a^2 - 5*a + 1)*q^10 + (-a^4 - 2*a^3 + 6*a^2 + 7*a - 6)*q^11 + (-a^4 + a^3 + 3*a^2 - 3*a - 1)*q^12 + (a^3 + a^2 - 2*a - 3)*q^13 + (-a^4 + a^3 + 3*a^2 - 5*a + 1)*q^14 + (-a^4 + 3*a^3 + a^2 - 9*a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-2*a^3 + 6*a + 2)*q^17 + (a^4 - a^3 - 5*a^2 + 6*a - 1)*q^18 + (-3*a^3 + 3*a^2 + 10*a - 8)*q^19 + (-a^3 + 3*a^2 + 3*a - 6)*q^20 + (3*a^4 - 3*a^3 - 11*a^2 + 11*a + 1)*q^21 + (-2*a^4 + 7*a^2 + 2*a - 1)*q^22 + (2*a^4 + a^3 - 9*a^2 - 4*a + 6)*q^23 + (-a^4 + 3*a^3 + 3*a^2 - 11*a + 1)*q^24 + (2*a^4 - 3*a^3 - 7*a^2 + 8*a + 2)*q^25 + (a^4 + a^3 - 2*a^2 - 3*a)*q^26 + (-3*a^4 + 7*a^3 + 11*a^2 - 23*a - 1)*q^27 + (-a^4 - a^3 + 5*a^2 + 3*a - 7)*q^28 + (2*a^3 - 2*a^2 - 4*a + 6)*q^29 + (3*a^4 - 5*a^3 - 9*a^2 + 11*a - 1)*q^30 + (-a^4 + 2*a^3 + 6*a^2 - 5*a - 6)*q^31 + (-2*a^3 + 4*a + 1)*q^32 + (-2*a^4 + 8*a^2 + 4*a - 4)*q^33 + (-2*a^4 + 6*a^2 + 2*a)*q^34 + (a^4 - a^3 - 7*a^2 + 3*a + 9)*q^35 + (a^4 - a^3 - 4*a^2 + a + 5)*q^36 + (2*a^4 - 2*a^3 - 10*a^2 + 4*a + 8)*q^37 + O(q^38)
*]> ;  // time = 1.02 seconds




J[82] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 82, 82, 41 ], new_dimensions := [ 1, 2, 3 ], dimensions := [ 1, 2, 6 ], intersection_graph := [ 0, 1, 1, 1, 0, 1, 1, 1, 0 ], ap_traces := [
[ -1, -2, -2, -4, -2, 4, -2, 6, -8, 0, -8, 2 ],
[ 2, 0, 0, -4, 0, 0, 4, -8, 8, 8, -8, 0 ]
], hecke_fields := [
x - 1,
x^2 - 2
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 7, 1 ]
], torsion_upper_bounds := [ 1, 7 ], torsion_lower_bounds := [ 1, 7 ], l_ratios := [ 0, 1/7 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ -1, -2, -2, -4, -2, 4, -2, 6, -8, 0, -8, 2 ],
[
1,
a,
-2*a,
-a - 2,
3*a,
0,
4*a + 2,
-a - 4,
-2*a + 4,
-4*a + 4,
2*a - 4,
6*a
]
*], q_expansions := [*
q - q^2 - 2*q^3 + q^4 - 2*q^5 + 2*q^6 - 4*q^7 - q^8 + q^9 + 2*q^10 - 2*q^11 - 2*q^12 + 4*q^13 + 4*q^14 + 4*q^15 + q^16 - 2*q^17 - q^18 + 6*q^19 - 2*q^20 + 8*q^21 + 2*q^22 - 8*q^23 + 2*q^24 - q^25 - 4*q^26 + 4*q^27 - 4*q^28 - 4*q^30 - 8*q^31 - q^32 + 4*q^33 + 2*q^34 + 8*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - 2*a*q^5 + a*q^6 + (-a - 2)*q^7 + q^8 - q^9 - 2*a*q^10 + 3*a*q^11 + a*q^12 + (-a - 2)*q^14 - 4*q^15 + q^16 + (4*a + 2)*q^17 - q^18 + (-a - 4)*q^19 - 2*a*q^20 + (-2*a - 2)*q^21 + 3*a*q^22 + (-2*a + 4)*q^23 + a*q^24 + 3*q^25 - 4*a*q^27 + (-a - 2)*q^28 + (-4*a + 4)*q^29 - 4*q^30 + (2*a - 4)*q^31 + q^32 + 6*q^33 + (4*a + 2)*q^34 + (4*a + 4)*q^35 - q^36 + 6*a*q^37 + O(q^38)
*]> ;  // time = 8.95 seconds




J[83] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 83, 83 ], new_dimensions := [ 1, 6 ], dimensions := [ 1, 6 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -1, -2, -3, 3, -6, 5, 2, -4, -7, 5, -11 ],
[ 1, 1, 2, 3, -3, 14, -5, -4, -5, -1, 3, 39 ]
], hecke_fields := [
x - 1,
x^6 - x^5 - 9*x^4 + 7*x^3 + 20*x^2 - 12*x - 8
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 41 ]
], tamagawa_numbers := [
[ 1 ],
[ 41 ]
], torsion_upper_bounds := [ 1, 41 ], torsion_lower_bounds := [ 1, 41 ], l_ratios := [ 0, 1/41 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ -1, -1, -2, -3, 3, -6, 5, 2, -4, -7, 5, -11 ],
[
a,
1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 3/2*a + 4,
-1/2*a^5 - 1/2*a^4 + 9/2*a^3 + 7/2*a^2 - 8*a - 2,
3/4*a^5 - 1/4*a^4 - 25/4*a^3 + 3/4*a^2 + 19/2*a,
-1/4*a^5 + 1/4*a^4 + 5/4*a^3 + 1/4*a^2 - 4,
a^3 - 5*a + 2,
1/4*a^5 - 3/4*a^4 - 7/4*a^3 + 17/4*a^2 + 7/2*a - 4,
3/2*a^5 - 1/2*a^4 - 23/2*a^3 - 1/2*a^2 + 16*a + 4,
-a^5 + 7*a^3 + 3*a^2 - 8*a - 7,
3/2*a^5 - 12*a^3 - 4*a^2 + 39/2*a + 8,
-3/4*a^5 + 3/4*a^4 + 23/4*a^3 - 21/4*a^2 - 8*a + 8,
-3/4*a^5 + 3/4*a^4 + 19/4*a^3 - 13/4*a^2 - 3*a + 8
]
*], q_expansions := [*
q - q^2 - q^3 - q^4 - 2*q^5 + q^6 - 3*q^7 + 3*q^8 - 2*q^9 + 2*q^10 + 3*q^11 + q^12 - 6*q^13 + 3*q^14 + 2*q^15 - q^16 + 5*q^17 + 2*q^18 + 2*q^19 + 2*q^20 + 3*q^21 - 3*q^22 - 4*q^23 - 3*q^24 - q^25 + 6*q^26 + 5*q^27 + 3*q^28 - 7*q^29 - 2*q^30 + 5*q^31 - 5*q^32 - 3*q^33 - 5*q^34 + 6*q^35 + 2*q^36 - 11*q^37 + O(q^38),
q + a*q^2 + (1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 3/2*a + 4)*q^3 + (a^2 - 2)*q^4 + (-1/2*a^5 - 1/2*a^4 + 9/2*a^3 + 7/2*a^2 - 8*a - 2)*q^5 + (1/2*a^5 - 1/2*a^4 - 7/2*a^3 + 3/2*a^2 + 4*a)*q^6 + (3/4*a^5 - 1/4*a^4 - 25/4*a^3 + 3/4*a^2 + 19/2*a)*q^7 + (a^3 - 4*a)*q^8 + (-1/4*a^5 + 1/4*a^4 + 9/4*a^3 - 7/4*a^2 - 5*a + 3)*q^9 + (-a^5 + 7*a^3 + 2*a^2 - 8*a - 4)*q^10 + (-1/4*a^5 + 1/4*a^4 + 5/4*a^3 + 1/4*a^2 - 4)*q^11 + (-a^3 + a^2 + 3*a - 4)*q^12 + (a^3 - 5*a + 2)*q^13 + (1/2*a^5 + 1/2*a^4 - 9/2*a^3 - 11/2*a^2 + 9*a + 6)*q^14 + (a^4 - 7*a^2 + 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/4*a^5 - 3/4*a^4 - 7/4*a^3 + 17/4*a^2 + 7/2*a - 4)*q^17 - 2*q^18 + (3/2*a^5 - 1/2*a^4 - 23/2*a^3 - 1/2*a^2 + 16*a + 4)*q^19 + (-a^4 + 5*a^2 - 4)*q^20 + (1/4*a^5 + 1/4*a^4 - 15/4*a^3 + 1/4*a^2 + 23/2*a - 5)*q^21 + (-a^4 + 2*a^3 + 5*a^2 - 7*a - 2)*q^22 + (-a^5 + 7*a^3 + 3*a^2 - 8*a - 7)*q^23 + (-a^5 + 8*a^3 - 12*a)*q^24 + (-a^5 - a^4 + 9*a^3 + 9*a^2 - 14*a - 9)*q^25 + (a^4 - 5*a^2 + 2*a)*q^26 + (-a^5 - 1/2*a^4 + 19/2*a^3 + 9/2*a^2 - 35/2*a - 3)*q^27 + (-1/2*a^5 + 1/2*a^4 + 7/2*a^3 - 5/2*a^2 - 7*a + 4)*q^28 + (3/2*a^5 - 12*a^3 - 4*a^2 + 39/2*a + 8)*q^29 + (a^5 - 7*a^3 + 6*a)*q^30 + (-3/4*a^5 + 3/4*a^4 + 23/4*a^3 - 21/4*a^2 - 8*a + 8)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^5 - a^4 - 4*a^3 + 8*a^2 + 9/2*a - 11)*q^33 + (-1/2*a^5 + 1/2*a^4 + 5/2*a^3 - 3/2*a^2 - a + 2)*q^34 + (a^5 - a^4 - 6*a^3 + 5*a^2 + 3*a - 6)*q^35 + (1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 7/2*a^2 + 8*a - 6)*q^36 + (-3/4*a^5 + 3/4*a^4 + 19/4*a^3 - 13/4*a^2 - 3*a + 8)*q^37 + O(q^38)
*]> ;  // time = 1.029 seconds




J[85] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 85, 85, 85, 17 ], new_dimensions := [ 1, 2, 2, 1 ], dimensions := [ 1, 2, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0 ], ap_traces := [
[ 1, 2, -1, -2, 2, 2, 1, 0, 6, -6, -10, 2 ],
[ -2, -4, -2, -4, -8, 0, -2, 0, -4, -4, 0, -4 ],
[ 0, 2, 2, -2, 6, -8, -2, 4, -6, 0, 10, -8 ]
], hecke_fields := [
x - 1,
x^2 + 2*x - 1,
x^2 - 3
], atkin_lehners := [
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 3 ], l_ratios := [ 1, 0, 1/3 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ 1, 2, -1, -2, 2, 2, 1, 0, 6, -6, -10, 2 ],
[
a,
-a - 3,
-1,
a - 1,
a - 3,
-2*a - 2,
-1,
-2*a - 2,
-a - 3,
-2*a - 4,
3*a + 3,
6*a + 4
],
[
a,
-a + 1,
1,
a - 1,
-a + 3,
-4,
-1,
2*a + 2,
3*a - 3,
2*a,
a + 5,
-2*a - 4
]
*], q_expansions := [*
q + q^2 + 2*q^3 - q^4 - q^5 + 2*q^6 - 2*q^7 - 3*q^8 + q^9 - q^10 + 2*q^11 - 2*q^12 + 2*q^13 - 2*q^14 - 2*q^15 - q^16 + q^17 + q^18 + q^20 - 4*q^21 + 2*q^22 + 6*q^23 - 6*q^24 + q^25 + 2*q^26 - 4*q^27 + 2*q^28 - 6*q^29 - 2*q^30 - 10*q^31 + 5*q^32 + 4*q^33 + q^34 + 2*q^35 - q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (-a - 3)*q^3 + (-2*a - 1)*q^4 - q^5 + (-a - 1)*q^6 + (a - 1)*q^7 + (a - 2)*q^8 + (4*a + 7)*q^9 - a*q^10 + (a - 3)*q^11 + (3*a + 5)*q^12 + (-2*a - 2)*q^13 + (-3*a + 1)*q^14 + (a + 3)*q^15 + 3*q^16 - q^17 + (-a + 4)*q^18 + (-2*a - 2)*q^19 + (2*a + 1)*q^20 + 2*q^21 + (-5*a + 1)*q^22 + (-a - 3)*q^23 + (a + 5)*q^24 + q^25 + (2*a - 2)*q^26 + (-8*a - 16)*q^27 + (5*a - 1)*q^28 + (-2*a - 4)*q^29 + (a + 1)*q^30 + (3*a + 3)*q^31 + (a + 4)*q^32 + (2*a + 8)*q^33 - a*q^34 + (-a + 1)*q^35 + (-2*a - 15)*q^36 + (6*a + 4)*q^37 + O(q^38),
q + a*q^2 + (-a + 1)*q^3 + q^4 + q^5 + (a - 3)*q^6 + (a - 1)*q^7 - a*q^8 + (-2*a + 1)*q^9 + a*q^10 + (-a + 3)*q^11 + (-a + 1)*q^12 - 4*q^13 + (-a + 3)*q^14 + (-a + 1)*q^15 - 5*q^16 - q^17 + (a - 6)*q^18 + (2*a + 2)*q^19 + q^20 + (2*a - 4)*q^21 + (3*a - 3)*q^22 + (3*a - 3)*q^23 + (-a + 3)*q^24 + q^25 - 4*a*q^26 + 4*q^27 + (a - 1)*q^28 + 2*a*q^29 + (a - 3)*q^30 + (a + 5)*q^31 - 3*a*q^32 + (-4*a + 6)*q^33 - a*q^34 + (a - 1)*q^35 + (-2*a + 1)*q^36 + (-2*a - 4)*q^37 + O(q^38)
*]> ;  // time = 6.431 seconds




J[86] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 86, 86, 43, 43 ], new_dimensions := [ 2, 2, 1, 2 ], dimensions := [ 2, 2, 2, 4 ], intersection_graph := [ 0, 1, 1, 7, 1, 0, 5, 1, 1, 5, 0, 1, 7, 1, 1, 0 ], ap_traces := [
[ -2, -1, 3, 4, 0, 4, -9, 1, -9, 3, 1, 1 ],
[ 2, 1, -3, 0, -4, 0, -1, 11, 3, -7, 13, -5 ]
], hecke_fields := [
x^2 + x - 5,
x^2 - x - 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 21, 3 ],
[ 55, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 55, 1 ]
], torsion_upper_bounds := [ 3, 11 ], torsion_lower_bounds := [ 3, 11 ], l_ratios := [ 1/3, 5/11 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
-1,
a,
-a + 1,
2,
0,
2,
a - 4,
-3*a - 1,
-a - 5,
a + 2,
3*a + 2,
3*a + 2
],
[
1,
a,
-a - 1,
-4*a + 2,
4*a - 4,
4*a - 2,
-a,
a + 5,
-3*a + 3,
-3*a - 2,
a + 6,
-a - 2
]
*], q_expansions := [*
q - q^2 + a*q^3 + q^4 + (-a + 1)*q^5 - a*q^6 + 2*q^7 - q^8 + (-a + 2)*q^9 + (a - 1)*q^10 + a*q^12 + 2*q^13 - 2*q^14 + (2*a - 5)*q^15 + q^16 + (a - 4)*q^17 + (a - 2)*q^18 + (-3*a - 1)*q^19 + (-a + 1)*q^20 + 2*a*q^21 + (-a - 5)*q^23 - a*q^24 + (-3*a + 1)*q^25 - 2*q^26 - 5*q^27 + 2*q^28 + (a + 2)*q^29 + (-2*a + 5)*q^30 + (3*a + 2)*q^31 - q^32 + (-a + 4)*q^34 + (-2*a + 2)*q^35 + (-a + 2)*q^36 + (3*a + 2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a - 1)*q^5 + a*q^6 + (-4*a + 2)*q^7 + q^8 + (a - 2)*q^9 + (-a - 1)*q^10 + (4*a - 4)*q^11 + a*q^12 + (4*a - 2)*q^13 + (-4*a + 2)*q^14 + (-2*a - 1)*q^15 + q^16 - a*q^17 + (a - 2)*q^18 + (a + 5)*q^19 + (-a - 1)*q^20 + (-2*a - 4)*q^21 + (4*a - 4)*q^22 + (-3*a + 3)*q^23 + a*q^24 + (3*a - 3)*q^25 + (4*a - 2)*q^26 + (-4*a + 1)*q^27 + (-4*a + 2)*q^28 + (-3*a - 2)*q^29 + (-2*a - 1)*q^30 + (a + 6)*q^31 + q^32 + 4*q^33 - a*q^34 + (6*a + 2)*q^35 + (a - 2)*q^36 + (-a - 2)*q^37 + O(q^38)
*]> ;  // time = 10.201 seconds




J[87] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 87, 87, 29 ], new_dimensions := [ 2, 3, 2 ], dimensions := [ 2, 3, 4 ], intersection_graph := [ 0, 1, 1, 1, 0, 23, 1, 23, 0 ], ap_traces := [
[ 1, 2, 2, -4, 4, -2, 6, -10, -2, -2, -6, 6 ],
[ 2, -3, 0, 4, -8, 4, 4, -2, 6, 3, 6, 8 ]
], hecke_fields := [
x^2 - x - 1,
x^3 - 2*x^2 - 4*x + 7
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 5, 1 ],
[ 23, 1 ]
], tamagawa_numbers := [
[ 5, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 5, 1 ], torsion_lower_bounds := [ 5, 1 ], l_ratios := [ 1/5, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
a,
1,
-2*a + 2,
-2*a - 1,
2*a + 1,
4*a - 3,
3,
2*a - 6,
6*a - 4,
-1,
-6*a,
-2*a + 4
],
[
a,
-1,
-2*a^2 + 8,
a^2 - a - 2,
a^2 - a - 6,
-a^2 - a + 6,
3*a^2 - a - 10,
2*a - 2,
-2*a^2 + 10,
1,
-2*a^2 + 10,
-2*a + 4
]
*], q_expansions := [*
q + a*q^2 + q^3 + (a - 1)*q^4 + (-2*a + 2)*q^5 + a*q^6 + (-2*a - 1)*q^7 + (-2*a + 1)*q^8 + q^9 - 2*q^10 + (2*a + 1)*q^11 + (a - 1)*q^12 + (4*a - 3)*q^13 + (-3*a - 2)*q^14 + (-2*a + 2)*q^15 - 3*a*q^16 + 3*q^17 + a*q^18 + (2*a - 6)*q^19 + (2*a - 4)*q^20 + (-2*a - 1)*q^21 + (3*a + 2)*q^22 + (6*a - 4)*q^23 + (-2*a + 1)*q^24 + (-4*a + 3)*q^25 + (a + 4)*q^26 + q^27 + (-a - 1)*q^28 - q^29 - 2*q^30 - 6*a*q^31 + (a - 5)*q^32 + (2*a + 1)*q^33 + 3*a*q^34 + (2*a + 2)*q^35 + (a - 1)*q^36 + (-2*a + 4)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-2*a^2 + 8)*q^5 - a*q^6 + (a^2 - a - 2)*q^7 + (2*a^2 - 7)*q^8 + q^9 + (-4*a^2 + 14)*q^10 + (a^2 - a - 6)*q^11 + (-a^2 + 2)*q^12 + (-a^2 - a + 6)*q^13 + (a^2 + 2*a - 7)*q^14 + (2*a^2 - 8)*q^15 + (2*a^2 + a - 10)*q^16 + (3*a^2 - a - 10)*q^17 + a*q^18 + (2*a - 2)*q^19 + (-4*a^2 - 2*a + 12)*q^20 + (-a^2 + a + 2)*q^21 + (a^2 - 2*a - 7)*q^22 + (-2*a^2 + 10)*q^23 + (-2*a^2 + 7)*q^24 + (4*a + 3)*q^25 + (-3*a^2 + 2*a + 7)*q^26 - q^27 + (2*a^2 - a - 3)*q^28 + q^29 + (4*a^2 - 14)*q^30 + (-2*a^2 + 10)*q^31 + (a^2 - 2*a)*q^32 + (-a^2 + a + 6)*q^33 + (5*a^2 + 2*a - 21)*q^34 + (-2*a - 2)*q^35 + (a^2 - 2)*q^36 + (-2*a + 4)*q^37 + O(q^38)
*]> ;  // time = 6.941 seconds




J[89] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 89, 89, 89 ], new_dimensions := [ 1, 1, 5 ], dimensions := [ 1, 1, 5 ], intersection_graph := [ 0, 1, 1, 1, 0, 5, 1, 5, 0 ], ap_traces := [
[ -1, -1, -1, -4, -2, 2, 3, -5, 7, 0, -9, -2 ],
[ 1, 2, -2, 2, -4, 2, 6, -2, 2, -6, 6, 10 ],
[ -1, -3, -1, 8, 6, 0, -13, 13, 1, 2, 19, -14 ]
], hecke_fields := [
x - 1,
x - 1,
x^5 + x^4 - 10*x^3 - 10*x^2 + 21*x + 17
], atkin_lehners := [
[ 1 ],
[ -1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 11 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 11 ]
], torsion_upper_bounds := [ 1, 1, 11 ], torsion_lower_bounds := [ 1, 1, 11 ], l_ratios := [ 0, 1, 1/11 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ -1, -1, -1, -4, -2, 2, 3, -5, 7, 0, -9, -2 ],
[ 1, 2, -2, 2, -4, 2, 6, -2, 2, -6, 6, 10 ],
[
a,
-1/2*a^4 + 1/2*a^3 + 7/2*a^2 - 5/2*a - 4,
-a^2 + 4,
1/2*a^4 - 4*a^2 - a + 13/2,
-a^3 + 5*a + 2,
-a^4 + a^3 + 8*a^2 - 5*a - 11,
a^4 - a^3 - 7*a^2 + 4*a + 4,
1/2*a^3 - 1/2*a^2 - 3/2*a + 9/2,
a^4 - 3/2*a^3 - 13/2*a^2 + 17/2*a + 11/2,
-a^4 + 9*a^2 - 14,
1/2*a^4 - 3/2*a^3 - 7/2*a^2 + 15/2*a + 8,
a^4 - 2*a^3 - 8*a^2 + 10*a + 9
]
*], q_expansions := [*
q - q^2 - q^3 - q^4 - q^5 + q^6 - 4*q^7 + 3*q^8 - 2*q^9 + q^10 - 2*q^11 + q^12 + 2*q^13 + 4*q^14 + q^15 - q^16 + 3*q^17 + 2*q^18 - 5*q^19 + q^20 + 4*q^21 + 2*q^22 + 7*q^23 - 3*q^24 - 4*q^25 - 2*q^26 + 5*q^27 + 4*q^28 - q^30 - 9*q^31 - 5*q^32 + 2*q^33 - 3*q^34 + 4*q^35 + 2*q^36 - 2*q^37 + O(q^38),
q + q^2 + 2*q^3 - q^4 - 2*q^5 + 2*q^6 + 2*q^7 - 3*q^8 + q^9 - 2*q^10 - 4*q^11 - 2*q^12 + 2*q^13 + 2*q^14 - 4*q^15 - q^16 + 6*q^17 + q^18 - 2*q^19 + 2*q^20 + 4*q^21 - 4*q^22 + 2*q^23 - 6*q^24 - q^25 + 2*q^26 - 4*q^27 - 2*q^28 - 6*q^29 - 4*q^30 + 6*q^31 + 5*q^32 - 8*q^33 + 6*q^34 - 4*q^35 - q^36 + 10*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^4 + 1/2*a^3 + 7/2*a^2 - 5/2*a - 4)*q^3 + (a^2 - 2)*q^4 + (-a^2 + 4)*q^5 + (a^4 - 3/2*a^3 - 15/2*a^2 + 13/2*a + 17/2)*q^6 + (1/2*a^4 - 4*a^2 - a + 13/2)*q^7 + (a^3 - 4*a)*q^8 + (a^2 - a - 4)*q^9 + (-a^3 + 4*a)*q^10 + (-a^3 + 5*a + 2)*q^11 + (-3/2*a^4 + 3/2*a^3 + 19/2*a^2 - 15/2*a - 9)*q^12 + (-a^4 + a^3 + 8*a^2 - 5*a - 11)*q^13 + (-1/2*a^4 + a^3 + 4*a^2 - 4*a - 17/2)*q^14 + (1/2*a^4 - 1/2*a^3 - 5/2*a^2 + 5/2*a + 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 - a^3 - 7*a^2 + 4*a + 4)*q^17 + (a^3 - a^2 - 4*a)*q^18 + (1/2*a^3 - 1/2*a^2 - 3/2*a + 9/2)*q^19 + (-a^4 + 6*a^2 - 8)*q^20 + (-a^4 + a^3 + 7*a^2 - 4*a - 9)*q^21 + (-a^4 + 5*a^2 + 2*a)*q^22 + (a^4 - 3/2*a^3 - 13/2*a^2 + 17/2*a + 11/2)*q^23 + (a^4 - 5/2*a^3 - 15/2*a^2 + 19/2*a + 17/2)*q^24 + (a^4 - 8*a^2 + 11)*q^25 + (2*a^4 - 2*a^3 - 15*a^2 + 10*a + 17)*q^26 + (1/2*a^3 - 1/2*a^2 - 3/2*a + 5/2)*q^27 + (1/2*a^4 - a^3 - a^2 + 4*a - 9/2)*q^28 + (-a^4 + 9*a^2 - 14)*q^29 + (-a^4 + 5/2*a^3 + 15/2*a^2 - 19/2*a - 17/2)*q^30 + (1/2*a^4 - 3/2*a^3 - 7/2*a^2 + 15/2*a + 8)*q^31 + (-a^4 + 2*a^3 + 10*a^2 - 9*a - 17)*q^32 + (-a^4 + 2*a^3 + 7*a^2 - 8*a - 8)*q^33 + (-2*a^4 + 3*a^3 + 14*a^2 - 17*a - 17)*q^34 + (1/2*a^4 + a^3 - 7*a^2 - 6*a + 35/2)*q^35 + (a^4 - a^3 - 6*a^2 + 2*a + 8)*q^36 + (a^4 - 2*a^3 - 8*a^2 + 10*a + 9)*q^37 + O(q^38)
*]> ;  // time = 1.161 seconds




J[91] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 91, 91, 91, 91 ], new_dimensions := [ 1, 1, 2, 3 ], dimensions := [ 1, 1, 2, 3 ], intersection_graph := [ 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0 ], ap_traces := [
[ -2, 0, -3, -1, -6, -1, 4, 5, 3, -5, -3, -4 ],
[ 0, -2, -3, 1, 0, 1, -6, -7, 3, -9, 5, 2 ],
[ 0, 0, 6, 2, 0, -2, 0, -6, -6, 6, -2, -4 ],
[ 1, -2, 2, -3, 2, 3, 4, -4, 10, 24, -4, 0 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2,
x^3 - x^2 - 4*x + 2
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 7, 1 ], torsion_lower_bounds := [ 1, 1, 7, 1 ], l_ratios := [ 0, 0, 1/7, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[ -2, 0, -3, -1, -6, -1, 4, 5, 3, -5, -3, -4 ],
[ 0, -2, -3, 1, 0, 1, -6, -7, 3, -9, 5, 2 ],
[
a,
-a,
a + 3,
1,
-3*a,
-1,
-a,
3*a - 3,
2*a - 3,
2*a + 3,
-3*a - 1,
-3*a - 2
],
[
a,
-a^2 + a + 2,
-a + 1,
-1,
a^2 - a - 2,
1,
a^2 + a - 2,
-a - 1,
-a^2 - 2*a + 7,
a^2 + 5,
2*a^2 - a - 7,
a^2 + 3*a - 4
]
*], q_expansions := [*
q - 2*q^2 + 2*q^4 - 3*q^5 - q^7 - 3*q^9 + 6*q^10 - 6*q^11 - q^13 + 2*q^14 - 4*q^16 + 4*q^17 + 6*q^18 + 5*q^19 - 6*q^20 + 12*q^22 + 3*q^23 + 4*q^25 + 2*q^26 - 2*q^28 - 5*q^29 - 3*q^31 + 8*q^32 - 8*q^34 + 3*q^35 - 6*q^36 - 4*q^37 + O(q^38),
q - 2*q^3 - 2*q^4 - 3*q^5 + q^7 + q^9 + 4*q^12 + q^13 + 6*q^15 + 4*q^16 - 6*q^17 - 7*q^19 + 6*q^20 - 2*q^21 + 3*q^23 + 4*q^25 + 4*q^27 - 2*q^28 - 9*q^29 + 5*q^31 - 3*q^35 - 2*q^36 + 2*q^37 + O(q^38),
q + a*q^2 - a*q^3 + (a + 3)*q^5 - 2*q^6 + q^7 - 2*a*q^8 - q^9 + (3*a + 2)*q^10 - 3*a*q^11 - q^13 + a*q^14 + (-3*a - 2)*q^15 - 4*q^16 - a*q^17 - a*q^18 + (3*a - 3)*q^19 - a*q^21 - 6*q^22 + (2*a - 3)*q^23 + 4*q^24 + (6*a + 6)*q^25 - a*q^26 + 4*a*q^27 + (2*a + 3)*q^29 + (-2*a - 6)*q^30 + (-3*a - 1)*q^31 + 6*q^33 - 2*q^34 + (a + 3)*q^35 + (-3*a - 2)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + a + 2)*q^3 + (a^2 - 2)*q^4 + (-a + 1)*q^5 + (-2*a + 2)*q^6 - q^7 + (a^2 - 2)*q^8 + (-2*a + 3)*q^9 + (-a^2 + a)*q^10 + (a^2 - a - 2)*q^11 - 4*q^12 + q^13 - a*q^14 + (-a^2 + 3*a)*q^15 + (-a^2 + 2*a + 2)*q^16 + (a^2 + a - 2)*q^17 + (-2*a^2 + 3*a)*q^18 + (-a - 1)*q^19 - 2*a*q^20 + (a^2 - a - 2)*q^21 + (2*a - 2)*q^22 + (-a^2 - 2*a + 7)*q^23 - 4*q^24 + (a^2 - 2*a - 4)*q^25 + a*q^26 + (4*a - 4)*q^27 + (-a^2 + 2)*q^28 + (a^2 + 5)*q^29 + (2*a^2 - 4*a + 2)*q^30 + (2*a^2 - a - 7)*q^31 + (-a^2 - 2*a + 6)*q^32 + (2*a - 6)*q^33 + (2*a^2 + 2*a - 2)*q^34 + (a - 1)*q^35 + (a^2 - 4*a - 2)*q^36 + (a^2 + 3*a - 4)*q^37 + O(q^38)
*]> ;  // time = 7.149 seconds




J[93] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 93, 93, 31 ], new_dimensions := [ 2, 3, 2 ], dimensions := [ 2, 3, 4 ], intersection_graph := [ 0, 1, 1, 1, 0, 1, 1, 1, 0 ], ap_traces := [
[ -3, -2, -4, -4, -6, -2, -4, -8, 2, 2, -2, 2 ],
[ 0, 3, -2, 4, -2, 4, -2, 4, -6, -8, -3, 0 ]
], hecke_fields := [
x^2 + 3*x + 1,
x^3 - 4*x + 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1 ], torsion_lower_bounds := [ 1, 1 ], l_ratios := [ 0, 1 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-1,
-2*a - 5,
2*a + 1,
2*a,
2*a + 2,
-4*a - 8,
-2*a - 7,
-2*a - 2,
2*a + 4,
-1,
-6*a - 8
],
[
a,
1,
-a^2 - a + 2,
-a^2 - a + 4,
2*a^2 - 6,
2*a^2 - 4,
2*a^2 + 2*a - 6,
-a^2 + 3*a + 4,
-2*a - 2,
-4*a^2 - 2*a + 8,
-1,
2*a
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-3*a - 3)*q^4 + (-2*a - 5)*q^5 - a*q^6 + (2*a + 1)*q^7 + (4*a + 3)*q^8 + q^9 + (a + 2)*q^10 + 2*a*q^11 + (3*a + 3)*q^12 + (2*a + 2)*q^13 + (-5*a - 2)*q^14 + (2*a + 5)*q^15 + (-3*a + 2)*q^16 + (-4*a - 8)*q^17 + a*q^18 + (-2*a - 7)*q^19 + (3*a + 9)*q^20 + (-2*a - 1)*q^21 + (-6*a - 2)*q^22 + (-2*a - 2)*q^23 + (-4*a - 3)*q^24 + (8*a + 16)*q^25 + (-4*a - 2)*q^26 - q^27 + (9*a + 3)*q^28 + (2*a + 4)*q^29 + (-a - 2)*q^30 - q^31 + (3*a - 3)*q^32 - 2*a*q^33 + (4*a + 4)*q^34 - q^35 + (-3*a - 3)*q^36 + (-6*a - 8)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^2 - a + 2)*q^5 + a*q^6 + (-a^2 - a + 4)*q^7 - q^8 + q^9 + (-a^2 - 2*a + 1)*q^10 + (2*a^2 - 6)*q^11 + (a^2 - 2)*q^12 + (2*a^2 - 4)*q^13 + (-a^2 + 1)*q^14 + (-a^2 - a + 2)*q^15 + (-2*a^2 - a + 4)*q^16 + (2*a^2 + 2*a - 6)*q^17 + a*q^18 + (-a^2 + 3*a + 4)*q^19 + (-a - 3)*q^20 + (-a^2 - a + 4)*q^21 + (2*a - 2)*q^22 + (-2*a - 2)*q^23 - q^24 + (a^2 + 3*a - 3)*q^25 + (4*a - 2)*q^26 + q^27 + (2*a^2 - a - 7)*q^28 + (-4*a^2 - 2*a + 8)*q^29 + (-a^2 - 2*a + 1)*q^30 - q^31 + (-a^2 - 4*a + 4)*q^32 + (2*a^2 - 6)*q^33 + (2*a^2 + 2*a - 2)*q^34 + (-a^2 + a + 6)*q^35 + (a^2 - 2)*q^36 + 2*a*q^37 + O(q^38)
*]> ;  // time = 7.289 seconds




J[94] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 94, 94, 47 ], new_dimensions := [ 1, 2, 4 ], dimensions := [ 1, 2, 8 ], intersection_graph := [ 0, 1, 1, 1, 0, 47, 1, 47, 0 ], ap_traces := [
[ 1, 0, 0, 0, 2, -4, -2, -2, 4, 4, 4, 2 ],
[ -2, 0, 4, -4, 8, -4, 0, -8, 0, 12, 0, 4 ]
], hecke_fields := [
x - 1,
x^2 - 8
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 47, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1 ], torsion_lower_bounds := [ 1, 1 ], l_ratios := [ 1, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ 1, 0, 0, 0, 2, -4, -2, -2, 4, 4, 4, 2 ],
[
-1,
a,
-1/2*a + 2,
-a - 2,
-1/2*a + 4,
-1/2*a - 2,
0,
3/2*a - 4,
-a,
3/2*a + 6,
-3*a,
3*a + 2
]
*], q_expansions := [*
q + q^2 + q^4 + q^8 - 3*q^9 + 2*q^11 - 4*q^13 + q^16 - 2*q^17 - 3*q^18 - 2*q^19 + 2*q^22 + 4*q^23 - 5*q^25 - 4*q^26 + 4*q^29 + 4*q^31 + q^32 - 2*q^34 - 3*q^36 + 2*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-1/2*a + 2)*q^5 - a*q^6 + (-a - 2)*q^7 - q^8 + 5*q^9 + (1/2*a - 2)*q^10 + (-1/2*a + 4)*q^11 + a*q^12 + (-1/2*a - 2)*q^13 + (a + 2)*q^14 + (2*a - 4)*q^15 + q^16 - 5*q^18 + (3/2*a - 4)*q^19 + (-1/2*a + 2)*q^20 + (-2*a - 8)*q^21 + (1/2*a - 4)*q^22 - a*q^23 - a*q^24 + (-2*a + 1)*q^25 + (1/2*a + 2)*q^26 + 2*a*q^27 + (-a - 2)*q^28 + (3/2*a + 6)*q^29 + (-2*a + 4)*q^30 - 3*a*q^31 - q^32 + (4*a - 4)*q^33 - a*q^35 + 5*q^36 + (3*a + 2)*q^37 + O(q^38)
*]> ;  // time = 9.529 seconds




J[95] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 95, 95, 19 ], new_dimensions := [ 3, 4, 1 ], dimensions := [ 3, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 0, 9, 1, 9, 0 ], ap_traces := [
[ 1, 2, 3, 0, -8, 8, 2, -3, -4, -10, 4, 20 ],
[ -2, 2, -4, 4, 4, 2, 4, 4, -8, 4, 4, -6 ]
], hecke_fields := [
x^3 - x^2 - 3*x + 1,
x^4 + 2*x^3 - 6*x^2 - 8*x + 9
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 5, 1 ],
[ 27, 3 ]
], tamagawa_numbers := [
[ 5, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 5, 3 ], torsion_lower_bounds := [ 5, 3 ], l_ratios := [ 1/5, 1/3 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
a,
-a^2 + 3,
1,
2*a^2 - 2*a - 4,
-2*a - 2,
a^2 - 2*a + 1,
-2*a^2 + 4*a + 4,
-1,
2*a - 2,
2*a^2 - 8,
4*a,
a^2 - 2*a + 5
],
[
a,
-a^3 + 5*a - 2,
-1,
-2*a^2 - 2*a + 8,
2*a^2 + 2*a - 6,
a^3 + 2*a^2 - 3*a - 4,
2*a^3 - 10*a + 6,
1,
-2*a^3 - 2*a^2 + 8*a,
2*a^3 - 10*a + 6,
2*a^3 - 2*a^2 - 10*a + 14,
a^3 - 3*a + 2
]
*], q_expansions := [*
q + a*q^2 + (-a^2 + 3)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^2 + 1)*q^6 + (2*a^2 - 2*a - 4)*q^7 + (a^2 - a - 1)*q^8 + (-2*a^2 + 2*a + 5)*q^9 + a*q^10 + (-2*a - 2)*q^11 + (a^2 - 2*a - 5)*q^12 + (a^2 - 2*a + 1)*q^13 + (2*a - 2)*q^14 + (-a^2 + 3)*q^15 + (-2*a^2 + 2*a + 3)*q^16 + (-2*a^2 + 4*a + 4)*q^17 + (-a + 2)*q^18 - q^19 + (a^2 - 2)*q^20 + (4*a^2 - 4*a - 12)*q^21 + (-2*a^2 - 2*a)*q^22 + (2*a - 2)*q^23 + (a^2 - 2*a - 3)*q^24 + q^25 + (-a^2 + 4*a - 1)*q^26 + (-2*a^2 + 4*a + 6)*q^27 + (-2*a^2 + 2*a + 8)*q^28 + (2*a^2 - 8)*q^29 + (-a^2 + 1)*q^30 + 4*a*q^31 + (-2*a^2 - a + 4)*q^32 + (4*a^2 - 8)*q^33 + (2*a^2 - 2*a + 2)*q^34 + (2*a^2 - 2*a - 4)*q^35 + (3*a^2 - 2*a - 10)*q^36 + (a^2 - 2*a + 5)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 5*a - 2)*q^3 + (a^2 - 2)*q^4 - q^5 + (2*a^3 - a^2 - 10*a + 9)*q^6 + (-2*a^2 - 2*a + 8)*q^7 + (a^3 - 4*a)*q^8 + (-2*a + 1)*q^9 - a*q^10 + (2*a^2 + 2*a - 6)*q^11 + (-3*a^3 + 2*a^2 + 15*a - 14)*q^12 + (a^3 + 2*a^2 - 3*a - 4)*q^13 + (-2*a^3 - 2*a^2 + 8*a)*q^14 + (a^3 - 5*a + 2)*q^15 + (-2*a^3 + 8*a - 5)*q^16 + (2*a^3 - 10*a + 6)*q^17 + (-2*a^2 + a)*q^18 + q^19 + (-a^2 + 2)*q^20 + (-2*a^3 - 2*a^2 + 10*a + 2)*q^21 + (2*a^3 + 2*a^2 - 6*a)*q^22 + (-2*a^3 - 2*a^2 + 8*a)*q^23 + (4*a^3 - a^2 - 18*a + 9)*q^24 + q^25 + (3*a^2 + 4*a - 9)*q^26 + (-2*a^3 + 2*a^2 + 10*a - 14)*q^27 + (2*a^3 - 12*a + 2)*q^28 + (2*a^3 - 10*a + 6)*q^29 + (-2*a^3 + a^2 + 10*a - 9)*q^30 + (2*a^3 - 2*a^2 - 10*a + 14)*q^31 + (2*a^3 - 4*a^2 - 13*a + 18)*q^32 + (2*a^2 - 6)*q^33 + (-4*a^3 + 2*a^2 + 22*a - 18)*q^34 + (2*a^2 + 2*a - 8)*q^35 + (-2*a^3 + a^2 + 4*a - 2)*q^36 + (a^3 - 3*a + 2)*q^37 + O(q^38)
*]> ;  // time = 7.601 seconds




J[97] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 97, 97 ], new_dimensions := [ 3, 4 ], dimensions := [ 3, 4 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -4, -4, -3, -7, -7, -2, -3, 5, -12, 1, -8, -2 ],
[ 3, 0, 1, 3, 5, -6, 3, -3, 22, 7, -4, -6 ]
], hecke_fields := [
x^3 + 4*x^2 + 3*x - 1,
x^4 - 3*x^3 - x^2 + 6*x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ]
], torsion_upper_bounds := [ 1, 1 ], torsion_lower_bounds := [ 1, 1 ], l_ratios := [ 0, 1 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^2 - 3*a - 2,
2*a^2 + 5*a - 1,
-a^2 - 3*a - 3,
a - 1,
-a - 2,
a^2 + 4*a + 1,
-4*a^2 - 6*a + 7,
-3*a - 8,
-4*a^2 - 14*a - 5,
a^2 - 6,
6*a^2 + 17*a + 2
],
[
a,
-a^2 + a + 2,
-a + 1,
a^3 - a^2 - 4*a + 2,
-2*a^3 + 4*a^2 + 3*a - 3,
-3*a^3 + 4*a^2 + 8*a - 5,
2*a^3 - 3*a^2 - 4*a + 3,
-a^3 + 2*a^2 + 3*a - 4,
-a^3 + 4*a^2 - 1,
a^3 - 2*a^2 + a + 2,
3*a^3 - 7*a^2 - 3*a + 7,
-3*a^3 + 6*a^2 + 6*a - 9
]
*], q_expansions := [*
q + a*q^2 + (-a^2 - 3*a - 2)*q^3 + (a^2 - 2)*q^4 + (2*a^2 + 5*a - 1)*q^5 + (a^2 + a - 1)*q^6 + (-a^2 - 3*a - 3)*q^7 + (-4*a^2 - 7*a + 1)*q^8 + (2*a^2 + 7*a + 3)*q^9 + (-3*a^2 - 7*a + 2)*q^10 + (a - 1)*q^11 + (-a^2 + 2*a + 5)*q^12 + (-a - 2)*q^13 + (a^2 - 1)*q^14 - q^15 + (7*a^2 + 13*a)*q^16 + (a^2 + 4*a + 1)*q^17 + (-a^2 - 3*a + 2)*q^18 + (-4*a^2 - 6*a + 7)*q^19 + (a^2 + a - 1)*q^20 + (3*a^2 + 10*a + 8)*q^21 + (a^2 - a)*q^22 + (-3*a - 8)*q^23 + (4*a^2 + 6*a + 1)*q^24 + (-7*a^2 - 18*a)*q^25 + (-a^2 - 2*a)*q^26 + (a^2 - a - 5)*q^27 + (-2*a^2 + 2*a + 7)*q^28 + (-4*a^2 - 14*a - 5)*q^29 - a*q^30 + (a^2 - 6)*q^31 + (-7*a^2 - 7*a + 5)*q^32 + (2*a^2 + 4*a + 1)*q^33 + (-2*a + 1)*q^34 + (-2*a^2 - 5*a)*q^35 + (-3*a^2 - 9*a - 7)*q^36 + (6*a^2 + 17*a + 2)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + a + 2)*q^3 + (a^2 - 2)*q^4 + (-a + 1)*q^5 + (-a^3 + a^2 + 2*a)*q^6 + (a^3 - a^2 - 4*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (a^3 - 2*a^2 - 2*a + 2)*q^9 + (-a^2 + a)*q^10 + (-2*a^3 + 4*a^2 + 3*a - 3)*q^11 + (-2*a^3 + 3*a^2 + 4*a - 5)*q^12 + (-3*a^3 + 4*a^2 + 8*a - 5)*q^13 + (2*a^3 - 3*a^2 - 4*a + 1)*q^14 + (a^3 - 2*a^2 - a + 2)*q^15 + (3*a^3 - 5*a^2 - 6*a + 5)*q^16 + (2*a^3 - 3*a^2 - 4*a + 3)*q^17 + (a^3 - a^2 - 4*a + 1)*q^18 + (-a^3 + 2*a^2 + 3*a - 4)*q^19 + (-a^3 + a^2 + 2*a - 2)*q^20 + (a^3 - 3*a^2 - a + 3)*q^21 + (-2*a^3 + a^2 + 9*a - 2)*q^22 + (-a^3 + 4*a^2 - 1)*q^23 + (-a^3 + 3*a - 2)*q^24 + (a^2 - 2*a - 4)*q^25 + (-5*a^3 + 5*a^2 + 13*a - 3)*q^26 + (a^3 + a^2 - 6*a - 2)*q^27 + (a^3 - 3*a - 2)*q^28 + (a^3 - 2*a^2 + a + 2)*q^29 + (a^3 - 4*a + 1)*q^30 + (3*a^3 - 7*a^2 - 3*a + 7)*q^31 + (2*a^3 - 3*a^2 - 5*a + 3)*q^32 + (-a^3 + 2*a^2 + 5*a - 6)*q^33 + (3*a^3 - 2*a^2 - 9*a + 2)*q^34 + (-a^3 + 2*a^2 + 1)*q^35 + (a^2 - a - 3)*q^36 + (-3*a^3 + 6*a^2 + 6*a - 9)*q^37 + O(q^38)
*]> ;  // time = 1.069 seconds




J[101] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 101, 101 ], new_dimensions := [ 1, 7 ], dimensions := [ 1, 7 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ 0, -2, -1, -2, -2, 1, 3, -5, 1, -4, -9, -2 ],
[ 0, 4, -3, 2, 8, -1, -7, 19, -7, -2, 7, 0 ]
], hecke_fields := [
x - 1,
x^7 - 13*x^5 + 2*x^4 + 47*x^3 - 16*x^2 - 43*x + 14
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 25 ]
], tamagawa_numbers := [
[ 1 ],
[ 25 ]
], torsion_upper_bounds := [ 1, 25 ], torsion_lower_bounds := [ 1, 25 ], l_ratios := [ 0, 1/25 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ 0, -2, -1, -2, -2, 1, 3, -5, 1, -4, -9, -2 ],
[
a,
1/4*a^6 + 1/4*a^5 - 5/2*a^4 - 5/2*a^3 + 19/4*a^2 + 17/4*a + 1/2,
-1/2*a^6 - 3/4*a^5 + 11/2*a^4 + 7*a^3 - 29/2*a^2 - 45/4*a + 15/2,
-1/4*a^5 - 1/2*a^4 + 5/2*a^3 + 4*a^2 - 21/4*a - 7/2,
-1/4*a^6 + 3*a^4 - 35/4*a^2 + 5,
3/4*a^6 + a^5 - 17/2*a^4 - 9*a^3 + 91/4*a^2 + 12*a - 10,
3/4*a^6 + 3/4*a^5 - 8*a^4 - 7*a^3 + 79/4*a^2 + 45/4*a - 21/2,
1/2*a^5 - 5*a^3 + 21/2*a + 2,
-1/2*a^6 - 1/2*a^5 + 5*a^4 + 4*a^3 - 21/2*a^2 - 7/2*a + 2,
-1/2*a^6 - 1/2*a^5 + 5*a^4 + 4*a^3 - 19/2*a^2 - 7/2*a - 1,
-a^6 - 3/2*a^5 + 11*a^4 + 15*a^3 - 28*a^2 - 55/2*a + 14,
-5/4*a^6 - 9/4*a^5 + 13*a^4 + 21*a^3 - 113/4*a^2 - 135/4*a + 13/2
]
*], q_expansions := [*
q - 2*q^3 - 2*q^4 - q^5 - 2*q^7 + q^9 - 2*q^11 + 4*q^12 + q^13 + 2*q^15 + 4*q^16 + 3*q^17 - 5*q^19 + 2*q^20 + 4*q^21 + q^23 - 4*q^25 + 4*q^27 + 4*q^28 - 4*q^29 - 9*q^31 + 4*q^33 + 2*q^35 - 2*q^36 - 2*q^37 + O(q^38),
q + a*q^2 + (1/4*a^6 + 1/4*a^5 - 5/2*a^4 - 5/2*a^3 + 19/4*a^2 + 17/4*a + 1/2)*q^3 + (a^2 - 2)*q^4 + (-1/2*a^6 - 3/4*a^5 + 11/2*a^4 + 7*a^3 - 29/2*a^2 - 45/4*a + 15/2)*q^5 + (1/4*a^6 + 3/4*a^5 - 3*a^4 - 7*a^3 + 33/4*a^2 + 45/4*a - 7/2)*q^6 + (-1/4*a^5 - 1/2*a^4 + 5/2*a^3 + 4*a^2 - 21/4*a - 7/2)*q^7 + (a^3 - 4*a)*q^8 + (1/4*a^6 + 1/2*a^5 - 5/2*a^4 - 5*a^3 + 21/4*a^2 + 17/2*a - 1)*q^9 + (-3/4*a^6 - a^5 + 8*a^4 + 9*a^3 - 77/4*a^2 - 14*a + 7)*q^10 + (-1/4*a^6 + 3*a^4 - 35/4*a^2 + 5)*q^11 + (1/4*a^6 - 1/4*a^5 - 5/2*a^4 + 3/2*a^3 + 23/4*a^2 - 5/4*a - 9/2)*q^12 + (3/4*a^6 + a^5 - 17/2*a^4 - 9*a^3 + 91/4*a^2 + 12*a - 10)*q^13 + (-1/4*a^6 - 1/2*a^5 + 5/2*a^4 + 4*a^3 - 21/4*a^2 - 7/2*a)*q^14 + (-3/4*a^6 - 3/4*a^5 + 17/2*a^4 + 15/2*a^3 - 93/4*a^2 - 55/4*a + 25/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (3/4*a^6 + 3/4*a^5 - 8*a^4 - 7*a^3 + 79/4*a^2 + 45/4*a - 21/2)*q^17 + (1/2*a^6 + 3/4*a^5 - 11/2*a^4 - 13/2*a^3 + 25/2*a^2 + 39/4*a - 7/2)*q^18 + (1/2*a^5 - 5*a^3 + 21/2*a + 2)*q^19 + (-1/4*a^5 - 1/2*a^4 + 2*a^3 + 3*a^2 - 11/4*a - 9/2)*q^20 + (3/4*a^6 + 1/2*a^5 - 17/2*a^4 - 4*a^3 + 95/4*a^2 + 7/2*a - 14)*q^21 + (-1/4*a^5 + 1/2*a^4 + 3*a^3 - 4*a^2 - 23/4*a + 7/2)*q^22 + (-1/2*a^6 - 1/2*a^5 + 5*a^4 + 4*a^3 - 21/2*a^2 - 7/2*a + 2)*q^23 + (-3/4*a^6 - 3/4*a^5 + 7*a^4 + 8*a^3 - 55/4*a^2 - 65/4*a + 7/2)*q^24 + (3/4*a^6 + 5/4*a^5 - 8*a^4 - 12*a^3 + 75/4*a^2 + 87/4*a - 13/2)*q^25 + (a^6 + 5/4*a^5 - 21/2*a^4 - 25/2*a^3 + 24*a^2 + 89/4*a - 21/2)*q^26 + (-1/2*a^6 - 3/4*a^5 + 11/2*a^4 + 13/2*a^3 - 25/2*a^2 - 31/4*a + 3/2)*q^27 + (-1/2*a^6 - 1/4*a^5 + 11/2*a^4 + 3/2*a^3 - 31/2*a^2 - 1/4*a + 21/2)*q^28 + (-1/2*a^6 - 1/2*a^5 + 5*a^4 + 4*a^3 - 19/2*a^2 - 7/2*a - 1)*q^29 + (-3/4*a^6 - 5/4*a^5 + 9*a^4 + 12*a^3 - 103/4*a^2 - 79/4*a + 21/2)*q^30 + (-a^6 - 3/2*a^5 + 11*a^4 + 15*a^3 - 28*a^2 - 55/2*a + 14)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-3/4*a^6 - 5/4*a^5 + 9*a^4 + 11*a^3 - 111/4*a^2 - 59/4*a + 33/2)*q^33 + (3/4*a^6 + 7/4*a^5 - 17/2*a^4 - 31/2*a^3 + 93/4*a^2 + 87/4*a - 21/2)*q^34 + (-1/4*a^6 - a^5 + 2*a^4 + 10*a^3 + 1/4*a^2 - 18*a - 7)*q^35 + (1/4*a^6 - 5/2*a^4 - a^3 + 29/4*a^2 + a - 5)*q^36 + (-5/4*a^6 - 9/4*a^5 + 13*a^4 + 21*a^3 - 113/4*a^2 - 135/4*a + 13/2)*q^37 + O(q^38)
*]> ;  // time = 1.149 seconds




J[102] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 102, 102, 102, 51, 51, 34, 17 ], new_dimensions := [ 1, 1, 1, 1, 2, 1, 1 ], dimensions := [ 1, 1, 1, 2, 4, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 0, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ -1, -1, -4, -2, 0, -6, -1, 4, 6, -4, -6, -4 ],
[ -1, 1, 0, 2, 0, 2, -1, -4, -6, 0, -10, 8 ],
[ 1, 1, -2, 0, -4, -2, 1, 4, 0, -10, 8, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 3, 3, 1 ],
[ 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 1 ], torsion_lower_bounds := [ 1, 3, 1 ], l_ratios := [ 0, 1/3, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ -1, -1, -4, -2, 0, -6, -1, 4, 6, -4, -6, -4 ],
[ -1, 1, 0, 2, 0, 2, -1, -4, -6, 0, -10, 8 ],
[ 1, 1, -2, 0, -4, -2, 1, 4, 0, -10, 8, -2 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - 4*q^5 + q^6 - 2*q^7 - q^8 + q^9 + 4*q^10 - q^12 - 6*q^13 + 2*q^14 + 4*q^15 + q^16 - q^17 - q^18 + 4*q^19 - 4*q^20 + 2*q^21 + 6*q^23 + q^24 + 11*q^25 + 6*q^26 - q^27 - 2*q^28 - 4*q^29 - 4*q^30 - 6*q^31 - q^32 + q^34 + 8*q^35 + q^36 - 4*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - q^6 + 2*q^7 - q^8 + q^9 + q^12 + 2*q^13 - 2*q^14 + q^16 - q^17 - q^18 - 4*q^19 + 2*q^21 - 6*q^23 - q^24 - 5*q^25 - 2*q^26 + q^27 + 2*q^28 - 10*q^31 - q^32 + q^34 + q^36 + 8*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - 2*q^5 + q^6 + q^8 + q^9 - 2*q^10 - 4*q^11 + q^12 - 2*q^13 - 2*q^15 + q^16 + q^17 + q^18 + 4*q^19 - 2*q^20 - 4*q^22 + q^24 - q^25 - 2*q^26 + q^27 - 10*q^29 - 2*q^30 + 8*q^31 + q^32 - 4*q^33 + q^34 + q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 37.689 seconds




J[103] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 103, 103 ], new_dimensions := [ 2, 6 ], dimensions := [ 2, 6 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -3, -2, -3, -2, -3, -3, -9, 5, 0, -6, 0, 0 ],
[ 4, 0, 3, -2, -1, -1, 21, -7, 12, 12, -16, 0 ]
], hecke_fields := [
x^2 + 3*x + 1,
x^6 - 4*x^5 - x^4 + 17*x^3 - 9*x^2 - 16*x + 11
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 17 ]
], tamagawa_numbers := [
[ 1 ],
[ 17 ]
], torsion_upper_bounds := [ 1, 17 ], torsion_lower_bounds := [ 1, 17 ], l_ratios := [ 0, 1/17 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-1,
-a - 3,
-1,
a,
3*a + 3,
a - 3,
-3*a - 2,
-4*a - 6,
2*a,
6*a + 9,
-6*a - 9
],
[
a,
-a^5 + 3*a^4 + 3*a^3 - 11*a^2 - a + 8,
2*a^5 - 5*a^4 - 9*a^3 + 19*a^2 + 9*a - 13,
-a^4 + 2*a^3 + 4*a^2 - 5*a - 3,
-a^5 + 2*a^4 + 4*a^3 - 4*a^2 - 4*a - 1,
2*a^5 - 4*a^4 - 11*a^3 + 15*a^2 + 14*a - 11,
-3*a^5 + 7*a^4 + 16*a^3 - 30*a^2 - 21*a + 30,
-a^5 + 3*a^4 + 4*a^3 - 14*a^2 - 3*a + 13,
-4*a^5 + 9*a^4 + 22*a^3 - 38*a^2 - 29*a + 34,
3*a^5 - 8*a^4 - 13*a^3 + 31*a^2 + 14*a - 21,
a^5 - 3*a^4 - 3*a^3 + 11*a^2 + 3*a - 12,
5*a^5 - 13*a^4 - 23*a^3 + 53*a^2 + 27*a - 44
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-3*a - 3)*q^4 + (-a - 3)*q^5 - a*q^6 - q^7 + (4*a + 3)*q^8 - 2*q^9 + q^10 + a*q^11 + (3*a + 3)*q^12 + (3*a + 3)*q^13 - a*q^14 + (a + 3)*q^15 + (-3*a + 2)*q^16 + (a - 3)*q^17 - 2*a*q^18 + (-3*a - 2)*q^19 + (3*a + 6)*q^20 + q^21 + (-3*a - 1)*q^22 + (-4*a - 6)*q^23 + (-4*a - 3)*q^24 + (3*a + 3)*q^25 + (-6*a - 3)*q^26 + 5*q^27 + (3*a + 3)*q^28 + 2*a*q^29 - q^30 + (6*a + 9)*q^31 + (3*a - 3)*q^32 - a*q^33 + (-6*a - 1)*q^34 + (a + 3)*q^35 + (6*a + 6)*q^36 + (-6*a - 9)*q^37 + O(q^38),
q + a*q^2 + (-a^5 + 3*a^4 + 3*a^3 - 11*a^2 - a + 8)*q^3 + (a^2 - 2)*q^4 + (2*a^5 - 5*a^4 - 9*a^3 + 19*a^2 + 9*a - 13)*q^5 + (-a^5 + 2*a^4 + 6*a^3 - 10*a^2 - 8*a + 11)*q^6 + (-a^4 + 2*a^3 + 4*a^2 - 5*a - 3)*q^7 + (a^3 - 4*a)*q^8 + (-a^5 + 3*a^4 + 5*a^3 - 15*a^2 - 7*a + 17)*q^9 + (3*a^5 - 7*a^4 - 15*a^3 + 27*a^2 + 19*a - 22)*q^10 + (-a^5 + 2*a^4 + 4*a^3 - 4*a^2 - 4*a - 1)*q^11 + (-a^4 + a^3 + 5*a^2 - 3*a - 5)*q^12 + (2*a^5 - 4*a^4 - 11*a^3 + 15*a^2 + 14*a - 11)*q^13 + (-a^5 + 2*a^4 + 4*a^3 - 5*a^2 - 3*a)*q^14 + (a^4 - 3*a^3 - a^2 + 7*a - 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3*a^5 + 7*a^4 + 16*a^3 - 30*a^2 - 21*a + 30)*q^17 + (-a^5 + 4*a^4 + 2*a^3 - 16*a^2 + a + 11)*q^18 + (-a^5 + 3*a^4 + 4*a^3 - 14*a^2 - 3*a + 13)*q^19 + (a^5 - 2*a^4 - 6*a^3 + 8*a^2 + 8*a - 7)*q^20 + (a^5 - 3*a^4 - 5*a^3 + 17*a^2 + 7*a - 24)*q^21 + (-2*a^5 + 3*a^4 + 13*a^3 - 13*a^2 - 17*a + 11)*q^22 + (-4*a^5 + 9*a^4 + 22*a^3 - 38*a^2 - 29*a + 34)*q^23 + (a^5 - 3*a^4 - 7*a^3 + 17*a^2 + 11*a - 22)*q^24 + (a^5 - 4*a^4 - 2*a^3 + 16*a^2 - 12)*q^25 + (4*a^5 - 9*a^4 - 19*a^3 + 32*a^2 + 21*a - 22)*q^26 + (a^5 - a^4 - 7*a^3 + a^2 + 13*a + 2)*q^27 + (-2*a^5 + 5*a^4 + 8*a^3 - 20*a^2 - 6*a + 17)*q^28 + (3*a^5 - 8*a^4 - 13*a^3 + 31*a^2 + 14*a - 21)*q^29 + (a^5 - 3*a^4 - a^3 + 7*a^2 - 5*a)*q^30 + (a^5 - 3*a^4 - 3*a^3 + 11*a^2 + 3*a - 12)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^5 - 4*a^4 - 2*a^3 + 20*a^2 - 4*a - 19)*q^33 + (-5*a^5 + 13*a^4 + 21*a^3 - 48*a^2 - 18*a + 33)*q^34 + (2*a^5 - 5*a^4 - 7*a^3 + 15*a^2 + 3*a - 5)*q^35 + (2*a^5 - 5*a^4 - 9*a^3 + 22*a^2 + 9*a - 23)*q^36 + (5*a^5 - 13*a^4 - 23*a^3 + 53*a^2 + 27*a - 44)*q^37 + O(q^38)
*]> ;  // time = 1.171 seconds




J[105] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 105, 105, 35, 35, 21, 15 ], new_dimensions := [ 1, 2, 1, 2, 1, 1 ], dimensions := [ 1, 2, 2, 4, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 0, 5, 1, 1, 1, 1, 5, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 1, 1, 1, 1, 0, -6, 2, -8, 8, -2, 4, -2 ],
[ 0, -2, -2, 2, 4, 0, -4, 4, 8, -4, 12, 4 ]
], hecke_fields := [
x - 1,
x^2 - 5
], atkin_lehners := [
[ -1, -1, -1 ],
[ 1, 1, -1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 5, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1 ], torsion_lower_bounds := [ 1, 1 ], l_ratios := [ 1, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ 1, 1, 1, 1, 0, -6, 2, -8, 8, -2, 4, -2 ],
[
a,
-1,
-1,
1,
-2*a + 2,
-2*a,
-2,
2*a + 2,
4,
-2,
2*a + 6,
4*a + 2
]
*], q_expansions := [*
q + q^2 + q^3 - q^4 + q^5 + q^6 + q^7 - 3*q^8 + q^9 + q^10 - q^12 - 6*q^13 + q^14 + q^15 - q^16 + 2*q^17 + q^18 - 8*q^19 - q^20 + q^21 + 8*q^23 - 3*q^24 + q^25 - 6*q^26 + q^27 - q^28 - 2*q^29 + q^30 + 4*q^31 + 5*q^32 + 2*q^34 + q^35 - q^36 - 2*q^37 + O(q^38),
q + a*q^2 - q^3 + 3*q^4 - q^5 - a*q^6 + q^7 + a*q^8 + q^9 - a*q^10 + (-2*a + 2)*q^11 - 3*q^12 - 2*a*q^13 + a*q^14 + q^15 - q^16 - 2*q^17 + a*q^18 + (2*a + 2)*q^19 - 3*q^20 - q^21 + (2*a - 10)*q^22 + 4*q^23 - a*q^24 + q^25 - 10*q^26 - q^27 + 3*q^28 - 2*q^29 + a*q^30 + (2*a + 6)*q^31 - 3*a*q^32 + (2*a - 2)*q^33 - 2*a*q^34 - q^35 + 3*q^36 + (4*a + 2)*q^37 + O(q^38)
*]> ;  // time = 17.341 seconds




J[106] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 106, 106, 106, 106, 53, 53 ], new_dimensions := [ 1, 1, 1, 1, 1, 3 ], dimensions := [ 1, 1, 1, 1, 2, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 0, 3, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 0 ], ap_traces := [
[ -1, -1, -4, 0, -4, 1, 5, -7, 1, 5, -4, 1 ],
[ -1, 2, 1, -2, 5, -4, 3, -4, -3, -6, 7, -6 ],
[ 1, 1, 0, -4, 0, 5, -3, -1, 3, 9, -4, 5 ],
[ 1, -2, 3, 2, -3, -4, 3, -4, -9, 6, 5, -10 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 5, 1 ],
[ 3, 1 ],
[ 3, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 3 ], torsion_lower_bounds := [ 1, 1, 3, 3 ], l_ratios := [ 0, 1, 1/3, 1/3 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1 ], eigenvalues := [*
[ -1, -1, -4, 0, -4, 1, 5, -7, 1, 5, -4, 1 ],
[ -1, 2, 1, -2, 5, -4, 3, -4, -3, -6, 7, -6 ],
[ 1, 1, 0, -4, 0, 5, -3, -1, 3, 9, -4, 5 ],
[ 1, -2, 3, 2, -3, -4, 3, -4, -9, 6, 5, -10 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - 4*q^5 + q^6 - q^8 - 2*q^9 + 4*q^10 - 4*q^11 - q^12 + q^13 + 4*q^15 + q^16 + 5*q^17 + 2*q^18 - 7*q^19 - 4*q^20 + 4*q^22 + q^23 + q^24 + 11*q^25 - q^26 + 5*q^27 + 5*q^29 - 4*q^30 - 4*q^31 - q^32 + 4*q^33 - 5*q^34 - 2*q^36 + q^37 + O(q^38),
q - q^2 + 2*q^3 + q^4 + q^5 - 2*q^6 - 2*q^7 - q^8 + q^9 - q^10 + 5*q^11 + 2*q^12 - 4*q^13 + 2*q^14 + 2*q^15 + q^16 + 3*q^17 - q^18 - 4*q^19 + q^20 - 4*q^21 - 5*q^22 - 3*q^23 - 2*q^24 - 4*q^25 + 4*q^26 - 4*q^27 - 2*q^28 - 6*q^29 - 2*q^30 + 7*q^31 - q^32 + 10*q^33 - 3*q^34 - 2*q^35 + q^36 - 6*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^6 - 4*q^7 + q^8 - 2*q^9 + q^12 + 5*q^13 - 4*q^14 + q^16 - 3*q^17 - 2*q^18 - q^19 - 4*q^21 + 3*q^23 + q^24 - 5*q^25 + 5*q^26 - 5*q^27 - 4*q^28 + 9*q^29 - 4*q^31 + q^32 - 3*q^34 - 2*q^36 + 5*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 + 3*q^5 - 2*q^6 + 2*q^7 + q^8 + q^9 + 3*q^10 - 3*q^11 - 2*q^12 - 4*q^13 + 2*q^14 - 6*q^15 + q^16 + 3*q^17 + q^18 - 4*q^19 + 3*q^20 - 4*q^21 - 3*q^22 - 9*q^23 - 2*q^24 + 4*q^25 - 4*q^26 + 4*q^27 + 2*q^28 + 6*q^29 - 6*q^30 + 5*q^31 + q^32 + 6*q^33 + 3*q^34 + 6*q^35 + q^36 - 10*q^37 + O(q^38)
*]> ;  // time = 12.181 seconds




J[107] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 107, 107 ], new_dimensions := [ 2, 7 ], dimensions := [ 2, 7 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -3, -3, -4, 4, -12, -3, 2, 6, -2, -2, -13 ],
[ -1, 3, 5, 4, -2, 18, -1, -4, 0, -3, 4, 25 ]
], hecke_fields := [
x^2 + x - 1,
x^7 + x^6 - 10*x^5 - 7*x^4 + 29*x^3 + 12*x^2 - 20*x - 8
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 53 ]
], tamagawa_numbers := [
[ 1 ],
[ 53 ]
], torsion_upper_bounds := [ 1, 53 ], torsion_lower_bounds := [ 1, 53 ], l_ratios := [ 0, 1/53 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a - 2,
-a - 2,
2*a - 1,
2*a + 3,
-6,
a - 1,
-6*a - 2,
-4*a + 1,
-4*a - 3,
4*a + 1,
-3*a - 8
],
[
a,
-1/4*a^6 - 1/4*a^5 + 5/2*a^4 + 3/4*a^3 - 29/4*a^2 + 2*a + 4,
1/2*a^6 + 1/2*a^5 - 4*a^4 - 5/2*a^3 + 15/2*a^2 + a,
-1/2*a^6 - 1/2*a^5 + 4*a^4 + 7/2*a^3 - 15/2*a^2 - 6*a + 2,
1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 11/2*a,
1/2*a^6 - 11/2*a^4 + 1/2*a^3 + 17*a^2 - 7/2*a - 8,
a^5 + a^4 - 7*a^3 - 5*a^2 + 10*a + 4,
-3/4*a^6 - 5/4*a^5 + 6*a^4 + 33/4*a^3 - 45/4*a^2 - 19/2*a,
3/4*a^6 - 3/4*a^5 - 9*a^4 + 23/4*a^3 + 113/4*a^2 - 21/2*a - 16,
a^5 + a^4 - 7*a^3 - 4*a^2 + 12*a + 1,
a^4 - 7*a^2 + 2*a + 8,
-1/4*a^6 + 3/4*a^5 + 7/2*a^4 - 21/4*a^3 - 49/4*a^2 + 7*a + 12
]
*], q_expansions := [*
q + a*q^2 + (-a - 2)*q^3 + (-a - 1)*q^4 + (-a - 2)*q^5 + (-a - 1)*q^6 + (2*a - 1)*q^7 + (-2*a - 1)*q^8 + (3*a + 2)*q^9 + (-a - 1)*q^10 + (2*a + 3)*q^11 + (2*a + 3)*q^12 - 6*q^13 + (-3*a + 2)*q^14 + (3*a + 5)*q^15 + 3*a*q^16 + (a - 1)*q^17 + (-a + 3)*q^18 + (-6*a - 2)*q^19 + (2*a + 3)*q^20 - a*q^21 + (a + 2)*q^22 + (-4*a + 1)*q^23 + (3*a + 4)*q^24 + 3*a*q^25 - 6*a*q^26 + (-2*a - 1)*q^27 + (a - 1)*q^28 + (-4*a - 3)*q^29 + (2*a + 3)*q^30 + (4*a + 1)*q^31 + (a + 5)*q^32 + (-5*a - 8)*q^33 + (-2*a + 1)*q^34 - a*q^35 + (-2*a - 5)*q^36 + (-3*a - 8)*q^37 + O(q^38),
q + a*q^2 + (-1/4*a^6 - 1/4*a^5 + 5/2*a^4 + 3/4*a^3 - 29/4*a^2 + 2*a + 4)*q^3 + (a^2 - 2)*q^4 + (1/2*a^6 + 1/2*a^5 - 4*a^4 - 5/2*a^3 + 15/2*a^2 + a)*q^5 + (-a^4 + 5*a^2 - a - 2)*q^6 + (-1/2*a^6 - 1/2*a^5 + 4*a^4 + 7/2*a^3 - 15/2*a^2 - 6*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (1/4*a^6 - 1/4*a^5 - 2*a^4 + 9/4*a^3 + 15/4*a^2 - 9/2*a - 1)*q^9 + (a^5 + a^4 - 7*a^3 - 5*a^2 + 10*a + 4)*q^10 + (1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 11/2*a)*q^11 + (1/2*a^6 - 1/2*a^5 - 5*a^4 + 7/2*a^3 + 27/2*a^2 - 6*a - 8)*q^12 + (1/2*a^6 - 11/2*a^4 + 1/2*a^3 + 17*a^2 - 7/2*a - 8)*q^13 + (-a^5 + 7*a^3 - 8*a - 4)*q^14 + (-1/2*a^6 + 1/2*a^5 + 6*a^4 - 11/2*a^3 - 39/2*a^2 + 14*a + 10)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^5 + a^4 - 7*a^3 - 5*a^2 + 10*a + 4)*q^17 + (-1/2*a^6 + 1/2*a^5 + 4*a^4 - 7/2*a^3 - 15/2*a^2 + 4*a + 2)*q^18 + (-3/4*a^6 - 5/4*a^5 + 6*a^4 + 33/4*a^3 - 45/4*a^2 - 19/2*a)*q^19 + (a^4 - 5*a^2 + 2*a)*q^20 + (-a^6 - a^5 + 9*a^4 + 6*a^3 - 22*a^2 - 5*a + 8)*q^21 + (1/2*a^6 - 1/2*a^5 - 4*a^4 + 5/2*a^3 + 11/2*a^2)*q^22 + (3/4*a^6 - 3/4*a^5 - 9*a^4 + 23/4*a^3 + 113/4*a^2 - 21/2*a - 16)*q^23 + (-a^6 + 9*a^4 - a^3 - 22*a^2 + 4*a + 8)*q^24 + (a^6 - 11*a^4 + 2*a^3 + 32*a^2 - 10*a - 13)*q^25 + (-1/2*a^6 - 1/2*a^5 + 4*a^4 + 5/2*a^3 - 19/2*a^2 + 2*a + 4)*q^26 + (1/4*a^6 + 1/4*a^5 - 3/2*a^4 - 3/4*a^3 + 13/4*a^2 - 2*a - 5)*q^27 + (a^5 - a^4 - 7*a^3 + 7*a^2 + 8*a - 4)*q^28 + (a^5 + a^4 - 7*a^3 - 4*a^2 + 12*a + 1)*q^29 + (a^6 + a^5 - 9*a^4 - 5*a^3 + 20*a^2 - 4)*q^30 + (a^4 - 7*a^2 + 2*a + 8)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^6 + a^5 - 9/2*a^4 - 11/2*a^3 + 11*a^2 + 11/2*a - 3)*q^33 + (a^6 + a^5 - 7*a^4 - 5*a^3 + 10*a^2 + 4*a)*q^34 + (-a^5 + 9*a^3 - 18*a - 4)*q^35 + (1/2*a^6 - 1/2*a^5 - 3*a^4 + 5/2*a^3 + 5/2*a^2 + a - 2)*q^36 + (-1/4*a^6 + 3/4*a^5 + 7/2*a^4 - 21/4*a^3 - 49/4*a^2 + 7*a + 12)*q^37 + O(q^38)
*]> ;  // time = 1.25 seconds




J[109] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 109, 109, 109 ], new_dimensions := [ 1, 3, 4 ], dimensions := [ 1, 3, 4 ], intersection_graph := [ 0, 1, 1, 1, 0, 1, 1, 1, 0 ], ap_traces := [
[ 1, 0, 3, 2, 1, 0, -8, -5, 7, -5, 6, 2 ],
[ -2, -4, -6, -1, -13, -1, 3, -5, 1, -6, -7, 0 ],
[ -1, 4, 1, -3, 12, -7, 11, 10, -2, 1, -5, -12 ]
], hecke_fields := [
x - 1,
x^3 + 2*x^2 - x - 1,
x^4 + x^3 - 5*x^2 - 4*x + 3
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 9 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 9 ]
], torsion_upper_bounds := [ 1, 1, 9 ], torsion_lower_bounds := [ 1, 1, 9 ], l_ratios := [ 1, 0, 1/9 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ 1, 0, 3, 2, 1, 0, -8, -5, 7, -5, 6, 2 ],
[
a,
-a - 2,
-2*a^2 - 3*a,
3*a^2 + 5*a - 3,
a^2 + 2*a - 5,
-2*a^2 - a + 3,
-a^2 - 3*a + 1,
-3*a^2 - 5*a + 1,
-5*a - 3,
4*a^2 + 9*a - 4,
-2*a^2 - 7*a - 3,
a^2 - 2
],
[
a,
-a^3 + 4*a + 1,
-a,
a^3 - a^2 - 4*a + 2,
a^3 + a^2 - 5*a,
2*a^2 + a - 7,
a^3 - a^2 - 2*a + 6,
-a^2 - a + 5,
-a^3 + 2*a^2 + 4*a - 6,
2*a^3 - 2*a^2 - 7*a + 6,
2*a^3 - 7*a - 1,
-3*a^3 - 3*a^2 + 11*a + 5
]
*], q_expansions := [*
q + q^2 - q^4 + 3*q^5 + 2*q^7 - 3*q^8 - 3*q^9 + 3*q^10 + q^11 + 2*q^14 - q^16 - 8*q^17 - 3*q^18 - 5*q^19 - 3*q^20 + q^22 + 7*q^23 + 4*q^25 - 2*q^28 - 5*q^29 + 6*q^31 + 5*q^32 - 8*q^34 + 6*q^35 + 3*q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (-a - 2)*q^3 + (a^2 - 2)*q^4 + (-2*a^2 - 3*a)*q^5 + (-a^2 - 2*a)*q^6 + (3*a^2 + 5*a - 3)*q^7 + (-2*a^2 - 3*a + 1)*q^8 + (a^2 + 4*a + 1)*q^9 + (a^2 - 2*a - 2)*q^10 + (a^2 + 2*a - 5)*q^11 + (a + 3)*q^12 + (-2*a^2 - a + 3)*q^13 + (-a^2 + 3)*q^14 + (3*a^2 + 8*a + 2)*q^15 + (-a^2 - a + 2)*q^16 + (-a^2 - 3*a + 1)*q^17 + (2*a^2 + 2*a + 1)*q^18 + (-3*a^2 - 5*a + 1)*q^19 + (5*a + 1)*q^20 + (-5*a^2 - 10*a + 3)*q^21 + (-4*a + 1)*q^22 + (-5*a - 3)*q^23 + (3*a^2 + 7*a)*q^24 + (5*a^2 + 8*a - 1)*q^25 + (3*a^2 + a - 2)*q^26 + (-4*a^2 - 7*a + 3)*q^27 + (-4*a^2 - 8*a + 5)*q^28 + (4*a^2 + 9*a - 4)*q^29 + (2*a^2 + 5*a + 3)*q^30 + (-2*a^2 - 7*a - 3)*q^31 + (5*a^2 + 7*a - 3)*q^32 + (-2*a^2 + 9)*q^33 + (-a^2 - 1)*q^34 + (-a^2 - 4*a - 7)*q^35 + (-4*a^2 - 5*a)*q^36 + (a^2 - 2)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 4*a + 1)*q^3 + (a^2 - 2)*q^4 - a*q^5 + (a^3 - a^2 - 3*a + 3)*q^6 + (a^3 - a^2 - 4*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (-a^3 - a^2 + 3*a + 4)*q^9 - a^2*q^10 + (a^3 + a^2 - 5*a)*q^11 + (2*a^2 - a - 5)*q^12 + (2*a^2 + a - 7)*q^13 + (-2*a^3 + a^2 + 6*a - 3)*q^14 + (-a^3 + a^2 + 3*a - 3)*q^15 + (-a^3 - a^2 + 4*a + 1)*q^16 + (a^3 - a^2 - 2*a + 6)*q^17 + (-2*a^2 + 3)*q^18 + (-a^2 - a + 5)*q^19 + (-a^3 + 2*a)*q^20 + (-a^2 + 2*a - 1)*q^21 + (4*a - 3)*q^22 + (-a^3 + 2*a^2 + 4*a - 6)*q^23 + (a^2 + a - 6)*q^24 + (a^2 - 5)*q^25 + (2*a^3 + a^2 - 7*a)*q^26 + (-2*a^2 - a + 7)*q^27 + (a^3 - 2*a^2 - 3*a + 2)*q^28 + (2*a^3 - 2*a^2 - 7*a + 6)*q^29 + (2*a^3 - 2*a^2 - 7*a + 3)*q^30 + (2*a^3 - 7*a - 1)*q^31 + (-2*a^3 - a^2 + 5*a + 3)*q^32 + (-3*a^3 + 4*a^2 + 11*a - 12)*q^33 + (-2*a^3 + 3*a^2 + 10*a - 3)*q^34 + (2*a^3 - a^2 - 6*a + 3)*q^35 + (2*a^2 - 3*a - 8)*q^36 + (-3*a^3 - 3*a^2 + 11*a + 5)*q^37 + O(q^38)
*]> ;  // time = 1.239 seconds




J[110] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 110, 110, 110, 110, 55, 55, 11 ], new_dimensions := [ 1, 1, 1, 2, 1, 2, 1 ], dimensions := [ 1, 1, 1, 2, 2, 4, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 1, 1, 0, 49, 1, 1, 5, 1, 1, 49, 0 ], ap_traces := [
[ -1, 1, -1, 5, 1, 2, 3, -7, -6, -3, -7, -7 ],
[ 1, 1, -1, -1, -1, 2, -3, -1, 6, -9, 5, 5 ],
[ 1, -1, 1, 3, 1, -6, -7, 5, -6, 5, -3, 3 ],
[ -2, -1, 2, 1, -2, 4, -3, 7, -6, -3, 1, 13 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 + x - 8
], atkin_lehners := [
[ 1, 1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ],
[ 1, -1, 1 ]
], component_group_orders := [
[ 7, 1, 3 ],
[ 3, 1, 1 ],
[ 5, 5, 1 ],
[ 1, 3, 1 ]
], tamagawa_numbers := [
[ 1, 1, 3 ],
[ 3, 1, 1 ],
[ 5, 5, 1 ],
[ 1, 3, 1 ]
], torsion_upper_bounds := [ 3, 3, 5, 3 ], torsion_lower_bounds := [ 3, 3, 1, 3 ], l_ratios := [ 1/3, 1/3, 1, 1/3 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1/25, 1 ], eigenvalues := [*
[ -1, 1, -1, 5, 1, 2, 3, -7, -6, -3, -7, -7 ],
[ 1, 1, -1, -1, -1, 2, -3, -1, 6, -9, 5, 5 ],
[ 1, -1, 1, 3, 1, -6, -7, 5, -6, 5, -3, 3 ],
[
-1,
a,
1,
-a,
-1,
2,
-a - 2,
a + 4,
-2*a - 4,
-a - 2,
-a,
-a + 6
]
*], q_expansions := [*
q - q^2 + q^3 + q^4 - q^5 - q^6 + 5*q^7 - q^8 - 2*q^9 + q^10 + q^11 + q^12 + 2*q^13 - 5*q^14 - q^15 + q^16 + 3*q^17 + 2*q^18 - 7*q^19 - q^20 + 5*q^21 - q^22 - 6*q^23 - q^24 + q^25 - 2*q^26 - 5*q^27 + 5*q^28 - 3*q^29 + q^30 - 7*q^31 - q^32 + q^33 - 3*q^34 - 5*q^35 - 2*q^36 - 7*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - q^5 + q^6 - q^7 + q^8 - 2*q^9 - q^10 - q^11 + q^12 + 2*q^13 - q^14 - q^15 + q^16 - 3*q^17 - 2*q^18 - q^19 - q^20 - q^21 - q^22 + 6*q^23 + q^24 + q^25 + 2*q^26 - 5*q^27 - q^28 - 9*q^29 - q^30 + 5*q^31 + q^32 - q^33 - 3*q^34 + q^35 - 2*q^36 + 5*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + 3*q^7 + q^8 - 2*q^9 + q^10 + q^11 - q^12 - 6*q^13 + 3*q^14 - q^15 + q^16 - 7*q^17 - 2*q^18 + 5*q^19 + q^20 - 3*q^21 + q^22 - 6*q^23 - q^24 + q^25 - 6*q^26 + 5*q^27 + 3*q^28 + 5*q^29 - q^30 - 3*q^31 + q^32 - q^33 - 7*q^34 + 3*q^35 - 2*q^36 + 3*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + q^5 - a*q^6 - a*q^7 - q^8 + (-a + 5)*q^9 - q^10 - q^11 + a*q^12 + 2*q^13 + a*q^14 + a*q^15 + q^16 + (-a - 2)*q^17 + (a - 5)*q^18 + (a + 4)*q^19 + q^20 + (a - 8)*q^21 + q^22 + (-2*a - 4)*q^23 - a*q^24 + q^25 - 2*q^26 + (3*a - 8)*q^27 - a*q^28 + (-a - 2)*q^29 - a*q^30 - a*q^31 - q^32 - a*q^33 + (a + 2)*q^34 - a*q^35 + (-a + 5)*q^36 + (-a + 6)*q^37 + O(q^38)
*]> ;  // time = 26.111 seconds




J[111] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 111, 111, 37, 37 ], new_dimensions := [ 3, 4, 1, 1 ], dimensions := [ 3, 4, 2, 2 ], intersection_graph := [ 0, 1, 1, 5, 1, 0, 7, 1, 1, 7, 0, 1, 5, 1, 1, 0 ], ap_traces := [
[ 3, -3, 4, -4, 4, -2, 4, -8, -2, 16, -8, 3 ],
[ 0, 4, -2, 4, 0, 4, -2, 8, -10, -2, 4, -4 ]
], hecke_fields := [
x^3 - 3*x^2 - x + 5,
x^4 - 6*x^2 + 2*x + 5
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 133, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 133, 1 ]
], torsion_upper_bounds := [ 1, 19 ], torsion_lower_bounds := [ 1, 19 ], l_ratios := [ 1, 7/19 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
a,
-1,
-a^2 + 5,
-2*a^2 + 2*a + 4,
2*a^2 - 4*a - 2,
2*a^2 - 4*a - 4,
-a^2 + 4*a + 1,
2*a^2 - 2*a - 8,
-a^2 + 2*a + 1,
-a^2 + 9,
-4*a^2 + 6*a + 6,
1
],
[
a,
1,
-a^3 - 2*a^2 + 3*a + 4,
2*a^3 + 2*a^2 - 8*a - 2,
2*a^2 - 6,
-2*a^3 - 4*a^2 + 6*a + 10,
-a^3 + 3*a - 2,
2*a^2 + 2*a - 4,
3*a^3 + 2*a^2 - 11*a - 4,
-a^3 + 7*a - 2,
-2*a^3 - 2*a^2 + 8*a + 4,
-1
]
*], q_expansions := [*
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 + 5)*q^5 - a*q^6 + (-2*a^2 + 2*a + 4)*q^7 + (3*a^2 - 3*a - 5)*q^8 + q^9 + (-3*a^2 + 4*a + 5)*q^10 + (2*a^2 - 4*a - 2)*q^11 + (-a^2 + 2)*q^12 + (2*a^2 - 4*a - 4)*q^13 + (-4*a^2 + 2*a + 10)*q^14 + (a^2 - 5)*q^15 + (4*a^2 - 2*a - 11)*q^16 + (-a^2 + 4*a + 1)*q^17 + a*q^18 + (2*a^2 - 2*a - 8)*q^19 + (-3*a^2 + 2*a + 5)*q^20 + (2*a^2 - 2*a - 4)*q^21 + (2*a^2 - 10)*q^22 + (-a^2 + 2*a + 1)*q^23 + (-3*a^2 + 3*a + 5)*q^24 + (-2*a + 5)*q^25 + (2*a^2 - 2*a - 10)*q^26 - q^27 + (-6*a^2 + 2*a + 12)*q^28 + (-a^2 + 9)*q^29 + (3*a^2 - 4*a - 5)*q^30 + (-4*a^2 + 6*a + 6)*q^31 + (4*a^2 - a - 10)*q^32 + (-2*a^2 + 4*a + 2)*q^33 + (a^2 + 5)*q^34 + 4*a*q^35 + (a^2 - 2)*q^36 + q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^3 - 2*a^2 + 3*a + 4)*q^5 + a*q^6 + (2*a^3 + 2*a^2 - 8*a - 2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-2*a^3 - 3*a^2 + 6*a + 5)*q^10 + (2*a^2 - 6)*q^11 + (a^2 - 2)*q^12 + (-2*a^3 - 4*a^2 + 6*a + 10)*q^13 + (2*a^3 + 4*a^2 - 6*a - 10)*q^14 + (-a^3 - 2*a^2 + 3*a + 4)*q^15 + (-2*a - 1)*q^16 + (-a^3 + 3*a - 2)*q^17 + a*q^18 + (2*a^2 + 2*a - 4)*q^19 + (-a^3 - 2*a^2 + 3*a + 2)*q^20 + (2*a^3 + 2*a^2 - 8*a - 2)*q^21 + (2*a^3 - 6*a)*q^22 + (3*a^3 + 2*a^2 - 11*a - 4)*q^23 + (a^3 - 4*a)*q^24 + (2*a^3 + 4*a^2 - 4*a - 9)*q^25 + (-4*a^3 - 6*a^2 + 14*a + 10)*q^26 + q^27 + (2*a^2 + 2*a - 6)*q^28 + (-a^3 + 7*a - 2)*q^29 + (-2*a^3 - 3*a^2 + 6*a + 5)*q^30 + (-2*a^3 - 2*a^2 + 8*a + 4)*q^31 + (-2*a^3 - 2*a^2 + 7*a)*q^32 + (2*a^2 - 6)*q^33 + (-3*a^2 + 5)*q^34 + (-2*a^2 - 4*a + 2)*q^35 + (a^2 - 2)*q^36 - q^37 + O(q^38)
*]> ;  // time = 9.719 seconds




J[113] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 113, 113, 113, 113 ], new_dimensions := [ 1, 2, 3, 3 ], dimensions := [ 1, 2, 3, 3 ], intersection_graph := [ 0, 1, 1, 3, 1, 0, 1, 11, 1, 1, 0, 1, 3, 11, 1, 0 ], ap_traces := [
[ -1, 2, 2, 0, 0, 2, -6, 6, -6, -6, -4, 2 ],
[ 2, 2, 0, 8, -4, -4, -4, -6, 2, 8, 4, -8 ],
[ -2, -5, -1, -10, 2, -8, -2, -4, -6, 5, -15, -2 ],
[ -2, -1, -3, 6, 2, 8, 10, 4, 4, -7, 9, 8 ]
], hecke_fields := [
x - 1,
x^2 - 8*x - 11,
x^3 + 2*x^2 - x - 1,
x^3 + 2*x^2 - 5*x - 9
], atkin_lehners := [
[ -1 ],
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 7 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 7 ]
], torsion_upper_bounds := [ 1, 1, 1, 7 ], torsion_lower_bounds := [ 1, 1, 1, 7 ], l_ratios := [ 1, 1, 0, 1/7 ], analytic_sha_upper_bounds := [ 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 1 ], eigenvalues := [*
[ -1, 2, 2, 0, 0, 2, -6, 6, -6, -6, -4, 2 ],
[
1,
1/3*a - 1/3,
-2/3*a + 8/3,
4,
-2/3*a + 2/3,
2/3*a - 14/3,
-2,
1/3*a - 13/3,
1/3*a - 1/3,
2/3*a + 4/3,
-2/3*a + 14/3,
2/3*a - 20/3
],
[
a,
-a^2 - 2*a - 1,
2*a^2 + 2*a - 3,
-a^2 - a - 2,
-3*a^2 - 4*a + 4,
a^2 + 4*a - 2,
-a^2 - 5*a - 2,
3*a^2 + 5*a - 4,
3*a,
-a^2 + 2*a + 5,
a^2 - 3*a - 9,
-6*a^2 - 11*a + 4
],
[
a,
a^2 - 5,
-1,
-a^2 - a + 6,
a^2 - 4,
a^2 - 2,
a^2 - a - 2,
-3*a^2 + a + 16,
-2*a^2 - a + 10,
a^2 - 7,
a^2 + a - 1,
-4*a^2 + a + 22
]
*], q_expansions := [*
q - q^2 + 2*q^3 - q^4 + 2*q^5 - 2*q^6 + 3*q^8 + q^9 - 2*q^10 - 2*q^12 + 2*q^13 + 4*q^15 - q^16 - 6*q^17 - q^18 + 6*q^19 - 2*q^20 - 6*q^23 + 6*q^24 - q^25 - 2*q^26 - 4*q^27 - 6*q^29 - 4*q^30 - 4*q^31 - 5*q^32 + 6*q^34 - q^36 + 2*q^37 + O(q^38),
q + q^2 + (1/3*a - 1/3)*q^3 - q^4 + (-2/3*a + 8/3)*q^5 + (1/3*a - 1/3)*q^6 + 4*q^7 - 3*q^8 + (2/3*a - 5/3)*q^9 + (-2/3*a + 8/3)*q^10 + (-2/3*a + 2/3)*q^11 + (-1/3*a + 1/3)*q^12 + (2/3*a - 14/3)*q^13 + 4*q^14 + (-2/3*a - 10/3)*q^15 - q^16 - 2*q^17 + (2/3*a - 5/3)*q^18 + (1/3*a - 13/3)*q^19 + (2/3*a - 8/3)*q^20 + (4/3*a - 4/3)*q^21 + (-2/3*a + 2/3)*q^22 + (1/3*a - 1/3)*q^23 + (-a + 1)*q^24 + 7*q^25 + (2/3*a - 14/3)*q^26 + 4*q^27 - 4*q^28 + (2/3*a + 4/3)*q^29 + (-2/3*a - 10/3)*q^30 + (-2/3*a + 14/3)*q^31 + 5*q^32 + (-4/3*a - 8/3)*q^33 - 2*q^34 + (-8/3*a + 32/3)*q^35 + (-2/3*a + 5/3)*q^36 + (2/3*a - 20/3)*q^37 + O(q^38),
q + a*q^2 + (-a^2 - 2*a - 1)*q^3 + (a^2 - 2)*q^4 + (2*a^2 + 2*a - 3)*q^5 + (-2*a - 1)*q^6 + (-a^2 - a - 2)*q^7 + (-2*a^2 - 3*a + 1)*q^8 + (3*a^2 + 7*a)*q^9 + (-2*a^2 - a + 2)*q^10 + (-3*a^2 - 4*a + 4)*q^11 + (3*a + 2)*q^12 + (a^2 + 4*a - 2)*q^13 + (a^2 - 3*a - 1)*q^14 + (-a^2 + 1)*q^15 + (-a^2 - a + 2)*q^16 + (-a^2 - 5*a - 2)*q^17 + (a^2 + 3*a + 3)*q^18 + (3*a^2 + 5*a - 4)*q^19 + (-a^2 - 4*a + 4)*q^20 + (4*a^2 + 7*a + 3)*q^21 + (2*a^2 + a - 3)*q^22 + 3*a*q^23 + (3*a^2 + 6*a + 2)*q^24 + (-4*a^2 - 8*a + 4)*q^25 + (2*a^2 - a + 1)*q^26 + (-3*a^2 - 11*a - 4)*q^27 + (-3*a^2 + 2*a + 5)*q^28 + (-a^2 + 2*a + 5)*q^29 + (2*a^2 - 1)*q^30 + (a^2 - 3*a - 9)*q^31 + (5*a^2 + 7*a - 3)*q^32 + (2*a^2 + 3*a)*q^33 + (-3*a^2 - 3*a - 1)*q^34 + (-5*a^2 - 3*a + 6)*q^35 + (-5*a^2 - 10*a + 1)*q^36 + (-6*a^2 - 11*a + 4)*q^37 + O(q^38),
q + a*q^2 + (a^2 - 5)*q^3 + (a^2 - 2)*q^4 - q^5 + (-2*a^2 + 9)*q^6 + (-a^2 - a + 6)*q^7 + (-2*a^2 + a + 9)*q^8 + (-a^2 - a + 4)*q^9 - a*q^10 + (a^2 - 4)*q^11 + (2*a^2 - a - 8)*q^12 + (a^2 - 2)*q^13 + (a^2 + a - 9)*q^14 + (-a^2 + 5)*q^15 + (3*a^2 - a - 14)*q^16 + (a^2 - a - 2)*q^17 + (a^2 - a - 9)*q^18 + (-3*a^2 + a + 16)*q^19 + (-a^2 + 2)*q^20 + (4*a^2 + a - 21)*q^21 + (-2*a^2 + a + 9)*q^22 + (-2*a^2 - a + 10)*q^23 + (-a^2 + 2*a)*q^24 - 4*q^25 + (-2*a^2 + 3*a + 9)*q^26 + (-a^2 + a + 4)*q^27 + (a^2 - 2*a - 3)*q^28 + (a^2 - 7)*q^29 + (2*a^2 - 9)*q^30 + (a^2 + a - 1)*q^31 + (-3*a^2 - a + 9)*q^32 + (-a + 2)*q^33 + (-3*a^2 + 3*a + 9)*q^34 + (a^2 + a - 6)*q^35 + (-a^2 - 2*a + 1)*q^36 + (-4*a^2 + a + 22)*q^37 + O(q^38)
*]> ;  // time = 1.421 seconds




J[114] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 114, 114, 114, 57, 57, 57, 38, 38, 19 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 2, 2, 2, 2, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 5, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 5, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 1, 9, 0, 1, 5, 1, 5, 1, 1, 1, 1, 1, 0, 1, 9, 1, 3, 1, 1, 1, 5, 1, 0, 1, 1, 1, 3, 1, 1, 1, 9, 1, 0 ], ap_traces := [
[ -1, -1, 0, 4, 4, 0, -2, 1, -2, -6, 6, -8 ],
[ 1, -1, 2, 0, -4, 2, -6, -1, -4, -2, 4, 10 ],
[ 1, 1, 0, -4, 0, -4, 6, 1, -6, 6, 2, -4 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 5, 1 ],
[ 5, 3, 1 ],
[ 3, 3, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 5, 1, 1 ],
[ 3, 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1 ], l_ratios := [ 1, 5, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1/9 ], eigenvalues := [*
[ -1, -1, 0, 4, 4, 0, -2, 1, -2, -6, 6, -8 ],
[ 1, -1, 2, 0, -4, 2, -6, -1, -4, -2, 4, 10 ],
[ 1, 1, 0, -4, 0, -4, 6, 1, -6, 6, 2, -4 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + q^6 + 4*q^7 - q^8 + q^9 + 4*q^11 - q^12 - 4*q^14 + q^16 - 2*q^17 - q^18 + q^19 - 4*q^21 - 4*q^22 - 2*q^23 + q^24 - 5*q^25 - q^27 + 4*q^28 - 6*q^29 + 6*q^31 - q^32 - 4*q^33 + 2*q^34 + q^36 - 8*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + 2*q^5 - q^6 + q^8 + q^9 + 2*q^10 - 4*q^11 - q^12 + 2*q^13 - 2*q^15 + q^16 - 6*q^17 + q^18 - q^19 + 2*q^20 - 4*q^22 - 4*q^23 - q^24 - q^25 + 2*q^26 - q^27 - 2*q^29 - 2*q^30 + 4*q^31 + q^32 + 4*q^33 - 6*q^34 + q^36 + 10*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^6 - 4*q^7 + q^8 + q^9 + q^12 - 4*q^13 - 4*q^14 + q^16 + 6*q^17 + q^18 + q^19 - 4*q^21 - 6*q^23 + q^24 - 5*q^25 - 4*q^26 + q^27 - 4*q^28 + 6*q^29 + 2*q^31 + q^32 + 6*q^34 + q^36 - 4*q^37 + O(q^38)
*]> ;  // time = 42.31 seconds




J[115] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 115, 115, 115, 23 ], new_dimensions := [ 1, 2, 4, 2 ], dimensions := [ 1, 2, 4, 4 ], intersection_graph := [ 0, 1, 1, 5, 1, 0, 1, 1, 1, 1, 0, 1, 5, 1, 1, 0 ], ap_traces := [
[ 2, 0, -1, 1, 2, -2, 3, -2, 1, 7, -5, 11 ],
[ -3, -2, -2, -2, -2, -8, -4, 2, -2, -10, 4, -6 ],
[ 2, -2, 4, -3, 4, 0, -1, -4, -4, 19, -1, -3 ]
], hecke_fields := [
x - 1,
x^2 + 3*x + 1,
x^4 - 2*x^3 - 4*x^2 + 5*x + 2
], atkin_lehners := [
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1 ], l_ratios := [ 1, 0, 1 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ 2, 0, -1, 1, 2, -2, 3, -2, 1, 7, -5, 11 ],
[
a,
-1,
-1,
-2*a - 4,
2*a + 2,
2*a - 1,
-4*a - 8,
6*a + 10,
-1,
-4*a - 11,
-2*a - 1,
6*a + 6
],
[
a,
-a^2 + a + 2,
1,
a^3 - 2*a^2 - 4*a + 3,
-2*a + 2,
-2*a^3 + 3*a^2 + 7*a - 4,
-a^3 + 2*a^2 + 2*a - 3,
2*a - 2,
-1,
a^3 - a^2 - 3*a + 5,
-3*a^3 + 5*a^2 + 9*a - 7,
a^3 + 2*a^2 - 8*a - 7
]
*], q_expansions := [*
q + 2*q^2 + 2*q^4 - q^5 + q^7 - 3*q^9 - 2*q^10 + 2*q^11 - 2*q^13 + 2*q^14 - 4*q^16 + 3*q^17 - 6*q^18 - 2*q^19 - 2*q^20 + 4*q^22 + q^23 + q^25 - 4*q^26 + 2*q^28 + 7*q^29 - 5*q^31 - 8*q^32 + 6*q^34 - q^35 - 6*q^36 + 11*q^37 + O(q^38),
q + a*q^2 - q^3 + (-3*a - 3)*q^4 - q^5 - a*q^6 + (-2*a - 4)*q^7 + (4*a + 3)*q^8 - 2*q^9 - a*q^10 + (2*a + 2)*q^11 + (3*a + 3)*q^12 + (2*a - 1)*q^13 + (2*a + 2)*q^14 + q^15 + (-3*a + 2)*q^16 + (-4*a - 8)*q^17 - 2*a*q^18 + (6*a + 10)*q^19 + (3*a + 3)*q^20 + (2*a + 4)*q^21 + (-4*a - 2)*q^22 - q^23 + (-4*a - 3)*q^24 + q^25 + (-7*a - 2)*q^26 + 5*q^27 + 6*q^28 + (-4*a - 11)*q^29 + a*q^30 + (-2*a - 1)*q^31 + (3*a - 3)*q^32 + (-2*a - 2)*q^33 + (4*a + 4)*q^34 + (2*a + 4)*q^35 + (6*a + 6)*q^36 + (6*a + 6)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + a + 2)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^3 + a^2 + 2*a)*q^6 + (a^3 - 2*a^2 - 4*a + 3)*q^7 + (a^3 - 4*a)*q^8 + (a^2 - a - 1)*q^9 + a*q^10 + (-2*a + 2)*q^11 + (-a^3 + 3*a - 2)*q^12 + (-2*a^3 + 3*a^2 + 7*a - 4)*q^13 + (-2*a - 2)*q^14 + (-a^2 + a + 2)*q^15 + (2*a^3 - 2*a^2 - 5*a + 2)*q^16 + (-a^3 + 2*a^2 + 2*a - 3)*q^17 + (a^3 - a^2 - a)*q^18 + (2*a - 2)*q^19 + (a^2 - 2)*q^20 + (2*a^3 - 2*a^2 - 8*a + 4)*q^21 + (-2*a^2 + 2*a)*q^22 - q^23 + (-3*a^2 - a + 2)*q^24 + q^25 + (-a^3 - a^2 + 6*a + 4)*q^26 + (a^2 - a - 6)*q^27 + (-2*a^3 + 2*a^2 + 6*a - 6)*q^28 + (a^3 - a^2 - 3*a + 5)*q^29 + (-a^3 + a^2 + 2*a)*q^30 + (-3*a^3 + 5*a^2 + 9*a - 7)*q^31 + (3*a^2 - 4)*q^32 + (2*a^3 - 4*a^2 - 2*a + 4)*q^33 + (-2*a^2 + 2*a + 2)*q^34 + (a^3 - 2*a^2 - 4*a + 3)*q^35 + (a^3 + a^2 - 3*a)*q^36 + (a^3 + 2*a^2 - 8*a - 7)*q^37 + O(q^38)
*]> ;  // time = 9.329 seconds




J[118] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 118, 118, 118, 118, 59 ], new_dimensions := [ 1, 1, 1, 1, 5 ], dimensions := [ 1, 1, 1, 1, 10 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 19, 1, 1, 0, 3, 1, 1, 1, 3, 0, 1, 1, 19, 1, 1, 0 ], ap_traces := [
[ -1, -1, -3, -1, -2, -2, -2, 3, 0, -1, 10, -12 ],
[ -1, 2, 2, -3, 1, 3, -1, -8, 8, -4, -4, -1 ],
[ 1, -1, 1, 3, 2, -6, -2, -5, 4, -5, 2, 8 ],
[ 1, 2, -2, -3, -1, -3, 7, 4, 4, 4, -4, -7 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 19, 1 ],
[ 5, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 5, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 5, 1 ], torsion_lower_bounds := [ 1, 1, 5, 1 ], l_ratios := [ 0, 1, 1/5, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1 ], eigenvalues := [*
[ -1, -1, -3, -1, -2, -2, -2, 3, 0, -1, 10, -12 ],
[ -1, 2, 2, -3, 1, 3, -1, -8, 8, -4, -4, -1 ],
[ 1, -1, 1, 3, 2, -6, -2, -5, 4, -5, 2, 8 ],
[ 1, 2, -2, -3, -1, -3, 7, 4, 4, 4, -4, -7 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - 3*q^5 + q^6 - q^7 - q^8 - 2*q^9 + 3*q^10 - 2*q^11 - q^12 - 2*q^13 + q^14 + 3*q^15 + q^16 - 2*q^17 + 2*q^18 + 3*q^19 - 3*q^20 + q^21 + 2*q^22 + q^24 + 4*q^25 + 2*q^26 + 5*q^27 - q^28 - q^29 - 3*q^30 + 10*q^31 - q^32 + 2*q^33 + 2*q^34 + 3*q^35 - 2*q^36 - 12*q^37 + O(q^38),
q - q^2 + 2*q^3 + q^4 + 2*q^5 - 2*q^6 - 3*q^7 - q^8 + q^9 - 2*q^10 + q^11 + 2*q^12 + 3*q^13 + 3*q^14 + 4*q^15 + q^16 - q^17 - q^18 - 8*q^19 + 2*q^20 - 6*q^21 - q^22 + 8*q^23 - 2*q^24 - q^25 - 3*q^26 - 4*q^27 - 3*q^28 - 4*q^29 - 4*q^30 - 4*q^31 - q^32 + 2*q^33 + q^34 - 6*q^35 + q^36 - q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + 3*q^7 + q^8 - 2*q^9 + q^10 + 2*q^11 - q^12 - 6*q^13 + 3*q^14 - q^15 + q^16 - 2*q^17 - 2*q^18 - 5*q^19 + q^20 - 3*q^21 + 2*q^22 + 4*q^23 - q^24 - 4*q^25 - 6*q^26 + 5*q^27 + 3*q^28 - 5*q^29 - q^30 + 2*q^31 + q^32 - 2*q^33 - 2*q^34 + 3*q^35 - 2*q^36 + 8*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 - 2*q^5 + 2*q^6 - 3*q^7 + q^8 + q^9 - 2*q^10 - q^11 + 2*q^12 - 3*q^13 - 3*q^14 - 4*q^15 + q^16 + 7*q^17 + q^18 + 4*q^19 - 2*q^20 - 6*q^21 - q^22 + 4*q^23 + 2*q^24 - q^25 - 3*q^26 - 4*q^27 - 3*q^28 + 4*q^29 - 4*q^30 - 4*q^31 + q^32 - 2*q^33 + 7*q^34 + 6*q^35 + q^36 - 7*q^37 + O(q^38)
*]> ;  // time = 13.88 seconds




J[119] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 119, 119, 17 ], new_dimensions := [ 4, 5, 1 ], dimensions := [ 4, 5, 2 ], intersection_graph := [ 0, 1, 1, 1, 0, 3, 1, 3, 0 ], ap_traces := [
[ -1, 2, 2, 4, 2, 8, -4, 10, -6, 2, 12, 6 ],
[ 2, -2, 0, -5, -2, 2, 5, 6, -10, -8, 0, 8 ]
], hecke_fields := [
x^4 + x^3 - 5*x^2 - x + 3,
x^5 - 2*x^4 - 8*x^3 + 14*x^2 + 14*x - 17
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 9, 3 ],
[ 3, 1 ]
], tamagawa_numbers := [
[ 9, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 9, 1 ], torsion_lower_bounds := [ 9, 1 ], l_ratios := [ 1/9, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
a,
-a^3 - a^2 + 4*a + 1,
a^3 + a^2 - 4*a,
1,
-2*a,
2*a^3 + 4*a^2 - 6*a - 4,
-1,
-2*a^3 - 4*a^2 + 4*a + 8,
2*a^2 + 4*a - 6,
-2*a,
a^3 - a^2 - 4*a + 8,
2*a^3 + 4*a^2 - 4*a - 4
],
[
a,
-a^4 + 6*a^2 + a - 4,
2*a^4 + a^3 - 15*a^2 - 6*a + 18,
-1,
-2*a^4 - 2*a^3 + 14*a^2 + 12*a - 14,
-2*a^4 + 14*a^2 - 14,
1,
-2*a^4 + 14*a^2 + 2*a - 14,
2*a^2 - 10,
4*a^4 - 28*a^2 - 2*a + 28,
2*a^4 + a^3 - 13*a^2 - 6*a + 10,
-2*a^3 + 8*a + 4
]
*], q_expansions := [*
q + a*q^2 + (-a^3 - a^2 + 4*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^3 + a^2 - 4*a)*q^5 + (-a^2 + 3)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (-a^3 - 3*a^2 + 2*a + 7)*q^9 + (a^2 + a - 3)*q^10 - 2*a*q^11 + (a^3 + 2*a^2 - 5*a - 2)*q^12 + (2*a^3 + 4*a^2 - 6*a - 4)*q^13 + a*q^14 + (2*a^2 + 2*a - 9)*q^15 + (-a^3 - a^2 + a + 1)*q^16 - q^17 + (-2*a^3 - 3*a^2 + 6*a + 3)*q^18 + (-2*a^3 - 4*a^2 + 4*a + 8)*q^19 + (-a^3 - a^2 + 5*a)*q^20 + (-a^3 - a^2 + 4*a + 1)*q^21 - 2*a^2*q^22 + (2*a^2 + 4*a - 6)*q^23 + (a^3 + 2*a^2 - a - 9)*q^24 + (a^3 - a^2 - 6*a + 4)*q^25 + (2*a^3 + 4*a^2 - 2*a - 6)*q^26 + (-2*a^3 - 4*a^2 + 8*a + 7)*q^27 + (a^2 - 2)*q^28 - 2*a*q^29 + (2*a^3 + 2*a^2 - 9*a)*q^30 + (a^3 - a^2 - 4*a + 8)*q^31 + (-2*a^3 - 4*a^2 + 8*a + 3)*q^32 + (2*a^2 - 6)*q^33 - a*q^34 + (a^3 + a^2 - 4*a)*q^35 + (a^3 + 2*a^2 - 3*a - 8)*q^36 + (2*a^3 + 4*a^2 - 4*a - 4)*q^37 + O(q^38),
q + a*q^2 + (-a^4 + 6*a^2 + a - 4)*q^3 + (a^2 - 2)*q^4 + (2*a^4 + a^3 - 15*a^2 - 6*a + 18)*q^5 + (-2*a^4 - 2*a^3 + 15*a^2 + 10*a - 17)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (2*a^4 + a^3 - 13*a^2 - 8*a + 13)*q^9 + (5*a^4 + a^3 - 34*a^2 - 10*a + 34)*q^10 + (-2*a^4 - 2*a^3 + 14*a^2 + 12*a - 14)*q^11 + (-4*a^4 - a^3 + 26*a^2 + 9*a - 26)*q^12 + (-2*a^4 + 14*a^2 - 14)*q^13 - a*q^14 + (-a^4 - a^3 + 7*a^2 + 3*a - 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + q^17 + (5*a^4 + 3*a^3 - 36*a^2 - 15*a + 34)*q^18 + (-2*a^4 + 14*a^2 + 2*a - 14)*q^19 + (7*a^4 + 4*a^3 - 50*a^2 - 24*a + 49)*q^20 + (a^4 - 6*a^2 - a + 4)*q^21 + (-6*a^4 - 2*a^3 + 40*a^2 + 14*a - 34)*q^22 + (2*a^2 - 10)*q^23 + (-5*a^4 - 2*a^3 + 35*a^2 + 10*a - 34)*q^24 + (-3*a^4 - 2*a^3 + 22*a^2 + 13*a - 21)*q^25 + (-4*a^4 - 2*a^3 + 28*a^2 + 14*a - 34)*q^26 + (-a^4 + a^3 + 5*a^2 - 3*a - 6)*q^27 + (-a^2 + 2)*q^28 + (4*a^4 - 28*a^2 - 2*a + 28)*q^29 + (-3*a^4 - a^3 + 17*a^2 + 10*a - 17)*q^30 + (2*a^4 + a^3 - 13*a^2 - 6*a + 10)*q^31 + (2*a^4 - 14*a^2 - 2*a + 17)*q^32 + (4*a^4 - 26*a^2 + 22)*q^33 + a*q^34 + (-2*a^4 - a^3 + 15*a^2 + 6*a - 18)*q^35 + (9*a^4 + 2*a^3 - 59*a^2 - 20*a + 59)*q^36 + (-2*a^3 + 8*a + 4)*q^37 + O(q^38)
*]> ;  // time = 9.91 seconds




J[122] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 122, 122, 122, 61, 61 ], new_dimensions := [ 1, 2, 3, 1, 3 ], dimensions := [ 1, 2, 3, 2, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 13, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 13, 1, 1, 0 ], ap_traces := [
[ -1, -2, 1, -5, -3, -3, 0, 0, 5, 6, 0, -12 ],
[ -2, 1, 0, 5, 2, 6, -2, 1, -3, -11, -1, -3 ],
[ 3, -1, 1, 4, -7, -1, -6, -3, 2, 1, -3, 7 ]
], hecke_fields := [
x - 1,
x^2 - x - 3,
x^3 + x^2 - 5*x + 2
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 39, 3 ],
[ 31, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 3 ],
[ 31, 1 ]
], torsion_upper_bounds := [ 1, 3, 31 ], torsion_lower_bounds := [ 1, 3, 31 ], l_ratios := [ 0, 1/3, 1/31 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ -1, -2, 1, -5, -3, -3, 0, 0, 5, 6, 0, -12 ],
[
-1,
a,
0,
-a + 3,
-2*a + 2,
-2*a + 4,
2*a - 2,
3*a - 1,
-3*a,
-a - 5,
-a,
a - 2
],
[
1,
a,
-a^2 - 3*a + 3,
2*a^2 + 3*a - 5,
-a^2 - a + 1,
-a^2 - a + 3,
-2*a^2 - 4*a + 4,
a^2 + 2*a - 4,
3*a^2 + 4*a - 9,
a^2 + 4*a - 2,
-2*a^2 - a + 6,
-4*a^2 - 9*a + 14
]
*], q_expansions := [*
q - q^2 - 2*q^3 + q^4 + q^5 + 2*q^6 - 5*q^7 - q^8 + q^9 - q^10 - 3*q^11 - 2*q^12 - 3*q^13 + 5*q^14 - 2*q^15 + q^16 - q^18 + q^20 + 10*q^21 + 3*q^22 + 5*q^23 + 2*q^24 - 4*q^25 + 3*q^26 + 4*q^27 - 5*q^28 + 6*q^29 + 2*q^30 - q^32 + 6*q^33 - 5*q^35 + q^36 - 12*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - a*q^6 + (-a + 3)*q^7 - q^8 + a*q^9 + (-2*a + 2)*q^11 + a*q^12 + (-2*a + 4)*q^13 + (a - 3)*q^14 + q^16 + (2*a - 2)*q^17 - a*q^18 + (3*a - 1)*q^19 + (2*a - 3)*q^21 + (2*a - 2)*q^22 - 3*a*q^23 - a*q^24 - 5*q^25 + (2*a - 4)*q^26 + (-2*a + 3)*q^27 + (-a + 3)*q^28 + (-a - 5)*q^29 - a*q^31 - q^32 - 6*q^33 + (-2*a + 2)*q^34 + a*q^36 + (a - 2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a^2 - 3*a + 3)*q^5 + a*q^6 + (2*a^2 + 3*a - 5)*q^7 + q^8 + (a^2 - 3)*q^9 + (-a^2 - 3*a + 3)*q^10 + (-a^2 - a + 1)*q^11 + a*q^12 + (-a^2 - a + 3)*q^13 + (2*a^2 + 3*a - 5)*q^14 + (-2*a^2 - 2*a + 2)*q^15 + q^16 + (-2*a^2 - 4*a + 4)*q^17 + (a^2 - 3)*q^18 + (a^2 + 2*a - 4)*q^19 + (-a^2 - 3*a + 3)*q^20 + (a^2 + 5*a - 4)*q^21 + (-a^2 - a + 1)*q^22 + (3*a^2 + 4*a - 9)*q^23 + a*q^24 + (3*a^2 + 5*a - 6)*q^25 + (-a^2 - a + 3)*q^26 + (-a^2 - a - 2)*q^27 + (2*a^2 + 3*a - 5)*q^28 + (a^2 + 4*a - 2)*q^29 + (-2*a^2 - 2*a + 2)*q^30 + (-2*a^2 - a + 6)*q^31 + q^32 + (-4*a + 2)*q^33 + (-2*a^2 - 4*a + 4)*q^34 + (-a^2 - 7*a - 1)*q^35 + (a^2 - 3)*q^36 + (-4*a^2 - 9*a + 14)*q^37 + O(q^38)
*]> ;  // time = 15.78 seconds




J[123] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 123, 123, 123, 123, 41 ], new_dimensions := [ 1, 1, 2, 3, 3 ], dimensions := [ 1, 1, 2, 3, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 0, 23, 1, 5, 1, 23, 0 ], ap_traces := [
[ 0, -1, -2, -4, 5, -4, -5, -2, 4, 1, -5, -7 ],
[ -2, 1, -4, -2, -3, -6, 3, 0, -6, 5, 7, -7 ],
[ 0, 2, 4, -4, 2, 4, 2, -8, 0, 2, -6, -2 ],
[ 1, -3, 4, 2, -4, 8, 2, 2, -10, -6, -2, 20 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2,
x^3 - x^2 - 4*x + 2
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 5, 1 ],
[ 7, 1 ],
[ 23, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 5, 1 ],
[ 7, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 5, 7, 1 ], torsion_lower_bounds := [ 1, 1, 7, 1 ], l_ratios := [ 0, 0, 1/7, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[ 0, -1, -2, -4, 5, -4, -5, -2, 4, 1, -5, -7 ],
[ -2, 1, -4, -2, -3, -6, 3, 0, -6, 5, 7, -7 ],
[
a,
1,
-a + 2,
a - 2,
-a + 1,
-3*a + 2,
a + 1,
a - 4,
a,
5*a + 1,
-3,
6*a - 1
],
[
a,
-1,
-a^2 + a + 4,
-a^2 - a + 4,
-a - 1,
a^2 - a,
2*a^2 - a - 5,
a^2 - a - 2,
a^2 - a - 6,
-3*a - 1,
a^2 + 4*a - 5,
-a^2 + 2*a + 9
]
*], q_expansions := [*
q - q^3 - 2*q^4 - 2*q^5 - 4*q^7 + q^9 + 5*q^11 + 2*q^12 - 4*q^13 + 2*q^15 + 4*q^16 - 5*q^17 - 2*q^19 + 4*q^20 + 4*q^21 + 4*q^23 - q^25 - q^27 + 8*q^28 + q^29 - 5*q^31 - 5*q^33 + 8*q^35 - 2*q^36 - 7*q^37 + O(q^38),
q - 2*q^2 + q^3 + 2*q^4 - 4*q^5 - 2*q^6 - 2*q^7 + q^9 + 8*q^10 - 3*q^11 + 2*q^12 - 6*q^13 + 4*q^14 - 4*q^15 - 4*q^16 + 3*q^17 - 2*q^18 - 8*q^20 - 2*q^21 + 6*q^22 - 6*q^23 + 11*q^25 + 12*q^26 + q^27 - 4*q^28 + 5*q^29 + 8*q^30 + 7*q^31 + 8*q^32 - 3*q^33 - 6*q^34 + 8*q^35 + 2*q^36 - 7*q^37 + O(q^38),
q + a*q^2 + q^3 + (-a + 2)*q^5 + a*q^6 + (a - 2)*q^7 - 2*a*q^8 + q^9 + (2*a - 2)*q^10 + (-a + 1)*q^11 + (-3*a + 2)*q^13 + (-2*a + 2)*q^14 + (-a + 2)*q^15 - 4*q^16 + (a + 1)*q^17 + a*q^18 + (a - 4)*q^19 + (a - 2)*q^21 + (a - 2)*q^22 + a*q^23 - 2*a*q^24 + (-4*a + 1)*q^25 + (2*a - 6)*q^26 + q^27 + (5*a + 1)*q^29 + (2*a - 2)*q^30 - 3*q^31 + (-a + 1)*q^33 + (a + 2)*q^34 + (4*a - 6)*q^35 + (6*a - 1)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 + a + 4)*q^5 - a*q^6 + (-a^2 - a + 4)*q^7 + (a^2 - 2)*q^8 + q^9 + 2*q^10 + (-a - 1)*q^11 + (-a^2 + 2)*q^12 + (a^2 - a)*q^13 + (-2*a^2 + 2)*q^14 + (a^2 - a - 4)*q^15 + (-a^2 + 2*a + 2)*q^16 + (2*a^2 - a - 5)*q^17 + a*q^18 + (a^2 - a - 2)*q^19 + (2*a^2 - 8)*q^20 + (a^2 + a - 4)*q^21 + (-a^2 - a)*q^22 + (a^2 - a - 6)*q^23 + (-a^2 + 2)*q^24 + (-4*a^2 + 2*a + 13)*q^25 + (4*a - 2)*q^26 - q^27 + (-4*a - 4)*q^28 + (-3*a - 1)*q^29 - 2*q^30 + (a^2 + 4*a - 5)*q^31 + (-a^2 - 2*a + 6)*q^32 + (a + 1)*q^33 + (a^2 + 3*a - 4)*q^34 + (-4*a^2 + 2*a + 14)*q^35 + (a^2 - 2)*q^36 + (-a^2 + 2*a + 9)*q^37 + O(q^38)
*]> ;  // time = 11.54 seconds




J[127] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 127, 127 ], new_dimensions := [ 3, 7 ], dimensions := [ 3, 7 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -3, -3, -6, -3, 0, -3, -18, 3, -9, 3, 12, 0 ],
[ 2, 3, 8, -3, 0, -1, 24, -5, -1, -7, -8, -6 ]
], hecke_fields := [
x^3 + 3*x^2 - 3,
x^7 - 2*x^6 - 8*x^5 + 15*x^4 + 17*x^3 - 28*x^2 - 11*x + 15
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 21 ]
], tamagawa_numbers := [
[ 1 ],
[ 21 ]
], torsion_upper_bounds := [ 1, 21 ], torsion_lower_bounds := [ 1, 21 ], l_ratios := [ 0, 1/21 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^2 - 2*a,
a^2 + a - 4,
a^2 + a - 3,
a^2 + 4*a + 1,
-3*a^2 - 4*a + 4,
-a - 7,
a^2 + a - 1,
-2*a^2 - 3*a,
a^2 - a - 3,
-3*a^2 - 5*a + 8,
-4*a^2 - 2*a + 10
],
[
a,
a^6 - 2*a^5 - 6*a^4 + 12*a^3 + 4*a^2 - 11*a + 4,
-a^6 + a^5 + 8*a^4 - 6*a^3 - 16*a^2 + 5*a + 9,
-a^5 + a^4 + 7*a^3 - 7*a^2 - 9*a + 8,
a^6 - 2*a^5 - 6*a^4 + 13*a^3 + 3*a^2 - 15*a + 6,
-2*a^6 + 6*a^5 + 11*a^4 - 38*a^3 - 2*a^2 + 39*a - 13,
a^6 - a^5 - 9*a^4 + 6*a^3 + 24*a^2 - 6*a - 15,
2*a^6 - 5*a^5 - 11*a^4 + 32*a^3 + 2*a^2 - 33*a + 11,
3*a^5 - 6*a^4 - 20*a^3 + 36*a^2 + 24*a - 33,
-2*a^6 + 5*a^5 + 13*a^4 - 31*a^3 - 15*a^2 + 29*a,
-a^6 + 5*a^5 - 33*a^3 + 33*a^2 + 39*a - 40,
-4*a^5 + 6*a^4 + 27*a^3 - 37*a^2 - 32*a + 35
]
*], q_expansions := [*
q + a*q^2 + (-a^2 - 2*a)*q^3 + (a^2 - 2)*q^4 + (a^2 + a - 4)*q^5 + (a^2 - 3)*q^6 + (a^2 + a - 3)*q^7 + (-3*a^2 - 4*a + 3)*q^8 + (a^2 + 3*a)*q^9 + (-2*a^2 - 4*a + 3)*q^10 + (a^2 + 4*a + 1)*q^11 + (-a^2 + a + 3)*q^12 + (-3*a^2 - 4*a + 4)*q^13 + (-2*a^2 - 3*a + 3)*q^14 + (2*a^2 + 5*a)*q^15 + (3*a^2 + 3*a - 5)*q^16 + (-a - 7)*q^17 + 3*q^18 + (a^2 + a - 1)*q^19 + (a + 2)*q^20 + (a^2 + 3*a)*q^21 + (a^2 + a + 3)*q^22 + (-2*a^2 - 3*a)*q^23 + (2*a^2 + 3*a + 3)*q^24 + (-4*a^2 - 5*a + 8)*q^25 + (5*a^2 + 4*a - 9)*q^26 + (3*a^2 + 3*a - 6)*q^27 + (a^2 + a)*q^28 + (a^2 - a - 3)*q^29 + (-a^2 + 6)*q^30 + (-3*a^2 - 5*a + 8)*q^31 + (3*a + 3)*q^32 + (-5*a - 9)*q^33 + (-a^2 - 7*a)*q^34 + (-3*a^2 - 4*a + 9)*q^35 + (-2*a^2 - 3*a)*q^36 + (-4*a^2 - 2*a + 10)*q^37 + O(q^38),
q + a*q^2 + (a^6 - 2*a^5 - 6*a^4 + 12*a^3 + 4*a^2 - 11*a + 4)*q^3 + (a^2 - 2)*q^4 + (-a^6 + a^5 + 8*a^4 - 6*a^3 - 16*a^2 + 5*a + 9)*q^5 + (2*a^5 - 3*a^4 - 13*a^3 + 17*a^2 + 15*a - 15)*q^6 + (-a^5 + a^4 + 7*a^3 - 7*a^2 - 9*a + 8)*q^7 + (a^3 - 4*a)*q^8 + (a^5 - 3*a^4 - 7*a^3 + 19*a^2 + 9*a - 17)*q^9 + (-a^6 + 9*a^4 + a^3 - 23*a^2 - 2*a + 15)*q^10 + (a^6 - 2*a^5 - 6*a^4 + 13*a^3 + 3*a^2 - 15*a + 6)*q^11 + (a^5 - a^4 - 7*a^3 + 7*a^2 + 7*a - 8)*q^12 + (-2*a^6 + 6*a^5 + 11*a^4 - 38*a^3 - 2*a^2 + 39*a - 13)*q^13 + (-a^6 + a^5 + 7*a^4 - 7*a^3 - 9*a^2 + 8*a)*q^14 + (-a^5 + 4*a^4 + 6*a^3 - 24*a^2 - 8*a + 21)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 - a^5 - 9*a^4 + 6*a^3 + 24*a^2 - 6*a - 15)*q^17 + (a^6 - 3*a^5 - 7*a^4 + 19*a^3 + 9*a^2 - 17*a)*q^18 + (2*a^6 - 5*a^5 - 11*a^4 + 32*a^3 + 2*a^2 - 33*a + 11)*q^19 + (-a^5 + 6*a^3 + 2*a^2 - 6*a - 3)*q^20 + (a^6 - 3*a^5 - 4*a^4 + 20*a^3 - 10*a^2 - 23*a + 17)*q^21 + (2*a^5 - 2*a^4 - 14*a^3 + 13*a^2 + 17*a - 15)*q^22 + (3*a^5 - 6*a^4 - 20*a^3 + 36*a^2 + 24*a - 33)*q^23 + (a^6 - 5*a^5 - a^4 + 33*a^3 - 27*a^2 - 38*a + 30)*q^24 + (-a^6 + a^5 + 7*a^4 - 7*a^3 - 9*a^2 + 10*a + 1)*q^25 + (2*a^6 - 5*a^5 - 8*a^4 + 32*a^3 - 17*a^2 - 35*a + 30)*q^26 + (a^6 + a^5 - 12*a^4 - 8*a^3 + 42*a^2 + 13*a - 35)*q^27 + (-a^6 + a^5 + 6*a^4 - 6*a^3 - 6*a^2 + 7*a - 1)*q^28 + (-2*a^6 + 5*a^5 + 13*a^4 - 31*a^3 - 15*a^2 + 29*a)*q^29 + (-a^6 + 4*a^5 + 6*a^4 - 24*a^3 - 8*a^2 + 21*a)*q^30 + (-a^6 + 5*a^5 - 33*a^3 + 33*a^2 + 39*a - 40)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^6 - 5*a^5 - 3*a^4 + 33*a^3 - 15*a^2 - 36*a + 24)*q^33 + (a^6 - a^5 - 9*a^4 + 7*a^3 + 22*a^2 - 4*a - 15)*q^34 + (-a^4 + a^3 + 5*a^2 - a - 3)*q^35 + (-a^6 - a^5 + 10*a^4 + 6*a^3 - 27*a^2 - 7*a + 19)*q^36 + (-4*a^5 + 6*a^4 + 27*a^3 - 37*a^2 - 32*a + 35)*q^37 + O(q^38)
*]> ;  // time = 1.39 seconds




J[129] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 129, 129, 129, 129, 43, 43 ], new_dimensions := [ 1, 1, 2, 3, 1, 2 ], dimensions := [ 1, 1, 2, 3, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 0, 1, 5, 3, 1, 1, 1, 0, 1, 1, 7, 1, 5, 1, 0, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 7, 1, 1, 0 ], ap_traces := [
[ 0, -1, -2, -2, -5, 3, -3, 2, -1, 0, -5, 8 ],
[ 1, 1, 2, 0, 0, -2, -6, 4, -4, -6, 8, 6 ],
[ 2, -2, 2, 2, 6, -10, -4, -2, 12, 6, 8, -8 ],
[ -2, 3, -4, 4, 1, 9, 1, -4, 11, 2, -5, 0 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2*x - 1,
x^3 + 2*x^2 - 5*x - 8
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 1 ],
[ 7, 1 ],
[ 11, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 11, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 11 ], torsion_lower_bounds := [ 1, 1, 1, 11 ], l_ratios := [ 0, 3, 1, 1/11 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1 ], eigenvalues := [*
[ 0, -1, -2, -2, -5, 3, -3, 2, -1, 0, -5, 8 ],
[ 1, 1, 2, 0, 0, -2, -6, 4, -4, -6, 8, 6 ],
[
a,
-1,
-a + 2,
-2*a + 3,
-a + 4,
-5,
-2*a,
4*a - 5,
6,
3*a,
4,
-2*a - 2
],
[
a,
1,
-a - 2,
-a^2 + 6,
a^2 - a - 5,
3,
-a^2 + 5,
-a^2 - 2*a + 2,
3*a^2 + 2*a - 9,
-a,
a^2 + 2*a - 5,
2*a^2 + 2*a - 8
]
*], q_expansions := [*
q - q^3 - 2*q^4 - 2*q^5 - 2*q^7 + q^9 - 5*q^11 + 2*q^12 + 3*q^13 + 2*q^15 + 4*q^16 - 3*q^17 + 2*q^19 + 4*q^20 + 2*q^21 - q^23 - q^25 - q^27 + 4*q^28 - 5*q^31 + 5*q^33 + 4*q^35 - 2*q^36 + 8*q^37 + O(q^38),
q + q^2 + q^3 - q^4 + 2*q^5 + q^6 - 3*q^8 + q^9 + 2*q^10 - q^12 - 2*q^13 + 2*q^15 - q^16 - 6*q^17 + q^18 + 4*q^19 - 2*q^20 - 4*q^23 - 3*q^24 - q^25 - 2*q^26 + q^27 - 6*q^29 + 2*q^30 + 8*q^31 + 5*q^32 - 6*q^34 - q^36 + 6*q^37 + O(q^38),
q + a*q^2 - q^3 + (2*a - 1)*q^4 + (-a + 2)*q^5 - a*q^6 + (-2*a + 3)*q^7 + (a + 2)*q^8 + q^9 - q^10 + (-a + 4)*q^11 + (-2*a + 1)*q^12 - 5*q^13 + (-a - 2)*q^14 + (a - 2)*q^15 + 3*q^16 - 2*a*q^17 + a*q^18 + (4*a - 5)*q^19 + (a - 4)*q^20 + (2*a - 3)*q^21 + (2*a - 1)*q^22 + 6*q^23 + (-a - 2)*q^24 - 2*a*q^25 - 5*a*q^26 - q^27 - 7*q^28 + 3*a*q^29 + q^30 + 4*q^31 + (a - 4)*q^32 + (a - 4)*q^33 + (-4*a - 2)*q^34 + (-3*a + 8)*q^35 + (2*a - 1)*q^36 + (-2*a - 2)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a - 2)*q^5 + a*q^6 + (-a^2 + 6)*q^7 + (-2*a^2 + a + 8)*q^8 + q^9 + (-a^2 - 2*a)*q^10 + (a^2 - a - 5)*q^11 + (a^2 - 2)*q^12 + 3*q^13 + (2*a^2 + a - 8)*q^14 + (-a - 2)*q^15 + (3*a^2 - 2*a - 12)*q^16 + (-a^2 + 5)*q^17 + a*q^18 + (-a^2 - 2*a + 2)*q^19 + (-3*a - 4)*q^20 + (-a^2 + 6)*q^21 + (-3*a^2 + 8)*q^22 + (3*a^2 + 2*a - 9)*q^23 + (-2*a^2 + a + 8)*q^24 + (a^2 + 4*a - 1)*q^25 + 3*a*q^26 + q^27 + (-a^2 + 2*a + 4)*q^28 - a*q^29 + (-a^2 - 2*a)*q^30 + (a^2 + 2*a - 5)*q^31 + (-4*a^2 + a + 8)*q^32 + (a^2 - a - 5)*q^33 + (2*a^2 - 8)*q^34 + (-a - 4)*q^35 + (a^2 - 2)*q^36 + (2*a^2 + 2*a - 8)*q^37 + O(q^38)
*]> ;  // time = 11.51 seconds




J[130] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 130, 130, 130, 65, 65, 65, 26, 26 ], new_dimensions := [ 1, 1, 1, 1, 2, 2, 1, 1 ], dimensions := [ 1, 1, 1, 2, 4, 4, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 7, 3, 1, 1, 1, 3, 1, 0, 1, 1, 5, 1, 1, 1, 7, 1, 0 ], ap_traces := [
[ -1, -2, 1, -4, -6, 1, -6, 2, 6, -6, 2, 2 ],
[ 1, 2, -1, -4, -2, -1, 2, 6, 6, 2, -6, -2 ],
[ 1, 0, 1, 0, 0, 1, 2, -8, -4, -2, -4, 6 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, -1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 3, 1 ],
[ 1, 5, 1 ],
[ 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 3, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1 ], l_ratios := [ 0, 1, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ -1, -2, 1, -4, -6, 1, -6, 2, 6, -6, 2, 2 ],
[ 1, 2, -1, -4, -2, -1, 2, 6, 6, 2, -6, -2 ],
[ 1, 0, 1, 0, 0, 1, 2, -8, -4, -2, -4, 6 ]
*], q_expansions := [*
q - q^2 - 2*q^3 + q^4 + q^5 + 2*q^6 - 4*q^7 - q^8 + q^9 - q^10 - 6*q^11 - 2*q^12 + q^13 + 4*q^14 - 2*q^15 + q^16 - 6*q^17 - q^18 + 2*q^19 + q^20 + 8*q^21 + 6*q^22 + 6*q^23 + 2*q^24 + q^25 - q^26 + 4*q^27 - 4*q^28 - 6*q^29 + 2*q^30 + 2*q^31 - q^32 + 12*q^33 + 6*q^34 - 4*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 - q^5 + 2*q^6 - 4*q^7 + q^8 + q^9 - q^10 - 2*q^11 + 2*q^12 - q^13 - 4*q^14 - 2*q^15 + q^16 + 2*q^17 + q^18 + 6*q^19 - q^20 - 8*q^21 - 2*q^22 + 6*q^23 + 2*q^24 + q^25 - q^26 - 4*q^27 - 4*q^28 + 2*q^29 - 2*q^30 - 6*q^31 + q^32 - 4*q^33 + 2*q^34 + 4*q^35 + q^36 - 2*q^37 + O(q^38),
q + q^2 + q^4 + q^5 + q^8 - 3*q^9 + q^10 + q^13 + q^16 + 2*q^17 - 3*q^18 - 8*q^19 + q^20 - 4*q^23 + q^25 + q^26 - 2*q^29 - 4*q^31 + q^32 + 2*q^34 - 3*q^36 + 6*q^37 + O(q^38)
*]> ;  // time = 33.3 seconds




J[131] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 131, 131 ], new_dimensions := [ 1, 10 ], dimensions := [ 1, 10 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ 0, -1, -2, -1, 0, -3, 4, -2, -2, 0, -2, -8 ],
[ 0, 1, 4, 1, 2, 11, -2, 0, -10, 16, 6, 34 ]
], hecke_fields := [
x - 1,
x^10 - 18*x^8 + 2*x^7 + 111*x^6 - 18*x^5 - 270*x^4 + 28*x^3 + 232*x^2 + 16*x - 32
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 65 ]
], tamagawa_numbers := [
[ 1 ],
[ 65 ]
], torsion_upper_bounds := [ 1, 65 ], torsion_lower_bounds := [ 1, 65 ], l_ratios := [ 0, 1/65 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ 0, -1, -2, -1, 0, -3, 4, -2, -2, 0, -2, -8 ],
[
a,
1/8*a^8 - 2*a^6 + 81/8*a^4 - 67/4*a^2 + 5,
-1/16*a^9 + 9/8*a^7 + 1/8*a^6 - 107/16*a^5 - 9/8*a^4 + 117/8*a^3 + 7/4*a^2 - 9*a + 1,
-1/8*a^9 - 1/4*a^8 + 7/4*a^7 + 7/2*a^6 - 57/8*a^5 - 63/4*a^4 + 11/2*a^3 + 47/2*a^2 + 15/2*a - 3,
-1/16*a^9 + 9/8*a^7 - 3/8*a^6 - 107/16*a^5 + 31/8*a^4 + 117/8*a^3 - 35/4*a^2 - 11*a + 2,
1/16*a^9 + 1/8*a^8 - 7/8*a^7 - 15/8*a^6 + 55/16*a^5 + 17/2*a^4 - 17/8*a^3 - 21/2*a^2 - 5*a + 1,
1/8*a^9 + 1/4*a^8 - 7/4*a^7 - 13/4*a^6 + 59/8*a^5 + 25/2*a^4 - 31/4*a^3 - 12*a^2 - 4*a - 4,
1/8*a^9 - 9/4*a^7 + 1/4*a^6 + 103/8*a^5 - 13/4*a^4 - 95/4*a^3 + 21/2*a^2 + 6*a - 6,
1/4*a^9 + 1/4*a^8 - 4*a^7 - 7/2*a^6 + 83/4*a^5 + 63/4*a^4 - 37*a^3 - 49/2*a^2 + 16*a + 6,
1/8*a^9 - 1/4*a^8 - 9/4*a^7 + 17/4*a^6 + 103/8*a^5 - 45/2*a^4 - 99/4*a^3 + 37*a^2 + 13*a - 10,
3/8*a^9 + 1/4*a^8 - 25/4*a^7 - 11/4*a^6 + 273/8*a^5 + 8*a^4 - 257/4*a^3 - 5*a^2 + 26*a - 2,
-1/4*a^8 + 7/2*a^6 - 1/2*a^5 - 59/4*a^4 + 7/2*a^3 + 35/2*a^2 - 2*a + 2
]
*], q_expansions := [*
q - q^3 - 2*q^4 - 2*q^5 - q^7 - 2*q^9 + 2*q^12 - 3*q^13 + 2*q^15 + 4*q^16 + 4*q^17 - 2*q^19 + 4*q^20 + q^21 - 2*q^23 - q^25 + 5*q^27 + 2*q^28 - 2*q^31 + 2*q^35 + 4*q^36 - 8*q^37 + O(q^38),
q + a*q^2 + (1/8*a^8 - 2*a^6 + 81/8*a^4 - 67/4*a^2 + 5)*q^3 + (a^2 - 2)*q^4 + (-1/16*a^9 + 9/8*a^7 + 1/8*a^6 - 107/16*a^5 - 9/8*a^4 + 117/8*a^3 + 7/4*a^2 - 9*a + 1)*q^5 + (1/8*a^9 - 2*a^7 + 81/8*a^5 - 67/4*a^3 + 5*a)*q^6 + (-1/8*a^9 - 1/4*a^8 + 7/4*a^7 + 7/2*a^6 - 57/8*a^5 - 63/4*a^4 + 11/2*a^3 + 47/2*a^2 + 15/2*a - 3)*q^7 + (a^3 - 4*a)*q^8 + (3/16*a^9 - 25/8*a^7 + 5/8*a^6 + 273/16*a^5 - 45/8*a^4 - 261/8*a^3 + 39/4*a^2 + 31/2*a + 1)*q^9 + (1/4*a^7 + 1/4*a^6 - 9/4*a^5 - 9/4*a^4 + 7/2*a^3 + 11/2*a^2 + 2*a - 2)*q^10 + (-1/16*a^9 + 9/8*a^7 - 3/8*a^6 - 107/16*a^5 + 31/8*a^4 + 117/8*a^3 - 35/4*a^2 - 11*a + 2)*q^11 + (-1/4*a^7 + 1/4*a^6 + 9/4*a^5 - 13/4*a^4 - 7/2*a^3 + 19/2*a^2 - 2*a - 6)*q^12 + (1/16*a^9 + 1/8*a^8 - 7/8*a^7 - 15/8*a^6 + 55/16*a^5 + 17/2*a^4 - 17/8*a^3 - 21/2*a^2 - 5*a + 1)*q^13 + (-1/4*a^9 - 1/2*a^8 + 15/4*a^7 + 27/4*a^6 - 18*a^5 - 113/4*a^4 + 27*a^3 + 73/2*a^2 - a - 4)*q^14 + (-1/8*a^9 + 1/8*a^8 + 9/4*a^7 - 5/2*a^6 - 109/8*a^5 + 121/8*a^4 + 61/2*a^3 - 109/4*a^2 - 41/2*a + 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/8*a^9 + 1/4*a^8 - 7/4*a^7 - 13/4*a^6 + 59/8*a^5 + 25/2*a^4 - 31/4*a^3 - 12*a^2 - 4*a - 4)*q^17 + (1/4*a^8 + 1/4*a^7 - 15/4*a^6 - 9/4*a^5 + 18*a^4 + 9/2*a^3 - 28*a^2 - 2*a + 6)*q^18 + (1/8*a^9 - 9/4*a^7 + 1/4*a^6 + 103/8*a^5 - 13/4*a^4 - 95/4*a^3 + 21/2*a^2 + 6*a - 6)*q^19 + (1/8*a^9 + 1/4*a^8 - 2*a^7 - 5/2*a^6 + 89/8*a^5 + 23/4*a^4 - 95/4*a^3 - 3/2*a^2 + 16*a - 2)*q^20 + (1/16*a^9 - 9/8*a^7 + 1/8*a^6 + 119/16*a^5 - 5/8*a^4 - 163/8*a^3 - 3/4*a^2 + 33/2*a + 3)*q^21 + (-1/4*a^7 + 1/4*a^6 + 11/4*a^5 - 9/4*a^4 - 7*a^3 + 7/2*a^2 + 3*a - 2)*q^22 + (1/4*a^9 + 1/4*a^8 - 4*a^7 - 7/2*a^6 + 83/4*a^5 + 63/4*a^4 - 37*a^3 - 49/2*a^2 + 16*a + 6)*q^23 + (-1/4*a^9 - 1/4*a^8 + 17/4*a^7 + 9/4*a^6 - 47/2*a^5 - 7/2*a^4 + 43*a^3 - 2*a^2 - 16*a)*q^24 + (-5/16*a^9 - 1/4*a^8 + 41/8*a^7 + 21/8*a^6 - 447/16*a^5 - 51/8*a^4 + 441/8*a^3 - 1/4*a^2 - 29*a + 5)*q^25 + (1/8*a^9 + 1/4*a^8 - 2*a^7 - 7/2*a^6 + 77/8*a^5 + 59/4*a^4 - 49/4*a^3 - 39/2*a^2 + 2)*q^26 + (-3/16*a^9 - 1/8*a^8 + 23/8*a^7 + 11/8*a^6 - 209/16*a^5 - 7/2*a^4 + 99/8*a^3 - a^2 + 16*a + 4)*q^27 + (-1/4*a^9 - 1/4*a^8 + 15/4*a^7 + 11/4*a^6 - 37/2*a^5 - 9*a^4 + 65/2*a^3 + 10*a^2 - 15*a - 2)*q^28 + (1/8*a^9 - 1/4*a^8 - 9/4*a^7 + 17/4*a^6 + 103/8*a^5 - 45/2*a^4 - 99/4*a^3 + 37*a^2 + 13*a - 10)*q^29 + (1/8*a^9 - 9/4*a^7 + 1/4*a^6 + 103/8*a^5 - 13/4*a^4 - 95/4*a^3 + 17/2*a^2 + 7*a - 4)*q^30 + (3/8*a^9 + 1/4*a^8 - 25/4*a^7 - 11/4*a^6 + 273/8*a^5 + 8*a^4 - 257/4*a^3 - 5*a^2 + 26*a - 2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-1/4*a^9 - 1/4*a^8 + 4*a^7 + 13/4*a^6 - 21*a^5 - 27/2*a^4 + 157/4*a^3 + 19*a^2 - 39/2*a - 4)*q^33 + (1/4*a^9 + 1/2*a^8 - 7/2*a^7 - 13/2*a^6 + 59/4*a^5 + 26*a^4 - 31/2*a^3 - 33*a^2 - 6*a + 4)*q^34 + (-1/16*a^9 - 3/8*a^8 + 7/8*a^7 + 47/8*a^6 - 55/16*a^5 - 119/4*a^4 + 1/8*a^3 + 50*a^2 + 13*a - 14)*q^35 + (-1/8*a^9 + 1/4*a^8 + 5/2*a^7 - 7/2*a^6 - 129/8*a^5 + 63/4*a^4 + 149/4*a^3 - 43/2*a^2 - 25*a - 2)*q^36 + (-1/4*a^8 + 7/2*a^6 - 1/2*a^5 - 59/4*a^4 + 7/2*a^3 + 35/2*a^2 - 2*a + 2)*q^37 + O(q^38)
*]> ;  // time = 1.479 seconds




J[133] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 133, 133, 133, 133, 19 ], new_dimensions := [ 2, 2, 2, 3, 1 ], dimensions := [ 2, 2, 2, 3, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 0, 7, 1, 1, 3, 7, 0 ], ap_traces := [
[ -3, -3, 0, -2, -9, 2, -3, -2, -6, -9, 5, -8 ],
[ 1, 3, 2, 2, -1, -2, 1, -2, -2, 5, -1, -14 ],
[ -1, -3, -6, 2, -5, -4, -7, 2, -6, 9, -1, 0 ],
[ 2, 3, -2, -3, 7, -2, 7, 3, 14, -3, -11, 0 ]
], hecke_fields := [
x^2 + 3*x + 1,
x^2 - x - 1,
x^2 + x - 3,
x^3 - 2*x^2 - 4*x + 7
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 5, 1 ],
[ 3, 1 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 5, 1 ],
[ 3, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 5, 9, 1 ], torsion_lower_bounds := [ 1, 5, 1, 1 ], l_ratios := [ 0, 1/5, 0, 1 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1 ], eigenvalues := [*
[
a,
a,
-2*a - 3,
-1,
a - 3,
1,
3*a + 3,
-1,
-3,
a - 3,
3*a + 7,
6*a + 5
],
[
a,
-a + 2,
1,
1,
a - 1,
-1,
3*a - 1,
-1,
-4*a + 1,
-a + 3,
9*a - 5,
4*a - 9
],
[
a,
-a - 2,
-3,
1,
-a - 3,
2*a - 1,
a - 3,
1,
-3,
-3*a + 3,
-a - 1,
-2*a - 1
],
[
a,
-a^2 + 5,
a^2 - a - 4,
-1,
-a + 3,
a^2 - a - 4,
-2*a^2 - a + 11,
1,
a^2 + a,
-4*a^2 + 3*a + 13,
2*a^2 - a - 11,
-a^2 + 3*a + 2
]
*], q_expansions := [*
q + a*q^2 + a*q^3 + (-3*a - 3)*q^4 + (-2*a - 3)*q^5 + (-3*a - 1)*q^6 - q^7 + (4*a + 3)*q^8 + (-3*a - 4)*q^9 + (3*a + 2)*q^10 + (a - 3)*q^11 + (6*a + 3)*q^12 + q^13 - a*q^14 + (3*a + 2)*q^15 + (-3*a + 2)*q^16 + (3*a + 3)*q^17 + (5*a + 3)*q^18 - q^19 + (-3*a + 3)*q^20 - a*q^21 + (-6*a - 1)*q^22 - 3*q^23 + (-9*a - 4)*q^24 + a*q^26 + (2*a + 3)*q^27 + (3*a + 3)*q^28 + (a - 3)*q^29 + (-7*a - 3)*q^30 + (3*a + 7)*q^31 + (3*a - 3)*q^32 + (-6*a - 1)*q^33 + (-6*a - 3)*q^34 + (2*a + 3)*q^35 + (-6*a + 3)*q^36 + (6*a + 5)*q^37 + O(q^38),
q + a*q^2 + (-a + 2)*q^3 + (a - 1)*q^4 + q^5 + (a - 1)*q^6 + q^7 + (-2*a + 1)*q^8 + (-3*a + 2)*q^9 + a*q^10 + (a - 1)*q^11 + (2*a - 3)*q^12 - q^13 + a*q^14 + (-a + 2)*q^15 - 3*a*q^16 + (3*a - 1)*q^17 + (-a - 3)*q^18 - q^19 + (a - 1)*q^20 + (-a + 2)*q^21 + q^22 + (-4*a + 1)*q^23 + (-3*a + 4)*q^24 - 4*q^25 - a*q^26 + (-2*a + 1)*q^27 + (a - 1)*q^28 + (-a + 3)*q^29 + (a - 1)*q^30 + (9*a - 5)*q^31 + (a - 5)*q^32 + (2*a - 3)*q^33 + (2*a + 3)*q^34 + q^35 + (2*a - 5)*q^36 + (4*a - 9)*q^37 + O(q^38),
q + a*q^2 + (-a - 2)*q^3 + (-a + 1)*q^4 - 3*q^5 + (-a - 3)*q^6 + q^7 - 3*q^8 + (3*a + 4)*q^9 - 3*a*q^10 + (-a - 3)*q^11 + q^12 + (2*a - 1)*q^13 + a*q^14 + (3*a + 6)*q^15 + (-a - 2)*q^16 + (a - 3)*q^17 + (a + 9)*q^18 + q^19 + (3*a - 3)*q^20 + (-a - 2)*q^21 + (-2*a - 3)*q^22 - 3*q^23 + (3*a + 6)*q^24 + 4*q^25 + (-3*a + 6)*q^26 + (-4*a - 11)*q^27 + (-a + 1)*q^28 + (-3*a + 3)*q^29 + (3*a + 9)*q^30 + (-a - 1)*q^31 + (-a + 3)*q^32 + (4*a + 9)*q^33 + (-4*a + 3)*q^34 - 3*q^35 + (2*a - 5)*q^36 + (-2*a - 1)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + 5)*q^3 + (a^2 - 2)*q^4 + (a^2 - a - 4)*q^5 + (-2*a^2 + a + 7)*q^6 - q^7 + (2*a^2 - 7)*q^8 + (-2*a^2 + a + 8)*q^9 + (a^2 - 7)*q^10 + (-a + 3)*q^11 + (-a^2 - a + 4)*q^12 + (a^2 - a - 4)*q^13 - a*q^14 + (3*a^2 - 2*a - 13)*q^15 + (2*a^2 + a - 10)*q^16 + (-2*a^2 - a + 11)*q^17 + (-3*a^2 + 14)*q^18 + q^19 + (-a + 1)*q^20 + (a^2 - 5)*q^21 + (-a^2 + 3*a)*q^22 + (a^2 + a)*q^23 + (a^2 - 2*a - 7)*q^24 + (-3*a^2 + a + 11)*q^25 + (a^2 - 7)*q^26 + (-a^2 + 3*a + 4)*q^27 + (-a^2 + 2)*q^28 + (-4*a^2 + 3*a + 13)*q^29 + (4*a^2 - a - 21)*q^30 + (2*a^2 - a - 11)*q^31 + (a^2 - 2*a)*q^32 + (-a^2 - a + 8)*q^33 + (-5*a^2 + 3*a + 14)*q^34 + (-a^2 + a + 4)*q^35 + (-2*a^2 + 5)*q^36 + (-a^2 + 3*a + 2)*q^37 + O(q^38)
*]> ;  // time = 10.539 seconds




J[134] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 134, 134, 67, 67, 67 ], new_dimensions := [ 3, 3, 1, 2, 2 ], dimensions := [ 3, 3, 2, 4, 4 ], intersection_graph := [ 0, 1, 5, 1, 5, 1, 0, 1, 19, 1, 5, 1, 0, 1, 25, 1, 19, 1, 0, 1, 5, 1, 25, 1, 0 ], ap_traces := [
[ -3, 1, 3, 0, -1, 11, -3, 6, -11, 0, 4, 4 ],
[ 3, 3, -3, 0, -3, -3, -3, 6, -3, -12, 12, 0 ]
], hecke_fields := [
x^3 - x^2 - 8*x + 11,
x^3 - 3*x^2 + 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 75, 3 ],
[ 323, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 323, 1 ]
], torsion_upper_bounds := [ 3, 17 ], torsion_lower_bounds := [ 3, 17 ], l_ratios := [ 1/3, 19/17 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
-1,
a,
a^2 + a - 5,
-2*a^2 - 2*a + 12,
-a^2 - 2*a + 6,
a^2 - 2,
-a^2 - a + 5,
2,
a - 4,
0,
4*a^2 + 2*a - 22,
-2*a^2 - 4*a + 14
],
[
1,
a,
-a^2 + a + 1,
2*a^2 - 6*a,
-3*a^2 + 6*a + 2,
3*a^2 - 8*a - 2,
-a^2 + 5*a - 3,
-4*a^2 + 12*a + 2,
4*a^2 - 9*a - 4,
-4,
-2*a + 6,
-6*a^2 + 16*a + 2
]
*], q_expansions := [*
q - q^2 + a*q^3 + q^4 + (a^2 + a - 5)*q^5 - a*q^6 + (-2*a^2 - 2*a + 12)*q^7 - q^8 + (a^2 - 3)*q^9 + (-a^2 - a + 5)*q^10 + (-a^2 - 2*a + 6)*q^11 + a*q^12 + (a^2 - 2)*q^13 + (2*a^2 + 2*a - 12)*q^14 + (2*a^2 + 3*a - 11)*q^15 + q^16 + (-a^2 - a + 5)*q^17 + (-a^2 + 3)*q^18 + 2*q^19 + (a^2 + a - 5)*q^20 + (-4*a^2 - 4*a + 22)*q^21 + (a^2 + 2*a - 6)*q^22 + (a - 4)*q^23 - a*q^24 + (2*a^2 + 3*a - 13)*q^25 + (-a^2 + 2)*q^26 + (a^2 + 2*a - 11)*q^27 + (-2*a^2 - 2*a + 12)*q^28 + (-2*a^2 - 3*a + 11)*q^30 + (4*a^2 + 2*a - 22)*q^31 - q^32 + (-3*a^2 - 2*a + 11)*q^33 + (a^2 + a - 5)*q^34 + (-2*a^2 - 4*a + 6)*q^35 + (a^2 - 3)*q^36 + (-2*a^2 - 4*a + 14)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a^2 + a + 1)*q^5 + a*q^6 + (2*a^2 - 6*a)*q^7 + q^8 + (a^2 - 3)*q^9 + (-a^2 + a + 1)*q^10 + (-3*a^2 + 6*a + 2)*q^11 + a*q^12 + (3*a^2 - 8*a - 2)*q^13 + (2*a^2 - 6*a)*q^14 + (-2*a^2 + a + 1)*q^15 + q^16 + (-a^2 + 5*a - 3)*q^17 + (a^2 - 3)*q^18 + (-4*a^2 + 12*a + 2)*q^19 + (-a^2 + a + 1)*q^20 - 2*q^21 + (-3*a^2 + 6*a + 2)*q^22 + (4*a^2 - 9*a - 4)*q^23 + a*q^24 + (2*a^2 + a - 5)*q^25 + (3*a^2 - 8*a - 2)*q^26 + (3*a^2 - 6*a - 1)*q^27 + (2*a^2 - 6*a)*q^28 - 4*q^29 + (-2*a^2 + a + 1)*q^30 + (-2*a + 6)*q^31 + q^32 + (-3*a^2 + 2*a + 3)*q^33 + (-a^2 + 5*a - 3)*q^34 + (2*a^2 - 4*a - 2)*q^35 + (a^2 - 3)*q^36 + (-6*a^2 + 16*a + 2)*q^37 + O(q^38)
*]> ;  // time = 17.249 seconds




J[137] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 137, 137 ], new_dimensions := [ 4, 7 ], dimensions := [ 4, 7 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -3, -5, -2, -13, 1, -8, -4, -10, -1, 11, -17, -4 ],
[ 0, 3, -2, 15, -3, 12, -6, 10, -3, -9, 13, -2 ]
], hecke_fields := [
x^4 + 3*x^3 - 4*x - 1,
x^7 - 10*x^5 + 28*x^3 + 3*x^2 - 19*x - 7
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 17 ]
], tamagawa_numbers := [
[ 1 ],
[ 17 ]
], torsion_upper_bounds := [ 1, 17 ], torsion_lower_bounds := [ 1, 17 ], l_ratios := [ 0, 1/17 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
a^3 + a^2 - 3*a - 2,
-2*a^3 - 3*a^2 + 3*a + 1,
-a^3 - 2*a^2 + 2*a - 1,
4*a^3 + 9*a^2 - 4*a - 8,
a^2 + 3*a - 2,
-a^3 - 5*a^2 - 2*a + 5,
-2*a^3 - 7*a^2 - a + 5,
a^2 - 2*a - 4,
-a^3 - 5*a^2 + a + 11,
5*a^3 + 9*a^2 - 7*a - 11,
2*a^3 + 7*a^2 + 3*a - 7
],
[
a,
-1/2*a^6 + 1/2*a^5 + 11/2*a^4 - 9/2*a^3 - 33/2*a^2 + 9*a + 21/2,
a^6 - a^5 - 10*a^4 + 8*a^3 + 26*a^2 - 13*a - 13,
-a^6 + 9*a^4 - a^3 - 21*a^2 + 3*a + 11,
2*a^6 - a^5 - 19*a^4 + 10*a^3 + 47*a^2 - 21*a - 22,
a^6 - 9*a^4 + 2*a^3 + 22*a^2 - 8*a - 10,
a^5 + a^4 - 7*a^3 - 5*a^2 + 9*a + 3,
a^6 - a^5 - 10*a^4 + 8*a^3 + 28*a^2 - 13*a - 17,
-1/2*a^6 + 1/2*a^5 + 7/2*a^4 - 11/2*a^3 - 9/2*a^2 + 12*a + 1/2,
-a^6 + a^5 + 11*a^4 - 8*a^3 - 32*a^2 + 15*a + 16,
1/2*a^6 + 1/2*a^5 - 9/2*a^4 - 3/2*a^3 + 21/2*a^2 - 2*a - 3/2,
-a^6 + 10*a^4 - 3*a^3 - 28*a^2 + 12*a + 16
]
*], q_expansions := [*
q + a*q^2 + (a^3 + a^2 - 3*a - 2)*q^3 + (a^2 - 2)*q^4 + (-2*a^3 - 3*a^2 + 3*a + 1)*q^5 + (-2*a^3 - 3*a^2 + 2*a + 1)*q^6 + (-a^3 - 2*a^2 + 2*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (2*a^2 + 3*a - 1)*q^9 + (3*a^3 + 3*a^2 - 7*a - 2)*q^10 + (4*a^3 + 9*a^2 - 4*a - 8)*q^11 + (a^3 - a + 2)*q^12 + (a^2 + 3*a - 2)*q^13 + (a^3 + 2*a^2 - 5*a - 1)*q^14 + (4*a + 1)*q^15 + (-3*a^3 - 6*a^2 + 4*a + 5)*q^16 + (-a^3 - 5*a^2 - 2*a + 5)*q^17 + (2*a^3 + 3*a^2 - a)*q^18 + (-2*a^3 - 7*a^2 - a + 5)*q^19 + (-2*a^3 - a^2 + 4*a + 1)*q^20 + (-4*a^3 - 4*a^2 + 11*a + 5)*q^21 + (-3*a^3 - 4*a^2 + 8*a + 4)*q^22 + (a^2 - 2*a - 4)*q^23 + (a^3 + 5*a^2 + 2*a - 1)*q^24 + (3*a^3 + 7*a^2 - 6*a - 7)*q^25 + (a^3 + 3*a^2 - 2*a)*q^26 + (-4*a^3 - 9*a^2 + 4*a + 7)*q^27 + (a^3 - a^2 - a + 3)*q^28 + (-a^3 - 5*a^2 + a + 11)*q^29 + (4*a^2 + a)*q^30 + (5*a^3 + 9*a^2 - 7*a - 11)*q^31 + (a^3 + 4*a^2 + a - 3)*q^32 + (-a^3 - 6*a^2 - 7*a + 6)*q^33 + (-2*a^3 - 2*a^2 + a - 1)*q^34 + (9*a^3 + 13*a^2 - 16*a - 5)*q^35 + (-3*a^3 - 5*a^2 + 2*a + 4)*q^36 + (2*a^3 + 7*a^2 + 3*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^6 + 1/2*a^5 + 11/2*a^4 - 9/2*a^3 - 33/2*a^2 + 9*a + 21/2)*q^3 + (a^2 - 2)*q^4 + (a^6 - a^5 - 10*a^4 + 8*a^3 + 26*a^2 - 13*a - 13)*q^5 + (1/2*a^6 + 1/2*a^5 - 9/2*a^4 - 5/2*a^3 + 21/2*a^2 + a - 7/2)*q^6 + (-a^6 + 9*a^4 - a^3 - 21*a^2 + 3*a + 11)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^6 + a^5 + 19*a^4 - 10*a^3 - 48*a^2 + 20*a + 25)*q^9 + (-a^6 + 8*a^4 - 2*a^3 - 16*a^2 + 6*a + 7)*q^10 + (2*a^6 - a^5 - 19*a^4 + 10*a^3 + 47*a^2 - 21*a - 22)*q^11 + (3/2*a^6 - 1/2*a^5 - 27/2*a^4 + 11/2*a^3 + 65/2*a^2 - 12*a - 35/2)*q^12 + (a^6 - 9*a^4 + 2*a^3 + 22*a^2 - 8*a - 10)*q^13 + (-a^5 - a^4 + 7*a^3 + 6*a^2 - 8*a - 7)*q^14 + (a^6 - 10*a^4 + a^3 + 27*a^2 - 5*a - 14)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^5 + a^4 - 7*a^3 - 5*a^2 + 9*a + 3)*q^17 + (a^6 - a^5 - 10*a^4 + 8*a^3 + 26*a^2 - 13*a - 14)*q^18 + (a^6 - a^5 - 10*a^4 + 8*a^3 + 28*a^2 - 13*a - 17)*q^19 + (-2*a^6 + 18*a^4 - 4*a^3 - 43*a^2 + 14*a + 19)*q^20 + (-3*a^6 + 2*a^5 + 31*a^4 - 18*a^3 - 87*a^2 + 34*a + 49)*q^21 + (-a^6 + a^5 + 10*a^4 - 9*a^3 - 27*a^2 + 16*a + 14)*q^22 + (-1/2*a^6 + 1/2*a^5 + 7/2*a^4 - 11/2*a^3 - 9/2*a^2 + 12*a + 1/2)*q^23 + (-3/2*a^6 + 1/2*a^5 + 29/2*a^4 - 9/2*a^3 - 75/2*a^2 + 9*a + 35/2)*q^24 + (a^6 - 9*a^4 + 3*a^3 + 22*a^2 - 11*a - 11)*q^25 + (a^5 + 2*a^4 - 6*a^3 - 11*a^2 + 9*a + 7)*q^26 + (-2*a^6 + 18*a^4 - 2*a^3 - 43*a^2 + 6*a + 21)*q^27 + (a^6 - a^5 - 11*a^4 + 8*a^3 + 34*a^2 - 13*a - 22)*q^28 + (-a^6 + a^5 + 11*a^4 - 8*a^3 - 32*a^2 + 15*a + 16)*q^29 + (a^4 - a^3 - 8*a^2 + 5*a + 7)*q^30 + (1/2*a^6 + 1/2*a^5 - 9/2*a^4 - 3/2*a^3 + 21/2*a^2 - 2*a - 3/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^6 - a^5 - 11*a^4 + 8*a^3 + 33*a^2 - 13*a - 21)*q^33 + (a^6 + a^5 - 7*a^4 - 5*a^3 + 9*a^2 + 3*a)*q^34 + (3*a^6 - 3*a^5 - 30*a^4 + 25*a^3 + 80*a^2 - 42*a - 45)*q^35 + (3*a^6 - 2*a^5 - 30*a^4 + 18*a^3 + 80*a^2 - 35*a - 43)*q^36 + (-a^6 + 10*a^4 - 3*a^3 - 28*a^2 + 12*a + 16)*q^37 + O(q^38)
*]> ;  // time = 1.5 seconds




J[138] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 138, 138, 138, 138, 69, 69, 46, 23 ], new_dimensions := [ 1, 1, 1, 2, 1, 2, 1, 2 ], dimensions := [ 1, 1, 1, 2, 2, 4, 2, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 11, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 121, 1, 1, 1, 1, 1, 1, 0, 25, 1, 1, 1, 11, 1, 121, 25, 0 ], ap_traces := [
[ -1, -1, -2, -2, -6, -2, 0, 0, -1, 6, 8, 0 ],
[ -1, 1, 0, 2, 0, 2, 0, 2, -1, -6, -4, -10 ],
[ 1, -1, 2, 0, 0, -2, 2, -8, -1, -2, -8, 2 ],
[ 2, 2, -2, 0, -6, 0, -8, -2, 2, 0, 4, 18 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 + 2*x - 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 11, 11, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 11, 11, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 11 ], torsion_lower_bounds := [ 1, 3, 1, 1 ], l_ratios := [ 0, 1/3, 1, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1/121 ], eigenvalues := [*
[ -1, -1, -2, -2, -6, -2, 0, 0, -1, 6, 8, 0 ],
[ -1, 1, 0, 2, 0, 2, 0, 2, -1, -6, -4, -10 ],
[ 1, -1, 2, 0, 0, -2, 2, -8, -1, -2, -8, 2 ],
[
1,
1,
a,
-2*a - 2,
-a - 4,
2*a + 2,
-4,
3*a + 2,
1,
-2*a - 2,
-2*a,
a + 10
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - 2*q^5 + q^6 - 2*q^7 - q^8 + q^9 + 2*q^10 - 6*q^11 - q^12 - 2*q^13 + 2*q^14 + 2*q^15 + q^16 - q^18 - 2*q^20 + 2*q^21 + 6*q^22 - q^23 + q^24 - q^25 + 2*q^26 - q^27 - 2*q^28 + 6*q^29 - 2*q^30 + 8*q^31 - q^32 + 6*q^33 + 4*q^35 + q^36 + O(q^38),
q - q^2 + q^3 + q^4 - q^6 + 2*q^7 - q^8 + q^9 + q^12 + 2*q^13 - 2*q^14 + q^16 - q^18 + 2*q^19 + 2*q^21 - q^23 - q^24 - 5*q^25 - 2*q^26 + q^27 + 2*q^28 - 6*q^29 - 4*q^31 - q^32 + q^36 - 10*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + 2*q^5 - q^6 + q^8 + q^9 + 2*q^10 - q^12 - 2*q^13 - 2*q^15 + q^16 + 2*q^17 + q^18 - 8*q^19 + 2*q^20 - q^23 - q^24 - q^25 - 2*q^26 - q^27 - 2*q^29 - 2*q^30 - 8*q^31 + q^32 + 2*q^34 + q^36 + 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + a*q^5 + q^6 + (-2*a - 2)*q^7 + q^8 + q^9 + a*q^10 + (-a - 4)*q^11 + q^12 + (2*a + 2)*q^13 + (-2*a - 2)*q^14 + a*q^15 + q^16 - 4*q^17 + q^18 + (3*a + 2)*q^19 + a*q^20 + (-2*a - 2)*q^21 + (-a - 4)*q^22 + q^23 + q^24 + (-2*a - 1)*q^25 + (2*a + 2)*q^26 + q^27 + (-2*a - 2)*q^28 + (-2*a - 2)*q^29 + a*q^30 - 2*a*q^31 + q^32 + (-a - 4)*q^33 - 4*q^34 + (2*a - 8)*q^35 + q^36 + (a + 10)*q^37 + O(q^38)
*]> ;  // time = 52.451 seconds




J[139] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 139, 139, 139 ], new_dimensions := [ 1, 3, 7 ], dimensions := [ 1, 3, 7 ], intersection_graph := [ 0, 1, 3, 1, 0, 1, 3, 1, 0 ], ap_traces := [
[ 1, 2, -1, 3, 5, -7, -6, -2, 2, 9, 9, 2 ],
[ -2, -2, -8, 0, -7, 1, -3, -2, -7, -15, 3, -9 ],
[ 1, -2, 11, -5, 2, 6, 5, -10, -1, 30, -20, 6 ]
], hecke_fields := [
x - 1,
x^3 + 2*x^2 - x - 1,
x^7 - x^6 - 11*x^5 + 8*x^4 + 35*x^3 - 10*x^2 - 32*x - 8
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 23 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 23 ]
], torsion_upper_bounds := [ 1, 1, 23 ], torsion_lower_bounds := [ 1, 1, 23 ], l_ratios := [ 1, 0, 1/23 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ 1, 2, -1, 3, 5, -7, -6, -2, 2, 9, 9, 2 ],
[
a,
-a^2 - 2*a,
a^2 + a - 4,
2*a^2 + 3*a - 2,
-3*a^2 - 4*a + 1,
-3*a^2 - 5*a + 3,
a^2 + 3*a - 1,
2*a^2 + 7*a,
4*a^2 + 5*a - 7,
-3*a - 7,
-3*a - 1,
-a^2 - 6*a - 5
],
[
a,
1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 4*a^3 + 19/2*a^2 - 6*a - 4,
-1/4*a^6 - 1/4*a^5 + 9/4*a^4 + 3/2*a^3 - 19/4*a^2 - a + 3,
-1/4*a^6 + 1/4*a^5 + 11/4*a^4 - 2*a^3 - 35/4*a^2 + 7/2*a + 6,
-1/2*a^6 + a^5 + 5*a^4 - 17/2*a^3 - 25/2*a^2 + 27/2*a + 7,
1/2*a^5 + 1/2*a^4 - 9/2*a^3 - 4*a^2 + 17/2*a + 7,
1/2*a^6 + 1/2*a^5 - 9/2*a^4 - 4*a^3 + 17/2*a^2 + 6*a + 2,
-a^4 + 7*a^2 - 8,
1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 5*a^3 + 21/2*a^2 - 10*a - 8,
-1/4*a^6 + 1/4*a^5 + 11/4*a^4 - a^3 - 27/4*a^2 - 7/2*a + 4,
-3/4*a^6 + 1/4*a^5 + 27/4*a^4 - 7/2*a^3 - 57/4*a^2 + 10*a + 3,
-2*a^4 + 13*a^2 - 9
]
*], q_expansions := [*
q + q^2 + 2*q^3 - q^4 - q^5 + 2*q^6 + 3*q^7 - 3*q^8 + q^9 - q^10 + 5*q^11 - 2*q^12 - 7*q^13 + 3*q^14 - 2*q^15 - q^16 - 6*q^17 + q^18 - 2*q^19 + q^20 + 6*q^21 + 5*q^22 + 2*q^23 - 6*q^24 - 4*q^25 - 7*q^26 - 4*q^27 - 3*q^28 + 9*q^29 - 2*q^30 + 9*q^31 + 5*q^32 + 10*q^33 - 6*q^34 - 3*q^35 - q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (-a^2 - 2*a)*q^3 + (a^2 - 2)*q^4 + (a^2 + a - 4)*q^5 + (-a - 1)*q^6 + (2*a^2 + 3*a - 2)*q^7 + (-2*a^2 - 3*a + 1)*q^8 + (a^2 + 3*a - 1)*q^9 + (-a^2 - 3*a + 1)*q^10 + (-3*a^2 - 4*a + 1)*q^11 + (a^2 + 3*a)*q^12 + (-3*a^2 - 5*a + 3)*q^13 + (-a^2 + 2)*q^14 + (3*a^2 + 6*a - 1)*q^15 + (-a^2 - a + 2)*q^16 + (a^2 + 3*a - 1)*q^17 + (a^2 + 1)*q^18 + (2*a^2 + 7*a)*q^19 + (-3*a^2 - 2*a + 7)*q^20 + (-a - 3)*q^21 + (2*a^2 - 2*a - 3)*q^22 + (4*a^2 + 5*a - 7)*q^23 + (a^2 + 3*a + 3)*q^24 + (-6*a^2 - 7*a + 11)*q^25 + (a^2 - 3)*q^26 + (3*a^2 + 4*a - 3)*q^27 + (-2*a^2 - 5*a + 3)*q^28 + (-3*a - 7)*q^29 + (2*a + 3)*q^30 + (-3*a - 1)*q^31 + (5*a^2 + 7*a - 3)*q^32 + (2*a^2 + 5*a + 4)*q^33 + (a^2 + 1)*q^34 + (-7*a^2 - 11*a + 9)*q^35 + (-4*a^2 - 4*a + 3)*q^36 + (-a^2 - 6*a - 5)*q^37 + O(q^38),
q + a*q^2 + (1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 4*a^3 + 19/2*a^2 - 6*a - 4)*q^3 + (a^2 - 2)*q^4 + (-1/4*a^6 - 1/4*a^5 + 9/4*a^4 + 3/2*a^3 - 19/4*a^2 - a + 3)*q^5 + (a^5 - 8*a^3 - a^2 + 12*a + 4)*q^6 + (-1/4*a^6 + 1/4*a^5 + 11/4*a^4 - 2*a^3 - 35/4*a^2 + 7/2*a + 6)*q^7 + (a^3 - 4*a)*q^8 + (-a^5 - a^4 + 9*a^3 + 7*a^2 - 18*a - 7)*q^9 + (-1/2*a^6 - 1/2*a^5 + 7/2*a^4 + 4*a^3 - 7/2*a^2 - 5*a - 2)*q^10 + (-1/2*a^6 + a^5 + 5*a^4 - 17/2*a^3 - 25/2*a^2 + 27/2*a + 7)*q^11 + (a^5 + a^4 - 9*a^3 - 7*a^2 + 16*a + 8)*q^12 + (1/2*a^5 + 1/2*a^4 - 9/2*a^3 - 4*a^2 + 17/2*a + 7)*q^13 + (a^2 - 2*a - 2)*q^14 + (a^6 - 9*a^4 + 19*a^2 - a - 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/2*a^6 + 1/2*a^5 - 9/2*a^4 - 4*a^3 + 17/2*a^2 + 6*a + 2)*q^17 + (-a^6 - a^5 + 9*a^4 + 7*a^3 - 18*a^2 - 7*a)*q^18 + (-a^4 + 7*a^2 - 8)*q^19 + (-1/2*a^6 - 3/2*a^5 + 7/2*a^4 + 11*a^3 - 1/2*a^2 - 16*a - 10)*q^20 + (-a^4 + a^3 + 7*a^2 - 5*a - 8)*q^21 + (1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 5*a^3 + 17/2*a^2 - 9*a - 4)*q^22 + (1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 5*a^3 + 21/2*a^2 - 10*a - 8)*q^23 + (a^6 - a^5 - 9*a^4 + 9*a^3 + 18*a^2 - 16*a - 8)*q^24 + (-3/4*a^6 - 1/4*a^5 + 29/4*a^4 + a^3 - 65/4*a^2 + 3/2*a + 5)*q^25 + (1/2*a^6 + 1/2*a^5 - 9/2*a^4 - 4*a^3 + 17/2*a^2 + 7*a)*q^26 + (a^6 - a^5 - 8*a^4 + 9*a^3 + 11*a^2 - 16*a)*q^27 + (1/2*a^6 - 1/2*a^5 - 11/2*a^4 + 5*a^3 + 31/2*a^2 - 9*a - 12)*q^28 + (-1/4*a^6 + 1/4*a^5 + 11/4*a^4 - a^3 - 27/4*a^2 - 7/2*a + 4)*q^29 + (a^6 + 2*a^5 - 8*a^4 - 16*a^3 + 9*a^2 + 26*a + 8)*q^30 + (-3/4*a^6 + 1/4*a^5 + 27/4*a^4 - 7/2*a^3 - 57/4*a^2 + 10*a + 3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^6 + a^5 + 10*a^4 - 10*a^3 - 24*a^2 + 22*a + 6)*q^33 + (a^6 + a^5 - 8*a^4 - 9*a^3 + 11*a^2 + 18*a + 4)*q^34 + (-3/4*a^6 + 5/4*a^5 + 31/4*a^4 - 19/2*a^3 - 93/4*a^2 + 14*a + 18)*q^35 + (-2*a^6 + 17*a^4 - a^3 - 31*a^2 + 4*a + 6)*q^36 + (-2*a^4 + 13*a^2 - 9)*q^37 + O(q^38)
*]> ;  // time = 1.641 seconds




J[141] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 141, 141, 141, 141, 141, 141, 47 ], new_dimensions := [ 1, 1, 1, 1, 1, 2, 4 ], dimensions := [ 1, 1, 1, 1, 1, 2, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 0, 3, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 7, 1, 1, 1, 1, 1, 0, 43, 1, 3, 1, 1, 7, 43, 0 ], ap_traces := [
[ 0, -1, -1, -3, -3, -4, 8, -6, 3, -1, 4, 1 ],
[ -1, -1, 0, 4, 0, 6, -6, 2, 4, 8, 6, -6 ],
[ -1, 1, 2, 0, 4, -2, 2, 0, 0, -6, -4, -10 ],
[ 2, 1, -1, -3, 1, -2, 2, 6, 3, 3, 2, -7 ],
[ -2, 1, -3, -3, -5, 2, -6, -6, 9, 1, -2, 1 ],
[ -1, -2, 1, 1, 7, -6, 2, 12, -3, -15, 6, 11 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 + x - 4
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 43, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 1, 1, 0, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 0, 1 ], eigenvalues := [*
[ 0, -1, -1, -3, -3, -4, 8, -6, 3, -1, 4, 1 ],
[ -1, -1, 0, 4, 0, 6, -6, 2, 4, 8, 6, -6 ],
[ -1, 1, 2, 0, 4, -2, 2, 0, 0, -6, -4, -10 ],
[ 2, 1, -1, -3, 1, -2, 2, 6, 3, 3, 2, -7 ],
[ -2, 1, -3, -3, -5, 2, -6, -6, 9, 1, -2, 1 ],
[
a,
-1,
a + 1,
a + 1,
-a + 3,
-2*a - 4,
-2*a,
6,
-3*a - 3,
a - 7,
2*a + 4,
-a + 5
]
*], q_expansions := [*
q - q^3 - 2*q^4 - q^5 - 3*q^7 + q^9 - 3*q^11 + 2*q^12 - 4*q^13 + q^15 + 4*q^16 + 8*q^17 - 6*q^19 + 2*q^20 + 3*q^21 + 3*q^23 - 4*q^25 - q^27 + 6*q^28 - q^29 + 4*q^31 + 3*q^33 + 3*q^35 - 2*q^36 + q^37 + O(q^38),
q - q^2 - q^3 - q^4 + q^6 + 4*q^7 + 3*q^8 + q^9 + q^12 + 6*q^13 - 4*q^14 - q^16 - 6*q^17 - q^18 + 2*q^19 - 4*q^21 + 4*q^23 - 3*q^24 - 5*q^25 - 6*q^26 - q^27 - 4*q^28 + 8*q^29 + 6*q^31 - 5*q^32 + 6*q^34 - q^36 - 6*q^37 + O(q^38),
q - q^2 + q^3 - q^4 + 2*q^5 - q^6 + 3*q^8 + q^9 - 2*q^10 + 4*q^11 - q^12 - 2*q^13 + 2*q^15 - q^16 + 2*q^17 - q^18 - 2*q^20 - 4*q^22 + 3*q^24 - q^25 + 2*q^26 + q^27 - 6*q^29 - 2*q^30 - 4*q^31 - 5*q^32 + 4*q^33 - 2*q^34 - q^36 - 10*q^37 + O(q^38),
q + 2*q^2 + q^3 + 2*q^4 - q^5 + 2*q^6 - 3*q^7 + q^9 - 2*q^10 + q^11 + 2*q^12 - 2*q^13 - 6*q^14 - q^15 - 4*q^16 + 2*q^17 + 2*q^18 + 6*q^19 - 2*q^20 - 3*q^21 + 2*q^22 + 3*q^23 - 4*q^25 - 4*q^26 + q^27 - 6*q^28 + 3*q^29 - 2*q^30 + 2*q^31 - 8*q^32 + q^33 + 4*q^34 + 3*q^35 + 2*q^36 - 7*q^37 + O(q^38),
q - 2*q^2 + q^3 + 2*q^4 - 3*q^5 - 2*q^6 - 3*q^7 + q^9 + 6*q^10 - 5*q^11 + 2*q^12 + 2*q^13 + 6*q^14 - 3*q^15 - 4*q^16 - 6*q^17 - 2*q^18 - 6*q^19 - 6*q^20 - 3*q^21 + 10*q^22 + 9*q^23 + 4*q^25 - 4*q^26 + q^27 - 6*q^28 + q^29 + 6*q^30 - 2*q^31 + 8*q^32 - 5*q^33 + 12*q^34 + 9*q^35 + 2*q^36 + q^37 + O(q^38),
q + a*q^2 - q^3 + (-a + 2)*q^4 + (a + 1)*q^5 - a*q^6 + (a + 1)*q^7 + (a - 4)*q^8 + q^9 + 4*q^10 + (-a + 3)*q^11 + (a - 2)*q^12 + (-2*a - 4)*q^13 + 4*q^14 + (-a - 1)*q^15 - 3*a*q^16 - 2*a*q^17 + a*q^18 + 6*q^19 + (2*a - 2)*q^20 + (-a - 1)*q^21 + (4*a - 4)*q^22 + (-3*a - 3)*q^23 + (-a + 4)*q^24 + a*q^25 + (-2*a - 8)*q^26 - q^27 + (2*a - 2)*q^28 + (a - 7)*q^29 - 4*q^30 + (2*a + 4)*q^31 + (a - 4)*q^32 + (a - 3)*q^33 + (2*a - 8)*q^34 + (a + 5)*q^35 + (-a + 2)*q^36 + (-a + 5)*q^37 + O(q^38)
*]> ;  // time = 12.77 seconds




J[142] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 142, 142, 142, 142, 142, 71, 71 ], new_dimensions := [ 1, 1, 1, 1, 1, 3, 3 ], dimensions := [ 1, 1, 1, 1, 1, 6, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 1, 3, 3, 1, 3, 0, 1, 1, 9, 9, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 3, 3, 1, 3, 9, 1, 3, 0, 81, 1, 3, 9, 1, 3, 81, 0 ], ap_traces := [
[ -1, -1, -2, -1, -2, -3, -6, 5, -1, 6, 1, 6 ],
[ -1, 0, 2, 0, 6, 4, 6, -8, -4, -2, -8, 10 ],
[ -1, 3, 2, -3, -6, -5, 6, 1, 5, -2, -5, -2 ],
[ 1, 1, 0, -1, 0, -1, 0, -1, 3, 0, 5, -4 ],
[ 1, -3, -4, -3, 0, 1, 0, -5, -7, -8, 7, 4 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 1 ],
[ 27, 1 ],
[ 3, 1 ],
[ 9, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 9, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 1 ], torsion_lower_bounds := [ 1, 1, 1, 3, 1 ], l_ratios := [ 0, 1, 1, 1/3, 0 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 0 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 0 ], eigenvalues := [*
[ -1, -1, -2, -1, -2, -3, -6, 5, -1, 6, 1, 6 ],
[ -1, 0, 2, 0, 6, 4, 6, -8, -4, -2, -8, 10 ],
[ -1, 3, 2, -3, -6, -5, 6, 1, 5, -2, -5, -2 ],
[ 1, 1, 0, -1, 0, -1, 0, -1, 3, 0, 5, -4 ],
[ 1, -3, -4, -3, 0, 1, 0, -5, -7, -8, 7, 4 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - 2*q^5 + q^6 - q^7 - q^8 - 2*q^9 + 2*q^10 - 2*q^11 - q^12 - 3*q^13 + q^14 + 2*q^15 + q^16 - 6*q^17 + 2*q^18 + 5*q^19 - 2*q^20 + q^21 + 2*q^22 - q^23 + q^24 - q^25 + 3*q^26 + 5*q^27 - q^28 + 6*q^29 - 2*q^30 + q^31 - q^32 + 2*q^33 + 6*q^34 + 2*q^35 - 2*q^36 + 6*q^37 + O(q^38),
q - q^2 + q^4 + 2*q^5 - q^8 - 3*q^9 - 2*q^10 + 6*q^11 + 4*q^13 + q^16 + 6*q^17 + 3*q^18 - 8*q^19 + 2*q^20 - 6*q^22 - 4*q^23 - q^25 - 4*q^26 - 2*q^29 - 8*q^31 - q^32 - 6*q^34 - 3*q^36 + 10*q^37 + O(q^38),
q - q^2 + 3*q^3 + q^4 + 2*q^5 - 3*q^6 - 3*q^7 - q^8 + 6*q^9 - 2*q^10 - 6*q^11 + 3*q^12 - 5*q^13 + 3*q^14 + 6*q^15 + q^16 + 6*q^17 - 6*q^18 + q^19 + 2*q^20 - 9*q^21 + 6*q^22 + 5*q^23 - 3*q^24 - q^25 + 5*q^26 + 9*q^27 - 3*q^28 - 2*q^29 - 6*q^30 - 5*q^31 - q^32 - 18*q^33 - 6*q^34 - 6*q^35 + 6*q^36 - 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^6 - q^7 + q^8 - 2*q^9 + q^12 - q^13 - q^14 + q^16 - 2*q^18 - q^19 - q^21 + 3*q^23 + q^24 - 5*q^25 - q^26 - 5*q^27 - q^28 + 5*q^31 + q^32 - 2*q^36 - 4*q^37 + O(q^38),
q + q^2 - 3*q^3 + q^4 - 4*q^5 - 3*q^6 - 3*q^7 + q^8 + 6*q^9 - 4*q^10 - 3*q^12 + q^13 - 3*q^14 + 12*q^15 + q^16 + 6*q^18 - 5*q^19 - 4*q^20 + 9*q^21 - 7*q^23 - 3*q^24 + 11*q^25 + q^26 - 9*q^27 - 3*q^28 - 8*q^29 + 12*q^30 + 7*q^31 + q^32 + 12*q^35 + 6*q^36 + 4*q^37 + O(q^38)
*]> ;  // time = 17.65 seconds




J[143] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 143, 143, 143, 11 ], new_dimensions := [ 1, 4, 6, 1 ], dimensions := [ 1, 4, 6, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 0, 1, 9, 1, 1, 0, 1, 1, 9, 1, 0 ], ap_traces := [
[ 0, -1, -1, -2, -1, -1, -4, 2, 7, -2, -3, -11 ],
[ 3, 0, 0, 6, 4, -4, 6, 8, -4, -10, 2, 12 ],
[ 0, 3, 1, 4, -6, 6, 0, -10, 11, 2, -9, 15 ]
], hecke_fields := [
x - 1,
x^4 - 3*x^3 - x^2 + 5*x + 1,
x^6 - 10*x^4 + 2*x^3 + 24*x^2 - 7*x - 12
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 7, 9 ],
[ 3, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 7, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 1, 7, 3 ], torsion_lower_bounds := [ 1, 7, 3 ], l_ratios := [ 0, 1/7, 1/3 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ 0, -1, -1, -2, -1, -1, -4, 2, 7, -2, -3, -11 ],
[
a,
-a^3 + 3*a^2 - 3,
-2*a^2 + 2*a + 4,
a^3 - a^2 - 4*a + 2,
1,
-1,
-4*a^2 + 6*a + 8,
-3*a^3 + 7*a^2 + 2*a - 3,
a^3 - a^2 - 2*a - 2,
-2*a^3 + 4*a^2 + 4*a - 6,
4*a^3 - 6*a^2 - 8*a + 2,
-4*a^2 + 8*a + 8
],
[
a,
-a^5 - a^4 + 8*a^3 + 6*a^2 - 11*a - 5,
a^5 + 2*a^4 - 8*a^3 - 14*a^2 + 12*a + 15,
2*a^5 + 2*a^4 - 17*a^3 - 13*a^2 + 26*a + 14,
-1,
1,
-2*a,
-2*a^5 - 3*a^4 + 16*a^3 + 20*a^2 - 23*a - 22,
-3*a^5 - 4*a^4 + 25*a^3 + 29*a^2 - 38*a - 33,
2*a^5 + 2*a^4 - 16*a^3 - 14*a^2 + 22*a + 18,
3*a^5 + 4*a^4 - 26*a^3 - 28*a^2 + 44*a + 29,
-a^5 - 2*a^4 + 8*a^3 + 16*a^2 - 10*a - 19
]
*], q_expansions := [*
q - q^3 - 2*q^4 - q^5 - 2*q^7 - 2*q^9 - q^11 + 2*q^12 - q^13 + q^15 + 4*q^16 - 4*q^17 + 2*q^19 + 2*q^20 + 2*q^21 + 7*q^23 - 4*q^25 + 5*q^27 + 4*q^28 - 2*q^29 - 3*q^31 + q^33 + 2*q^35 + 4*q^36 - 11*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 3*a^2 - 3)*q^3 + (a^2 - 2)*q^4 + (-2*a^2 + 2*a + 4)*q^5 + (-a^2 + 2*a + 1)*q^6 + (a^3 - a^2 - 4*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (a^3 - 3*a^2 - 2*a + 5)*q^9 + (-2*a^3 + 2*a^2 + 4*a)*q^10 + q^11 + (a^3 - 4*a^2 + a + 6)*q^12 - q^13 + (2*a^3 - 3*a^2 - 3*a - 1)*q^14 + (-2*a^3 + 6*a^2 + 2*a - 10)*q^15 + (3*a^3 - 5*a^2 - 5*a + 3)*q^16 + (-4*a^2 + 6*a + 8)*q^17 + (-a^2 - 1)*q^18 + (-3*a^3 + 7*a^2 + 2*a - 3)*q^19 + (-4*a^3 + 6*a^2 + 6*a - 6)*q^20 + (-2*a^3 + 8*a^2 - 4*a - 9)*q^21 + a*q^22 + (a^3 - a^2 - 2*a - 2)*q^23 + (-a^3 + 4*a^2 - 3*a - 3)*q^24 + (4*a^3 - 8*a^2 - 4*a + 7)*q^25 - a*q^26 + (2*a^2 - 2*a - 7)*q^27 + (a^3 + a^2 - 3*a - 6)*q^28 + (-2*a^3 + 4*a^2 + 4*a - 6)*q^29 + 2*q^30 + (4*a^3 - 6*a^2 - 8*a + 2)*q^31 + (2*a^3 - 2*a^2 - 4*a - 3)*q^32 + (-a^3 + 3*a^2 - 3)*q^33 + (-4*a^3 + 6*a^2 + 8*a)*q^34 + (2*a^3 - 8*a^2 + 10)*q^35 + (-3*a^3 + 6*a^2 + 3*a - 10)*q^36 + (-4*a^2 + 8*a + 8)*q^37 + O(q^38),
q + a*q^2 + (-a^5 - a^4 + 8*a^3 + 6*a^2 - 11*a - 5)*q^3 + (a^2 - 2)*q^4 + (a^5 + 2*a^4 - 8*a^3 - 14*a^2 + 12*a + 15)*q^5 + (-a^5 - 2*a^4 + 8*a^3 + 13*a^2 - 12*a - 12)*q^6 + (2*a^5 + 2*a^4 - 17*a^3 - 13*a^2 + 26*a + 14)*q^7 + (a^3 - 4*a)*q^8 + (-3*a^5 - 4*a^4 + 25*a^3 + 27*a^2 - 38*a - 26)*q^9 + (2*a^5 + 2*a^4 - 16*a^3 - 12*a^2 + 22*a + 12)*q^10 - q^11 + (-a^3 + 3*a - 2)*q^12 + q^13 + (2*a^5 + 3*a^4 - 17*a^3 - 22*a^2 + 28*a + 24)*q^14 + (3*a^5 + 4*a^4 - 24*a^3 - 28*a^2 + 30*a + 33)*q^15 + (a^4 - 6*a^2 + 4)*q^16 - 2*a*q^17 + (-4*a^5 - 5*a^4 + 33*a^3 + 34*a^2 - 47*a - 36)*q^18 + (-2*a^5 - 3*a^4 + 16*a^3 + 20*a^2 - 23*a - 22)*q^19 + (2*a^2 + 2*a - 6)*q^20 + (2*a^5 + 3*a^4 - 17*a^3 - 19*a^2 + 29*a + 14)*q^21 - a*q^22 + (-3*a^5 - 4*a^4 + 25*a^3 + 29*a^2 - 38*a - 33)*q^23 + (2*a^5 + 3*a^4 - 16*a^3 - 23*a^2 + 22*a + 24)*q^24 + (-3*a^5 - 4*a^4 + 26*a^3 + 26*a^2 - 44*a - 20)*q^25 + a*q^26 + (-5*a^5 - 7*a^4 + 41*a^3 + 47*a^2 - 59*a - 47)*q^27 + (-a^5 - a^4 + 8*a^3 + 6*a^2 - 14*a - 4)*q^28 + (2*a^5 + 2*a^4 - 16*a^3 - 14*a^2 + 22*a + 18)*q^29 + (4*a^5 + 6*a^4 - 34*a^3 - 42*a^2 + 54*a + 36)*q^30 + (3*a^5 + 4*a^4 - 26*a^3 - 28*a^2 + 44*a + 29)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^5 + a^4 - 8*a^3 - 6*a^2 + 11*a + 5)*q^33 - 2*a^2*q^34 + (-2*a^3 + 12*a - 6)*q^35 + (a^5 + a^4 - 8*a^3 - 5*a^2 + 12*a + 4)*q^36 + (-a^5 - 2*a^4 + 8*a^3 + 16*a^2 - 10*a - 19)*q^37 + O(q^38)
*]> ;  // time = 12.87 seconds




J[145] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 145, 145, 145, 145, 29 ], new_dimensions := [ 1, 2, 3, 3, 2 ], dimensions := [ 1, 2, 3, 3, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 0, 1, 25, 1, 1, 1, 0, 1, 1, 7, 25, 1, 0 ], ap_traces := [
[ -1, 0, -1, -2, -6, 2, -2, -2, 2, -1, 2, 10 ],
[ -2, -4, 2, -4, -4, -4, 0, -4, -12, 2, -4, 0 ],
[ 3, -2, -3, -2, 8, -6, 0, 0, 14, 3, 12, 4 ],
[ 1, 2, 3, 4, 2, -2, -4, -10, 16, -3, -14, -8 ]
], hecke_fields := [
x - 1,
x^2 + 2*x - 1,
x^3 - 3*x^2 - x + 5,
x^3 - x^2 - 3*x + 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 7, 1 ],
[ 25, 1 ],
[ 5, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 5, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 5 ], torsion_lower_bounds := [ 1, 1, 1, 5 ], l_ratios := [ 0, 0, 1, 1/5 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[ -1, 0, -1, -2, -6, 2, -2, -2, 2, -1, 2, 10 ],
[
a,
-2,
1,
-2*a - 4,
2*a,
-2,
2*a + 2,
-2*a - 4,
2*a - 4,
1,
6*a + 4,
-6*a - 6
],
[
a,
-a^2 + 2*a + 1,
-1,
-a^2 + 3,
a^2 - 2*a + 1,
2*a - 4,
-3*a^2 + 2*a + 9,
3*a^2 - 4*a - 7,
a^2 - 2*a + 3,
1,
-3*a^2 + 4*a + 11,
-a^2 - 2*a + 7
],
[
a,
-a^2 + 3,
1,
a^2 - 1,
a^2 - 2*a - 1,
-2*a,
3*a^2 - 4*a - 7,
-a^2 - 1,
-a^2 + 2*a + 7,
-1,
a^2 - 7,
-3*a^2 + 4*a + 3
]
*], q_expansions := [*
q - q^2 - q^4 - q^5 - 2*q^7 + 3*q^8 - 3*q^9 + q^10 - 6*q^11 + 2*q^13 + 2*q^14 - q^16 - 2*q^17 + 3*q^18 - 2*q^19 + q^20 + 6*q^22 + 2*q^23 + q^25 - 2*q^26 + 2*q^28 - q^29 + 2*q^31 - 5*q^32 + 2*q^34 + 2*q^35 + 3*q^36 + 10*q^37 + O(q^38),
q + a*q^2 - 2*q^3 + (-2*a - 1)*q^4 + q^5 - 2*a*q^6 + (-2*a - 4)*q^7 + (a - 2)*q^8 + q^9 + a*q^10 + 2*a*q^11 + (4*a + 2)*q^12 - 2*q^13 - 2*q^14 - 2*q^15 + 3*q^16 + (2*a + 2)*q^17 + a*q^18 + (-2*a - 4)*q^19 + (-2*a - 1)*q^20 + (4*a + 8)*q^21 + (-4*a + 2)*q^22 + (2*a - 4)*q^23 + (-2*a + 4)*q^24 + q^25 - 2*a*q^26 + 4*q^27 + (2*a + 8)*q^28 + q^29 - 2*a*q^30 + (6*a + 4)*q^31 + (a + 4)*q^32 - 4*a*q^33 + (-2*a + 2)*q^34 + (-2*a - 4)*q^35 + (-2*a - 1)*q^36 + (-6*a - 6)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + 2*a + 1)*q^3 + (a^2 - 2)*q^4 - q^5 + (-a^2 + 5)*q^6 + (-a^2 + 3)*q^7 + (3*a^2 - 3*a - 5)*q^8 + (-2*a + 3)*q^9 - a*q^10 + (a^2 - 2*a + 1)*q^11 + (-a^2 + 3)*q^12 + (2*a - 4)*q^13 + (-3*a^2 + 2*a + 5)*q^14 + (a^2 - 2*a - 1)*q^15 + (4*a^2 - 2*a - 11)*q^16 + (-3*a^2 + 2*a + 9)*q^17 + (-2*a^2 + 3*a)*q^18 + (3*a^2 - 4*a - 7)*q^19 + (-a^2 + 2)*q^20 + (2*a - 2)*q^21 + (a^2 + 2*a - 5)*q^22 + (a^2 - 2*a + 3)*q^23 + (-a^2 + 2*a - 5)*q^24 + q^25 + (2*a^2 - 4*a)*q^26 + (2*a^2 - 10)*q^27 + (-5*a^2 + 2*a + 9)*q^28 + q^29 + (a^2 - 5)*q^30 + (-3*a^2 + 4*a + 11)*q^31 + (4*a^2 - a - 10)*q^32 + (-2*a^2 + 6*a - 4)*q^33 + (-7*a^2 + 6*a + 15)*q^34 + (a^2 - 3)*q^35 + (-3*a^2 + 2*a + 4)*q^36 + (-a^2 - 2*a + 7)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + 3)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^2 + 1)*q^6 + (a^2 - 1)*q^7 + (a^2 - a - 1)*q^8 + (-2*a^2 + 2*a + 5)*q^9 + a*q^10 + (a^2 - 2*a - 1)*q^11 + (a^2 - 2*a - 5)*q^12 - 2*a*q^13 + (a^2 + 2*a - 1)*q^14 + (-a^2 + 3)*q^15 + (-2*a^2 + 2*a + 3)*q^16 + (3*a^2 - 4*a - 7)*q^17 + (-a + 2)*q^18 + (-a^2 - 1)*q^19 + (a^2 - 2)*q^20 + (-2*a - 2)*q^21 + (-a^2 + 2*a - 1)*q^22 + (-a^2 + 2*a + 7)*q^23 + (a^2 - 2*a - 3)*q^24 + q^25 - 2*a^2*q^26 + (-2*a^2 + 4*a + 6)*q^27 + (a^2 + 2*a + 1)*q^28 - q^29 + (-a^2 + 1)*q^30 + (a^2 - 7)*q^31 + (-2*a^2 - a + 4)*q^32 + (2*a^2 - 2*a - 4)*q^33 + (-a^2 + 2*a - 3)*q^34 + (a^2 - 1)*q^35 + (3*a^2 - 2*a - 10)*q^36 + (-3*a^2 + 4*a + 3)*q^37 + O(q^38)
*]> ;  // time = 12.571 seconds




J[146] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 146, 146, 73, 73, 73 ], new_dimensions := [ 3, 4, 1, 2, 2 ], dimensions := [ 3, 4, 2, 4, 4 ], intersection_graph := [ 0, 1, 1, 1, 9, 1, 0, 1, 19, 1, 1, 1, 0, 1, 9, 1, 19, 1, 0, 1, 9, 1, 9, 1, 0 ], ap_traces := [
[ -3, 0, -2, 8, 2, 4, -2, 8, 4, -6, 2, -14 ],
[ 4, 0, 2, 0, 0, -4, -4, 0, -12, 2, -6, 12 ]
], hecke_fields := [
x^3 - 8*x + 4,
x^4 - 8*x^2 + 4*x + 4
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 27, 3 ],
[ 703, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 703, 1 ]
], torsion_upper_bounds := [ 3, 37 ], torsion_lower_bounds := [ 3, 37 ], l_ratios := [ 1/3, 19/37 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
-1,
a,
-1/2*a^2 + 2,
1/2*a^2,
-a^2 - 2*a + 6,
-1/2*a^2 + 4,
a^2 + 2*a - 6,
-a^2 - 2*a + 8,
a^2 - 4,
3/2*a^2 - 2*a - 10,
1/2*a^2 + 2*a - 2,
-2*a^2 - 2*a + 6
],
[
1,
a,
-1/2*a^3 - 1/2*a^2 + 2*a + 1,
a^3 + 1/2*a^2 - 7*a + 1,
a^2 - 4,
-3/2*a^2 - a + 5,
-a^3 - a^2 + 6*a,
a^2 + 2*a - 4,
-a^3 - a^2 + 8*a - 2,
3/2*a^3 + 1/2*a^2 - 10*a + 3,
-1/2*a^3 + 1/2*a^2 + 6*a - 5,
a^3 - 8*a + 6
]
*], q_expansions := [*
q - q^2 + a*q^3 + q^4 + (-1/2*a^2 + 2)*q^5 - a*q^6 + 1/2*a^2*q^7 - q^8 + (a^2 - 3)*q^9 + (1/2*a^2 - 2)*q^10 + (-a^2 - 2*a + 6)*q^11 + a*q^12 + (-1/2*a^2 + 4)*q^13 - 1/2*a^2*q^14 + (-2*a + 2)*q^15 + q^16 + (a^2 + 2*a - 6)*q^17 + (-a^2 + 3)*q^18 + (-a^2 - 2*a + 8)*q^19 + (-1/2*a^2 + 2)*q^20 + (4*a - 2)*q^21 + (a^2 + 2*a - 6)*q^22 + (a^2 - 4)*q^23 - a*q^24 + (-a - 1)*q^25 + (1/2*a^2 - 4)*q^26 + (2*a - 4)*q^27 + 1/2*a^2*q^28 + (3/2*a^2 - 2*a - 10)*q^29 + (2*a - 2)*q^30 + (1/2*a^2 + 2*a - 2)*q^31 - q^32 + (-2*a^2 - 2*a + 4)*q^33 + (-a^2 - 2*a + 6)*q^34 + (-a^2 + a)*q^35 + (a^2 - 3)*q^36 + (-2*a^2 - 2*a + 6)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-1/2*a^3 - 1/2*a^2 + 2*a + 1)*q^5 + a*q^6 + (a^3 + 1/2*a^2 - 7*a + 1)*q^7 + q^8 + (a^2 - 3)*q^9 + (-1/2*a^3 - 1/2*a^2 + 2*a + 1)*q^10 + (a^2 - 4)*q^11 + a*q^12 + (-3/2*a^2 - a + 5)*q^13 + (a^3 + 1/2*a^2 - 7*a + 1)*q^14 + (-1/2*a^3 - 2*a^2 + 3*a + 2)*q^15 + q^16 + (-a^3 - a^2 + 6*a)*q^17 + (a^2 - 3)*q^18 + (a^2 + 2*a - 4)*q^19 + (-1/2*a^3 - 1/2*a^2 + 2*a + 1)*q^20 + (1/2*a^3 + a^2 - 3*a - 4)*q^21 + (a^2 - 4)*q^22 + (-a^3 - a^2 + 8*a - 2)*q^23 + a*q^24 + (2*a^2 + a - 5)*q^25 + (-3/2*a^2 - a + 5)*q^26 + (a^3 - 6*a)*q^27 + (a^3 + 1/2*a^2 - 7*a + 1)*q^28 + (3/2*a^3 + 1/2*a^2 - 10*a + 3)*q^29 + (-1/2*a^3 - 2*a^2 + 3*a + 2)*q^30 + (-1/2*a^3 + 1/2*a^2 + 6*a - 5)*q^31 + q^32 + (a^3 - 4*a)*q^33 + (-a^3 - a^2 + 6*a)*q^34 + (a^3 + a^2 - 7*a - 4)*q^35 + (a^2 - 3)*q^36 + (a^3 - 8*a + 6)*q^37 + O(q^38)
*]> ;  // time = 20.321 seconds




J[149] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 149, 149 ], new_dimensions := [ 3, 9 ], dimensions := [ 3, 9 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -4, -3, -5, -5, -3, 5, -18, 8, -2, -18, 3 ],
[ -1, 6, -1, 3, 5, 7, -5, 30, -4, -16, 22, -7 ]
], hecke_fields := [
x^3 + x^2 - 2*x - 1,
x^9 + x^8 - 15*x^7 - 12*x^6 + 75*x^5 + 48*x^4 - 137*x^3 - 76*x^2 + 68*x + 39
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 37 ]
], tamagawa_numbers := [
[ 1 ],
[ 37 ]
], torsion_upper_bounds := [ 1, 37 ], torsion_lower_bounds := [ 1, 37 ], l_ratios := [ 0, 1/37 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^2 - a,
a^2 - a - 3,
a^2 + a - 3,
-2*a^2 + a + 2,
-2*a^2 - a + 2,
4*a^2 + 3*a - 4,
-2*a^2 - a - 3,
-a^2 - a + 4,
-4*a^2 - 3*a + 5,
3*a^2 - 11,
6*a + 3
],
[
a,
-3/4*a^8 - 1/4*a^7 + 23/2*a^6 + 5/4*a^5 - 233/4*a^4 + 13/4*a^3 + 209/2*a^2 - 49/4*a - 44,
-1/4*a^8 - 1/4*a^7 + 7/2*a^6 + 9/4*a^5 - 63/4*a^4 - 19/4*a^3 + 23*a^2 + 3/4*a - 13/2,
a^8 + 1/2*a^7 - 29/2*a^6 - 3*a^5 + 139/2*a^4 - 3/2*a^3 - 237/2*a^2 + 14*a + 101/2,
3/4*a^8 - 49/4*a^6 + 3/4*a^5 + 129/2*a^4 - 15/2*a^3 - 471/4*a^2 + 63/4*a + 207/4,
a^8 + 1/2*a^7 - 29/2*a^6 - 3*a^5 + 139/2*a^4 - 3/2*a^3 - 235/2*a^2 + 14*a + 95/2,
-1/4*a^8 - 1/2*a^7 + 11/4*a^6 + 19/4*a^5 - 10*a^4 - 25/2*a^3 + 59/4*a^2 + 29/4*a - 25/4,
-1/2*a^8 + 15/2*a^6 - 3/2*a^5 - 37*a^4 + 12*a^3 + 131/2*a^2 - 41/2*a - 55/2,
1/2*a^8 - 1/4*a^7 - 33/4*a^6 + 7/2*a^5 + 177/4*a^4 - 57/4*a^3 - 335/4*a^2 + 15*a + 149/4,
1/4*a^7 + 3/4*a^6 - 5/2*a^5 - 31/4*a^4 + 27/4*a^3 + 89/4*a^2 - 7/2*a - 61/4,
3/2*a^8 + 1/2*a^7 - 23*a^6 - 7/2*a^5 + 231/2*a^4 + 1/2*a^3 - 204*a^2 + 37/2*a + 88,
5/4*a^8 + 3/4*a^7 - 18*a^6 - 21/4*a^5 + 345/4*a^4 + 17/4*a^3 - 299/2*a^2 + 41/4*a + 66
]
*], q_expansions := [*
q + a*q^2 + (-a^2 - a)*q^3 + (a^2 - 2)*q^4 + (a^2 - a - 3)*q^5 + (-2*a - 1)*q^6 + (a^2 + a - 3)*q^7 + (-a^2 - 2*a + 1)*q^8 + (2*a^2 + 3*a - 2)*q^9 + (-2*a^2 - a + 1)*q^10 + (-2*a^2 + a + 2)*q^11 + a*q^12 + (-2*a^2 - a + 2)*q^13 + (-a + 1)*q^14 + (a^2 + 4*a + 1)*q^15 + (-3*a^2 - a + 3)*q^16 + (4*a^2 + 3*a - 4)*q^17 + (a^2 + 2*a + 2)*q^18 + (-2*a^2 - a - 3)*q^19 + (-a^2 - a + 4)*q^20 + (a^2 - 1)*q^21 + (3*a^2 - 2*a - 2)*q^22 + (-a^2 - a + 4)*q^23 + (a^2 + 4*a + 2)*q^24 + (a + 1)*q^25 + (a^2 - 2*a - 2)*q^26 + (a^2 - 3*a - 3)*q^27 + (-3*a^2 - a + 6)*q^28 + (-4*a^2 - 3*a + 5)*q^29 + (3*a^2 + 3*a + 1)*q^30 + (3*a^2 - 11)*q^31 + (4*a^2 + a - 5)*q^32 + (2*a^2 - 2*a - 1)*q^33 + (-a^2 + 4*a + 4)*q^34 + (-4*a^2 - a + 8)*q^35 + (-3*a^2 - 2*a + 5)*q^36 + (6*a + 3)*q^37 + O(q^38),
q + a*q^2 + (-3/4*a^8 - 1/4*a^7 + 23/2*a^6 + 5/4*a^5 - 233/4*a^4 + 13/4*a^3 + 209/2*a^2 - 49/4*a - 44)*q^3 + (a^2 - 2)*q^4 + (-1/4*a^8 - 1/4*a^7 + 7/2*a^6 + 9/4*a^5 - 63/4*a^4 - 19/4*a^3 + 23*a^2 + 3/4*a - 13/2)*q^5 + (1/2*a^8 + 1/4*a^7 - 31/4*a^6 - 2*a^5 + 157/4*a^4 + 7/4*a^3 - 277/4*a^2 + 7*a + 117/4)*q^6 + (a^8 + 1/2*a^7 - 29/2*a^6 - 3*a^5 + 139/2*a^4 - 3/2*a^3 - 237/2*a^2 + 14*a + 101/2)*q^7 + (a^3 - 4*a)*q^8 + (-3/4*a^8 + 47/4*a^6 - 7/4*a^5 - 121/2*a^4 + 14*a^3 + 439/4*a^2 - 93/4*a - 185/4)*q^9 + (-1/4*a^7 - 3/4*a^6 + 3*a^5 + 29/4*a^4 - 45/4*a^3 - 73/4*a^2 + 21/2*a + 39/4)*q^10 + (3/4*a^8 - 49/4*a^6 + 3/4*a^5 + 129/2*a^4 - 15/2*a^3 - 471/4*a^2 + 63/4*a + 207/4)*q^11 + (5/4*a^8 + 1/4*a^7 - 19*a^6 - 3/4*a^5 + 377/4*a^4 - 29/4*a^3 - 164*a^2 + 79/4*a + 137/2)*q^12 + (a^8 + 1/2*a^7 - 29/2*a^6 - 3*a^5 + 139/2*a^4 - 3/2*a^3 - 235/2*a^2 + 14*a + 95/2)*q^13 + (-1/2*a^8 + 1/2*a^7 + 9*a^6 - 11/2*a^5 - 99/2*a^4 + 37/2*a^3 + 90*a^2 - 35/2*a - 39)*q^14 + (-7/4*a^8 - 3/4*a^7 + 26*a^6 + 21/4*a^5 - 503/4*a^4 - 9/4*a^3 + 211*a^2 - 77/4*a - 169/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/4*a^8 - 1/2*a^7 + 11/4*a^6 + 19/4*a^5 - 10*a^4 - 25/2*a^3 + 59/4*a^2 + 29/4*a - 25/4)*q^17 + (3/4*a^8 + 1/2*a^7 - 43/4*a^6 - 17/4*a^5 + 50*a^4 + 7*a^3 - 321/4*a^2 + 19/4*a + 117/4)*q^18 + (-1/2*a^8 + 15/2*a^6 - 3/2*a^5 - 37*a^4 + 12*a^3 + 131/2*a^2 - 41/2*a - 55/2)*q^19 + (1/4*a^8 - 1/4*a^7 - 4*a^6 + 11/4*a^5 + 81/4*a^4 - 35/4*a^3 - 71/2*a^2 + 33/4*a + 13)*q^20 + (1/2*a^8 - 15/2*a^6 + 3/2*a^5 + 36*a^4 - 12*a^3 - 115/2*a^2 + 37/2*a + 41/2)*q^21 + (-3/4*a^8 - a^7 + 39/4*a^6 + 33/4*a^5 - 87/2*a^4 - 15*a^3 + 291/4*a^2 + 3/4*a - 117/4)*q^22 + (1/2*a^8 - 1/4*a^7 - 33/4*a^6 + 7/2*a^5 + 177/4*a^4 - 57/4*a^3 - 335/4*a^2 + 15*a + 149/4)*q^23 + (-2*a^8 - 3/4*a^7 + 119/4*a^6 + 9/2*a^5 - 583/4*a^4 + 15/4*a^3 + 1013/4*a^2 - 61/2*a - 429/4)*q^24 + (-1/2*a^8 + 1/4*a^7 + 33/4*a^6 - 4*a^5 - 179/4*a^4 + 71/4*a^3 + 347/4*a^2 - 19*a - 163/4)*q^25 + (-1/2*a^8 + 1/2*a^7 + 9*a^6 - 11/2*a^5 - 99/2*a^4 + 39/2*a^3 + 90*a^2 - 41/2*a - 39)*q^26 + (-7/4*a^8 + 109/4*a^6 - 15/4*a^5 - 277/2*a^4 + 61/2*a^3 + 987/4*a^2 - 203/4*a - 419/4)*q^27 + (-a^8 + 1/2*a^7 + 35/2*a^6 - 6*a^5 - 193/2*a^4 + 49/2*a^3 + 363/2*a^2 - 33*a - 163/2)*q^28 + (1/4*a^7 + 3/4*a^6 - 5/2*a^5 - 31/4*a^4 + 27/4*a^3 + 89/4*a^2 - 7/2*a - 61/4)*q^29 + (a^8 - 1/4*a^7 - 63/4*a^6 + 11/2*a^5 + 327/4*a^4 - 115/4*a^3 - 609/4*a^2 + 69/2*a + 273/4)*q^30 + (3/2*a^8 + 1/2*a^7 - 23*a^6 - 7/2*a^5 + 231/2*a^4 + 1/2*a^3 - 204*a^2 + 37/2*a + 88)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-1/4*a^8 + 17/4*a^6 - 1/4*a^5 - 47/2*a^4 + 2*a^3 + 185/4*a^2 - 3/4*a - 99/4)*q^33 + (-1/4*a^8 - a^7 + 7/4*a^6 + 35/4*a^5 - 1/2*a^4 - 39/2*a^3 - 47/4*a^2 + 43/4*a + 39/4)*q^34 + (3/2*a^8 + 1/2*a^7 - 23*a^6 - 5/2*a^5 + 233/2*a^4 - 15/2*a^3 - 210*a^2 + 59/2*a + 91)*q^35 + (5/4*a^8 + 1/2*a^7 - 75/4*a^6 - 11/4*a^5 + 92*a^4 - 11/2*a^3 - 631/4*a^2 + 99/4*a + 253/4)*q^36 + (5/4*a^8 + 3/4*a^7 - 18*a^6 - 21/4*a^5 + 345/4*a^4 + 17/4*a^3 - 299/2*a^2 + 41/4*a + 66)*q^37 + O(q^38)
*]> ;  // time = 1.66 seconds




J[151] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 151, 151, 151 ], new_dimensions := [ 3, 3, 6 ], dimensions := [ 3, 3, 6 ], intersection_graph := [ 0, 1, 1, 1, 0, 67, 1, 67, 0 ], ap_traces := [
[ -2, -1, -7, -3, -5, -1, -8, -3, 0, -1, -1, 13 ],
[ 0, 6, 5, -6, -1, -2, 9, 3, 0, 3, -1, 3 ],
[ 1, -5, 6, 3, 8, -1, 9, -6, -4, -2, -8, -12 ]
], hecke_fields := [
x^3 + 2*x^2 - x - 1,
x^3 - 5*x + 3,
x^6 - x^5 - 7*x^4 + 3*x^3 + 13*x^2 + 3*x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 25 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 25 ]
], torsion_upper_bounds := [ 1, 1, 25 ], torsion_lower_bounds := [ 1, 1, 25 ], l_ratios := [ 0, 1, 1/25 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[
a,
-a - 1,
-a^2 - a - 1,
-1,
2*a^2 + 4*a - 3,
3*a^2 + 5*a - 3,
-3*a^2 - 5*a,
-5*a^2 - 6*a + 5,
3*a^2 + 6*a - 2,
-a^2 - 7*a - 3,
-4*a^2 - 7*a + 3,
-3*a^2 - 5*a + 7
],
[
a,
2,
-a^2 - 2*a + 5,
-2,
2*a^2 + a - 7,
-2*a^2 + 6,
-a + 3,
3*a^2 + 3*a - 9,
2*a,
3*a^2 + 5*a - 9,
-a^2 + 3,
-3*a + 1
],
[
a,
-a^5 + a^4 + 7*a^3 - 4*a^2 - 12*a - 1,
a^5 - a^4 - 6*a^3 + 3*a^2 + 9*a + 2,
-a^4 + 3*a^2 + 3*a + 3,
a^3 - 5*a,
2*a^5 - 3*a^4 - 11*a^3 + 12*a^2 + 13*a - 4,
-a^4 - 2*a^3 + 6*a^2 + 8*a,
2*a^5 - a^4 - 12*a^3 + 2*a^2 + 15*a + 1,
-a^5 + 6*a^3 - 7*a + 1,
3*a^5 - 5*a^4 - 17*a^3 + 19*a^2 + 24*a - 3,
-2*a^5 + 3*a^4 + 10*a^3 - 9*a^2 - 12*a - 3,
a^2 + 3*a - 5
]
*], q_expansions := [*
q + a*q^2 + (-a - 1)*q^3 + (a^2 - 2)*q^4 + (-a^2 - a - 1)*q^5 + (-a^2 - a)*q^6 - q^7 + (-2*a^2 - 3*a + 1)*q^8 + (a^2 + 2*a - 2)*q^9 + (a^2 - 2*a - 1)*q^10 + (2*a^2 + 4*a - 3)*q^11 + (a^2 + a + 1)*q^12 + (3*a^2 + 5*a - 3)*q^13 - a*q^14 + (3*a + 2)*q^15 + (-a^2 - a + 2)*q^16 + (-3*a^2 - 5*a)*q^17 + (-a + 1)*q^18 + (-5*a^2 - 6*a + 5)*q^19 + (-2*a^2 + 2*a + 3)*q^20 + (a + 1)*q^21 + (-a + 2)*q^22 + (3*a^2 + 6*a - 2)*q^23 + (a^2 + 4*a + 1)*q^24 + (4*a^2 + 3*a - 4)*q^25 + (-a^2 + 3)*q^26 + (-a^2 + 2*a + 4)*q^27 + (-a^2 + 2)*q^28 + (-a^2 - 7*a - 3)*q^29 + (3*a^2 + 2*a)*q^30 + (-4*a^2 - 7*a + 3)*q^31 + (5*a^2 + 7*a - 3)*q^32 + (-2*a^2 - 3*a + 1)*q^33 + (a^2 - 3*a - 3)*q^34 + (a^2 + a + 1)*q^35 + (-3*a^2 - 3*a + 4)*q^36 + (-3*a^2 - 5*a + 7)*q^37 + O(q^38),
q + a*q^2 + 2*q^3 + (a^2 - 2)*q^4 + (-a^2 - 2*a + 5)*q^5 + 2*a*q^6 - 2*q^7 + (a - 3)*q^8 + q^9 + (-2*a^2 + 3)*q^10 + (2*a^2 + a - 7)*q^11 + (2*a^2 - 4)*q^12 + (-2*a^2 + 6)*q^13 - 2*a*q^14 + (-2*a^2 - 4*a + 10)*q^15 + (-a^2 - 3*a + 4)*q^16 + (-a + 3)*q^17 + a*q^18 + (3*a^2 + 3*a - 9)*q^19 + (2*a^2 - 3*a - 4)*q^20 - 4*q^21 + (a^2 + 3*a - 6)*q^22 + 2*a*q^23 + (2*a - 6)*q^24 + (-a^2 - 3*a + 8)*q^25 + (-4*a + 6)*q^26 - 4*q^27 + (-2*a^2 + 4)*q^28 + (3*a^2 + 5*a - 9)*q^29 + (-4*a^2 + 6)*q^30 + (-a^2 + 3)*q^31 + (-3*a^2 - 3*a + 9)*q^32 + (4*a^2 + 2*a - 14)*q^33 + (-a^2 + 3*a)*q^34 + (2*a^2 + 4*a - 10)*q^35 + (a^2 - 2)*q^36 + (-3*a + 1)*q^37 + O(q^38),
q + a*q^2 + (-a^5 + a^4 + 7*a^3 - 4*a^2 - 12*a - 1)*q^3 + (a^2 - 2)*q^4 + (a^5 - a^4 - 6*a^3 + 3*a^2 + 9*a + 2)*q^5 + (-a^3 + a^2 + 2*a - 1)*q^6 + (-a^4 + 3*a^2 + 3*a + 3)*q^7 + (a^3 - 4*a)*q^8 + (-a^5 + 3*a^4 + 4*a^3 - 13*a^2 - 4*a + 9)*q^9 + (a^4 - 4*a^2 - a + 1)*q^10 + (a^3 - 5*a)*q^11 + (2*a^5 - 3*a^4 - 13*a^3 + 10*a^2 + 23*a + 2)*q^12 + (2*a^5 - 3*a^4 - 11*a^3 + 12*a^2 + 13*a - 4)*q^13 + (-a^5 + 3*a^3 + 3*a^2 + 3*a)*q^14 + (-a^5 + 7*a^3 + 3*a^2 - 13*a - 10)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 - 2*a^3 + 6*a^2 + 8*a)*q^17 + (2*a^5 - 3*a^4 - 10*a^3 + 9*a^2 + 12*a - 1)*q^18 + (2*a^5 - a^4 - 12*a^3 + 2*a^2 + 15*a + 1)*q^19 + (-a^5 + 2*a^4 + 8*a^3 - 7*a^2 - 17*a - 4)*q^20 + (-3*a^5 + 5*a^4 + 19*a^3 - 16*a^2 - 36*a - 5)*q^21 + (a^4 - 5*a^2)*q^22 + (-a^5 + 6*a^3 - 7*a + 1)*q^23 + (-a^5 + a^4 + 6*a^3 - 5*a^2 - 8*a + 4)*q^24 + (2*a^5 - a^4 - 13*a^3 + a^2 + 21*a + 5)*q^25 + (-a^5 + 3*a^4 + 6*a^3 - 13*a^2 - 10*a + 2)*q^26 + (-5*a^5 + 6*a^4 + 34*a^3 - 22*a^2 - 57*a - 5)*q^27 + (-a^5 - 2*a^4 + 6*a^3 + 10*a^2 - 3*a - 7)*q^28 + (3*a^5 - 5*a^4 - 17*a^3 + 19*a^2 + 24*a - 3)*q^29 + (-a^5 + 6*a^3 - 7*a - 1)*q^30 + (-2*a^5 + 3*a^4 + 10*a^3 - 9*a^2 - 12*a - 3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^5 + a^4 + 7*a^3 - 6*a^2 - 10*a + 5)*q^33 + (-a^5 - 2*a^4 + 6*a^3 + 8*a^2)*q^34 + (2*a^5 - 3*a^4 - 15*a^3 + 10*a^2 + 29*a + 8)*q^35 + (a^5 - 2*a^4 - 5*a^3 + 12*a^2 + a - 16)*q^36 + (a^2 + 3*a - 5)*q^37 + O(q^38)
*]> ;  // time = 1.71 seconds




J[154] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 154, 154, 154, 154, 77, 77, 77, 77, 14, 11 ], new_dimensions := [ 1, 1, 1, 2, 1, 1, 1, 2, 1, 1 ], dimensions := [ 1, 1, 1, 2, 2, 2, 2, 4, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 5, 3, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 0, 25, 3, 1, 1, 1, 1, 1, 1, 1, 25, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 5, 1, 9, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, -4, -1, -1, 2, -4, -6, 4, -2, -2, 10 ],
[ -1, 2, 2, -1, 1, -4, 0, 4, 4, 2, -10, -6 ],
[ 1, 0, 2, -1, -1, 2, 2, 0, -8, -2, -8, -2 ],
[ 2, -2, 2, 2, 2, -2, -4, -10, 8, 0, 4, -4 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 + 2*x - 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 5, 5, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 5, 5, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 5 ], torsion_lower_bounds := [ 1, 1, 1, 1 ], l_ratios := [ 0, 1, 3, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1/25 ], eigenvalues := [*
[ -1, 0, -4, -1, -1, 2, -4, -6, 4, -2, -2, 10 ],
[ -1, 2, 2, -1, 1, -4, 0, 4, 4, 2, -10, -6 ],
[ 1, 0, 2, -1, -1, 2, 2, 0, -8, -2, -8, -2 ],
[
1,
a,
-a,
1,
1,
-a - 2,
2*a,
-a - 6,
4,
2*a + 2,
2,
4*a + 2
]
*], q_expansions := [*
q - q^2 + q^4 - 4*q^5 - q^7 - q^8 - 3*q^9 + 4*q^10 - q^11 + 2*q^13 + q^14 + q^16 - 4*q^17 + 3*q^18 - 6*q^19 - 4*q^20 + q^22 + 4*q^23 + 11*q^25 - 2*q^26 - q^28 - 2*q^29 - 2*q^31 - q^32 + 4*q^34 + 4*q^35 - 3*q^36 + 10*q^37 + O(q^38),
q - q^2 + 2*q^3 + q^4 + 2*q^5 - 2*q^6 - q^7 - q^8 + q^9 - 2*q^10 + q^11 + 2*q^12 - 4*q^13 + q^14 + 4*q^15 + q^16 - q^18 + 4*q^19 + 2*q^20 - 2*q^21 - q^22 + 4*q^23 - 2*q^24 - q^25 + 4*q^26 - 4*q^27 - q^28 + 2*q^29 - 4*q^30 - 10*q^31 - q^32 + 2*q^33 - 2*q^35 + q^36 - 6*q^37 + O(q^38),
q + q^2 + q^4 + 2*q^5 - q^7 + q^8 - 3*q^9 + 2*q^10 - q^11 + 2*q^13 - q^14 + q^16 + 2*q^17 - 3*q^18 + 2*q^20 - q^22 - 8*q^23 - q^25 + 2*q^26 - q^28 - 2*q^29 - 8*q^31 + q^32 + 2*q^34 - 2*q^35 - 3*q^36 - 2*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - a*q^5 + a*q^6 + q^7 + q^8 + (-2*a + 1)*q^9 - a*q^10 + q^11 + a*q^12 + (-a - 2)*q^13 + q^14 + (2*a - 4)*q^15 + q^16 + 2*a*q^17 + (-2*a + 1)*q^18 + (-a - 6)*q^19 - a*q^20 + a*q^21 + q^22 + 4*q^23 + a*q^24 + (-2*a - 1)*q^25 + (-a - 2)*q^26 + (2*a - 8)*q^27 + q^28 + (2*a + 2)*q^29 + (2*a - 4)*q^30 + 2*q^31 + q^32 + a*q^33 + 2*a*q^34 - a*q^35 + (-2*a + 1)*q^36 + (4*a + 2)*q^37 + O(q^38)
*]> ;  // time = 42.359 seconds




J[155] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 155, 155, 155, 155, 155, 31 ], new_dimensions := [ 1, 1, 1, 4, 4, 2 ], dimensions := [ 1, 1, 1, 4, 4, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 0, 1, 49, 1, 1, 1, 1, 0, 1, 1, 1, 5, 49, 1, 0 ], ap_traces := [
[ 0, -1, -1, 0, -4, -6, 5, -1, 8, -10, -1, 1 ],
[ -1, 2, -1, 4, 4, 0, -8, 4, 2, -6, 1, -4 ],
[ -2, -1, 1, -2, 2, -6, -7, -5, 4, 0, 1, -7 ],
[ -1, -1, -4, 0, -6, 16, 1, 5, 0, 6, 4, 9 ],
[ 1, 1, 4, 2, -4, 10, 11, -3, -2, -8, -4, 3 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^4 + x^3 - 8*x^2 - 4*x + 12,
x^4 - x^3 - 6*x^2 + 4*x + 4
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 5, 1 ],
[ 147, 3 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 5, 1 ],
[ 1, 3 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 5, 3, 1 ], torsion_lower_bounds := [ 1, 1, 1, 3, 1 ], l_ratios := [ 0, 1, 0, 1/3, 1 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1, 1 ], eigenvalues := [*
[ 0, -1, -1, 0, -4, -6, 5, -1, 8, -10, -1, 1 ],
[ -1, 2, -1, 4, 4, 0, -8, 4, 2, -6, 1, -4 ],
[ -2, -1, 1, -2, 2, -6, -7, -5, 4, 0, 1, -7 ],
[
a,
-1/2*a^3 - 1/2*a^2 + 3*a + 1,
-1,
a^2 + a - 4,
a^2 - a - 6,
-a^2 - a + 8,
-1/2*a^3 + 1/2*a^2 + 2*a - 3,
a^3 + a^2 - 5*a - 1,
-a^3 - 2*a^2 + 3*a + 6,
-a^3 + 7*a,
1,
1/2*a^3 - 1/2*a^2 - 4*a + 5
],
[
a,
-1/2*a^3 + 1/2*a^2 + 2*a - 1,
1,
-a^2 - a + 4,
-a^2 + a + 2,
a^3 - 5*a + 2,
1/2*a^3 + 1/2*a^2 - 3*a + 1,
-a^3 + a^2 + 3*a - 3,
a^2 + a - 4,
a^3 - 2*a^2 - 5*a + 4,
-1,
-1/2*a^3 - 5/2*a^2 + 3*a + 9
]
*], q_expansions := [*
q - q^3 - 2*q^4 - q^5 - 2*q^9 - 4*q^11 + 2*q^12 - 6*q^13 + q^15 + 4*q^16 + 5*q^17 - q^19 + 2*q^20 + 8*q^23 + q^25 + 5*q^27 - 10*q^29 - q^31 + 4*q^33 + 4*q^36 + q^37 + O(q^38),
q - q^2 + 2*q^3 - q^4 - q^5 - 2*q^6 + 4*q^7 + 3*q^8 + q^9 + q^10 + 4*q^11 - 2*q^12 - 4*q^14 - 2*q^15 - q^16 - 8*q^17 - q^18 + 4*q^19 + q^20 + 8*q^21 - 4*q^22 + 2*q^23 + 6*q^24 + q^25 - 4*q^27 - 4*q^28 - 6*q^29 + 2*q^30 + q^31 - 5*q^32 + 8*q^33 + 8*q^34 - 4*q^35 - q^36 - 4*q^37 + O(q^38),
q - 2*q^2 - q^3 + 2*q^4 + q^5 + 2*q^6 - 2*q^7 - 2*q^9 - 2*q^10 + 2*q^11 - 2*q^12 - 6*q^13 + 4*q^14 - q^15 - 4*q^16 - 7*q^17 + 4*q^18 - 5*q^19 + 2*q^20 + 2*q^21 - 4*q^22 + 4*q^23 + q^25 + 12*q^26 + 5*q^27 - 4*q^28 + 2*q^30 + q^31 + 8*q^32 - 2*q^33 + 14*q^34 - 2*q^35 - 4*q^36 - 7*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^3 - 1/2*a^2 + 3*a + 1)*q^3 + (a^2 - 2)*q^4 - q^5 + (-a^2 - a + 6)*q^6 + (a^2 + a - 4)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^2 - a + 10)*q^9 - a*q^10 + (a^2 - a - 6)*q^11 - 2*q^12 + (-a^2 - a + 8)*q^13 + (a^3 + a^2 - 4*a)*q^14 + (1/2*a^3 + 1/2*a^2 - 3*a - 1)*q^15 + (-a^3 + 2*a^2 + 4*a - 8)*q^16 + (-1/2*a^3 + 1/2*a^2 + 2*a - 3)*q^17 + (-2*a^3 - a^2 + 10*a)*q^18 + (a^3 + a^2 - 5*a - 1)*q^19 + (-a^2 + 2)*q^20 + (a^3 - 7*a + 2)*q^21 + (a^3 - a^2 - 6*a)*q^22 + (-a^3 - 2*a^2 + 3*a + 6)*q^23 + (2*a^2 - 12)*q^24 + q^25 + (-a^3 - a^2 + 8*a)*q^26 + (-3/2*a^3 - 1/2*a^2 + 10*a + 1)*q^27 + (2*a^2 + 2*a - 4)*q^28 + (-a^3 + 7*a)*q^29 + (a^2 + a - 6)*q^30 + q^31 + (a^3 - 4*a^2 - 4*a + 12)*q^32 + (2*a^3 + 3*a^2 - 11*a - 12)*q^33 + (a^3 - 2*a^2 - 5*a + 6)*q^34 + (-a^2 - a + 4)*q^35 + (a^3 - 2*a^2 - 6*a + 4)*q^36 + (1/2*a^3 - 1/2*a^2 - 4*a + 5)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^3 + 1/2*a^2 + 2*a - 1)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^2 + a + 2)*q^6 + (-a^2 - a + 4)*q^7 + (a^3 - 4*a)*q^8 - a*q^9 + a*q^10 + (-a^2 + a + 2)*q^11 + (-2*a + 2)*q^12 + (a^3 - 5*a + 2)*q^13 + (-a^3 - a^2 + 4*a)*q^14 + (-1/2*a^3 + 1/2*a^2 + 2*a - 1)*q^15 + (a^3 - 4*a)*q^16 + (1/2*a^3 + 1/2*a^2 - 3*a + 1)*q^17 - a^2*q^18 + (-a^3 + a^2 + 3*a - 3)*q^19 + (a^2 - 2)*q^20 + (-a^3 + 2*a^2 + 5*a - 6)*q^21 + (-a^3 + a^2 + 2*a)*q^22 + (a^2 + a - 4)*q^23 - 4*q^24 + q^25 + (a^3 + a^2 - 2*a - 4)*q^26 + (3/2*a^3 - 1/2*a^2 - 7*a + 1)*q^27 + (-2*a^3 + 6*a - 4)*q^28 + (a^3 - 2*a^2 - 5*a + 4)*q^29 + (-a^2 + a + 2)*q^30 - q^31 + (-a^3 + 2*a^2 + 4*a - 4)*q^32 + (-a^2 + 3*a)*q^33 + (a^3 - a - 2)*q^34 + (-a^2 - a + 4)*q^35 + (-a^3 + 2*a)*q^36 + (-1/2*a^3 - 5/2*a^2 + 3*a + 9)*q^37 + O(q^38)
*]> ;  // time = 15.101 seconds




J[157] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 157, 157 ], new_dimensions := [ 5, 7 ], dimensions := [ 5, 7 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -5, -7, -3, -3, -14, -7, -9, -3, -13, -2, 3, 3 ],
[ 5, 5, -1, 1, 10, -5, 5, -3, 15, 8, -13, -15 ]
], hecke_fields := [
x^5 + 5*x^4 + 5*x^3 - 6*x^2 - 7*x + 1,
x^7 - 5*x^6 + 2*x^5 + 21*x^4 - 22*x^3 - 21*x^2 + 27*x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 13 ]
], tamagawa_numbers := [
[ 1 ],
[ 13 ]
], torsion_upper_bounds := [ 1, 13 ], torsion_lower_bounds := [ 1, 13 ], l_ratios := [ 0, 1/13 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^4 - 3*a^3 + 3*a - 1,
2*a^4 + 7*a^3 + a^2 - 10*a - 2,
-a^4 - 5*a^3 - 4*a^2 + 6*a + 2,
-a^4 - 2*a^3 + 4*a^2 + 5*a - 6,
a^3 + 3*a^2 + a - 3,
a^4 + a^3 - 3*a^2 + 3*a,
-a^3 - 5*a^2 - 3*a + 5,
-a^4 - 5*a^3 - 6*a^2 + 3*a + 3,
a^4 + 5*a^3 + 3*a^2 - 8*a - 2,
-2*a^4 - 2*a^3 + 14*a^2 + 9*a - 12,
a^4 - 9*a^2 - 4*a + 7
],
[
a,
a^4 - 3*a^3 - 2*a^2 + 7*a + 1,
a^6 - 4*a^5 - 2*a^4 + 18*a^3 - 2*a^2 - 20*a + 3,
-a^6 + 3*a^5 + 4*a^4 - 13*a^3 - 5*a^2 + 13*a + 2,
-a^6 + 4*a^5 + a^4 - 15*a^3 + 3*a^2 + 13*a + 1,
a^6 - 3*a^5 - 5*a^4 + 17*a^3 + 4*a^2 - 22*a + 3,
a^6 - 3*a^5 - 4*a^4 + 13*a^3 + 6*a^2 - 16*a - 2,
4*a^6 - 14*a^5 - 12*a^4 + 61*a^3 + 9*a^2 - 65*a - 3,
a^5 - 4*a^4 + 12*a^2 - 4*a - 4,
-4*a^6 + 13*a^5 + 16*a^4 - 62*a^3 - 17*a^2 + 71*a + 1,
2*a^6 - 7*a^5 - 7*a^4 + 35*a^3 + 2*a^2 - 42*a + 5,
-2*a^6 + 8*a^5 + a^4 - 30*a^3 + 13*a^2 + 28*a - 11
]
*], q_expansions := [*
q + a*q^2 + (-a^4 - 3*a^3 + 3*a - 1)*q^3 + (a^2 - 2)*q^4 + (2*a^4 + 7*a^3 + a^2 - 10*a - 2)*q^5 + (2*a^4 + 5*a^3 - 3*a^2 - 8*a + 1)*q^6 + (-a^4 - 5*a^3 - 4*a^2 + 6*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (2*a^4 + 6*a^3 + a^2 - 5*a - 2)*q^9 + (-3*a^4 - 9*a^3 + 2*a^2 + 12*a - 2)*q^10 + (-a^4 - 2*a^3 + 4*a^2 + 5*a - 6)*q^11 + (-3*a^4 - 7*a^3 + 4*a^2 + 9*a)*q^12 + (a^3 + 3*a^2 + a - 3)*q^13 + (a^3 - 5*a + 1)*q^14 + (-a^4 - 4*a^3 - a^2 + 8*a + 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 + a^3 - 3*a^2 + 3*a)*q^17 + (-4*a^4 - 9*a^3 + 7*a^2 + 12*a - 2)*q^18 + (-a^3 - 5*a^2 - 3*a + 5)*q^19 + (2*a^4 + 3*a^3 - 8*a^2 - 3*a + 7)*q^20 + (a^4 + 6*a^3 + 6*a^2 - 6*a - 1)*q^21 + (3*a^4 + 9*a^3 - a^2 - 13*a + 1)*q^22 + (-a^4 - 5*a^3 - 6*a^2 + 3*a + 3)*q^23 + (4*a^4 + 9*a^3 - 3*a^2 - 5*a + 1)*q^24 + (-a^4 - 3*a^3 - 3*a^2 - 2*a + 6)*q^25 + (a^4 + 3*a^3 + a^2 - 3*a)*q^26 + (a^3 - a^2 - 4*a + 4)*q^27 + (3*a^4 + 10*a^3 + 3*a^2 - 11*a - 4)*q^28 + (a^4 + 5*a^3 + 3*a^2 - 8*a - 2)*q^29 + (a^4 + 4*a^3 + 2*a^2 - 6*a + 1)*q^30 + (-2*a^4 - 2*a^3 + 14*a^2 + 9*a - 12)*q^31 + (-5*a^4 - 13*a^3 + 6*a^2 + 19*a - 1)*q^32 + (3*a^4 + 8*a^3 - 4*a^2 - 13*a + 5)*q^33 + (-4*a^4 - 8*a^3 + 9*a^2 + 7*a - 1)*q^34 + (-2*a^4 - 6*a^3 + 6*a^2 + 16*a - 11)*q^35 + (7*a^4 + 15*a^3 - 14*a^2 - 20*a + 8)*q^36 + (a^4 - 9*a^2 - 4*a + 7)*q^37 + O(q^38),
q + a*q^2 + (a^4 - 3*a^3 - 2*a^2 + 7*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^6 - 4*a^5 - 2*a^4 + 18*a^3 - 2*a^2 - 20*a + 3)*q^5 + (a^5 - 3*a^4 - 2*a^3 + 7*a^2 + a)*q^6 + (-a^6 + 3*a^5 + 4*a^4 - 13*a^3 - 5*a^2 + 13*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^6 + 7*a^5 + 7*a^4 - 35*a^3 - 3*a^2 + 42*a - 3)*q^9 + (a^6 - 4*a^5 - 3*a^4 + 20*a^3 + a^2 - 24*a + 1)*q^10 + (-a^6 + 4*a^5 + a^4 - 15*a^3 + 3*a^2 + 13*a + 1)*q^11 + (a^6 - 3*a^5 - 4*a^4 + 13*a^3 + 5*a^2 - 14*a - 2)*q^12 + (a^6 - 3*a^5 - 5*a^4 + 17*a^3 + 4*a^2 - 22*a + 3)*q^13 + (-2*a^6 + 6*a^5 + 8*a^4 - 27*a^3 - 8*a^2 + 29*a - 1)*q^14 + (3*a^6 - 11*a^5 - 8*a^4 + 50*a^3 - 57*a + 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 - 3*a^5 - 4*a^4 + 13*a^3 + 6*a^2 - 16*a - 2)*q^17 + (-3*a^6 + 11*a^5 + 7*a^4 - 47*a^3 + 51*a - 2)*q^18 + (4*a^6 - 14*a^5 - 12*a^4 + 61*a^3 + 9*a^2 - 65*a - 3)*q^19 + (-a^6 + 3*a^5 + 3*a^4 - 13*a^3 + a^2 + 14*a - 5)*q^20 + (a^4 - 2*a^3 - 4*a^2 + 4*a + 3)*q^21 + (-a^6 + 3*a^5 + 6*a^4 - 19*a^3 - 8*a^2 + 28*a - 1)*q^22 + (a^5 - 4*a^4 + 12*a^2 - 4*a - 4)*q^23 + (2*a^6 - 8*a^5 - 2*a^4 + 31*a^3 - 7*a^2 - 31*a + 1)*q^24 + (-a^6 + 4*a^5 + 3*a^4 - 20*a^3 - 2*a^2 + 26*a - 1)*q^25 + (2*a^6 - 7*a^5 - 4*a^4 + 26*a^3 - a^2 - 24*a + 1)*q^26 + (-5*a^6 + 18*a^5 + 14*a^4 - 82*a^3 + 90*a - 9)*q^27 + (-2*a^6 + 6*a^5 + 7*a^4 - 26*a^3 - 3*a^2 + 27*a - 6)*q^28 + (-4*a^6 + 13*a^5 + 16*a^4 - 62*a^3 - 17*a^2 + 71*a + 1)*q^29 + (4*a^6 - 14*a^5 - 13*a^4 + 66*a^3 + 6*a^2 - 76*a + 3)*q^30 + (2*a^6 - 7*a^5 - 7*a^4 + 35*a^3 + 2*a^2 - 42*a + 5)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-2*a^6 + 7*a^5 + 8*a^4 - 37*a^3 - 8*a^2 + 50*a)*q^33 + (2*a^6 - 6*a^5 - 8*a^4 + 28*a^3 + 5*a^2 - 29*a + 1)*q^34 + (-a^6 + 3*a^5 + 5*a^4 - 14*a^3 - 9*a^2 + 15*a + 5)*q^35 + (-a^5 + 2*a^4 + 4*a^3 - 6*a^2 - 5*a + 3)*q^36 + (-2*a^6 + 8*a^5 + a^4 - 30*a^3 + 13*a^2 + 28*a - 11)*q^37 + O(q^38)
*]> ;  // time = 1.641 seconds




J[158] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 158, 158, 158, 158, 158, 158, 79, 79 ], new_dimensions := [ 1, 1, 1, 1, 1, 2, 1, 5 ], dimensions := [ 1, 1, 1, 1, 1, 2, 2, 10 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 53, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 53, 1, 0 ], ap_traces := [
[ -1, -1, -1, -3, 4, -7, -4, -6, 6, 4, 8, 10 ],
[ -1, 1, 3, -1, 0, 5, 0, 2, -6, 0, -4, 2 ],
[ 1, -1, 1, 3, 2, -1, -2, 0, -6, -10, 2, -2 ],
[ 1, 2, -2, 0, -4, 2, -2, 0, 0, 8, 8, 4 ],
[ 1, -3, -3, -3, -2, -5, 6, 0, -2, 6, -10, -10 ],
[ -2, 0, -4, 8, 0, 4, 4, 0, 4, -4, -4, -4 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 6
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 3 ],
[ 5, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 53, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 3 ],
[ 5, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 5, 1, 1, 1 ], torsion_lower_bounds := [ 1, 3, 5, 1, 1, 1 ], l_ratios := [ 0, 1/3, 1/5, 1, 0, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 0, 1 ], eigenvalues := [*
[ -1, -1, -1, -3, 4, -7, -4, -6, 6, 4, 8, 10 ],
[ -1, 1, 3, -1, 0, 5, 0, 2, -6, 0, -4, 2 ],
[ 1, -1, 1, 3, 2, -1, -2, 0, -6, -10, 2, -2 ],
[ 1, 2, -2, 0, -4, 2, -2, 0, 0, 8, 8, 4 ],
[ 1, -3, -3, -3, -2, -5, 6, 0, -2, 6, -10, -10 ],
[
-1,
a,
-2,
4,
0,
-2*a + 2,
-2*a + 2,
2*a,
2*a + 2,
-3*a - 2,
-2*a - 2,
-a - 2
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - q^5 + q^6 - 3*q^7 - q^8 - 2*q^9 + q^10 + 4*q^11 - q^12 - 7*q^13 + 3*q^14 + q^15 + q^16 - 4*q^17 + 2*q^18 - 6*q^19 - q^20 + 3*q^21 - 4*q^22 + 6*q^23 + q^24 - 4*q^25 + 7*q^26 + 5*q^27 - 3*q^28 + 4*q^29 - q^30 + 8*q^31 - q^32 - 4*q^33 + 4*q^34 + 3*q^35 - 2*q^36 + 10*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + 3*q^5 - q^6 - q^7 - q^8 - 2*q^9 - 3*q^10 + q^12 + 5*q^13 + q^14 + 3*q^15 + q^16 + 2*q^18 + 2*q^19 + 3*q^20 - q^21 - 6*q^23 - q^24 + 4*q^25 - 5*q^26 - 5*q^27 - q^28 - 3*q^30 - 4*q^31 - q^32 - 3*q^35 - 2*q^36 + 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + 3*q^7 + q^8 - 2*q^9 + q^10 + 2*q^11 - q^12 - q^13 + 3*q^14 - q^15 + q^16 - 2*q^17 - 2*q^18 + q^20 - 3*q^21 + 2*q^22 - 6*q^23 - q^24 - 4*q^25 - q^26 + 5*q^27 + 3*q^28 - 10*q^29 - q^30 + 2*q^31 + q^32 - 2*q^33 - 2*q^34 + 3*q^35 - 2*q^36 - 2*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 - 2*q^5 + 2*q^6 + q^8 + q^9 - 2*q^10 - 4*q^11 + 2*q^12 + 2*q^13 - 4*q^15 + q^16 - 2*q^17 + q^18 - 2*q^20 - 4*q^22 + 2*q^24 - q^25 + 2*q^26 - 4*q^27 + 8*q^29 - 4*q^30 + 8*q^31 + q^32 - 8*q^33 - 2*q^34 + q^36 + 4*q^37 + O(q^38),
q + q^2 - 3*q^3 + q^4 - 3*q^5 - 3*q^6 - 3*q^7 + q^8 + 6*q^9 - 3*q^10 - 2*q^11 - 3*q^12 - 5*q^13 - 3*q^14 + 9*q^15 + q^16 + 6*q^17 + 6*q^18 - 3*q^20 + 9*q^21 - 2*q^22 - 2*q^23 - 3*q^24 + 4*q^25 - 5*q^26 - 9*q^27 - 3*q^28 + 6*q^29 + 9*q^30 - 10*q^31 + q^32 + 6*q^33 + 6*q^34 + 9*q^35 + 6*q^36 - 10*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - 2*q^5 - a*q^6 + 4*q^7 - q^8 + 3*q^9 + 2*q^10 + a*q^12 + (-2*a + 2)*q^13 - 4*q^14 - 2*a*q^15 + q^16 + (-2*a + 2)*q^17 - 3*q^18 + 2*a*q^19 - 2*q^20 + 4*a*q^21 + (2*a + 2)*q^23 - a*q^24 - q^25 + (2*a - 2)*q^26 + 4*q^28 + (-3*a - 2)*q^29 + 2*a*q^30 + (-2*a - 2)*q^31 - q^32 + (2*a - 2)*q^34 - 8*q^35 + 3*q^36 + (-a - 2)*q^37 + O(q^38)
*]> ;  // time = 21.38 seconds




J[159] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 159, 159, 53, 53 ], new_dimensions := [ 4, 5, 1, 3 ], dimensions := [ 4, 5, 2, 6 ], intersection_graph := [ 0, 1, 7, 1, 1, 0, 1, 107, 7, 1, 0, 1, 1, 107, 1, 0 ], ap_traces := [
[ 3, 4, 2, -4, 6, -6, 10, -6, 2, 6, -12, -10 ],
[ 0, -5, 0, 4, 2, 8, 0, 2, -6, 20, 8, 4 ]
], hecke_fields := [
x^4 - 3*x^3 - x^2 + 7*x - 3,
x^5 - 10*x^3 + 22*x + 5
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 63, 1 ],
[ 107, 1 ]
], tamagawa_numbers := [
[ 63, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 9, 1 ], torsion_lower_bounds := [ 9, 1 ], l_ratios := [ 7/9, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
a,
1,
-a^3 + a^2 + 2*a,
a^3 - 3*a^2 - 2*a + 5,
4*a^3 - 6*a^2 - 12*a + 12,
-3*a^3 + 5*a^2 + 8*a - 10,
-4*a^3 + 8*a^2 + 10*a - 12,
2*a^2 - 4*a - 4,
-a^3 + a^2 + 6*a - 3,
4*a^3 - 6*a^2 - 12*a + 12,
2*a^2 + 2*a - 10,
a^3 - 3*a^2 - 4*a + 5
],
[
a,
-1,
-a^3 - a^2 + 6*a + 4,
1/3*a^4 + 4/3*a^3 - 2*a^2 - 7*a + 4/3,
-2/3*a^4 - 2/3*a^3 + 4*a^2 + 2*a - 2/3,
2/3*a^4 - 1/3*a^3 - 5*a^2 + 2*a + 20/3,
-2*a,
-2/3*a^4 - 2/3*a^3 + 4*a^2 + 2*a - 2/3,
1/3*a^4 + 4/3*a^3 - 7*a - 26/3,
2*a^2 - 4,
2/3*a^4 + 2/3*a^3 - 4*a^2 - 4*a + 8/3,
1/3*a^4 + 4/3*a^3 - 2*a^2 - 5*a + 4/3
]
*], q_expansions := [*
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^3 + a^2 + 2*a)*q^5 + a*q^6 + (a^3 - 3*a^2 - 2*a + 5)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-2*a^3 + a^2 + 7*a - 3)*q^10 + (4*a^3 - 6*a^2 - 12*a + 12)*q^11 + (a^2 - 2)*q^12 + (-3*a^3 + 5*a^2 + 8*a - 10)*q^13 + (-a^2 - 2*a + 3)*q^14 + (-a^3 + a^2 + 2*a)*q^15 + (3*a^3 - 5*a^2 - 7*a + 7)*q^16 + (-4*a^3 + 8*a^2 + 10*a - 12)*q^17 + a*q^18 + (2*a^2 - 4*a - 4)*q^19 + (-3*a^3 + 3*a^2 + 7*a - 6)*q^20 + (a^3 - 3*a^2 - 2*a + 5)*q^21 + (6*a^3 - 8*a^2 - 16*a + 12)*q^22 + (-a^3 + a^2 + 6*a - 3)*q^23 + (a^3 - 4*a)*q^24 + (a^3 + a^2 - 4*a - 2)*q^25 + (-4*a^3 + 5*a^2 + 11*a - 9)*q^26 + q^27 + (-3*a^3 + 4*a^2 + 7*a - 10)*q^28 + (4*a^3 - 6*a^2 - 12*a + 12)*q^29 + (-2*a^3 + a^2 + 7*a - 3)*q^30 + (2*a^2 + 2*a - 10)*q^31 + (2*a^3 - 4*a^2 - 6*a + 9)*q^32 + (4*a^3 - 6*a^2 - 12*a + 12)*q^33 + (-4*a^3 + 6*a^2 + 16*a - 12)*q^34 + (4*a^3 - 6*a^2 - 8*a + 9)*q^35 + (a^2 - 2)*q^36 + (a^3 - 3*a^2 - 4*a + 5)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^3 - a^2 + 6*a + 4)*q^5 - a*q^6 + (1/3*a^4 + 4/3*a^3 - 2*a^2 - 7*a + 4/3)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^4 - a^3 + 6*a^2 + 4*a)*q^10 + (-2/3*a^4 - 2/3*a^3 + 4*a^2 + 2*a - 2/3)*q^11 + (-a^2 + 2)*q^12 + (2/3*a^4 - 1/3*a^3 - 5*a^2 + 2*a + 20/3)*q^13 + (4/3*a^4 + 4/3*a^3 - 7*a^2 - 6*a - 5/3)*q^14 + (a^3 + a^2 - 6*a - 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 - 2*a*q^17 + a*q^18 + (-2/3*a^4 - 2/3*a^3 + 4*a^2 + 2*a - 2/3)*q^19 + (-a^4 - 2*a^3 + 6*a^2 + 10*a - 3)*q^20 + (-1/3*a^4 - 4/3*a^3 + 2*a^2 + 7*a - 4/3)*q^21 + (-2/3*a^4 - 8/3*a^3 + 2*a^2 + 14*a + 10/3)*q^22 + (1/3*a^4 + 4/3*a^3 - 7*a - 26/3)*q^23 + (-a^3 + 4*a)*q^24 + (-a^4 + 6*a^2 - a + 1)*q^25 + (-1/3*a^4 + 5/3*a^3 + 2*a^2 - 8*a - 10/3)*q^26 - q^27 + (2/3*a^4 + 11/3*a^3 - 2*a^2 - 17*a - 28/3)*q^28 + (2*a^2 - 4)*q^29 + (a^4 + a^3 - 6*a^2 - 4*a)*q^30 + (2/3*a^4 + 2/3*a^3 - 4*a^2 - 4*a + 8/3)*q^31 + (2*a^3 - 10*a - 5)*q^32 + (2/3*a^4 + 2/3*a^3 - 4*a^2 - 2*a + 2/3)*q^33 - 2*a^2*q^34 + (5/3*a^4 - 1/3*a^3 - 13*a^2 + 3*a + 26/3)*q^35 + (a^2 - 2)*q^36 + (1/3*a^4 + 4/3*a^3 - 2*a^2 - 5*a + 4/3)*q^37 + O(q^38)
*]> ;  // time = 15.679 seconds




J[161] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 161, 161, 161, 161, 23 ], new_dimensions := [ 1, 2, 3, 5, 2 ], dimensions := [ 1, 2, 3, 5, 4 ], intersection_graph := [ 0, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 19, 5, 1, 1, 0, 1, 1, 1, 19, 1, 0 ], ap_traces := [
[ -1, 0, 2, 1, 4, 6, -2, 4, -1, -2, -4, -2 ],
[ -1, -2, -2, -2, 0, -4, 0, -10, -2, 6, -18, 2 ],
[ -1, 2, 2, -3, 4, 2, 4, 8, 3, -2, 16, -6 ],
[ 2, 0, -4, 5, -4, -6, -12, 6, -5, -4, 30, 4 ]
], hecke_fields := [
x - 1,
x^2 + x - 1,
x^3 + x^2 - 5*x - 1,
x^5 - 2*x^4 - 9*x^3 + 17*x^2 + 16*x - 27
], atkin_lehners := [
[ -1, 1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 19, 1 ],
[ 3, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1, 3 ], l_ratios := [ 1, 0, 1, 1/3 ], analytic_sha_upper_bounds := [ 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1, 1 ], eigenvalues := [*
[ -1, 0, 2, 1, 4, 6, -2, 4, -1, -2, -4, -2 ],
[
a,
-1,
-2*a - 2,
-1,
4*a + 2,
2*a - 1,
0,
-2*a - 6,
-1,
-4*a + 1,
-9,
-6*a - 2
],
[
a,
-1/2*a^2 + 5/2,
-1/2*a^2 + 5/2,
-1,
-a + 1,
a^2 - 3,
1/2*a^2 - 1/2,
2*a^2 + 2*a - 4,
1,
a^2 + a - 4,
-3/2*a^2 - 4*a + 19/2,
a^2 + 2*a - 5
],
[
a,
1/2*a^4 - 1/2*a^3 - 4*a^2 + 5/2*a + 11/2,
-1/2*a^4 - 1/2*a^3 + 5*a^2 + 5/2*a - 21/2,
1,
-a^4 + 8*a^2 + a - 12,
a^4 - 9*a^2 + 14,
1/2*a^4 + 1/2*a^3 - 3*a^2 - 5/2*a - 3/2,
-2*a + 2,
-1,
-3*a^2 + a + 12,
-1/2*a^4 + 1/2*a^3 + 4*a^2 - 5/2*a + 1/2,
a^4 - a^3 - 8*a^2 + 7*a + 11
]
*], q_expansions := [*
q - q^2 - q^4 + 2*q^5 + q^7 + 3*q^8 - 3*q^9 - 2*q^10 + 4*q^11 + 6*q^13 - q^14 - q^16 - 2*q^17 + 3*q^18 + 4*q^19 - 2*q^20 - 4*q^22 - q^23 - q^25 - 6*q^26 - q^28 - 2*q^29 - 4*q^31 - 5*q^32 + 2*q^34 + 2*q^35 + 3*q^36 - 2*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a - 1)*q^4 + (-2*a - 2)*q^5 - a*q^6 - q^7 + (-2*a - 1)*q^8 - 2*q^9 - 2*q^10 + (4*a + 2)*q^11 + (a + 1)*q^12 + (2*a - 1)*q^13 - a*q^14 + (2*a + 2)*q^15 + 3*a*q^16 - 2*a*q^18 + (-2*a - 6)*q^19 + (2*a + 4)*q^20 + q^21 + (-2*a + 4)*q^22 - q^23 + (2*a + 1)*q^24 + (4*a + 3)*q^25 + (-3*a + 2)*q^26 + 5*q^27 + (a + 1)*q^28 + (-4*a + 1)*q^29 + 2*q^30 - 9*q^31 + (a + 5)*q^32 + (-4*a - 2)*q^33 + (2*a + 2)*q^35 + (2*a + 2)*q^36 + (-6*a - 2)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^2 + 5/2)*q^3 + (a^2 - 2)*q^4 + (-1/2*a^2 + 5/2)*q^5 + (1/2*a^2 - 1/2)*q^6 - q^7 + (-a^2 + a + 1)*q^8 + (-a^2 - a + 3)*q^9 + (1/2*a^2 - 1/2)*q^10 + (-a + 1)*q^11 + (1/2*a^2 + 2*a - 9/2)*q^12 + (a^2 - 3)*q^13 - a*q^14 + (-a^2 - a + 6)*q^15 + (-4*a + 3)*q^16 + (1/2*a^2 - 1/2)*q^17 + (-2*a - 1)*q^18 + (2*a^2 + 2*a - 4)*q^19 + (1/2*a^2 + 2*a - 9/2)*q^20 + (1/2*a^2 - 5/2)*q^21 + (-a^2 + a)*q^22 + q^23 + (1/2*a^2 - 2*a + 3/2)*q^24 + (-a^2 - a + 1)*q^25 + (-a^2 + 2*a + 1)*q^26 - 2*a*q^27 + (-a^2 + 2)*q^28 + (a^2 + a - 4)*q^29 + (a - 1)*q^30 + (-3/2*a^2 - 4*a + 19/2)*q^31 + (-2*a^2 + a - 2)*q^32 + (-a^2 + 3)*q^33 + (-1/2*a^2 + 2*a + 1/2)*q^34 + (1/2*a^2 - 5/2)*q^35 + (a - 6)*q^36 + (a^2 + 2*a - 5)*q^37 + O(q^38),
q + a*q^2 + (1/2*a^4 - 1/2*a^3 - 4*a^2 + 5/2*a + 11/2)*q^3 + (a^2 - 2)*q^4 + (-1/2*a^4 - 1/2*a^3 + 5*a^2 + 5/2*a - 21/2)*q^5 + (1/2*a^4 + 1/2*a^3 - 6*a^2 - 5/2*a + 27/2)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (-a^2 - a + 7)*q^9 + (-3/2*a^4 + 1/2*a^3 + 11*a^2 - 5/2*a - 27/2)*q^10 + (-a^4 + 8*a^2 + a - 12)*q^11 + (1/2*a^4 - 1/2*a^3 - 3*a^2 + 1/2*a + 5/2)*q^12 + (a^4 - 9*a^2 + 14)*q^13 + a*q^14 + (a^3 - 8*a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/2*a^4 + 1/2*a^3 - 3*a^2 - 5/2*a - 3/2)*q^17 + (-a^3 - a^2 + 7*a)*q^18 + (-2*a + 2)*q^19 + (-3/2*a^4 - 3/2*a^3 + 13*a^2 + 11/2*a - 39/2)*q^20 + (1/2*a^4 - 1/2*a^3 - 4*a^2 + 5/2*a + 11/2)*q^21 + (-2*a^4 - a^3 + 18*a^2 + 4*a - 27)*q^22 - q^23 + (-1/2*a^4 + 1/2*a^3 + 4*a^2 - 1/2*a - 27/2)*q^24 + (a^3 - 6*a + 4)*q^25 + (2*a^4 - 17*a^2 - 2*a + 27)*q^26 + (-a^3 + a^2 + 7*a - 5)*q^27 + (a^2 - 2)*q^28 + (-3*a^2 + a + 12)*q^29 + (a^4 - 8*a^2 + 3*a)*q^30 + (-1/2*a^4 + 1/2*a^3 + 4*a^2 - 5/2*a + 1/2)*q^31 + (2*a^4 + a^3 - 17*a^2 - 4*a + 27)*q^32 + (a^4 + a^3 - 10*a^2 - 5*a + 15)*q^33 + (3/2*a^4 + 3/2*a^3 - 11*a^2 - 19/2*a + 27/2)*q^34 + (-1/2*a^4 - 1/2*a^3 + 5*a^2 + 5/2*a - 21/2)*q^35 + (-a^4 - a^3 + 9*a^2 + 2*a - 14)*q^36 + (a^4 - a^3 - 8*a^2 + 7*a + 11)*q^37 + O(q^38)
*]> ;  // time = 15.02 seconds




J[163] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 163, 163, 163 ], new_dimensions := [ 1, 5, 7 ], dimensions := [ 1, 5, 7 ], intersection_graph := [ 0, 3, 1, 3, 0, 1, 1, 1, 0 ], ap_traces := [
[ 0, 0, -4, 2, -6, 4, 0, -6, 6, -4, -6, -8 ],
[ -5, -5, -9, -6, 2, -14, -21, 7, -8, -13, 7, -1 ],
[ 3, 1, 11, 0, 2, 10, 13, -5, 2, 7, -11, 3 ]
], hecke_fields := [
x - 1,
x^5 + 5*x^4 + 3*x^3 - 15*x^2 - 16*x + 3,
x^7 - 3*x^6 - 5*x^5 + 19*x^4 - 23*x^2 + 4*x + 6
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 27 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 27 ]
], torsion_upper_bounds := [ 1, 1, 27 ], torsion_lower_bounds := [ 1, 1, 27 ], l_ratios := [ 0, 0, 1/27 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[ 0, 0, -4, 2, -6, 4, 0, -6, 6, -4, -6, -8 ],
[
a,
-2*a^4 - 5*a^3 + 6*a^2 + 13*a - 3,
2*a^4 + 5*a^3 - 7*a^2 - 15*a + 2,
3*a^4 + 8*a^3 - 8*a^2 - 22*a - 1,
-a^4 - 4*a^3 + a^2 + 13*a + 3,
-a^4 - 3*a^3 + 2*a^2 + 8*a - 2,
-a^4 - 2*a^3 + 4*a^2 + 6*a - 6,
-2*a^4 - 3*a^3 + 9*a^2 + 8*a - 3,
2*a^4 + 3*a^3 - 8*a^2 - 7*a,
-2*a^4 - 6*a^3 + 4*a^2 + 16*a - 1,
4*a^4 + 11*a^3 - 14*a^2 - 34*a + 12,
-3*a^4 - 7*a^3 + 10*a^2 + 18*a - 5
],
[
a,
a^5 - a^4 - 6*a^3 + 5*a^2 + 5*a - 2,
-a^6 + a^5 + 7*a^4 - 6*a^3 - 11*a^2 + 6*a + 6,
a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 11*a^2 - 11*a - 4,
a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 12*a^2 - 12*a - 6,
-a^6 + a^5 + 8*a^4 - 6*a^3 - 16*a^2 + 5*a + 8,
a^6 - a^5 - 6*a^4 + 5*a^3 + 6*a^2 - 3*a,
a^6 - 6*a^4 - a^3 + 4*a^2 + 3*a + 2,
a^6 - a^5 - 7*a^4 + 6*a^3 + 12*a^2 - 8*a - 6,
a^6 - 6*a^4 + 3*a^2 - a + 6,
-a^6 + a^5 + 5*a^4 - 4*a^3 + 2*a^2 - a - 10,
3*a^6 - 6*a^5 - 17*a^4 + 33*a^3 + 11*a^2 - 21*a + 2
]
*], q_expansions := [*
q - 2*q^4 - 4*q^5 + 2*q^7 - 3*q^9 - 6*q^11 + 4*q^13 + 4*q^16 - 6*q^19 + 8*q^20 + 6*q^23 + 11*q^25 - 4*q^28 - 4*q^29 - 6*q^31 - 8*q^35 + 6*q^36 - 8*q^37 + O(q^38),
q + a*q^2 + (-2*a^4 - 5*a^3 + 6*a^2 + 13*a - 3)*q^3 + (a^2 - 2)*q^4 + (2*a^4 + 5*a^3 - 7*a^2 - 15*a + 2)*q^5 + (5*a^4 + 12*a^3 - 17*a^2 - 35*a + 6)*q^6 + (3*a^4 + 8*a^3 - 8*a^2 - 22*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (2*a^2 + 3*a - 3)*q^9 + (-5*a^4 - 13*a^3 + 15*a^2 + 34*a - 6)*q^10 + (-a^4 - 4*a^3 + a^2 + 13*a + 3)*q^11 + (-9*a^4 - 22*a^3 + 28*a^2 + 60*a - 9)*q^12 + (-a^4 - 3*a^3 + 2*a^2 + 8*a - 2)*q^13 + (-7*a^4 - 17*a^3 + 23*a^2 + 47*a - 9)*q^14 + (5*a^4 + 13*a^3 - 14*a^2 - 32*a + 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 - 2*a^3 + 4*a^2 + 6*a - 6)*q^17 + (2*a^3 + 3*a^2 - 3*a)*q^18 + (-2*a^4 - 3*a^3 + 9*a^2 + 8*a - 3)*q^19 + (8*a^4 + 20*a^3 - 27*a^2 - 56*a + 11)*q^20 + (2*a^4 + 5*a^3 - 8*a^2 - 14*a + 6)*q^21 + (a^4 + 4*a^3 - 2*a^2 - 13*a + 3)*q^22 + (2*a^4 + 3*a^3 - 8*a^2 - 7*a)*q^23 + (13*a^4 + 31*a^3 - 41*a^2 - 83*a + 15)*q^24 + (-9*a^4 - 22*a^3 + 32*a^2 + 65*a - 16)*q^25 + (2*a^4 + 5*a^3 - 7*a^2 - 18*a + 3)*q^26 + (a^4 + 2*a^3 - 7*a^2 - 11*a + 6)*q^27 + (12*a^4 + 28*a^3 - 42*a^2 - 77*a + 23)*q^28 + (-2*a^4 - 6*a^3 + 4*a^2 + 16*a - 1)*q^29 + (-12*a^4 - 29*a^3 + 43*a^2 + 86*a - 15)*q^30 + (4*a^4 + 11*a^3 - 14*a^2 - 34*a + 12)*q^31 + (-5*a^4 - 11*a^3 + 15*a^2 + 28*a - 3)*q^32 + (a^3 + a^2 - 5*a - 3)*q^33 + (3*a^4 + 7*a^3 - 9*a^2 - 22*a + 3)*q^34 + (-9*a^4 - 23*a^3 + 28*a^2 + 63*a - 8)*q^35 + (2*a^4 + 3*a^3 - 7*a^2 - 6*a + 6)*q^36 + (-3*a^4 - 7*a^3 + 10*a^2 + 18*a - 5)*q^37 + O(q^38),
q + a*q^2 + (a^5 - a^4 - 6*a^3 + 5*a^2 + 5*a - 2)*q^3 + (a^2 - 2)*q^4 + (-a^6 + a^5 + 7*a^4 - 6*a^3 - 11*a^2 + 6*a + 6)*q^5 + (a^6 - a^5 - 6*a^4 + 5*a^3 + 5*a^2 - 2*a)*q^6 + (a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 11*a^2 - 11*a - 4)*q^7 + (a^3 - 4*a)*q^8 + (-a^6 + a^5 + 7*a^4 - 5*a^3 - 12*a^2 + 2*a + 7)*q^9 + (-2*a^6 + 2*a^5 + 13*a^4 - 11*a^3 - 17*a^2 + 10*a + 6)*q^10 + (a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 12*a^2 - 12*a - 6)*q^11 + (2*a^6 - 3*a^5 - 12*a^4 + 17*a^3 + 11*a^2 - 14*a - 2)*q^12 + (-a^6 + a^5 + 8*a^4 - 6*a^3 - 16*a^2 + 5*a + 8)*q^13 + (a^6 - 2*a^5 - 7*a^4 + 11*a^3 + 12*a^2 - 8*a - 6)*q^14 + (2*a^5 - a^4 - 13*a^3 + 4*a^2 + 14*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 - a^5 - 6*a^4 + 5*a^3 + 6*a^2 - 3*a)*q^17 + (-2*a^6 + 2*a^5 + 14*a^4 - 12*a^3 - 21*a^2 + 11*a + 6)*q^18 + (a^6 - 6*a^4 - a^3 + 4*a^2 + 3*a + 2)*q^19 + (-2*a^6 + a^5 + 13*a^4 - 5*a^3 - 14*a^2 + 2*a)*q^20 + (-2*a^4 + a^3 + 12*a^2 - 4*a - 10)*q^21 + (a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 11*a^2 - 10*a - 6)*q^22 + (a^6 - a^5 - 7*a^4 + 6*a^3 + 12*a^2 - 8*a - 6)*q^23 + (a^6 - 9*a^4 + a^3 + 22*a^2 - 6*a - 12)*q^24 + (-3*a^6 + 4*a^5 + 21*a^4 - 24*a^3 - 33*a^2 + 24*a + 13)*q^25 + (-2*a^6 + 3*a^5 + 13*a^4 - 16*a^3 - 18*a^2 + 12*a + 6)*q^26 + (-a^6 + a^5 + 6*a^4 - 5*a^3 - 5*a^2 + 2*a - 2)*q^27 + (-a^6 + 2*a^5 + 6*a^4 - 12*a^3 - 7*a^2 + 12*a + 2)*q^28 + (a^6 - 6*a^4 + 3*a^2 - a + 6)*q^29 + (2*a^6 - a^5 - 13*a^4 + 4*a^3 + 14*a^2)*q^30 + (-a^6 + a^5 + 5*a^4 - 4*a^3 + 2*a^2 - a - 10)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^6 - 2*a^5 - 8*a^4 + 13*a^3 + 18*a^2 - 16*a - 12)*q^33 + (2*a^6 - a^5 - 14*a^4 + 6*a^3 + 20*a^2 - 4*a - 6)*q^34 + (3*a^6 - 5*a^5 - 20*a^4 + 30*a^3 + 28*a^2 - 28*a - 12)*q^35 + (-2*a^6 + 2*a^5 + 12*a^4 - 11*a^3 - 11*a^2 + 10*a - 2)*q^36 + (3*a^6 - 6*a^5 - 17*a^4 + 33*a^3 + 11*a^2 - 21*a + 2)*q^37 + O(q^38)
*]> ;  // time = 1.87 seconds




J[165] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 165, 165, 165, 55, 55, 33, 15, 11 ], new_dimensions := [ 2, 2, 3, 1, 2, 1, 1, 1 ], dimensions := [ 2, 2, 3, 2, 4, 2, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 49, 1, 1, 1, 1, 1, 0, 1, 9, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 49, 9, 1, 0 ], ap_traces := [
[ -2, -2, -2, -4, -2, 0, -8, -8, -8, -4, 0, 12 ],
[ 0, 2, -2, 4, -2, 4, 0, 4, 0, 0, -8, 4 ],
[ -1, 3, 3, 0, 3, -2, -2, 8, 0, -10, 8, -6 ]
], hecke_fields := [
x^2 + 2*x - 1,
x^2 - 3,
x^3 + x^2 - 5*x - 1
], atkin_lehners := [
[ 1, 1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 5, 5, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 5, 5, 1 ]
], torsion_upper_bounds := [ 1, 3, 5 ], torsion_lower_bounds := [ 1, 3, 1 ], l_ratios := [ 0, 1/3, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1/25 ], eigenvalues := [*
[
a,
-1,
-1,
-2*a - 4,
-1,
4*a + 4,
-2*a - 6,
2*a - 2,
-4,
2*a,
0,
-4*a + 2
],
[
a,
1,
-1,
2,
-1,
-2*a + 2,
0,
-2*a + 2,
-4*a,
2*a,
4*a - 4,
4*a + 2
],
[
a,
1,
1,
-a^2 - 2*a + 3,
1,
-a^2 + 3,
a^2 - 2*a - 5,
2*a^2 + 2*a - 4,
2*a^2 + 4*a - 6,
-2*a - 4,
-2*a^2 + 10,
-2
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-2*a - 1)*q^4 - q^5 - a*q^6 + (-2*a - 4)*q^7 + (a - 2)*q^8 + q^9 - a*q^10 - q^11 + (2*a + 1)*q^12 + (4*a + 4)*q^13 - 2*q^14 + q^15 + 3*q^16 + (-2*a - 6)*q^17 + a*q^18 + (2*a - 2)*q^19 + (2*a + 1)*q^20 + (2*a + 4)*q^21 - a*q^22 - 4*q^23 + (-a + 2)*q^24 + q^25 + (-4*a + 4)*q^26 - q^27 + (2*a + 8)*q^28 + 2*a*q^29 + a*q^30 + (a + 4)*q^32 + q^33 + (-2*a - 2)*q^34 + (2*a + 4)*q^35 + (-2*a - 1)*q^36 + (-4*a + 2)*q^37 + O(q^38),
q + a*q^2 + q^3 + q^4 - q^5 + a*q^6 + 2*q^7 - a*q^8 + q^9 - a*q^10 - q^11 + q^12 + (-2*a + 2)*q^13 + 2*a*q^14 - q^15 - 5*q^16 + a*q^18 + (-2*a + 2)*q^19 - q^20 + 2*q^21 - a*q^22 - 4*a*q^23 - a*q^24 + q^25 + (2*a - 6)*q^26 + q^27 + 2*q^28 + 2*a*q^29 - a*q^30 + (4*a - 4)*q^31 - 3*a*q^32 - q^33 - 2*q^35 + q^36 + (4*a + 2)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + q^5 + a*q^6 + (-a^2 - 2*a + 3)*q^7 + (-a^2 + a + 1)*q^8 + q^9 + a*q^10 + q^11 + (a^2 - 2)*q^12 + (-a^2 + 3)*q^13 + (-a^2 - 2*a - 1)*q^14 + q^15 + (-4*a + 3)*q^16 + (a^2 - 2*a - 5)*q^17 + a*q^18 + (2*a^2 + 2*a - 4)*q^19 + (a^2 - 2)*q^20 + (-a^2 - 2*a + 3)*q^21 + a*q^22 + (2*a^2 + 4*a - 6)*q^23 + (-a^2 + a + 1)*q^24 + q^25 + (a^2 - 2*a - 1)*q^26 + q^27 + (a^2 - 2*a - 7)*q^28 + (-2*a - 4)*q^29 + a*q^30 + (-2*a^2 + 10)*q^31 + (-2*a^2 + a - 2)*q^32 + q^33 + (-3*a^2 + 1)*q^34 + (-a^2 - 2*a + 3)*q^35 + (a^2 - 2)*q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 33.04 seconds




J[166] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 166, 166, 166, 83, 83 ], new_dimensions := [ 1, 2, 3, 1, 6 ], dimensions := [ 1, 2, 3, 2, 12 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 131, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 131, 1, 1, 0 ], ap_traces := [
[ -1, -1, -2, 1, -5, -2, -3, -2, 4, -3, 1, 1 ],
[ -2, -2, 3, -3, 6, 3, 7, -1, 3, 8, -9, -4 ],
[ 3, 1, -1, 2, 5, -9, -4, -5, 7, 13, -4, -19 ]
], hecke_fields := [
x - 1,
x^2 + 2*x - 4,
x^3 - x^2 - 6*x + 4
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 131, 1 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ]
], torsion_upper_bounds := [ 1, 1, 7 ], torsion_lower_bounds := [ 1, 1, 7 ], l_ratios := [ 0, 1, 1/7 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ -1, -1, -2, 1, -5, -2, -3, -2, 4, -3, 1, 1 ],
[
-1,
a,
1/2*a + 2,
1/2*a - 1,
-a + 2,
-1/2*a + 1,
1/2*a + 4,
-1/2*a - 1,
-3/2*a,
4,
1/2*a - 4,
-4*a - 6
],
[
1,
a,
-1/2*a^2 - 1/2*a + 2,
1/2*a^2 - 3/2*a - 1,
-a + 2,
-1/2*a^2 + 1/2*a - 1,
3/2*a^2 + 1/2*a - 8,
-5/2*a^2 + 1/2*a + 9,
1/2*a^2 + 1/2*a,
a^2,
3/2*a^2 + 1/2*a - 8,
-a^2 - 2
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - 2*q^5 + q^6 + q^7 - q^8 - 2*q^9 + 2*q^10 - 5*q^11 - q^12 - 2*q^13 - q^14 + 2*q^15 + q^16 - 3*q^17 + 2*q^18 - 2*q^19 - 2*q^20 - q^21 + 5*q^22 + 4*q^23 + q^24 - q^25 + 2*q^26 + 5*q^27 + q^28 - 3*q^29 - 2*q^30 + q^31 - q^32 + 5*q^33 + 3*q^34 - 2*q^35 - 2*q^36 + q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (1/2*a + 2)*q^5 - a*q^6 + (1/2*a - 1)*q^7 - q^8 + (-2*a + 1)*q^9 + (-1/2*a - 2)*q^10 + (-a + 2)*q^11 + a*q^12 + (-1/2*a + 1)*q^13 + (-1/2*a + 1)*q^14 + (a + 2)*q^15 + q^16 + (1/2*a + 4)*q^17 + (2*a - 1)*q^18 + (-1/2*a - 1)*q^19 + (1/2*a + 2)*q^20 + (-2*a + 2)*q^21 + (a - 2)*q^22 - 3/2*a*q^23 - a*q^24 + 3/2*a*q^25 + (1/2*a - 1)*q^26 + (2*a - 8)*q^27 + (1/2*a - 1)*q^28 + 4*q^29 + (-a - 2)*q^30 + (1/2*a - 4)*q^31 - q^32 + (4*a - 4)*q^33 + (-1/2*a - 4)*q^34 - q^35 + (-2*a + 1)*q^36 + (-4*a - 6)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-1/2*a^2 - 1/2*a + 2)*q^5 + a*q^6 + (1/2*a^2 - 3/2*a - 1)*q^7 + q^8 + (a^2 - 3)*q^9 + (-1/2*a^2 - 1/2*a + 2)*q^10 + (-a + 2)*q^11 + a*q^12 + (-1/2*a^2 + 1/2*a - 1)*q^13 + (1/2*a^2 - 3/2*a - 1)*q^14 + (-a^2 - a + 2)*q^15 + q^16 + (3/2*a^2 + 1/2*a - 8)*q^17 + (a^2 - 3)*q^18 + (-5/2*a^2 + 1/2*a + 9)*q^19 + (-1/2*a^2 - 1/2*a + 2)*q^20 + (-a^2 + 2*a - 2)*q^21 + (-a + 2)*q^22 + (1/2*a^2 + 1/2*a)*q^23 + a*q^24 + (1/2*a^2 + 3/2*a - 4)*q^25 + (-1/2*a^2 + 1/2*a - 1)*q^26 + (a^2 - 4)*q^27 + (1/2*a^2 - 3/2*a - 1)*q^28 + a^2*q^29 + (-a^2 - a + 2)*q^30 + (3/2*a^2 + 1/2*a - 8)*q^31 + q^32 + (-a^2 + 2*a)*q^33 + (3/2*a^2 + 1/2*a - 8)*q^34 + (a^2 - 3)*q^35 + (a^2 - 3)*q^36 + (-a^2 - 2)*q^37 + O(q^38)
*]> ;  // time = 22.089 seconds




J[167] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 167, 167 ], new_dimensions := [ 2, 12 ], dimensions := [ 2, 12 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -1, -2, -5, 0, -5, -5, 0, 1, 8, 6, -12 ],
[ 2, 3, 4, 11, 0, 9, 3, 0, 1, -6, 2, 34 ]
], hecke_fields := [
x^2 + x - 1,
x^12 - 2*x^11 - 17*x^10 + 33*x^9 + 103*x^8 - 189*x^7 - 277*x^6 + 447*x^5 + 363*x^4 - 433*x^3 - 205*x^2 + 120*x + 9
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 83 ]
], tamagawa_numbers := [
[ 1 ],
[ 83 ]
], torsion_upper_bounds := [ 1, 83 ], torsion_lower_bounds := [ 1, 83 ], l_ratios := [ 0, 1/83 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a - 1,
-1,
a - 2,
0,
-a - 3,
a - 2,
4*a + 2,
-a,
-2*a + 3,
-2*a + 2,
2*a - 5
],
[
a,
544/933*a^11 + 157/933*a^10 - 10187/933*a^9 - 1063/311*a^8 + 68788/933*a^7 + 7637/311*a^6 - 200347/933*a^5 - 23356/311*a^4 + 76833/311*a^3 + 80543/933*a^2 - 60181/933*a - 1147/311,
-779/933*a^11 + 631/933*a^10 + 13207/933*a^9 - 2957/311*a^8 - 78341/933*a^7 + 12545/311*a^6 + 193997/933*a^5 - 13559/311*a^4 - 64281/311*a^3 - 12787/933*a^2 + 42281/933*a + 1204/311,
-98/311*a^11 - 34/311*a^10 + 1802/311*a^9 + 754/311*a^8 - 11866/311*a^7 - 5855/311*a^6 + 33461/311*a^5 + 18902/311*a^4 - 37164/311*a^3 - 21634/311*a^2 + 8350/311*a + 2112/311,
-623/933*a^11 + 628/933*a^10 + 10567/933*a^9 - 3008/311*a^8 - 62594/933*a^7 + 13132/311*a^6 + 154004/933*a^5 - 15052/311*a^4 - 49696/311*a^3 - 12775/933*a^2 + 24248/933*a + 1943/311,
652/933*a^11 - 491/933*a^10 - 11297/933*a^9 + 2227/311*a^8 + 69355/933*a^7 - 8631/311*a^6 - 182461/933*a^5 + 5275/311*a^4 + 67433/311*a^3 + 30887/933*a^2 - 59101/933*a - 755/311,
7/933*a^11 + 580/933*a^10 - 884/933*a^9 - 3202/311*a^8 + 12088/933*a^7 + 18170/311*a^6 - 54838/933*a^5 - 41428/311*a^4 + 26298/311*a^3 + 107774/933*a^2 - 19834/933*a - 3027/311,
973/933*a^11 + 382/933*a^10 - 18380/933*a^9 - 2525/311*a^8 + 125854/933*a^7 + 17726/311*a^6 - 374938/933*a^5 - 52886/311*a^4 + 149519/311*a^3 + 179474/933*a^2 - 131464/933*a - 4635/311,
125/933*a^11 - 1372/933*a^10 - 58/933*a^9 + 7154/311*a^8 - 17926/933*a^7 - 37362/311*a^6 + 112360/933*a^5 + 74590/311*a^4 - 63980/311*a^3 - 164318/933*a^2 + 79000/933*a + 2815/311,
938/933*a^11 - 1585/933*a^10 - 14893/933*a^9 + 7887/311*a^8 + 79409/933*a^7 - 37670/311*a^6 - 164192/933*a^5 + 60643/311*a^4 + 42909/311*a^3 - 78563/933*a^2 - 10835/933*a + 237/311,
1466/933*a^11 - 1021/933*a^10 - 25192/933*a^9 + 4724/311*a^8 + 152156/933*a^7 - 19272/311*a^6 - 385676/933*a^5 + 16332/311*a^4 + 130096/311*a^3 + 48868/933*a^2 - 83927/933*a - 2166/311,
91/311*a^11 - 235/311*a^10 - 1229/311*a^9 + 3565/311*a^8 + 4443/311*a^7 - 17555/311*a^6 - 393/311*a^5 + 31053/311*a^4 - 10941/311*a^3 - 19897/311*a^2 + 4953/311*a + 2304/311
]
*], q_expansions := [*
q + a*q^2 + (-a - 1)*q^3 + (-a - 1)*q^4 - q^5 - q^6 + (a - 2)*q^7 + (-2*a - 1)*q^8 + (a - 1)*q^9 - a*q^10 + (a + 2)*q^12 + (-a - 3)*q^13 + (-3*a + 1)*q^14 + (a + 1)*q^15 + 3*a*q^16 + (a - 2)*q^17 + (-2*a + 1)*q^18 + (4*a + 2)*q^19 + (a + 1)*q^20 + (2*a + 1)*q^21 - a*q^23 + (a + 3)*q^24 - 4*q^25 + (-2*a - 1)*q^26 + (4*a + 3)*q^27 + (2*a + 1)*q^28 + (-2*a + 3)*q^29 + q^30 + (-2*a + 2)*q^31 + (a + 5)*q^32 + (-3*a + 1)*q^34 + (-a + 2)*q^35 + a*q^36 + (2*a - 5)*q^37 + O(q^38),
q + a*q^2 + (544/933*a^11 + 157/933*a^10 - 10187/933*a^9 - 1063/311*a^8 + 68788/933*a^7 + 7637/311*a^6 - 200347/933*a^5 - 23356/311*a^4 + 76833/311*a^3 + 80543/933*a^2 - 60181/933*a - 1147/311)*q^3 + (a^2 - 2)*q^4 + (-779/933*a^11 + 631/933*a^10 + 13207/933*a^9 - 2957/311*a^8 - 78341/933*a^7 + 12545/311*a^6 + 193997/933*a^5 - 13559/311*a^4 - 64281/311*a^3 - 12787/933*a^2 + 42281/933*a + 1204/311)*q^5 + (415/311*a^11 - 313/311*a^10 - 7047/311*a^9 + 4252/311*a^8 + 41909/311*a^7 - 16553/311*a^6 - 104412/311*a^5 + 11009/311*a^4 + 105365/311*a^3 + 17113/311*a^2 - 22907/311*a - 1632/311)*q^6 + (-98/311*a^11 - 34/311*a^10 + 1802/311*a^9 + 754/311*a^8 - 11866/311*a^7 - 5855/311*a^6 + 33461/311*a^5 + 18902/311*a^4 - 37164/311*a^3 - 21634/311*a^2 + 8350/311*a + 2112/311)*q^7 + (a^3 - 4*a)*q^8 + (-324/311*a^11 + 78/311*a^10 + 5818/311*a^9 - 687/311*a^8 - 37466/311*a^7 - 1002/311*a^6 + 104330/311*a^5 + 19422/311*a^4 - 119105/311*a^3 - 33278/311*a^2 + 32836/311*a + 1759/311)*q^9 + (-309/311*a^11 - 12/311*a^10 + 5612/311*a^9 + 632/311*a^8 - 36532/311*a^7 - 7262/311*a^6 + 102512/311*a^5 + 29978/311*a^4 - 116698/311*a^3 - 39138/311*a^2 + 32364/311*a + 2337/311)*q^10 + (-623/933*a^11 + 628/933*a^10 + 10567/933*a^9 - 3008/311*a^8 - 62594/933*a^7 + 13132/311*a^6 + 154004/933*a^5 - 15052/311*a^4 - 49696/311*a^3 - 12775/933*a^2 + 24248/933*a + 1943/311)*q^11 + (463/933*a^11 - 290/933*a^10 - 7955/933*a^9 + 1290/311*a^8 + 48070/933*a^7 - 4731/311*a^6 - 122794/933*a^5 + 1432/311*a^4 + 43142/311*a^3 + 25418/933*a^2 - 33934/933*a - 1441/311)*q^12 + (652/933*a^11 - 491/933*a^10 - 11297/933*a^9 + 2227/311*a^8 + 69355/933*a^7 - 8631/311*a^6 - 182461/933*a^5 + 5275/311*a^4 + 67433/311*a^3 + 30887/933*a^2 - 59101/933*a - 755/311)*q^13 + (-230/311*a^11 + 136/311*a^10 + 3988/311*a^9 - 1772/311*a^8 - 24377/311*a^7 + 6315/311*a^6 + 62708/311*a^5 - 1590/311*a^4 - 64068/311*a^3 - 11740/311*a^2 + 13872/311*a + 882/311)*q^14 + (2158/933*a^11 - 2063/933*a^10 - 36209/933*a^9 + 9713/311*a^8 + 211147/933*a^7 - 41277/311*a^6 - 508297/933*a^5 + 44605/311*a^4 + 161381/311*a^3 + 35309/933*a^2 - 83227/933*a - 1647/311)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (7/933*a^11 + 580/933*a^10 - 884/933*a^9 - 3202/311*a^8 + 12088/933*a^7 + 18170/311*a^6 - 54838/933*a^5 - 41428/311*a^4 + 26298/311*a^3 + 107774/933*a^2 - 19834/933*a - 3027/311)*q^17 + (-570/311*a^11 + 310/311*a^10 + 10005/311*a^9 - 4094/311*a^8 - 62238/311*a^7 + 14582/311*a^6 + 164250/311*a^5 - 1493/311*a^4 - 173570/311*a^3 - 33584/311*a^2 + 40639/311*a + 2916/311)*q^18 + (973/933*a^11 + 382/933*a^10 - 18380/933*a^9 - 2525/311*a^8 + 125854/933*a^7 + 17726/311*a^6 - 374938/933*a^5 - 52886/311*a^4 + 149519/311*a^3 + 179474/933*a^2 - 131464/933*a - 4635/311)*q^19 + (-332/933*a^11 - 185/933*a^10 + 6073/933*a^9 + 1209/311*a^8 - 40307/933*a^7 - 8171/311*a^6 + 116309/933*a^5 + 22587/311*a^4 - 44373/311*a^3 - 67369/933*a^2 + 33689/933*a + 373/311)*q^20 + (510/311*a^11 + 50/311*a^10 - 9492/311*a^9 - 1493/311*a^8 + 63789/311*a^7 + 13879/311*a^6 - 185901/311*a^5 - 51305/311*a^4 + 218367/311*a^3 + 65732/311*a^2 - 63320/311*a - 3051/311)*q^21 + (-206/311*a^11 - 8/311*a^10 + 3845/311*a^9 + 525/311*a^8 - 26117/311*a^7 - 6189/311*a^6 + 77775/311*a^5 + 25687/311*a^4 - 94178/311*a^3 - 34489/311*a^2 + 26863/311*a + 1869/311)*q^22 + (125/933*a^11 - 1372/933*a^10 - 58/933*a^9 + 7154/311*a^8 - 17926/933*a^7 - 37362/311*a^6 + 112360/933*a^5 + 74590/311*a^4 - 63980/311*a^3 - 164318/933*a^2 + 79000/933*a + 2815/311)*q^23 + (-618/311*a^11 + 598/311*a^10 + 10291/311*a^9 - 8377/311*a^8 - 59380/311*a^7 + 34925/311*a^6 + 141269/311*a^5 - 34899/311*a^4 - 135431/311*a^3 - 13899/311*a^2 + 25853/311*a + 1875/311)*q^24 + (-2245/933*a^11 + 719/933*a^10 + 40265/933*a^9 - 2705/311*a^8 - 258487/933*a^7 + 5071/311*a^6 + 714025/933*a^5 + 25467/311*a^4 - 266529/311*a^3 - 184811/933*a^2 + 212977/933*a + 3681/311)*q^25 + (271/311*a^11 - 71/311*a^10 - 4945/311*a^9 + 733/311*a^8 + 32445/311*a^7 - 619/311*a^6 - 91873/311*a^5 - 11459/311*a^4 + 104401/311*a^3 + 24853/311*a^2 - 26835/311*a - 1956/311)*q^26 + (167/933*a^11 + 2108/933*a^10 - 6295/933*a^9 - 11125/311*a^8 + 67664/933*a^7 + 58907/311*a^6 - 277313/933*a^5 - 119864/311*a^4 + 131439/311*a^3 + 272401/933*a^2 - 137036/933*a - 5084/311)*q^27 + (-128/311*a^11 + 146/311*a^10 + 2214/311*a^9 - 2195/311*a^8 - 13423/311*a^7 + 10708/311*a^6 + 34298/311*a^5 - 18382/311*a^4 - 37002/311*a^3 + 9990/311*a^2 + 11782/311*a - 2154/311)*q^28 + (938/933*a^11 - 1585/933*a^10 - 14893/933*a^9 + 7887/311*a^8 + 79409/933*a^7 - 37670/311*a^6 - 164192/933*a^5 + 60643/311*a^4 + 42909/311*a^3 - 78563/933*a^2 - 10835/933*a + 237/311)*q^29 + (751/311*a^11 + 159/311*a^10 - 14025/311*a^9 - 3709/311*a^8 + 94677/311*a^7 + 29823/311*a^6 - 276937/311*a^5 - 99737/311*a^4 + 323241/311*a^3 + 119721/311*a^2 - 87967/311*a - 6474/311)*q^30 + (1466/933*a^11 - 1021/933*a^10 - 25192/933*a^9 + 4724/311*a^8 + 152156/933*a^7 - 19272/311*a^6 - 385676/933*a^5 + 16332/311*a^4 + 130096/311*a^3 + 48868/933*a^2 - 83927/933*a - 2166/311)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-124/311*a^11 - 500/311*a^10 + 3175/311*a^9 + 8088/311*a^8 - 28330/311*a^7 - 44557/311*a^6 + 105281/311*a^5 + 98176/311*a^4 - 144754/311*a^3 - 84147/311*a^2 + 47276/311*a + 5008/311)*q^33 + (198/311*a^11 - 255/311*a^10 - 3279/311*a^9 + 3789/311*a^8 + 18611/311*a^7 - 17633/311*a^6 - 42471/311*a^5 + 25451/311*a^4 + 36935/311*a^3 - 6133/311*a^2 - 3307/311*a - 21/311)*q^34 + (-673/311*a^11 + 306/311*a^10 + 11772/311*a^9 - 3676/311*a^8 - 72964/311*a^7 + 9466/311*a^6 + 191786/311*a^5 + 18970/311*a^4 - 201066/311*a^3 - 57826/311*a^2 + 43652/311*a + 4317/311)*q^35 + (-182/311*a^11 + 159/311*a^10 + 3080/311*a^9 - 2154/311*a^8 - 18216/311*a^7 + 8364/311*a^6 + 44637/311*a^5 - 5504/311*a^4 - 42184/311*a^3 - 9655/311*a^2 + 5644/311*a + 1612/311)*q^36 + (91/311*a^11 - 235/311*a^10 - 1229/311*a^9 + 3565/311*a^8 + 4443/311*a^7 - 17555/311*a^6 - 393/311*a^5 + 31053/311*a^4 - 10941/311*a^3 - 19897/311*a^2 + 4953/311*a + 2304/311)*q^37 + O(q^38)
*]> ;  // time = 1.961 seconds




J[170] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 170, 170, 170, 170, 170, 170, 85, 85, 85, 34, 17 ], new_dimensions := [ 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 2, 2, 4, 4, 2, 4 ], intersection_graph := [ 0, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ -1, -2, -1, 2, 6, 2, 1, 8, -6, -6, 2, 2 ],
[ -1, 3, -1, 2, -4, -3, 1, 3, -6, 9, -3, -8 ],
[ -1, 1, 1, 2, 0, 5, -1, -1, 6, -9, -1, -4 ],
[ -1, -2, 1, -2, -2, -6, 1, -8, -2, 6, -2, 6 ],
[ 1, 1, -1, 2, 0, -1, -1, -1, -6, -3, 5, 8 ],
[ 2, -1, 2, 2, -8, 5, 2, -1, -2, 1, -9, -6 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 + x - 4
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ 1, -1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 1, 3 ],
[ 1, 1, 1 ],
[ 3, 3, 1 ],
[ 1, 1, 1 ],
[ 21, 3, 1 ],
[ 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 3 ],
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 21, 1, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 3, 1, 3, 1, 3, 1 ], torsion_lower_bounds := [ 3, 1, 3, 1, 3, 1 ], l_ratios := [ 1/3, 1, 1/3, 0, 7/3, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 0, 1, 1 ], eigenvalues := [*
[ -1, -2, -1, 2, 6, 2, 1, 8, -6, -6, 2, 2 ],
[ -1, 3, -1, 2, -4, -3, 1, 3, -6, 9, -3, -8 ],
[ -1, 1, 1, 2, 0, 5, -1, -1, 6, -9, -1, -4 ],
[ -1, -2, 1, -2, -2, -6, 1, -8, -2, 6, -2, 6 ],
[ 1, 1, -1, 2, 0, -1, -1, -1, -6, -3, 5, 8 ],
[
1,
a,
1,
-2*a,
-4,
-a + 2,
1,
a,
2*a,
3*a + 2,
a - 4,
2*a - 2
]
*], q_expansions := [*
q - q^2 - 2*q^3 + q^4 - q^5 + 2*q^6 + 2*q^7 - q^8 + q^9 + q^10 + 6*q^11 - 2*q^12 + 2*q^13 - 2*q^14 + 2*q^15 + q^16 + q^17 - q^18 + 8*q^19 - q^20 - 4*q^21 - 6*q^22 - 6*q^23 + 2*q^24 + q^25 - 2*q^26 + 4*q^27 + 2*q^28 - 6*q^29 - 2*q^30 + 2*q^31 - q^32 - 12*q^33 - q^34 - 2*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 + 3*q^3 + q^4 - q^5 - 3*q^6 + 2*q^7 - q^8 + 6*q^9 + q^10 - 4*q^11 + 3*q^12 - 3*q^13 - 2*q^14 - 3*q^15 + q^16 + q^17 - 6*q^18 + 3*q^19 - q^20 + 6*q^21 + 4*q^22 - 6*q^23 - 3*q^24 + q^25 + 3*q^26 + 9*q^27 + 2*q^28 + 9*q^29 + 3*q^30 - 3*q^31 - q^32 - 12*q^33 - q^34 - 2*q^35 + 6*q^36 - 8*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + q^5 - q^6 + 2*q^7 - q^8 - 2*q^9 - q^10 + q^12 + 5*q^13 - 2*q^14 + q^15 + q^16 - q^17 + 2*q^18 - q^19 + q^20 + 2*q^21 + 6*q^23 - q^24 + q^25 - 5*q^26 - 5*q^27 + 2*q^28 - 9*q^29 - q^30 - q^31 - q^32 + q^34 + 2*q^35 - 2*q^36 - 4*q^37 + O(q^38),
q - q^2 - 2*q^3 + q^4 + q^5 + 2*q^6 - 2*q^7 - q^8 + q^9 - q^10 - 2*q^11 - 2*q^12 - 6*q^13 + 2*q^14 - 2*q^15 + q^16 + q^17 - q^18 - 8*q^19 + q^20 + 4*q^21 + 2*q^22 - 2*q^23 + 2*q^24 + q^25 + 6*q^26 + 4*q^27 - 2*q^28 + 6*q^29 + 2*q^30 - 2*q^31 - q^32 + 4*q^33 - q^34 - 2*q^35 + q^36 + 6*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - q^5 + q^6 + 2*q^7 + q^8 - 2*q^9 - q^10 + q^12 - q^13 + 2*q^14 - q^15 + q^16 - q^17 - 2*q^18 - q^19 - q^20 + 2*q^21 - 6*q^23 + q^24 + q^25 - q^26 - 5*q^27 + 2*q^28 - 3*q^29 - q^30 + 5*q^31 + q^32 - q^34 - 2*q^35 - 2*q^36 + 8*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + q^5 + a*q^6 - 2*a*q^7 + q^8 + (-a + 1)*q^9 + q^10 - 4*q^11 + a*q^12 + (-a + 2)*q^13 - 2*a*q^14 + a*q^15 + q^16 + q^17 + (-a + 1)*q^18 + a*q^19 + q^20 + (2*a - 8)*q^21 - 4*q^22 + 2*a*q^23 + a*q^24 + q^25 + (-a + 2)*q^26 + (-a - 4)*q^27 - 2*a*q^28 + (3*a + 2)*q^29 + a*q^30 + (a - 4)*q^31 + q^32 - 4*a*q^33 + q^34 - 2*a*q^35 + (-a + 1)*q^36 + (2*a - 2)*q^37 + O(q^38)
*]> ;  // time = 50.219 seconds




J[173] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 173, 173 ], new_dimensions := [ 4, 10 ], dimensions := [ 4, 10 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -6, -1, -9, -5, -5, 2, -7, -11, 9, 3, -14 ],
[ 1, 8, 1, 11, 5, 1, -2, 7, 5, -5, 3, 8 ]
], hecke_fields := [
x^4 + x^3 - 3*x^2 - x + 1,
x^10 - x^9 - 16*x^8 + 16*x^7 + 85*x^6 - 80*x^5 - 175*x^4 + 136*x^3 + 138*x^2 - 71*x - 25
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 43 ]
], tamagawa_numbers := [
[ 1 ],
[ 43 ]
], torsion_upper_bounds := [ 1, 43 ], torsion_lower_bounds := [ 1, 43 ], l_ratios := [ 0, 1/43 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^2 - a,
a^2 - 2,
a^3 + a^2 - 3*a - 3,
-3*a^3 - 4*a^2 + 6*a + 2,
-4*a^3 - 5*a^2 + 10*a + 3,
4*a^3 + 5*a^2 - 7*a - 3,
2*a^3 + 3*a^2 - 2*a - 4,
3*a^3 + 2*a^2 - 8*a - 3,
-2*a^3 - 2*a^2 + 3*a + 3,
2*a^3 + 4*a^2 - a - 3,
3*a^3 - a^2 - 10*a + 1
],
[
a,
9/116*a^9 - 11/58*a^8 - 69/58*a^7 + 81/29*a^6 + 645/116*a^5 - 1439/116*a^4 - 235/29*a^3 + 465/29*a^2 + 98/29*a - 303/116,
-7/58*a^9 + 15/29*a^8 + 44/29*a^7 - 213/29*a^6 - 231/58*a^5 + 1783/58*a^4 - 179/29*a^3 - 1023/29*a^2 + 376/29*a + 371/58,
-1/58*a^9 - 37/116*a^8 + 79/116*a^7 + 537/116*a^6 - 849/116*a^5 - 579/29*a^4 + 3125/116*a^3 + 2767/116*a^2 - 2913/116*a - 387/116,
23/116*a^9 + 5/116*a^8 - 343/116*a^7 - 71/116*a^6 + 400/29*a^5 + 389/116*a^4 - 2399/116*a^3 - 921/116*a^2 + 715/116*a + 275/58,
-25/116*a^9 - 13/116*a^8 + 393/116*a^7 + 173/116*a^6 - 1007/58*a^5 - 791/116*a^4 + 3755/116*a^3 + 1455/116*a^2 - 2265/116*a - 140/29,
-5/58*a^9 + 9/58*a^8 + 67/58*a^7 - 151/58*a^6 - 126/29*a^5 + 735/58*a^4 + 171/58*a^3 - 927/58*a^2 + 127/58*a + 31/29,
-47/116*a^9 + 73/116*a^8 + 653/116*a^7 - 1083/116*a^6 - 1283/58*a^5 + 4647/116*a^4 + 2141/116*a^3 - 5141/116*a^2 + 463/116*a + 224/29,
5/58*a^9 + 10/29*a^8 - 48/29*a^7 - 142/29*a^6 + 687/58*a^5 + 1237/58*a^4 - 1028/29*a^3 - 827/29*a^2 + 908/29*a + 489/58,
1/116*a^9 - 27/58*a^8 + 1/29*a^7 + 183/29*a^6 - 257/116*a^5 - 2815/116*a^4 + 338/29*a^3 + 1215/58*a^2 - 292/29*a + 179/116,
-35/58*a^9 + 17/29*a^8 + 249/29*a^7 - 253/29*a^6 - 2083/58*a^5 + 2129/58*a^4 + 1164/29*a^3 - 1026/29*a^2 - 150/29*a - 1/58,
-53/116*a^9 + 5/29*a^8 + 387/58*a^7 - 171/58*a^6 - 3489/116*a^5 + 1643/116*a^4 + 2481/58*a^3 - 515/29*a^2 - 687/58*a + 547/116
]
*], q_expansions := [*
q + a*q^2 + (-a^2 - a)*q^3 + (a^2 - 2)*q^4 + (a^2 - 2)*q^5 + (-a^3 - a^2)*q^6 + (a^3 + a^2 - 3*a - 3)*q^7 + (a^3 - 4*a)*q^8 + (a^3 + 4*a^2 + a - 4)*q^9 + (a^3 - 2*a)*q^10 + (-3*a^3 - 4*a^2 + 6*a + 2)*q^11 + (-a^2 + a + 1)*q^12 + (-4*a^3 - 5*a^2 + 10*a + 3)*q^13 + (-2*a - 1)*q^14 + (-a^2 + a + 1)*q^15 + (-a^3 - 3*a^2 + a + 3)*q^16 + (4*a^3 + 5*a^2 - 7*a - 3)*q^17 + (3*a^3 + 4*a^2 - 3*a - 1)*q^18 + (2*a^3 + 3*a^2 - 2*a - 4)*q^19 + (-a^3 - a^2 + a + 3)*q^20 + (2*a^2 + 3*a + 1)*q^21 + (-a^3 - 3*a^2 - a + 3)*q^22 + (3*a^3 + 2*a^2 - 8*a - 3)*q^23 + (a^3 + 3*a^2 + a)*q^24 + (-a^3 - a^2 + a - 2)*q^25 + (-a^3 - 2*a^2 - a + 4)*q^26 + (-4*a^3 - 7*a^2 + 4*a + 4)*q^27 + (-2*a^3 - 4*a^2 + 5*a + 6)*q^28 + (-2*a^3 - 2*a^2 + 3*a + 3)*q^29 + (-a^3 + a^2 + a)*q^30 + (2*a^3 + 4*a^2 - a - 3)*q^31 + (-4*a^3 - 2*a^2 + 10*a + 1)*q^32 + (3*a^3 + 7*a^2 - a - 4)*q^33 + (a^3 + 5*a^2 + a - 4)*q^34 + (-2*a^3 - 4*a^2 + 5*a + 6)*q^35 + (-a^3 - 2*a^2 + 5)*q^36 + (3*a^3 - a^2 - 10*a + 1)*q^37 + O(q^38),
q + a*q^2 + (9/116*a^9 - 11/58*a^8 - 69/58*a^7 + 81/29*a^6 + 645/116*a^5 - 1439/116*a^4 - 235/29*a^3 + 465/29*a^2 + 98/29*a - 303/116)*q^3 + (a^2 - 2)*q^4 + (-7/58*a^9 + 15/29*a^8 + 44/29*a^7 - 213/29*a^6 - 231/58*a^5 + 1783/58*a^4 - 179/29*a^3 - 1023/29*a^2 + 376/29*a + 371/58)*q^5 + (-13/116*a^9 + 3/58*a^8 + 45/29*a^7 - 30/29*a^6 - 719/116*a^5 + 635/116*a^4 + 159/29*a^3 - 425/58*a^2 + 84/29*a + 225/116)*q^6 + (-1/58*a^9 - 37/116*a^8 + 79/116*a^7 + 537/116*a^6 - 849/116*a^5 - 579/29*a^4 + 3125/116*a^3 + 2767/116*a^2 - 2913/116*a - 387/116)*q^7 + (a^3 - 4*a)*q^8 + (9/29*a^9 - 59/116*a^8 - 523/116*a^7 + 861/116*a^6 + 2261/116*a^5 - 1805/58*a^4 - 2745/116*a^3 + 3641/116*a^2 + 611/116*a + 151/116)*q^9 + (23/58*a^9 - 12/29*a^8 - 157/29*a^7 + 182/29*a^6 + 1223/58*a^5 - 1583/58*a^4 - 547/29*a^3 + 859/29*a^2 - 63/29*a - 175/58)*q^10 + (23/116*a^9 + 5/116*a^8 - 343/116*a^7 - 71/116*a^6 + 400/29*a^5 + 389/116*a^4 - 2399/116*a^3 - 921/116*a^2 + 715/116*a + 275/58)*q^11 + (-25/116*a^9 + 4/29*a^8 + 91/29*a^7 - 131/58*a^6 - 1695/116*a^5 + 1239/116*a^4 + 1399/58*a^3 - 795/58*a^2 - 741/58*a + 281/116)*q^12 + (-25/116*a^9 - 13/116*a^8 + 393/116*a^7 + 173/116*a^6 - 1007/58*a^5 - 791/116*a^4 + 3755/116*a^3 + 1455/116*a^2 - 2265/116*a - 140/29)*q^13 + (-39/116*a^9 + 47/116*a^8 + 569/116*a^7 - 679/116*a^6 - 619/29*a^5 + 2775/116*a^4 + 3039/116*a^3 - 2637/116*a^2 - 529/116*a - 25/58)*q^14 + (-11/29*a^9 + 57/58*a^8 + 289/58*a^7 - 821/58*a^6 - 929/58*a^5 + 1733/29*a^4 - 251/58*a^3 - 3899/58*a^2 + 1597/58*a + 557/58)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-5/58*a^9 + 9/58*a^8 + 67/58*a^7 - 151/58*a^6 - 126/29*a^5 + 735/58*a^4 + 171/58*a^3 - 927/58*a^2 + 127/58*a + 31/29)*q^17 + (-23/116*a^9 + 53/116*a^8 + 285/116*a^7 - 799/116*a^6 - 365/58*a^5 + 3555/116*a^4 - 1255/116*a^3 - 4357/116*a^2 + 2707/116*a + 225/29)*q^18 + (-47/116*a^9 + 73/116*a^8 + 653/116*a^7 - 1083/116*a^6 - 1283/58*a^5 + 4647/116*a^4 + 2141/116*a^3 - 5141/116*a^2 + 463/116*a + 224/29)*q^19 + (13/58*a^9 - 3/29*a^8 - 90/29*a^7 + 60/29*a^6 + 719/58*a^5 - 635/58*a^4 - 347/29*a^3 + 396/29*a^2 - 23/29*a - 167/58)*q^20 + (27/116*a^9 - 31/29*a^8 - 149/58*a^7 + 921/58*a^6 + 311/116*a^5 - 8261/116*a^4 + 1867/58*a^3 + 2758/29*a^2 - 2689/58*a - 3229/116)*q^21 + (7/29*a^9 + 25/116*a^8 - 439/116*a^7 - 355/116*a^6 + 2229/116*a^5 + 813/58*a^4 - 4049/116*a^3 - 2459/116*a^2 + 2183/116*a + 575/116)*q^22 + (5/58*a^9 + 10/29*a^8 - 48/29*a^7 - 142/29*a^6 + 687/58*a^5 + 1237/58*a^4 - 1028/29*a^3 - 827/29*a^2 + 908/29*a + 489/58)*q^23 + (17/116*a^9 - 12/29*a^8 - 111/58*a^7 + 335/58*a^6 + 677/116*a^5 - 2847/116*a^4 + 269/58*a^3 + 917/29*a^2 - 1083/58*a - 1075/116)*q^24 + (6/29*a^9 - 5/29*a^8 - 92/29*a^7 + 71/29*a^6 + 430/29*a^5 - 302/29*a^4 - 588/29*a^3 + 399/29*a^2 + 68/29*a - 144/29)*q^25 + (-19/58*a^9 - 7/116*a^8 + 573/116*a^7 + 111/116*a^6 - 2791/116*a^5 - 155/29*a^4 + 4855/116*a^3 + 1185/116*a^2 - 2335/116*a - 625/116)*q^26 + (111/116*a^9 - 107/116*a^8 - 1615/116*a^7 + 1589/116*a^6 + 1793/29*a^5 - 6631/116*a^4 - 9863/116*a^3 + 6207/116*a^2 + 3491/116*a + 263/58)*q^27 + (3/29*a^9 + 19/116*a^8 - 213/116*a^7 - 235/116*a^6 + 1353/116*a^5 + 423/58*a^4 - 3583/116*a^3 - 681/116*a^2 + 3007/116*a - 201/116)*q^28 + (1/116*a^9 - 27/58*a^8 + 1/29*a^7 + 183/29*a^6 - 257/116*a^5 - 2815/116*a^4 + 338/29*a^3 + 1215/58*a^2 - 292/29*a + 179/116)*q^29 + (35/58*a^9 - 63/58*a^8 - 469/58*a^7 + 941/58*a^6 + 853/29*a^5 - 4101/58*a^4 - 907/58*a^3 + 4633/58*a^2 - 1005/58*a - 275/29)*q^30 + (-35/58*a^9 + 17/29*a^8 + 249/29*a^7 - 253/29*a^6 - 2083/58*a^5 + 2129/58*a^4 + 1164/29*a^3 - 1026/29*a^2 - 150/29*a - 1/58)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (9/29*a^9 - 59/116*a^8 - 523/116*a^7 + 861/116*a^6 + 2261/116*a^5 - 1863/58*a^4 - 2629/116*a^3 + 4569/116*a^2 + 31/116*a - 1125/116)*q^33 + (2/29*a^9 - 13/58*a^8 - 71/58*a^7 + 173/58*a^6 + 335/58*a^5 - 352/29*a^4 - 247/58*a^3 + 817/58*a^2 - 293/58*a - 125/58)*q^34 + (-16/29*a^9 + 23/29*a^8 + 226/29*a^7 - 344/29*a^6 - 934/29*a^5 + 1511/29*a^4 + 988/29*a^3 - 1789/29*a^2 + 12/29*a + 239/29)*q^35 + (-21/58*a^9 + 35/116*a^8 + 615/116*a^7 - 497/116*a^6 - 2807/116*a^5 + 485/29*a^4 + 4261/116*a^3 - 1401/116*a^2 - 1955/116*a - 877/116)*q^36 + (-53/116*a^9 + 5/29*a^8 + 387/58*a^7 - 171/58*a^6 - 3489/116*a^5 + 1643/116*a^4 + 2481/58*a^3 - 515/29*a^2 - 687/58*a + 547/116)*q^37 + O(q^38)
*]> ;  // time = 1.931 seconds




J[174] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 174, 174, 174, 174, 174, 87, 87, 58, 58, 29 ], new_dimensions := [ 1, 1, 1, 1, 1, 2, 3, 1, 1, 2 ], dimensions := [ 1, 1, 1, 1, 1, 4, 6, 2, 2, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 0, 5, 1, 1, 1, 1, 1, 1, 1, 1, 5, 0, 1, 1, 11, 1, 7, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 7, 1, 1, 11, 1, 1, 0, 1, 1, 5, 1, 13, 1, 1, 1, 1, 1, 0, 1, 1, 529, 1, 1, 7, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 7, 1, 529, 1, 1, 0 ], ap_traces := [
[ -1, -1, 3, -3, 6, 0, 7, 5, -8, 1, -8, -3 ],
[ -1, 1, 2, 0, -4, 6, -2, 4, 0, -1, -4, -6 ],
[ -1, 1, -3, 5, 6, -4, 3, -1, 0, -1, -4, -1 ],
[ 1, -1, 1, 1, 6, -4, -7, -3, 4, -1, 0, -7 ],
[ 1, 1, -1, 1, -2, 0, -3, -1, -4, 1, 4, 3 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 13, 1, 1 ],
[ 1, 1, 1 ],
[ 11, 21, 1 ],
[ 1, 3, 1 ],
[ 7, 7, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 21, 1 ],
[ 1, 1, 1 ],
[ 7, 7, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 7 ], torsion_lower_bounds := [ 1, 1, 3, 1, 1 ], l_ratios := [ 1, 1, 7/3, 1, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1, 1/49 ], eigenvalues := [*
[ -1, -1, 3, -3, 6, 0, 7, 5, -8, 1, -8, -3 ],
[ -1, 1, 2, 0, -4, 6, -2, 4, 0, -1, -4, -6 ],
[ -1, 1, -3, 5, 6, -4, 3, -1, 0, -1, -4, -1 ],
[ 1, -1, 1, 1, 6, -4, -7, -3, 4, -1, 0, -7 ],
[ 1, 1, -1, 1, -2, 0, -3, -1, -4, 1, 4, 3 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + 3*q^5 + q^6 - 3*q^7 - q^8 + q^9 - 3*q^10 + 6*q^11 - q^12 + 3*q^14 - 3*q^15 + q^16 + 7*q^17 - q^18 + 5*q^19 + 3*q^20 + 3*q^21 - 6*q^22 - 8*q^23 + q^24 + 4*q^25 - q^27 - 3*q^28 + q^29 + 3*q^30 - 8*q^31 - q^32 - 6*q^33 - 7*q^34 - 9*q^35 + q^36 - 3*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + 2*q^5 - q^6 - q^8 + q^9 - 2*q^10 - 4*q^11 + q^12 + 6*q^13 + 2*q^15 + q^16 - 2*q^17 - q^18 + 4*q^19 + 2*q^20 + 4*q^22 - q^24 - q^25 - 6*q^26 + q^27 - q^29 - 2*q^30 - 4*q^31 - q^32 - 4*q^33 + 2*q^34 + q^36 - 6*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - 3*q^5 - q^6 + 5*q^7 - q^8 + q^9 + 3*q^10 + 6*q^11 + q^12 - 4*q^13 - 5*q^14 - 3*q^15 + q^16 + 3*q^17 - q^18 - q^19 - 3*q^20 + 5*q^21 - 6*q^22 - q^24 + 4*q^25 + 4*q^26 + q^27 + 5*q^28 - q^29 + 3*q^30 - 4*q^31 - q^32 + 6*q^33 - 3*q^34 - 15*q^35 + q^36 - q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + q^7 + q^8 + q^9 + q^10 + 6*q^11 - q^12 - 4*q^13 + q^14 - q^15 + q^16 - 7*q^17 + q^18 - 3*q^19 + q^20 - q^21 + 6*q^22 + 4*q^23 - q^24 - 4*q^25 - 4*q^26 - q^27 + q^28 - q^29 - q^30 + q^32 - 6*q^33 - 7*q^34 + q^35 + q^36 - 7*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - q^5 + q^6 + q^7 + q^8 + q^9 - q^10 - 2*q^11 + q^12 + q^14 - q^15 + q^16 - 3*q^17 + q^18 - q^19 - q^20 + q^21 - 2*q^22 - 4*q^23 + q^24 - 4*q^25 + q^27 + q^28 + q^29 - q^30 + 4*q^31 + q^32 - 2*q^33 - 3*q^34 - q^35 + q^36 + 3*q^37 + O(q^38)
*]> ;  // time = 71.159 seconds




J[177] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 177, 177, 177, 177, 59 ], new_dimensions := [ 2, 2, 2, 3, 5 ], dimensions := [ 2, 2, 2, 3, 10 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 31, 1, 1, 1, 0, 229, 1, 1, 31, 229, 0 ], ap_traces := [
[ -1, -2, 0, -7, 0, -8, -3, -5, -7, 15, -1, -7 ],
[ 1, 2, 2, 1, 4, -2, 1, -5, 3, 5, -1, -9 ],
[ -3, 2, -6, -7, -2, 0, -3, -5, -5, -11, -7, -1 ],
[ 0, -3, -2, 9, -2, 4, 3, 7, 1, -11, 13, -5 ]
], hecke_fields := [
x^2 + x - 1,
x^2 - x - 1,
x^2 + 3*x + 1,
x^3 - 4*x - 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 5, 1 ],
[ 31, 1 ],
[ 229, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 5, 1 ],
[ 31, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 5, 1, 1 ], torsion_lower_bounds := [ 1, 5, 1, 1 ], l_ratios := [ 0, 1/5, 0, 1 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1 ], eigenvalues := [*
[
a,
-1,
-2*a - 1,
a - 3,
2*a + 1,
-2*a - 5,
3*a,
5*a,
-a - 4,
-a + 7,
-9*a - 5,
3*a - 2
],
[
a,
1,
1,
-a + 1,
-2*a + 3,
-1,
-3*a + 2,
3*a - 4,
3*a,
-a + 3,
-3*a + 1,
-a - 4
],
[
a,
1,
-3,
-a - 5,
-4*a - 7,
6*a + 9,
a,
3*a + 2,
-a - 4,
-a - 7,
-a - 5,
-5*a - 8
],
[
a,
-1,
-a^2 + a + 2,
a + 3,
-a^2 - a + 2,
-a^2 - a + 4,
3*a^2 - 2*a - 7,
-a^2 + 5,
-a^2 - 2*a + 3,
2*a^2 + a - 9,
2*a^2 - a - 1,
-a^2 - 2*a + 1
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-a - 1)*q^4 + (-2*a - 1)*q^5 - a*q^6 + (a - 3)*q^7 + (-2*a - 1)*q^8 + q^9 + (a - 2)*q^10 + (2*a + 1)*q^11 + (a + 1)*q^12 + (-2*a - 5)*q^13 + (-4*a + 1)*q^14 + (2*a + 1)*q^15 + 3*a*q^16 + 3*a*q^17 + a*q^18 + 5*a*q^19 + (a + 3)*q^20 + (-a + 3)*q^21 + (-a + 2)*q^22 + (-a - 4)*q^23 + (2*a + 1)*q^24 + (-3*a - 2)*q^26 - q^27 + (3*a + 2)*q^28 + (-a + 7)*q^29 + (-a + 2)*q^30 + (-9*a - 5)*q^31 + (a + 5)*q^32 + (-2*a - 1)*q^33 + (-3*a + 3)*q^34 + (7*a + 1)*q^35 + (-a - 1)*q^36 + (3*a - 2)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a - 1)*q^4 + q^5 + a*q^6 + (-a + 1)*q^7 + (-2*a + 1)*q^8 + q^9 + a*q^10 + (-2*a + 3)*q^11 + (a - 1)*q^12 - q^13 - q^14 + q^15 - 3*a*q^16 + (-3*a + 2)*q^17 + a*q^18 + (3*a - 4)*q^19 + (a - 1)*q^20 + (-a + 1)*q^21 + (a - 2)*q^22 + 3*a*q^23 + (-2*a + 1)*q^24 - 4*q^25 - a*q^26 + q^27 + (a - 2)*q^28 + (-a + 3)*q^29 + a*q^30 + (-3*a + 1)*q^31 + (a - 5)*q^32 + (-2*a + 3)*q^33 + (-a - 3)*q^34 + (-a + 1)*q^35 + (a - 1)*q^36 + (-a - 4)*q^37 + O(q^38),
q + a*q^2 + q^3 + (-3*a - 3)*q^4 - 3*q^5 + a*q^6 + (-a - 5)*q^7 + (4*a + 3)*q^8 + q^9 - 3*a*q^10 + (-4*a - 7)*q^11 + (-3*a - 3)*q^12 + (6*a + 9)*q^13 + (-2*a + 1)*q^14 - 3*q^15 + (-3*a + 2)*q^16 + a*q^17 + a*q^18 + (3*a + 2)*q^19 + (9*a + 9)*q^20 + (-a - 5)*q^21 + (5*a + 4)*q^22 + (-a - 4)*q^23 + (4*a + 3)*q^24 + 4*q^25 + (-9*a - 6)*q^26 + q^27 + (9*a + 12)*q^28 + (-a - 7)*q^29 - 3*a*q^30 + (-a - 5)*q^31 + (3*a - 3)*q^32 + (-4*a - 7)*q^33 + (-3*a - 1)*q^34 + (3*a + 15)*q^35 + (-3*a - 3)*q^36 + (-5*a - 8)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 + a + 2)*q^5 - a*q^6 + (a + 3)*q^7 + q^8 + q^9 + (a^2 - 2*a - 1)*q^10 + (-a^2 - a + 2)*q^11 + (-a^2 + 2)*q^12 + (-a^2 - a + 4)*q^13 + (a^2 + 3*a)*q^14 + (a^2 - a - 2)*q^15 + (-2*a^2 + a + 4)*q^16 + (3*a^2 - 2*a - 7)*q^17 + a*q^18 + (-a^2 + 5)*q^19 + (a - 3)*q^20 + (-a - 3)*q^21 + (-a^2 - 2*a - 1)*q^22 + (-a^2 - 2*a + 3)*q^23 - q^24 + (a^2 - 3*a - 3)*q^25 + (-a^2 - 1)*q^26 - q^27 + (3*a^2 + 2*a - 5)*q^28 + (2*a^2 + a - 9)*q^29 + (-a^2 + 2*a + 1)*q^30 + (2*a^2 - a - 1)*q^31 + (a^2 - 4*a - 4)*q^32 + (a^2 + a - 2)*q^33 + (-2*a^2 + 5*a + 3)*q^34 + (-2*a^2 + a + 5)*q^35 + (a^2 - 2)*q^36 + (-a^2 - 2*a + 1)*q^37 + O(q^38)
*]> ;  // time = 17.36 seconds




J[178] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 178, 178, 178, 178, 89, 89, 89 ], new_dimensions := [ 1, 1, 2, 3, 1, 1, 5 ], dimensions := [ 1, 1, 2, 3, 2, 2, 10 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 7, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 25, 7, 1, 1, 1, 1, 25, 0 ], ap_traces := [
[ -1, 2, 2, 0, 0, -4, 2, -2, 8, 0, 0, 0 ],
[ 1, 1, 3, -4, -6, 2, 3, 5, -3, 0, 5, -10 ],
[ -2, -2, -2, -4, -4, -4, -6, 2, -14, 0, 6, 12 ],
[ 3, 1, -1, 0, 6, -2, -5, -11, 5, 4, -19, 10 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + 2*x - 1,
x^3 - x^2 - 8*x + 4
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 7, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 5, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 5, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 5 ], torsion_lower_bounds := [ 1, 3, 1, 5 ], l_ratios := [ 1, 1/3, 0, 1/5 ], analytic_sha_upper_bounds := [ 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 1 ], eigenvalues := [*
[ -1, 2, 2, 0, 0, -4, 2, -2, 8, 0, 0, 0 ],
[ 1, 1, 3, -4, -6, 2, 3, 5, -3, 0, 5, -10 ],
[
-1,
a,
-2*a - 3,
-2,
2*a,
-2,
2*a - 1,
a + 2,
-a - 8,
-4*a - 4,
-a + 2,
4*a + 10
],
[
1,
a,
-a,
-1/2*a^2 - 1/2*a + 3,
2,
1/2*a^2 - 3/2*a - 3,
-a^2 + 4,
a - 4,
3/2*a^2 + 1/2*a - 7,
-3/2*a^2 + 5/2*a + 9,
1/2*a^2 - 1/2*a - 9,
1/2*a^2 - 3/2*a + 1
]
*], q_expansions := [*
q - q^2 + 2*q^3 + q^4 + 2*q^5 - 2*q^6 - q^8 + q^9 - 2*q^10 + 2*q^12 - 4*q^13 + 4*q^15 + q^16 + 2*q^17 - q^18 - 2*q^19 + 2*q^20 + 8*q^23 - 2*q^24 - q^25 + 4*q^26 - 4*q^27 - 4*q^30 - q^32 - 2*q^34 + q^36 + O(q^38),
q + q^2 + q^3 + q^4 + 3*q^5 + q^6 - 4*q^7 + q^8 - 2*q^9 + 3*q^10 - 6*q^11 + q^12 + 2*q^13 - 4*q^14 + 3*q^15 + q^16 + 3*q^17 - 2*q^18 + 5*q^19 + 3*q^20 - 4*q^21 - 6*q^22 - 3*q^23 + q^24 + 4*q^25 + 2*q^26 - 5*q^27 - 4*q^28 + 3*q^30 + 5*q^31 + q^32 - 6*q^33 + 3*q^34 - 12*q^35 - 2*q^36 - 10*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-2*a - 3)*q^5 - a*q^6 - 2*q^7 - q^8 + (-2*a - 2)*q^9 + (2*a + 3)*q^10 + 2*a*q^11 + a*q^12 - 2*q^13 + 2*q^14 + (a - 2)*q^15 + q^16 + (2*a - 1)*q^17 + (2*a + 2)*q^18 + (a + 2)*q^19 + (-2*a - 3)*q^20 - 2*a*q^21 - 2*a*q^22 + (-a - 8)*q^23 - a*q^24 + (4*a + 8)*q^25 + 2*q^26 + (-a - 2)*q^27 - 2*q^28 + (-4*a - 4)*q^29 + (-a + 2)*q^30 + (-a + 2)*q^31 - q^32 + (-4*a + 2)*q^33 + (-2*a + 1)*q^34 + (4*a + 6)*q^35 + (-2*a - 2)*q^36 + (4*a + 10)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - a*q^5 + a*q^6 + (-1/2*a^2 - 1/2*a + 3)*q^7 + q^8 + (a^2 - 3)*q^9 - a*q^10 + 2*q^11 + a*q^12 + (1/2*a^2 - 3/2*a - 3)*q^13 + (-1/2*a^2 - 1/2*a + 3)*q^14 - a^2*q^15 + q^16 + (-a^2 + 4)*q^17 + (a^2 - 3)*q^18 + (a - 4)*q^19 - a*q^20 + (-a^2 - a + 2)*q^21 + 2*q^22 + (3/2*a^2 + 1/2*a - 7)*q^23 + a*q^24 + (a^2 - 5)*q^25 + (1/2*a^2 - 3/2*a - 3)*q^26 + (a^2 + 2*a - 4)*q^27 + (-1/2*a^2 - 1/2*a + 3)*q^28 + (-3/2*a^2 + 5/2*a + 9)*q^29 - a^2*q^30 + (1/2*a^2 - 1/2*a - 9)*q^31 + q^32 + 2*a*q^33 + (-a^2 + 4)*q^34 + (a^2 + a - 2)*q^35 + (a^2 - 3)*q^36 + (1/2*a^2 - 3/2*a + 1)*q^37 + O(q^38)
*]> ;  // time = 26.441 seconds




J[179] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 179, 179, 179 ], new_dimensions := [ 1, 3, 11 ], dimensions := [ 1, 3, 11 ], intersection_graph := [ 0, 1, 9, 1, 0, 1, 9, 1, 0 ], ap_traces := [
[ 2, 0, 3, -4, 4, -1, 1, -3, 6, 3, -8, 2 ],
[ -1, -2, -4, -4, -3, -11, 2, -9, 9, -1, -1, -2 ],
[ -3, 0, 3, 8, -9, 24, 7, 20, -9, 6, 13, 0 ]
], hecke_fields := [
x - 1,
x^3 + x^2 - 2*x - 1,
x^11 + 3*x^10 - 14*x^9 - 45*x^8 + 59*x^7 + 225*x^6 - 58*x^5 - 427*x^4 - 76*x^3 + 240*x^2 + 56*x - 16
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 89 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 89 ]
], torsion_upper_bounds := [ 1, 1, 89 ], torsion_lower_bounds := [ 1, 1, 89 ], l_ratios := [ 1, 0, 1/89 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ 2, 0, 3, -4, 4, -1, 1, -3, 6, 3, -8, 2 ],
[
a,
-a - 1,
-a^2 - a,
a - 1,
2*a^2 + a - 4,
-a^2 - 2,
5*a^2 + 2*a - 7,
-3*a^2 + 2,
-3*a^2 + 8,
-5*a^2 + 8,
-5*a - 2,
3*a^2 - 4*a - 7
],
[
a,
-21/68*a^10 - 1/2*a^9 + 345/68*a^8 + 471/68*a^7 - 57/2*a^6 - 514/17*a^5 + 4241/68*a^4 + 2993/68*a^3 - 2895/68*a^2 - 311/34*a + 45/17,
-3/136*a^10 - 1/8*a^9 + 21/68*a^8 + 247/136*a^7 - 13/8*a^6 - 1151/136*a^5 + 309/68*a^4 + 1841/136*a^3 - 223/34*a^2 - 157/34*a + 53/17,
7/68*a^10 + 1/4*a^9 - 49/34*a^8 - 259/68*a^7 + 25/4*a^6 + 1303/68*a^5 - 279/34*a^4 - 2369/68*a^3 - 18/17*a^2 + 270/17*a + 36/17,
5/17*a^10 + 1/2*a^9 - 157/34*a^8 - 117/17*a^7 + 49/2*a^6 + 1009/34*a^5 - 1703/34*a^4 - 711/17*a^3 + 1041/34*a^2 + 123/17*a - 4/17,
-1/8*a^10 - 1/8*a^9 + 2*a^8 + 13/8*a^7 - 89/8*a^6 - 51/8*a^5 + 51/2*a^4 + 59/8*a^3 - 81/4*a^2 - a + 3,
39/136*a^10 + 3/8*a^9 - 81/17*a^8 - 695/136*a^7 + 219/8*a^6 + 3029/136*a^5 - 2119/34*a^4 - 4689/136*a^3 + 2993/68*a^2 + 375/34*a + 8/17,
79/136*a^10 + 7/8*a^9 - 319/34*a^8 - 1631/136*a^7 + 415/8*a^6 + 7065/136*a^5 - 1928/17*a^4 - 10377/136*a^3 + 5687/68*a^2 + 621/34*a - 166/17,
-22/17*a^10 - 2*a^9 + 359/17*a^8 + 474/17*a^7 - 118*a^6 - 2111/17*a^5 + 4413/17*a^4 + 3278/17*a^3 - 3164/17*a^2 - 1041/17*a + 242/17,
155/136*a^10 + 13/8*a^9 - 1289/68*a^8 - 3083/136*a^7 + 873/8*a^6 + 13727/136*a^5 - 17189/68*a^4 - 21293/136*a^3 + 3429/17*a^2 + 857/17*a - 415/17,
31/68*a^10 + 1/2*a^9 - 519/68*a^8 - 433/68*a^7 + 89/2*a^6 + 405/17*a^5 - 7219/68*a^4 - 1627/68*a^3 + 6197/68*a^2 - 161/34*a - 166/17,
13/17*a^10 + 3/2*a^9 - 415/34*a^8 - 362/17*a^7 + 133/2*a^6 + 3317/34*a^5 - 4829/34*a^4 - 2702/17*a^3 + 3305/34*a^2 + 1010/17*a - 126/17
]
*], q_expansions := [*
q + 2*q^2 + 2*q^4 + 3*q^5 - 4*q^7 - 3*q^9 + 6*q^10 + 4*q^11 - q^13 - 8*q^14 - 4*q^16 + q^17 - 6*q^18 - 3*q^19 + 6*q^20 + 8*q^22 + 6*q^23 + 4*q^25 - 2*q^26 - 8*q^28 + 3*q^29 - 8*q^31 - 8*q^32 + 2*q^34 - 12*q^35 - 6*q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (a^2 - 2)*q^4 + (-a^2 - a)*q^5 + (-a^2 - a)*q^6 + (a - 1)*q^7 + (-a^2 - 2*a + 1)*q^8 + (a^2 + 2*a - 2)*q^9 + (-2*a - 1)*q^10 + (2*a^2 + a - 4)*q^11 + q^12 + (-a^2 - 2)*q^13 + (a^2 - a)*q^14 + (a^2 + 3*a + 1)*q^15 + (-3*a^2 - a + 3)*q^16 + (5*a^2 + 2*a - 7)*q^17 + (a^2 + 1)*q^18 + (-3*a^2 + 2)*q^19 + a*q^20 + (-a^2 + 1)*q^21 + (-a^2 + 2)*q^22 + (-3*a^2 + 8)*q^23 + (2*a^2 + 3*a)*q^24 + (2*a^2 + 3*a - 4)*q^25 + (a^2 - 4*a - 1)*q^26 + (-2*a^2 + a + 4)*q^27 + (-2*a^2 + 3)*q^28 + (-5*a^2 + 8)*q^29 + (2*a^2 + 3*a + 1)*q^30 + (-5*a - 2)*q^31 + (4*a^2 + a - 5)*q^32 + (-a^2 - a + 2)*q^33 + (-3*a^2 + 3*a + 5)*q^34 + (a^2 - a - 1)*q^35 + (-3*a^2 - a + 5)*q^36 + (3*a^2 - 4*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-21/68*a^10 - 1/2*a^9 + 345/68*a^8 + 471/68*a^7 - 57/2*a^6 - 514/17*a^5 + 4241/68*a^4 + 2993/68*a^3 - 2895/68*a^2 - 311/34*a + 45/17)*q^3 + (a^2 - 2)*q^4 + (-3/136*a^10 - 1/8*a^9 + 21/68*a^8 + 247/136*a^7 - 13/8*a^6 - 1151/136*a^5 + 309/68*a^4 + 1841/136*a^3 - 223/34*a^2 - 157/34*a + 53/17)*q^5 + (29/68*a^10 + 3/4*a^9 - 237/34*a^8 - 699/68*a^7 + 157/4*a^6 + 3023/68*a^5 - 2987/34*a^4 - 4491/68*a^3 + 2209/34*a^2 + 339/17*a - 84/17)*q^6 + (7/68*a^10 + 1/4*a^9 - 49/34*a^8 - 259/68*a^7 + 25/4*a^6 + 1303/68*a^5 - 279/34*a^4 - 2369/68*a^3 - 18/17*a^2 + 270/17*a + 36/17)*q^7 + (a^3 - 4*a)*q^8 + (-12/17*a^10 - 5/4*a^9 + 757/68*a^8 + 599/34*a^7 - 237/4*a^6 - 5445/68*a^5 + 8205/68*a^4 + 4409/34*a^3 - 5041/68*a^2 - 1641/34*a + 115/17)*q^9 + (-1/17*a^10 + 14/17*a^8 - 11/34*a^7 - 7/2*a^6 + 111/34*a^5 + 70/17*a^4 - 140/17*a^3 + 23/34*a^2 + 74/17*a - 6/17)*q^10 + (5/17*a^10 + 1/2*a^9 - 157/34*a^8 - 117/17*a^7 + 49/2*a^6 + 1009/34*a^5 - 1703/34*a^4 - 711/17*a^3 + 1041/34*a^2 + 123/17*a - 4/17)*q^11 + (3/34*a^10 - 21/17*a^8 + 4/17*a^7 + 11/2*a^6 - 45/17*a^5 - 295/34*a^4 + 159/17*a^3 + 93/34*a^2 - 179/17*a + 26/17)*q^12 + (-1/8*a^10 - 1/8*a^9 + 2*a^8 + 13/8*a^7 - 89/8*a^6 - 51/8*a^5 + 51/2*a^4 + 59/8*a^3 - 81/4*a^2 - a + 3)*q^13 + (-1/17*a^10 + 14/17*a^8 + 3/17*a^7 - 4*a^6 - 38/17*a^5 + 155/17*a^4 + 115/17*a^3 - 150/17*a^2 - 62/17*a + 28/17)*q^14 + (35/34*a^10 + 7/4*a^9 - 1133/68*a^8 - 418/17*a^7 + 369/4*a^6 + 7573/68*a^5 - 13655/68*a^4 - 3075/17*a^3 + 9701/68*a^2 + 1170/17*a - 252/17)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (39/136*a^10 + 3/8*a^9 - 81/17*a^8 - 695/136*a^7 + 219/8*a^6 + 3029/136*a^5 - 2119/34*a^4 - 4689/136*a^3 + 2993/68*a^2 + 375/34*a + 8/17)*q^17 + (59/68*a^10 + 5/4*a^9 - 481/34*a^8 - 1197/68*a^7 + 315/4*a^6 + 5421/68*a^5 - 5839/34*a^4 - 8689/68*a^3 + 4119/34*a^2 + 787/17*a - 192/17)*q^18 + (79/136*a^10 + 7/8*a^9 - 319/34*a^8 - 1631/136*a^7 + 415/8*a^6 + 7065/136*a^5 - 1928/17*a^4 - 10377/136*a^3 + 5687/68*a^2 + 621/34*a - 166/17)*q^19 + (15/68*a^10 + 1/4*a^9 - 61/17*a^8 - 249/68*a^7 + 79/4*a^6 + 1199/68*a^5 - 1443/34*a^4 - 2099/68*a^3 + 537/17*a^2 + 207/17*a - 122/17)*q^20 + (-75/68*a^10 - 7/4*a^9 + 305/17*a^8 + 1687/68*a^7 - 399/4*a^6 - 7729/68*a^5 + 3701/17*a^4 + 12637/68*a^3 - 5251/34*a^2 - 1188/17*a + 270/17)*q^21 + (-13/34*a^10 - 1/2*a^9 + 108/17*a^8 + 243/34*a^7 - 73/2*a^6 - 1123/34*a^5 + 1424/17*a^4 + 1801/34*a^3 - 1077/17*a^2 - 284/17*a + 80/17)*q^22 + (-22/17*a^10 - 2*a^9 + 359/17*a^8 + 474/17*a^7 - 118*a^6 - 2111/17*a^5 + 4413/17*a^4 + 3278/17*a^3 - 3164/17*a^2 - 1041/17*a + 242/17)*q^23 + (-19/17*a^10 - 3/2*a^9 + 617/34*a^8 + 709/34*a^7 - 101*a^6 - 1572/17*a^5 + 7573/34*a^4 + 2406/17*a^3 - 2748/17*a^2 - 736/17*a + 192/17)*q^24 + (59/136*a^10 + 5/8*a^9 - 481/68*a^8 - 1163/136*a^7 + 313/8*a^6 + 5047/136*a^5 - 5669/68*a^4 - 7533/136*a^3 + 949/17*a^2 + 215/17*a - 62/17)*q^25 + (1/4*a^10 + 1/4*a^9 - 4*a^8 - 15/4*a^7 + 87/4*a^6 + 73/4*a^5 - 46*a^4 - 119/4*a^3 + 29*a^2 + 10*a - 2)*q^26 + (-15/34*a^10 - 1/2*a^9 + 122/17*a^8 + 215/34*a^7 - 79/2*a^6 - 791/34*a^5 + 1409/17*a^4 + 739/34*a^3 - 870/17*a^2 + 147/17*a - 11/17)*q^27 + (-1/34*a^10 - 1/2*a^9 + 7/17*a^8 + 241/34*a^7 - 3/2*a^6 - 1109/34*a^5 - 33/17*a^4 + 1917/34*a^3 + 214/17*a^2 - 456/17*a - 88/17)*q^28 + (155/136*a^10 + 13/8*a^9 - 1289/68*a^8 - 3083/136*a^7 + 873/8*a^6 + 13727/136*a^5 - 17189/68*a^4 - 21293/136*a^3 + 3429/17*a^2 + 857/17*a - 415/17)*q^29 + (-91/68*a^10 - 9/4*a^9 + 739/34*a^8 + 2143/68*a^7 - 481/4*a^6 - 9595/68*a^5 + 8795/34*a^4 + 15021/68*a^3 - 3030/17*a^2 - 1232/17*a + 280/17)*q^30 + (31/68*a^10 + 1/2*a^9 - 519/68*a^8 - 433/68*a^7 + 89/2*a^6 + 405/17*a^5 - 7219/68*a^4 - 1627/68*a^3 + 6197/68*a^2 - 161/34*a - 166/17)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (5/34*a^10 + 1/2*a^9 - 35/17*a^8 - 253/34*a^7 + 17/2*a^6 + 1227/34*a^5 - 124/17*a^4 - 2139/34*a^3 - 152/17*a^2 + 478/17*a - 70/17)*q^33 + (-33/68*a^10 - 3/4*a^9 + 265/34*a^8 + 711/68*a^7 - 169/4*a^6 - 3107/68*a^5 + 2991/34*a^4 + 4475/68*a^3 - 1965/34*a^2 - 265/17*a + 78/17)*q^34 + (-5/34*a^10 + 87/34*a^8 - 19/34*a^7 - 16*a^6 + 109/17*a^5 + 1489/34*a^4 - 717/34*a^3 - 1651/34*a^2 + 355/17*a + 138/17)*q^35 + (1/17*a^10 + 1/2*a^9 - 14/17*a^8 - 261/34*a^7 + 3*a^6 + 1317/34*a^5 + 47/34*a^4 - 2457/34*a^3 - 465/34*a^2 + 623/17*a + 6/17)*q^36 + (13/17*a^10 + 3/2*a^9 - 415/34*a^8 - 362/17*a^7 + 133/2*a^6 + 3317/34*a^5 - 4829/34*a^4 - 2702/17*a^3 + 3305/34*a^2 + 1010/17*a - 126/17)*q^37 + O(q^38)
*]> ;  // time = 2.28 seconds




J[181] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 181, 181 ], new_dimensions := [ 5, 9 ], dimensions := [ 5, 9 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -3, -5, -5, -2, -20, -2, -5, -6, -6, -17, 5, 2 ],
[ 3, 3, 1, 2, 24, -8, -1, 4, 14, 13, -7, -20 ]
], hecke_fields := [
x^5 + 3*x^4 - x^3 - 7*x^2 - 2*x + 1,
x^9 - 3*x^8 - 9*x^7 + 29*x^6 + 23*x^5 - 84*x^4 - 23*x^3 + 89*x^2 + 8*x - 27
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 15 ]
], tamagawa_numbers := [
[ 1 ],
[ 15 ]
], torsion_upper_bounds := [ 1, 15 ], torsion_lower_bounds := [ 1, 15 ], l_ratios := [ 0, 1/15 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^4 - 2*a^3 + 2*a^2 + 3*a - 1,
2*a^4 + 5*a^3 - 4*a^2 - 11*a - 1,
-2*a^3 - 2*a^2 + 5*a + 1,
-a^4 - 3*a^3 + a^2 + 6*a - 3,
-2*a^4 - 3*a^3 + 8*a^2 + 8*a - 5,
2*a^4 + 4*a^3 - 5*a^2 - 8*a,
-3*a^4 - 5*a^3 + 8*a^2 + 10*a - 2,
2*a^4 + 3*a^3 - 6*a^2 - 3*a + 2,
-a^4 - a^3 + 3*a^2 - a - 5,
-2*a^4 - 4*a^3 + 2*a^2 + 7*a + 6,
a^4 + 6*a^3 + 3*a^2 - 17*a - 7
],
[
a,
1/2*a^8 - 2*a^7 - 5/2*a^6 + 16*a^5 - 7/2*a^4 - 59/2*a^3 + 12*a^2 + 25/2*a - 7/2,
1/4*a^7 - 1/4*a^6 - 5/2*a^5 + 2*a^4 + 25/4*a^3 - 9/2*a^2 - 5/2*a + 15/4,
1/4*a^8 - 3/4*a^7 - a^6 + 5*a^5 - 19/4*a^4 - 5*a^3 + 29/2*a^2 - 1/4*a - 11/2,
-1/2*a^8 + 1/2*a^7 + 6*a^6 - 4*a^5 - 47/2*a^4 + 8*a^3 + 35*a^2 - 9/2*a - 12,
-1/2*a^8 + 7/4*a^7 + 11/4*a^6 - 29/2*a^5 + 7/2*a^4 + 121/4*a^3 - 41/2*a^2 - 18*a + 47/4,
3/2*a^8 - 9/2*a^7 - 10*a^6 + 35*a^5 + 13/2*a^4 - 61*a^3 + 17*a^2 + 45/2*a - 12,
-3/4*a^8 + 11/4*a^7 + 7/2*a^6 - 21*a^5 + 33/4*a^4 + 67/2*a^3 - 53/2*a^2 - 33/4*a + 11,
-5/4*a^8 + 19/4*a^7 + 6*a^6 - 38*a^5 + 51/4*a^4 + 72*a^3 - 91/2*a^2 - 147/4*a + 45/2,
3/4*a^7 - 11/4*a^6 - 9/2*a^5 + 22*a^4 + 7/4*a^3 - 79/2*a^2 + 5/2*a + 57/4,
3/4*a^8 - 11/4*a^7 - 9/2*a^6 + 23*a^5 + 3/4*a^4 - 97/2*a^3 + 15/2*a^2 + 113/4*a - 4,
1/2*a^8 - 5/4*a^7 - 13/4*a^6 + 17/2*a^5 + 1/2*a^4 - 31/4*a^3 + 23/2*a^2 - 6*a - 37/4
]
*], q_expansions := [*
q + a*q^2 + (-a^4 - 2*a^3 + 2*a^2 + 3*a - 1)*q^3 + (a^2 - 2)*q^4 + (2*a^4 + 5*a^3 - 4*a^2 - 11*a - 1)*q^5 + (a^4 + a^3 - 4*a^2 - 3*a + 1)*q^6 + (-2*a^3 - 2*a^2 + 5*a + 1)*q^7 + (a^3 - 4*a)*q^8 + (a^4 + 3*a^3 - 4*a - 2)*q^9 + (-a^4 - 2*a^3 + 3*a^2 + 3*a - 2)*q^10 + (-a^4 - 3*a^3 + a^2 + 6*a - 3)*q^11 + (a^3 - 3*a + 1)*q^12 + (-2*a^4 - 3*a^3 + 8*a^2 + 8*a - 5)*q^13 + (-2*a^4 - 2*a^3 + 5*a^2 + a)*q^14 + (-a^4 - 3*a^3 + 3*a^2 + 9*a - 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^4 + 4*a^3 - 5*a^2 - 8*a)*q^17 + (a^3 + 3*a^2 - 1)*q^18 + (-3*a^4 - 5*a^3 + 8*a^2 + 10*a - 2)*q^19 + (-3*a^4 - 8*a^3 + 4*a^2 + 18*a + 3)*q^20 + (2*a^4 + 5*a^3 - 4*a^2 - 8*a + 2)*q^21 + (-a^2 - 5*a + 1)*q^22 + (2*a^4 + 3*a^3 - 6*a^2 - 3*a + 2)*q^23 + (-a^4 - 2*a^3 + 5*a^2 + 7*a - 2)*q^24 + (-2*a^3 - 6*a^2 + 3*a + 11)*q^25 + (3*a^4 + 6*a^3 - 6*a^2 - 9*a + 2)*q^26 + (3*a^4 + 4*a^3 - 11*a^2 - 10*a + 4)*q^27 + (4*a^4 + 7*a^3 - 9*a^2 - 14*a)*q^28 + (-a^4 - a^3 + 3*a^2 - a - 5)*q^29 + (2*a^3 + 2*a^2 - 4*a + 1)*q^30 + (-2*a^4 - 4*a^3 + 2*a^2 + 7*a + 6)*q^31 + (-3*a^4 - 7*a^3 + 7*a^2 + 14*a - 1)*q^32 + (5*a^4 + 11*a^3 - 9*a^2 - 17*a + 5)*q^33 + (-2*a^4 - 3*a^3 + 6*a^2 + 4*a - 2)*q^34 + (-3*a^4 - 3*a^3 + 13*a^2 + 6*a - 11)*q^35 + (-a^4 - 3*a^3 + 7*a + 4)*q^36 + (a^4 + 6*a^3 + 3*a^2 - 17*a - 7)*q^37 + O(q^38),
q + a*q^2 + (1/2*a^8 - 2*a^7 - 5/2*a^6 + 16*a^5 - 7/2*a^4 - 59/2*a^3 + 12*a^2 + 25/2*a - 7/2)*q^3 + (a^2 - 2)*q^4 + (1/4*a^7 - 1/4*a^6 - 5/2*a^5 + 2*a^4 + 25/4*a^3 - 9/2*a^2 - 5/2*a + 15/4)*q^5 + (-1/2*a^8 + 2*a^7 + 3/2*a^6 - 15*a^5 + 25/2*a^4 + 47/2*a^3 - 32*a^2 - 15/2*a + 27/2)*q^6 + (1/4*a^8 - 3/4*a^7 - a^6 + 5*a^5 - 19/4*a^4 - 5*a^3 + 29/2*a^2 - 1/4*a - 11/2)*q^7 + (a^3 - 4*a)*q^8 + (-a^7 + 2*a^6 + 9*a^5 - 16*a^4 - 21*a^3 + 30*a^2 + 13*a - 11)*q^9 + (1/4*a^8 - 1/4*a^7 - 5/2*a^6 + 2*a^5 + 25/4*a^4 - 9/2*a^3 - 5/2*a^2 + 15/4*a)*q^10 + (-1/2*a^8 + 1/2*a^7 + 6*a^6 - 4*a^5 - 47/2*a^4 + 8*a^3 + 35*a^2 - 9/2*a - 12)*q^11 + (-1/2*a^8 + a^7 + 9/2*a^6 - 8*a^5 - 23/2*a^4 + 31/2*a^3 + 13*a^2 - 15/2*a - 13/2)*q^12 + (-1/2*a^8 + 7/4*a^7 + 11/4*a^6 - 29/2*a^5 + 7/2*a^4 + 121/4*a^3 - 41/2*a^2 - 18*a + 47/4)*q^13 + (5/4*a^7 - 9/4*a^6 - 21/2*a^5 + 16*a^4 + 81/4*a^3 - 45/2*a^2 - 15/2*a + 27/4)*q^14 + (5/2*a^7 - 13/2*a^6 - 19*a^5 + 51*a^4 + 59/2*a^3 - 92*a^2 - 10*a + 75/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (3/2*a^8 - 9/2*a^7 - 10*a^6 + 35*a^5 + 13/2*a^4 - 61*a^3 + 17*a^2 + 45/2*a - 12)*q^17 + (-a^8 + 2*a^7 + 9*a^6 - 16*a^5 - 21*a^4 + 30*a^3 + 13*a^2 - 11*a)*q^18 + (-3/4*a^8 + 11/4*a^7 + 7/2*a^6 - 21*a^5 + 33/4*a^4 + 67/2*a^3 - 53/2*a^2 - 33/4*a + 11)*q^19 + (1/2*a^8 - 3/4*a^7 - 19/4*a^6 + 11/2*a^5 + 25/2*a^4 - 37/4*a^3 - 19/2*a^2 + 3*a - 3/4)*q^20 + (a^8 - 3/2*a^7 - 21/2*a^6 + 12*a^5 + 34*a^4 - 45/2*a^3 - 41*a^2 + 5*a + 25/2)*q^21 + (-a^8 + 3/2*a^7 + 21/2*a^6 - 12*a^5 - 34*a^4 + 47/2*a^3 + 40*a^2 - 8*a - 27/2)*q^22 + (-5/4*a^8 + 19/4*a^7 + 6*a^6 - 38*a^5 + 51/4*a^4 + 72*a^3 - 91/2*a^2 - 147/4*a + 45/2)*q^23 + (1/2*a^8 - 4*a^7 + 7/2*a^6 + 30*a^5 - 103/2*a^4 - 91/2*a^3 + 101*a^2 + 25/2*a - 81/2)*q^24 + (-a^8 + 5/4*a^7 + 43/4*a^6 - 19/2*a^5 - 36*a^4 + 65/4*a^3 + 91/2*a^2 - 9/2*a - 65/4)*q^25 + (1/4*a^8 - 7/4*a^7 + 15*a^5 - 47/4*a^4 - 32*a^3 + 53/2*a^2 + 63/4*a - 27/2)*q^26 + (a^8 - 5*a^7 - 2*a^6 + 40*a^5 - 32*a^4 - 74*a^3 + 75*a^2 + 33*a - 32)*q^27 + (3/4*a^8 - 3/4*a^7 - 17/2*a^6 + 6*a^5 + 119/4*a^4 - 25/2*a^3 - 73/2*a^2 + 29/4*a + 11)*q^28 + (3/4*a^7 - 11/4*a^6 - 9/2*a^5 + 22*a^4 + 7/4*a^3 - 79/2*a^2 + 5/2*a + 57/4)*q^29 + (5/2*a^8 - 13/2*a^7 - 19*a^6 + 51*a^5 + 59/2*a^4 - 92*a^3 - 10*a^2 + 75/2*a)*q^30 + (3/4*a^8 - 11/4*a^7 - 9/2*a^6 + 23*a^5 + 3/4*a^4 - 97/2*a^3 + 15/2*a^2 + 113/4*a - 4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2*a^8 - 9*a^7 - 7*a^6 + 71*a^5 - 38*a^4 - 125*a^3 + 94*a^2 + 45*a - 39)*q^33 + (7/2*a^7 - 17/2*a^6 - 28*a^5 + 65*a^4 + 103/2*a^3 - 111*a^2 - 24*a + 81/2)*q^34 + (-2*a^8 + 9/2*a^7 + 35/2*a^6 - 36*a^5 - 42*a^4 + 137/2*a^3 + 41*a^2 - 29*a - 21/2)*q^35 + (-a^8 + 2*a^7 + 9*a^6 - 16*a^5 - 22*a^4 + 32*a^3 + 18*a^2 - 18*a - 5)*q^36 + (1/2*a^8 - 5/4*a^7 - 13/4*a^6 + 17/2*a^5 + 1/2*a^4 - 31/4*a^3 + 23/2*a^2 - 6*a - 37/4)*q^37 + O(q^38)
*]> ;  // time = 1.919 seconds




J[182] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 182, 182, 182, 182, 182, 91, 91, 91, 91, 26, 26, 14 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 2, 2, 4, 6, 2, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 11, 7, 1, 1, 1, 0, 1, 1, 1, 1, 1, 7, 1, 1, 1, 5, 1, 1, 0, 3, 1, 5, 1, 1, 1, 1, 3, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 3, 1, 3, 1, 7, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 11, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 1, 1, 3, 1, 1, 0, 1, 3, 1, 1, 3, 3, 1, 1, 1, 7, 1, 1, 0, 1, 1, 5, 1, 1, 1, 1, 3, 1, 1, 3, 1, 0 ], ap_traces := [
[ -1, 1, 4, -1, -1, 1, 4, 2, -7, -8, 3, 7 ],
[ -1, 3, 0, 1, -5, -1, -4, 2, 5, 4, 1, 7 ],
[ 1, 0, 2, -1, 4, -1, -6, 0, 8, -10, -8, 6 ],
[ 1, 3, -4, -1, 1, -1, 0, -6, -7, -4, 7, 9 ],
[ 1, 1, 0, 1, -3, 1, 0, 2, -3, 0, 5, -7 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 11, 7, 1 ],
[ 7, 1, 5 ],
[ 5, 3, 1 ],
[ 1, 3, 1 ],
[ 9, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 5, 1, 1 ],
[ 1, 1, 1 ],
[ 9, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 1, 1, 5, 1, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1, 1/9 ], eigenvalues := [*
[ -1, 1, 4, -1, -1, 1, 4, 2, -7, -8, 3, 7 ],
[ -1, 3, 0, 1, -5, -1, -4, 2, 5, 4, 1, 7 ],
[ 1, 0, 2, -1, 4, -1, -6, 0, 8, -10, -8, 6 ],
[ 1, 3, -4, -1, 1, -1, 0, -6, -7, -4, 7, 9 ],
[ 1, 1, 0, 1, -3, 1, 0, 2, -3, 0, 5, -7 ]
*], q_expansions := [*
q - q^2 + q^3 + q^4 + 4*q^5 - q^6 - q^7 - q^8 - 2*q^9 - 4*q^10 - q^11 + q^12 + q^13 + q^14 + 4*q^15 + q^16 + 4*q^17 + 2*q^18 + 2*q^19 + 4*q^20 - q^21 + q^22 - 7*q^23 - q^24 + 11*q^25 - q^26 - 5*q^27 - q^28 - 8*q^29 - 4*q^30 + 3*q^31 - q^32 - q^33 - 4*q^34 - 4*q^35 - 2*q^36 + 7*q^37 + O(q^38),
q - q^2 + 3*q^3 + q^4 - 3*q^6 + q^7 - q^8 + 6*q^9 - 5*q^11 + 3*q^12 - q^13 - q^14 + q^16 - 4*q^17 - 6*q^18 + 2*q^19 + 3*q^21 + 5*q^22 + 5*q^23 - 3*q^24 - 5*q^25 + q^26 + 9*q^27 + q^28 + 4*q^29 + q^31 - q^32 - 15*q^33 + 4*q^34 + 6*q^36 + 7*q^37 + O(q^38),
q + q^2 + q^4 + 2*q^5 - q^7 + q^8 - 3*q^9 + 2*q^10 + 4*q^11 - q^13 - q^14 + q^16 - 6*q^17 - 3*q^18 + 2*q^20 + 4*q^22 + 8*q^23 - q^25 - q^26 - q^28 - 10*q^29 - 8*q^31 + q^32 - 6*q^34 - 2*q^35 - 3*q^36 + 6*q^37 + O(q^38),
q + q^2 + 3*q^3 + q^4 - 4*q^5 + 3*q^6 - q^7 + q^8 + 6*q^9 - 4*q^10 + q^11 + 3*q^12 - q^13 - q^14 - 12*q^15 + q^16 + 6*q^18 - 6*q^19 - 4*q^20 - 3*q^21 + q^22 - 7*q^23 + 3*q^24 + 11*q^25 - q^26 + 9*q^27 - q^28 - 4*q^29 - 12*q^30 + 7*q^31 + q^32 + 3*q^33 + 4*q^35 + 6*q^36 + 9*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^6 + q^7 + q^8 - 2*q^9 - 3*q^11 + q^12 + q^13 + q^14 + q^16 - 2*q^18 + 2*q^19 + q^21 - 3*q^22 - 3*q^23 + q^24 - 5*q^25 + q^26 - 5*q^27 + q^28 + 5*q^31 + q^32 - 3*q^33 - 2*q^36 - 7*q^37 + O(q^38)
*]> ;  // time = 53.88 seconds




J[183] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 183, 183, 183, 61, 61 ], new_dimensions := [ 2, 3, 6, 1, 3 ], dimensions := [ 2, 3, 6, 2, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 19, 1, 1, 0, 3, 1, 1, 1, 3, 0, 1, 1, 19, 1, 1, 0 ], ap_traces := [
[ -2, -2, -2, -2, -2, -6, -12, 4, -2, 0, 4, -4 ],
[ 1, -3, 6, 0, 2, 6, 12, -8, 2, 4, -8, -6 ],
[ 0, 6, 2, 2, -8, 6, 10, 8, 0, -10, 0, -4 ]
], hecke_fields := [
x^2 + 2*x - 1,
x^3 - x^2 - 3*x + 1,
x^6 - 11*x^4 + 2*x^3 + 31*x^2 - 10*x - 17
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 19, 1 ],
[ 93, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 93, 1 ]
], torsion_upper_bounds := [ 1, 1, 31 ], torsion_lower_bounds := [ 1, 1, 31 ], l_ratios := [ 0, 1, 3/31 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[
a,
-1,
-1,
-a - 2,
-a - 2,
-3,
-6,
4*a + 6,
3*a + 2,
-4*a - 4,
4*a + 6,
2*a
],
[
a,
-1,
2,
-2*a^2 + 2*a + 4,
-a^2 + 3,
2*a^2 - 2*a - 2,
-a^2 - 2*a + 7,
-2*a - 2,
3*a^2 - 4*a - 5,
-a^2 + 2*a + 3,
2*a^2 + 2*a - 8,
4*a^2 - 4*a - 10
],
[
a,
1,
1/2*a^5 + a^4 - 5*a^3 - 8*a^2 + 21/2*a + 10,
-a^5 - 3/2*a^4 + 9*a^3 + 11*a^2 - 17*a - 23/2,
-1/2*a^4 + 3*a^2 - a - 5/2,
-1/2*a^5 + 5*a^3 - 21/2*a + 1,
a^5 + a^4 - 9*a^3 - 6*a^2 + 16*a + 5,
a^5 + a^4 - 8*a^3 - 8*a^2 + 11*a + 13,
-1/2*a^4 + 5*a^2 - a - 17/2,
a^4 + a^3 - 8*a^2 - 5*a + 9,
-2*a^5 - 3*a^4 + 18*a^3 + 24*a^2 - 32*a - 31,
-a^5 - a^4 + 8*a^3 + 6*a^2 - 9*a - 5
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-2*a - 1)*q^4 - q^5 - a*q^6 + (-a - 2)*q^7 + (a - 2)*q^8 + q^9 - a*q^10 + (-a - 2)*q^11 + (2*a + 1)*q^12 - 3*q^13 - q^14 + q^15 + 3*q^16 - 6*q^17 + a*q^18 + (4*a + 6)*q^19 + (2*a + 1)*q^20 + (a + 2)*q^21 - q^22 + (3*a + 2)*q^23 + (-a + 2)*q^24 - 4*q^25 - 3*a*q^26 - q^27 + (a + 4)*q^28 + (-4*a - 4)*q^29 + a*q^30 + (4*a + 6)*q^31 + (a + 4)*q^32 + (a + 2)*q^33 - 6*a*q^34 + (a + 2)*q^35 + (-2*a - 1)*q^36 + 2*a*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + 2*q^5 - a*q^6 + (-2*a^2 + 2*a + 4)*q^7 + (a^2 - a - 1)*q^8 + q^9 + 2*a*q^10 + (-a^2 + 3)*q^11 + (-a^2 + 2)*q^12 + (2*a^2 - 2*a - 2)*q^13 + (-2*a + 2)*q^14 - 2*q^15 + (-2*a^2 + 2*a + 3)*q^16 + (-a^2 - 2*a + 7)*q^17 + a*q^18 + (-2*a - 2)*q^19 + (2*a^2 - 4)*q^20 + (2*a^2 - 2*a - 4)*q^21 + (-a^2 + 1)*q^22 + (3*a^2 - 4*a - 5)*q^23 + (-a^2 + a + 1)*q^24 - q^25 + (4*a - 2)*q^26 - q^27 + (2*a^2 - 2*a - 8)*q^28 + (-a^2 + 2*a + 3)*q^29 - 2*a*q^30 + (2*a^2 + 2*a - 8)*q^31 + (-2*a^2 - a + 4)*q^32 + (a^2 - 3)*q^33 + (-3*a^2 + 4*a + 1)*q^34 + (-4*a^2 + 4*a + 8)*q^35 + (a^2 - 2)*q^36 + (4*a^2 - 4*a - 10)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (1/2*a^5 + a^4 - 5*a^3 - 8*a^2 + 21/2*a + 10)*q^5 + a*q^6 + (-a^5 - 3/2*a^4 + 9*a^3 + 11*a^2 - 17*a - 23/2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (a^5 + 1/2*a^4 - 9*a^3 - 5*a^2 + 15*a + 17/2)*q^10 + (-1/2*a^4 + 3*a^2 - a - 5/2)*q^11 + (a^2 - 2)*q^12 + (-1/2*a^5 + 5*a^3 - 21/2*a + 1)*q^13 + (-3/2*a^5 - 2*a^4 + 13*a^3 + 14*a^2 - 43/2*a - 17)*q^14 + (1/2*a^5 + a^4 - 5*a^3 - 8*a^2 + 21/2*a + 10)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^5 + a^4 - 9*a^3 - 6*a^2 + 16*a + 5)*q^17 + a*q^18 + (a^5 + a^4 - 8*a^3 - 8*a^2 + 11*a + 13)*q^19 + (-1/2*a^5 + 3*a^3 - 5/2*a - 3)*q^20 + (-a^5 - 3/2*a^4 + 9*a^3 + 11*a^2 - 17*a - 23/2)*q^21 + (-1/2*a^5 + 3*a^3 - a^2 - 5/2*a)*q^22 + (-1/2*a^4 + 5*a^2 - a - 17/2)*q^23 + (a^3 - 4*a)*q^24 + (5/2*a^5 + 3*a^4 - 23*a^3 - 22*a^2 + 85/2*a + 27)*q^25 + (-1/2*a^4 + a^3 + 5*a^2 - 4*a - 17/2)*q^26 + q^27 + (-1/2*a^4 - a^3 + 3*a^2 + 2*a - 5/2)*q^28 + (a^4 + a^3 - 8*a^2 - 5*a + 9)*q^29 + (a^5 + 1/2*a^4 - 9*a^3 - 5*a^2 + 15*a + 17/2)*q^30 + (-2*a^5 - 3*a^4 + 18*a^3 + 24*a^2 - 32*a - 31)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-1/2*a^4 + 3*a^2 - a - 5/2)*q^33 + (a^5 + 2*a^4 - 8*a^3 - 15*a^2 + 15*a + 17)*q^34 + (-2*a^5 - 3/2*a^4 + 19*a^3 + 13*a^2 - 36*a - 43/2)*q^35 + (a^2 - 2)*q^36 + (-a^5 - a^4 + 8*a^3 + 6*a^2 - 9*a - 5)*q^37 + O(q^38)
*]> ;  // time = 19.031 seconds




J[185] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 185, 185, 185, 185, 185, 37, 37 ], new_dimensions := [ 1, 1, 1, 5, 5, 1, 1 ], dimensions := [ 1, 1, 1, 5, 5, 2, 2 ], intersection_graph := [ 0, 3, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 0 ], ap_traces := [
[ 1, -2, -1, -2, 0, -2, 2, 2, -8, 2, -6, -1 ],
[ -2, 1, -1, -5, 3, -2, -4, -4, -2, 2, 0, -1 ],
[ 0, -1, 1, -3, -5, 4, -4, -8, 4, 4, 2, 1 ],
[ 2, 3, -5, 11, -5, 4, 0, -4, 4, -4, 8, 5 ],
[ 0, -1, 5, 7, 7, 2, -8, 14, 2, 2, 8, -5 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^5 - 2*x^4 - 8*x^3 + 14*x^2 + 11*x - 12,
x^5 - 8*x^3 + 2*x^2 + 11*x - 2
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 9, 3 ],
[ 19, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 3 ],
[ 19, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 19 ], torsion_lower_bounds := [ 1, 1, 1, 3, 19 ], l_ratios := [ 0, 0, 0, 1/3, 1/19 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ 1, -2, -1, -2, 0, -2, 2, 2, -8, 2, -6, -1 ],
[ -2, 1, -1, -5, 3, -2, -4, -4, -2, 2, 0, -1 ],
[ 0, -1, 1, -3, -5, 4, -4, -8, 4, 4, 2, 1 ],
[
a,
-1/2*a^3 + 5/2*a + 1,
-1,
1/2*a^4 - 7/2*a^2 - a + 5,
-a^2 + 3,
-1/2*a^4 + 1/2*a^3 + 5/2*a^2 - 5/2*a + 2,
-1/2*a^4 + 1/2*a^3 + 9/2*a^2 - 9/2*a - 6,
-a^4 + 1/2*a^3 + 8*a^2 - 5/2*a - 10,
-a^4 + 9*a^2 - 12,
-a^3 + 5*a,
-1/2*a^4 + a^3 + 5/2*a^2 - 4*a + 2,
1
],
[
a,
-1/2*a^4 + 7/2*a^2 - a - 3,
1,
-1/2*a^3 - a^2 + 5/2*a + 4,
a^4 + a^3 - 6*a^2 - 3*a + 5,
-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 1/2*a - 3,
-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 5/2*a - 5,
-1/2*a^4 - a^3 + 5/2*a^2 + 2*a + 2,
a^4 - 7*a^2 + 6,
a^4 + 2*a^3 - 5*a^2 - 8*a + 2,
a^4 + 3/2*a^3 - 7*a^2 - 11/2*a + 9,
-1
]
*], q_expansions := [*
q + q^2 - 2*q^3 - q^4 - q^5 - 2*q^6 - 2*q^7 - 3*q^8 + q^9 - q^10 + 2*q^12 - 2*q^13 - 2*q^14 + 2*q^15 - q^16 + 2*q^17 + q^18 + 2*q^19 + q^20 + 4*q^21 - 8*q^23 + 6*q^24 + q^25 - 2*q^26 + 4*q^27 + 2*q^28 + 2*q^29 + 2*q^30 - 6*q^31 + 5*q^32 + 2*q^34 + 2*q^35 - q^36 - q^37 + O(q^38),
q - 2*q^2 + q^3 + 2*q^4 - q^5 - 2*q^6 - 5*q^7 - 2*q^9 + 2*q^10 + 3*q^11 + 2*q^12 - 2*q^13 + 10*q^14 - q^15 - 4*q^16 - 4*q^17 + 4*q^18 - 4*q^19 - 2*q^20 - 5*q^21 - 6*q^22 - 2*q^23 + q^25 + 4*q^26 - 5*q^27 - 10*q^28 + 2*q^29 + 2*q^30 + 8*q^32 + 3*q^33 + 8*q^34 + 5*q^35 - 4*q^36 - q^37 + O(q^38),
q - q^3 - 2*q^4 + q^5 - 3*q^7 - 2*q^9 - 5*q^11 + 2*q^12 + 4*q^13 - q^15 + 4*q^16 - 4*q^17 - 8*q^19 - 2*q^20 + 3*q^21 + 4*q^23 + q^25 + 5*q^27 + 6*q^28 + 4*q^29 + 2*q^31 + 5*q^33 - 3*q^35 + 4*q^36 + q^37 + O(q^38),
q + a*q^2 + (-1/2*a^3 + 5/2*a + 1)*q^3 + (a^2 - 2)*q^4 - q^5 + (-1/2*a^4 + 5/2*a^2 + a)*q^6 + (1/2*a^4 - 7/2*a^2 - a + 5)*q^7 + (a^3 - 4*a)*q^8 + (1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 5/2*a + 4)*q^9 - a*q^10 + (-a^2 + 3)*q^11 + (-a^4 - 1/2*a^3 + 8*a^2 + 1/2*a - 8)*q^12 + (-1/2*a^4 + 1/2*a^3 + 5/2*a^2 - 5/2*a + 2)*q^13 + (a^4 + 1/2*a^3 - 8*a^2 - 1/2*a + 6)*q^14 + (1/2*a^3 - 5/2*a - 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^4 + 1/2*a^3 + 9/2*a^2 - 9/2*a - 6)*q^17 + (1/2*a^4 + 1/2*a^3 - 9/2*a^2 - 3/2*a + 6)*q^18 + (-a^4 + 1/2*a^3 + 8*a^2 - 5/2*a - 10)*q^19 + (-a^2 + 2)*q^20 + (1/2*a^4 - 3/2*a^3 - 7/2*a^2 + 11/2*a + 5)*q^21 + (-a^3 + 3*a)*q^22 + (-a^4 + 9*a^2 - 12)*q^23 + (-3/2*a^4 + 19/2*a^2 + a - 12)*q^24 + q^25 + (-1/2*a^4 - 3/2*a^3 + 9/2*a^2 + 15/2*a - 6)*q^26 + (1/2*a^4 + 1/2*a^3 - 9/2*a^2 - 7/2*a + 7)*q^27 + (3/2*a^4 - 15/2*a^2 - 3*a + 2)*q^28 + (-a^3 + 5*a)*q^29 + (1/2*a^4 - 5/2*a^2 - a)*q^30 + (-1/2*a^4 + a^3 + 5/2*a^2 - 4*a + 2)*q^31 + (2*a^4 - 14*a^2 + a + 12)*q^32 + (a^4 - 8*a^2 + 2*a + 9)*q^33 + (-1/2*a^4 + 1/2*a^3 + 5/2*a^2 - 1/2*a - 6)*q^34 + (-1/2*a^4 + 7/2*a^2 + a - 5)*q^35 + (1/2*a^4 + 1/2*a^3 - 3/2*a^2 - 9/2*a - 2)*q^36 + q^37 + O(q^38),
q + a*q^2 + (-1/2*a^4 + 7/2*a^2 - a - 3)*q^3 + (a^2 - 2)*q^4 + q^5 + (-1/2*a^3 + 5/2*a - 1)*q^6 + (-1/2*a^3 - a^2 + 5/2*a + 4)*q^7 + (a^3 - 4*a)*q^8 + (1/2*a^4 + 1/2*a^3 - 9/2*a^2 - 5/2*a + 7)*q^9 + a*q^10 + (a^4 + a^3 - 6*a^2 - 3*a + 5)*q^11 + (1/2*a^4 - 9/2*a^2 + a + 6)*q^12 + (-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 1/2*a - 3)*q^13 + (-1/2*a^4 - a^3 + 5/2*a^2 + 4*a)*q^14 + (-1/2*a^4 + 7/2*a^2 - a - 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 5/2*a - 5)*q^17 + (1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 3/2*a + 1)*q^18 + (-1/2*a^4 - a^3 + 5/2*a^2 + 2*a + 2)*q^19 + (a^2 - 2)*q^20 + (-3/2*a^4 - 1/2*a^3 + 23/2*a^2 + 1/2*a - 14)*q^21 + (a^4 + 2*a^3 - 5*a^2 - 6*a + 2)*q^22 + (a^4 - 7*a^2 + 6)*q^23 + (1/2*a^3 - 9/2*a + 3)*q^24 + q^25 + (-1/2*a^4 - 1/2*a^3 + 3/2*a^2 + 5/2*a - 1)*q^26 + (-1/2*a^4 + 1/2*a^3 + 11/2*a^2 - 7/2*a - 10)*q^27 + (-a^4 - 1/2*a^3 + 7*a^2 + 1/2*a - 9)*q^28 + (a^4 + 2*a^3 - 5*a^2 - 8*a + 2)*q^29 + (-1/2*a^3 + 5/2*a - 1)*q^30 + (a^4 + 3/2*a^3 - 7*a^2 - 11/2*a + 9)*q^31 + (-2*a^2 + a + 2)*q^32 + (-a^4 + 8*a^2 - 2*a - 13)*q^33 + (-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 1/2*a - 1)*q^34 + (-1/2*a^3 - a^2 + 5/2*a + 4)*q^35 + (-3/2*a^4 - 1/2*a^3 + 19/2*a^2 + 1/2*a - 13)*q^36 - q^37 + O(q^38)
*]> ;  // time = 18.759 seconds




J[186] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 186, 186, 186, 186, 93, 93, 62, 62, 31 ], new_dimensions := [ 1, 1, 1, 2, 2, 3, 1, 2, 2 ], dimensions := [ 1, 1, 1, 2, 4, 6, 2, 4, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 11, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 5, 1, 1, 1, 0, 19, 1, 1, 1, 1, 1, 1, 1, 19, 0, 1, 1, 1, 1, 1, 7, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 11, 1, 1, 1, 1, 1, 1, 0, 121, 1, 1, 5, 1, 1, 1, 1, 121, 0 ], ap_traces := [
[ -1, -1, -1, 2, 3, 3, 1, 7, 0, 4, 1, -10 ],
[ -1, 1, 3, -2, 5, -7, -1, 7, 4, -8, -1, -6 ],
[ 1, 1, 1, -2, -3, -1, 3, -5, 4, 0, 1, -2 ],
[ 2, -2, 3, 2, -1, 3, -1, -1, -16, -6, -2, 0 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 - 3*x - 2
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 1, 11, 1 ],
[ 7, 1, 1 ],
[ 5, 5, 1 ],
[ 19, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 5, 5, 1 ],
[ 19, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 5, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1 ], l_ratios := [ 1, 1, 1, 19 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1/25, 1 ], eigenvalues := [*
[ -1, -1, -1, 2, 3, 3, 1, 7, 0, 4, 1, -10 ],
[ -1, 1, 3, -2, 5, -7, -1, 7, 4, -8, -1, -6 ],
[ 1, 1, 1, -2, -3, -1, 3, -5, 4, 0, 1, -2 ],
[
1,
-1,
a,
-2*a + 4,
a - 2,
a,
-3*a + 4,
a - 2,
-8,
2*a - 6,
-1,
-4*a + 6
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - q^5 + q^6 + 2*q^7 - q^8 + q^9 + q^10 + 3*q^11 - q^12 + 3*q^13 - 2*q^14 + q^15 + q^16 + q^17 - q^18 + 7*q^19 - q^20 - 2*q^21 - 3*q^22 + q^24 - 4*q^25 - 3*q^26 - q^27 + 2*q^28 + 4*q^29 - q^30 + q^31 - q^32 - 3*q^33 - q^34 - 2*q^35 + q^36 - 10*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + 3*q^5 - q^6 - 2*q^7 - q^8 + q^9 - 3*q^10 + 5*q^11 + q^12 - 7*q^13 + 2*q^14 + 3*q^15 + q^16 - q^17 - q^18 + 7*q^19 + 3*q^20 - 2*q^21 - 5*q^22 + 4*q^23 - q^24 + 4*q^25 + 7*q^26 + q^27 - 2*q^28 - 8*q^29 - 3*q^30 - q^31 - q^32 + 5*q^33 + q^34 - 6*q^35 + q^36 - 6*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^5 + q^6 - 2*q^7 + q^8 + q^9 + q^10 - 3*q^11 + q^12 - q^13 - 2*q^14 + q^15 + q^16 + 3*q^17 + q^18 - 5*q^19 + q^20 - 2*q^21 - 3*q^22 + 4*q^23 + q^24 - 4*q^25 - q^26 + q^27 - 2*q^28 + q^30 + q^31 + q^32 - 3*q^33 + 3*q^34 - 2*q^35 + q^36 - 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + a*q^5 - q^6 + (-2*a + 4)*q^7 + q^8 + q^9 + a*q^10 + (a - 2)*q^11 - q^12 + a*q^13 + (-2*a + 4)*q^14 - a*q^15 + q^16 + (-3*a + 4)*q^17 + q^18 + (a - 2)*q^19 + a*q^20 + (2*a - 4)*q^21 + (a - 2)*q^22 - 8*q^23 - q^24 + (3*a - 3)*q^25 + a*q^26 - q^27 + (-2*a + 4)*q^28 + (2*a - 6)*q^29 - a*q^30 - q^31 + q^32 + (-a + 2)*q^33 + (-3*a + 4)*q^34 + (-2*a - 4)*q^35 + q^36 + (-4*a + 6)*q^37 + O(q^38)
*]> ;  // time = 87.76 seconds




J[187] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 187, 187, 187, 187, 187, 187, 17, 11 ], new_dimensions := [ 1, 1, 2, 2, 3, 4, 1, 1 ], dimensions := [ 1, 1, 2, 2, 3, 4, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 5, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 2, 0, 4, -5, -1, 4, 1, 2, -2, -3, 4, -2 ],
[ 0, 1, 3, 2, 1, 2, -1, 2, -3, -6, -7, -7 ],
[ 4, -1, 1, 3, 2, 0, -2, -6, 1, 15, -1, 5 ],
[ -2, 0, -4, -4, 2, -10, 2, -2, -4, -6, 8, -4 ],
[ -2, -3, -7, 0, -3, 0, -3, 6, -15, -14, -9, -11 ],
[ 1, 1, 3, 0, -4, -2, 4, -2, 5, 12, -17, 19 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2*x - 16,
x^2 + 2*x - 2,
x^3 + 2*x^2 - 2*x - 2,
x^4 - x^3 - 6*x^2 + 2*x + 2
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 3, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 3, 1, 1, 1, 1 ], l_ratios := [ 1, 1/3, 1, 0, 0, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1, 0, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 0, 0, 1 ], eigenvalues := [*
[ 2, 0, 4, -5, -1, 4, 1, 2, -2, -3, 4, -2 ],
[ 0, 1, 3, 2, 1, 2, -1, 2, -3, -6, -7, -7 ],
[
2,
1/2*a - 1,
-1/2*a + 1,
-1/2*a + 2,
1,
0,
-1,
a - 4,
3/2*a - 1,
-1/2*a + 8,
1/2*a - 1,
-1/2*a + 3
],
[
a,
-a - 1,
a - 1,
-2,
1,
-a - 6,
1,
3*a + 2,
a - 1,
-a - 4,
a + 5,
a - 1
],
[
a,
-a^2 - a + 1,
-a - 3,
2*a^2 + 2*a - 4,
-1,
3*a + 2,
-1,
-2*a^2 - 5*a + 4,
-a^2 - a - 3,
-a^2 - 3*a - 4,
2*a^2 + 5*a - 5,
-5*a^2 - 7*a + 5
],
[
a,
-a^3 + a^2 + 5*a - 1,
-a + 1,
0,
-1,
a^3 - 2*a^2 - 5*a + 4,
1,
a^3 - 7*a - 2,
a^3 - a^2 - 7*a + 3,
a^2 - a,
-2*a^3 + 13*a - 1,
-a^3 + a^2 + 7*a + 3
]
*], q_expansions := [*
q + 2*q^2 + 2*q^4 + 4*q^5 - 5*q^7 - 3*q^9 + 8*q^10 - q^11 + 4*q^13 - 10*q^14 - 4*q^16 + q^17 - 6*q^18 + 2*q^19 + 8*q^20 - 2*q^22 - 2*q^23 + 11*q^25 + 8*q^26 - 10*q^28 - 3*q^29 + 4*q^31 - 8*q^32 + 2*q^34 - 20*q^35 - 6*q^36 - 2*q^37 + O(q^38),
q + q^3 - 2*q^4 + 3*q^5 + 2*q^7 - 2*q^9 + q^11 - 2*q^12 + 2*q^13 + 3*q^15 + 4*q^16 - q^17 + 2*q^19 - 6*q^20 + 2*q^21 - 3*q^23 + 4*q^25 - 5*q^27 - 4*q^28 - 6*q^29 - 7*q^31 + q^33 + 6*q^35 + 4*q^36 - 7*q^37 + O(q^38),
q + 2*q^2 + (1/2*a - 1)*q^3 + 2*q^4 + (-1/2*a + 1)*q^5 + (a - 2)*q^6 + (-1/2*a + 2)*q^7 + (-1/2*a + 2)*q^9 + (-a + 2)*q^10 + q^11 + (a - 2)*q^12 + (-a + 4)*q^14 + (1/2*a - 5)*q^15 - 4*q^16 - q^17 + (-a + 4)*q^18 + (a - 4)*q^19 + (-a + 2)*q^20 + (a - 6)*q^21 + 2*q^22 + (3/2*a - 1)*q^23 - 1/2*a*q^25 + (-1/2*a - 3)*q^27 + (-a + 4)*q^28 + (-1/2*a + 8)*q^29 + (a - 10)*q^30 + (1/2*a - 1)*q^31 - 8*q^32 + (1/2*a - 1)*q^33 - 2*q^34 + (-a + 6)*q^35 + (-a + 4)*q^36 + (-1/2*a + 3)*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 - 2*a*q^4 + (a - 1)*q^5 + (a - 2)*q^6 - 2*q^7 + (2*a - 4)*q^8 + (-3*a + 2)*q^10 + q^11 + (-2*a + 4)*q^12 + (-a - 6)*q^13 - 2*a*q^14 + (2*a - 1)*q^15 + (-4*a + 4)*q^16 + q^17 + (3*a + 2)*q^19 + (6*a - 4)*q^20 + (2*a + 2)*q^21 + a*q^22 + (a - 1)*q^23 + 6*a*q^24 + (-4*a - 2)*q^25 + (-4*a - 2)*q^26 + (3*a + 3)*q^27 + 4*a*q^28 + (-a - 4)*q^29 + (-5*a + 4)*q^30 + (a + 5)*q^31 + 8*a*q^32 + (-a - 1)*q^33 + a*q^34 + (-2*a + 2)*q^35 + (a - 1)*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 1)*q^3 + (a^2 - 2)*q^4 + (-a - 3)*q^5 + (a^2 - a - 2)*q^6 + (2*a^2 + 2*a - 4)*q^7 + (-2*a^2 - 2*a + 2)*q^8 + (a^2 - 2)*q^9 + (-a^2 - 3*a)*q^10 - q^11 + (-a^2 + 2*a)*q^12 + (3*a + 2)*q^13 + (-2*a^2 + 4)*q^14 + (2*a^2 + 4*a - 1)*q^15 - 2*a*q^16 - q^17 + (-2*a^2 + 2)*q^18 + (-2*a^2 - 5*a + 4)*q^19 + (-a^2 + 4)*q^20 + (2*a - 4)*q^21 - a*q^22 + (-a^2 - a - 3)*q^23 + (2*a^2 + 2)*q^24 + (a^2 + 6*a + 4)*q^25 + (3*a^2 + 2*a)*q^26 + (2*a^2 + 5*a - 3)*q^27 + (-4*a + 4)*q^28 + (-a^2 - 3*a - 4)*q^29 + (3*a + 4)*q^30 + (2*a^2 + 5*a - 5)*q^31 + (2*a^2 + 4*a - 4)*q^32 + (a^2 + a - 1)*q^33 - a*q^34 + (-4*a^2 - 6*a + 8)*q^35 + (2*a^2 - 2*a)*q^36 + (-5*a^2 - 7*a + 5)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + a^2 + 5*a - 1)*q^3 + (a^2 - 2)*q^4 + (-a + 1)*q^5 + (-a^2 + a + 2)*q^6 + (a^3 - 4*a)*q^8 + (-a^2 + 6)*q^9 + (-a^2 + a)*q^10 - q^11 + (a^3 - a^2 - 8*a + 2)*q^12 + (a^3 - 2*a^2 - 5*a + 4)*q^13 + (-a^3 + 2*a^2 + 4*a - 3)*q^15 + (a^3 - 2*a + 2)*q^16 + q^17 + (-a^3 + 6*a)*q^18 + (a^3 - 7*a - 2)*q^19 + (-a^3 + a^2 + 2*a - 2)*q^20 - a*q^22 + (a^3 - a^2 - 7*a + 3)*q^23 + (-2*a - 6)*q^24 + (a^2 - 2*a - 4)*q^25 + (-a^3 + a^2 + 2*a - 2)*q^26 + (-2*a^3 + 2*a^2 + 13*a - 3)*q^27 + (a^2 - a)*q^29 + (a^3 - 2*a^2 - a + 2)*q^30 + (-2*a^3 + 13*a - 1)*q^31 + (-a^3 + 4*a^2 + 8*a - 2)*q^32 + (a^3 - a^2 - 5*a + 1)*q^33 + a*q^34 + (-a^3 + 2*a^2 + 2*a - 10)*q^36 + (-a^3 + a^2 + 7*a + 3)*q^37 + O(q^38)
*]> ;  // time = 21.429 seconds




J[190] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 190, 190, 190, 190, 95, 95, 38, 38, 19 ], new_dimensions := [ 1, 1, 1, 2, 3, 4, 1, 1, 1 ], dimensions := [ 1, 1, 1, 2, 6, 8, 2, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 11, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0, 13, 1, 1, 1, 1, 1, 1, 1, 13, 0, 1, 1, 5, 1, 1, 11, 1, 1, 1, 0, 3, 1, 81, 1, 1, 1, 1, 1, 3, 0, 1, 9, 1, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 3, 1, 1, 81, 9, 1, 0 ], ap_traces := [
[ -1, -1, -1, -1, 0, -3, -7, -1, -5, -5, 10, 2 ],
[ 1, -3, -1, -5, -4, -1, -3, 1, 7, -3, -2, -2 ],
[ 1, 1, 1, -1, 0, -1, -3, 1, 3, -3, 2, -10 ],
[ -2, -1, 2, -1, 8, -1, 11, -2, 3, 1, -2, -12 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 + x - 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ -1, 1, -1 ],
[ -1, -1, -1 ],
[ 1, -1, 1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 11, 1, 1 ],
[ 3, 3, 1 ],
[ 13, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 11, 1, 1 ],
[ 3, 3, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1 ], l_ratios := [ 0, 0, 1, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1/9, 1 ], eigenvalues := [*
[ -1, -1, -1, -1, 0, -3, -7, -1, -5, -5, 10, 2 ],
[ 1, -3, -1, -5, -4, -1, -3, 1, 7, -3, -2, -2 ],
[ 1, 1, 1, -1, 0, -1, -3, 1, 3, -3, 2, -10 ],
[
-1,
a,
1,
a,
4,
-3*a - 2,
a + 6,
-1,
-3*a,
3*a + 2,
2*a,
-6
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - q^5 + q^6 - q^7 - q^8 - 2*q^9 + q^10 - q^12 - 3*q^13 + q^14 + q^15 + q^16 - 7*q^17 + 2*q^18 - q^19 - q^20 + q^21 - 5*q^23 + q^24 + q^25 + 3*q^26 + 5*q^27 - q^28 - 5*q^29 - q^30 + 10*q^31 - q^32 + 7*q^34 + q^35 - 2*q^36 + 2*q^37 + O(q^38),
q + q^2 - 3*q^3 + q^4 - q^5 - 3*q^6 - 5*q^7 + q^8 + 6*q^9 - q^10 - 4*q^11 - 3*q^12 - q^13 - 5*q^14 + 3*q^15 + q^16 - 3*q^17 + 6*q^18 + q^19 - q^20 + 15*q^21 - 4*q^22 + 7*q^23 - 3*q^24 + q^25 - q^26 - 9*q^27 - 5*q^28 - 3*q^29 + 3*q^30 - 2*q^31 + q^32 + 12*q^33 - 3*q^34 + 5*q^35 + 6*q^36 - 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^5 + q^6 - q^7 + q^8 - 2*q^9 + q^10 + q^12 - q^13 - q^14 + q^15 + q^16 - 3*q^17 - 2*q^18 + q^19 + q^20 - q^21 + 3*q^23 + q^24 + q^25 - q^26 - 5*q^27 - q^28 - 3*q^29 + q^30 + 2*q^31 + q^32 - 3*q^34 - q^35 - 2*q^36 - 10*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + q^5 - a*q^6 + a*q^7 - q^8 + (-a + 1)*q^9 - q^10 + 4*q^11 + a*q^12 + (-3*a - 2)*q^13 - a*q^14 + a*q^15 + q^16 + (a + 6)*q^17 + (a - 1)*q^18 - q^19 + q^20 + (-a + 4)*q^21 - 4*q^22 - 3*a*q^23 - a*q^24 + q^25 + (3*a + 2)*q^26 + (-a - 4)*q^27 + a*q^28 + (3*a + 2)*q^29 - a*q^30 + 2*a*q^31 - q^32 + 4*a*q^33 + (-a - 6)*q^34 + a*q^35 + (-a + 1)*q^36 - 6*q^37 + O(q^38)
*]> ;  // time = 59.75 seconds




J[191] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 191, 191 ], new_dimensions := [ 2, 14 ], dimensions := [ 2, 14 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -2, -1, -1, -1, -7, 0, -6, -1, 0, -5, 2 ],
[ 0, 2, 1, 3, -3, 19, 14, 20, -13, 6, 15, -8 ]
], hecke_fields := [
x^2 + x - 1,
x^14 - 23*x^12 + x^11 + 205*x^10 - 13*x^9 - 895*x^8 + 35*x^7 + 1993*x^6 + 103*x^5 - 2135*x^4 - 465*x^3 + 853*x^2 + 374*x + 41
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 95 ]
], tamagawa_numbers := [
[ 1 ],
[ 95 ]
], torsion_upper_bounds := [ 1, 95 ], torsion_lower_bounds := [ 1, 95 ], l_ratios := [ 0, 1/95 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-1,
-a - 1,
-a - 1,
a,
3*a - 2,
0,
-3,
a,
-2*a - 1,
5*a,
-4*a - 1
],
[
a,
-145153/114035*a^13 + 32777/114035*a^12 + 3364061/114035*a^11 - 874037/114035*a^10 - 30238352/114035*a^9 + 8179107/114035*a^8 + 133274007/114035*a^7 - 31876833/114035*a^6 - 300314067/114035*a^5 + 43961084/114035*a^4 + 328052329/114035*a^3 + 4557079/114035*a^2 - 27781803/22807*a - 29013772/114035,
-44318/114035*a^13 - 468/114035*a^12 + 996676/114035*a^11 - 67192/114035*a^10 - 8645332/114035*a^9 + 1110732/114035*a^8 + 36541877/114035*a^7 - 5434583/114035*a^6 - 78444822/114035*a^5 + 7801444/114035*a^4 + 81404284/114035*a^3 + 2785164/114035*a^2 - 6622972/22807*a - 6986182/114035,
148787/114035*a^13 - 73368/114035*a^12 - 3418414/114035*a^11 + 1764598/114035*a^10 + 30273378/114035*a^9 - 15485288/114035*a^8 - 130230738/114035*a^7 + 59339692/114035*a^6 + 282975218/114035*a^5 - 90112966/114035*a^4 - 296004726/114035*a^3 + 24031844/114035*a^2 + 24591132/22807*a + 24473743/114035,
-317749/114035*a^13 + 87501/114035*a^12 + 7255723/114035*a^11 - 2329051/114035*a^10 - 63902811/114035*a^9 + 21925031/114035*a^8 + 273703901/114035*a^7 - 87350029/114035*a^6 - 592597121/114035*a^5 + 131174117/114035*a^4 + 615896407/114035*a^3 - 20228013/114035*a^2 - 50237157/22807*a - 50606546/114035,
169418/114035*a^13 - 44707/114035*a^12 - 3873501/114035*a^11 + 1208972/114035*a^10 + 34207957/114035*a^9 - 11502337/114035*a^8 - 147297467/114035*a^7 + 46178043/114035*a^6 + 321976277/114035*a^5 - 69816889/114035*a^4 - 339639974/114035*a^3 + 10698151/114035*a^2 + 28096743/22807*a + 28321417/114035,
303228/114035*a^13 - 86692/114035*a^12 - 6907461/114035*a^11 + 2286332/114035*a^10 + 60603762/114035*a^9 - 21383092/114035*a^8 - 257968172/114035*a^7 + 84810468/114035*a^6 + 552823792/114035*a^5 - 127305184/114035*a^4 - 565213084/114035*a^3 + 21919331/114035*a^2 + 45132248/22807*a + 45171892/114035,
-24374/114035*a^13 + 60751/114035*a^12 + 524093/114035*a^11 - 1347011/114035*a^10 - 4102891/114035*a^9 + 11125891/114035*a^8 + 13791251/114035*a^7 - 41743519/114035*a^6 - 16672401/114035*a^5 + 68606947/114035*a^4 - 1099913/114035*a^3 - 38565303/114035*a^2 + 1095165/22807*a + 3360679/114035,
39921/22807*a^13 - 4913/22807*a^12 - 908173/22807*a^11 + 165777/22807*a^10 + 7973795/22807*a^9 - 1768332/22807*a^8 - 34094825/22807*a^7 + 7468373/22807*a^6 + 73831676/22807*a^5 - 10996563/22807*a^4 - 76780679/22807*a^3 - 206151/22807*a^2 + 31072819/22807*a + 6279936/22807,
29682/22807*a^13 + 685/22807*a^12 - 686101/22807*a^11 + 22129/22807*a^10 + 6157277/22807*a^9 - 428091/22807*a^8 - 27138725/22807*a^7 + 1952471/22807*a^6 + 61244391/22807*a^5 - 1415669/22807*a^4 - 66926471/22807*a^3 - 5457861/22807*a^2 + 28139201/22807*a + 6245485/22807,
141063/114035*a^13 - 75647/114035*a^12 - 3159481/114035*a^11 + 1847727/114035*a^10 + 27001997/114035*a^9 - 16450667/114035*a^8 - 110256147/114035*a^7 + 64132173/114035*a^6 + 221254747/114035*a^5 - 101220029/114035*a^4 - 206018409/114035*a^3 + 37764231/114035*a^2 + 15179661/22807*a + 14145902/114035,
167816/114035*a^13 - 78339/114035*a^12 - 3890397/114035*a^11 + 1890079/114035*a^10 + 34906349/114035*a^9 - 16634679/114035*a^8 - 153103989/114035*a^7 + 63896051/114035*a^6 + 342297969/114035*a^5 - 96779723/114035*a^4 - 371525683/114035*a^3 + 22562677/114035*a^2 + 31806965/22807*a + 31900929/114035
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-a - 1)*q^4 + (-a - 1)*q^5 - a*q^6 + (-a - 1)*q^7 + (-2*a - 1)*q^8 - 2*q^9 - q^10 + a*q^11 + (a + 1)*q^12 + (3*a - 2)*q^13 - q^14 + (a + 1)*q^15 + 3*a*q^16 - 2*a*q^18 - 3*q^19 + (a + 2)*q^20 + (a + 1)*q^21 + (-a + 1)*q^22 + a*q^23 + (2*a + 1)*q^24 + (a - 3)*q^25 + (-5*a + 3)*q^26 + 5*q^27 + (a + 2)*q^28 + (-2*a - 1)*q^29 + q^30 + 5*a*q^31 + (a + 5)*q^32 - a*q^33 + (a + 2)*q^35 + (2*a + 2)*q^36 + (-4*a - 1)*q^37 + O(q^38),
q + a*q^2 + (-145153/114035*a^13 + 32777/114035*a^12 + 3364061/114035*a^11 - 874037/114035*a^10 - 30238352/114035*a^9 + 8179107/114035*a^8 + 133274007/114035*a^7 - 31876833/114035*a^6 - 300314067/114035*a^5 + 43961084/114035*a^4 + 328052329/114035*a^3 + 4557079/114035*a^2 - 27781803/22807*a - 29013772/114035)*q^3 + (a^2 - 2)*q^4 + (-44318/114035*a^13 - 468/114035*a^12 + 996676/114035*a^11 - 67192/114035*a^10 - 8645332/114035*a^9 + 1110732/114035*a^8 + 36541877/114035*a^7 - 5434583/114035*a^6 - 78444822/114035*a^5 + 7801444/114035*a^4 + 81404284/114035*a^3 + 2785164/114035*a^2 - 6622972/22807*a - 6986182/114035)*q^5 + (32777/114035*a^13 + 25542/114035*a^12 - 728884/114035*a^11 - 481987/114035*a^10 + 6292118/114035*a^9 + 3362072/114035*a^8 - 26796478/114035*a^7 - 11024138/114035*a^6 + 58911843/114035*a^5 + 18150674/114035*a^4 - 62939066/114035*a^3 - 15093506/114035*a^2 + 5054690/22807*a + 5951273/114035)*q^6 + (148787/114035*a^13 - 73368/114035*a^12 - 3418414/114035*a^11 + 1764598/114035*a^10 + 30273378/114035*a^9 - 15485288/114035*a^8 - 130230738/114035*a^7 + 59339692/114035*a^6 + 282975218/114035*a^5 - 90112966/114035*a^4 - 296004726/114035*a^3 + 24031844/114035*a^2 + 24591132/22807*a + 24473743/114035)*q^7 + (a^3 - 4*a)*q^8 + (34542/114035*a^13 + 21737/114035*a^12 - 802949/114035*a^11 - 412297/114035*a^10 + 7331993/114035*a^9 + 2916102/114035*a^8 - 33454383/114035*a^7 - 9948713/114035*a^6 + 79726068/114035*a^5 + 18237999/114035*a^4 - 92932081/114035*a^3 - 19074881/114035*a^2 + 8100797/22807*a + 10072718/114035)*q^9 + (-468/114035*a^13 - 22638/114035*a^12 - 22874/114035*a^11 + 439858/114035*a^10 + 534598/114035*a^9 - 3122733/114035*a^8 - 3883453/114035*a^7 + 9880952/114035*a^6 + 12366198/114035*a^5 - 13214646/114035*a^4 - 17822706/114035*a^3 + 4688394/114035*a^2 + 1917750/22807*a + 1817038/114035)*q^10 + (-317749/114035*a^13 + 87501/114035*a^12 + 7255723/114035*a^11 - 2329051/114035*a^10 - 63902811/114035*a^9 + 21925031/114035*a^8 + 273703901/114035*a^7 - 87350029/114035*a^6 - 592597121/114035*a^5 + 131174117/114035*a^4 + 615896407/114035*a^3 - 20228013/114035*a^2 - 50237157/22807*a - 50606546/114035)*q^11 + (315848/114035*a^13 - 40567/114035*a^12 - 7242886/114035*a^11 + 1320907/114035*a^10 + 64264877/114035*a^9 - 13819277/114035*a^8 - 278719347/114035*a^7 + 57340948/114035*a^6 + 615402777/114035*a^5 - 80882339/114035*a^4 - 655956859/114035*a^3 - 11799489/114035*a^2 + 54302141/22807*a + 56683687/114035)*q^12 + (169418/114035*a^13 - 44707/114035*a^12 - 3873501/114035*a^11 + 1208972/114035*a^10 + 34207957/114035*a^9 - 11502337/114035*a^8 - 147297467/114035*a^7 + 46178043/114035*a^6 + 321976277/114035*a^5 - 69816889/114035*a^4 - 339639974/114035*a^3 + 10698151/114035*a^2 + 28096743/22807*a + 28321417/114035)*q^13 + (-73368/114035*a^13 + 3687/114035*a^12 + 1615811/114035*a^11 - 227957/114035*a^10 - 13551057/114035*a^9 + 2933627/114035*a^8 + 54132147/114035*a^7 - 13557273/114035*a^6 - 105438027/114035*a^5 + 21655519/114035*a^4 + 93217799/114035*a^3 - 3959651/114035*a^2 - 6234519/22807*a - 6100267/114035)*q^14 + (101858/114035*a^13 - 58322/114035*a^12 - 2292531/114035*a^11 + 1387757/114035*a^10 + 19694912/114035*a^9 - 12095462/114035*a^8 - 80836142/114035*a^7 + 46393178/114035*a^6 + 162965222/114035*a^5 - 72409694/114035*a^4 - 152342989/114035*a^3 + 26703391/114035*a^2 + 11332620/22807*a + 10449012/114035)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (303228/114035*a^13 - 86692/114035*a^12 - 6907461/114035*a^11 + 2286332/114035*a^10 + 60603762/114035*a^9 - 21383092/114035*a^8 - 257968172/114035*a^7 + 84810468/114035*a^6 + 552823792/114035*a^5 - 127305184/114035*a^4 - 565213084/114035*a^3 + 21919331/114035*a^2 + 45132248/22807*a + 45171892/114035)*q^17 + (21737/114035*a^13 - 8483/114035*a^12 - 446839/114035*a^11 + 250883/114035*a^10 + 3365148/114035*a^9 - 2539293/114035*a^8 - 11157683/114035*a^7 + 10883862/114035*a^6 + 14680173/114035*a^5 - 19184911/114035*a^4 - 3012851/114035*a^3 + 11039659/114035*a^2 - 569198/22807*a - 1416222/114035)*q^18 + (-24374/114035*a^13 + 60751/114035*a^12 + 524093/114035*a^11 - 1347011/114035*a^10 - 4102891/114035*a^9 + 11125891/114035*a^8 + 13791251/114035*a^7 - 41743519/114035*a^6 - 16672401/114035*a^5 + 68606947/114035*a^4 - 1099913/114035*a^3 - 38565303/114035*a^2 + 1095165/22807*a + 3360679/114035)*q^19 + (65998/114035*a^13 - 32702/114035*a^12 - 1553026/114035*a^11 + 764922/114035*a^10 + 14161847/114035*a^9 - 6523777/114035*a^8 - 63186422/114035*a^7 + 24168088/114035*a^6 + 143723202/114035*a^5 - 34424774/114035*a^4 - 158337794/114035*a^3 + 4417626/114035*a^2 + 13644358/22807*a + 13991552/114035)*q^20 + (-504737/114035*a^13 + 144888/114035*a^12 + 11503414/114035*a^11 - 3823758/114035*a^10 - 101029758/114035*a^9 + 35742508/114035*a^8 + 430936308/114035*a^7 - 141443112/114035*a^6 - 927320908/114035*a^5 + 210797716/114035*a^4 + 955568936/114035*a^3 - 32381654/114035*a^2 - 77251470/22807*a - 78729853/114035)*q^21 + (87501/114035*a^13 - 52504/114035*a^12 - 2011302/114035*a^11 + 1235734/114035*a^10 + 17794294/114035*a^9 - 10681454/114035*a^8 - 76228814/114035*a^7 + 40676636/114035*a^6 + 163902264/114035*a^5 - 62497708/114035*a^4 - 167981298/114035*a^3 + 19854112/114035*a^2 + 13646316/22807*a + 13027709/114035)*q^22 + (39921/22807*a^13 - 4913/22807*a^12 - 908173/22807*a^11 + 165777/22807*a^10 + 7973795/22807*a^9 - 1768332/22807*a^8 - 34094825/22807*a^7 + 7468373/22807*a^6 + 73831676/22807*a^5 - 10996563/22807*a^4 - 76780679/22807*a^3 - 206151/22807*a^2 + 31072819/22807*a + 6279936/22807)*q^23 + (-106121/114035*a^13 - 29466/114035*a^12 + 2462827/114035*a^11 + 480011/114035*a^10 - 22297489/114035*a^9 - 2759531/114035*a^8 + 99879224/114035*a^7 + 7965989/114035*a^6 - 231238369/114035*a^5 - 17922727/114035*a^4 + 260947963/114035*a^3 + 32279373/114035*a^2 - 22398073/22807*a - 24852314/114035)*q^24 + (35334/114035*a^13 - 1356/114035*a^12 - 781783/114035*a^11 + 88941/114035*a^10 + 6620271/114035*a^9 - 1141371/114035*a^8 - 26952561/114035*a^7 + 5136669/114035*a^6 + 54351291/114035*a^5 - 7626787/114035*a^4 - 50630237/114035*a^3 + 447033/114035*a^2 + 3478182/22807*a + 2962646/114035)*q^25 + (-44707/114035*a^13 + 23113/114035*a^12 + 1039554/114035*a^11 - 522733/114035*a^10 - 9299903/114035*a^9 + 4331643/114035*a^8 + 40248413/114035*a^7 - 15673797/114035*a^6 - 87266943/114035*a^5 + 22067456/114035*a^4 + 89477521/114035*a^3 - 4029839/114035*a^2 - 7008183/22807*a - 6946138/114035)*q^26 + (-557464/114035*a^13 + 145556/114035*a^12 + 12789383/114035*a^11 - 3857481/114035*a^10 - 113360386/114035*a^9 + 36119091/114035*a^8 + 489914611/114035*a^7 - 142576889/114035*a^6 - 1074302751/114035*a^5 + 208584342/114035*a^4 + 1134739817/114035*a^3 - 17430173/114035*a^2 - 93655848/22807*a - 96218141/114035)*q^27 + (-293887/114035*a^13 + 75083/114035*a^12 + 6682239/114035*a^11 - 2039813/114035*a^10 - 58566913/114035*a^9 + 19438363/114035*a^8 + 249472083/114035*a^7 - 77894987/114035*a^6 - 536738013/114035*a^5 + 116803051/114035*a^4 + 553933681/114035*a^3 - 16653379/114035*a^2 - 44914391/22807*a - 45939398/114035)*q^28 + (29682/22807*a^13 + 685/22807*a^12 - 686101/22807*a^11 + 22129/22807*a^10 + 6157277/22807*a^9 - 428091/22807*a^8 - 27138725/22807*a^7 + 1952471/22807*a^6 + 61244391/22807*a^5 - 1415669/22807*a^4 - 66926471/22807*a^3 - 5457861/22807*a^2 + 28139201/22807*a + 6245485/22807)*q^29 + (-58322/114035*a^13 + 50203/114035*a^12 + 1285899/114035*a^11 - 1185978/114035*a^10 - 10771308/114035*a^9 + 10326768/114035*a^8 + 42828148/114035*a^7 - 40037772/114035*a^6 - 82901068/114035*a^5 + 65123841/114035*a^4 + 74067361/114035*a^3 - 30221774/114035*a^2 - 5529176/22807*a - 4176178/114035)*q^30 + (141063/114035*a^13 - 75647/114035*a^12 - 3159481/114035*a^11 + 1847727/114035*a^10 + 27001997/114035*a^9 - 16450667/114035*a^8 - 110256147/114035*a^7 + 64132173/114035*a^6 + 221254747/114035*a^5 - 101220029/114035*a^4 - 206018409/114035*a^3 + 37764231/114035*a^2 + 15179661/22807*a + 14145902/114035)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-98063/114035*a^13 + 9437/114035*a^12 + 2327431/114035*a^11 - 306897/114035*a^10 - 21575277/114035*a^9 + 3187387/114035*a^8 + 98962207/114035*a^7 - 12871453/114035*a^6 - 234448567/114035*a^5 + 15650379/114035*a^4 + 270634419/114035*a^3 + 12054799/114035*a^2 - 23802029/22807*a - 23649702/114035)*q^33 + (-86692/114035*a^13 + 66783/114035*a^12 + 1983104/114035*a^11 - 1557978/114035*a^10 - 17441128/114035*a^9 + 13420888/114035*a^8 + 74197488/114035*a^7 - 51509612/114035*a^6 - 158537668/114035*a^5 + 82178696/114035*a^4 + 162920351/114035*a^3 - 32992244/114035*a^2 - 13647076/22807*a - 12432348/114035)*q^34 + (-58851/114035*a^13 - 52871/114035*a^12 + 1399907/114035*a^11 + 1088501/114035*a^10 - 13111959/114035*a^9 - 8471251/114035*a^8 + 61447029/114035*a^7 + 31363979/114035*a^6 - 150287009/114035*a^5 - 56984197/114035*a^4 + 178560403/114035*a^3 + 48184383/114035*a^2 - 15433091/22807*a - 18678334/114035)*q^35 + (-77567/114035*a^13 + 9638/114035*a^12 + 1835044/114035*a^11 - 266343/114035*a^10 - 16920698/114035*a^9 + 2464728/114035*a^8 + 77031833/114035*a^7 - 8744242/114035*a^6 - 180875958/114035*a^5 + 6919646/114035*a^4 + 207011526/114035*a^3 + 16762111/114035*a^2 - 18110766/22807*a - 21036653/114035)*q^36 + (167816/114035*a^13 - 78339/114035*a^12 - 3890397/114035*a^11 + 1890079/114035*a^10 + 34906349/114035*a^9 - 16634679/114035*a^8 - 153103989/114035*a^7 + 63896051/114035*a^6 + 342297969/114035*a^5 - 96779723/114035*a^4 - 371525683/114035*a^3 + 22562677/114035*a^2 + 31806965/22807*a + 31900929/114035)*q^37 + O(q^38)
*]> ;  // time = 2.459 seconds




J[193] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 193, 193, 193 ], new_dimensions := [ 2, 5, 8 ], dimensions := [ 2, 5, 8 ], intersection_graph := [ 0, 11, 1, 11, 0, 1, 1, 1, 0 ], ap_traces := [
[ -3, -2, 0, -1, 3, -6, -6, -14, -9, 9, 1, 1 ],
[ -2, -5, -8, -10, -10, 2, -9, 14, -20, -3, -6, -6 ],
[ 2, 5, 8, 5, 9, -4, 7, 0, 23, -2, 7, -13 ]
], hecke_fields := [
x^2 + 3*x + 1,
x^5 + 2*x^4 - 5*x^3 - 7*x^2 + 7*x + 1,
x^8 - 2*x^7 - 9*x^6 + 18*x^5 + 21*x^4 - 44*x^3 - 11*x^2 + 27*x + 1
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ]
], torsion_upper_bounds := [ 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1 ], l_ratios := [ 0, 0, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[
a,
-1,
2*a + 3,
-3*a - 5,
-3*a - 3,
-3,
2*a,
-7,
3*a,
a + 6,
3*a + 5,
3*a + 5
],
[
a,
a^4 - 5*a^2 + a + 1,
-a^4 + 5*a^2 - 2*a - 4,
-a^4 - a^3 + 3*a^2 + a - 1,
a^4 + 3*a^3 - 3*a^2 - 8*a + 1,
-a^4 - 4*a^3 + 3*a^2 + 13*a - 4,
2*a^4 + 2*a^3 - 7*a^2 - 2*a - 1,
2*a^3 - 9*a + 6,
-a^4 - 2*a^3 + 2*a^2 + 5*a - 2,
-4*a^3 + 18*a - 7,
a^4 - 4*a^2 + a - 2,
-2*a^4 + 2*a^3 + 10*a^2 - 11*a - 2
],
[
a,
-1/7*a^7 + 4/7*a^6 + 8/7*a^5 - 34/7*a^4 - 16/7*a^3 + 69/7*a^2 + 6/7*a - 18/7,
-8/7*a^7 + 4/7*a^6 + 78/7*a^5 - 27/7*a^4 - 212/7*a^3 + 41/7*a^2 + 160/7*a + 10/7,
15/7*a^7 - 11/7*a^6 - 148/7*a^5 + 83/7*a^4 + 408/7*a^3 - 146/7*a^2 - 307/7*a + 18/7,
3/7*a^7 - 5/7*a^6 - 31/7*a^5 + 39/7*a^4 + 97/7*a^3 - 67/7*a^2 - 95/7*a + 19/7,
-4/7*a^7 + 2/7*a^6 + 39/7*a^5 - 17/7*a^4 - 99/7*a^3 + 38/7*a^2 + 52/7*a - 9/7,
23/7*a^7 - 15/7*a^6 - 219/7*a^5 + 110/7*a^4 + 564/7*a^3 - 187/7*a^2 - 383/7*a + 15/7,
-26/7*a^7 + 13/7*a^6 + 264/7*a^5 - 93/7*a^4 - 759/7*a^3 + 149/7*a^2 + 604/7*a + 22/7,
-19/7*a^7 + 13/7*a^6 + 187/7*a^5 - 93/7*a^4 - 514/7*a^3 + 142/7*a^2 + 380/7*a + 36/7,
26/7*a^7 - 13/7*a^6 - 250/7*a^5 + 79/7*a^4 + 661/7*a^3 - 79/7*a^2 - 485/7*a - 57/7,
-13/7*a^7 + 10/7*a^6 + 132/7*a^5 - 64/7*a^4 - 390/7*a^3 + 50/7*a^2 + 344/7*a + 81/7,
-3*a^7 + 2*a^6 + 29*a^5 - 15*a^4 - 77*a^3 + 25*a^2 + 57*a
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-3*a - 3)*q^4 + (2*a + 3)*q^5 - a*q^6 + (-3*a - 5)*q^7 + (4*a + 3)*q^8 - 2*q^9 + (-3*a - 2)*q^10 + (-3*a - 3)*q^11 + (3*a + 3)*q^12 - 3*q^13 + (4*a + 3)*q^14 + (-2*a - 3)*q^15 + (-3*a + 2)*q^16 + 2*a*q^17 - 2*a*q^18 - 7*q^19 + (3*a - 3)*q^20 + (3*a + 5)*q^21 + (6*a + 3)*q^22 + 3*a*q^23 + (-4*a - 3)*q^24 - 3*a*q^26 + 5*q^27 + (-3*a + 6)*q^28 + (a + 6)*q^29 + (3*a + 2)*q^30 + (3*a + 5)*q^31 + (3*a - 3)*q^32 + (3*a + 3)*q^33 + (-6*a - 2)*q^34 + (-a - 9)*q^35 + (6*a + 6)*q^36 + (3*a + 5)*q^37 + O(q^38),
q + a*q^2 + (a^4 - 5*a^2 + a + 1)*q^3 + (a^2 - 2)*q^4 + (-a^4 + 5*a^2 - 2*a - 4)*q^5 + (-2*a^4 + 8*a^2 - 6*a - 1)*q^6 + (-a^4 - a^3 + 3*a^2 + a - 1)*q^7 + (a^3 - 4*a)*q^8 + (-a^4 + a^3 + 7*a^2 - 4*a - 3)*q^9 + (2*a^4 - 9*a^2 + 3*a + 1)*q^10 + (a^4 + 3*a^3 - 3*a^2 - 8*a + 1)*q^11 + (2*a^4 - 2*a^3 - 10*a^2 + 11*a)*q^12 + (-a^4 - 4*a^3 + 3*a^2 + 13*a - 4)*q^13 + (a^4 - 2*a^3 - 6*a^2 + 6*a + 1)*q^14 + (-a^3 + 7*a - 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^4 + 2*a^3 - 7*a^2 - 2*a - 1)*q^17 + (3*a^4 + 2*a^3 - 11*a^2 + 4*a + 1)*q^18 + (2*a^3 - 9*a + 6)*q^19 + (-2*a^4 + a^3 + 7*a^2 - 9*a + 6)*q^20 + (-a^4 + 3*a^3 + 8*a^2 - 8*a - 2)*q^21 + (a^4 + 2*a^3 - a^2 - 6*a - 1)*q^22 + (-a^4 - 2*a^3 + 2*a^2 + 5*a - 2)*q^23 + (-2*a^4 + 9*a^2 - 2*a)*q^24 + (a^4 + a^3 - 6*a^2 - 4*a + 8)*q^25 + (-2*a^4 - 2*a^3 + 6*a^2 + 3*a + 1)*q^26 + (-5*a^3 - 5*a^2 + 17*a - 2)*q^27 + (-2*a^4 + a^3 + 7*a^2 - 8*a + 1)*q^28 + (-4*a^3 + 18*a - 7)*q^29 + (-a^4 + 7*a^2 - 2*a)*q^30 + (a^4 - 4*a^2 + a - 2)*q^31 + (-2*a^4 - 3*a^3 + 7*a^2 + 5*a - 1)*q^32 + (-5*a^4 - 3*a^3 + 18*a^2 - 2*a + 1)*q^33 + (-2*a^4 + 3*a^3 + 12*a^2 - 15*a - 2)*q^34 + (3*a^4 + 2*a^3 - 11*a^2 - a + 4)*q^35 + (-2*a^4 + 2*a^3 + 11*a^2 - 12*a + 3)*q^36 + (-2*a^4 + 2*a^3 + 10*a^2 - 11*a - 2)*q^37 + O(q^38),
q + a*q^2 + (-1/7*a^7 + 4/7*a^6 + 8/7*a^5 - 34/7*a^4 - 16/7*a^3 + 69/7*a^2 + 6/7*a - 18/7)*q^3 + (a^2 - 2)*q^4 + (-8/7*a^7 + 4/7*a^6 + 78/7*a^5 - 27/7*a^4 - 212/7*a^3 + 41/7*a^2 + 160/7*a + 10/7)*q^5 + (2/7*a^7 - 1/7*a^6 - 16/7*a^5 + 5/7*a^4 + 25/7*a^3 - 5/7*a^2 + 9/7*a + 1/7)*q^6 + (15/7*a^7 - 11/7*a^6 - 148/7*a^5 + 83/7*a^4 + 408/7*a^3 - 146/7*a^2 - 307/7*a + 18/7)*q^7 + (a^3 - 4*a)*q^8 + (-5/7*a^7 + 6/7*a^6 + 47/7*a^5 - 44/7*a^4 - 122/7*a^3 + 58/7*a^2 + 86/7*a + 29/7)*q^9 + (-12/7*a^7 + 6/7*a^6 + 117/7*a^5 - 44/7*a^4 - 311/7*a^3 + 72/7*a^2 + 226/7*a + 8/7)*q^10 + (3/7*a^7 - 5/7*a^6 - 31/7*a^5 + 39/7*a^4 + 97/7*a^3 - 67/7*a^2 - 95/7*a + 19/7)*q^11 + (5/7*a^7 - 6/7*a^6 - 47/7*a^5 + 51/7*a^4 + 115/7*a^3 - 107/7*a^2 - 65/7*a + 34/7)*q^12 + (-4/7*a^7 + 2/7*a^6 + 39/7*a^5 - 17/7*a^4 - 99/7*a^3 + 38/7*a^2 + 52/7*a - 9/7)*q^13 + (19/7*a^7 - 13/7*a^6 - 187/7*a^5 + 93/7*a^4 + 514/7*a^3 - 142/7*a^2 - 387/7*a - 15/7)*q^14 + (-11/7*a^7 + 9/7*a^6 + 109/7*a^5 - 66/7*a^4 - 309/7*a^3 + 108/7*a^2 + 248/7*a - 2/7)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (23/7*a^7 - 15/7*a^6 - 219/7*a^5 + 110/7*a^4 + 564/7*a^3 - 187/7*a^2 - 383/7*a + 15/7)*q^17 + (-4/7*a^7 + 2/7*a^6 + 46/7*a^5 - 17/7*a^4 - 162/7*a^3 + 31/7*a^2 + 164/7*a + 5/7)*q^18 + (-26/7*a^7 + 13/7*a^6 + 264/7*a^5 - 93/7*a^4 - 759/7*a^3 + 149/7*a^2 + 604/7*a + 22/7)*q^19 + (-2/7*a^7 + 1/7*a^6 + 16/7*a^5 - 5/7*a^4 - 32/7*a^3 + 12/7*a^2 + 12/7*a - 8/7)*q^20 + (4*a^7 - 2*a^6 - 40*a^5 + 13*a^4 + 113*a^3 - 14*a^2 - 90*a - 14)*q^21 + (1/7*a^7 - 4/7*a^6 - 15/7*a^5 + 34/7*a^4 + 65/7*a^3 - 62/7*a^2 - 62/7*a - 3/7)*q^22 + (-19/7*a^7 + 13/7*a^6 + 187/7*a^5 - 93/7*a^4 - 514/7*a^3 + 142/7*a^2 + 380/7*a + 36/7)*q^23 + (-a^5 + 9*a^3 - 17*a - 1)*q^24 + (-10/7*a^7 + 5/7*a^6 + 94/7*a^5 - 32/7*a^4 - 244/7*a^3 + 53/7*a^2 + 179/7*a - 26/7)*q^25 + (-6/7*a^7 + 3/7*a^6 + 55/7*a^5 - 15/7*a^4 - 138/7*a^3 + 8/7*a^2 + 99/7*a + 4/7)*q^26 + (-3*a^7 + 2*a^6 + 29*a^5 - 15*a^4 - 76*a^3 + 26*a^2 + 51*a)*q^27 + (-5/7*a^7 + 6/7*a^6 + 47/7*a^5 - 51/7*a^4 - 122/7*a^3 + 114/7*a^2 + 86/7*a - 55/7)*q^28 + (26/7*a^7 - 13/7*a^6 - 250/7*a^5 + 79/7*a^4 + 661/7*a^3 - 79/7*a^2 - 485/7*a - 57/7)*q^29 + (-13/7*a^7 + 10/7*a^6 + 132/7*a^5 - 78/7*a^4 - 376/7*a^3 + 127/7*a^2 + 295/7*a + 11/7)*q^30 + (-13/7*a^7 + 10/7*a^6 + 132/7*a^5 - 64/7*a^4 - 390/7*a^3 + 50/7*a^2 + 344/7*a + 81/7)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (15/7*a^7 - 4/7*a^6 - 155/7*a^5 + 20/7*a^4 + 464/7*a^3 + 1/7*a^2 - 412/7*a - 73/7)*q^33 + (31/7*a^7 - 12/7*a^6 - 304/7*a^5 + 81/7*a^4 + 825/7*a^3 - 130/7*a^2 - 606/7*a - 23/7)*q^34 + (-1/7*a^7 - 3/7*a^6 + 8/7*a^5 + 29/7*a^4 - 9/7*a^3 - 64/7*a^2 - 15/7*a + 17/7)*q^35 + (4/7*a^7 - 2/7*a^6 - 39/7*a^5 + 10/7*a^4 + 99/7*a^3 + 4/7*a^2 - 59/7*a - 54/7)*q^36 + (-3*a^7 + 2*a^6 + 29*a^5 - 15*a^4 - 77*a^3 + 25*a^2 + 57*a)*q^37 + O(q^38)
*]> ;  // time = 2.459 seconds




J[194] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 194, 194, 194, 97, 97 ], new_dimensions := [ 1, 4, 4, 3, 4 ], dimensions := [ 1, 4, 4, 6, 8 ], intersection_graph := [ 0, 1, 7, 1, 1, 1, 0, 1, 1, 67, 7, 1, 0, 71, 1, 1, 1, 71, 0, 1, 1, 67, 1, 1, 0 ], ap_traces := [
[ 1, 0, 4, -4, 4, -4, 6, -6, -4, 0, 0, -8 ],
[ -4, 2, -2, 6, 2, 4, -8, 8, 10, -6, 8, -2 ],
[ 4, 2, -2, 2, -2, 4, -8, 0, -10, 6, 8, 14 ]
], hecke_fields := [
x - 1,
x^4 - 2*x^3 - 9*x^2 + 18*x + 1,
x^4 - 2*x^3 - 9*x^2 + 18*x - 7
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 201, 3 ],
[ 3479, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 3 ],
[ 3479, 1 ]
], torsion_upper_bounds := [ 1, 3, 49 ], torsion_lower_bounds := [ 1, 3, 49 ], l_ratios := [ 1, 1/3, 71/49 ], analytic_sha_upper_bounds := [ 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1 ], eigenvalues := [*
[ 1, 0, 4, -4, 4, -4, 6, -6, -4, 0, 0, -8 ],
[
-1,
a,
-1/2*a^3 - 1/2*a^2 + 9/2*a + 1,
1/2*a^3 - 4*a + 5/2,
-a + 1,
a^3 - 8*a + 3,
a^3 - a^2 - 9*a + 6,
-a^3 - a^2 + 7*a + 6,
-1/2*a^3 + 3/2*a^2 + 9/2*a - 7,
1/2*a^3 - 2*a - 3/2,
-a^2 - 3*a + 9,
-3/2*a^3 + a^2 + 11*a - 17/2
],
[
1,
a,
1/2*a^3 - 1/2*a^2 - 11/2*a + 4,
-1/2*a^3 + 4*a - 1/2,
-2*a^3 + 2*a^2 + 19*a - 17,
a^3 - a^2 - 11*a + 10,
a^3 - a^2 - 9*a + 6,
a^3 - a^2 - 9*a + 8,
3/2*a^3 - 3/2*a^2 - 29/2*a + 10,
-1/2*a^3 + 2*a^2 + 4*a - 21/2,
-2*a^3 + 3*a^2 + 21*a - 21,
1/2*a^3 - a^2 - 3*a + 19/2
]
*], q_expansions := [*
q + q^2 + q^4 + 4*q^5 - 4*q^7 + q^8 - 3*q^9 + 4*q^10 + 4*q^11 - 4*q^13 - 4*q^14 + q^16 + 6*q^17 - 3*q^18 - 6*q^19 + 4*q^20 + 4*q^22 - 4*q^23 + 11*q^25 - 4*q^26 - 4*q^28 + q^32 + 6*q^34 - 16*q^35 - 3*q^36 - 8*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-1/2*a^3 - 1/2*a^2 + 9/2*a + 1)*q^5 - a*q^6 + (1/2*a^3 - 4*a + 5/2)*q^7 - q^8 + (a^2 - 3)*q^9 + (1/2*a^3 + 1/2*a^2 - 9/2*a - 1)*q^10 + (-a + 1)*q^11 + a*q^12 + (a^3 - 8*a + 3)*q^13 + (-1/2*a^3 + 4*a - 5/2)*q^14 + (-3/2*a^3 + 10*a + 1/2)*q^15 + q^16 + (a^3 - a^2 - 9*a + 6)*q^17 + (-a^2 + 3)*q^18 + (-a^3 - a^2 + 7*a + 6)*q^19 + (-1/2*a^3 - 1/2*a^2 + 9/2*a + 1)*q^20 + (a^3 + 1/2*a^2 - 13/2*a - 1/2)*q^21 + (a - 1)*q^22 + (-1/2*a^3 + 3/2*a^2 + 9/2*a - 7)*q^23 - a*q^24 + (-a^3 + a^2 + 8*a - 4)*q^25 + (-a^3 + 8*a - 3)*q^26 + (a^3 - 6*a)*q^27 + (1/2*a^3 - 4*a + 5/2)*q^28 + (1/2*a^3 - 2*a - 3/2)*q^29 + (3/2*a^3 - 10*a - 1/2)*q^30 + (-a^2 - 3*a + 9)*q^31 - q^32 + (-a^2 + a)*q^33 + (-a^3 + a^2 + 9*a - 6)*q^34 + (-a^2 - a + 2)*q^35 + (a^2 - 3)*q^36 + (-3/2*a^3 + a^2 + 11*a - 17/2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (1/2*a^3 - 1/2*a^2 - 11/2*a + 4)*q^5 + a*q^6 + (-1/2*a^3 + 4*a - 1/2)*q^7 + q^8 + (a^2 - 3)*q^9 + (1/2*a^3 - 1/2*a^2 - 11/2*a + 4)*q^10 + (-2*a^3 + 2*a^2 + 19*a - 17)*q^11 + a*q^12 + (a^3 - a^2 - 11*a + 10)*q^13 + (-1/2*a^3 + 4*a - 1/2)*q^14 + (1/2*a^3 - a^2 - 5*a + 7/2)*q^15 + q^16 + (a^3 - a^2 - 9*a + 6)*q^17 + (a^2 - 3)*q^18 + (a^3 - a^2 - 9*a + 8)*q^19 + (1/2*a^3 - 1/2*a^2 - 11/2*a + 4)*q^20 + (-a^3 - 1/2*a^2 + 17/2*a - 7/2)*q^21 + (-2*a^3 + 2*a^2 + 19*a - 17)*q^22 + (3/2*a^3 - 3/2*a^2 - 29/2*a + 10)*q^23 + a*q^24 + (-a^3 + a^2 + 10*a - 10)*q^25 + (a^3 - a^2 - 11*a + 10)*q^26 + (a^3 - 6*a)*q^27 + (-1/2*a^3 + 4*a - 1/2)*q^28 + (-1/2*a^3 + 2*a^2 + 4*a - 21/2)*q^29 + (1/2*a^3 - a^2 - 5*a + 7/2)*q^30 + (-2*a^3 + 3*a^2 + 21*a - 21)*q^31 + q^32 + (-2*a^3 + a^2 + 19*a - 14)*q^33 + (a^3 - a^2 - 9*a + 6)*q^34 + (2*a^3 - a^2 - 19*a + 12)*q^35 + (a^2 - 3)*q^36 + (1/2*a^3 - a^2 - 3*a + 19/2)*q^37 + O(q^38)
*]> ;  // time = 33.49 seconds




J[195] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 195, 195, 195, 195, 195, 65, 65, 65, 39, 39, 15 ], new_dimensions := [ 1, 1, 1, 1, 3, 1, 2, 2, 1, 2, 1 ], dimensions := [ 1, 1, 1, 1, 3, 2, 4, 4, 2, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 7, 1, 1, 3, 1, 0, 1, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 11, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 0, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 0, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 2, -1, 1, 3, -1, -1, -1, -2, -3, -2, -6, 11 ],
[ 2, 1, -1, -1, 5, -1, -7, -6, 3, 2, 2, 7 ],
[ -1, 1, 1, 0, 4, 1, 2, -4, 8, -2, -8, 6 ],
[ 2, 1, 1, -3, -5, 1, 5, 2, -1, 10, -2, -3 ],
[ 0, -3, -3, 1, 1, 3, -1, 6, -7, 18, 6, 13 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^3 - 7*x - 2
], atkin_lehners := [
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ],
[ -1, -1, -1 ],
[ 1, 1, -1 ]
], component_group_orders := [
[ 7, 1, 3 ],
[ 3, 7, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 11, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 1, 3, 1, 1, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1, 1 ], eigenvalues := [*
[ 2, -1, 1, 3, -1, -1, -1, -2, -3, -2, -6, 11 ],
[ 2, 1, -1, -1, 5, -1, -7, -6, 3, 2, 2, 7 ],
[ -1, 1, 1, 0, 4, 1, 2, -4, 8, -2, -8, 6 ],
[ 2, 1, 1, -3, -5, 1, 5, 2, -1, 10, -2, -3 ],
[
a,
-1,
-1,
-a^2 + 5,
-a^2 + 5,
1,
a^2 - 2*a - 5,
-2*a + 2,
a^2 - 2*a - 7,
6,
2*a + 2,
-a^2 - 2*a + 9
]
*], q_expansions := [*
q + 2*q^2 - q^3 + 2*q^4 + q^5 - 2*q^6 + 3*q^7 + q^9 + 2*q^10 - q^11 - 2*q^12 - q^13 + 6*q^14 - q^15 - 4*q^16 - q^17 + 2*q^18 - 2*q^19 + 2*q^20 - 3*q^21 - 2*q^22 - 3*q^23 + q^25 - 2*q^26 - q^27 + 6*q^28 - 2*q^29 - 2*q^30 - 6*q^31 - 8*q^32 + q^33 - 2*q^34 + 3*q^35 + 2*q^36 + 11*q^37 + O(q^38),
q + 2*q^2 + q^3 + 2*q^4 - q^5 + 2*q^6 - q^7 + q^9 - 2*q^10 + 5*q^11 + 2*q^12 - q^13 - 2*q^14 - q^15 - 4*q^16 - 7*q^17 + 2*q^18 - 6*q^19 - 2*q^20 - q^21 + 10*q^22 + 3*q^23 + q^25 - 2*q^26 + q^27 - 2*q^28 + 2*q^29 - 2*q^30 + 2*q^31 - 8*q^32 + 5*q^33 - 14*q^34 + q^35 + 2*q^36 + 7*q^37 + O(q^38),
q - q^2 + q^3 - q^4 + q^5 - q^6 + 3*q^8 + q^9 - q^10 + 4*q^11 - q^12 + q^13 + q^15 - q^16 + 2*q^17 - q^18 - 4*q^19 - q^20 - 4*q^22 + 8*q^23 + 3*q^24 + q^25 - q^26 + q^27 - 2*q^29 - q^30 - 8*q^31 - 5*q^32 + 4*q^33 - 2*q^34 - q^36 + 6*q^37 + O(q^38),
q + 2*q^2 + q^3 + 2*q^4 + q^5 + 2*q^6 - 3*q^7 + q^9 + 2*q^10 - 5*q^11 + 2*q^12 + q^13 - 6*q^14 + q^15 - 4*q^16 + 5*q^17 + 2*q^18 + 2*q^19 + 2*q^20 - 3*q^21 - 10*q^22 - q^23 + q^25 + 2*q^26 + q^27 - 6*q^28 + 10*q^29 + 2*q^30 - 2*q^31 - 8*q^32 - 5*q^33 + 10*q^34 - 3*q^35 + 2*q^36 - 3*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 - q^5 - a*q^6 + (-a^2 + 5)*q^7 + (3*a + 2)*q^8 + q^9 - a*q^10 + (-a^2 + 5)*q^11 + (-a^2 + 2)*q^12 + q^13 + (-2*a - 2)*q^14 + q^15 + (a^2 + 2*a + 4)*q^16 + (a^2 - 2*a - 5)*q^17 + a*q^18 + (-2*a + 2)*q^19 + (-a^2 + 2)*q^20 + (a^2 - 5)*q^21 + (-2*a - 2)*q^22 + (a^2 - 2*a - 7)*q^23 + (-3*a - 2)*q^24 + q^25 + a*q^26 - q^27 + (-2*a - 10)*q^28 + 6*q^29 + a*q^30 + (2*a + 2)*q^31 + (2*a^2 + 5*a - 2)*q^32 + (a^2 - 5)*q^33 + (-2*a^2 + 2*a + 2)*q^34 + (a^2 - 5)*q^35 + (a^2 - 2)*q^36 + (-a^2 - 2*a + 9)*q^37 + O(q^38)
*]> ;  // time = 47.569 seconds




J[197] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 197, 197, 197 ], new_dimensions := [ 1, 5, 10 ], dimensions := [ 1, 5, 10 ], intersection_graph := [ 0, 5, 1, 5, 0, 1, 1, 1, 0 ], ap_traces := [
[ -2, 0, 0, -3, 4, -2, -8, -3, -3, 7, -10, 7 ],
[ 0, -8, -4, -10, -8, -8, 9, -16, -1, 2, 2, -17 ],
[ 0, 10, 2, 11, 2, 8, -3, 17, -4, -9, 20, 12 ]
], hecke_fields := [
x - 1,
x^5 - 5*x^3 + x^2 + 3*x - 1,
x^10 - 15*x^8 + x^7 + 78*x^6 - 7*x^5 - 165*x^4 + 15*x^3 + 123*x^2 - 9*x - 26
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 49 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 49 ]
], torsion_upper_bounds := [ 1, 1, 49 ], torsion_lower_bounds := [ 1, 1, 49 ], l_ratios := [ 0, 0, 1/49 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[ -2, 0, 0, -3, 4, -2, -8, -3, -3, 7, -10, 7 ],
[
a,
-a^4 + 4*a^2 - a - 2,
3*a^4 + a^3 - 14*a^2 - 3*a + 5,
-2*a^4 - 2*a^3 + 9*a^2 + 6*a - 6,
-3*a^4 - 2*a^3 + 15*a^2 + 7*a - 10,
2*a^4 + 3*a^3 - 9*a^2 - 9*a + 3,
-3*a^4 - a^3 + 14*a^2 - 4,
4*a^4 + a^3 - 19*a^2 - a + 5,
-3*a^4 - a^3 + 13*a^2 + 3*a - 4,
-4*a^4 - 3*a^3 + 17*a^2 + 8*a - 5,
a^3 - 6*a + 1,
9*a^4 + 3*a^3 - 43*a^2 - 4*a + 16
],
[
a,
1/4*a^8 + 1/2*a^7 - 5/2*a^6 - 17/4*a^5 + 15/2*a^4 + 9*a^3 - 27/4*a^2 - 7/4*a + 5/2,
-1/2*a^8 + 5*a^6 - 3/2*a^5 - 13*a^4 + 7*a^3 + 11/2*a^2 - 9/2*a + 1,
-a^7 - a^6 + 10*a^5 + 8*a^4 - 27*a^3 - 18*a^2 + 14*a + 9,
-1/2*a^9 + 1/4*a^8 + 13/2*a^7 - 3*a^6 - 109/4*a^5 + 15/2*a^4 + 85/2*a^3 + 3/4*a^2 - 75/4*a - 3/2,
1/2*a^9 + 1/2*a^8 - 7*a^7 - 11/2*a^6 + 67/2*a^5 + 20*a^4 - 121/2*a^3 - 27*a^2 + 53/2*a + 11,
-1/2*a^9 + 1/2*a^8 + 7*a^7 - 11/2*a^6 - 63/2*a^5 + 16*a^4 + 105/2*a^3 - 11*a^2 - 49/2*a + 1,
a^3 + a^2 - 5*a - 1,
a^9 + 1/2*a^8 - 12*a^7 - 4*a^6 + 91/2*a^5 + 11*a^4 - 60*a^3 - 23/2*a^2 + 41/2*a + 2,
1/4*a^9 + a^8 - 7/2*a^7 - 45/4*a^6 + 18*a^5 + 38*a^4 - 143/4*a^3 - 157/4*a^2 + 17*a + 8,
-3/4*a^8 + 1/2*a^7 + 19/2*a^6 - 25/4*a^5 - 75/2*a^4 + 19*a^3 + 205/4*a^2 - 43/4*a - 31/2,
-1/4*a^9 + 9/2*a^7 + 9/4*a^6 - 25*a^5 - 19*a^4 + 195/4*a^3 + 165/4*a^2 - 22*a - 16
]
*], q_expansions := [*
q - 2*q^2 + 2*q^4 - 3*q^7 - 3*q^9 + 4*q^11 - 2*q^13 + 6*q^14 - 4*q^16 - 8*q^17 + 6*q^18 - 3*q^19 - 8*q^22 - 3*q^23 - 5*q^25 + 4*q^26 - 6*q^28 + 7*q^29 - 10*q^31 + 8*q^32 + 16*q^34 - 6*q^36 + 7*q^37 + O(q^38),
q + a*q^2 + (-a^4 + 4*a^2 - a - 2)*q^3 + (a^2 - 2)*q^4 + (3*a^4 + a^3 - 14*a^2 - 3*a + 5)*q^5 + (-a^3 + a - 1)*q^6 + (-2*a^4 - 2*a^3 + 9*a^2 + 6*a - 6)*q^7 + (a^3 - 4*a)*q^8 + (2*a^4 + a^3 - 7*a^2 - 2*a + 2)*q^9 + (a^4 + a^3 - 6*a^2 - 4*a + 3)*q^10 + (-3*a^4 - 2*a^3 + 15*a^2 + 7*a - 10)*q^11 + (a^4 - 7*a^2 + a + 4)*q^12 + (2*a^4 + 3*a^3 - 9*a^2 - 9*a + 3)*q^13 + (-2*a^4 - a^3 + 8*a^2 - 2)*q^14 + (-3*a^4 - a^3 + 15*a^2 + 6*a - 8)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3*a^4 - a^3 + 14*a^2 - 4)*q^17 + (a^4 + 3*a^3 - 4*a^2 - 4*a + 2)*q^18 + (4*a^4 + a^3 - 19*a^2 - a + 5)*q^19 + (-5*a^4 - 3*a^3 + 23*a^2 + 6*a - 9)*q^20 + (5*a^4 + 2*a^3 - 21*a^2 - a + 8)*q^21 + (-2*a^4 + 10*a^2 - a - 3)*q^22 + (-3*a^4 - a^3 + 13*a^2 + 3*a - 4)*q^23 + (-a + 3)*q^24 + (-3*a^4 - 2*a^3 + 14*a^2 + 7*a - 5)*q^25 + (3*a^4 + a^3 - 11*a^2 - 3*a + 2)*q^26 + (-2*a^3 - 5*a^2 + 7*a + 3)*q^27 + (3*a^4 + 2*a^3 - 16*a^2 - 8*a + 10)*q^28 + (-4*a^4 - 3*a^3 + 17*a^2 + 8*a - 5)*q^29 + (-a^4 + 9*a^2 + a - 3)*q^30 + (a^3 - 6*a + 1)*q^31 + (-3*a^3 - a^2 + 9*a + 1)*q^32 + (7*a^4 + a^3 - 34*a^2 - a + 15)*q^33 + (-a^4 - a^3 + 3*a^2 + 5*a - 3)*q^34 + (-a^4 + 3*a^3 + 7*a^2 - 10*a - 3)*q^35 + (-a^4 - a^3 + 9*a^2 + 3*a - 3)*q^36 + (9*a^4 + 3*a^3 - 43*a^2 - 4*a + 16)*q^37 + O(q^38),
q + a*q^2 + (1/4*a^8 + 1/2*a^7 - 5/2*a^6 - 17/4*a^5 + 15/2*a^4 + 9*a^3 - 27/4*a^2 - 7/4*a + 5/2)*q^3 + (a^2 - 2)*q^4 + (-1/2*a^8 + 5*a^6 - 3/2*a^5 - 13*a^4 + 7*a^3 + 11/2*a^2 - 9/2*a + 1)*q^5 + (1/4*a^9 + 1/2*a^8 - 5/2*a^7 - 17/4*a^6 + 15/2*a^5 + 9*a^4 - 27/4*a^3 - 7/4*a^2 + 5/2*a)*q^6 + (-a^7 - a^6 + 10*a^5 + 8*a^4 - 27*a^3 - 18*a^2 + 14*a + 9)*q^7 + (a^3 - 4*a)*q^8 + (-1/4*a^9 - 1/2*a^8 + 7/2*a^7 + 25/4*a^6 - 33/2*a^5 - 26*a^4 + 111/4*a^3 + 159/4*a^2 - 19/2*a - 13)*q^9 + (-1/2*a^9 + 5*a^7 - 3/2*a^6 - 13*a^5 + 7*a^4 + 11/2*a^3 - 9/2*a^2 + a)*q^10 + (-1/2*a^9 + 1/4*a^8 + 13/2*a^7 - 3*a^6 - 109/4*a^5 + 15/2*a^4 + 85/2*a^3 + 3/4*a^2 - 75/4*a - 3/2)*q^11 + (1/2*a^9 + 3/4*a^8 - 11/2*a^7 - 7*a^6 + 77/4*a^5 + 39/2*a^4 - 47/2*a^3 - 59/4*a^2 + 23/4*a + 3/2)*q^12 + (1/2*a^9 + 1/2*a^8 - 7*a^7 - 11/2*a^6 + 67/2*a^5 + 20*a^4 - 121/2*a^3 - 27*a^2 + 53/2*a + 11)*q^13 + (-a^8 - a^7 + 10*a^6 + 8*a^5 - 27*a^4 - 18*a^3 + 14*a^2 + 9*a)*q^14 + (1/2*a^9 - a^8 - 6*a^7 + 23/2*a^6 + 20*a^5 - 36*a^4 - 35/2*a^3 + 57/2*a^2 + a - 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^9 + 1/2*a^8 + 7*a^7 - 11/2*a^6 - 63/2*a^5 + 16*a^4 + 105/2*a^3 - 11*a^2 - 49/2*a + 1)*q^17 + (-1/2*a^9 - 1/4*a^8 + 13/2*a^7 + 3*a^6 - 111/4*a^5 - 27/2*a^4 + 87/2*a^3 + 85/4*a^2 - 61/4*a - 13/2)*q^18 + (a^3 + a^2 - 5*a - 1)*q^19 + (-3/2*a^8 - a^7 + 16*a^6 + 13/2*a^5 - 51*a^4 - 11*a^3 + 103/2*a^2 + 9/2*a - 15)*q^20 + (1/2*a^9 + 3/2*a^8 - 7*a^7 - 35/2*a^6 + 71/2*a^5 + 65*a^4 - 141/2*a^3 - 85*a^2 + 69/2*a + 29)*q^21 + (1/4*a^9 - a^8 - 5/2*a^7 + 47/4*a^6 + 4*a^5 - 40*a^4 + 33/4*a^3 + 171/4*a^2 - 6*a - 13)*q^22 + (a^9 + 1/2*a^8 - 12*a^7 - 4*a^6 + 91/2*a^5 + 11*a^4 - 60*a^3 - 23/2*a^2 + 41/2*a + 2)*q^23 + (1/4*a^9 + a^8 - 5/2*a^7 - 45/4*a^6 + 8*a^5 + 41*a^4 - 35/4*a^3 - 209/4*a^2 + a + 13)*q^24 + (a^8 + a^7 - 11*a^6 - 8*a^5 + 37*a^4 + 18*a^3 - 39*a^2 - 11*a + 9)*q^25 + (1/2*a^9 + 1/2*a^8 - 6*a^7 - 11/2*a^6 + 47/2*a^5 + 22*a^4 - 69/2*a^3 - 35*a^2 + 31/2*a + 13)*q^26 + (-a^9 - 2*a^8 + 13*a^7 + 23*a^6 - 58*a^5 - 87*a^4 + 97*a^3 + 120*a^2 - 38*a - 40)*q^27 + (-a^9 - a^8 + 12*a^7 + 10*a^6 - 47*a^5 - 34*a^4 + 68*a^3 + 45*a^2 - 28*a - 18)*q^28 + (1/4*a^9 + a^8 - 7/2*a^7 - 45/4*a^6 + 18*a^5 + 38*a^4 - 143/4*a^3 - 157/4*a^2 + 17*a + 8)*q^29 + (-a^9 + 3/2*a^8 + 11*a^7 - 19*a^6 - 65/2*a^5 + 65*a^4 + 21*a^3 - 121/2*a^2 + 1/2*a + 13)*q^30 + (-3/4*a^8 + 1/2*a^7 + 19/2*a^6 - 25/4*a^5 - 75/2*a^4 + 19*a^3 + 205/4*a^2 - 43/4*a - 31/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-3/2*a^9 + 1/2*a^8 + 19*a^7 - 13/2*a^6 - 153/2*a^5 + 16*a^4 + 221/2*a^3 + 5*a^2 - 81/2*a - 7)*q^33 + (1/2*a^9 - 1/2*a^8 - 5*a^7 + 15/2*a^6 + 25/2*a^5 - 30*a^4 - 7/2*a^3 + 37*a^2 - 7/2*a - 13)*q^34 + (-a^8 + 11*a^6 - 2*a^5 - 34*a^4 + 9*a^3 + 26*a^2 - 5*a - 4)*q^35 + (1/4*a^9 - 7/2*a^7 - 5/4*a^6 + 16*a^5 + 13*a^4 - 107/4*a^3 - 133/4*a^2 + 8*a + 13)*q^36 + (-1/4*a^9 + 9/2*a^7 + 9/4*a^6 - 25*a^5 - 19*a^4 + 195/4*a^3 + 165/4*a^2 - 22*a - 16)*q^37 + O(q^38)
*]> ;  // time = 2.719 seconds




J[199] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 199, 199, 199 ], new_dimensions := [ 2, 4, 10 ], dimensions := [ 2, 4, 10 ], intersection_graph := [ 0, 1, 71, 1, 0, 1, 71, 1, 0 ], ap_traces := [
[ -1, 4, 6, 0, -6, 2, 2, 2, 0, 8, -4, -6 ],
[ -3, -2, -5, -3, -7, 0, -13, 0, -4, -19, -2, 11 ],
[ 5, -4, -1, -3, 17, 0, 13, -8, 4, 31, -10, -1 ]
], hecke_fields := [
x^2 + x - 1,
x^4 + 3*x^3 - 4*x - 1,
x^10 - 5*x^9 - 4*x^8 + 51*x^7 - 32*x^6 - 154*x^5 + 151*x^4 + 168*x^3 - 168*x^2 - 54*x + 27
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 33 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 33 ]
], torsion_upper_bounds := [ 1, 1, 33 ], torsion_lower_bounds := [ 1, 1, 33 ], l_ratios := [ 1, 0, 1/33 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[
a,
2,
3,
0,
2*a - 2,
-4*a - 1,
-2*a,
6*a + 4,
-6*a - 3,
-4*a + 2,
-2*a - 3,
6*a
],
[
a,
-a^3 - 2*a^2 + a + 1,
a^3 + a^2 - 3*a - 2,
2*a^3 + 5*a^2 - 2*a - 6,
-2*a^3 - 4*a^2 + 3*a + 2,
-2*a^3 - 3*a^2 + 5*a + 3,
-2*a^3 - 3*a^2 + 4*a - 1,
3*a^3 + 5*a^2 - 4*a - 3,
-4*a^2 - 4*a + 5,
3*a^2 + 6*a - 7,
-a^3 - 4*a^2 - a + 4,
-2*a^3 - 4*a^2 + a + 5
],
[
a,
-2/9*a^9 + 7/9*a^8 + 23/9*a^7 - 9*a^6 - 89/9*a^5 + 287/9*a^4 + 151/9*a^3 - 107/3*a^2 - 35/3*a + 3,
4/9*a^9 - 14/9*a^8 - 37/9*a^7 + 16*a^6 + 97/9*a^5 - 430/9*a^4 - 122/9*a^3 + 136/3*a^2 + 37/3*a - 4,
7/9*a^9 - 29/9*a^8 - 58/9*a^7 + 34*a^6 + 109/9*a^5 - 964/9*a^4 - 74/9*a^3 + 337/3*a^2 + 40/3*a - 14,
11/9*a^9 - 34/9*a^8 - 104/9*a^7 + 39*a^6 + 278/9*a^5 - 1070/9*a^4 - 313/9*a^3 + 362/3*a^2 + 68/3*a - 14,
-1/3*a^9 + 4/3*a^8 + 3*a^7 - 44/3*a^6 - 22/3*a^5 + 50*a^4 + 8*a^3 - 181/3*a^2 - 6*a + 13,
-17/9*a^9 + 55/9*a^8 + 164/9*a^7 - 64*a^6 - 473/9*a^5 + 1796/9*a^4 + 658/9*a^3 - 623/3*a^2 - 182/3*a + 29,
1/3*a^8 + 1/3*a^7 - 16/3*a^6 - 3*a^5 + 79/3*a^4 + 20/3*a^3 - 119/3*a^2 - 7*a + 6,
19/9*a^9 - 68/9*a^8 - 175/9*a^7 + 239/3*a^6 + 454/9*a^5 - 2260/9*a^4 - 569/9*a^3 + 797/3*a^2 + 178/3*a - 36,
-17/9*a^9 + 58/9*a^8 + 158/9*a^7 - 202/3*a^6 - 410/9*a^5 + 1880/9*a^4 + 466/9*a^3 - 646/3*a^2 - 128/3*a + 30,
10/9*a^9 - 23/9*a^8 - 112/9*a^7 + 83/3*a^6 + 400/9*a^5 - 820/9*a^4 - 569/9*a^3 + 296/3*a^2 + 103/3*a - 13,
-5/3*a^9 + 17/3*a^8 + 16*a^7 - 181/3*a^6 - 137/3*a^5 + 194*a^4 + 63*a^3 - 635/3*a^2 - 54*a + 30
]
*], q_expansions := [*
q + a*q^2 + 2*q^3 + (-a - 1)*q^4 + 3*q^5 + 2*a*q^6 + (-2*a - 1)*q^8 + q^9 + 3*a*q^10 + (2*a - 2)*q^11 + (-2*a - 2)*q^12 + (-4*a - 1)*q^13 + 6*q^15 + 3*a*q^16 - 2*a*q^17 + a*q^18 + (6*a + 4)*q^19 + (-3*a - 3)*q^20 + (-4*a + 2)*q^22 + (-6*a - 3)*q^23 + (-4*a - 2)*q^24 + 4*q^25 + (3*a - 4)*q^26 - 4*q^27 + (-4*a + 2)*q^29 + 6*a*q^30 + (-2*a - 3)*q^31 + (a + 5)*q^32 + (4*a - 4)*q^33 + (2*a - 2)*q^34 + (-a - 1)*q^36 + 6*a*q^37 + O(q^38),
q + a*q^2 + (-a^3 - 2*a^2 + a + 1)*q^3 + (a^2 - 2)*q^4 + (a^3 + a^2 - 3*a - 2)*q^5 + (a^3 + a^2 - 3*a - 1)*q^6 + (2*a^3 + 5*a^2 - 2*a - 6)*q^7 + (a^3 - 4*a)*q^8 + (a^3 + 2*a^2 - a - 3)*q^9 + (-2*a^3 - 3*a^2 + 2*a + 1)*q^10 + (-2*a^3 - 4*a^2 + 3*a + 2)*q^11 + (a^2 + a - 1)*q^12 + (-2*a^3 - 3*a^2 + 5*a + 3)*q^13 + (-a^3 - 2*a^2 + 2*a + 2)*q^14 + (a^2 + 3*a)*q^15 + (-3*a^3 - 6*a^2 + 4*a + 5)*q^16 + (-2*a^3 - 3*a^2 + 4*a - 1)*q^17 + (-a^3 - a^2 + a + 1)*q^18 + (3*a^3 + 5*a^2 - 4*a - 3)*q^19 + (a^3 - a + 2)*q^20 + (a^2 + a - 3)*q^21 + (2*a^3 + 3*a^2 - 6*a - 2)*q^22 + (-4*a^2 - 4*a + 5)*q^23 + (-a^3 - a^2 + 5*a + 2)*q^24 + (2*a^2 + 3*a - 3)*q^25 + (3*a^3 + 5*a^2 - 5*a - 2)*q^26 + (4*a^3 + 8*a^2 - 4*a - 5)*q^27 + (-3*a^3 - 8*a^2 + 2*a + 11)*q^28 + (3*a^2 + 6*a - 7)*q^29 + (a^3 + 3*a^2)*q^30 + (-a^3 - 4*a^2 - a + 4)*q^31 + (a^3 + 4*a^2 + a - 3)*q^32 + (3*a^3 + 5*a^2 - 5*a - 1)*q^33 + (3*a^3 + 4*a^2 - 9*a - 2)*q^34 + (-a^3 - 4*a^2 - a + 6)*q^35 + (-3*a^2 - a + 5)*q^36 + (-2*a^3 - 4*a^2 + a + 5)*q^37 + O(q^38),
q + a*q^2 + (-2/9*a^9 + 7/9*a^8 + 23/9*a^7 - 9*a^6 - 89/9*a^5 + 287/9*a^4 + 151/9*a^3 - 107/3*a^2 - 35/3*a + 3)*q^3 + (a^2 - 2)*q^4 + (4/9*a^9 - 14/9*a^8 - 37/9*a^7 + 16*a^6 + 97/9*a^5 - 430/9*a^4 - 122/9*a^3 + 136/3*a^2 + 37/3*a - 4)*q^5 + (-1/3*a^9 + 5/3*a^8 + 7/3*a^7 - 17*a^6 - 7/3*a^5 + 151/3*a^4 + 5/3*a^3 - 49*a^2 - 9*a + 6)*q^6 + (7/9*a^9 - 29/9*a^8 - 58/9*a^7 + 34*a^6 + 109/9*a^5 - 964/9*a^4 - 74/9*a^3 + 337/3*a^2 + 40/3*a - 14)*q^7 + (a^3 - 4*a)*q^8 + (-8/3*a^9 + 26/3*a^8 + 25*a^7 - 271/3*a^6 - 194/3*a^5 + 279*a^4 + 65*a^3 - 860/3*a^2 - 41*a + 44)*q^9 + (2/3*a^9 - 7/3*a^8 - 20/3*a^7 + 25*a^6 + 62/3*a^5 - 242/3*a^4 - 88/3*a^3 + 87*a^2 + 20*a - 12)*q^10 + (11/9*a^9 - 34/9*a^8 - 104/9*a^7 + 39*a^6 + 278/9*a^5 - 1070/9*a^4 - 313/9*a^3 + 362/3*a^2 + 68/3*a - 14)*q^11 + (4/9*a^9 - 5/9*a^8 - 46/9*a^7 + 5*a^6 + 169/9*a^5 - 106/9*a^4 - 239/9*a^3 + 19/3*a^2 + 34/3*a + 3)*q^12 + (-1/3*a^9 + 4/3*a^8 + 3*a^7 - 44/3*a^6 - 22/3*a^5 + 50*a^4 + 8*a^3 - 181/3*a^2 - 6*a + 13)*q^13 + (2/3*a^9 - 10/3*a^8 - 17/3*a^7 + 37*a^6 + 38/3*a^5 - 377/3*a^4 - 55/3*a^3 + 144*a^2 + 28*a - 21)*q^14 + (14/9*a^9 - 46/9*a^8 - 140/9*a^7 + 167/3*a^6 + 416/9*a^5 - 1664/9*a^4 - 493/9*a^3 + 208*a^2 + 86/3*a - 37)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-17/9*a^9 + 55/9*a^8 + 164/9*a^7 - 64*a^6 - 473/9*a^5 + 1796/9*a^4 + 658/9*a^3 - 623/3*a^2 - 182/3*a + 29)*q^17 + (-14/3*a^9 + 43/3*a^8 + 137/3*a^7 - 150*a^6 - 395/3*a^5 + 1403/3*a^4 + 484/3*a^3 - 489*a^2 - 100*a + 72)*q^18 + (1/3*a^8 + 1/3*a^7 - 16/3*a^6 - 3*a^5 + 79/3*a^4 + 20/3*a^3 - 119/3*a^2 - 7*a + 6)*q^19 + (1/9*a^9 - 8/9*a^8 - 7/9*a^7 + 10*a^6 + 4/9*a^5 - 310/9*a^4 + 19/9*a^3 + 124/3*a^2 - 2/3*a - 10)*q^20 + (34/9*a^9 - 107/9*a^8 - 334/9*a^7 + 377/3*a^6 + 973/9*a^5 - 3580/9*a^4 - 1229/9*a^3 + 1265/3*a^2 + 274/3*a - 61)*q^21 + (7/3*a^9 - 20/3*a^8 - 70/3*a^7 + 70*a^6 + 208/3*a^5 - 658/3*a^4 - 254/3*a^3 + 228*a^2 + 52*a - 33)*q^22 + (19/9*a^9 - 68/9*a^8 - 175/9*a^7 + 239/3*a^6 + 454/9*a^5 - 2260/9*a^4 - 569/9*a^3 + 797/3*a^2 + 178/3*a - 36)*q^23 + (7/3*a^9 - 20/3*a^8 - 67/3*a^7 + 67*a^6 + 184/3*a^5 - 583/3*a^4 - 215/3*a^3 + 184*a^2 + 45*a - 24)*q^24 + (-5/9*a^9 + 25/9*a^8 + 29/9*a^7 - 85/3*a^6 + 34/9*a^5 + 761/9*a^4 - 197/9*a^3 - 256/3*a^2 + 16/3*a + 13)*q^25 + (-1/3*a^9 + 5/3*a^8 + 7/3*a^7 - 18*a^6 - 4/3*a^5 + 175/3*a^4 - 13/3*a^3 - 62*a^2 - 5*a + 9)*q^26 + (-34/9*a^9 + 113/9*a^8 + 340/9*a^7 - 406/3*a^6 - 1045/9*a^5 + 3964/9*a^4 + 1484/9*a^3 - 475*a^2 - 376/3*a + 60)*q^27 + (-14/9*a^9 + 31/9*a^8 + 143/9*a^7 - 34*a^6 - 425/9*a^5 + 857/9*a^4 + 436/9*a^3 - 254/3*a^2 - 35/3*a + 10)*q^28 + (-17/9*a^9 + 58/9*a^8 + 158/9*a^7 - 202/3*a^6 - 410/9*a^5 + 1880/9*a^4 + 466/9*a^3 - 646/3*a^2 - 128/3*a + 30)*q^29 + (8/3*a^9 - 28/3*a^8 - 71/3*a^7 + 96*a^6 + 164/3*a^5 - 869/3*a^4 - 160/3*a^3 + 290*a^2 + 47*a - 42)*q^30 + (10/9*a^9 - 23/9*a^8 - 112/9*a^7 + 83/3*a^6 + 400/9*a^5 - 820/9*a^4 - 569/9*a^3 + 296/3*a^2 + 103/3*a - 13)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (13/9*a^9 - 53/9*a^8 - 103/9*a^7 + 181/3*a^6 + 169/9*a^5 - 1639/9*a^4 - 101/9*a^3 + 189*a^2 + 67/3*a - 32)*q^33 + (-10/3*a^9 + 32/3*a^8 + 97/3*a^7 - 113*a^6 - 274/3*a^5 + 1075/3*a^4 + 329/3*a^3 - 378*a^2 - 73*a + 51)*q^34 + (-7/3*a^9 + 8*a^8 + 65/3*a^7 - 250/3*a^6 - 169/3*a^5 + 770/3*a^4 + 196/3*a^3 - 788/3*a^2 - 53*a + 37)*q^35 + (-11/3*a^9 + 29/3*a^8 + 38*a^7 - 301/3*a^6 - 365/3*a^5 + 308*a^4 + 165*a^3 - 932/3*a^2 - 98*a + 38)*q^36 + (-5/3*a^9 + 17/3*a^8 + 16*a^7 - 181/3*a^6 - 137/3*a^5 + 194*a^4 + 63*a^3 - 635/3*a^2 - 54*a + 30)*q^37 + O(q^38)
*]> ;  // time = 2.789 seconds




J[201] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 201, 201, 201, 201, 201, 67, 67, 67 ], new_dimensions := [ 1, 1, 1, 3, 5, 1, 2, 2 ], dimensions := [ 1, 1, 1, 3, 5, 2, 4, 4 ], intersection_graph := [ 0, 3, 1, 1, 1, 1, 5, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 19, 1, 1, 1, 1, 0, 1, 29, 1, 1, 1, 3, 1, 1, 0, 1, 25, 5, 1, 1, 1, 29, 1, 0, 1, 1, 1, 1, 19, 1, 25, 1, 0 ], ap_traces := [
[ 1, -1, -3, -3, 0, 4, 2, -2, -7, -8, -1, -3 ],
[ -2, -1, 0, 0, -6, 4, -7, -5, -1, 1, -4, 3 ],
[ -1, 1, -1, -5, -4, -4, 6, -2, -3, 4, -7, 5 ],
[ 3, -3, 1, 1, 10, -8, 0, -2, 3, 4, 11, -9 ],
[ 0, 5, -3, 7, 0, 10, -5, 5, -2, 3, 9, 8 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^3 - 3*x^2 - x + 5,
x^5 - 8*x^3 + 13*x + 2
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 19, 1 ],
[ 493, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 493, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 17 ], torsion_lower_bounds := [ 1, 1, 1, 1, 17 ], l_ratios := [ 0, 0, 0, 1, 29/17 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ 1, -1, -3, -3, 0, 4, 2, -2, -7, -8, -1, -3 ],
[ -2, -1, 0, 0, -6, 4, -7, -5, -1, 1, -4, 3 ],
[ -1, 1, -1, -5, -4, -4, 6, -2, -3, 4, -7, 5 ],
[
a,
-1,
-a^2 + a + 3,
-a^2 + 2*a + 2,
-a^2 + 7,
-a^2 + 1,
3*a^2 - 4*a - 7,
-a^2 - 2*a + 5,
3*a^2 - 5*a - 5,
-4*a^2 + 4*a + 12,
4*a^2 - 6*a - 5,
3*a^2 - 2*a - 12
],
[
a,
1,
1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 5/2*a + 3,
-1/2*a^4 - 1/2*a^3 + 5/2*a^2 + 3/2*a + 1,
a^3 - 5*a,
a^3 - 5*a + 2,
-a^4 - a^3 + 6*a^2 + 3*a - 5,
a^4 - a^3 - 6*a^2 + 5*a + 5,
1/2*a^4 + 1/2*a^3 - 5/2*a^2 - 5/2*a,
a^3 + 3*a^2 - 5*a - 9,
-1/2*a^4 + 1/2*a^3 + 9/2*a^2 - 7/2*a - 5,
-1/2*a^4 + 1/2*a^3 + 7/2*a^2 + 1/2*a - 2
]
*], q_expansions := [*
q + q^2 - q^3 - q^4 - 3*q^5 - q^6 - 3*q^7 - 3*q^8 + q^9 - 3*q^10 + q^12 + 4*q^13 - 3*q^14 + 3*q^15 - q^16 + 2*q^17 + q^18 - 2*q^19 + 3*q^20 + 3*q^21 - 7*q^23 + 3*q^24 + 4*q^25 + 4*q^26 - q^27 + 3*q^28 - 8*q^29 + 3*q^30 - q^31 + 5*q^32 + 2*q^34 + 9*q^35 - q^36 - 3*q^37 + O(q^38),
q - 2*q^2 - q^3 + 2*q^4 + 2*q^6 + q^9 - 6*q^11 - 2*q^12 + 4*q^13 - 4*q^16 - 7*q^17 - 2*q^18 - 5*q^19 + 12*q^22 - q^23 - 5*q^25 - 8*q^26 - q^27 + q^29 - 4*q^31 + 8*q^32 + 6*q^33 + 14*q^34 + 2*q^36 + 3*q^37 + O(q^38),
q - q^2 + q^3 - q^4 - q^5 - q^6 - 5*q^7 + 3*q^8 + q^9 + q^10 - 4*q^11 - q^12 - 4*q^13 + 5*q^14 - q^15 - q^16 + 6*q^17 - q^18 - 2*q^19 + q^20 - 5*q^21 + 4*q^22 - 3*q^23 + 3*q^24 - 4*q^25 + 4*q^26 + q^27 + 5*q^28 + 4*q^29 + q^30 - 7*q^31 - 5*q^32 - 4*q^33 - 6*q^34 + 5*q^35 - q^36 + 5*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 + a + 3)*q^5 - a*q^6 + (-a^2 + 2*a + 2)*q^7 + (3*a^2 - 3*a - 5)*q^8 + q^9 + (-2*a^2 + 2*a + 5)*q^10 + (-a^2 + 7)*q^11 + (-a^2 + 2)*q^12 + (-a^2 + 1)*q^13 + (-a^2 + a + 5)*q^14 + (a^2 - a - 3)*q^15 + (4*a^2 - 2*a - 11)*q^16 + (3*a^2 - 4*a - 7)*q^17 + a*q^18 + (-a^2 - 2*a + 5)*q^19 + (-2*a^2 + a + 4)*q^20 + (a^2 - 2*a - 2)*q^21 + (-3*a^2 + 6*a + 5)*q^22 + (3*a^2 - 5*a - 5)*q^23 + (-3*a^2 + 3*a + 5)*q^24 + (-a^2 + 2*a - 1)*q^25 + (-3*a^2 + 5)*q^26 - q^27 + q^28 + (-4*a^2 + 4*a + 12)*q^29 + (2*a^2 - 2*a - 5)*q^30 + (4*a^2 - 6*a - 5)*q^31 + (4*a^2 - a - 10)*q^32 + (a^2 - 7)*q^33 + (5*a^2 - 4*a - 15)*q^34 + (-2*a^2 + 3*a + 6)*q^35 + (a^2 - 2)*q^36 + (3*a^2 - 2*a - 12)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 5/2*a + 3)*q^5 + a*q^6 + (-1/2*a^4 - 1/2*a^3 + 5/2*a^2 + 3/2*a + 1)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-1/2*a^4 + 1/2*a^3 + 5/2*a^2 - 7/2*a - 1)*q^10 + (a^3 - 5*a)*q^11 + (a^2 - 2)*q^12 + (a^3 - 5*a + 2)*q^13 + (-1/2*a^4 - 3/2*a^3 + 3/2*a^2 + 15/2*a + 1)*q^14 + (1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 5/2*a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 - a^3 + 6*a^2 + 3*a - 5)*q^17 + a*q^18 + (a^4 - a^3 - 6*a^2 + 5*a + 5)*q^19 + (-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 1/2*a - 5)*q^20 + (-1/2*a^4 - 1/2*a^3 + 5/2*a^2 + 3/2*a + 1)*q^21 + (a^4 - 5*a^2)*q^22 + (1/2*a^4 + 1/2*a^3 - 5/2*a^2 - 5/2*a)*q^23 + (a^3 - 4*a)*q^24 + (-1/2*a^4 + 3/2*a^3 + 5/2*a^2 - 17/2*a)*q^25 + (a^4 - 5*a^2 + 2*a)*q^26 + q^27 + (-1/2*a^4 - 3/2*a^3 + 5/2*a^2 + 9/2*a - 1)*q^28 + (a^3 + 3*a^2 - 5*a - 9)*q^29 + (-1/2*a^4 + 1/2*a^3 + 5/2*a^2 - 7/2*a - 1)*q^30 + (-1/2*a^4 + 1/2*a^3 + 9/2*a^2 - 7/2*a - 5)*q^31 + (-a - 2)*q^32 + (a^3 - 5*a)*q^33 + (-a^4 - 2*a^3 + 3*a^2 + 8*a + 2)*q^34 + (3/2*a^4 - 1/2*a^3 - 17/2*a^2 + 9/2*a + 3)*q^35 + (a^2 - 2)*q^36 + (-1/2*a^4 + 1/2*a^3 + 7/2*a^2 + 1/2*a - 2)*q^37 + O(q^38)
*]> ;  // time = 24.319 seconds




J[202] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 202, 202, 202, 101, 101 ], new_dimensions := [ 1, 3, 4, 1, 7 ], dimensions := [ 1, 3, 4, 2, 14 ], intersection_graph := [ 0, 1, 1, 1, 17, 1, 0, 1, 3, 1, 1, 1, 0, 3, 1, 1, 3, 3, 0, 1, 17, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, 2, 1, 4, 0, 5, 1, 6, -5, 0, -8 ],
[ -3, -3, -3, -3, -9, -3, -9, -6, -12, 0, 12, 3 ],
[ 4, -1, 3, 2, 1, 1, 4, -13, 2, 9, -8, -1 ]
], hecke_fields := [
x - 1,
x^3 + 3*x^2 - 1,
x^4 + x^3 - 8*x^2 + x + 8
], atkin_lehners := [
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 17, 1 ],
[ 3, 1 ],
[ 51, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 51, 1 ]
], torsion_upper_bounds := [ 1, 1, 17 ], torsion_lower_bounds := [ 1, 1, 17 ], l_ratios := [ 1, 0, 3/17 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ -1, 0, 2, 1, 4, 0, 5, 1, 6, -5, 0, -8 ],
[
-1,
a,
a^2 + a - 3,
-3*a^2 - 8*a,
a^2 + 3*a - 3,
3*a^2 + 10*a,
-2*a^2 - 5*a - 2,
-2,
2*a^2 + 6*a - 4,
-4*a^2 - 6*a + 6,
4*a^2 + 8*a,
4*a^2 + 7*a - 4
],
[
1,
a,
a^3 + 2*a^2 - 5*a - 2,
-a^3 - 2*a^2 + 4*a + 3,
-3*a^3 - 8*a^2 + 11*a + 16,
-a^2 - 2*a + 4,
3*a^3 + 9*a^2 - 11*a - 19,
3*a^3 + 7*a^2 - 12*a - 15,
-2*a^3 - 4*a^2 + 10*a + 6,
-a^3 - a^2 + 6*a + 1,
4*a^3 + 12*a^2 - 12*a - 28,
a
]
*], q_expansions := [*
q - q^2 + q^4 + 2*q^5 + q^7 - q^8 - 3*q^9 - 2*q^10 + 4*q^11 - q^14 + q^16 + 5*q^17 + 3*q^18 + q^19 + 2*q^20 - 4*q^22 + 6*q^23 - q^25 + q^28 - 5*q^29 - q^32 - 5*q^34 + 2*q^35 - 3*q^36 - 8*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (a^2 + a - 3)*q^5 - a*q^6 + (-3*a^2 - 8*a)*q^7 - q^8 + (a^2 - 3)*q^9 + (-a^2 - a + 3)*q^10 + (a^2 + 3*a - 3)*q^11 + a*q^12 + (3*a^2 + 10*a)*q^13 + (3*a^2 + 8*a)*q^14 + (-2*a^2 - 3*a + 1)*q^15 + q^16 + (-2*a^2 - 5*a - 2)*q^17 + (-a^2 + 3)*q^18 - 2*q^19 + (a^2 + a - 3)*q^20 + (a^2 - 3)*q^21 + (-a^2 - 3*a + 3)*q^22 + (2*a^2 + 6*a - 4)*q^23 - a*q^24 + (-2*a^2 - 5*a + 3)*q^25 + (-3*a^2 - 10*a)*q^26 + (-3*a^2 - 6*a + 1)*q^27 + (-3*a^2 - 8*a)*q^28 + (-4*a^2 - 6*a + 6)*q^29 + (2*a^2 + 3*a - 1)*q^30 + (4*a^2 + 8*a)*q^31 - q^32 + (-3*a + 1)*q^33 + (2*a^2 + 5*a + 2)*q^34 + (7*a^2 + 21*a - 2)*q^35 + (a^2 - 3)*q^36 + (4*a^2 + 7*a - 4)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (a^3 + 2*a^2 - 5*a - 2)*q^5 + a*q^6 + (-a^3 - 2*a^2 + 4*a + 3)*q^7 + q^8 + (a^2 - 3)*q^9 + (a^3 + 2*a^2 - 5*a - 2)*q^10 + (-3*a^3 - 8*a^2 + 11*a + 16)*q^11 + a*q^12 + (-a^2 - 2*a + 4)*q^13 + (-a^3 - 2*a^2 + 4*a + 3)*q^14 + (a^3 + 3*a^2 - 3*a - 8)*q^15 + q^16 + (3*a^3 + 9*a^2 - 11*a - 19)*q^17 + (a^2 - 3)*q^18 + (3*a^3 + 7*a^2 - 12*a - 15)*q^19 + (a^3 + 2*a^2 - 5*a - 2)*q^20 + (-a^3 - 4*a^2 + 4*a + 8)*q^21 + (-3*a^3 - 8*a^2 + 11*a + 16)*q^22 + (-2*a^3 - 4*a^2 + 10*a + 6)*q^23 + a*q^24 + (-2*a^2 - 3*a + 7)*q^25 + (-a^2 - 2*a + 4)*q^26 + (a^3 - 6*a)*q^27 + (-a^3 - 2*a^2 + 4*a + 3)*q^28 + (-a^3 - a^2 + 6*a + 1)*q^29 + (a^3 + 3*a^2 - 3*a - 8)*q^30 + (4*a^3 + 12*a^2 - 12*a - 28)*q^31 + q^32 + (-5*a^3 - 13*a^2 + 19*a + 24)*q^33 + (3*a^3 + 9*a^2 - 11*a - 19)*q^34 + (a^2 + a - 6)*q^35 + (a^2 - 3)*q^36 + a*q^37 + O(q^38)
*]> ;  // time = 31.339 seconds




J[203] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 203, 203, 203, 203, 203, 203, 203, 29 ], new_dimensions := [ 1, 1, 1, 2, 2, 3, 5, 2 ], dimensions := [ 1, 1, 1, 2, 2, 3, 5, 4 ], intersection_graph := [ 0, 3, 1, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 9, 0, 1, 1, 7, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 7, 1, 1, 0 ], ap_traces := [
[ 1, 2, 2, 1, -4, -2, 4, 2, 0, -1, -2, 2 ],
[ -2, -1, -4, 1, 2, 4, -2, 5, 9, -1, -8, 8 ],
[ -1, -1, 1, 1, -5, -5, -4, -4, 6, 1, 7, -10 ],
[ -2, -1, 3, -2, -1, 5, 6, 8, -2, 2, -5, 12 ],
[ 4, 2, 0, -2, -4, 8, 0, 2, -2, 2, 4, 0 ],
[ -1, -3, -5, -3, 5, -15, 2, -6, 2, -3, -5, -12 ],
[ 2, -2, 5, 5, 3, 15, -4, -15, -5, -5, 9, 14 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 - 17,
x^2 - 6*x + 7,
x^3 + x^2 - 3*x - 1,
x^5 - 2*x^4 - 8*x^3 + 14*x^2 + 9*x - 6
], atkin_lehners := [
[ -1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 5, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 3, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 5, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ]
], torsion_upper_bounds := [ 1, 5, 1, 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 5, 1, 1, 1, 1, 3 ], l_ratios := [ 1, 1/5, 0, 1, 1, 0, 1/3 ], analytic_sha_upper_bounds := [ 1, 1, 0, 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 1, 1, 0, 1 ], eigenvalues := [*
[ 1, 2, 2, 1, -4, -2, 4, 2, 0, -1, -2, 2 ],
[ -2, -1, -4, 1, 2, 4, -2, 5, 9, -1, -8, 8 ],
[ -1, -1, 1, 1, -5, -5, -4, -4, 6, 1, 7, -10 ],
[
-1,
-1/2*a - 1/2,
-1/2*a + 3/2,
-1,
-1/2*a - 1/2,
1/2*a + 5/2,
a + 3,
4,
-a - 1,
1,
3/2*a - 5/2,
6
],
[
2,
a - 2,
-2*a + 6,
-1,
-2*a + 4,
2*a - 2,
-2*a + 6,
3*a - 8,
2*a - 7,
1,
2,
6*a - 18
],
[
a,
-a^2 - a + 1,
a^2 - 4,
-1,
a^2 - a - 1,
-5,
-3*a^2 - 2*a + 7,
a^2 + 4*a - 3,
4*a + 2,
-1,
2*a^2 + a - 6,
a^2 - 2*a - 7
],
[
a,
-1/2*a^4 + 1/2*a^3 + 7/2*a^2 - 7/2*a - 2,
1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 5/2*a + 3,
1,
-1/2*a^4 - 1/2*a^3 + 5/2*a^2 + 7/2*a + 3,
1/2*a^4 + 1/2*a^3 - 7/2*a^2 - 9/2*a + 5,
-a^3 + 5*a,
a^2 - 7,
-a^3 - a^2 + 7*a + 3,
-1,
-3/2*a^4 + 3/2*a^3 + 23/2*a^2 - 21/2*a - 7,
-a^3 + 9*a + 2
]
*], q_expansions := [*
q + q^2 + 2*q^3 - q^4 + 2*q^5 + 2*q^6 + q^7 - 3*q^8 + q^9 + 2*q^10 - 4*q^11 - 2*q^12 - 2*q^13 + q^14 + 4*q^15 - q^16 + 4*q^17 + q^18 + 2*q^19 - 2*q^20 + 2*q^21 - 4*q^22 - 6*q^24 - q^25 - 2*q^26 - 4*q^27 - q^28 - q^29 + 4*q^30 - 2*q^31 + 5*q^32 - 8*q^33 + 4*q^34 + 2*q^35 - q^36 + 2*q^37 + O(q^38),
q - 2*q^2 - q^3 + 2*q^4 - 4*q^5 + 2*q^6 + q^7 - 2*q^9 + 8*q^10 + 2*q^11 - 2*q^12 + 4*q^13 - 2*q^14 + 4*q^15 - 4*q^16 - 2*q^17 + 4*q^18 + 5*q^19 - 8*q^20 - q^21 - 4*q^22 + 9*q^23 + 11*q^25 - 8*q^26 + 5*q^27 + 2*q^28 - q^29 - 8*q^30 - 8*q^31 + 8*q^32 - 2*q^33 + 4*q^34 - 4*q^35 - 4*q^36 + 8*q^37 + O(q^38),
q - q^2 - q^3 - q^4 + q^5 + q^6 + q^7 + 3*q^8 - 2*q^9 - q^10 - 5*q^11 + q^12 - 5*q^13 - q^14 - q^15 - q^16 - 4*q^17 + 2*q^18 - 4*q^19 - q^20 - q^21 + 5*q^22 + 6*q^23 - 3*q^24 - 4*q^25 + 5*q^26 + 5*q^27 - q^28 + q^29 + q^30 + 7*q^31 - 5*q^32 + 5*q^33 + 4*q^34 + q^35 + 2*q^36 - 10*q^37 + O(q^38),
q - q^2 + (-1/2*a - 1/2)*q^3 - q^4 + (-1/2*a + 3/2)*q^5 + (1/2*a + 1/2)*q^6 - q^7 + 3*q^8 + (1/2*a + 3/2)*q^9 + (1/2*a - 3/2)*q^10 + (-1/2*a - 1/2)*q^11 + (1/2*a + 1/2)*q^12 + (1/2*a + 5/2)*q^13 + q^14 + (-1/2*a + 7/2)*q^15 - q^16 + (a + 3)*q^17 + (-1/2*a - 3/2)*q^18 + 4*q^19 + (1/2*a - 3/2)*q^20 + (1/2*a + 1/2)*q^21 + (1/2*a + 1/2)*q^22 + (-a - 1)*q^23 + (-3/2*a - 3/2)*q^24 + (-3/2*a + 3/2)*q^25 + (-1/2*a - 5/2)*q^26 + (1/2*a - 7/2)*q^27 + q^28 + q^29 + (1/2*a - 7/2)*q^30 + (3/2*a - 5/2)*q^31 - 5*q^32 + (1/2*a + 9/2)*q^33 + (-a - 3)*q^34 + (1/2*a - 3/2)*q^35 + (-1/2*a - 3/2)*q^36 + 6*q^37 + O(q^38),
q + 2*q^2 + (a - 2)*q^3 + 2*q^4 + (-2*a + 6)*q^5 + (2*a - 4)*q^6 - q^7 + (2*a - 6)*q^9 + (-4*a + 12)*q^10 + (-2*a + 4)*q^11 + (2*a - 4)*q^12 + (2*a - 2)*q^13 - 2*q^14 + (-2*a + 2)*q^15 - 4*q^16 + (-2*a + 6)*q^17 + (4*a - 12)*q^18 + (3*a - 8)*q^19 + (-4*a + 12)*q^20 + (-a + 2)*q^21 + (-4*a + 8)*q^22 + (2*a - 7)*q^23 + 3*q^25 + (4*a - 4)*q^26 + (-a + 4)*q^27 - 2*q^28 + q^29 + (-4*a + 4)*q^30 + 2*q^31 - 8*q^32 + (-4*a + 6)*q^33 + (-4*a + 12)*q^34 + (2*a - 6)*q^35 + (4*a - 12)*q^36 + (6*a - 18)*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 1)*q^3 + (a^2 - 2)*q^4 + (a^2 - 4)*q^5 + (-2*a - 1)*q^6 - q^7 + (-a^2 - a + 1)*q^8 + (a^2 + 2*a - 1)*q^9 + (-a^2 - a + 1)*q^10 + (a^2 - a - 1)*q^11 + (a - 2)*q^12 - 5*q^13 - a*q^14 + (2*a^2 + 3*a - 4)*q^15 + (-2*a^2 - 2*a + 3)*q^16 + (-3*a^2 - 2*a + 7)*q^17 + (a^2 + 2*a + 1)*q^18 + (a^2 + 4*a - 3)*q^19 + (-2*a^2 - 2*a + 7)*q^20 + (a^2 + a - 1)*q^21 + (-2*a^2 + 2*a + 1)*q^22 + (4*a + 2)*q^23 + (a^2 + 2*a + 2)*q^24 + (-4*a^2 - 2*a + 10)*q^25 - 5*a*q^26 + (2*a^2 - a - 6)*q^27 + (-a^2 + 2)*q^28 - q^29 + (a^2 + 2*a + 2)*q^30 + (2*a^2 + a - 6)*q^31 + (2*a^2 - a - 4)*q^32 + (-a^2 + 2*a)*q^33 + (a^2 - 2*a - 3)*q^34 + (-a^2 + 4)*q^35 + (-a^2 + 3)*q^36 + (a^2 - 2*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^4 + 1/2*a^3 + 7/2*a^2 - 7/2*a - 2)*q^3 + (a^2 - 2)*q^4 + (1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 5/2*a + 3)*q^5 + (-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 5/2*a - 3)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (1/2*a^4 + 1/2*a^3 - 9/2*a^2 - 5/2*a + 7)*q^9 + (1/2*a^4 + 1/2*a^3 - 9/2*a^2 - 3/2*a + 3)*q^10 + (-1/2*a^4 - 1/2*a^3 + 5/2*a^2 + 7/2*a + 3)*q^11 + (-1/2*a^4 - 3/2*a^3 + 5/2*a^2 + 17/2*a + 1)*q^12 + (1/2*a^4 + 1/2*a^3 - 7/2*a^2 - 9/2*a + 5)*q^13 + a*q^14 + (-1/2*a^4 + 1/2*a^3 + 9/2*a^2 - 7/2*a - 9)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^3 + 5*a)*q^17 + (3/2*a^4 - 1/2*a^3 - 19/2*a^2 + 5/2*a + 3)*q^18 + (a^2 - 7)*q^19 + (1/2*a^4 + 1/2*a^3 - 3/2*a^2 - 13/2*a - 3)*q^20 + (-1/2*a^4 + 1/2*a^3 + 7/2*a^2 - 7/2*a - 2)*q^21 + (-3/2*a^4 - 3/2*a^3 + 21/2*a^2 + 15/2*a - 3)*q^22 + (-a^3 - a^2 + 7*a + 3)*q^23 + (-3/2*a^4 - 1/2*a^3 + 17/2*a^2 + 1/2*a + 3)*q^24 + (1/2*a^4 - 3/2*a^3 - 7/2*a^2 + 15/2*a + 4)*q^25 + (3/2*a^4 + 1/2*a^3 - 23/2*a^2 + 1/2*a + 3)*q^26 + (-1/2*a^4 + 3/2*a^3 + 7/2*a^2 - 21/2*a - 2)*q^27 + (a^2 - 2)*q^28 - q^29 + (-1/2*a^4 + 1/2*a^3 + 7/2*a^2 - 9/2*a - 3)*q^30 + (-3/2*a^4 + 3/2*a^3 + 23/2*a^2 - 21/2*a - 7)*q^31 + (2*a^4 - 14*a^2 + 3*a + 6)*q^32 + (-1/2*a^4 + 5/2*a^3 + 11/2*a^2 - 29/2*a - 9)*q^33 + (-a^4 + 5*a^2)*q^34 + (1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 5/2*a + 3)*q^35 + (3/2*a^4 + 3/2*a^3 - 19/2*a^2 - 11/2*a - 5)*q^36 + (-a^3 + 9*a + 2)*q^37 + O(q^38)
*]> ;  // time = 24.459 seconds




J[205] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 205, 205, 205, 205, 205, 205, 205, 41 ], new_dimensions := [ 1, 1, 1, 2, 2, 3, 3, 3 ], dimensions := [ 1, 1, 1, 2, 2, 3, 3, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 13, 1, 1, 1, 1, 1, 0, 1, 31, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 13, 31, 1, 0 ], ap_traces := [
[ -1, 2, -1, 2, 6, 2, 2, -6, -4, 10, 0, -6 ],
[ 1, 2, 1, 2, 0, -4, 4, 0, -8, 2, 0, -6 ],
[ -1, 0, 1, -4, 0, -2, -6, 0, -8, 6, 0, 6 ],
[ -1, -2, -2, 3, -8, -3, 0, -5, -6, -3, -7, 1 ],
[ -1, -6, 2, -3, -6, -1, -4, -3, 4, -5, -3, -3 ],
[ 2, 2, -3, -9, 4, -3, 4, 15, 6, 1, 1, -17 ],
[ 0, 2, 3, 1, 4, 1, -2, -5, 20, -13, -11, 11 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 + x - 1,
x^2 + x - 3,
x^3 - 2*x^2 - 4*x + 7,
x^3 - 4*x - 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 13, 1 ],
[ 31, 1 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 13, 1 ],
[ 1, 1 ],
[ 7, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 7 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 7 ], l_ratios := [ 1, 1, 0, 0, 0, 1, 1/7 ], analytic_sha_upper_bounds := [ 1, 1, 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 0, 0, 1, 1 ], eigenvalues := [*
[ -1, 2, -1, 2, 6, 2, 2, -6, -4, 10, 0, -6 ],
[ 1, 2, 1, 2, 0, -4, 4, 0, -8, 2, 0, -6 ],
[ -1, 0, 1, -4, 0, -2, -6, 0, -8, 6, 0, 6 ],
[
a,
-1,
-1,
-3*a,
2*a - 3,
3*a,
2*a + 1,
-3*a - 4,
-3,
-a - 2,
5*a - 1,
-a
],
[
a,
-3,
1,
-a - 2,
-3,
-3*a - 2,
2*a - 1,
3*a,
2*a + 3,
a - 2,
-3*a - 3,
3*a
],
[
a,
-a^2 + a + 4,
-1,
a^2 - 7,
-a^2 - a + 6,
-a^2 + 3,
3*a^2 - a - 10,
a^2 + 1,
a^2 - 3*a,
a^2 + 2*a - 5,
-2*a^2 - a + 9,
-a^2 + 2*a - 3
],
[
a,
a^2 - a - 2,
1,
-a^2 + 3,
-a^2 + a + 4,
-a^2 + 2*a + 3,
-a^2 - a + 2,
-a^2 + 1,
a^2 - a + 4,
a^2 - 7,
2*a^2 + 3*a - 9,
a^2 + 1
]
*], q_expansions := [*
q - q^2 + 2*q^3 - q^4 - q^5 - 2*q^6 + 2*q^7 + 3*q^8 + q^9 + q^10 + 6*q^11 - 2*q^12 + 2*q^13 - 2*q^14 - 2*q^15 - q^16 + 2*q^17 - q^18 - 6*q^19 + q^20 + 4*q^21 - 6*q^22 - 4*q^23 + 6*q^24 + q^25 - 2*q^26 - 4*q^27 - 2*q^28 + 10*q^29 + 2*q^30 - 5*q^32 + 12*q^33 - 2*q^34 - 2*q^35 - q^36 - 6*q^37 + O(q^38),
q + q^2 + 2*q^3 - q^4 + q^5 + 2*q^6 + 2*q^7 - 3*q^8 + q^9 + q^10 - 2*q^12 - 4*q^13 + 2*q^14 + 2*q^15 - q^16 + 4*q^17 + q^18 - q^20 + 4*q^21 - 8*q^23 - 6*q^24 + q^25 - 4*q^26 - 4*q^27 - 2*q^28 + 2*q^29 + 2*q^30 + 5*q^32 + 4*q^34 + 2*q^35 - q^36 - 6*q^37 + O(q^38),
q - q^2 - q^4 + q^5 - 4*q^7 + 3*q^8 - 3*q^9 - q^10 - 2*q^13 + 4*q^14 - q^16 - 6*q^17 + 3*q^18 - q^20 - 8*q^23 + q^25 + 2*q^26 + 4*q^28 + 6*q^29 - 5*q^32 + 6*q^34 - 4*q^35 + 3*q^36 + 6*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a - 1)*q^4 - q^5 - a*q^6 - 3*a*q^7 + (-2*a - 1)*q^8 - 2*q^9 - a*q^10 + (2*a - 3)*q^11 + (a + 1)*q^12 + 3*a*q^13 + (3*a - 3)*q^14 + q^15 + 3*a*q^16 + (2*a + 1)*q^17 - 2*a*q^18 + (-3*a - 4)*q^19 + (a + 1)*q^20 + 3*a*q^21 + (-5*a + 2)*q^22 - 3*q^23 + (2*a + 1)*q^24 + q^25 + (-3*a + 3)*q^26 + 5*q^27 + 3*q^28 + (-a - 2)*q^29 + a*q^30 + (5*a - 1)*q^31 + (a + 5)*q^32 + (-2*a + 3)*q^33 + (-a + 2)*q^34 + 3*a*q^35 + (2*a + 2)*q^36 - a*q^37 + O(q^38),
q + a*q^2 - 3*q^3 + (-a + 1)*q^4 + q^5 - 3*a*q^6 + (-a - 2)*q^7 - 3*q^8 + 6*q^9 + a*q^10 - 3*q^11 + (3*a - 3)*q^12 + (-3*a - 2)*q^13 + (-a - 3)*q^14 - 3*q^15 + (-a - 2)*q^16 + (2*a - 1)*q^17 + 6*a*q^18 + 3*a*q^19 + (-a + 1)*q^20 + (3*a + 6)*q^21 - 3*a*q^22 + (2*a + 3)*q^23 + 9*q^24 + q^25 + (a - 9)*q^26 - 9*q^27 + q^28 + (a - 2)*q^29 - 3*a*q^30 + (-3*a - 3)*q^31 + (-a + 3)*q^32 + 9*q^33 + (-3*a + 6)*q^34 + (-a - 2)*q^35 + (-6*a + 6)*q^36 + 3*a*q^37 + O(q^38),
q + a*q^2 + (-a^2 + a + 4)*q^3 + (a^2 - 2)*q^4 - q^5 + (-a^2 + 7)*q^6 + (a^2 - 7)*q^7 + (2*a^2 - 7)*q^8 + (-3*a^2 + a + 13)*q^9 - a*q^10 + (-a^2 - a + 6)*q^11 + (a - 1)*q^12 + (-a^2 + 3)*q^13 + (2*a^2 - 3*a - 7)*q^14 + (a^2 - a - 4)*q^15 + (2*a^2 + a - 10)*q^16 + (3*a^2 - a - 10)*q^17 + (-5*a^2 + a + 21)*q^18 + (a^2 + 1)*q^19 + (-a^2 + 2)*q^20 + (5*a^2 - 4*a - 21)*q^21 + (-3*a^2 + 2*a + 7)*q^22 + (a^2 - 3*a)*q^23 + (3*a^2 - a - 14)*q^24 + q^25 + (-2*a^2 - a + 7)*q^26 + (-5*a^2 + a + 26)*q^27 + (-a^2 + a)*q^28 + (a^2 + 2*a - 5)*q^29 + (a^2 - 7)*q^30 + (-2*a^2 - a + 9)*q^31 + (a^2 - 2*a)*q^32 + (-3*a^2 + 3*a + 10)*q^33 + (5*a^2 + 2*a - 21)*q^34 + (-a^2 + 7)*q^35 + (-3*a^2 - a + 9)*q^36 + (-a^2 + 2*a - 3)*q^37 + O(q^38),
q + a*q^2 + (a^2 - a - 2)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^2 + 2*a + 1)*q^6 + (-a^2 + 3)*q^7 + q^8 + (a^2 - 3*a - 1)*q^9 + a*q^10 + (-a^2 + a + 4)*q^11 + (-a + 3)*q^12 + (-a^2 + 2*a + 3)*q^13 + (-a - 1)*q^14 + (a^2 - a - 2)*q^15 + (-2*a^2 + a + 4)*q^16 + (-a^2 - a + 2)*q^17 + (-3*a^2 + 3*a + 1)*q^18 + (-a^2 + 1)*q^19 + (a^2 - 2)*q^20 + (a^2 - 5)*q^21 + (a^2 - 1)*q^22 + (a^2 - a + 4)*q^23 + (a^2 - a - 2)*q^24 + q^25 + (2*a^2 - a - 1)*q^26 + (a^2 - 5*a + 4)*q^27 + (a^2 - a - 6)*q^28 + (a^2 - 7)*q^29 + (-a^2 + 2*a + 1)*q^30 + (2*a^2 + 3*a - 9)*q^31 + (a^2 - 4*a - 4)*q^32 + (a^2 + a - 6)*q^33 + (-a^2 - 2*a - 1)*q^34 + (-a^2 + 3)*q^35 + (a^2 - 5*a - 1)*q^36 + (a^2 + 1)*q^37 + O(q^38)
*]> ;  // time = 23.091 seconds




J[206] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 206, 206, 206, 206, 103, 103 ], new_dimensions := [ 1, 2, 2, 4, 2, 6 ], dimensions := [ 1, 2, 2, 4, 4, 12 ], intersection_graph := [ 0, 5, 3, 1, 1, 1, 5, 0, 1, 1, 1, 67, 3, 1, 0, 1, 1, 17, 1, 1, 1, 0, 19, 1, 1, 1, 1, 19, 0, 1, 1, 67, 17, 1, 1, 0 ], ap_traces := [
[ -1, 2, 4, 0, -6, -2, 2, -4, 0, -6, 8, 8 ],
[ -2, 1, 1, -3, 8, 2, -3, 12, -7, -12, 16, -7 ],
[ -2, -3, -5, 5, 0, 6, 5, 4, -3, 12, -8, 1 ],
[ 4, 2, 0, 2, 4, 0, -14, 0, 2, 0, 8, 10 ]
], hecke_fields := [
x - 1,
x^2 - x - 7,
x^2 + 3*x - 1,
x^4 - 2*x^3 - 5*x^2 + 12*x - 5
], atkin_lehners := [
[ 1, -1 ],
[ 1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 67, 1 ],
[ 51, 3 ],
[ 247, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 3 ],
[ 247, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 13 ], torsion_lower_bounds := [ 1, 1, 3, 13 ], l_ratios := [ 1, 1, 1/3, 19/13 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1 ], eigenvalues := [*
[ -1, 2, 4, 0, -6, -2, 2, -4, 0, -6, 8, 8 ],
[
-1,
a,
-a + 1,
a - 2,
4,
-2*a + 2,
-a - 1,
6,
-a - 3,
-6,
8,
a - 4
],
[
-1,
a,
a - 1,
a + 4,
0,
2*a + 6,
-a + 1,
2,
3*a + 3,
6,
-4,
-3*a - 4
],
[
1,
a,
-a^3 + 5*a - 2,
2*a^3 - a^2 - 12*a + 9,
-2*a^3 + 2*a^2 + 10*a - 10,
2*a^3 - 10*a + 4,
2*a^3 - 3*a^2 - 12*a + 12,
-2*a^2 - 2*a + 8,
-4*a^3 + 3*a^2 + 24*a - 20,
-4*a^3 + 2*a^2 + 22*a - 16,
-4*a^3 + 2*a^2 + 22*a - 14,
2*a^3 + 2*a^2 - 11*a
]
*], q_expansions := [*
q - q^2 + 2*q^3 + q^4 + 4*q^5 - 2*q^6 - q^8 + q^9 - 4*q^10 - 6*q^11 + 2*q^12 - 2*q^13 + 8*q^15 + q^16 + 2*q^17 - q^18 - 4*q^19 + 4*q^20 + 6*q^22 - 2*q^24 + 11*q^25 + 2*q^26 - 4*q^27 - 6*q^29 - 8*q^30 + 8*q^31 - q^32 - 12*q^33 - 2*q^34 + q^36 + 8*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a + 1)*q^5 - a*q^6 + (a - 2)*q^7 - q^8 + (a + 4)*q^9 + (a - 1)*q^10 + 4*q^11 + a*q^12 + (-2*a + 2)*q^13 + (-a + 2)*q^14 - 7*q^15 + q^16 + (-a - 1)*q^17 + (-a - 4)*q^18 + 6*q^19 + (-a + 1)*q^20 + (-a + 7)*q^21 - 4*q^22 + (-a - 3)*q^23 - a*q^24 + (-a + 3)*q^25 + (2*a - 2)*q^26 + (2*a + 7)*q^27 + (a - 2)*q^28 - 6*q^29 + 7*q^30 + 8*q^31 - q^32 + 4*a*q^33 + (a + 1)*q^34 + (2*a - 9)*q^35 + (a + 4)*q^36 + (a - 4)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (a - 1)*q^5 - a*q^6 + (a + 4)*q^7 - q^8 + (-3*a - 2)*q^9 + (-a + 1)*q^10 + a*q^12 + (2*a + 6)*q^13 + (-a - 4)*q^14 + (-4*a + 1)*q^15 + q^16 + (-a + 1)*q^17 + (3*a + 2)*q^18 + 2*q^19 + (a - 1)*q^20 + (a + 1)*q^21 + (3*a + 3)*q^23 - a*q^24 + (-5*a - 3)*q^25 + (-2*a - 6)*q^26 + (4*a - 3)*q^27 + (a + 4)*q^28 + 6*q^29 + (4*a - 1)*q^30 - 4*q^31 - q^32 + (a - 1)*q^34 - 3*q^35 + (-3*a - 2)*q^36 + (-3*a - 4)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a^3 + 5*a - 2)*q^5 + a*q^6 + (2*a^3 - a^2 - 12*a + 9)*q^7 + q^8 + (a^2 - 3)*q^9 + (-a^3 + 5*a - 2)*q^10 + (-2*a^3 + 2*a^2 + 10*a - 10)*q^11 + a*q^12 + (2*a^3 - 10*a + 4)*q^13 + (2*a^3 - a^2 - 12*a + 9)*q^14 + (-2*a^3 + 10*a - 5)*q^15 + q^16 + (2*a^3 - 3*a^2 - 12*a + 12)*q^17 + (a^2 - 3)*q^18 + (-2*a^2 - 2*a + 8)*q^19 + (-a^3 + 5*a - 2)*q^20 + (3*a^3 - 2*a^2 - 15*a + 10)*q^21 + (-2*a^3 + 2*a^2 + 10*a - 10)*q^22 + (-4*a^3 + 3*a^2 + 24*a - 20)*q^23 + a*q^24 + (a^2 + 2*a - 6)*q^25 + (2*a^3 - 10*a + 4)*q^26 + (a^3 - 6*a)*q^27 + (2*a^3 - a^2 - 12*a + 9)*q^28 + (-4*a^3 + 2*a^2 + 22*a - 16)*q^29 + (-2*a^3 + 10*a - 5)*q^30 + (-4*a^3 + 2*a^2 + 22*a - 14)*q^31 + q^32 + (-2*a^3 + 14*a - 10)*q^33 + (2*a^3 - 3*a^2 - 12*a + 12)*q^34 + (3*a^3 - 2*a^2 - 18*a + 12)*q^35 + (a^2 - 3)*q^36 + (2*a^3 + 2*a^2 - 11*a)*q^37 + O(q^38)
*]> ;  // time = 34.639 seconds




J[209] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 209, 209, 209, 209, 19, 11 ], new_dimensions := [ 1, 2, 5, 7, 1, 1 ], dimensions := [ 1, 2, 5, 7, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 0, 15, 1, 3, 1, 1, 15, 0, 1, 1, 1, 5, 1, 1, 0 ], ap_traces := [
[ 0, 1, -3, -4, 1, 2, 0, 1, 3, -6, -7, -7 ],
[ 0, -2, -2, -4, -2, -4, 4, -2, -6, -4, -10, 6 ],
[ 2, 1, -5, 6, 5, 4, -4, -5, 3, 10, 11, 1 ],
[ -1, 2, 2, 10, -7, -4, 2, 7, 10, -18, 24, 0 ]
], hecke_fields := [
x - 1,
x^2 - 2,
x^5 - 2*x^4 - 6*x^3 + 10*x^2 + 5*x - 4,
x^7 + x^6 - 14*x^5 - 10*x^4 + 59*x^3 + 27*x^2 - 66*x - 30
], atkin_lehners := [
[ -1, -1 ],
[ 1, 1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 3, 1 ],
[ 1, 1 ],
[ 5, 5 ],
[ 45, 3 ]
], tamagawa_numbers := [
[ 3, 1 ],
[ 1, 1 ],
[ 5, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 3, 1, 5, 3 ], torsion_lower_bounds := [ 1, 1, 5, 3 ], l_ratios := [ 0, 0, 1/5, 1/3 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[ 0, 1, -3, -4, 1, 2, 0, 1, 3, -6, -7, -7 ],
[
a,
-a - 1,
-1,
-a - 2,
-1,
3*a - 2,
a + 2,
-1,
-3,
-3*a - 2,
-a - 5,
5*a + 3
],
[
a,
1/2*a^4 - a^3 - 5/2*a^2 + 4*a + 1,
-1/2*a^3 + 7/2*a - 1,
-1/2*a^3 + 3/2*a + 2,
1,
-1/2*a^4 + 7/2*a^2 - 2,
a^4 - a^3 - 5*a^2 + 3*a,
-1,
-a^4 + a^3 + 8*a^2 - 5*a - 9,
3/2*a^4 - a^3 - 17/2*a^2 + 2*a + 6,
-1/2*a^4 + 2*a^3 + 5/2*a^2 - 10*a + 1,
a^4 - 8*a^2 + 9
],
[
a,
-1/2*a^4 + 7/2*a^2 - a - 2,
1/2*a^5 - 9/2*a^3 + 7*a + 3,
-1/4*a^6 + 3*a^4 - 37/4*a^2 + 13/2,
-1,
-1/4*a^6 - 1/2*a^5 + 5/2*a^4 + 9/2*a^3 - 27/4*a^2 - 9*a + 7/2,
a^4 - a^3 - 9*a^2 + 7*a + 12,
1,
1/2*a^6 - 5*a^4 + 21/2*a^2 + 2*a,
-1/2*a^4 + 9/2*a^2 - a - 9,
1/4*a^6 + 1/2*a^5 - 5/2*a^4 - 9/2*a^3 + 23/4*a^2 + 9*a + 7/2,
-a^5 - a^4 + 10*a^3 + 8*a^2 - 21*a - 13
]
*], q_expansions := [*
q + q^3 - 2*q^4 - 3*q^5 - 4*q^7 - 2*q^9 + q^11 - 2*q^12 + 2*q^13 - 3*q^15 + 4*q^16 + q^19 + 6*q^20 - 4*q^21 + 3*q^23 + 4*q^25 - 5*q^27 + 8*q^28 - 6*q^29 - 7*q^31 + q^33 + 12*q^35 + 4*q^36 - 7*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 - q^5 + (-a - 2)*q^6 + (-a - 2)*q^7 - 2*a*q^8 + 2*a*q^9 - a*q^10 - q^11 + (3*a - 2)*q^13 + (-2*a - 2)*q^14 + (a + 1)*q^15 - 4*q^16 + (a + 2)*q^17 + 4*q^18 - q^19 + (3*a + 4)*q^21 - a*q^22 - 3*q^23 + (2*a + 4)*q^24 - 4*q^25 + (-2*a + 6)*q^26 + (a - 1)*q^27 + (-3*a - 2)*q^29 + (a + 2)*q^30 + (-a - 5)*q^31 + (a + 1)*q^33 + (2*a + 2)*q^34 + (a + 2)*q^35 + (5*a + 3)*q^37 + O(q^38),
q + a*q^2 + (1/2*a^4 - a^3 - 5/2*a^2 + 4*a + 1)*q^3 + (a^2 - 2)*q^4 + (-1/2*a^3 + 7/2*a - 1)*q^5 + (1/2*a^3 - a^2 - 3/2*a + 2)*q^6 + (-1/2*a^3 + 3/2*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (1/2*a^3 - a^2 - 7/2*a + 4)*q^9 + (-1/2*a^4 + 7/2*a^2 - a)*q^10 + q^11 + (-1/2*a^4 + a^3 + 7/2*a^2 - 6*a - 2)*q^12 + (-1/2*a^4 + 7/2*a^2 - 2)*q^13 + (-1/2*a^4 + 3/2*a^2 + 2*a)*q^14 + (-1/2*a^4 + 2*a^3 + 1/2*a^2 - 8*a + 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 - a^3 - 5*a^2 + 3*a)*q^17 + (1/2*a^4 - a^3 - 7/2*a^2 + 4*a)*q^18 - q^19 + (-a^4 + 3/2*a^3 + 4*a^2 - 9/2*a)*q^20 + (a^4 - 2*a^3 - 5*a^2 + 7*a + 4)*q^21 + a*q^22 + (-a^4 + a^3 + 8*a^2 - 5*a - 9)*q^23 + (-1/2*a^3 + a^2 + 7/2*a - 6)*q^24 + (-a^4 + 3/2*a^3 + 6*a^2 - 17/2*a - 2)*q^25 + (-a^4 + 1/2*a^3 + 5*a^2 + 1/2*a - 2)*q^26 + (-a^3 + a^2 + 6*a - 5)*q^27 + (-a^4 - 1/2*a^3 + 7*a^2 - 1/2*a - 6)*q^28 + (3/2*a^4 - a^3 - 17/2*a^2 + 2*a + 6)*q^29 + (a^4 - 5/2*a^3 - 3*a^2 + 15/2*a - 2)*q^30 + (-1/2*a^4 + 2*a^3 + 5/2*a^2 - 10*a + 1)*q^31 + (2*a^4 - 2*a^3 - 10*a^2 + 7*a + 4)*q^32 + (1/2*a^4 - a^3 - 5/2*a^2 + 4*a + 1)*q^33 + (a^4 + a^3 - 7*a^2 - 5*a + 4)*q^34 + (-a^2 + 4*a)*q^35 + (-3/2*a^3 + a^2 + 9/2*a - 6)*q^36 + (a^4 - 8*a^2 + 9)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^4 + 7/2*a^2 - a - 2)*q^3 + (a^2 - 2)*q^4 + (1/2*a^5 - 9/2*a^3 + 7*a + 3)*q^5 + (-1/2*a^5 + 7/2*a^3 - a^2 - 2*a)*q^6 + (-1/4*a^6 + 3*a^4 - 37/4*a^2 + 13/2)*q^7 + (a^3 - 4*a)*q^8 + (1/4*a^6 - 3*a^4 + a^3 + 41/4*a^2 - 5*a - 13/2)*q^9 + (1/2*a^6 - 9/2*a^4 + 7*a^2 + 3*a)*q^10 - q^11 + (-1/2*a^6 + 9/2*a^4 - a^3 - 9*a^2 + 2*a + 4)*q^12 + (-1/4*a^6 - 1/2*a^5 + 5/2*a^4 + 9/2*a^3 - 27/4*a^2 - 9*a + 7/2)*q^13 + (1/4*a^6 - 1/2*a^5 - 5/2*a^4 + 11/2*a^3 + 27/4*a^2 - 10*a - 15/2)*q^14 + (1/4*a^6 + 1/2*a^5 - 5/2*a^4 - 9/2*a^3 + 23/4*a^2 + 7*a + 3/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 - a^3 - 9*a^2 + 7*a + 12)*q^17 + (-1/4*a^6 + 1/2*a^5 + 7/2*a^4 - 9/2*a^3 - 47/4*a^2 + 10*a + 15/2)*q^18 + q^19 + (-1/2*a^6 + 3/2*a^5 + 5*a^4 - 27/2*a^3 - 21/2*a^2 + 19*a + 9)*q^20 + (-1/4*a^6 - 1/2*a^5 + 2*a^4 + 7/2*a^3 - 9/4*a^2 - 5*a - 11/2)*q^21 - a*q^22 + (1/2*a^6 - 5*a^4 + 21/2*a^2 + 2*a)*q^23 + (1/2*a^6 - 3/2*a^5 - 6*a^4 + 27/2*a^3 + 35/2*a^2 - 25*a - 15)*q^24 + (-1/4*a^6 + 2*a^4 - a^3 - 5/4*a^2 + 3*a - 7/2)*q^25 + (-1/4*a^6 - a^5 + 2*a^4 + 8*a^3 - 9/4*a^2 - 13*a - 15/2)*q^26 + (1/4*a^6 - 1/2*a^5 - 3*a^4 + 11/2*a^3 + 33/4*a^2 - 15*a - 7/2)*q^27 + (-1/4*a^6 + a^5 + 2*a^4 - 8*a^3 + 7/4*a^2 + 9*a - 11/2)*q^28 + (-1/2*a^4 + 9/2*a^2 - a - 9)*q^29 + (1/4*a^6 + a^5 - 2*a^4 - 9*a^3 + 1/4*a^2 + 18*a + 15/2)*q^30 + (1/4*a^6 + 1/2*a^5 - 5/2*a^4 - 9/2*a^3 + 23/4*a^2 + 9*a + 7/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^4 - 7/2*a^2 + a + 2)*q^33 + (a^5 - a^4 - 9*a^3 + 7*a^2 + 12*a)*q^34 + (-1/4*a^6 + 1/2*a^5 + 3*a^4 - 9/2*a^3 - 33/4*a^2 + 5*a + 9/2)*q^35 + (1/4*a^6 - a^4 + a^3 - 15/4*a^2 + a + 11/2)*q^36 + (-a^5 - a^4 + 10*a^3 + 8*a^2 - 21*a - 13)*q^37 + O(q^38)
*]> ;  // time = 22.899 seconds




J[210] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 210, 210, 210, 210, 210, 105, 105, 70, 42, 35, 35, 30, 21, 15, 14 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 2, 4, 2, 2, 4, 8, 2, 4, 4, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 25, 1, 1, 0, 1, 3, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 9, 1, 3, 1, 1, 0 ], ap_traces := [
[ -1, -1, -1, -1, -4, -2, -6, 0, -8, 10, -8, 2 ],
[ -1, 1, 1, 1, 0, 2, -6, 8, 0, 6, -4, -10 ],
[ 1, -1, 1, 1, 4, -2, 2, -4, -8, 6, -8, -2 ],
[ 1, 1, -1, 1, 0, 2, -6, -4, 0, -6, -4, 2 ],
[ 1, 1, 1, -1, -4, -2, 2, 4, -8, -2, 0, 6 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, 1, 1 ],
[ 1, -1, -1, -1 ],
[ -1, 1, -1, -1 ],
[ -1, -1, 1, -1 ],
[ -1, -1, -1, 1 ]
], component_group_orders := [
[ 1, 1, 1, 1 ],
[ 1, 3, 3, 1 ],
[ 1, 1, 1, 1 ],
[ 3, 3, 1, 1 ],
[ 1, 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1, 1 ],
[ 1, 3, 3, 1 ],
[ 1, 1, 1, 1 ],
[ 3, 3, 1, 1 ],
[ 1, 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 3, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 1, 1, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1/9, 1, 1/9, 1 ], eigenvalues := [*
[ -1, -1, -1, -1, -4, -2, -6, 0, -8, 10, -8, 2 ],
[ -1, 1, 1, 1, 0, 2, -6, 8, 0, 6, -4, -10 ],
[ 1, -1, 1, 1, 4, -2, 2, -4, -8, 6, -8, -2 ],
[ 1, 1, -1, 1, 0, 2, -6, -4, 0, -6, -4, 2 ],
[ 1, 1, 1, -1, -4, -2, 2, 4, -8, -2, 0, 6 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - q^5 + q^6 - q^7 - q^8 + q^9 + q^10 - 4*q^11 - q^12 - 2*q^13 + q^14 + q^15 + q^16 - 6*q^17 - q^18 - q^20 + q^21 + 4*q^22 - 8*q^23 + q^24 + q^25 + 2*q^26 - q^27 - q^28 + 10*q^29 - q^30 - 8*q^31 - q^32 + 4*q^33 + 6*q^34 + q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + q^5 - q^6 + q^7 - q^8 + q^9 - q^10 + q^12 + 2*q^13 - q^14 + q^15 + q^16 - 6*q^17 - q^18 + 8*q^19 + q^20 + q^21 - q^24 + q^25 - 2*q^26 + q^27 + q^28 + 6*q^29 - q^30 - 4*q^31 - q^32 + 6*q^34 + q^35 + q^36 - 10*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + q^7 + q^8 + q^9 + q^10 + 4*q^11 - q^12 - 2*q^13 + q^14 - q^15 + q^16 + 2*q^17 + q^18 - 4*q^19 + q^20 - q^21 + 4*q^22 - 8*q^23 - q^24 + q^25 - 2*q^26 - q^27 + q^28 + 6*q^29 - q^30 - 8*q^31 + q^32 - 4*q^33 + 2*q^34 + q^35 + q^36 - 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - q^5 + q^6 + q^7 + q^8 + q^9 - q^10 + q^12 + 2*q^13 + q^14 - q^15 + q^16 - 6*q^17 + q^18 - 4*q^19 - q^20 + q^21 + q^24 + q^25 + 2*q^26 + q^27 + q^28 - 6*q^29 - q^30 - 4*q^31 + q^32 - 6*q^34 - q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^5 + q^6 - q^7 + q^8 + q^9 + q^10 - 4*q^11 + q^12 - 2*q^13 - q^14 + q^15 + q^16 + 2*q^17 + q^18 + 4*q^19 + q^20 - q^21 - 4*q^22 - 8*q^23 + q^24 + q^25 - 2*q^26 + q^27 - q^28 - 2*q^29 + q^30 + q^32 - 4*q^33 + 2*q^34 - q^35 + q^36 + 6*q^37 + O(q^38)
*]> ;  // time = 502.771 seconds




J[211] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 211, 211, 211, 211 ], new_dimensions := [ 2, 3, 3, 9 ], dimensions := [ 2, 3, 3, 9 ], intersection_graph := [ 0, 1, 1, 41, 1, 0, 7, 1, 1, 7, 0, 1, 41, 1, 1, 0 ], ap_traces := [
[ 1, 3, 2, 1, -6, 8, 11, -5, 8, 0, -11, -4 ],
[ 0, -3, -5, -3, -9, 1, -17, 2, 16, -20, 3, 5 ],
[ -2, -1, -8, 2, -2, -3, 6, -7, -19, -6, -5, -2 ],
[ -1, -1, 15, -2, 13, -4, 4, -2, -3, 26, 5, 5 ]
], hecke_fields := [
x^2 - x - 1,
x^3 - 4*x + 1,
x^3 + 2*x^2 - x - 1,
x^9 + x^8 - 14*x^7 - 11*x^6 + 66*x^5 + 36*x^4 - 123*x^3 - 38*x^2 + 72*x + 8
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 5 ],
[ 1 ],
[ 1 ],
[ 7 ]
], tamagawa_numbers := [
[ 5 ],
[ 1 ],
[ 1 ],
[ 7 ]
], torsion_upper_bounds := [ 5, 1, 1, 7 ], torsion_lower_bounds := [ 5, 1, 1, 7 ], l_ratios := [ 1/5, 0, 0, 1/7 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1 ], eigenvalues := [*
[
a,
a + 1,
-2*a + 2,
-a + 1,
-3,
-2*a + 5,
-a + 6,
-3*a - 1,
2*a + 3,
2*a - 1,
5*a - 8,
8*a - 6
],
[
a,
-a - 1,
-a^2 - a + 1,
a - 1,
-3,
2*a^2 - 5,
-a^2 - 3,
a^2 - 2,
-a^2 + a + 8,
-a^2 + a - 4,
-3*a^2 + 9,
a^2 - a - 1
],
[
a,
-a^2 - a + 1,
a^2 + a - 4,
-a^2 - 4*a,
3*a^2 + 7*a - 2,
2*a^2 + 3*a - 3,
a^2 + 3*a + 2,
-2*a^2 - a + 1,
-a - 7,
-7*a^2 - 12*a + 4,
-a^2 - 5*a - 3,
-2*a^2 + a + 4
],
[
a,
9/58*a^8 + 15/58*a^7 - 2*a^6 - 157/58*a^5 + 235/29*a^4 + 222/29*a^3 - 637/58*a^2 - 161/29*a + 62/29,
7/116*a^8 + 31/116*a^7 - 1/2*a^6 - 309/116*a^5 + 41/58*a^4 + 183/29*a^3 + 91/116*a^2 - 93/58*a + 8/29,
-13/58*a^8 - 41/58*a^7 + 2*a^6 + 433/58*a^5 - 101/29*a^4 - 630/29*a^3 - 111/58*a^2 + 500/29*a + 78/29,
3/29*a^8 - 19/58*a^7 - 3/2*a^6 + 112/29*a^5 + 381/58*a^4 - 374/29*a^3 - 280/29*a^2 + 665/58*a + 167/29,
3/116*a^8 + 5/116*a^7 - 33/116*a^5 - 43/29*a^4 + 8/29*a^3 + 271/116*a^2 + 7/29*a + 49/29,
-5/29*a^8 - 18/29*a^7 + 2*a^6 + 200/29*a^5 - 216/29*a^4 - 614/29*a^3 + 341/29*a^2 + 456/29*a - 172/29,
33/116*a^8 + 55/116*a^7 - 3*a^6 - 595/116*a^5 + 223/29*a^4 + 465/29*a^3 - 151/116*a^2 - 416/29*a - 99/29,
7/29*a^8 + 2/29*a^7 - 3*a^6 - 19/29*a^5 + 314/29*a^4 + 65/29*a^3 - 286/29*a^2 - 128/29*a - 84/29,
-4/29*a^8 + 3/29*a^7 + 2*a^6 - 43/29*a^5 - 283/29*a^4 + 170/29*a^3 + 499/29*a^2 - 192/29*a - 68/29,
17/58*a^8 + 9/58*a^7 - 3*a^6 - 13/58*a^5 + 228/29*a^4 - 180/29*a^3 - 301/58*a^2 + 350/29*a + 72/29,
25/58*a^8 + 16/29*a^7 - 9/2*a^6 - 275/58*a^5 + 703/58*a^4 + 259/29*a^3 - 313/58*a^2 - 105/58*a - 121/29
]
*], q_expansions := [*
q + a*q^2 + (a + 1)*q^3 + (a - 1)*q^4 + (-2*a + 2)*q^5 + (2*a + 1)*q^6 + (-a + 1)*q^7 + (-2*a + 1)*q^8 + (3*a - 1)*q^9 - 2*q^10 - 3*q^11 + a*q^12 + (-2*a + 5)*q^13 - q^14 - 2*a*q^15 - 3*a*q^16 + (-a + 6)*q^17 + (2*a + 3)*q^18 + (-3*a - 1)*q^19 + (2*a - 4)*q^20 - a*q^21 - 3*a*q^22 + (2*a + 3)*q^23 + (-3*a - 1)*q^24 + (-4*a + 3)*q^25 + (3*a - 2)*q^26 + (2*a - 1)*q^27 + (a - 2)*q^28 + (2*a - 1)*q^29 + (-2*a - 2)*q^30 + (5*a - 8)*q^31 + (a - 5)*q^32 + (-3*a - 3)*q^33 + (5*a - 1)*q^34 + (-2*a + 4)*q^35 + (-a + 4)*q^36 + (8*a - 6)*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (a^2 - 2)*q^4 + (-a^2 - a + 1)*q^5 + (-a^2 - a)*q^6 + (a - 1)*q^7 - q^8 + (a^2 + 2*a - 2)*q^9 + (-a^2 - 3*a + 1)*q^10 - 3*q^11 + (-a^2 - 2*a + 3)*q^12 + (2*a^2 - 5)*q^13 + (a^2 - a)*q^14 + (2*a^2 + 4*a - 2)*q^15 + (-2*a^2 - a + 4)*q^16 + (-a^2 - 3)*q^17 + (2*a^2 + 2*a - 1)*q^18 + (a^2 - 2)*q^19 + (-a^2 - a - 1)*q^20 + (-a^2 + 1)*q^21 - 3*a*q^22 + (-a^2 + a + 8)*q^23 + (a + 1)*q^24 + (3*a^2 + 5*a - 6)*q^25 + (3*a - 2)*q^26 + (-3*a^2 - a + 6)*q^27 + (-a^2 + 2*a + 1)*q^28 + (-a^2 + a - 4)*q^29 + (4*a^2 + 6*a - 2)*q^30 + (-3*a^2 + 9)*q^31 + (-a^2 - 4*a + 4)*q^32 + (3*a + 3)*q^33 + (-7*a + 1)*q^34 - 2*a*q^35 + (3*a + 2)*q^36 + (a^2 - a - 1)*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 1)*q^3 + (a^2 - 2)*q^4 + (a^2 + a - 4)*q^5 + (a^2 - 1)*q^6 + (-a^2 - 4*a)*q^7 + (-2*a^2 - 3*a + 1)*q^8 + (-a - 2)*q^9 + (-a^2 - 3*a + 1)*q^10 + (3*a^2 + 7*a - 2)*q^11 + (2*a - 1)*q^12 + (2*a^2 + 3*a - 3)*q^13 + (-2*a^2 - a - 1)*q^14 + (3*a^2 + 4*a - 4)*q^15 + (-a^2 - a + 2)*q^16 + (a^2 + 3*a + 2)*q^17 + (-a^2 - 2*a)*q^18 + (-2*a^2 - a + 1)*q^19 + (-3*a^2 - 2*a + 7)*q^20 + (-2*a^2 + 3)*q^21 + (a^2 + a + 3)*q^22 + (-a - 7)*q^23 + (-a + 2)*q^24 + (-6*a^2 - 7*a + 11)*q^25 + (-a^2 - a + 2)*q^26 + (4*a^2 + 5*a - 4)*q^27 + (5*a^2 + 5*a - 2)*q^28 + (-7*a^2 - 12*a + 4)*q^29 + (-2*a^2 - a + 3)*q^30 + (-a^2 - 5*a - 3)*q^31 + (5*a^2 + 7*a - 3)*q^32 + (3*a^2 + 2*a - 6)*q^33 + (a^2 + 3*a + 1)*q^34 + (5*a^2 + 12*a - 3)*q^35 + (a + 3)*q^36 + (-2*a^2 + a + 4)*q^37 + O(q^38),
q + a*q^2 + (9/58*a^8 + 15/58*a^7 - 2*a^6 - 157/58*a^5 + 235/29*a^4 + 222/29*a^3 - 637/58*a^2 - 161/29*a + 62/29)*q^3 + (a^2 - 2)*q^4 + (7/116*a^8 + 31/116*a^7 - 1/2*a^6 - 309/116*a^5 + 41/58*a^4 + 183/29*a^3 + 91/116*a^2 - 93/58*a + 8/29)*q^5 + (3/29*a^8 + 5/29*a^7 - a^6 - 62/29*a^5 + 60/29*a^4 + 235/29*a^3 + 10/29*a^2 - 262/29*a - 36/29)*q^6 + (-13/58*a^8 - 41/58*a^7 + 2*a^6 + 433/58*a^5 - 101/29*a^4 - 630/29*a^3 - 111/58*a^2 + 500/29*a + 78/29)*q^7 + (a^3 - 4*a)*q^8 + (-7/29*a^8 - 2/29*a^7 + 3*a^6 + 19/29*a^5 - 314/29*a^4 - 65/29*a^3 + 286/29*a^2 + 70/29*a + 113/29)*q^9 + (6/29*a^8 + 10/29*a^7 - 2*a^6 - 95/29*a^5 + 120/29*a^4 + 238/29*a^3 + 20/29*a^2 - 118/29*a - 14/29)*q^10 + (3/29*a^8 - 19/58*a^7 - 3/2*a^6 + 112/29*a^5 + 381/58*a^4 - 374/29*a^3 - 280/29*a^2 + 665/58*a + 167/29)*q^11 + (-7/29*a^8 - 2/29*a^7 + 3*a^6 + 19/29*a^5 - 343/29*a^4 - 65/29*a^3 + 489/29*a^2 + 70/29*a - 148/29)*q^12 + (3/116*a^8 + 5/116*a^7 - 33/116*a^5 - 43/29*a^4 + 8/29*a^3 + 271/116*a^2 + 7/29*a + 49/29)*q^13 + (-14/29*a^8 - 33/29*a^7 + 5*a^6 + 328/29*a^5 - 396/29*a^4 - 855/29*a^3 + 253/29*a^2 + 546/29*a + 52/29)*q^14 + (11/58*a^8 + 57/58*a^7 - 2*a^6 - 643/58*a^5 + 168/29*a^4 + 1035/29*a^3 - 205/58*a^2 - 954/29*a - 66/29)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-5/29*a^8 - 18/29*a^7 + 2*a^6 + 200/29*a^5 - 216/29*a^4 - 614/29*a^3 + 341/29*a^2 + 456/29*a - 172/29)*q^17 + (5/29*a^8 - 11/29*a^7 - 2*a^6 + 148/29*a^5 + 187/29*a^4 - 575/29*a^3 - 196/29*a^2 + 617/29*a + 56/29)*q^18 + (33/116*a^8 + 55/116*a^7 - 3*a^6 - 595/116*a^5 + 223/29*a^4 + 465/29*a^3 - 151/116*a^2 - 416/29*a - 99/29)*q^19 + (1/58*a^8 + 21/58*a^7 - 243/58*a^5 - 19/29*a^4 + 392/29*a^3 + 129/58*a^2 - 353/29*a - 64/29)*q^20 + (-3/29*a^8 - 5/29*a^7 + a^6 + 33/29*a^5 - 60/29*a^4 + 26/29*a^3 - 10/29*a^2 - 260/29*a + 36/29)*q^21 + (-25/58*a^8 - 3/58*a^7 + 5*a^6 - 15/58*a^5 - 482/29*a^4 + 89/29*a^3 + 893/58*a^2 - 49/29*a - 24/29)*q^22 + (7/29*a^8 + 2/29*a^7 - 3*a^6 - 19/29*a^5 + 314/29*a^4 + 65/29*a^3 - 286/29*a^2 - 128/29*a - 84/29)*q^23 + (-1/29*a^8 - 21/29*a^7 + 243/29*a^5 + 67/29*a^4 - 842/29*a^3 - 216/29*a^2 + 880/29*a + 128/29)*q^24 + (13/58*a^8 + 35/29*a^7 - 3/2*a^6 - 723/58*a^5 - 59/58*a^4 + 949/29*a^3 + 691/58*a^2 - 971/58*a - 194/29)*q^25 + (1/58*a^8 + 21/58*a^7 - 185/58*a^5 - 19/29*a^4 + 160/29*a^3 + 71/58*a^2 - 5/29*a - 6/29)*q^26 + (-1/29*a^8 + 8/29*a^7 - 105/29*a^5 + 96/29*a^4 + 405/29*a^3 - 303/29*a^2 - 454/29*a + 12/29)*q^27 + (-6/29*a^8 - 10/29*a^7 + 2*a^6 + 95/29*a^5 - 149/29*a^4 - 209/29*a^3 + 125/29*a^2 + 60/29*a - 44/29)*q^28 + (-4/29*a^8 + 3/29*a^7 + 2*a^6 - 43/29*a^5 - 283/29*a^4 + 170/29*a^3 + 499/29*a^2 - 192/29*a - 68/29)*q^29 + (23/29*a^8 + 19/29*a^7 - 9*a^6 - 195/29*a^5 + 837/29*a^4 + 574/29*a^3 - 745/29*a^2 - 462/29*a - 44/29)*q^30 + (17/58*a^8 + 9/58*a^7 - 3*a^6 - 13/58*a^5 + 228/29*a^4 - 180/29*a^3 - 301/58*a^2 + 350/29*a + 72/29)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (37/58*a^8 + 23/58*a^7 - 8*a^6 - 233/58*a^5 + 892/29*a^4 + 381/29*a^3 - 2303/58*a^2 - 446/29*a + 300/29)*q^33 + (-13/29*a^8 - 12/29*a^7 + 5*a^6 + 114/29*a^5 - 434/29*a^4 - 274/29*a^3 + 266/29*a^2 + 188/29*a + 40/29)*q^34 + (-49/58*a^8 - 101/58*a^7 + 9*a^6 + 1061/58*a^5 - 751/29*a^4 - 1518/29*a^3 + 987/58*a^2 + 1086/29*a + 120/29)*q^35 + (-2/29*a^8 + 16/29*a^7 + a^6 - 181/29*a^5 - 127/29*a^4 + 549/29*a^3 + 235/29*a^2 - 444/29*a - 266/29)*q^36 + (25/58*a^8 + 16/29*a^7 - 9/2*a^6 - 275/58*a^5 + 703/58*a^4 + 259/29*a^3 - 313/58*a^2 - 105/58*a - 121/29)*q^37 + O(q^38)
*]> ;  // time = 2.99 seconds




J[213] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 213, 213, 213, 213, 213, 71, 71 ], new_dimensions := [ 1, 2, 2, 2, 4, 3, 3 ], dimensions := [ 1, 2, 2, 2, 4, 6, 6 ], intersection_graph := [ 0, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 9, 5, 1, 1, 1, 1, 0, 19, 61, 1, 1, 1, 9, 19, 0, 81, 1, 1, 1, 5, 61, 81, 0 ], ap_traces := [
[ 1, 1, 2, 2, 0, -2, 0, 0, 0, -2, -10, -6 ],
[ -1, -2, 1, -6, -4, -5, 0, -8, -3, 3, -4, 3 ],
[ 1, 2, -1, -2, 6, -3, 6, -4, 3, 7, 4, -1 ],
[ -3, 2, -5, -4, -8, -1, -4, -8, -3, 3, 8, -1 ],
[ 3, -4, -3, 6, 2, 5, -8, 8, -1, -5, 2, 19 ]
], hecke_fields := [
x - 1,
x^2 + x - 1,
x^2 - x - 3,
x^2 + 3*x + 1,
x^4 - 3*x^3 - 2*x^2 + 7*x + 1
], atkin_lehners := [
[ -1, 1 ],
[ 1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 45, 1 ],
[ 1159, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 45, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 1 ], torsion_lower_bounds := [ 1, 1, 3, 1, 1 ], l_ratios := [ 1, 0, 1/3, 0, 1 ], analytic_sha_upper_bounds := [ 1, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1, 0, 1 ], eigenvalues := [*
[ 1, 1, 2, 2, 0, -2, 0, 0, 0, -2, -10, -6 ],
[
a,
-1,
-a,
-3,
-2*a - 3,
3*a - 1,
2*a + 1,
-2*a - 5,
5*a + 1,
3*a + 3,
-2,
-9*a - 3
],
[
a,
1,
-a,
-1,
3,
-a - 1,
3,
-2*a - 1,
-3*a + 3,
a + 3,
2,
a - 1
],
[
a,
1,
-a - 4,
2*a + 1,
-2*a - 7,
-3*a - 5,
2*a + 1,
2*a - 1,
3*a + 3,
-7*a - 9,
4*a + 10,
5*a + 7
],
[
a,
-1,
-a^2 + 2*a + 1,
-a^2 + a + 4,
-a^3 + a^2 + 3*a + 1,
-a^3 + 2*a^2 + a,
2*a^3 - 5*a^2 - 5*a + 6,
3*a^3 - 5*a^2 - 9*a + 7,
-a^3 + 4*a^2 + a - 8,
-a^3 + 4*a^2 - 3*a - 6,
-a^3 - 2*a^2 + 8*a + 7,
-a^3 + 2*a^2 + 3*a + 2
]
*], q_expansions := [*
q + q^2 + q^3 - q^4 + 2*q^5 + q^6 + 2*q^7 - 3*q^8 + q^9 + 2*q^10 - q^12 - 2*q^13 + 2*q^14 + 2*q^15 - q^16 + q^18 - 2*q^20 + 2*q^21 - 3*q^24 - q^25 - 2*q^26 + q^27 - 2*q^28 - 2*q^29 + 2*q^30 - 10*q^31 + 5*q^32 + 4*q^35 - q^36 - 6*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a - 1)*q^4 - a*q^5 - a*q^6 - 3*q^7 + (-2*a - 1)*q^8 + q^9 + (a - 1)*q^10 + (-2*a - 3)*q^11 + (a + 1)*q^12 + (3*a - 1)*q^13 - 3*a*q^14 + a*q^15 + 3*a*q^16 + (2*a + 1)*q^17 + a*q^18 + (-2*a - 5)*q^19 + q^20 + 3*q^21 + (-a - 2)*q^22 + (5*a + 1)*q^23 + (2*a + 1)*q^24 + (-a - 4)*q^25 + (-4*a + 3)*q^26 - q^27 + (3*a + 3)*q^28 + (3*a + 3)*q^29 + (-a + 1)*q^30 - 2*q^31 + (a + 5)*q^32 + (2*a + 3)*q^33 + (-a + 2)*q^34 + 3*a*q^35 + (-a - 1)*q^36 + (-9*a - 3)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a + 1)*q^4 - a*q^5 + a*q^6 - q^7 + 3*q^8 + q^9 + (-a - 3)*q^10 + 3*q^11 + (a + 1)*q^12 + (-a - 1)*q^13 - a*q^14 - a*q^15 + (a - 2)*q^16 + 3*q^17 + a*q^18 + (-2*a - 1)*q^19 + (-2*a - 3)*q^20 - q^21 + 3*a*q^22 + (-3*a + 3)*q^23 + 3*q^24 + (a - 2)*q^25 + (-2*a - 3)*q^26 + q^27 + (-a - 1)*q^28 + (a + 3)*q^29 + (-a - 3)*q^30 + 2*q^31 + (-a - 3)*q^32 + 3*q^33 + 3*a*q^34 + a*q^35 + (a + 1)*q^36 + (a - 1)*q^37 + O(q^38),
q + a*q^2 + q^3 + (-3*a - 3)*q^4 + (-a - 4)*q^5 + a*q^6 + (2*a + 1)*q^7 + (4*a + 3)*q^8 + q^9 + (-a + 1)*q^10 + (-2*a - 7)*q^11 + (-3*a - 3)*q^12 + (-3*a - 5)*q^13 + (-5*a - 2)*q^14 + (-a - 4)*q^15 + (-3*a + 2)*q^16 + (2*a + 1)*q^17 + a*q^18 + (2*a - 1)*q^19 + (6*a + 9)*q^20 + (2*a + 1)*q^21 + (-a + 2)*q^22 + (3*a + 3)*q^23 + (4*a + 3)*q^24 + (5*a + 10)*q^25 + (4*a + 3)*q^26 + q^27 + (9*a + 3)*q^28 + (-7*a - 9)*q^29 + (-a + 1)*q^30 + (4*a + 10)*q^31 + (3*a - 3)*q^32 + (-2*a - 7)*q^33 + (-5*a - 2)*q^34 + (-3*a - 2)*q^35 + (-3*a - 3)*q^36 + (5*a + 7)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 + 2*a + 1)*q^5 - a*q^6 + (-a^2 + a + 4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^3 + 2*a^2 + a)*q^10 + (-a^3 + a^2 + 3*a + 1)*q^11 + (-a^2 + 2)*q^12 + (-a^3 + 2*a^2 + a)*q^13 + (-a^3 + a^2 + 4*a)*q^14 + (a^2 - 2*a - 1)*q^15 + (3*a^3 - 4*a^2 - 7*a + 3)*q^16 + (2*a^3 - 5*a^2 - 5*a + 6)*q^17 + a*q^18 + (3*a^3 - 5*a^2 - 9*a + 7)*q^19 + (-a^3 + a^2 + 3*a - 1)*q^20 + (a^2 - a - 4)*q^21 + (-2*a^3 + a^2 + 8*a + 1)*q^22 + (-a^3 + 4*a^2 + a - 8)*q^23 + (-a^3 + 4*a)*q^24 + (-a^3 + 4*a^2 - 3*a - 5)*q^25 + (-a^3 - a^2 + 7*a + 1)*q^26 - q^27 + (-2*a^3 + 4*a^2 + 5*a - 7)*q^28 + (-a^3 + 4*a^2 - 3*a - 6)*q^29 + (a^3 - 2*a^2 - a)*q^30 + (-a^3 - 2*a^2 + 8*a + 7)*q^31 + (3*a^3 - a^2 - 10*a - 3)*q^32 + (a^3 - a^2 - 3*a - 1)*q^33 + (a^3 - a^2 - 8*a - 2)*q^34 + (-a^2 + 2*a + 3)*q^35 + (a^2 - 2)*q^36 + (-a^3 + 2*a^2 + 3*a + 2)*q^37 + O(q^38)
*]> ;  // time = 24.339 seconds




J[214] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 214, 214, 214, 214, 214, 214, 107, 107 ], new_dimensions := [ 1, 1, 1, 1, 2, 2, 2, 7 ], dimensions := [ 1, 1, 1, 1, 2, 2, 4, 14 ], intersection_graph := [ 0, 3, 1, 1, 1, 1, 5, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 1, 0, 1, 1, 109, 1, 1, 3, 1, 1, 0, 11, 1, 5, 1, 1, 1, 1, 11, 0, 1, 1, 1, 1, 7, 109, 1, 1, 0 ], ap_traces := [
[ -1, 1, -4, -2, -3, -1, 6, 1, -7, -6, 4, -9 ],
[ -1, -2, -1, 4, -6, -4, -6, -2, 5, 0, -2, 0 ],
[ 1, 1, 0, 2, -3, -1, 6, -7, 9, -6, -4, -1 ],
[ 1, -2, -3, -4, -2, 4, -2, -2, 1, -4, -10, 12 ],
[ -2, -2, 4, -2, 2, 2, 10, 4, 0, 10, -4, -8 ],
[ 2, 2, 0, -2, 6, -2, -6, 4, -12, 6, 4, -8 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 + 2*x - 2,
x^2 - 2*x - 2
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 7, 1 ],
[ 109, 1 ],
[ 33, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 33, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 3, 1, 1, 3 ], l_ratios := [ 0, 0, 1/3, 0, 1, 11/3 ], analytic_sha_upper_bounds := [ 0, 0, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 0, 1, 1 ], eigenvalues := [*
[ -1, 1, -4, -2, -3, -1, 6, 1, -7, -6, 4, -9 ],
[ -1, -2, -1, 4, -6, -4, -6, -2, 5, 0, -2, 0 ],
[ 1, 1, 0, 2, -3, -1, 6, -7, 9, -6, -4, -1 ],
[ 1, -2, -3, -4, -2, 4, -2, -2, 1, -4, -10, 12 ],
[
-1,
a,
a + 3,
a,
-a,
-a,
-a + 4,
2,
-a - 1,
-a + 4,
-4*a - 6,
-4
],
[
1,
a,
-a + 1,
-a,
-a + 4,
-a,
a - 4,
2,
-a - 5,
3*a,
2,
4*a - 8
]
*], q_expansions := [*
q - q^2 + q^3 + q^4 - 4*q^5 - q^6 - 2*q^7 - q^8 - 2*q^9 + 4*q^10 - 3*q^11 + q^12 - q^13 + 2*q^14 - 4*q^15 + q^16 + 6*q^17 + 2*q^18 + q^19 - 4*q^20 - 2*q^21 + 3*q^22 - 7*q^23 - q^24 + 11*q^25 + q^26 - 5*q^27 - 2*q^28 - 6*q^29 + 4*q^30 + 4*q^31 - q^32 - 3*q^33 - 6*q^34 + 8*q^35 - 2*q^36 - 9*q^37 + O(q^38),
q - q^2 - 2*q^3 + q^4 - q^5 + 2*q^6 + 4*q^7 - q^8 + q^9 + q^10 - 6*q^11 - 2*q^12 - 4*q^13 - 4*q^14 + 2*q^15 + q^16 - 6*q^17 - q^18 - 2*q^19 - q^20 - 8*q^21 + 6*q^22 + 5*q^23 + 2*q^24 - 4*q^25 + 4*q^26 + 4*q^27 + 4*q^28 - 2*q^30 - 2*q^31 - q^32 + 12*q^33 + 6*q^34 - 4*q^35 + q^36 + O(q^38),
q + q^2 + q^3 + q^4 + q^6 + 2*q^7 + q^8 - 2*q^9 - 3*q^11 + q^12 - q^13 + 2*q^14 + q^16 + 6*q^17 - 2*q^18 - 7*q^19 + 2*q^21 - 3*q^22 + 9*q^23 + q^24 - 5*q^25 - q^26 - 5*q^27 + 2*q^28 - 6*q^29 - 4*q^31 + q^32 - 3*q^33 + 6*q^34 - 2*q^36 - q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 3*q^5 - 2*q^6 - 4*q^7 + q^8 + q^9 - 3*q^10 - 2*q^11 - 2*q^12 + 4*q^13 - 4*q^14 + 6*q^15 + q^16 - 2*q^17 + q^18 - 2*q^19 - 3*q^20 + 8*q^21 - 2*q^22 + q^23 - 2*q^24 + 4*q^25 + 4*q^26 + 4*q^27 - 4*q^28 - 4*q^29 + 6*q^30 - 10*q^31 + q^32 + 4*q^33 - 2*q^34 + 12*q^35 + q^36 + 12*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (a + 3)*q^5 - a*q^6 + a*q^7 - q^8 + (-2*a - 1)*q^9 + (-a - 3)*q^10 - a*q^11 + a*q^12 - a*q^13 - a*q^14 + (a + 2)*q^15 + q^16 + (-a + 4)*q^17 + (2*a + 1)*q^18 + 2*q^19 + (a + 3)*q^20 + (-2*a + 2)*q^21 + a*q^22 + (-a - 1)*q^23 - a*q^24 + (4*a + 6)*q^25 + a*q^26 - 4*q^27 + a*q^28 + (-a + 4)*q^29 + (-a - 2)*q^30 + (-4*a - 6)*q^31 - q^32 + (2*a - 2)*q^33 + (a - 4)*q^34 + (a + 2)*q^35 + (-2*a - 1)*q^36 - 4*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a + 1)*q^5 + a*q^6 - a*q^7 + q^8 + (2*a - 1)*q^9 + (-a + 1)*q^10 + (-a + 4)*q^11 + a*q^12 - a*q^13 - a*q^14 + (-a - 2)*q^15 + q^16 + (a - 4)*q^17 + (2*a - 1)*q^18 + 2*q^19 + (-a + 1)*q^20 + (-2*a - 2)*q^21 + (-a + 4)*q^22 + (-a - 5)*q^23 + a*q^24 - 2*q^25 - a*q^26 + 4*q^27 - a*q^28 + 3*a*q^29 + (-a - 2)*q^30 + 2*q^31 + q^32 + (2*a - 2)*q^33 + (a - 4)*q^34 + (a + 2)*q^35 + (2*a - 1)*q^36 + (4*a - 8)*q^37 + O(q^38)
*]> ;  // time = 36.25 seconds




J[215] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 215, 215, 215, 215, 43, 43 ], new_dimensions := [ 1, 3, 5, 6, 1, 2 ], dimensions := [ 1, 3, 5, 6, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 0, 49, 1, 1, 1, 1, 49, 0, 1, 5, 1, 1, 1, 1, 0, 1, 31, 1, 1, 5, 1, 0, 1, 1, 1, 1, 31, 1, 0 ], ap_traces := [
[ 0, 0, -1, -2, -1, -1, -3, -2, -1, 4, 3, -8 ],
[ -2, 1, 3, -3, 9, -2, 10, 6, -6, 2, 13, 9 ],
[ 2, -1, 5, 5, -6, 5, -17, -6, 1, 6, 6, 5 ],
[ 3, 4, -6, 8, 0, 6, 6, 6, 0, -10, 0, 28 ]
], hecke_fields := [
x - 1,
x^3 + 2*x^2 - 3*x - 3,
x^5 - 2*x^4 - 7*x^3 + 13*x^2 + 5*x - 4,
x^6 - 3*x^5 - 5*x^4 + 17*x^3 + 3*x^2 - 17*x - 3
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 11, 1 ],
[ 5, 1 ],
[ 93, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 11, 1 ],
[ 5, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 1, 11, 1, 3 ], torsion_lower_bounds := [ 1, 11, 1, 3 ], l_ratios := [ 0, 1/11, 5, 1/3 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1 ], eigenvalues := [*
[ 0, 0, -1, -2, -1, -1, -3, -2, -1, 4, 3, -8 ],
[
a,
a + 1,
1,
-a^2 - 2*a + 1,
-a^2 + a + 7,
-2*a - 2,
-2*a + 2,
-2*a^2 - 4*a + 6,
2*a^2 + 4*a - 6,
2*a + 2,
a^2 + 1,
a^2 - a - 1
],
[
a,
-a^3 + 5*a,
1,
a^4 - a^3 - 6*a^2 + 6*a + 2,
a^3 - 6*a - 1,
-a^4 + 5*a^2 + a + 3,
a^4 - 7*a^2 + a + 1,
-2*a^4 + 14*a^2 - 2*a - 10,
-a^4 + 5*a^2 - a + 3,
-2*a^4 + 2*a^3 + 14*a^2 - 12*a - 8,
2*a^4 + a^3 - 13*a^2 - 5*a + 7,
-a^4 + a^3 + 7*a^2 - 5*a - 4
],
[
a,
a^5 - 2*a^4 - 6*a^3 + 9*a^2 + 6*a - 2,
-1,
-2*a^5 + 3*a^4 + 13*a^3 - 12*a^2 - 16*a + 2,
-3*a^5 + 3*a^4 + 23*a^3 - 9*a^2 - 38*a - 9,
-2*a + 2,
4*a^5 - 4*a^4 - 30*a^3 + 12*a^2 + 48*a + 12,
2*a^5 - 2*a^4 - 16*a^3 + 6*a^2 + 28*a + 8,
-2*a^5 + 4*a^4 + 12*a^3 - 16*a^2 - 14*a,
2*a^5 - 2*a^4 - 16*a^3 + 8*a^2 + 26*a,
2*a^5 - 3*a^4 - 15*a^3 + 14*a^2 + 24*a - 4,
-a^5 + a^4 + 9*a^3 - 5*a^2 - 16*a + 5
]
*], q_expansions := [*
q - 2*q^4 - q^5 - 2*q^7 - 3*q^9 - q^11 - q^13 + 4*q^16 - 3*q^17 - 2*q^19 + 2*q^20 - q^23 + q^25 + 4*q^28 + 4*q^29 + 3*q^31 + 2*q^35 + 6*q^36 - 8*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + (a^2 - 2)*q^4 + q^5 + (a^2 + a)*q^6 + (-a^2 - 2*a + 1)*q^7 + (-2*a^2 - a + 3)*q^8 + (a^2 + 2*a - 2)*q^9 + a*q^10 + (-a^2 + a + 7)*q^11 + (-a^2 + a + 1)*q^12 + (-2*a - 2)*q^13 + (-2*a - 3)*q^14 + (a + 1)*q^15 + (a^2 - 3*a - 2)*q^16 + (-2*a + 2)*q^17 + (a + 3)*q^18 + (-2*a^2 - 4*a + 6)*q^19 + (a^2 - 2)*q^20 + (-a^2 - 4*a - 2)*q^21 + (3*a^2 + 4*a - 3)*q^22 + (2*a^2 + 4*a - 6)*q^23 + (a^2 - 4*a - 3)*q^24 + q^25 + (-2*a^2 - 2*a)*q^26 + (a^2 - 2)*q^27 + (a - 2)*q^28 + (2*a + 2)*q^29 + (a^2 + a)*q^30 + (a^2 + 1)*q^31 + (-a^2 + 3*a - 3)*q^32 + (2*a^2 + 5*a + 4)*q^33 + (-2*a^2 + 2*a)*q^34 + (-a^2 - 2*a + 1)*q^35 + (-a^2 - a + 4)*q^36 + (a^2 - a - 1)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 5*a)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^4 + 5*a^2)*q^6 + (a^4 - a^3 - 6*a^2 + 6*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (a^4 + a^3 - 6*a^2 - 6*a + 5)*q^9 + a*q^10 + (a^3 - 6*a - 1)*q^11 + (-2*a^4 + 13*a^2 - 5*a - 4)*q^12 + (-a^4 + 5*a^2 + a + 3)*q^13 + (a^4 + a^3 - 7*a^2 - 3*a + 4)*q^14 + (-a^3 + 5*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 - 7*a^2 + a + 1)*q^17 + (3*a^4 + a^3 - 19*a^2 + 4)*q^18 + (-2*a^4 + 14*a^2 - 2*a - 10)*q^19 + (a^2 - 2)*q^20 + (-a^4 + 5*a^2 - 4*a + 8)*q^21 + (a^4 - 6*a^2 - a)*q^22 + (-a^4 + 5*a^2 - a + 3)*q^23 + (-2*a^4 - a^3 + 11*a^2 + 6*a - 8)*q^24 + q^25 + (-2*a^4 - 2*a^3 + 14*a^2 + 8*a - 4)*q^26 + (-a^4 - 2*a^3 + 7*a^2 + 8*a - 8)*q^27 + (a^4 + 2*a^3 - 4*a^2 - 13*a)*q^28 + (-2*a^4 + 2*a^3 + 14*a^2 - 12*a - 8)*q^29 + (-a^4 + 5*a^2)*q^30 + (2*a^4 + a^3 - 13*a^2 - 5*a + 7)*q^31 + (2*a^4 - a^3 - 13*a^2 + 7*a + 4)*q^32 + (a^2 + a - 8)*q^33 + (2*a^4 - 12*a^2 - 4*a + 4)*q^34 + (a^4 - a^3 - 6*a^2 + 6*a + 2)*q^35 + (5*a^4 - 27*a^2 + a + 2)*q^36 + (-a^4 + a^3 + 7*a^2 - 5*a - 4)*q^37 + O(q^38),
q + a*q^2 + (a^5 - 2*a^4 - 6*a^3 + 9*a^2 + 6*a - 2)*q^3 + (a^2 - 2)*q^4 - q^5 + (a^5 - a^4 - 8*a^3 + 3*a^2 + 15*a + 3)*q^6 + (-2*a^5 + 3*a^4 + 13*a^3 - 12*a^2 - 16*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (2*a^5 - 3*a^4 - 13*a^3 + 10*a^2 + 16*a + 7)*q^9 - a*q^10 + (-3*a^5 + 3*a^4 + 23*a^3 - 9*a^2 - 38*a - 9)*q^11 + (a^4 - 2*a^3 - 6*a^2 + 8*a + 7)*q^12 + (-2*a + 2)*q^13 + (-3*a^5 + 3*a^4 + 22*a^3 - 10*a^2 - 32*a - 6)*q^14 + (-a^5 + 2*a^4 + 6*a^3 - 9*a^2 - 6*a + 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (4*a^5 - 4*a^4 - 30*a^3 + 12*a^2 + 48*a + 12)*q^17 + (3*a^5 - 3*a^4 - 24*a^3 + 10*a^2 + 41*a + 6)*q^18 + (2*a^5 - 2*a^4 - 16*a^3 + 6*a^2 + 28*a + 8)*q^19 + (-a^2 + 2)*q^20 + (-a^4 + a^3 + 8*a^2 - 4*a - 13)*q^21 + (-6*a^5 + 8*a^4 + 42*a^3 - 29*a^2 - 60*a - 9)*q^22 + (-2*a^5 + 4*a^4 + 12*a^3 - 16*a^2 - 14*a)*q^23 + (-a^5 + 10*a^3 + 2*a^2 - 23*a - 6)*q^24 + q^25 + (-2*a^2 + 2*a)*q^26 + (2*a^5 - 5*a^4 - 9*a^3 + 22*a^2 - 5)*q^27 + (-2*a^5 + a^4 + 15*a^3 + a^2 - 25*a - 13)*q^28 + (2*a^5 - 2*a^4 - 16*a^3 + 8*a^2 + 26*a)*q^29 + (-a^5 + a^4 + 8*a^3 - 3*a^2 - 15*a - 3)*q^30 + (2*a^5 - 3*a^4 - 15*a^3 + 14*a^2 + 24*a - 4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-5*a^5 + 6*a^4 + 38*a^3 - 23*a^2 - 64*a - 3)*q^33 + (8*a^5 - 10*a^4 - 56*a^3 + 36*a^2 + 80*a + 12)*q^34 + (2*a^5 - 3*a^4 - 13*a^3 + 12*a^2 + 16*a - 2)*q^35 + (2*a^5 - 3*a^4 - 15*a^3 + 12*a^2 + 25*a - 5)*q^36 + (-a^5 + a^4 + 9*a^3 - 5*a^2 - 16*a + 5)*q^37 + O(q^38)
*]> ;  // time = 24.949 seconds




J[217] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 217, 217, 217, 217, 31 ], new_dimensions := [ 3, 3, 4, 5, 2 ], dimensions := [ 3, 3, 4, 5, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 19, 1, 1, 0, 1, 1, 1, 1, 1, 0, 31, 1, 19, 1, 31, 0 ], ap_traces := [
[ -3, -3, 0, -3, -6, -3, -6, 3, -18, -15, -3, 0 ],
[ -3, -3, -6, 3, 0, -3, -12, -3, -12, 9, 3, 6 ],
[ 0, 3, 4, 4, 2, -1, 8, 5, 20, -7, -4, 0 ],
[ 3, 3, 0, -5, 4, -3, -4, -9, 18, -1, 5, -12 ]
], hecke_fields := [
x^3 + 3*x^2 - 3,
x^3 + 3*x^2 - 3,
x^4 - 5*x^2 + x + 1,
x^5 - 3*x^4 - 5*x^3 + 16*x^2 + 6*x - 19
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 19, 1 ],
[ 1, 1 ],
[ 31, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 19, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1 ], l_ratios := [ 0, 0, 1, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
a,
a^2 + a - 3,
-2*a^2 - 3*a + 3,
-1,
a^2 - 5,
2*a^2 + 5*a - 2,
a - 1,
-a,
a^2 + 3*a - 6,
-a^2 + a - 1,
-1,
-a^2 + a + 4
],
[
a,
-a^2 - a + 1,
-a - 3,
1,
3*a^2 + 6*a - 3,
-3*a - 4,
a - 3,
3*a + 2,
-3*a^2 - 5*a,
3*a^2 + 3*a - 3,
1,
-a^2 - 3*a + 2
],
[
a,
-a^3 + 5*a,
-a + 1,
1,
-a^2 - 2*a + 3,
a^3 - a^2 - 5*a + 3,
2*a^2 + a - 3,
3*a^3 + a^2 - 13*a + 1,
2*a^3 + a^2 - 9*a + 4,
a^3 + 2*a^2 - 3*a - 6,
-1,
-6*a^3 - a^2 + 25*a - 2
],
[
a,
-a^3 + 2*a^2 + 3*a - 4,
a^4 - 2*a^3 - 5*a^2 + 6*a + 6,
-1,
-a^4 + 2*a^3 + 4*a^2 - 5*a - 2,
-a^4 + a^3 + 6*a^2 - 2*a - 8,
2*a^3 - 4*a^2 - 7*a + 9,
2*a^4 - 3*a^3 - 11*a^2 + 9*a + 11,
-a^2 - a + 8,
-2*a^4 + a^3 + 16*a^2 - 3*a - 26,
1,
-a^4 + 4*a^3 + 2*a^2 - 12*a - 3
]
*], q_expansions := [*
q + a*q^2 + (a^2 + a - 3)*q^3 + (a^2 - 2)*q^4 + (-2*a^2 - 3*a + 3)*q^5 + (-2*a^2 - 3*a + 3)*q^6 - q^7 + (-3*a^2 - 4*a + 3)*q^8 + (-2*a^2 - 3*a + 3)*q^9 + (3*a^2 + 3*a - 6)*q^10 + (a^2 - 5)*q^11 + (a^2 + a)*q^12 + (2*a^2 + 5*a - 2)*q^13 - a*q^14 + (3*a^2 + 6*a - 6)*q^15 + (3*a^2 + 3*a - 5)*q^16 + (a - 1)*q^17 + (3*a^2 + 3*a - 6)*q^18 - a*q^19 + (-2*a^2 + 3)*q^20 + (-a^2 - a + 3)*q^21 + (-3*a^2 - 5*a + 3)*q^22 + (a^2 + 3*a - 6)*q^23 + (2*a^2 + 6*a - 3)*q^24 + (-3*a^2 - 6*a + 4)*q^25 + (-a^2 - 2*a + 6)*q^26 + (3*a + 3)*q^27 + (-a^2 + 2)*q^28 + (-a^2 + a - 1)*q^29 + (-3*a^2 - 6*a + 9)*q^30 - q^31 + (3*a + 3)*q^32 + (-2*a^2 - 2*a + 9)*q^33 + (a^2 - a)*q^34 + (2*a^2 + 3*a - 3)*q^35 + (-2*a^2 + 3)*q^36 + (-a^2 + a + 4)*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 1)*q^3 + (a^2 - 2)*q^4 + (-a - 3)*q^5 + (2*a^2 + a - 3)*q^6 + q^7 + (-3*a^2 - 4*a + 3)*q^8 + (2*a^2 + a - 5)*q^9 + (-a^2 - 3*a)*q^10 + (3*a^2 + 6*a - 3)*q^11 + (-3*a^2 - a + 4)*q^12 + (-3*a - 4)*q^13 + a*q^14 + (a^2 + 2*a)*q^15 + (3*a^2 + 3*a - 5)*q^16 + (a - 3)*q^17 + (-5*a^2 - 5*a + 6)*q^18 + (3*a + 2)*q^19 + (2*a + 3)*q^20 + (-a^2 - a + 1)*q^21 + (-3*a^2 - 3*a + 9)*q^22 + (-3*a^2 - 5*a)*q^23 + (4*a^2 + 2*a - 3)*q^24 + (a^2 + 6*a + 4)*q^25 + (-3*a^2 - 4*a)*q^26 + (3*a + 1)*q^27 + (a^2 - 2)*q^28 + (3*a^2 + 3*a - 3)*q^29 + (-a^2 + 3)*q^30 + q^31 + (3*a + 3)*q^32 - 3*q^33 + (a^2 - 3*a)*q^34 + (-a - 3)*q^35 + (6*a^2 + 4*a - 5)*q^36 + (-a^2 - 3*a + 2)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 5*a)*q^3 + (a^2 - 2)*q^4 + (-a + 1)*q^5 + (a + 1)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (-a^3 - a^2 + 5*a + 2)*q^9 + (-a^2 + a)*q^10 + (-a^2 - 2*a + 3)*q^11 + (2*a^3 + a^2 - 9*a)*q^12 + (a^3 - a^2 - 5*a + 3)*q^13 + a*q^14 + (-a^3 + 4*a - 1)*q^15 + (-a^2 - a + 3)*q^16 + (2*a^2 + a - 3)*q^17 + (-a^3 + 3*a + 1)*q^18 + (3*a^3 + a^2 - 13*a + 1)*q^19 + (-a^3 + a^2 + 2*a - 2)*q^20 + (-a^3 + 5*a)*q^21 + (-a^3 - 2*a^2 + 3*a)*q^22 + (2*a^3 + a^2 - 9*a + 4)*q^23 + (a^3 + a^2 - 4*a - 4)*q^24 + (a^2 - 2*a - 4)*q^25 + (-a^3 + 2*a - 1)*q^26 + (-2*a^2 - a + 5)*q^27 + (a^2 - 2)*q^28 + (a^3 + 2*a^2 - 3*a - 6)*q^29 + (-a^2 + 1)*q^30 - q^31 + (-3*a^3 - a^2 + 11*a)*q^32 + (-3*a^3 - a^2 + 12*a - 2)*q^33 + (2*a^3 + a^2 - 3*a)*q^34 + (-a + 1)*q^35 + (2*a^3 - 8*a - 3)*q^36 + (-6*a^3 - a^2 + 25*a - 2)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 2*a^2 + 3*a - 4)*q^3 + (a^2 - 2)*q^4 + (a^4 - 2*a^3 - 5*a^2 + 6*a + 6)*q^5 + (-a^4 + 2*a^3 + 3*a^2 - 4*a)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-a^3 + 3*a^2 + a - 6)*q^9 + (a^4 - 10*a^2 + 19)*q^10 + (-a^4 + 2*a^3 + 4*a^2 - 5*a - 2)*q^11 + (-a^4 + 8*a^2 - 11)*q^12 + (-a^4 + a^3 + 6*a^2 - 2*a - 8)*q^13 - a*q^14 + (a^4 - a^3 - 7*a^2 + a + 14)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^3 - 4*a^2 - 7*a + 9)*q^17 + (-a^4 + 3*a^3 + a^2 - 6*a)*q^18 + (2*a^4 - 3*a^3 - 11*a^2 + 9*a + 11)*q^19 + (a^4 - a^3 - 6*a^2 + a + 7)*q^20 + (a^3 - 2*a^2 - 3*a + 4)*q^21 + (-a^4 - a^3 + 11*a^2 + 4*a - 19)*q^22 + (-a^2 - a + 8)*q^23 + (-a^4 - a^3 + 10*a^2 + 3*a - 19)*q^24 + (-3*a^2 + 2*a + 12)*q^25 + (-2*a^4 + a^3 + 14*a^2 - 2*a - 19)*q^26 + (a^4 - 2*a^3 - a^2 - 2)*q^27 + (-a^2 + 2)*q^28 + (-2*a^4 + a^3 + 16*a^2 - 3*a - 26)*q^29 + (2*a^4 - 2*a^3 - 15*a^2 + 8*a + 19)*q^30 + q^31 + (3*a^4 - 3*a^3 - 16*a^2 + 6*a + 19)*q^32 + (-a^4 + a^3 + 6*a^2 + a - 11)*q^33 + (2*a^4 - 4*a^3 - 7*a^2 + 9*a)*q^34 + (-a^4 + 2*a^3 + 5*a^2 - 6*a - 6)*q^35 + (-2*a^3 + 4*a^2 + 4*a - 7)*q^36 + (-a^4 + 4*a^3 + 2*a^2 - 12*a - 3)*q^37 + O(q^38)
*]> ;  // time = 23.439 seconds




J[218] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 218, 218, 218, 218, 218, 109, 109, 109 ], new_dimensions := [ 1, 2, 2, 2, 3, 1, 3, 4 ], dimensions := [ 1, 2, 2, 2, 3, 2, 6, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 7, 1, 1, 1, 0, 11, 1, 1, 1, 1, 1, 1, 11, 0, 1, 1, 41, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 1, 41, 1, 1, 0, 1, 3, 1, 1, 1, 3, 1, 1, 0 ], ap_traces := [
[ 1, -2, -3, -4, 3, -4, -6, 5, 3, -3, -4, -4 ],
[ -2, -4, 2, -4, -2, -8, -4, -10, -2, 6, -4, -4 ],
[ 2, -2, 0, 6, 2, 4, 2, -2, -8, -16, 6, 2 ],
[ 2, 3, 2, -4, -6, 3, -4, 0, 3, 10, -6, 1 ],
[ -3, 3, -3, 6, 3, 9, 0, 3, 0, -3, 0, -3 ]
], hecke_fields := [
x - 1,
x^2 + 4*x + 2,
x^2 + 2*x - 2,
x^2 - 3*x + 1,
x^3 - 3*x^2 - 3*x + 8
], atkin_lehners := [
[ -1, -1 ],
[ 1, 1 ],
[ -1, 1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 3, 1 ],
[ 7, 1 ],
[ 11, 1 ],
[ 205, 1 ],
[ 9, 3 ]
], tamagawa_numbers := [
[ 3, 1 ],
[ 1, 1 ],
[ 11, 1 ],
[ 205, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 3, 1, 11, 5, 3 ], torsion_lower_bounds := [ 1, 1, 11, 5, 3 ], l_ratios := [ 0, 0, 1/11, 41/5, 1/3 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1, 1 ], eigenvalues := [*
[ 1, -2, -3, -4, 3, -4, -6, 5, 3, -3, -4, -4 ],
[
-1,
a,
-a - 1,
-a - 4,
2*a + 3,
2*a,
a,
-2*a - 9,
-5*a - 11,
3*a + 9,
3*a + 4,
3*a + 4
],
[
1,
a,
-a - 1,
a + 4,
1,
-2*a,
-a,
2*a + 1,
-a - 5,
a - 7,
-3*a,
3*a + 4
],
[
1,
a,
-2*a + 4,
-2,
-2*a,
3*a - 3,
-4*a + 4,
0,
3*a - 3,
-2*a + 8,
6*a - 12,
-a + 2
],
[
-1,
a,
-a^2 + a + 3,
2,
a^2 - a - 3,
a^2 - 2*a,
0,
-a^2 - a + 7,
-3*a + 3,
-a^2 + a + 3,
-2*a^2 + 4*a + 6,
-3*a + 2
]
*], q_expansions := [*
q + q^2 - 2*q^3 + q^4 - 3*q^5 - 2*q^6 - 4*q^7 + q^8 + q^9 - 3*q^10 + 3*q^11 - 2*q^12 - 4*q^13 - 4*q^14 + 6*q^15 + q^16 - 6*q^17 + q^18 + 5*q^19 - 3*q^20 + 8*q^21 + 3*q^22 + 3*q^23 - 2*q^24 + 4*q^25 - 4*q^26 + 4*q^27 - 4*q^28 - 3*q^29 + 6*q^30 - 4*q^31 + q^32 - 6*q^33 - 6*q^34 + 12*q^35 + q^36 - 4*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a - 1)*q^5 - a*q^6 + (-a - 4)*q^7 - q^8 + (-4*a - 5)*q^9 + (a + 1)*q^10 + (2*a + 3)*q^11 + a*q^12 + 2*a*q^13 + (a + 4)*q^14 + (3*a + 2)*q^15 + q^16 + a*q^17 + (4*a + 5)*q^18 + (-2*a - 9)*q^19 + (-a - 1)*q^20 + 2*q^21 + (-2*a - 3)*q^22 + (-5*a - 11)*q^23 - a*q^24 + (-2*a - 6)*q^25 - 2*a*q^26 + (8*a + 8)*q^27 + (-a - 4)*q^28 + (3*a + 9)*q^29 + (-3*a - 2)*q^30 + (3*a + 4)*q^31 - q^32 + (-5*a - 4)*q^33 - a*q^34 + (a + 2)*q^35 + (-4*a - 5)*q^36 + (3*a + 4)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a - 1)*q^5 + a*q^6 + (a + 4)*q^7 + q^8 + (-2*a - 1)*q^9 + (-a - 1)*q^10 + q^11 + a*q^12 - 2*a*q^13 + (a + 4)*q^14 + (a - 2)*q^15 + q^16 - a*q^17 + (-2*a - 1)*q^18 + (2*a + 1)*q^19 + (-a - 1)*q^20 + (2*a + 2)*q^21 + q^22 + (-a - 5)*q^23 + a*q^24 - 2*q^25 - 2*a*q^26 - 4*q^27 + (a + 4)*q^28 + (a - 7)*q^29 + (a - 2)*q^30 - 3*a*q^31 + q^32 + a*q^33 - a*q^34 + (-3*a - 6)*q^35 + (-2*a - 1)*q^36 + (3*a + 4)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-2*a + 4)*q^5 + a*q^6 - 2*q^7 + q^8 + (3*a - 4)*q^9 + (-2*a + 4)*q^10 - 2*a*q^11 + a*q^12 + (3*a - 3)*q^13 - 2*q^14 + (-2*a + 2)*q^15 + q^16 + (-4*a + 4)*q^17 + (3*a - 4)*q^18 + (-2*a + 4)*q^20 - 2*a*q^21 - 2*a*q^22 + (3*a - 3)*q^23 + a*q^24 + (-4*a + 7)*q^25 + (3*a - 3)*q^26 + (2*a - 3)*q^27 - 2*q^28 + (-2*a + 8)*q^29 + (-2*a + 2)*q^30 + (6*a - 12)*q^31 + q^32 + (-6*a + 2)*q^33 + (-4*a + 4)*q^34 + (4*a - 8)*q^35 + (3*a - 4)*q^36 + (-a + 2)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a^2 + a + 3)*q^5 - a*q^6 + 2*q^7 - q^8 + (a^2 - 3)*q^9 + (a^2 - a - 3)*q^10 + (a^2 - a - 3)*q^11 + a*q^12 + (a^2 - 2*a)*q^13 - 2*q^14 + (-2*a^2 + 8)*q^15 + q^16 + (-a^2 + 3)*q^18 + (-a^2 - a + 7)*q^19 + (-a^2 + a + 3)*q^20 + 2*a*q^21 + (-a^2 + a + 3)*q^22 + (-3*a + 3)*q^23 - a*q^24 + (a^2 + a - 4)*q^25 + (-a^2 + 2*a)*q^26 + (3*a^2 - 3*a - 8)*q^27 + 2*q^28 + (-a^2 + a + 3)*q^29 + (2*a^2 - 8)*q^30 + (-2*a^2 + 4*a + 6)*q^31 - q^32 + (2*a^2 - 8)*q^33 + (-2*a^2 + 2*a + 6)*q^35 + (a^2 - 3)*q^36 + (-3*a + 2)*q^37 + O(q^38)
*]> ;  // time = 39.05 seconds




J[219] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 219, 219, 219, 219, 219, 73, 73, 73 ], new_dimensions := [ 1, 1, 1, 4, 6, 1, 2, 2 ], dimensions := [ 1, 1, 1, 4, 6, 2, 4, 4 ], intersection_graph := [ 0, 3, 1, 1, 1, 1, 5, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 17, 1, 1, 1, 1, 0, 1, 29, 1, 1, 1, 1, 1, 1, 0, 1, 9, 5, 1, 1, 1, 29, 1, 0, 1, 1, 1, 3, 17, 1, 9, 1, 0 ], ap_traces := [
[ 1, -1, -4, 2, -4, -2, 0, -4, 0, 8, 6, -2 ],
[ -2, -1, -1, 2, -4, -2, -3, -1, 0, -10, -6, 1 ],
[ 0, 1, -3, -4, 0, -4, 3, -1, 6, -6, -10, -7 ],
[ 1, -4, 9, -4, 2, 6, 9, 1, 4, 10, -10, -11 ],
[ -1, 6, 5, 8, -2, 4, -3, 5, -6, -4, 4, 13 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^4 - x^3 - 6*x^2 + 4*x + 4,
x^6 + x^5 - 9*x^4 - 5*x^3 + 20*x^2 + 4*x - 4
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 17, 1 ],
[ 1073, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1073, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 37 ], torsion_lower_bounds := [ 1, 1, 1, 1, 37 ], l_ratios := [ 0, 0, 0, 1, 29/37 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ 1, -1, -4, 2, -4, -2, 0, -4, 0, 8, 6, -2 ],
[ -2, -1, -1, 2, -4, -2, -3, -1, 0, -10, -6, 1 ],
[ 0, 1, -3, -4, 0, -4, 3, -1, 6, -6, -10, -7 ],
[
a,
-1,
-1/2*a^3 + 1/2*a^2 + 2*a + 1,
-a^2 + a + 2,
-a^2 - a + 4,
-a^3 + 5*a + 2,
3/2*a^3 - 1/2*a^2 - 7*a + 3,
a^3 + a^2 - 7*a - 3,
-a^3 + 3*a + 2,
a^3 - 5*a + 2,
a^3 + a^2 - 6*a - 6,
2*a^3 - 2*a^2 - 11*a + 3
],
[
a,
1,
-1/2*a^5 - 1/2*a^4 + 7/2*a^3 + 3/2*a^2 - 5*a + 1,
1/2*a^5 + a^4 - 7/2*a^3 - 5*a^2 + 5*a + 4,
1/2*a^5 - 11/2*a^3 + 13*a,
a^3 - 5*a + 2,
-1/2*a^5 - 1/2*a^4 + 9/2*a^3 + 3/2*a^2 - 10*a + 1,
a^3 + a^2 - 5*a - 1,
a^3 + 2*a^2 - 5*a - 6,
-a^4 - a^3 + 7*a^2 + 3*a - 8,
1/2*a^5 - a^4 - 13/2*a^3 + 5*a^2 + 16*a,
-a^5 - a^4 + 8*a^3 + 4*a^2 - 13*a + 1
]
*], q_expansions := [*
q + q^2 - q^3 - q^4 - 4*q^5 - q^6 + 2*q^7 - 3*q^8 + q^9 - 4*q^10 - 4*q^11 + q^12 - 2*q^13 + 2*q^14 + 4*q^15 - q^16 + q^18 - 4*q^19 + 4*q^20 - 2*q^21 - 4*q^22 + 3*q^24 + 11*q^25 - 2*q^26 - q^27 - 2*q^28 + 8*q^29 + 4*q^30 + 6*q^31 + 5*q^32 + 4*q^33 - 8*q^35 - q^36 - 2*q^37 + O(q^38),
q - 2*q^2 - q^3 + 2*q^4 - q^5 + 2*q^6 + 2*q^7 + q^9 + 2*q^10 - 4*q^11 - 2*q^12 - 2*q^13 - 4*q^14 + q^15 - 4*q^16 - 3*q^17 - 2*q^18 - q^19 - 2*q^20 - 2*q^21 + 8*q^22 - 4*q^25 + 4*q^26 - q^27 + 4*q^28 - 10*q^29 - 2*q^30 - 6*q^31 + 8*q^32 + 4*q^33 + 6*q^34 - 2*q^35 + 2*q^36 + q^37 + O(q^38),
q + q^3 - 2*q^4 - 3*q^5 - 4*q^7 + q^9 - 2*q^12 - 4*q^13 - 3*q^15 + 4*q^16 + 3*q^17 - q^19 + 6*q^20 - 4*q^21 + 6*q^23 + 4*q^25 + q^27 + 8*q^28 - 6*q^29 - 10*q^31 + 12*q^35 - 2*q^36 - 7*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-1/2*a^3 + 1/2*a^2 + 2*a + 1)*q^5 - a*q^6 + (-a^2 + a + 2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^2 + 3*a + 2)*q^10 + (-a^2 - a + 4)*q^11 + (-a^2 + 2)*q^12 + (-a^3 + 5*a + 2)*q^13 + (-a^3 + a^2 + 2*a)*q^14 + (1/2*a^3 - 1/2*a^2 - 2*a - 1)*q^15 + (a^3 - 4*a)*q^16 + (3/2*a^3 - 1/2*a^2 - 7*a + 3)*q^17 + a*q^18 + (a^3 + a^2 - 7*a - 3)*q^19 + (2*a^2 - 2*a - 2)*q^20 + (a^2 - a - 2)*q^21 + (-a^3 - a^2 + 4*a)*q^22 + (-a^3 + 3*a + 2)*q^23 + (-a^3 + 4*a)*q^24 + (-2*a^3 + 2*a^2 + 7*a - 2)*q^25 + (-a^3 - a^2 + 6*a + 4)*q^26 - q^27 + (-2*a^2 + 2*a)*q^28 + (a^3 - 5*a + 2)*q^29 + (a^2 - 3*a - 2)*q^30 + (a^3 + a^2 - 6*a - 6)*q^31 + (-a^3 + 2*a^2 + 4*a - 4)*q^32 + (a^2 + a - 4)*q^33 + (a^3 + 2*a^2 - 3*a - 6)*q^34 + (-3*a^2 + 5*a + 4)*q^35 + (a^2 - 2)*q^36 + (2*a^3 - 2*a^2 - 11*a + 3)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-1/2*a^5 - 1/2*a^4 + 7/2*a^3 + 3/2*a^2 - 5*a + 1)*q^5 + a*q^6 + (1/2*a^5 + a^4 - 7/2*a^3 - 5*a^2 + 5*a + 4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^4 - a^3 + 5*a^2 + 3*a - 2)*q^10 + (1/2*a^5 - 11/2*a^3 + 13*a)*q^11 + (a^2 - 2)*q^12 + (a^3 - 5*a + 2)*q^13 + (1/2*a^5 + a^4 - 5/2*a^3 - 5*a^2 + 2*a + 2)*q^14 + (-1/2*a^5 - 1/2*a^4 + 7/2*a^3 + 3/2*a^2 - 5*a + 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^5 - 1/2*a^4 + 9/2*a^3 + 3/2*a^2 - 10*a + 1)*q^17 + a*q^18 + (a^3 + a^2 - 5*a - 1)*q^19 + (-2*a^3 + 8*a - 2)*q^20 + (1/2*a^5 + a^4 - 7/2*a^3 - 5*a^2 + 5*a + 4)*q^21 + (-1/2*a^5 - a^4 + 5/2*a^3 + 3*a^2 - 2*a + 2)*q^22 + (a^3 + 2*a^2 - 5*a - 6)*q^23 + (a^3 - 4*a)*q^24 + (-a^5 - a^4 + 8*a^3 + 4*a^2 - 15*a)*q^25 + (a^4 - 5*a^2 + 2*a)*q^26 + q^27 + (-1/2*a^5 + 9/2*a^3 + 2*a^2 - 10*a - 6)*q^28 + (-a^4 - a^3 + 7*a^2 + 3*a - 8)*q^29 + (-a^4 - a^3 + 5*a^2 + 3*a - 2)*q^30 + (1/2*a^5 - a^4 - 13/2*a^3 + 5*a^2 + 16*a)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^5 - 11/2*a^3 + 13*a)*q^33 + (-a^3 + 3*a - 2)*q^34 + (a^4 + a^3 - 5*a^2 - 5*a)*q^35 + (a^2 - 2)*q^36 + (-a^5 - a^4 + 8*a^3 + 4*a^2 - 13*a + 1)*q^37 + O(q^38)
*]> ;  // time = 28.249 seconds




J[221] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 221, 221, 221, 221, 221, 221, 221, 17 ], new_dimensions := [ 1, 1, 2, 2, 2, 3, 6, 1 ], dimensions := [ 1, 1, 2, 2, 2, 3, 6, 2 ], intersection_graph := [ 0, 1, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 5, 1, 1, 1, 3, 5, 1, 5, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 1, 2, 2, 2, -6, -1, 1, 4, 6, -6, -2, 2 ],
[ -1, 0, 4, -2, 6, -1, 1, 8, 4, -6, -2, -8 ],
[ -1, -3, 0, -1, -3, -2, -2, -7, 6, -8, -14, 10 ],
[ 0, 2, -2, 4, 4, -2, 2, 4, -6, -12, 0, 10 ],
[ -1, 1, -2, -5, 3, -2, 2, 5, 6, 18, 8, -8 ],
[ 0, -3, -2, -9, -7, 3, 3, -17, 2, 4, -6, -4 ],
[ 1, 1, -2, 7, -1, 6, -6, 23, -10, -4, 16, 4 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + x - 1,
x^2 - 5,
x^2 + x - 5,
x^3 - 4*x + 1,
x^6 - x^5 - 9*x^4 + 6*x^3 + 19*x^2 - 5*x - 3
], atkin_lehners := [
[ 1, -1 ],
[ 1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ 1, -1 ],
[ -1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 7 ],
[ 1, 1 ],
[ 9, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 7 ],
[ 1, 1 ],
[ 9, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 7, 1, 9 ], torsion_lower_bounds := [ 1, 1, 1, 1, 7, 1, 9 ], l_ratios := [ 1, 1, 0, 1, 1/7, 0, 1/9 ], analytic_sha_upper_bounds := [ 1, 1, 0, 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 1, 1, 0, 1 ], eigenvalues := [*
[ 1, 2, 2, 2, -6, -1, 1, 4, 6, -6, -2, 2 ],
[ -1, 0, 4, -2, 6, -1, 1, 8, 4, -6, -2, -8 ],
[
a,
a - 1,
-2*a - 1,
-a - 1,
3*a,
-1,
-1,
3*a - 2,
-2*a + 2,
2*a - 3,
-7,
4*a + 7
],
[
a,
-a + 1,
a - 1,
2,
2,
-1,
1,
-2*a + 2,
-a - 3,
-6,
2*a,
-a + 5
],
[
a,
a + 1,
-1,
-a - 3,
a + 2,
-1,
1,
-a + 2,
-2*a + 2,
9,
2*a + 5,
-2*a - 5
],
[
a,
-a - 1,
-a^2 - a + 2,
a - 3,
a^2 - 5,
1,
1,
-a^2 - 3,
4*a^2 + 2*a - 10,
-a^2 + a + 4,
-3*a^2 - a + 6,
a^2 - 5*a - 4
],
[
a,
-1/2*a^5 + 1/2*a^4 + 4*a^3 - 5/2*a^2 - 13/2*a + 1,
1/2*a^4 - 1/2*a^3 - 3*a^2 + 3/2*a + 3/2,
-a^3 + 5*a + 2,
-a^2 + 3,
1,
-1,
a^5 - a^4 - 8*a^3 + 6*a^2 + 13*a - 1,
1/2*a^5 + 1/2*a^4 - 4*a^3 - 7/2*a^2 + 13/2*a,
-a^3 + a^2 + 5*a - 3,
a^3 + a^2 - 7*a - 1,
-a^5 + 1/2*a^4 + 17/2*a^3 - 2*a^2 - 29/2*a + 1/2
]
*], q_expansions := [*
q + q^2 + 2*q^3 - q^4 + 2*q^5 + 2*q^6 + 2*q^7 - 3*q^8 + q^9 + 2*q^10 - 6*q^11 - 2*q^12 - q^13 + 2*q^14 + 4*q^15 - q^16 + q^17 + q^18 + 4*q^19 - 2*q^20 + 4*q^21 - 6*q^22 + 6*q^23 - 6*q^24 - q^25 - q^26 - 4*q^27 - 2*q^28 - 6*q^29 + 4*q^30 - 2*q^31 + 5*q^32 - 12*q^33 + q^34 + 4*q^35 - q^36 + 2*q^37 + O(q^38),
q - q^2 - q^4 + 4*q^5 - 2*q^7 + 3*q^8 - 3*q^9 - 4*q^10 + 6*q^11 - q^13 + 2*q^14 - q^16 + q^17 + 3*q^18 + 8*q^19 - 4*q^20 - 6*q^22 + 4*q^23 + 11*q^25 + q^26 + 2*q^28 - 6*q^29 - 2*q^31 - 5*q^32 - q^34 - 8*q^35 + 3*q^36 - 8*q^37 + O(q^38),
q + a*q^2 + (a - 1)*q^3 + (-a - 1)*q^4 + (-2*a - 1)*q^5 + (-2*a + 1)*q^6 + (-a - 1)*q^7 + (-2*a - 1)*q^8 + (-3*a - 1)*q^9 + (a - 2)*q^10 + 3*a*q^11 + a*q^12 - q^13 - q^14 + (3*a - 1)*q^15 + 3*a*q^16 - q^17 + (2*a - 3)*q^18 + (3*a - 2)*q^19 + (a + 3)*q^20 + a*q^21 + (-3*a + 3)*q^22 + (-2*a + 2)*q^23 + (3*a - 1)*q^24 - a*q^26 + (2*a + 1)*q^27 + (a + 2)*q^28 + (2*a - 3)*q^29 + (-4*a + 3)*q^30 - 7*q^31 + (a + 5)*q^32 + (-6*a + 3)*q^33 - a*q^34 + (a + 3)*q^35 + (a + 4)*q^36 + (4*a + 7)*q^37 + O(q^38),
q + a*q^2 + (-a + 1)*q^3 + 3*q^4 + (a - 1)*q^5 + (a - 5)*q^6 + 2*q^7 + a*q^8 + (-2*a + 3)*q^9 + (-a + 5)*q^10 + 2*q^11 + (-3*a + 3)*q^12 - q^13 + 2*a*q^14 + (2*a - 6)*q^15 - q^16 + q^17 + (3*a - 10)*q^18 + (-2*a + 2)*q^19 + (3*a - 3)*q^20 + (-2*a + 2)*q^21 + 2*a*q^22 + (-a - 3)*q^23 + (a - 5)*q^24 + (-2*a + 1)*q^25 - a*q^26 + (-2*a + 10)*q^27 + 6*q^28 - 6*q^29 + (-6*a + 10)*q^30 + 2*a*q^31 - 3*a*q^32 + (-2*a + 2)*q^33 + a*q^34 + (2*a - 2)*q^35 + (-6*a + 9)*q^36 + (-a + 5)*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + (-a + 3)*q^4 - q^5 + 5*q^6 + (-a - 3)*q^7 + (2*a - 5)*q^8 + (a + 3)*q^9 - a*q^10 + (a + 2)*q^11 + (3*a - 2)*q^12 - q^13 + (-2*a - 5)*q^14 + (-a - 1)*q^15 + (-5*a + 4)*q^16 + q^17 + (2*a + 5)*q^18 + (-a + 2)*q^19 + (a - 3)*q^20 + (-3*a - 8)*q^21 + (a + 5)*q^22 + (-2*a + 2)*q^23 + (-5*a + 5)*q^24 - 4*q^25 - a*q^26 + 5*q^27 + (-a - 4)*q^28 + 9*q^29 - 5*q^30 + (2*a + 5)*q^31 + (5*a - 15)*q^32 + (2*a + 7)*q^33 + a*q^34 + (a + 3)*q^35 + (a + 4)*q^36 + (-2*a - 5)*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (a^2 - 2)*q^4 + (-a^2 - a + 2)*q^5 + (-a^2 - a)*q^6 + (a - 3)*q^7 - q^8 + (a^2 + 2*a - 2)*q^9 + (-a^2 - 2*a + 1)*q^10 + (a^2 - 5)*q^11 + (-a^2 - 2*a + 3)*q^12 + q^13 + (a^2 - 3*a)*q^14 + (2*a^2 + 3*a - 3)*q^15 + (-2*a^2 - a + 4)*q^16 + q^17 + (2*a^2 + 2*a - 1)*q^18 + (-a^2 - 3)*q^19 + (-a - 3)*q^20 + (-a^2 + 2*a + 3)*q^21 + (-a - 1)*q^22 + (4*a^2 + 2*a - 10)*q^23 + (a + 1)*q^24 + (a^2 + 3*a - 3)*q^25 + a*q^26 + (-3*a^2 - a + 6)*q^27 + (-3*a^2 + 2*a + 5)*q^28 + (-a^2 + a + 4)*q^29 + (3*a^2 + 5*a - 2)*q^30 + (-3*a^2 - a + 6)*q^31 + (-a^2 - 4*a + 4)*q^32 + (-a^2 + a + 6)*q^33 + a*q^34 + (2*a^2 + a - 5)*q^35 + (3*a + 2)*q^36 + (a^2 - 5*a - 4)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^5 + 1/2*a^4 + 4*a^3 - 5/2*a^2 - 13/2*a + 1)*q^3 + (a^2 - 2)*q^4 + (1/2*a^4 - 1/2*a^3 - 3*a^2 + 3/2*a + 3/2)*q^5 + (-1/2*a^4 + 1/2*a^3 + 3*a^2 - 3/2*a - 3/2)*q^6 + (-a^3 + 5*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (-a^2 + 4)*q^9 + (1/2*a^5 - 1/2*a^4 - 3*a^3 + 3/2*a^2 + 3/2*a)*q^10 + (-a^2 + 3)*q^11 + (1/2*a^5 - 1/2*a^4 - 5*a^3 + 7/2*a^2 + 23/2*a - 2)*q^12 + q^13 + (-a^4 + 5*a^2 + 2*a)*q^14 + (a^3 - 7*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 - q^17 + (-a^3 + 4*a)*q^18 + (a^5 - a^4 - 8*a^3 + 6*a^2 + 13*a - 1)*q^19 + (1/2*a^4 - 1/2*a^3 - 2*a^2 - 1/2*a - 3/2)*q^20 + (-a^5 + 9*a^3 + 2*a^2 - 18*a - 4)*q^21 + (-a^3 + 3*a)*q^22 + (1/2*a^5 + 1/2*a^4 - 4*a^3 - 7/2*a^2 + 13/2*a)*q^23 + (1/2*a^4 - 1/2*a^3 - 4*a^2 + 7/2*a + 9/2)*q^24 + (-a^4 + 7*a^2 - 5)*q^25 + a*q^26 + (a^3 - a^2 - 5*a + 1)*q^27 + (-a^5 + 7*a^3 + 2*a^2 - 10*a - 4)*q^28 + (-a^3 + a^2 + 5*a - 3)*q^29 + (a^4 - 7*a^2)*q^30 + (a^3 + a^2 - 7*a - 1)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^5 + a^4 + 9*a^3 - 6*a^2 - 18*a + 3)*q^33 - a*q^34 + (a^5 - 8*a^3 - a^2 + 9*a + 3)*q^35 + (-a^4 + 6*a^2 - 8)*q^36 + (-a^5 + 1/2*a^4 + 17/2*a^3 - 2*a^2 - 29/2*a + 1/2)*q^37 + O(q^38)
*]> ;  // time = 26.56 seconds




J[222] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 222, 222, 222, 222, 222, 111, 111, 74, 74, 37, 37 ], new_dimensions := [ 1, 1, 1, 1, 1, 3, 4, 2, 2, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 6, 8, 4, 4, 4, 4 ], intersection_graph := [ 0, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 0, 1, 1, 1, 23, 1, 9, 1, 1, 1, 1, 1, 0, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 23, 1, 1, 1, 0, 1, 1, 1, 1, 25, 1, 1, 13, 1, 1, 1, 0, 1, 19, 49, 1, 3, 9, 1, 1, 1, 1, 1, 0, 1, 1, 9, 1, 1, 1, 11, 1, 1, 19, 1, 0, 25, 1, 1, 1, 1, 1, 1, 1, 49, 1, 25, 0, 1, 1, 1, 1, 1, 3, 25, 1, 9, 1, 1, 0 ], ap_traces := [
[ -1, -1, 2, 0, -4, 6, 6, 8, 0, -6, 4, 1 ],
[ -1, -1, -4, 3, 5, 3, 3, -7, 9, 0, -2, 1 ],
[ -1, 1, 4, -1, -1, -3, 3, -5, 5, 4, -10, -1 ],
[ 1, -1, 0, 3, 1, 1, -3, 3, -1, -4, -6, -1 ],
[ 1, 1, 0, -1, 3, -1, -3, -7, 3, 0, 2, 1 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 3, 1 ],
[ 23, 9, 1 ],
[ 13, 1, 1 ],
[ 1, 11, 1 ],
[ 3, 3, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 3, 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 1, 1, 1, 1, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1, 1/9 ], eigenvalues := [*
[ -1, -1, 2, 0, -4, 6, 6, 8, 0, -6, 4, 1 ],
[ -1, -1, -4, 3, 5, 3, 3, -7, 9, 0, -2, 1 ],
[ -1, 1, 4, -1, -1, -3, 3, -5, 5, 4, -10, -1 ],
[ 1, -1, 0, 3, 1, 1, -3, 3, -1, -4, -6, -1 ],
[ 1, 1, 0, -1, 3, -1, -3, -7, 3, 0, 2, 1 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + 2*q^5 + q^6 - q^8 + q^9 - 2*q^10 - 4*q^11 - q^12 + 6*q^13 - 2*q^15 + q^16 + 6*q^17 - q^18 + 8*q^19 + 2*q^20 + 4*q^22 + q^24 - q^25 - 6*q^26 - q^27 - 6*q^29 + 2*q^30 + 4*q^31 - q^32 + 4*q^33 - 6*q^34 + q^36 + q^37 + O(q^38),
q - q^2 - q^3 + q^4 - 4*q^5 + q^6 + 3*q^7 - q^8 + q^9 + 4*q^10 + 5*q^11 - q^12 + 3*q^13 - 3*q^14 + 4*q^15 + q^16 + 3*q^17 - q^18 - 7*q^19 - 4*q^20 - 3*q^21 - 5*q^22 + 9*q^23 + q^24 + 11*q^25 - 3*q^26 - q^27 + 3*q^28 - 4*q^30 - 2*q^31 - q^32 - 5*q^33 - 3*q^34 - 12*q^35 + q^36 + q^37 + O(q^38),
q - q^2 + q^3 + q^4 + 4*q^5 - q^6 - q^7 - q^8 + q^9 - 4*q^10 - q^11 + q^12 - 3*q^13 + q^14 + 4*q^15 + q^16 + 3*q^17 - q^18 - 5*q^19 + 4*q^20 - q^21 + q^22 + 5*q^23 - q^24 + 11*q^25 + 3*q^26 + q^27 - q^28 + 4*q^29 - 4*q^30 - 10*q^31 - q^32 - q^33 - 3*q^34 - 4*q^35 + q^36 - q^37 + O(q^38),
q + q^2 - q^3 + q^4 - q^6 + 3*q^7 + q^8 + q^9 + q^11 - q^12 + q^13 + 3*q^14 + q^16 - 3*q^17 + q^18 + 3*q^19 - 3*q^21 + q^22 - q^23 - q^24 - 5*q^25 + q^26 - q^27 + 3*q^28 - 4*q^29 - 6*q^31 + q^32 - q^33 - 3*q^34 + q^36 - q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^6 - q^7 + q^8 + q^9 + 3*q^11 + q^12 - q^13 - q^14 + q^16 - 3*q^17 + q^18 - 7*q^19 - q^21 + 3*q^22 + 3*q^23 + q^24 - 5*q^25 - q^26 + q^27 - q^28 + 2*q^31 + q^32 + 3*q^33 - 3*q^34 + q^36 + q^37 + O(q^38)
*]> ;  // time = 108.04 seconds




J[223] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 223, 223, 223 ], new_dimensions := [ 2, 4, 12 ], dimensions := [ 2, 4, 12 ], intersection_graph := [ 0, 7, 1, 7, 0, 1, 1, 1, 0 ], ap_traces := [
[ -2, -2, -4, 0, 2, 4, -6, -4, -6, -14, 8, 2 ],
[ -4, 0, -3, -6, -10, -9, -17, 7, -2, 7, 0, -2 ],
[ 7, 0, 7, 2, 6, 1, 27, -5, 12, 3, -12, 2 ]
], hecke_fields := [
x^2 + 2*x - 1,
x^4 + 4*x^3 + 2*x^2 - 5*x - 3,
x^12 - 7*x^11 + 6*x^10 + 57*x^9 - 122*x^8 - 105*x^7 + 430*x^6 - 73*x^5 - 499*x^4 + 242*x^3 + 143*x^2 - 52*x - 19
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 37 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 37 ]
], torsion_upper_bounds := [ 1, 1, 37 ], torsion_lower_bounds := [ 1, 1, 37 ], l_ratios := [ 0, 0, 1/37 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[
a,
a,
-a - 3,
-a - 1,
-a,
a + 3,
2*a - 1,
-a - 3,
3*a,
-7,
-2*a + 2,
2*a + 3
],
[
a,
-a - 1,
-a^3 - 3*a^2 + a + 3,
2*a^3 + 5*a^2 - 2*a - 6,
-2*a^3 - 6*a^2 + a + 4,
a^3 + 4*a^2 - 8,
a^3 + a^2 - 4*a - 5,
a^3 + 4*a^2 + 3*a - 1,
-2*a^3 - 2*a^2 + 8*a + 1,
a^3 + 4*a^2 + a - 3,
-4*a^3 - 12*a^2 + 3*a + 14,
-2*a^3 - 7*a^2 - 2*a + 6
],
[
a,
2*a^11 - 11*a^10 - 2*a^9 + 98*a^8 - 103*a^7 - 245*a^6 + 397*a^5 + 123*a^4 - 412*a^3 + 129*a^2 + 41*a - 18,
4*a^11 - 21*a^10 - 10*a^9 + 196*a^8 - 152*a^7 - 550*a^6 + 654*a^5 + 468*a^4 - 731*a^3 + 20*a^2 + 114*a + 4,
-9*a^11 + 45*a^10 + 34*a^9 - 435*a^8 + 235*a^7 + 1320*a^6 - 1172*a^5 - 1412*a^4 + 1388*a^3 + 350*a^2 - 263*a - 61,
-12*a^11 + 60*a^10 + 45*a^9 - 578*a^8 + 315*a^7 + 1739*a^6 - 1559*a^5 - 1813*a^4 + 1827*a^3 + 390*a^2 - 327*a - 68,
a^11 - 7*a^10 + 6*a^9 + 56*a^8 - 119*a^7 - 96*a^6 + 400*a^5 - 95*a^4 - 403*a^3 + 248*a^2 + 36*a - 31,
14*a^11 - 66*a^10 - 73*a^9 + 663*a^8 - 176*a^7 - 2169*a^6 + 1282*a^5 + 2737*a^4 - 1683*a^3 - 1153*a^2 + 418*a + 185,
10*a^11 - 50*a^10 - 37*a^9 + 481*a^8 - 268*a^7 - 1444*a^6 + 1319*a^5 + 1500*a^4 - 1550*a^3 - 318*a^2 + 285*a + 56,
a^11 - 4*a^10 - 8*a^9 + 42*a^8 + 15*a^7 - 147*a^6 + 5*a^5 + 204*a^4 - 23*a^3 - 97*a^2 + a + 10,
3*a^11 - 14*a^10 - 17*a^9 + 144*a^8 - 26*a^7 - 492*a^6 + 245*a^5 + 674*a^4 - 335*a^3 - 336*a^2 + 86*a + 53,
13*a^11 - 63*a^10 - 59*a^9 + 620*a^8 - 244*a^7 - 1951*a^6 + 1410*a^5 + 2273*a^4 - 1739*a^3 - 773*a^2 + 371*a + 120,
-2*a^11 + 12*a^10 - 3*a^9 - 101*a^8 + 150*a^7 + 211*a^6 - 533*a^5 + 32*a^4 + 544*a^3 - 306*a^2 - 56*a + 43
]
*], q_expansions := [*
q + a*q^2 + a*q^3 + (-2*a - 1)*q^4 + (-a - 3)*q^5 + (-2*a + 1)*q^6 + (-a - 1)*q^7 + (a - 2)*q^8 + (-2*a - 2)*q^9 + (-a - 1)*q^10 - a*q^11 + (3*a - 2)*q^12 + (a + 3)*q^13 + (a - 1)*q^14 + (-a - 1)*q^15 + 3*q^16 + (2*a - 1)*q^17 + (2*a - 2)*q^18 + (-a - 3)*q^19 + (3*a + 5)*q^20 + (a - 1)*q^21 + (2*a - 1)*q^22 + 3*a*q^23 + (-4*a + 1)*q^24 + (4*a + 5)*q^25 + (a + 1)*q^26 + (-a - 2)*q^27 + (-a + 3)*q^28 - 7*q^29 + (a - 1)*q^30 + (-2*a + 2)*q^31 + (a + 4)*q^32 + (2*a - 1)*q^33 + (-5*a + 2)*q^34 + (2*a + 4)*q^35 + (-2*a + 6)*q^36 + (2*a + 3)*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (a^2 - 2)*q^4 + (-a^3 - 3*a^2 + a + 3)*q^5 + (-a^2 - a)*q^6 + (2*a^3 + 5*a^2 - 2*a - 6)*q^7 + (a^3 - 4*a)*q^8 + (a^2 + 2*a - 2)*q^9 + (a^3 + 3*a^2 - 2*a - 3)*q^10 + (-2*a^3 - 6*a^2 + a + 4)*q^11 + (-a^3 - a^2 + 2*a + 2)*q^12 + (a^3 + 4*a^2 - 8)*q^13 + (-3*a^3 - 6*a^2 + 4*a + 6)*q^14 + a*q^15 + (-4*a^3 - 8*a^2 + 5*a + 7)*q^16 + (a^3 + a^2 - 4*a - 5)*q^17 + (a^3 + 2*a^2 - 2*a)*q^18 + (a^3 + 4*a^2 + 3*a - 1)*q^19 + (a^3 + 2*a^2 - 3)*q^20 + (a^3 + a^2 - 2*a)*q^21 + (2*a^3 + 5*a^2 - 6*a - 6)*q^22 + (-2*a^3 - 2*a^2 + 8*a + 1)*q^23 + (3*a^3 + 6*a^2 - a - 3)*q^24 + (a^3 + 2*a^2 - 3*a - 5)*q^25 + (-2*a^2 - 3*a + 3)*q^26 + (-a^3 - 3*a^2 + 3*a + 5)*q^27 + (2*a^3 - 5*a + 3)*q^28 + (a^3 + 4*a^2 + a - 3)*q^29 + a^2*q^30 + (-4*a^3 - 12*a^2 + 3*a + 14)*q^31 + (6*a^3 + 13*a^2 - 5*a - 12)*q^32 + (a^2 + 5*a + 2)*q^33 + (-3*a^3 - 6*a^2 + 3)*q^34 + (-a^3 + 4*a - 3)*q^35 + (-2*a^3 - 6*a^2 + a + 7)*q^36 + (-2*a^3 - 7*a^2 - 2*a + 6)*q^37 + O(q^38),
q + a*q^2 + (2*a^11 - 11*a^10 - 2*a^9 + 98*a^8 - 103*a^7 - 245*a^6 + 397*a^5 + 123*a^4 - 412*a^3 + 129*a^2 + 41*a - 18)*q^3 + (a^2 - 2)*q^4 + (4*a^11 - 21*a^10 - 10*a^9 + 196*a^8 - 152*a^7 - 550*a^6 + 654*a^5 + 468*a^4 - 731*a^3 + 20*a^2 + 114*a + 4)*q^5 + (3*a^11 - 14*a^10 - 16*a^9 + 141*a^8 - 35*a^7 - 463*a^6 + 269*a^5 + 586*a^4 - 355*a^3 - 245*a^2 + 86*a + 38)*q^6 + (-9*a^11 + 45*a^10 + 34*a^9 - 435*a^8 + 235*a^7 + 1320*a^6 - 1172*a^5 - 1412*a^4 + 1388*a^3 + 350*a^2 - 263*a - 61)*q^7 + (a^3 - 4*a)*q^8 + (-a^9 + 3*a^8 + 9*a^7 - 29*a^6 - 23*a^5 + 87*a^4 + 13*a^3 - 88*a^2 + 10*a + 17)*q^9 + (7*a^11 - 34*a^10 - 32*a^9 + 336*a^8 - 130*a^7 - 1066*a^6 + 760*a^5 + 1265*a^4 - 948*a^3 - 458*a^2 + 212*a + 76)*q^10 + (-12*a^11 + 60*a^10 + 45*a^9 - 578*a^8 + 315*a^7 + 1739*a^6 - 1559*a^5 - 1813*a^4 + 1827*a^3 + 390*a^2 - 327*a - 68)*q^11 + (3*a^11 - 12*a^10 - 26*a^9 + 135*a^8 + 58*a^7 - 531*a^6 + 11*a^5 + 896*a^4 - 147*a^3 - 601*a^2 + 112*a + 93)*q^12 + (a^11 - 7*a^10 + 6*a^9 + 56*a^8 - 119*a^7 - 96*a^6 + 400*a^5 - 95*a^4 - 403*a^3 + 248*a^2 + 36*a - 31)*q^13 + (-18*a^11 + 88*a^10 + 78*a^9 - 863*a^8 + 375*a^7 + 2698*a^6 - 2069*a^5 - 3103*a^4 + 2528*a^3 + 1024*a^2 - 529*a - 171)*q^14 + (2*a^11 - 9*a^10 - 12*a^9 + 91*a^8 - 9*a^7 - 300*a^6 + 128*a^5 + 380*a^4 - 165*a^3 - 158*a^2 + 25*a + 23)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (14*a^11 - 66*a^10 - 73*a^9 + 663*a^8 - 176*a^7 - 2169*a^6 + 1282*a^5 + 2737*a^4 - 1683*a^3 - 1153*a^2 + 418*a + 185)*q^17 + (-a^10 + 3*a^9 + 9*a^8 - 29*a^7 - 23*a^6 + 87*a^5 + 13*a^4 - 88*a^3 + 10*a^2 + 17*a)*q^18 + (10*a^11 - 50*a^10 - 37*a^9 + 481*a^8 - 268*a^7 - 1444*a^6 + 1319*a^5 + 1500*a^4 - 1550*a^3 - 318*a^2 + 285*a + 56)*q^19 + (7*a^11 - 32*a^10 - 43*a^9 + 332*a^8 - 27*a^7 - 1150*a^6 + 468*a^5 + 1609*a^4 - 690*a^3 - 829*a^2 + 212*a + 125)*q^20 + (-a^11 + 3*a^10 + 15*a^9 - 46*a^8 - 78*a^7 + 250*a^6 + 158*a^5 - 573*a^4 - 79*a^3 + 503*a^2 - 60*a - 80)*q^21 + (-24*a^11 + 117*a^10 + 106*a^9 - 1149*a^8 + 479*a^7 + 3601*a^6 - 2689*a^5 - 4161*a^4 + 3294*a^3 + 1389*a^2 - 692*a - 228)*q^22 + (a^11 - 4*a^10 - 8*a^9 + 42*a^8 + 15*a^7 - 147*a^6 + 5*a^5 + 204*a^4 - 23*a^3 - 97*a^2 + a + 10)*q^23 + (3*a^11 - 16*a^10 - 4*a^9 + 142*a^8 - 146*a^7 - 353*a^6 + 577*a^5 + 178*a^4 - 617*a^3 + 173*a^2 + 77*a - 19)*q^24 + (13*a^11 - 64*a^10 - 54*a^9 + 625*a^8 - 294*a^7 - 1938*a^6 + 1568*a^5 + 2191*a^4 - 1912*a^3 - 692*a^2 + 407*a + 125)*q^25 + (-a^9 + 3*a^8 + 9*a^7 - 30*a^6 - 22*a^5 + 96*a^4 + 6*a^3 - 107*a^2 + 21*a + 19)*q^26 + (-6*a^11 + 28*a^10 + 33*a^9 - 283*a^8 + 58*a^7 + 935*a^6 - 493*a^5 - 1199*a^4 + 657*a^3 + 522*a^2 - 164*a - 81)*q^27 + (-20*a^11 + 96*a^10 + 95*a^9 - 951*a^8 + 338*a^7 + 3031*a^6 - 2073*a^5 - 3630*a^4 + 2604*a^3 + 1345*a^2 - 581*a - 220)*q^28 + (3*a^11 - 14*a^10 - 17*a^9 + 144*a^8 - 26*a^7 - 492*a^6 + 245*a^5 + 674*a^4 - 335*a^3 - 336*a^2 + 86*a + 53)*q^29 + (5*a^11 - 24*a^10 - 23*a^9 + 235*a^8 - 90*a^7 - 732*a^6 + 526*a^5 + 833*a^4 - 642*a^3 - 261*a^2 + 127*a + 38)*q^30 + (13*a^11 - 63*a^10 - 59*a^9 + 620*a^8 - 244*a^7 - 1951*a^6 + 1410*a^5 + 2273*a^4 - 1739*a^3 - 773*a^2 + 371*a + 120)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^11 + 4*a^10 + 8*a^9 - 43*a^8 - 13*a^7 + 157*a^6 - 21*a^5 - 238*a^4 + 59*a^3 + 147*a^2 - 30*a - 30)*q^33 + (32*a^11 - 157*a^10 - 135*a^9 + 1532*a^8 - 699*a^7 - 4738*a^6 + 3759*a^5 + 5303*a^4 - 4541*a^3 - 1584*a^2 + 913*a + 266)*q^34 + (-16*a^11 + 76*a^10 + 81*a^9 - 761*a^8 + 224*a^7 + 2476*a^6 - 1530*a^5 - 3096*a^4 + 1978*a^3 + 1283*a^2 - 473*a - 206)*q^35 + (-a^11 + 3*a^10 + 11*a^9 - 35*a^8 - 41*a^7 + 145*a^6 + 59*a^5 - 262*a^4 - 16*a^3 + 193*a^2 - 20*a - 34)*q^36 + (-2*a^11 + 12*a^10 - 3*a^9 - 101*a^8 + 150*a^7 + 211*a^6 - 533*a^5 + 32*a^4 + 544*a^3 - 306*a^2 - 56*a + 43)*q^37 + O(q^38)
*]> ;  // time = 3.179 seconds




J[226] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 226, 226, 226, 226, 113, 113, 113, 113 ], new_dimensions := [ 1, 2, 2, 4, 1, 2, 3, 3 ], dimensions := [ 1, 2, 2, 4, 2, 4, 6, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 7, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 41, 1, 1, 1, 1, 1, 0, 1, 1, 9, 1, 1, 1, 1, 1, 0, 1, 121, 1, 7, 1, 41, 1, 1, 0, 1, 3, 1, 3, 1, 9, 121, 1, 0 ], ap_traces := [
[ 1, -2, -4, 0, -4, -2, -2, -2, 4, -4, 8, -8 ],
[ -2, 0, -4, -4, -8, 4, -4, 0, 0, -4, -12, 12 ],
[ -2, 2, 4, 0, 4, -4, -4, 2, 14, 4, 4, -4 ],
[ 4, 2, 4, -4, 0, 4, 0, -6, -6, 0, 0, -8 ]
], hecke_fields := [
x - 1,
x^2 - 2,
x^2 - 2*x - 2,
x^4 - 2*x^3 - 6*x^2 + 12*x - 4
], atkin_lehners := [
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 1 ],
[ 7, 1 ],
[ 3, 1 ],
[ 779, 1 ]
], tamagawa_numbers := [
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 779, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 19 ], torsion_lower_bounds := [ 1, 1, 1, 19 ], l_ratios := [ 0, 0, 1, 41/19 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[ 1, -2, -4, 0, -4, -2, -2, -2, 4, -4, 8, -8 ],
[
-1,
a,
-a - 2,
-2*a - 2,
-4,
2,
2*a - 2,
5*a,
4*a,
-5*a - 2,
-2*a - 6,
-3*a + 6
],
[
-1,
a,
2,
0,
-2*a + 4,
-2*a,
-2,
-3*a + 4,
-a + 8,
2,
2*a,
4*a - 6
],
[
1,
a,
1/2*a^3 - a^2 - 4*a + 6,
-a^3 + a^2 + 6*a - 6,
a^2 - 4,
2*a^3 - 2*a^2 - 14*a + 12,
-2*a^3 + 2*a^2 + 12*a - 10,
-2*a^3 + 2*a^2 + 13*a - 12,
3/2*a^3 - 3*a^2 - 9*a + 12,
-3/2*a^3 + a^2 + 10*a - 6,
2*a^3 - a^2 - 12*a + 6,
-1/2*a^3 - a^2 + 2*a + 2
]
*], q_expansions := [*
q + q^2 - 2*q^3 + q^4 - 4*q^5 - 2*q^6 + q^8 + q^9 - 4*q^10 - 4*q^11 - 2*q^12 - 2*q^13 + 8*q^15 + q^16 - 2*q^17 + q^18 - 2*q^19 - 4*q^20 - 4*q^22 + 4*q^23 - 2*q^24 + 11*q^25 - 2*q^26 + 4*q^27 - 4*q^29 + 8*q^30 + 8*q^31 + q^32 + 8*q^33 - 2*q^34 + q^36 - 8*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a - 2)*q^5 - a*q^6 + (-2*a - 2)*q^7 - q^8 - q^9 + (a + 2)*q^10 - 4*q^11 + a*q^12 + 2*q^13 + (2*a + 2)*q^14 + (-2*a - 2)*q^15 + q^16 + (2*a - 2)*q^17 + q^18 + 5*a*q^19 + (-a - 2)*q^20 + (-2*a - 4)*q^21 + 4*q^22 + 4*a*q^23 - a*q^24 + (4*a + 1)*q^25 - 2*q^26 - 4*a*q^27 + (-2*a - 2)*q^28 + (-5*a - 2)*q^29 + (2*a + 2)*q^30 + (-2*a - 6)*q^31 - q^32 - 4*a*q^33 + (-2*a + 2)*q^34 + (6*a + 8)*q^35 - q^36 + (-3*a + 6)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + 2*q^5 - a*q^6 - q^8 + (2*a - 1)*q^9 - 2*q^10 + (-2*a + 4)*q^11 + a*q^12 - 2*a*q^13 + 2*a*q^15 + q^16 - 2*q^17 + (-2*a + 1)*q^18 + (-3*a + 4)*q^19 + 2*q^20 + (2*a - 4)*q^22 + (-a + 8)*q^23 - a*q^24 - q^25 + 2*a*q^26 + 4*q^27 + 2*q^29 - 2*a*q^30 + 2*a*q^31 - q^32 - 4*q^33 + 2*q^34 + (2*a - 1)*q^36 + (4*a - 6)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (1/2*a^3 - a^2 - 4*a + 6)*q^5 + a*q^6 + (-a^3 + a^2 + 6*a - 6)*q^7 + q^8 + (a^2 - 3)*q^9 + (1/2*a^3 - a^2 - 4*a + 6)*q^10 + (a^2 - 4)*q^11 + a*q^12 + (2*a^3 - 2*a^2 - 14*a + 12)*q^13 + (-a^3 + a^2 + 6*a - 6)*q^14 + (-a^2 + 2)*q^15 + q^16 + (-2*a^3 + 2*a^2 + 12*a - 10)*q^17 + (a^2 - 3)*q^18 + (-2*a^3 + 2*a^2 + 13*a - 12)*q^19 + (1/2*a^3 - a^2 - 4*a + 6)*q^20 + (-a^3 + 6*a - 4)*q^21 + (a^2 - 4)*q^22 + (3/2*a^3 - 3*a^2 - 9*a + 12)*q^23 + a*q^24 + (3*a^3 - 4*a^2 - 20*a + 21)*q^25 + (2*a^3 - 2*a^2 - 14*a + 12)*q^26 + (a^3 - 6*a)*q^27 + (-a^3 + a^2 + 6*a - 6)*q^28 + (-3/2*a^3 + a^2 + 10*a - 6)*q^29 + (-a^2 + 2)*q^30 + (2*a^3 - a^2 - 12*a + 6)*q^31 + q^32 + (a^3 - 4*a)*q^33 + (-2*a^3 + 2*a^2 + 12*a - 10)*q^34 + (-2*a^3 + 4*a^2 + 14*a - 20)*q^35 + (a^2 - 3)*q^36 + (-1/2*a^3 - a^2 + 2*a + 2)*q^37 + O(q^38)
*]> ;  // time = 41.27 seconds




J[227] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 227, 227, 227, 227, 227 ], new_dimensions := [ 2, 2, 2, 3, 10 ], dimensions := [ 2, 2, 2, 3, 10 ], intersection_graph := [ 0, 1, 1, 7, 1, 1, 0, 1, 1, 31, 1, 1, 0, 1, 65, 7, 1, 1, 0, 1, 1, 31, 65, 1, 0 ], ap_traces := [
[ 0, -4, 0, -2, 2, -8, -8, 10, -6, -6, -4, -20 ],
[ 0, 3, -4, 7, 1, -2, -8, 13, 11, -3, 0, 8 ],
[ 2, -1, 4, 3, 5, 2, -8, 1, 7, 5, -12, 16 ],
[ -2, 1, -5, -6, -1, -9, 7, -10, 2, -1, 2, -14 ],
[ 0, 1, 7, 0, -3, 23, 17, -16, -16, -3, 14, 38 ]
], hecke_fields := [
x^2 - 2,
x^2 - 5,
x^2 - x - 7,
x^3 + 2*x^2 - x - 1,
x^10 - 17*x^8 - 3*x^7 + 98*x^6 + 40*x^5 - 218*x^4 - 148*x^3 + 136*x^2 + 144*x + 32
], atkin_lehners := [
[ 1 ],
[ -1 ],
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ 113 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ 113 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 113 ], torsion_lower_bounds := [ 1, 1, 1, 1, 113 ], l_ratios := [ 0, 1, 1, 0, 1/113 ], analytic_sha_upper_bounds := [ 0, 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 0, 1 ], eigenvalues := [*
[
a,
-2,
-a,
-2*a - 1,
2*a + 1,
2*a - 4,
a - 4,
2*a + 5,
-2*a - 3,
-4*a - 3,
3*a - 2,
-a - 10
],
[
a,
-1/2*a + 3/2,
-2,
1/2*a + 7/2,
-1/2*a + 1/2,
-a - 1,
-4,
1/2*a + 13/2,
-1/2*a + 11/2,
-3/2*a - 3/2,
-2*a,
4
],
[
1,
a - 1,
2,
-a + 2,
a + 2,
-2*a + 2,
-4,
-a + 1,
a + 3,
-a + 3,
-6,
8
],
[
a,
-a^2 - 2*a + 1,
a^2 + a - 3,
a^2 + 3*a - 2,
a^2 - a - 3,
-3,
a + 3,
-4*a^2 - 7*a,
-2*a^2 + 2*a + 6,
2*a^2 + 2*a - 3,
4*a^2 + 8*a - 2,
a^2 + 4*a - 4
],
[
a,
1/16*a^9 - 21/16*a^7 - 3/16*a^6 + 75/8*a^5 + 9/4*a^4 - 209/8*a^3 - 33/4*a^2 + 23*a + 10,
-3/4*a^9 + 3/4*a^8 + 49/4*a^7 - 19/2*a^6 - 269/4*a^5 + 31*a^4 + 289/2*a^3 - 21/2*a^2 - 101*a - 30,
13/16*a^9 - 1/2*a^8 - 213/16*a^7 + 97/16*a^6 + 589/8*a^5 - 16*a^4 - 1281/8*a^3 - 53/4*a^2 + 227/2*a + 42,
1/8*a^9 - 1/4*a^8 - 15/8*a^7 + 27/8*a^6 + 35/4*a^5 - 51/4*a^4 - 53/4*a^3 + 11*a^2 + 7/2*a + 1,
-1/4*a^8 + 13/4*a^6 - 1/4*a^5 - 25/2*a^4 + a^3 + 29/2*a^2 + a,
-9/8*a^9 + a^8 + 149/8*a^7 - 101/8*a^6 - 415/4*a^5 + 81/2*a^4 + 901/4*a^3 - 19/2*a^2 - 157*a - 46,
3/8*a^9 - 1/8*a^8 - 49/8*a^7 + a^6 + 271/8*a^5 + 2*a^4 - 297/4*a^3 - 85/4*a^2 + 53*a + 23,
-15/16*a^9 + 3/8*a^8 + 247/16*a^7 - 73/16*a^6 - 173/2*a^5 + 43/4*a^4 + 1539/8*a^3 + 20*a^2 - 140*a - 51,
3/4*a^9 - 3/8*a^8 - 25/2*a^7 + 33/8*a^6 + 563/8*a^5 - 15/2*a^4 - 154*a^3 - 85/4*a^2 + 105*a + 37,
1/8*a^9 - 1/4*a^8 - 21/8*a^7 + 23/8*a^6 + 37/2*a^5 - 8*a^4 - 201/4*a^3 - 2*a^2 + 42*a + 18,
-3/8*a^9 + 51/8*a^7 + 9/8*a^6 - 147/4*a^5 - 14*a^4 + 335/4*a^3 + 95/2*a^2 - 66*a - 38
]
*], q_expansions := [*
q + a*q^2 - 2*q^3 - a*q^5 - 2*a*q^6 + (-2*a - 1)*q^7 - 2*a*q^8 + q^9 - 2*q^10 + (2*a + 1)*q^11 + (2*a - 4)*q^13 + (-a - 4)*q^14 + 2*a*q^15 - 4*q^16 + (a - 4)*q^17 + a*q^18 + (2*a + 5)*q^19 + (4*a + 2)*q^21 + (a + 4)*q^22 + (-2*a - 3)*q^23 + 4*a*q^24 - 3*q^25 + (-4*a + 4)*q^26 + 4*q^27 + (-4*a - 3)*q^29 + 4*q^30 + (3*a - 2)*q^31 + (-4*a - 2)*q^33 + (-4*a + 2)*q^34 + (a + 4)*q^35 + (-a - 10)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a + 3/2)*q^3 + 3*q^4 - 2*q^5 + (3/2*a - 5/2)*q^6 + (1/2*a + 7/2)*q^7 + a*q^8 + (-3/2*a + 1/2)*q^9 - 2*a*q^10 + (-1/2*a + 1/2)*q^11 + (-3/2*a + 9/2)*q^12 + (-a - 1)*q^13 + (7/2*a + 5/2)*q^14 + (a - 3)*q^15 - q^16 - 4*q^17 + (1/2*a - 15/2)*q^18 + (1/2*a + 13/2)*q^19 - 6*q^20 + (-a + 4)*q^21 + (1/2*a - 5/2)*q^22 + (-1/2*a + 11/2)*q^23 + (3/2*a - 5/2)*q^24 - q^25 + (-a - 5)*q^26 - a*q^27 + (3/2*a + 21/2)*q^28 + (-3/2*a - 3/2)*q^29 + (-3*a + 5)*q^30 - 2*a*q^31 - 3*a*q^32 + (-a + 2)*q^33 - 4*a*q^34 + (-a - 7)*q^35 + (-9/2*a + 3/2)*q^36 + 4*q^37 + O(q^38),
q + q^2 + (a - 1)*q^3 - q^4 + 2*q^5 + (a - 1)*q^6 + (-a + 2)*q^7 - 3*q^8 + (-a + 5)*q^9 + 2*q^10 + (a + 2)*q^11 + (-a + 1)*q^12 + (-2*a + 2)*q^13 + (-a + 2)*q^14 + (2*a - 2)*q^15 - q^16 - 4*q^17 + (-a + 5)*q^18 + (-a + 1)*q^19 - 2*q^20 + (2*a - 9)*q^21 + (a + 2)*q^22 + (a + 3)*q^23 + (-3*a + 3)*q^24 - q^25 + (-2*a + 2)*q^26 + (2*a - 9)*q^27 + (a - 2)*q^28 + (-a + 3)*q^29 + (2*a - 2)*q^30 - 6*q^31 + 5*q^32 + (2*a + 5)*q^33 - 4*q^34 + (-2*a + 4)*q^35 + (a - 5)*q^36 + 8*q^37 + O(q^38),
q + a*q^2 + (-a^2 - 2*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^2 + a - 3)*q^5 - q^6 + (a^2 + 3*a - 2)*q^7 + (-2*a^2 - 3*a + 1)*q^8 + (-a^2 - a)*q^9 + (-a^2 - 2*a + 1)*q^10 + (a^2 - a - 3)*q^11 + (2*a^2 + 3*a - 2)*q^12 - 3*q^13 + (a^2 - a + 1)*q^14 + (3*a^2 + 5*a - 4)*q^15 + (-a^2 - a + 2)*q^16 + (a + 3)*q^17 + (a^2 - a - 1)*q^18 + (-4*a^2 - 7*a)*q^19 + (-2*a^2 - 2*a + 5)*q^20 + (2*a^2 + 3*a - 5)*q^21 + (-3*a^2 - 2*a + 1)*q^22 + (-2*a^2 + 2*a + 6)*q^23 + (-a^2 + 4)*q^24 + (-4*a^2 - 5*a + 4)*q^25 - 3*a*q^26 + (3*a^2 + 7*a - 2)*q^27 + (-5*a^2 - 4*a + 5)*q^28 + (2*a^2 + 2*a - 3)*q^29 + (-a^2 - a + 3)*q^30 + (4*a^2 + 8*a - 2)*q^31 + (5*a^2 + 7*a - 3)*q^32 + (3*a^2 + 5*a - 2)*q^33 + (a^2 + 3*a)*q^34 + (-5*a^2 - 8*a + 8)*q^35 + (-a^2 + 2*a + 1)*q^36 + (a^2 + 4*a - 4)*q^37 + O(q^38),
q + a*q^2 + (1/16*a^9 - 21/16*a^7 - 3/16*a^6 + 75/8*a^5 + 9/4*a^4 - 209/8*a^3 - 33/4*a^2 + 23*a + 10)*q^3 + (a^2 - 2)*q^4 + (-3/4*a^9 + 3/4*a^8 + 49/4*a^7 - 19/2*a^6 - 269/4*a^5 + 31*a^4 + 289/2*a^3 - 21/2*a^2 - 101*a - 30)*q^5 + (-1/4*a^8 + 13/4*a^6 - 1/4*a^5 - 25/2*a^4 + a^3 + 29/2*a^2 + a - 2)*q^6 + (13/16*a^9 - 1/2*a^8 - 213/16*a^7 + 97/16*a^6 + 589/8*a^5 - 16*a^4 - 1281/8*a^3 - 53/4*a^2 + 227/2*a + 42)*q^7 + (a^3 - 4*a)*q^8 + (-5/16*a^9 + 1/4*a^8 + 81/16*a^7 - 45/16*a^6 - 217/8*a^5 + 25/4*a^4 + 441/8*a^3 + 31/4*a^2 - 35*a - 14)*q^9 + (3/4*a^9 - 1/2*a^8 - 47/4*a^7 + 25/4*a^6 + 61*a^5 - 19*a^4 - 243/2*a^3 + a^2 + 78*a + 24)*q^10 + (1/8*a^9 - 1/4*a^8 - 15/8*a^7 + 27/8*a^6 + 35/4*a^5 - 51/4*a^4 - 53/4*a^3 + 11*a^2 + 7/2*a + 1)*q^11 + (-3/8*a^9 + 47/8*a^7 + 1/8*a^6 - 125/4*a^5 - 7/2*a^4 + 267/4*a^3 + 35/2*a^2 - 48*a - 20)*q^12 + (-1/4*a^8 + 13/4*a^6 - 1/4*a^5 - 25/2*a^4 + a^3 + 29/2*a^2 + a)*q^13 + (-1/2*a^9 + 1/2*a^8 + 17/2*a^7 - 6*a^6 - 97/2*a^5 + 17*a^4 + 107*a^3 + 3*a^2 - 75*a - 26)*q^14 + (5/4*a^9 - 3/4*a^8 - 83/4*a^7 + 9*a^6 + 465/4*a^5 - 24*a^4 - 507/2*a^3 - 31/2*a^2 + 172*a + 58)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-9/8*a^9 + a^8 + 149/8*a^7 - 101/8*a^6 - 415/4*a^5 + 81/2*a^4 + 901/4*a^3 - 19/2*a^2 - 157*a - 46)*q^17 + (1/4*a^9 - 1/4*a^8 - 15/4*a^7 + 7/2*a^6 + 75/4*a^5 - 13*a^4 - 77/2*a^3 + 15/2*a^2 + 31*a + 10)*q^18 + (3/8*a^9 - 1/8*a^8 - 49/8*a^7 + a^6 + 271/8*a^5 + 2*a^4 - 297/4*a^3 - 85/4*a^2 + 53*a + 23)*q^19 + (a^9 - 1/2*a^8 - 16*a^7 + 13/2*a^6 + 171/2*a^5 - 20*a^4 - 177*a^3 - 3*a^2 + 118*a + 36)*q^20 + (-13/16*a^9 + 5/8*a^8 + 217/16*a^7 - 123/16*a^6 - 305/4*a^5 + 23*a^4 + 1329/8*a^3 - 225/2*a - 32)*q^21 + (-1/4*a^9 + 1/4*a^8 + 15/4*a^7 - 7/2*a^6 - 71/4*a^5 + 14*a^4 + 59/2*a^3 - 27/2*a^2 - 17*a - 4)*q^22 + (-15/16*a^9 + 3/8*a^8 + 247/16*a^7 - 73/16*a^6 - 173/2*a^5 + 43/4*a^4 + 1539/8*a^3 + 20*a^2 - 140*a - 51)*q^23 + (-a^7 - a^6 + 12*a^5 + 10*a^4 - 40*a^3 - 26*a^2 + 32*a + 16)*q^24 + (-1/4*a^9 + 17/4*a^7 + 3/4*a^6 - 51/2*a^5 - 10*a^4 + 129/2*a^3 + 36*a^2 - 58*a - 29)*q^25 + (-1/4*a^9 + 13/4*a^7 - 1/4*a^6 - 25/2*a^5 + a^4 + 29/2*a^3 + a^2)*q^26 + (-1/2*a^9 + 1/4*a^8 + 17/2*a^7 - 9/4*a^6 - 195/4*a^5 - a^4 + 217/2*a^3 + 67/2*a^2 - 77*a - 35)*q^27 + (-9/8*a^9 + a^8 + 153/8*a^7 - 93/8*a^6 - 441/4*a^5 + 30*a^4 + 997/4*a^3 + 39/2*a^2 - 181*a - 68)*q^28 + (3/4*a^9 - 3/8*a^8 - 25/2*a^7 + 33/8*a^6 + 563/8*a^5 - 15/2*a^4 - 154*a^3 - 85/4*a^2 + 105*a + 37)*q^29 + (-3/4*a^9 + 1/2*a^8 + 51/4*a^7 - 25/4*a^6 - 74*a^5 + 19*a^4 + 339/2*a^3 + 2*a^2 - 122*a - 40)*q^30 + (1/8*a^9 - 1/4*a^8 - 21/8*a^7 + 23/8*a^6 + 37/2*a^5 - 8*a^4 - 201/4*a^3 - 2*a^2 + 42*a + 18)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (9/16*a^9 - 3/8*a^8 - 149/16*a^7 + 59/16*a^6 + 52*a^5 - 3*a^4 - 913/8*a^3 - 63/2*a^2 + 163/2*a + 33)*q^33 + (a^9 - 1/2*a^8 - 16*a^7 + 13/2*a^6 + 171/2*a^5 - 20*a^4 - 176*a^3 - 4*a^2 + 116*a + 36)*q^34 + (9/8*a^9 - 3/4*a^8 - 153/8*a^7 + 67/8*a^6 + 221/2*a^5 - 33/2*a^4 - 1009/4*a^3 - 39*a^2 + 187*a + 70)*q^35 + (3/8*a^9 - 47/8*a^7 - 1/8*a^6 + 125/4*a^5 + 7/2*a^4 - 263/4*a^3 - 37/2*a^2 + 44*a + 20)*q^36 + (-3/8*a^9 + 51/8*a^7 + 9/8*a^6 - 147/4*a^5 - 14*a^4 + 335/4*a^3 + 95/2*a^2 - 66*a - 38)*q^37 + O(q^38)
*]> ;  // time = 3.87 seconds




J[229] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 229, 229, 229 ], new_dimensions := [ 1, 6, 11 ], dimensions := [ 1, 6, 11 ], intersection_graph := [ 0, 1, 1, 1, 0, 1, 1, 1, 0 ], ap_traces := [
[ -1, 1, -3, 2, -3, -6, -7, 3, 4, -6, 4, 2 ],
[ -4, -6, -3, -5, -22, 1, 6, -19, -10, -7, -3, 2 ],
[ 5, 3, 0, 1, 27, -7, 1, 8, -2, 17, -3, -14 ]
], hecke_fields := [
x - 1,
x^6 + 4*x^5 - 12*x^3 - 3*x^2 + 9*x - 1,
x^11 - 5*x^10 - 4*x^9 + 50*x^8 - 26*x^7 - 165*x^6 + 152*x^5 + 193*x^4 - 207*x^3 - 50*x^2 + 52*x + 1
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 19 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 19 ]
], torsion_upper_bounds := [ 1, 1, 19 ], torsion_lower_bounds := [ 1, 1, 19 ], l_ratios := [ 0, 0, 1/19 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[ -1, 1, -3, 2, -3, -6, -7, 3, 4, -6, 4, 2 ],
[
a,
a^4 + 2*a^3 - 3*a^2 - 4*a + 1,
-a^5 - 4*a^4 - a^3 + 8*a^2 + 3*a - 2,
a^5 + 2*a^4 - 3*a^3 - 2*a^2 + 4*a - 4,
a^4 + 3*a^3 - 2*a^2 - 6*a - 1,
a^5 + 5*a^4 + 4*a^3 - 11*a^2 - 12*a + 5,
-a^4 - 4*a^3 + a^2 + 10*a - 1,
a^5 + 4*a^4 + a^3 - 8*a^2 - 2*a - 1,
-3*a^4 - 9*a^3 + 4*a^2 + 17*a - 5,
3*a^5 + 9*a^4 - 6*a^3 - 25*a^2 + 3*a + 10,
-a^5 - a^4 + 7*a^3 + 5*a^2 - 8*a - 2,
-4*a^5 - 10*a^4 + 13*a^3 + 28*a^2 - 14*a - 9
],
[
a,
1/4*a^9 - 1/4*a^8 - 13/4*a^7 + 11/4*a^6 + 55/4*a^5 - 10*a^4 - 83/4*a^3 + 53/4*a^2 + 8*a - 11/4,
-1/4*a^9 + 1/4*a^8 + 11/4*a^7 - 5/4*a^6 - 43/4*a^5 + 65/4*a^3 + 15/4*a^2 - 6*a - 3/4,
-1/4*a^10 + 3/4*a^9 + 9/4*a^8 - 31/4*a^7 - 21/4*a^6 + 53/2*a^5 - 3/4*a^4 - 131/4*a^3 + 13/2*a^2 + 41/4*a + 3/2,
1/2*a^10 - 7/4*a^9 - 17/4*a^8 + 71/4*a^7 + 39/4*a^6 - 235/4*a^5 - 1/2*a^4 + 265/4*a^3 - 49/4*a^2 - 27/2*a + 23/4,
1/2*a^10 - 3/2*a^9 - 9/2*a^8 + 29/2*a^7 + 25/2*a^6 - 46*a^5 - 19/2*a^4 + 105/2*a^3 - 3*a^2 - 31/2*a + 2,
-1/2*a^10 + 5/2*a^9 + 5/2*a^8 - 25*a^7 + 6*a^6 + 82*a^5 - 89/2*a^4 - 93*a^3 + 54*a^2 + 39/2*a - 15/2,
-1/2*a^10 + 5/4*a^9 + 19/4*a^8 - 45/4*a^7 - 57/4*a^6 + 121/4*a^5 + 23/2*a^4 - 75/4*a^3 + 27/4*a^2 - 23/2*a - 13/4,
1/2*a^8 - 1/2*a^7 - 6*a^6 + 3*a^5 + 49/2*a^4 - 2*a^3 - 34*a^2 - 11/2*a + 7,
-1/2*a^9 + 3/2*a^8 + 9/2*a^7 - 29/2*a^6 - 25/2*a^5 + 46*a^4 + 17/2*a^3 - 99/2*a^2 + 4*a + 17/2,
1/2*a^10 - 2*a^9 - 7/2*a^8 + 41/2*a^7 + 2*a^6 - 141/2*a^5 + 26*a^4 + 88*a^3 - 85/2*a^2 - 23*a + 15/2,
3/4*a^9 - 3/4*a^8 - 33/4*a^7 + 15/4*a^6 + 125/4*a^5 + 2*a^4 - 179/4*a^3 - 77/4*a^2 + 19*a + 21/4
]
*], q_expansions := [*
q - q^2 + q^3 - q^4 - 3*q^5 - q^6 + 2*q^7 + 3*q^8 - 2*q^9 + 3*q^10 - 3*q^11 - q^12 - 6*q^13 - 2*q^14 - 3*q^15 - q^16 - 7*q^17 + 2*q^18 + 3*q^19 + 3*q^20 + 2*q^21 + 3*q^22 + 4*q^23 + 3*q^24 + 4*q^25 + 6*q^26 - 5*q^27 - 2*q^28 - 6*q^29 + 3*q^30 + 4*q^31 - 5*q^32 - 3*q^33 + 7*q^34 - 6*q^35 + 2*q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (a^4 + 2*a^3 - 3*a^2 - 4*a + 1)*q^3 + (a^2 - 2)*q^4 + (-a^5 - 4*a^4 - a^3 + 8*a^2 + 3*a - 2)*q^5 + (a^5 + 2*a^4 - 3*a^3 - 4*a^2 + a)*q^6 + (a^5 + 2*a^4 - 3*a^3 - 2*a^2 + 4*a - 4)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^4 - 5*a^3 + 5*a^2 + 10*a - 4)*q^9 + (-a^4 - 4*a^3 + 7*a - 1)*q^10 + (a^4 + 3*a^3 - 2*a^2 - 6*a - 1)*q^11 + (-2*a^5 - 5*a^4 + 4*a^3 + 10*a^2 - a - 1)*q^12 + (a^5 + 5*a^4 + 4*a^3 - 11*a^2 - 12*a + 5)*q^13 + (-2*a^5 - 3*a^4 + 10*a^3 + 7*a^2 - 13*a + 1)*q^14 + (2*a^5 + 7*a^4 + a^3 - 12*a^2 - 5*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 - 4*a^3 + a^2 + 10*a - 1)*q^17 + (-2*a^5 - 5*a^4 + 5*a^3 + 10*a^2 - 4*a)*q^18 + (a^5 + 4*a^4 + a^3 - 8*a^2 - 2*a - 1)*q^19 + (a^5 + 4*a^4 + 2*a^3 - 9*a^2 - 7*a + 4)*q^20 + (-3*a^5 - 9*a^4 + 4*a^3 + 18*a^2 - 2)*q^21 + (a^5 + 3*a^4 - 2*a^3 - 6*a^2 - a)*q^22 + (-3*a^4 - 9*a^3 + 4*a^2 + 17*a - 5)*q^23 + (a^5 - 8*a^3 + a^2 + 15*a - 2)*q^24 + (-a^5 - 3*a^4 + 2*a^3 + 9*a^2 + 2*a - 3)*q^25 + (a^5 + 4*a^4 + a^3 - 9*a^2 - 4*a + 1)*q^26 + (-a^5 - 2*a^4 + 6*a^3 + 8*a^2 - 8*a - 2)*q^27 + (3*a^5 + 6*a^4 - 11*a^3 - 15*a^2 + 11*a + 6)*q^28 + (3*a^5 + 9*a^4 - 6*a^3 - 25*a^2 + 3*a + 10)*q^29 + (-a^5 + a^4 + 12*a^3 + a^2 - 18*a + 2)*q^30 + (-a^5 - a^4 + 7*a^3 + 5*a^2 - 8*a - 2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^5 - 3*a^4 - 15*a^3 + 8*a^2 + 26*a - 4)*q^33 + (-a^5 - 4*a^4 + a^3 + 10*a^2 - a)*q^34 + (a^5 + 6*a^4 + 4*a^3 - 17*a^2 - 11*a + 7)*q^35 + (3*a^5 + 9*a^4 - 4*a^3 - 20*a^2 - 2*a + 6)*q^36 + (-4*a^5 - 10*a^4 + 13*a^3 + 28*a^2 - 14*a - 9)*q^37 + O(q^38),
q + a*q^2 + (1/4*a^9 - 1/4*a^8 - 13/4*a^7 + 11/4*a^6 + 55/4*a^5 - 10*a^4 - 83/4*a^3 + 53/4*a^2 + 8*a - 11/4)*q^3 + (a^2 - 2)*q^4 + (-1/4*a^9 + 1/4*a^8 + 11/4*a^7 - 5/4*a^6 - 43/4*a^5 + 65/4*a^3 + 15/4*a^2 - 6*a - 3/4)*q^5 + (1/4*a^10 - 1/4*a^9 - 13/4*a^8 + 11/4*a^7 + 55/4*a^6 - 10*a^5 - 83/4*a^4 + 53/4*a^3 + 8*a^2 - 11/4*a)*q^6 + (-1/4*a^10 + 3/4*a^9 + 9/4*a^8 - 31/4*a^7 - 21/4*a^6 + 53/2*a^5 - 3/4*a^4 - 131/4*a^3 + 13/2*a^2 + 41/4*a + 3/2)*q^7 + (a^3 - 4*a)*q^8 + (-1/2*a^10 + 5/4*a^9 + 23/4*a^8 - 53/4*a^7 - 97/4*a^6 + 189/4*a^5 + 89/2*a^4 - 247/4*a^3 - 125/4*a^2 + 37/2*a + 23/4)*q^9 + (-1/4*a^10 + 1/4*a^9 + 11/4*a^8 - 5/4*a^7 - 43/4*a^6 + 65/4*a^4 + 15/4*a^3 - 6*a^2 - 3/4*a)*q^10 + (1/2*a^10 - 7/4*a^9 - 17/4*a^8 + 71/4*a^7 + 39/4*a^6 - 235/4*a^5 - 1/2*a^4 + 265/4*a^3 - 49/4*a^2 - 27/2*a + 23/4)*q^11 + (a^10 - 11/4*a^9 - 37/4*a^8 + 107/4*a^7 + 103/4*a^6 - 345/4*a^5 - 15*a^4 + 405/4*a^3 - 67/4*a^2 - 29*a + 21/4)*q^12 + (1/2*a^10 - 3/2*a^9 - 9/2*a^8 + 29/2*a^7 + 25/2*a^6 - 46*a^5 - 19/2*a^4 + 105/2*a^3 - 3*a^2 - 31/2*a + 2)*q^13 + (-1/2*a^10 + 5/4*a^9 + 19/4*a^8 - 47/4*a^7 - 59/4*a^6 + 149/4*a^5 + 31/2*a^4 - 181/4*a^3 - 9/4*a^2 + 29/2*a + 1/4)*q^14 + (-1/4*a^9 + 1/4*a^8 + 13/4*a^7 - 11/4*a^6 - 55/4*a^5 + 10*a^4 + 79/4*a^3 - 49/4*a^2 - 5*a + 7/4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^10 + 5/2*a^9 + 5/2*a^8 - 25*a^7 + 6*a^6 + 82*a^5 - 89/2*a^4 - 93*a^3 + 54*a^2 + 39/2*a - 15/2)*q^17 + (-5/4*a^10 + 15/4*a^9 + 47/4*a^8 - 149/4*a^7 - 141/4*a^6 + 241/2*a^5 + 139/4*a^4 - 539/4*a^3 - 13/2*a^2 + 127/4*a + 1/2)*q^18 + (-1/2*a^10 + 5/4*a^9 + 19/4*a^8 - 45/4*a^7 - 57/4*a^6 + 121/4*a^5 + 23/2*a^4 - 75/4*a^3 + 27/4*a^2 - 23/2*a - 13/4)*q^19 + (-a^10 + 9/4*a^9 + 43/4*a^8 - 91/4*a^7 - 155/4*a^6 + 303/4*a^5 + 52*a^4 - 361/4*a^3 - 83/4*a^2 + 25*a + 7/4)*q^20 + (1/2*a^9 - 3/2*a^8 - 9/2*a^7 + 27/2*a^6 + 29/2*a^5 - 38*a^4 - 45/2*a^3 + 67/2*a^2 + 16*a - 7/2)*q^21 + (3/4*a^10 - 9/4*a^9 - 29/4*a^8 + 91/4*a^7 + 95/4*a^6 - 153/2*a^5 - 121/4*a^4 + 365/4*a^3 + 23/2*a^2 - 81/4*a - 1/2)*q^22 + (1/2*a^8 - 1/2*a^7 - 6*a^6 + 3*a^5 + 49/2*a^4 - 2*a^3 - 34*a^2 - 11/2*a + 7)*q^23 + (7/4*a^10 - 19/4*a^9 - 67/4*a^8 + 185/4*a^7 + 205/4*a^6 - 147*a^5 - 201/4*a^4 + 655/4*a^3 + 5*a^2 - 165/4*a - 1)*q^24 + (3/2*a^10 - 9/2*a^9 - 29/2*a^8 + 46*a^7 + 46*a^6 - 156*a^5 - 105/2*a^4 + 188*a^3 + 18*a^2 - 95/2*a - 11/2)*q^25 + (a^10 - 5/2*a^9 - 21/2*a^8 + 51/2*a^7 + 73/2*a^6 - 171/2*a^5 - 44*a^4 + 201/2*a^3 + 19/2*a^2 - 24*a - 1/2)*q^26 + (-1/2*a^10 + 7/4*a^9 + 17/4*a^8 - 71/4*a^7 - 39/4*a^6 + 239/4*a^5 - 5/2*a^4 - 277/4*a^3 + 97/4*a^2 + 19/2*a - 27/4)*q^27 + (-3/4*a^10 + 5/4*a^9 + 35/4*a^8 - 49/4*a^7 - 139/4*a^6 + 77/2*a^5 + 211/4*a^4 - 161/4*a^3 - 47/2*a^2 + 23/4*a - 5/2)*q^28 + (-1/2*a^9 + 3/2*a^8 + 9/2*a^7 - 29/2*a^6 - 25/2*a^5 + 46*a^4 + 17/2*a^3 - 99/2*a^2 + 4*a + 17/2)*q^29 + (-1/4*a^10 + 1/4*a^9 + 13/4*a^8 - 11/4*a^7 - 55/4*a^6 + 10*a^5 + 79/4*a^4 - 49/4*a^3 - 5*a^2 + 7/4*a)*q^30 + (1/2*a^10 - 2*a^9 - 7/2*a^8 + 41/2*a^7 + 2*a^6 - 141/2*a^5 + 26*a^4 + 88*a^3 - 85/2*a^2 - 23*a + 15/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^10 - 3/4*a^9 - 25/4*a^8 + 23/4*a^7 + 127/4*a^6 - 43/4*a^5 - 159/2*a^4 - 11/4*a^3 + 343/4*a^2 + 17/2*a - 69/4)*q^33 + (1/2*a^9 - 7*a^7 - 1/2*a^6 + 63/2*a^5 + 7/2*a^4 - 99/2*a^3 - 11/2*a^2 + 37/2*a + 1/2)*q^34 + (1/4*a^10 - 1/4*a^9 - 13/4*a^8 + 11/4*a^7 + 55/4*a^6 - 10*a^5 - 83/4*a^4 + 57/4*a^3 + 9*a^2 - 35/4*a - 1)*q^35 + (-3/2*a^10 + 17/4*a^9 + 55/4*a^8 - 165/4*a^7 - 149/4*a^6 + 521/4*a^5 + 35/2*a^4 - 567/4*a^3 + 127/4*a^2 + 57/2*a - 41/4)*q^36 + (3/4*a^9 - 3/4*a^8 - 33/4*a^7 + 15/4*a^6 + 125/4*a^5 + 2*a^4 - 179/4*a^3 - 77/4*a^2 + 19*a + 21/4)*q^37 + O(q^38)
*]> ;  // time = 3.08 seconds




J[230] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 230, 230, 230, 230, 115, 115, 115, 46, 23 ], new_dimensions := [ 2, 2, 2, 3, 1, 2, 4, 1, 2 ], dimensions := [ 2, 2, 2, 3, 2, 4, 8, 2, 8 ], intersection_graph := [ 0, 1, 1, 1, 5, 1, 1, 5, 5, 1, 0, 1, 1, 1, 1, 43, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 11, 1, 1, 1, 0, 1, 19, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 5, 25, 1, 1, 1, 19, 1, 0, 1, 1, 1, 1, 43, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 5, 1, 1, 0, 25, 5, 1, 11, 1, 25, 1, 1, 25, 0 ], ap_traces := [
[ -2, -1, -2, 1, 3, 7, -3, 7, 2, 6, 7, -8 ],
[ -2, 3, 2, 3, -7, 3, 3, 1, -2, 2, -5, 16 ],
[ 2, 1, 2, 1, 1, -3, 1, -3, 2, -14, 7, 4 ],
[ 3, 1, -3, 3, 3, -1, -7, 3, -3, -4, -5, -2 ]
], hecke_fields := [
x^2 + x - 5,
x^2 - 3*x - 1,
x^2 - x - 1,
x^3 - x^2 - 9*x + 12
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 5, 5, 3 ],
[ 43, 3, 1 ],
[ 11, 11, 1 ],
[ 57, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 3 ],
[ 1, 3, 1 ],
[ 11, 11, 1 ],
[ 57, 1, 1 ]
], torsion_upper_bounds := [ 3, 3, 11, 3 ], torsion_lower_bounds := [ 3, 3, 1, 3 ], l_ratios := [ 1/3, 1/3, 1, 19/3 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1/121, 1 ], eigenvalues := [*
[
-1,
a,
-1,
a + 1,
a + 2,
-a + 3,
-a - 2,
-a + 3,
1,
-2*a + 2,
3*a + 5,
-4
],
[
-1,
a,
1,
-a + 3,
-a - 2,
-a + 3,
-3*a + 6,
-3*a + 5,
-1,
2*a - 2,
3*a - 7,
8
],
[
1,
a,
1,
-a + 1,
-3*a + 2,
-5*a + 1,
5*a - 2,
3*a - 3,
1,
-2*a - 6,
5*a + 1,
4*a
],
[
1,
a,
-1,
-a^2 - 2*a + 8,
2*a^2 + a - 12,
-a^2 + 6,
-a - 2,
-a^2 - 2*a + 8,
-1,
2*a - 2,
a^2 - 8,
2*a^2 + 2*a - 14
]
*], q_expansions := [*
q - q^2 + a*q^3 + q^4 - q^5 - a*q^6 + (a + 1)*q^7 - q^8 + (-a + 2)*q^9 + q^10 + (a + 2)*q^11 + a*q^12 + (-a + 3)*q^13 + (-a - 1)*q^14 - a*q^15 + q^16 + (-a - 2)*q^17 + (a - 2)*q^18 + (-a + 3)*q^19 - q^20 + 5*q^21 + (-a - 2)*q^22 + q^23 - a*q^24 + q^25 + (a - 3)*q^26 - 5*q^27 + (a + 1)*q^28 + (-2*a + 2)*q^29 + a*q^30 + (3*a + 5)*q^31 - q^32 + (a + 5)*q^33 + (a + 2)*q^34 + (-a - 1)*q^35 + (-a + 2)*q^36 - 4*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + q^5 - a*q^6 + (-a + 3)*q^7 - q^8 + (3*a - 2)*q^9 - q^10 + (-a - 2)*q^11 + a*q^12 + (-a + 3)*q^13 + (a - 3)*q^14 + a*q^15 + q^16 + (-3*a + 6)*q^17 + (-3*a + 2)*q^18 + (-3*a + 5)*q^19 + q^20 - q^21 + (a + 2)*q^22 - q^23 - a*q^24 + q^25 + (a - 3)*q^26 + (4*a + 3)*q^27 + (-a + 3)*q^28 + (2*a - 2)*q^29 - a*q^30 + (3*a - 7)*q^31 - q^32 + (-5*a - 1)*q^33 + (3*a - 6)*q^34 + (-a + 3)*q^35 + (3*a - 2)*q^36 + 8*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + q^5 + a*q^6 + (-a + 1)*q^7 + q^8 + (a - 2)*q^9 + q^10 + (-3*a + 2)*q^11 + a*q^12 + (-5*a + 1)*q^13 + (-a + 1)*q^14 + a*q^15 + q^16 + (5*a - 2)*q^17 + (a - 2)*q^18 + (3*a - 3)*q^19 + q^20 - q^21 + (-3*a + 2)*q^22 + q^23 + a*q^24 + q^25 + (-5*a + 1)*q^26 + (-4*a + 1)*q^27 + (-a + 1)*q^28 + (-2*a - 6)*q^29 + a*q^30 + (5*a + 1)*q^31 + q^32 + (-a - 3)*q^33 + (5*a - 2)*q^34 + (-a + 1)*q^35 + (a - 2)*q^36 + 4*a*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - q^5 + a*q^6 + (-a^2 - 2*a + 8)*q^7 + q^8 + (a^2 - 3)*q^9 - q^10 + (2*a^2 + a - 12)*q^11 + a*q^12 + (-a^2 + 6)*q^13 + (-a^2 - 2*a + 8)*q^14 - a*q^15 + q^16 + (-a - 2)*q^17 + (a^2 - 3)*q^18 + (-a^2 - 2*a + 8)*q^19 - q^20 + (-3*a^2 - a + 12)*q^21 + (2*a^2 + a - 12)*q^22 - q^23 + a*q^24 + q^25 + (-a^2 + 6)*q^26 + (a^2 + 3*a - 12)*q^27 + (-a^2 - 2*a + 8)*q^28 + (2*a - 2)*q^29 - a*q^30 + (a^2 - 8)*q^31 + q^32 + (3*a^2 + 6*a - 24)*q^33 + (-a - 2)*q^34 + (a^2 + 2*a - 8)*q^35 + (a^2 - 3)*q^36 + (2*a^2 + 2*a - 14)*q^37 + O(q^38)
*]> ;  // time = 83.25 seconds




J[231] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 231, 231, 231, 231, 231, 77, 77, 77, 77, 33, 21, 11 ], new_dimensions := [ 1, 2, 2, 3, 3, 1, 1, 1, 2, 1, 1, 1 ], dimensions := [ 1, 2, 2, 3, 3, 2, 2, 2, 4, 2, 2, 4 ], intersection_graph := [ 0, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 0, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 3, 1, 1, 3, 1, 3, 1, 1, 1, 1, 0, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 3, 1, 9, 1, 5, 1, 1, 1, 1, 1, 0, 25, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 25, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 0, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 3, 1, 1, 9, 1, 1, 9, 1, 0 ], ap_traces := [
[ -1, -1, -2, 1, -1, 6, 2, 4, 0, -2, 8, 6 ],
[ -1, -2, 6, 2, -2, 2, 6, -4, -2, 2, -2, 2 ],
[ 1, 2, 2, 2, 2, -2, 6, 0, -2, 10, -6, -14 ],
[ 0, -3, 0, -3, 3, 0, 0, 12, -6, 12, -6, 0 ],
[ 2, 3, 4, -3, -3, -4, 8, -8, 10, -4, -2, 0 ]
], hecke_fields := [
x - 1,
x^2 + x - 5,
x^2 - x - 1,
x^3 - 6*x - 1,
x^3 - 2*x^2 - 4*x + 7
], atkin_lehners := [
[ 1, -1, 1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ],
[ 1, 1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 25, 1, 1 ],
[ 5, 5, 1 ],
[ 3, 3, 1 ],
[ 7, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 5, 5, 1 ],
[ 1, 1, 1 ],
[ 7, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 5, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 1, 1, 1, 1, 7 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1/25, 1, 1 ], eigenvalues := [*
[ -1, -1, -2, 1, -1, 6, 2, 4, 0, -2, 8, 6 ],
[
a,
-1,
3,
1,
-1,
1,
2*a + 4,
-2*a - 3,
-2*a - 2,
-4*a - 1,
2*a,
1
],
[
a,
1,
1,
1,
1,
-4*a + 1,
-2*a + 4,
6*a - 3,
-6*a + 2,
5,
2*a - 4,
-7
],
[
a,
-1,
-a^2 + a + 4,
-1,
1,
-a^2 + a + 4,
-2*a,
-a^2 - a + 8,
-2*a - 2,
a^2 - a,
2*a^2 - 10,
a^2 + 3*a - 4
],
[
a,
1,
-a^2 - a + 6,
-1,
-1,
-3*a^2 + a + 10,
4*a^2 - 2*a - 12,
a^2 - a - 6,
2*a + 2,
-3*a^2 + a + 10,
2*a^2 - 4*a - 6,
-a^2 + 3*a + 2
]
*], q_expansions := [*
q - q^2 - q^3 - q^4 - 2*q^5 + q^6 + q^7 + 3*q^8 + q^9 + 2*q^10 - q^11 + q^12 + 6*q^13 - q^14 + 2*q^15 - q^16 + 2*q^17 - q^18 + 4*q^19 + 2*q^20 - q^21 + q^22 - 3*q^24 - q^25 - 6*q^26 - q^27 - q^28 - 2*q^29 - 2*q^30 + 8*q^31 - 5*q^32 + q^33 - 2*q^34 - 2*q^35 - q^36 + 6*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a + 3)*q^4 + 3*q^5 - a*q^6 + q^7 + (2*a - 5)*q^8 + q^9 + 3*a*q^10 - q^11 + (a - 3)*q^12 + q^13 + a*q^14 - 3*q^15 + (-5*a + 4)*q^16 + (2*a + 4)*q^17 + a*q^18 + (-2*a - 3)*q^19 + (-3*a + 9)*q^20 - q^21 - a*q^22 + (-2*a - 2)*q^23 + (-2*a + 5)*q^24 + 4*q^25 + a*q^26 - q^27 + (-a + 3)*q^28 + (-4*a - 1)*q^29 - 3*a*q^30 + 2*a*q^31 + (5*a - 15)*q^32 + q^33 + (2*a + 10)*q^34 + 3*q^35 + (-a + 3)*q^36 + q^37 + O(q^38),
q + a*q^2 + q^3 + (a - 1)*q^4 + q^5 + a*q^6 + q^7 + (-2*a + 1)*q^8 + q^9 + a*q^10 + q^11 + (a - 1)*q^12 + (-4*a + 1)*q^13 + a*q^14 + q^15 - 3*a*q^16 + (-2*a + 4)*q^17 + a*q^18 + (6*a - 3)*q^19 + (a - 1)*q^20 + q^21 + a*q^22 + (-6*a + 2)*q^23 + (-2*a + 1)*q^24 - 4*q^25 + (-3*a - 4)*q^26 + q^27 + (a - 1)*q^28 + 5*q^29 + a*q^30 + (2*a - 4)*q^31 + (a - 5)*q^32 + q^33 + (2*a - 2)*q^34 + q^35 + (a - 1)*q^36 - 7*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 + a + 4)*q^5 - a*q^6 - q^7 + (2*a + 1)*q^8 + q^9 + (a^2 - 2*a - 1)*q^10 + q^11 + (-a^2 + 2)*q^12 + (-a^2 + a + 4)*q^13 - a*q^14 + (a^2 - a - 4)*q^15 + (a + 4)*q^16 - 2*a*q^17 + a*q^18 + (-a^2 - a + 8)*q^19 + (3*a - 7)*q^20 + q^21 + a*q^22 + (-2*a - 2)*q^23 + (-2*a - 1)*q^24 + (-a^2 - 3*a + 9)*q^25 + (a^2 - 2*a - 1)*q^26 - q^27 + (-a^2 + 2)*q^28 + (a^2 - a)*q^29 + (-a^2 + 2*a + 1)*q^30 + (2*a^2 - 10)*q^31 + (a^2 - 2)*q^32 - q^33 - 2*a^2*q^34 + (a^2 - a - 4)*q^35 + (a^2 - 2)*q^36 + (a^2 + 3*a - 4)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^2 - a + 6)*q^5 + a*q^6 - q^7 + (2*a^2 - 7)*q^8 + q^9 + (-3*a^2 + 2*a + 7)*q^10 - q^11 + (a^2 - 2)*q^12 + (-3*a^2 + a + 10)*q^13 - a*q^14 + (-a^2 - a + 6)*q^15 + (2*a^2 + a - 10)*q^16 + (4*a^2 - 2*a - 12)*q^17 + a*q^18 + (a^2 - a - 6)*q^19 + (-2*a^2 - 3*a + 9)*q^20 - q^21 - a*q^22 + (2*a + 2)*q^23 + (2*a^2 - 7)*q^24 + (a^2 - 3*a + 3)*q^25 + (-5*a^2 - 2*a + 21)*q^26 + q^27 + (-a^2 + 2)*q^28 + (-3*a^2 + a + 10)*q^29 + (-3*a^2 + 2*a + 7)*q^30 + (2*a^2 - 4*a - 6)*q^31 + (a^2 - 2*a)*q^32 - q^33 + (6*a^2 + 4*a - 28)*q^34 + (a^2 + a - 6)*q^35 + (a^2 - 2)*q^36 + (-a^2 + 3*a + 2)*q^37 + O(q^38)
*]> ;  // time = 56.311 seconds




J[233] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 233, 233, 233 ], new_dimensions := [ 1, 7, 11 ], dimensions := [ 1, 7, 11 ], intersection_graph := [ 0, 1, 27, 1, 0, 1, 27, 1, 0 ], ap_traces := [
[ 1, -2, 2, 4, 6, 6, -6, -4, 0, -2, 4, -6 ],
[ -2, -8, -3, -17, 1, -12, -5, -8, -16, 3, -24, -10 ],
[ -2, 10, -1, 15, -5, 4, 7, 8, 8, -9, 24, 14 ]
], hecke_fields := [
x - 1,
x^7 + 2*x^6 - 6*x^5 - 10*x^4 + 10*x^3 + 8*x^2 - 7*x + 1,
x^11 + 2*x^10 - 16*x^9 - 30*x^8 + 91*x^7 + 158*x^6 - 213*x^5 - 349*x^4 + 152*x^3 + 290*x^2 + 41*x - 19
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 29 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 29 ]
], torsion_upper_bounds := [ 1, 1, 29 ], torsion_lower_bounds := [ 1, 1, 29 ], l_ratios := [ 1, 0, 1/29 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ 1, -2, 2, 4, 6, 6, -6, -4, 0, -2, 4, -6 ],
[
a,
a^5 + a^4 - 5*a^3 - 4*a^2 + 3*a,
-a^5 - 2*a^4 + 4*a^3 + 8*a^2 - a - 3,
-a^6 - 3*a^5 + 5*a^4 + 16*a^3 - 6*a^2 - 16*a + 3,
-a^6 - 2*a^5 + 7*a^4 + 11*a^3 - 13*a^2 - 11*a + 5,
6*a^6 + 14*a^5 - 29*a^4 - 68*a^3 + 25*a^2 + 52*a - 16,
5*a^6 + 13*a^5 - 24*a^4 - 65*a^3 + 22*a^2 + 53*a - 17,
-5*a^6 - 10*a^5 + 24*a^4 + 46*a^3 - 18*a^2 - 28*a + 6,
-3*a^6 - 7*a^5 + 17*a^4 + 35*a^3 - 26*a^2 - 29*a + 14,
-4*a^6 - 11*a^5 + 19*a^4 + 57*a^3 - 16*a^2 - 51*a + 13,
a^6 + a^5 - 7*a^4 - 5*a^3 + 11*a^2 + 4*a - 4,
3*a^6 + 7*a^5 - 13*a^4 - 34*a^3 + 6*a^2 + 24*a - 8
],
[
a,
7/4*a^10 - 1/2*a^9 - 107/4*a^8 + 8*a^7 + 139*a^6 - 65/2*a^5 - 1147/4*a^4 + 31/4*a^3 + 883/4*a^2 + 203/4*a - 16,
27/2*a^10 - 9/2*a^9 - 409/2*a^8 + 145/2*a^7 + 1046*a^6 - 310*a^5 - 4193/2*a^4 + 183*a^3 + 1550*a^2 + 294*a - 219/2,
a^10 - 1/2*a^9 - 15*a^8 + 15/2*a^7 + 75*a^6 - 31*a^5 - 143*a^4 + 43/2*a^3 + 195/2*a^2 + 41/2*a - 5/2,
9/4*a^10 - 3/4*a^9 - 135/4*a^8 + 49/4*a^7 + 170*a^6 - 107/2*a^5 - 1331/4*a^4 + 75/2*a^3 + 242*a^2 + 37*a - 81/4,
-a^10 + 15*a^8 - a^7 - 76*a^6 + 6*a^5 + 150*a^4 + 3*a^3 - 104*a^2 - 20*a + 7,
-21/2*a^10 + 4*a^9 + 319/2*a^8 - 63*a^7 - 819*a^6 + 268*a^5 + 3305/2*a^4 - 349/2*a^3 - 2477/2*a^2 - 455/2*a + 92,
33/2*a^10 - 13/2*a^9 - 499/2*a^8 + 205/2*a^7 + 1271*a^6 - 439*a^5 - 5055/2*a^4 + 306*a^3 + 1855*a^2 + 332*a - 249/2,
-9/2*a^10 + 2*a^9 + 135/2*a^8 - 31*a^7 - 339*a^6 + 132*a^5 + 1315/2*a^4 - 197/2*a^3 - 941/2*a^2 - 163/2*a + 31,
-33*a^10 + 12*a^9 + 500*a^8 - 191*a^7 - 2556*a^6 + 819*a^5 + 5112*a^4 - 544*a^3 - 3768*a^2 - 670*a + 264,
14*a^10 - 5*a^9 - 212*a^8 + 80*a^7 + 1083*a^6 - 345*a^5 - 2165*a^4 + 236*a^3 + 1600*a^2 + 268*a - 118,
29*a^10 - 23/2*a^9 - 438*a^8 + 363/2*a^7 + 2227*a^6 - 781*a^5 - 4415*a^4 + 1137/2*a^3 + 6467/2*a^2 + 1091/2*a - 455/2
]
*], q_expansions := [*
q + q^2 - 2*q^3 - q^4 + 2*q^5 - 2*q^6 + 4*q^7 - 3*q^8 + q^9 + 2*q^10 + 6*q^11 + 2*q^12 + 6*q^13 + 4*q^14 - 4*q^15 - q^16 - 6*q^17 + q^18 - 4*q^19 - 2*q^20 - 8*q^21 + 6*q^22 + 6*q^24 - q^25 + 6*q^26 + 4*q^27 - 4*q^28 - 2*q^29 - 4*q^30 + 4*q^31 + 5*q^32 - 12*q^33 - 6*q^34 + 8*q^35 - q^36 - 6*q^37 + O(q^38),
q + a*q^2 + (a^5 + a^4 - 5*a^3 - 4*a^2 + 3*a)*q^3 + (a^2 - 2)*q^4 + (-a^5 - 2*a^4 + 4*a^3 + 8*a^2 - a - 3)*q^5 + (a^6 + a^5 - 5*a^4 - 4*a^3 + 3*a^2)*q^6 + (-a^6 - 3*a^5 + 5*a^4 + 16*a^3 - 6*a^2 - 16*a + 3)*q^7 + (a^3 - 4*a)*q^8 + (-a^6 - 4*a^5 + 3*a^4 + 19*a^3 + 4*a^2 - 11*a - 1)*q^9 + (-a^6 - 2*a^5 + 4*a^4 + 8*a^3 - a^2 - 3*a)*q^10 + (-a^6 - 2*a^5 + 7*a^4 + 11*a^3 - 13*a^2 - 11*a + 5)*q^11 + (-a^6 - a^5 + 4*a^4 + 3*a^3 + a - 1)*q^12 + (6*a^6 + 14*a^5 - 29*a^4 - 68*a^3 + 25*a^2 + 52*a - 16)*q^13 + (-a^6 - a^5 + 6*a^4 + 4*a^3 - 8*a^2 - 4*a + 1)*q^14 + (2*a^6 + 6*a^5 - 7*a^4 - 27*a^3 - a^2 + 16*a - 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (5*a^6 + 13*a^5 - 24*a^4 - 65*a^3 + 22*a^2 + 53*a - 17)*q^17 + (-2*a^6 - 3*a^5 + 9*a^4 + 14*a^3 - 3*a^2 - 8*a + 1)*q^18 + (-5*a^6 - 10*a^5 + 24*a^4 + 46*a^3 - 18*a^2 - 28*a + 6)*q^19 + (2*a^4 + a^3 - 11*a^2 - 5*a + 7)*q^20 + (-a^6 - 5*a^5 + 2*a^4 + 24*a^3 + 7*a^2 - 13*a + 2)*q^21 + (a^5 + a^4 - 3*a^3 - 3*a^2 - 2*a + 1)*q^22 + (-3*a^6 - 7*a^5 + 17*a^4 + 35*a^3 - 26*a^2 - 29*a + 14)*q^23 + (-a^6 - 4*a^5 + 3*a^4 + 18*a^3 + 3*a^2 - 8*a + 1)*q^24 + (-4*a^6 - 10*a^5 + 19*a^4 + 49*a^3 - 15*a^2 - 34*a + 10)*q^25 + (2*a^6 + 7*a^5 - 8*a^4 - 35*a^3 + 4*a^2 + 26*a - 6)*q^26 + (2*a^6 + 5*a^5 - 10*a^4 - 23*a^3 + 9*a^2 + 13*a - 5)*q^27 + (3*a^6 + 6*a^5 - 16*a^4 - 30*a^3 + 16*a^2 + 26*a - 5)*q^28 + (-4*a^6 - 11*a^5 + 19*a^4 + 57*a^3 - 16*a^2 - 51*a + 13)*q^29 + (2*a^6 + 5*a^5 - 7*a^4 - 21*a^3 + 10*a - 2)*q^30 + (a^6 + a^5 - 7*a^4 - 5*a^3 + 11*a^2 + 4*a - 4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-3*a^6 - 7*a^5 + 11*a^4 + 31*a^3 + a^2 - 17*a + 4)*q^33 + (3*a^6 + 6*a^5 - 15*a^4 - 28*a^3 + 13*a^2 + 18*a - 5)*q^34 + (4*a^6 + 12*a^5 - 15*a^4 - 56*a^3 + a^2 + 36*a - 6)*q^35 + (3*a^6 + 5*a^5 - 12*a^4 - 21*a^3 + 9*a + 4)*q^36 + (3*a^6 + 7*a^5 - 13*a^4 - 34*a^3 + 6*a^2 + 24*a - 8)*q^37 + O(q^38),
q + a*q^2 + (7/4*a^10 - 1/2*a^9 - 107/4*a^8 + 8*a^7 + 139*a^6 - 65/2*a^5 - 1147/4*a^4 + 31/4*a^3 + 883/4*a^2 + 203/4*a - 16)*q^3 + (a^2 - 2)*q^4 + (27/2*a^10 - 9/2*a^9 - 409/2*a^8 + 145/2*a^7 + 1046*a^6 - 310*a^5 - 4193/2*a^4 + 183*a^3 + 1550*a^2 + 294*a - 219/2)*q^5 + (-4*a^10 + 5/4*a^9 + 121/2*a^8 - 81/4*a^7 - 309*a^6 + 86*a^5 + 1237/2*a^4 - 181/4*a^3 - 1827/4*a^2 - 351/4*a + 133/4)*q^6 + (a^10 - 1/2*a^9 - 15*a^8 + 15/2*a^7 + 75*a^6 - 31*a^5 - 143*a^4 + 43/2*a^3 + 195/2*a^2 + 41/2*a - 5/2)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^10 + 1/2*a^9 + 30*a^8 - 17/2*a^7 - 151*a^6 + 36*a^5 + 294*a^4 - 23/2*a^3 - 417/2*a^2 - 95/2*a + 31/2)*q^9 + (-63/2*a^10 + 23/2*a^9 + 955/2*a^8 - 365/2*a^7 - 2443*a^6 + 779*a^5 + 9789/2*a^4 - 502*a^3 - 3621*a^2 - 663*a + 513/2)*q^10 + (9/4*a^10 - 3/4*a^9 - 135/4*a^8 + 49/4*a^7 + 170*a^6 - 107/2*a^5 - 1331/4*a^4 + 75/2*a^3 + 242*a^2 + 37*a - 81/4)*q^11 + (23/4*a^10 - 5/2*a^9 - 347/4*a^8 + 39*a^7 + 440*a^6 - 337/2*a^5 - 3471/4*a^4 + 543/4*a^3 + 2523/4*a^2 + 383/4*a - 44)*q^12 + (-a^10 + 15*a^8 - a^7 - 76*a^6 + 6*a^5 + 150*a^4 + 3*a^3 - 104*a^2 - 20*a + 7)*q^13 + (-5/2*a^10 + a^9 + 75/2*a^8 - 16*a^7 - 189*a^6 + 70*a^5 + 741/2*a^4 - 109/2*a^3 - 539/2*a^2 - 87/2*a + 19)*q^14 + (-17/2*a^10 + 7/2*a^9 + 257/2*a^8 - 109/2*a^7 - 654*a^6 + 231*a^5 + 2597/2*a^4 - 158*a^3 - 956*a^2 - 175*a + 141/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-21/2*a^10 + 4*a^9 + 319/2*a^8 - 63*a^7 - 819*a^6 + 268*a^5 + 3305/2*a^4 - 349/2*a^3 - 2477/2*a^2 - 455/2*a + 92)*q^17 + (9/2*a^10 - 2*a^9 - 137/2*a^8 + 31*a^7 + 352*a^6 - 132*a^5 - 1419/2*a^4 + 191/2*a^3 + 1065/2*a^2 + 195/2*a - 38)*q^18 + (33/2*a^10 - 13/2*a^9 - 499/2*a^8 + 205/2*a^7 + 1271*a^6 - 439*a^5 - 5055/2*a^4 + 306*a^3 + 1855*a^2 + 332*a - 249/2)*q^19 + (95/2*a^10 - 35/2*a^9 - 1437/2*a^8 + 557/2*a^7 + 3664*a^6 - 1195*a^5 - 14605/2*a^4 + 801*a^3 + 5372*a^2 + 960*a - 759/2)*q^20 + (3/2*a^10 - 1/2*a^9 - 45/2*a^8 + 15/2*a^7 + 113*a^6 - 28*a^5 - 437/2*a^4 - a^3 + 153*a^2 + 49*a - 15/2)*q^21 + (-21/4*a^10 + 9/4*a^9 + 319/4*a^8 - 139/4*a^7 - 409*a^6 + 293/2*a^5 + 3291/4*a^4 - 100*a^3 - 1231/2*a^2 - 225/2*a + 171/4)*q^22 + (-9/2*a^10 + 2*a^9 + 135/2*a^8 - 31*a^7 - 339*a^6 + 132*a^5 + 1315/2*a^4 - 197/2*a^3 - 941/2*a^2 - 163/2*a + 31)*q^23 + (-6*a^10 + 11/4*a^9 + 181/2*a^8 - 171/4*a^7 - 459*a^6 + 185*a^5 + 1811/2*a^4 - 611/4*a^3 - 2633/4*a^2 - 417/4*a + 171/4)*q^24 + (-10*a^10 + 4*a^9 + 151*a^8 - 63*a^7 - 768*a^6 + 270*a^5 + 1525*a^4 - 191*a^3 - 1120*a^2 - 200*a + 77)*q^25 + (2*a^10 - a^9 - 31*a^8 + 15*a^7 + 164*a^6 - 63*a^5 - 346*a^4 + 48*a^3 + 270*a^2 + 48*a - 19)*q^26 + (-15/2*a^10 + 11/4*a^9 + 113*a^8 - 175/4*a^7 - 572*a^6 + 187*a^5 + 1124*a^4 - 489/4*a^3 - 3239/4*a^2 - 595/4*a + 207/4)*q^27 + (4*a^10 - 3/2*a^9 - 61*a^8 + 47/2*a^7 + 315*a^6 - 100*a^5 - 641*a^4 + 135/2*a^3 + 973/2*a^2 + 161/2*a - 85/2)*q^28 + (-33*a^10 + 12*a^9 + 500*a^8 - 191*a^7 - 2556*a^6 + 819*a^5 + 5112*a^4 - 544*a^3 - 3768*a^2 - 670*a + 264)*q^29 + (41/2*a^10 - 15/2*a^9 - 619/2*a^8 + 239/2*a^7 + 1574*a^6 - 512*a^5 - 6249/2*a^4 + 336*a^3 + 2290*a^2 + 419*a - 323/2)*q^30 + (14*a^10 - 5*a^9 - 212*a^8 + 80*a^7 + 1083*a^6 - 345*a^5 - 2165*a^4 + 236*a^3 + 1600*a^2 + 268*a - 118)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-4*a^10 + 3/2*a^9 + 61*a^8 - 47/2*a^7 - 315*a^6 + 99*a^5 + 640*a^4 - 117/2*a^3 - 955/2*a^2 - 199/2*a + 59/2)*q^33 + (25*a^10 - 17/2*a^9 - 378*a^8 + 273/2*a^7 + 1927*a^6 - 584*a^5 - 3839*a^4 + 715/2*a^3 + 5635/2*a^2 + 1045/2*a - 399/2)*q^34 + (17*a^10 - 6*a^9 - 257*a^8 + 96*a^7 + 1310*a^6 - 410*a^5 - 2610*a^4 + 251*a^3 + 1916*a^2 + 371*a - 130)*q^35 + (-7*a^10 + 5/2*a^9 + 106*a^8 - 81/2*a^7 - 541*a^6 + 177*a^5 + 1078*a^4 - 257/2*a^3 - 1581/2*a^2 - 255/2*a + 109/2)*q^36 + (29*a^10 - 23/2*a^9 - 438*a^8 + 363/2*a^7 + 2227*a^6 - 781*a^5 - 4415*a^4 + 1137/2*a^3 + 6467/2*a^2 + 1091/2*a - 455/2)*q^37 + O(q^38)
*]> ;  // time = 3.2 seconds




J[235] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 235, 235, 235, 235, 235, 47 ], new_dimensions := [ 1, 1, 1, 5, 7, 4 ], dimensions := [ 1, 1, 1, 5, 7, 8 ], intersection_graph := [ 0, 3, 1, 1, 1, 9, 3, 0, 1, 1, 1, 3, 1, 1, 0, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 9, 3, 3, 1, 1, 0 ], ap_traces := [
[ -1, -1, -1, 1, 3, 3, 6, -1, 4, 2, -3, 0 ],
[ 2, 2, -1, -2, 0, 3, 0, -4, 1, 8, 6, -6 ],
[ -1, -1, 1, 1, -3, -3, -6, -7, 4, -10, 3, 12 ],
[ -4, -5, -5, -5, -1, -11, -14, 5, -6, -16, 3, -16 ],
[ 1, 1, 7, -3, 1, 2, 12, 3, 1, 26, -5, 0 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^5 + 4*x^4 - 12*x^2 - 4*x + 7,
x^7 - x^6 - 10*x^5 + 8*x^4 + 28*x^3 - 17*x^2 - 19*x + 2
], atkin_lehners := [
[ 1, -1 ],
[ 1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 9, 1 ],
[ 3, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 1, 1, 0, 0, 1 ], analytic_sha_upper_bounds := [ 1, 1, 0, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 0, 1 ], eigenvalues := [*
[ -1, -1, -1, 1, 3, 3, 6, -1, 4, 2, -3, 0 ],
[ 2, 2, -1, -2, 0, 3, 0, -4, 1, 8, 6, -6 ],
[ -1, -1, 1, 1, -3, -3, -6, -7, 4, -10, 3, 12 ],
[
a,
a^4 + 2*a^3 - 4*a^2 - 5*a + 3,
-1,
-2*a^4 - 5*a^3 + 5*a^2 + 10*a - 5,
a^4 + 3*a^3 + a^2 - 3*a - 5,
a^4 + a^3 - 5*a^2 - 3*a + 1,
a^3 + a^2 - 2*a - 2,
-a^4 - a^3 + 3*a^2 - a + 1,
-2*a^4 - 2*a^3 + 12*a^2 + 6*a - 14,
-4*a^3 - 8*a^2 + 10*a + 8,
a^4 + a^3 - 9*a^2 - 5*a + 15,
2*a^4 + 5*a^3 - 3*a^2 - 8*a - 4
],
[
a,
1/2*a^6 - 5*a^4 + 12*a^2 - 3/2*a - 3,
1,
-1/2*a^6 + 4*a^4 + a^3 - 7*a^2 - 3/2*a + 1,
-3/2*a^6 + 13*a^4 + 3*a^3 - 25*a^2 - 15/2*a + 3,
-1/2*a^6 - a^5 + 5*a^4 + 9*a^3 - 11*a^2 - 33/2*a + 2,
a^6 - 8*a^4 - 3*a^3 + 13*a^2 + 9*a + 2,
1/2*a^6 + 2*a^5 - 5*a^4 - 17*a^3 + 9*a^2 + 57/2*a + 3,
a^6 + a^5 - 10*a^4 - 10*a^3 + 24*a^2 + 17*a - 7,
-2*a + 4,
-1/2*a^6 + 5*a^4 + a^3 - 11*a^2 - 5/2*a - 1,
2*a^6 + 2*a^5 - 18*a^4 - 19*a^3 + 33*a^2 + 34*a + 2
]
*], q_expansions := [*
q - q^2 - q^3 - q^4 - q^5 + q^6 + q^7 + 3*q^8 - 2*q^9 + q^10 + 3*q^11 + q^12 + 3*q^13 - q^14 + q^15 - q^16 + 6*q^17 + 2*q^18 - q^19 + q^20 - q^21 - 3*q^22 + 4*q^23 - 3*q^24 + q^25 - 3*q^26 + 5*q^27 - q^28 + 2*q^29 - q^30 - 3*q^31 - 5*q^32 - 3*q^33 - 6*q^34 - q^35 + 2*q^36 + O(q^38),
q + 2*q^2 + 2*q^3 + 2*q^4 - q^5 + 4*q^6 - 2*q^7 + q^9 - 2*q^10 + 4*q^12 + 3*q^13 - 4*q^14 - 2*q^15 - 4*q^16 + 2*q^18 - 4*q^19 - 2*q^20 - 4*q^21 + q^23 + q^25 + 6*q^26 - 4*q^27 - 4*q^28 + 8*q^29 - 4*q^30 + 6*q^31 - 8*q^32 + 2*q^35 + 2*q^36 - 6*q^37 + O(q^38),
q - q^2 - q^3 - q^4 + q^5 + q^6 + q^7 + 3*q^8 - 2*q^9 - q^10 - 3*q^11 + q^12 - 3*q^13 - q^14 - q^15 - q^16 - 6*q^17 + 2*q^18 - 7*q^19 - q^20 - q^21 + 3*q^22 + 4*q^23 - 3*q^24 + q^25 + 3*q^26 + 5*q^27 - q^28 - 10*q^29 + q^30 + 3*q^31 - 5*q^32 + 3*q^33 + 6*q^34 + q^35 + 2*q^36 + 12*q^37 + O(q^38),
q + a*q^2 + (a^4 + 2*a^3 - 4*a^2 - 5*a + 3)*q^3 + (a^2 - 2)*q^4 - q^5 + (-2*a^4 - 4*a^3 + 7*a^2 + 7*a - 7)*q^6 + (-2*a^4 - 5*a^3 + 5*a^2 + 10*a - 5)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^4 - 3*a^3 + 9*a^2 + 6*a - 8)*q^9 - a*q^10 + (a^4 + 3*a^3 + a^2 - 3*a - 5)*q^11 + (2*a^4 + 3*a^3 - 9*a^2 - 5*a + 8)*q^12 + (a^4 + a^3 - 5*a^2 - 3*a + 1)*q^13 + (3*a^4 + 5*a^3 - 14*a^2 - 13*a + 14)*q^14 + (-a^4 - 2*a^3 + 4*a^2 + 5*a - 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^3 + a^2 - 2*a - 2)*q^17 + (5*a^4 + 9*a^3 - 18*a^2 - 16*a + 14)*q^18 + (-a^4 - a^3 + 3*a^2 - a + 1)*q^19 + (-a^2 + 2)*q^20 + (2*a^4 + 4*a^3 - 4*a^2 - 2*a - 1)*q^21 + (-a^4 + a^3 + 9*a^2 - a - 7)*q^22 + (-2*a^4 - 2*a^3 + 12*a^2 + 6*a - 14)*q^23 + (-a^4 - a^3 + 5*a^2 + 2*a)*q^24 + q^25 + (-3*a^4 - 5*a^3 + 9*a^2 + 5*a - 7)*q^26 + (2*a^4 + 2*a^3 - 10*a^2 + 9)*q^27 + (-3*a^4 - 4*a^3 + 13*a^2 + 6*a - 11)*q^28 + (-4*a^3 - 8*a^2 + 10*a + 8)*q^29 + (2*a^4 + 4*a^3 - 7*a^2 - 7*a + 7)*q^30 + (a^4 + a^3 - 9*a^2 - 5*a + 15)*q^31 + (-4*a^4 - 8*a^3 + 12*a^2 + 16*a - 7)*q^32 + (-3*a^4 - 9*a^3 + 3*a^2 + 15*a - 1)*q^33 + (a^4 + a^3 - 2*a^2 - 2*a)*q^34 + (2*a^4 + 5*a^3 - 5*a^2 - 10*a + 5)*q^35 + (-7*a^4 - 12*a^3 + 26*a^2 + 22*a - 19)*q^36 + (2*a^4 + 5*a^3 - 3*a^2 - 8*a - 4)*q^37 + O(q^38),
q + a*q^2 + (1/2*a^6 - 5*a^4 + 12*a^2 - 3/2*a - 3)*q^3 + (a^2 - 2)*q^4 + q^5 + (1/2*a^6 - 4*a^4 - 2*a^3 + 7*a^2 + 13/2*a - 1)*q^6 + (-1/2*a^6 + 4*a^4 + a^3 - 7*a^2 - 3/2*a + 1)*q^7 + (a^3 - 4*a)*q^8 + (1/2*a^6 - 4*a^4 - a^3 + 5*a^2 + 3/2*a + 6)*q^9 + a*q^10 + (-3/2*a^6 + 13*a^4 + 3*a^3 - 25*a^2 - 15/2*a + 3)*q^11 + (-1/2*a^6 + a^5 + 4*a^4 - 7*a^3 - 9*a^2 + 23/2*a + 5)*q^12 + (-1/2*a^6 - a^5 + 5*a^4 + 9*a^3 - 11*a^2 - 33/2*a + 2)*q^13 + (-1/2*a^6 - a^5 + 5*a^4 + 7*a^3 - 10*a^2 - 17/2*a + 1)*q^14 + (1/2*a^6 - 5*a^4 + 12*a^2 - 3/2*a - 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 - 8*a^4 - 3*a^3 + 13*a^2 + 9*a + 2)*q^17 + (1/2*a^6 + a^5 - 5*a^4 - 9*a^3 + 10*a^2 + 31/2*a - 1)*q^18 + (1/2*a^6 + 2*a^5 - 5*a^4 - 17*a^3 + 9*a^2 + 57/2*a + 3)*q^19 + (a^2 - 2)*q^20 + (1/2*a^6 - 4*a^4 - 2*a^3 + 8*a^2 + 11/2*a - 3)*q^21 + (-3/2*a^6 - 2*a^5 + 15*a^4 + 17*a^3 - 33*a^2 - 51/2*a + 3)*q^22 + (a^6 + a^5 - 10*a^4 - 10*a^3 + 24*a^2 + 17*a - 7)*q^23 + (-1/2*a^6 - a^5 + 5*a^4 + 9*a^3 - 11*a^2 - 35/2*a + 3)*q^24 + q^25 + (-3/2*a^6 + 13*a^4 + 3*a^3 - 25*a^2 - 15/2*a + 1)*q^26 + (1/2*a^6 - 2*a^5 - 4*a^4 + 16*a^3 + 10*a^2 - 57/2*a - 7)*q^27 + (-1/2*a^6 + 3*a^4 + 2*a^3 - 3*a^2 - 11/2*a - 1)*q^28 + (-2*a + 4)*q^29 + (1/2*a^6 - 4*a^4 - 2*a^3 + 7*a^2 + 13/2*a - 1)*q^30 + (-1/2*a^6 + 5*a^4 + a^3 - 11*a^2 - 5/2*a - 1)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-3/2*a^6 + 13*a^4 + 3*a^3 - 23*a^2 - 19/2*a - 5)*q^33 + (a^6 + 2*a^5 - 11*a^4 - 15*a^3 + 26*a^2 + 21*a - 2)*q^34 + (-1/2*a^6 + 4*a^4 + a^3 - 7*a^2 - 3/2*a + 1)*q^35 + (1/2*a^6 - 5*a^4 - 2*a^3 + 14*a^2 + 11/2*a - 13)*q^36 + (2*a^6 + 2*a^5 - 18*a^4 - 19*a^3 + 33*a^2 + 34*a + 2)*q^37 + O(q^38)
*]> ;  // time = 26.59 seconds




J[237] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 237, 237, 237, 79, 79 ], new_dimensions := [ 2, 4, 7, 1, 5 ], dimensions := [ 2, 4, 7, 2, 10 ], intersection_graph := [ 0, 1, 1, 1, 31, 1, 0, 1, 3, 1, 1, 1, 0, 5, 1, 1, 3, 5, 0, 1, 31, 1, 1, 1, 0 ], ap_traces := [
[ 2, -2, 0, 2, 6, -2, 2, -4, 6, 6, -4, 0 ],
[ -3, -4, -4, -2, -8, -6, -8, -4, -18, -2, 0, 4 ],
[ 2, 7, -2, 4, 2, 6, -8, 4, 8, -10, 4, 10 ]
], hecke_fields := [
x^2 - 2*x - 1,
x^4 + 3*x^3 - x^2 - 5*x + 1,
x^7 - 2*x^6 - 11*x^5 + 22*x^4 + 30*x^3 - 65*x^2 - 2*x + 23
], atkin_lehners := [
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 31, 1 ],
[ 3, 1 ],
[ 25, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 25, 1 ]
], torsion_upper_bounds := [ 1, 1, 5 ], torsion_lower_bounds := [ 1, 1, 5 ], l_ratios := [ 1, 0, 1 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[
a,
-1,
0,
1,
-a + 4,
-2*a + 1,
-a + 2,
-2,
-3*a + 6,
-a + 4,
-2*a,
6*a - 6
],
[
a,
-1,
-a^3 - 3*a^2 + 2,
2*a^3 + 4*a^2 - 4*a - 4,
-a^3 - a^2 + 2*a - 3,
-a^3 + a^2 + 6*a - 5,
2*a^3 + 4*a^2 - 2*a - 4,
-a^3 - 5*a^2 - 2*a + 6,
a^3 + 5*a^2 + 4*a - 10,
-2*a^3 - 8*a^2 - 4*a + 8,
3*a^3 + 5*a^2 - 4*a - 1,
-2*a^3 - 4*a^2 + 6*a + 6
],
[
a,
1,
-a^6 + 12*a^4 - a^3 - 37*a^2 + 9*a + 16,
3/2*a^6 - 1/2*a^5 - 17*a^4 + 4*a^3 + 49*a^2 - 25/2*a - 37/2,
1/2*a^6 + 1/2*a^5 - 6*a^4 - 4*a^3 + 17*a^2 + 7/2*a - 7/2,
5/2*a^6 - 1/2*a^5 - 28*a^4 + 4*a^3 + 79*a^2 - 33/2*a - 57/2,
-5/2*a^6 + 1/2*a^5 + 27*a^4 - 2*a^3 - 73*a^2 + 11/2*a + 53/2,
-3*a^6 + 34*a^4 + a^3 - 97*a^2 + 7*a + 38,
-3/2*a^6 + 1/2*a^5 + 17*a^4 - 5*a^3 - 48*a^2 + 33/2*a + 33/2,
5/2*a^6 - 1/2*a^5 - 29*a^4 + 4*a^3 + 87*a^2 - 35/2*a - 81/2,
-3*a^6 + 35*a^4 - 104*a^2 + 12*a + 44,
-a^6 + a^5 + 10*a^4 - 6*a^3 - 26*a^2 + 5*a + 15
]
*], q_expansions := [*
q + a*q^2 - q^3 + (2*a - 1)*q^4 - a*q^6 + q^7 + (a + 2)*q^8 + q^9 + (-a + 4)*q^11 + (-2*a + 1)*q^12 + (-2*a + 1)*q^13 + a*q^14 + 3*q^16 + (-a + 2)*q^17 + a*q^18 - 2*q^19 - q^21 + (2*a - 1)*q^22 + (-3*a + 6)*q^23 + (-a - 2)*q^24 - 5*q^25 + (-3*a - 2)*q^26 - q^27 + (2*a - 1)*q^28 + (-a + 4)*q^29 - 2*a*q^31 + (a - 4)*q^32 + (a - 4)*q^33 - q^34 + (2*a - 1)*q^36 + (6*a - 6)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^3 - 3*a^2 + 2)*q^5 - a*q^6 + (2*a^3 + 4*a^2 - 4*a - 4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^2 - 3*a + 1)*q^10 + (-a^3 - a^2 + 2*a - 3)*q^11 + (-a^2 + 2)*q^12 + (-a^3 + a^2 + 6*a - 5)*q^13 + (-2*a^3 - 2*a^2 + 6*a - 2)*q^14 + (a^3 + 3*a^2 - 2)*q^15 + (-3*a^3 - 5*a^2 + 5*a + 3)*q^16 + (2*a^3 + 4*a^2 - 2*a - 4)*q^17 + a*q^18 + (-a^3 - 5*a^2 - 2*a + 6)*q^19 + (a^3 + 3*a^2 + a - 4)*q^20 + (-2*a^3 - 4*a^2 + 4*a + 4)*q^21 + (2*a^3 + a^2 - 8*a + 1)*q^22 + (a^3 + 5*a^2 + 4*a - 10)*q^23 + (-a^3 + 4*a)*q^24 + (a^3 + 3*a^2 + 2*a - 2)*q^25 + (4*a^3 + 5*a^2 - 10*a + 1)*q^26 - q^27 + (-4*a^2 - 4*a + 10)*q^28 + (-2*a^3 - 8*a^2 - 4*a + 8)*q^29 + (a^2 + 3*a - 1)*q^30 + (3*a^3 + 5*a^2 - 4*a - 1)*q^31 + (2*a^3 + 2*a^2 - 4*a + 3)*q^32 + (a^3 + a^2 - 2*a + 3)*q^33 + (-2*a^3 + 6*a - 2)*q^34 + (4*a^2 + 6*a - 10)*q^35 + (a^2 - 2)*q^36 + (-2*a^3 - 4*a^2 + 6*a + 6)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^6 + 12*a^4 - a^3 - 37*a^2 + 9*a + 16)*q^5 + a*q^6 + (3/2*a^6 - 1/2*a^5 - 17*a^4 + 4*a^3 + 49*a^2 - 25/2*a - 37/2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-2*a^6 + a^5 + 21*a^4 - 7*a^3 - 56*a^2 + 14*a + 23)*q^10 + (1/2*a^6 + 1/2*a^5 - 6*a^4 - 4*a^3 + 17*a^2 + 7/2*a - 7/2)*q^11 + (a^2 - 2)*q^12 + (5/2*a^6 - 1/2*a^5 - 28*a^4 + 4*a^3 + 79*a^2 - 33/2*a - 57/2)*q^13 + (5/2*a^6 - 1/2*a^5 - 29*a^4 + 4*a^3 + 85*a^2 - 31/2*a - 69/2)*q^14 + (-a^6 + 12*a^4 - a^3 - 37*a^2 + 9*a + 16)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-5/2*a^6 + 1/2*a^5 + 27*a^4 - 2*a^3 - 73*a^2 + 11/2*a + 53/2)*q^17 + a*q^18 + (-3*a^6 + 34*a^4 + a^3 - 97*a^2 + 7*a + 38)*q^19 + (-a^6 - a^5 + 13*a^4 + 6*a^3 - 42*a^2 + a + 14)*q^20 + (3/2*a^6 - 1/2*a^5 - 17*a^4 + 4*a^3 + 49*a^2 - 25/2*a - 37/2)*q^21 + (3/2*a^6 - 1/2*a^5 - 15*a^4 + 2*a^3 + 36*a^2 - 5/2*a - 23/2)*q^22 + (-3/2*a^6 + 1/2*a^5 + 17*a^4 - 5*a^3 - 48*a^2 + 33/2*a + 33/2)*q^23 + (a^3 - 4*a)*q^24 + (a^5 - a^4 - 8*a^3 + 6*a^2 + 11*a - 2)*q^25 + (9/2*a^6 - 1/2*a^5 - 51*a^4 + 4*a^3 + 146*a^2 - 47/2*a - 115/2)*q^26 + q^27 + (3/2*a^6 - 1/2*a^5 - 17*a^4 + 2*a^3 + 49*a^2 - 9/2*a - 41/2)*q^28 + (5/2*a^6 - 1/2*a^5 - 29*a^4 + 4*a^3 + 87*a^2 - 35/2*a - 81/2)*q^29 + (-2*a^6 + a^5 + 21*a^4 - 7*a^3 - 56*a^2 + 14*a + 23)*q^30 + (-3*a^6 + 35*a^4 - 104*a^2 + 12*a + 44)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^6 + 1/2*a^5 - 6*a^4 - 4*a^3 + 17*a^2 + 7/2*a - 7/2)*q^33 + (-9/2*a^6 - 1/2*a^5 + 53*a^4 + 2*a^3 - 157*a^2 + 43/2*a + 115/2)*q^34 + (-2*a^6 + 24*a^4 - 72*a^2 + 8*a + 26)*q^35 + (a^2 - 2)*q^36 + (-a^6 + a^5 + 10*a^4 - 6*a^3 - 26*a^2 + 5*a + 15)*q^37 + O(q^38)
*]> ;  // time = 29.42 seconds




J[238] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 238, 238, 238, 238, 238, 238, 119, 119, 34, 17, 14 ], new_dimensions := [ 1, 1, 1, 1, 1, 2, 4, 5, 1, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 2, 8, 10, 2, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 61, 1, 1, 1, 1, 5, 1, 7, 1, 1, 0, 1, 3, 1, 3, 1, 1, 1, 1, 1, 61, 1, 0, 1, 9, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, -2, -1, -2, 0, -1, -2, -8, 0, 8, -4 ],
[ -1, 2, 4, 1, -4, -4, -1, -6, 0, 6, 4, -10 ],
[ 1, 2, 0, -1, -2, -2, -1, 0, 4, 4, 0, 8 ],
[ 1, -2, -4, 1, -6, -2, -1, 0, -4, 8, 0, 4 ],
[ 1, 0, 2, 1, 0, -2, 1, 4, 0, -6, 0, -6 ],
[ -2, 2, 2, -2, 6, 4, 2, -8, 16, 2, -12, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 2*x - 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, 1 ],
[ -1, -1, -1 ],
[ 1, 1, -1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 5, 1, 1 ],
[ 1, 1, 1 ],
[ 7, 1, 1 ],
[ 1, 1, 1 ],
[ 61, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 7, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 1, 0, 1, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 0, 1, 1 ], eigenvalues := [*
[ -1, 0, -2, -1, -2, 0, -1, -2, -8, 0, 8, -4 ],
[ -1, 2, 4, 1, -4, -4, -1, -6, 0, 6, 4, -10 ],
[ 1, 2, 0, -1, -2, -2, -1, 0, 4, 4, 0, 8 ],
[ 1, -2, -4, 1, -6, -2, -1, 0, -4, 8, 0, 4 ],
[ 1, 0, 2, 1, 0, -2, 1, 4, 0, -6, 0, -6 ],
[
-1,
a,
-a + 2,
-1,
a + 2,
-2*a + 4,
1,
-2*a - 2,
8,
-3*a + 4,
2*a - 8,
-a
]
*], q_expansions := [*
q - q^2 + q^4 - 2*q^5 - q^7 - q^8 - 3*q^9 + 2*q^10 - 2*q^11 + q^14 + q^16 - q^17 + 3*q^18 - 2*q^19 - 2*q^20 + 2*q^22 - 8*q^23 - q^25 - q^28 + 8*q^31 - q^32 + q^34 + 2*q^35 - 3*q^36 - 4*q^37 + O(q^38),
q - q^2 + 2*q^3 + q^4 + 4*q^5 - 2*q^6 + q^7 - q^8 + q^9 - 4*q^10 - 4*q^11 + 2*q^12 - 4*q^13 - q^14 + 8*q^15 + q^16 - q^17 - q^18 - 6*q^19 + 4*q^20 + 2*q^21 + 4*q^22 - 2*q^24 + 11*q^25 + 4*q^26 - 4*q^27 + q^28 + 6*q^29 - 8*q^30 + 4*q^31 - q^32 - 8*q^33 + q^34 + 4*q^35 + q^36 - 10*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 + 2*q^6 - q^7 + q^8 + q^9 - 2*q^11 + 2*q^12 - 2*q^13 - q^14 + q^16 - q^17 + q^18 - 2*q^21 - 2*q^22 + 4*q^23 + 2*q^24 - 5*q^25 - 2*q^26 - 4*q^27 - q^28 + 4*q^29 + q^32 - 4*q^33 - q^34 + q^36 + 8*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 4*q^5 - 2*q^6 + q^7 + q^8 + q^9 - 4*q^10 - 6*q^11 - 2*q^12 - 2*q^13 + q^14 + 8*q^15 + q^16 - q^17 + q^18 - 4*q^20 - 2*q^21 - 6*q^22 - 4*q^23 - 2*q^24 + 11*q^25 - 2*q^26 + 4*q^27 + q^28 + 8*q^29 + 8*q^30 + q^32 + 12*q^33 - q^34 - 4*q^35 + q^36 + 4*q^37 + O(q^38),
q + q^2 + q^4 + 2*q^5 + q^7 + q^8 - 3*q^9 + 2*q^10 - 2*q^13 + q^14 + q^16 + q^17 - 3*q^18 + 4*q^19 + 2*q^20 - q^25 - 2*q^26 + q^28 - 6*q^29 + q^32 + q^34 + 2*q^35 - 3*q^36 - 6*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a + 2)*q^5 - a*q^6 - q^7 - q^8 + (2*a + 1)*q^9 + (a - 2)*q^10 + (a + 2)*q^11 + a*q^12 + (-2*a + 4)*q^13 + q^14 - 4*q^15 + q^16 + q^17 + (-2*a - 1)*q^18 + (-2*a - 2)*q^19 + (-a + 2)*q^20 - a*q^21 + (-a - 2)*q^22 + 8*q^23 - a*q^24 + (-2*a + 3)*q^25 + (2*a - 4)*q^26 + (2*a + 8)*q^27 - q^28 + (-3*a + 4)*q^29 + 4*q^30 + (2*a - 8)*q^31 - q^32 + (4*a + 4)*q^33 - q^34 + (a - 2)*q^35 + (2*a + 1)*q^36 - a*q^37 + O(q^38)
*]> ;  // time = 81.379 seconds




J[239] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 239, 239 ], new_dimensions := [ 3, 17 ], dimensions := [ 3, 17 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -1, -4, -3, -1, -7, -2, -10, 3, 4, -8, -3 ],
[ 0, 3, 6, 5, -1, 15, 4, 24, -9, -2, 28, 11 ]
], hecke_fields := [
x^3 + x^2 - 2*x - 1,
x^17 - 28*x^15 + x^14 + 319*x^13 - 17*x^12 - 1903*x^11 + 91*x^10 + 6377*x^9 - 125*x^8 - 11967*x^7 - 233*x^6 + 11733*x^5 + 503*x^4 - 5015*x^3 - 94*x^2 + 609*x + 49
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 119 ]
], tamagawa_numbers := [
[ 1 ],
[ 119 ]
], torsion_upper_bounds := [ 1, 119 ], torsion_lower_bounds := [ 1, 119 ], l_ratios := [ 0, 1/119 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^2 - a + 1,
a^2 - 3,
-1,
a^2 - 2,
a^2 - 4,
-a^2 + 1,
a^2 + 3*a - 4,
-a^2 + a + 3,
-6*a^2 - a + 11,
-2*a^2 - 2*a,
3*a
],
[
a,
16771351/11107271*a^16 - 2866545/1586753*a^15 - 63196242/1586753*a^14 + 548454202/11107271*a^13 + 4613893796/11107271*a^12 - 5855599700/11107271*a^11 - 24126751696/11107271*a^10 + 4398458577/1586753*a^9 + 9469941088/1586753*a^8 - 82906055202/11107271*a^7 - 91822850183/11107271*a^6 + 108744026520/11107271*a^5 + 54627655140/11107271*a^4 - 59185678764/11107271*a^3 - 7102994828/11107271*a^2 + 7384450585/11107271*a + 86905773/1586753,
22511799/11107271*a^16 - 4122295/1586753*a^15 - 85029894/1586753*a^14 + 783888478/11107271*a^13 + 6223382488/11107271*a^12 - 8326382581/11107271*a^11 - 32632212856/11107271*a^10 + 6229020626/1586753*a^9 + 12852845780/1586753*a^8 - 117052738164/11107271*a^7 - 125297104388/11107271*a^6 + 153180936380/11107271*a^5 + 75340597103/11107271*a^4 - 83236570496/11107271*a^3 - 10250253852/11107271*a^2 + 10451957825/11107271*a + 132668371/1586753,
25677032/11107271*a^16 - 4808908/1586753*a^15 - 96911585/1586753*a^14 + 913041769/11107271*a^13 + 7082868525/11107271*a^12 - 9683160111/11107271*a^11 - 37044681867/11107271*a^10 + 7231854089/1586753*a^9 + 2075098395/226679*a^8 - 135617406635/11107271*a^7 - 140464578889/11107271*a^6 + 176959976663/11107271*a^5 + 83052116143/11107271*a^4 - 95724702685/11107271*a^3 - 10472865097/11107271*a^2 + 11880604573/11107271*a + 142368927/1586753,
11795867/11107271*a^16 - 1932394/1586753*a^15 - 44322451/1586753*a^14 + 372521827/11107271*a^13 + 3225743447/11107271*a^12 - 4005866463/11107271*a^11 - 16804920021/11107271*a^10 + 3031135855/1586753*a^9 + 6564330462/1586753*a^8 - 57627409134/11107271*a^7 - 63241803565/11107271*a^6 + 76509429271/11107271*a^5 + 37396414775/11107271*a^4 - 42451276279/11107271*a^3 - 5056555641/11107271*a^2 + 5464612926/11107271*a + 75908807/1586753,
12932667/11107271*a^16 - 2279337/1586753*a^15 - 48752987/1586753*a^14 + 433764071/11107271*a^13 + 3560780261/11107271*a^12 - 4604482467/11107271*a^11 - 18627365653/11107271*a^10 + 3435101051/1586753*a^9 + 7316629361/1586753*a^8 - 64145365971/11107271*a^7 - 71086180147/11107271*a^6 + 82910826763/11107271*a^5 + 42558283977/11107271*a^4 - 44016310883/11107271*a^3 - 5687517959/11107271*a^2 + 5215960508/11107271*a + 67672208/1586753,
21279582/11107271*a^16 - 576557/226679*a^15 - 11490920/226679*a^14 + 764328658/11107271*a^13 + 5888803376/11107271*a^12 - 8085603784/11107271*a^11 - 30866495077/11107271*a^10 + 6022752188/1586753*a^9 + 12144661700/1586753*a^8 - 112598812800/11107271*a^7 - 118266415576/11107271*a^6 + 146376439975/11107271*a^5 + 71289580280/11107271*a^4 - 78898734658/11107271*a^3 - 10026490116/11107271*a^2 + 9892317506/11107271*a + 131645167/1586753,
17310495/11107271*a^16 - 3414606/1586753*a^15 - 65437688/1586753*a^14 + 645668596/11107271*a^13 + 4788816728/11107271*a^12 - 6824305772/11107271*a^11 - 25069140146/11107271*a^10 + 5083421254/1586753*a^9 + 9834005994/1586753*a^8 - 95167008616/11107271*a^7 - 95086769046/11107271*a^6 + 124129226300/11107271*a^5 + 56185475128/11107271*a^4 - 67333009400/11107271*a^3 - 7048228324/11107271*a^2 + 8503642143/11107271*a + 97915806/1586753,
31722361/11107271*a^16 - 5850154/1586753*a^15 - 119732695/1586753*a^14 + 1112154343/11107271*a^13 + 8752755413/11107271*a^12 - 11810292925/11107271*a^11 - 45803042055/11107271*a^10 + 8833142877/1586753*a^9 + 17978970083/1586753*a^8 - 165930762117/11107271*a^7 - 174209659179/11107271*a^6 + 216989136849/11107271*a^5 + 103470227181/11107271*a^4 - 117637416119/11107271*a^3 - 13353180733/11107271*a^2 + 14550510082/11107271*a + 176544419/1586753,
37599616/11107271*a^16 - 6005504/1586753*a^15 - 141443329/1586753*a^14 + 1156074400/11107271*a^13 + 10313257723/11107271*a^12 - 12402758789/11107271*a^11 - 53893343681/11107271*a^10 + 9348637439/1586753*a^9 + 21162527937/1586753*a^8 - 176565199519/11107271*a^7 - 205761663785/11107271*a^6 + 231733252097/11107271*a^5 + 123644621259/11107271*a^4 - 126013913667/11107271*a^3 - 17196071544/11107271*a^2 + 15589598961/11107271*a + 203454605/1586753,
-24153904/11107271*a^16 + 4321005/1586753*a^15 + 91255413/1586753*a^14 - 822194252/11107271*a^13 - 6682216498/11107271*a^12 + 8733648358/11107271*a^11 + 35066854706/11107271*a^10 - 6528082826/1586753*a^9 - 1975726498/226679*a^8 + 122383812294/11107271*a^7 + 135081794294/11107271*a^6 - 159364496414/11107271*a^5 - 81358052074/11107271*a^4 + 85759333630/11107271*a^3 + 10925236722/11107271*a^2 - 10535502669/11107271*a - 128905963/1586753,
58834648/11107271*a^16 - 10469071/1586753*a^15 - 221869889/1586753*a^14 + 1994193703/11107271*a^13 + 16206951361/11107271*a^12 - 21201818723/11107271*a^11 - 84762261663/11107271*a^10 + 15858972953/1586753*a^9 + 33262149523/1586753*a^8 - 297518575153/11107271*a^7 - 322391208789/11107271*a^6 + 387851937953/11107271*a^5 + 191863930809/11107271*a^4 - 209242126735/11107271*a^3 - 25038696915/11107271*a^2 + 25744954717/11107271*a + 307195088/1586753
]
*], q_expansions := [*
q + a*q^2 + (-a^2 - a + 1)*q^3 + (a^2 - 2)*q^4 + (a^2 - 3)*q^5 + (-a - 1)*q^6 - q^7 + (-a^2 - 2*a + 1)*q^8 + (a - 1)*q^9 + (-a^2 - a + 1)*q^10 + (a^2 - 2)*q^11 + (a^2 + a - 2)*q^12 + (a^2 - 4)*q^13 - a*q^14 + (2*a^2 + 2*a - 3)*q^15 + (-3*a^2 - a + 3)*q^16 + (-a^2 + 1)*q^17 + (a^2 - a)*q^18 + (a^2 + 3*a - 4)*q^19 + (-2*a^2 - a + 5)*q^20 + (a^2 + a - 1)*q^21 + (-a^2 + 1)*q^22 + (-a^2 + a + 3)*q^23 + (2*a + 3)*q^24 + (-3*a^2 - a + 3)*q^25 + (-a^2 - 2*a + 1)*q^26 + (4*a^2 + 3*a - 5)*q^27 + (-a^2 + 2)*q^28 + (-6*a^2 - a + 11)*q^29 + (a + 2)*q^30 + (-2*a^2 - 2*a)*q^31 + (4*a^2 + a - 5)*q^32 + (a^2 + a - 2)*q^33 + (a^2 - a - 1)*q^34 + (-a^2 + 3)*q^35 + (-2*a^2 + 3)*q^36 + 3*a*q^37 + O(q^38),
q + a*q^2 + (16771351/11107271*a^16 - 2866545/1586753*a^15 - 63196242/1586753*a^14 + 548454202/11107271*a^13 + 4613893796/11107271*a^12 - 5855599700/11107271*a^11 - 24126751696/11107271*a^10 + 4398458577/1586753*a^9 + 9469941088/1586753*a^8 - 82906055202/11107271*a^7 - 91822850183/11107271*a^6 + 108744026520/11107271*a^5 + 54627655140/11107271*a^4 - 59185678764/11107271*a^3 - 7102994828/11107271*a^2 + 7384450585/11107271*a + 86905773/1586753)*q^3 + (a^2 - 2)*q^4 + (22511799/11107271*a^16 - 4122295/1586753*a^15 - 85029894/1586753*a^14 + 783888478/11107271*a^13 + 6223382488/11107271*a^12 - 8326382581/11107271*a^11 - 32632212856/11107271*a^10 + 6229020626/1586753*a^9 + 12852845780/1586753*a^8 - 117052738164/11107271*a^7 - 125297104388/11107271*a^6 + 153180936380/11107271*a^5 + 75340597103/11107271*a^4 - 83236570496/11107271*a^3 - 10250253852/11107271*a^2 + 10451957825/11107271*a + 132668371/1586753)*q^5 + (-2866545/1586753*a^16 + 3889162/1586753*a^15 + 75954693/1586753*a^14 - 105166739/1586753*a^13 - 795783819/1586753*a^12 + 1112732751/1586753*a^11 + 4180431014/1586753*a^10 - 5808759673/1586753*a^9 - 11544233761/1586753*a^8 + 15554272462/1586753*a^7 + 16093107329/1586753*a^6 - 20307229449/1586753*a^5 - 9660238331/1586753*a^4 + 11000761491/1586753*a^3 + 1280136797/1586753*a^2 - 1372201764/1586753*a - 16771351/226679)*q^6 + (25677032/11107271*a^16 - 4808908/1586753*a^15 - 96911585/1586753*a^14 + 913041769/11107271*a^13 + 7082868525/11107271*a^12 - 9683160111/11107271*a^11 - 37044681867/11107271*a^10 + 7231854089/1586753*a^9 + 2075098395/226679*a^8 - 135617406635/11107271*a^7 - 140464578889/11107271*a^6 + 176959976663/11107271*a^5 + 83052116143/11107271*a^4 - 95724702685/11107271*a^3 - 10472865097/11107271*a^2 + 11880604573/11107271*a + 142368927/1586753)*q^7 + (a^3 - 4*a)*q^8 + (-40326507/11107271*a^16 + 7012377/1586753*a^15 + 151773551/1586753*a^14 - 1340855037/11107271*a^13 - 11062061824/11107271*a^12 + 14306805063/11107271*a^11 + 57702618949/11107271*a^10 - 10739526779/1586753*a^9 - 3223836327/226679*a^8 + 202279847143/11107271*a^7 + 217699265401/11107271*a^6 - 265111857765/11107271*a^5 - 128705356679/11107271*a^4 + 144216800690/11107271*a^3 + 16680675317/11107271*a^2 - 17999251300/11107271*a - 216160587/1586753)*q^9 + (-4122295/1586753*a^16 + 5017302/1586753*a^15 + 108768097/1586753*a^14 - 136840199/1586753*a^13 - 1134811714/1586753*a^12 + 1458248663/1586753*a^11 + 5936367239/1586753*a^10 - 7655403109/1586753*a^9 - 16319823327/1586753*a^8 + 20585942035/1586753*a^7 + 22632312221/1586753*a^6 - 26970048652/1586753*a^5 - 13508572199/1586753*a^4 + 14663774019/1586753*a^3 + 1795438133/1586753*a^2 - 1825858142/1586753*a - 22511799/226679)*q^10 + (11795867/11107271*a^16 - 1932394/1586753*a^15 - 44322451/1586753*a^14 + 372521827/11107271*a^13 + 3225743447/11107271*a^12 - 4005866463/11107271*a^11 - 16804920021/11107271*a^10 + 3031135855/1586753*a^9 + 6564330462/1586753*a^8 - 57627409134/11107271*a^7 - 63241803565/11107271*a^6 + 76509429271/11107271*a^5 + 37396414775/11107271*a^4 - 42451276279/11107271*a^3 - 5056555641/11107271*a^2 + 5464612926/11107271*a + 75908807/1586753)*q^11 + (-6318568/11107271*a^16 + 1424523/1586753*a^15 + 24092290/1586753*a^14 - 266400152/11107271*a^13 - 1779777190/11107271*a^12 + 2788970553/11107271*a^11 + 9418174846/11107271*a^10 - 2061193450/1586753*a^9 - 3743927839/1586753*a^8 + 38336253602/11107271*a^7 + 36819759328/11107271*a^6 - 49677513962/11107271*a^5 - 22156874898/11107271*a^4 + 26702252882/11107271*a^3 + 2714390698/11107271*a^2 - 3370616034/11107271*a - 33350841/1586753)*q^12 + (12932667/11107271*a^16 - 2279337/1586753*a^15 - 48752987/1586753*a^14 + 433764071/11107271*a^13 + 3560780261/11107271*a^12 - 4604482467/11107271*a^11 - 18627365653/11107271*a^10 + 3435101051/1586753*a^9 + 7316629361/1586753*a^8 - 64145365971/11107271*a^7 - 71086180147/11107271*a^6 + 82910826763/11107271*a^5 + 42558283977/11107271*a^4 - 44016310883/11107271*a^3 - 5687517959/11107271*a^2 + 5215960508/11107271*a + 67672208/1586753)*q^13 + (-4808908/1586753*a^16 + 5796543/1586753*a^15 + 126766391/1586753*a^14 - 158300669/1586753*a^13 - 1320950081/1586753*a^12 + 1688387147/1586753*a^11 + 6898052673/1586753*a^10 - 8866087387/1586753*a^9 - 18915396805/1586753*a^8 + 23830351865/1586753*a^7 + 26134675017/1586753*a^6 - 31173785759/1586753*a^5 - 15520035683/1586753*a^4 + 16899635769/1586753*a^3 + 2042035083/1586753*a^2 - 2091532857/1586753*a - 25677032/226679)*q^14 + (-36280233/11107271*a^16 + 6756275/1586753*a^15 + 137081748/1586753*a^14 - 1281596277/11107271*a^13 - 10034246150/11107271*a^12 + 13578645544/11107271*a^11 + 52603913191/11107271*a^10 - 10129810610/1586753*a^9 - 20707252022/1586753*a^8 + 189684933246/11107271*a^7 + 201718786246/11107271*a^6 - 247013229219/11107271*a^5 - 121377536570/11107271*a^4 + 133344739412/11107271*a^3 + 16781354739/11107271*a^2 - 16683671513/11107271*a - 215351389/1586753)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (21279582/11107271*a^16 - 576557/226679*a^15 - 11490920/226679*a^14 + 764328658/11107271*a^13 + 5888803376/11107271*a^12 - 8085603784/11107271*a^11 - 30866495077/11107271*a^10 + 6022752188/1586753*a^9 + 12144661700/1586753*a^8 - 112598812800/11107271*a^7 - 118266415576/11107271*a^6 + 146376439975/11107271*a^5 + 71289580280/11107271*a^4 - 78898734658/11107271*a^3 - 10026490116/11107271*a^2 + 9892317506/11107271*a + 131645167/1586753)*q^17 + (7012377/1586753*a^16 - 9532477/1586753*a^15 - 185789790/1586753*a^14 + 257441987/1586753*a^13 + 1945893492/1586753*a^12 - 2719817696/1586753*a^11 - 10215282188/1586753*a^10 + 14170593588/1586753*a^9 + 28177004824/1586753*a^8 - 37841149124/1586753*a^7 - 39215419128/1586753*a^6 + 49206507136/1586753*a^5 + 23500147673/1586753*a^4 - 26508108184/1586753*a^3 - 3112848994/1586753*a^2 + 3292245522/1586753*a + 40326507/226679)*q^18 + (17310495/11107271*a^16 - 3414606/1586753*a^15 - 65437688/1586753*a^14 + 645668596/11107271*a^13 + 4788816728/11107271*a^12 - 6824305772/11107271*a^11 - 25069140146/11107271*a^10 + 5083421254/1586753*a^9 + 9834005994/1586753*a^8 - 95167008616/11107271*a^7 - 95086769046/11107271*a^6 + 124129226300/11107271*a^5 + 56185475128/11107271*a^4 - 67333009400/11107271*a^3 - 7048228324/11107271*a^2 + 8503642143/11107271*a + 97915806/1586753)*q^19 + (-9902484/11107271*a^16 + 1588427/1586753*a^15 + 37341884/1586753*a^14 - 306374219/11107271*a^13 - 2729577440/11107271*a^12 + 3294244140/11107271*a^11 + 14302505864/11107271*a^10 - 2489989364/1586753*a^9 - 805005200/226679*a^8 + 47211132020/11107271*a^7 + 55080405067/11107271*a^6 - 62353667508/11107271*a^5 - 33520175378/11107271*a^4 + 34328041948/11107271*a^3 + 5007030600/11107271*a^2 - 4433650216/11107271*a - 63344287/1586753)*q^20 + (-60389393/11107271*a^16 + 11166166/1586753*a^15 + 228189755/1586753*a^14 - 2121785233/11107271*a^13 - 16704515587/11107271*a^12 + 22522996135/11107271*a^11 + 87572121447/11107271*a^10 - 16839940973/1586753*a^9 - 34457385811/1586753*a^8 + 316253630139/11107271*a^7 + 334942204895/11107271*a^6 - 413450505207/11107271*a^5 - 199657525257/11107271*a^4 + 224025771901/11107271*a^3 + 25793598659/11107271*a^2 - 27640305732/11107271*a - 332347363/1586753)*q^21 + (-1932394/1586753*a^16 + 2861017/1586753*a^15 + 51532280/1586753*a^14 - 76734018/1586753*a^13 - 543619532/1586753*a^12 + 806087840/1586753*a^11 + 2877789584/1586753*a^10 - 4181704375/1586753*a^9 - 8021846537/1586753*a^8 + 11131333832/1586753*a^7 + 11322552326/1586753*a^6 - 14429213248/1586753*a^5 - 6912085340/1586753*a^4 + 7728531052/1586753*a^3 + 939060632/1586753*a^2 - 950331622/1586753*a - 11795867/226679)*q^22 + (31722361/11107271*a^16 - 5850154/1586753*a^15 - 119732695/1586753*a^14 + 1112154343/11107271*a^13 + 8752755413/11107271*a^12 - 11810292925/11107271*a^11 - 45803042055/11107271*a^10 + 8833142877/1586753*a^9 + 17978970083/1586753*a^8 - 165930762117/11107271*a^7 - 174209659179/11107271*a^6 + 216989136849/11107271*a^5 + 103470227181/11107271*a^4 - 117637416119/11107271*a^3 - 13353180733/11107271*a^2 + 14550510082/11107271*a + 176544419/1586753)*q^23 + (7157613/1586753*a^16 - 8960306/1586753*a^15 - 189063898/1586753*a^14 + 244025764/1586753*a^13 + 1974646909/1586753*a^12 - 2597759796/1586753*a^11 - 10339914094/1586753*a^10 + 13629806955/1586753*a^9 + 28452243608/1586753*a^8 - 36650622628/1586753*a^7 - 39493320416/1586753*a^6 + 48040013676/1586753*a^5 + 23589118460/1586753*a^4 - 26140555528/1586753*a^3 - 3126639512/1586753*a^2 + 3260768103/1586753*a + 39861270/226679)*q^24 + (-25462033/11107271*a^16 + 4395613/1586753*a^15 + 95804186/1586753*a^14 - 839651038/11107271*a^13 - 6980479892/11107271*a^12 + 8946254792/11107271*a^11 + 36397594000/11107271*a^10 - 957366636/226679*a^9 - 14228060939/1586753*a^8 + 125828529167/11107271*a^7 + 137208083944/11107271*a^6 - 164162253174/11107271*a^5 - 81202433244/11107271*a^4 + 88842208296/11107271*a^3 + 10692881072/11107271*a^2 - 11137228887/11107271*a - 134495476/1586753)*q^25 + (-2279337/1586753*a^16 + 425383/226679*a^15 + 8588396/226679*a^14 - 80677216/1586753*a^13 - 626375304/1586753*a^12 + 854785664/1586753*a^11 + 3266976380/1586753*a^10 - 637861468/226679*a^9 - 1276097604/226679*a^8 + 11954149406/1586753*a^7 + 12274876882/1586753*a^6 - 15597242562/1586753*a^5 - 7217348912/1586753*a^4 + 8452829578/1586753*a^3 + 918804458/1586753*a^2 - 1057469821/1586753*a - 12932667/226679)*q^26 + (42256325/11107271*a^16 - 6785852/1586753*a^15 - 159054515/1586753*a^14 + 1305111919/11107271*a^13 + 11603698718/11107271*a^12 - 13991580215/11107271*a^11 - 60661871593/11107271*a^10 + 10540136738/1586753*a^9 + 23820822709/1586753*a^8 - 198956641101/11107271*a^7 - 231309666626/11107271*a^6 + 260869534865/11107271*a^5 + 138106652683/11107271*a^4 - 141473618446/11107271*a^3 - 18317061865/11107271*a^2 + 17298885530/11107271*a + 214943577/1586753)*q^27 + (-10778263/11107271*a^16 + 1734783/1586753*a^15 + 40331409/1586753*a^14 - 334442541/11107271*a^13 - 2919287073/11107271*a^12 + 3593225465/11107271*a^11 + 15090026421/11107271*a^10 - 387528381/226679*a^9 - 5822139165/1586753*a^8 + 51340124137/11107271*a^7 + 54869328517/11107271*a^6 - 67599780159/11107271*a^5 - 30874616835/11107271*a^4 + 36926935611/11107271*a^3 + 3140738731/11107271*a^2 - 4519008910/11107271*a - 49101362/1586753)*q^28 + (37599616/11107271*a^16 - 6005504/1586753*a^15 - 141443329/1586753*a^14 + 1156074400/11107271*a^13 + 10313257723/11107271*a^12 - 12402758789/11107271*a^11 - 53893343681/11107271*a^10 + 9348637439/1586753*a^9 + 21162527937/1586753*a^8 - 176565199519/11107271*a^7 - 205761663785/11107271*a^6 + 231733252097/11107271*a^5 + 123644621259/11107271*a^4 - 126013913667/11107271*a^3 - 17196071544/11107271*a^2 + 15589598961/11107271*a + 203454605/1586753)*q^29 + (6756275/1586753*a^16 - 8039184/1586753*a^15 - 177902292/1586753*a^14 + 219878311/1586753*a^13 + 1851697369/1586753*a^12 - 2348195744/1586753*a^11 - 9658167581/1586753*a^10 + 12344040241/1586753*a^9 + 26449986303/1586753*a^8 - 33206680295/1586753*a^7 - 36495217644/1586753*a^6 + 43471205317/1586753*a^5 + 21656242373/1586753*a^4 - 23594859108/1586753*a^3 - 2870573345/1586753*a^2 + 2941028882/1586753*a + 36280233/226679)*q^30 + (-24153904/11107271*a^16 + 4321005/1586753*a^15 + 91255413/1586753*a^14 - 822194252/11107271*a^13 - 6682216498/11107271*a^12 + 8733648358/11107271*a^11 + 35066854706/11107271*a^10 - 6528082826/1586753*a^9 - 1975726498/226679*a^8 + 122383812294/11107271*a^7 + 135081794294/11107271*a^6 - 159364496414/11107271*a^5 - 81358052074/11107271*a^4 + 85759333630/11107271*a^3 + 10925236722/11107271*a^2 - 10535502669/11107271*a - 128905963/1586753)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-67423899/11107271*a^16 + 1675760/226679*a^15 + 36336930/226679*a^14 - 2238101394/11107271*a^13 - 18596294425/11107271*a^12 + 23828089507/11107271*a^11 + 97422150367/11107271*a^10 - 17843348701/1586753*a^9 - 38348772811/1586753*a^8 + 335017240785/11107271*a^7 + 373830398447/11107271*a^6 - 436921975895/11107271*a^5 - 225166281001/11107271*a^4 + 235699120185/11107271*a^3 + 31079452962/11107271*a^2 - 29079193803/11107271*a - 381202163/1586753)*q^33 + (-576557/226679*a^16 + 4681888/1586753*a^15 + 106149868/1586753*a^14 - 128483326/1586753*a^13 - 157629610/226679*a^12 + 1375507067/1586753*a^11 + 820873946/226679*a^10 - 7241037502/1586753*a^9 - 15705552150/1586753*a^8 + 19483763174/1586753*a^7 + 3088460869/226679*a^6 - 25483393618/1586753*a^5 - 12800337772/1586753*a^4 + 13812944802/1586753*a^3 + 242706086/226679*a^2 - 1719678467/1586753*a - 21279582/226679)*q^34 + (-53415365/11107271*a^16 + 9336701/1586753*a^15 + 201488144/1586753*a^14 - 1783241386/11107271*a^13 - 14727403738/11107271*a^12 + 19012774104/11107271*a^11 + 77112264086/11107271*a^10 - 14267804958/1586753*a^9 - 30314587188/1586753*a^8 + 268767500488/11107271*a^7 + 294505713500/11107271*a^6 - 352301417140/11107271*a^5 - 175561828396/11107271*a^4 + 191294580606/11107271*a^3 + 22872039584/11107271*a^2 - 23488614189/11107271*a - 295067627/1586753)*q^35 + (13925675/11107271*a^16 - 3467988/1586753*a^15 - 53117492/1586753*a^14 + 644326677/11107271*a^13 + 3919872639/11107271*a^12 - 6708711425/11107271*a^11 - 20677966931/11107271*a^10 + 705447179/226679*a^9 + 8169106579/1586753*a^8 - 91647819269/11107271*a^7 - 79515793963/11107271*a^6 + 118791213854/11107271*a^5 + 47163376653/11107271*a^4 - 64054049753/11107271*a^3 - 5701487914/11107271*a^2 + 8080738292/11107271*a + 88714701/1586753)*q^36 + (58834648/11107271*a^16 - 10469071/1586753*a^15 - 221869889/1586753*a^14 + 1994193703/11107271*a^13 + 16206951361/11107271*a^12 - 21201818723/11107271*a^11 - 84762261663/11107271*a^10 + 15858972953/1586753*a^9 + 33262149523/1586753*a^8 - 297518575153/11107271*a^7 - 322391208789/11107271*a^6 + 387851937953/11107271*a^5 + 191863930809/11107271*a^4 - 209242126735/11107271*a^3 - 25038696915/11107271*a^2 + 25744954717/11107271*a + 307195088/1586753)*q^37 + O(q^38)
*]> ;  // time = 3.649 seconds




J[241] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 241, 241 ], new_dimensions := [ 7, 12 ], dimensions := [ 7, 12 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -4, -3, -8, -7, -18, -1, -2, -6, -22, -16, -18, 8 ],
[ 3, 1, 6, 3, 22, -5, -4, -6, 32, 6, 8, -8 ]
], hecke_fields := [
x^7 + 4*x^6 - 14*x^4 - 10*x^3 + 6*x^2 + 3*x - 1,
x^12 - 3*x^11 - 14*x^10 + 44*x^9 + 65*x^8 - 219*x^7 - 123*x^6 + 444*x^5 + 105*x^4 - 328*x^3 - 45*x^2 + 18*x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 5 ]
], tamagawa_numbers := [
[ 1 ],
[ 5 ]
], torsion_upper_bounds := [ 1, 5 ], torsion_lower_bounds := [ 1, 5 ], l_ratios := [ 0, 1/5 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^6 - 3*a^5 + 3*a^4 + 11*a^3 - a^2 - 6*a + 1,
a^6 + 2*a^5 - 6*a^4 - 9*a^3 + 10*a^2 + 8*a - 4,
2*a^6 + 9*a^5 + 3*a^4 - 29*a^3 - 28*a^2 + 4*a + 3,
-2*a^6 - 8*a^5 - 2*a^4 + 23*a^3 + 26*a^2 + 3*a - 8,
2*a^6 + 7*a^5 - a^4 - 21*a^3 - 15*a^2 + 2*a + 1,
-5*a^6 - 21*a^5 - 4*a^4 + 68*a^3 + 60*a^2 - 12*a - 10,
-2*a^6 - 4*a^5 + 11*a^4 + 17*a^3 - 16*a^2 - 14*a + 4,
a^6 + 4*a^5 + a^4 - 13*a^3 - 15*a^2 + 3*a + 2,
5*a^6 + 20*a^5 + 3*a^4 - 63*a^3 - 60*a^2 + 8*a + 12,
3*a^6 + 13*a^5 + 5*a^4 - 39*a^3 - 46*a^2 - a + 8,
a^5 + a^4 - 6*a^3 - 5*a^2 + 6*a + 6
],
[
a,
11/8*a^11 - 15/4*a^10 - 79/4*a^9 + 54*a^8 + 773/8*a^7 - 1043/4*a^6 - 1631/8*a^5 + 4025/8*a^4 + 827/4*a^3 - 1375/4*a^2 - 741/8*a + 93/8,
11/8*a^11 - 17/4*a^10 - 75/4*a^9 + 123/2*a^8 + 669/8*a^7 - 1199/4*a^6 - 1223/8*a^5 + 4717/8*a^4 + 589/4*a^3 - 1677/4*a^2 - 737/8*a + 117/8,
-15/16*a^11 + 7/4*a^10 + 61/4*a^9 - 205/8*a^8 - 1415/16*a^7 + 1011/8*a^6 + 3567/16*a^5 - 3951/16*a^4 - 1809/8*a^3 + 1283/8*a^2 + 813/16*a - 71/16,
-5/4*a^11 + 31/8*a^10 + 135/8*a^9 - 445/8*a^8 - 589/8*a^7 + 535/2*a^6 + 255/2*a^5 - 4119/8*a^4 - 443/4*a^3 + 711/2*a^2 + 65*a - 85/8,
7/8*a^11 - 5/2*a^10 - 25/2*a^9 + 145/4*a^8 + 487/8*a^7 - 707/4*a^6 - 1039/8*a^5 + 2759/8*a^4 + 569/4*a^3 - 947/4*a^2 - 613/8*a + 47/8,
-13/8*a^11 + 7/2*a^10 + 53/2*a^9 - 215/4*a^8 - 1237/8*a^7 + 1141/4*a^6 + 3173/8*a^5 - 4981/8*a^4 - 1715/4*a^3 + 1909/4*a^2 + 1127/8*a - 133/8,
5/16*a^11 - 7/8*a^10 - 27/8*a^9 + 41/4*a^8 + 111/16*a^7 - 249/8*a^6 + 287/16*a^5 + 99/16*a^4 - 423/8*a^3 + 311/8*a^2 + 501/16*a + 15/16,
9/16*a^11 - 15/8*a^10 - 59/8*a^9 + 107/4*a^8 + 483/16*a^7 - 1013/8*a^6 - 709/16*a^5 + 3751/16*a^4 + 205/8*a^3 - 1189/8*a^2 - 167/16*a + 99/16,
-11/4*a^11 + 17/2*a^10 + 38*a^9 - 124*a^8 - 695/4*a^7 + 1223/2*a^6 + 1323/4*a^5 - 4881/4*a^4 - 321*a^3 + 876*a^2 + 727/4*a - 115/4,
1/2*a^11 + 1/8*a^10 - 71/8*a^9 - 39/8*a^8 + 447/8*a^7 + 49*a^6 - 575/4*a^5 - 1439/8*a^4 + 425/4*a^3 + 219*a^2 + 233/4*a - 73/8,
-a^11 + 13/4*a^10 + 57/4*a^9 - 199/4*a^8 - 273/4*a^7 + 264*a^6 + 275/2*a^5 - 2335/4*a^4 - 277/2*a^3 + 471*a^2 + 181/2*a - 81/4
]
*], q_expansions := [*
q + a*q^2 + (-a^6 - 3*a^5 + 3*a^4 + 11*a^3 - a^2 - 6*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^6 + 2*a^5 - 6*a^4 - 9*a^3 + 10*a^2 + 8*a - 4)*q^5 + (a^6 + 3*a^5 - 3*a^4 - 11*a^3 + 4*a - 1)*q^6 + (2*a^6 + 9*a^5 + 3*a^4 - 29*a^3 - 28*a^2 + 4*a + 3)*q^7 + (a^3 - 4*a)*q^8 + (-a^5 - 2*a^4 + 5*a^3 + 7*a^2 - 5*a - 2)*q^9 + (-2*a^6 - 6*a^5 + 5*a^4 + 20*a^3 + 2*a^2 - 7*a + 1)*q^10 + (-2*a^6 - 8*a^5 - 2*a^4 + 23*a^3 + 26*a^2 + 3*a - 8)*q^11 + (a^6 + 3*a^5 - 3*a^4 - 12*a^3 + 8*a - 1)*q^12 + (2*a^6 + 7*a^5 - a^4 - 21*a^3 - 15*a^2 + 2*a + 1)*q^13 + (a^6 + 3*a^5 - a^4 - 8*a^3 - 8*a^2 - 3*a + 2)*q^14 + (a^6 + 5*a^5 + 2*a^4 - 18*a^3 - 14*a^2 + 11*a - 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-5*a^6 - 21*a^5 - 4*a^4 + 68*a^3 + 60*a^2 - 12*a - 10)*q^17 + (-a^6 - 2*a^5 + 5*a^4 + 7*a^3 - 5*a^2 - 2*a)*q^18 + (-2*a^6 - 4*a^5 + 11*a^4 + 17*a^3 - 16*a^2 - 14*a + 4)*q^19 + (a^5 + 4*a^4 - 15*a^2 - 9*a + 6)*q^20 + (a^6 + 2*a^5 - 7*a^4 - 11*a^3 + 15*a^2 + 16*a - 6)*q^21 + (-2*a^5 - 5*a^4 + 6*a^3 + 15*a^2 - 2*a - 2)*q^22 + (a^6 + 4*a^5 + a^4 - 13*a^3 - 15*a^2 + 3*a + 2)*q^23 + (-3*a^6 - 9*a^5 + 8*a^4 + 32*a^3 + 2*a^2 - 12*a + 3)*q^24 + (-2*a^6 - 7*a^5 + 4*a^4 + 28*a^3 + 6*a^2 - 20*a + 1)*q^25 + (-a^6 - a^5 + 7*a^4 + 5*a^3 - 10*a^2 - 5*a + 2)*q^26 + (-a^4 - 2*a^3 + 3*a^2 + 6*a + 1)*q^27 + (-5*a^6 - 19*a^5 + 60*a^3 + 47*a^2 - 9*a - 5)*q^28 + (5*a^6 + 20*a^5 + 3*a^4 - 63*a^3 - 60*a^2 + 8*a + 12)*q^29 + (a^6 + 2*a^5 - 4*a^4 - 4*a^3 + 5*a^2 - 4*a + 1)*q^30 + (3*a^6 + 13*a^5 + 5*a^4 - 39*a^3 - 46*a^2 - a + 8)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (6*a^6 + 20*a^5 - 11*a^4 - 69*a^3 - 18*a^2 + 26*a - 2)*q^33 + (-a^6 - 4*a^5 - 2*a^4 + 10*a^3 + 18*a^2 + 5*a - 5)*q^34 + (-2*a^6 - 7*a^5 + 6*a^4 + 31*a^3 - 2*a^2 - 26*a + 5)*q^35 + (2*a^6 + 7*a^5 - 3*a^4 - 25*a^3 - 10*a^2 + 13*a + 3)*q^36 + (a^5 + a^4 - 6*a^3 - 5*a^2 + 6*a + 6)*q^37 + O(q^38),
q + a*q^2 + (11/8*a^11 - 15/4*a^10 - 79/4*a^9 + 54*a^8 + 773/8*a^7 - 1043/4*a^6 - 1631/8*a^5 + 4025/8*a^4 + 827/4*a^3 - 1375/4*a^2 - 741/8*a + 93/8)*q^3 + (a^2 - 2)*q^4 + (11/8*a^11 - 17/4*a^10 - 75/4*a^9 + 123/2*a^8 + 669/8*a^7 - 1199/4*a^6 - 1223/8*a^5 + 4717/8*a^4 + 589/4*a^3 - 1677/4*a^2 - 737/8*a + 117/8)*q^5 + (3/8*a^11 - 1/2*a^10 - 13/2*a^9 + 29/4*a^8 + 323/8*a^7 - 139/4*a^6 - 859/8*a^5 + 499/8*a^4 + 429/4*a^3 - 123/4*a^2 - 105/8*a + 11/8)*q^6 + (-15/16*a^11 + 7/4*a^10 + 61/4*a^9 - 205/8*a^8 - 1415/16*a^7 + 1011/8*a^6 + 3567/16*a^5 - 3951/16*a^4 - 1809/8*a^3 + 1283/8*a^2 + 813/16*a - 71/16)*q^7 + (a^3 - 4*a)*q^8 + (-3/2*a^11 + 5*a^10 + 20*a^9 - 73*a^8 - 171/2*a^7 + 361*a^6 + 293/2*a^5 - 1453/2*a^4 - 149*a^3 + 532*a^2 + 251/2*a - 27/2)*q^9 + (-1/8*a^11 + 1/2*a^10 + a^9 - 23/4*a^8 + 11/8*a^7 + 65/4*a^6 - 167/8*a^5 + 23/8*a^4 + 127/4*a^3 - 121/4*a^2 - 81/8*a + 11/8)*q^10 + (-5/4*a^11 + 31/8*a^10 + 135/8*a^9 - 445/8*a^8 - 589/8*a^7 + 535/2*a^6 + 255/2*a^5 - 4119/8*a^4 - 443/4*a^3 + 711/2*a^2 + 65*a - 85/8)*q^11 + (-17/8*a^11 + 25/4*a^10 + 121/4*a^9 - 92*a^8 - 1167/8*a^7 + 1841/4*a^6 + 2429/8*a^5 - 7507/8*a^4 - 1285/4*a^3 + 2765/4*a^2 + 1439/8*a - 183/8)*q^12 + (7/8*a^11 - 5/2*a^10 - 25/2*a^9 + 145/4*a^8 + 487/8*a^7 - 707/4*a^6 - 1039/8*a^5 + 2759/8*a^4 + 569/4*a^3 - 947/4*a^2 - 613/8*a + 47/8)*q^13 + (-17/16*a^11 + 17/8*a^10 + 125/8*a^9 - 55/2*a^8 - 1263/16*a^7 + 861/8*a^6 + 2709/16*a^5 - 2043/16*a^4 - 1177/8*a^3 + 69/8*a^2 + 199/16*a - 15/16)*q^14 + (7/8*a^11 - 2*a^10 - 14*a^9 + 123/4*a^8 + 635/8*a^7 - 655/4*a^6 - 1559/8*a^5 + 2883/8*a^4 + 785/4*a^3 - 1127/4*a^2 - 461/8*a + 115/8)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-13/8*a^11 + 7/2*a^10 + 53/2*a^9 - 215/4*a^8 - 1237/8*a^7 + 1141/4*a^6 + 3173/8*a^5 - 4981/8*a^4 - 1715/4*a^3 + 1909/4*a^2 + 1127/8*a - 133/8)*q^17 + (1/2*a^11 - a^10 - 7*a^9 + 12*a^8 + 65/2*a^7 - 38*a^6 - 121/2*a^5 + 17/2*a^4 + 40*a^3 + 58*a^2 + 27/2*a - 3/2)*q^18 + (5/16*a^11 - 7/8*a^10 - 27/8*a^9 + 41/4*a^8 + 111/16*a^7 - 249/8*a^6 + 287/16*a^5 + 99/16*a^4 - 423/8*a^3 + 311/8*a^2 + 501/16*a + 15/16)*q^19 + (-21/8*a^11 + 31/4*a^10 + 149/4*a^9 - 227/2*a^8 - 1427/8*a^7 + 2253/4*a^6 + 2913/8*a^5 - 9075/8*a^4 - 1463/4*a^3 + 3291/4*a^2 + 1503/8*a - 235/8)*q^20 + (2*a^11 - 23/4*a^10 - 119/4*a^9 + 349/4*a^8 + 615/4*a^7 - 457*a^6 - 701/2*a^5 + 3969/4*a^4 + 779/2*a^3 - 780*a^2 - 425/2*a + 95/4)*q^21 + (1/8*a^11 - 5/8*a^10 - 5/8*a^9 + 61/8*a^8 - 25/4*a^7 - 105/4*a^6 + 321/8*a^5 + 41/2*a^4 - 109/2*a^3 + 35/4*a^2 + 95/8*a - 5/4)*q^22 + (9/16*a^11 - 15/8*a^10 - 59/8*a^9 + 107/4*a^8 + 483/16*a^7 - 1013/8*a^6 - 709/16*a^5 + 3751/16*a^4 + 205/8*a^3 - 1189/8*a^2 - 167/16*a + 99/16)*q^23 + (-7/8*a^11 + 3/2*a^10 + 29/2*a^9 - 89/4*a^8 - 687/8*a^7 + 447/4*a^6 + 1759/8*a^5 - 1783/8*a^4 - 881/4*a^3 + 583/4*a^2 + 333/8*a - 39/8)*q^24 + (7/2*a^11 - 10*a^10 - 103/2*a^9 + 150*a^8 + 261*a^7 - 772*a^6 - 1147/2*a^5 + 3271/2*a^4 + 1187/2*a^3 - 2503/2*a^2 - 283*a + 45)*q^25 + (1/8*a^11 - 1/4*a^10 - 9/4*a^9 + 4*a^8 + 119/8*a^7 - 89/4*a^6 - 349/8*a^5 + 403/8*a^4 + 201/4*a^3 - 149/4*a^2 - 79/8*a + 7/8)*q^26 + (9/4*a^11 - 13/2*a^10 - 65/2*a^9 + 96*a^8 + 643/4*a^7 - 965/2*a^6 - 1389/4*a^5 + 3951/4*a^4 + 745/2*a^3 - 1443/2*a^2 - 779/4*a + 63/4)*q^27 + (13/16*a^11 - 11/4*a^10 - 45/4*a^9 + 331/8*a^8 + 829/16*a^7 - 1713/8*a^6 - 1629/16*a^5 + 7333/16*a^4 + 899/8*a^3 - 2849/8*a^2 - 1335/16*a + 125/16)*q^28 + (-11/4*a^11 + 17/2*a^10 + 38*a^9 - 124*a^8 - 695/4*a^7 + 1223/2*a^6 + 1323/4*a^5 - 4881/4*a^4 - 321*a^3 + 876*a^2 + 727/4*a - 115/4)*q^29 + (5/8*a^11 - 7/4*a^10 - 31/4*a^9 + 45/2*a^8 + 223/8*a^7 - 349/4*a^6 - 225/8*a^5 + 835/8*a^4 + 21/4*a^3 - 73/4*a^2 - 11/8*a + 7/8)*q^30 + (1/2*a^11 + 1/8*a^10 - 71/8*a^9 - 39/8*a^8 + 447/8*a^7 + 49*a^6 - 575/4*a^5 - 1439/8*a^4 + 425/4*a^3 + 219*a^2 + 233/4*a - 73/8)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^9 - 3*a^8 - 12*a^7 + 38*a^6 + 40*a^5 - 143*a^4 - 30*a^3 + 156*a^2 - 5*a - 6)*q^33 + (-11/8*a^11 + 15/4*a^10 + 71/4*a^9 - 49*a^8 - 565/8*a^7 + 787/4*a^6 + 791/8*a^5 - 2065/8*a^4 - 223/4*a^3 + 271/4*a^2 + 101/8*a - 13/8)*q^34 + (11/16*a^11 - 19/8*a^10 - 87/8*a^9 + 79/2*a^8 + 981/16*a^7 - 1863/8*a^6 - 2487/16*a^5 + 9241/16*a^4 + 1531/8*a^3 - 4071/8*a^2 - 1949/16*a + 261/16)*q^35 + (7/2*a^11 - 10*a^10 - 50*a^9 + 146*a^8 + 485/2*a^7 - 721*a^6 - 1013/2*a^5 + 2881/2*a^4 + 520*a^3 - 1028*a^2 - 523/2*a + 55/2)*q^36 + (-a^11 + 13/4*a^10 + 57/4*a^9 - 199/4*a^8 - 273/4*a^7 + 264*a^6 + 275/2*a^5 - 2335/4*a^4 - 277/2*a^3 + 471*a^2 + 181/2*a - 81/4)*q^37 + O(q^38)
*]> ;  // time = 3.16 seconds




J[246] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 246, 246, 246, 246, 246, 246, 246, 123, 123, 123, 123, 82, 82, 41 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 2, 3 ], dimensions := [ 1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 6, 2, 4, 12 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 0, 5, 1, 1, 1, 1, 1, 7, 1, 3, 1, 1, 1, 1, 5, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 0, 3, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 25, 1, 1, 7, 1, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 529, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 1, 5, 1, 1, 25, 1, 529, 1, 1, 0 ], ap_traces := [
[ -1, -1, -2, 2, -4, -4, -2, -8, 4, -8, 4, 2 ],
[ -1, -1, 3, -2, 2, 1, 5, -1, 6, 8, 3, -6 ],
[ -1, 1, -2, 2, 4, 4, -2, 0, 4, 0, 4, 2 ],
[ -1, 1, 3, 2, -6, -1, 3, 5, -6, 0, -1, 2 ],
[ 1, -1, 1, 2, 2, -7, 7, 7, -2, -8, -5, -10 ],
[ 1, 1, 1, -2, 2, -1, -7, 5, -6, 0, 7, -2 ],
[ 1, 1, -2, 4, -4, 2, 2, -4, 0, -6, -8, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 3, 1, 1 ],
[ 11, 1, 1 ],
[ 7, 3, 1 ],
[ 1, 3, 1 ],
[ 3, 7, 1 ],
[ 25, 5, 1 ],
[ 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 3, 1 ],
[ 3, 1, 1 ],
[ 25, 5, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 1, 5, 1 ], torsion_lower_bounds := [ 1, 1, 1, 3, 1, 1, 1 ], l_ratios := [ 0, 1, 3, 1/3, 3, 5, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 1, 1/25, 1 ], eigenvalues := [*
[ -1, -1, -2, 2, -4, -4, -2, -8, 4, -8, 4, 2 ],
[ -1, -1, 3, -2, 2, 1, 5, -1, 6, 8, 3, -6 ],
[ -1, 1, -2, 2, 4, 4, -2, 0, 4, 0, 4, 2 ],
[ -1, 1, 3, 2, -6, -1, 3, 5, -6, 0, -1, 2 ],
[ 1, -1, 1, 2, 2, -7, 7, 7, -2, -8, -5, -10 ],
[ 1, 1, 1, -2, 2, -1, -7, 5, -6, 0, 7, -2 ],
[ 1, 1, -2, 4, -4, 2, 2, -4, 0, -6, -8, -2 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - 2*q^5 + q^6 + 2*q^7 - q^8 + q^9 + 2*q^10 - 4*q^11 - q^12 - 4*q^13 - 2*q^14 + 2*q^15 + q^16 - 2*q^17 - q^18 - 8*q^19 - 2*q^20 - 2*q^21 + 4*q^22 + 4*q^23 + q^24 - q^25 + 4*q^26 - q^27 + 2*q^28 - 8*q^29 - 2*q^30 + 4*q^31 - q^32 + 4*q^33 + 2*q^34 - 4*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + 3*q^5 + q^6 - 2*q^7 - q^8 + q^9 - 3*q^10 + 2*q^11 - q^12 + q^13 + 2*q^14 - 3*q^15 + q^16 + 5*q^17 - q^18 - q^19 + 3*q^20 + 2*q^21 - 2*q^22 + 6*q^23 + q^24 + 4*q^25 - q^26 - q^27 - 2*q^28 + 8*q^29 + 3*q^30 + 3*q^31 - q^32 - 2*q^33 - 5*q^34 - 6*q^35 + q^36 - 6*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - 2*q^5 - q^6 + 2*q^7 - q^8 + q^9 + 2*q^10 + 4*q^11 + q^12 + 4*q^13 - 2*q^14 - 2*q^15 + q^16 - 2*q^17 - q^18 - 2*q^20 + 2*q^21 - 4*q^22 + 4*q^23 - q^24 - q^25 - 4*q^26 + q^27 + 2*q^28 + 2*q^30 + 4*q^31 - q^32 + 4*q^33 + 2*q^34 - 4*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + 3*q^5 - q^6 + 2*q^7 - q^8 + q^9 - 3*q^10 - 6*q^11 + q^12 - q^13 - 2*q^14 + 3*q^15 + q^16 + 3*q^17 - q^18 + 5*q^19 + 3*q^20 + 2*q^21 + 6*q^22 - 6*q^23 - q^24 + 4*q^25 + q^26 + q^27 + 2*q^28 - 3*q^30 - q^31 - q^32 - 6*q^33 - 3*q^34 + 6*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + 2*q^7 + q^8 + q^9 + q^10 + 2*q^11 - q^12 - 7*q^13 + 2*q^14 - q^15 + q^16 + 7*q^17 + q^18 + 7*q^19 + q^20 - 2*q^21 + 2*q^22 - 2*q^23 - q^24 - 4*q^25 - 7*q^26 - q^27 + 2*q^28 - 8*q^29 - q^30 - 5*q^31 + q^32 - 2*q^33 + 7*q^34 + 2*q^35 + q^36 - 10*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^5 + q^6 - 2*q^7 + q^8 + q^9 + q^10 + 2*q^11 + q^12 - q^13 - 2*q^14 + q^15 + q^16 - 7*q^17 + q^18 + 5*q^19 + q^20 - 2*q^21 + 2*q^22 - 6*q^23 + q^24 - 4*q^25 - q^26 + q^27 - 2*q^28 + q^30 + 7*q^31 + q^32 + 2*q^33 - 7*q^34 - 2*q^35 + q^36 - 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - 2*q^5 + q^6 + 4*q^7 + q^8 + q^9 - 2*q^10 - 4*q^11 + q^12 + 2*q^13 + 4*q^14 - 2*q^15 + q^16 + 2*q^17 + q^18 - 4*q^19 - 2*q^20 + 4*q^21 - 4*q^22 + q^24 - q^25 + 2*q^26 + q^27 + 4*q^28 - 6*q^29 - 2*q^30 - 8*q^31 + q^32 - 4*q^33 + 2*q^34 - 8*q^35 + q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 140.95 seconds




J[247] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 247, 247, 247, 247, 247, 19 ], new_dimensions := [ 2, 3, 4, 5, 5, 1 ], dimensions := [ 2, 3, 4, 5, 5, 2 ], intersection_graph := [ 0, 1, 1, 1, 31, 1, 1, 0, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 5, 31, 1, 1, 1, 0, 1, 1, 3, 1, 5, 1, 0 ], ap_traces := [
[ 1, -2, 2, -4, -6, 2, 6, -2, 8, 0, 4, 6 ],
[ -3, -3, -3, -3, 0, 3, -12, 3, -6, -15, -3, 6 ],
[ -3, -1, -8, -2, -5, -4, -15, -4, -2, 1, 7, 2 ],
[ 4, 3, 3, -1, -2, -5, 14, 5, -6, -9, -3, 6 ],
[ 0, 3, 2, 4, 7, 5, 23, -5, -2, 5, -9, -18 ]
], hecke_fields := [
x^2 - x - 1,
x^3 + 3*x^2 - 3,
x^4 + 3*x^3 - 2*x^2 - 9*x - 4,
x^5 - 4*x^4 + 12*x^2 - 5*x - 5,
x^5 - 9*x^3 - x^2 + 19*x + 4
], atkin_lehners := [
[ -1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 5, 7 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 5, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 7 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 5, 3, 1, 7, 1 ], torsion_lower_bounds := [ 5, 1, 1, 7, 1 ], l_ratios := [ 1/5, 0, 0, 1/7, 1 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 1 ], eigenvalues := [*
[
a,
2*a - 2,
2*a,
-2,
2*a - 4,
1,
-4*a + 5,
-1,
-2*a + 5,
4*a - 2,
2*a + 1,
4*a + 1
],
[
a,
-a^2 - a + 1,
-a^2 - 2*a,
2*a^2 + 3*a - 4,
a^2 - 3,
1,
a^2 + 4*a - 3,
1,
-a^2 - 4*a - 3,
2*a^2 + 5*a - 6,
-4*a^2 - 3*a + 8,
5*a^2 + 6*a - 7
],
[
a,
-a^3 - 2*a^2 + 3*a + 4,
a^3 + 2*a^2 - 4*a - 7,
a^3 + a^2 - 5*a - 3,
a^2 + 2*a - 3,
-1,
a^2 - 7,
-1,
-3*a^3 - 6*a^2 + 14*a + 16,
2*a^3 + 2*a^2 - 9*a - 4,
2*a^3 + 6*a^2 - 7*a - 14,
-5*a^3 - 10*a^2 + 18*a + 24
],
[
a,
-a^2 + a + 3,
a^3 - 2*a^2 - 2*a + 3,
-a^4 + 2*a^3 + 3*a^2 - 4*a - 1,
a^4 - 4*a^3 + 9*a - 2,
-1,
a^3 - 6*a + 2,
1,
-2*a^4 + 3*a^3 + 10*a^2 - 8*a - 10,
-3*a^4 + 6*a^3 + 11*a^2 - 14*a - 9,
a^3 - a^2 - 5*a + 1,
2*a^4 - 5*a^3 - 4*a^2 + 8*a + 2
],
[
a,
a^3 - 5*a,
-a^3 + 4*a + 1,
-a^3 - a^2 + 5*a + 5,
-a^2 + 5,
1,
a^2 + 1,
-1,
a^4 - 6*a^2 - a + 4,
-a^4 + a^3 + 6*a^2 - 6*a - 4,
a^4 + a^3 - 6*a^2 - 4*a + 2,
-a^4 + 6*a^2 - a - 8
]
*], q_expansions := [*
q + a*q^2 + (2*a - 2)*q^3 + (a - 1)*q^4 + 2*a*q^5 + 2*q^6 - 2*q^7 + (-2*a + 1)*q^8 + (-4*a + 5)*q^9 + (2*a + 2)*q^10 + (2*a - 4)*q^11 + (-2*a + 4)*q^12 + q^13 - 2*a*q^14 + 4*q^15 - 3*a*q^16 + (-4*a + 5)*q^17 + (a - 4)*q^18 - q^19 + 2*q^20 + (-4*a + 4)*q^21 + (-2*a + 2)*q^22 + (-2*a + 5)*q^23 + (2*a - 6)*q^24 + (4*a - 1)*q^25 + a*q^26 + (4*a - 12)*q^27 + (-2*a + 2)*q^28 + (4*a - 2)*q^29 + 4*a*q^30 + (2*a + 1)*q^31 + (a - 5)*q^32 + (-8*a + 12)*q^33 + (a - 4)*q^34 - 4*a*q^35 + (5*a - 9)*q^36 + (4*a + 1)*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 1)*q^3 + (a^2 - 2)*q^4 + (-a^2 - 2*a)*q^5 + (2*a^2 + a - 3)*q^6 + (2*a^2 + 3*a - 4)*q^7 + (-3*a^2 - 4*a + 3)*q^8 + (2*a^2 + a - 5)*q^9 + (a^2 - 3)*q^10 + (a^2 - 3)*q^11 + (-3*a^2 - a + 4)*q^12 + q^13 + (-3*a^2 - 4*a + 6)*q^14 + (a^2 + a)*q^15 + (3*a^2 + 3*a - 5)*q^16 + (a^2 + 4*a - 3)*q^17 + (-5*a^2 - 5*a + 6)*q^18 + q^19 + (-a^2 + a + 3)*q^20 + (a - 1)*q^21 + (-3*a^2 - 3*a + 3)*q^22 + (-a^2 - 4*a - 3)*q^23 + (4*a^2 + 2*a - 3)*q^24 + (a^2 + 3*a - 2)*q^25 + a*q^26 + (3*a + 1)*q^27 + (a^2 - 1)*q^28 + (2*a^2 + 5*a - 6)*q^29 + (-2*a^2 + 3)*q^30 + (-4*a^2 - 3*a + 8)*q^31 + (3*a + 3)*q^32 + (-2*a^2 + 3)*q^33 + (a^2 - 3*a + 3)*q^34 + (a^2 + 2*a - 3)*q^35 + (6*a^2 + 4*a - 5)*q^36 + (5*a^2 + 6*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-a^3 - 2*a^2 + 3*a + 4)*q^3 + (a^2 - 2)*q^4 + (a^3 + 2*a^2 - 4*a - 7)*q^5 + (a^3 + a^2 - 5*a - 4)*q^6 + (a^3 + a^2 - 5*a - 3)*q^7 + (a^3 - 4*a)*q^8 + (a + 1)*q^9 + (-a^3 - 2*a^2 + 2*a + 4)*q^10 + (a^2 + 2*a - 3)*q^11 + (a^2 - a - 4)*q^12 - q^13 + (-2*a^3 - 3*a^2 + 6*a + 4)*q^14 + (2*a^3 + 5*a^2 - 5*a - 12)*q^15 + (-3*a^3 - 4*a^2 + 9*a + 8)*q^16 + (a^2 - 7)*q^17 + (a^2 + a)*q^18 - q^19 + (-a^3 - 4*a^2 + 3*a + 10)*q^20 + (-a^3 - a^2 + 7*a + 4)*q^21 + (a^3 + 2*a^2 - 3*a)*q^22 + (-3*a^3 - 6*a^2 + 14*a + 16)*q^23 + (-a^3 - 3*a^2 + 6*a + 8)*q^24 + (-4*a^3 - 9*a^2 + 15*a + 24)*q^25 - a*q^26 + (3*a^3 + 5*a^2 - 11*a - 12)*q^27 + (a^3 - 4*a - 2)*q^28 + (2*a^3 + 2*a^2 - 9*a - 4)*q^29 + (-a^3 - a^2 + 6*a + 8)*q^30 + (2*a^3 + 6*a^2 - 7*a - 14)*q^31 + (3*a^3 + 3*a^2 - 11*a - 12)*q^32 + (3*a^3 + 5*a^2 - 14*a - 16)*q^33 + (a^3 - 7*a)*q^34 + (a^2 + 2*a + 1)*q^35 + (a^3 + a^2 - 2*a - 2)*q^36 + (-5*a^3 - 10*a^2 + 18*a + 24)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + a + 3)*q^3 + (a^2 - 2)*q^4 + (a^3 - 2*a^2 - 2*a + 3)*q^5 + (-a^3 + a^2 + 3*a)*q^6 + (-a^4 + 2*a^3 + 3*a^2 - 4*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (a^4 - 2*a^3 - 5*a^2 + 6*a + 6)*q^9 + (a^4 - 2*a^3 - 2*a^2 + 3*a)*q^10 + (a^4 - 4*a^3 + 9*a - 2)*q^11 + (-a^4 + a^3 + 5*a^2 - 2*a - 6)*q^12 - q^13 + (-2*a^4 + 3*a^3 + 8*a^2 - 6*a - 5)*q^14 + (-a^4 + 3*a^3 + a^2 - 8*a + 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^3 - 6*a + 2)*q^17 + (2*a^4 - 5*a^3 - 6*a^2 + 11*a + 5)*q^18 + q^19 + (2*a^4 - 4*a^3 - 5*a^2 + 9*a - 1)*q^20 + (a^3 - a^2 - 3*a + 2)*q^21 + (-3*a^2 + 3*a + 5)*q^22 + (-2*a^4 + 3*a^3 + 10*a^2 - 8*a - 10)*q^23 + (-3*a^4 + 7*a^3 + 8*a^2 - 17*a - 5)*q^24 + (2*a^3 - 3*a^2 - 7*a + 4)*q^25 - a*q^26 + (2*a^4 - 5*a^3 - 5*a^2 + 11*a + 4)*q^27 + (-3*a^4 + 4*a^3 + 12*a^2 - 7*a - 8)*q^28 + (-3*a^4 + 6*a^3 + 11*a^2 - 14*a - 9)*q^29 + (-a^4 + a^3 + 4*a^2 - a - 5)*q^30 + (a^3 - a^2 - 5*a + 1)*q^31 + (4*a^4 - 8*a^3 - 12*a^2 + 17*a + 5)*q^32 + (3*a^4 - 9*a^3 - 6*a^2 + 25*a - 1)*q^33 + (a^4 - 6*a^2 + 2*a)*q^34 + (-a^4 + 2*a^3 + 2*a^2 - 5*a + 2)*q^35 + (a^4 - 2*a^3 - 3*a^2 + 3*a - 2)*q^36 + (2*a^4 - 5*a^3 - 4*a^2 + 8*a + 2)*q^37 + O(q^38),
q + a*q^2 + (a^3 - 5*a)*q^3 + (a^2 - 2)*q^4 + (-a^3 + 4*a + 1)*q^5 + (a^4 - 5*a^2)*q^6 + (-a^3 - a^2 + 5*a + 5)*q^7 + (a^3 - 4*a)*q^8 + (-a^4 + a^3 + 6*a^2 - 4*a - 3)*q^9 + (-a^4 + 4*a^2 + a)*q^10 + (-a^2 + 5)*q^11 + (2*a^3 + a^2 - 9*a - 4)*q^12 + q^13 + (-a^4 - a^3 + 5*a^2 + 5*a)*q^14 + (-a^2 - a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^2 + 1)*q^17 + (a^4 - 3*a^3 - 5*a^2 + 16*a + 4)*q^18 - q^19 + (-3*a^3 + 11*a + 2)*q^20 + (a^4 - 7*a^2 - 2*a + 4)*q^21 + (-a^3 + 5*a)*q^22 + (a^4 - 6*a^2 - a + 4)*q^23 + (a^3 + a^2 - 4*a)*q^24 + (a^4 - a^3 - 3*a^2 + 4*a - 4)*q^25 + a*q^26 + (-a^4 + 2*a^3 + 7*a^2 - 12*a - 8)*q^27 + (-a^4 - 2*a^3 + 6*a^2 + 9*a - 6)*q^28 + (-a^4 + a^3 + 6*a^2 - 6*a - 4)*q^29 + (-a^3 - a^2)*q^30 + (a^4 + a^3 - 6*a^2 - 4*a + 2)*q^31 + (a^3 + a^2 - 7*a - 4)*q^32 + (a^3 - a^2 - 6*a + 4)*q^33 + (a^3 + a)*q^34 + (a^2 + 2*a + 1)*q^35 + (-a^4 + 2*a^3 + 5*a^2 - 7*a + 2)*q^36 + (-a^4 + 6*a^2 - a - 8)*q^37 + O(q^38)
*]> ;  // time = 29.739 seconds




J[249] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 249, 249, 249, 249, 249, 83, 83 ], new_dimensions := [ 1, 1, 2, 4, 5, 1, 6 ], dimensions := [ 1, 1, 2, 4, 5, 2, 12 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 31, 1, 1, 1, 0, 1, 5, 1, 1, 1, 1, 1, 0, 1, 2711, 1, 3, 1, 5, 1, 0, 1, 1, 1, 31, 1, 2711, 1, 0 ], ap_traces := [
[ 1, -1, -1, -4, -3, 2, 4, -1, -3, 4, -6, -9 ],
[ -1, -1, 1, 0, -3, -6, -4, -7, 5, 8, -10, 7 ],
[ -2, 2, -6, -4, -6, 0, 0, -2, -2, -12, -16, -2 ],
[ 2, 4, 6, 0, 4, -6, 0, -2, 8, 0, 8, -16 ],
[ -3, -5, -2, 8, 4, 4, 2, 12, 8, -2, 24, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + 2*x - 1,
x^4 - 2*x^3 - 4*x^2 + 8*x - 1,
x^5 + 3*x^4 - 4*x^3 - 14*x^2 - 3*x + 1
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 1 ],
[ 31, 1 ],
[ 35, 1 ],
[ 2711, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 31, 1 ],
[ 35, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 7, 1 ], torsion_lower_bounds := [ 1, 1, 1, 7, 1 ], l_ratios := [ 0, 0, 0, 5/7, 1 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ 1, -1, -1, -4, -3, 2, 4, -1, -3, 4, -6, -9 ],
[ -1, -1, 1, 0, -3, -6, -4, -7, 5, 8, -10, 7 ],
[
a,
1,
-a - 4,
-2,
2*a - 1,
0,
-4*a - 4,
a,
4*a + 3,
-6,
-8,
-1
],
[
a,
1,
-a + 2,
-a^2 + 3,
-2*a^3 + a^2 + 8*a - 2,
-a^3 + 5*a - 2,
2*a^3 - 2*a^2 - 8*a + 6,
2*a^3 - 9*a,
4*a^3 - 2*a^2 - 18*a + 9,
-2*a^3 + 3*a^2 + 8*a - 9,
-2*a^3 + 3*a^2 + 8*a - 7,
2*a^3 - 6*a - 5
],
[
a,
-1,
-1/2*a^4 - 2*a^3 + 2*a^2 + 10*a + 1/2,
a^4 + 2*a^3 - 5*a^2 - 8*a + 2,
-1/2*a^4 - 2*a^3 + a^2 + 9*a + 9/2,
a^3 - 5*a + 2,
2*a^4 + 4*a^3 - 10*a^2 - 18*a,
-5/2*a^4 - 6*a^3 + 12*a^2 + 26*a + 5/2,
-1/2*a^4 + 4*a^2 - a - 5/2,
-a^4 - 2*a^3 + 5*a^2 + 6*a - 2,
a^4 + 2*a^3 - 5*a^2 - 10*a + 4,
1/2*a^4 - 4*a^2 - a + 5/2
]
*], q_expansions := [*
q + q^2 - q^3 - q^4 - q^5 - q^6 - 4*q^7 - 3*q^8 + q^9 - q^10 - 3*q^11 + q^12 + 2*q^13 - 4*q^14 + q^15 - q^16 + 4*q^17 + q^18 - q^19 + q^20 + 4*q^21 - 3*q^22 - 3*q^23 + 3*q^24 - 4*q^25 + 2*q^26 - q^27 + 4*q^28 + 4*q^29 + q^30 - 6*q^31 + 5*q^32 + 3*q^33 + 4*q^34 + 4*q^35 - q^36 - 9*q^37 + O(q^38),
q - q^2 - q^3 - q^4 + q^5 + q^6 + 3*q^8 + q^9 - q^10 - 3*q^11 + q^12 - 6*q^13 - q^15 - q^16 - 4*q^17 - q^18 - 7*q^19 - q^20 + 3*q^22 + 5*q^23 - 3*q^24 - 4*q^25 + 6*q^26 - q^27 + 8*q^29 + q^30 - 10*q^31 - 5*q^32 + 3*q^33 + 4*q^34 - q^36 + 7*q^37 + O(q^38),
q + a*q^2 + q^3 + (-2*a - 1)*q^4 + (-a - 4)*q^5 + a*q^6 - 2*q^7 + (a - 2)*q^8 + q^9 + (-2*a - 1)*q^10 + (2*a - 1)*q^11 + (-2*a - 1)*q^12 - 2*a*q^14 + (-a - 4)*q^15 + 3*q^16 + (-4*a - 4)*q^17 + a*q^18 + a*q^19 + (5*a + 6)*q^20 - 2*q^21 + (-5*a + 2)*q^22 + (4*a + 3)*q^23 + (a - 2)*q^24 + (6*a + 12)*q^25 + q^27 + (4*a + 2)*q^28 - 6*q^29 + (-2*a - 1)*q^30 - 8*q^31 + (a + 4)*q^32 + (2*a - 1)*q^33 + (4*a - 4)*q^34 + (2*a + 8)*q^35 + (-2*a - 1)*q^36 - q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a + 2)*q^5 + a*q^6 + (-a^2 + 3)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^2 + 2*a)*q^10 + (-2*a^3 + a^2 + 8*a - 2)*q^11 + (a^2 - 2)*q^12 + (-a^3 + 5*a - 2)*q^13 + (-a^3 + 3*a)*q^14 + (-a + 2)*q^15 + (2*a^3 - 2*a^2 - 8*a + 5)*q^16 + (2*a^3 - 2*a^2 - 8*a + 6)*q^17 + a*q^18 + (2*a^3 - 9*a)*q^19 + (-a^3 + 2*a^2 + 2*a - 4)*q^20 + (-a^2 + 3)*q^21 + (-3*a^3 + 14*a - 2)*q^22 + (4*a^3 - 2*a^2 - 18*a + 9)*q^23 + (a^3 - 4*a)*q^24 + (a^2 - 4*a - 1)*q^25 + (-2*a^3 + a^2 + 6*a - 1)*q^26 + q^27 + (-2*a^3 + a^2 + 8*a - 7)*q^28 + (-2*a^3 + 3*a^2 + 8*a - 9)*q^29 + (-a^2 + 2*a)*q^30 + (-2*a^3 + 3*a^2 + 8*a - 7)*q^31 + (-3*a + 2)*q^32 + (-2*a^3 + a^2 + 8*a - 2)*q^33 + (2*a^3 - 10*a + 2)*q^34 + (a^3 - 2*a^2 - 3*a + 6)*q^35 + (a^2 - 2)*q^36 + (2*a^3 - 6*a - 5)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-1/2*a^4 - 2*a^3 + 2*a^2 + 10*a + 1/2)*q^5 - a*q^6 + (a^4 + 2*a^3 - 5*a^2 - 8*a + 2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-1/2*a^4 + 3*a^2 - a + 1/2)*q^10 + (-1/2*a^4 - 2*a^3 + a^2 + 9*a + 9/2)*q^11 + (-a^2 + 2)*q^12 + (a^3 - 5*a + 2)*q^13 + (-a^4 - a^3 + 6*a^2 + 5*a - 1)*q^14 + (1/2*a^4 + 2*a^3 - 2*a^2 - 10*a - 1/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^4 + 4*a^3 - 10*a^2 - 18*a)*q^17 + a*q^18 + (-5/2*a^4 - 6*a^3 + 12*a^2 + 26*a + 5/2)*q^19 + (5/2*a^4 + 5*a^3 - 12*a^2 - 21*a - 1/2)*q^20 + (-a^4 - 2*a^3 + 5*a^2 + 8*a - 2)*q^21 + (-1/2*a^4 - a^3 + 2*a^2 + 3*a + 1/2)*q^22 + (-1/2*a^4 + 4*a^2 - a - 5/2)*q^23 + (-a^3 + 4*a)*q^24 + (1/2*a^4 + 2*a^3 - 3*a^2 - 11*a + 5/2)*q^25 + (a^4 - 5*a^2 + 2*a)*q^26 - q^27 + (-2*a^3 + a^2 + 12*a - 3)*q^28 + (-a^4 - 2*a^3 + 5*a^2 + 6*a - 2)*q^29 + (1/2*a^4 - 3*a^2 + a - 1/2)*q^30 + (a^4 + 2*a^3 - 5*a^2 - 10*a + 4)*q^31 + (-3*a^4 - 4*a^3 + 14*a^2 + 15*a - 1)*q^32 + (1/2*a^4 + 2*a^3 - a^2 - 9*a - 9/2)*q^33 + (-2*a^4 - 2*a^3 + 10*a^2 + 6*a - 2)*q^34 + (-3*a^4 - 7*a^3 + 16*a^2 + 31*a - 5)*q^35 + (a^2 - 2)*q^36 + (1/2*a^4 - 4*a^2 - a + 5/2)*q^37 + O(q^38)
*]> ;  // time = 32.129 seconds




J[251] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 251, 251 ], new_dimensions := [ 4, 17 ], dimensions := [ 4, 17 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -2, -2, -3, -3, -3, -12, 1, -9, 4, -12, -2, -13 ],
[ 2, 0, 3, 3, -1, 22, -1, 13, -2, 28, 12, 27 ]
], hecke_fields := [
x^4 + 6*x^3 - 3*x^2 - 16*x + 11,
x^17 - 2*x^16 - 28*x^15 + 54*x^14 + 317*x^13 - 582*x^12 - 1867*x^11 + 3178*x^10 + 6186*x^9 - 9216*x^8 - 11921*x^7 + 13680*x^6 + 13752*x^5 - 9400*x^4 - 8800*x^3 + 1920*x^2 + 2240*x + 256
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 125 ]
], tamagawa_numbers := [
[ 1 ],
[ 125 ]
], torsion_upper_bounds := [ 1, 125 ], torsion_lower_bounds := [ 1, 125 ], l_ratios := [ 0, 1/125 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
2/7*a^3 + 13/7*a^2 + 4/7*a - 23/7,
-1/7*a^3 - 13/14*a^2 + 3/14*a + 23/14,
-3/14*a^3 - 23/14*a^2 - 27/14*a + 12/7,
3/14*a^3 + 23/14*a^2 + 13/14*a - 33/7,
5/14*a^3 + 18/7*a^2 + 12/7*a - 75/14,
1/7*a^3 + 13/14*a^2 + 11/14*a - 51/14,
5/14*a^3 + 43/14*a^2 + 59/14*a - 41/7,
-9/14*a^3 - 69/14*a^2 - 53/14*a + 57/7,
-1/7*a^3 - 10/7*a^2 - 23/7*a + 22/7,
-1/7*a^3 - 3/7*a^2 + 26/7*a - 6/7,
6/7*a^3 + 85/14*a^2 + 31/14*a - 187/14,
1/14*a^3 - 2/7*a^2 - 27/7*a - 29/14
],
[
a,
69/1216*a^16 - 53/304*a^15 - 219/152*a^14 + 2819/608*a^13 + 903/64*a^12 - 1857/38*a^11 - 79979/1216*a^10 + 9809/38*a^9 + 87207/608*a^8 - 216513/304*a^7 - 7719/64*a^6 + 31535/32*a^5 + 6777/152*a^4 - 97473/152*a^3 - 3451/76*a^2 + 5735/38*a + 434/19,
-21/304*a^16 - 37/608*a^15 + 653/304*a^14 + 287/152*a^13 - 109/4*a^12 - 14297/608*a^11 + 27443/152*a^10 + 91723/608*a^9 - 200943/304*a^8 - 161767/304*a^7 + 20607/16*a^6 + 32619/32*a^5 - 21707/19*a^4 - 146925/152*a^3 + 5341/19*a^2 + 5948/19*a + 743/19,
7/19*a^16 - 85/304*a^15 - 801/76*a^14 + 1009/152*a^13 + 973/8*a^12 - 17893/304*a^11 - 13748/19*a^10 + 68557/304*a^9 + 89407/38*a^8 - 18169/76*a^7 - 4087*a^6 - 9741/16*a^5 + 518077/152*a^4 + 205791/152*a^3 - 68487/76*a^2 - 10829/19*a - 1119/19,
-4/19*a^16 - 11/152*a^15 + 967/152*a^14 + 203/76*a^13 - 313/4*a^12 - 5829/152*a^11 + 76243/152*a^10 + 42431/152*a^9 - 269993/152*a^8 - 42051/38*a^7 + 13471/4*a^6 + 18769/8*a^5 - 451977/152*a^4 - 89797/38*a^3 + 29179/38*a^2 + 14852/19*a + 1622/19,
-277/1216*a^16 + 47/304*a^15 + 2007/304*a^14 - 2231/608*a^13 - 4951/64*a^12 + 616/19*a^11 + 569887/1216*a^10 - 9297/76*a^9 - 946677/608*a^8 + 34695/304*a^7 + 177391/64*a^6 + 12773/32*a^5 - 720659/304*a^4 - 127435/152*a^3 + 25057/38*a^2 + 6630/19*a + 606/19,
17/64*a^16 - 11/32*a^15 - 59/8*a^14 + 275/32*a^13 + 5253/64*a^12 - 2657/32*a^11 - 29879/64*a^10 + 12219/32*a^9 + 45967/32*a^8 - 6455/8*a^7 - 150313/64*a^6 + 8557/16*a^5 + 30275/16*a^4 + 857/4*a^3 - 1051/2*a^2 - 379/2*a - 11,
167/304*a^16 - 113/304*a^15 - 1203/76*a^14 + 1315/152*a^13 + 2947/16*a^12 - 22429/304*a^11 - 336329/304*a^10 + 77359/304*a^9 + 552825/152*a^8 - 13795/152*a^7 - 102241/16*a^6 - 22063/16*a^5 + 815887/152*a^4 + 184777/76*a^3 - 26577/19*a^2 - 18561/19*a - 2086/19,
-301/1216*a^16 + 59/608*a^15 + 2199/304*a^14 - 1219/608*a^13 - 5483/64*a^12 + 8133/608*a^11 + 639823/1216*a^10 - 7751/608*a^9 - 1080393/608*a^8 - 8365/38*a^7 + 205535/64*a^6 + 14891/16*a^5 - 208521/76*a^4 - 47879/38*a^3 + 27539/38*a^2 + 17769/38*a + 973/19,
-455/608*a^16 + 127/152*a^15 + 3203/152*a^14 - 6385/304*a^13 - 7629/32*a^12 + 15531/76*a^11 + 840781/608*a^10 - 36001/38*a^9 - 1323811/304*a^8 + 306159/152*a^7 + 233493/32*a^6 - 20781/16*a^5 - 906415/152*a^4 - 26099/38*a^3 + 31473/19*a^2 + 10806/19*a + 902/19,
443/608*a^16 - 505/608*a^15 - 6233/304*a^14 + 6321/304*a^13 + 7423/32*a^12 - 122337/608*a^11 - 818923/608*a^10 + 562955/608*a^9 + 646365/152*a^8 - 591193/304*a^7 - 229025/32*a^6 + 38505/32*a^5 + 892785/152*a^4 + 110843/152*a^3 - 123189/76*a^2 - 10727/19*a - 991/19,
-71/304*a^16 + 2/19*a^15 + 511/76*a^14 - 309/152*a^13 - 1253/16*a^12 + 821/76*a^11 + 143605/304*a^10 + 1771/76*a^9 - 238323/152*a^8 - 31575/76*a^7 + 44837/16*a^6 + 11253/8*a^5 - 182785/76*a^4 - 65537/38*a^3 + 23569/38*a^2 + 11673/19*a + 1306/19
]
*], q_expansions := [*
q + (2/7*a^3 + 13/7*a^2 + 4/7*a - 23/7)*q^2 + (-1/7*a^3 - 13/14*a^2 + 3/14*a + 23/14)*q^3 + (-2/7*a^3 - 13/7*a^2 - 4/7*a + 16/7)*q^4 + (-3/14*a^3 - 23/14*a^2 - 27/14*a + 12/7)*q^5 + (3/14*a^3 + 23/14*a^2 + 13/14*a - 26/7)*q^6 + (3/14*a^3 + 23/14*a^2 + 13/14*a - 33/7)*q^7 + (-4/7*a^3 - 26/7*a^2 - 8/7*a + 39/7)*q^8 + (-1/7*a^3 - 13/14*a^2 - 11/14*a - 5/14)*q^9 + (-5/14*a^3 - 18/7*a^2 - 12/7*a + 61/14)*q^10 + (5/14*a^3 + 18/7*a^2 + 12/7*a - 75/14)*q^11 + (-1/14*a^3 - 5/7*a^2 - 8/7*a + 29/14)*q^12 + (1/7*a^3 + 13/14*a^2 + 11/14*a - 51/14)*q^13 + (-9/14*a^3 - 31/7*a^2 - 9/7*a + 121/14)*q^14 - q^15 + (6/7*a^3 + 39/7*a^2 + 12/7*a - 69/7)*q^16 + (5/14*a^3 + 43/14*a^2 + 59/14*a - 41/7)*q^17 + (-1/2*a^3 - 7/2*a^2 - 3/2*a + 6)*q^18 + (-9/14*a^3 - 69/14*a^2 - 53/14*a + 57/7)*q^19 + (4/7*a^3 + 59/14*a^2 + 51/14*a - 85/14)*q^20 + (1/2*a^3 + 3*a^2 - 11/2)*q^21 + (-3/7*a^3 - 39/14*a^2 - 5/14*a + 83/14)*q^22 + (-1/7*a^3 - 10/7*a^2 - 23/7*a + 22/7)*q^23 + (-2/7*a^3 - 33/14*a^2 - 29/14*a + 81/14)*q^24 + (15/14*a^3 + 54/7*a^2 + 43/7*a - 197/14)*q^25 + (-9/14*a^3 - 55/14*a^2 - 11/14*a + 50/7)*q^26 + (9/14*a^3 + 55/14*a^2 - 17/14*a - 50/7)*q^27 + (3/7*a^3 + 39/14*a^2 + 5/14*a - 55/14)*q^28 + (-1/7*a^3 - 3/7*a^2 + 26/7*a - 6/7)*q^29 + (-2/7*a^3 - 13/7*a^2 - 4/7*a + 23/7)*q^30 + (6/7*a^3 + 85/14*a^2 + 31/14*a - 187/14)*q^31 + (2/7*a^3 + 13/7*a^2 + 4/7*a + 12/7)*q^32 + (3/7*a^3 + 39/14*a^2 + 5/14*a - 69/14)*q^33 + (1/14*a^3 + 5/7*a^2 + 15/7*a - 15/14)*q^34 + (-1/14*a^3 - 3/14*a^2 + 19/14*a + 11/7)*q^35 + (9/14*a^3 + 31/7*a^2 + 16/7*a - 79/14)*q^36 + (1/14*a^3 - 2/7*a^2 - 27/7*a - 29/14)*q^37 + O(q^38),
q + a*q^2 + (69/1216*a^16 - 53/304*a^15 - 219/152*a^14 + 2819/608*a^13 + 903/64*a^12 - 1857/38*a^11 - 79979/1216*a^10 + 9809/38*a^9 + 87207/608*a^8 - 216513/304*a^7 - 7719/64*a^6 + 31535/32*a^5 + 6777/152*a^4 - 97473/152*a^3 - 3451/76*a^2 + 5735/38*a + 434/19)*q^3 + (a^2 - 2)*q^4 + (-21/304*a^16 - 37/608*a^15 + 653/304*a^14 + 287/152*a^13 - 109/4*a^12 - 14297/608*a^11 + 27443/152*a^10 + 91723/608*a^9 - 200943/304*a^8 - 161767/304*a^7 + 20607/16*a^6 + 32619/32*a^5 - 21707/19*a^4 - 146925/152*a^3 + 5341/19*a^2 + 5948/19*a + 743/19)*q^5 + (-37/608*a^16 + 45/304*a^15 + 239/152*a^14 - 1179/304*a^13 - 507/32*a^12 + 12211/304*a^11 + 47303/608*a^10 - 63105/304*a^9 - 57537/304*a^8 + 42243/76*a^7 + 6695/32*a^6 - 2943/4*a^5 - 8199/76*a^4 + 34499/76*a^3 + 1595/38*a^2 - 1981/19*a - 276/19)*q^6 + (7/19*a^16 - 85/304*a^15 - 801/76*a^14 + 1009/152*a^13 + 973/8*a^12 - 17893/304*a^11 - 13748/19*a^10 + 68557/304*a^9 + 89407/38*a^8 - 18169/76*a^7 - 4087*a^6 - 9741/16*a^5 + 518077/152*a^4 + 205791/152*a^3 - 68487/76*a^2 - 10829/19*a - 1119/19)*q^7 + (a^3 - 4*a)*q^8 + (-85/1216*a^16 + 89/608*a^15 + 283/152*a^14 - 2347/608*a^13 - 1243/64*a^12 + 24279/608*a^11 + 120979/1216*a^10 - 123313/608*a^9 - 156211/608*a^8 + 78283/152*a^7 + 20239/64*a^6 - 4757/8*a^5 - 58625/304*a^4 + 41921/152*a^3 + 4151/76*a^2 - 1323/38*a - 31/19)*q^9 + (-121/608*a^16 + 65/304*a^15 + 427/76*a^14 - 1627/304*a^13 - 2039/32*a^12 + 15679/304*a^11 + 225199/608*a^10 - 71037/304*a^9 - 355303/304*a^8 + 17649/38*a^7 + 62859/32*a^6 - 385/2*a^5 - 245625/152*a^4 - 6209/19*a^3 + 8468/19*a^2 + 3683/19*a + 336/19)*q^10 + (-4/19*a^16 - 11/152*a^15 + 967/152*a^14 + 203/76*a^13 - 313/4*a^12 - 5829/152*a^11 + 76243/152*a^10 + 42431/152*a^9 - 269993/152*a^8 - 42051/38*a^7 + 13471/4*a^6 + 18769/8*a^5 - 451977/152*a^4 - 89797/38*a^3 + 29179/38*a^2 + 14852/19*a + 1622/19)*q^11 + (-53/608*a^16 + 33/152*a^15 + 87/38*a^14 - 1771/304*a^13 - 751/32*a^12 + 2353/38*a^11 + 71355/608*a^10 - 12505/38*a^9 - 88731/304*a^8 + 138045/152*a^7 + 10815/32*a^6 - 19871/16*a^5 - 15753/76*a^4 + 59963/76*a^3 + 3929/38*a^2 - 3421/19*a - 572/19)*q^12 + (-277/1216*a^16 + 47/304*a^15 + 2007/304*a^14 - 2231/608*a^13 - 4951/64*a^12 + 616/19*a^11 + 569887/1216*a^10 - 9297/76*a^9 - 946677/608*a^8 + 34695/304*a^7 + 177391/64*a^6 + 12773/32*a^5 - 720659/304*a^4 - 127435/152*a^3 + 25057/38*a^2 + 6630/19*a + 606/19)*q^13 + (139/304*a^16 - 17/76*a^15 - 2015/152*a^14 + 735/152*a^13 + 2489/16*a^12 - 679/19*a^11 - 287379/304*a^10 + 2803/38*a^9 + 239879/76*a^8 + 5794/19*a^7 - 90381/16*a^6 - 13265/8*a^5 + 732191/152*a^4 + 177913/76*a^3 - 24269/19*a^2 - 16799/19*a - 1792/19)*q^14 + (-259/608*a^16 + 91/152*a^15 + 1787/152*a^14 - 4605/304*a^13 - 4153/32*a^12 + 11323/76*a^11 + 443753/608*a^10 - 13419/19*a^9 - 671799/304*a^8 + 242391/152*a^7 + 113153/32*a^6 - 21817/16*a^5 - 423745/152*a^4 + 1231/19*a^3 + 28721/38*a^2 + 7169/38*a + 386/19)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (17/64*a^16 - 11/32*a^15 - 59/8*a^14 + 275/32*a^13 + 5253/64*a^12 - 2657/32*a^11 - 29879/64*a^10 + 12219/32*a^9 + 45967/32*a^8 - 6455/8*a^7 - 150313/64*a^6 + 8557/16*a^5 + 30275/16*a^4 + 857/4*a^3 - 1051/2*a^2 - 379/2*a - 11)*q^17 + (1/152*a^16 - 29/304*a^15 - 13/152*a^14 + 52/19*a^13 - 3/4*a^12 - 9429/304*a^11 + 1469/76*a^10 + 53347/304*a^9 - 19637/152*a^8 - 78593/152*a^7 + 2893/8*a^6 + 12295/16*a^5 - 28977/76*a^4 - 42599/76*a^3 + 3777/38*a^2 + 2944/19*a + 340/19)*q^18 + (167/304*a^16 - 113/304*a^15 - 1203/76*a^14 + 1315/152*a^13 + 2947/16*a^12 - 22429/304*a^11 - 336329/304*a^10 + 77359/304*a^9 + 552825/152*a^8 - 13795/152*a^7 - 102241/16*a^6 - 22063/16*a^5 + 815887/152*a^4 + 184777/76*a^3 - 26577/19*a^2 - 18561/19*a - 2086/19)*q^19 + (-7/152*a^16 + 51/304*a^15 + 167/152*a^14 - 335/76*a^13 - 39/4*a^12 + 13943/304*a^11 + 2865/76*a^10 - 72773/304*a^9 - 7245/152*a^8 + 99737/152*a^7 - 367/8*a^6 - 14685/16*a^5 + 6645/76*a^4 + 47697/76*a^3 + 261/19*a^2 - 3090/19*a - 518/19)*q^20 + (939/1216*a^16 - 105/304*a^15 - 6847/304*a^14 + 4457/608*a^13 + 17033/64*a^12 - 3939/76*a^11 - 1982345/1216*a^10 + 6169/76*a^9 + 3338887/608*a^8 + 191863/304*a^7 - 634721/64*a^6 - 94955/32*a^5 + 2589711/304*a^4 + 623103/152*a^3 - 173497/76*a^2 - 29432/19*a - 3080/19)*q^21 + (-75/152*a^16 + 71/152*a^15 + 1067/76*a^14 - 875/76*a^13 - 1287/8*a^12 + 16499/152*a^11 + 144127/152*a^10 - 72041/152*a^9 - 115779/38*a^8 + 65213/76*a^7 + 41809/8*a^6 - 627/8*a^5 - 164997/38*a^4 - 41221/38*a^3 + 22532/19*a^2 + 10582/19*a + 1024/19)*q^22 + (-301/1216*a^16 + 59/608*a^15 + 2199/304*a^14 - 1219/608*a^13 - 5483/64*a^12 + 8133/608*a^11 + 639823/1216*a^10 - 7751/608*a^9 - 1080393/608*a^8 - 8365/38*a^7 + 205535/64*a^6 + 14891/16*a^5 - 208521/76*a^4 - 47879/38*a^3 + 27539/38*a^2 + 17769/38*a + 973/19)*q^23 + (25/152*a^16 - 17/38*a^15 - 81/19*a^14 + 453/38*a^13 + 343/8*a^12 - 9555/76*a^11 - 31563/152*a^10 + 12588/19*a^9 + 36735/76*a^8 - 137777/76*a^7 - 3743/8*a^6 + 2463*a^5 + 7043/38*a^4 - 29860/19*a^3 - 1836/19*a^2 + 7100/19*a + 976/19)*q^24 + (-97/1216*a^16 + 157/608*a^15 + 605/304*a^14 - 4159/608*a^13 - 1215/64*a^12 + 43655/608*a^11 + 102595/1216*a^10 - 229565/608*a^9 - 98961/608*a^8 + 157517/152*a^7 + 4443/64*a^6 - 11381/8*a^5 + 5387/76*a^4 + 69241/76*a^3 - 180/19*a^2 - 8103/38*a - 446/19)*q^25 + (-183/608*a^16 + 17/76*a^15 + 164/19*a^14 - 1565/304*a^13 - 3205/32*a^12 + 6591/152*a^11 + 365777/608*a^10 - 22479/152*a^9 - 603513/304*a^8 + 8539/152*a^7 + 112493/32*a^6 + 12193/16*a^5 - 226455/76*a^4 - 25559/19*a^3 + 14940/19*a^2 + 10301/19*a + 1108/19)*q^26 + (-3/304*a^16 - 23/304*a^15 + 153/304*a^14 + 36/19*a^13 - 139/16*a^12 - 5645/304*a^11 + 10793/152*a^10 + 27339/304*a^9 - 91037/304*a^8 - 4284/19*a^7 + 10131/16*a^6 + 4663/16*a^5 - 174807/304*a^4 - 15531/76*a^3 + 11545/76*a^2 + 1941/38*a + 98/19)*q^27 + (-7/152*a^16 + 2/19*a^15 + 93/76*a^14 - 101/38*a^13 - 103/8*a^12 + 495/19*a^11 + 10309/152*a^10 - 9363/76*a^9 - 3549/19*a^8 + 21283/76*a^7 + 2087/8*a^6 - 1013/4*a^5 - 6757/38*a^4 + 2933/76*a^3 + 1529/38*a^2 + 406/19*a + 14/19)*q^28 + (-455/608*a^16 + 127/152*a^15 + 3203/152*a^14 - 6385/304*a^13 - 7629/32*a^12 + 15531/76*a^11 + 840781/608*a^10 - 36001/38*a^9 - 1323811/304*a^8 + 306159/152*a^7 + 233493/32*a^6 - 20781/16*a^5 - 906415/152*a^4 - 26099/38*a^3 + 31473/19*a^2 + 10806/19*a + 902/19)*q^29 + (-77/304*a^16 - 13/76*a^15 + 597/76*a^14 + 799/152*a^13 - 1583/16*a^12 - 4975/76*a^11 + 196847/304*a^10 + 16161/38*a^9 - 354345/152*a^8 - 29301/19*a^7 + 71423/16*a^6 + 24563/8*a^5 - 299401/76*a^4 - 113729/38*a^3 + 38249/38*a^2 + 18516/19*a + 2072/19)*q^30 + (443/608*a^16 - 505/608*a^15 - 6233/304*a^14 + 6321/304*a^13 + 7423/32*a^12 - 122337/608*a^11 - 818923/608*a^10 + 562955/608*a^9 + 646365/152*a^8 - 591193/304*a^7 - 229025/32*a^6 + 38505/32*a^5 + 892785/152*a^4 + 110843/152*a^3 - 123189/76*a^2 - 10727/19*a - 991/19)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-365/608*a^16 + 29/304*a^15 + 673/38*a^14 - 243/304*a^13 - 6787/32*a^12 - 4669/304*a^11 + 802531/608*a^10 + 79083/304*a^9 - 1376815/304*a^8 - 114347/76*a^7 + 266727/32*a^6 + 3982*a^5 - 1100343/152*a^4 - 343253/76*a^3 + 36216/19*a^2 + 29660/19*a + 3080/19)*q^33 + (3/16*a^16 + 1/16*a^15 - 23/4*a^14 - 17/8*a^13 + 1145/16*a^12 + 465/16*a^11 - 7397/16*a^10 - 3307/16*a^9 + 13129/8*a^8 + 6543/8*a^7 - 49583/16*a^6 - 28171/16*a^5 + 21689/8*a^4 + 1812*a^3 - 1399/2*a^2 - 606*a - 68)*q^34 + (-245/1216*a^16 + 159/304*a^15 + 1561/304*a^14 - 8267/608*a^13 - 3239/64*a^12 + 10553/76*a^11 + 290743/1216*a^10 - 106327/152*a^9 - 327817/608*a^8 + 542797/304*a^7 + 32143/64*a^6 - 68883/32*a^5 - 60821/304*a^4 + 21692/19*a^3 + 2735/38*a^2 - 8047/38*a - 485/19)*q^35 + (35/608*a^16 - 59/304*a^15 - 51/38*a^14 + 1485/304*a^13 + 373/32*a^12 - 14669/304*a^11 - 26997/608*a^10 + 71667/304*a^9 + 17457/304*a^8 - 44839/76*a^7 + 1471/32*a^6 + 1435/2*a^5 - 17173/152*a^4 - 29967/76*a^3 + 1257/38*a^2 + 1383/19*a + 30/19)*q^36 + (-71/304*a^16 + 2/19*a^15 + 511/76*a^14 - 309/152*a^13 - 1253/16*a^12 + 821/76*a^11 + 143605/304*a^10 + 1771/76*a^9 - 238323/152*a^8 - 31575/76*a^7 + 44837/16*a^6 + 11253/8*a^5 - 182785/76*a^4 - 65537/38*a^3 + 23569/38*a^2 + 11673/19*a + 1306/19)*q^37 + O(q^38)
*]> ;  // time = 3.881 seconds




J[253] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 253, 253, 253, 253, 23, 11 ], new_dimensions := [ 3, 3, 5, 6, 2, 1 ], dimensions := [ 3, 3, 5, 6, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 19, 1, 1, 0, 1, 1, 5, 5, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 23, 19, 5, 1, 1, 0, 1, 1, 5, 1, 23, 1, 0 ], ap_traces := [
[ 3, 3, 3, 3, -3, -3, 3, 9, 3, 0, 0, -18 ],
[ -1, -5, -5, -3, 3, -1, -9, -5, 3, 12, -4, -14 ],
[ -4, -5, -3, -3, -5, -15, -9, -5, -5, -8, -4, 8 ],
[ 3, 7, 3, -1, 6, -3, 5, 1, -6, 6, -8, 2 ]
], hecke_fields := [
x^3 - 3*x^2 + 3,
x^3 + x^2 - 4*x + 1,
x^5 + 4*x^4 - 14*x^2 - 13*x - 1,
x^6 - 3*x^5 - 4*x^4 + 16*x^3 - 3*x^2 - 10*x + 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 19, 1 ],
[ 5, 5 ],
[ 1, 1 ],
[ 1, 23 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 5, 5 ],
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 5, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1 ], l_ratios := [ 1, 0, 0, 1 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1 ], eigenvalues := [*
[
a,
-a^2 + a + 3,
a^2 - 2*a,
-a^2 + a + 3,
-1,
a^2 - 3*a - 1,
-a^2 + 2*a + 2,
2*a^2 - 4*a + 1,
1,
-a^2 - 3*a + 6,
3*a^2 - 4*a - 5,
-3*a^2 + 6*a - 3
],
[
a,
-a^2 - a + 1,
a^2 + 2*a - 4,
-a^2 - 3*a + 1,
1,
a^2 + a - 3,
a^2 - 6,
2*a - 1,
1,
a^2 + 3*a + 2,
-5*a^2 - 8*a + 11,
a^2 + 2*a - 7
],
[
a,
-a^4 - 3*a^3 + 3*a^2 + 10*a + 1,
2*a^4 + 5*a^3 - 8*a^2 - 18*a - 1,
-2*a^4 - 4*a^3 + 9*a^2 + 13*a - 3,
-1,
-a^4 - 3*a^3 + 3*a^2 + 10*a - 1,
-a^3 - 2*a^2 + 6*a + 5,
a^4 + 3*a^3 - 2*a^2 - 11*a - 7,
-1,
2*a^4 + 4*a^3 - 7*a^2 - 11*a - 4,
-2*a^4 - 5*a^3 + 6*a^2 + 18*a + 6,
-a^4 - 4*a^3 + 2*a^2 + 17*a + 8
],
[
a,
a^4 - a^3 - 5*a^2 + 4*a + 3,
-a^3 + 4*a + 1,
-a^5 + 6*a^3 + a^2 - 6*a - 2,
1,
-2*a^5 + 3*a^4 + 11*a^3 - 15*a^2 - 6*a + 5,
2*a^5 - 4*a^4 - 9*a^3 + 20*a^2 - 2*a - 7,
4*a^5 - 5*a^4 - 21*a^3 + 22*a^2 + 11*a - 3,
-1,
-2*a^5 + 14*a^3 + 3*a^2 - 21*a - 6,
a^5 - 7*a^3 + 2*a^2 + 9*a - 7,
4*a^5 - 5*a^4 - 22*a^3 + 24*a^2 + 15*a - 8
]
*], q_expansions := [*
q + a*q^2 + (-a^2 + a + 3)*q^3 + (a^2 - 2)*q^4 + (a^2 - 2*a)*q^5 + (-2*a^2 + 3*a + 3)*q^6 + (-a^2 + a + 3)*q^7 + (3*a^2 - 4*a - 3)*q^8 + (-2*a^2 + 3*a + 3)*q^9 + (a^2 - 3)*q^10 - q^11 + (-a^2 + a)*q^12 + (a^2 - 3*a - 1)*q^13 + (-2*a^2 + 3*a + 3)*q^14 + (a^2 - 3*a)*q^15 + (3*a^2 - 3*a - 5)*q^16 + (-a^2 + 2*a + 2)*q^17 + (-3*a^2 + 3*a + 6)*q^18 + (2*a^2 - 4*a + 1)*q^19 + (a^2 + a - 3)*q^20 + (-2*a^2 + 3*a + 6)*q^21 - a*q^22 + q^23 + (2*a^2 - 6*a - 3)*q^24 + (a^2 - 3*a - 2)*q^25 + (-a - 3)*q^26 + (3*a - 3)*q^27 + (-a^2 + a)*q^28 + (-a^2 - 3*a + 6)*q^29 - 3*q^30 + (3*a^2 - 4*a - 5)*q^31 + (3*a - 3)*q^32 + (a^2 - a - 3)*q^33 + (-a^2 + 2*a + 3)*q^34 + (a^2 - 3*a)*q^35 + (-2*a^2 + 3)*q^36 + (-3*a^2 + 6*a - 3)*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 1)*q^3 + (a^2 - 2)*q^4 + (a^2 + 2*a - 4)*q^5 + (-3*a + 1)*q^6 + (-a^2 - 3*a + 1)*q^7 + (-a^2 - 1)*q^8 + (2*a^2 + a - 3)*q^9 + (a^2 - 1)*q^10 + q^11 + (-a^2 + 3*a - 2)*q^12 + (a^2 + a - 3)*q^13 + (-2*a^2 - 3*a + 1)*q^14 + (a^2 - a - 2)*q^15 + (-a^2 - 5*a + 5)*q^16 + (a^2 - 6)*q^17 + (-a^2 + 5*a - 2)*q^18 + (2*a - 1)*q^19 + (-3*a^2 - a + 7)*q^20 + (2*a^2 + 7*a - 2)*q^21 + a*q^22 + q^23 + (4*a^2 - 1)*q^24 + (-3*a^2 - 5*a + 8)*q^25 + (a - 1)*q^26 + (5*a - 5)*q^27 + (a^2 - a)*q^28 + (a^2 + 3*a + 2)*q^29 + (-2*a^2 + 2*a - 1)*q^30 + (-5*a^2 - 8*a + 11)*q^31 + (-2*a^2 + a + 3)*q^32 + (-a^2 - a + 1)*q^33 + (-a^2 - 2*a - 1)*q^34 + (-a^2 - a)*q^35 + (2*a^2 - 8*a + 7)*q^36 + (a^2 + 2*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-a^4 - 3*a^3 + 3*a^2 + 10*a + 1)*q^3 + (a^2 - 2)*q^4 + (2*a^4 + 5*a^3 - 8*a^2 - 18*a - 1)*q^5 + (a^4 + 3*a^3 - 4*a^2 - 12*a - 1)*q^6 + (-2*a^4 - 4*a^3 + 9*a^2 + 13*a - 3)*q^7 + (a^3 - 4*a)*q^8 + (4*a^4 + 11*a^3 - 13*a^2 - 37*a - 6)*q^9 + (-3*a^4 - 8*a^3 + 10*a^2 + 25*a + 2)*q^10 - q^11 + (a^4 + 2*a^3 - 4*a^2 - 8*a - 1)*q^12 + (-a^4 - 3*a^3 + 3*a^2 + 10*a - 1)*q^13 + (4*a^4 + 9*a^3 - 15*a^2 - 29*a - 2)*q^14 + (-5*a^4 - 13*a^3 + 19*a^2 + 48*a + 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^3 - 2*a^2 + 6*a + 5)*q^17 + (-5*a^4 - 13*a^3 + 19*a^2 + 46*a + 4)*q^18 + (a^4 + 3*a^3 - 2*a^2 - 11*a - 7)*q^19 + (-a^2 - a - 1)*q^20 + (3*a^4 + 8*a^3 - 11*a^2 - 28*a - 3)*q^21 - a*q^22 - q^23 + (-4*a^4 - 10*a^3 + 14*a^2 + 36*a + 3)*q^24 + (4*a^4 + 12*a^3 - 11*a^2 - 39*a - 8)*q^25 + (a^4 + 3*a^3 - 4*a^2 - 14*a - 1)*q^26 + (-7*a^4 - 18*a^3 + 25*a^2 + 62*a + 4)*q^27 + (-3*a^4 - 7*a^3 + 9*a^2 + 24*a + 10)*q^28 + (2*a^4 + 4*a^3 - 7*a^2 - 11*a - 4)*q^29 + (7*a^4 + 19*a^3 - 22*a^2 - 61*a - 5)*q^30 + (-2*a^4 - 5*a^3 + 6*a^2 + 18*a + 6)*q^31 + (-4*a^4 - 8*a^3 + 14*a^2 + 25*a + 1)*q^32 + (a^4 + 3*a^3 - 3*a^2 - 10*a - 1)*q^33 + (-a^4 - 2*a^3 + 6*a^2 + 5*a)*q^34 + (a^4 + a^3 - 5*a^2 - 2*a - 2)*q^35 + (-a^4 - 3*a^3 + 2*a^2 + 13*a + 7)*q^36 + (-a^4 - 4*a^3 + 2*a^2 + 17*a + 8)*q^37 + O(q^38),
q + a*q^2 + (a^4 - a^3 - 5*a^2 + 4*a + 3)*q^3 + (a^2 - 2)*q^4 + (-a^3 + 4*a + 1)*q^5 + (a^5 - a^4 - 5*a^3 + 4*a^2 + 3*a)*q^6 + (-a^5 + 6*a^3 + a^2 - 6*a - 2)*q^7 + (a^3 - 4*a)*q^8 + (2*a^4 - a^3 - 11*a^2 + 3*a + 8)*q^9 + (-a^4 + 4*a^2 + a)*q^10 + q^11 + (2*a^5 - 3*a^4 - 10*a^3 + 16*a^2 + 2*a - 7)*q^12 + (-2*a^5 + 3*a^4 + 11*a^3 - 15*a^2 - 6*a + 5)*q^13 + (-3*a^5 + 2*a^4 + 17*a^3 - 9*a^2 - 12*a + 1)*q^14 + (-a^5 + a^4 + 5*a^3 - 5*a^2 - 3*a + 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^5 - 4*a^4 - 9*a^3 + 20*a^2 - 2*a - 7)*q^17 + (2*a^5 - a^4 - 11*a^3 + 3*a^2 + 8*a)*q^18 + (4*a^5 - 5*a^4 - 21*a^3 + 22*a^2 + 11*a - 3)*q^19 + (-a^5 + 6*a^3 + a^2 - 8*a - 2)*q^20 + (-a^5 - a^4 + 6*a^3 + 7*a^2 - 7*a - 8)*q^21 + a*q^22 - q^23 + (a^5 - 6*a^3 + 7*a - 2)*q^24 + (3*a^5 - 4*a^4 - 18*a^3 + 19*a^2 + 18*a - 5)*q^25 + (-3*a^5 + 3*a^4 + 17*a^3 - 12*a^2 - 15*a + 2)*q^26 + (-2*a^5 + 5*a^4 + 10*a^3 - 27*a^2 - 4*a + 18)*q^27 + (-5*a^5 + 5*a^4 + 27*a^3 - 23*a^2 - 17*a + 7)*q^28 + (-2*a^5 + 14*a^3 + 3*a^2 - 21*a - 6)*q^29 + (-2*a^5 + a^4 + 11*a^3 - 6*a^2 - 5*a + 1)*q^30 + (a^5 - 7*a^3 + 2*a^2 + 9*a - 7)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^4 - a^3 - 5*a^2 + 4*a + 3)*q^33 + (2*a^5 - a^4 - 12*a^3 + 4*a^2 + 13*a - 2)*q^34 + (3*a^5 - 3*a^4 - 17*a^3 + 15*a^2 + 13*a - 5)*q^35 + (5*a^5 - 7*a^4 - 27*a^3 + 36*a^2 + 14*a - 18)*q^36 + (4*a^5 - 5*a^4 - 22*a^3 + 24*a^2 + 15*a - 8)*q^37 + O(q^38)
*]> ;  // time = 29.17 seconds




J[254] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 254, 254, 254, 254, 254, 254, 127, 127 ], new_dimensions := [ 1, 1, 1, 1, 2, 5, 3, 7 ], dimensions := [ 1, 1, 1, 1, 2, 5, 6, 14 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 9, 1, 1, 1, 1, 0, 1, 17, 1, 1, 1, 1, 1, 1, 0, 1, 1149, 3, 3, 1, 1, 17, 1, 0, 1, 1, 1, 1, 9, 1, 1149, 1, 0 ], ap_traces := [
[ -1, 0, -1, -3, 1, -2, -1, -7, 9, -6, -10, 4 ],
[ 1, 0, 2, 0, 4, -2, 2, -4, 0, -6, 8, -2 ],
[ 1, -2, 0, 4, 0, 6, -6, 8, 4, -8, -8, -6 ],
[ 1, -2, -3, -1, -3, -4, 3, -7, 3, 6, -4, 2 ],
[ 2, 4, -1, 1, -7, -2, -3, 5, -3, 6, 0, 4 ],
[ -5, -2, -1, 3, 1, 10, 7, 17, -1, 0, 14, 8 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 6*x - 8,
x^5 + 2*x^4 - 10*x^3 - 16*x^2 + 10*x + 16
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 3, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 9, 1 ],
[ 17, 1 ],
[ 3447, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 9, 1 ],
[ 17, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 3 ], l_ratios := [ 0, 3, 1, 0, 17, 1/3 ], analytic_sha_upper_bounds := [ 0, 1, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 0, 1, 1 ], eigenvalues := [*
[ -1, 0, -1, -3, 1, -2, -1, -7, 9, -6, -10, 4 ],
[ 1, 0, 2, 0, 4, -2, 2, -4, 0, -6, 8, -2 ],
[ 1, -2, 0, 4, 0, 6, -6, 8, 4, -8, -8, -6 ],
[ 1, -2, -3, -1, -3, -4, 3, -7, 3, 6, -4, 2 ],
[
1,
2,
-1/2*a + 1,
1/2*a - 1,
1/2*a - 5,
a - 4,
1/2*a - 3,
-3/2*a + 7,
-3/2*a + 3,
-a + 6,
0,
2
],
[
-1,
a,
-5/2*a^4 - 2*a^3 + 27*a^2 + 7*a - 31,
3/2*a^4 + a^3 - 17*a^2 - 2*a + 23,
1/2*a^4 + a^3 - 5*a^2 - 6*a + 5,
2,
3/2*a^4 + a^3 - 17*a^2 - 4*a + 23,
-3/2*a^4 - a^3 + 17*a^2 + 2*a - 19,
-1/2*a^4 - a^3 + 5*a^2 + 6*a - 5,
-2*a^4 - a^3 + 22*a^2 + a - 26,
3*a^4 + 2*a^3 - 33*a^2 - 6*a + 42,
-5*a^4 - 4*a^3 + 54*a^2 + 14*a - 60
]
*], q_expansions := [*
q - q^2 + q^4 - q^5 - 3*q^7 - q^8 - 3*q^9 + q^10 + q^11 - 2*q^13 + 3*q^14 + q^16 - q^17 + 3*q^18 - 7*q^19 - q^20 - q^22 + 9*q^23 - 4*q^25 + 2*q^26 - 3*q^28 - 6*q^29 - 10*q^31 - q^32 + q^34 + 3*q^35 - 3*q^36 + 4*q^37 + O(q^38),
q + q^2 + q^4 + 2*q^5 + q^8 - 3*q^9 + 2*q^10 + 4*q^11 - 2*q^13 + q^16 + 2*q^17 - 3*q^18 - 4*q^19 + 2*q^20 + 4*q^22 - q^25 - 2*q^26 - 6*q^29 + 8*q^31 + q^32 + 2*q^34 - 3*q^36 - 2*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 2*q^6 + 4*q^7 + q^8 + q^9 - 2*q^12 + 6*q^13 + 4*q^14 + q^16 - 6*q^17 + q^18 + 8*q^19 - 8*q^21 + 4*q^23 - 2*q^24 - 5*q^25 + 6*q^26 + 4*q^27 + 4*q^28 - 8*q^29 - 8*q^31 + q^32 - 6*q^34 + q^36 - 6*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 3*q^5 - 2*q^6 - q^7 + q^8 + q^9 - 3*q^10 - 3*q^11 - 2*q^12 - 4*q^13 - q^14 + 6*q^15 + q^16 + 3*q^17 + q^18 - 7*q^19 - 3*q^20 + 2*q^21 - 3*q^22 + 3*q^23 - 2*q^24 + 4*q^25 - 4*q^26 + 4*q^27 - q^28 + 6*q^29 + 6*q^30 - 4*q^31 + q^32 + 6*q^33 + 3*q^34 + 3*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 + (-1/2*a + 1)*q^5 + 2*q^6 + (1/2*a - 1)*q^7 + q^8 + q^9 + (-1/2*a + 1)*q^10 + (1/2*a - 5)*q^11 + 2*q^12 + (a - 4)*q^13 + (1/2*a - 1)*q^14 + (-a + 2)*q^15 + q^16 + (1/2*a - 3)*q^17 + q^18 + (-3/2*a + 7)*q^19 + (-1/2*a + 1)*q^20 + (a - 2)*q^21 + (1/2*a - 5)*q^22 + (-3/2*a + 3)*q^23 + 2*q^24 + (1/2*a - 2)*q^25 + (a - 4)*q^26 - 4*q^27 + (1/2*a - 1)*q^28 + (-a + 6)*q^29 + (-a + 2)*q^30 + q^32 + (a - 10)*q^33 + (1/2*a - 3)*q^34 + (-1/2*a - 3)*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-5/2*a^4 - 2*a^3 + 27*a^2 + 7*a - 31)*q^5 - a*q^6 + (3/2*a^4 + a^3 - 17*a^2 - 2*a + 23)*q^7 - q^8 + (a^2 - 3)*q^9 + (5/2*a^4 + 2*a^3 - 27*a^2 - 7*a + 31)*q^10 + (1/2*a^4 + a^3 - 5*a^2 - 6*a + 5)*q^11 + a*q^12 + 2*q^13 + (-3/2*a^4 - a^3 + 17*a^2 + 2*a - 23)*q^14 + (3*a^4 + 2*a^3 - 33*a^2 - 6*a + 40)*q^15 + q^16 + (3/2*a^4 + a^3 - 17*a^2 - 4*a + 23)*q^17 + (-a^2 + 3)*q^18 + (-3/2*a^4 - a^3 + 17*a^2 + 2*a - 19)*q^19 + (-5/2*a^4 - 2*a^3 + 27*a^2 + 7*a - 31)*q^20 + (-2*a^4 - 2*a^3 + 22*a^2 + 8*a - 24)*q^21 + (-1/2*a^4 - a^3 + 5*a^2 + 6*a - 5)*q^22 + (-1/2*a^4 - a^3 + 5*a^2 + 6*a - 5)*q^23 - a*q^24 + (1/2*a^4 + a^3 - 6*a^2 - 8*a + 12)*q^25 - 2*q^26 + (a^3 - 6*a)*q^27 + (3/2*a^4 + a^3 - 17*a^2 - 2*a + 23)*q^28 + (-2*a^4 - a^3 + 22*a^2 + a - 26)*q^29 + (-3*a^4 - 2*a^3 + 33*a^2 + 6*a - 40)*q^30 + (3*a^4 + 2*a^3 - 33*a^2 - 6*a + 42)*q^31 - q^32 + (2*a^2 - 8)*q^33 + (-3/2*a^4 - a^3 + 17*a^2 + 4*a - 23)*q^34 + (-5/2*a^4 - 3*a^3 + 27*a^2 + 16*a - 33)*q^35 + (a^2 - 3)*q^36 + (-5*a^4 - 4*a^3 + 54*a^2 + 14*a - 60)*q^37 + O(q^38)
*]> ;  // time = 47.83 seconds




J[255] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 255, 255, 255, 255, 85, 85, 85, 51, 51, 17, 15 ], new_dimensions := [ 2, 2, 3, 4, 1, 2, 2, 1, 2, 1, 1 ], dimensions := [ 2, 2, 3, 4, 2, 4, 4, 2, 4, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 3, 1, 1, 1, 13, 1, 1, 1, 0, 1, 1, 1, 1, 11, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 17, 1, 9, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17, 1, 0, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 9, 1, 1, 3, 0, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 1, -2, -2, 0, 10, -6, 2, -4, 2, 8, -6, 2 ],
[ 3, -2, 2, 0, 2, 6, -2, -12, 10, -4, -10, 10 ],
[ 0, 3, 3, 4, -2, 4, 3, 0, -6, -6, 2, 16 ],
[ 1, 4, -4, 4, 2, -2, -4, 12, 2, 4, 6, -2 ]
], hecke_fields := [
x^2 - x - 3,
x^2 - 3*x + 1,
x^3 - 4*x + 1,
x^4 - x^3 - 8*x^2 + 7*x + 9
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 3, 13, 1 ],
[ 11, 1, 5 ],
[ 1, 1, 1 ],
[ 51, 9, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 51, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1, 3 ], l_ratios := [ 1, 1, 1, 17/3 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1 ], eigenvalues := [*
[
a,
-1,
-1,
2*a - 1,
5,
-2*a - 2,
1,
-2*a - 1,
-2*a + 2,
-2*a + 5,
-2*a - 2,
-4*a + 3
],
[
a,
-1,
1,
-2*a + 3,
-4*a + 7,
-2*a + 6,
-1,
2*a - 9,
2*a + 2,
-6*a + 7,
-2*a - 2,
4*a - 1
],
[
a,
1,
1,
-a^2 - a + 4,
-a^2 + a + 2,
2*a^2 - 4,
1,
-3*a^2 - 3*a + 8,
-2*a - 2,
3*a^2 - a - 10,
4*a^2 + 2*a - 10,
-a^2 - 3*a + 8
],
[
a,
1,
-1,
-a^3 - a^2 + 5*a + 5,
a^3 + a^2 - 7*a - 3,
-2*a^2 + 8,
-1,
a^3 + a^2 - 5*a - 1,
-2*a^3 + 10*a,
a^3 + a^2 - 5*a - 3,
-2*a + 2,
a^3 + 3*a^2 - 5*a - 13
]
*], q_expansions := [*
q + a*q^2 - q^3 + (a + 1)*q^4 - q^5 - a*q^6 + (2*a - 1)*q^7 + 3*q^8 + q^9 - a*q^10 + 5*q^11 + (-a - 1)*q^12 + (-2*a - 2)*q^13 + (a + 6)*q^14 + q^15 + (a - 2)*q^16 + q^17 + a*q^18 + (-2*a - 1)*q^19 + (-a - 1)*q^20 + (-2*a + 1)*q^21 + 5*a*q^22 + (-2*a + 2)*q^23 - 3*q^24 + q^25 + (-4*a - 6)*q^26 - q^27 + (3*a + 5)*q^28 + (-2*a + 5)*q^29 + a*q^30 + (-2*a - 2)*q^31 + (-a - 3)*q^32 - 5*q^33 + a*q^34 + (-2*a + 1)*q^35 + (a + 1)*q^36 + (-4*a + 3)*q^37 + O(q^38),
q + a*q^2 - q^3 + (3*a - 3)*q^4 + q^5 - a*q^6 + (-2*a + 3)*q^7 + (4*a - 3)*q^8 + q^9 + a*q^10 + (-4*a + 7)*q^11 + (-3*a + 3)*q^12 + (-2*a + 6)*q^13 + (-3*a + 2)*q^14 - q^15 + (3*a + 2)*q^16 - q^17 + a*q^18 + (2*a - 9)*q^19 + (3*a - 3)*q^20 + (2*a - 3)*q^21 + (-5*a + 4)*q^22 + (2*a + 2)*q^23 + (-4*a + 3)*q^24 + q^25 + 2*q^26 - q^27 + (-3*a - 3)*q^28 + (-6*a + 7)*q^29 - a*q^30 + (-2*a - 2)*q^31 + (3*a + 3)*q^32 + (4*a - 7)*q^33 - a*q^34 + (-2*a + 3)*q^35 + (3*a - 3)*q^36 + (4*a - 1)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + q^5 + a*q^6 + (-a^2 - a + 4)*q^7 - q^8 + q^9 + a*q^10 + (-a^2 + a + 2)*q^11 + (a^2 - 2)*q^12 + (2*a^2 - 4)*q^13 + (-a^2 + 1)*q^14 + q^15 + (-2*a^2 - a + 4)*q^16 + q^17 + a*q^18 + (-3*a^2 - 3*a + 8)*q^19 + (a^2 - 2)*q^20 + (-a^2 - a + 4)*q^21 + (a^2 - 2*a + 1)*q^22 + (-2*a - 2)*q^23 - q^24 + q^25 + (4*a - 2)*q^26 + q^27 + (2*a^2 - a - 7)*q^28 + (3*a^2 - a - 10)*q^29 + a*q^30 + (4*a^2 + 2*a - 10)*q^31 + (-a^2 - 4*a + 4)*q^32 + (-a^2 + a + 2)*q^33 + a*q^34 + (-a^2 - a + 4)*q^35 + (a^2 - 2)*q^36 + (-a^2 - 3*a + 8)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 - q^5 + a*q^6 + (-a^3 - a^2 + 5*a + 5)*q^7 + (a^3 - 4*a)*q^8 + q^9 - a*q^10 + (a^3 + a^2 - 7*a - 3)*q^11 + (a^2 - 2)*q^12 + (-2*a^2 + 8)*q^13 + (-2*a^3 - 3*a^2 + 12*a + 9)*q^14 - q^15 + (a^3 + 2*a^2 - 7*a - 5)*q^16 - q^17 + a*q^18 + (a^3 + a^2 - 5*a - 1)*q^19 + (-a^2 + 2)*q^20 + (-a^3 - a^2 + 5*a + 5)*q^21 + (2*a^3 + a^2 - 10*a - 9)*q^22 + (-2*a^3 + 10*a)*q^23 + (a^3 - 4*a)*q^24 + q^25 + (-2*a^3 + 8*a)*q^26 + q^27 + (-3*a^3 - 2*a^2 + 13*a + 8)*q^28 + (a^3 + a^2 - 5*a - 3)*q^29 - a*q^30 + (-2*a + 2)*q^31 + (a^3 + a^2 - 4*a - 9)*q^32 + (a^3 + a^2 - 7*a - 3)*q^33 - a*q^34 + (a^3 + a^2 - 5*a - 5)*q^35 + (a^2 - 2)*q^36 + (a^3 + 3*a^2 - 5*a - 13)*q^37 + O(q^38)
*]> ;  // time = 68.171 seconds




J[257] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 257, 257 ], new_dimensions := [ 7, 14 ], dimensions := [ 7, 14 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -3, -5, -1, -18, -2, -10, -10, -7, -12, 7, -9, -11 ],
[ 2, 3, -1, 24, 2, 12, -4, 9, 20, -3, 3, 5 ]
], hecke_fields := [
x^7 + 3*x^6 - 3*x^5 - 11*x^4 + 3*x^3 + 10*x^2 - x - 1,
x^14 - 2*x^13 - 21*x^12 + 42*x^11 + 163*x^10 - 327*x^9 - 568*x^8 + 1153*x^7 + 830*x^6 - 1755*x^5 - 318*x^4 + 825*x^3 + 10*x^2 - 96*x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ]
], torsion_upper_bounds := [ 1, 1 ], torsion_lower_bounds := [ 1, 1 ], l_ratios := [ 0, 1 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
a^4 + 2*a^3 - 3*a^2 - 4*a + 1,
-a^5 - 4*a^4 - a^3 + 9*a^2 + 4*a - 3,
a^6 + 4*a^5 - 12*a^3 - 4*a^2 + 8*a - 1,
-a^6 - 2*a^5 + 6*a^4 + 9*a^3 - 9*a^2 - 7*a,
a^6 + 2*a^5 - 5*a^4 - 5*a^3 + 11*a^2 - 6,
2*a^6 + 8*a^5 + a^4 - 22*a^3 - 9*a^2 + 14*a,
-3*a^6 - 8*a^5 + 11*a^4 + 28*a^3 - 15*a^2 - 20*a + 4,
-a^6 - 5*a^5 - 2*a^4 + 16*a^3 + 9*a^2 - 12*a - 4,
a^5 + a^4 - 7*a^3 - 8*a^2 + 6*a + 9,
-a^6 - 5*a^5 - 6*a^4 + 4*a^3 + 12*a^2 + 9*a - 1,
3*a^6 + 7*a^5 - 13*a^4 - 27*a^3 + 17*a^2 + 25*a - 6
],
[
a,
1755/144512*a^13 - 14949/144512*a^12 - 15147/72256*a^11 + 77379/36128*a^10 + 155093/144512*a^9 - 1184607/72256*a^8 - 21849/72256*a^7 + 8189141/144512*a^6 - 1591687/144512*a^5 - 6092391/72256*a^4 + 826663/36128*a^3 + 5567751/144512*a^2 - 838701/144512*a - 479015/144512,
6245/72256*a^13 - 7803/72256*a^12 - 66405/36128*a^11 + 40205/18064*a^10 + 1060043/72256*a^9 - 610385/36128*a^8 - 1969527/36128*a^7 + 4165227/72256*a^6 + 6795559/72256*a^5 - 3048569/36128*a^4 - 1165231/18064*a^3 + 2740441/72256*a^2 + 1042445/72256*a - 214841/72256,
3085/144512*a^13 - 803/144512*a^12 - 29405/72256*a^11 + 2701/36128*a^10 + 376483/144512*a^9 - 13089/72256*a^8 - 389111/72256*a^7 - 168493/144512*a^6 - 729569/144512*a^5 + 434759/72256*a^4 + 866533/36128*a^3 - 1185999/144512*a^2 - 1265867/144512*a + 477775/144512,
7307/36128*a^13 - 11013/36128*a^12 - 78211/18064*a^11 + 57571/9032*a^10 + 1255701/36128*a^9 - 887991/18064*a^8 - 2333329/18064*a^7 + 6124677/36128*a^6 + 7879545/36128*a^5 - 4385815/18064*a^4 - 1210133/9032*a^3 + 3144647/36128*a^2 + 698611/36128*a - 95719/36128,
215/36128*a^13 - 905/36128*a^12 - 2203/18064*a^11 + 4481/9032*a^10 + 29473/36128*a^9 - 63719/18064*a^8 - 22053/18064*a^7 + 383777/36128*a^6 - 252067/36128*a^5 - 201971/18064*a^4 + 208273/9032*a^3 - 46029/36128*a^2 - 424425/36128*a + 76437/36128,
255/4516*a^13 - 261/2258*a^12 - 5357/4516*a^11 + 5667/2258*a^10 + 10321/1129*a^9 - 91783/4516*a^8 - 140295/4516*a^7 + 338339/4516*a^6 + 47119/1129*a^5 - 135015/1129*a^4 - 35287/4516*a^3 + 66268/1129*a^2 - 7256/1129*a - 6788/1129,
-24769/144512*a^13 + 44607/144512*a^12 + 263521/72256*a^11 - 233793/36128*a^10 - 4182639/144512*a^9 + 3614269/72256*a^8 + 7602267/72256*a^7 - 24927727/144512*a^6 - 24546683/144512*a^5 + 17660933/72256*a^4 + 3435315/36128*a^3 - 11568517/144512*a^2 - 2663753/144512*a + 320581/144512,
-4017/36128*a^13 + 8927/36128*a^12 + 40089/18064*a^11 - 46449/9032*a^10 - 567343/36128*a^9 + 711749/18064*a^8 + 804483/18064*a^7 - 4870079/36128*a^6 - 1036987/36128*a^5 + 3480933/18064*a^4 - 481241/9032*a^3 - 2725669/36128*a^2 + 1005655/36128*a + 299589/36128,
1823/36128*a^13 - 5153/36128*a^12 - 21431/18064*a^11 + 25749/9032*a^10 + 391601/36128*a^9 - 373879/18064*a^8 - 873757/18064*a^7 + 2364609/36128*a^6 + 3881085/36128*a^5 - 1449695/18064*a^4 - 944983/9032*a^3 + 540475/36128*a^2 + 999399/36128*a - 27731/36128,
-8595/72256*a^13 + 9293/72256*a^12 + 93635/36128*a^11 - 46859/18064*a^10 - 1541405/72256*a^9 + 694983/36128*a^8 + 2976401/36128*a^7 - 4612349/72256*a^6 - 10800545/72256*a^5 + 3178799/36128*a^4 + 2019817/18064*a^3 - 1991999/72256*a^2 - 2301067/72256*a - 59809/72256,
-12759/72256*a^13 + 10857/72256*a^12 + 143191/36128*a^11 - 54583/18064*a^10 - 2452665/72256*a^9 + 799931/36128*a^8 + 5001293/36128*a^7 - 5150393/72256*a^6 - 19579405/72256*a^5 + 3307859/36128*a^4 + 4006917/18064*a^3 - 1552051/72256*a^2 - 3973391/72256*a - 162125/72256
]
*], q_expansions := [*
q + a*q^2 + (a^4 + 2*a^3 - 3*a^2 - 4*a + 1)*q^3 + (a^2 - 2)*q^4 + (-a^5 - 4*a^4 - a^3 + 9*a^2 + 4*a - 3)*q^5 + (a^5 + 2*a^4 - 3*a^3 - 4*a^2 + a)*q^6 + (a^6 + 4*a^5 - 12*a^3 - 4*a^2 + 8*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^6 - 6*a^5 + 3*a^4 + 15*a^3 + a^2 - 6*a - 1)*q^9 + (-a^6 - 4*a^5 - a^4 + 9*a^3 + 4*a^2 - 3*a)*q^10 + (-a^6 - 2*a^5 + 6*a^4 + 9*a^3 - 9*a^2 - 7*a)*q^11 + (a^6 + 2*a^5 - 5*a^4 - 8*a^3 + 7*a^2 + 8*a - 2)*q^12 + (a^6 + 2*a^5 - 5*a^4 - 5*a^3 + 11*a^2 - 6)*q^13 + (a^6 + 3*a^5 - a^4 - 7*a^3 - 2*a^2 + 1)*q^14 + (3*a^6 + 10*a^5 - 3*a^4 - 26*a^3 - 2*a^2 + 13*a - 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^6 + 8*a^5 + a^4 - 22*a^3 - 9*a^2 + 14*a)*q^17 + (-3*a^5 - 7*a^4 + 7*a^3 + 14*a^2 - 3*a - 2)*q^18 + (-3*a^6 - 8*a^5 + 11*a^4 + 28*a^3 - 15*a^2 - 20*a + 4)*q^19 + (-a^6 - 2*a^5 + 6*a^4 + 9*a^3 - 11*a^2 - 9*a + 5)*q^20 + (-a^6 - 5*a^5 - 6*a^4 + 7*a^3 + 19*a^2 + 6*a - 6)*q^21 + (a^6 + 3*a^5 - 2*a^4 - 6*a^3 + 3*a^2 - a - 1)*q^22 + (-a^6 - 5*a^5 - 2*a^4 + 16*a^3 + 9*a^2 - 12*a - 4)*q^23 + (-a^6 - 4*a^5 - a^4 + 10*a^3 + 6*a^2 - 3*a + 1)*q^24 + (-3*a^6 - 9*a^5 + 8*a^4 + 30*a^3 - 7*a^2 - 20*a + 2)*q^25 + (-a^6 - 2*a^5 + 6*a^4 + 8*a^3 - 10*a^2 - 5*a + 1)*q^26 + (3*a^6 + 10*a^5 - 3*a^4 - 27*a^3 - 4*a^2 + 17*a)*q^27 + (-2*a^6 - 6*a^5 + 4*a^4 + 19*a^3 - 2*a^2 - 14*a + 3)*q^28 + (a^5 + a^4 - 7*a^3 - 8*a^2 + 6*a + 9)*q^29 + (a^6 + 6*a^5 + 7*a^4 - 11*a^3 - 17*a^2 + 3)*q^30 + (-a^6 - 5*a^5 - 6*a^4 + 4*a^3 + 12*a^2 + 9*a - 1)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^6 - 4*a^5 - a^4 + 8*a^3 + 3*a^2 + 2)*q^33 + (2*a^6 + 7*a^5 - 15*a^3 - 6*a^2 + 2*a + 2)*q^34 + (4*a^5 + 15*a^4 + 2*a^3 - 34*a^2 - 15*a + 10)*q^35 + (a^6 + 5*a^5 + a^4 - 16*a^3 - 5*a^2 + 10*a + 2)*q^36 + (3*a^6 + 7*a^5 - 13*a^4 - 27*a^3 + 17*a^2 + 25*a - 6)*q^37 + O(q^38),
q + a*q^2 + (1755/144512*a^13 - 14949/144512*a^12 - 15147/72256*a^11 + 77379/36128*a^10 + 155093/144512*a^9 - 1184607/72256*a^8 - 21849/72256*a^7 + 8189141/144512*a^6 - 1591687/144512*a^5 - 6092391/72256*a^4 + 826663/36128*a^3 + 5567751/144512*a^2 - 838701/144512*a - 479015/144512)*q^3 + (a^2 - 2)*q^4 + (6245/72256*a^13 - 7803/72256*a^12 - 66405/36128*a^11 + 40205/18064*a^10 + 1060043/72256*a^9 - 610385/36128*a^8 - 1969527/36128*a^7 + 4165227/72256*a^6 + 6795559/72256*a^5 - 3048569/36128*a^4 - 1165231/18064*a^3 + 2740441/72256*a^2 + 1042445/72256*a - 214841/72256)*q^5 + (-11439/144512*a^13 + 6561/144512*a^12 + 117903/72256*a^11 - 32743/36128*a^10 - 1795329/144512*a^9 + 476571/72256*a^8 + 3082813/72256*a^7 - 3048337/144512*a^6 - 9104757/144512*a^5 + 1932371/72256*a^4 + 1029969/36128*a^3 - 856251/144512*a^2 - 310535/144512*a + 1755/144512)*q^6 + (3085/144512*a^13 - 803/144512*a^12 - 29405/72256*a^11 + 2701/36128*a^10 + 376483/144512*a^9 - 13089/72256*a^8 - 389111/72256*a^7 - 168493/144512*a^6 - 729569/144512*a^5 + 434759/72256*a^4 + 866533/36128*a^3 - 1185999/144512*a^2 - 1265867/144512*a + 477775/144512)*q^7 + (a^3 - 4*a)*q^8 + (-2903/18064*a^13 + 4973/18064*a^12 + 31447/9032*a^11 - 12931/2258*a^10 - 510665/18064*a^9 + 396635/9032*a^8 + 955811/9032*a^7 - 2725157/18064*a^6 - 3211105/18064*a^5 + 1967487/9032*a^4 + 472569/4516*a^3 - 1557671/18064*a^2 - 246359/18064*a + 134227/18064)*q^9 + (4687/72256*a^13 - 1665/72256*a^12 - 50735/36128*a^11 + 10527/18064*a^10 + 821345/72256*a^9 - 195947/36128*a^8 - 1517629/36128*a^7 + 1612209/72256*a^6 + 4862837/72256*a^5 - 1337507/36128*a^4 - 602921/18064*a^3 + 979995/72256*a^2 + 384679/72256*a + 6245/72256)*q^10 + (7307/36128*a^13 - 11013/36128*a^12 - 78211/18064*a^11 + 57571/9032*a^10 + 1255701/36128*a^9 - 887991/18064*a^8 - 2333329/18064*a^7 + 6124677/36128*a^6 + 7879545/36128*a^5 - 4385815/18064*a^4 - 1210133/9032*a^3 + 3144647/36128*a^2 + 698611/36128*a - 95719/36128)*q^11 + (-19827/144512*a^13 + 25485/144512*a^12 + 205027/72256*a^11 - 137451/36128*a^10 - 3097597/144512*a^9 + 2203351/72256*a^8 + 5114113/72256*a^7 - 15988669/144512*a^6 - 13027329/144512*a^5 + 12425919/72256*a^4 + 491905/36128*a^3 - 11331647/144512*a^2 + 581013/144512*a + 946591/144512)*q^12 + (215/36128*a^13 - 905/36128*a^12 - 2203/18064*a^11 + 4481/9032*a^10 + 29473/36128*a^9 - 63719/18064*a^8 - 22053/18064*a^7 + 383777/36128*a^6 - 252067/36128*a^5 - 201971/18064*a^4 + 208273/9032*a^3 - 46029/36128*a^2 - 424425/36128*a + 76437/36128)*q^13 + (5367/144512*a^13 + 5975/144512*a^12 - 59383/72256*a^11 - 31593/36128*a^10 + 982617/144512*a^9 + 487029/72256*a^8 - 1862749/72256*a^7 - 3290119/144512*a^6 + 6283693/144512*a^5 + 2223581/72256*a^4 - 932781/36128*a^3 - 1296717/144512*a^2 + 773935/144512*a + 3085/144512)*q^14 + (-6555/72256*a^13 + 14149/72256*a^12 + 67691/36128*a^11 - 73867/18064*a^10 - 1021461/72256*a^9 + 1145247/36128*a^8 + 1679113/36128*a^7 - 8065461/72256*a^6 - 4117401/72256*a^5 + 6157767/36128*a^4 - 21991/18064*a^3 - 5841575/72256*a^2 + 998253/72256*a + 743591/72256)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (255/4516*a^13 - 261/2258*a^12 - 5357/4516*a^11 + 5667/2258*a^10 + 10321/1129*a^9 - 91783/4516*a^8 - 140295/4516*a^7 + 338339/4516*a^6 + 47119/1129*a^5 - 135015/1129*a^4 - 35287/4516*a^3 + 66268/1129*a^2 - 7256/1129*a - 6788/1129)*q^17 + (-833/18064*a^13 + 1931/18064*a^12 + 9239/9032*a^11 - 9369/4516*a^10 - 156011/18064*a^9 + 131359/9032*a^8 + 311001/9032*a^7 - 801615/18064*a^6 - 1159791/18064*a^5 + 483561/9032*a^4 + 104663/2258*a^3 - 217329/18064*a^2 - 144461/18064*a - 2903/18064)*q^18 + (-24769/144512*a^13 + 44607/144512*a^12 + 263521/72256*a^11 - 233793/36128*a^10 - 4182639/144512*a^9 + 3614269/72256*a^8 + 7602267/72256*a^7 - 24927727/144512*a^6 - 24546683/144512*a^5 + 17660933/72256*a^4 + 3435315/36128*a^3 - 11568517/144512*a^2 - 2663753/144512*a + 320581/144512)*q^19 + (-4781/72256*a^13 + 12563/72256*a^12 + 55437/36128*a^11 - 66069/18064*a^10 - 979331/72256*a^9 + 1034249/36128*a^8 + 2043103/36128*a^7 - 7357827/72256*a^6 - 8040447/72256*a^5 + 5636529/36128*a^4 + 1608767/18064*a^3 - 5143073/72256*a^2 - 1628693/72256*a + 434369/72256)*q^20 + (3189/36128*a^13 - 11323/36128*a^12 - 32109/18064*a^11 + 58819/9032*a^10 + 459803/36128*a^9 - 905501/18064*a^8 - 663975/18064*a^7 + 6317115/36128*a^6 + 919151/36128*a^5 - 4772341/18064*a^4 + 368867/9032*a^3 + 4469209/36128*a^2 - 770035/36128*a - 407313/36128)*q^21 + (3601/36128*a^13 - 2975/36128*a^12 - 38305/18064*a^11 + 16165/9032*a^10 + 613407/36128*a^9 - 258141/18064*a^8 - 1150147/18064*a^7 + 1814735/36128*a^6 + 4052155/36128*a^5 - 1258453/18064*a^4 - 720907/9032*a^3 + 625541/36128*a^2 + 605753/36128*a + 7307/36128)*q^22 + (-4017/36128*a^13 + 8927/36128*a^12 + 40089/18064*a^11 - 46449/9032*a^10 - 567343/36128*a^9 + 711749/18064*a^8 + 804483/18064*a^7 - 4870079/36128*a^6 - 1036987/36128*a^5 + 3480933/18064*a^4 - 481241/9032*a^3 - 2725669/36128*a^2 + 1005655/36128*a + 299589/36128)*q^23 + (8709/144512*a^13 - 19435/144512*a^12 - 94341/72256*a^11 + 99037/36128*a^10 + 1513931/144512*a^9 - 1469897/72256*a^8 - 2729695/72256*a^7 + 9525755/144512*a^6 + 8264967/144512*a^5 - 6033425/72256*a^4 - 803531/36128*a^3 + 2491785/144512*a^2 - 335731/144512*a - 23337/144512)*q^24 + (2075/18064*a^13 - 2853/18064*a^12 - 23467/9032*a^11 + 14523/4516*a^10 + 403125/18064*a^9 - 215559/9032*a^8 - 817561/9032*a^7 + 1394853/18064*a^6 + 3151977/18064*a^5 - 865415/9032*a^4 - 636877/4516*a^3 + 243879/18064*a^2 + 653587/18064*a + 92233/18064)*q^25 + (-475/36128*a^13 + 109/36128*a^12 + 4447/18064*a^11 - 1393/9032*a^10 - 57133/36128*a^9 + 39007/18064*a^8 + 67941/18064*a^7 - 430517/36128*a^6 - 26617/36128*a^5 + 450731/18064*a^4 - 55851/9032*a^3 - 426575/36128*a^2 + 97077/36128*a + 215/36128)*q^26 + (-5133/72256*a^13 + 6483/72256*a^12 + 55557/36128*a^11 - 31249/18064*a^10 - 912563/72256*a^9 + 418993/36128*a^8 + 1783967/36128*a^7 - 2136691/72256*a^6 - 6789759/72256*a^5 + 345681/36128*a^4 + 1391939/18064*a^3 + 3390271/72256*a^2 - 1207301/72256*a - 1084559/72256)*q^27 + (10539/144512*a^13 - 4453/144512*a^12 - 117083/72256*a^11 + 21547/36128*a^10 + 1976101/144512*a^9 - 312343/72256*a^8 - 3960913/72256*a^7 + 2166069/144512*a^6 + 15325385/144512*a^5 - 1881727/72256*a^4 - 3164189/36128*a^3 + 3092263/144512*a^2 + 3050051/144512*a - 950183/144512)*q^28 + (1823/36128*a^13 - 5153/36128*a^12 - 21431/18064*a^11 + 25749/9032*a^10 + 391601/36128*a^9 - 373879/18064*a^8 - 873757/18064*a^7 + 2364609/36128*a^6 + 3881085/36128*a^5 - 1449695/18064*a^4 - 944983/9032*a^3 + 540475/36128*a^2 + 999399/36128*a - 27731/36128)*q^29 + (1039/72256*a^13 - 2273/72256*a^12 - 10079/36128*a^11 + 11751/18064*a^10 + 147009/72256*a^9 - 182507/36128*a^8 - 253773/36128*a^7 + 1323249/72256*a^6 + 811509/72256*a^5 - 1086227/36128*a^4 - 108425/18064*a^3 + 1063803/72256*a^2 + 114311/72256*a - 6555/72256)*q^30 + (-8595/72256*a^13 + 9293/72256*a^12 + 93635/36128*a^11 - 46859/18064*a^10 - 1541405/72256*a^9 + 694983/36128*a^8 + 2976401/36128*a^7 - 4612349/72256*a^6 - 10800545/72256*a^5 + 3178799/36128*a^4 + 2019817/18064*a^3 - 1991999/72256*a^2 - 2301067/72256*a - 59809/72256)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (6729/36128*a^13 - 12991/36128*a^12 - 74473/18064*a^11 + 66277/9032*a^10 + 1250487/36128*a^9 - 984857/18064*a^8 - 2471255/18064*a^7 + 6372671/36128*a^6 + 9135747/36128*a^5 - 3952129/18064*a^4 - 1639893/9032*a^3 + 1086805/36128*a^2 + 1106561/36128*a + 345019/36128)*q^33 + (-3/1129*a^13 - 1/2258*a^12 + 156/1129*a^11 - 281/4516*a^10 - 4199/2258*a^9 + 4545/4516*a^8 + 11081/1129*a^7 - 11587/2258*a^6 - 92535/4516*a^5 + 45803/4516*a^4 + 54697/4516*a^3 - 15787/2258*a^2 - 668/1129*a + 255/4516)*q^34 + (8695/72256*a^13 - 5513/72256*a^12 - 91719/36128*a^11 + 30039/18064*a^10 + 1445049/72256*a^9 - 486427/36128*a^8 - 2619917/36128*a^7 + 3594425/72256*a^6 + 8571917/72256*a^5 - 2983715/36128*a^4 - 1295957/18064*a^3 + 3762707/72256*a^2 + 1141647/72256*a - 754067/72256)*q^35 + (6071/18064*a^13 - 8961/18064*a^12 - 64139/9032*a^11 + 23333/2258*a^10 + 1011657/18064*a^9 - 718841/9032*a^8 - 1832205/9032*a^7 + 4981913/18064*a^6 + 5927417/18064*a^5 - 3648769/9032*a^4 - 206916/1129*a^3 + 2979211/18064*a^2 + 409847/18064*a - 269287/18064)*q^36 + (-12759/72256*a^13 + 10857/72256*a^12 + 143191/36128*a^11 - 54583/18064*a^10 - 2452665/72256*a^9 + 799931/36128*a^8 + 5001293/36128*a^7 - 5150393/72256*a^6 - 19579405/72256*a^5 + 3307859/36128*a^4 + 4006917/18064*a^3 - 1552051/72256*a^2 - 3973391/72256*a - 162125/72256)*q^37 + O(q^38)
*]> ;  // time = 3.641 seconds




J[258] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 258, 258, 258, 258, 258, 258, 258, 129, 129, 129, 129, 86, 86, 43, 43 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 1, 2 ], dimensions := [ 1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 6, 4, 4, 4, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 7, 1, 7, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 0, 5, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 0, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 25, 1, 1, 9, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 0, 1, 7, 1, 1, 49, 1, 1, 1, 1, 1, 1, 1, 1, 25, 1, 0, 1, 11, 1, 1, 1, 7, 5, 1, 1, 1, 1, 1, 1, 7, 1, 0, 1, 1, 49, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 11, 1, 0, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 25, 0, 1, 1, 7, 1, 1, 1, 7, 1, 1, 1, 49, 1, 49, 1, 1, 0 ], ap_traces := [
[ -1, -1, 1, -5, 1, -3, 0, -7, -4, -3, -2, 2 ],
[ -1, -1, -2, 2, 0, 2, 6, 4, 6, -2, 4, 4 ],
[ -1, 1, -3, -3, -5, -3, 0, 7, -4, 1, -6, -6 ],
[ 1, -1, -2, 4, 4, 6, -6, -4, -4, 6, -8, 2 ],
[ 1, -1, 3, -1, -1, 1, 4, 1, -4, -9, 2, 2 ],
[ 1, 1, -1, 1, 5, -7, 4, -1, -4, -5, -10, 10 ],
[ 1, 1, 2, -2, -4, 2, -2, -4, 2, 10, -4, -8 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ 1, -1, -1 ],
[ -1, 1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 3, 1, 1 ],
[ 7, 7, 1 ],
[ 1, 5, 1 ],
[ 3, 1, 1 ],
[ 1, 19, 1 ],
[ 7, 7, 1 ],
[ 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 5, 1 ],
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 7, 7, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 7, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 0, 3, 1, 1, 1 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1, 1, 1/49, 1 ], eigenvalues := [*
[ -1, -1, 1, -5, 1, -3, 0, -7, -4, -3, -2, 2 ],
[ -1, -1, -2, 2, 0, 2, 6, 4, 6, -2, 4, 4 ],
[ -1, 1, -3, -3, -5, -3, 0, 7, -4, 1, -6, -6 ],
[ 1, -1, -2, 4, 4, 6, -6, -4, -4, 6, -8, 2 ],
[ 1, -1, 3, -1, -1, 1, 4, 1, -4, -9, 2, 2 ],
[ 1, 1, -1, 1, 5, -7, 4, -1, -4, -5, -10, 10 ],
[ 1, 1, 2, -2, -4, 2, -2, -4, 2, 10, -4, -8 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + q^5 + q^6 - 5*q^7 - q^8 + q^9 - q^10 + q^11 - q^12 - 3*q^13 + 5*q^14 - q^15 + q^16 - q^18 - 7*q^19 + q^20 + 5*q^21 - q^22 - 4*q^23 + q^24 - 4*q^25 + 3*q^26 - q^27 - 5*q^28 - 3*q^29 + q^30 - 2*q^31 - q^32 - q^33 - 5*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 - q^3 + q^4 - 2*q^5 + q^6 + 2*q^7 - q^8 + q^9 + 2*q^10 - q^12 + 2*q^13 - 2*q^14 + 2*q^15 + q^16 + 6*q^17 - q^18 + 4*q^19 - 2*q^20 - 2*q^21 + 6*q^23 + q^24 - q^25 - 2*q^26 - q^27 + 2*q^28 - 2*q^29 - 2*q^30 + 4*q^31 - q^32 - 6*q^34 - 4*q^35 + q^36 + 4*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - 3*q^5 - q^6 - 3*q^7 - q^8 + q^9 + 3*q^10 - 5*q^11 + q^12 - 3*q^13 + 3*q^14 - 3*q^15 + q^16 - q^18 + 7*q^19 - 3*q^20 - 3*q^21 + 5*q^22 - 4*q^23 - q^24 + 4*q^25 + 3*q^26 + q^27 - 3*q^28 + q^29 + 3*q^30 - 6*q^31 - q^32 - 5*q^33 + 9*q^35 + q^36 - 6*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 2*q^5 - q^6 + 4*q^7 + q^8 + q^9 - 2*q^10 + 4*q^11 - q^12 + 6*q^13 + 4*q^14 + 2*q^15 + q^16 - 6*q^17 + q^18 - 4*q^19 - 2*q^20 - 4*q^21 + 4*q^22 - 4*q^23 - q^24 - q^25 + 6*q^26 - q^27 + 4*q^28 + 6*q^29 + 2*q^30 - 8*q^31 + q^32 - 4*q^33 - 6*q^34 - 8*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + 3*q^5 - q^6 - q^7 + q^8 + q^9 + 3*q^10 - q^11 - q^12 + q^13 - q^14 - 3*q^15 + q^16 + 4*q^17 + q^18 + q^19 + 3*q^20 + q^21 - q^22 - 4*q^23 - q^24 + 4*q^25 + q^26 - q^27 - q^28 - 9*q^29 - 3*q^30 + 2*q^31 + q^32 + q^33 + 4*q^34 - 3*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - q^5 + q^6 + q^7 + q^8 + q^9 - q^10 + 5*q^11 + q^12 - 7*q^13 + q^14 - q^15 + q^16 + 4*q^17 + q^18 - q^19 - q^20 + q^21 + 5*q^22 - 4*q^23 + q^24 - 4*q^25 - 7*q^26 + q^27 + q^28 - 5*q^29 - q^30 - 10*q^31 + q^32 + 5*q^33 + 4*q^34 - q^35 + q^36 + 10*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + 2*q^5 + q^6 - 2*q^7 + q^8 + q^9 + 2*q^10 - 4*q^11 + q^12 + 2*q^13 - 2*q^14 + 2*q^15 + q^16 - 2*q^17 + q^18 - 4*q^19 + 2*q^20 - 2*q^21 - 4*q^22 + 2*q^23 + q^24 - q^25 + 2*q^26 + q^27 - 2*q^28 + 10*q^29 + 2*q^30 - 4*q^31 + q^32 - 4*q^33 - 2*q^34 - 4*q^35 + q^36 - 8*q^37 + O(q^38)
*]> ;  // time = 140.949 seconds




J[259] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 259, 259, 259, 259, 259, 259, 259, 37, 37 ], new_dimensions := [ 1, 2, 2, 3, 3, 4, 4, 1, 1 ], dimensions := [ 1, 2, 2, 3, 3, 4, 4, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 3, 3, 1, 1, 0, 1, 1, 1, 17, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 1, 1, 0, 1, 1, 1, 3, 1, 17, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 3, 1, 3, 1, 1, 7, 1, 1, 3, 0, 1, 1, 7, 1, 1, 3, 1, 1, 1, 0 ], ap_traces := [
[ 1, 0, 4, 1, 4, 4, 0, -6, -4, -6, 2, -1 ],
[ 0, 0, 6, -2, -6, 2, 0, 4, 0, 0, 2, 2 ],
[ 1, 0, 1, 2, -1, 1, 2, 6, 8, 6, -5, -2 ],
[ 1, -2, -6, -3, -1, 1, -7, -7, -1, -10, 2, -3 ],
[ -3, 0, -6, 3, -9, -3, -3, -3, -9, -18, 6, 3 ],
[ 0, 2, 6, -4, 3, 5, 13, -7, -5, 20, 10, 4 ],
[ 1, 0, 1, 4, 10, -8, -3, -3, -1, 18, -13, -4 ]
], hecke_fields := [
x - 1,
x^2 - 32,
x^2 - x - 4,
x^3 - x^2 - 2*x + 1,
x^3 + 3*x^2 - 3,
x^4 - 9*x^2 + x + 17,
x^4 - x^3 - 6*x^2 + 5*x + 4
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 57, 1 ]
], tamagawa_numbers := [
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 57, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 3, 1, 19 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 19 ], l_ratios := [ 3, 1, 1, 0, 0, 1, 3/19 ], analytic_sha_upper_bounds := [ 1, 1, 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 0, 0, 1, 1 ], eigenvalues := [*
[ 1, 0, 4, 1, 4, 4, 0, -6, -4, -6, 2, -1 ],
[
0,
-1/2*a,
-1/4*a + 3,
-1,
1/2*a - 3,
3/4*a + 1,
1/2*a,
2,
1/2*a,
-1/2*a,
3/4*a + 1,
1
],
[
a,
0,
-a + 1,
1,
a - 1,
-a + 1,
-2*a + 2,
-2*a + 4,
4,
-2*a + 4,
a - 3,
-1
],
[
a,
-a^2 + 1,
a^2 - 2*a - 3,
-1,
a^2 - 2,
-3*a^2 + a + 5,
3*a^2 + 2*a - 8,
-2*a^2 + 1,
-2*a^2 + 3*a + 2,
-4*a^2 + a + 3,
6*a^2 - a - 9,
-1
],
[
a,
-a^2 - 2*a + 1,
a^2 + 2*a - 3,
1,
a^2 - 6,
3*a^2 + 3*a - 7,
-a^2 - 2*a,
-2*a^2 + 5,
2*a^2 + 3*a - 6,
3*a - 3,
-4*a^2 - 3*a + 11,
1
],
[
a,
-a^2 + 5,
a^2 - 3,
-1,
-a^3 - 2*a^2 + 4*a + 9,
a^3 - 5*a + 2,
a^3 + 2*a^2 - 6*a - 5,
-a^3 - a^2 + 6*a + 2,
a^3 + a^2 - 5*a - 5,
-a + 5,
-2*a^3 - 4*a^2 + 9*a + 19,
1
],
[
a,
-a^3 + 4*a,
a^2 - 3,
1,
a^3 - 6*a + 3,
-a^2 + a + 1,
-a^2 + 2*a + 2,
a^3 + a^2 - 4*a - 4,
-2*a^3 + 7*a,
a^3 - a^2 - 5*a + 8,
-a - 3,
-1
]
*], q_expansions := [*
q + q^2 - q^4 + 4*q^5 + q^7 - 3*q^8 - 3*q^9 + 4*q^10 + 4*q^11 + 4*q^13 + q^14 - q^16 - 3*q^18 - 6*q^19 - 4*q^20 + 4*q^22 - 4*q^23 + 11*q^25 + 4*q^26 - q^28 - 6*q^29 + 2*q^31 + 5*q^32 + 4*q^35 + 3*q^36 - q^37 + O(q^38),
q - 1/2*a*q^3 - 2*q^4 + (-1/4*a + 3)*q^5 - q^7 + 5*q^9 + (1/2*a - 3)*q^11 + a*q^12 + (3/4*a + 1)*q^13 + (-3/2*a + 4)*q^15 + 4*q^16 + 1/2*a*q^17 + 2*q^19 + (1/2*a - 6)*q^20 + 1/2*a*q^21 + 1/2*a*q^23 + (-3/2*a + 6)*q^25 - a*q^27 + 2*q^28 - 1/2*a*q^29 + (3/4*a + 1)*q^31 + (3/2*a - 8)*q^33 + (1/4*a - 3)*q^35 - 10*q^36 + q^37 + O(q^38),
q + a*q^2 + (a + 2)*q^4 + (-a + 1)*q^5 + q^7 + (a + 4)*q^8 - 3*q^9 - 4*q^10 + (a - 1)*q^11 + (-a + 1)*q^13 + a*q^14 + 3*a*q^16 + (-2*a + 2)*q^17 - 3*a*q^18 + (-2*a + 4)*q^19 + (-2*a - 2)*q^20 + 4*q^22 + 4*q^23 - a*q^25 - 4*q^26 + (a + 2)*q^28 + (-2*a + 4)*q^29 + (a - 3)*q^31 + (a + 4)*q^32 - 8*q^34 + (-a + 1)*q^35 + (-3*a - 6)*q^36 - q^37 + O(q^38),
q + a*q^2 + (-a^2 + 1)*q^3 + (a^2 - 2)*q^4 + (a^2 - 2*a - 3)*q^5 + (-a^2 - a + 1)*q^6 - q^7 + (a^2 - 2*a - 1)*q^8 + (a^2 + a - 3)*q^9 + (-a^2 - a - 1)*q^10 + (a^2 - 2)*q^11 + (-a - 1)*q^12 + (-3*a^2 + a + 5)*q^13 - a*q^14 + (3*a^2 + a - 4)*q^15 + (-3*a^2 + a + 3)*q^16 + (3*a^2 + 2*a - 8)*q^17 + (2*a^2 - a - 1)*q^18 + (-2*a^2 + 1)*q^19 + (-4*a^2 + a + 7)*q^20 + (a^2 - 1)*q^21 + (a^2 - 1)*q^22 + (-2*a^2 + 3*a + 2)*q^23 + (a^2 + a - 2)*q^24 + (-3*a^2 + 5*a + 7)*q^25 + (-2*a^2 - a + 3)*q^26 + (3*a^2 - 2*a - 4)*q^27 + (-a^2 + 2)*q^28 + (-4*a^2 + a + 3)*q^29 + (4*a^2 + 2*a - 3)*q^30 + (6*a^2 - a - 9)*q^31 + (-4*a^2 + a + 5)*q^32 + (-a - 1)*q^33 + (5*a^2 - 2*a - 3)*q^34 + (-a^2 + 2*a + 3)*q^35 + (-a^2 + a + 4)*q^36 - q^37 + O(q^38),
q + a*q^2 + (-a^2 - 2*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^2 + 2*a - 3)*q^5 + (a^2 + a - 3)*q^6 + q^7 + (-3*a^2 - 4*a + 3)*q^8 + (-a^2 - a + 1)*q^9 + (-a^2 - 3*a + 3)*q^10 + (a^2 - 6)*q^11 + (a + 1)*q^12 + (3*a^2 + 3*a - 7)*q^13 + a*q^14 + (3*a^2 + 5*a - 6)*q^15 + (3*a^2 + 3*a - 5)*q^16 + (-a^2 - 2*a)*q^17 + (2*a^2 + a - 3)*q^18 + (-2*a^2 + 5)*q^19 + (-2*a^2 - a + 3)*q^20 + (-a^2 - 2*a + 1)*q^21 + (-3*a^2 - 6*a + 3)*q^22 + (2*a^2 + 3*a - 6)*q^23 + (-a^2 - a + 6)*q^24 + (-5*a^2 - 9*a + 7)*q^25 + (-6*a^2 - 7*a + 9)*q^26 + (3*a^2 + 6*a - 2)*q^27 + (a^2 - 2)*q^28 + (3*a - 3)*q^29 + (-4*a^2 - 6*a + 9)*q^30 + (-4*a^2 - 3*a + 11)*q^31 + (3*a + 3)*q^32 + (4*a^2 + 9*a - 3)*q^33 + (a^2 - 3)*q^34 + (a^2 + 2*a - 3)*q^35 + (-3*a^2 - a + 4)*q^36 + q^37 + O(q^38),
q + a*q^2 + (-a^2 + 5)*q^3 + (a^2 - 2)*q^4 + (a^2 - 3)*q^5 + (-a^3 + 5*a)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-a^2 - a + 5)*q^9 + (a^3 - 3*a)*q^10 + (-a^3 - 2*a^2 + 4*a + 9)*q^11 + (-2*a^2 + a + 7)*q^12 + (a^3 - 5*a + 2)*q^13 - a*q^14 + (-a^2 + a + 2)*q^15 + (3*a^2 - a - 13)*q^16 + (a^3 + 2*a^2 - 6*a - 5)*q^17 + (-a^3 - a^2 + 5*a)*q^18 + (-a^3 - a^2 + 6*a + 2)*q^19 + (4*a^2 - a - 11)*q^20 + (a^2 - 5)*q^21 + (-2*a^3 - 5*a^2 + 10*a + 17)*q^22 + (a^3 + a^2 - 5*a - 5)*q^23 + (a^2 - 3*a)*q^24 + (3*a^2 - a - 13)*q^25 + (4*a^2 + a - 17)*q^26 + (a^3 + 2*a^2 - 6*a - 7)*q^27 + (-a^2 + 2)*q^28 + (-a + 5)*q^29 + (-a^3 + a^2 + 2*a)*q^30 + (-2*a^3 - 4*a^2 + 9*a + 19)*q^31 + (a^3 - a^2 - 5*a)*q^32 + (-2*a^2 + a + 11)*q^33 + (2*a^3 + 3*a^2 - 6*a - 17)*q^34 + (-a^2 + 3)*q^35 + (-a^3 - 2*a^2 + 3*a + 7)*q^36 + q^37 + O(q^38),
q + a*q^2 + (-a^3 + 4*a)*q^3 + (a^2 - 2)*q^4 + (a^2 - 3)*q^5 + (-a^3 - 2*a^2 + 5*a + 4)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (a^2 + a + 1)*q^9 + (a^3 - 3*a)*q^10 + (a^3 - 6*a + 3)*q^11 + (-a^3 - a^2 + a + 4)*q^12 + (-a^2 + a + 1)*q^13 + a*q^14 + (-a^2 - 3*a + 4)*q^15 + (a^3 - 5*a)*q^16 + (-a^2 + 2*a + 2)*q^17 + (a^3 + a^2 + a)*q^18 + (a^3 + a^2 - 4*a - 4)*q^19 + (a^3 + a^2 - 5*a + 2)*q^20 + (-a^3 + 4*a)*q^21 + (a^3 - 2*a - 4)*q^22 + (-2*a^3 + 7*a)*q^23 + (-a^2 - a - 4)*q^24 + (a^3 - 5*a)*q^25 + (-a^3 + a^2 + a)*q^26 + (-2*a^3 - 3*a^2 + 6*a + 8)*q^27 + (a^2 - 2)*q^28 + (a^3 - a^2 - 5*a + 8)*q^29 + (-a^3 - 3*a^2 + 4*a)*q^30 + (-a - 3)*q^31 + (-a^3 + a^2 + 3*a - 4)*q^32 + (-a^3 + 3*a^2 + a - 12)*q^33 + (-a^3 + 2*a^2 + 2*a)*q^34 + (a^2 - 3)*q^35 + (2*a^3 + 5*a^2 - 7*a - 6)*q^36 - q^37 + O(q^38)
*]> ;  // time = 32.27 seconds




J[262] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 262, 262, 262, 262, 262, 262, 131, 131 ], new_dimensions := [ 1, 1, 2, 2, 2, 2, 1, 10 ], dimensions := [ 1, 1, 2, 2, 2, 2, 2, 20 ], intersection_graph := [ 0, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 11, 3, 1, 0, 1, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 313, 1, 1, 1, 1, 0, 11, 3, 1, 1, 1, 1, 1, 11, 0, 1, 1, 1, 1, 3, 1, 3, 1, 0, 1, 1, 11, 1, 313, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, 0, -5, 2, -2, -6, 7, -6, -3, 2, -1 ],
[ 1, -2, -2, -3, -6, 4, -4, 3, -4, 3, -4, -3 ],
[ -2, -1, -5, 3, -7, -5, -2, -4, -2, -12, 6, -6 ],
[ -2, 0, 4, 2, 4, 0, 8, -2, 12, 6, -4, 6 ],
[ 2, -2, 2, 4, 0, -6, 2, 8, 14, -6, -10, -10 ],
[ 2, 3, -1, -1, 5, 3, -2, -8, -6, 0, 2, -6 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + x - 3,
x^2 - 2,
x^2 + 2*x - 2,
x^2 - 3*x + 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 11, 1 ],
[ 3, 1 ],
[ 313, 1 ],
[ 33, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 11, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 33, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 11, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 11, 1 ], l_ratios := [ 0, 0, 0, 1, 3/11, 1 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1, 1 ], eigenvalues := [*
[ -1, 0, 0, -5, 2, -2, -6, 7, -6, -3, 2, -1 ],
[ 1, -2, -2, -3, -6, 4, -4, 3, -4, 3, -4, -3 ],
[
-1,
a,
-a - 3,
-a + 1,
-a - 4,
a - 2,
2*a,
-2,
2*a,
-6,
-2*a + 2,
-2*a - 4
],
[
-1,
a,
-a + 2,
a + 1,
2*a + 2,
-3*a,
-a + 4,
-a - 1,
a + 6,
2*a + 3,
-3*a - 2,
6*a + 3
],
[
1,
a,
a + 2,
-a + 1,
-2*a - 2,
-a - 4,
-a,
a + 5,
-a + 6,
-3,
3*a - 2,
2*a - 3
],
[
1,
a,
-a + 1,
-a + 1,
-a + 4,
-3*a + 6,
2*a - 4,
4*a - 10,
-2*a,
-4*a + 6,
-6*a + 10,
6*a - 12
]
*], q_expansions := [*
q - q^2 + q^4 - 5*q^7 - q^8 - 3*q^9 + 2*q^11 - 2*q^13 + 5*q^14 + q^16 - 6*q^17 + 3*q^18 + 7*q^19 - 2*q^22 - 6*q^23 - 5*q^25 + 2*q^26 - 5*q^28 - 3*q^29 + 2*q^31 - q^32 + 6*q^34 - 3*q^36 - q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 2*q^5 - 2*q^6 - 3*q^7 + q^8 + q^9 - 2*q^10 - 6*q^11 - 2*q^12 + 4*q^13 - 3*q^14 + 4*q^15 + q^16 - 4*q^17 + q^18 + 3*q^19 - 2*q^20 + 6*q^21 - 6*q^22 - 4*q^23 - 2*q^24 - q^25 + 4*q^26 + 4*q^27 - 3*q^28 + 3*q^29 + 4*q^30 - 4*q^31 + q^32 + 12*q^33 - 4*q^34 + 6*q^35 + q^36 - 3*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a - 3)*q^5 - a*q^6 + (-a + 1)*q^7 - q^8 - a*q^9 + (a + 3)*q^10 + (-a - 4)*q^11 + a*q^12 + (a - 2)*q^13 + (a - 1)*q^14 + (-2*a - 3)*q^15 + q^16 + 2*a*q^17 + a*q^18 - 2*q^19 + (-a - 3)*q^20 + (2*a - 3)*q^21 + (a + 4)*q^22 + 2*a*q^23 - a*q^24 + (5*a + 7)*q^25 + (-a + 2)*q^26 + (-2*a - 3)*q^27 + (-a + 1)*q^28 - 6*q^29 + (2*a + 3)*q^30 + (-2*a + 2)*q^31 - q^32 + (-3*a - 3)*q^33 - 2*a*q^34 + a*q^35 - a*q^36 + (-2*a - 4)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a + 2)*q^5 - a*q^6 + (a + 1)*q^7 - q^8 - q^9 + (a - 2)*q^10 + (2*a + 2)*q^11 + a*q^12 - 3*a*q^13 + (-a - 1)*q^14 + (2*a - 2)*q^15 + q^16 + (-a + 4)*q^17 + q^18 + (-a - 1)*q^19 + (-a + 2)*q^20 + (a + 2)*q^21 + (-2*a - 2)*q^22 + (a + 6)*q^23 - a*q^24 + (-4*a + 1)*q^25 + 3*a*q^26 - 4*a*q^27 + (a + 1)*q^28 + (2*a + 3)*q^29 + (-2*a + 2)*q^30 + (-3*a - 2)*q^31 - q^32 + (2*a + 4)*q^33 + (a - 4)*q^34 + a*q^35 - q^36 + (6*a + 3)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (a + 2)*q^5 + a*q^6 + (-a + 1)*q^7 + q^8 + (-2*a - 1)*q^9 + (a + 2)*q^10 + (-2*a - 2)*q^11 + a*q^12 + (-a - 4)*q^13 + (-a + 1)*q^14 + 2*q^15 + q^16 - a*q^17 + (-2*a - 1)*q^18 + (a + 5)*q^19 + (a + 2)*q^20 + (3*a - 2)*q^21 + (-2*a - 2)*q^22 + (-a + 6)*q^23 + a*q^24 + (2*a + 1)*q^25 + (-a - 4)*q^26 - 4*q^27 + (-a + 1)*q^28 - 3*q^29 + 2*q^30 + (3*a - 2)*q^31 + q^32 + (2*a - 4)*q^33 - a*q^34 + a*q^35 + (-2*a - 1)*q^36 + (2*a - 3)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a + 1)*q^5 + a*q^6 + (-a + 1)*q^7 + q^8 + (3*a - 4)*q^9 + (-a + 1)*q^10 + (-a + 4)*q^11 + a*q^12 + (-3*a + 6)*q^13 + (-a + 1)*q^14 + (-2*a + 1)*q^15 + q^16 + (2*a - 4)*q^17 + (3*a - 4)*q^18 + (4*a - 10)*q^19 + (-a + 1)*q^20 + (-2*a + 1)*q^21 + (-a + 4)*q^22 - 2*a*q^23 + a*q^24 + (a - 5)*q^25 + (-3*a + 6)*q^26 + (2*a - 3)*q^27 + (-a + 1)*q^28 + (-4*a + 6)*q^29 + (-2*a + 1)*q^30 + (-6*a + 10)*q^31 + q^32 + (a + 1)*q^33 + (2*a - 4)*q^34 + a*q^35 + (3*a - 4)*q^36 + (6*a - 12)*q^37 + O(q^38)
*]> ;  // time = 48.29 seconds




J[263] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 263, 263 ], new_dimensions := [ 5, 17 ], dimensions := [ 5, 17 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -2, -5, -3, -5, 2, -15, -10, -5, 0, -2, -5, -9 ],
[ 1, 7, 3, 7, -2, 27, 16, 5, -4, -12, 11, 17 ]
], hecke_fields := [
x^5 + 2*x^4 - 3*x^3 - 6*x^2 + 1,
x^17 - x^16 - 26*x^15 + 24*x^14 + 274*x^13 - 225*x^12 - 1505*x^11 + 1041*x^10 + 4613*x^9 - 2467*x^8 - 7815*x^7 + 2761*x^6 + 6709*x^5 - 974*x^4 - 2284*x^3 - 239*x^2 + 135*x + 19
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 131 ]
], tamagawa_numbers := [
[ 1 ],
[ 131 ]
], torsion_upper_bounds := [ 1, 131 ], torsion_lower_bounds := [ 1, 131 ], l_ratios := [ 0, 1/131 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^4 - a^3 + 3*a^2 + 2*a - 1,
a^4 + a^3 - 4*a^2 - 3*a + 1,
a^4 + 2*a^3 - 3*a^2 - 6*a - 1,
-a^3 + a^2 + 3*a - 2,
-a^3 - a^2 + 4*a - 1,
-4*a^4 - 5*a^3 + 14*a^2 + 12*a - 6,
-a^4 - 3*a^3 + 3*a^2 + 10*a - 1,
3*a^4 + 4*a^3 - 10*a^2 - 10*a + 2,
-a^4 + 2*a^3 + 6*a^2 - 4*a - 4,
-2*a^4 - 4*a^3 + 5*a^2 + 12*a + 1,
-a^4 + 2*a^3 + 5*a^2 - 8*a - 5
],
[
a,
85010/668441*a^16 - 176339/668441*a^15 - 2241538/668441*a^14 + 4190472/668441*a^13 + 23933223/668441*a^12 - 39391493/668441*a^11 - 132842471/668441*a^10 + 186205893/668441*a^9 + 408643734/668441*a^8 - 465256935/668441*a^7 - 683138027/668441*a^6 + 586757546/668441*a^5 + 555506577/668441*a^4 - 303194375/668441*a^3 - 158959094/668441*a^2 + 17326687/668441*a + 6750715/668441,
143848/668441*a^16 - 199927/668441*a^15 - 3606981/668441*a^14 + 4857661/668441*a^13 + 36214213/668441*a^12 - 46276983/668441*a^11 - 186415557/668441*a^10 + 219401931/668441*a^9 + 523834133/668441*a^8 - 543663031/668441*a^7 - 789092227/668441*a^6 + 674003695/668441*a^5 + 572350237/668441*a^4 - 346151879/668441*a^3 - 145298876/668441*a^2 + 28757148/668441*a + 6281260/668441,
-43514/668441*a^16 + 387440/668441*a^15 + 1361549/668441*a^14 - 9030537/668441*a^13 - 16703058/668441*a^12 + 83027396/668441*a^11 + 103963774/668441*a^10 - 382002286/668441*a^9 - 350947554/668441*a^8 + 922397046/668441*a^7 + 629731852/668441*a^6 - 1116987852/668441*a^5 - 539197064/668441*a^4 + 560122572/668441*a^3 + 159965080/668441*a^2 - 45325035/668441*a - 6004853/668441,
-47976/668441*a^16 - 59269/668441*a^15 + 1131843/668441*a^14 + 1309592/668441*a^13 - 10511458/668441*a^12 - 11592732/668441*a^11 + 48829796/668441*a^10 + 52587277/668441*a^9 - 120312720/668441*a^8 - 129264310/668441*a^7 + 158327476/668441*a^6 + 165877480/668441*a^5 - 115340775/668441*a^4 - 92636576/668441*a^3 + 50139863/668441*a^2 + 9500135/668441*a - 3596410/668441,
81195/668441*a^16 - 58067/668441*a^15 - 2131430/668441*a^14 + 1449193/668441*a^13 + 22632202/668441*a^12 - 14341944/668441*a^11 - 124620842/668441*a^10 + 71906730/668441*a^9 + 378754518/668441*a^8 - 193643585/668441*a^7 - 622117679/668441*a^6 + 271133268/668441*a^5 + 494039702/668441*a^4 - 164894323/668441*a^3 - 139152381/668441*a^2 + 15752546/668441*a + 8602445/668441,
-163352/668441*a^16 - 181517/668441*a^15 + 3926005/668441*a^14 + 3879384/668441*a^13 - 37768822/668441*a^12 - 31928283/668441*a^11 + 185718644/668441*a^10 + 125556894/668441*a^9 - 494068580/668441*a^8 - 234706784/668441*a^7 + 687597052/668441*a^6 + 170902912/668441*a^5 - 422743240/668441*a^4 - 10753004/668441*a^3 + 54574006/668441*a^2 + 56457/668441*a + 1613950/668441,
-305545/668441*a^16 + 396376/668441*a^15 + 7729643/668441*a^14 - 9663251/668441*a^13 - 78677679/668441*a^12 + 92893507/668441*a^11 + 412897535/668441*a^10 - 447731635/668441*a^9 - 1189364747/668441*a^8 + 1138378461/668441*a^7 + 1843017565/668441*a^6 - 1462656613/668441*a^5 - 1374163219/668441*a^4 + 784387360/668441*a^3 + 357763439/668441*a^2 - 64709348/668441*a - 17273024/668441,
190268/668441*a^16 + 65799/668441*a^15 - 4573543/668441*a^14 - 1121760/668441*a^13 + 43799157/668441*a^12 + 6118939/668441*a^11 - 212988923/668441*a^10 - 5212643/668441*a^9 + 555260801/668441*a^8 - 59217770/668441*a^7 - 748409934/668441*a^6 + 192621427/668441*a^5 + 440494369/668441*a^4 - 187017515/668441*a^3 - 54965704/668441*a^2 + 29420594/668441*a + 739471/668441,
-27439/668441*a^16 - 331684/668441*a^15 + 234410/668441*a^14 + 7633817/668441*a^13 + 2530626/668441*a^12 - 68791754/668441*a^11 - 41010444/668441*a^10 + 306568660/668441*a^9 + 205630004/668441*a^8 - 704262848/668441*a^7 - 470330618/668441*a^6 + 790737304/668441*a^5 + 490154914/668441*a^4 - 351151409/668441*a^3 - 185873264/668441*a^2 + 19154680/668441*a + 8867071/668441,
28575/668441*a^16 + 481667/668441*a^15 - 172932/668441*a^14 - 11146025/668441*a^13 - 4279251/668441*a^12 + 101607191/668441*a^11 + 57300348/668441*a^10 - 462224165/668441*a^9 - 275732201/668441*a^8 + 1097405047/668441*a^7 + 612026151/668441*a^6 - 1291804681/668441*a^5 - 600172325/668441*a^4 + 610391623/668441*a^3 + 189762478/668441*a^2 - 35697637/668441*a - 5682028/668441,
-31476/668441*a^16 - 25008/668441*a^15 + 626712/668441*a^14 + 749181/668441*a^13 - 4650589/668441*a^12 - 8830599/668441*a^11 + 15488313/668441*a^10 + 52716960/668441*a^9 - 21329231/668441*a^8 - 170031529/668441*a^7 + 10613449/668441*a^6 + 287525021/668441*a^5 - 23987414/668441*a^4 - 215749803/668441*a^3 + 42275405/668441*a^2 + 38387049/668441*a - 1957926/668441
]
*], q_expansions := [*
q + a*q^2 + (-a^4 - a^3 + 3*a^2 + 2*a - 1)*q^3 + (a^2 - 2)*q^4 + (a^4 + a^3 - 4*a^2 - 3*a + 1)*q^5 + (a^4 - 4*a^2 - a + 1)*q^6 + (a^4 + 2*a^3 - 3*a^2 - 6*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (a^4 + a^3 - 2*a^2 - 2*a - 2)*q^9 + (-a^4 - a^3 + 3*a^2 + a - 1)*q^10 + (-a^3 + a^2 + 3*a - 2)*q^11 + (a^3 - a^2 - 3*a + 1)*q^12 + (-a^3 - a^2 + 4*a - 1)*q^13 + (-a - 1)*q^14 + (a^2 + 2*a - 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-4*a^4 - 5*a^3 + 14*a^2 + 12*a - 6)*q^17 + (-a^4 + a^3 + 4*a^2 - 2*a - 1)*q^18 + (-a^4 - 3*a^3 + 3*a^2 + 10*a - 1)*q^19 + (-a^4 - 2*a^3 + 3*a^2 + 5*a - 1)*q^20 + (a^2 + a - 1)*q^21 + (-a^4 + a^3 + 3*a^2 - 2*a)*q^22 + (3*a^4 + 4*a^3 - 10*a^2 - 10*a + 2)*q^23 + (-a^4 - a^3 + 5*a^2 + 3*a - 2)*q^24 + (a^3 + a^2 - 2*a - 4)*q^25 + (-a^4 - a^3 + 4*a^2 - a)*q^26 + (3*a^4 + 4*a^3 - 11*a^2 - 9*a + 4)*q^27 + (-2*a^4 - 4*a^3 + 5*a^2 + 11*a + 2)*q^28 + (-a^4 + 2*a^3 + 6*a^2 - 4*a - 4)*q^29 + (a^3 + 2*a^2 - a)*q^30 + (-2*a^4 - 4*a^3 + 5*a^2 + 12*a + 1)*q^31 + (-2*a^4 - 5*a^3 + 6*a^2 + 12*a - 1)*q^32 + (2*a^3 - 2*a^2 - 5*a + 2)*q^33 + (3*a^4 + 2*a^3 - 12*a^2 - 6*a + 4)*q^34 + (a + 2)*q^35 + (a^4 - a^3 - 4*a^2 + 3*a + 5)*q^36 + (-a^4 + 2*a^3 + 5*a^2 - 8*a - 5)*q^37 + O(q^38),
q + a*q^2 + (85010/668441*a^16 - 176339/668441*a^15 - 2241538/668441*a^14 + 4190472/668441*a^13 + 23933223/668441*a^12 - 39391493/668441*a^11 - 132842471/668441*a^10 + 186205893/668441*a^9 + 408643734/668441*a^8 - 465256935/668441*a^7 - 683138027/668441*a^6 + 586757546/668441*a^5 + 555506577/668441*a^4 - 303194375/668441*a^3 - 158959094/668441*a^2 + 17326687/668441*a + 6750715/668441)*q^3 + (a^2 - 2)*q^4 + (143848/668441*a^16 - 199927/668441*a^15 - 3606981/668441*a^14 + 4857661/668441*a^13 + 36214213/668441*a^12 - 46276983/668441*a^11 - 186415557/668441*a^10 + 219401931/668441*a^9 + 523834133/668441*a^8 - 543663031/668441*a^7 - 789092227/668441*a^6 + 674003695/668441*a^5 + 572350237/668441*a^4 - 346151879/668441*a^3 - 145298876/668441*a^2 + 28757148/668441*a + 6281260/668441)*q^5 + (-91329/668441*a^16 - 31278/668441*a^15 + 2150232/668441*a^14 + 640483/668441*a^13 - 20264243/668441*a^12 - 4902421/668441*a^11 + 97710483/668441*a^10 + 16492604/668441*a^9 - 255537265/668441*a^8 - 18784877/668441*a^7 + 352044936/668441*a^6 - 14825513/668441*a^5 - 220394635/668441*a^4 + 35203746/668441*a^3 + 37644077/668441*a^2 - 4725635/668441*a - 1615190/668441)*q^6 + (-43514/668441*a^16 + 387440/668441*a^15 + 1361549/668441*a^14 - 9030537/668441*a^13 - 16703058/668441*a^12 + 83027396/668441*a^11 + 103963774/668441*a^10 - 382002286/668441*a^9 - 350947554/668441*a^8 + 922397046/668441*a^7 + 629731852/668441*a^6 - 1116987852/668441*a^5 - 539197064/668441*a^4 + 560122572/668441*a^3 + 159965080/668441*a^2 - 45325035/668441*a - 6004853/668441)*q^7 + (a^3 - 4*a)*q^8 + (42054/668441*a^16 - 262455/668441*a^15 - 1209902/668441*a^14 + 6116298/668441*a^13 + 14043018/668441*a^12 - 56453950/668441*a^11 - 84463769/668441*a^10 + 262318806/668441*a^9 + 280220078/668441*a^8 - 644775138/668441*a^7 - 501512106/668441*a^6 + 801919566/668441*a^5 + 434439282/668441*a^4 - 416801437/668441*a^3 - 135528601/668441*a^2 + 35976810/668441*a + 9629069/668441)*q^9 + (-56079/668441*a^16 + 133067/668441*a^15 + 1405309/668441*a^14 - 3200139/668441*a^13 - 13911183/668441*a^12 + 30075683/668441*a^11 + 69656163/668441*a^10 - 139736691/668441*a^9 - 188790015/668441*a^8 + 335079893/668441*a^7 + 276839367/668441*a^6 - 392725995/668441*a^5 - 206043927/668441*a^4 + 183249956/668441*a^3 + 63136820/668441*a^2 - 13138220/668441*a - 2733112/668441)*q^10 + (-47976/668441*a^16 - 59269/668441*a^15 + 1131843/668441*a^14 + 1309592/668441*a^13 - 10511458/668441*a^12 - 11592732/668441*a^11 + 48829796/668441*a^10 + 52587277/668441*a^9 - 120312720/668441*a^8 - 129264310/668441*a^7 + 158327476/668441*a^6 + 165877480/668441*a^5 - 115340775/668441*a^4 - 92636576/668441*a^3 + 50139863/668441*a^2 + 9500135/668441*a - 3596410/668441)*q^11 + (-292627/668441*a^16 + 128356/668441*a^15 + 7315455/668441*a^14 - 3621041/668441*a^13 - 73317892/668441*a^12 + 39043324/668441*a^11 + 377251035/668441*a^10 - 206648374/668441*a^9 - 1061380988/668441*a^8 + 568822671/668441*a^7 + 1603609910/668441*a^6 - 781183466/668441*a^5 - 1164763854/668441*a^4 + 435437391/668441*a^3 + 291364922/668441*a^2 - 23939149/668441*a - 11766179/668441)*q^12 + (81195/668441*a^16 - 58067/668441*a^15 - 2131430/668441*a^14 + 1449193/668441*a^13 + 22632202/668441*a^12 - 14341944/668441*a^11 - 124620842/668441*a^10 + 71906730/668441*a^9 + 378754518/668441*a^8 - 193643585/668441*a^7 - 622117679/668441*a^6 + 271133268/668441*a^5 + 494039702/668441*a^4 - 164894323/668441*a^3 - 139152381/668441*a^2 + 15752546/668441*a + 8602445/668441)*q^13 + (343926/668441*a^16 + 230185/668441*a^15 - 7986201/668441*a^14 - 4780222/668441*a^13 + 73236746/668441*a^12 + 38475204/668441*a^11 - 336704212/668441*a^10 - 150217472/668441*a^9 + 815048008/668441*a^8 + 289669942/668441*a^7 - 996845698/668441*a^6 - 247261638/668441*a^5 + 517739936/668441*a^4 + 60579104/668441*a^3 - 55724881/668441*a^2 - 130463/668441*a + 826766/668441)*q^14 + (33901/668441*a^16 + 195128/668441*a^15 - 734373/668441*a^14 - 4348962/668441*a^13 + 5964676/668441*a^12 + 38079778/668441*a^11 - 21329382/668441*a^10 - 165695826/668441*a^9 + 24034258/668441*a^8 + 373508124/668441*a^7 + 41245074/668441*a^6 - 413682388/668441*a^5 - 118411148/668441*a^4 + 187871331/668441*a^3 + 74098916/668441*a^2 - 21479655/668441*a - 4189942/668441)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-163352/668441*a^16 - 181517/668441*a^15 + 3926005/668441*a^14 + 3879384/668441*a^13 - 37768822/668441*a^12 - 31928283/668441*a^11 + 185718644/668441*a^10 + 125556894/668441*a^9 - 494068580/668441*a^8 - 234706784/668441*a^7 + 687597052/668441*a^6 + 170902912/668441*a^5 - 422743240/668441*a^4 - 10753004/668441*a^3 + 54574006/668441*a^2 + 56457/668441*a + 1613950/668441)*q^17 + (-220401/668441*a^16 - 116498/668441*a^15 + 5107002/668441*a^14 + 2520222/668441*a^13 - 46991800/668441*a^12 - 21172499/668441*a^11 + 218540592/668441*a^10 + 86224976/668441*a^9 - 541027920/668441*a^8 - 172860096/668441*a^7 + 685808472/668441*a^6 + 152298996/668441*a^5 - 375840841/668441*a^4 - 39477265/668441*a^3 + 46027716/668441*a^2 + 3951779/668441*a - 799026/668441)*q^18 + (-305545/668441*a^16 + 396376/668441*a^15 + 7729643/668441*a^14 - 9663251/668441*a^13 - 78677679/668441*a^12 + 92893507/668441*a^11 + 412897535/668441*a^10 - 447731635/668441*a^9 - 1189364747/668441*a^8 + 1138378461/668441*a^7 + 1843017565/668441*a^6 - 1462656613/668441*a^5 - 1374163219/668441*a^4 + 784387360/668441*a^3 + 357763439/668441*a^2 - 64709348/668441*a - 17273024/668441)*q^19 + (-210708/668441*a^16 + 347109/668441*a^15 + 5359719/668441*a^14 - 8260859/668441*a^13 - 54970518/668441*a^12 + 77811234/668441*a^11 + 291472662/668441*a^10 - 368901450/668441*a^9 - 850935266/668441*a^8 + 925908044/668441*a^7 + 1340292578/668441*a^6 - 1177817306/668441*a^5 - 1016071464/668441*a^4 + 627356142/668441*a^3 + 264056651/668441*a^2 - 52676743/668441*a - 11497019/668441)*q^20 + (230655/668441*a^16 + 104003/668441*a^15 - 5477067/668441*a^14 - 2081190/668441*a^13 + 51975564/668441*a^12 + 15945274/668441*a^11 - 252394580/668441*a^10 - 57891692/668441*a^9 + 669784150/668441*a^8 + 98335400/668441*a^7 - 965614658/668441*a^6 - 62142906/668441*a^5 + 701195070/668441*a^4 - 2680705/668441*a^3 - 205873841/668441*a^2 + 3745997/668441*a + 11268782/668441)*q^21 + (-107245/668441*a^16 - 115533/668441*a^15 + 2461016/668441*a^14 + 2633966/668441*a^13 - 22387332/668441*a^12 - 23374084/668441*a^11 + 102530293/668441*a^10 + 101000568/668441*a^9 - 247621102/668441*a^8 - 216604964/668441*a^7 + 298339216/668441*a^6 + 206530209/668441*a^5 - 139365200/668441*a^4 - 59437321/668441*a^3 - 1966129/668441*a^2 + 2880350/668441*a + 911544/668441)*q^22 + (190268/668441*a^16 + 65799/668441*a^15 - 4573543/668441*a^14 - 1121760/668441*a^13 + 43799157/668441*a^12 + 6118939/668441*a^11 - 212988923/668441*a^10 - 5212643/668441*a^9 + 555260801/668441*a^8 - 59217770/668441*a^7 - 748409934/668441*a^6 + 192621427/668441*a^5 + 440494369/668441*a^4 - 187017515/668441*a^3 - 54965704/668441*a^2 + 29420594/668441*a + 739471/668441)*q^23 + (18387/668441*a^16 - 230291/668441*a^15 - 898457/668441*a^14 + 5580940/668441*a^13 + 13730735/668441*a^12 - 53347758/668441*a^11 - 97444633/668441*a^10 + 255522155/668441*a^9 + 357986392/668441*a^8 - 645700341/668441*a^7 - 677330191/668441*a^6 + 828121715/668441*a^5 + 591207963/668441*a^4 - 447402638/668441*a^3 - 169165156/668441*a^2 + 37189736/668441*a + 8790293/668441)*q^24 + (-182820/668441*a^16 + 74928/668441*a^15 + 4741247/668441*a^14 - 2266478/668441*a^13 - 49751449/668441*a^12 + 26239789/668441*a^11 + 271136067/668441*a^10 - 150472493/668441*a^9 - 818451701/668441*a^8 + 455230155/668441*a^7 + 1341380923/668441*a^6 - 699413509/668441*a^5 - 1060536893/668441*a^4 + 448490811/668441*a^3 + 286306875/668441*a^2 - 41781650/668441*a - 14197232/668441)*q^25 + (23128/668441*a^16 - 20360/668441*a^15 - 499487/668441*a^14 + 384772/668441*a^13 + 3926931/668441*a^12 - 2422367/668441*a^11 - 12617265/668441*a^10 + 4201983/668441*a^9 + 6664480/668441*a^8 + 12421246/668441*a^7 + 46953873/668441*a^6 - 50697553/668441*a^5 - 85810393/668441*a^4 + 46296999/668441*a^3 + 35158151/668441*a^2 - 2358880/668441*a - 1542705/668441)*q^26 + (128760/668441*a^16 - 318437/668441*a^15 - 3246680/668441*a^14 + 7454516/668441*a^13 + 32880147/668441*a^12 - 68497690/668441*a^11 - 171530087/668441*a^10 + 312449599/668441*a^9 + 491846360/668441*a^8 - 736724891/668441*a^7 - 763948559/668441*a^6 + 842473872/668441*a^5 + 582381989/668441*a^4 - 362325457/668441*a^3 - 161338545/668441*a^2 + 2263337/668441*a + 4329747/668441)*q^27 + (661139/668441*a^16 + 180995/668441*a^15 - 15757544/668441*a^14 - 2937904/668441*a^13 + 149264670/668441*a^12 + 14849626/668441*a^11 - 716171986/668441*a^10 - 7478058/668441*a^9 + 1840030492/668441*a^8 - 153858100/668441*a^7 - 2456305028/668441*a^6 + 444316106/668441*a^5 + 1473957156/668441*a^4 - 390443041/668441*a^3 - 237862309/668441*a^2 + 45046826/668441*a + 5475112/668441)*q^28 + (-27439/668441*a^16 - 331684/668441*a^15 + 234410/668441*a^14 + 7633817/668441*a^13 + 2530626/668441*a^12 - 68791754/668441*a^11 - 41010444/668441*a^10 + 306568660/668441*a^9 + 205630004/668441*a^8 - 704262848/668441*a^7 - 470330618/668441*a^6 + 790737304/668441*a^5 + 490154914/668441*a^4 - 351151409/668441*a^3 - 185873264/668441*a^2 + 19154680/668441*a + 8867071/668441)*q^29 + (229029/668441*a^16 + 147053/668441*a^15 - 5162586/668441*a^14 - 3324198/668441*a^13 + 45707503/668441*a^12 + 29691623/668441*a^11 - 200986767/668441*a^10 - 132351055/668441*a^9 + 457141891/668441*a^8 + 306181389/668441*a^7 - 507283049/668441*a^6 - 345852957/668441*a^5 + 220890905/668441*a^4 + 151528800/668441*a^3 - 13377316/668441*a^2 - 8766577/668441*a - 644119/668441)*q^30 + (28575/668441*a^16 + 481667/668441*a^15 - 172932/668441*a^14 - 11146025/668441*a^13 - 4279251/668441*a^12 + 101607191/668441*a^11 + 57300348/668441*a^10 - 462224165/668441*a^9 - 275732201/668441*a^8 + 1097405047/668441*a^7 + 612026151/668441*a^6 - 1291804681/668441*a^5 - 600172325/668441*a^4 + 610391623/668441*a^3 + 189762478/668441*a^2 - 35697637/668441*a - 5682028/668441)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (205441/668441*a^16 - 333455/668441*a^15 - 5210507/668441*a^14 + 8210575/668441*a^13 + 53148393/668441*a^12 - 80180890/668441*a^11 - 279076356/668441*a^10 + 395460805/668441*a^9 + 800405168/668441*a^8 - 1037595482/668441*a^7 - 1215830164/668441*a^6 + 1386834420/668441*a^5 + 840048083/668441*a^4 - 778443043/668441*a^3 - 148601811/668441*a^2 + 65640558/668441*a + 712737/668441)*q^33 + (-344869/668441*a^16 - 321147/668441*a^15 + 7799832/668441*a^14 + 6989626/668441*a^13 - 68682483/668441*a^12 - 60126116/668441*a^11 + 295606326/668441*a^10 + 259474196/668441*a^9 - 637696168/668441*a^8 - 588998828/668441*a^7 + 621917784/668441*a^6 + 673185328/668441*a^5 - 169857852/668441*a^4 - 318521962/668441*a^3 - 38984671/668441*a^2 + 23666470/668441*a + 3103688/668441)*q^34 + (-89862/668441*a^16 - 607831/668441*a^15 + 1315224/668441*a^14 + 13973940/668441*a^13 - 2363814/668441*a^12 - 127097854/668441*a^11 - 54181682/668441*a^10 + 580558106/668441*a^9 + 377224866/668441*a^8 - 1397435006/668441*a^7 - 973215626/668441*a^6 + 1694572898/668441*a^5 + 1056590290/668441*a^4 - 854379516/668441*a^3 - 381027413/668441*a^2 + 71394762/668441*a + 16294488/668441)*q^35 + (-421007/668441*a^16 - 98514/668441*a^15 + 10229650/668441*a^14 + 1165478/668441*a^13 - 98848760/668441*a^12 - 255013/668441*a^11 + 484589955/668441*a^10 - 48955719/668441*a^9 - 1277029519/668441*a^8 + 252924933/668441*a^7 + 1763850369/668441*a^6 - 501009664/668441*a^5 - 1123026403/668441*a^4 + 376234706/668441*a^3 + 222333142/668441*a^2 - 42998511/668441*a - 15070519/668441)*q^36 + (-31476/668441*a^16 - 25008/668441*a^15 + 626712/668441*a^14 + 749181/668441*a^13 - 4650589/668441*a^12 - 8830599/668441*a^11 + 15488313/668441*a^10 + 52716960/668441*a^9 - 21329231/668441*a^8 - 170031529/668441*a^7 + 10613449/668441*a^6 + 287525021/668441*a^5 - 23987414/668441*a^4 - 215749803/668441*a^3 + 42275405/668441*a^2 + 38387049/668441*a - 1957926/668441)*q^37 + O(q^38)
*]> ;  // time = 4.281 seconds




J[265] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 265, 265, 265, 265, 265, 265, 265, 265, 53, 53 ], new_dimensions := [ 1, 2, 2, 2, 2, 2, 2, 4, 1, 3 ], dimensions := [ 1, 2, 2, 2, 2, 2, 2, 4, 2, 6 ], intersection_graph := [ 0, 5, 1, 1, 1, 1, 1, 1, 3, 1, 5, 0, 7, 1, 1, 1, 1, 1, 1, 1, 1, 7, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 11, 1, 1, 1, 1, 1, 1, 1, 1, 11, 0, 1, 1, 1, 1, 31, 1, 1, 1, 1, 1, 0, 1, 17, 3, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 1, 1, 17, 1, 0, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 31, 1, 5, 1, 1, 0 ], ap_traces := [
[ -1, 0, -1, 2, 0, -6, -6, -2, -8, 2, 10, 2 ],
[ -1, -1, -2, -6, -10, 0, -3, 6, -7, 6, 2, 0 ],
[ -2, -2, -2, -4, 4, 2, 2, -2, -10, -10, -12, -10 ],
[ 0, 4, -2, 2, 4, 0, 4, -2, 8, 12, -6, 4 ],
[ 3, -3, -2, 4, 6, 2, 3, -14, 1, 2, -2, -4 ],
[ -1, 1, 2, -2, 6, -4, 3, 0, 1, 2, 6, 4 ],
[ -1, -1, 2, -4, -10, 2, 1, -8, -11, -2, -6, 8 ],
[ 4, -2, 4, 4, 4, -2, -2, 14, 14, -2, 0, -14 ]
], hecke_fields := [
x - 1,
x^2 + x - 5,
x^2 + 2*x - 1,
x^2 - 3,
x^2 - 3*x + 1,
x^2 + x - 3,
x^2 + x - 1,
x^4 - 10*x^3 - 37*x^2 + 220*x - 92
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, -1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 31, 1 ],
[ 27, 1 ],
[ 5, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 27, 1 ],
[ 5, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 9, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 9, 1, 1 ], l_ratios := [ 0, 0, 0, 1, 1, 1/3, 0, 1 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1, 1, 0, 1 ], eigenvalues := [*
[ -1, 0, -1, 2, 0, -6, -6, -2, -8, 2, 10, 2 ],
[
a,
-a - 1,
-1,
-3,
-5,
2*a + 1,
-a - 2,
3,
-a - 4,
2*a + 4,
2*a + 2,
-4*a - 2
],
[
a,
a,
-1,
-2*a - 4,
2,
-2*a - 1,
2*a + 3,
a,
3*a - 2,
2*a - 3,
-6,
-4*a - 9
],
[
a,
2,
-1,
a + 1,
-2*a + 2,
-2*a,
2,
a - 1,
-2*a + 4,
2*a + 6,
-a - 3,
-4*a + 2
],
[
a,
a - 3,
-1,
-2*a + 5,
3,
1,
-3*a + 6,
-7,
-5*a + 8,
-2*a + 4,
-2*a + 2,
8*a - 14
],
[
a,
a + 1,
1,
-1,
3,
2*a - 1,
-3*a,
-2*a - 1,
-a,
-2*a,
-2*a + 2,
2
],
[
a,
-a - 1,
1,
2*a - 1,
-5,
-4*a - 1,
-a,
2*a - 3,
3*a - 4,
2*a,
-6*a - 6,
4*a + 6
],
[
5/286*a^3 - 21/143*a^2 - 15/22*a + 394/143,
5/858*a^3 - 7/143*a^2 - 37/66*a + 394/429,
1,
-2/143*a^3 + 79/429*a^2 + 7/33*a - 1060/429,
-20/429*a^3 + 56/143*a^2 + 82/33*a - 2294/429,
-19/429*a^3 + 131/429*a^2 + 79/33*a - 531/143,
3/143*a^3 - 47/429*a^2 - 71/33*a + 875/429,
7/858*a^3 - 58/429*a^2 + 23/66*a + 794/143,
35/858*a^3 - 49/143*a^2 - 127/66*a + 3616/429,
-7/429*a^3 - 9/143*a^2 + 65/33*a + 1385/429,
1/39*a^3 - 11/39*a^2 - 4/3*a + 82/13,
4/429*a^3 - 5/429*a^2 - 34/33*a - 543/143
]
*], q_expansions := [*
q - q^2 - q^4 - q^5 + 2*q^7 + 3*q^8 - 3*q^9 + q^10 - 6*q^13 - 2*q^14 - q^16 - 6*q^17 + 3*q^18 - 2*q^19 + q^20 - 8*q^23 + q^25 + 6*q^26 - 2*q^28 + 2*q^29 + 10*q^31 - 5*q^32 + 6*q^34 - 2*q^35 + 3*q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (-a + 3)*q^4 - q^5 - 5*q^6 - 3*q^7 + (2*a - 5)*q^8 + (a + 3)*q^9 - a*q^10 - 5*q^11 + (-3*a + 2)*q^12 + (2*a + 1)*q^13 - 3*a*q^14 + (a + 1)*q^15 + (-5*a + 4)*q^16 + (-a - 2)*q^17 + (2*a + 5)*q^18 + 3*q^19 + (a - 3)*q^20 + (3*a + 3)*q^21 - 5*a*q^22 + (-a - 4)*q^23 + (5*a - 5)*q^24 + q^25 + (-a + 10)*q^26 - 5*q^27 + (3*a - 9)*q^28 + (2*a + 4)*q^29 + 5*q^30 + (2*a + 2)*q^31 + (5*a - 15)*q^32 + (5*a + 5)*q^33 + (-a - 5)*q^34 + 3*q^35 + (a + 4)*q^36 + (-4*a - 2)*q^37 + O(q^38),
q + a*q^2 + a*q^3 + (-2*a - 1)*q^4 - q^5 + (-2*a + 1)*q^6 + (-2*a - 4)*q^7 + (a - 2)*q^8 + (-2*a - 2)*q^9 - a*q^10 + 2*q^11 + (3*a - 2)*q^12 + (-2*a - 1)*q^13 - 2*q^14 - a*q^15 + 3*q^16 + (2*a + 3)*q^17 + (2*a - 2)*q^18 + a*q^19 + (2*a + 1)*q^20 - 2*q^21 + 2*a*q^22 + (3*a - 2)*q^23 + (-4*a + 1)*q^24 + q^25 + (3*a - 2)*q^26 + (-a - 2)*q^27 + (2*a + 8)*q^28 + (2*a - 3)*q^29 + (2*a - 1)*q^30 - 6*q^31 + (a + 4)*q^32 + 2*a*q^33 + (-a + 2)*q^34 + (2*a + 4)*q^35 + (-2*a + 6)*q^36 + (-4*a - 9)*q^37 + O(q^38),
q + a*q^2 + 2*q^3 + q^4 - q^5 + 2*a*q^6 + (a + 1)*q^7 - a*q^8 + q^9 - a*q^10 + (-2*a + 2)*q^11 + 2*q^12 - 2*a*q^13 + (a + 3)*q^14 - 2*q^15 - 5*q^16 + 2*q^17 + a*q^18 + (a - 1)*q^19 - q^20 + (2*a + 2)*q^21 + (2*a - 6)*q^22 + (-2*a + 4)*q^23 - 2*a*q^24 + q^25 - 6*q^26 - 4*q^27 + (a + 1)*q^28 + (2*a + 6)*q^29 - 2*a*q^30 + (-a - 3)*q^31 - 3*a*q^32 + (-4*a + 4)*q^33 + 2*a*q^34 + (-a - 1)*q^35 + q^36 + (-4*a + 2)*q^37 + O(q^38),
q + a*q^2 + (a - 3)*q^3 + (3*a - 3)*q^4 - q^5 - q^6 + (-2*a + 5)*q^7 + (4*a - 3)*q^8 + (-3*a + 5)*q^9 - a*q^10 + 3*q^11 + (-3*a + 6)*q^12 + q^13 + (-a + 2)*q^14 + (-a + 3)*q^15 + (3*a + 2)*q^16 + (-3*a + 6)*q^17 + (-4*a + 3)*q^18 - 7*q^19 + (-3*a + 3)*q^20 + (5*a - 13)*q^21 + 3*a*q^22 + (-5*a + 8)*q^23 + (-3*a + 5)*q^24 + q^25 + a*q^26 + (2*a - 3)*q^27 + (3*a - 9)*q^28 + (-2*a + 4)*q^29 + q^30 + (-2*a + 2)*q^31 + (3*a + 3)*q^32 + (3*a - 9)*q^33 + (-3*a + 3)*q^34 + (2*a - 5)*q^35 + (-3*a - 6)*q^36 + (8*a - 14)*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + (-a + 1)*q^4 + q^5 + 3*q^6 - q^7 - 3*q^8 + (a + 1)*q^9 + a*q^10 + 3*q^11 + (a - 2)*q^12 + (2*a - 1)*q^13 - a*q^14 + (a + 1)*q^15 + (-a - 2)*q^16 - 3*a*q^17 + 3*q^18 + (-2*a - 1)*q^19 + (-a + 1)*q^20 + (-a - 1)*q^21 + 3*a*q^22 - a*q^23 + (-3*a - 3)*q^24 + q^25 + (-3*a + 6)*q^26 + (-2*a + 1)*q^27 + (a - 1)*q^28 - 2*a*q^29 + 3*q^30 + (-2*a + 2)*q^31 + (-a + 3)*q^32 + (3*a + 3)*q^33 + (3*a - 9)*q^34 - q^35 + (a - 2)*q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (-a - 1)*q^4 + q^5 - q^6 + (2*a - 1)*q^7 + (-2*a - 1)*q^8 + (a - 1)*q^9 + a*q^10 - 5*q^11 + (a + 2)*q^12 + (-4*a - 1)*q^13 + (-3*a + 2)*q^14 + (-a - 1)*q^15 + 3*a*q^16 - a*q^17 + (-2*a + 1)*q^18 + (2*a - 3)*q^19 + (-a - 1)*q^20 + (a - 1)*q^21 - 5*a*q^22 + (3*a - 4)*q^23 + (a + 3)*q^24 + q^25 + (3*a - 4)*q^26 + (4*a + 3)*q^27 + (a - 1)*q^28 + 2*a*q^29 - q^30 + (-6*a - 6)*q^31 + (a + 5)*q^32 + (5*a + 5)*q^33 + (a - 1)*q^34 + (2*a - 1)*q^35 + a*q^36 + (4*a + 6)*q^37 + O(q^38),
q + (5/286*a^3 - 21/143*a^2 - 15/22*a + 394/143)*q^2 + (5/858*a^3 - 7/143*a^2 - 37/66*a + 394/429)*q^3 + (5/143*a^3 - 42/143*a^2 - 15/11*a + 645/143)*q^4 + q^5 + (1/429*a^3 - 37/429*a^2 - 1/11*a + 701/429)*q^6 + (-2/143*a^3 + 79/429*a^2 + 7/33*a - 1060/429)*q^7 + (5/286*a^3 - 21/143*a^2 - 15/22*a + 680/143)*q^8 + (-1/429*a^3 + 37/429*a^2 + 1/11*a - 1130/429)*q^9 + (5/286*a^3 - 21/143*a^2 - 15/22*a + 394/143)*q^10 + (-20/429*a^3 + 56/143*a^2 + 82/33*a - 2294/429)*q^11 + (-1/858*a^3 - 53/429*a^2 + 25/66*a + 336/143)*q^12 + (-19/429*a^3 + 131/429*a^2 + 79/33*a - 531/143)*q^13 + (-1/39*a^3 + 11/39*a^2 + 4/3*a - 82/13)*q^14 + (5/858*a^3 - 7/143*a^2 - 37/66*a + 394/429)*q^15 + 3*q^16 + (3/143*a^3 - 47/429*a^2 - 71/33*a + 875/429)*q^17 + (-4/143*a^3 + 158/429*a^2 + 47/33*a - 2978/429)*q^18 + (7/858*a^3 - 58/429*a^2 + 23/66*a + 794/143)*q^19 + (5/143*a^3 - 42/143*a^2 - 15/11*a + 645/143)*q^20 + (-10/429*a^3 + 28/143*a^2 + 8/33*a - 718/429)*q^21 + (-17/429*a^3 + 200/429*a^2 + 17/11*a - 4624/429)*q^22 + (35/858*a^3 - 49/143*a^2 - 127/66*a + 3616/429)*q^23 + (2/143*a^3 - 79/429*a^2 - 40/33*a + 1489/429)*q^24 + q^25 + (-25/858*a^3 + 35/143*a^2 + 53/66*a - 2828/429)*q^26 + (-41/858*a^3 + 115/429*a^2 + 63/22*a - 2144/429)*q^27 + (-16/429*a^3 + 163/429*a^2 + 27/11*a - 4352/429)*q^28 + (-7/429*a^3 - 9/143*a^2 + 65/33*a + 1385/429)*q^29 + (1/429*a^3 - 37/429*a^2 - 1/11*a + 701/429)*q^30 + (1/39*a^3 - 11/39*a^2 - 4/3*a + 82/13)*q^31 + (5/286*a^3 - 21/143*a^2 - 15/22*a - 178/143)*q^32 + (5/429*a^3 - 14/143*a^2 - 37/33*a - 928/429)*q^33 + (-1/858*a^3 - 53/429*a^2 + 25/66*a + 336/143)*q^34 + (-2/143*a^3 + 79/429*a^2 + 7/33*a - 1060/429)*q^35 + (-23/429*a^3 + 93/143*a^2 + 91/33*a - 4826/429)*q^36 + (4/429*a^3 - 5/429*a^2 - 34/33*a - 543/143)*q^37 + O(q^38)
*]> ;  // time = 32.659 seconds




J[266] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 266, 266, 266, 266, 133, 133, 133, 133, 38, 38, 19, 14 ], new_dimensions := [ 2, 2, 2, 3, 2, 2, 2, 3, 1, 1, 1, 1 ], dimensions := [ 2, 2, 2, 3, 4, 4, 4, 6, 2, 2, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 13, 7, 1, 1, 1, 1, 0, 1, 1, 1, 11, 1, 1, 1, 1, 1, 11, 1, 1, 0, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 1, 0, 19, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 19, 0, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 9, 1, 1, 1, 0, 1, 3, 1, 9, 3, 13, 1, 1, 1, 1, 1, 1, 0, 1, 1, 49, 1, 7, 1, 1, 1, 1, 1, 3, 1, 0, 1, 9, 3, 1, 1, 1, 11, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 1, 9, 49, 9, 1, 0, 3, 1, 11, 1, 1, 1, 1, 3, 1, 3, 1, 3, 0 ], ap_traces := [
[ -2, 1, -1, -2, 3, -2, -8, 2, -6, 5, 20, 3 ],
[ -2, 3, 1, 2, 7, 6, -4, -2, 2, -11, 8, 3 ],
[ 2, 1, 1, 2, -5, 6, 0, 2, -2, -9, 0, 1 ],
[ 3, -1, 5, -3, 3, -4, 6, -3, -2, 5, 4, 7 ]
], hecke_fields := [
x^2 - x - 7,
x^2 - 3*x + 1,
x^2 - x - 3,
x^3 + x^2 - 7*x + 4
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 13, 7, 1 ],
[ 11, 1, 11 ],
[ 81, 3, 1 ],
[ 19, 11, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 81, 3, 1 ],
[ 19, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 9, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1 ], l_ratios := [ 1, 1, 3, 19 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1/81, 1 ], eigenvalues := [*
[
-1,
a,
a - 1,
-1,
-a + 2,
-2*a,
-4,
1,
-2*a - 2,
-a + 3,
10,
a + 1
],
[
-1,
a,
-3*a + 5,
1,
a + 2,
2*a,
4*a - 8,
-1,
-6*a + 10,
-3*a - 1,
-4*a + 10,
3*a - 3
],
[
1,
a,
-a + 1,
1,
-a - 2,
-2*a + 4,
0,
1,
2*a - 2,
-3*a - 3,
4*a - 2,
3*a - 1
],
[
1,
a,
-a^2 - 2*a + 6,
-1,
2*a^2 + 3*a - 8,
2*a^2 + 4*a - 10,
-2*a^2 - 6*a + 10,
-1,
-2*a^2 - 4*a + 8,
a^2 + 4*a - 2,
2*a^2 + 2*a - 8,
-a^2 - 4*a + 6
]
*], q_expansions := [*
q - q^2 + a*q^3 + q^4 + (a - 1)*q^5 - a*q^6 - q^7 - q^8 + (a + 4)*q^9 + (-a + 1)*q^10 + (-a + 2)*q^11 + a*q^12 - 2*a*q^13 + q^14 + 7*q^15 + q^16 - 4*q^17 + (-a - 4)*q^18 + q^19 + (a - 1)*q^20 - a*q^21 + (a - 2)*q^22 + (-2*a - 2)*q^23 - a*q^24 + (-a + 3)*q^25 + 2*a*q^26 + (2*a + 7)*q^27 - q^28 + (-a + 3)*q^29 - 7*q^30 + 10*q^31 - q^32 + (a - 7)*q^33 + 4*q^34 + (-a + 1)*q^35 + (a + 4)*q^36 + (a + 1)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-3*a + 5)*q^5 - a*q^6 + q^7 - q^8 + (3*a - 4)*q^9 + (3*a - 5)*q^10 + (a + 2)*q^11 + a*q^12 + 2*a*q^13 - q^14 + (-4*a + 3)*q^15 + q^16 + (4*a - 8)*q^17 + (-3*a + 4)*q^18 - q^19 + (-3*a + 5)*q^20 + a*q^21 + (-a - 2)*q^22 + (-6*a + 10)*q^23 - a*q^24 + (-3*a + 11)*q^25 - 2*a*q^26 + (2*a - 3)*q^27 + q^28 + (-3*a - 1)*q^29 + (4*a - 3)*q^30 + (-4*a + 10)*q^31 - q^32 + (5*a - 1)*q^33 + (-4*a + 8)*q^34 + (-3*a + 5)*q^35 + (3*a - 4)*q^36 + (3*a - 3)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a + 1)*q^5 + a*q^6 + q^7 + q^8 + a*q^9 + (-a + 1)*q^10 + (-a - 2)*q^11 + a*q^12 + (-2*a + 4)*q^13 + q^14 - 3*q^15 + q^16 + a*q^18 + q^19 + (-a + 1)*q^20 + a*q^21 + (-a - 2)*q^22 + (2*a - 2)*q^23 + a*q^24 + (-a - 1)*q^25 + (-2*a + 4)*q^26 + (-2*a + 3)*q^27 + q^28 + (-3*a - 3)*q^29 - 3*q^30 + (4*a - 2)*q^31 + q^32 + (-3*a - 3)*q^33 + (-a + 1)*q^35 + a*q^36 + (3*a - 1)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a^2 - 2*a + 6)*q^5 + a*q^6 - q^7 + q^8 + (a^2 - 3)*q^9 + (-a^2 - 2*a + 6)*q^10 + (2*a^2 + 3*a - 8)*q^11 + a*q^12 + (2*a^2 + 4*a - 10)*q^13 - q^14 + (-a^2 - a + 4)*q^15 + q^16 + (-2*a^2 - 6*a + 10)*q^17 + (a^2 - 3)*q^18 - q^19 + (-a^2 - 2*a + 6)*q^20 - a*q^21 + (2*a^2 + 3*a - 8)*q^22 + (-2*a^2 - 4*a + 8)*q^23 + a*q^24 + (-4*a^2 - 7*a + 19)*q^25 + (2*a^2 + 4*a - 10)*q^26 + (-a^2 + a - 4)*q^27 - q^28 + (a^2 + 4*a - 2)*q^29 + (-a^2 - a + 4)*q^30 + (2*a^2 + 2*a - 8)*q^31 + q^32 + (a^2 + 6*a - 8)*q^33 + (-2*a^2 - 6*a + 10)*q^34 + (a^2 + 2*a - 6)*q^35 + (a^2 - 3)*q^36 + (-a^2 - 4*a + 6)*q^37 + O(q^38)
*]> ;  // time = 102.28 seconds




J[267] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 267, 267, 267, 267, 267, 267, 89, 89, 89 ], new_dimensions := [ 1, 1, 3, 3, 3, 4, 1, 1, 5 ], dimensions := [ 1, 1, 3, 3, 3, 4, 2, 2, 10 ], intersection_graph := [ 0, 1, 1, 1, 1, 7, 1, 1, 17, 1, 0, 1, 5, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 5, 1, 0, 1, 1, 5, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 113, 7, 1, 1, 1, 1, 0, 1, 3, 13, 1, 1, 3, 5, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 25, 17, 1, 1, 1, 113, 13, 1, 25, 0 ], ap_traces := [
[ 0, -1, 4, -2, 2, 6, 4, -4, -3, 3, 8, -8 ],
[ 0, 1, 0, 2, 6, 2, 0, -4, 3, -3, -4, -4 ],
[ 0, -3, -3, -6, 6, -15, -6, -6, 3, -6, -9, -9 ],
[ 2, 3, 5, -4, -4, 3, 6, -4, -1, 12, -1, 7 ],
[ -4, 3, -7, -4, -8, -11, -4, 0, -7, -6, -3, -11 ],
[ 1, -4, 3, 6, -6, 9, 2, 10, 1, -2, -11, 23 ]
], hecke_fields := [
x - 1,
x - 1,
x^3 - 3*x + 1,
x^3 - 2*x^2 - 3*x + 5,
x^3 + 4*x^2 + 3*x - 1,
x^4 - x^3 - 7*x^2 + 6*x + 7
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ],
[ 1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ]
], component_group_orders := [
[ 17, 1 ],
[ 3, 1 ],
[ 3, 1 ],
[ 25, 1 ],
[ 113, 1 ],
[ 39, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 25, 1 ],
[ 113, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 5, 1, 1 ], torsion_lower_bounds := [ 1, 3, 1, 5, 1, 1 ], l_ratios := [ 1, 1/3, 0, 1, 0, 1 ], analytic_sha_upper_bounds := [ 1, 1, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 1, 0, 1 ], eigenvalues := [*
[ 0, -1, 4, -2, 2, 6, 4, -4, -3, 3, 8, -8 ],
[ 0, 1, 0, 2, 6, 2, 0, -4, 3, -3, -4, -4 ],
[
a,
-1,
-a^2 - 2*a + 1,
-a^2,
3*a^2 + a - 4,
a^2 + a - 7,
3*a^2 + 4*a - 8,
-3*a - 2,
-3*a^2 + 7,
-5*a^2 + 8,
-3*a^2 + 3,
-4*a^2 - 3*a + 5
],
[
a,
1,
-a^2 + 5,
-a^2 + 2,
a^2 - a - 4,
a^2 + a - 3,
a^2 - 2*a,
-2*a^2 - a + 6,
-a^2 + 3,
a^2 - 2*a + 2,
3*a^2 - 2*a - 9,
4*a^2 - 3*a - 9
],
[
a,
1,
a^2 + 2*a - 3,
-3*a^2 - 8*a - 2,
a^2 + 3*a - 2,
a^2 + 3*a - 3,
a^2 + 2*a - 2,
4*a^2 + 13*a + 4,
-a^2 - 6*a - 7,
-a^2 + 2*a + 4,
5*a^2 + 14*a + 1,
-6*a^2 - 13*a - 1
],
[
a,
-1,
a^2 - 3,
-a^3 - a^2 + 5*a + 5,
-a^2 + a + 2,
-a^3 - a^2 + 4*a + 6,
a^3 + a^2 - 5*a - 3,
a^3 - 6*a + 3,
a^2 - 2*a - 3,
-a^3 - a^2 + 5*a + 3,
-a^2 + 1,
2*a^3 + 2*a^2 - 11*a - 1
]
*], q_expansions := [*
q - q^3 - 2*q^4 + 4*q^5 - 2*q^7 + q^9 + 2*q^11 + 2*q^12 + 6*q^13 - 4*q^15 + 4*q^16 + 4*q^17 - 4*q^19 - 8*q^20 + 2*q^21 - 3*q^23 + 11*q^25 - q^27 + 4*q^28 + 3*q^29 + 8*q^31 - 2*q^33 - 8*q^35 - 2*q^36 - 8*q^37 + O(q^38),
q + q^3 - 2*q^4 + 2*q^7 + q^9 + 6*q^11 - 2*q^12 + 2*q^13 + 4*q^16 - 4*q^19 + 2*q^21 + 3*q^23 - 5*q^25 + q^27 - 4*q^28 - 3*q^29 - 4*q^31 + 6*q^33 - 2*q^36 - 4*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 - 2*a + 1)*q^5 - a*q^6 - a^2*q^7 + (-a - 1)*q^8 + q^9 + (-2*a^2 - 2*a + 1)*q^10 + (3*a^2 + a - 4)*q^11 + (-a^2 + 2)*q^12 + (a^2 + a - 7)*q^13 + (-3*a + 1)*q^14 + (a^2 + 2*a - 1)*q^15 + (-3*a^2 - a + 4)*q^16 + (3*a^2 + 4*a - 8)*q^17 + a*q^18 + (-3*a - 2)*q^19 - a*q^20 + a^2*q^21 + (a^2 + 5*a - 3)*q^22 + (-3*a^2 + 7)*q^23 + (a + 1)*q^24 + (5*a^2 + 7*a - 8)*q^25 + (a^2 - 4*a - 1)*q^26 - q^27 + (-a^2 + a)*q^28 + (-5*a^2 + 8)*q^29 + (2*a^2 + 2*a - 1)*q^30 + (-3*a^2 + 3)*q^31 + (-a^2 - 3*a + 5)*q^32 + (-3*a^2 - a + 4)*q^33 + (4*a^2 + a - 3)*q^34 + (2*a^2 + 5*a - 2)*q^35 + (a^2 - 2)*q^36 + (-4*a^2 - 3*a + 5)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^2 + 5)*q^5 + a*q^6 + (-a^2 + 2)*q^7 + (2*a^2 - a - 5)*q^8 + q^9 + (-2*a^2 + 2*a + 5)*q^10 + (a^2 - a - 4)*q^11 + (a^2 - 2)*q^12 + (a^2 + a - 3)*q^13 + (-2*a^2 - a + 5)*q^14 + (-a^2 + 5)*q^15 + (a^2 + a - 6)*q^16 + (a^2 - 2*a)*q^17 + a*q^18 + (-2*a^2 - a + 6)*q^19 - a*q^20 + (-a^2 + 2)*q^21 + (a^2 - a - 5)*q^22 + (-a^2 + 3)*q^23 + (2*a^2 - a - 5)*q^24 + (-3*a^2 + a + 10)*q^25 + (3*a^2 - 5)*q^26 + q^27 + (-3*a^2 - a + 6)*q^28 + (a^2 - 2*a + 2)*q^29 + (-2*a^2 + 2*a + 5)*q^30 + (3*a^2 - 2*a - 9)*q^31 + (-a^2 - a + 5)*q^32 + (a^2 - a - 4)*q^33 + (3*a - 5)*q^34 + a*q^35 + (a^2 - 2)*q^36 + (4*a^2 - 3*a - 9)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (a^2 + 2*a - 3)*q^5 + a*q^6 + (-3*a^2 - 8*a - 2)*q^7 + (-4*a^2 - 7*a + 1)*q^8 + q^9 + (-2*a^2 - 6*a + 1)*q^10 + (a^2 + 3*a - 2)*q^11 + (a^2 - 2)*q^12 + (a^2 + 3*a - 3)*q^13 + (4*a^2 + 7*a - 3)*q^14 + (a^2 + 2*a - 3)*q^15 + (7*a^2 + 13*a)*q^16 + (a^2 + 2*a - 2)*q^17 + a*q^18 + (4*a^2 + 13*a + 4)*q^19 + (3*a + 4)*q^20 + (-3*a^2 - 8*a - 2)*q^21 + (-a^2 - 5*a + 1)*q^22 + (-a^2 - 6*a - 7)*q^23 + (-4*a^2 - 7*a + 1)*q^24 + (-5*a^2 - 11*a + 4)*q^25 + (-a^2 - 6*a + 1)*q^26 + q^27 + (-3*a^2 + a + 8)*q^28 + (-a^2 + 2*a + 4)*q^29 + (-2*a^2 - 6*a + 1)*q^30 + (5*a^2 + 14*a + 1)*q^31 + (-7*a^2 - 7*a + 5)*q^32 + (a^2 + 3*a - 2)*q^33 + (-2*a^2 - 5*a + 1)*q^34 + (8*a^2 + 23*a + 4)*q^35 + (a^2 - 2)*q^36 + (-6*a^2 - 13*a - 1)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (a^2 - 3)*q^5 - a*q^6 + (-a^3 - a^2 + 5*a + 5)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (a^3 - 3*a)*q^10 + (-a^2 + a + 2)*q^11 + (-a^2 + 2)*q^12 + (-a^3 - a^2 + 4*a + 6)*q^13 + (-2*a^3 - 2*a^2 + 11*a + 7)*q^14 + (-a^2 + 3)*q^15 + (a^3 + a^2 - 6*a - 3)*q^16 + (a^3 + a^2 - 5*a - 3)*q^17 + a*q^18 + (a^3 - 6*a + 3)*q^19 + (a^3 + 2*a^2 - 6*a - 1)*q^20 + (a^3 + a^2 - 5*a - 5)*q^21 + (-a^3 + a^2 + 2*a)*q^22 + (a^2 - 2*a - 3)*q^23 + (-a^3 + 4*a)*q^24 + (a^3 + a^2 - 6*a - 3)*q^25 + (-2*a^3 - 3*a^2 + 12*a + 7)*q^26 - q^27 + (-2*a^3 - a^2 + 9*a + 4)*q^28 + (-a^3 - a^2 + 5*a + 3)*q^29 + (-a^3 + 3*a)*q^30 + (-a^2 + 1)*q^31 + (a^2 - a - 7)*q^32 + (a^2 - a - 2)*q^33 + (2*a^3 + 2*a^2 - 9*a - 7)*q^34 + (-a^3 + 4*a - 1)*q^35 + (a^2 - 2)*q^36 + (2*a^3 + 2*a^2 - 11*a - 1)*q^37 + O(q^38)
*]> ;  // time = 41.039 seconds




J[269] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 269, 269, 269 ], new_dimensions := [ 1, 5, 16 ], dimensions := [ 1, 5, 16 ], intersection_graph := [ 0, 3, 1, 3, 0, 1, 1, 1, 0 ], ap_traces := [
[ 0, 0, 1, -4, -3, 2, -4, 2, -1, -2, -8, 7 ],
[ -1, -5, -4, -5, -9, -5, 6, -25, 2, -2, 1, -9 ],
[ 1, 5, -1, 11, 16, -1, -2, 35, 1, 2, 13, 4 ]
], hecke_fields := [
x - 1,
x^5 + x^4 - 5*x^3 - 4*x^2 + 5*x + 3,
x^16 - x^15 - 28*x^14 + 27*x^13 + 314*x^12 - 283*x^11 - 1803*x^10 + 1435*x^9 + 5637*x^8 - 3547*x^7 - 9470*x^6 + 3701*x^5 + 7860*x^4 - 1001*x^3 - 2363*x^2 - 43*x + 172
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 67 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 67 ]
], torsion_upper_bounds := [ 1, 1, 67 ], torsion_lower_bounds := [ 1, 1, 67 ], l_ratios := [ 0, 0, 1/67 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[ 0, 0, 1, -4, -3, 2, -4, 2, -1, -2, -8, 7 ],
[
a,
a^4 - 5*a^2 + 3,
-a^4 + 5*a^2 - a - 5,
-a^4 - a^3 + 3*a^2 + 2*a - 1,
a^4 - 4*a^2,
2*a^3 + 3*a^2 - 5*a - 7,
-a^3 + a^2 + 4*a - 1,
-a^4 - a^3 + 4*a^2 + 3*a - 7,
2*a^4 + a^3 - 11*a^2 - 2*a + 11,
-2*a^4 - a^3 + 7*a^2 + 3*a - 2,
3*a^4 + a^3 - 15*a^2 + 13,
-a^3 + 3*a - 2
],
[
a,
18/683*a^15 - 991/10928*a^14 - 9143/10928*a^13 + 26463/10928*a^12 + 58569/5464*a^11 - 279911/10928*a^10 - 773187/10928*a^9 + 92792/683*a^8 + 693889/2732*a^7 - 4097871/10928*a^6 - 5203557/10928*a^5 + 5451909/10928*a^4 + 2147933/5464*a^3 - 2720323/10928*a^2 - 840769/10928*a + 79841/2732,
70/683*a^15 - 363/10928*a^14 - 30851/10928*a^13 + 11845/10928*a^12 + 84629/2732*a^11 - 148583/10928*a^10 - 1882165/10928*a^9 + 454851/5464*a^8 + 1392713/2732*a^7 - 2841689/10928*a^6 - 8410593/10928*a^5 + 4298529/10928*a^4 + 695081/1366*a^3 - 2654109/10928*a^2 - 976295/10928*a + 93147/2732,
2287/10928*a^15 - 333/1366*a^14 - 15109/2732*a^13 + 72055/10928*a^12 + 624789/10928*a^11 - 377619/5464*a^10 - 3183057/10928*a^9 + 478169/1366*a^8 + 8282669/10928*a^7 - 4746505/5464*a^6 - 5240293/5464*a^5 + 10399189/10928*a^4 + 5962023/10928*a^3 - 528717/1366*a^2 - 999017/10928*a + 117181/2732,
-581/2732*a^15 + 1717/5464*a^14 + 31231/5464*a^13 - 46055/5464*a^12 - 164865/2732*a^11 + 480091/5464*a^10 + 1727655/5464*a^9 - 1215601/2732*a^8 - 585729/683*a^7 + 6088951/5464*a^6 + 6340331/5464*a^5 - 6839219/5464*a^4 - 990813/1366*a^3 + 2851401/5464*a^2 + 722503/5464*a - 73529/1366,
3/2732*a^15 + 49/683*a^14 + 42/683*a^13 - 5167/2732*a^12 - 5311/2732*a^11 + 53695/2732*a^10 + 27423/1366*a^9 - 277997/2732*a^8 - 266457/2732*a^7 + 370859/1366*a^6 + 317525/1366*a^5 - 469565/1366*a^4 - 654743/2732*a^3 + 437761/2732*a^2 + 42097/683*a - 12622/683,
291/2732*a^15 - 2273/5464*a^14 - 15901/5464*a^13 + 59667/5464*a^12 + 42595/1366*a^11 - 610205/5464*a^10 - 905991/5464*a^9 + 380726/683*a^8 + 1259209/2732*a^7 - 7570837/5464*a^6 - 3661403/5464*a^5 + 8479841/5464*a^4 + 696685/1366*a^3 - 3408805/5464*a^2 - 632393/5464*a + 88677/1366,
91/2732*a^15 + 13/1366*a^14 - 2417/2732*a^13 - 553/2732*a^12 + 25131/2732*a^11 + 2401/1366*a^10 - 64265/1366*a^9 - 23935/2732*a^8 + 82837/683*a^7 + 77483/2732*a^6 - 391963/2732*a^5 - 34814/683*a^4 + 42337/683*a^3 + 81369/2732*a^2 - 6187/683*a - 1298/683,
117/1366*a^15 - 1525/5464*a^14 - 12723/5464*a^13 + 40185/5464*a^12 + 16985/683*a^11 - 413107/5464*a^10 - 721213/5464*a^9 + 1038961/2732*a^8 + 999273/2732*a^7 - 5235583/5464*a^6 - 2858339/5464*a^5 + 6047185/5464*a^4 + 1027237/2732*a^3 - 2636785/5464*a^2 - 427893/5464*a + 72455/1366,
1439/5464*a^15 - 575/2732*a^14 - 19129/2732*a^13 + 31815/5464*a^12 + 399863/5464*a^11 - 85489/1366*a^10 - 2075633/5464*a^9 + 892031/2732*a^8 + 5569797/5464*a^7 - 2303547/2732*a^6 - 921679/683*a^5 + 5392391/5464*a^4 + 4341637/5464*a^3 - 307307/683*a^2 - 774853/5464*a + 66921/1366,
-2125/5464*a^15 + 4369/5464*a^14 + 57897/5464*a^13 - 29201/1366*a^12 - 623357/5464*a^11 + 1218507/5464*a^10 + 1682807/2732*a^9 - 1554179/1366*a^8 - 9590531/5464*a^7 + 15858173/5464*a^6 + 14111367/5464*a^5 - 2303174/683*a^4 - 9912439/5464*a^3 + 7889031/5464*a^2 + 969499/2732*a - 105353/683,
-43/2732*a^15 - 247/683*a^14 + 845/1366*a^13 + 6278/683*a^12 - 26781/2732*a^11 - 61328/683*a^10 + 106893/1366*a^9 + 285096/683*a^8 - 879823/2732*a^7 - 2495623/2732*a^6 + 1688789/2732*a^5 + 1045595/1366*a^4 - 1082553/2732*a^3 - 288307/2732*a^2 + 110579/2732*a - 6682/683
]
*], q_expansions := [*
q - 2*q^4 + q^5 - 4*q^7 - 3*q^9 - 3*q^11 + 2*q^13 + 4*q^16 - 4*q^17 + 2*q^19 - 2*q^20 - q^23 - 4*q^25 + 8*q^28 - 2*q^29 - 8*q^31 - 4*q^35 + 6*q^36 + 7*q^37 + O(q^38),
q + a*q^2 + (a^4 - 5*a^2 + 3)*q^3 + (a^2 - 2)*q^4 + (-a^4 + 5*a^2 - a - 5)*q^5 + (-a^4 + 4*a^2 - 2*a - 3)*q^6 + (-a^4 - a^3 + 3*a^2 + 2*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (-a^4 + a^3 + 5*a^2 - 3*a - 3)*q^9 + (a^4 - 5*a^2 + 3)*q^10 + (a^4 - 4*a^2)*q^11 + (-a^4 - a^3 + 4*a^2 + 2*a - 3)*q^12 + (2*a^3 + 3*a^2 - 5*a - 7)*q^13 + (-2*a^3 - 2*a^2 + 4*a + 3)*q^14 + (-a^3 + a^2 + 5*a - 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^3 + a^2 + 4*a - 1)*q^17 + (2*a^4 - 7*a^2 + 2*a + 3)*q^18 + (-a^4 - a^3 + 4*a^2 + 3*a - 7)*q^19 + (a^4 - 6*a^2 + 7)*q^20 + (a^4 + 2*a^3 - a^2 - 3*a - 3)*q^21 + (-a^4 + a^3 + 4*a^2 - 5*a - 3)*q^22 + (2*a^4 + a^3 - 11*a^2 - 2*a + 11)*q^23 + (2*a^4 - a^3 - 10*a^2 + 6*a + 9)*q^24 + (a^4 + a^3 - 6*a^2 - 3*a + 5)*q^25 + (2*a^4 + 3*a^3 - 5*a^2 - 7*a)*q^26 + (-a^4 - 2*a^3 + 4*a^2 + 7*a - 3)*q^27 + (-2*a^2 - a + 2)*q^28 + (-2*a^4 - a^3 + 7*a^2 + 3*a - 2)*q^29 + (-a^4 + a^3 + 5*a^2 - 3*a)*q^30 + (3*a^4 + a^3 - 15*a^2 + 13)*q^31 + (-a^4 - 3*a^3 + 4*a^2 + 7*a - 3)*q^32 + (-3*a^4 + 14*a^2 - a - 6)*q^33 + (-a^4 + a^3 + 4*a^2 - a)*q^34 + (a^4 + 2*a^3 - 3*a^2 - 5*a + 2)*q^35 + (a^3 - a)*q^36 + (-a^3 + 3*a - 2)*q^37 + O(q^38),
q + a*q^2 + (18/683*a^15 - 991/10928*a^14 - 9143/10928*a^13 + 26463/10928*a^12 + 58569/5464*a^11 - 279911/10928*a^10 - 773187/10928*a^9 + 92792/683*a^8 + 693889/2732*a^7 - 4097871/10928*a^6 - 5203557/10928*a^5 + 5451909/10928*a^4 + 2147933/5464*a^3 - 2720323/10928*a^2 - 840769/10928*a + 79841/2732)*q^3 + (a^2 - 2)*q^4 + (70/683*a^15 - 363/10928*a^14 - 30851/10928*a^13 + 11845/10928*a^12 + 84629/2732*a^11 - 148583/10928*a^10 - 1882165/10928*a^9 + 454851/5464*a^8 + 1392713/2732*a^7 - 2841689/10928*a^6 - 8410593/10928*a^5 + 4298529/10928*a^4 + 695081/1366*a^3 - 2654109/10928*a^2 - 976295/10928*a + 93147/2732)*q^5 + (-703/10928*a^15 - 1079/10928*a^14 + 18687/10928*a^13 + 13353/5464*a^12 - 198407/10928*a^11 - 253923/10928*a^10 + 66962/683*a^9 + 288025/2732*a^8 - 3076335/10928*a^7 - 2476197/10928*a^6 + 4386021/10928*a^5 + 1016093/5464*a^4 - 2432035/10928*a^3 - 160225/10928*a^2 + 82937/2732*a - 3096/683)*q^6 + (2287/10928*a^15 - 333/1366*a^14 - 15109/2732*a^13 + 72055/10928*a^12 + 624789/10928*a^11 - 377619/5464*a^10 - 3183057/10928*a^9 + 478169/1366*a^8 + 8282669/10928*a^7 - 4746505/5464*a^6 - 5240293/5464*a^5 + 10399189/10928*a^4 + 5962023/10928*a^3 - 528717/1366*a^2 - 999017/10928*a + 117181/2732)*q^7 + (a^3 - 4*a)*q^8 + (-170/683*a^15 + 879/2732*a^14 + 8963/1366*a^13 - 5902/683*a^12 - 184257/2732*a^11 + 122809/1366*a^10 + 231930/683*a^9 - 1234197/2732*a^8 - 2359169/2732*a^7 + 3034549/2732*a^6 + 715749/683*a^5 - 3283869/2732*a^4 - 778493/1366*a^3 + 329537/683*a^2 + 135419/1366*a - 33795/683)*q^9 + (757/10928*a^15 + 509/10928*a^14 - 18395/10928*a^13 - 3291/2732*a^12 + 168377/10928*a^11 + 137195/10928*a^10 - 348749/5464*a^9 - 185647/2732*a^8 + 1130951/10928*a^7 + 2195807/10928*a^6 + 153409/10928*a^5 - 405319/1366*a^4 - 1532989/10928*a^3 + 1670265/10928*a^2 + 105187/2732*a - 12040/683)*q^10 + (-581/2732*a^15 + 1717/5464*a^14 + 31231/5464*a^13 - 46055/5464*a^12 - 164865/2732*a^11 + 480091/5464*a^10 + 1727655/5464*a^9 - 1215601/2732*a^8 - 585729/683*a^7 + 6088951/5464*a^6 + 6340331/5464*a^5 - 6839219/5464*a^4 - 990813/1366*a^3 + 2851401/5464*a^2 + 722503/5464*a - 73529/1366)*q^11 + (-1179/5464*a^15 + 985/10928*a^14 + 63973/10928*a^13 - 30591/10928*a^12 - 171787/2732*a^11 + 363705/10928*a^10 + 3707279/10928*a^9 - 520717/2732*a^8 - 5260425/5464*a^7 + 5924353/10928*a^6 + 15041103/10928*a^5 - 7810273/10928*a^4 - 2363915/2732*a^3 + 4111205/10928*a^2 + 1601773/10928*a - 129453/2732)*q^12 + (3/2732*a^15 + 49/683*a^14 + 42/683*a^13 - 5167/2732*a^12 - 5311/2732*a^11 + 53695/2732*a^10 + 27423/1366*a^9 - 277997/2732*a^8 - 266457/2732*a^7 + 370859/1366*a^6 + 317525/1366*a^5 - 469565/1366*a^4 - 654743/2732*a^3 + 437761/2732*a^2 + 42097/683*a - 12622/683)*q^13 + (-377/10928*a^15 + 225/683*a^14 + 5153/5464*a^13 - 93329/10928*a^12 - 108017/10928*a^11 + 235101/2732*a^10 + 543507/10928*a^9 - 2304575/5464*a^8 - 1381021/10928*a^7 + 1397163/1366*a^6 + 967501/5464*a^5 - 12013797/10928*a^4 - 1940449/10928*a^3 + 1101291/2732*a^2 + 567065/10928*a - 98341/2732)*q^14 + (439/5464*a^15 + 223/5464*a^14 - 11615/5464*a^13 - 629/683*a^12 + 120741/5464*a^11 + 43393/5464*a^10 - 155587/1366*a^9 - 22604/683*a^8 + 1646959/5464*a^7 + 375683/5464*a^6 - 2092481/5464*a^5 - 41043/683*a^4 + 1086029/5464*a^3 - 2731/5464*a^2 - 50097/1366*a + 2866/683)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (291/2732*a^15 - 2273/5464*a^14 - 15901/5464*a^13 + 59667/5464*a^12 + 42595/1366*a^11 - 610205/5464*a^10 - 905991/5464*a^9 + 380726/683*a^8 + 1259209/2732*a^7 - 7570837/5464*a^6 - 3661403/5464*a^5 + 8479841/5464*a^4 + 696685/1366*a^3 - 3408805/5464*a^2 - 632393/5464*a + 88677/1366)*q^17 + (199/2732*a^15 - 557/1366*a^14 - 1312/683*a^13 + 29263/2732*a^12 + 26589/1366*a^11 - 74580/683*a^10 - 258397/2732*a^9 + 1473991/2732*a^8 + 622589/2732*a^7 - 894151/683*a^6 - 767189/2732*a^5 + 1893907/1366*a^4 + 159367/683*a^3 - 668001/1366*a^2 - 41105/683*a + 29240/683)*q^18 + (91/2732*a^15 + 13/1366*a^14 - 2417/2732*a^13 - 553/2732*a^12 + 25131/2732*a^11 + 2401/1366*a^10 - 64265/1366*a^9 - 23935/2732*a^8 + 82837/683*a^7 + 77483/2732*a^6 - 391963/2732*a^5 - 34814/683*a^4 + 42337/683*a^3 + 81369/2732*a^2 - 6187/683*a - 1298/683)*q^19 + (-487/5464*a^15 + 3527/10928*a^14 + 28099/10928*a^13 - 93011/10928*a^12 - 162803/5464*a^11 + 964539/10928*a^10 + 1935447/10928*a^9 - 2477831/5464*a^8 - 3130409/5464*a^7 + 13005577/10928*a^6 + 10776977/10928*a^5 - 16080067/10928*a^4 - 4346637/5464*a^3 + 7517757/10928*a^2 + 1792501/10928*a - 218845/2732)*q^20 + (849/10928*a^15 - 269/5464*a^14 - 5189/2732*a^13 + 13019/10928*a^12 + 189461/10928*a^11 - 56197/5464*a^10 - 767449/10928*a^9 + 185561/5464*a^8 + 1143309/10928*a^7 - 22637/5464*a^6 + 24673/683*a^5 - 1808633/10928*a^4 - 1566635/10928*a^3 + 946159/5464*a^2 + 375861/10928*a - 62089/2732)*q^21 + (555/5464*a^15 - 1305/5464*a^14 - 14681/5464*a^13 + 17569/2732*a^12 + 151245/5464*a^11 - 367431/5464*a^10 - 190933/1366*a^9 + 932181/2732*a^8 + 1967337/5464*a^7 - 4663809/5464*a^6 - 2538657/5464*a^5 + 1292517/1366*a^4 + 1688239/5464*a^3 - 2023303/5464*a^2 - 172041/2732*a + 24983/683)*q^22 + (117/1366*a^15 - 1525/5464*a^14 - 12723/5464*a^13 + 40185/5464*a^12 + 16985/683*a^11 - 413107/5464*a^10 - 721213/5464*a^9 + 1038961/2732*a^8 + 999273/2732*a^7 - 5235583/5464*a^6 - 2858339/5464*a^5 + 6047185/5464*a^4 + 1027237/2732*a^3 - 2636785/5464*a^2 - 427893/5464*a + 72455/1366)*q^23 + (33/10928*a^15 + 107/10928*a^14 - 4299/10928*a^13 - 37/2732*a^12 + 93205/10928*a^11 - 36349/10928*a^10 - 420961/5464*a^9 + 116749/2732*a^8 + 3713197/10928*a^7 - 2336763/10928*a^6 - 7855357/10928*a^5 + 626731/1366*a^4 + 6614917/10928*a^3 - 3649731/10928*a^2 - 641351/5464*a + 63081/1366)*q^24 + (3283/10928*a^15 - 1473/2732*a^14 - 43993/5464*a^13 + 156999/10928*a^12 + 925563/10928*a^11 - 203459/1366*a^10 - 4827629/10928*a^9 + 4105865/5464*a^8 + 13036151/10928*a^7 - 5133891/2732*a^6 - 8839721/5464*a^5 + 23072643/10928*a^4 + 11420195/10928*a^3 - 597851/683*a^2 - 2243543/10928*a + 255531/2732)*q^25 + (199/2732*a^15 + 63/683*a^14 - 1312/683*a^13 - 6253/2732*a^12 + 13636/683*a^11 + 60255/2732*a^10 - 141151/1366*a^9 - 70842/683*a^8 + 752359/2732*a^7 + 165865/683*a^6 - 950233/2732*a^5 - 678323/2732*a^4 + 110191/683*a^3 + 175477/2732*a^2 - 50359/2732*a - 129/683)*q^26 + (-2373/10928*a^15 + 43/683*a^14 + 15271/2732*a^13 - 20465/10928*a^12 - 610051/10928*a^11 + 113183/5464*a^10 + 2956315/10928*a^9 - 142531/1366*a^8 - 7072631/10928*a^7 + 1265313/5464*a^6 + 3781135/5464*a^5 - 1942595/10928*a^4 - 3089321/10928*a^3 + 62037/1366*a^2 + 485267/10928*a - 11703/2732)*q^27 + (-1351/10928*a^15 + 2539/5464*a^14 + 18861/5464*a^13 - 133749/10928*a^12 - 415865/10928*a^11 + 343563/2732*a^10 + 2297959/10928*a^9 - 431661/683*a^8 - 6725253/10928*a^7 + 1084427/683*a^6 + 2585663/2732*a^5 - 19775607/10928*a^4 - 7896259/10928*a^3 + 4067843/5464*a^2 + 1588459/10928*a - 218151/2732)*q^28 + (1439/5464*a^15 - 575/2732*a^14 - 19129/2732*a^13 + 31815/5464*a^12 + 399863/5464*a^11 - 85489/1366*a^10 - 2075633/5464*a^9 + 892031/2732*a^8 + 5569797/5464*a^7 - 2303547/2732*a^6 - 921679/683*a^5 + 5392391/5464*a^4 + 4341637/5464*a^3 - 307307/683*a^2 - 774853/5464*a + 66921/1366)*q^29 + (331/2732*a^15 + 677/5464*a^14 - 16885/5464*a^13 - 17105/5464*a^12 + 83815/2732*a^11 + 169169/5464*a^10 - 810797/5464*a^9 - 206921/1366*a^8 + 241602/683*a^7 + 2064849/5464*a^6 - 1953083/5464*a^5 - 2364511/5464*a^4 + 109177/1366*a^3 + 836969/5464*a^2 + 41805/5464*a - 18877/1366)*q^30 + (-2125/5464*a^15 + 4369/5464*a^14 + 57897/5464*a^13 - 29201/1366*a^12 - 623357/5464*a^11 + 1218507/5464*a^10 + 1682807/2732*a^9 - 1554179/1366*a^8 - 9590531/5464*a^7 + 15858173/5464*a^6 + 14111367/5464*a^5 - 2303174/683*a^4 - 9912439/5464*a^3 + 7889031/5464*a^2 + 969499/2732*a - 105353/683)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (961/5464*a^15 - 1189/5464*a^14 - 27461/5464*a^13 + 16493/2732*a^12 + 315381/5464*a^11 - 362819/5464*a^10 - 464221/1366*a^9 + 499813/1366*a^8 + 5911499/5464*a^7 - 5721523/5464*a^6 - 9788297/5464*a^5 + 3952517/2732*a^4 + 7191167/5464*a^3 - 4191365/5464*a^2 - 658799/2732*a + 61071/683)*q^33 + (-1691/5464*a^15 + 395/5464*a^14 + 43953/5464*a^13 - 1546/683*a^12 - 445499/5464*a^11 + 143355/5464*a^10 + 1105319/2732*a^9 - 190579/1366*a^8 - 5506483/5464*a^7 + 1850137/5464*a^6 + 6325859/5464*a^5 - 446945/1366*a^4 - 2826223/5464*a^3 + 742873/5464*a^2 + 189867/2732*a - 12513/683)*q^34 + (-903/10928*a^15 + 425/10928*a^14 + 22513/10928*a^13 - 2713/2732*a^12 - 214071/10928*a^11 + 102767/10928*a^10 + 475783/5464*a^9 - 26336/683*a^8 - 1886213/10928*a^7 + 572227/10928*a^6 + 1057761/10928*a^5 + 111193/2732*a^4 + 553955/10928*a^3 - 921019/10928*a^2 - 17291/683*a + 11705/683)*q^35 + (445/2732*a^15 - 717/1366*a^14 - 5981/1366*a^13 + 9477/683*a^12 + 126511/2732*a^11 - 97709/683*a^10 - 333507/1366*a^9 + 492305/683*a^8 + 1847587/2732*a^7 - 4951757/2732*a^6 - 2674677/2732*a^5 + 2820533/1366*a^4 + 1977169/2732*a^3 - 2330479/2732*a^2 - 416159/2732*a + 59033/683)*q^36 + (-43/2732*a^15 - 247/683*a^14 + 845/1366*a^13 + 6278/683*a^12 - 26781/2732*a^11 - 61328/683*a^10 + 106893/1366*a^9 + 285096/683*a^8 - 879823/2732*a^7 - 2495623/2732*a^6 + 1688789/2732*a^5 + 1045595/1366*a^4 - 1082553/2732*a^3 - 288307/2732*a^2 + 110579/2732*a - 6682/683)*q^37 + O(q^38)
*]> ;  // time = 4.431 seconds




J[271] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 271, 271 ], new_dimensions := [ 6, 16 ], dimensions := [ 6, 16 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -4, -1, -8, -3, -11, -2, -10, -5, -3, -17, -6, 0 ],
[ 5, 1, 10, -3, 17, -4, 12, -3, 5, 21, -10, 2 ]
], hecke_fields := [
x^6 + 4*x^5 + x^4 - 9*x^3 - 4*x^2 + 5*x + 1,
x^16 - 5*x^15 - 12*x^14 + 91*x^13 + 11*x^12 - 620*x^11 + 381*x^10 + 1953*x^9 - 1863*x^8 - 2853*x^7 + 3137*x^6 + 1830*x^5 - 1758*x^4 - 831*x^3 + 308*x^2 + 204*x + 27
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 45 ]
], tamagawa_numbers := [
[ 1 ],
[ 45 ]
], torsion_upper_bounds := [ 1, 45 ], torsion_lower_bounds := [ 1, 45 ], l_ratios := [ 0, 1/45 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^5 - 3*a^4 + a^3 + 5*a^2 - a - 1,
a^5 + 4*a^4 + 2*a^3 - 6*a^2 - 4*a,
a^5 + 2*a^4 - 5*a^3 - 7*a^2 + 5*a + 2,
a^5 + 3*a^4 - a^3 - 4*a^2 + 3*a - 2,
-a^5 - 5*a^4 - 4*a^3 + 9*a^2 + 7*a - 4,
a^4 + 2*a^3 - 2*a^2 - 2*a - 1,
-2*a^5 - 7*a^4 + a^3 + 15*a^2 - 6,
-a^5 - a^4 + 9*a^3 + 10*a^2 - 9*a - 7,
-a^5 - 4*a^4 - 3*a^3 + a^2 + 2*a + 2,
a^5 + 6*a^4 + 8*a^3 - 10*a^2 - 14*a + 6,
-2*a^4 - 8*a^3 - 4*a^2 + 9*a + 4
],
[
a,
4966/763*a^15 - 26858/763*a^14 - 49243/763*a^13 + 474081/763*a^12 - 128875/763*a^11 - 3063997/763*a^10 + 3087453/763*a^9 + 8695891/763*a^8 - 1814217/109*a^7 - 9799739/763*a^6 + 19637291/763*a^5 + 2259965/763*a^4 - 1419203/109*a^3 - 760516/763*a^2 + 1897494/763*a + 406918/763,
-2931/763*a^15 + 15816/763*a^14 + 29560/763*a^13 - 280031/763*a^12 + 67017/763*a^11 + 1819457/763*a^10 - 1760793/763*a^9 - 5219351/763*a^8 + 1043544/109*a^7 + 6055573/763*a^6 - 11326071/763*a^5 - 1666627/763*a^4 + 817097/109*a^3 + 533915/763*a^2 - 1063246/763*a - 229968/763,
4747/763*a^15 - 25342/763*a^14 - 48836/763*a^13 + 449248/763*a^12 - 91214/763*a^11 - 2925197/763*a^10 + 2735429/763*a^9 + 8428341/763*a^8 - 1639143/109*a^7 - 9899208/763*a^6 + 17856212/763*a^5 + 2928854/763*a^4 - 1289523/109*a^3 - 966229/763*a^2 + 1684731/763*a + 377795/763,
7251/763*a^15 - 38561/763*a^14 - 74756/763*a^13 + 683219/763*a^12 - 136608/763*a^11 - 4444746/763*a^10 + 4161832/763*a^9 + 12784879/763*a^8 - 2498112/109*a^7 - 14949252/763*a^6 + 27259040/763*a^5 + 4317273/763*a^4 - 1977730/109*a^3 - 1421394/763*a^2 + 2608957/763*a + 583200/763,
-5580/763*a^15 + 29983/763*a^14 + 56725/763*a^13 - 531848/763*a^12 + 121076/763*a^11 + 3466885/763*a^10 - 3325823/763*a^9 - 10012231/763*a^8 + 1988907/109*a^7 + 11833721/763*a^6 - 21864055/763*a^5 - 3620923/763*a^4 + 1631536/109*a^3 + 1218208/763*a^2 - 2212377/763*a - 498223/763,
-5031/763*a^15 + 26862/763*a^14 + 51827/763*a^13 - 477424/763*a^12 + 97635/763*a^11 + 3122927/763*a^10 - 2930010/763*a^9 - 9083295/763*a^8 + 1770391/109*a^7 + 10944961/763*a^6 - 19647573/763*a^5 - 3696284/763*a^4 + 1497695/109*a^3 + 1294955/763*a^2 - 2085085/763*a - 491712/763,
-5161/763*a^15 + 27633/763*a^14 + 51654/763*a^13 - 486399/763*a^12 + 123663/763*a^11 + 3127863/763*a^10 - 3120993/763*a^9 - 8782273/763*a^8 + 1831851/109*a^7 + 9580635/763*a^6 - 19581155/763*a^5 - 1649098/763*a^4 + 1355256/109*a^3 + 456333/763*a^2 - 1725498/763*a - 336262/763,
4806/763*a^15 - 25733/763*a^14 - 49632/763*a^13 + 458046/763*a^12 - 91030/763*a^11 - 3003925/763*a^10 + 2783727/763*a^9 + 8782661/763*a^8 - 1684359/109*a^7 - 10728587/763*a^6 + 18698377/763*a^5 + 3857405/763*a^4 - 1423894/109*a^3 - 1364271/763*a^2 + 1967073/763*a + 474459/763,
-1888/109*a^15 + 10114/109*a^14 + 19041/109*a^13 - 178640/109*a^12 + 43162/109*a^11 + 1155815/109*a^10 - 1133843/109*a^9 - 3287391/109*a^8 + 4701383/109*a^7 + 3725665/109*a^6 - 7280339/109*a^5 - 887819/109*a^4 + 3667367/109*a^3 + 287364/109*a^2 - 692847/109*a - 147741/109,
-647/109*a^15 + 3449/109*a^14 + 6743/109*a^13 - 61391/109*a^12 + 11053/109*a^11 + 402563/109*a^10 - 365690/109*a^9 - 1176425/109*a^8 + 1554123/109*a^7 + 1433995/109*a^6 - 2456291/109*a^5 - 506978/109*a^4 + 1288760/109*a^3 + 171449/109*a^2 - 246702/109*a - 58720/109,
13014/763*a^15 - 68567/763*a^14 - 136420/763*a^13 + 1216931/763*a^12 - 206238/763*a^11 - 7940319/763*a^10 + 7225376/763*a^9 + 22976028/763*a^8 - 4390072/109*a^7 - 27292612/763*a^6 + 48299044/763*a^5 + 8542042/763*a^4 - 3555707/109*a^3 - 2811128/763*a^2 + 4741176/763*a + 1077998/763
]
*], q_expansions := [*
q + a*q^2 + (-a^5 - 3*a^4 + a^3 + 5*a^2 - a - 1)*q^3 + (a^2 - 2)*q^4 + (a^5 + 4*a^4 + 2*a^3 - 6*a^2 - 4*a)*q^5 + (a^5 + 2*a^4 - 4*a^3 - 5*a^2 + 4*a + 1)*q^6 + (a^5 + 2*a^4 - 5*a^3 - 7*a^2 + 5*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (a^3 + 2*a^2 - 2*a - 3)*q^9 + (a^4 + 3*a^3 - 5*a - 1)*q^10 + (a^5 + 3*a^4 - a^3 - 4*a^2 + 3*a - 2)*q^11 + (a^4 + 2*a^3 - 2*a^2 - 2*a + 1)*q^12 + (-a^5 - 5*a^4 - 4*a^3 + 9*a^2 + 7*a - 4)*q^13 + (-2*a^5 - 6*a^4 + 2*a^3 + 9*a^2 - 3*a - 1)*q^14 + (a^5 + 3*a^4 - a^3 - 5*a^2 + a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 + 2*a^3 - 2*a^2 - 2*a - 1)*q^17 + (a^4 + 2*a^3 - 2*a^2 - 3*a)*q^18 + (-2*a^5 - 7*a^4 + a^3 + 15*a^2 - 6)*q^19 + (-a^5 - 5*a^4 - 4*a^3 + 7*a^2 + 7*a)*q^20 + (a^5 + 4*a^4 + a^3 - 6*a^2 + 2*a)*q^21 + (-a^5 - 2*a^4 + 5*a^3 + 7*a^2 - 7*a - 1)*q^22 + (-a^5 - a^4 + 9*a^3 + 10*a^2 - 9*a - 7)*q^23 + (-a^5 - 2*a^4 + 6*a^3 + 8*a^2 - 7*a - 2)*q^24 + (-3*a^5 - 13*a^4 - 10*a^3 + 16*a^2 + 18*a - 2)*q^25 + (-a^5 - 3*a^4 + 3*a^2 + a + 1)*q^26 + (3*a^5 + 10*a^4 - 16*a^2 - a + 4)*q^27 + (a^3 + 3*a^2 - a - 2)*q^28 + (-a^5 - 4*a^4 - 3*a^3 + a^2 + 2*a + 2)*q^29 + (-a^5 - 2*a^4 + 4*a^3 + 5*a^2 - 5*a - 1)*q^30 + (a^5 + 6*a^4 + 8*a^3 - 10*a^2 - 14*a + 6)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (3*a^5 + 8*a^4 - 8*a^3 - 19*a^2 + 9*a + 4)*q^33 + (a^5 + 2*a^4 - 2*a^3 - 2*a^2 - a)*q^34 + (-a^5 - 2*a^4 + 5*a^3 + 6*a^2 - 7*a - 1)*q^35 + (a^5 + 2*a^4 - 4*a^3 - 7*a^2 + 4*a + 6)*q^36 + (-2*a^4 - 8*a^3 - 4*a^2 + 9*a + 4)*q^37 + O(q^38),
q + a*q^2 + (4966/763*a^15 - 26858/763*a^14 - 49243/763*a^13 + 474081/763*a^12 - 128875/763*a^11 - 3063997/763*a^10 + 3087453/763*a^9 + 8695891/763*a^8 - 1814217/109*a^7 - 9799739/763*a^6 + 19637291/763*a^5 + 2259965/763*a^4 - 1419203/109*a^3 - 760516/763*a^2 + 1897494/763*a + 406918/763)*q^3 + (a^2 - 2)*q^4 + (-2931/763*a^15 + 15816/763*a^14 + 29560/763*a^13 - 280031/763*a^12 + 67017/763*a^11 + 1819457/763*a^10 - 1760793/763*a^9 - 5219351/763*a^8 + 1043544/109*a^7 + 6055573/763*a^6 - 11326071/763*a^5 - 1666627/763*a^4 + 817097/109*a^3 + 533915/763*a^2 - 1063246/763*a - 229968/763)*q^5 + (-2028/763*a^15 + 10349/763*a^14 + 22175/763*a^13 - 183501/763*a^12 + 14923/763*a^11 + 1195407/763*a^10 - 1002707/763*a^9 - 3447861/763*a^8 + 624037/109*a^7 + 4058949/763*a^6 - 6827815/763*a^5 - 1204193/763*a^4 + 480890/109*a^3 + 367966/763*a^2 - 606146/763*a - 134082/763)*q^6 + (4747/763*a^15 - 25342/763*a^14 - 48836/763*a^13 + 449248/763*a^12 - 91214/763*a^11 - 2925197/763*a^10 + 2735429/763*a^9 + 8428341/763*a^8 - 1639143/109*a^7 - 9899208/763*a^6 + 17856212/763*a^5 + 2928854/763*a^4 - 1289523/109*a^3 - 966229/763*a^2 + 1684731/763*a + 377795/763)*q^7 + (a^3 - 4*a)*q^8 + (-711/763*a^15 + 4117/763*a^14 + 6631/763*a^13 - 73473/763*a^12 + 26518/763*a^11 + 483904/763*a^10 - 502266/763*a^9 - 1426970/763*a^8 + 291298/109*a^7 + 1785758/763*a^6 - 3224758/763*a^5 - 727467/763*a^4 + 254767/109*a^3 + 299893/763*a^2 - 373803/763*a - 96515/763)*q^9 + (1161/763*a^15 - 5612/763*a^14 - 13310/763*a^13 + 99258/763*a^12 + 2237/763*a^11 - 644082/763*a^10 + 504892/763*a^9 + 1844355/763*a^8 - 329510/109*a^7 - 2131524/763*a^6 + 3697103/763*a^5 + 566981/763*a^4 - 271678/109*a^3 - 160498/763*a^2 + 367956/763*a + 79137/763)*q^10 + (7251/763*a^15 - 38561/763*a^14 - 74756/763*a^13 + 683219/763*a^12 - 136608/763*a^11 - 4444746/763*a^10 + 4161832/763*a^9 + 12784879/763*a^8 - 2498112/109*a^7 - 14949252/763*a^6 + 27259040/763*a^5 + 4317273/763*a^4 - 1977730/109*a^3 - 1421394/763*a^2 + 2608957/763*a + 583200/763)*q^11 + (-1389/109*a^15 + 7365/109*a^14 + 14219/109*a^13 - 130133/109*a^12 + 27971/109*a^11 + 842565/109*a^10 - 808869/109*a^9 - 2400241/109*a^8 + 3381729/109*a^7 + 2733357/109*a^6 - 5252505/109*a^5 - 674132/109*a^4 + 2650220/109*a^3 + 219930/109*a^2 - 502194/109*a - 108440/109)*q^12 + (-5580/763*a^15 + 29983/763*a^14 + 56725/763*a^13 - 531848/763*a^12 + 121076/763*a^11 + 3466885/763*a^10 - 3325823/763*a^9 - 10012231/763*a^8 + 1988907/109*a^7 + 11833721/763*a^6 - 21864055/763*a^5 - 3620923/763*a^4 + 1631536/109*a^3 + 1218208/763*a^2 - 2212377/763*a - 498223/763)*q^13 + (-1607/763*a^15 + 8128/763*a^14 + 17271/763*a^13 - 143431/763*a^12 + 17943/763*a^11 + 926822/763*a^10 - 842550/763*a^9 - 2630340/763*a^8 + 520569/109*a^7 + 2964873/763*a^6 - 5758156/763*a^5 - 681435/763*a^4 + 425504/109*a^3 + 222655/763*a^2 - 590593/763*a - 128169/763)*q^14 + (7319/763*a^15 - 39516/763*a^14 - 73656/763*a^13 + 700239/763*a^12 - 172244/763*a^11 - 4556343/763*a^10 + 4452023/763*a^9 + 13109473/763*a^8 - 2647603/109*a^7 - 15335651/763*a^6 + 29041283/763*a^5 + 4437222/763*a^4 - 2165241/109*a^3 - 1487261/763*a^2 + 2952512/763*a + 659007/763)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-5031/763*a^15 + 26862/763*a^14 + 51827/763*a^13 - 477424/763*a^12 + 97635/763*a^11 + 3122927/763*a^10 - 2930010/763*a^9 - 9083295/763*a^8 + 1770391/109*a^7 + 10944961/763*a^6 - 19647573/763*a^5 - 3696284/763*a^4 + 1497695/109*a^3 + 1294955/763*a^2 - 2085085/763*a - 491712/763)*q^17 + (562/763*a^15 - 1901/763*a^14 - 8772/763*a^13 + 34339/763*a^12 + 43084/763*a^11 - 231375/763*a^10 - 38387/763*a^9 + 714493/763*a^8 - 34675/109*a^7 - 994351/763*a^6 + 573663/763*a^5 + 533431/763*a^4 - 41564/109*a^3 - 154815/763*a^2 + 48529/763*a + 19197/763)*q^18 + (-5161/763*a^15 + 27633/763*a^14 + 51654/763*a^13 - 486399/763*a^12 + 123663/763*a^11 + 3127863/763*a^10 - 3120993/763*a^9 - 8782273/763*a^8 + 1831851/109*a^7 + 9580635/763*a^6 - 19581155/763*a^5 - 1649098/763*a^4 + 1355256/109*a^3 + 456333/763*a^2 - 1725498/763*a - 336262/763)*q^19 + (865/109*a^15 - 4430/109*a^14 - 9359/109*a^13 + 78504/109*a^12 - 8328/109*a^11 - 510909/109*a^10 + 442644/109*a^9 + 1470725/109*a^8 - 1918401/109*a^7 - 1722300/109*a^6 + 3013499/109*a^5 + 496078/109*a^4 - 1519295/109*a^3 - 151066/109*a^2 + 281255/109*a + 61227/109)*q^20 + (-2050/763*a^15 + 11219/763*a^14 + 20338/763*a^13 - 198343/763*a^12 + 52125/763*a^11 + 1285079/763*a^10 - 1258281/763*a^9 - 3663781/763*a^8 + 735221/109*a^7 + 4175545/763*a^6 - 7851743/763*a^5 - 1027273/763*a^4 + 545412/109*a^3 + 323815/763*a^2 - 696942/763*a - 146512/763)*q^21 + (-2306/763*a^15 + 12256/763*a^14 + 23378/763*a^13 - 216369/763*a^12 + 50874/763*a^11 + 1399201/763*a^10 - 1376324/763*a^9 - 3978171/763*a^8 + 819693/109*a^7 + 4512653/763*a^6 - 8952057/763*a^5 - 1096852/763*a^4 + 657741/109*a^3 + 375649/763*a^2 - 896004/763*a - 195777/763)*q^22 + (4806/763*a^15 - 25733/763*a^14 - 49632/763*a^13 + 458046/763*a^12 - 91030/763*a^11 - 3003925/763*a^10 + 2783727/763*a^9 + 8782661/763*a^8 - 1684359/109*a^7 - 10728587/763*a^6 + 18698377/763*a^5 + 3857405/763*a^4 - 1423894/109*a^3 - 1364271/763*a^2 + 1967073/763*a + 474459/763)*q^23 + (6996/763*a^15 - 37841/763*a^14 - 70488/763*a^13 + 669752/763*a^12 - 160151/763*a^11 - 4348434/763*a^10 + 4192746/763*a^9 + 12453876/763*a^8 - 2477534/109*a^7 - 14384382/763*a^6 + 26729796/763*a^5 + 3866892/763*a^4 - 1896109/109*a^3 - 1256606/763*a^2 + 2436704/763*a + 530685/763)*q^24 + (-10230/763*a^15 + 54333/763*a^14 + 105649/763*a^13 - 962338/763*a^12 + 188655/763*a^11 + 6256893/763*a^10 - 5834743/763*a^9 - 17975910/763*a^8 + 3500215/109*a^7 + 20951103/763*a^6 - 38052359/763*a^5 - 5938815/763*a^4 + 2725589/109*a^3 + 1931742/763*a^2 - 3529173/763*a - 780011/763)*q^25 + (2083/763*a^15 - 10235/763*a^14 - 24068/763*a^13 + 182456/763*a^12 + 7285/763*a^11 - 1199843/763*a^10 + 885509/763*a^9 + 3526809/763*a^8 - 583717/109*a^7 - 4359595/763*a^6 + 6590477/763*a^5 + 1611112/763*a^4 - 488396/109*a^3 - 493737/763*a^2 + 640097/763*a + 150660/763)*q^26 + (-5756/763*a^15 + 29313/763*a^14 + 64156/763*a^13 - 523926/763*a^12 + 24221/763*a^11 + 3460174/763*a^10 - 2766296/763*a^9 - 10254030/763*a^8 + 1769958/109*a^7 + 12933586/763*a^6 - 20054838/763*a^5 - 5194234/763*a^4 + 1542871/109*a^3 + 1693618/763*a^2 - 2092578/763*a - 512207/763)*q^27 + (-1343/109*a^15 + 6953/109*a^14 + 14354/109*a^13 - 123268/109*a^12 + 16130/109*a^11 + 802873/109*a^10 - 708961/109*a^9 - 2315220/109*a^8 + 3046872/109*a^7 + 2725917/109*a^6 - 4779007/109*a^5 - 814898/109*a^4 + 2420080/109*a^3 + 262403/109*a^2 - 452829/109*a - 101743/109)*q^28 + (-1888/109*a^15 + 10114/109*a^14 + 19041/109*a^13 - 178640/109*a^12 + 43162/109*a^11 + 1155815/109*a^10 - 1133843/109*a^9 - 3287391/109*a^8 + 4701383/109*a^7 + 3725665/109*a^6 - 7280339/109*a^5 - 887819/109*a^4 + 3667367/109*a^3 + 287364/109*a^2 - 692847/109*a - 147741/109)*q^29 + (-2921/763*a^15 + 14172/763*a^14 + 34210/763*a^13 - 252753/763*a^12 - 18563/763*a^11 + 1663484/763*a^10 - 1184534/763*a^9 - 4897924/763*a^8 + 792208/109*a^7 + 6081580/763*a^6 - 8956548/763*a^5 - 2289885/763*a^4 + 656404/109*a^3 + 698260/763*a^2 - 834069/763*a - 197613/763)*q^30 + (-647/109*a^15 + 3449/109*a^14 + 6743/109*a^13 - 61391/109*a^12 + 11053/109*a^11 + 402563/109*a^10 - 365690/109*a^9 - 1176425/109*a^8 + 1554123/109*a^7 + 1433995/109*a^6 - 2456291/109*a^5 - 506978/109*a^4 + 1288760/109*a^3 + 171449/109*a^2 - 246702/109*a - 58720/109)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2112/763*a^15 - 11798/763*a^14 - 19739/763*a^13 + 207847/763*a^12 - 76852/763*a^11 - 1338648/763*a^10 + 1465036/763*a^9 + 3771408/763*a^8 - 841428/109*a^7 - 4161408/763*a^6 + 9088654/763*a^5 + 822574/763*a^4 - 669338/109*a^3 - 303643/763*a^2 + 920845/763*a + 199854/763)*q^33 + (1707/763*a^15 - 8545/763*a^14 - 19603/763*a^13 + 152976/763*a^12 + 3707/763*a^11 - 1013199/763*a^10 + 742248/763*a^9 + 3019984/763*a^8 - 486926/109*a^7 - 3865326/763*a^6 + 5510446/763*a^5 + 1639367/763*a^4 - 412258/109*a^3 - 535537/763*a^2 + 534612/763*a + 135837/763)*q^34 + (9169/763*a^15 - 48375/763*a^14 - 96197/763*a^13 + 858891/763*a^12 - 143300/763*a^11 - 5607628/763*a^10 + 5071608/763*a^9 + 16244993/763*a^8 - 3080273/109*a^7 - 19351503/763*a^6 + 33813791/763*a^5 + 6129860/763*a^4 - 2469550/109*a^3 - 1988751/763*a^2 + 3232657/763*a + 732195/763)*q^35 + (333/109*a^15 - 1466/109*a^14 - 4295/109*a^13 + 26264/109*a^12 + 9147/109*a^11 - 174331/109*a^10 + 88777/109*a^9 + 522603/109*a^8 - 495591/109*a^7 - 680121/109*a^6 + 850641/109*a^5 + 307426/109*a^4 - 464933/109*a^3 - 103479/109*a^2 + 93165/109*a + 25408/109)*q^36 + (13014/763*a^15 - 68567/763*a^14 - 136420/763*a^13 + 1216931/763*a^12 - 206238/763*a^11 - 7940319/763*a^10 + 7225376/763*a^9 + 22976028/763*a^8 - 4390072/109*a^7 - 27292612/763*a^6 + 48299044/763*a^5 + 8542042/763*a^4 - 3555707/109*a^3 - 2811128/763*a^2 + 4741176/763*a + 1077998/763)*q^37 + O(q^38)
*]> ;  // time = 3.97 seconds




J[273] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 273, 273, 273, 273, 273, 91, 91, 91, 91, 39, 39, 21 ], new_dimensions := [ 1, 1, 2, 3, 4, 1, 1, 2, 3, 1, 2, 1 ], dimensions := [ 1, 1, 2, 3, 4, 2, 2, 4, 6, 2, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 7, 3, 1, 1, 0, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ -2, -1, -1, 1, -2, 1, -4, 3, -9, -1, -5, -8 ],
[ 2, 1, 1, -1, -2, -1, 0, 1, 3, -5, 9, 0 ],
[ 2, -2, 0, 2, 4, -2, 4, 0, 8, 4, -8, -4 ],
[ -2, -3, -3, -3, -2, -3, -8, -7, -9, -1, -7, 12 ],
[ 1, 4, -3, 4, -2, 4, -2, 7, 3, 1, 3, 10 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2*x - 1,
x^3 + 2*x^2 - 3*x - 2,
x^4 - x^3 - 7*x^2 + 5*x + 6
], atkin_lehners := [
[ 1, -1, -1 ],
[ -1, 1, 1 ],
[ 1, -1, 1 ],
[ 1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 3, 1 ],
[ 1, 7, 3 ],
[ 7, 1, 1 ],
[ 1, 1, 1 ],
[ 9, 1, 1 ]
], tamagawa_numbers := [
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 9, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 1, 0, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 0, 1/9 ], eigenvalues := [*
[ -2, -1, -1, 1, -2, 1, -4, 3, -9, -1, -5, -8 ],
[ 2, 1, 1, -1, -2, -1, 0, 1, 3, -5, 9, 0 ],
[
a,
-1,
0,
1,
2,
-1,
-2*a + 4,
-4*a + 4,
-2*a + 6,
-4*a + 6,
4*a - 8,
-4*a + 2
],
[
a,
-1,
-a^2 - 2*a + 1,
-1,
2*a^2 + 2*a - 6,
-1,
-2*a - 4,
a^2 + 4*a - 3,
a^2 + 2*a - 5,
a^2 + 4*a - 1,
-3*a^2 - 4*a + 5,
-2*a^2 - 4*a + 8
],
[
a,
1,
-a^2 + 3,
1,
-a^3 + 5*a,
1,
-2*a,
a^3 - a^2 - 5*a + 5,
a^3 + a^2 - 7*a - 3,
-a^3 + a^2 + 5*a - 3,
a^3 - a^2 - 9*a + 5,
-2*a^3 + 2*a^2 + 10*a - 4
]
*], q_expansions := [*
q - 2*q^2 - q^3 + 2*q^4 - q^5 + 2*q^6 + q^7 + q^9 + 2*q^10 - 2*q^11 - 2*q^12 + q^13 - 2*q^14 + q^15 - 4*q^16 - 4*q^17 - 2*q^18 + 3*q^19 - 2*q^20 - q^21 + 4*q^22 - 9*q^23 - 4*q^25 - 2*q^26 - q^27 + 2*q^28 - q^29 - 2*q^30 - 5*q^31 + 8*q^32 + 2*q^33 + 8*q^34 - q^35 + 2*q^36 - 8*q^37 + O(q^38),
q + 2*q^2 + q^3 + 2*q^4 + q^5 + 2*q^6 - q^7 + q^9 + 2*q^10 - 2*q^11 + 2*q^12 - q^13 - 2*q^14 + q^15 - 4*q^16 + 2*q^18 + q^19 + 2*q^20 - q^21 - 4*q^22 + 3*q^23 - 4*q^25 - 2*q^26 + q^27 - 2*q^28 - 5*q^29 + 2*q^30 + 9*q^31 - 8*q^32 - 2*q^33 - q^35 + 2*q^36 + O(q^38),
q + a*q^2 - q^3 + (2*a - 1)*q^4 - a*q^6 + q^7 + (a + 2)*q^8 + q^9 + 2*q^11 + (-2*a + 1)*q^12 - q^13 + a*q^14 + 3*q^16 + (-2*a + 4)*q^17 + a*q^18 + (-4*a + 4)*q^19 - q^21 + 2*a*q^22 + (-2*a + 6)*q^23 + (-a - 2)*q^24 - 5*q^25 - a*q^26 - q^27 + (2*a - 1)*q^28 + (-4*a + 6)*q^29 + (4*a - 8)*q^31 + (a - 4)*q^32 - 2*q^33 - 2*q^34 + (2*a - 1)*q^36 + (-4*a + 2)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 - 2*a + 1)*q^5 - a*q^6 - q^7 + (-2*a^2 - a + 2)*q^8 + q^9 + (-2*a - 2)*q^10 + (2*a^2 + 2*a - 6)*q^11 + (-a^2 + 2)*q^12 - q^13 - a*q^14 + (a^2 + 2*a - 1)*q^15 + (a^2 - 4*a)*q^16 + (-2*a - 4)*q^17 + a*q^18 + (a^2 + 4*a - 3)*q^19 + (2*a - 2)*q^20 + q^21 + (-2*a^2 + 4)*q^22 + (a^2 + 2*a - 5)*q^23 + (2*a^2 + a - 2)*q^24 + (a^2 + 4*a)*q^25 - a*q^26 - q^27 + (-a^2 + 2)*q^28 + (a^2 + 4*a - 1)*q^29 + (2*a + 2)*q^30 + (-3*a^2 - 4*a + 5)*q^31 + (-2*a^2 + 5*a - 2)*q^32 + (-2*a^2 - 2*a + 6)*q^33 + (-2*a^2 - 4*a)*q^34 + (a^2 + 2*a - 1)*q^35 + (a^2 - 2)*q^36 + (-2*a^2 - 4*a + 8)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^2 + 3)*q^5 + a*q^6 + q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^3 + 3*a)*q^10 + (-a^3 + 5*a)*q^11 + (a^2 - 2)*q^12 + q^13 + a*q^14 + (-a^2 + 3)*q^15 + (a^3 + a^2 - 5*a - 2)*q^16 - 2*a*q^17 + a*q^18 + (a^3 - a^2 - 5*a + 5)*q^19 + (-a^3 - 2*a^2 + 5*a)*q^20 + q^21 + (-a^3 - 2*a^2 + 5*a + 6)*q^22 + (a^3 + a^2 - 7*a - 3)*q^23 + (a^3 - 4*a)*q^24 + (a^3 + a^2 - 5*a - 2)*q^25 + a*q^26 + q^27 + (a^2 - 2)*q^28 + (-a^3 + a^2 + 5*a - 3)*q^29 + (-a^3 + 3*a)*q^30 + (a^3 - a^2 - 9*a + 5)*q^31 + (2*a^2 + a - 6)*q^32 + (-a^3 + 5*a)*q^33 - 2*a^2*q^34 + (-a^2 + 3)*q^35 + (a^2 - 2)*q^36 + (-2*a^3 + 2*a^2 + 10*a - 4)*q^37 + O(q^38)
*]> ;  // time = 74.71 seconds




J[274] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 274, 274, 274, 274, 274, 137, 137 ], new_dimensions := [ 1, 1, 1, 3, 5, 4, 7 ], dimensions := [ 1, 1, 1, 3, 5, 8, 14 ], intersection_graph := [ 0, 3, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 11, 1, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 0, 1, 1, 109, 1, 1, 1, 1, 0, 149, 1, 1, 11, 1, 1, 149, 0, 1, 1, 1, 7, 109, 1, 1, 0 ], ap_traces := [
[ -1, 0, 0, -4, -4, 4, 2, -4, -6, -8, 10, -2 ],
[ -1, 0, -3, 2, -1, -2, -7, -1, 0, 1, -11, 4 ],
[ 1, -2, -3, 0, -3, -6, 1, -3, 0, -3, 7, 10 ],
[ -3, 2, 5, 2, 5, -8, 3, -3, 10, 11, 13, -12 ],
[ 5, 2, 5, -4, -1, 4, 7, -1, -8, -5, -11, 2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^3 - 2*x^2 - 4*x + 4,
x^5 - 2*x^4 - 10*x^3 + 20*x^2 - 8
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 11, 1 ],
[ 7, 1 ],
[ 109, 1 ],
[ 3427, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 3427, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 23 ], torsion_lower_bounds := [ 1, 1, 1, 1, 23 ], l_ratios := [ 0, 0, 0, 1, 149/23 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ -1, 0, 0, -4, -4, 4, 2, -4, -6, -8, 10, -2 ],
[ -1, 0, -3, 2, -1, -2, -7, -1, 0, 1, -11, 4 ],
[ 1, -2, -3, 0, -3, -6, 1, -3, 0, -3, 7, 10 ],
[
-1,
a,
-1/2*a^2 + a + 3,
-a^2 + a + 4,
a^2 - 2*a - 1,
a^2 - a - 6,
-2*a^2 + 9,
a^2 - 3*a - 3,
-a + 4,
5/2*a^2 - 2*a - 5,
1/2*a^2 - a + 3,
a^2 - 3*a - 6
],
[
1,
a,
1/2*a^4 - 1/2*a^3 - 11/2*a^2 + 4*a + 5,
-1/2*a^4 + 1/2*a^3 + 5*a^2 - 5*a - 2,
-3/4*a^4 + 1/2*a^3 + 8*a^2 - 5*a - 5,
1/2*a^3 - 5*a + 2,
-1/4*a^4 + 1/2*a^3 + 3*a^2 - 5*a - 1,
1/4*a^4 - a^3 - 2*a^2 + 8*a - 3,
-1/2*a^4 + a^3 + 5*a^2 - 9*a - 2,
a^4 - a^3 - 23/2*a^2 + 9*a + 9,
1/2*a^4 - a^3 - 11/2*a^2 + 8*a + 1,
a^4 - 1/2*a^3 - 11*a^2 + 7*a + 8
]
*], q_expansions := [*
q - q^2 + q^4 - 4*q^7 - q^8 - 3*q^9 - 4*q^11 + 4*q^13 + 4*q^14 + q^16 + 2*q^17 + 3*q^18 - 4*q^19 + 4*q^22 - 6*q^23 - 5*q^25 - 4*q^26 - 4*q^28 - 8*q^29 + 10*q^31 - q^32 - 2*q^34 - 3*q^36 - 2*q^37 + O(q^38),
q - q^2 + q^4 - 3*q^5 + 2*q^7 - q^8 - 3*q^9 + 3*q^10 - q^11 - 2*q^13 - 2*q^14 + q^16 - 7*q^17 + 3*q^18 - q^19 - 3*q^20 + q^22 + 4*q^25 + 2*q^26 + 2*q^28 + q^29 - 11*q^31 - q^32 + 7*q^34 - 6*q^35 - 3*q^36 + 4*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 3*q^5 - 2*q^6 + q^8 + q^9 - 3*q^10 - 3*q^11 - 2*q^12 - 6*q^13 + 6*q^15 + q^16 + q^17 + q^18 - 3*q^19 - 3*q^20 - 3*q^22 - 2*q^24 + 4*q^25 - 6*q^26 + 4*q^27 - 3*q^29 + 6*q^30 + 7*q^31 + q^32 + 6*q^33 + q^34 + q^36 + 10*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-1/2*a^2 + a + 3)*q^5 - a*q^6 + (-a^2 + a + 4)*q^7 - q^8 + (a^2 - 3)*q^9 + (1/2*a^2 - a - 3)*q^10 + (a^2 - 2*a - 1)*q^11 + a*q^12 + (a^2 - a - 6)*q^13 + (a^2 - a - 4)*q^14 + (a + 2)*q^15 + q^16 + (-2*a^2 + 9)*q^17 + (-a^2 + 3)*q^18 + (a^2 - 3*a - 3)*q^19 + (-1/2*a^2 + a + 3)*q^20 + (-a^2 + 4)*q^21 + (-a^2 + 2*a + 1)*q^22 + (-a + 4)*q^23 - a*q^24 + (-2*a^2 + 3*a + 6)*q^25 + (-a^2 + a + 6)*q^26 + (2*a^2 - 2*a - 4)*q^27 + (-a^2 + a + 4)*q^28 + (5/2*a^2 - 2*a - 5)*q^29 + (-a - 2)*q^30 + (1/2*a^2 - a + 3)*q^31 - q^32 + (3*a - 4)*q^33 + (2*a^2 - 9)*q^34 + (-3*a^2 + 3*a + 14)*q^35 + (a^2 - 3)*q^36 + (a^2 - 3*a - 6)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (1/2*a^4 - 1/2*a^3 - 11/2*a^2 + 4*a + 5)*q^5 + a*q^6 + (-1/2*a^4 + 1/2*a^3 + 5*a^2 - 5*a - 2)*q^7 + q^8 + (a^2 - 3)*q^9 + (1/2*a^4 - 1/2*a^3 - 11/2*a^2 + 4*a + 5)*q^10 + (-3/4*a^4 + 1/2*a^3 + 8*a^2 - 5*a - 5)*q^11 + a*q^12 + (1/2*a^3 - 5*a + 2)*q^13 + (-1/2*a^4 + 1/2*a^3 + 5*a^2 - 5*a - 2)*q^14 + (1/2*a^4 - 1/2*a^3 - 6*a^2 + 5*a + 4)*q^15 + q^16 + (-1/4*a^4 + 1/2*a^3 + 3*a^2 - 5*a - 1)*q^17 + (a^2 - 3)*q^18 + (1/4*a^4 - a^3 - 2*a^2 + 8*a - 3)*q^19 + (1/2*a^4 - 1/2*a^3 - 11/2*a^2 + 4*a + 5)*q^20 + (-1/2*a^4 + 5*a^2 - 2*a - 4)*q^21 + (-3/4*a^4 + 1/2*a^3 + 8*a^2 - 5*a - 5)*q^22 + (-1/2*a^4 + a^3 + 5*a^2 - 9*a - 2)*q^23 + a*q^24 + (7/4*a^4 - 2*a^3 - 19*a^2 + 18*a + 12)*q^25 + (1/2*a^3 - 5*a + 2)*q^26 + (a^3 - 6*a)*q^27 + (-1/2*a^4 + 1/2*a^3 + 5*a^2 - 5*a - 2)*q^28 + (a^4 - a^3 - 23/2*a^2 + 9*a + 9)*q^29 + (1/2*a^4 - 1/2*a^3 - 6*a^2 + 5*a + 4)*q^30 + (1/2*a^4 - a^3 - 11/2*a^2 + 8*a + 1)*q^31 + q^32 + (-a^4 + 1/2*a^3 + 10*a^2 - 5*a - 6)*q^33 + (-1/4*a^4 + 1/2*a^3 + 3*a^2 - 5*a - 1)*q^34 + (-a^4 + 3/2*a^3 + 11*a^2 - 13*a - 8)*q^35 + (a^2 - 3)*q^36 + (a^4 - 1/2*a^3 - 11*a^2 + 7*a + 8)*q^37 + O(q^38)
*]> ;  // time = 62.839 seconds




J[277] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 277, 277, 277, 277 ], new_dimensions := [ 1, 3, 9, 9 ], dimensions := [ 1, 3, 9, 9 ], intersection_graph := [ 0, 1, 5, 1, 1, 0, 1, 137, 5, 1, 0, 1, 1, 137, 1, 0 ], ap_traces := [
[ 1, -2, 2, -4, 1, -5, 2, -6, 0, 5, -3, -4 ],
[ -1, 6, 4, 4, 11, 1, -4, -10, -8, 3, -11, 12 ],
[ -6, -10, -12, -2, -14, -2, -19, 1, -30, -8, 0, 1 ],
[ 4, 6, 4, -2, 2, -2, 15, 13, 26, -4, 12, -25 ]
], hecke_fields := [
x - 1,
x^3 + x^2 - 3*x - 1,
x^9 + 6*x^8 + 4*x^7 - 37*x^6 - 69*x^5 + 24*x^4 + 119*x^3 + 34*x^2 - 52*x - 25,
x^9 - 4*x^8 - 6*x^7 + 37*x^6 - 3*x^5 - 100*x^4 + 49*x^3 + 64*x^2 - 20*x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 23 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 23 ]
], torsion_upper_bounds := [ 1, 1, 1, 23 ], torsion_lower_bounds := [ 1, 1, 1, 23 ], l_ratios := [ 0, 1, 0, 1/23 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1 ], eigenvalues := [*
[ 1, -2, 2, -4, 1, -5, 2, -6, 0, 5, -3, -4 ],
[
a,
2,
a^2 - 1,
-a^2 - 2*a + 3,
a + 4,
2*a + 1,
-3*a^2 - 2*a + 5,
-a^2 - 1,
-a^2 - 2*a - 1,
a^2 - 2*a - 2,
3*a^2 + 5*a - 9,
4
],
[
a,
-6*a^8 - 26*a^7 + 19*a^6 + 189*a^5 + 101*a^4 - 302*a^3 - 213*a^2 + 131*a + 95,
8*a^8 + 34*a^7 - 27*a^6 - 247*a^5 - 122*a^4 + 394*a^3 + 260*a^2 - 171*a - 117,
-6*a^8 - 24*a^7 + 25*a^6 + 175*a^5 + 55*a^4 - 281*a^3 - 129*a^2 + 118*a + 58,
5*a^8 + 20*a^7 - 22*a^6 - 149*a^5 - 40*a^4 + 253*a^3 + 111*a^2 - 113*a - 59,
8*a^8 + 34*a^7 - 26*a^6 - 244*a^5 - 127*a^4 + 375*a^3 + 258*a^2 - 152*a - 111,
-7*a^8 - 28*a^7 + 30*a^6 + 208*a^5 + 63*a^4 - 352*a^3 - 170*a^2 + 160*a + 83,
2*a^8 + 7*a^7 - 12*a^6 - 52*a^5 + 10*a^4 + 86*a^3 - 9*a^2 - 32*a + 4,
-7*a^8 - 31*a^7 + 19*a^6 + 222*a^5 + 139*a^4 - 340*a^3 - 273*a^2 + 142*a + 114,
6*a^8 + 25*a^7 - 23*a^6 - 184*a^5 - 70*a^4 + 305*a^3 + 156*a^2 - 139*a - 71,
-10*a^8 - 42*a^7 + 36*a^6 + 304*a^5 + 131*a^4 - 477*a^3 - 269*a^2 + 196*a + 113,
9*a^8 + 38*a^7 - 33*a^6 - 280*a^5 - 119*a^4 + 463*a^3 + 267*a^2 - 205*a - 119
],
[
a,
2*a^8 - 4*a^7 - 19*a^6 + 33*a^5 + 55*a^4 - 74*a^3 - 43*a^2 + 27*a + 1,
-2*a^8 + 4*a^7 + 19*a^6 - 33*a^5 - 54*a^4 + 72*a^3 + 38*a^2 - 19*a + 3,
-2*a^8 + 4*a^7 + 19*a^6 - 33*a^5 - 55*a^4 + 73*a^3 + 43*a^2 - 22*a,
-a^8 + 2*a^7 + 10*a^6 - 19*a^5 - 28*a^4 + 51*a^3 + 15*a^2 - 29*a + 1,
-2*a^8 + 4*a^7 + 20*a^6 - 36*a^5 - 59*a^4 + 89*a^3 + 42*a^2 - 38*a + 1,
a^8 - 2*a^7 - 10*a^6 + 18*a^5 + 29*a^4 - 44*a^3 - 18*a^2 + 16*a - 1,
2*a^8 - 3*a^7 - 22*a^6 + 26*a^5 + 76*a^4 - 58*a^3 - 79*a^2 + 10*a + 6,
a^8 - a^7 - 11*a^6 + 8*a^5 + 37*a^4 - 16*a^3 - 35*a^2 + 4,
2*a^8 - 3*a^7 - 21*a^6 + 26*a^5 + 64*a^4 - 57*a^3 - 44*a^2 + 7*a - 5,
2*a^5 - 3*a^4 - 11*a^3 + 11*a^2 + 10*a + 3,
3*a^8 - 6*a^7 - 29*a^6 + 52*a^5 + 83*a^4 - 123*a^3 - 57*a^2 + 45*a - 7
]
*], q_expansions := [*
q + q^2 - 2*q^3 - q^4 + 2*q^5 - 2*q^6 - 4*q^7 - 3*q^8 + q^9 + 2*q^10 + q^11 + 2*q^12 - 5*q^13 - 4*q^14 - 4*q^15 - q^16 + 2*q^17 + q^18 - 6*q^19 - 2*q^20 + 8*q^21 + q^22 + 6*q^24 - q^25 - 5*q^26 + 4*q^27 + 4*q^28 + 5*q^29 - 4*q^30 - 3*q^31 + 5*q^32 - 2*q^33 + 2*q^34 - 8*q^35 - q^36 - 4*q^37 + O(q^38),
q + a*q^2 + 2*q^3 + (a^2 - 2)*q^4 + (a^2 - 1)*q^5 + 2*a*q^6 + (-a^2 - 2*a + 3)*q^7 + (-a^2 - a + 1)*q^8 + q^9 + (-a^2 + 2*a + 1)*q^10 + (a + 4)*q^11 + (2*a^2 - 4)*q^12 + (2*a + 1)*q^13 + (-a^2 - 1)*q^14 + (2*a^2 - 2)*q^15 + (-2*a^2 - 2*a + 3)*q^16 + (-3*a^2 - 2*a + 5)*q^17 + a*q^18 + (-a^2 - 1)*q^19 + (a^2 - 2*a + 1)*q^20 + (-2*a^2 - 4*a + 6)*q^21 + (a^2 + 4*a)*q^22 + (-a^2 - 2*a - 1)*q^23 + (-2*a^2 - 2*a + 2)*q^24 + (2*a^2 - 2*a - 5)*q^25 + (2*a^2 + a)*q^26 - 4*q^27 + (3*a^2 - 7)*q^28 + (a^2 - 2*a - 2)*q^29 + (-2*a^2 + 4*a + 2)*q^30 + (3*a^2 + 5*a - 9)*q^31 + (2*a^2 - a - 4)*q^32 + (2*a + 8)*q^33 + (a^2 - 4*a - 3)*q^34 + (2*a^2 - 2*a - 4)*q^35 + (a^2 - 2)*q^36 + 4*q^37 + O(q^38),
q + a*q^2 + (-6*a^8 - 26*a^7 + 19*a^6 + 189*a^5 + 101*a^4 - 302*a^3 - 213*a^2 + 131*a + 95)*q^3 + (a^2 - 2)*q^4 + (8*a^8 + 34*a^7 - 27*a^6 - 247*a^5 - 122*a^4 + 394*a^3 + 260*a^2 - 171*a - 117)*q^5 + (10*a^8 + 43*a^7 - 33*a^6 - 313*a^5 - 158*a^4 + 501*a^3 + 335*a^2 - 217*a - 150)*q^6 + (-6*a^8 - 24*a^7 + 25*a^6 + 175*a^5 + 55*a^4 - 281*a^3 - 129*a^2 + 118*a + 58)*q^7 + (a^3 - 4*a)*q^8 + (10*a^8 + 43*a^7 - 33*a^6 - 313*a^5 - 158*a^4 + 502*a^3 + 337*a^2 - 219*a - 153)*q^9 + (-14*a^8 - 59*a^7 + 49*a^6 + 430*a^5 + 202*a^4 - 692*a^3 - 443*a^2 + 299*a + 200)*q^10 + (5*a^8 + 20*a^7 - 22*a^6 - 149*a^5 - 40*a^4 + 253*a^3 + 111*a^2 - 113*a - 59)*q^11 + (-5*a^8 - 21*a^7 + 19*a^6 + 154*a^5 + 59*a^4 - 251*a^3 - 131*a^2 + 108*a + 60)*q^12 + (8*a^8 + 34*a^7 - 26*a^6 - 244*a^5 - 127*a^4 + 375*a^3 + 258*a^2 - 152*a - 111)*q^13 + (12*a^8 + 49*a^7 - 47*a^6 - 359*a^5 - 137*a^4 + 585*a^3 + 322*a^2 - 254*a - 150)*q^14 + (-6*a^8 - 25*a^7 + 21*a^6 + 181*a^5 + 87*a^4 - 286*a^3 - 190*a^2 + 124*a + 85)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-7*a^8 - 28*a^7 + 30*a^6 + 208*a^5 + 63*a^4 - 352*a^3 - 170*a^2 + 160*a + 83)*q^17 + (-17*a^8 - 73*a^7 + 57*a^6 + 532*a^5 + 262*a^4 - 853*a^3 - 559*a^2 + 367*a + 250)*q^18 + (2*a^8 + 7*a^7 - 12*a^6 - 52*a^5 + 10*a^4 + 86*a^3 - 9*a^2 - 32*a + 4)*q^19 + (9*a^8 + 37*a^7 - 34*a^6 - 270*a^5 - 112*a^4 + 435*a^3 + 255*a^2 - 186*a - 116)*q^20 + (11*a^8 + 45*a^7 - 42*a^6 - 327*a^5 - 132*a^4 + 521*a^3 + 301*a^2 - 219*a - 140)*q^21 + (-10*a^8 - 42*a^7 + 36*a^6 + 305*a^5 + 133*a^4 - 484*a^3 - 283*a^2 + 201*a + 125)*q^22 + (-7*a^8 - 31*a^7 + 19*a^6 + 222*a^5 + 139*a^4 - 340*a^3 - 273*a^2 + 142*a + 114)*q^23 + (-11*a^8 - 47*a^7 + 35*a^6 + 340*a^5 + 185*a^4 - 538*a^3 - 392*a^2 + 234*a + 175)*q^24 + (-5*a^8 - 21*a^7 + 17*a^6 + 151*a^5 + 73*a^4 - 234*a^3 - 145*a^2 + 99*a + 59)*q^25 + (-14*a^8 - 58*a^7 + 52*a^6 + 425*a^5 + 183*a^4 - 694*a^3 - 424*a^2 + 305*a + 200)*q^26 + (-6*a^8 - 24*a^7 + 26*a^6 + 176*a^5 + 47*a^4 - 287*a^3 - 117*a^2 + 124*a + 55)*q^27 + (-11*a^8 - 47*a^7 + 35*a^6 + 341*a^5 + 187*a^4 - 544*a^3 - 404*a^2 + 238*a + 184)*q^28 + (6*a^8 + 25*a^7 - 23*a^6 - 184*a^5 - 70*a^4 + 305*a^3 + 156*a^2 - 139*a - 71)*q^29 + (11*a^8 + 45*a^7 - 41*a^6 - 327*a^5 - 142*a^4 + 524*a^3 + 328*a^2 - 227*a - 150)*q^30 + (-10*a^8 - 42*a^7 + 36*a^6 + 304*a^5 + 131*a^4 - 477*a^3 - 269*a^2 + 196*a + 113)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (3*a^8 + 15*a^7 - 2*a^6 - 106*a^5 - 106*a^4 + 159*a^3 + 197*a^2 - 72*a - 80)*q^33 + (14*a^8 + 58*a^7 - 51*a^6 - 420*a^5 - 184*a^4 + 663*a^3 + 398*a^2 - 281*a - 175)*q^34 + (-3*a^8 - 12*a^7 + 14*a^6 + 91*a^5 + 20*a^4 - 160*a^3 - 69*a^2 + 72*a + 39)*q^35 + (9*a^8 + 39*a^7 - 31*a^6 - 285*a^5 - 129*a^4 + 460*a^3 + 271*a^2 - 196*a - 119)*q^36 + (9*a^8 + 38*a^7 - 33*a^6 - 280*a^5 - 119*a^4 + 463*a^3 + 267*a^2 - 205*a - 119)*q^37 + O(q^38),
q + a*q^2 + (2*a^8 - 4*a^7 - 19*a^6 + 33*a^5 + 55*a^4 - 74*a^3 - 43*a^2 + 27*a + 1)*q^3 + (a^2 - 2)*q^4 + (-2*a^8 + 4*a^7 + 19*a^6 - 33*a^5 - 54*a^4 + 72*a^3 + 38*a^2 - 19*a + 3)*q^5 + (4*a^8 - 7*a^7 - 41*a^6 + 61*a^5 + 126*a^4 - 141*a^3 - 101*a^2 + 41*a + 2)*q^6 + (-2*a^8 + 4*a^7 + 19*a^6 - 33*a^5 - 55*a^4 + 73*a^3 + 43*a^2 - 22*a)*q^7 + (a^3 - 4*a)*q^8 + (2*a^8 - 5*a^7 - 17*a^6 + 41*a^5 + 42*a^4 - 94*a^3 - 23*a^2 + 43*a - 1)*q^9 + (-4*a^8 + 7*a^7 + 41*a^6 - 60*a^5 - 128*a^4 + 136*a^3 + 109*a^2 - 37*a - 2)*q^10 + (-a^8 + 2*a^7 + 10*a^6 - 19*a^5 - 28*a^4 + 51*a^3 + 15*a^2 - 29*a + 1)*q^11 + (5*a^8 - 9*a^7 - 49*a^6 + 72*a^5 + 149*a^4 - 149*a^3 - 129*a^2 + 28*a + 2)*q^12 + (-2*a^8 + 4*a^7 + 20*a^6 - 36*a^5 - 59*a^4 + 89*a^3 + 42*a^2 - 38*a + 1)*q^13 + (-4*a^8 + 7*a^7 + 41*a^6 - 61*a^5 - 127*a^4 + 141*a^3 + 106*a^2 - 40*a - 2)*q^14 + (-2*a^8 + 3*a^7 + 21*a^6 - 23*a^5 - 71*a^4 + 42*a^3 + 74*a^2 + 4*a - 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^8 - 2*a^7 - 10*a^6 + 18*a^5 + 29*a^4 - 44*a^3 - 18*a^2 + 16*a - 1)*q^17 + (3*a^8 - 5*a^7 - 33*a^6 + 48*a^5 + 106*a^4 - 121*a^3 - 85*a^2 + 39*a + 2)*q^18 + (2*a^8 - 3*a^7 - 22*a^6 + 26*a^5 + 76*a^4 - 58*a^3 - 79*a^2 + 10*a + 6)*q^19 + (-5*a^8 + 9*a^7 + 50*a^6 - 74*a^5 - 156*a^4 + 161*a^3 + 143*a^2 - 44*a - 10)*q^20 + (a^8 - a^7 - 12*a^6 + 11*a^5 + 40*a^4 - 29*a^3 - 31*a^2 + 5*a)*q^21 + (-2*a^8 + 4*a^7 + 18*a^6 - 31*a^5 - 49*a^4 + 64*a^3 + 35*a^2 - 19*a - 1)*q^22 + (a^8 - a^7 - 11*a^6 + 8*a^5 + 37*a^4 - 16*a^3 - 35*a^2 + 4)*q^23 + (3*a^8 - 5*a^7 - 31*a^6 + 42*a^5 + 99*a^4 - 92*a^3 - 90*a^2 + 20*a + 1)*q^24 + (3*a^8 - 5*a^7 - 31*a^6 + 41*a^5 + 101*a^4 - 86*a^3 - 101*a^2 + 13*a + 11)*q^25 + (-4*a^8 + 8*a^7 + 38*a^6 - 65*a^5 - 111*a^4 + 140*a^3 + 90*a^2 - 39*a - 2)*q^26 + (-2*a^7 + 4*a^6 + 16*a^5 - 25*a^4 - 41*a^3 + 35*a^2 + 34*a + 3)*q^27 + (-5*a^8 + 9*a^7 + 49*a^6 - 73*a^5 - 149*a^4 + 156*a^3 + 130*a^2 - 38*a - 4)*q^28 + (2*a^8 - 3*a^7 - 21*a^6 + 26*a^5 + 64*a^4 - 57*a^3 - 44*a^2 + 7*a - 5)*q^29 + (-5*a^8 + 9*a^7 + 51*a^6 - 77*a^5 - 158*a^4 + 172*a^3 + 132*a^2 - 41*a - 2)*q^30 + (2*a^5 - 3*a^4 - 11*a^3 + 11*a^2 + 10*a + 3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^8 - a^7 - 10*a^6 + 2*a^5 + 38*a^4 + 17*a^3 - 55*a^2 - 34*a - 2)*q^33 + (2*a^8 - 4*a^7 - 19*a^6 + 32*a^5 + 56*a^4 - 67*a^3 - 48*a^2 + 19*a + 1)*q^34 + (-a^8 + 2*a^7 + 10*a^6 - 19*a^5 - 28*a^4 + 50*a^3 + 15*a^2 - 24*a + 3)*q^35 + (3*a^8 - 5*a^7 - 29*a^6 + 33*a^5 + 95*a^4 - 44*a^3 - 107*a^2 - 24*a + 5)*q^36 + (3*a^8 - 6*a^7 - 29*a^6 + 52*a^5 + 83*a^4 - 123*a^3 - 57*a^2 + 45*a - 7)*q^37 + O(q^38)
*]> ;  // time = 3.71 seconds




J[278] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 278, 278, 278, 278, 278, 139, 139, 139 ], new_dimensions := [ 1, 1, 2, 3, 5, 1, 3, 7 ], dimensions := [ 1, 1, 2, 3, 5, 2, 6, 14 ], intersection_graph := [ 0, 1, 1, 17, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 1, 17, 1, 1, 0, 1, 1, 1, 271, 1, 1, 1, 1, 0, 1, 41, 1, 1, 1, 1, 1, 1, 0, 1, 9, 1, 1, 7, 1, 41, 1, 0, 1, 1, 1, 1, 271, 1, 9, 1, 0 ], ap_traces := [
[ -1, -2, 3, -1, -3, 5, 6, 2, 6, -3, 5, 2 ],
[ 1, -2, -1, -5, -3, 1, 2, -2, -6, 1, 9, -6 ],
[ -2, 0, -2, -6, 2, -10, 0, 0, 4, -6, -6, -8 ],
[ -3, 3, 0, 9, 0, 0, 0, 9, -6, 6, -3, 12 ],
[ 5, 1, -2, 7, 6, 2, 0, -1, -2, -20, 3, 8 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2,
x^3 - 3*x^2 + 3,
x^5 - x^4 - 10*x^3 + 11*x^2 + 12*x - 2
], atkin_lehners := [
[ 1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 3 ],
[ 1, 1 ],
[ 7, 1 ],
[ 271, 1 ],
[ 1435, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1435, 1 ]
], torsion_upper_bounds := [ 3, 1, 1, 1, 35 ], torsion_lower_bounds := [ 3, 1, 1, 1, 35 ], l_ratios := [ 1/3, 0, 0, 1, 41/35 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 1 ], eigenvalues := [*
[ -1, -2, 3, -1, -3, 5, 6, 2, 6, -3, 5, 2 ],
[ 1, -2, -1, -5, -3, 1, 2, -2, -6, 1, 9, -6 ],
[
-1,
a,
-a - 1,
-a - 3,
-2*a + 1,
-a - 5,
5*a,
a,
3*a + 2,
3*a - 3,
a - 3,
2*a - 4
],
[
-1,
a,
-2*a^2 + 4*a + 2,
-a^2 + a + 5,
2*a^2 - 4*a - 2,
4*a^2 - 6*a - 6,
-2*a + 2,
-a^2 + 6,
2*a^2 - 2*a - 6,
-4*a + 6,
5*a^2 - 6*a - 10,
-2*a^2 + 10
],
[
1,
a,
1/5*a^4 + 2/5*a^3 - 9/5*a^2 - 11/5*a + 9/5,
-2/5*a^4 - 4/5*a^3 + 13/5*a^2 + 17/5*a + 7/5,
a^3 + a^2 - 8*a - 1,
3/5*a^4 - 4/5*a^3 - 27/5*a^2 + 37/5*a + 17/5,
-7/5*a^4 + 1/5*a^3 + 58/5*a^2 - 33/5*a - 28/5,
3/5*a^4 + 1/5*a^3 - 27/5*a^2 + 7/5*a + 22/5,
3/5*a^4 + 1/5*a^3 - 22/5*a^2 - 3/5*a + 2/5,
a^4 - 9*a^2 + 5*a + 3,
-3/5*a^4 - 6/5*a^3 + 22/5*a^2 + 23/5*a - 7/5,
2/5*a^4 + 4/5*a^3 - 8/5*a^2 - 22/5*a - 12/5
]
*], q_expansions := [*
q - q^2 - 2*q^3 + q^4 + 3*q^5 + 2*q^6 - q^7 - q^8 + q^9 - 3*q^10 - 3*q^11 - 2*q^12 + 5*q^13 + q^14 - 6*q^15 + q^16 + 6*q^17 - q^18 + 2*q^19 + 3*q^20 + 2*q^21 + 3*q^22 + 6*q^23 + 2*q^24 + 4*q^25 - 5*q^26 + 4*q^27 - q^28 - 3*q^29 + 6*q^30 + 5*q^31 - q^32 + 6*q^33 - 6*q^34 - 3*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - q^5 - 2*q^6 - 5*q^7 + q^8 + q^9 - q^10 - 3*q^11 - 2*q^12 + q^13 - 5*q^14 + 2*q^15 + q^16 + 2*q^17 + q^18 - 2*q^19 - q^20 + 10*q^21 - 3*q^22 - 6*q^23 - 2*q^24 - 4*q^25 + q^26 + 4*q^27 - 5*q^28 + q^29 + 2*q^30 + 9*q^31 + q^32 + 6*q^33 + 2*q^34 + 5*q^35 + q^36 - 6*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a - 1)*q^5 - a*q^6 + (-a - 3)*q^7 - q^8 - q^9 + (a + 1)*q^10 + (-2*a + 1)*q^11 + a*q^12 + (-a - 5)*q^13 + (a + 3)*q^14 + (-a - 2)*q^15 + q^16 + 5*a*q^17 + q^18 + a*q^19 + (-a - 1)*q^20 + (-3*a - 2)*q^21 + (2*a - 1)*q^22 + (3*a + 2)*q^23 - a*q^24 + (2*a - 2)*q^25 + (a + 5)*q^26 - 4*a*q^27 + (-a - 3)*q^28 + (3*a - 3)*q^29 + (a + 2)*q^30 + (a - 3)*q^31 - q^32 + (a - 4)*q^33 - 5*a*q^34 + (4*a + 5)*q^35 - q^36 + (2*a - 4)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-2*a^2 + 4*a + 2)*q^5 - a*q^6 + (-a^2 + a + 5)*q^7 - q^8 + (a^2 - 3)*q^9 + (2*a^2 - 4*a - 2)*q^10 + (2*a^2 - 4*a - 2)*q^11 + a*q^12 + (4*a^2 - 6*a - 6)*q^13 + (a^2 - a - 5)*q^14 + (-2*a^2 + 2*a + 6)*q^15 + q^16 + (-2*a + 2)*q^17 + (-a^2 + 3)*q^18 + (-a^2 + 6)*q^19 + (-2*a^2 + 4*a + 2)*q^20 + (-2*a^2 + 5*a + 3)*q^21 + (-2*a^2 + 4*a + 2)*q^22 + (2*a^2 - 2*a - 6)*q^23 - a*q^24 + (-4*a^2 + 4*a + 11)*q^25 + (-4*a^2 + 6*a + 6)*q^26 + (3*a^2 - 6*a - 3)*q^27 + (-a^2 + a + 5)*q^28 + (-4*a + 6)*q^29 + (2*a^2 - 2*a - 6)*q^30 + (5*a^2 - 6*a - 10)*q^31 - q^32 + (2*a^2 - 2*a - 6)*q^33 + (2*a - 2)*q^34 + (-8*a^2 + 16*a + 10)*q^35 + (a^2 - 3)*q^36 + (-2*a^2 + 10)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (1/5*a^4 + 2/5*a^3 - 9/5*a^2 - 11/5*a + 9/5)*q^5 + a*q^6 + (-2/5*a^4 - 4/5*a^3 + 13/5*a^2 + 17/5*a + 7/5)*q^7 + q^8 + (a^2 - 3)*q^9 + (1/5*a^4 + 2/5*a^3 - 9/5*a^2 - 11/5*a + 9/5)*q^10 + (a^3 + a^2 - 8*a - 1)*q^11 + a*q^12 + (3/5*a^4 - 4/5*a^3 - 27/5*a^2 + 37/5*a + 17/5)*q^13 + (-2/5*a^4 - 4/5*a^3 + 13/5*a^2 + 17/5*a + 7/5)*q^14 + (3/5*a^4 + 1/5*a^3 - 22/5*a^2 - 3/5*a + 2/5)*q^15 + q^16 + (-7/5*a^4 + 1/5*a^3 + 58/5*a^2 - 33/5*a - 28/5)*q^17 + (a^2 - 3)*q^18 + (3/5*a^4 + 1/5*a^3 - 27/5*a^2 + 7/5*a + 22/5)*q^19 + (1/5*a^4 + 2/5*a^3 - 9/5*a^2 - 11/5*a + 9/5)*q^20 + (-6/5*a^4 - 7/5*a^3 + 39/5*a^2 + 31/5*a - 4/5)*q^21 + (a^3 + a^2 - 8*a - 1)*q^22 + (3/5*a^4 + 1/5*a^3 - 22/5*a^2 - 3/5*a + 2/5)*q^23 + a*q^24 + (-4/5*a^4 - 3/5*a^3 + 31/5*a^2 + 4/5*a - 16/5)*q^25 + (3/5*a^4 - 4/5*a^3 - 27/5*a^2 + 37/5*a + 17/5)*q^26 + (a^3 - 6*a)*q^27 + (-2/5*a^4 - 4/5*a^3 + 13/5*a^2 + 17/5*a + 7/5)*q^28 + (a^4 - 9*a^2 + 5*a + 3)*q^29 + (3/5*a^4 + 1/5*a^3 - 22/5*a^2 - 3/5*a + 2/5)*q^30 + (-3/5*a^4 - 6/5*a^3 + 22/5*a^2 + 23/5*a - 7/5)*q^31 + q^32 + (a^4 + a^3 - 8*a^2 - a)*q^33 + (-7/5*a^4 + 1/5*a^3 + 58/5*a^2 - 33/5*a - 28/5)*q^34 + (6/5*a^4 + 7/5*a^3 - 49/5*a^2 - 26/5*a + 19/5)*q^35 + (a^2 - 3)*q^36 + (2/5*a^4 + 4/5*a^3 - 8/5*a^2 - 22/5*a - 12/5)*q^37 + O(q^38)
*]> ;  // time = 56.26 seconds




J[281] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 281, 281 ], new_dimensions := [ 7, 16 ], dimensions := [ 7, 16 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -2, -4, -4, -12, -7, -7, -4, -20, 1, -2, -41, -2 ],
[ -1, 4, 2, 16, 1, 9, -6, 28, 7, -8, 59, 2 ]
], hecke_fields := [
x^7 + 2*x^6 - 5*x^5 - 9*x^4 + 7*x^3 + 10*x^2 - 2*x - 1,
x^16 + x^15 - 27*x^14 - 24*x^13 + 294*x^12 + 229*x^11 - 1650*x^10 - 1115*x^9 + 5054*x^8 + 2991*x^7 - 8223*x^6 - 4526*x^5 + 6338*x^4 + 3707*x^3 - 1604*x^2 - 1215*x - 167
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 35 ]
], tamagawa_numbers := [
[ 1 ],
[ 35 ]
], torsion_upper_bounds := [ 1, 35 ], torsion_lower_bounds := [ 1, 35 ], l_ratios := [ 0, 1/35 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
a^6 + a^5 - 6*a^4 - 4*a^3 + 9*a^2 + 3*a - 2,
-a^6 - a^5 + 7*a^4 + 5*a^3 - 13*a^2 - 6*a + 3,
-a^6 - a^5 + 5*a^4 + 3*a^3 - 6*a^2 - 2*a - 1,
-a^6 - 2*a^5 + 2*a^4 + 4*a^3 + 3*a^2 + 2*a - 4,
a^4 - 3*a^2 + 2*a - 1,
2*a^6 + 5*a^5 - 8*a^4 - 21*a^3 + 8*a^2 + 19*a - 2,
a^6 + a^5 - 6*a^4 - 4*a^3 + 8*a^2 + 4*a - 2,
a^6 - a^5 - 9*a^4 + 6*a^3 + 20*a^2 - 7*a - 7,
3*a^6 + 6*a^5 - 12*a^4 - 20*a^3 + 15*a^2 + 13*a - 7,
2*a^6 + 5*a^5 - 7*a^4 - 20*a^3 + 4*a^2 + 20*a - 4,
-a^6 + 2*a^5 + 10*a^4 - 7*a^3 - 19*a^2 + 4*a + 4
],
[
a,
-13665/151856*a^15 - 4453/75928*a^14 + 360823/151856*a^13 + 192549/151856*a^12 - 3808793/151856*a^11 - 393525/37964*a^10 + 10220589/75928*a^9 + 6015201/151856*a^8 - 58521373/151856*a^7 - 5496873/75928*a^6 + 85533697/151856*a^5 + 10360255/151856*a^4 - 55824393/151856*a^3 - 495365/9491*a^2 + 6299351/75928*a + 2953595/151856,
-5097/75928*a^15 - 73/9491*a^14 + 142687/75928*a^13 - 599/75928*a^12 - 1608837/75928*a^11 + 87021/37964*a^10 + 4649421/37964*a^9 - 1750371/75928*a^8 - 28958277/75928*a^7 + 3301675/37964*a^6 + 46755675/75928*a^5 - 9261139/75928*a^4 - 34843841/75928*a^3 + 249793/9491*a^2 + 1195511/9491*a + 1626197/75928,
599/18982*a^15 + 3543/37964*a^14 - 15197/18982*a^13 - 42087/18982*a^12 + 305459/37964*a^11 + 777481/37964*a^10 - 1529371/37964*a^9 - 3507895/37964*a^8 + 975791/9491*a^7 + 1985247/9491*a^6 - 2259949/18982*a^5 - 8255973/37964*a^4 + 1467147/37964*a^3 + 739551/9491*a^2 + 371647/37964*a + 33381/18982,
-12727/151856*a^15 + 204/9491*a^14 + 346247/151856*a^13 - 99493/151856*a^12 - 3793561/151856*a^11 + 144027/18982*a^10 + 10706791/75928*a^9 - 6451005/151856*a^8 - 66041481/151856*a^7 + 8902335/75928*a^6 + 108659163/151856*a^5 - 20422589/151856*a^4 - 86268599/151856*a^3 + 1062797/75928*a^2 + 1623433/9491*a + 5250719/151856,
1845/18982*a^15 + 1311/37964*a^14 - 101841/37964*a^13 - 8453/18982*a^12 + 1130421/37964*a^11 - 2887/9491*a^10 - 3205285/18982*a^9 + 515547/18982*a^8 + 19453149/37964*a^7 - 2577655/18982*a^6 - 7543373/9491*a^5 + 8568847/37964*a^4 + 5259886/9491*a^3 - 3199653/37964*a^2 - 5388413/37964*a - 668059/37964,
-12825/151856*a^15 - 137/75928*a^14 + 331621/151856*a^13 - 23651/151856*a^12 - 3407013/151856*a^11 + 270075/75928*a^10 + 1104410/9491*a^9 - 4198049/151856*a^8 - 48509991/151856*a^7 + 7224269/75928*a^6 + 67546421/151856*a^5 - 20784153/151856*a^4 - 42201483/151856*a^3 + 3879829/75928*a^2 + 4946355/75928*a + 1356261/151856,
7373/37964*a^15 + 5081/37964*a^14 - 48131/9491*a^13 - 55551/18982*a^12 + 1999655/37964*a^11 + 920249/37964*a^10 - 5237881/18982*a^9 - 1776419/18982*a^8 + 7219115/9491*a^7 + 6374821/37964*a^6 - 9890044/9491*a^5 - 5068599/37964*a^4 + 5685979/9491*a^3 + 2717221/37964*a^2 - 1985371/18982*a - 746545/37964,
-1471/151856*a^15 - 10767/75928*a^14 + 497/151856*a^13 + 534079/151856*a^12 + 470353/151856*a^11 - 327182/9491*a^10 - 2801443/75928*a^9 + 25536335/151856*a^8 + 27102325/151856*a^7 - 31740777/75928*a^6 - 61392841/151856*a^5 + 71502829/151856*a^4 + 61901993/151856*a^3 - 1415021/9491*a^2 - 11374473/75928*a - 3762107/151856,
4133/37964*a^15 + 5553/18982*a^14 - 105649/37964*a^13 - 65385/9491*a^12 + 1068203/37964*a^11 + 2386447/37964*a^10 - 5365733/37964*a^9 - 10595625/37964*a^8 + 13688985/37964*a^7 + 23574929/37964*a^6 - 15887983/37964*a^5 - 6124297/9491*a^4 + 5799147/37964*a^3 + 2425273/9491*a^2 + 228357/37964*a - 494225/37964,
-5857/37964*a^15 - 3745/18982*a^14 + 74385/18982*a^13 + 171509/37964*a^12 - 1490571/37964*a^11 - 1509711/37964*a^10 + 7426625/37964*a^9 + 1589060/9491*a^8 - 9479359/18982*a^7 - 3229211/9491*a^6 + 22656067/37964*a^5 + 11247503/37964*a^4 - 4702321/18982*a^3 - 2987479/37964*a^2 + 86059/18982*a - 48488/9491,
1299/75928*a^15 - 527/18982*a^14 - 30041/75928*a^13 + 56149/75928*a^12 + 251853/75928*a^11 - 293769/37964*a^10 - 208019/18982*a^9 + 3077775/75928*a^8 + 56775/75928*a^7 - 4253999/37964*a^6 + 5693565/75928*a^5 + 11955561/75928*a^4 - 10735111/75928*a^3 - 1814201/18982*a^2 + 619469/9491*a + 1419859/75928
]
*], q_expansions := [*
q + a*q^2 + (a^6 + a^5 - 6*a^4 - 4*a^3 + 9*a^2 + 3*a - 2)*q^3 + (a^2 - 2)*q^4 + (-a^6 - a^5 + 7*a^4 + 5*a^3 - 13*a^2 - 6*a + 3)*q^5 + (-a^6 - a^5 + 5*a^4 + 2*a^3 - 7*a^2 + 1)*q^6 + (-a^6 - a^5 + 5*a^4 + 3*a^3 - 6*a^2 - 2*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (a^4 + 3*a^3 - 2*a^2 - 7*a)*q^9 + (a^6 + 2*a^5 - 4*a^4 - 6*a^3 + 4*a^2 + a - 1)*q^10 + (-a^6 - 2*a^5 + 2*a^4 + 4*a^3 + 3*a^2 + 2*a - 4)*q^11 + (-a^6 - 2*a^5 + 5*a^4 + 8*a^3 - 8*a^2 - 7*a + 3)*q^12 + (a^4 - 3*a^2 + 2*a - 1)*q^13 + (a^6 - 6*a^4 + a^3 + 8*a^2 - 3*a - 1)*q^14 + (a^5 - 7*a^3 + 2*a^2 + 12*a - 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^6 + 5*a^5 - 8*a^4 - 21*a^3 + 8*a^2 + 19*a - 2)*q^17 + (a^5 + 3*a^4 - 2*a^3 - 7*a^2)*q^18 + (a^6 + a^5 - 6*a^4 - 4*a^3 + 8*a^2 + 4*a - 2)*q^19 + (2*a^6 + 3*a^5 - 11*a^4 - 13*a^3 + 17*a^2 + 13*a - 5)*q^20 + (-a^6 - a^5 + 7*a^4 + 5*a^3 - 12*a^2 - 3*a + 2)*q^21 + (-3*a^5 - 5*a^4 + 10*a^3 + 12*a^2 - 6*a - 1)*q^22 + (a^6 - a^5 - 9*a^4 + 6*a^3 + 20*a^2 - 7*a - 7)*q^23 + (2*a^6 + 2*a^5 - 11*a^4 - 5*a^3 + 17*a^2 + a - 3)*q^24 + (-2*a^6 - 7*a^5 + 4*a^4 + 27*a^3 + a^2 - 22*a + 3)*q^25 + (a^5 - 3*a^3 + 2*a^2 - a)*q^26 + (-2*a^6 - 3*a^5 + 9*a^4 + 10*a^3 - 10*a^2 - 7*a + 2)*q^27 + (a^5 - 5*a^3 - a^2 + 5*a + 3)*q^28 + (3*a^6 + 6*a^5 - 12*a^4 - 20*a^3 + 15*a^2 + 13*a - 7)*q^29 + (a^6 - 7*a^4 + 2*a^3 + 12*a^2 - 5*a)*q^30 + (2*a^6 + 5*a^5 - 7*a^4 - 20*a^3 + 4*a^2 + 20*a - 4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-2*a^6 - 2*a^5 + 15*a^4 + 12*a^3 - 28*a^2 - 13*a + 8)*q^33 + (a^6 + 2*a^5 - 3*a^4 - 6*a^3 - a^2 + 2*a + 2)*q^34 + (2*a^6 + 2*a^5 - 13*a^4 - 8*a^3 + 22*a^2 + 7*a - 3)*q^35 + (a^6 + 3*a^5 - 4*a^4 - 13*a^3 + 4*a^2 + 14*a)*q^36 + (-a^6 + 2*a^5 + 10*a^4 - 7*a^3 - 19*a^2 + 4*a + 4)*q^37 + O(q^38),
q + a*q^2 + (-13665/151856*a^15 - 4453/75928*a^14 + 360823/151856*a^13 + 192549/151856*a^12 - 3808793/151856*a^11 - 393525/37964*a^10 + 10220589/75928*a^9 + 6015201/151856*a^8 - 58521373/151856*a^7 - 5496873/75928*a^6 + 85533697/151856*a^5 + 10360255/151856*a^4 - 55824393/151856*a^3 - 495365/9491*a^2 + 6299351/75928*a + 2953595/151856)*q^3 + (a^2 - 2)*q^4 + (-5097/75928*a^15 - 73/9491*a^14 + 142687/75928*a^13 - 599/75928*a^12 - 1608837/75928*a^11 + 87021/37964*a^10 + 4649421/37964*a^9 - 1750371/75928*a^8 - 28958277/75928*a^7 + 3301675/37964*a^6 + 46755675/75928*a^5 - 9261139/75928*a^4 - 34843841/75928*a^3 + 249793/9491*a^2 + 1195511/9491*a + 1626197/75928)*q^5 + (4759/151856*a^15 - 2033/37964*a^14 - 135411/151856*a^13 + 208717/151856*a^12 + 1555185/151856*a^11 - 263259/18982*a^10 - 4610637/75928*a^9 + 10541537/151856*a^8 + 29878269/151856*a^7 - 13416799/75928*a^6 - 51487535/151856*a^5 + 30784377/151856*a^4 + 42730315/151856*a^3 - 4659979/75928*a^2 - 3412345/37964*a - 2282055/151856)*q^6 + (599/18982*a^15 + 3543/37964*a^14 - 15197/18982*a^13 - 42087/18982*a^12 + 305459/37964*a^11 + 777481/37964*a^10 - 1529371/37964*a^9 - 3507895/37964*a^8 + 975791/9491*a^7 + 1985247/9491*a^6 - 2259949/18982*a^5 - 8255973/37964*a^4 + 1467147/37964*a^3 + 739551/9491*a^2 + 371647/37964*a + 33381/18982)*q^7 + (a^3 - 4*a)*q^8 + (-4843/151856*a^15 - 9653/75928*a^14 + 117451/151856*a^13 + 458291/151856*a^12 - 1101831/151856*a^11 - 2104033/75928*a^10 + 610951/18982*a^9 + 18715513/151856*a^8 - 9503777/151856*a^7 - 20597367/75928*a^6 + 2873867/151856*a^5 + 40752581/151856*a^4 + 10907739/151856*a^3 - 6622291/75928*a^2 - 3428859/75928*a - 475745/151856)*q^9 + (4513/75928*a^15 + 1267/18982*a^14 - 122927/75928*a^13 - 110319/75928*a^12 + 1341255/75928*a^11 + 111099/9491*a^10 - 3716763/37964*a^9 - 3198039/75928*a^8 + 21848477/75928*a^7 + 1210761/18982*a^6 - 32330161/75928*a^5 - 2539055/75928*a^4 + 20892923/75928*a^3 + 347125/18982*a^2 - 2283329/37964*a - 851199/75928)*q^10 + (-12727/151856*a^15 + 204/9491*a^14 + 346247/151856*a^13 - 99493/151856*a^12 - 3793561/151856*a^11 + 144027/18982*a^10 + 10706791/75928*a^9 - 6451005/151856*a^8 - 66041481/151856*a^7 + 8902335/75928*a^6 + 108659163/151856*a^5 - 20422589/151856*a^4 - 86268599/151856*a^3 + 1062797/75928*a^2 + 1623433/9491*a + 5250719/151856)*q^11 + (14439/151856*a^15 + 5447/75928*a^14 - 398713/151856*a^13 - 229059/151856*a^12 + 4421703/151856*a^11 + 444819/37964*a^10 - 12517267/75928*a^9 - 6204119/151856*a^8 + 75974979/151856*a^7 + 4816607/75928*a^6 - 118743783/151856*a^5 - 8152737/151856*a^4 + 84687215/151856*a^3 + 1229467/18982*a^2 - 10848637/75928*a - 5112437/151856)*q^12 + (1845/18982*a^15 + 1311/37964*a^14 - 101841/37964*a^13 - 8453/18982*a^12 + 1130421/37964*a^11 - 2887/9491*a^10 - 3205285/18982*a^9 + 515547/18982*a^8 + 19453149/37964*a^7 - 2577655/18982*a^6 - 7543373/9491*a^5 + 8568847/37964*a^4 + 5259886/9491*a^3 - 3199653/37964*a^2 - 5388413/37964*a - 668059/37964)*q^13 + (2345/37964*a^15 + 488/9491*a^14 - 27711/18982*a^13 - 46753/37964*a^12 + 503139/37964*a^11 + 447329/37964*a^10 - 2172125/37964*a^9 - 537882/9491*a^8 + 2178885/18982*a^7 + 1332814/9491*a^6 - 2833825/37964*a^5 - 6125777/37964*a^4 - 741391/18982*a^3 + 2293239/37964*a^2 + 380583/9491*a + 100033/18982)*q^14 + (-3707/151856*a^15 - 3093/75928*a^14 + 109957/151856*a^13 + 120711/151856*a^12 - 1283403/151856*a^11 - 47861/9491*a^10 + 3671003/75928*a^9 + 1194587/151856*a^8 - 20653287/151856*a^7 + 2306125/75928*a^6 + 23719231/151856*a^5 - 15391871/151856*a^4 - 2615603/151856*a^3 + 695142/9491*a^2 - 2669661/75928*a - 2017859/151856)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-12825/151856*a^15 - 137/75928*a^14 + 331621/151856*a^13 - 23651/151856*a^12 - 3407013/151856*a^11 + 270075/75928*a^10 + 1104410/9491*a^9 - 4198049/151856*a^8 - 48509991/151856*a^7 + 7224269/75928*a^6 + 67546421/151856*a^5 - 20784153/151856*a^4 - 42201483/151856*a^3 + 3879829/75928*a^2 + 4946355/75928*a + 1356261/151856)*q^17 + (-14463/151856*a^15 - 6655/75928*a^14 + 342059/151856*a^13 + 322011/151856*a^12 - 3099019/151856*a^11 - 1551671/75928*a^10 + 832223/9491*a^9 + 14972745/151856*a^8 - 26709321/151856*a^7 - 18475061/75928*a^6 + 18833163/151856*a^5 + 41602673/151856*a^4 + 4708419/151856*a^3 - 7312945/75928*a^2 - 3179995/75928*a - 808781/151856)*q^18 + (7373/37964*a^15 + 5081/37964*a^14 - 48131/9491*a^13 - 55551/18982*a^12 + 1999655/37964*a^11 + 920249/37964*a^10 - 5237881/18982*a^9 - 1776419/18982*a^8 + 7219115/9491*a^7 + 6374821/37964*a^6 - 9890044/9491*a^5 - 5068599/37964*a^4 + 5685979/9491*a^3 + 2717221/37964*a^2 - 1985371/18982*a - 746545/37964)*q^19 + (10749/75928*a^15 + 23/18982*a^14 - 287381/75928*a^13 + 15631/75928*a^12 + 3072989/75928*a^11 - 41895/9491*a^10 - 2095466/9491*a^9 + 2540517/75928*a^8 + 49261215/75928*a^7 - 4213231/37964*a^6 - 75624567/75928*a^5 + 10811807/75928*a^4 + 54346491/75928*a^3 - 662247/37964*a^2 - 1812010/9491*a - 2498723/75928)*q^20 + (2407/37964*a^15 + 933/18982*a^14 - 14835/9491*a^13 - 40113/37964*a^12 + 563075/37964*a^11 + 316617/37964*a^10 - 2520841/37964*a^9 - 263937/9491*a^8 + 1246031/9491*a^7 + 484245/18982*a^6 - 1814107/37964*a^5 + 1758137/37964*a^4 - 2618509/18982*a^3 - 2999693/37964*a^2 + 850803/9491*a + 267161/9491)*q^21 + (15991/151856*a^15 + 1309/75928*a^14 - 404941/151856*a^13 - 51823/151856*a^12 + 4066699/151856*a^11 + 25877/9491*a^10 - 10320805/75928*a^9 - 1719223/151856*a^8 + 55871127/151856*a^7 + 2002521/75928*a^6 - 78024991/151856*a^5 - 5604873/151856*a^4 + 49304583/151856*a^3 + 1390205/37964*a^2 - 5106293/75928*a - 2125409/151856)*q^22 + (-1471/151856*a^15 - 10767/75928*a^14 + 497/151856*a^13 + 534079/151856*a^12 + 470353/151856*a^11 - 327182/9491*a^10 - 2801443/75928*a^9 + 25536335/151856*a^8 + 27102325/151856*a^7 - 31740777/75928*a^6 - 61392841/151856*a^5 + 71502829/151856*a^4 + 61901993/151856*a^3 - 1415021/9491*a^2 - 11374473/75928*a - 3762107/151856)*q^23 + (-13063/151856*a^15 + 1851/37964*a^14 + 388299/151856*a^13 - 240797/151856*a^12 - 4637625/151856*a^11 + 375245/18982*a^10 + 14168957/75928*a^9 - 18082801/151856*a^8 - 93310373/151856*a^7 + 26827655/75928*a^6 + 160173247/151856*a^5 - 68395921/151856*a^4 - 129150267/151856*a^3 + 10051399/75928*a^2 + 9932427/37964*a + 6975423/151856)*q^24 + (-18787/151856*a^15 + 9815/75928*a^14 + 514887/151856*a^13 - 546433/151856*a^12 - 5645395/151856*a^11 + 2983727/75928*a^10 + 7872913/37964*a^9 - 32258431/151856*a^8 - 93641125/151856*a^7 + 44336255/75928*a^6 + 141315311/151856*a^5 - 111563159/151856*a^4 - 93387109/151856*a^3 + 22080703/75928*a^2 + 10720555/75928*a + 1245711/151856)*q^25 + (-2379/37964*a^15 - 2211/37964*a^14 + 35827/18982*a^13 + 45561/37964*a^12 - 428279/18982*a^11 - 161035/18982*a^10 + 1286361/9491*a^9 + 803889/37964*a^8 - 4048025/9491*a^7 + 84689/18982*a^6 + 25269787/37964*a^5 - 586919/9491*a^4 - 16878483/37964*a^3 + 530347/37964*a^2 + 3815291/37964*a + 308115/18982)*q^26 + (9697/75928*a^15 - 14063/75928*a^14 - 135709/37964*a^13 + 369555/75928*a^12 + 382183/9491*a^11 - 950825/18982*a^10 - 2216470/9491*a^9 + 19296375/75928*a^8 + 7013062/9491*a^7 - 6174524/9491*a^6 - 94400127/75928*a^5 + 28322871/37964*a^4 + 76302919/75928*a^3 - 17391781/75928*a^2 - 23743103/75928*a - 483117/9491)*q^27 + (-2789/37964*a^15 + 807/37964*a^14 + 70315/37964*a^13 - 17943/37964*a^12 - 350297/18982*a^11 + 142163/37964*a^10 + 3521889/37964*a^9 - 239035/18982*a^8 - 9488967/37964*a^7 + 283567/18982*a^6 + 13527489/37964*a^5 + 83277/18982*a^4 - 4666985/18982*a^3 - 158174/9491*a^2 + 2305947/37964*a + 258091/37964)*q^28 + (4133/37964*a^15 + 5553/18982*a^14 - 105649/37964*a^13 - 65385/9491*a^12 + 1068203/37964*a^11 + 2386447/37964*a^10 - 5365733/37964*a^9 - 10595625/37964*a^8 + 13688985/37964*a^7 + 23574929/37964*a^6 - 15887983/37964*a^5 - 6124297/9491*a^4 + 5799147/37964*a^3 + 2425273/9491*a^2 + 228357/37964*a - 494225/37964)*q^29 + (-2479/151856*a^15 + 2467/37964*a^14 + 31743/151856*a^13 - 193545/151856*a^12 + 83127/151856*a^11 + 76591/9491*a^10 - 1469359/75928*a^9 - 1918109/151856*a^8 + 15699887/151856*a^7 - 3381715/75928*a^6 - 32169753/151856*a^5 + 20879363/151856*a^4 + 24864121/151856*a^3 - 5642675/75928*a^2 - 815233/18982*a - 619069/151856)*q^30 + (-5857/37964*a^15 - 3745/18982*a^14 + 74385/18982*a^13 + 171509/37964*a^12 - 1490571/37964*a^11 - 1509711/37964*a^10 + 7426625/37964*a^9 + 1589060/9491*a^8 - 9479359/18982*a^7 - 3229211/9491*a^6 + 22656067/37964*a^5 + 11247503/37964*a^4 - 4702321/18982*a^3 - 2987479/37964*a^2 + 86059/18982*a - 48488/9491)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-25091/151856*a^15 + 2553/75928*a^14 + 692823/151856*a^13 - 200217/151856*a^12 - 7666363/151856*a^11 + 1376685/75928*a^10 + 10799969/37964*a^9 - 17553207/151856*a^8 - 129821653/151856*a^7 + 26926159/75928*a^6 + 198180323/151856*a^5 - 69615435/151856*a^4 - 132831349/151856*a^3 + 10002703/75928*a^2 + 14910685/75928*a + 5436963/151856)*q^33 + (12551/151856*a^15 - 7327/75928*a^14 - 331451/151856*a^13 + 363537/151856*a^12 + 3477075/151856*a^11 - 1745345/75928*a^10 - 4624481/37964*a^9 + 16307559/151856*a^8 + 52808113/151856*a^7 - 18956777/75928*a^6 - 78830103/151856*a^5 + 39083367/151856*a^4 + 55301933/151856*a^3 - 5339295/75928*a^2 - 7113057/75928*a - 2141775/151856)*q^34 + (9111/75928*a^15 + 3019/37964*a^14 - 219997/75928*a^13 - 132239/75928*a^12 + 2052243/75928*a^11 + 277131/18982*a^10 - 4589521/37964*a^9 - 4350975/75928*a^8 + 19335935/75928*a^7 + 3818453/37964*a^6 - 13615819/75928*a^5 - 3963197/75928*a^4 - 7149809/75928*a^3 - 399003/18982*a^2 + 3882849/37964*a + 1562331/75928)*q^35 + (10839/151856*a^15 - 4915/75928*a^14 - 260003/151856*a^13 + 236521/151856*a^12 + 2412347/151856*a^11 - 1066125/75928*a^10 - 2732179/37964*a^9 + 8955655/151856*a^8 + 25316265/151856*a^7 - 8853309/75928*a^6 - 29604599/151856*a^5 + 14869751/151856*a^4 + 17172973/151856*a^3 - 1534739/75928*a^2 - 2332945/75928*a - 1463831/151856)*q^36 + (1299/75928*a^15 - 527/18982*a^14 - 30041/75928*a^13 + 56149/75928*a^12 + 251853/75928*a^11 - 293769/37964*a^10 - 208019/18982*a^9 + 3077775/75928*a^8 + 56775/75928*a^7 - 4253999/37964*a^6 + 5693565/75928*a^5 + 11955561/75928*a^4 - 10735111/75928*a^3 - 1814201/18982*a^2 + 619469/9491*a + 1419859/75928)*q^37 + O(q^38)
*]> ;  // time = 4.099 seconds




J[282] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 282, 282, 282, 282, 282, 141, 141, 141, 141, 141, 141, 94, 94, 47 ], new_dimensions := [ 1, 1, 2, 2, 3, 1, 1, 1, 1, 1, 2, 1, 2, 4 ], dimensions := [ 1, 1, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 4, 16 ], intersection_graph := [ 0, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 23, 3, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 9, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 1, 49, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1849, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2209, 1, 1, 1, 1, 23, 1, 9, 1, 1, 49, 1849, 1, 2209, 0 ], ap_traces := [
[ 1, -1, 2, 0, 0, 2, 2, 0, 0, 2, -8, -2 ],
[ 1, -1, -4, -4, 0, -2, -6, 6, -4, 4, 2, -6 ],
[ -2, -2, -2, 0, -6, -2, -8, -6, -12, -2, -4, -4 ],
[ -2, 2, 0, 4, 0, 4, 0, 4, 0, 0, 4, 4 ],
[ 3, 3, 2, 0, -6, 0, -2, -4, -8, -6, 6, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + 2*x - 2,
x^2 - 6,
x^3 - 2*x^2 - 8*x - 4
], atkin_lehners := [
[ -1, 1, 1 ],
[ -1, 1, -1 ],
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 5, 3, 1 ],
[ 115, 23, 1 ]
], tamagawa_numbers := [
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 115, 23, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 23 ], torsion_lower_bounds := [ 1, 1, 1, 3, 1 ], l_ratios := [ 3, 0, 0, 1/3, 5 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 1/529 ], eigenvalues := [*
[ 1, -1, 2, 0, 0, 2, 2, 0, 0, 2, -8, -2 ],
[ 1, -1, -4, -4, 0, -2, -6, 6, -4, 4, 2, -6 ],
[
-1,
-1,
a,
-2*a - 2,
-a - 4,
3*a + 2,
-4,
a - 2,
-2*a - 8,
-3*a - 4,
4*a + 2,
-4*a - 6
],
[
-1,
1,
a,
2,
-a,
-a + 2,
-2*a,
a + 2,
2*a,
-3*a,
2,
4*a + 2
],
[
1,
1,
a,
a^2 - 4*a - 4,
-2*a^2 + 5*a + 8,
-2*a^2 + 5*a + 10,
a^2 - 2*a - 6,
2*a^2 - 7*a - 10,
2*a^2 - 6*a - 12,
2*a^2 - 5*a - 12,
-2*a^2 + 8*a + 10,
-4*a^2 + 12*a + 18
]
*], q_expansions := [*
q + q^2 - q^3 + q^4 + 2*q^5 - q^6 + q^8 + q^9 + 2*q^10 - q^12 + 2*q^13 - 2*q^15 + q^16 + 2*q^17 + q^18 + 2*q^20 - q^24 - q^25 + 2*q^26 - q^27 + 2*q^29 - 2*q^30 - 8*q^31 + q^32 + 2*q^34 + q^36 - 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 4*q^5 - q^6 - 4*q^7 + q^8 + q^9 - 4*q^10 - q^12 - 2*q^13 - 4*q^14 + 4*q^15 + q^16 - 6*q^17 + q^18 + 6*q^19 - 4*q^20 + 4*q^21 - 4*q^23 - q^24 + 11*q^25 - 2*q^26 - q^27 - 4*q^28 + 4*q^29 + 4*q^30 + 2*q^31 + q^32 - 6*q^34 + 16*q^35 + q^36 - 6*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + a*q^5 + q^6 + (-2*a - 2)*q^7 - q^8 + q^9 - a*q^10 + (-a - 4)*q^11 - q^12 + (3*a + 2)*q^13 + (2*a + 2)*q^14 - a*q^15 + q^16 - 4*q^17 - q^18 + (a - 2)*q^19 + a*q^20 + (2*a + 2)*q^21 + (a + 4)*q^22 + (-2*a - 8)*q^23 + q^24 + (-2*a - 3)*q^25 + (-3*a - 2)*q^26 - q^27 + (-2*a - 2)*q^28 + (-3*a - 4)*q^29 + a*q^30 + (4*a + 2)*q^31 - q^32 + (a + 4)*q^33 + 4*q^34 + (2*a - 4)*q^35 + q^36 + (-4*a - 6)*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + a*q^5 - q^6 + 2*q^7 - q^8 + q^9 - a*q^10 - a*q^11 + q^12 + (-a + 2)*q^13 - 2*q^14 + a*q^15 + q^16 - 2*a*q^17 - q^18 + (a + 2)*q^19 + a*q^20 + 2*q^21 + a*q^22 + 2*a*q^23 - q^24 + q^25 + (a - 2)*q^26 + q^27 + 2*q^28 - 3*a*q^29 - a*q^30 + 2*q^31 - q^32 - a*q^33 + 2*a*q^34 + 2*a*q^35 + q^36 + (4*a + 2)*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + a*q^5 + q^6 + (a^2 - 4*a - 4)*q^7 + q^8 + q^9 + a*q^10 + (-2*a^2 + 5*a + 8)*q^11 + q^12 + (-2*a^2 + 5*a + 10)*q^13 + (a^2 - 4*a - 4)*q^14 + a*q^15 + q^16 + (a^2 - 2*a - 6)*q^17 + q^18 + (2*a^2 - 7*a - 10)*q^19 + a*q^20 + (a^2 - 4*a - 4)*q^21 + (-2*a^2 + 5*a + 8)*q^22 + (2*a^2 - 6*a - 12)*q^23 + q^24 + (a^2 - 5)*q^25 + (-2*a^2 + 5*a + 10)*q^26 + q^27 + (a^2 - 4*a - 4)*q^28 + (2*a^2 - 5*a - 12)*q^29 + a*q^30 + (-2*a^2 + 8*a + 10)*q^31 + q^32 + (-2*a^2 + 5*a + 8)*q^33 + (a^2 - 2*a - 6)*q^34 + (-2*a^2 + 4*a + 4)*q^35 + q^36 + (-4*a^2 + 12*a + 18)*q^37 + O(q^38)
*]> ;  // time = 160.61 seconds




J[283] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 283, 283 ], new_dimensions := [ 9, 14 ], dimensions := [ 9, 14 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -6, -6, -14, -2, -5, -9, -13, 3, -24, -33, -1, -24 ],
[ 6, 4, 14, 0, 5, 9, 13, -7, 22, 33, -13, 16 ]
], hecke_fields := [
x^9 + 6*x^8 + 5*x^7 - 29*x^6 - 50*x^5 + 27*x^4 + 83*x^3 + 19*x^2 - 13*x + 1,
x^14 - 6*x^13 - 4*x^12 + 83*x^11 - 77*x^10 - 394*x^9 + 617*x^8 + 724*x^7 - 1566*x^6 - 370*x^5 + 1489*x^4 - 153*x^3 - 410*x^2 + 120*x - 8
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 47 ]
], tamagawa_numbers := [
[ 1 ],
[ 47 ]
], torsion_upper_bounds := [ 1, 47 ], torsion_lower_bounds := [ 1, 47 ], l_ratios := [ 0, 1/47 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
1/5*a^8 + 2/5*a^7 - 13/5*a^6 - 22/5*a^5 + 53/5*a^4 + 13*a^3 - 77/5*a^2 - 53/5*a + 14/5,
a^7 + 4*a^6 - 3*a^5 - 23*a^4 - 4*a^3 + 34*a^2 + 12*a - 5,
3/5*a^8 + 16/5*a^7 + 11/5*a^6 - 66/5*a^5 - 111/5*a^4 + 6*a^3 + 169/5*a^2 + 76/5*a - 23/5,
-3/5*a^8 - 21/5*a^7 - 31/5*a^6 + 76/5*a^5 + 216/5*a^4 + 3*a^3 - 309/5*a^2 - 176/5*a + 28/5,
2/5*a^8 + 14/5*a^7 + 19/5*a^6 - 64/5*a^5 - 169/5*a^4 + 2*a^3 + 291/5*a^2 + 164/5*a - 42/5,
-2/5*a^8 - 19/5*a^7 - 39/5*a^6 + 79/5*a^5 + 284/5*a^4 + a^3 - 461/5*a^2 - 199/5*a + 42/5,
-2*a^8 - 9*a^7 + 2*a^6 + 49*a^5 + 30*a^4 - 66*a^3 - 54*a^2,
3/5*a^8 + 21/5*a^7 + 31/5*a^6 - 86/5*a^5 - 251/5*a^4 - a^3 + 409/5*a^2 + 216/5*a - 53/5,
-a^8 - 5*a^7 - a^6 + 26*a^5 + 26*a^4 - 33*a^3 - 45*a^2 - 2*a + 2,
-19/5*a^8 - 93/5*a^7 - 3/5*a^6 + 513/5*a^5 + 438/5*a^4 - 138*a^3 - 797/5*a^2 - 48/5*a + 59/5,
a^8 + 5*a^7 + a^6 - 24*a^5 - 20*a^4 + 27*a^3 + 23*a^2 + 4*a + 3
],
[
a,
17/94*a^13 - 41/47*a^12 - 85/47*a^11 + 1211/94*a^10 + 265/94*a^9 - 3265/47*a^8 + 1745/94*a^7 + 7844/47*a^6 - 2764/47*a^5 - 8227/47*a^4 + 4197/94*a^3 + 5787/94*a^2 - 526/47*a - 102/47,
-19/94*a^13 + 32/47*a^12 + 142/47*a^11 - 983/94*a^10 - 1673/94*a^9 + 2781/47*a^8 + 5343/94*a^7 - 7014/47*a^6 - 5357/47*a^5 + 7384/47*a^4 + 11621/94*a^3 - 4151/94*a^2 - 1552/47*a + 302/47,
-39/188*a^13 + 65/47*a^12 + 27/47*a^11 - 3685/188*a^10 + 3705/188*a^9 + 4587/47*a^8 - 27647/188*a^7 - 18971/94*a^6 + 34223/94*a^5 + 15263/94*a^4 - 63131/188*a^3 - 6403/188*a^2 + 4062/47*a - 447/47,
3/188*a^13 + 37/94*a^12 - 78/47*a^11 - 1047/188*a^10 + 4321/188*a^9 + 2559/94*a^8 - 22993/188*a^7 - 2526/47*a^6 + 27057/94*a^5 + 3779/94*a^4 - 53525/188*a^3 - 1279/188*a^2 + 7911/94*a - 432/47,
-79/94*a^13 + 323/94*a^12 + 489/47*a^11 - 4859/94*a^10 - 1911/47*a^9 + 26671/94*a^8 + 4509/94*a^7 - 64761/94*a^6 - 28/47*a^5 + 33230/47*a^4 + 745/94*a^3 - 9848/47*a^2 + 1231/94*a + 239/47,
-57/47*a^13 + 239/47*a^12 + 664/47*a^11 - 3560/47*a^10 - 2058/47*a^9 + 19130/47*a^8 - 797/47*a^7 - 44810/47*a^6 + 9594/47*a^5 + 44069/47*a^4 - 8189/47*a^3 - 13064/47*a^2 + 2297/47*a + 214/47,
73/47*a^13 - 330/47*a^12 - 777/47*a^11 + 4885/47*a^10 + 1572/47*a^9 - 26003/47*a^8 + 6556/47*a^7 + 59871/47*a^6 - 24794/47*a^5 - 56619/47*a^4 + 22598/47*a^3 + 14358/47*a^2 - 7260/47*a + 816/47,
73/47*a^13 - 613/94*a^12 - 871/47*a^11 + 4603/47*a^10 + 5917/94*a^9 - 49985/94*a^8 - 870/47*a^7 + 118379/94*a^6 - 7310/47*a^5 - 58123/47*a^4 + 5302/47*a^3 + 31301/94*a^2 - 4885/94*a + 17/47,
-231/188*a^13 + 535/94*a^12 + 554/47*a^11 - 15449/188*a^10 - 1461/188*a^9 + 39743/94*a^8 - 39791/188*a^7 - 43506/47*a^6 + 62913/94*a^5 + 76087/94*a^4 - 122299/188*a^3 - 32929/188*a^2 + 18491/94*a - 1046/47,
-12/47*a^13 + 33/47*a^12 + 214/47*a^11 - 559/47*a^10 - 1492/47*a^9 + 3451/47*a^8 + 5351/47*a^7 - 9451/47*a^6 - 10784/47*a^5 + 11034/47*a^4 + 10966/47*a^3 - 4002/47*a^2 - 3175/47*a + 520/47,
143/94*a^13 - 320/47*a^12 - 762/47*a^11 + 9407/94*a^10 + 3241/94*a^9 - 24896/47*a^8 + 11477/94*a^7 + 57121/47*a^6 - 22382/47*a^5 - 53959/47*a^4 + 39689/94*a^3 + 27833/94*a^2 - 5724/47*a + 552/47
]
*], q_expansions := [*
q + a*q^2 + (1/5*a^8 + 2/5*a^7 - 13/5*a^6 - 22/5*a^5 + 53/5*a^4 + 13*a^3 - 77/5*a^2 - 53/5*a + 14/5)*q^3 + (a^2 - 2)*q^4 + (a^7 + 4*a^6 - 3*a^5 - 23*a^4 - 4*a^3 + 34*a^2 + 12*a - 5)*q^5 + (-4/5*a^8 - 18/5*a^7 + 7/5*a^6 + 103/5*a^5 + 38/5*a^4 - 32*a^3 - 72/5*a^2 + 27/5*a - 1/5)*q^6 + (3/5*a^8 + 16/5*a^7 + 11/5*a^6 - 66/5*a^5 - 111/5*a^4 + 6*a^3 + 169/5*a^2 + 76/5*a - 23/5)*q^7 + (a^3 - 4*a)*q^8 + (-7/5*a^8 - 34/5*a^7 + 1/5*a^6 + 189/5*a^5 + 144/5*a^4 - 52*a^3 - 251/5*a^2 - 9/5*a + 2/5)*q^9 + (a^8 + 4*a^7 - 3*a^6 - 23*a^5 - 4*a^4 + 34*a^3 + 12*a^2 - 5*a)*q^10 + (-3/5*a^8 - 21/5*a^7 - 31/5*a^6 + 76/5*a^5 + 216/5*a^4 + 3*a^3 - 309/5*a^2 - 176/5*a + 28/5)*q^11 + (4/5*a^8 + 23/5*a^7 + 13/5*a^6 - 118/5*a^5 - 158/5*a^4 + 26*a^3 + 257/5*a^2 + 53/5*a - 24/5)*q^12 + (2/5*a^8 + 14/5*a^7 + 19/5*a^6 - 64/5*a^5 - 169/5*a^4 + 2*a^3 + 291/5*a^2 + 164/5*a - 42/5)*q^13 + (-2/5*a^8 - 4/5*a^7 + 21/5*a^6 + 39/5*a^5 - 51/5*a^4 - 16*a^3 + 19/5*a^2 + 16/5*a - 3/5)*q^14 + (1/5*a^8 + 12/5*a^7 + 32/5*a^6 - 37/5*a^5 - 197/5*a^4 - 8*a^3 + 298/5*a^2 + 147/5*a - 46/5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-2/5*a^8 - 19/5*a^7 - 39/5*a^6 + 79/5*a^5 + 284/5*a^4 + a^3 - 461/5*a^2 - 199/5*a + 42/5)*q^17 + (8/5*a^8 + 36/5*a^7 - 14/5*a^6 - 206/5*a^5 - 71/5*a^4 + 66*a^3 + 124/5*a^2 - 89/5*a + 7/5)*q^18 + (-2*a^8 - 9*a^7 + 2*a^6 + 49*a^5 + 30*a^4 - 66*a^3 - 54*a^2)*q^19 + (-2*a^8 - 10*a^7 - 2*a^6 + 52*a^5 + 53*a^4 - 63*a^3 - 92*a^2 - 11*a + 9)*q^20 + (13/5*a^8 + 61/5*a^7 - 9/5*a^6 - 346/5*a^5 - 241/5*a^4 + 98*a^3 + 459/5*a^2 + 1/5*a - 28/5)*q^21 + (-3/5*a^8 - 16/5*a^7 - 11/5*a^6 + 66/5*a^5 + 96/5*a^4 - 12*a^3 - 119/5*a^2 - 11/5*a + 3/5)*q^22 + (3/5*a^8 + 21/5*a^7 + 31/5*a^6 - 86/5*a^5 - 251/5*a^4 - a^3 + 409/5*a^2 + 216/5*a - 53/5)*q^23 + (7/5*a^8 + 29/5*a^7 - 16/5*a^6 - 164/5*a^5 - 54/5*a^4 + 49*a^3 + 121/5*a^2 - 26/5*a - 2/5)*q^24 + (a^8 + a^7 - 16*a^6 - 17*a^5 + 71*a^4 + 65*a^3 - 100*a^2 - 69*a + 15)*q^25 + (2/5*a^8 + 9/5*a^7 - 6/5*a^6 - 69/5*a^5 - 44/5*a^4 + 25*a^3 + 126/5*a^2 - 16/5*a - 2/5)*q^26 + (9/5*a^8 + 48/5*a^7 + 18/5*a^6 - 253/5*a^5 - 298/5*a^4 + 62*a^3 + 502/5*a^2 + 73/5*a - 39/5)*q^27 + (2/5*a^8 - 1/5*a^7 - 41/5*a^6 - 19/5*a^5 + 196/5*a^4 + 25*a^3 - 284/5*a^2 - 181/5*a + 48/5)*q^28 + (-a^8 - 5*a^7 - a^6 + 26*a^5 + 26*a^4 - 33*a^3 - 45*a^2 - 2*a + 2)*q^29 + (6/5*a^8 + 27/5*a^7 - 8/5*a^6 - 147/5*a^5 - 67/5*a^4 + 43*a^3 + 128/5*a^2 - 33/5*a - 1/5)*q^30 + (-19/5*a^8 - 93/5*a^7 - 3/5*a^6 + 513/5*a^5 + 438/5*a^4 - 138*a^3 - 797/5*a^2 - 48/5*a + 59/5)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-8/5*a^8 - 36/5*a^7 + 14/5*a^6 + 221/5*a^5 + 121/5*a^4 - 69*a^3 - 264/5*a^2 + 34/5*a + 13/5)*q^33 + (-7/5*a^8 - 29/5*a^7 + 21/5*a^6 + 184/5*a^5 + 59/5*a^4 - 59*a^3 - 161/5*a^2 + 16/5*a + 2/5)*q^34 + (-22/5*a^8 - 109/5*a^7 - 19/5*a^6 + 554/5*a^5 + 529/5*a^4 - 132*a^3 - 871/5*a^2 - 89/5*a + 67/5)*q^35 + (2/5*a^8 + 14/5*a^7 + 24/5*a^6 - 49/5*a^5 - 174/5*a^4 - 4*a^3 + 261/5*a^2 + 129/5*a - 12/5)*q^36 + (a^8 + 5*a^7 + a^6 - 24*a^5 - 20*a^4 + 27*a^3 + 23*a^2 + 4*a + 3)*q^37 + O(q^38),
q + a*q^2 + (17/94*a^13 - 41/47*a^12 - 85/47*a^11 + 1211/94*a^10 + 265/94*a^9 - 3265/47*a^8 + 1745/94*a^7 + 7844/47*a^6 - 2764/47*a^5 - 8227/47*a^4 + 4197/94*a^3 + 5787/94*a^2 - 526/47*a - 102/47)*q^3 + (a^2 - 2)*q^4 + (-19/94*a^13 + 32/47*a^12 + 142/47*a^11 - 983/94*a^10 - 1673/94*a^9 + 2781/47*a^8 + 5343/94*a^7 - 7014/47*a^6 - 5357/47*a^5 + 7384/47*a^4 + 11621/94*a^3 - 4151/94*a^2 - 1552/47*a + 302/47)*q^5 + (10/47*a^13 - 51/47*a^12 - 100/47*a^11 + 787/47*a^10 + 84/47*a^9 - 4372/47*a^8 + 1690/47*a^7 + 10547/47*a^6 - 5082/47*a^5 - 10558/47*a^4 + 4194/47*a^3 + 2959/47*a^2 - 1122/47*a + 68/47)*q^6 + (-39/188*a^13 + 65/47*a^12 + 27/47*a^11 - 3685/188*a^10 + 3705/188*a^9 + 4587/47*a^8 - 27647/188*a^7 - 18971/94*a^6 + 34223/94*a^5 + 15263/94*a^4 - 63131/188*a^3 - 6403/188*a^2 + 4062/47*a - 447/47)*q^7 + (a^3 - 4*a)*q^8 + (45/47*a^13 - 206/47*a^12 - 450/47*a^11 + 3001/47*a^10 + 566/47*a^9 - 15679/47*a^8 + 6148/47*a^7 + 35312/47*a^6 - 20331/47*a^5 - 32659/47*a^4 + 18920/47*a^3 + 8357/47*a^2 - 5378/47*a + 635/47)*q^9 + (-25/47*a^13 + 104/47*a^12 + 297/47*a^11 - 1568/47*a^10 - 962/47*a^9 + 8533/47*a^8 - 136/47*a^7 - 20234/47*a^6 + 3869/47*a^5 + 19956/47*a^4 - 3529/47*a^3 - 5447/47*a^2 + 1442/47*a - 76/47)*q^10 + (3/188*a^13 + 37/94*a^12 - 78/47*a^11 - 1047/188*a^10 + 4321/188*a^9 + 2559/94*a^8 - 22993/188*a^7 - 2526/47*a^6 + 27057/94*a^5 + 3779/94*a^4 - 53525/188*a^3 - 1279/188*a^2 + 7911/94*a - 432/47)*q^11 + (-8/47*a^13 + 22/47*a^12 + 127/47*a^11 - 357/47*a^10 - 697/47*a^9 + 2050/47*a^8 + 1562/47*a^7 - 5110/47*a^6 - 1330/47*a^5 + 5758/47*a^4 + 292/47*a^3 - 2809/47*a^2 - 80/47*a + 284/47)*q^12 + (-79/94*a^13 + 323/94*a^12 + 489/47*a^11 - 4859/94*a^10 - 1911/47*a^9 + 26671/94*a^8 + 4509/94*a^7 - 64761/94*a^6 - 28/47*a^5 + 33230/47*a^4 + 745/94*a^3 - 9848/47*a^2 + 1231/94*a + 239/47)*q^13 + (13/94*a^13 - 12/47*a^12 - 112/47*a^11 + 351/94*a^10 + 1491/94*a^9 - 896/47*a^8 - 4853/94*a^7 + 1843/47*a^6 + 4024/47*a^5 - 1265/47*a^4 - 6185/94*a^3 + 129/94*a^2 + 723/47*a - 78/47)*q^14 + (-13/47*a^13 + 71/47*a^12 + 83/47*a^11 - 1009/47*a^10 + 577/47*a^9 + 4941/47*a^8 - 5863/47*a^7 - 9514/47*a^6 + 15358/47*a^5 + 5632/47*a^4 - 14542/47*a^3 + 1093/47*a^2 + 4382/47*a - 784/47)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-57/47*a^13 + 239/47*a^12 + 664/47*a^11 - 3560/47*a^10 - 2058/47*a^9 + 19130/47*a^8 - 797/47*a^7 - 44810/47*a^6 + 9594/47*a^5 + 44069/47*a^4 - 8189/47*a^3 - 13064/47*a^2 + 2297/47*a + 214/47)*q^17 + (64/47*a^13 - 270/47*a^12 - 734/47*a^11 + 4031/47*a^10 + 2051/47*a^9 - 21617/47*a^8 + 2732/47*a^7 + 50139/47*a^6 - 16009/47*a^5 - 48085/47*a^4 + 15242/47*a^3 + 13072/47*a^2 - 4765/47*a + 360/47)*q^18 + (73/47*a^13 - 330/47*a^12 - 777/47*a^11 + 4885/47*a^10 + 1572/47*a^9 - 26003/47*a^8 + 6556/47*a^7 + 59871/47*a^6 - 24794/47*a^5 - 56619/47*a^4 + 22598/47*a^3 + 14358/47*a^2 - 7260/47*a + 816/47)*q^19 + (-27/47*a^13 + 133/47*a^12 + 223/47*a^11 - 1904/47*a^10 + 356/47*a^9 + 9727/47*a^8 - 7477/47*a^7 - 21253/47*a^6 + 21420/47*a^5 + 18928/47*a^4 - 20893/47*a^3 - 4657/47*a^2 + 6028/47*a - 804/47)*q^20 + (43/94*a^13 - 112/47*a^12 - 168/47*a^11 + 3229/94*a^10 - 889/94*a^9 - 8253/47*a^8 + 13753/94*a^7 + 17734/47*a^6 - 19297/47*a^5 - 14658/47*a^4 + 38451/94*a^3 + 4541/94*a^2 - 6365/47*a + 776/47)*q^21 + (23/47*a^13 - 75/47*a^12 - 324/47*a^11 + 1138/47*a^10 + 1575/47*a^9 - 6211/47*a^8 - 3069/47*a^7 + 14703/47*a^6 + 2167/47*a^5 - 14498/47*a^4 - 205/47*a^3 + 4263/47*a^2 - 522/47*a + 6/47)*q^22 + (73/47*a^13 - 613/94*a^12 - 871/47*a^11 + 4603/47*a^10 + 5917/94*a^9 - 49985/94*a^8 - 870/47*a^7 + 118379/94*a^6 - 7310/47*a^5 - 58123/47*a^4 + 5302/47*a^3 + 31301/94*a^2 - 4885/94*a + 17/47)*q^23 + (-46/47*a^13 + 197/47*a^12 + 507/47*a^11 - 2887/47*a^10 - 1270/47*a^9 + 15242/47*a^8 - 2698/47*a^7 - 34952/47*a^6 + 12962/47*a^5 + 33320/47*a^4 - 12421/47*a^3 - 9278/47*a^2 + 3488/47*a - 200/47)*q^24 + (-40/47*a^13 + 157/47*a^12 + 494/47*a^11 - 2302/47*a^10 - 1981/47*a^9 + 12224/47*a^8 + 2875/47*a^7 - 28323/47*a^6 - 2279/47*a^5 + 26957/47*a^4 + 3575/47*a^3 - 6713/47*a^2 - 682/47*a + 245/47)*q^25 + (-151/94*a^13 + 331/47*a^12 + 849/47*a^11 - 9905/94*a^10 - 4455/94*a^9 + 26626/47*a^8 - 7565/94*a^7 - 61885/47*a^6 + 18615/47*a^5 + 59188/47*a^4 - 31783/94*a^3 - 31159/94*a^2 + 4979/47*a - 316/47)*q^26 + (-28/47*a^13 + 124/47*a^12 + 280/47*a^11 - 1790/47*a^10 - 301/47*a^9 + 9149/47*a^8 - 4403/47*a^7 - 19671/47*a^6 + 14897/47*a^5 + 16581/47*a^4 - 15381/47*a^3 - 3275/47*a^2 + 5172/47*a - 604/47)*q^27 + (93/94*a^13 - 216/47*a^12 - 418/47*a^11 + 6177/94*a^10 - 375/94*a^9 - 15611/47*a^8 + 21921/94*a^7 + 33174/47*a^6 - 33083/47*a^5 - 28034/47*a^4 + 65249/94*a^3 + 13179/94*a^2 - 8982/47*a + 946/47)*q^28 + (-231/188*a^13 + 535/94*a^12 + 554/47*a^11 - 15449/188*a^10 - 1461/188*a^9 + 39743/94*a^8 - 39791/188*a^7 - 43506/47*a^6 + 62913/94*a^5 + 76087/94*a^4 - 122299/188*a^3 - 32929/188*a^2 + 18491/94*a - 1046/47)*q^29 + (-7/47*a^13 + 31/47*a^12 + 70/47*a^11 - 424/47*a^10 - 181/47*a^9 + 2158/47*a^8 - 102/47*a^7 - 5000/47*a^6 + 822/47*a^5 + 4815/47*a^4 - 896/47*a^3 - 948/47*a^2 + 776/47*a - 104/47)*q^30 + (-12/47*a^13 + 33/47*a^12 + 214/47*a^11 - 559/47*a^10 - 1492/47*a^9 + 3451/47*a^8 + 5351/47*a^7 - 9451/47*a^6 - 10784/47*a^5 + 11034/47*a^4 + 10966/47*a^3 - 4002/47*a^2 - 3175/47*a + 520/47)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (83/94*a^13 - 214/47*a^12 - 321/47*a^11 + 6095/94*a^10 - 1681/94*a^9 - 15352/47*a^8 + 25495/94*a^7 + 32483/47*a^6 - 34584/47*a^5 - 26985/47*a^4 + 63875/94*a^3 + 11301/94*a^2 - 8656/47*a + 912/47)*q^33 + (-103/47*a^13 + 436/47*a^12 + 1171/47*a^11 - 6447/47*a^10 - 3328/47*a^9 + 34372/47*a^8 - 3542/47*a^7 - 79668/47*a^6 + 22979/47*a^5 + 76684/47*a^4 - 21785/47*a^3 - 21073/47*a^2 + 7054/47*a - 456/47)*q^34 + (-51/94*a^13 + 123/47*a^12 + 255/47*a^11 - 3633/94*a^10 - 701/94*a^9 + 9654/47*a^8 - 5987/94*a^7 - 22263/47*a^6 + 8950/47*a^5 + 21344/47*a^4 - 11839/94*a^3 - 11627/94*a^2 + 591/47*a - 164/47)*q^35 + (24/47*a^13 - 66/47*a^12 - 381/47*a^11 + 977/47*a^10 + 2467/47*a^9 - 5398/47*a^8 - 8493/47*a^7 + 13591/47*a^6 + 16257/47*a^5 - 14736/47*a^4 - 14976/47*a^3 + 4761/47*a^2 + 3436/47*a - 758/47)*q^36 + (143/94*a^13 - 320/47*a^12 - 762/47*a^11 + 9407/94*a^10 + 3241/94*a^9 - 24896/47*a^8 + 11477/94*a^7 + 57121/47*a^6 - 22382/47*a^5 - 53959/47*a^4 + 39689/94*a^3 + 27833/94*a^2 - 5724/47*a + 552/47)*q^37 + O(q^38)
*]> ;  // time = 4.181 seconds




J[285] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 285, 285, 285, 285, 285, 285, 285, 95, 95, 57, 57, 57, 19, 15 ], new_dimensions := [ 1, 1, 1, 2, 2, 2, 2, 3, 4, 1, 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 2, 2, 2, 2, 6, 8, 2, 2, 2, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 47, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 19, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 19, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 5, 47, 1, 1, 1, 1, 0, 1, 1, 1, 81, 1, 3, 3, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 1, 7, 1, 5, 1, 1, 9, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 81, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 1, -1, -1, -2, -2, -4, 2, -1, -4, 4, 0, 0 ],
[ 1, -1, 1, 4, 4, 2, 2, -1, -4, -2, 0, -6 ],
[ -1, 1, -1, -2, -6, 0, -6, 1, -8, 4, 0, 4 ],
[ 2, -2, -2, 4, 0, 8, -8, 2, 4, -4, -4, 8 ],
[ 0, -2, 2, -2, 6, -6, -8, -2, 8, 2, 12, 2 ],
[ 2, 2, -2, 0, 4, -4, 8, -2, 4, 0, -12, -4 ],
[ 0, 2, 2, -2, 6, -2, 0, 2, 0, 6, 4, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 - 2*x - 1,
x^2 - 7,
x^2 - 2*x - 1,
x^2 - 3
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ -1, 1, -1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 3, 1 ],
[ 1, 3, 1 ],
[ 5, 1, 1 ],
[ 47, 1, 1 ],
[ 19, 3, 3 ],
[ 1, 7, 1 ],
[ 3, 3, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 5, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 3, 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 3, 0, 1, 3, 1, 1 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1, 1, 1, 1/9 ], eigenvalues := [*
[ 1, -1, -1, -2, -2, -4, 2, -1, -4, 4, 0, 0 ],
[ 1, -1, 1, 4, 4, 2, 2, -1, -4, -2, 0, -6 ],
[ -1, 1, -1, -2, -6, 0, -6, 1, -8, 4, 0, 4 ],
[
a,
-1,
-1,
a + 1,
-a + 1,
-a + 5,
-2*a - 2,
1,
-4*a + 6,
5*a - 7,
-6*a + 4,
-5*a + 9
],
[
a,
-1,
1,
-a - 1,
a + 3,
-a - 3,
-4,
-1,
-2*a + 4,
-3*a + 1,
6,
-a + 1
],
[
a,
1,
-1,
-a + 1,
-3*a + 5,
-a - 1,
-2*a + 6,
-1,
4*a - 2,
a - 1,
2*a - 8,
-a - 1
],
[
a,
1,
1,
a - 1,
-a + 3,
-a - 1,
0,
1,
-2*a,
-3*a + 3,
-4*a + 2,
3*a - 1
]
*], q_expansions := [*
q + q^2 - q^3 - q^4 - q^5 - q^6 - 2*q^7 - 3*q^8 + q^9 - q^10 - 2*q^11 + q^12 - 4*q^13 - 2*q^14 + q^15 - q^16 + 2*q^17 + q^18 - q^19 + q^20 + 2*q^21 - 2*q^22 - 4*q^23 + 3*q^24 + q^25 - 4*q^26 - q^27 + 2*q^28 + 4*q^29 + q^30 + 5*q^32 + 2*q^33 + 2*q^34 + 2*q^35 - q^36 + O(q^38),
q + q^2 - q^3 - q^4 + q^5 - q^6 + 4*q^7 - 3*q^8 + q^9 + q^10 + 4*q^11 + q^12 + 2*q^13 + 4*q^14 - q^15 - q^16 + 2*q^17 + q^18 - q^19 - q^20 - 4*q^21 + 4*q^22 - 4*q^23 + 3*q^24 + q^25 + 2*q^26 - q^27 - 4*q^28 - 2*q^29 - q^30 + 5*q^32 - 4*q^33 + 2*q^34 + 4*q^35 - q^36 - 6*q^37 + O(q^38),
q - q^2 + q^3 - q^4 - q^5 - q^6 - 2*q^7 + 3*q^8 + q^9 + q^10 - 6*q^11 - q^12 + 2*q^14 - q^15 - q^16 - 6*q^17 - q^18 + q^19 + q^20 - 2*q^21 + 6*q^22 - 8*q^23 + 3*q^24 + q^25 + q^27 + 2*q^28 + 4*q^29 + q^30 - 5*q^32 - 6*q^33 + 6*q^34 + 2*q^35 - q^36 + 4*q^37 + O(q^38),
q + a*q^2 - q^3 + (2*a - 1)*q^4 - q^5 - a*q^6 + (a + 1)*q^7 + (a + 2)*q^8 + q^9 - a*q^10 + (-a + 1)*q^11 + (-2*a + 1)*q^12 + (-a + 5)*q^13 + (3*a + 1)*q^14 + q^15 + 3*q^16 + (-2*a - 2)*q^17 + a*q^18 + q^19 + (-2*a + 1)*q^20 + (-a - 1)*q^21 + (-a - 1)*q^22 + (-4*a + 6)*q^23 + (-a - 2)*q^24 + q^25 + (3*a - 1)*q^26 - q^27 + (5*a + 1)*q^28 + (5*a - 7)*q^29 + a*q^30 + (-6*a + 4)*q^31 + (a - 4)*q^32 + (a - 1)*q^33 + (-6*a - 2)*q^34 + (-a - 1)*q^35 + (2*a - 1)*q^36 + (-5*a + 9)*q^37 + O(q^38),
q + a*q^2 - q^3 + 5*q^4 + q^5 - a*q^6 + (-a - 1)*q^7 + 3*a*q^8 + q^9 + a*q^10 + (a + 3)*q^11 - 5*q^12 + (-a - 3)*q^13 + (-a - 7)*q^14 - q^15 + 11*q^16 - 4*q^17 + a*q^18 - q^19 + 5*q^20 + (a + 1)*q^21 + (3*a + 7)*q^22 + (-2*a + 4)*q^23 - 3*a*q^24 + q^25 + (-3*a - 7)*q^26 - q^27 + (-5*a - 5)*q^28 + (-3*a + 1)*q^29 - a*q^30 + 6*q^31 + 5*a*q^32 + (-a - 3)*q^33 - 4*a*q^34 + (-a - 1)*q^35 + 5*q^36 + (-a + 1)*q^37 + O(q^38),
q + a*q^2 + q^3 + (2*a - 1)*q^4 - q^5 + a*q^6 + (-a + 1)*q^7 + (a + 2)*q^8 + q^9 - a*q^10 + (-3*a + 5)*q^11 + (2*a - 1)*q^12 + (-a - 1)*q^13 + (-a - 1)*q^14 - q^15 + 3*q^16 + (-2*a + 6)*q^17 + a*q^18 - q^19 + (-2*a + 1)*q^20 + (-a + 1)*q^21 + (-a - 3)*q^22 + (4*a - 2)*q^23 + (a + 2)*q^24 + q^25 + (-3*a - 1)*q^26 + q^27 + (-a - 3)*q^28 + (a - 1)*q^29 - a*q^30 + (2*a - 8)*q^31 + (a - 4)*q^32 + (-3*a + 5)*q^33 + (2*a - 2)*q^34 + (a - 1)*q^35 + (2*a - 1)*q^36 + (-a - 1)*q^37 + O(q^38),
q + a*q^2 + q^3 + q^4 + q^5 + a*q^6 + (a - 1)*q^7 - a*q^8 + q^9 + a*q^10 + (-a + 3)*q^11 + q^12 + (-a - 1)*q^13 + (-a + 3)*q^14 + q^15 - 5*q^16 + a*q^18 + q^19 + q^20 + (a - 1)*q^21 + (3*a - 3)*q^22 - 2*a*q^23 - a*q^24 + q^25 + (-a - 3)*q^26 + q^27 + (a - 1)*q^28 + (-3*a + 3)*q^29 + a*q^30 + (-4*a + 2)*q^31 - 3*a*q^32 + (-a + 3)*q^33 + (a - 1)*q^35 + q^36 + (3*a - 1)*q^37 + O(q^38)
*]> ;  // time = 82.009 seconds




J[286] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 286, 286, 286, 286, 286, 286, 286, 143, 143, 143, 26, 26, 11 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 3, 1, 4, 6, 1, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 1, 3, 2, 8, 12, 2, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 15, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 139, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 139, 1, 0, 1, 1, 7, 81, 1, 15, 1, 13, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 9, 0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 5, 1, 1, 1, 81, 1, 1, 1, 0 ], ap_traces := [
[ -1, -1, -1, 1, -1, -1, -1, -4, -8, -8, 0, 7 ],
[ -1, -2, 3, -1, -1, 1, 6, 8, -3, 9, 2, -10 ],
[ 1, 2, -1, 1, -1, -1, 2, -4, 1, 7, -6, -2 ],
[ 1, -1, -3, -5, -1, 1, 7, 0, -4, -8, 0, -3 ],
[ 1, -1, 1, 3, 1, 1, 3, 0, 4, 0, -8, -7 ],
[ 1, 2, 1, -3, 1, 1, -6, 0, 1, -3, 10, 2 ],
[ -3, 1, 2, -4, 3, -3, 3, -12, 5, 13, -2, 7 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^3 - x^2 - 10*x + 8
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ -1, 1, 1 ],
[ -1, 1, -1 ],
[ -1, -1, -1 ],
[ -1, -1, -1 ],
[ 1, -1, 1 ]
], component_group_orders := [
[ 3, 1, 1 ],
[ 5, 1, 3 ],
[ 3, 5, 1 ],
[ 13, 1, 1 ],
[ 5, 1, 5 ],
[ 1, 1, 1 ],
[ 139, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 3 ],
[ 3, 1, 1 ],
[ 13, 1, 1 ],
[ 5, 1, 5 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 1, 5, 1, 1 ], torsion_lower_bounds := [ 1, 3, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1/3, 3, 0, 1, 1, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 0, 1/25, 1, 1 ], eigenvalues := [*
[ -1, -1, -1, 1, -1, -1, -1, -4, -8, -8, 0, 7 ],
[ -1, -2, 3, -1, -1, 1, 6, 8, -3, 9, 2, -10 ],
[ 1, 2, -1, 1, -1, -1, 2, -4, 1, 7, -6, -2 ],
[ 1, -1, -3, -5, -1, 1, 7, 0, -4, -8, 0, -3 ],
[ 1, -1, 1, 3, 1, 1, 3, 0, 4, 0, -8, -7 ],
[ 1, 2, 1, -3, 1, 1, -6, 0, 1, -3, 10, 2 ],
[
-1,
a,
-1/2*a^2 + 1/2*a + 4,
-1/2*a^2 + 1/2*a + 2,
1,
-1,
a^2 - 6,
-4,
-1/2*a^2 - 5/2*a + 6,
-1/2*a^2 - 1/2*a + 8,
a^2 + a - 8,
-a^2 - 2*a + 10
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - q^5 + q^6 + q^7 - q^8 - 2*q^9 + q^10 - q^11 - q^12 - q^13 - q^14 + q^15 + q^16 - q^17 + 2*q^18 - 4*q^19 - q^20 - q^21 + q^22 - 8*q^23 + q^24 - 4*q^25 + q^26 + 5*q^27 + q^28 - 8*q^29 - q^30 - q^32 + q^33 + q^34 - q^35 - 2*q^36 + 7*q^37 + O(q^38),
q - q^2 - 2*q^3 + q^4 + 3*q^5 + 2*q^6 - q^7 - q^8 + q^9 - 3*q^10 - q^11 - 2*q^12 + q^13 + q^14 - 6*q^15 + q^16 + 6*q^17 - q^18 + 8*q^19 + 3*q^20 + 2*q^21 + q^22 - 3*q^23 + 2*q^24 + 4*q^25 - q^26 + 4*q^27 - q^28 + 9*q^29 + 6*q^30 + 2*q^31 - q^32 + 2*q^33 - 6*q^34 - 3*q^35 + q^36 - 10*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 - q^5 + 2*q^6 + q^7 + q^8 + q^9 - q^10 - q^11 + 2*q^12 - q^13 + q^14 - 2*q^15 + q^16 + 2*q^17 + q^18 - 4*q^19 - q^20 + 2*q^21 - q^22 + q^23 + 2*q^24 - 4*q^25 - q^26 - 4*q^27 + q^28 + 7*q^29 - 2*q^30 - 6*q^31 + q^32 - 2*q^33 + 2*q^34 - q^35 + q^36 - 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 3*q^5 - q^6 - 5*q^7 + q^8 - 2*q^9 - 3*q^10 - q^11 - q^12 + q^13 - 5*q^14 + 3*q^15 + q^16 + 7*q^17 - 2*q^18 - 3*q^20 + 5*q^21 - q^22 - 4*q^23 - q^24 + 4*q^25 + q^26 + 5*q^27 - 5*q^28 - 8*q^29 + 3*q^30 + q^32 + q^33 + 7*q^34 + 15*q^35 - 2*q^36 - 3*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + 3*q^7 + q^8 - 2*q^9 + q^10 + q^11 - q^12 + q^13 + 3*q^14 - q^15 + q^16 + 3*q^17 - 2*q^18 + q^20 - 3*q^21 + q^22 + 4*q^23 - q^24 - 4*q^25 + q^26 + 5*q^27 + 3*q^28 - q^30 - 8*q^31 + q^32 - q^33 + 3*q^34 + 3*q^35 - 2*q^36 - 7*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 + q^5 + 2*q^6 - 3*q^7 + q^8 + q^9 + q^10 + q^11 + 2*q^12 + q^13 - 3*q^14 + 2*q^15 + q^16 - 6*q^17 + q^18 + q^20 - 6*q^21 + q^22 + q^23 + 2*q^24 - 4*q^25 + q^26 - 4*q^27 - 3*q^28 - 3*q^29 + 2*q^30 + 10*q^31 + q^32 + 2*q^33 - 6*q^34 - 3*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-1/2*a^2 + 1/2*a + 4)*q^5 - a*q^6 + (-1/2*a^2 + 1/2*a + 2)*q^7 - q^8 + (a^2 - 3)*q^9 + (1/2*a^2 - 1/2*a - 4)*q^10 + q^11 + a*q^12 - q^13 + (1/2*a^2 - 1/2*a - 2)*q^14 + (-a + 4)*q^15 + q^16 + (a^2 - 6)*q^17 + (-a^2 + 3)*q^18 - 4*q^19 + (-1/2*a^2 + 1/2*a + 4)*q^20 + (-3*a + 4)*q^21 - q^22 + (-1/2*a^2 - 5/2*a + 6)*q^23 - a*q^24 + (-3/2*a^2 - 1/2*a + 13)*q^25 + q^26 + (a^2 + 4*a - 8)*q^27 + (-1/2*a^2 + 1/2*a + 2)*q^28 + (-1/2*a^2 - 1/2*a + 8)*q^29 + (a - 4)*q^30 + (a^2 + a - 8)*q^31 - q^32 + a*q^33 + (-a^2 + 6)*q^34 + (-1/2*a^2 - 3/2*a + 10)*q^35 + (a^2 - 3)*q^36 + (-a^2 - 2*a + 10)*q^37 + O(q^38)
*]> ;  // time = 107.98 seconds




J[287] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 287, 287, 287, 287, 287, 287, 41 ], new_dimensions := [ 2, 2, 3, 3, 5, 6, 3 ], dimensions := [ 2, 2, 3, 3, 5, 6, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 19, 1, 1, 0, 1, 1, 97, 13, 1, 1, 1, 0, 61, 1, 1, 1, 1, 1, 61, 0, 1, 1, 1, 1, 97, 1, 1, 0, 37, 1, 19, 13, 1, 1, 37, 0 ], ap_traces := [
[ -1, -1, 1, -2, -2, -8, -4, -1, -5, -5, 5, -10 ],
[ -1, -3, -1, 2, 0, -6, -6, -3, 3, 9, -17, 2 ],
[ 4, 5, 2, -3, -4, 7, 3, -11, -13, 2, 0, 3 ],
[ 1, -1, 6, 3, -6, 9, 1, 13, -11, 10, -2, 3 ],
[ -1, 4, -5, 5, 2, 5, 13, 0, 2, -5, 17, -7 ],
[ -1, -4, -1, -6, 6, 7, 7, 2, 20, -9, -27, 19 ]
], hecke_fields := [
x^2 + x - 1,
x^2 + x - 1,
x^3 - 4*x^2 + 3*x + 1,
x^3 - x^2 - 4*x + 3,
x^5 + x^4 - 6*x^3 - 4*x^2 + 6*x + 3,
x^6 + x^5 - 10*x^4 - 10*x^3 + 23*x^2 + 24*x + 5
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 19, 1 ],
[ 13, 1 ],
[ 1, 1 ],
[ 21, 3 ],
[ 37, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 19, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 21, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 21, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 21, 1 ], l_ratios := [ 0, 0, 1, 1, 1/21, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1, 1, 1 ], eigenvalues := [*
[
a,
-a - 1,
a + 1,
-1,
-1,
-2*a - 5,
-2*a - 3,
3*a + 1,
-a - 3,
-3*a - 4,
5*a + 5,
2*a - 4
],
[
a,
a - 1,
-a - 1,
1,
-2*a - 1,
-3,
4*a - 1,
-3*a - 3,
-a + 1,
3*a + 6,
-a - 9,
6*a + 4
],
[
a,
-a + 3,
-2*a^2 + 4*a + 2,
-1,
2*a^2 - 6*a,
-a^2 + 5*a - 1,
-a^2 - 2*a + 7,
3*a^2 - 8*a - 3,
-2*a^2 + 7*a - 7,
-4*a^2 + 12*a - 2,
-6*a^2 + 18*a - 4,
3*a^2 - 9*a + 3
],
[
a,
a^2 - a - 3,
2,
1,
-2,
-a^2 + 6,
-2*a^2 + a + 6,
a + 4,
-a^2 + a - 1,
-2*a + 4,
-2*a,
5*a^2 - 14
],
[
a,
a + 1,
a^4 - 7*a^2 + a + 6,
1,
-a^4 - a^3 + 3*a^2 + 2*a + 3,
-a^4 - a^3 + 6*a^2 + 3*a - 4,
a^4 + 2*a^3 - 4*a^2 - 7*a + 3,
-a^4 + a^3 + 6*a^2 - 6*a - 4,
2*a^4 - 12*a^2 + a + 9,
2*a^4 + a^3 - 10*a^2 - 3*a + 3,
-a^4 + 7*a^2 - 3*a - 4,
-2*a^4 + 13*a^2 - 3*a - 13
],
[
a,
-a^3 + 5*a,
a^5 - 9*a^3 - a^2 + 19*a + 6,
-1,
a^5 + a^4 - 11*a^3 - 8*a^2 + 30*a + 15,
a^5 + a^4 - 10*a^3 - 8*a^2 + 22*a + 14,
a^3 + a^2 - 5*a - 3,
-a^4 - a^3 + 6*a^2 + 4*a - 2,
-a^3 + 5*a + 4,
2*a^5 + a^4 - 22*a^3 - 11*a^2 + 59*a + 27,
a^5 - 11*a^3 - 3*a^2 + 29*a + 10,
2*a^5 - 19*a^3 - 4*a^2 + 42*a + 23
]
*], q_expansions := [*
q + a*q^2 + (-a - 1)*q^3 + (-a - 1)*q^4 + (a + 1)*q^5 - q^6 - q^7 + (-2*a - 1)*q^8 + (a - 1)*q^9 + q^10 - q^11 + (a + 2)*q^12 + (-2*a - 5)*q^13 - a*q^14 + (-a - 2)*q^15 + 3*a*q^16 + (-2*a - 3)*q^17 + (-2*a + 1)*q^18 + (3*a + 1)*q^19 + (-a - 2)*q^20 + (a + 1)*q^21 - a*q^22 + (-a - 3)*q^23 + (a + 3)*q^24 + (a - 3)*q^25 + (-3*a - 2)*q^26 + (4*a + 3)*q^27 + (a + 1)*q^28 + (-3*a - 4)*q^29 + (-a - 1)*q^30 + (5*a + 5)*q^31 + (a + 5)*q^32 + (a + 1)*q^33 + (-a - 2)*q^34 + (-a - 1)*q^35 + a*q^36 + (2*a - 4)*q^37 + O(q^38),
q + a*q^2 + (a - 1)*q^3 + (-a - 1)*q^4 + (-a - 1)*q^5 + (-2*a + 1)*q^6 + q^7 + (-2*a - 1)*q^8 + (-3*a - 1)*q^9 - q^10 + (-2*a - 1)*q^11 + a*q^12 - 3*q^13 + a*q^14 + a*q^15 + 3*a*q^16 + (4*a - 1)*q^17 + (2*a - 3)*q^18 + (-3*a - 3)*q^19 + (a + 2)*q^20 + (a - 1)*q^21 + (a - 2)*q^22 + (-a + 1)*q^23 + (3*a - 1)*q^24 + (a - 3)*q^25 - 3*a*q^26 + (2*a + 1)*q^27 + (-a - 1)*q^28 + (3*a + 6)*q^29 + (-a + 1)*q^30 + (-a - 9)*q^31 + (a + 5)*q^32 + (3*a - 1)*q^33 + (-5*a + 4)*q^34 + (-a - 1)*q^35 + (a + 4)*q^36 + (6*a + 4)*q^37 + O(q^38),
q + a*q^2 + (-a + 3)*q^3 + (a^2 - 2)*q^4 + (-2*a^2 + 4*a + 2)*q^5 + (-a^2 + 3*a)*q^6 - q^7 + (4*a^2 - 7*a - 1)*q^8 + (a^2 - 6*a + 6)*q^9 + (-4*a^2 + 8*a + 2)*q^10 + (2*a^2 - 6*a)*q^11 + (-a^2 + 5*a - 5)*q^12 + (-a^2 + 5*a - 1)*q^13 - a*q^14 + (-2*a^2 + 4*a + 4)*q^15 + (7*a^2 - 13*a)*q^16 + (-a^2 - 2*a + 7)*q^17 + (-2*a^2 + 3*a - 1)*q^18 + (3*a^2 - 8*a - 3)*q^19 + (-4*a^2 + 6*a)*q^20 + (a - 3)*q^21 + (2*a^2 - 6*a - 2)*q^22 + (-2*a^2 + 7*a - 7)*q^23 + (3*a^2 - 8*a + 1)*q^24 + (-4*a^2 + 12*a - 1)*q^25 + (a^2 + 2*a + 1)*q^26 + (5*a^2 - 18*a + 10)*q^27 + (-a^2 + 2)*q^28 + (-4*a^2 + 12*a - 2)*q^29 + (-4*a^2 + 10*a + 2)*q^30 + (-6*a^2 + 18*a - 4)*q^31 + (7*a^2 - 7*a - 5)*q^32 + (4*a^2 - 12*a + 2)*q^33 + (-6*a^2 + 10*a + 1)*q^34 + (2*a^2 - 4*a - 2)*q^35 + (-7*a^2 + 17*a - 10)*q^36 + (3*a^2 - 9*a + 3)*q^37 + O(q^38),
q + a*q^2 + (a^2 - a - 3)*q^3 + (a^2 - 2)*q^4 + 2*q^5 + (a - 3)*q^6 + q^7 + (a^2 - 3)*q^8 + (-2*a^2 - a + 9)*q^9 + 2*a*q^10 - 2*q^11 + (-a^2 - a + 6)*q^12 + (-a^2 + 6)*q^13 + a*q^14 + (2*a^2 - 2*a - 6)*q^15 + (-a^2 + a + 1)*q^16 + (-2*a^2 + a + 6)*q^17 + (-3*a^2 + a + 6)*q^18 + (a + 4)*q^19 + (2*a^2 - 4)*q^20 + (a^2 - a - 3)*q^21 - 2*a*q^22 + (-a^2 + a - 1)*q^23 + (-2*a^2 + 9)*q^24 - q^25 + (-a^2 + 2*a + 3)*q^26 + (4*a^2 - a - 15)*q^27 + (a^2 - 2)*q^28 + (-2*a + 4)*q^29 + (2*a - 6)*q^30 - 2*a*q^31 + (-2*a^2 - 3*a + 9)*q^32 + (-2*a^2 + 2*a + 6)*q^33 + (-a^2 - 2*a + 6)*q^34 + 2*q^35 + (2*a^2 - 4*a - 9)*q^36 + (5*a^2 - 14)*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + (a^2 - 2)*q^4 + (a^4 - 7*a^2 + a + 6)*q^5 + (a^2 + a)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (a^2 + 2*a - 2)*q^9 + (-a^4 - a^3 + 5*a^2 - 3)*q^10 + (-a^4 - a^3 + 3*a^2 + 2*a + 3)*q^11 + (a^3 + a^2 - 2*a - 2)*q^12 + (-a^4 - a^3 + 6*a^2 + 3*a - 4)*q^13 + a*q^14 + (-a^3 - 2*a^2 + a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 + 2*a^3 - 4*a^2 - 7*a + 3)*q^17 + (a^3 + 2*a^2 - 2*a)*q^18 + (-a^4 + a^3 + 6*a^2 - 6*a - 4)*q^19 + (-2*a^4 - a^3 + 10*a^2 + a - 9)*q^20 + (a + 1)*q^21 + (-3*a^3 - 2*a^2 + 9*a + 3)*q^22 + (2*a^4 - 12*a^2 + a + 9)*q^23 + (a^4 + a^3 - 4*a^2 - 4*a)*q^24 + (2*a^4 + 3*a^3 - 10*a^2 - 9*a + 10)*q^25 + (-a^2 + 2*a + 3)*q^26 + (a^3 + 3*a^2 - 3*a - 5)*q^27 + (a^2 - 2)*q^28 + (2*a^4 + a^3 - 10*a^2 - 3*a + 3)*q^29 + (-a^4 - 2*a^3 + a^2 + 3*a)*q^30 + (-a^4 + 7*a^2 - 3*a - 4)*q^31 + (-a^4 - 2*a^3 + 4*a^2 + 6*a - 3)*q^32 + (-a^4 - 4*a^3 + a^2 + 11*a + 6)*q^33 + (a^4 + 2*a^3 - 3*a^2 - 3*a - 3)*q^34 + (a^4 - 7*a^2 + a + 6)*q^35 + (a^4 + 2*a^3 - 4*a^2 - 4*a + 4)*q^36 + (-2*a^4 + 13*a^2 - 3*a - 13)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 5*a)*q^3 + (a^2 - 2)*q^4 + (a^5 - 9*a^3 - a^2 + 19*a + 6)*q^5 + (-a^4 + 5*a^2)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-a^5 + 10*a^3 + 2*a^2 - 24*a - 8)*q^9 + (-a^5 + a^4 + 9*a^3 - 4*a^2 - 18*a - 5)*q^10 + (a^5 + a^4 - 11*a^3 - 8*a^2 + 30*a + 15)*q^11 + (-a^5 + 7*a^3 - 10*a)*q^12 + (a^5 + a^4 - 10*a^3 - 8*a^2 + 22*a + 14)*q^13 - a*q^14 + (-2*a^5 - a^4 + 20*a^3 + 7*a^2 - 47*a - 15)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^3 + a^2 - 5*a - 3)*q^17 + (a^5 - 8*a^3 - a^2 + 16*a + 5)*q^18 + (-a^4 - a^3 + 6*a^2 + 4*a - 2)*q^19 + (-a^4 + 4*a^3 + 7*a^2 - 19*a - 7)*q^20 + (a^3 - 5*a)*q^21 + (-a^4 + 2*a^3 + 7*a^2 - 9*a - 5)*q^22 + (-a^3 + 5*a + 4)*q^23 + (a^5 - a^4 - 10*a^3 + 3*a^2 + 24*a + 5)*q^24 + (-2*a^5 - a^4 + 22*a^3 + 11*a^2 - 61*a - 24)*q^25 + (2*a^3 - a^2 - 10*a - 5)*q^26 + (2*a^5 + a^4 - 20*a^3 - 9*a^2 + 46*a + 20)*q^27 + (-a^2 + 2)*q^28 + (2*a^5 + a^4 - 22*a^3 - 11*a^2 + 59*a + 27)*q^29 + (a^5 - 13*a^3 - a^2 + 33*a + 10)*q^30 + (a^5 - 11*a^3 - 3*a^2 + 29*a + 10)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-3*a^5 - 2*a^4 + 29*a^3 + 17*a^2 - 69*a - 30)*q^33 + (a^4 + a^3 - 5*a^2 - 3*a)*q^34 + (-a^5 + 9*a^3 + a^2 - 19*a - 6)*q^35 + (a^5 + 2*a^4 - 11*a^3 - 11*a^2 + 29*a + 11)*q^36 + (2*a^5 - 19*a^3 - 4*a^2 + 42*a + 23)*q^37 + O(q^38)
*]> ;  // time = 40.08 seconds




J[290] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 290, 290, 290, 290, 290, 145, 145, 145, 145, 58, 58, 29 ], new_dimensions := [ 1, 2, 2, 3, 3, 1, 2, 3, 3, 1, 1, 2 ], dimensions := [ 1, 2, 2, 3, 3, 2, 4, 6, 6, 2, 2, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 13, 9, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 0, 1, 7, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 0, 1, 1, 1, 1, 49, 1, 23, 1, 1, 1, 1, 1, 0, 1, 1, 1, 625, 1, 1, 13, 1, 1, 1, 1, 1, 0, 1, 5, 1, 3, 1, 9, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 5, 1, 0, 1, 1, 1, 1, 1, 7, 1, 49, 625, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, -1, -2, 2, -6, 2, -2, -6, -1, -6, -2 ],
[ -2, 1, -2, 5, -2, 9, 3, 6, 7, 2, -5, -2 ],
[ -2, 1, 2, 3, 2, -1, -1, 6, -3, -2, 17, 6 ],
[ 3, 3, -3, 3, 0, 3, 3, 0, -15, -3, -9, 0 ],
[ 3, -1, 3, -1, 2, 5, -5, 2, 1, 3, -5, -4 ]
], hecke_fields := [
x - 1,
x^2 - x - 3,
x^2 - x - 3,
x^3 - 3*x^2 - 3*x + 8,
x^3 + x^2 - 7*x + 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 3, 1 ],
[ 23, 1, 3 ],
[ 13, 27, 1 ],
[ 3, 7, 1 ],
[ 49, 7, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 3 ],
[ 1, 27, 1 ],
[ 3, 1, 1 ],
[ 49, 7, 1 ]
], torsion_upper_bounds := [ 1, 3, 3, 3, 7 ], torsion_lower_bounds := [ 1, 3, 3, 3, 1 ], l_ratios := [ 0, 1/3, 3, 1/3, 7 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 1/49 ], eigenvalues := [*
[ -1, 0, -1, -2, 2, -6, 2, -2, -6, -1, -6, -2 ],
[
-1,
a,
-1,
-a + 3,
2*a - 2,
a + 4,
-3*a + 3,
-2*a + 4,
-a + 4,
1,
-3*a - 1,
6*a - 4
],
[
-1,
a,
1,
a + 1,
-2*a + 2,
-a,
a - 1,
-2*a + 4,
-3*a,
-1,
-a + 9,
-2*a + 4
],
[
1,
a,
-1,
-a^2 + 6,
-2*a + 2,
2*a^2 - 3*a - 6,
a^2 - 2*a - 2,
-2*a^2 + 4*a + 6,
-2*a^2 + 3*a + 2,
-1,
a^2 - 2*a - 6,
-2*a^2 + 10
],
[
1,
a,
1,
-a^2 - 2*a + 4,
2*a^2 + 4*a - 8,
-2*a^2 - 5*a + 10,
a^2 + 2*a - 6,
-2*a,
-a,
1,
-3*a^2 - 4*a + 12,
2*a^2 + 4*a - 10
]
*], q_expansions := [*
q - q^2 + q^4 - q^5 - 2*q^7 - q^8 - 3*q^9 + q^10 + 2*q^11 - 6*q^13 + 2*q^14 + q^16 + 2*q^17 + 3*q^18 - 2*q^19 - q^20 - 2*q^22 - 6*q^23 + q^25 + 6*q^26 - 2*q^28 - q^29 - 6*q^31 - q^32 - 2*q^34 + 2*q^35 - 3*q^36 - 2*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - q^5 - a*q^6 + (-a + 3)*q^7 - q^8 + a*q^9 + q^10 + (2*a - 2)*q^11 + a*q^12 + (a + 4)*q^13 + (a - 3)*q^14 - a*q^15 + q^16 + (-3*a + 3)*q^17 - a*q^18 + (-2*a + 4)*q^19 - q^20 + (2*a - 3)*q^21 + (-2*a + 2)*q^22 + (-a + 4)*q^23 - a*q^24 + q^25 + (-a - 4)*q^26 + (-2*a + 3)*q^27 + (-a + 3)*q^28 + q^29 + a*q^30 + (-3*a - 1)*q^31 - q^32 + 6*q^33 + (3*a - 3)*q^34 + (a - 3)*q^35 + a*q^36 + (6*a - 4)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + q^5 - a*q^6 + (a + 1)*q^7 - q^8 + a*q^9 - q^10 + (-2*a + 2)*q^11 + a*q^12 - a*q^13 + (-a - 1)*q^14 + a*q^15 + q^16 + (a - 1)*q^17 - a*q^18 + (-2*a + 4)*q^19 + q^20 + (2*a + 3)*q^21 + (2*a - 2)*q^22 - 3*a*q^23 - a*q^24 + q^25 + a*q^26 + (-2*a + 3)*q^27 + (a + 1)*q^28 - q^29 - a*q^30 + (-a + 9)*q^31 - q^32 - 6*q^33 + (-a + 1)*q^34 + (a + 1)*q^35 + a*q^36 + (-2*a + 4)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - q^5 + a*q^6 + (-a^2 + 6)*q^7 + q^8 + (a^2 - 3)*q^9 - q^10 + (-2*a + 2)*q^11 + a*q^12 + (2*a^2 - 3*a - 6)*q^13 + (-a^2 + 6)*q^14 - a*q^15 + q^16 + (a^2 - 2*a - 2)*q^17 + (a^2 - 3)*q^18 + (-2*a^2 + 4*a + 6)*q^19 - q^20 + (-3*a^2 + 3*a + 8)*q^21 + (-2*a + 2)*q^22 + (-2*a^2 + 3*a + 2)*q^23 + a*q^24 + q^25 + (2*a^2 - 3*a - 6)*q^26 + (3*a^2 - 3*a - 8)*q^27 + (-a^2 + 6)*q^28 - q^29 - a*q^30 + (a^2 - 2*a - 6)*q^31 + q^32 + (-2*a^2 + 2*a)*q^33 + (a^2 - 2*a - 2)*q^34 + (a^2 - 6)*q^35 + (a^2 - 3)*q^36 + (-2*a^2 + 10)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + q^5 + a*q^6 + (-a^2 - 2*a + 4)*q^7 + q^8 + (a^2 - 3)*q^9 + q^10 + (2*a^2 + 4*a - 8)*q^11 + a*q^12 + (-2*a^2 - 5*a + 10)*q^13 + (-a^2 - 2*a + 4)*q^14 + a*q^15 + q^16 + (a^2 + 2*a - 6)*q^17 + (a^2 - 3)*q^18 - 2*a*q^19 + q^20 + (-a^2 - 3*a + 4)*q^21 + (2*a^2 + 4*a - 8)*q^22 - a*q^23 + a*q^24 + q^25 + (-2*a^2 - 5*a + 10)*q^26 + (-a^2 + a - 4)*q^27 + (-a^2 - 2*a + 4)*q^28 + q^29 + a*q^30 + (-3*a^2 - 4*a + 12)*q^31 + q^32 + (2*a^2 + 6*a - 8)*q^33 + (a^2 + 2*a - 6)*q^34 + (-a^2 - 2*a + 4)*q^35 + (a^2 - 3)*q^36 + (2*a^2 + 4*a - 10)*q^37 + O(q^38)
*]> ;  // time = 119.99 seconds




J[291] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 291, 291, 291, 291, 291, 291, 291, 291, 97, 97 ], new_dimensions := [ 1, 1, 1, 1, 2, 2, 2, 7, 3, 4 ], dimensions := [ 1, 1, 1, 1, 2, 2, 2, 7, 6, 8 ], intersection_graph := [ 0, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 3, 1, 1, 5, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 11, 1, 1, 1, 23, 3, 1, 1, 1, 0, 1, 1, 1, 13, 1, 1, 5, 1, 11, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 0, 139, 1, 1, 1, 1, 1, 13, 1, 1, 139, 0, 1, 1, 1, 1, 23, 1, 1, 11, 1, 1, 0 ], ap_traces := [
[ -1, -1, 0, 2, -4, -2, -8, -2, -4, 0, 8, 10 ],
[ -1, -1, -2, -4, 4, 6, 2, -8, 4, 6, 8, -2 ],
[ 2, -1, 1, 2, 4, 0, 2, -2, -8, -3, -1, 4 ],
[ -2, -1, 3, -2, 0, -4, 6, 6, 0, 7, 7, 4 ],
[ -1, -2, -6, 3, -3, -3, 5, -8, 0, -11, -5, -10 ],
[ 3, -2, 6, -3, -7, 7, -1, 4, 8, 7, -9, -14 ],
[ -1, 2, -4, -7, 1, -9, 1, -8, 6, -7, -5, -6 ],
[ 0, 7, 4, 9, -3, 11, -5, 6, -10, 3, 9, 4 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 + x - 3,
x^2 - 3*x + 1,
x^2 + x - 1,
x^7 - 11*x^5 + x^4 + 34*x^3 - 5*x^2 - 24*x - 4
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ 1, -1 ],
[ 1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 23, 1 ],
[ 13, 1 ],
[ 1, 1 ],
[ 11, 1 ],
[ 6811, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 11, 1 ],
[ 6811, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 1, 49 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 49 ], l_ratios := [ 0, 1, 1, 1, 0, 1, 0, 139/49 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 0, 1, 0, 1 ], eigenvalues := [*
[ -1, -1, 0, 2, -4, -2, -8, -2, -4, 0, 8, 10 ],
[ -1, -1, -2, -4, 4, 6, 2, -8, 4, 6, 8, -2 ],
[ 2, -1, 1, 2, 4, 0, 2, -2, -8, -3, -1, 4 ],
[ -2, -1, 3, -2, 0, -4, 6, 6, 0, 7, 7, 4 ],
[
a,
-1,
-3,
-a + 1,
-a - 2,
a - 1,
-3*a + 1,
2*a - 3,
2*a + 1,
a - 5,
3*a - 1,
-5
],
[
a,
-1,
3,
-3*a + 3,
-a - 2,
-a + 5,
-5*a + 7,
2*a - 1,
-2*a + 7,
-a + 5,
3*a - 9,
-7
],
[
a,
1,
-2*a - 3,
a - 3,
3*a + 2,
-a - 5,
a + 1,
-2*a - 5,
-4*a + 1,
5*a - 1,
-a - 3,
8*a + 1
],
[
a,
1,
-1/2*a^6 + 9/2*a^4 - 1/2*a^3 - 10*a^2 + 5/2*a + 4,
1/2*a^6 + 1/2*a^5 - 5*a^4 - 7/2*a^3 + 25/2*a^2 + 3*a - 2,
a^4 - a^3 - 7*a^2 + 5*a + 6,
a^3 - 5*a + 2,
-a^5 - a^4 + 9*a^3 + 7*a^2 - 18*a - 8,
1/2*a^6 + 1/2*a^5 - 4*a^4 - 9/2*a^3 + 11/2*a^2 + 8*a + 4,
1/2*a^6 - 1/2*a^5 - 5*a^4 + 7/2*a^3 + 25/2*a^2 - 5*a - 6,
-1/2*a^6 + 11/2*a^4 - 3/2*a^3 - 15*a^2 + 15/2*a + 4,
a^4 - 6*a^2 + 5,
-2*a^5 - a^4 + 16*a^3 + 7*a^2 - 26*a - 8
]
*], q_expansions := [*
q - q^2 - q^3 - q^4 + q^6 + 2*q^7 + 3*q^8 + q^9 - 4*q^11 + q^12 - 2*q^13 - 2*q^14 - q^16 - 8*q^17 - q^18 - 2*q^19 - 2*q^21 + 4*q^22 - 4*q^23 - 3*q^24 - 5*q^25 + 2*q^26 - q^27 - 2*q^28 + 8*q^31 - 5*q^32 + 4*q^33 + 8*q^34 - q^36 + 10*q^37 + O(q^38),
q - q^2 - q^3 - q^4 - 2*q^5 + q^6 - 4*q^7 + 3*q^8 + q^9 + 2*q^10 + 4*q^11 + q^12 + 6*q^13 + 4*q^14 + 2*q^15 - q^16 + 2*q^17 - q^18 - 8*q^19 + 2*q^20 + 4*q^21 - 4*q^22 + 4*q^23 - 3*q^24 - q^25 - 6*q^26 - q^27 + 4*q^28 + 6*q^29 - 2*q^30 + 8*q^31 - 5*q^32 - 4*q^33 - 2*q^34 + 8*q^35 - q^36 - 2*q^37 + O(q^38),
q + 2*q^2 - q^3 + 2*q^4 + q^5 - 2*q^6 + 2*q^7 + q^9 + 2*q^10 + 4*q^11 - 2*q^12 + 4*q^14 - q^15 - 4*q^16 + 2*q^17 + 2*q^18 - 2*q^19 + 2*q^20 - 2*q^21 + 8*q^22 - 8*q^23 - 4*q^25 - q^27 + 4*q^28 - 3*q^29 - 2*q^30 - q^31 - 8*q^32 - 4*q^33 + 4*q^34 + 2*q^35 + 2*q^36 + 4*q^37 + O(q^38),
q - 2*q^2 - q^3 + 2*q^4 + 3*q^5 + 2*q^6 - 2*q^7 + q^9 - 6*q^10 - 2*q^12 - 4*q^13 + 4*q^14 - 3*q^15 - 4*q^16 + 6*q^17 - 2*q^18 + 6*q^19 + 6*q^20 + 2*q^21 + 4*q^25 + 8*q^26 - q^27 - 4*q^28 + 7*q^29 + 6*q^30 + 7*q^31 + 8*q^32 - 12*q^34 - 6*q^35 + 2*q^36 + 4*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a + 1)*q^4 - 3*q^5 - a*q^6 + (-a + 1)*q^7 - 3*q^8 + q^9 - 3*a*q^10 + (-a - 2)*q^11 + (a - 1)*q^12 + (a - 1)*q^13 + (2*a - 3)*q^14 + 3*q^15 + (-a - 2)*q^16 + (-3*a + 1)*q^17 + a*q^18 + (2*a - 3)*q^19 + (3*a - 3)*q^20 + (a - 1)*q^21 + (-a - 3)*q^22 + (2*a + 1)*q^23 + 3*q^24 + 4*q^25 + (-2*a + 3)*q^26 - q^27 + (-3*a + 4)*q^28 + (a - 5)*q^29 + 3*a*q^30 + (3*a - 1)*q^31 + (-a + 3)*q^32 + (a + 2)*q^33 + (4*a - 9)*q^34 + (3*a - 3)*q^35 + (-a + 1)*q^36 - 5*q^37 + O(q^38),
q + a*q^2 - q^3 + (3*a - 3)*q^4 + 3*q^5 - a*q^6 + (-3*a + 3)*q^7 + (4*a - 3)*q^8 + q^9 + 3*a*q^10 + (-a - 2)*q^11 + (-3*a + 3)*q^12 + (-a + 5)*q^13 + (-6*a + 3)*q^14 - 3*q^15 + (3*a + 2)*q^16 + (-5*a + 7)*q^17 + a*q^18 + (2*a - 1)*q^19 + (9*a - 9)*q^20 + (3*a - 3)*q^21 + (-5*a + 1)*q^22 + (-2*a + 7)*q^23 + (-4*a + 3)*q^24 + 4*q^25 + (2*a + 1)*q^26 - q^27 - 9*a*q^28 + (-a + 5)*q^29 - 3*a*q^30 + (3*a - 9)*q^31 + (3*a + 3)*q^32 + (a + 2)*q^33 + (-8*a + 5)*q^34 + (-9*a + 9)*q^35 + (3*a - 3)*q^36 - 7*q^37 + O(q^38),
q + a*q^2 + q^3 + (-a - 1)*q^4 + (-2*a - 3)*q^5 + a*q^6 + (a - 3)*q^7 + (-2*a - 1)*q^8 + q^9 + (-a - 2)*q^10 + (3*a + 2)*q^11 + (-a - 1)*q^12 + (-a - 5)*q^13 + (-4*a + 1)*q^14 + (-2*a - 3)*q^15 + 3*a*q^16 + (a + 1)*q^17 + a*q^18 + (-2*a - 5)*q^19 + (3*a + 5)*q^20 + (a - 3)*q^21 + (-a + 3)*q^22 + (-4*a + 1)*q^23 + (-2*a - 1)*q^24 + (8*a + 8)*q^25 + (-4*a - 1)*q^26 + q^27 + (3*a + 2)*q^28 + (5*a - 1)*q^29 + (-a - 2)*q^30 + (-a - 3)*q^31 + (a + 5)*q^32 + (3*a + 2)*q^33 + q^34 + (5*a + 7)*q^35 + (-a - 1)*q^36 + (8*a + 1)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-1/2*a^6 + 9/2*a^4 - 1/2*a^3 - 10*a^2 + 5/2*a + 4)*q^5 + a*q^6 + (1/2*a^6 + 1/2*a^5 - 5*a^4 - 7/2*a^3 + 25/2*a^2 + 3*a - 2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^5 + 7*a^3 - 8*a - 2)*q^10 + (a^4 - a^3 - 7*a^2 + 5*a + 6)*q^11 + (a^2 - 2)*q^12 + (a^3 - 5*a + 2)*q^13 + (1/2*a^6 + 1/2*a^5 - 4*a^4 - 9/2*a^3 + 11/2*a^2 + 10*a + 2)*q^14 + (-1/2*a^6 + 9/2*a^4 - 1/2*a^3 - 10*a^2 + 5/2*a + 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^5 - a^4 + 9*a^3 + 7*a^2 - 18*a - 8)*q^17 + a*q^18 + (1/2*a^6 + 1/2*a^5 - 4*a^4 - 9/2*a^3 + 11/2*a^2 + 8*a + 4)*q^19 + (-2*a^4 + a^3 + 12*a^2 - 7*a - 8)*q^20 + (1/2*a^6 + 1/2*a^5 - 5*a^4 - 7/2*a^3 + 25/2*a^2 + 3*a - 2)*q^21 + (a^5 - a^4 - 7*a^3 + 5*a^2 + 6*a)*q^22 + (1/2*a^6 - 1/2*a^5 - 5*a^4 + 7/2*a^3 + 25/2*a^2 - 5*a - 6)*q^23 + (a^3 - 4*a)*q^24 + (-a^6 + 9*a^4 - 19*a^2 + 6)*q^25 + (a^4 - 5*a^2 + 2*a)*q^26 + q^27 + (-1/2*a^6 + 1/2*a^5 + 5*a^4 - 9/2*a^3 - 25/2*a^2 + 8*a + 6)*q^28 + (-1/2*a^6 + 11/2*a^4 - 3/2*a^3 - 15*a^2 + 15/2*a + 4)*q^29 + (-a^5 + 7*a^3 - 8*a - 2)*q^30 + (a^4 - 6*a^2 + 5)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^4 - a^3 - 7*a^2 + 5*a + 6)*q^33 + (-a^6 - a^5 + 9*a^4 + 7*a^3 - 18*a^2 - 8*a)*q^34 + (a^5 - a^4 - 7*a^3 + 7*a^2 + 6*a - 6)*q^35 + (a^2 - 2)*q^36 + (-2*a^5 - a^4 + 16*a^3 + 7*a^2 - 26*a - 8)*q^37 + O(q^38)
*]> ;  // time = 47.281 seconds




J[293] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 293, 293 ], new_dimensions := [ 8, 16 ], dimensions := [ 8, 16 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -3, -8, -1, -13, -9, -8, -2, -15, -8, 7, -9, -23 ],
[ 3, 10, 1, 15, 9, 10, -4, 19, 4, -7, 7, 19 ]
], hecke_fields := [
x^8 + 3*x^7 - 4*x^6 - 15*x^5 + 4*x^4 + 21*x^3 - 2*x^2 - 8*x + 1,
x^16 - 3*x^15 - 22*x^14 + 69*x^13 + 184*x^12 - 621*x^11 - 716*x^10 + 2758*x^9 + 1234*x^8 - 6287*x^7 - 554*x^6 + 7023*x^5 - 572*x^4 - 3385*x^3 + 508*x^2 + 526*x - 111
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 73 ]
], tamagawa_numbers := [
[ 1 ],
[ 73 ]
], torsion_upper_bounds := [ 1, 73 ], torsion_lower_bounds := [ 1, 73 ], l_ratios := [ 0, 1/73 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
a^5 + a^4 - 5*a^3 - 3*a^2 + 5*a,
-a^6 - 3*a^5 + 3*a^4 + 12*a^3 - a^2 - 10*a,
a^6 + 2*a^5 - 4*a^4 - 6*a^3 + 4*a^2 + a - 2,
-2*a^7 - 4*a^6 + 10*a^5 + 17*a^4 - 16*a^3 - 17*a^2 + 9*a + 1,
a^7 + 3*a^6 - 4*a^5 - 15*a^4 + 2*a^3 + 19*a^2 + 4*a - 6,
2*a^7 + 7*a^6 - 3*a^5 - 29*a^4 - 12*a^3 + 30*a^2 + 14*a - 9,
-a^7 - 5*a^6 + 25*a^4 + 13*a^3 - 34*a^2 - 12*a + 8,
2*a^7 + 6*a^6 - 6*a^5 - 27*a^4 - 2*a^3 + 29*a^2 + 8*a - 5,
-a^7 - 5*a^6 + 23*a^4 + 12*a^3 - 25*a^2 - 11*a + 5,
-a^6 - 2*a^5 + 6*a^4 + 10*a^3 - 13*a^2 - 12*a + 8,
-3*a^7 - 9*a^6 + 9*a^5 + 38*a^4 - 2*a^3 - 37*a^2 + a + 2
],
[
a,
-577/16858*a^15 + 4393/33716*a^14 + 16563/33716*a^13 - 18220/8429*a^12 - 74523/33716*a^11 + 435367/33716*a^10 + 21555/8429*a^9 - 286976/8429*a^8 + 130715/33716*a^7 + 1398031/33716*a^6 - 320453/33716*a^5 - 230781/8429*a^4 + 82231/8429*a^3 + 483617/33716*a^2 - 38240/8429*a - 18467/8429,
761/33716*a^15 - 713/33716*a^14 - 17781/33716*a^13 + 6135/16858*a^12 + 163023/33716*a^11 - 65719/33716*a^10 - 739285/33716*a^9 + 44693/33716*a^8 + 1715335/33716*a^7 + 154804/8429*a^6 - 1882511/33716*a^5 - 1693565/33716*a^4 + 697325/33716*a^3 + 319291/8429*a^2 + 78445/33716*a - 86901/16858,
297/16858*a^15 - 479/33716*a^14 - 3143/8429*a^13 + 949/33716*a^12 + 115053/33716*a^11 + 34451/16858*a^10 - 597641/33716*a^9 - 139484/8429*a^8 + 1843485/33716*a^7 + 751603/16858*a^6 - 1559611/16858*a^5 - 1306309/33716*a^4 + 1221403/16858*a^3 - 53941/33716*a^2 - 576815/33716*a + 54207/8429,
-233/33716*a^15 + 1511/67432*a^14 + 8529/67432*a^13 - 16297/67432*a^12 - 49515/33716*a^11 + 18855/67432*a^10 + 844103/67432*a^9 + 245827/67432*a^8 - 4050371/67432*a^7 - 567485/67432*a^6 + 4635547/33716*a^5 - 340967/67432*a^4 - 8679221/67432*a^3 + 1068839/67432*a^2 + 1152697/33716*a - 303691/67432,
-623/33716*a^15 + 193/8429*a^14 + 5855/16858*a^13 - 9325/33716*a^12 - 82399/33716*a^11 + 6083/16858*a^10 + 130703/16858*a^9 + 62912/8429*a^8 - 155665/16858*a^7 - 1292109/33716*a^6 - 175301/33716*a^5 + 611969/8429*a^4 + 172165/8429*a^3 - 1923829/33716*a^2 - 471027/33716*a + 411913/33716,
5121/67432*a^15 - 20349/67432*a^14 - 59089/67432*a^13 + 79407/16858*a^12 + 58193/67432*a^11 - 1662399/67432*a^10 + 1575357/67432*a^9 + 2934123/67432*a^8 - 7273265/67432*a^7 + 145400/8429*a^6 + 12534279/67432*a^5 - 7704035/67432*a^4 - 9352905/67432*a^3 + 1452333/16858*a^2 + 2408533/67432*a - 229595/16858,
-1175/16858*a^15 - 6285/67432*a^14 + 169263/67432*a^13 + 8299/67432*a^12 - 248807/8429*a^11 + 947657/67432*a^10 + 10419633/67432*a^9 - 7553201/67432*a^8 - 25892511/67432*a^7 + 21334795/67432*a^6 + 14788541/33716*a^5 - 24100153/67432*a^4 - 14102421/67432*a^3 + 9874977/67432*a^2 + 1128119/33716*a - 1024209/67432,
-89/16858*a^15 - 763/67432*a^14 + 19937/67432*a^13 - 25799/67432*a^12 - 59937/16858*a^11 + 571695/67432*a^10 + 1027195/67432*a^9 - 3749195/67432*a^8 - 1173729/67432*a^7 + 10430077/67432*a^6 - 867699/33716*a^5 - 12637907/67432*a^4 + 3065513/67432*a^3 + 5895535/67432*a^2 - 301955/33716*a - 589459/67432,
3885/33716*a^15 - 11349/33716*a^14 - 71413/33716*a^13 + 103847/16858*a^12 + 522739/33716*a^11 - 1459075/33716*a^10 - 2073633/33716*a^9 + 5057349/33716*a^8 + 5231307/33716*a^7 - 2358918/8429*a^6 - 8467211/33716*a^5 + 9665959/33716*a^4 + 7114909/33716*a^3 - 1254647/8429*a^2 - 1876887/33716*a + 443941/16858,
5441/33716*a^15 - 2335/8429*a^14 - 66207/16858*a^13 + 220255/33716*a^12 + 1248809/33716*a^11 - 997553/16858*a^10 - 2874303/16858*a^9 + 2172635/8429*a^8 + 6711855/16858*a^7 - 18695269/33716*a^6 - 15276237/33716*a^5 + 4657938/8429*a^4 + 1932769/8429*a^3 - 7449369/33716*a^2 - 1475651/33716*a + 857921/33716,
4927/33716*a^15 - 2054/8429*a^14 - 110779/33716*a^13 + 171783/33716*a^12 + 244061/8429*a^11 - 1399111/33716*a^10 - 2122319/16858*a^9 + 5594357/33716*a^8 + 2351622/8429*a^7 - 2849107/8429*a^6 - 9947321/33716*a^5 + 2797941/8429*a^4 + 4322749/33716*a^3 - 4462107/33716*a^2 - 395485/16858*a + 225443/16858
]
*], q_expansions := [*
q + a*q^2 + (a^5 + a^4 - 5*a^3 - 3*a^2 + 5*a)*q^3 + (a^2 - 2)*q^4 + (-a^6 - 3*a^5 + 3*a^4 + 12*a^3 - a^2 - 10*a)*q^5 + (a^6 + a^5 - 5*a^4 - 3*a^3 + 5*a^2)*q^6 + (a^6 + 2*a^5 - 4*a^4 - 6*a^3 + 4*a^2 + a - 2)*q^7 + (a^3 - 4*a)*q^8 + (a^7 + 2*a^6 - 7*a^5 - 10*a^4 + 18*a^3 + 12*a^2 - 15*a - 1)*q^9 + (-a^7 - 3*a^6 + 3*a^5 + 12*a^4 - a^3 - 10*a^2)*q^10 + (-2*a^7 - 4*a^6 + 10*a^5 + 17*a^4 - 16*a^3 - 17*a^2 + 9*a + 1)*q^11 + (a^7 + a^6 - 7*a^5 - 5*a^4 + 15*a^3 + 6*a^2 - 10*a)*q^12 + (a^7 + 3*a^6 - 4*a^5 - 15*a^4 + 2*a^3 + 19*a^2 + 4*a - 6)*q^13 + (a^7 + 2*a^6 - 4*a^5 - 6*a^4 + 4*a^3 + a^2 - 2*a)*q^14 + (-a^7 - 2*a^6 + 7*a^5 + 11*a^4 - 16*a^3 - 13*a^2 + 12*a - 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^7 + 7*a^6 - 3*a^5 - 29*a^4 - 12*a^3 + 30*a^2 + 14*a - 9)*q^17 + (-a^7 - 3*a^6 + 5*a^5 + 14*a^4 - 9*a^3 - 13*a^2 + 7*a - 1)*q^18 + (-a^7 - 5*a^6 + 25*a^4 + 13*a^3 - 34*a^2 - 12*a + 8)*q^19 + (a^6 + 3*a^5 - 3*a^4 - 13*a^3 + 12*a + 1)*q^20 + (-2*a^7 - 5*a^6 + 6*a^5 + 18*a^4 - a^3 - 11*a^2 + a - 1)*q^21 + (2*a^7 + 2*a^6 - 13*a^5 - 8*a^4 + 25*a^3 + 5*a^2 - 15*a + 2)*q^22 + (2*a^7 + 6*a^6 - 6*a^5 - 27*a^4 - 2*a^3 + 29*a^2 + 8*a - 5)*q^23 + (-2*a^7 - 5*a^6 + 8*a^5 + 21*a^4 - 9*a^3 - 18*a^2 + 8*a - 1)*q^24 + (2*a^7 + 6*a^6 - 7*a^5 - 27*a^4 + 4*a^3 + 28*a^2 + a - 4)*q^25 + (-2*a^4 - 2*a^3 + 6*a^2 + 2*a - 1)*q^26 + (-3*a^7 - 7*a^6 + 14*a^5 + 29*a^4 - 22*a^3 - 23*a^2 + 17*a - 5)*q^27 + (-a^7 - 2*a^6 + 5*a^5 + 8*a^4 - 8*a^3 - 8*a^2 + 6*a + 3)*q^28 + (-a^7 - 5*a^6 + 23*a^4 + 12*a^3 - 25*a^2 - 11*a + 5)*q^29 + (a^7 + 3*a^6 - 4*a^5 - 12*a^4 + 8*a^3 + 10*a^2 - 10*a + 1)*q^30 + (-a^6 - 2*a^5 + 6*a^4 + 10*a^3 - 13*a^2 - 12*a + 8)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2*a^7 + 4*a^6 - 12*a^5 - 18*a^4 + 29*a^3 + 18*a^2 - 26*a + 4)*q^33 + (a^7 + 5*a^6 + a^5 - 20*a^4 - 12*a^3 + 18*a^2 + 7*a - 2)*q^34 + (2*a^7 + 7*a^6 - 3*a^5 - 27*a^4 - 10*a^3 + 19*a^2 + 8*a + 1)*q^35 + (-2*a^7 - 3*a^6 + 13*a^5 + 15*a^4 - 28*a^3 - 19*a^2 + 21*a + 3)*q^36 + (-3*a^7 - 9*a^6 + 9*a^5 + 38*a^4 - 2*a^3 - 37*a^2 + a + 2)*q^37 + O(q^38),
q + a*q^2 + (-577/16858*a^15 + 4393/33716*a^14 + 16563/33716*a^13 - 18220/8429*a^12 - 74523/33716*a^11 + 435367/33716*a^10 + 21555/8429*a^9 - 286976/8429*a^8 + 130715/33716*a^7 + 1398031/33716*a^6 - 320453/33716*a^5 - 230781/8429*a^4 + 82231/8429*a^3 + 483617/33716*a^2 - 38240/8429*a - 18467/8429)*q^3 + (a^2 - 2)*q^4 + (761/33716*a^15 - 713/33716*a^14 - 17781/33716*a^13 + 6135/16858*a^12 + 163023/33716*a^11 - 65719/33716*a^10 - 739285/33716*a^9 + 44693/33716*a^8 + 1715335/33716*a^7 + 154804/8429*a^6 - 1882511/33716*a^5 - 1693565/33716*a^4 + 697325/33716*a^3 + 319291/8429*a^2 + 78445/33716*a - 86901/16858)*q^5 + (931/33716*a^15 - 8825/33716*a^14 + 3373/16858*a^13 + 137813/33716*a^12 - 281267/33716*a^11 - 185011/8429*a^10 + 508707/8429*a^9 + 1554751/33716*a^8 - 5857167/33716*a^7 - 959769/33716*a^6 + 3590709/16858*a^5 - 82791/8429*a^4 - 3422673/33716*a^3 + 108318/8429*a^2 + 133284/8429*a - 64047/16858)*q^6 + (297/16858*a^15 - 479/33716*a^14 - 3143/8429*a^13 + 949/33716*a^12 + 115053/33716*a^11 + 34451/16858*a^10 - 597641/33716*a^9 - 139484/8429*a^8 + 1843485/33716*a^7 + 751603/16858*a^6 - 1559611/16858*a^5 - 1306309/33716*a^4 + 1221403/16858*a^3 - 53941/33716*a^2 - 576815/33716*a + 54207/8429)*q^7 + (a^3 - 4*a)*q^8 + (-6493/67432*a^15 + 15609/67432*a^14 + 114805/67432*a^13 - 122391/33716*a^12 - 789151/67432*a^11 + 1292555/67432*a^10 + 2819513/67432*a^9 - 2376333/67432*a^8 - 6046011/67432*a^7 - 62305/16858*a^6 + 7703439/67432*a^5 + 3916345/67432*a^4 - 4410473/67432*a^3 - 252993/8429*a^2 + 589083/67432*a + 103289/33716)*q^9 + (785/16858*a^15 - 1039/33716*a^14 - 40239/33716*a^13 + 22999/33716*a^12 + 203431/16858*a^11 - 194409/33716*a^10 - 2054145/33716*a^9 + 776261/33716*a^8 + 5403623/33716*a^7 - 1460917/33716*a^6 - 1759517/8429*a^5 + 1132617/33716*a^4 + 3853149/33716*a^3 - 308143/33716*a^2 - 143522/8429*a + 84471/33716)*q^10 + (-233/33716*a^15 + 1511/67432*a^14 + 8529/67432*a^13 - 16297/67432*a^12 - 49515/33716*a^11 + 18855/67432*a^10 + 844103/67432*a^9 + 245827/67432*a^8 - 4050371/67432*a^7 - 567485/67432*a^6 + 4635547/33716*a^5 - 340967/67432*a^4 - 8679221/67432*a^3 + 1068839/67432*a^2 + 1152697/33716*a - 303691/67432)*q^11 + (-931/8429*a^15 + 9221/16858*a^14 + 10112/8429*a^13 - 306811/33716*a^12 - 12847/33716*a^11 + 915345/16858*a^10 - 1185387/33716*a^9 - 4710213/33716*a^8 + 2315999/16858*a^7 + 2450565/16858*a^6 - 6228671/33716*a^5 - 1043893/33716*a^4 + 2926859/33716*a^3 - 453523/16858*a^2 - 77970/8429*a + 251077/33716)*q^12 + (-623/33716*a^15 + 193/8429*a^14 + 5855/16858*a^13 - 9325/33716*a^12 - 82399/33716*a^11 + 6083/16858*a^10 + 130703/16858*a^9 + 62912/8429*a^8 - 155665/16858*a^7 - 1292109/33716*a^6 - 175301/33716*a^5 + 611969/8429*a^4 + 172165/8429*a^3 - 1923829/33716*a^2 - 471027/33716*a + 411913/33716)*q^13 + (1303/33716*a^15 + 124/8429*a^14 - 40037/33716*a^13 + 5757/33716*a^12 + 109444/8429*a^11 - 172337/33716*a^10 - 549047/8429*a^9 + 1110489/33716*a^8 + 1309421/8429*a^7 - 1395073/16858*a^6 - 5477971/33716*a^5 + 1391287/16858*a^4 + 1956749/33716*a^3 - 878567/33716*a^2 - 23904/8429*a + 32967/16858)*q^14 + (3143/33716*a^15 - 1527/33716*a^14 - 92887/33716*a^13 + 37965/16858*a^12 + 1004213/33716*a^11 - 987525/33716*a^10 - 5120447/33716*a^9 + 5359527/33716*a^8 + 12997241/33716*a^7 - 3321223/8429*a^6 - 15984413/33716*a^5 + 14449993/33716*a^4 + 8619091/33716*a^3 - 1483825/8429*a^2 - 1584757/33716*a + 378501/16858)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (5121/67432*a^15 - 20349/67432*a^14 - 59089/67432*a^13 + 79407/16858*a^12 + 58193/67432*a^11 - 1662399/67432*a^10 + 1575357/67432*a^9 + 2934123/67432*a^8 - 7273265/67432*a^7 + 145400/8429*a^6 + 12534279/67432*a^5 - 7704035/67432*a^4 - 9352905/67432*a^3 + 1452333/16858*a^2 + 2408533/67432*a - 229595/16858)*q^17 + (-1935/33716*a^15 - 28041/67432*a^14 + 203235/67432*a^13 + 405561/67432*a^12 - 1369799/33716*a^11 - 1829475/67432*a^10 + 15531361/67432*a^9 + 1966351/67432*a^8 - 41070711/67432*a^7 + 4106317/67432*a^6 + 12379171/16858*a^5 - 8124469/67432*a^4 - 24002749/67432*a^3 + 3887527/67432*a^2 + 452737/8429*a - 720723/67432)*q^18 + (-1175/16858*a^15 - 6285/67432*a^14 + 169263/67432*a^13 + 8299/67432*a^12 - 248807/8429*a^11 + 947657/67432*a^10 + 10419633/67432*a^9 - 7553201/67432*a^8 - 25892511/67432*a^7 + 21334795/67432*a^6 + 14788541/33716*a^5 - 24100153/67432*a^4 - 14102421/67432*a^3 + 9874977/67432*a^2 + 1128119/33716*a - 1024209/67432)*q^19 + (2149/33716*a^15 - 4273/33716*a^14 - 49769/33716*a^13 + 46721/16858*a^12 + 454515/33716*a^11 - 798587/33716*a^10 - 2075229/33716*a^9 + 3376857/33716*a^8 + 4979003/33716*a^7 - 1851680/8429*a^6 - 6128471/33716*a^5 + 8138319/33716*a^4 + 3611657/33716*a^3 - 981494/8429*a^2 - 898239/33716*a + 260937/16858)*q^20 + (-3727/67432*a^15 + 34749/67432*a^14 + 2283/67432*a^13 - 315879/33716*a^12 + 698567/67432*a^11 + 4351209/67432*a^10 - 6199965/67432*a^9 - 14307941/67432*a^8 + 21373537/67432*a^7 + 5839007/16858*a^6 - 33476305/67432*a^5 - 17215569/67432*a^4 + 22724119/67432*a^3 + 1910969/33716*a^2 - 4949557/67432*a + 28470/8429)*q^21 + (113/67432*a^15 - 1723/67432*a^14 + 15857/67432*a^13 - 6643/33716*a^12 - 270531/67432*a^11 + 510447/67432*a^10 + 1531055/67432*a^9 - 3475327/67432*a^8 - 3497227/67432*a^7 + 4506465/33716*a^6 + 2931751/67432*a^5 - 8945773/67432*a^4 - 508571/67432*a^3 + 1271061/33716*a^2 - 58575/67432*a - 25863/33716)*q^22 + (-89/16858*a^15 - 763/67432*a^14 + 19937/67432*a^13 - 25799/67432*a^12 - 59937/16858*a^11 + 571695/67432*a^10 + 1027195/67432*a^9 - 3749195/67432*a^8 - 1173729/67432*a^7 + 10430077/67432*a^6 - 867699/33716*a^5 - 12637907/67432*a^4 + 3065513/67432*a^3 + 5895535/67432*a^2 - 301955/33716*a - 589459/67432)*q^23 + (1352/8429*a^15 - 11915/16858*a^14 - 63347/33716*a^13 + 396743/33716*a^12 + 20155/8429*a^11 - 2371683/33716*a^10 + 1490923/33716*a^9 + 1529478/8429*a^8 - 1699331/8429*a^7 - 6372229/33716*a^6 + 10746923/33716*a^5 + 1459059/33716*a^4 - 1666860/8429*a^3 + 178342/8429*a^2 + 1143629/33716*a - 39294/8429)*q^24 + (a^5 - a^4 - 8*a^3 + 6*a^2 + 11*a - 2)*q^25 + (-1097/33716*a^15 - 499/8429*a^14 + 16831/16858*a^13 + 32233/33716*a^12 - 374717/33716*a^11 - 92331/16858*a^10 + 984941/16858*a^9 + 114363/8429*a^8 - 2604455/16858*a^7 - 520443/33716*a^6 + 6823205/33716*a^5 + 83076/8429*a^4 - 1008171/8429*a^3 - 154543/33716*a^2 + 739611/33716*a - 69153/33716)*q^26 + (-2391/16858*a^15 + 21931/67432*a^14 + 188033/67432*a^13 - 386241/67432*a^12 - 743351/33716*a^11 + 2535427/67432*a^10 + 6212625/67432*a^9 - 7797103/67432*a^8 - 15059699/67432*a^7 + 12008445/67432*a^6 + 10430123/33716*a^5 - 9886125/67432*a^4 - 14378143/67432*a^3 + 4822557/67432*a^2 + 865695/16858*a - 859003/67432)*q^27 + (3217/33716*a^15 - 10413/33716*a^14 - 29503/16858*a^13 + 98063/16858*a^12 + 101680/8429*a^11 - 350261/8429*a^10 - 1287903/33716*a^9 + 2372827/16858*a^8 + 1714845/33716*a^7 - 7762521/33716*a^6 - 129951/33716*a^5 + 5314683/33716*a^4 - 338381/8429*a^3 - 324829/16858*a^2 + 267093/16858*a - 289023/33716)*q^28 + (3885/33716*a^15 - 11349/33716*a^14 - 71413/33716*a^13 + 103847/16858*a^12 + 522739/33716*a^11 - 1459075/33716*a^10 - 2073633/33716*a^9 + 5057349/33716*a^8 + 5231307/33716*a^7 - 2358918/8429*a^6 - 8467211/33716*a^5 + 9665959/33716*a^4 + 7114909/33716*a^3 - 1254647/8429*a^2 - 1876887/33716*a + 443941/16858)*q^29 + (3951/16858*a^15 - 23741/33716*a^14 - 140937/33716*a^13 + 425901/33716*a^12 + 482139/16858*a^11 - 2870059/33716*a^10 - 3308867/33716*a^9 + 9118779/33716*a^8 + 6475149/33716*a^7 - 14243191/33716*a^6 - 1905824/8429*a^5 + 10416887/33716*a^4 + 4703755/33716*a^3 - 3181401/33716*a^2 - 224054/8429*a + 348873/33716)*q^30 + (5441/33716*a^15 - 2335/8429*a^14 - 66207/16858*a^13 + 220255/33716*a^12 + 1248809/33716*a^11 - 997553/16858*a^10 - 2874303/16858*a^9 + 2172635/8429*a^8 + 6711855/16858*a^7 - 18695269/33716*a^6 - 15276237/33716*a^5 + 4657938/8429*a^4 + 1932769/8429*a^3 - 7449369/33716*a^2 - 1475651/33716*a + 857921/33716)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (7627/67432*a^15 - 26485/67432*a^14 - 118883/67432*a^13 + 120843/16858*a^12 + 557463/67432*a^11 - 3324969/67432*a^10 - 57837/67432*a^9 + 10753195/67432*a^8 - 6422889/67432*a^7 - 4137811/16858*a^6 + 17473811/67432*a^5 + 10022511/67432*a^4 - 15934065/67432*a^3 + 92679/33716*a^2 + 3452181/67432*a - 559909/33716)*q^33 + (-2493/33716*a^15 + 53573/67432*a^14 - 35721/67432*a^13 - 884071/67432*a^12 + 758871/33716*a^11 + 5241993/67432*a^10 - 11189595/67432*a^9 - 13592579/67432*a^8 + 33358927/67432*a^7 + 15371313/67432*a^6 - 21834409/33716*a^5 - 6423693/67432*a^4 + 23143917/67432*a^3 - 192935/67432*a^2 - 1806013/33716*a + 568431/67432)*q^34 + (-310/8429*a^15 + 1323/16858*a^14 + 16159/16858*a^13 - 19198/8429*a^12 - 153209/16858*a^11 + 408081/16858*a^10 + 328446/8429*a^9 - 1017757/8429*a^8 - 1273781/16858*a^7 + 4983679/16858*a^6 + 1043581/16858*a^5 - 2853271/8429*a^4 - 265542/8429*a^3 + 2585371/16858*a^2 + 127797/8429*a - 153261/8429)*q^35 + (-26665/67432*a^15 + 86877/67432*a^14 + 442981/67432*a^13 - 768977/33716*a^12 - 2654443/67432*a^11 + 10175331/67432*a^10 + 7000785/67432*a^9 - 31542465/67432*a^8 - 8132351/67432*a^7 + 5983893/8429*a^6 + 3647663/67432*a^5 - 34049079/67432*a^4 - 391477/67432*a^3 + 1204468/8429*a^2 + 136731/67432*a - 421363/33716)*q^36 + (4927/33716*a^15 - 2054/8429*a^14 - 110779/33716*a^13 + 171783/33716*a^12 + 244061/8429*a^11 - 1399111/33716*a^10 - 2122319/16858*a^9 + 5594357/33716*a^8 + 2351622/8429*a^7 - 2849107/8429*a^6 - 9947321/33716*a^5 + 2797941/8429*a^4 + 4322749/33716*a^3 - 4462107/33716*a^2 - 395485/16858*a + 225443/16858)*q^37 + O(q^38)
*]> ;  // time = 4.84 seconds




J[295] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 295, 295, 295, 295, 59 ], new_dimensions := [ 3, 3, 6, 7, 5 ], dimensions := [ 3, 3, 6, 7, 10 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 107, 1, 1, 0, 1, 1, 1, 1, 1, 0, 6629, 1, 107, 1, 6629, 0 ], ap_traces := [
[ -1, -1, -3, 0, -9, 1, -12, -1, -3, -12, -7, 6 ],
[ -3, -3, 3, -6, 3, -9, -18, 3, -3, -12, 3, -6 ],
[ 2, 1, 6, 2, 3, 11, 16, -5, 11, 6, -11, 10 ],
[ 1, 3, -7, -4, 3, -9, 24, 3, 3, 4, -1, -24 ]
], hecke_fields := [
x^3 + x^2 - 2*x - 1,
x^3 + 3*x^2 - 3,
x^6 - 2*x^5 - 6*x^4 + 11*x^3 + 8*x^2 - 11*x - 3,
x^7 - x^6 - 10*x^5 + 7*x^4 + 27*x^3 - 11*x^2 - 10*x - 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 107, 1 ],
[ 5, 1 ],
[ 6629, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 107, 1 ],
[ 5, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 5, 1 ], torsion_lower_bounds := [ 1, 1, 5, 1 ], l_ratios := [ 0, 0, 1/5, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
a,
-a^2 - a + 1,
-1,
2*a^2 + a - 3,
-a^2 - 2*a - 2,
2*a^2 - 3,
-a^2 - 2*a - 3,
2*a^2 + 5*a - 2,
-3*a^2 + 4,
-3*a^2 + 1,
-2*a^2 - 3*a,
-4*a^2 + 4*a + 10
],
[
a,
a^2 + a - 3,
1,
-2*a^2 - 3*a + 1,
-a^2 + 4,
2*a^2 + 2*a - 7,
-a^2 - 2*a - 5,
-3*a - 2,
3*a^2 + 8*a - 2,
a^2 + 4*a - 3,
-2*a^2 - 5*a + 2,
-4*a^2 - 8*a + 2
],
[
a,
-a^5 + a^4 + 6*a^3 - 4*a^2 - 7*a + 1,
1,
a^5 - 7*a^3 - a^2 + 10*a + 3,
a^4 - a^3 - 5*a^2 + 3*a + 4,
-a^4 + a^3 + 4*a^2 - 3*a + 1,
a^5 - a^4 - 7*a^3 + 5*a^2 + 10*a,
a^3 - a^2 - 3*a + 1,
a^5 - 2*a^4 - 6*a^3 + 9*a^2 + 5*a - 1,
-a^5 - a^4 + 9*a^3 + 7*a^2 - 18*a - 8,
-a^3 + a^2 + a - 3,
-a^5 - a^4 + 7*a^3 + 8*a^2 - 10*a - 9
],
[
a,
a^5 - 3*a^4 - 4*a^3 + 14*a^2 - a - 3,
-1,
a^6 - a^5 - 10*a^4 + 8*a^3 + 25*a^2 - 15*a - 4,
-a^6 + 2*a^5 + 5*a^4 - 8*a^3 - 3*a^2 - 2*a + 3,
-2*a^6 + 4*a^5 + 15*a^4 - 23*a^3 - 30*a^2 + 23*a + 7,
a^6 - a^5 - 9*a^4 + 6*a^3 + 21*a^2 - 9*a - 1,
a^6 - 2*a^5 - 10*a^4 + 16*a^3 + 27*a^2 - 30*a - 6,
3*a^6 - 5*a^5 - 24*a^4 + 31*a^3 + 51*a^2 - 40*a - 14,
-a^6 + 3*a^5 + 5*a^4 - 14*a^3 - 5*a^2 + a + 5,
-3*a^6 + 4*a^5 + 26*a^4 - 24*a^3 - 59*a^2 + 30*a + 12,
-3*a^5 + 9*a^4 + 9*a^3 - 40*a^2 + 18*a + 3
]
*], q_expansions := [*
q + a*q^2 + (-a^2 - a + 1)*q^3 + (a^2 - 2)*q^4 - q^5 + (-a - 1)*q^6 + (2*a^2 + a - 3)*q^7 + (-a^2 - 2*a + 1)*q^8 + (a - 1)*q^9 - a*q^10 + (-a^2 - 2*a - 2)*q^11 + (a^2 + a - 2)*q^12 + (2*a^2 - 3)*q^13 + (-a^2 + a + 2)*q^14 + (a^2 + a - 1)*q^15 + (-3*a^2 - a + 3)*q^16 + (-a^2 - 2*a - 3)*q^17 + (a^2 - a)*q^18 + (2*a^2 + 5*a - 2)*q^19 + (-a^2 + 2)*q^20 + (a^2 - 4)*q^21 + (-a^2 - 4*a - 1)*q^22 + (-3*a^2 + 4)*q^23 + (2*a + 3)*q^24 + q^25 + (-2*a^2 + a + 2)*q^26 + (4*a^2 + 3*a - 5)*q^27 + (-2*a^2 - 2*a + 5)*q^28 + (-3*a^2 + 1)*q^29 + (a + 1)*q^30 + (-2*a^2 - 3*a)*q^31 + (4*a^2 + a - 5)*q^32 + (3*a^2 + 5*a)*q^33 + (-a^2 - 5*a - 1)*q^34 + (-2*a^2 - a + 3)*q^35 + (-2*a^2 + 3)*q^36 + (-4*a^2 + 4*a + 10)*q^37 + O(q^38),
q + a*q^2 + (a^2 + a - 3)*q^3 + (a^2 - 2)*q^4 + q^5 + (-2*a^2 - 3*a + 3)*q^6 + (-2*a^2 - 3*a + 1)*q^7 + (-3*a^2 - 4*a + 3)*q^8 + (-2*a^2 - 3*a + 3)*q^9 + a*q^10 + (-a^2 + 4)*q^11 + (a^2 + a)*q^12 + (2*a^2 + 2*a - 7)*q^13 + (3*a^2 + a - 6)*q^14 + (a^2 + a - 3)*q^15 + (3*a^2 + 3*a - 5)*q^16 + (-a^2 - 2*a - 5)*q^17 + (3*a^2 + 3*a - 6)*q^18 + (-3*a - 2)*q^19 + (a^2 - 2)*q^20 + (a^2 + 4*a)*q^21 + (3*a^2 + 4*a - 3)*q^22 + (3*a^2 + 8*a - 2)*q^23 + (2*a^2 + 6*a - 3)*q^24 + q^25 + (-4*a^2 - 7*a + 6)*q^26 + (3*a + 3)*q^27 + (-4*a^2 + 7)*q^28 + (a^2 + 4*a - 3)*q^29 + (-2*a^2 - 3*a + 3)*q^30 + (-2*a^2 - 5*a + 2)*q^31 + (3*a + 3)*q^32 + (a^2 + a - 6)*q^33 + (a^2 - 5*a - 3)*q^34 + (-2*a^2 - 3*a + 1)*q^35 + (-2*a^2 + 3)*q^36 + (-4*a^2 - 8*a + 2)*q^37 + O(q^38),
q + a*q^2 + (-a^5 + a^4 + 6*a^3 - 4*a^2 - 7*a + 1)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^5 + 7*a^3 + a^2 - 10*a - 3)*q^6 + (a^5 - 7*a^3 - a^2 + 10*a + 3)*q^7 + (a^3 - 4*a)*q^8 + (-a^3 - a^2 + 5*a + 4)*q^9 + a*q^10 + (a^4 - a^3 - 5*a^2 + 3*a + 4)*q^11 + (-a^4 + 6*a^2 - 5)*q^12 + (-a^4 + a^3 + 4*a^2 - 3*a + 1)*q^13 + (2*a^5 - a^4 - 12*a^3 + 2*a^2 + 14*a + 3)*q^14 + (-a^5 + a^4 + 6*a^3 - 4*a^2 - 7*a + 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^5 - a^4 - 7*a^3 + 5*a^2 + 10*a)*q^17 + (-a^4 - a^3 + 5*a^2 + 4*a)*q^18 + (a^3 - a^2 - 3*a + 1)*q^19 + (a^2 - 2)*q^20 + (a^4 + a^3 - 5*a^2 - 7*a)*q^21 + (a^5 - a^4 - 5*a^3 + 3*a^2 + 4*a)*q^22 + (a^5 - 2*a^4 - 6*a^3 + 9*a^2 + 5*a - 1)*q^23 + (a^5 - 8*a^3 - 2*a^2 + 15*a + 6)*q^24 + q^25 + (-a^5 + a^4 + 4*a^3 - 3*a^2 + a)*q^26 + (-a^5 + 9*a^3 + a^2 - 18*a - 5)*q^27 + (a^5 - 6*a^3 + 5*a)*q^28 + (-a^5 - a^4 + 9*a^3 + 7*a^2 - 18*a - 8)*q^29 + (-a^5 + 7*a^3 + a^2 - 10*a - 3)*q^30 + (-a^3 + a^2 + a - 3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^4 - 6*a^2 - 2*a + 7)*q^33 + (a^5 - a^4 - 6*a^3 + 2*a^2 + 11*a + 3)*q^34 + (a^5 - 7*a^3 - a^2 + 10*a + 3)*q^35 + (-a^5 - a^4 + 7*a^3 + 6*a^2 - 10*a - 8)*q^36 + (-a^5 - a^4 + 7*a^3 + 8*a^2 - 10*a - 9)*q^37 + O(q^38),
q + a*q^2 + (a^5 - 3*a^4 - 4*a^3 + 14*a^2 - a - 3)*q^3 + (a^2 - 2)*q^4 - q^5 + (a^6 - 3*a^5 - 4*a^4 + 14*a^3 - a^2 - 3*a)*q^6 + (a^6 - a^5 - 10*a^4 + 8*a^3 + 25*a^2 - 15*a - 4)*q^7 + (a^3 - 4*a)*q^8 + (-a^6 + 2*a^5 + 8*a^4 - 14*a^3 - 17*a^2 + 22*a + 7)*q^9 - a*q^10 + (-a^6 + 2*a^5 + 5*a^4 - 8*a^3 - 3*a^2 - 2*a + 3)*q^11 + (-2*a^6 + 4*a^5 + 13*a^4 - 20*a^3 - 20*a^2 + 12*a + 7)*q^12 + (-2*a^6 + 4*a^5 + 15*a^4 - 23*a^3 - 30*a^2 + 23*a + 7)*q^13 + (a^4 - 2*a^3 - 4*a^2 + 6*a + 1)*q^14 + (-a^5 + 3*a^4 + 4*a^3 - 14*a^2 + a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 - a^5 - 9*a^4 + 6*a^3 + 21*a^2 - 9*a - 1)*q^17 + (a^6 - 2*a^5 - 7*a^4 + 10*a^3 + 11*a^2 - 3*a - 1)*q^18 + (a^6 - 2*a^5 - 10*a^4 + 16*a^3 + 27*a^2 - 30*a - 6)*q^19 + (-a^2 + 2)*q^20 + (a^6 - 4*a^5 + a^4 + 14*a^3 - 25*a^2 + 14*a + 7)*q^21 + (a^6 - 5*a^5 - a^4 + 24*a^3 - 13*a^2 - 7*a - 1)*q^22 + (3*a^6 - 5*a^5 - 24*a^4 + 31*a^3 + 51*a^2 - 40*a - 14)*q^23 + (-a^5 + 2*a^4 + 6*a^3 - 8*a^2 - 7*a - 2)*q^24 + q^25 + (2*a^6 - 5*a^5 - 9*a^4 + 24*a^3 + a^2 - 13*a - 2)*q^26 + (a^6 + a^5 - 14*a^4 - 4*a^3 + 43*a^2 - 3*a - 4)*q^27 + (-2*a^6 + 3*a^5 + 18*a^4 - 20*a^3 - 44*a^2 + 31*a + 8)*q^28 + (-a^6 + 3*a^5 + 5*a^4 - 14*a^3 - 5*a^2 + a + 5)*q^29 + (-a^6 + 3*a^5 + 4*a^4 - 14*a^3 + a^2 + 3*a)*q^30 + (-3*a^6 + 4*a^5 + 26*a^4 - 24*a^3 - 59*a^2 + 30*a + 12)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-3*a^4 + 4*a^3 + 18*a^2 - 18*a - 11)*q^33 + (a^5 - a^4 - 6*a^3 + 2*a^2 + 9*a + 1)*q^34 + (-a^6 + a^5 + 10*a^4 - 8*a^3 - 25*a^2 + 15*a + 4)*q^35 + (a^6 - a^5 - 13*a^4 + 12*a^3 + 42*a^2 - 35*a - 13)*q^36 + (-3*a^5 + 9*a^4 + 9*a^3 - 40*a^2 + 18*a + 3)*q^37 + O(q^38)
*]> ;  // time = 41.311 seconds




J[298] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 298, 298, 298, 298, 298, 149, 149 ], new_dimensions := [ 1, 1, 2, 3, 5, 3, 9 ], dimensions := [ 1, 1, 2, 3, 5, 6, 18 ], intersection_graph := [ 0, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 1, 1, 9, 1, 1, 0, 1, 1, 1, 69, 5, 1, 1, 0, 1, 13, 1, 1, 1, 1, 1, 0, 29, 1, 1, 1, 1, 13, 29, 0, 1, 1, 9, 69, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, -4, 4, 2, -5, -7, -7, 3, -8, 2, -4 ],
[ 1, -2, -2, -2, 0, -5, -7, 1, -1, 8, 4, 0 ],
[ -2, 2, 2, 2, 6, -4, 10, 2, 4, 4, -10, 0 ],
[ -3, -5, 1, -4, -5, 0, -9, -2, -19, -1, -4, 7 ],
[ 5, 1, 5, 0, -3, 6, 9, -8, 1, 7, 0, -13 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2*x - 2,
x^3 + 5*x^2 + 4*x - 5,
x^5 - x^4 - 10*x^3 + 11*x^2 + 12*x - 2
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 9, 1 ],
[ 69, 1 ],
[ 13, 1 ],
[ 725, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 9, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 725, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 25 ], torsion_lower_bounds := [ 1, 1, 1, 1, 25 ], l_ratios := [ 0, 0, 1, 0, 29/25 ], analytic_sha_upper_bounds := [ 0, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 0, 1 ], eigenvalues := [*
[ -1, 0, -4, 4, 2, -5, -7, -7, 3, -8, 2, -4 ],
[ 1, -2, -2, -2, 0, -5, -7, 1, -1, 8, 4, 0 ],
[
-1,
a,
-a + 2,
-a + 2,
a + 2,
a - 3,
5,
-2*a + 3,
-a + 3,
-2*a + 4,
-a - 4,
0
],
[
-1,
a,
-a^2 - 3*a + 1,
2*a^2 + 4*a - 6,
-3*a^2 - 8*a + 2,
0,
a^2 + 4*a - 2,
2*a^2 + 6*a - 2,
a^2 + 3*a - 7,
4*a^2 + 9*a - 8,
2*a + 2,
-3*a^2 - 5*a + 11
],
[
1,
a,
2/5*a^4 - 1/5*a^3 - 18/5*a^2 + 13/5*a + 18/5,
-3/5*a^4 - 1/5*a^3 + 22/5*a^2 - 7/5*a - 2/5,
-1/5*a^4 + 3/5*a^3 + 9/5*a^2 - 29/5*a - 4/5,
3/5*a^4 + 6/5*a^3 - 17/5*a^2 - 33/5*a - 3/5,
-2/5*a^4 + 1/5*a^3 + 18/5*a^2 - 18/5*a - 3/5,
-a^3 - a^2 + 6*a + 1,
-4/5*a^4 - 8/5*a^3 + 31/5*a^2 + 39/5*a - 21/5,
1/5*a^4 + 7/5*a^3 - 4/5*a^2 - 36/5*a + 4/5,
-1/5*a^4 + 3/5*a^3 + 14/5*a^2 - 19/5*a - 24/5,
7/5*a^4 - 6/5*a^3 - 68/5*a^2 + 68/5*a + 48/5
]
*], q_expansions := [*
q - q^2 + q^4 - 4*q^5 + 4*q^7 - q^8 - 3*q^9 + 4*q^10 + 2*q^11 - 5*q^13 - 4*q^14 + q^16 - 7*q^17 + 3*q^18 - 7*q^19 - 4*q^20 - 2*q^22 + 3*q^23 + 11*q^25 + 5*q^26 + 4*q^28 - 8*q^29 + 2*q^31 - q^32 + 7*q^34 - 16*q^35 - 3*q^36 - 4*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 2*q^5 - 2*q^6 - 2*q^7 + q^8 + q^9 - 2*q^10 - 2*q^12 - 5*q^13 - 2*q^14 + 4*q^15 + q^16 - 7*q^17 + q^18 + q^19 - 2*q^20 + 4*q^21 - q^23 - 2*q^24 - q^25 - 5*q^26 + 4*q^27 - 2*q^28 + 8*q^29 + 4*q^30 + 4*q^31 + q^32 - 7*q^34 + 4*q^35 + q^36 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a + 2)*q^5 - a*q^6 + (-a + 2)*q^7 - q^8 + (2*a - 1)*q^9 + (a - 2)*q^10 + (a + 2)*q^11 + a*q^12 + (a - 3)*q^13 + (a - 2)*q^14 - 2*q^15 + q^16 + 5*q^17 + (-2*a + 1)*q^18 + (-2*a + 3)*q^19 + (-a + 2)*q^20 - 2*q^21 + (-a - 2)*q^22 + (-a + 3)*q^23 - a*q^24 + (-2*a + 1)*q^25 + (-a + 3)*q^26 + 4*q^27 + (-a + 2)*q^28 + (-2*a + 4)*q^29 + 2*q^30 + (-a - 4)*q^31 - q^32 + (4*a + 2)*q^33 - 5*q^34 + (-2*a + 6)*q^35 + (2*a - 1)*q^36 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a^2 - 3*a + 1)*q^5 - a*q^6 + (2*a^2 + 4*a - 6)*q^7 - q^8 + (a^2 - 3)*q^9 + (a^2 + 3*a - 1)*q^10 + (-3*a^2 - 8*a + 2)*q^11 + a*q^12 + (-2*a^2 - 4*a + 6)*q^14 + (2*a^2 + 5*a - 5)*q^15 + q^16 + (a^2 + 4*a - 2)*q^17 + (-a^2 + 3)*q^18 + (2*a^2 + 6*a - 2)*q^19 + (-a^2 - 3*a + 1)*q^20 + (-6*a^2 - 14*a + 10)*q^21 + (3*a^2 + 8*a - 2)*q^22 + (a^2 + 3*a - 7)*q^23 - a*q^24 + (-2*a^2 - 5*a + 1)*q^25 + (-5*a^2 - 10*a + 5)*q^27 + (2*a^2 + 4*a - 6)*q^28 + (4*a^2 + 9*a - 8)*q^29 + (-2*a^2 - 5*a + 5)*q^30 + (2*a + 2)*q^31 - q^32 + (7*a^2 + 14*a - 15)*q^33 + (-a^2 - 4*a + 2)*q^34 + (4*a^2 + 12*a - 6)*q^35 + (a^2 - 3)*q^36 + (-3*a^2 - 5*a + 11)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (2/5*a^4 - 1/5*a^3 - 18/5*a^2 + 13/5*a + 18/5)*q^5 + a*q^6 + (-3/5*a^4 - 1/5*a^3 + 22/5*a^2 - 7/5*a - 2/5)*q^7 + q^8 + (a^2 - 3)*q^9 + (2/5*a^4 - 1/5*a^3 - 18/5*a^2 + 13/5*a + 18/5)*q^10 + (-1/5*a^4 + 3/5*a^3 + 9/5*a^2 - 29/5*a - 4/5)*q^11 + a*q^12 + (3/5*a^4 + 6/5*a^3 - 17/5*a^2 - 33/5*a - 3/5)*q^13 + (-3/5*a^4 - 1/5*a^3 + 22/5*a^2 - 7/5*a - 2/5)*q^14 + (1/5*a^4 + 2/5*a^3 - 9/5*a^2 - 6/5*a + 4/5)*q^15 + q^16 + (-2/5*a^4 + 1/5*a^3 + 18/5*a^2 - 18/5*a - 3/5)*q^17 + (a^2 - 3)*q^18 + (-a^3 - a^2 + 6*a + 1)*q^19 + (2/5*a^4 - 1/5*a^3 - 18/5*a^2 + 13/5*a + 18/5)*q^20 + (-4/5*a^4 - 8/5*a^3 + 26/5*a^2 + 34/5*a - 6/5)*q^21 + (-1/5*a^4 + 3/5*a^3 + 9/5*a^2 - 29/5*a - 4/5)*q^22 + (-4/5*a^4 - 8/5*a^3 + 31/5*a^2 + 39/5*a - 21/5)*q^23 + a*q^24 + (a^4 - a^3 - 10*a^2 + 10*a + 9)*q^25 + (3/5*a^4 + 6/5*a^3 - 17/5*a^2 - 33/5*a - 3/5)*q^26 + (a^3 - 6*a)*q^27 + (-3/5*a^4 - 1/5*a^3 + 22/5*a^2 - 7/5*a - 2/5)*q^28 + (1/5*a^4 + 7/5*a^3 - 4/5*a^2 - 36/5*a + 4/5)*q^29 + (1/5*a^4 + 2/5*a^3 - 9/5*a^2 - 6/5*a + 4/5)*q^30 + (-1/5*a^4 + 3/5*a^3 + 14/5*a^2 - 19/5*a - 24/5)*q^31 + q^32 + (2/5*a^4 - 1/5*a^3 - 18/5*a^2 + 8/5*a - 2/5)*q^33 + (-2/5*a^4 + 1/5*a^3 + 18/5*a^2 - 18/5*a - 3/5)*q^34 - 2*q^35 + (a^2 - 3)*q^36 + (7/5*a^4 - 6/5*a^3 - 68/5*a^2 + 68/5*a + 48/5)*q^37 + O(q^38)
*]> ;  // time = 60.9 seconds




J[299] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 299, 299, 299, 299, 299, 299, 299, 23 ], new_dimensions := [ 2, 2, 2, 2, 2, 3, 10, 2 ], dimensions := [ 2, 2, 2, 2, 2, 3, 10, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 5, 1, 5, 1, 1, 1, 1, 0, 17, 1, 1, 1, 1, 1, 5, 17, 0, 1, 5, 1, 1, 1, 1, 1, 1, 0, 1, 1, 11, 1, 5, 1, 5, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 289, 1, 1, 1, 1, 11, 1, 289, 0 ], ap_traces := [
[ 1, -1, -3, -2, -3, -2, -1, -4, -2, 1, 1, -6 ],
[ 0, 0, 2, 2, -6, 2, 4, 10, -2, 8, 12, 2 ],
[ 1, 1, 1, 2, 5, 2, -12, 5, -2, 4, -4, 10 ],
[ -1, -1, 3, 2, 3, 2, 3, -8, -2, -11, 11, 14 ],
[ -1, -1, -1, -4, 1, 2, -3, 2, 2, -7, -13, -14 ],
[ 0, -1, 1, 2, 5, 3, 2, 1, -3, 10, -12, 8 ],
[ 1, 3, 3, -2, 3, -10, -3, 2, 10, 17, 5, 16 ]
], hecke_fields := [
x^2 - x - 1,
x^2 - 5,
x^2 - x - 4,
x^2 + x - 5,
x^2 + x - 1,
x^3 + x^2 - 9*x - 5,
x^10 - x^9 - 19*x^8 + 18*x^7 + 127*x^6 - 109*x^5 - 357*x^4 + 252*x^3 + 400*x^2 - 192*x - 128
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ -1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 11, 1 ],
[ 3, 3 ],
[ 289, 7 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 11, 1 ],
[ 3, 1 ],
[ 1, 7 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 3, 7 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 3, 7 ], l_ratios := [ 0, 1, 1, 1, 0, 1/3, 1/7 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 0, 1, 1 ], eigenvalues := [*
[
a,
-a,
-a - 1,
-1,
a - 2,
-1,
3*a - 2,
2*a - 3,
-1,
-3*a + 2,
-3*a + 2,
-2*a - 2
],
[
a,
0,
a + 1,
-a + 1,
-a - 3,
1,
2,
-a + 5,
-1,
-2*a + 4,
-2*a + 6,
a + 1
],
[
a,
-a + 1,
-a + 1,
2*a,
-a + 3,
1,
-6,
-a + 3,
-1,
2,
-4*a,
-2*a + 6
],
[
a,
a,
-a + 1,
1,
a + 2,
1,
a + 2,
-2*a - 5,
-1,
-a - 6,
a + 6,
-2*a + 6
],
[
a,
a,
-a - 1,
-2*a - 3,
-a,
1,
3*a,
4*a + 3,
1,
3*a - 2,
a - 6,
2*a - 6
],
[
0,
a,
-1/2*a^2 + 7/2,
a + 1,
-1/2*a^2 - a + 9/2,
1,
-a^2 + 7,
1/2*a^2 + a - 5/2,
-1,
-a^2 - 2*a + 9,
-4,
a^2 - a - 4
],
[
a,
-3/16*a^9 - 3/16*a^8 + 47/16*a^7 + 11/4*a^6 - 233/16*a^5 - 195/16*a^4 + 397/16*a^3 + 141/8*a^2 - 23/2*a - 7,
7/32*a^9 + 9/32*a^8 - 117/32*a^7 - 65/16*a^6 + 649/32*a^5 + 565/32*a^4 - 1379/32*a^3 - 199/8*a^2 + 61/2*a + 11,
-3/16*a^9 + 1/16*a^8 + 51/16*a^7 - a^6 - 289/16*a^5 + 73/16*a^4 + 617/16*a^3 - 29/8*a^2 - 25*a - 4,
7/32*a^9 + 13/32*a^8 - 105/32*a^7 - 95/16*a^6 + 481/32*a^5 + 849/32*a^4 - 711/32*a^3 - 39*a^2 + 21/2*a + 15,
-1,
5/16*a^9 + 3/16*a^8 - 87/16*a^7 - 23/8*a^6 + 507/16*a^5 + 231/16*a^4 - 1121/16*a^3 - 119/4*a^2 + 47*a + 22,
-13/32*a^9 - 15/32*a^8 + 227/32*a^7 + 117/16*a^6 - 1355/32*a^5 - 1179/32*a^4 + 3245/32*a^3 + 68*a^2 - 165/2*a - 35,
1,
-1/16*a^9 - 7/16*a^8 + 11/16*a^7 + 51/8*a^6 - 15/16*a^5 - 443/16*a^4 - 99/16*a^3 + 143/4*a^2 + 9*a - 8,
-5/8*a^9 - 7/8*a^8 + 83/8*a^7 + 53/4*a^6 - 459/8*a^5 - 499/8*a^4 + 989/8*a^3 + 100*a^2 - 93*a - 44,
-1/8*a^8 - 3/8*a^7 + 11/8*a^6 + 23/4*a^5 - 15/8*a^4 - 203/8*a^3 - 107/8*a^2 + 27*a + 22
]
*], q_expansions := [*
q + a*q^2 - a*q^3 + (a - 1)*q^4 + (-a - 1)*q^5 + (-a - 1)*q^6 - q^7 + (-2*a + 1)*q^8 + (a - 2)*q^9 + (-2*a - 1)*q^10 + (a - 2)*q^11 - q^12 - q^13 - a*q^14 + (2*a + 1)*q^15 - 3*a*q^16 + (3*a - 2)*q^17 + (-a + 1)*q^18 + (2*a - 3)*q^19 - a*q^20 + a*q^21 + (-a + 1)*q^22 - q^23 + (a + 2)*q^24 + (3*a - 3)*q^25 - a*q^26 + (4*a - 1)*q^27 + (-a + 1)*q^28 + (-3*a + 2)*q^29 + (3*a + 2)*q^30 + (-3*a + 2)*q^31 + (a - 5)*q^32 + (a - 1)*q^33 + (a + 3)*q^34 + (a + 1)*q^35 + (-2*a + 3)*q^36 + (-2*a - 2)*q^37 + O(q^38),
q + a*q^2 + 3*q^4 + (a + 1)*q^5 + (-a + 1)*q^7 + a*q^8 - 3*q^9 + (a + 5)*q^10 + (-a - 3)*q^11 + q^13 + (a - 5)*q^14 - q^16 + 2*q^17 - 3*a*q^18 + (-a + 5)*q^19 + (3*a + 3)*q^20 + (-3*a - 5)*q^22 - q^23 + (2*a + 1)*q^25 + a*q^26 + (-3*a + 3)*q^28 + (-2*a + 4)*q^29 + (-2*a + 6)*q^31 - 3*a*q^32 + 2*a*q^34 - 4*q^35 - 9*q^36 + (a + 1)*q^37 + O(q^38),
q + a*q^2 + (-a + 1)*q^3 + (a + 2)*q^4 + (-a + 1)*q^5 - 4*q^6 + 2*a*q^7 + (a + 4)*q^8 + (-a + 2)*q^9 - 4*q^10 + (-a + 3)*q^11 + (-2*a - 2)*q^12 + q^13 + (2*a + 8)*q^14 + (-a + 5)*q^15 + 3*a*q^16 - 6*q^17 + (a - 4)*q^18 + (-a + 3)*q^19 + (-2*a - 2)*q^20 - 8*q^21 + (2*a - 4)*q^22 - q^23 - 4*a*q^24 - a*q^25 + a*q^26 + (a + 3)*q^27 + (6*a + 8)*q^28 + 2*q^29 + (4*a - 4)*q^30 - 4*a*q^31 + (a + 4)*q^32 + (-3*a + 7)*q^33 - 6*a*q^34 - 8*q^35 - a*q^36 + (-2*a + 6)*q^37 + O(q^38),
q + a*q^2 + a*q^3 + (-a + 3)*q^4 + (-a + 1)*q^5 + (-a + 5)*q^6 + q^7 + (2*a - 5)*q^8 + (-a + 2)*q^9 + (2*a - 5)*q^10 + (a + 2)*q^11 + (4*a - 5)*q^12 + q^13 + a*q^14 + (2*a - 5)*q^15 + (-5*a + 4)*q^16 + (a + 2)*q^17 + (3*a - 5)*q^18 + (-2*a - 5)*q^19 + (-5*a + 8)*q^20 + a*q^21 + (a + 5)*q^22 - q^23 + (-7*a + 10)*q^24 + (-3*a + 1)*q^25 + a*q^26 - 5*q^27 + (-a + 3)*q^28 + (-a - 6)*q^29 + (-7*a + 10)*q^30 + (a + 6)*q^31 + (5*a - 15)*q^32 + (a + 5)*q^33 + (a + 5)*q^34 + (-a + 1)*q^35 + (-6*a + 11)*q^36 + (-2*a + 6)*q^37 + O(q^38),
q + a*q^2 + a*q^3 + (-a - 1)*q^4 + (-a - 1)*q^5 + (-a + 1)*q^6 + (-2*a - 3)*q^7 + (-2*a - 1)*q^8 + (-a - 2)*q^9 - q^10 - a*q^11 - q^12 + q^13 + (-a - 2)*q^14 - q^15 + 3*a*q^16 + 3*a*q^17 + (-a - 1)*q^18 + (4*a + 3)*q^19 + (a + 2)*q^20 + (-a - 2)*q^21 + (a - 1)*q^22 + q^23 + (a - 2)*q^24 + (a - 3)*q^25 + a*q^26 + (-4*a - 1)*q^27 + (3*a + 5)*q^28 + (3*a - 2)*q^29 - a*q^30 + (a - 6)*q^31 + (a + 5)*q^32 + (a - 1)*q^33 + (-3*a + 3)*q^34 + (3*a + 5)*q^35 + (2*a + 3)*q^36 + (2*a - 6)*q^37 + O(q^38),
q + a*q^3 - 2*q^4 + (-1/2*a^2 + 7/2)*q^5 + (a + 1)*q^7 + (a^2 - 3)*q^9 + (-1/2*a^2 - a + 9/2)*q^11 - 2*a*q^12 + q^13 + (1/2*a^2 - a - 5/2)*q^15 + 4*q^16 + (-a^2 + 7)*q^17 + (1/2*a^2 + a - 5/2)*q^19 + (a^2 - 7)*q^20 + (a^2 + a)*q^21 - q^23 + (-a^2 - a + 6)*q^25 + (-a^2 + 3*a + 5)*q^27 + (-2*a - 2)*q^28 + (-a^2 - 2*a + 9)*q^29 - 4*q^31 + (-1/2*a^2 - 5/2)*q^33 + (-a + 1)*q^35 + (-2*a^2 + 6)*q^36 + (a^2 - a - 4)*q^37 + O(q^38),
q + a*q^2 + (-3/16*a^9 - 3/16*a^8 + 47/16*a^7 + 11/4*a^6 - 233/16*a^5 - 195/16*a^4 + 397/16*a^3 + 141/8*a^2 - 23/2*a - 7)*q^3 + (a^2 - 2)*q^4 + (7/32*a^9 + 9/32*a^8 - 117/32*a^7 - 65/16*a^6 + 649/32*a^5 + 565/32*a^4 - 1379/32*a^3 - 199/8*a^2 + 61/2*a + 11)*q^5 + (-3/8*a^9 - 5/8*a^8 + 49/8*a^7 + 37/4*a^6 - 261/8*a^5 - 337/8*a^4 + 519/8*a^3 + 127/2*a^2 - 43*a - 24)*q^6 + (-3/16*a^9 + 1/16*a^8 + 51/16*a^7 - a^6 - 289/16*a^5 + 73/16*a^4 + 617/16*a^3 - 29/8*a^2 - 25*a - 4)*q^7 + (a^3 - 4*a)*q^8 + (5/16*a^9 + 3/16*a^8 - 87/16*a^7 - 23/8*a^6 + 507/16*a^5 + 231/16*a^4 - 1137/16*a^3 - 115/4*a^2 + 52*a + 20)*q^9 + (1/2*a^9 + 1/2*a^8 - 8*a^7 - 15/2*a^6 + 83/2*a^5 + 35*a^4 - 80*a^3 - 57*a^2 + 53*a + 28)*q^10 + (7/32*a^9 + 13/32*a^8 - 105/32*a^7 - 95/16*a^6 + 481/32*a^5 + 849/32*a^4 - 711/32*a^3 - 39*a^2 + 21/2*a + 15)*q^11 + (-5/8*a^9 - 5/8*a^8 + 81/8*a^7 + 19/2*a^6 - 431/8*a^5 - 357/8*a^4 + 867/8*a^3 + 287/4*a^2 - 73*a - 34)*q^12 - q^13 + (-1/8*a^9 - 3/8*a^8 + 19/8*a^7 + 23/4*a^6 - 127/8*a^5 - 227/8*a^4 + 349/8*a^3 + 50*a^2 - 40*a - 24)*q^14 + (-3/32*a^9 - 1/32*a^8 + 45/32*a^7 + 3/16*a^6 - 181/32*a^5 + 43/32*a^4 + 51/32*a^3 - 17/2*a^2 + 21/2*a + 9)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (5/16*a^9 + 3/16*a^8 - 87/16*a^7 - 23/8*a^6 + 507/16*a^5 + 231/16*a^4 - 1121/16*a^3 - 119/4*a^2 + 47*a + 22)*q^17 + (1/2*a^9 + 1/2*a^8 - 17/2*a^7 - 8*a^6 + 97/2*a^5 + 81/2*a^4 - 215/2*a^3 - 73*a^2 + 80*a + 40)*q^18 + (-13/32*a^9 - 15/32*a^8 + 227/32*a^7 + 117/16*a^6 - 1355/32*a^5 - 1179/32*a^4 + 3245/32*a^3 + 68*a^2 - 165/2*a - 35)*q^19 + (9/16*a^9 + 15/16*a^8 - 147/16*a^7 - 111/8*a^6 + 783/16*a^5 + 1011/16*a^4 - 1549/16*a^3 - 389/4*a^2 + 63*a + 42)*q^20 + (-3/16*a^9 - 3/16*a^8 + 55/16*a^7 + 13/4*a^6 - 353/16*a^5 - 307/16*a^4 + 933/16*a^3 + 361/8*a^2 - 54*a - 30)*q^21 + (5/8*a^9 + 7/8*a^8 - 79/8*a^7 - 51/4*a^6 + 403/8*a^5 + 447/8*a^4 - 753/8*a^3 - 77*a^2 + 57*a + 28)*q^22 + q^23 + (-1/2*a^9 - 1/2*a^8 + 17/2*a^7 + 7*a^6 - 95/2*a^5 - 61/2*a^4 + 199/2*a^3 + 50*a^2 - 68*a - 32)*q^24 + (1/8*a^8 - 1/8*a^7 - 19/8*a^6 + 9/4*a^5 + 111/8*a^4 - 93/8*a^3 - 205/8*a^2 + 27/2*a + 14)*q^25 - a*q^26 + (-1/4*a^9 - 5/8*a^8 + 29/8*a^7 + 73/8*a^6 - 31/2*a^5 - 311/8*a^4 + 149/8*a^3 + 355/8*a^2 - 9/2*a - 3)*q^27 + (-1/8*a^9 - 1/8*a^8 + 13/8*a^7 + 2*a^6 - 47/8*a^5 - 81/8*a^4 + 35/8*a^3 + 69/4*a^2 + 2*a - 8)*q^28 + (-1/16*a^9 - 7/16*a^8 + 11/16*a^7 + 51/8*a^6 - 15/16*a^5 - 443/16*a^4 - 99/16*a^3 + 143/4*a^2 + 9*a - 8)*q^29 + (-1/8*a^9 - 3/8*a^8 + 15/8*a^7 + 25/4*a^6 - 71/8*a^5 - 255/8*a^4 + 121/8*a^3 + 48*a^2 - 9*a - 12)*q^30 + (-5/8*a^9 - 7/8*a^8 + 83/8*a^7 + 53/4*a^6 - 459/8*a^5 - 499/8*a^4 + 989/8*a^3 + 100*a^2 - 93*a - 44)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-3/32*a^9 - 5/32*a^8 + 65/32*a^7 + 49/16*a^6 - 493/32*a^5 - 625/32*a^4 + 1495/32*a^3 + 357/8*a^2 - 91/2*a - 29)*q^33 + (1/2*a^9 + 1/2*a^8 - 17/2*a^7 - 8*a^6 + 97/2*a^5 + 83/2*a^4 - 217/2*a^3 - 78*a^2 + 82*a + 40)*q^34 + (-3/16*a^9 + 5/16*a^8 + 55/16*a^7 - 19/4*a^6 - 329/16*a^5 + 325/16*a^4 + 693/16*a^3 - 119/8*a^2 - 49/2*a - 16)*q^35 + (3/8*a^9 + 5/8*a^8 - 49/8*a^7 - 37/4*a^6 + 253/8*a^5 + 337/8*a^4 - 455/8*a^3 - 125/2*a^2 + 32*a + 24)*q^36 + (-1/8*a^8 - 3/8*a^7 + 11/8*a^6 + 23/4*a^5 - 15/8*a^4 - 203/8*a^3 - 107/8*a^2 + 27*a + 22)*q^37 + O(q^38)
*]> ;  // time = 43.43 seconds




J[301] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 301, 301, 301, 301, 43, 43 ], new_dimensions := [ 4, 5, 5, 7, 1, 2 ], dimensions := [ 4, 5, 5, 7, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 7, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 17, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 7, 1, 17, 1, 1, 0 ], ap_traces := [
[ -4, -3, -4, 4, -15, 1, -1, -8, -5, -16, 3, -11 ],
[ 0, -3, -6, -5, -16, -2, -8, -10, -2, -4, -6, 9 ],
[ 1, 5, 4, -5, 13, -1, 1, 18, -5, 2, -3, -9 ],
[ 4, 1, 0, 7, 16, -2, 4, 0, 6, 12, 8, -7 ]
], hecke_fields := [
x^4 + 4*x^3 + 2*x^2 - 5*x - 3,
x^5 - 6*x^3 + x^2 + 5*x - 2,
x^5 - x^4 - 6*x^3 + 5*x^2 + 6*x - 1,
x^7 - 4*x^6 - 3*x^5 + 25*x^4 - 13*x^3 - 23*x^2 + 11*x + 2
], atkin_lehners := [
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 7, 1 ],
[ 1, 1 ],
[ 17, 1 ],
[ 11, 1 ]
], tamagawa_numbers := [
[ 7, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 11, 1 ]
], torsion_upper_bounds := [ 21, 1, 1, 11 ], torsion_lower_bounds := [ 1, 1, 1, 11 ], l_ratios := [ 0, 0, 1, 1/11 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
a,
-a^3 - 2*a^2 + 2*a + 1,
-a^2 - 2*a,
1,
-a^3 - 3*a^2 + a,
3*a^3 + 8*a^2 - 2*a - 7,
a^3 + 3*a^2 - 3*a - 6,
a^2 + 4*a - 1,
a^3 + 5*a^2 + a - 9,
-4*a^3 - 12*a^2 + 2*a + 9,
5*a^3 + 13*a^2 - 6*a - 13,
-a^3 - 6*a^2 - 4*a + 5
],
[
a,
a^4 + a^3 - 6*a^2 - 5*a + 4,
-2*a^4 - 2*a^3 + 11*a^2 + 8*a - 8,
-1,
3*a^4 + a^3 - 17*a^2 - 4*a + 7,
-2*a^4 - a^3 + 12*a^2 + 2*a - 9,
5*a^4 + 3*a^3 - 27*a^2 - 10*a + 13,
3*a^4 + 2*a^3 - 15*a^2 - 7*a + 4,
-4*a^4 - 3*a^3 + 21*a^2 + 13*a - 11,
-3*a^4 + 16*a^2 - a - 8,
4*a^4 + 3*a^3 - 25*a^2 - 12*a + 19,
7*a^4 + 3*a^3 - 38*a^2 - 9*a + 22
],
[
a,
-a^3 + 4*a + 1,
a^4 - 5*a^2 + a + 3,
-1,
a^4 - a^3 - 5*a^2 + 4*a + 5,
-a^3 - 2*a^2 + 4*a + 5,
-a^4 + a^3 + 7*a^2 - 6*a - 7,
2*a^3 + a^2 - 8*a + 1,
-2*a^4 + a^3 + 9*a^2 - 5*a - 3,
a^4 - 6*a^2 - 3*a + 6,
a^4 + a^3 - 5*a^2 - 5*a + 2,
-a^3 + 2*a^2 + 4*a - 7
],
[
a,
-a^5 + a^4 + 7*a^3 - 5*a^2 - 8*a + 2,
a^6 - 2*a^5 - 6*a^4 + 11*a^3 + 4*a^2 - 6*a,
1,
-a^6 + 3*a^5 + 5*a^4 - 18*a^3 + a^2 + 13*a + 1,
a^6 - a^5 - 8*a^4 + 6*a^3 + 14*a^2 - 7*a - 3,
-a^6 + a^5 + 7*a^4 - 4*a^3 - 9*a^2 - 3*a + 3,
-a^6 + 2*a^5 + 7*a^4 - 13*a^3 - 10*a^2 + 15*a + 4,
2*a^6 - 2*a^5 - 16*a^4 + 11*a^3 + 29*a^2 - 9*a - 7,
-3*a^6 + 5*a^5 + 19*a^4 - 29*a^3 - 14*a^2 + 22*a - 2,
-a^5 + 2*a^4 + 5*a^3 - 10*a^2 - a + 5,
3*a^5 - 5*a^4 - 19*a^3 + 25*a^2 + 18*a - 8
]
*], q_expansions := [*
q + a*q^2 + (-a^3 - 2*a^2 + 2*a + 1)*q^3 + (a^2 - 2)*q^4 + (-a^2 - 2*a)*q^5 + (2*a^3 + 4*a^2 - 4*a - 3)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (3*a^3 + 7*a^2 - 6*a - 8)*q^9 + (-a^3 - 2*a^2)*q^10 + (-a^3 - 3*a^2 + a)*q^11 + (-2*a^3 - 4*a^2 + 3*a + 4)*q^12 + (3*a^3 + 8*a^2 - 2*a - 7)*q^13 + a*q^14 + a*q^15 + (-4*a^3 - 8*a^2 + 5*a + 7)*q^16 + (a^3 + 3*a^2 - 3*a - 6)*q^17 + (-5*a^3 - 12*a^2 + 7*a + 9)*q^18 + (a^2 + 4*a - 1)*q^19 + (2*a^3 + 4*a^2 - a - 3)*q^20 + (-a^3 - 2*a^2 + 2*a + 1)*q^21 + (a^3 + 3*a^2 - 5*a - 3)*q^22 + (a^3 + 5*a^2 + a - 9)*q^23 + (-a^2 + 2*a)*q^24 + (2*a^2 + 5*a - 2)*q^25 + (-4*a^3 - 8*a^2 + 8*a + 9)*q^26 + (-5*a^3 - 13*a^2 + 9*a + 13)*q^27 + (a^2 - 2)*q^28 + (-4*a^3 - 12*a^2 + 2*a + 9)*q^29 + a^2*q^30 + (5*a^3 + 13*a^2 - 6*a - 13)*q^31 + (6*a^3 + 13*a^2 - 5*a - 12)*q^32 + (6*a^3 + 13*a^2 - 11*a - 9)*q^33 + (-a^3 - 5*a^2 - a + 3)*q^34 + (-a^2 - 2*a)*q^35 + (2*a^3 + 3*a^2 - 4*a + 1)*q^36 + (-a^3 - 6*a^2 - 4*a + 5)*q^37 + O(q^38),
q + a*q^2 + (a^4 + a^3 - 6*a^2 - 5*a + 4)*q^3 + (a^2 - 2)*q^4 + (-2*a^4 - 2*a^3 + 11*a^2 + 8*a - 8)*q^5 + (a^4 - 6*a^2 - a + 2)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-3*a^4 - a^3 + 17*a^2 + 5*a - 9)*q^9 + (-2*a^4 - a^3 + 10*a^2 + 2*a - 4)*q^10 + (3*a^4 + a^3 - 17*a^2 - 4*a + 7)*q^11 + (-2*a^4 - 2*a^3 + 10*a^2 + 7*a - 6)*q^12 + (-2*a^4 - a^3 + 12*a^2 + 2*a - 9)*q^13 - a*q^14 + (4*a^4 + 2*a^3 - 20*a^2 - 5*a + 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (5*a^4 + 3*a^3 - 27*a^2 - 10*a + 13)*q^17 + (-a^4 - a^3 + 8*a^2 + 6*a - 6)*q^18 + (3*a^4 + 2*a^3 - 15*a^2 - 7*a + 4)*q^19 + (3*a^4 + 2*a^3 - 18*a^2 - 10*a + 12)*q^20 + (-a^4 - a^3 + 6*a^2 + 5*a - 4)*q^21 + (a^4 + a^3 - 7*a^2 - 8*a + 6)*q^22 + (-4*a^4 - 3*a^3 + 21*a^2 + 13*a - 11)*q^23 + (-4*a^4 - 2*a^3 + 21*a^2 + 6*a - 8)*q^24 + (-3*a^4 + 16*a^2 - 5)*q^25 + (-a^4 + 4*a^2 + a - 4)*q^26 + (-a^4 - a^3 + 5*a^2 + 2*a - 4)*q^27 + (-a^2 + 2)*q^28 + (-3*a^4 + 16*a^2 - a - 8)*q^29 + (2*a^4 + 4*a^3 - 9*a^2 - 14*a + 8)*q^30 + (4*a^4 + 3*a^3 - 25*a^2 - 12*a + 19)*q^31 + (-2*a^3 - a^2 + 7*a + 2)*q^32 + (-3*a^4 - 4*a^3 + 19*a^2 + 22*a - 14)*q^33 + (3*a^4 + 3*a^3 - 15*a^2 - 12*a + 10)*q^34 + (2*a^4 + 2*a^3 - 11*a^2 - 8*a + 8)*q^35 + (5*a^4 + 4*a^3 - 27*a^2 - 11*a + 16)*q^36 + (7*a^4 + 3*a^3 - 38*a^2 - 9*a + 22)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 4*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^4 - 5*a^2 + a + 3)*q^5 + (-a^4 + 4*a^2 + a)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-a^4 - a^3 + 5*a^2 + 3*a - 1)*q^9 + (a^4 + a^3 - 4*a^2 - 3*a + 1)*q^10 + (a^4 - a^3 - 5*a^2 + 4*a + 5)*q^11 + (-a^4 + 6*a^2 - 2*a - 3)*q^12 + (-a^3 - 2*a^2 + 4*a + 5)*q^13 - a*q^14 + (a^4 - 6*a^2 + 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 + a^3 + 7*a^2 - 6*a - 7)*q^17 + (-2*a^4 - a^3 + 8*a^2 + 5*a - 1)*q^18 + (2*a^3 + a^2 - 8*a + 1)*q^19 + (2*a^3 + 2*a^2 - 7*a - 5)*q^20 + (a^3 - 4*a - 1)*q^21 + (a^3 - a^2 - a + 1)*q^22 + (-2*a^4 + a^3 + 9*a^2 - 5*a - 3)*q^23 + (a^4 - 5*a^2 + a - 1)*q^24 + (2*a^4 - 10*a^2 + 3*a + 4)*q^25 + (-a^4 - 2*a^3 + 4*a^2 + 5*a)*q^26 + (-2*a^4 + a^3 + 11*a^2 - 5*a - 5)*q^27 + (-a^2 + 2)*q^28 + (a^4 - 6*a^2 - 3*a + 6)*q^29 + (a^4 - 5*a^2 - a + 1)*q^30 + (a^4 + a^3 - 5*a^2 - 5*a + 2)*q^31 + (a^4 - 2*a^3 - 5*a^2 + 6*a + 1)*q^32 + (a^4 - 2*a^3 - 5*a^2 + 6*a + 8)*q^33 + (a^3 - a^2 - a - 1)*q^34 + (-a^4 + 5*a^2 - a - 3)*q^35 + (-a^4 - 2*a^3 + 5*a^2 + 5*a)*q^36 + (-a^3 + 2*a^2 + 4*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-a^5 + a^4 + 7*a^3 - 5*a^2 - 8*a + 2)*q^3 + (a^2 - 2)*q^4 + (a^6 - 2*a^5 - 6*a^4 + 11*a^3 + 4*a^2 - 6*a)*q^5 + (-a^6 + a^5 + 7*a^4 - 5*a^3 - 8*a^2 + 2*a)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (a^4 - a^3 - 7*a^2 + 5*a + 7)*q^9 + (2*a^6 - 3*a^5 - 14*a^4 + 17*a^3 + 17*a^2 - 11*a - 2)*q^10 + (-a^6 + 3*a^5 + 5*a^4 - 18*a^3 + a^2 + 13*a + 1)*q^11 + (-3*a^6 + 6*a^5 + 18*a^4 - 35*a^3 - 11*a^2 + 27*a - 2)*q^12 + (a^6 - a^5 - 8*a^4 + 6*a^3 + 14*a^2 - 7*a - 3)*q^13 + a*q^14 + (a^6 - 2*a^5 - 6*a^4 + 11*a^3 + 3*a^2 - 5*a + 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^6 + a^5 + 7*a^4 - 4*a^3 - 9*a^2 - 3*a + 3)*q^17 + (a^5 - a^4 - 7*a^3 + 5*a^2 + 7*a)*q^18 + (-a^6 + 2*a^5 + 7*a^4 - 13*a^3 - 10*a^2 + 15*a + 4)*q^19 + (3*a^6 - 4*a^5 - 21*a^4 + 21*a^3 + 27*a^2 - 12*a - 4)*q^20 + (-a^5 + a^4 + 7*a^3 - 5*a^2 - 8*a + 2)*q^21 + (-a^6 + 2*a^5 + 7*a^4 - 12*a^3 - 10*a^2 + 12*a + 2)*q^22 + (2*a^6 - 2*a^5 - 16*a^4 + 11*a^3 + 29*a^2 - 9*a - 7)*q^23 + (-4*a^6 + 7*a^5 + 26*a^4 - 40*a^3 - 26*a^2 + 27*a + 6)*q^24 + (-2*a^6 + 3*a^5 + 13*a^4 - 16*a^3 - 11*a^2 + 7*a - 3)*q^25 + (3*a^6 - 5*a^5 - 19*a^4 + 27*a^3 + 16*a^2 - 14*a - 2)*q^26 + (3*a^6 - 8*a^5 - 15*a^4 + 48*a^3 - 4*a^2 - 40*a + 4)*q^27 + (a^2 - 2)*q^28 + (-3*a^6 + 5*a^5 + 19*a^4 - 29*a^3 - 14*a^2 + 22*a - 2)*q^29 + (2*a^6 - 3*a^5 - 14*a^4 + 16*a^3 + 18*a^2 - 9*a - 2)*q^30 + (-a^5 + 2*a^4 + 5*a^3 - 10*a^2 - a + 5)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-2*a^5 + a^4 + 16*a^3 - 3*a^2 - 26*a - 6)*q^33 + (-3*a^6 + 4*a^5 + 21*a^4 - 22*a^3 - 26*a^2 + 14*a + 2)*q^34 + (a^6 - 2*a^5 - 6*a^4 + 11*a^3 + 4*a^2 - 6*a)*q^35 + (a^6 - a^5 - 9*a^4 + 7*a^3 + 21*a^2 - 10*a - 14)*q^36 + (3*a^5 - 5*a^4 - 19*a^3 + 25*a^2 + 18*a - 8)*q^37 + O(q^38)
*]> ;  // time = 39.449 seconds




J[302] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 302, 302, 302, 302, 302, 302, 151, 151, 151 ], new_dimensions := [ 1, 1, 1, 2, 4, 4, 3, 3, 6 ], dimensions := [ 1, 1, 1, 2, 4, 4, 6, 6, 12 ], intersection_graph := [ 0, 1, 1, 1, 9, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 3, 5, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 9, 1, 1, 1, 0, 1, 1, 3, 431, 1, 1, 1, 1, 1, 0, 41, 1, 1, 1, 1, 1, 7, 1, 41, 0, 1, 1, 3, 3, 5, 1, 3, 1, 1, 0, 4489, 1, 5, 1, 1, 431, 1, 1, 4489, 0 ], ap_traces := [
[ -1, 2, 2, 4, -4, 0, -6, 0, 0, 6, 0, -2 ],
[ 1, -1, -4, -2, 2, -6, 3, 0, -6, 0, -3, -2 ],
[ 1, -3, 0, -2, -6, -2, -5, -8, 6, 8, 9, 2 ],
[ -2, -2, 0, -4, 4, -8, -10, 0, 4, 0, -6, -12 ],
[ -4, 0, -4, 2, 0, 14, 12, 12, 2, -4, 0, 12 ],
[ 4, 2, 0, 6, 0, 6, -4, 4, -6, -4, 4, -8 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 + 2*x - 1,
x^4 - 10*x^2 - 6*x + 9,
x^4 - 2*x^3 - 4*x^2 + 8*x - 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 1 ],
[ 15, 1 ],
[ 5, 1 ],
[ 7, 1 ],
[ 3879, 3 ],
[ 779, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 15, 1 ],
[ 5, 1 ],
[ 1, 1 ],
[ 1, 3 ],
[ 779, 1 ]
], torsion_upper_bounds := [ 1, 5, 1, 1, 3, 19 ], torsion_lower_bounds := [ 1, 1, 1, 1, 3, 19 ], l_ratios := [ 1, 0, 0, 0, 1/3, 41/19 ], analytic_sha_upper_bounds := [ 1, 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 0, 1, 1 ], eigenvalues := [*
[ -1, 2, 2, 4, -4, 0, -6, 0, 0, 6, 0, -2 ],
[ 1, -1, -4, -2, 2, -6, 3, 0, -6, 0, -3, -2 ],
[ 1, -3, 0, -2, -6, -2, -5, -8, 6, 8, 9, 2 ],
[
-1,
a,
0,
-2*a - 4,
-2*a,
2*a - 2,
-5,
2*a + 2,
4*a + 6,
-4*a - 4,
4*a + 1,
-2*a - 8
],
[
-1,
a,
2/3*a^3 - a^2 - 14/3*a + 1,
-1/3*a^3 + 7/3*a + 2,
-a^2 + 2*a + 5,
1/3*a^3 - 7/3*a + 2,
3,
-2/3*a^3 + a^2 + 14/3*a + 1,
-1/3*a^3 + 1/3*a + 2,
2/3*a^3 - 20/3*a - 4,
2/3*a^3 - 3*a^2 - 8/3*a + 12,
2/3*a^3 - 2*a^2 - 14/3*a + 10
],
[
1,
a,
-a^2 + 3,
a^3 - 5*a + 2,
-2*a^3 + a^2 + 8*a - 3,
-a^3 + 2*a^2 + 3*a - 4,
-1,
2*a^3 - a^2 - 10*a + 5,
a^3 - 2*a^2 - 3*a + 4,
-2*a,
-2*a^3 + a^2 + 8*a - 2,
2*a^2 + 4*a - 10
]
*], q_expansions := [*
q - q^2 + 2*q^3 + q^4 + 2*q^5 - 2*q^6 + 4*q^7 - q^8 + q^9 - 2*q^10 - 4*q^11 + 2*q^12 - 4*q^14 + 4*q^15 + q^16 - 6*q^17 - q^18 + 2*q^20 + 8*q^21 + 4*q^22 - 2*q^24 - q^25 - 4*q^27 + 4*q^28 + 6*q^29 - 4*q^30 - q^32 - 8*q^33 + 6*q^34 + 8*q^35 + q^36 - 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 4*q^5 - q^6 - 2*q^7 + q^8 - 2*q^9 - 4*q^10 + 2*q^11 - q^12 - 6*q^13 - 2*q^14 + 4*q^15 + q^16 + 3*q^17 - 2*q^18 - 4*q^20 + 2*q^21 + 2*q^22 - 6*q^23 - q^24 + 11*q^25 - 6*q^26 + 5*q^27 - 2*q^28 + 4*q^30 - 3*q^31 + q^32 - 2*q^33 + 3*q^34 + 8*q^35 - 2*q^36 - 2*q^37 + O(q^38),
q + q^2 - 3*q^3 + q^4 - 3*q^6 - 2*q^7 + q^8 + 6*q^9 - 6*q^11 - 3*q^12 - 2*q^13 - 2*q^14 + q^16 - 5*q^17 + 6*q^18 - 8*q^19 + 6*q^21 - 6*q^22 + 6*q^23 - 3*q^24 - 5*q^25 - 2*q^26 - 9*q^27 - 2*q^28 + 8*q^29 + 9*q^31 + q^32 + 18*q^33 - 5*q^34 + 6*q^36 + 2*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - a*q^6 + (-2*a - 4)*q^7 - q^8 + (-2*a - 2)*q^9 - 2*a*q^11 + a*q^12 + (2*a - 2)*q^13 + (2*a + 4)*q^14 + q^16 - 5*q^17 + (2*a + 2)*q^18 + (2*a + 2)*q^19 - 2*q^21 + 2*a*q^22 + (4*a + 6)*q^23 - a*q^24 - 5*q^25 + (-2*a + 2)*q^26 + (-a - 2)*q^27 + (-2*a - 4)*q^28 + (-4*a - 4)*q^29 + (4*a + 1)*q^31 - q^32 + (4*a - 2)*q^33 + 5*q^34 + (-2*a - 2)*q^36 + (-2*a - 8)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (2/3*a^3 - a^2 - 14/3*a + 1)*q^5 - a*q^6 + (-1/3*a^3 + 7/3*a + 2)*q^7 - q^8 + (a^2 - 3)*q^9 + (-2/3*a^3 + a^2 + 14/3*a - 1)*q^10 + (-a^2 + 2*a + 5)*q^11 + a*q^12 + (1/3*a^3 - 7/3*a + 2)*q^13 + (1/3*a^3 - 7/3*a - 2)*q^14 + (-a^3 + 2*a^2 + 5*a - 6)*q^15 + q^16 + 3*q^17 + (-a^2 + 3)*q^18 + (-2/3*a^3 + a^2 + 14/3*a + 1)*q^19 + (2/3*a^3 - a^2 - 14/3*a + 1)*q^20 + (-a^2 + 3)*q^21 + (a^2 - 2*a - 5)*q^22 + (-1/3*a^3 + 1/3*a + 2)*q^23 - a*q^24 + (-2*a + 3)*q^25 + (-1/3*a^3 + 7/3*a - 2)*q^26 + (a^3 - 6*a)*q^27 + (-1/3*a^3 + 7/3*a + 2)*q^28 + (2/3*a^3 - 20/3*a - 4)*q^29 + (a^3 - 2*a^2 - 5*a + 6)*q^30 + (2/3*a^3 - 3*a^2 - 8/3*a + 12)*q^31 - q^32 + (-a^3 + 2*a^2 + 5*a)*q^33 - 3*q^34 + (2/3*a^3 - 14/3*a - 6)*q^35 + (a^2 - 3)*q^36 + (2/3*a^3 - 2*a^2 - 14/3*a + 10)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a^2 + 3)*q^5 + a*q^6 + (a^3 - 5*a + 2)*q^7 + q^8 + (a^2 - 3)*q^9 + (-a^2 + 3)*q^10 + (-2*a^3 + a^2 + 8*a - 3)*q^11 + a*q^12 + (-a^3 + 2*a^2 + 3*a - 4)*q^13 + (a^3 - 5*a + 2)*q^14 + (-a^3 + 3*a)*q^15 + q^16 - q^17 + (a^2 - 3)*q^18 + (2*a^3 - a^2 - 10*a + 5)*q^19 + (-a^2 + 3)*q^20 + (2*a^3 - a^2 - 6*a + 1)*q^21 + (-2*a^3 + a^2 + 8*a - 3)*q^22 + (a^3 - 2*a^2 - 3*a + 4)*q^23 + a*q^24 + (2*a^3 - 2*a^2 - 8*a + 5)*q^25 + (-a^3 + 2*a^2 + 3*a - 4)*q^26 + (a^3 - 6*a)*q^27 + (a^3 - 5*a + 2)*q^28 - 2*a*q^29 + (-a^3 + 3*a)*q^30 + (-2*a^3 + a^2 + 8*a - 2)*q^31 + q^32 + (-3*a^3 + 13*a - 2)*q^33 - q^34 + (-2*a^2 + 4)*q^35 + (a^2 - 3)*q^36 + (2*a^2 + 4*a - 10)*q^37 + O(q^38)
*]> ;  // time = 64.231 seconds




J[303] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 303, 303, 303, 303, 303, 101, 101 ], new_dimensions := [ 1, 1, 2, 6, 7, 1, 7 ], dimensions := [ 1, 1, 2, 6, 7, 2, 14 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 7, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1103, 1, 1, 1, 3, 1, 0, 1, 7, 1, 1, 1, 1103, 1, 0 ], ap_traces := [
[ 0, 1, -3, 0, -2, -3, -7, -5, -5, 6, 7, 10 ],
[ -2, 1, -1, -2, -6, 1, -5, 7, -3, -6, -1, -10 ],
[ 0, -2, -2, -4, 4, -6, -6, -6, 2, 4, 2, -8 ],
[ 1, 6, 6, 0, 10, 0, 12, -10, 4, 8, -2, -6 ],
[ 0, -7, 6, 6, -10, 10, 20, 2, 6, -10, 10, 8 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2,
x^6 - x^5 - 7*x^4 + 5*x^3 + 13*x^2 - 4*x - 6,
x^7 - 12*x^5 + 40*x^3 + x^2 - 24*x - 4
], atkin_lehners := [
[ -1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 7, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 51, 1 ],
[ 1103, 1 ]
], tamagawa_numbers := [
[ 7, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 51, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 17, 1 ], torsion_lower_bounds := [ 1, 1, 1, 17, 1 ], l_ratios := [ 0, 0, 0, 3/17, 1 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ 0, 1, -3, 0, -2, -3, -7, -5, -5, 6, 7, 10 ],
[ -2, 1, -1, -2, -6, 1, -5, 7, -3, -6, -1, -10 ],
[
a,
-1,
-a - 1,
-a - 2,
2,
2*a - 3,
-a - 3,
-3,
3*a + 1,
2*a + 2,
2*a + 1,
-4
],
[
a,
1,
a^4 - a^3 - 5*a^2 + 3*a + 5,
-a^5 + a^4 + 5*a^3 - 5*a^2 - 3*a + 4,
-2*a^4 + a^3 + 11*a^2 - 4*a - 8,
2*a^5 - 2*a^4 - 11*a^3 + 9*a^2 + 10*a - 5,
-a^4 + a^3 + 3*a^2 - 3*a + 3,
-a^5 + 2*a^4 + 7*a^3 - 11*a^2 - 10*a + 7,
-2*a^5 + 3*a^4 + 11*a^3 - 13*a^2 - 13*a + 7,
2*a^5 - 11*a^3 - 3*a^2 + 10*a + 8,
-2*a^4 - a^3 + 11*a^2 + 4*a - 9,
2*a^4 + a^3 - 7*a^2 - 6*a - 2
],
[
a,
-1,
a^6 + a^5 - 8*a^4 - 6*a^3 + 14*a^2 + 3*a - 3,
-a^6 - 2*a^5 + 8*a^4 + 12*a^3 - 14*a^2 - 5*a + 4,
-a^3 - a^2 + 6*a + 2,
-a^6 - 3*a^5 + 5*a^4 + 20*a^3 + 4*a^2 - 18*a - 3,
a^6 + 3*a^5 - 6*a^4 - 20*a^3 + 2*a^2 + 17*a + 5,
-a^5 + 7*a^3 - a^2 - 8*a + 3,
a^6 + 3*a^5 - 6*a^4 - 18*a^3 + 2*a^2 + 7*a + 3,
a^3 - a^2 - 6*a + 2,
-a^6 - a^5 + 7*a^4 + 8*a^3 - 8*a^2 - 14*a + 3,
-2*a^5 - 4*a^4 + 13*a^3 + 23*a^2 - 12*a - 6
]
*], q_expansions := [*
q + q^3 - 2*q^4 - 3*q^5 + q^9 - 2*q^11 - 2*q^12 - 3*q^13 - 3*q^15 + 4*q^16 - 7*q^17 - 5*q^19 + 6*q^20 - 5*q^23 + 4*q^25 + q^27 + 6*q^29 + 7*q^31 - 2*q^33 - 2*q^36 + 10*q^37 + O(q^38),
q - 2*q^2 + q^3 + 2*q^4 - q^5 - 2*q^6 - 2*q^7 + q^9 + 2*q^10 - 6*q^11 + 2*q^12 + q^13 + 4*q^14 - q^15 - 4*q^16 - 5*q^17 - 2*q^18 + 7*q^19 - 2*q^20 - 2*q^21 + 12*q^22 - 3*q^23 - 4*q^25 - 2*q^26 + q^27 - 4*q^28 - 6*q^29 + 2*q^30 - q^31 + 8*q^32 - 6*q^33 + 10*q^34 + 2*q^35 + 2*q^36 - 10*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a - 1)*q^5 - a*q^6 + (-a - 2)*q^7 - 2*a*q^8 + q^9 + (-a - 2)*q^10 + 2*q^11 + (2*a - 3)*q^13 + (-2*a - 2)*q^14 + (a + 1)*q^15 - 4*q^16 + (-a - 3)*q^17 + a*q^18 - 3*q^19 + (a + 2)*q^21 + 2*a*q^22 + (3*a + 1)*q^23 + 2*a*q^24 + (2*a - 2)*q^25 + (-3*a + 4)*q^26 - q^27 + (2*a + 2)*q^29 + (a + 2)*q^30 + (2*a + 1)*q^31 - 2*q^33 + (-3*a - 2)*q^34 + (3*a + 4)*q^35 - 4*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (a^4 - a^3 - 5*a^2 + 3*a + 5)*q^5 + a*q^6 + (-a^5 + a^4 + 5*a^3 - 5*a^2 - 3*a + 4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (a^5 - a^4 - 5*a^3 + 3*a^2 + 5*a)*q^10 + (-2*a^4 + a^3 + 11*a^2 - 4*a - 8)*q^11 + (a^2 - 2)*q^12 + (2*a^5 - 2*a^4 - 11*a^3 + 9*a^2 + 10*a - 5)*q^13 + (-2*a^4 + 10*a^2 - 6)*q^14 + (a^4 - a^3 - 5*a^2 + 3*a + 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 + a^3 + 3*a^2 - 3*a + 3)*q^17 + a*q^18 + (-a^5 + 2*a^4 + 7*a^3 - 11*a^2 - 10*a + 7)*q^19 + (2*a^2 - 2*a - 4)*q^20 + (-a^5 + a^4 + 5*a^3 - 5*a^2 - 3*a + 4)*q^21 + (-2*a^5 + a^4 + 11*a^3 - 4*a^2 - 8*a)*q^22 + (-2*a^5 + 3*a^4 + 11*a^3 - 13*a^2 - 13*a + 7)*q^23 + (a^3 - 4*a)*q^24 + (a^5 - 8*a^3 + 12*a + 2)*q^25 + (3*a^4 - a^3 - 16*a^2 + 3*a + 12)*q^26 + q^27 + (-2*a^4 + 10*a^2 - 8)*q^28 + (2*a^5 - 11*a^3 - 3*a^2 + 10*a + 8)*q^29 + (a^5 - a^4 - 5*a^3 + 3*a^2 + 5*a)*q^30 + (-2*a^4 - a^3 + 11*a^2 + 4*a - 9)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-2*a^4 + a^3 + 11*a^2 - 4*a - 8)*q^33 + (-a^5 + a^4 + 3*a^3 - 3*a^2 + 3*a)*q^34 + (a^5 - a^4 - 5*a^3 + 3*a^2 + 3*a + 2)*q^35 + (a^2 - 2)*q^36 + (2*a^4 + a^3 - 7*a^2 - 6*a - 2)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (a^6 + a^5 - 8*a^4 - 6*a^3 + 14*a^2 + 3*a - 3)*q^5 - a*q^6 + (-a^6 - 2*a^5 + 8*a^4 + 12*a^3 - 14*a^2 - 5*a + 4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (a^6 + 4*a^5 - 6*a^4 - 26*a^3 + 2*a^2 + 21*a + 4)*q^10 + (-a^3 - a^2 + 6*a + 2)*q^11 + (-a^2 + 2)*q^12 + (-a^6 - 3*a^5 + 5*a^4 + 20*a^3 + 4*a^2 - 18*a - 3)*q^13 + (-2*a^6 - 4*a^5 + 12*a^4 + 26*a^3 - 4*a^2 - 20*a - 4)*q^14 + (-a^6 - a^5 + 8*a^4 + 6*a^3 - 14*a^2 - 3*a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 + 3*a^5 - 6*a^4 - 20*a^3 + 2*a^2 + 17*a + 5)*q^17 + a*q^18 + (-a^5 + 7*a^3 - a^2 - 8*a + 3)*q^19 + (2*a^6 + 4*a^5 - 10*a^4 - 26*a^3 - 8*a^2 + 22*a + 10)*q^20 + (a^6 + 2*a^5 - 8*a^4 - 12*a^3 + 14*a^2 + 5*a - 4)*q^21 + (-a^4 - a^3 + 6*a^2 + 2*a)*q^22 + (a^6 + 3*a^5 - 6*a^4 - 18*a^3 + 2*a^2 + 7*a + 3)*q^23 + (-a^3 + 4*a)*q^24 + (2*a^6 + 5*a^5 - 12*a^4 - 32*a^3 + 4*a^2 + 22*a + 8)*q^25 + (-3*a^6 - 7*a^5 + 20*a^4 + 44*a^3 - 17*a^2 - 27*a - 4)*q^26 - q^27 + (-2*a^6 - 8*a^5 + 10*a^4 + 52*a^3 + 10*a^2 - 42*a - 16)*q^28 + (a^3 - a^2 - 6*a + 2)*q^29 + (-a^6 - 4*a^5 + 6*a^4 + 26*a^3 - 2*a^2 - 21*a - 4)*q^30 + (-a^6 - a^5 + 7*a^4 + 8*a^3 - 8*a^2 - 14*a + 3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^3 + a^2 - 6*a - 2)*q^33 + (3*a^6 + 6*a^5 - 20*a^4 - 38*a^3 + 16*a^2 + 29*a + 4)*q^34 + (-a^6 - 4*a^5 + 4*a^4 + 24*a^3 + 12*a^2 - 13*a - 16)*q^35 + (a^2 - 2)*q^36 + (-2*a^5 - 4*a^4 + 13*a^3 + 23*a^2 - 12*a - 6)*q^37 + O(q^38)
*]> ;  // time = 46.139 seconds




J[305] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 305, 305, 305, 305, 61, 61 ], new_dimensions := [ 3, 4, 7, 7, 1, 3 ], dimensions := [ 3, 4, 7, 7, 2, 6 ], intersection_graph := [ 0, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 37, 1, 1, 0, 1, 1, 139, 1, 1, 1, 0, 9, 1, 3, 1, 1, 9, 0, 1, 1, 37, 139, 1, 1, 0 ], ap_traces := [
[ 0, 0, -3, -6, -6, -3, 0, -15, 9, 3, -15, 3 ],
[ -3, -6, 4, -10, -2, -1, -4, -7, -13, 5, -21, -15 ],
[ -2, 0, -7, 12, 2, 9, -4, 13, -5, 7, 35, 9 ],
[ 2, 6, 7, 8, -6, 5, -2, 9, 5, -13, 17, 1 ]
], hecke_fields := [
x^3 - 3*x + 1,
x^4 + 3*x^3 - x^2 - 6*x - 1,
x^7 + 2*x^6 - 11*x^5 - 19*x^4 + 35*x^3 + 48*x^2 - 25*x - 27,
x^7 - 2*x^6 - 9*x^5 + 17*x^4 + 19*x^3 - 36*x^2 + 5*x + 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 1 ],
[ 37, 1 ],
[ 417, 3 ],
[ 279, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 37, 1 ],
[ 1, 3 ],
[ 279, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 31 ], torsion_lower_bounds := [ 1, 1, 3, 31 ], l_ratios := [ 0, 0, 1/3, 9/31 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
a,
-a,
-1,
-2*a^2 - a + 2,
-a^2 + a,
3*a^2 + 4*a - 7,
3*a^2 - a - 6,
-a - 5,
a^2 + 2*a + 1,
-3*a^2 - 5*a + 7,
a - 5,
-2*a^2 + a + 5
],
[
a,
-a^3 - 2*a^2 + 2*a + 1,
1,
a^3 + 2*a^2 - 2*a - 5,
a^2 - a - 4,
-a^2 - 2*a + 1,
-2*a^3 - a^2 + 7*a - 2,
-2*a^2 - a + 3,
2*a^3 + a^2 - 8*a - 3,
3*a^3 + 5*a^2 - 4*a - 2,
2*a^2 + 5*a - 7,
-2*a^2 - a + 1
],
[
a,
-1/2*a^5 + 4*a^3 - 1/2*a^2 - 11/2*a - 1/2,
-1,
a^4 - 7*a^2 + 2*a + 8,
1/2*a^6 - 5*a^4 + 1/2*a^3 + 25/2*a^2 - 3/2*a - 6,
-a^2 + 5,
a^4 + a^3 - 6*a^2 - 3*a + 3,
-a^4 - a^3 + 5*a^2 + 3*a + 2,
-a^6 + 10*a^4 - a^3 - 26*a^2 + a + 15,
a^6 - 11*a^4 + a^3 + 33*a^2 - 3*a - 21,
1/2*a^6 + a^5 - 5*a^4 - 15/2*a^3 + 29/2*a^2 + 19/2*a - 4,
-a^5 - a^4 + 7*a^3 + 6*a^2 - 8*a - 7
],
[
a,
-1/2*a^6 + a^5 + 4*a^4 - 15/2*a^3 - 15/2*a^2 + 27/2*a,
1,
a^4 - 2*a^3 - 5*a^2 + 8*a + 2,
a^6 - 3/2*a^5 - 10*a^4 + 13*a^3 + 49/2*a^2 - 55/2*a - 1/2,
a^6 - a^5 - 10*a^4 + 9*a^3 + 25*a^2 - 22*a - 2,
-a^5 + a^4 + 7*a^3 - 5*a^2 - 10*a + 4,
a^4 - a^3 - 5*a^2 + 3*a + 2,
-a^5 + 10*a^3 - 23*a + 4,
-a^5 + 3*a^4 + 2*a^3 - 13*a^2 + 11*a - 2,
-a^6 + 3/2*a^5 + 8*a^4 - 9*a^3 - 31/2*a^2 + 23/2*a + 7/2,
-a^4 + a^3 + 5*a^2 - 5*a
]
*], q_expansions := [*
q + a*q^2 - a*q^3 + (a^2 - 2)*q^4 - q^5 - a^2*q^6 + (-2*a^2 - a + 2)*q^7 + (-a - 1)*q^8 + (a^2 - 3)*q^9 - a*q^10 + (-a^2 + a)*q^11 + (-a + 1)*q^12 + (3*a^2 + 4*a - 7)*q^13 + (-a^2 - 4*a + 2)*q^14 + a*q^15 + (-3*a^2 - a + 4)*q^16 + (3*a^2 - a - 6)*q^17 - q^18 + (-a - 5)*q^19 + (-a^2 + 2)*q^20 + (a^2 + 4*a - 2)*q^21 + (a^2 - 3*a + 1)*q^22 + (a^2 + 2*a + 1)*q^23 + (a^2 + a)*q^24 + q^25 + (4*a^2 + 2*a - 3)*q^26 + (3*a + 1)*q^27 + (a - 3)*q^28 + (-3*a^2 - 5*a + 7)*q^29 + a^2*q^30 + (a - 5)*q^31 + (-a^2 - 3*a + 5)*q^32 + (-a^2 + 3*a - 1)*q^33 + (-a^2 + 3*a - 3)*q^34 + (2*a^2 + a - 2)*q^35 + (-2*a^2 - a + 6)*q^36 + (-2*a^2 + a + 5)*q^37 + O(q^38),
q + a*q^2 + (-a^3 - 2*a^2 + 2*a + 1)*q^3 + (a^2 - 2)*q^4 + q^5 + (a^3 + a^2 - 5*a - 1)*q^6 + (a^3 + 2*a^2 - 2*a - 5)*q^7 + (a^3 - 4*a)*q^8 + (3*a^3 + 5*a^2 - 7*a - 4)*q^9 + a*q^10 + (a^2 - a - 4)*q^11 + (a - 1)*q^12 + (-a^2 - 2*a + 1)*q^13 + (-a^3 - a^2 + a + 1)*q^14 + (-a^3 - 2*a^2 + 2*a + 1)*q^15 + (-3*a^3 - 5*a^2 + 6*a + 5)*q^16 + (-2*a^3 - a^2 + 7*a - 2)*q^17 + (-4*a^3 - 4*a^2 + 14*a + 3)*q^18 + (-2*a^2 - a + 3)*q^19 + (a^2 - 2)*q^20 + (a^3 + 3*a^2 - a - 3)*q^21 + (a^3 - a^2 - 4*a)*q^22 + (2*a^3 + a^2 - 8*a - 3)*q^23 + (-2*a^3 - a^2 + 9*a + 2)*q^24 + q^25 + (-a^3 - 2*a^2 + a)*q^26 + (-4*a^3 - 4*a^2 + 13*a - 1)*q^27 + (-4*a^2 - a + 9)*q^28 + (3*a^3 + 5*a^2 - 4*a - 2)*q^29 + (a^3 + a^2 - 5*a - 1)*q^30 + (2*a^2 + 5*a - 7)*q^31 + (2*a^3 + 3*a^2 - 5*a - 3)*q^32 + (a^3 + 3*a^2 + 2*a - 2)*q^33 + (5*a^3 + 5*a^2 - 14*a - 2)*q^34 + (a^3 + 2*a^2 - 2*a - 5)*q^35 + (2*a^3 - 7*a + 4)*q^36 + (-2*a^2 - a + 1)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^5 + 4*a^3 - 1/2*a^2 - 11/2*a - 1/2)*q^3 + (a^2 - 2)*q^4 - q^5 + (-1/2*a^6 + 4*a^4 - 1/2*a^3 - 11/2*a^2 - 1/2*a)*q^6 + (a^4 - 7*a^2 + 2*a + 8)*q^7 + (a^3 - 4*a)*q^8 + (-a^3 - a^2 + 5*a + 4)*q^9 - a*q^10 + (1/2*a^6 - 5*a^4 + 1/2*a^3 + 25/2*a^2 - 3/2*a - 6)*q^11 + (a^6 - 1/2*a^5 - 10*a^4 + 4*a^3 + 49/2*a^2 - 3/2*a - 25/2)*q^12 + (-a^2 + 5)*q^13 + (a^5 - 7*a^3 + 2*a^2 + 8*a)*q^14 + (1/2*a^5 - 4*a^3 + 1/2*a^2 + 11/2*a + 1/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 + a^3 - 6*a^2 - 3*a + 3)*q^17 + (-a^4 - a^3 + 5*a^2 + 4*a)*q^18 + (-a^4 - a^3 + 5*a^2 + 3*a + 2)*q^19 + (-a^2 + 2)*q^20 + (-a^5 + 9*a^3 - 18*a - 4)*q^21 + (-a^6 + 1/2*a^5 + 10*a^4 - 5*a^3 - 51/2*a^2 + 13/2*a + 27/2)*q^22 + (-a^6 + 10*a^4 - a^3 - 26*a^2 + a + 15)*q^23 + (-3/2*a^6 + a^5 + 15*a^4 - 19/2*a^3 - 77/2*a^2 + 27/2*a + 27)*q^24 + q^25 + (-a^3 + 5*a)*q^26 + (-a^4 + a^3 + 9*a^2 - 7*a - 14)*q^27 + (a^6 - 9*a^4 + 2*a^3 + 22*a^2 - 4*a - 16)*q^28 + (a^6 - 11*a^4 + a^3 + 33*a^2 - 3*a - 21)*q^29 + (1/2*a^6 - 4*a^4 + 1/2*a^3 + 11/2*a^2 + 1/2*a)*q^30 + (1/2*a^6 + a^5 - 5*a^4 - 15/2*a^3 + 29/2*a^2 + 19/2*a - 4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^4 - 6*a^2 + 3)*q^33 + (a^5 + a^4 - 6*a^3 - 3*a^2 + 3*a)*q^34 + (-a^4 + 7*a^2 - 2*a - 8)*q^35 + (-a^5 - a^4 + 7*a^3 + 6*a^2 - 10*a - 8)*q^36 + (-a^5 - a^4 + 7*a^3 + 6*a^2 - 8*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^6 + a^5 + 4*a^4 - 15/2*a^3 - 15/2*a^2 + 27/2*a)*q^3 + (a^2 - 2)*q^4 + q^5 + (-1/2*a^5 + a^4 + 2*a^3 - 9/2*a^2 + 5/2*a + 1/2)*q^6 + (a^4 - 2*a^3 - 5*a^2 + 8*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (-a^6 + 2*a^5 + 8*a^4 - 14*a^3 - 16*a^2 + 22*a + 2)*q^9 + a*q^10 + (a^6 - 3/2*a^5 - 10*a^4 + 13*a^3 + 49/2*a^2 - 55/2*a - 1/2)*q^11 + (1/2*a^6 - a^5 - 6*a^4 + 21/2*a^3 + 35/2*a^2 - 53/2*a)*q^12 + (a^6 - a^5 - 10*a^4 + 9*a^3 + 25*a^2 - 22*a - 2)*q^13 + (a^5 - 2*a^4 - 5*a^3 + 8*a^2 + 2*a)*q^14 + (-1/2*a^6 + a^5 + 4*a^4 - 15/2*a^3 - 15/2*a^2 + 27/2*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^5 + a^4 + 7*a^3 - 5*a^2 - 10*a + 4)*q^17 + (-a^5 + 3*a^4 + 3*a^3 - 14*a^2 + 7*a + 1)*q^18 + (a^4 - a^3 - 5*a^2 + 3*a + 2)*q^19 + (a^2 - 2)*q^20 + (-a^6 + 2*a^5 + 10*a^4 - 18*a^3 - 26*a^2 + 40*a + 3)*q^21 + (1/2*a^6 - a^5 - 4*a^4 + 11/2*a^3 + 17/2*a^2 - 11/2*a - 1)*q^22 + (-a^5 + 10*a^3 - 23*a + 4)*q^23 + (-1/2*a^5 + 4*a^3 + 1/2*a^2 - 15/2*a - 3/2)*q^24 + q^25 + (a^6 - a^5 - 8*a^4 + 6*a^3 + 14*a^2 - 7*a - 1)*q^26 + (-a^6 + 2*a^5 + 9*a^4 - 14*a^3 - 22*a^2 + 20*a + 8)*q^27 + (a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 12*a^2 - 16*a - 4)*q^28 + (-a^5 + 3*a^4 + 2*a^3 - 13*a^2 + 11*a - 2)*q^29 + (-1/2*a^5 + a^4 + 2*a^3 - 9/2*a^2 + 5/2*a + 1/2)*q^30 + (-a^6 + 3/2*a^5 + 8*a^4 - 9*a^3 - 31/2*a^2 + 23/2*a + 7/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2*a^6 - 3*a^5 - 19*a^4 + 24*a^3 + 47*a^2 - 47*a - 10)*q^33 + (-a^6 + a^5 + 7*a^4 - 5*a^3 - 10*a^2 + 4*a)*q^34 + (a^4 - 2*a^3 - 5*a^2 + 8*a + 2)*q^35 + (a^6 - a^5 - 13*a^4 + 14*a^3 + 39*a^2 - 43*a - 4)*q^36 + (-a^4 + a^3 + 5*a^2 - 5*a)*q^37 + O(q^38)
*]> ;  // time = 42.32 seconds




J[307] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 307, 307, 307, 307, 307, 307, 307 ], new_dimensions := [ 1, 1, 1, 1, 2, 9, 10 ], dimensions := [ 1, 1, 1, 1, 2, 9, 10 ], intersection_graph := [ 0, 1, 1, 1, 1, 13, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 11, 1, 1, 1, 1, 0, 3, 5, 1, 1, 1, 1, 3, 0, 107, 1, 13, 5, 11, 5, 107, 0, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 0, 0, 4, 0, 3, 6, -1, -1, -2, 0, 4, 3 ],
[ 1, 2, 0, 3, 5, 0, -5, -1, 6, -6, -4, -9 ],
[ 2, 0, 2, 3, -4, 0, 3, 1, 2, 6, -4, -6 ],
[ 2, 2, 0, -3, 1, 6, 2, -4, -6, 0, 2, 3 ],
[ -1, -3, 6, 5, 7, -4, 11, 1, 0, -3, -5, 8 ],
[ 3, 1, 5, -5, 0, -3, 3, -1, 16, 21, -4, 23 ],
[ -7, -4, -15, -3, -10, -11, -17, 1, -20, -22, 1, -28 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 + x - 3,
x^9 - 3*x^8 - 11*x^7 + 30*x^6 + 46*x^5 - 87*x^4 - 91*x^3 + 50*x^2 + 62*x + 13,
x^10 + 7*x^9 + 10*x^8 - 28*x^7 - 73*x^6 + 16*x^5 + 128*x^4 + 26*x^3 - 69*x^2 - 18*x - 1
], atkin_lehners := [
[ -1 ],
[ -1 ],
[ -1 ],
[ -1 ],
[ -1 ],
[ -1 ],
[ 1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ 3 ],
[ 17 ],
[ 1 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ 3 ],
[ 17 ],
[ 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 3, 17, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 3, 17, 1 ], l_ratios := [ 1, 1, 1, 1, 1/3, 1/17, 0 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 1, 1, 0 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1, 1, 1, 0 ], eigenvalues := [*
[ 0, 0, 4, 0, 3, 6, -1, -1, -2, 0, 4, 3 ],
[ 1, 2, 0, 3, 5, 0, -5, -1, 6, -6, -4, -9 ],
[ 2, 0, 2, 3, -4, 0, 3, 1, 2, 6, -4, -6 ],
[ 2, 2, 0, -3, 1, 6, 2, -4, -6, 0, 2, 3 ],
[
a,
-a - 2,
3,
-a + 2,
-a + 3,
2*a - 1,
a + 6,
3*a + 2,
0,
-3*a - 3,
-3*a - 4,
2*a + 5
],
[
a,
-a^8 + 2*a^7 + 11*a^6 - 18*a^5 - 38*a^4 + 44*a^3 + 39*a^2 - 24*a - 13,
a^7 - a^6 - 11*a^5 + 5*a^4 + 36*a^3 + 3*a^2 - 24*a - 9,
a^7 - a^6 - 12*a^5 + 5*a^4 + 44*a^3 + 5*a^2 - 36*a - 13,
a^8 - 2*a^7 - 10*a^6 + 15*a^5 + 31*a^4 - 26*a^3 - 23*a^2 + 6*a + 3,
a^8 - a^7 - 12*a^6 + 6*a^5 + 45*a^4 - 2*a^3 - 45*a^2 - 8*a + 6,
-a^8 + 3*a^7 + 9*a^6 - 27*a^5 - 26*a^4 + 71*a^3 + 27*a^2 - 47*a - 14,
-a^8 + 13*a^6 + 6*a^5 - 52*a^4 - 39*a^3 + 51*a^2 + 32*a - 1,
-a^8 - 2*a^7 + 15*a^6 + 29*a^5 - 61*a^4 - 120*a^3 + 38*a^2 + 94*a + 24,
-a^6 + 2*a^5 + 8*a^4 - 12*a^3 - 19*a^2 + 13*a + 13,
-2*a^8 + 2*a^7 + 23*a^6 - 10*a^5 - 80*a^4 - 9*a^3 + 59*a^2 + 29*a + 4,
-a^7 + 2*a^6 + 9*a^5 - 13*a^4 - 26*a^3 + 17*a^2 + 20*a + 3
],
[
a,
a^9 + 6*a^8 + 5*a^7 - 29*a^6 - 48*a^5 + 37*a^4 + 91*a^3 - 7*a^2 - 52*a - 6,
-a^9 - 6*a^8 - 4*a^7 + 34*a^6 + 50*a^5 - 57*a^4 - 111*a^3 + 22*a^2 + 69*a + 7,
-a^9 - 8*a^8 - 16*a^7 + 22*a^6 + 95*a^5 + 21*a^4 - 143*a^3 - 56*a^2 + 71*a + 9,
2*a^8 + 10*a^7 + 3*a^6 - 46*a^5 - 42*a^4 + 58*a^3 + 50*a^2 - 23*a - 6,
a^9 + 7*a^8 + 8*a^7 - 35*a^6 - 67*a^5 + 49*a^4 + 129*a^3 - 12*a^2 - 75*a - 12,
-a^9 - 7*a^8 - 10*a^7 + 24*a^6 + 58*a^5 - 10*a^4 - 68*a^3 - 6*a^2 + 20*a - 2,
2*a^8 + 12*a^7 + 10*a^6 - 51*a^5 - 71*a^4 + 57*a^3 + 76*a^2 - 23*a - 6,
2*a^9 + 12*a^8 + 10*a^7 - 56*a^6 - 88*a^5 + 72*a^4 + 150*a^3 - 25*a^2 - 75*a - 7,
3*a^9 + 19*a^8 + 23*a^7 - 67*a^6 - 146*a^5 + 25*a^4 + 173*a^3 + 35*a^2 - 41*a - 8,
-2*a^9 - 11*a^8 - 6*a^7 + 50*a^6 + 55*a^5 - 63*a^4 - 61*a^3 + 28*a^2 + 2*a + 1,
-2*a^9 - 14*a^8 - 21*a^7 + 48*a^6 + 131*a^5 - 11*a^4 - 180*a^3 - 35*a^2 + 70*a + 3
]
*], q_expansions := [*
q - 2*q^4 + 4*q^5 - 3*q^9 + 3*q^11 + 6*q^13 + 4*q^16 - q^17 - q^19 - 8*q^20 - 2*q^23 + 11*q^25 + 4*q^31 + 6*q^36 + 3*q^37 + O(q^38),
q + q^2 + 2*q^3 - q^4 + 2*q^6 + 3*q^7 - 3*q^8 + q^9 + 5*q^11 - 2*q^12 + 3*q^14 - q^16 - 5*q^17 + q^18 - q^19 + 6*q^21 + 5*q^22 + 6*q^23 - 6*q^24 - 5*q^25 - 4*q^27 - 3*q^28 - 6*q^29 - 4*q^31 + 5*q^32 + 10*q^33 - 5*q^34 - q^36 - 9*q^37 + O(q^38),
q + 2*q^2 + 2*q^4 + 2*q^5 + 3*q^7 - 3*q^9 + 4*q^10 - 4*q^11 + 6*q^14 - 4*q^16 + 3*q^17 - 6*q^18 + q^19 + 4*q^20 - 8*q^22 + 2*q^23 - q^25 + 6*q^28 + 6*q^29 - 4*q^31 - 8*q^32 + 6*q^34 + 6*q^35 - 6*q^36 - 6*q^37 + O(q^38),
q + 2*q^2 + 2*q^3 + 2*q^4 + 4*q^6 - 3*q^7 + q^9 + q^11 + 4*q^12 + 6*q^13 - 6*q^14 - 4*q^16 + 2*q^17 + 2*q^18 - 4*q^19 - 6*q^21 + 2*q^22 - 6*q^23 - 5*q^25 + 12*q^26 - 4*q^27 - 6*q^28 + 2*q^31 - 8*q^32 + 2*q^33 + 4*q^34 + 2*q^36 + 3*q^37 + O(q^38),
q + a*q^2 + (-a - 2)*q^3 + (-a + 1)*q^4 + 3*q^5 + (-a - 3)*q^6 + (-a + 2)*q^7 - 3*q^8 + (3*a + 4)*q^9 + 3*a*q^10 + (-a + 3)*q^11 + q^12 + (2*a - 1)*q^13 + (3*a - 3)*q^14 + (-3*a - 6)*q^15 + (-a - 2)*q^16 + (a + 6)*q^17 + (a + 9)*q^18 + (3*a + 2)*q^19 + (-3*a + 3)*q^20 + (-a - 1)*q^21 + (4*a - 3)*q^22 + (3*a + 6)*q^24 + 4*q^25 + (-3*a + 6)*q^26 + (-4*a - 11)*q^27 + (-4*a + 5)*q^28 + (-3*a - 3)*q^29 + (-3*a - 9)*q^30 + (-3*a - 4)*q^31 + (-a + 3)*q^32 + (-2*a - 3)*q^33 + (5*a + 3)*q^34 + (-3*a + 6)*q^35 + (2*a - 5)*q^36 + (2*a + 5)*q^37 + O(q^38),
q + a*q^2 + (-a^8 + 2*a^7 + 11*a^6 - 18*a^5 - 38*a^4 + 44*a^3 + 39*a^2 - 24*a - 13)*q^3 + (a^2 - 2)*q^4 + (a^7 - a^6 - 11*a^5 + 5*a^4 + 36*a^3 + 3*a^2 - 24*a - 9)*q^5 + (-a^8 + 12*a^6 + 8*a^5 - 43*a^4 - 52*a^3 + 26*a^2 + 49*a + 13)*q^6 + (a^7 - a^6 - 12*a^5 + 5*a^4 + 44*a^3 + 5*a^2 - 36*a - 13)*q^7 + (a^3 - 4*a)*q^8 + (a^7 - a^6 - 12*a^5 + 7*a^4 + 41*a^3 - 6*a^2 - 26*a - 3)*q^9 + (a^8 - a^7 - 11*a^6 + 5*a^5 + 36*a^4 + 3*a^3 - 24*a^2 - 9*a)*q^10 + (a^8 - 2*a^7 - 10*a^6 + 15*a^5 + 31*a^4 - 26*a^3 - 23*a^2 + 6*a + 3)*q^11 + (-a^8 - 3*a^7 + 16*a^6 + 39*a^5 - 63*a^4 - 153*a^3 + 21*a^2 + 123*a + 39)*q^12 + (a^8 - a^7 - 12*a^6 + 6*a^5 + 45*a^4 - 2*a^3 - 45*a^2 - 8*a + 6)*q^13 + (a^8 - a^7 - 12*a^6 + 5*a^5 + 44*a^4 + 5*a^3 - 36*a^2 - 13*a)*q^14 + (a^8 - 2*a^7 - 10*a^6 + 15*a^5 + 32*a^4 - 29*a^3 - 29*a^2 + 19*a + 13)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^8 + 3*a^7 + 9*a^6 - 27*a^5 - 26*a^4 + 71*a^3 + 27*a^2 - 47*a - 14)*q^17 + (a^8 - a^7 - 12*a^6 + 7*a^5 + 41*a^4 - 6*a^3 - 26*a^2 - 3*a)*q^18 + (-a^8 + 13*a^6 + 6*a^5 - 52*a^4 - 39*a^3 + 51*a^2 + 32*a - 1)*q^19 + (2*a^8 - 2*a^7 - 23*a^6 + 12*a^5 + 80*a^4 - 5*a^3 - 65*a^2 - 14*a + 5)*q^20 + (-a^8 + 2*a^7 + 10*a^6 - 15*a^5 - 30*a^4 + 27*a^3 + 16*a^2 - 13*a)*q^21 + (a^8 + a^7 - 15*a^6 - 15*a^5 + 61*a^4 + 68*a^3 - 44*a^2 - 59*a - 13)*q^22 + (-a^8 - 2*a^7 + 15*a^6 + 29*a^5 - 61*a^4 - 120*a^3 + 38*a^2 + 94*a + 24)*q^23 + (-4*a^8 + 5*a^7 + 45*a^6 - 33*a^5 - 154*a^4 + 34*a^3 + 121*a^2 + 3*a - 13)*q^24 + (-a^7 + a^6 + 13*a^5 - 7*a^4 - 50*a^3 + 4*a^2 + 44*a + 11)*q^25 + (2*a^8 - a^7 - 24*a^6 - a^5 + 85*a^4 + 46*a^3 - 58*a^2 - 56*a - 13)*q^26 + (a^8 - 12*a^6 - 7*a^5 + 41*a^4 + 46*a^3 - 17*a^2 - 43*a - 13)*q^27 + (2*a^8 - 3*a^7 - 23*a^6 + 22*a^5 + 82*a^4 - 33*a^3 - 73*a^2 + 10*a + 13)*q^28 + (-a^6 + 2*a^5 + 8*a^4 - 12*a^3 - 19*a^2 + 13*a + 13)*q^29 + (a^8 + a^7 - 15*a^6 - 14*a^5 + 58*a^4 + 62*a^3 - 31*a^2 - 49*a - 13)*q^30 + (-2*a^8 + 2*a^7 + 23*a^6 - 10*a^5 - 80*a^4 - 9*a^3 + 59*a^2 + 29*a + 4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^8 + 12*a^6 + 8*a^5 - 41*a^4 - 53*a^3 + 16*a^2 + 46*a + 13)*q^33 + (-2*a^7 + 3*a^6 + 20*a^5 - 16*a^4 - 64*a^3 + 3*a^2 + 48*a + 13)*q^34 + (-a^8 + 12*a^6 + 6*a^5 - 40*a^4 - 40*a^3 + 14*a^2 + 36*a + 13)*q^35 + (2*a^8 - 3*a^7 - 21*a^6 + 19*a^5 + 67*a^4 - 17*a^3 - 41*a^2 - 10*a - 7)*q^36 + (-a^7 + 2*a^6 + 9*a^5 - 13*a^4 - 26*a^3 + 17*a^2 + 20*a + 3)*q^37 + O(q^38),
q + a*q^2 + (a^9 + 6*a^8 + 5*a^7 - 29*a^6 - 48*a^5 + 37*a^4 + 91*a^3 - 7*a^2 - 52*a - 6)*q^3 + (a^2 - 2)*q^4 + (-a^9 - 6*a^8 - 4*a^7 + 34*a^6 + 50*a^5 - 57*a^4 - 111*a^3 + 22*a^2 + 69*a + 7)*q^5 + (-a^9 - 5*a^8 - a^7 + 25*a^6 + 21*a^5 - 37*a^4 - 33*a^3 + 17*a^2 + 12*a + 1)*q^6 + (-a^9 - 8*a^8 - 16*a^7 + 22*a^6 + 95*a^5 + 21*a^4 - 143*a^3 - 56*a^2 + 71*a + 9)*q^7 + (a^3 - 4*a)*q^8 + (a^8 + 5*a^7 - 27*a^5 - 14*a^4 + 47*a^3 + 17*a^2 - 29*a - 2)*q^9 + (a^9 + 6*a^8 + 6*a^7 - 23*a^6 - 41*a^5 + 17*a^4 + 48*a^3 - 11*a - 1)*q^10 + (2*a^8 + 10*a^7 + 3*a^6 - 46*a^5 - 42*a^4 + 58*a^3 + 50*a^2 - 23*a - 6)*q^11 + (-3*a^8 - 13*a^7 + 6*a^6 + 75*a^5 + 21*a^4 - 139*a^3 - 43*a^2 + 87*a + 11)*q^12 + (a^9 + 7*a^8 + 8*a^7 - 35*a^6 - 67*a^5 + 49*a^4 + 129*a^3 - 12*a^2 - 75*a - 12)*q^13 + (-a^9 - 6*a^8 - 6*a^7 + 22*a^6 + 37*a^5 - 15*a^4 - 30*a^3 + 2*a^2 - 9*a - 1)*q^14 + (-2*a^9 - 12*a^8 - 10*a^7 + 57*a^6 + 92*a^5 - 73*a^4 - 165*a^3 + 22*a^2 + 88*a + 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^9 - 7*a^8 - 10*a^7 + 24*a^6 + 58*a^5 - 10*a^4 - 68*a^3 - 6*a^2 + 20*a - 2)*q^17 + (a^9 + 5*a^8 - 27*a^6 - 14*a^5 + 47*a^4 + 17*a^3 - 29*a^2 - 2*a)*q^18 + (2*a^8 + 12*a^7 + 10*a^6 - 51*a^5 - 71*a^4 + 57*a^3 + 76*a^2 - 23*a - 6)*q^19 + (a^9 + 8*a^8 + 13*a^7 - 36*a^6 - 99*a^5 + 34*a^4 + 196*a^3 + 14*a^2 - 121*a - 13)*q^20 + (-a^8 - 4*a^7 + 6*a^6 + 33*a^5 - 8*a^4 - 85*a^3 - 2*a^2 + 67*a)*q^21 + (2*a^9 + 10*a^8 + 3*a^7 - 46*a^6 - 42*a^5 + 58*a^4 + 50*a^3 - 23*a^2 - 6*a)*q^22 + (2*a^9 + 12*a^8 + 10*a^7 - 56*a^6 - 88*a^5 + 72*a^4 + 150*a^3 - 25*a^2 - 75*a - 7)*q^23 + (-a^9 - 3*a^8 + 8*a^7 + 25*a^6 - 21*a^5 - 65*a^4 + 23*a^3 + 53*a^2 - 13*a - 2)*q^24 + (2*a^9 + 11*a^8 + a^7 - 80*a^6 - 84*a^5 + 174*a^4 + 246*a^3 - 95*a^2 - 175*a - 16)*q^25 + (-2*a^8 - 7*a^7 + 6*a^6 + 33*a^5 + a^4 - 38*a^3 - 6*a^2 + 6*a + 1)*q^26 + (3*a^6 + 10*a^5 - 8*a^4 - 42*a^3 - 4*a^2 + 40*a + 8)*q^27 + (3*a^9 + 20*a^8 + 26*a^7 - 80*a^6 - 189*a^5 + 56*a^4 + 314*a^3 + 34*a^2 - 161*a - 19)*q^28 + (3*a^9 + 19*a^8 + 23*a^7 - 67*a^6 - 146*a^5 + 25*a^4 + 173*a^3 + 35*a^2 - 41*a - 8)*q^29 + (2*a^9 + 10*a^8 + a^7 - 54*a^6 - 41*a^5 + 91*a^4 + 74*a^3 - 50*a^2 - 32*a - 2)*q^30 + (-2*a^9 - 11*a^8 - 6*a^7 + 50*a^6 + 55*a^5 - 63*a^4 - 61*a^3 + 28*a^2 + 2*a + 1)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-2*a^9 - 13*a^8 - 16*a^7 + 52*a^6 + 118*a^5 - 35*a^4 - 193*a^3 - 26*a^2 + 96*a + 15)*q^33 + (-4*a^7 - 15*a^6 + 6*a^5 + 60*a^4 + 20*a^3 - 49*a^2 - 20*a - 1)*q^34 + (2*a^9 + 15*a^8 + 26*a^7 - 50*a^6 - 166*a^5 + 2*a^4 + 266*a^3 + 54*a^2 - 140*a - 7)*q^35 + (-2*a^9 - 12*a^8 - 9*a^7 + 59*a^6 + 85*a^5 - 83*a^4 - 149*a^3 + 33*a^2 + 76*a + 5)*q^36 + (-2*a^9 - 14*a^8 - 21*a^7 + 48*a^6 + 131*a^5 - 11*a^4 - 180*a^3 - 35*a^2 + 70*a + 3)*q^37 + O(q^38)
*]> ;  // time = 6.809 seconds




J[309] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 309, 309, 309, 309, 103, 103 ], new_dimensions := [ 1, 3, 5, 8, 2, 6 ], dimensions := [ 1, 3, 5, 8, 4, 12 ], intersection_graph := [ 0, 1, 1, 1, 1, 5, 1, 0, 1, 1, 1, 89, 1, 1, 0, 1, 9, 1, 1, 1, 1, 0, 25, 1, 1, 1, 9, 25, 0, 1, 5, 89, 1, 1, 1, 0 ], ap_traces := [
[ -1, 1, -1, -2, -2, -5, 0, -8, 1, -2, 5, 2 ],
[ 1, -3, 1, -2, 8, -3, 4, 12, 7, 0, 7, -6 ],
[ -2, -5, -5, -2, -12, 1, -10, -16, -5, -16, -13, 4 ],
[ -1, 8, -1, 6, 6, 9, -4, 16, -11, 0, 17, -6 ]
], hecke_fields := [
x - 1,
x^3 - x^2 - 3*x + 1,
x^5 + 2*x^4 - 4*x^3 - 6*x^2 + 4*x + 1,
x^8 + x^7 - 13*x^6 - 11*x^5 + 52*x^4 + 35*x^3 - 59*x^2 - 27*x + 1
], atkin_lehners := [
[ -1, -1 ],
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 89, 1 ],
[ 9, 1 ],
[ 325, 1 ]
], tamagawa_numbers := [
[ 5, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 325, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 13 ], torsion_lower_bounds := [ 1, 1, 1, 13 ], l_ratios := [ 0, 1, 0, 25/13 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1 ], eigenvalues := [*
[ -1, 1, -1, -2, -2, -5, 0, -8, 1, -2, 5, 2 ],
[
a,
-1,
a,
-a^2 + 2*a + 1,
-a^2 + 5,
-2*a^2 + 2*a + 3,
-2*a + 2,
2*a^2 - 2*a,
a + 2,
-a^2 - 2*a + 3,
-2*a + 3,
a^2 - 4*a - 3
],
[
a,
-1,
a^4 + a^3 - 5*a^2 - 3*a + 3,
-2*a^4 - 3*a^3 + 7*a^2 + 6*a - 4,
2*a^3 + 2*a^2 - 6*a - 4,
2*a^4 + 3*a^3 - 5*a^2 - 6*a - 1,
-3*a^3 - a^2 + 10*a - 4,
-a^4 - 2*a^3 + 4*a^2 + 7*a - 6,
3*a^3 + a^2 - 10*a + 1,
-2*a^4 - 3*a^3 + 7*a^2 + 8*a - 6,
-a^4 - 3*a^3 + 3*a^2 + 9*a - 5,
-2*a^3 - 2*a^2 + 10*a + 4
],
[
a,
1,
-1/2*a^7 + 11/2*a^5 - 18*a^3 - 3/2*a^2 + 17*a + 7/2,
a^6 - 8*a^4 + a^3 + 13*a^2 - 3*a,
-a^6 - a^5 + 8*a^4 + 6*a^3 - 14*a^2 - 5*a + 3,
1/2*a^7 - 11/2*a^5 - a^4 + 18*a^3 + 15/2*a^2 - 18*a - 11/2,
-a^5 + 7*a^3 - a^2 - 8*a + 1,
a^5 + a^4 - 6*a^3 - 6*a^2 + 3*a + 7,
1/2*a^7 - 9/2*a^5 - a^4 + 10*a^3 + 15/2*a^2 - 6*a - 13/2,
a^6 + 2*a^5 - 6*a^4 - 13*a^3 + 3*a^2 + 13*a + 2,
-1/2*a^7 + 13/2*a^5 - 26*a^3 + 1/2*a^2 + 29*a + 1/2,
a^6 - 3*a^5 - 10*a^4 + 24*a^3 + 24*a^2 - 37*a - 9
]
*], q_expansions := [*
q - q^2 + q^3 - q^4 - q^5 - q^6 - 2*q^7 + 3*q^8 + q^9 + q^10 - 2*q^11 - q^12 - 5*q^13 + 2*q^14 - q^15 - q^16 - q^18 - 8*q^19 + q^20 - 2*q^21 + 2*q^22 + q^23 + 3*q^24 - 4*q^25 + 5*q^26 + q^27 + 2*q^28 - 2*q^29 + q^30 + 5*q^31 - 5*q^32 - 2*q^33 + 2*q^35 - q^36 + 2*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + a*q^5 - a*q^6 + (-a^2 + 2*a + 1)*q^7 + (a^2 - a - 1)*q^8 + q^9 + a^2*q^10 + (-a^2 + 5)*q^11 + (-a^2 + 2)*q^12 + (-2*a^2 + 2*a + 3)*q^13 + (a^2 - 2*a + 1)*q^14 - a*q^15 + (-2*a^2 + 2*a + 3)*q^16 + (-2*a + 2)*q^17 + a*q^18 + (2*a^2 - 2*a)*q^19 + (a^2 + a - 1)*q^20 + (a^2 - 2*a - 1)*q^21 + (-a^2 + 2*a + 1)*q^22 + (a + 2)*q^23 + (-a^2 + a + 1)*q^24 + (a^2 - 5)*q^25 + (-3*a + 2)*q^26 - q^27 + (a^2 - 3)*q^28 + (-a^2 - 2*a + 3)*q^29 - a^2*q^30 + (-2*a + 3)*q^31 + (-2*a^2 - a + 4)*q^32 + (a^2 - 5)*q^33 + (-2*a^2 + 2*a)*q^34 + (a^2 - 2*a + 1)*q^35 + (a^2 - 2)*q^36 + (a^2 - 4*a - 3)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (a^4 + a^3 - 5*a^2 - 3*a + 3)*q^5 - a*q^6 + (-2*a^4 - 3*a^3 + 7*a^2 + 6*a - 4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^4 - a^3 + 3*a^2 - a - 1)*q^10 + (2*a^3 + 2*a^2 - 6*a - 4)*q^11 + (-a^2 + 2)*q^12 + (2*a^4 + 3*a^3 - 5*a^2 - 6*a - 1)*q^13 + (a^4 - a^3 - 6*a^2 + 4*a + 2)*q^14 + (-a^4 - a^3 + 5*a^2 + 3*a - 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3*a^3 - a^2 + 10*a - 4)*q^17 + a*q^18 + (-a^4 - 2*a^3 + 4*a^2 + 7*a - 6)*q^19 + (-a^4 - 3*a^3 + 3*a^2 + 9*a - 5)*q^20 + (2*a^4 + 3*a^3 - 7*a^2 - 6*a + 4)*q^21 + (2*a^4 + 2*a^3 - 6*a^2 - 4*a)*q^22 + (3*a^3 + a^2 - 10*a + 1)*q^23 + (-a^3 + 4*a)*q^24 + (a^4 + 5*a^3 - a^2 - 13*a + 4)*q^25 + (-a^4 + 3*a^3 + 6*a^2 - 9*a - 2)*q^26 - q^27 + (a^4 + 4*a^3 - 4*a^2 - 14*a + 7)*q^28 + (-2*a^4 - 3*a^3 + 7*a^2 + 8*a - 6)*q^29 + (a^4 + a^3 - 3*a^2 + a + 1)*q^30 + (-a^4 - 3*a^3 + 3*a^2 + 9*a - 5)*q^31 + (-2*a^4 - 4*a^3 + 6*a^2 + 8*a - 1)*q^32 + (-2*a^3 - 2*a^2 + 6*a + 4)*q^33 + (-3*a^4 - a^3 + 10*a^2 - 4*a)*q^34 + (-2*a^3 + 4*a^2 + 14*a - 14)*q^35 + (a^2 - 2)*q^36 + (-2*a^3 - 2*a^2 + 10*a + 4)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-1/2*a^7 + 11/2*a^5 - 18*a^3 - 3/2*a^2 + 17*a + 7/2)*q^5 + a*q^6 + (a^6 - 8*a^4 + a^3 + 13*a^2 - 3*a)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (1/2*a^7 - a^6 - 11/2*a^5 + 8*a^4 + 16*a^3 - 25/2*a^2 - 10*a + 1/2)*q^10 + (-a^6 - a^5 + 8*a^4 + 6*a^3 - 14*a^2 - 5*a + 3)*q^11 + (a^2 - 2)*q^12 + (1/2*a^7 - 11/2*a^5 - a^4 + 18*a^3 + 15/2*a^2 - 18*a - 11/2)*q^13 + (a^7 - 8*a^5 + a^4 + 13*a^3 - 3*a^2)*q^14 + (-1/2*a^7 + 11/2*a^5 - 18*a^3 - 3/2*a^2 + 17*a + 7/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^5 + 7*a^3 - a^2 - 8*a + 1)*q^17 + a*q^18 + (a^5 + a^4 - 6*a^3 - 6*a^2 + 3*a + 7)*q^19 + (-1/2*a^7 + a^6 + 5/2*a^5 - 10*a^4 + 6*a^3 + 45/2*a^2 - 20*a - 15/2)*q^20 + (a^6 - 8*a^4 + a^3 + 13*a^2 - 3*a)*q^21 + (-a^7 - a^6 + 8*a^5 + 6*a^4 - 14*a^3 - 5*a^2 + 3*a)*q^22 + (1/2*a^7 - 9/2*a^5 - a^4 + 10*a^3 + 15/2*a^2 - 6*a - 13/2)*q^23 + (a^3 - 4*a)*q^24 + (1/2*a^7 - a^6 - 7/2*a^5 + 10*a^4 + 2*a^3 - 49/2*a^2 + 6*a + 23/2)*q^25 + (-1/2*a^7 + a^6 + 9/2*a^5 - 8*a^4 - 10*a^3 + 23/2*a^2 + 8*a - 1/2)*q^26 + q^27 + (-a^7 + 3*a^6 + 12*a^5 - 23*a^4 - 40*a^3 + 33*a^2 + 33*a - 1)*q^28 + (a^6 + 2*a^5 - 6*a^4 - 13*a^3 + 3*a^2 + 13*a + 2)*q^29 + (1/2*a^7 - a^6 - 11/2*a^5 + 8*a^4 + 16*a^3 - 25/2*a^2 - 10*a + 1/2)*q^30 + (-1/2*a^7 + 13/2*a^5 - 26*a^3 + 1/2*a^2 + 29*a + 1/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^6 - a^5 + 8*a^4 + 6*a^3 - 14*a^2 - 5*a + 3)*q^33 + (-a^6 + 7*a^4 - a^3 - 8*a^2 + a)*q^34 + (-a^6 + a^5 + 8*a^4 - 10*a^3 - 12*a^2 + 19*a - 1)*q^35 + (a^2 - 2)*q^36 + (a^6 - 3*a^5 - 10*a^4 + 24*a^3 + 24*a^2 - 37*a - 9)*q^37 + O(q^38)
*]> ;  // time = 45.05 seconds




J[310] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 310, 310, 310, 310, 310, 155, 155, 155, 155, 155, 62, 62, 31 ], new_dimensions := [ 1, 1, 2, 2, 3, 1, 1, 1, 4, 4, 1, 2, 2 ], dimensions := [ 1, 1, 2, 2, 3, 2, 2, 2, 8, 8, 2, 4, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 1, 5, 3, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 25, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 2401, 1, 1, 1, 23, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0, 121, 1, 1, 1, 1, 5, 1, 1, 25, 2401, 1, 1, 121, 0 ], ap_traces := [
[ 1, 2, -1, 0, 2, 0, 2, -4, -4, -4, -1, -8 ],
[ 1, -2, -1, -4, 0, -4, 0, -4, -6, 6, 1, 8 ],
[ -2, -2, -2, 0, -2, -6, -8, 4, -8, -2, -2, -10 ],
[ -2, 0, 2, -4, 4, 4, 0, 0, 4, 16, -2, 4 ],
[ 3, 2, 3, 0, 0, -8, 0, 8, -2, -2, 3, -8 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + 2*x - 2,
x^2 - 6,
x^3 - 2*x^2 - 4*x + 4
], atkin_lehners := [
[ -1, 1, 1 ],
[ -1, 1, -1 ],
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 3, 1, 1 ],
[ 3, 1, 1 ],
[ 3, 1, 1 ],
[ 23, 1, 1 ],
[ 25, 5, 1 ]
], tamagawa_numbers := [
[ 3, 1, 1 ],
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 25, 5, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 1, 5 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 3, 0, 0, 1, 5 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 1/25 ], eigenvalues := [*
[ 1, 2, -1, 0, 2, 0, 2, -4, -4, -4, -1, -8 ],
[ 1, -2, -1, -4, 0, -4, 0, -4, -6, 6, 1, 8 ],
[
-1,
a,
-1,
-2*a - 2,
-a - 2,
a - 2,
-4,
2*a + 4,
2*a - 2,
a,
-1,
-a - 6
],
[
-1,
a,
1,
-2,
a + 2,
a + 2,
-2*a,
-2*a,
2,
-a + 8,
-1,
-a + 2
],
[
1,
a,
1,
-a^2 + 4,
a^2 - 3*a - 2,
-a - 2,
-a^2 + 4,
2*a^2 - 2*a - 4,
-a^2 + 2*a + 2,
-3*a^2 + 5*a + 8,
1,
2*a^2 - a - 10
]
*], q_expansions := [*
q + q^2 + 2*q^3 + q^4 - q^5 + 2*q^6 + q^8 + q^9 - q^10 + 2*q^11 + 2*q^12 - 2*q^15 + q^16 + 2*q^17 + q^18 - 4*q^19 - q^20 + 2*q^22 - 4*q^23 + 2*q^24 + q^25 - 4*q^27 - 4*q^29 - 2*q^30 - q^31 + q^32 + 4*q^33 + 2*q^34 + q^36 - 8*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - q^5 - 2*q^6 - 4*q^7 + q^8 + q^9 - q^10 - 2*q^12 - 4*q^13 - 4*q^14 + 2*q^15 + q^16 + q^18 - 4*q^19 - q^20 + 8*q^21 - 6*q^23 - 2*q^24 + q^25 - 4*q^26 + 4*q^27 - 4*q^28 + 6*q^29 + 2*q^30 + q^31 + q^32 + 4*q^35 + q^36 + 8*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - q^5 - a*q^6 + (-2*a - 2)*q^7 - q^8 + (-2*a - 1)*q^9 + q^10 + (-a - 2)*q^11 + a*q^12 + (a - 2)*q^13 + (2*a + 2)*q^14 - a*q^15 + q^16 - 4*q^17 + (2*a + 1)*q^18 + (2*a + 4)*q^19 - q^20 + (2*a - 4)*q^21 + (a + 2)*q^22 + (2*a - 2)*q^23 - a*q^24 + q^25 + (-a + 2)*q^26 - 4*q^27 + (-2*a - 2)*q^28 + a*q^29 + a*q^30 - q^31 - q^32 - 2*q^33 + 4*q^34 + (2*a + 2)*q^35 + (-2*a - 1)*q^36 + (-a - 6)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + q^5 - a*q^6 - 2*q^7 - q^8 + 3*q^9 - q^10 + (a + 2)*q^11 + a*q^12 + (a + 2)*q^13 + 2*q^14 + a*q^15 + q^16 - 2*a*q^17 - 3*q^18 - 2*a*q^19 + q^20 - 2*a*q^21 + (-a - 2)*q^22 + 2*q^23 - a*q^24 + q^25 + (-a - 2)*q^26 - 2*q^28 + (-a + 8)*q^29 - a*q^30 - q^31 - q^32 + (2*a + 6)*q^33 + 2*a*q^34 - 2*q^35 + 3*q^36 + (-a + 2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + q^5 + a*q^6 + (-a^2 + 4)*q^7 + q^8 + (a^2 - 3)*q^9 + q^10 + (a^2 - 3*a - 2)*q^11 + a*q^12 + (-a - 2)*q^13 + (-a^2 + 4)*q^14 + a*q^15 + q^16 + (-a^2 + 4)*q^17 + (a^2 - 3)*q^18 + (2*a^2 - 2*a - 4)*q^19 + q^20 + (-2*a^2 + 4)*q^21 + (a^2 - 3*a - 2)*q^22 + (-a^2 + 2*a + 2)*q^23 + a*q^24 + q^25 + (-a - 2)*q^26 + (2*a^2 - 2*a - 4)*q^27 + (-a^2 + 4)*q^28 + (-3*a^2 + 5*a + 8)*q^29 + a*q^30 + q^31 + q^32 + (-a^2 + 2*a - 4)*q^33 + (-a^2 + 4)*q^34 + (-a^2 + 4)*q^35 + (a^2 - 3)*q^36 + (2*a^2 - a - 10)*q^37 + O(q^38)
*]> ;  // time = 129.66 seconds




J[311] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 311, 311 ], new_dimensions := [ 4, 22 ], dimensions := [ 4, 22 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -2, -1, -4, -4, -6, -7, -6, 2, -6, -6, -11 ],
[ 2, 2, 1, 8, 6, 12, 9, 16, -2, 24, 10, 27 ]
], hecke_fields := [
x^4 + x^3 - 3*x^2 - x + 1,
x^22 - 2*x^21 - 35*x^20 + 70*x^19 + 517*x^18 - 1033*x^17 - 4195*x^16 + 8357*x^15 + 20417*x^14 - 40403*x^13 - 61287*x^12 + 119701*x^11 + 113017*x^10 - 215615*x^9 - 124399*x^8 + 228609*x^7 + 76453*x^6 - 133295*x^5 - 23503*x^4 + 36742*x^3 + 3587*x^2 - 3200*x - 473
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 155 ]
], tamagawa_numbers := [
[ 1 ],
[ 155 ]
], torsion_upper_bounds := [ 1, 155 ], torsion_lower_bounds := [ 1, 155 ], l_ratios := [ 0, 1/155 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^3 - a^2 + 2*a,
a^3 + a^2 - 3*a - 1,
a^3 - 3*a,
-1,
a^2 + a - 3,
-3*a^3 - 3*a^2 + 7*a,
-a^3 - a^2 + 2*a - 1,
3*a^2 + 3*a - 4,
-a^3 - 2*a^2 + 3*a + 1,
a^3 + 2*a^2 + a - 3,
-4*a^3 - 8*a^2 + 7*a + 6
],
[
a,
-1333218028123436678/106341562018576649119*a^21 + 1367946423136236257/106341562018576649119*a^20 + 49328489263264063408/106341562018576649119*a^19 - 48698618113739814119/106341562018576649119*a^18 - 780071490285978038489/106341562018576649119*a^17 + 731764058773877640305/106341562018576649119*a^16 + 6883435129930837071209/106341562018576649119*a^15 - 6029718454604453812991/106341562018576649119*a^14 - 37117408682963362048611/106341562018576649119*a^13 + 29643589741202443321628/106341562018576649119*a^12 + 125904278451589035925849/106341562018576649119*a^11 - 88764078616540344648331/106341562018576649119*a^10 - 266400248133720180154691/106341562018576649119*a^9 + 159042733994278329421197/106341562018576649119*a^8 + 336261615438596631255820/106341562018576649119*a^7 - 162008001244132052237259/106341562018576649119*a^6 - 230084343080867524283273/106341562018576649119*a^5 + 85032171085335940948597/106341562018576649119*a^4 + 71086649415902837709445/106341562018576649119*a^3 - 17051195074052769029465/106341562018576649119*a^2 - 6284781941061791629214/106341562018576649119*a - 2035191172956196509/2473059581827363933,
-21242974024529590/106341562018576649119*a^21 - 1434491652110563978/106341562018576649119*a^20 + 3209217338769634321/106341562018576649119*a^19 + 48282217898366329351/106341562018576649119*a^18 - 94578303848943192367/106341562018576649119*a^17 - 676590780104692901915/106341562018576649119*a^16 + 1270815302353166006692/106341562018576649119*a^15 + 5102603103564094427213/106341562018576649119*a^14 - 9439579417621543494677/106341562018576649119*a^13 - 22357866355125222974699/106341562018576649119*a^12 + 41280678241435124160901/106341562018576649119*a^11 + 57441564627509462184517/106341562018576649119*a^10 - 106882614769975285857639/106341562018576649119*a^9 - 83882843771650414225579/106341562018576649119*a^8 + 158593036380613931304765/106341562018576649119*a^7 + 66319079553842412941717/106341562018576649119*a^6 - 126427357236440356717803/106341562018576649119*a^5 - 28369596568106140688094/106341562018576649119*a^4 + 47782658911006380501745/106341562018576649119*a^3 + 8238984211089590694971/106341562018576649119*a^2 - 6439892278957108980653/106341562018576649119*a - 30557112079337671866/2473059581827363933,
504418815307781939/106341562018576649119*a^21 - 1021065885099576655/106341562018576649119*a^20 - 16604493185137817773/106341562018576649119*a^19 + 33056103831567470983/106341562018576649119*a^18 + 226015020692329680027/106341562018576649119*a^17 - 435479859114799908685/106341562018576649119*a^16 - 1641199345467818455453/106341562018576649119*a^15 + 2956466065705411278227/106341562018576649119*a^14 + 6861291586789371631471/106341562018576649119*a^13 - 10597470554231302540041/106341562018576649119*a^12 - 16835996047441621774817/106341562018576649119*a^11 + 16674122550262725807072/106341562018576649119*a^10 + 24918511100968457522896/106341562018576649119*a^9 + 4438859628397342489851/106341562018576649119*a^8 - 26019738542206463779319/106341562018576649119*a^7 - 47775179818655449476697/106341562018576649119*a^6 + 24030985031406062666739/106341562018576649119*a^5 + 52435121331955185077307/106341562018576649119*a^4 - 16943596953875463472297/106341562018576649119*a^3 - 19178717695756638586794/106341562018576649119*a^2 + 5034806783502259963324/106341562018576649119*a + 39595990210148060592/2473059581827363933,
-949531404212230610/106341562018576649119*a^21 + 1404606076267666588/106341562018576649119*a^20 + 31860596932911204463/106341562018576649119*a^19 - 46971051976902102427/106341562018576649119*a^18 - 443194299396015920727/106341562018576649119*a^17 + 654211796697056201475/106341562018576649119*a^16 + 3289263238009343513027/106341562018576649119*a^15 - 4909640949988760976063/106341562018576649119*a^14 - 13911354804136965503755/106341562018576649119*a^13 + 21492498277511827879899/106341562018576649119*a^12 + 32809246067622506014675/106341562018576649119*a^11 - 55848212667582391995663/106341562018576649119*a^10 - 37152948138636735453445/106341562018576649119*a^9 + 85393270687204170694965/106341562018576649119*a^8 + 5583375858342452495631/106341562018576649119*a^7 - 76499001320510405514675/106341562018576649119*a^6 + 25817695878266203276277/106341562018576649119*a^5 + 39666285577392711382787/106341562018576649119*a^4 - 19730812320902394420787/106341562018576649119*a^3 - 10921342107175992074971/106341562018576649119*a^2 + 3730720089149782086801/106341562018576649119*a + 28348484555942980958/2473059581827363933,
321226424163746048/106341562018576649119*a^21 + 3801901583102434231/106341562018576649119*a^20 - 18552232937067380885/106341562018576649119*a^19 - 129228358922459727636/106341562018576649119*a^18 + 415822499184604316188/106341562018576649119*a^17 + 1838181668057575308290/106341562018576649119*a^16 - 4909941181790293676126/106341562018576649119*a^15 - 14192061774488959599914/106341562018576649119*a^14 + 33996329744624815911691/106341562018576649119*a^13 + 64611826293534390239510/106341562018576649119*a^12 - 143009619717835957566812/106341562018576649119*a^11 - 177164866440755054595842/106341562018576649119*a^10 + 363135701598845915429974/106341562018576649119*a^9 + 289742407609106508486970/106341562018576649119*a^8 - 534122568544790467437490/106341562018576649119*a^7 - 275603753317877822408499/106341562018576649119*a^6 + 420748487273236095304854/106341562018576649119*a^5 + 145078038418898400990846/106341562018576649119*a^4 - 153245015674186693664582/106341562018576649119*a^3 - 38930610655526174141722/106341562018576649119*a^2 + 18299352733124579928085/106341562018576649119*a + 96767738356241061887/2473059581827363933,
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]
*], q_expansions := [*
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*]> ;  // time = 6.64 seconds




J[313] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 313, 313, 313 ], new_dimensions := [ 2, 11, 12 ], dimensions := [ 2, 11, 12 ], intersection_graph := [ 0, 1, 41, 1, 0, 1, 41, 1, 0 ], ap_traces := [
[ 1, 3, 3, 2, 0, 7, 4, -2, 5, -16, 13, -16 ],
[ -8, -8, -6, -14, -11, -7, -15, 1, -44, -17, -3, -3 ],
[ 6, 1, -1, 6, 9, -8, 7, -1, 41, 29, -14, 5 ]
], hecke_fields := [
x^2 - x - 1,
x^11 + 8*x^10 + 16*x^9 - 26*x^8 - 121*x^7 - 62*x^6 + 190*x^5 + 196*x^4 - 76*x^3 - 122*x^2 + 2*x + 17,
x^12 - 6*x^11 - 2*x^10 + 69*x^9 - 68*x^8 - 268*x^7 + 399*x^6 + 368*x^5 - 701*x^4 - 57*x^3 + 262*x^2 - 22*x - 19
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 13 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 13 ]
], torsion_upper_bounds := [ 1, 1, 13 ], torsion_lower_bounds := [ 1, 1, 13 ], l_ratios := [ 1, 0, 1/13 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[
a,
-a + 2,
a + 1,
2*a,
-2*a + 1,
-3*a + 5,
2*a + 1,
-2*a,
a + 2,
-8,
3*a + 5,
-2*a - 7
],
[
a,
-29/13*a^10 - 184/13*a^9 - 159/13*a^8 + 1023/13*a^7 + 1831/13*a^6 - 1251/13*a^5 - 3525/13*a^4 + 133/13*a^3 + 2052/13*a^2 + 138/13*a - 290/13,
3/13*a^10 + 15/13*a^9 - 10/13*a^8 - 126/13*a^7 - 37/13*a^6 + 341/13*a^5 + 132/13*a^4 - 302/13*a^3 - 76/13*a^2 + 31/13*a + 4/13,
73/13*a^10 + 482/13*a^9 + 502/13*a^8 - 2559/13*a^7 - 5238/13*a^6 + 2582/13*a^5 + 9959/13*a^4 + 577/13*a^3 - 5875/13*a^2 - 602/13*a + 834/13,
-8/13*a^10 - 66/13*a^9 - 125/13*a^8 + 271/13*a^7 + 1013/13*a^6 + 135/13*a^5 - 1860/13*a^4 - 850/13*a^3 + 1117/13*a^2 + 368/13*a - 197/13,
73/13*a^10 + 482/13*a^9 + 502/13*a^8 - 2546/13*a^7 - 5199/13*a^6 + 2517/13*a^5 + 9751/13*a^4 + 655/13*a^3 - 5641/13*a^2 - 641/13*a + 795/13,
-3*a^10 - 20*a^9 - 21*a^8 + 107*a^7 + 217*a^6 - 114*a^5 - 408*a^4 - 6*a^3 + 232*a^2 + 11*a - 31,
-36/13*a^10 - 232/13*a^9 - 218/13*a^8 + 1252/13*a^7 + 2368/13*a^6 - 1349/13*a^5 - 4405/13*a^4 - 211/13*a^3 + 2459/13*a^2 + 395/13*a - 373/13,
16/13*a^10 + 106/13*a^9 + 107/13*a^8 - 581/13*a^7 - 1142/13*a^6 + 692/13*a^5 + 2225/13*a^4 - 120/13*a^3 - 1389/13*a^2 + 31/13*a + 186/13,
18/13*a^10 + 116/13*a^9 + 109/13*a^8 - 639/13*a^7 - 1236/13*a^6 + 720/13*a^5 + 2495/13*a^4 + 99/13*a^3 - 1587/13*a^2 - 152/13*a + 245/13,
-47/13*a^10 - 300/13*a^9 - 268/13*a^8 + 1662/13*a^7 + 3054/13*a^6 - 2010/13*a^5 - 5981/13*a^4 + 190/13*a^3 + 3678/13*a^2 + 251/13*a - 561/13,
16/13*a^10 + 132/13*a^9 + 237/13*a^8 - 607/13*a^7 - 2026/13*a^6 + 107/13*a^5 + 4019/13*a^4 + 1167/13*a^3 - 2663/13*a^2 - 567/13*a + 433/13
],
[
a,
a^10 - 3*a^9 - 12*a^8 + 35*a^7 + 54*a^6 - 139*a^5 - 112*a^4 + 200*a^3 + 100*a^2 - 47*a - 17,
a^11 - 4*a^10 - 9*a^9 + 47*a^8 + 18*a^7 - 190*a^6 + 34*a^5 + 290*a^4 - 113*a^3 - 105*a^2 + 33*a + 8,
-3/2*a^11 + 11/2*a^10 + 31/2*a^9 - 67*a^8 - 47*a^7 + 283*a^6 + 27/2*a^5 - 919/2*a^4 + 99*a^3 + 387/2*a^2 - 69/2*a - 33/2,
a^11 - 5*a^10 - 7*a^9 + 63*a^8 - 11*a^7 - 279*a^6 + 172*a^5 + 491*a^4 - 344*a^3 - 260*a^2 + 95*a + 32,
-a^11 + 2*a^10 + 15*a^9 - 22*a^8 - 92*a^7 + 77*a^6 + 276*a^5 - 72*a^4 - 355*a^3 - 52*a^2 + 80*a + 14,
a^11 - 4*a^10 - 9*a^9 + 47*a^8 + 19*a^7 - 193*a^6 + 27*a^5 + 313*a^4 - 102*a^3 - 151*a^2 + 36*a + 18,
3*a^11 - 12*a^10 - 27*a^9 + 141*a^8 + 55*a^7 - 573*a^6 + 95*a^5 + 892*a^4 - 326*a^3 - 357*a^2 + 96*a + 33,
-7/2*a^11 + 29/2*a^10 + 63/2*a^9 - 176*a^8 - 57*a^7 + 743*a^6 - 333/2*a^5 - 2431/2*a^4 + 498*a^3 + 1075/2*a^2 - 307/2*a - 101/2,
-a^11 + 4*a^10 + 9*a^9 - 46*a^8 - 22*a^7 + 185*a^6 - 2*a^5 - 296*a^4 + 46*a^3 + 147*a^2 - 19*a - 15,
3/2*a^11 - 15/2*a^10 - 17/2*a^9 + 88*a^8 - 32*a^7 - 364*a^6 + 581/2*a^5 + 1225/2*a^4 - 527*a^3 - 689/2*a^2 + 285/2*a + 77/2,
4*a^11 - 14*a^10 - 44*a^9 + 171*a^8 + 159*a^7 - 720*a^6 - 183*a^5 + 1141*a^4 - 31*a^3 - 411*a^2 + 39*a + 31
]
*], q_expansions := [*
q + a*q^2 + (-a + 2)*q^3 + (a - 1)*q^4 + (a + 1)*q^5 + (a - 1)*q^6 + 2*a*q^7 + (-2*a + 1)*q^8 + (-3*a + 2)*q^9 + (2*a + 1)*q^10 + (-2*a + 1)*q^11 + (2*a - 3)*q^12 + (-3*a + 5)*q^13 + (2*a + 2)*q^14 + q^15 - 3*a*q^16 + (2*a + 1)*q^17 + (-a - 3)*q^18 - 2*a*q^19 + a*q^20 + (2*a - 2)*q^21 + (-a - 2)*q^22 + (a + 2)*q^23 + (-3*a + 4)*q^24 + (3*a - 3)*q^25 + (2*a - 3)*q^26 + (-2*a + 1)*q^27 + 2*q^28 - 8*q^29 + a*q^30 + (3*a + 5)*q^31 + (a - 5)*q^32 + (-3*a + 4)*q^33 + (3*a + 2)*q^34 + (4*a + 2)*q^35 + (2*a - 5)*q^36 + (-2*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-29/13*a^10 - 184/13*a^9 - 159/13*a^8 + 1023/13*a^7 + 1831/13*a^6 - 1251/13*a^5 - 3525/13*a^4 + 133/13*a^3 + 2052/13*a^2 + 138/13*a - 290/13)*q^3 + (a^2 - 2)*q^4 + (3/13*a^10 + 15/13*a^9 - 10/13*a^8 - 126/13*a^7 - 37/13*a^6 + 341/13*a^5 + 132/13*a^4 - 302/13*a^3 - 76/13*a^2 + 31/13*a + 4/13)*q^5 + (48/13*a^10 + 305/13*a^9 + 269/13*a^8 - 1678/13*a^7 - 3049/13*a^6 + 1985/13*a^5 + 5817/13*a^4 - 152/13*a^3 - 3400/13*a^2 - 232/13*a + 493/13)*q^6 + (73/13*a^10 + 482/13*a^9 + 502/13*a^8 - 2559/13*a^7 - 5238/13*a^6 + 2582/13*a^5 + 9959/13*a^4 + 577/13*a^3 - 5875/13*a^2 - 602/13*a + 834/13)*q^7 + (a^3 - 4*a)*q^8 + (-4*a^10 - 27*a^9 - 30*a^8 + 142*a^7 + 303*a^6 - 138*a^5 - 576*a^4 - 39*a^3 + 348*a^2 + 35*a - 55)*q^9 + (-9/13*a^10 - 58/13*a^9 - 48/13*a^8 + 326/13*a^7 + 527/13*a^6 - 438/13*a^5 - 890/13*a^4 + 152/13*a^3 + 397/13*a^2 - 2/13*a - 51/13)*q^10 + (-8/13*a^10 - 66/13*a^9 - 125/13*a^8 + 271/13*a^7 + 1013/13*a^6 + 135/13*a^5 - 1860/13*a^4 - 850/13*a^3 + 1117/13*a^2 + 368/13*a - 197/13)*q^11 + (-21/13*a^10 - 131/13*a^9 - 112/13*a^8 + 713/13*a^7 + 1299/13*a^6 - 801/13*a^5 - 2510/13*a^4 - 18/13*a^3 + 1520/13*a^2 + 121/13*a - 236/13)*q^12 + (73/13*a^10 + 482/13*a^9 + 502/13*a^8 - 2546/13*a^7 - 5199/13*a^6 + 2517/13*a^5 + 9751/13*a^4 + 655/13*a^3 - 5641/13*a^2 - 641/13*a + 795/13)*q^13 + (-102/13*a^10 - 666/13*a^9 - 661/13*a^8 + 3595/13*a^7 + 7108/13*a^6 - 3911/13*a^5 - 13731/13*a^4 - 327/13*a^3 + 8304/13*a^2 + 688/13*a - 1241/13)*q^14 + (10*a^10 + 66*a^9 + 68*a^8 - 353*a^7 - 715*a^6 + 369*a^5 + 1371*a^4 + 58*a^3 - 826*a^2 - 77*a + 123)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3*a^10 - 20*a^9 - 21*a^8 + 107*a^7 + 217*a^6 - 114*a^5 - 408*a^4 - 6*a^3 + 232*a^2 + 11*a - 31)*q^17 + (5*a^10 + 34*a^9 + 38*a^8 - 181*a^7 - 386*a^6 + 184*a^5 + 745*a^4 + 44*a^3 - 453*a^2 - 47*a + 68)*q^18 + (-36/13*a^10 - 232/13*a^9 - 218/13*a^8 + 1252/13*a^7 + 2368/13*a^6 - 1349/13*a^5 - 4405/13*a^4 - 211/13*a^3 + 2459/13*a^2 + 395/13*a - 373/13)*q^19 + (8/13*a^10 + 66/13*a^9 + 112/13*a^8 - 310/13*a^7 - 922/13*a^6 + 138/13*a^5 + 1652/13*a^4 + 317/13*a^3 - 948/13*a^2 - 95/13*a + 145/13)*q^20 + (-64/13*a^10 - 437/13*a^9 - 506/13*a^8 + 2285/13*a^7 + 5062/13*a^6 - 2131/13*a^5 - 9784/13*a^4 - 820/13*a^3 + 6063/13*a^2 + 617/13*a - 939/13)*q^21 + (-2/13*a^10 + 3/13*a^9 + 63/13*a^8 + 45/13*a^7 - 361/13*a^6 - 340/13*a^5 + 718/13*a^4 + 509/13*a^3 - 608/13*a^2 - 181/13*a + 136/13)*q^22 + (16/13*a^10 + 106/13*a^9 + 107/13*a^8 - 581/13*a^7 - 1142/13*a^6 + 692/13*a^5 + 2225/13*a^4 - 120/13*a^3 - 1389/13*a^2 + 31/13*a + 186/13)*q^23 + (-59/13*a^10 - 386/13*a^9 - 371/13*a^8 + 2114/13*a^7 + 3995/13*a^6 - 2490/13*a^5 - 7536/13*a^4 + 228/13*a^3 + 4359/13*a^2 + 270/13*a - 629/13)*q^24 + (-12*a^10 - 79*a^9 - 80*a^8 + 427*a^7 + 854*a^6 - 465*a^5 - 1660*a^4 - 45*a^3 + 1019*a^2 + 90*a - 157)*q^25 + (-102/13*a^10 - 666/13*a^9 - 648/13*a^8 + 3634/13*a^7 + 7043/13*a^6 - 4119/13*a^5 - 13653/13*a^4 - 93/13*a^3 + 8265/13*a^2 + 649/13*a - 1241/13)*q^26 + (68/13*a^10 + 457/13*a^9 + 497/13*a^8 - 2427/13*a^7 - 5081/13*a^6 + 2473/13*a^5 + 9687/13*a^4 + 478/13*a^3 - 5770/13*a^2 - 554/13*a + 823/13)*q^27 + (4/13*a^10 + 7/13*a^9 - 61/13*a^8 - 116/13*a^7 + 241/13*a^6 + 485/13*a^5 - 253/13*a^4 - 602/13*a^3 - 6/13*a^2 + 167/13*a + 66/13)*q^28 + (18/13*a^10 + 116/13*a^9 + 109/13*a^8 - 639/13*a^7 - 1236/13*a^6 + 720/13*a^5 + 2495/13*a^4 + 99/13*a^3 - 1587/13*a^2 - 152/13*a + 245/13)*q^29 + (-14*a^10 - 92*a^9 - 93*a^8 + 495*a^7 + 989*a^6 - 529*a^5 - 1902*a^4 - 66*a^3 + 1143*a^2 + 103*a - 170)*q^30 + (-47/13*a^10 - 300/13*a^9 - 268/13*a^8 + 1662/13*a^7 + 3054/13*a^6 - 2010/13*a^5 - 5981/13*a^4 + 190/13*a^3 + 3678/13*a^2 + 251/13*a - 561/13)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (105/13*a^10 + 694/13*a^9 + 716/13*a^8 - 3734/13*a^7 - 7587/13*a^6 + 3966/13*a^5 + 14760/13*a^4 + 597/13*a^3 - 9017/13*a^2 - 787/13*a + 1349/13)*q^33 + (4*a^10 + 27*a^9 + 29*a^8 - 146*a^7 - 300*a^6 + 162*a^5 + 582*a^4 + 4*a^3 - 355*a^2 - 25*a + 51)*q^34 + (-14/13*a^10 - 83/13*a^9 - 40/13*a^8 + 497/13*a^7 + 593/13*a^6 - 794/13*a^5 - 915/13*a^4 + 430/13*a^3 + 190/13*a^2 - 32/13*a + 16/13)*q^35 + (2*a^10 + 12*a^9 + 9*a^8 - 65*a^7 - 112*a^6 + 71*a^5 + 216*a^4 + 5*a^3 - 133*a^2 - 12*a + 25)*q^36 + (16/13*a^10 + 132/13*a^9 + 237/13*a^8 - 607/13*a^7 - 2026/13*a^6 + 107/13*a^5 + 4019/13*a^4 + 1167/13*a^3 - 2663/13*a^2 - 567/13*a + 433/13)*q^37 + O(q^38),
q + a*q^2 + (a^10 - 3*a^9 - 12*a^8 + 35*a^7 + 54*a^6 - 139*a^5 - 112*a^4 + 200*a^3 + 100*a^2 - 47*a - 17)*q^3 + (a^2 - 2)*q^4 + (a^11 - 4*a^10 - 9*a^9 + 47*a^8 + 18*a^7 - 190*a^6 + 34*a^5 + 290*a^4 - 113*a^3 - 105*a^2 + 33*a + 8)*q^5 + (a^11 - 3*a^10 - 12*a^9 + 35*a^8 + 54*a^7 - 139*a^6 - 112*a^5 + 200*a^4 + 100*a^3 - 47*a^2 - 17*a)*q^6 + (-3/2*a^11 + 11/2*a^10 + 31/2*a^9 - 67*a^8 - 47*a^7 + 283*a^6 + 27/2*a^5 - 919/2*a^4 + 99*a^3 + 387/2*a^2 - 69/2*a - 33/2)*q^7 + (a^3 - 4*a)*q^8 + (-3*a^11 + 12*a^10 + 28*a^9 - 145*a^8 - 61*a^7 + 608*a^6 - 94*a^5 - 981*a^4 + 356*a^3 + 412*a^2 - 106*a - 37)*q^9 + (2*a^11 - 7*a^10 - 22*a^9 + 86*a^8 + 78*a^7 - 365*a^6 - 78*a^5 + 588*a^4 - 48*a^3 - 229*a^2 + 30*a + 19)*q^10 + (a^11 - 5*a^10 - 7*a^9 + 63*a^8 - 11*a^7 - 279*a^6 + 172*a^5 + 491*a^4 - 344*a^3 - 260*a^2 + 95*a + 32)*q^11 + (3*a^11 - 12*a^10 - 28*a^9 + 146*a^8 + 59*a^7 - 619*a^6 + 110*a^5 + 1025*a^4 - 390*a^3 - 479*a^2 + 116*a + 53)*q^12 + (-a^11 + 2*a^10 + 15*a^9 - 22*a^8 - 92*a^7 + 77*a^6 + 276*a^5 - 72*a^4 - 355*a^3 - 52*a^2 + 80*a + 14)*q^13 + (-7/2*a^11 + 25/2*a^10 + 73/2*a^9 - 149*a^8 - 119*a^7 + 612*a^6 + 185/2*a^5 - 1905/2*a^4 + 108*a^3 + 717/2*a^2 - 99/2*a - 57/2)*q^14 + (-a^11 + 4*a^10 + 9*a^9 - 47*a^8 - 18*a^7 + 190*a^6 - 35*a^5 - 288*a^4 + 119*a^3 + 96*a^2 - 42*a - 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^11 - 4*a^10 - 9*a^9 + 47*a^8 + 19*a^7 - 193*a^6 + 27*a^5 + 313*a^4 - 102*a^3 - 151*a^2 + 36*a + 18)*q^17 + (-6*a^11 + 22*a^10 + 62*a^9 - 265*a^8 - 196*a^7 + 1103*a^6 + 123*a^5 - 1747*a^4 + 241*a^3 + 680*a^2 - 103*a - 57)*q^18 + (3*a^11 - 12*a^10 - 27*a^9 + 141*a^8 + 55*a^7 - 573*a^6 + 95*a^5 + 892*a^4 - 326*a^3 - 357*a^2 + 96*a + 33)*q^19 + (3*a^11 - 10*a^10 - 34*a^9 + 120*a^8 + 135*a^7 - 496*a^6 - 216*a^5 + 774*a^4 + 111*a^3 - 284*a^2 - 3*a + 22)*q^20 + (2*a^11 - 4*a^10 - 31*a^9 + 48*a^8 + 189*a^7 - 186*a^6 - 545*a^5 + 208*a^4 + 662*a^3 + 103*a^2 - 141*a - 33)*q^21 + (a^11 - 5*a^10 - 6*a^9 + 57*a^8 - 11*a^7 - 227*a^6 + 123*a^5 + 357*a^4 - 203*a^3 - 167*a^2 + 54*a + 19)*q^22 + (-7/2*a^11 + 29/2*a^10 + 63/2*a^9 - 176*a^8 - 57*a^7 + 743*a^6 - 333/2*a^5 - 2431/2*a^4 + 498*a^3 + 1075/2*a^2 - 307/2*a - 101/2)*q^23 + (4*a^11 - 16*a^10 - 37*a^9 + 193*a^8 + 77*a^7 - 809*a^6 + 145*a^5 + 1313*a^4 - 508*a^3 - 576*a^2 + 153*a + 57)*q^24 + (2*a^11 - 7*a^10 - 22*a^9 + 86*a^8 + 78*a^7 - 364*a^6 - 80*a^5 + 581*a^4 - 35*a^3 - 218*a^2 + 9*a + 21)*q^25 + (-4*a^11 + 13*a^10 + 47*a^9 - 160*a^8 - 191*a^7 + 675*a^6 + 296*a^5 - 1056*a^4 - 109*a^3 + 342*a^2 - 8*a - 19)*q^26 + (2*a^11 - 6*a^10 - 24*a^9 + 70*a^8 + 107*a^7 - 276*a^6 - 215*a^5 + 386*a^4 + 175*a^3 - 70*a^2 - 17*a - 4)*q^27 + (-11/2*a^11 + 37/2*a^10 + 123/2*a^9 - 223*a^8 - 232*a^7 + 923*a^6 + 617/2*a^5 - 2853/2*a^4 - 39*a^3 + 961/2*a^2 - 73/2*a - 67/2)*q^28 + (-a^11 + 4*a^10 + 9*a^9 - 46*a^8 - 22*a^7 + 185*a^6 - 2*a^5 - 296*a^4 + 46*a^3 + 147*a^2 - 19*a - 15)*q^29 + (-2*a^11 + 7*a^10 + 22*a^9 - 86*a^8 - 78*a^7 + 364*a^6 + 80*a^5 - 582*a^4 + 39*a^3 + 220*a^2 - 25*a - 19)*q^30 + (3/2*a^11 - 15/2*a^10 - 17/2*a^9 + 88*a^8 - 32*a^7 - 364*a^6 + 581/2*a^5 + 1225/2*a^4 - 527*a^3 - 689/2*a^2 + 285/2*a + 77/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2*a^11 - 7*a^10 - 22*a^9 + 84*a^8 + 84*a^7 - 347*a^6 - 130*a^5 + 536*a^4 + 73*a^3 - 177*a^2 - 11*a + 7)*q^33 + (2*a^11 - 7*a^10 - 22*a^9 + 87*a^8 + 75*a^7 - 372*a^6 - 55*a^5 + 599*a^4 - 94*a^3 - 226*a^2 + 40*a + 19)*q^34 + (-a^11 + 3*a^10 + 12*a^9 - 34*a^8 - 57*a^7 + 131*a^6 + 137*a^5 - 184*a^4 - 154*a^3 + 47*a^2 + 27*a + 1)*q^35 + (-8*a^11 + 26*a^10 + 93*a^9 - 314*a^8 - 383*a^7 + 1301*a^6 + 649*a^5 - 2003*a^4 - 374*a^3 + 645*a^2 + 23*a - 40)*q^36 + (4*a^11 - 14*a^10 - 44*a^9 + 171*a^8 + 159*a^7 - 720*a^6 - 183*a^5 + 1141*a^4 - 31*a^3 - 411*a^2 + 39*a + 31)*q^37 + O(q^38)
*]> ;  // time = 4.889 seconds




J[314] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 314, 314, 314, 157, 157 ], new_dimensions := [ 1, 6, 7, 5, 7 ], dimensions := [ 1, 6, 7, 10, 14 ], intersection_graph := [ 0, 1, 1, 5, 1, 1, 0, 1, 1, 2147, 1, 1, 0, 709, 1, 5, 1, 709, 0, 1, 1, 2147, 1, 1, 0 ], ap_traces := [
[ -1, 0, 0, -3, -2, -1, 3, -4, -1, 0, -6, -1 ],
[ -6, 3, 1, 3, 9, 4, -7, 17, -3, -5, 18, 14 ],
[ 7, -1, 3, 4, -1, 7, 4, 1, 0, 5, 0, -3 ]
], hecke_fields := [
x - 1,
x^6 - 3*x^5 - 9*x^4 + 26*x^3 + 20*x^2 - 43*x - 25,
x^7 + x^6 - 17*x^5 - 6*x^4 + 84*x^3 - 19*x^2 - 73*x + 4
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 6441, 3 ],
[ 56011, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 3 ],
[ 56011, 1 ]
], torsion_upper_bounds := [ 1, 3, 79 ], torsion_lower_bounds := [ 1, 3, 79 ], l_ratios := [ 0, 1/3, 709/79 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ -1, 0, 0, -3, -2, -1, 3, -4, -1, 0, -6, -1 ],
[
-1,
a,
-5/13*a^5 + 8/13*a^4 + 51/13*a^3 - 56/13*a^2 - 103/13*a + 24/13,
-2/13*a^5 - 2/13*a^4 + 23/13*a^3 + 14/13*a^2 - 49/13*a - 6/13,
5/13*a^5 + 5/13*a^4 - 64/13*a^3 - 61/13*a^2 + 181/13*a + 171/13,
8/13*a^5 - 18/13*a^4 - 66/13*a^3 + 126/13*a^2 + 92/13*a - 80/13,
8/13*a^5 - 5/13*a^4 - 92/13*a^3 - 4/13*a^2 + 248/13*a + 154/13,
6/13*a^5 - 7/13*a^4 - 56/13*a^3 + 36/13*a^2 + 82/13*a + 70/13,
-6/13*a^5 - 6/13*a^4 + 82/13*a^3 + 81/13*a^2 - 264/13*a - 226/13,
7/13*a^5 - 19/13*a^4 - 48/13*a^3 + 133/13*a^2 + 9/13*a - 109/13,
2/13*a^5 + 2/13*a^4 - 10/13*a^3 - 40/13*a^2 - 16/13*a + 136/13,
-10/13*a^5 + 16/13*a^4 + 76/13*a^3 - 86/13*a^2 - 76/13*a + 22/13
],
[
1,
a,
-1/3*a^5 + 11/3*a^3 - 4/3*a^2 - 19/3*a + 4/3,
1/15*a^6 + 7/15*a^5 - a^4 - 71/15*a^3 + 26/5*a^2 + 28/5*a + 1/15,
-1/15*a^6 - 2/15*a^5 + 4/3*a^4 + 2/5*a^3 - 41/5*a^2 + 86/15*a + 74/15,
-1/15*a^6 + 1/5*a^5 + a^4 - 8/5*a^3 - 38/15*a^2 - 29/15*a + 49/15,
1/15*a^6 - 1/5*a^5 - 4/3*a^4 + 34/15*a^3 + 88/15*a^2 - 91/15*a - 13/5,
2/15*a^6 + 4/15*a^5 - a^4 - 32/15*a^3 - 4/15*a^2 + 68/15*a + 4/5,
1/5*a^6 + 1/15*a^5 - 3*a^4 - 8/15*a^3 + 169/15*a^2 + 7/15*a - 97/15,
-1/3*a^6 - 2/3*a^5 + 14/3*a^4 + 6*a^3 - 17*a^2 - 16/3*a + 8/3,
2/15*a^6 + 4/15*a^5 - 8/3*a^4 - 14/5*a^3 + 72/5*a^2 + 38/15*a - 118/15,
-7/15*a^6 - 3/5*a^5 + 19/3*a^4 + 62/15*a^3 - 346/15*a^2 + 37/15*a + 51/5
]
*], q_expansions := [*
q - q^2 + q^4 - 3*q^7 - q^8 - 3*q^9 - 2*q^11 - q^13 + 3*q^14 + q^16 + 3*q^17 + 3*q^18 - 4*q^19 + 2*q^22 - q^23 - 5*q^25 + q^26 - 3*q^28 - 6*q^31 - q^32 - 3*q^34 - 3*q^36 - q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-5/13*a^5 + 8/13*a^4 + 51/13*a^3 - 56/13*a^2 - 103/13*a + 24/13)*q^5 - a*q^6 + (-2/13*a^5 - 2/13*a^4 + 23/13*a^3 + 14/13*a^2 - 49/13*a - 6/13)*q^7 - q^8 + (a^2 - 3)*q^9 + (5/13*a^5 - 8/13*a^4 - 51/13*a^3 + 56/13*a^2 + 103/13*a - 24/13)*q^10 + (5/13*a^5 + 5/13*a^4 - 64/13*a^3 - 61/13*a^2 + 181/13*a + 171/13)*q^11 + a*q^12 + (8/13*a^5 - 18/13*a^4 - 66/13*a^3 + 126/13*a^2 + 92/13*a - 80/13)*q^13 + (2/13*a^5 + 2/13*a^4 - 23/13*a^3 - 14/13*a^2 + 49/13*a + 6/13)*q^14 + (-7/13*a^5 + 6/13*a^4 + 74/13*a^3 - 3/13*a^2 - 191/13*a - 125/13)*q^15 + q^16 + (8/13*a^5 - 5/13*a^4 - 92/13*a^3 - 4/13*a^2 + 248/13*a + 154/13)*q^17 + (-a^2 + 3)*q^18 + (6/13*a^5 - 7/13*a^4 - 56/13*a^3 + 36/13*a^2 + 82/13*a + 70/13)*q^19 + (-5/13*a^5 + 8/13*a^4 + 51/13*a^3 - 56/13*a^2 - 103/13*a + 24/13)*q^20 + (-8/13*a^5 + 5/13*a^4 + 66/13*a^3 - 9/13*a^2 - 92/13*a - 50/13)*q^21 + (-5/13*a^5 - 5/13*a^4 + 64/13*a^3 + 61/13*a^2 - 181/13*a - 171/13)*q^22 + (-6/13*a^5 - 6/13*a^4 + 82/13*a^3 + 81/13*a^2 - 264/13*a - 226/13)*q^23 - a*q^24 + (-4/13*a^5 + 22/13*a^4 + 7/13*a^3 - 180/13*a^2 + 97/13*a + 287/13)*q^25 + (-8/13*a^5 + 18/13*a^4 + 66/13*a^3 - 126/13*a^2 - 92/13*a + 80/13)*q^26 + (a^3 - 6*a)*q^27 + (-2/13*a^5 - 2/13*a^4 + 23/13*a^3 + 14/13*a^2 - 49/13*a - 6/13)*q^28 + (7/13*a^5 - 19/13*a^4 - 48/13*a^3 + 133/13*a^2 + 9/13*a - 109/13)*q^29 + (7/13*a^5 - 6/13*a^4 - 74/13*a^3 + 3/13*a^2 + 191/13*a + 125/13)*q^30 + (2/13*a^5 + 2/13*a^4 - 10/13*a^3 - 40/13*a^2 - 16/13*a + 136/13)*q^31 - q^32 + (20/13*a^5 - 19/13*a^4 - 191/13*a^3 + 81/13*a^2 + 386/13*a + 125/13)*q^33 + (-8/13*a^5 + 5/13*a^4 + 92/13*a^3 + 4/13*a^2 - 248/13*a - 154/13)*q^34 + (-17/13*a^5 + 22/13*a^4 + 163/13*a^3 - 115/13*a^2 - 345/13*a - 38/13)*q^35 + (a^2 - 3)*q^36 + (-10/13*a^5 + 16/13*a^4 + 76/13*a^3 - 86/13*a^2 - 76/13*a + 22/13)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-1/3*a^5 + 11/3*a^3 - 4/3*a^2 - 19/3*a + 4/3)*q^5 + a*q^6 + (1/15*a^6 + 7/15*a^5 - a^4 - 71/15*a^3 + 26/5*a^2 + 28/5*a + 1/15)*q^7 + q^8 + (a^2 - 3)*q^9 + (-1/3*a^5 + 11/3*a^3 - 4/3*a^2 - 19/3*a + 4/3)*q^10 + (-1/15*a^6 - 2/15*a^5 + 4/3*a^4 + 2/5*a^3 - 41/5*a^2 + 86/15*a + 74/15)*q^11 + a*q^12 + (-1/15*a^6 + 1/5*a^5 + a^4 - 8/5*a^3 - 38/15*a^2 - 29/15*a + 49/15)*q^13 + (1/15*a^6 + 7/15*a^5 - a^4 - 71/15*a^3 + 26/5*a^2 + 28/5*a + 1/15)*q^14 + (-1/3*a^6 + 11/3*a^4 - 4/3*a^3 - 19/3*a^2 + 4/3*a)*q^15 + q^16 + (1/15*a^6 - 1/5*a^5 - 4/3*a^4 + 34/15*a^3 + 88/15*a^2 - 91/15*a - 13/5)*q^17 + (a^2 - 3)*q^18 + (2/15*a^6 + 4/15*a^5 - a^4 - 32/15*a^3 - 4/15*a^2 + 68/15*a + 4/5)*q^19 + (-1/3*a^5 + 11/3*a^3 - 4/3*a^2 - 19/3*a + 4/3)*q^20 + (2/5*a^6 + 2/15*a^5 - 13/3*a^4 - 2/5*a^3 + 103/15*a^2 + 74/15*a - 4/15)*q^21 + (-1/15*a^6 - 2/15*a^5 + 4/3*a^4 + 2/5*a^3 - 41/5*a^2 + 86/15*a + 74/15)*q^22 + (1/5*a^6 + 1/15*a^5 - 3*a^4 - 8/15*a^3 + 169/15*a^2 + 7/15*a - 97/15)*q^23 + a*q^24 + (-2/3*a^4 + 1/3*a^3 + 20/3*a^2 - 7*a - 11/3)*q^25 + (-1/15*a^6 + 1/5*a^5 + a^4 - 8/5*a^3 - 38/15*a^2 - 29/15*a + 49/15)*q^26 + (a^3 - 6*a)*q^27 + (1/15*a^6 + 7/15*a^5 - a^4 - 71/15*a^3 + 26/5*a^2 + 28/5*a + 1/15)*q^28 + (-1/3*a^6 - 2/3*a^5 + 14/3*a^4 + 6*a^3 - 17*a^2 - 16/3*a + 8/3)*q^29 + (-1/3*a^6 + 11/3*a^4 - 4/3*a^3 - 19/3*a^2 + 4/3*a)*q^30 + (2/15*a^6 + 4/15*a^5 - 8/3*a^4 - 14/5*a^3 + 72/5*a^2 + 38/15*a - 118/15)*q^31 + q^32 + (-1/15*a^6 + 1/5*a^5 - 13/5*a^3 + 67/15*a^2 + 1/15*a + 4/15)*q^33 + (1/15*a^6 - 1/5*a^5 - 4/3*a^4 + 34/15*a^3 + 88/15*a^2 - 91/15*a - 13/5)*q^34 + (2/15*a^6 - 1/15*a^5 - 4/3*a^4 + 11/5*a^3 + 11/15*a^2 - 39/5*a + 4/5)*q^35 + (a^2 - 3)*q^36 + (-7/15*a^6 - 3/5*a^5 + 19/3*a^4 + 62/15*a^3 - 346/15*a^2 + 37/15*a + 51/5)*q^37 + O(q^38)
*]> ;  // time = 68.721 seconds




J[317] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 317, 317 ], new_dimensions := [ 11, 15 ], dimensions := [ 11, 15 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -3, -11, -4, -20, -10, -16, -7, -31, 0, 12, -12, -16 ],
[ 1, 11, 2, 20, 6, 14, 5, 31, 0, -2, 12, 14 ]
], hecke_fields := [
x^11 + 3*x^10 - 10*x^9 - 32*x^8 + 31*x^7 + 109*x^6 - 42*x^5 - 147*x^4 + 35*x^3 + 68*x^2 - 19*x - 1,
x^15 - x^14 - 22*x^13 + 22*x^12 + 188*x^11 - 184*x^10 - 786*x^9 + 723*x^8 + 1666*x^7 - 1315*x^6 - 1715*x^5 + 910*x^4 + 829*x^3 - 168*x^2 - 129*x + 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 79 ]
], tamagawa_numbers := [
[ 1 ],
[ 79 ]
], torsion_upper_bounds := [ 1, 79 ], torsion_lower_bounds := [ 1, 79 ], l_ratios := [ 0, 1/79 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
113/1046*a^10 - 154/523*a^9 - 1081/523*a^8 + 2021/523*a^7 + 12971/1046*a^6 - 9125/523*a^5 - 14011/523*a^4 + 33587/1046*a^3 + 8762/523*a^2 - 10392/523*a + 1175/1046,
234/523*a^10 + 834/523*a^9 - 1950/523*a^8 - 8588/523*a^7 + 3603/523*a^6 + 27458/523*a^5 + 2/523*a^4 - 33780/523*a^3 - 1733/523*a^2 + 13352/523*a - 964/523,
-250/523*a^10 - 596/523*a^9 + 2432/523*a^8 + 5322/523*a^7 - 7041/523*a^6 - 12072/523*a^5 + 7673/523*a^4 + 5045/523*a^3 - 2109/523*a^2 + 3374/523*a - 1822/523,
7/523*a^10 + 92/523*a^9 + 116/523*a^8 - 990/523*a^7 - 1830/523*a^6 + 3271/523*a^5 + 6285/523*a^4 - 4001/523*a^3 - 4922/523*a^2 + 2031/523*a - 1723/523,
59/523*a^10 + 103/523*a^9 - 666/523*a^8 - 574/523*a^7 + 2806/523*a^6 - 1494/523*a^5 - 5976/523*a^4 + 9761/523*a^3 + 4165/523*a^2 - 9704/523*a + 794/523,
-677/523*a^10 - 1501/523*a^9 + 7385/523*a^8 + 14981/523*a^7 - 25638/523*a^6 - 44243/523*a^5 + 33797/523*a^4 + 43567/523*a^3 - 13575/523*a^2 - 8595/523*a - 273/523,
365/1046*a^10 + 456/523*a^9 - 1608/523*a^8 - 3770/523*a^7 + 7759/1046*a^6 + 6867/523*a^5 - 4435/523*a^4 + 427/1046*a^3 + 5415/523*a^2 - 3645/523*a - 7507/1046,
-77/523*a^10 - 1012/523*a^9 - 753/523*a^8 + 10890/523*a^7 + 11239/523*a^6 - 37550/523*a^5 - 28341/523*a^4 + 51333/523*a^3 + 14917/523*a^2 - 22864/523*a + 2740/523,
-573/523*a^10 - 956/523*a^9 + 6867/523*a^8 + 9014/523*a^7 - 28395/523*a^6 - 24485/523*a^5 + 50592/523*a^4 + 24021/523*a^3 - 33580/523*a^2 - 8530/523*a + 3715/523,
182/523*a^10 + 823/523*a^9 - 1168/523*a^8 - 9004/523*a^7 - 1033/523*a^6 + 32223/523*a^5 + 12786/523*a^4 - 47542/523*a^3 - 13958/523*a^2 + 26133/523*a - 1912/523,
-947/1046*a^10 - 769/523*a^9 + 6125/523*a^8 + 8241/523*a^7 - 54497/1046*a^6 - 27563/523*a^5 + 49786/523*a^4 + 65647/1046*a^3 - 33909/523*a^2 - 9285/523*a + 8805/1046
],
[
a,
-2929/9028*a^14 + 3305/4514*a^13 + 31073/4514*a^12 - 35302/2257*a^11 - 248773/4514*a^10 + 573563/4514*a^9 + 919473/4514*a^8 - 4378801/9028*a^7 - 3005667/9028*a^6 + 1935368/2257*a^5 + 1592783/9028*a^4 - 5224775/9028*a^3 - 38286/2257*a^2 + 248643/2257*a - 29861/9028,
6887/4514*a^14 - 10787/4514*a^13 - 144831/4514*a^12 + 232879/4514*a^11 + 1153635/4514*a^10 - 1909601/4514*a^9 - 4281777/4514*a^8 + 3670378/2257*a^7 + 7216765/4514*a^6 - 12991581/4514*a^5 - 2205724/2257*a^4 + 8622515/4514*a^3 + 846049/4514*a^2 - 1576987/4514*a + 2893/2257,
-175/122*a^14 + 251/122*a^13 + 3703/122*a^12 - 5485/122*a^11 - 29711/122*a^10 + 45521/122*a^9 + 111249/122*a^8 - 88481/61*a^7 - 189781/122*a^6 + 316101/122*a^5 + 59244/61*a^4 - 210853/122*a^3 - 22725/122*a^2 + 38633/122*a - 55/61,
93/4514*a^14 - 1741/4514*a^13 - 2817/4514*a^12 + 35583/4514*a^11 + 30911/4514*a^10 - 277307/4514*a^9 - 158111/4514*a^8 + 512581/2257*a^7 + 392617/4514*a^6 - 1800053/4514*a^5 - 224672/2257*a^4 + 1279815/4514*a^3 + 214893/4514*a^2 - 246421/4514*a - 3148/2257,
-2172/2257*a^14 + 2583/2257*a^13 + 45696/2257*a^12 - 56593/2257*a^11 - 365097/2257*a^10 + 469928/2257*a^9 + 1366782/2257*a^8 - 1822073/2257*a^7 - 2356643/2257*a^6 + 3225372/2257*a^5 + 1542585/2257*a^4 - 2096010/2257*a^3 - 333769/2257*a^2 + 368683/2257*a + 6380/2257,
-1331/2257*a^14 + 3359/4514*a^13 + 55369/4514*a^12 - 73415/4514*a^11 - 434575/4514*a^10 + 608867/4514*a^9 + 1576641/4514*a^8 - 2363585/4514*a^7 - 1269561/2257*a^6 + 4210995/4514*a^5 + 1333379/4514*a^4 - 1396928/2257*a^3 - 103501/4514*a^2 + 509893/4514*a - 20707/4514,
-5113/9028*a^14 + 2227/2257*a^13 + 27379/2257*a^12 - 96937/4514*a^11 - 222537/2257*a^10 + 400941/2257*a^9 + 845411/2257*a^8 - 6220667/9028*a^7 - 5890799/9028*a^6 + 5556089/4514*a^5 + 3910273/9028*a^4 - 7456363/9028*a^3 - 501477/4514*a^2 + 676885/4514*a + 58729/9028,
16115/4514*a^14 - 24093/4514*a^13 - 339749/4514*a^12 + 524035/4514*a^11 + 2711963/4514*a^10 - 4328791/4514*a^9 - 10072577/4514*a^8 + 8377156/2257*a^7 + 16914173/4514*a^6 - 29824007/4514*a^5 - 5050561/2257*a^4 + 19893597/4514*a^3 + 1706727/4514*a^2 - 3701483/4514*a + 27260/2257,
1553/2257*a^14 - 921/2257*a^13 - 32698/2257*a^12 + 22740/2257*a^11 + 261188/2257*a^10 - 208659/2257*a^9 - 974375/2257*a^8 + 875377/2257*a^7 + 1658616/2257*a^6 - 1630991/2257*a^5 - 1029345/2257*a^4 + 1063558/2257*a^3 + 161992/2257*a^2 - 187810/2257*a + 11815/2257,
6683/4514*a^14 - 5559/2257*a^13 - 70600/2257*a^12 + 120478/2257*a^11 + 564211/2257*a^10 - 992156/2257*a^9 - 2093468/2257*a^8 + 7663319/4514*a^7 + 6987355/4514*a^6 - 6818910/2257*a^5 - 4089421/4514*a^4 + 9143453/4514*a^3 + 354317/2257*a^2 - 866859/2257*a + 10787/4514,
20437/9028*a^14 - 6599/2257*a^13 - 216293/4514*a^12 + 292305/4514*a^11 + 1735175/4514*a^10 - 1228459/2257*a^9 - 6487451/4514*a^8 + 19324327/9028*a^7 + 22018405/9028*a^6 - 8716942/2257*a^5 - 13481329/9028*a^4 + 23502269/9028*a^3 + 606540/2257*a^2 - 2236959/4514*a + 8909/9028
]
*], q_expansions := [*
q + a*q^2 + (113/1046*a^10 - 154/523*a^9 - 1081/523*a^8 + 2021/523*a^7 + 12971/1046*a^6 - 9125/523*a^5 - 14011/523*a^4 + 33587/1046*a^3 + 8762/523*a^2 - 10392/523*a + 1175/1046)*q^3 + (a^2 - 2)*q^4 + (234/523*a^10 + 834/523*a^9 - 1950/523*a^8 - 8588/523*a^7 + 3603/523*a^6 + 27458/523*a^5 + 2/523*a^4 - 33780/523*a^3 - 1733/523*a^2 + 13352/523*a - 964/523)*q^5 + (-647/1046*a^10 - 516/523*a^9 + 3829/523*a^8 + 4734/523*a^7 - 30567/1046*a^6 - 11638/523*a^5 + 25099/523*a^4 + 13569/1046*a^3 - 14234/523*a^2 + 1661/523*a + 113/1046)*q^6 + (-250/523*a^10 - 596/523*a^9 + 2432/523*a^8 + 5322/523*a^7 - 7041/523*a^6 - 12072/523*a^5 + 7673/523*a^4 + 5045/523*a^3 - 2109/523*a^2 + 3374/523*a - 1822/523)*q^7 + (a^3 - 4*a)*q^8 + (-385/1046*a^10 + 85/523*a^9 + 3086/523*a^8 - 1540/523*a^7 - 33761/1046*a^6 + 9156/523*a^5 + 36624/523*a^4 - 41445/1046*a^3 - 27298/523*a^2 + 14491/523*a + 2717/1046)*q^9 + (132/523*a^10 + 390/523*a^9 - 1100/523*a^8 - 3651/523*a^7 + 1952/523*a^6 + 9830/523*a^5 + 618/523*a^4 - 9923/523*a^3 - 2560/523*a^2 + 3482/523*a + 234/523)*q^10 + (7/523*a^10 + 92/523*a^9 + 116/523*a^8 - 990/523*a^7 - 1830/523*a^6 + 3271/523*a^5 + 6285/523*a^4 - 4001/523*a^3 - 4922/523*a^2 + 2031/523*a - 1723/523)*q^11 + (683/1046*a^10 + 902/523*a^9 - 3456/523*a^8 - 9297/523*a^7 + 21305/1046*a^6 + 29762/523*a^5 - 12748/523*a^4 - 72997/1046*a^3 + 6135/523*a^2 + 14694/523*a - 2997/1046)*q^12 + (59/523*a^10 + 103/523*a^9 - 666/523*a^8 - 574/523*a^7 + 2806/523*a^6 - 1494/523*a^5 - 5976/523*a^4 + 9761/523*a^3 + 4165/523*a^2 - 9704/523*a + 794/523)*q^13 + (154/523*a^10 - 68/523*a^9 - 2678/523*a^8 + 709/523*a^7 + 15178/523*a^6 - 2827/523*a^5 - 31705/523*a^4 + 6641/523*a^3 + 20374/523*a^2 - 6572/523*a - 250/523)*q^14 + (-418/523*a^10 - 1235/523*a^9 + 3832/523*a^8 + 12346/523*a^7 - 9145/523*a^6 - 37230/523*a^5 + 3796/523*a^4 + 41447/523*a^3 + 6712/523*a^2 - 13990/523*a - 3879/523)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-677/523*a^10 - 1501/523*a^9 + 7385/523*a^8 + 14981/523*a^7 - 25638/523*a^6 - 44243/523*a^5 + 33797/523*a^4 + 43567/523*a^3 - 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47373/9028)*q^36 + (20437/9028*a^14 - 6599/2257*a^13 - 216293/4514*a^12 + 292305/4514*a^11 + 1735175/4514*a^10 - 1228459/2257*a^9 - 6487451/4514*a^8 + 19324327/9028*a^7 + 22018405/9028*a^6 - 8716942/2257*a^5 - 13481329/9028*a^4 + 23502269/9028*a^3 + 606540/2257*a^2 - 2236959/4514*a + 8909/9028)*q^37 + O(q^38)
*]> ;  // time = 5.511 seconds




J[318] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 318, 318, 318, 318, 318, 318, 318, 159, 159, 106, 106, 106, 106, 53, 53 ], new_dimensions := [ 1, 1, 1, 1, 1, 2, 2, 4, 5, 1, 1, 1, 1, 1, 3 ], dimensions := [ 1, 1, 1, 1, 1, 2, 2, 8, 10, 2, 2, 2, 2, 4, 12 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 17, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 0, 1, 43, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 3, 1, 1, 43, 1, 0, 1, 1, 1, 3, 3, 49, 1, 1, 17, 1, 1, 11, 1, 1, 1, 0, 1, 1, 1, 1, 1, 11449, 3, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 25, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 9, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 49, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 13, 1, 11449, 1, 25, 1, 1, 1, 0 ], ap_traces := [
[ -1, -1, -1, 0, -1, -2, -7, 2, -5, -4, -1, -2 ],
[ -1, -1, 4, 1, -1, -4, 6, -1, 9, -3, -8, 12 ],
[ -1, 1, 0, 5, -3, -4, 6, 5, -3, 3, 8, -4 ],
[ 1, -1, 0, 1, 5, 0, 2, -1, 3, -1, -4, 0 ],
[ 1, -1, -3, -4, -5, -2, 5, 6, -7, -8, 1, 2 ],
[ -2, 2, 1, 0, 3, 12, -9, -2, 3, -2, -1, 12 ],
[ 2, 2, 1, 1, -2, -2, -5, 3, 0, -7, 1, 2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - x - 10,
x^2 - x - 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 3, 1 ],
[ 17, 3, 1 ],
[ 3, 3, 1 ],
[ 1, 5, 1 ],
[ 11, 1, 1 ],
[ 43, 5, 1 ],
[ 13, 13, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 11, 1, 1 ],
[ 1, 5, 1 ],
[ 13, 13, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 1, 1, 13 ], torsion_lower_bounds := [ 1, 1, 3, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 1/3, 1, 0, 5, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 0, 1, 1/169 ], eigenvalues := [*
[ -1, -1, -1, 0, -1, -2, -7, 2, -5, -4, -1, -2 ],
[ -1, -1, 4, 1, -1, -4, 6, -1, 9, -3, -8, 12 ],
[ -1, 1, 0, 5, -3, -4, 6, 5, -3, 3, 8, -4 ],
[ 1, -1, 0, 1, 5, 0, 2, -1, 3, -1, -4, 0 ],
[ 1, -1, -3, -4, -5, -2, 5, 6, -7, -8, 1, 2 ],
[
-1,
1,
a,
0,
-a + 2,
6,
-a - 4,
-2*a,
-a + 2,
2*a - 2,
3*a - 2,
6
],
[
1,
1,
a,
-a + 1,
-1,
-2*a,
-a - 2,
a + 1,
2*a - 1,
-a - 3,
a,
2*a
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - q^5 + q^6 - q^8 + q^9 + q^10 - q^11 - q^12 - 2*q^13 + q^15 + q^16 - 7*q^17 - q^18 + 2*q^19 - q^20 + q^22 - 5*q^23 + q^24 - 4*q^25 + 2*q^26 - q^27 - 4*q^29 - q^30 - q^31 - q^32 + q^33 + 7*q^34 + q^36 - 2*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + 4*q^5 + q^6 + q^7 - q^8 + q^9 - 4*q^10 - q^11 - q^12 - 4*q^13 - q^14 - 4*q^15 + q^16 + 6*q^17 - q^18 - q^19 + 4*q^20 - q^21 + q^22 + 9*q^23 + q^24 + 11*q^25 + 4*q^26 - q^27 + q^28 - 3*q^29 + 4*q^30 - 8*q^31 - q^32 + q^33 - 6*q^34 + 4*q^35 + q^36 + 12*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - q^6 + 5*q^7 - q^8 + q^9 - 3*q^11 + q^12 - 4*q^13 - 5*q^14 + q^16 + 6*q^17 - q^18 + 5*q^19 + 5*q^21 + 3*q^22 - 3*q^23 - q^24 - 5*q^25 + 4*q^26 + q^27 + 5*q^28 + 3*q^29 + 8*q^31 - q^32 - 3*q^33 - 6*q^34 + q^36 - 4*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - q^6 + q^7 + q^8 + q^9 + 5*q^11 - q^12 + q^14 + q^16 + 2*q^17 + q^18 - q^19 - q^21 + 5*q^22 + 3*q^23 - q^24 - 5*q^25 - q^27 + q^28 - q^29 - 4*q^31 + q^32 - 5*q^33 + 2*q^34 + q^36 + O(q^38),
q + q^2 - q^3 + q^4 - 3*q^5 - q^6 - 4*q^7 + q^8 + q^9 - 3*q^10 - 5*q^11 - q^12 - 2*q^13 - 4*q^14 + 3*q^15 + q^16 + 5*q^17 + q^18 + 6*q^19 - 3*q^20 + 4*q^21 - 5*q^22 - 7*q^23 - q^24 + 4*q^25 - 2*q^26 - q^27 - 4*q^28 - 8*q^29 + 3*q^30 + q^31 + q^32 + 5*q^33 + 5*q^34 + 12*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + a*q^5 - q^6 - q^8 + q^9 - a*q^10 + (-a + 2)*q^11 + q^12 + 6*q^13 + a*q^15 + q^16 + (-a - 4)*q^17 - q^18 - 2*a*q^19 + a*q^20 + (a - 2)*q^22 + (-a + 2)*q^23 - q^24 + (a + 5)*q^25 - 6*q^26 + q^27 + (2*a - 2)*q^29 - a*q^30 + (3*a - 2)*q^31 - q^32 + (-a + 2)*q^33 + (a + 4)*q^34 + q^36 + 6*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + a*q^5 + q^6 + (-a + 1)*q^7 + q^8 + q^9 + a*q^10 - q^11 + q^12 - 2*a*q^13 + (-a + 1)*q^14 + a*q^15 + q^16 + (-a - 2)*q^17 + q^18 + (a + 1)*q^19 + a*q^20 + (-a + 1)*q^21 - q^22 + (2*a - 1)*q^23 + q^24 + (a - 1)*q^25 - 2*a*q^26 + q^27 + (-a + 1)*q^28 + (-a - 3)*q^29 + a*q^30 + a*q^31 + q^32 - q^33 + (-a - 2)*q^34 - 4*q^35 + q^36 + 2*a*q^37 + O(q^38)
*]> ;  // time = 190.27 seconds




J[319] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 319, 319, 319, 319, 319, 29, 11 ], new_dimensions := [ 1, 3, 4, 7, 8, 2, 1 ], dimensions := [ 1, 3, 4, 7, 8, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 23, 1, 1, 1, 0, 1, 1, 1, 17, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 15, 23, 1, 1, 1, 0, 167, 1, 1, 17, 1, 1, 167, 0, 1, 1, 3, 1, 15, 1, 1, 0 ], ap_traces := [
[ 2, -3, 1, 4, -1, 6, 4, -2, 3, 1, -7, -11 ],
[ 0, 0, -6, -3, 3, -6, -12, -12, 0, 3, -9, 15 ],
[ -2, -3, -5, 1, -4, -2, -4, -2, -1, -4, -10, -8 ],
[ 3, 0, 4, 1, 7, 0, 18, 10, 4, -7, -13, -5 ],
[ 0, 4, 10, -7, -8, -4, 12, -10, 0, 8, 5, 9 ]
], hecke_fields := [
x - 1,
x^3 - 3*x - 1,
x^4 + 2*x^3 - 3*x^2 - 3*x + 2,
x^7 - 3*x^6 - 4*x^5 + 15*x^4 + x^3 - 14*x^2 + 1,
x^8 - 13*x^6 - x^5 + 50*x^4 + 7*x^3 - 54*x^2 - 5*x + 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 17, 3 ],
[ 1, 1 ],
[ 5, 15 ],
[ 167, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 17, 3 ],
[ 1, 1 ],
[ 5, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 5, 1 ], torsion_lower_bounds := [ 1, 1, 1, 5, 1 ], l_ratios := [ 1, 0, 0, 1/5, 1 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 1 ], eigenvalues := [*
[ 2, -3, 1, 4, -1, 6, 4, -2, 3, 1, -7, -11 ],
[
a,
-a,
-2*a^2 + a + 2,
2*a^2 - 2*a - 5,
1,
a^2 + a - 4,
-a^2 + a - 2,
a - 4,
-4*a^2 + 4*a + 8,
1,
3*a^2 - 2*a - 9,
4*a^2 - a - 3
],
[
a,
-a^3 - 2*a^2 + 2*a + 1,
a^3 + 2*a^2 - 2*a - 3,
a^3 + 2*a^2 - 3*a - 2,
-1,
-2*a^3 - 5*a^2 + a + 4,
3*a^2 + 5*a - 6,
a,
-a^3 - 4*a^2 - a + 5,
-1,
-a^2 + 2*a + 1,
2*a^3 + 2*a^2 - 5*a - 1
],
[
a,
-a^4 + a^3 + 5*a^2 - 3*a - 3,
a^5 - a^4 - 6*a^3 + 4*a^2 + 7*a - 1,
a^6 - 3*a^5 - 4*a^4 + 14*a^3 + 2*a^2 - 11*a - 1,
1,
a^5 - 2*a^4 - 4*a^3 + 6*a^2 + 2*a + 1,
a^6 - 3*a^5 - 4*a^4 + 15*a^3 + a^2 - 15*a + 3,
-3*a^6 + 8*a^5 + 13*a^4 - 38*a^3 - 6*a^2 + 28*a + 1,
a^6 - 4*a^5 - 2*a^4 + 19*a^3 - 7*a^2 - 15*a + 4,
-1,
a^6 - 4*a^5 - a^4 + 17*a^3 - 13*a^2 - 6*a + 7,
-a^6 + 5*a^5 + a^4 - 25*a^3 + 9*a^2 + 20*a
],
[
a,
-1/9*a^7 - 1/9*a^6 + 16/9*a^5 + 10/9*a^4 - 26/3*a^3 - 25/9*a^2 + 113/9*a + 14/9,
4/9*a^7 - 2/9*a^6 - 49/9*a^5 + 17/9*a^4 + 56/3*a^3 - 26/9*a^2 - 143/9*a + 13/9,
-2/9*a^7 - 1/3*a^6 + 3*a^5 + 34/9*a^4 - 12*a^3 - 98/9*a^2 + 13*a + 29/9,
-1,
2/3*a^7 - 2/9*a^6 - 73/9*a^5 + 16/9*a^4 + 86/3*a^3 - 2*a^2 - 254/9*a - 13/9,
1/3*a^6 - 1/3*a^5 - 8/3*a^4 + 3*a^3 + 3*a^2 - 17/3*a + 11/3,
1/9*a^7 + 2/9*a^6 - 20/9*a^5 - 8/3*a^4 + 37/3*a^3 + 64/9*a^2 - 148/9*a - 2/3,
-4/9*a^7 - 5/9*a^6 + 50/9*a^5 + 6*a^4 - 61/3*a^3 - 139/9*a^2 + 181/9*a + 10/3,
1,
1/9*a^7 - 4/3*a^5 + 4/9*a^4 + 4*a^3 - 23/9*a^2 - 2/3*a + 14/9,
7/9*a^7 - 31/3*a^5 - 8/9*a^4 + 40*a^3 + 55/9*a^2 - 116/3*a - 19/9
]
*], q_expansions := [*
q + 2*q^2 - 3*q^3 + 2*q^4 + q^5 - 6*q^6 + 4*q^7 + 6*q^9 + 2*q^10 - q^11 - 6*q^12 + 6*q^13 + 8*q^14 - 3*q^15 - 4*q^16 + 4*q^17 + 12*q^18 - 2*q^19 + 2*q^20 - 12*q^21 - 2*q^22 + 3*q^23 - 4*q^25 + 12*q^26 - 9*q^27 + 8*q^28 + q^29 - 6*q^30 - 7*q^31 - 8*q^32 + 3*q^33 + 8*q^34 + 4*q^35 + 12*q^36 - 11*q^37 + O(q^38),
q + a*q^2 - a*q^3 + (a^2 - 2)*q^4 + (-2*a^2 + a + 2)*q^5 - a^2*q^6 + (2*a^2 - 2*a - 5)*q^7 + (-a + 1)*q^8 + (a^2 - 3)*q^9 + (a^2 - 4*a - 2)*q^10 + q^11 + (-a - 1)*q^12 + (a^2 + a - 4)*q^13 + (-2*a^2 + a + 2)*q^14 + (-a^2 + 4*a + 2)*q^15 + (-3*a^2 + a + 4)*q^16 + (-a^2 + a - 2)*q^17 + q^18 + (a - 4)*q^19 + (-a - 3)*q^20 + (2*a^2 - a - 2)*q^21 + a*q^22 + (-4*a^2 + 4*a + 8)*q^23 + (a^2 - a)*q^24 + (5*a^2 - 4*a - 5)*q^25 + (a^2 - a + 1)*q^26 + (3*a - 1)*q^27 + (-3*a^2 + 8)*q^28 + q^29 + (4*a^2 - a - 1)*q^30 + (3*a^2 - 2*a - 9)*q^31 + (a^2 - 3*a - 5)*q^32 - a*q^33 + (a^2 - 5*a - 1)*q^34 + (5*a - 4)*q^35 + (-2*a^2 + a + 6)*q^36 + (4*a^2 - a - 3)*q^37 + O(q^38),
q + a*q^2 + (-a^3 - 2*a^2 + 2*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^3 + 2*a^2 - 2*a - 3)*q^5 + (-a^2 - 2*a + 2)*q^6 + (a^3 + 2*a^2 - 3*a - 2)*q^7 + (a^3 - 4*a)*q^8 + (a^3 + a^2 - 3*a)*q^9 + (a^2 - 2)*q^10 - q^11 + (a^3 + 2*a^2 - 2*a - 2)*q^12 + (-2*a^3 - 5*a^2 + a + 4)*q^13 + (a - 2)*q^14 + (a^3 + 3*a^2 - a - 5)*q^15 + (-2*a^3 - 3*a^2 + 3*a + 2)*q^16 + (3*a^2 + 5*a - 6)*q^17 + (-a^3 + 3*a - 2)*q^18 + a*q^19 + (-a^3 - 4*a^2 + 2*a + 6)*q^20 + (2*a^2 + 3*a - 6)*q^21 - a*q^22 + (-a^3 - 4*a^2 - a + 5)*q^23 + (3*a^2 + 5*a - 6)*q^24 + (-3*a^3 - 7*a^2 + 5*a + 6)*q^25 + (-a^3 - 5*a^2 - 2*a + 4)*q^26 + (2*a^3 + 6*a^2 - a - 7)*q^27 + (-2*a^3 - 3*a^2 + 4*a + 4)*q^28 - q^29 + (a^3 + 2*a^2 - 2*a - 2)*q^30 + (-a^2 + 2*a + 1)*q^31 + (-a^3 - 3*a^2 + 4*a + 4)*q^32 + (a^3 + 2*a^2 - 2*a - 1)*q^33 + (3*a^3 + 5*a^2 - 6*a)*q^34 + (-2*a^3 - 6*a^2 + 3*a + 10)*q^35 + (-2*a^2 + a + 2)*q^36 + (2*a^3 + 2*a^2 - 5*a - 1)*q^37 + O(q^38),
q + a*q^2 + (-a^4 + a^3 + 5*a^2 - 3*a - 3)*q^3 + (a^2 - 2)*q^4 + (a^5 - a^4 - 6*a^3 + 4*a^2 + 7*a - 1)*q^5 + (-a^5 + a^4 + 5*a^3 - 3*a^2 - 3*a)*q^6 + (a^6 - 3*a^5 - 4*a^4 + 14*a^3 + 2*a^2 - 11*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^6 + 5*a^5 + 9*a^4 - 23*a^3 - 7*a^2 + 17*a + 5)*q^9 + (a^6 - a^5 - 6*a^4 + 4*a^3 + 7*a^2 - a)*q^10 + q^11 + (-a^6 + a^5 + 7*a^4 - 5*a^3 - 13*a^2 + 6*a + 6)*q^12 + (a^5 - 2*a^4 - 4*a^3 + 6*a^2 + 2*a + 1)*q^13 + (-a^4 + a^3 + 3*a^2 - a - 1)*q^14 + (2*a^6 - 5*a^5 - 9*a^4 + 23*a^3 + 5*a^2 - 17*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 - 3*a^5 - 4*a^4 + 15*a^3 + a^2 - 15*a + 3)*q^17 + (-a^6 + a^5 + 7*a^4 - 5*a^3 - 11*a^2 + 5*a + 2)*q^18 + (-3*a^6 + 8*a^5 + 13*a^4 - 38*a^3 - 6*a^2 + 28*a + 1)*q^19 + (2*a^6 - 4*a^5 - 9*a^4 + 18*a^3 + 5*a^2 - 14*a + 1)*q^20 + (-2*a^6 + 6*a^5 + 9*a^4 - 31*a^3 - 7*a^2 + 31*a + 5)*q^21 + a*q^22 + (a^6 - 4*a^5 - 2*a^4 + 19*a^3 - 7*a^2 - 15*a + 4)*q^23 + (-2*a^6 + 5*a^5 + 8*a^4 - 22*a^3 - 2*a^2 + 12*a + 1)*q^24 + (a^6 - 3*a^5 - 3*a^4 + 14*a^3 - 2*a^2 - 10*a - 1)*q^25 + (a^6 - 2*a^5 - 4*a^4 + 6*a^3 + 2*a^2 + a)*q^26 + (3*a^6 - 9*a^5 - 13*a^4 + 47*a^3 + 9*a^2 - 48*a - 8)*q^27 + (-2*a^6 + 5*a^5 + 9*a^4 - 25*a^3 - 5*a^2 + 21*a + 2)*q^28 - q^29 + (a^6 - a^5 - 7*a^4 + 3*a^3 + 11*a^2 - 2)*q^30 + (a^6 - 4*a^5 - a^4 + 17*a^3 - 13*a^2 - 6*a + 7)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^4 + a^3 + 5*a^2 - 3*a - 3)*q^33 + (-a^2 + 3*a - 1)*q^34 + (-a^4 - a^3 + 7*a^2 + a - 5)*q^35 + (2*a^6 - 7*a^5 - 8*a^4 + 36*a^3 + 5*a^2 - 32*a - 9)*q^36 + (-a^6 + 5*a^5 + a^4 - 25*a^3 + 9*a^2 + 20*a)*q^37 + O(q^38),
q + a*q^2 + (-1/9*a^7 - 1/9*a^6 + 16/9*a^5 + 10/9*a^4 - 26/3*a^3 - 25/9*a^2 + 113/9*a + 14/9)*q^3 + (a^2 - 2)*q^4 + (4/9*a^7 - 2/9*a^6 - 49/9*a^5 + 17/9*a^4 + 56/3*a^3 - 26/9*a^2 - 143/9*a + 13/9)*q^5 + (-1/9*a^7 + 1/3*a^6 + a^5 - 28/9*a^4 - 2*a^3 + 59/9*a^2 + a + 1/9)*q^6 + (-2/9*a^7 - 1/3*a^6 + 3*a^5 + 34/9*a^4 - 12*a^3 - 98/9*a^2 + 13*a + 29/9)*q^7 + (a^3 - 4*a)*q^8 + (-1/3*a^7 + 1/9*a^6 + 41/9*a^5 - 8/9*a^4 - 58/3*a^3 + a^2 + 217/9*a + 20/9)*q^9 + (-2/9*a^7 + 1/3*a^6 + 7/3*a^5 - 32/9*a^4 - 6*a^3 + 73/9*a^2 + 11/3*a - 4/9)*q^10 - q^11 + (5/9*a^7 - 2/9*a^6 - 61/9*a^5 + 4/3*a^4 + 74/3*a^3 + 5/9*a^2 - 230/9*a - 3)*q^12 + (2/3*a^7 - 2/9*a^6 - 73/9*a^5 + 16/9*a^4 + 86/3*a^3 - 2*a^2 - 254/9*a - 13/9)*q^13 + (-1/3*a^7 + 1/9*a^6 + 32/9*a^5 - 8/9*a^4 - 28/3*a^3 + a^2 + 19/9*a + 2/9)*q^14 + (-1/9*a^7 + 1/9*a^6 + 17/9*a^5 - 2*a^4 - 28/3*a^3 + 71/9*a^2 + 115/9*a - 5/3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/3*a^6 - 1/3*a^5 - 8/3*a^4 + 3*a^3 + 3*a^2 - 17/3*a + 11/3)*q^17 + (1/9*a^7 + 2/9*a^6 - 11/9*a^5 - 8/3*a^4 + 10/3*a^3 + 55/9*a^2 + 5/9*a + 1/3)*q^18 + (1/9*a^7 + 2/9*a^6 - 20/9*a^5 - 8/3*a^4 + 37/3*a^3 + 64/9*a^2 - 148/9*a - 2/3)*q^19 + (-5/9*a^7 - 1/9*a^6 + 64/9*a^5 + 4/3*a^4 - 83/3*a^3 - 23/9*a^2 + 272/9*a - 8/3)*q^20 + (-11/9*a^7 - 1/9*a^6 + 136/9*a^5 + 8/3*a^4 - 158/3*a^3 - 119/9*a^2 + 389/9*a + 8)*q^21 - a*q^22 + (-4/9*a^7 - 5/9*a^6 + 50/9*a^5 + 6*a^4 - 61/3*a^3 - 139/9*a^2 + 181/9*a + 10/3)*q^23 + (-2/9*a^6 - 1/9*a^5 + 28/9*a^4 + 2/3*a^3 - 26/3*a^2 - 20/9*a - 7/9)*q^24 + (11/9*a^7 - 47/3*a^5 - 10/9*a^4 + 59*a^3 + 62/9*a^2 - 190/3*a + 10/9)*q^25 + (-2/9*a^7 + 5/9*a^6 + 22/9*a^5 - 14/3*a^4 - 20/3*a^3 + 70/9*a^2 + 17/9*a - 2/3)*q^26 + (1/9*a^7 + 2/9*a^6 - 11/9*a^5 - 8/3*a^4 + 10/3*a^3 + 55/9*a^2 - 4/9*a + 13/3)*q^27 + (5/9*a^7 - 1/9*a^6 - 65/9*a^5 - 2/9*a^4 + 82/3*a^3 + 53/9*a^2 - 247/9*a - 55/9)*q^28 + q^29 + (1/9*a^7 + 4/9*a^6 - 19/9*a^5 - 34/9*a^4 + 26/3*a^3 + 61/9*a^2 - 20/9*a + 1/9)*q^30 + (1/9*a^7 - 4/3*a^5 + 4/9*a^4 + 4*a^3 - 23/9*a^2 - 2/3*a + 14/9)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/9*a^7 + 1/9*a^6 - 16/9*a^5 - 10/9*a^4 + 26/3*a^3 + 25/9*a^2 - 113/9*a - 14/9)*q^33 + (1/3*a^7 - 1/3*a^6 - 8/3*a^5 + 3*a^4 + 3*a^3 - 17/3*a^2 + 11/3*a)*q^34 + (-1/3*a^7 + 1/9*a^6 + 32/9*a^5 - 8/9*a^4 - 22/3*a^3 + a^2 - 71/9*a + 2/9)*q^35 + (8/9*a^7 - 35/3*a^5 - 4/9*a^4 + 44*a^3 + 41/9*a^2 - 142/3*a - 41/9)*q^36 + (7/9*a^7 - 31/3*a^5 - 8/9*a^4 + 40*a^3 + 55/9*a^2 - 116/3*a - 19/9)*q^37 + O(q^38)
*]> ;  // time = 44.041 seconds




J[321] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 321, 321, 321, 321, 107, 107 ], new_dimensions := [ 2, 2, 6, 7, 2, 7 ], dimensions := [ 2, 2, 6, 7, 4, 14 ], intersection_graph := [ 0, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 41, 1, 1, 0, 1, 29, 1, 1, 1, 1, 0, 1, 14051, 5, 1, 29, 1, 0, 1, 1, 41, 1, 14051, 1, 0 ], ap_traces := [
[ -1, -2, 2, -4, -6, -2, 2, -8, -4, -2, -12, 2 ],
[ -1, 2, -6, -2, -4, -2, -6, 0, -8, -2, -4, 2 ],
[ 3, 6, 6, 0, 6, -8, 4, -4, 14, 10, 12, -12 ],
[ 0, -7, -8, 6, 4, 6, -10, 8, 6, 0, 16, 10 ]
], hecke_fields := [
x^2 + x - 1,
x^2 + x - 1,
x^6 - 3*x^5 - 5*x^4 + 18*x^3 + x^2 - 19*x + 3,
x^7 - 14*x^5 - x^4 + 55*x^3 + 8*x^2 - 46*x - 19
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 5, 1 ],
[ 41, 1 ],
[ 261, 1 ],
[ 14051, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 41, 1 ],
[ 261, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 9, 1 ], torsion_lower_bounds := [ 1, 1, 9, 1 ], l_ratios := [ 0, 0, 29/9, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
a,
-1,
1,
-2,
-2*a - 4,
-1,
-4*a - 1,
2*a - 3,
4*a,
2*a,
-6,
1
],
[
a,
1,
-3,
-2*a - 2,
-2,
-1,
4*a - 1,
2*a + 1,
-4,
-2*a - 2,
-2,
8*a + 5
],
[
a,
1,
1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 13/2*a,
-1/2*a^5 + 1/2*a^4 + 3*a^3 - 5/2*a^2 - 5/2*a + 2,
-a^5 + 3/2*a^4 + 13/2*a^3 - 7*a^2 - 19/2*a + 9/2,
1/2*a^4 + 1/2*a^3 - 4*a^2 - 5/2*a + 7/2,
-1/2*a^5 - 1/2*a^4 + 5*a^3 + 5/2*a^2 - 21/2*a,
a^5 - a^4 - 7*a^3 + 4*a^2 + 10*a - 1,
a^5 - 3/2*a^4 - 11/2*a^3 + 6*a^2 + 9/2*a + 3/2,
-2*a^5 + 4*a^4 + 12*a^3 - 20*a^2 - 12*a + 12,
5/2*a^5 - 9/2*a^4 - 15*a^3 + 47/2*a^2 + 27/2*a - 13,
-a^5 + 1/2*a^4 + 13/2*a^3 - 19/2*a - 11/2
],
[
a,
-1,
-1/4*a^6 + 1/4*a^5 + 11/4*a^4 - 5/2*a^3 - 31/4*a^2 + 25/4*a + 13/4,
1/2*a^6 - 7*a^4 + a^3 + 26*a^2 - 7*a - 27/2,
-3/4*a^6 + 1/4*a^5 + 41/4*a^4 - 4*a^3 - 151/4*a^2 + 67/4*a + 93/4,
-1/2*a^6 + 1/2*a^5 + 7*a^4 - 11/2*a^3 - 55/2*a^2 + 15*a + 21,
a^6 - 1/2*a^5 - 27/2*a^4 + 6*a^3 + 97/2*a^2 - 39/2*a - 28,
-1/2*a^6 + 1/2*a^5 + 11/2*a^4 - 4*a^3 - 33/2*a^2 + 11/2*a + 27/2,
a^6 - a^5 - 27/2*a^4 + 21/2*a^3 + 50*a^2 - 55/2*a - 63/2,
-2*a,
-3/4*a^6 + 3/4*a^5 + 41/4*a^4 - 17/2*a^3 - 153/4*a^2 + 87/4*a + 107/4,
1/4*a^6 - 3/4*a^5 - 11/4*a^4 + 7*a^3 + 33/4*a^2 - 53/4*a - 19/4
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-a - 1)*q^4 + q^5 - a*q^6 - 2*q^7 + (-2*a - 1)*q^8 + q^9 + a*q^10 + (-2*a - 4)*q^11 + (a + 1)*q^12 - q^13 - 2*a*q^14 - q^15 + 3*a*q^16 + (-4*a - 1)*q^17 + a*q^18 + (2*a - 3)*q^19 + (-a - 1)*q^20 + 2*q^21 + (-2*a - 2)*q^22 + 4*a*q^23 + (2*a + 1)*q^24 - 4*q^25 - a*q^26 - q^27 + (2*a + 2)*q^28 + 2*a*q^29 - a*q^30 - 6*q^31 + (a + 5)*q^32 + (2*a + 4)*q^33 + (3*a - 4)*q^34 - 2*q^35 + (-a - 1)*q^36 + q^37 + O(q^38),
q + a*q^2 + q^3 + (-a - 1)*q^4 - 3*q^5 + a*q^6 + (-2*a - 2)*q^7 + (-2*a - 1)*q^8 + q^9 - 3*a*q^10 - 2*q^11 + (-a - 1)*q^12 - q^13 - 2*q^14 - 3*q^15 + 3*a*q^16 + (4*a - 1)*q^17 + a*q^18 + (2*a + 1)*q^19 + (3*a + 3)*q^20 + (-2*a - 2)*q^21 - 2*a*q^22 - 4*q^23 + (-2*a - 1)*q^24 + 4*q^25 - a*q^26 + q^27 + (2*a + 4)*q^28 + (-2*a - 2)*q^29 - 3*a*q^30 - 2*q^31 + (a + 5)*q^32 - 2*q^33 + (-5*a + 4)*q^34 + (6*a + 6)*q^35 + (-a - 1)*q^36 + (8*a + 5)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 13/2*a)*q^5 + a*q^6 + (-1/2*a^5 + 1/2*a^4 + 3*a^3 - 5/2*a^2 - 5/2*a + 2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (a^5 - 3/2*a^4 - 13/2*a^3 + 6*a^2 + 19/2*a - 3/2)*q^10 + (-a^5 + 3/2*a^4 + 13/2*a^3 - 7*a^2 - 19/2*a + 9/2)*q^11 + (a^2 - 2)*q^12 + (1/2*a^4 + 1/2*a^3 - 4*a^2 - 5/2*a + 7/2)*q^13 + (-a^5 + 1/2*a^4 + 13/2*a^3 - 2*a^2 - 15/2*a + 3/2)*q^14 + (1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 13/2*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^5 - 1/2*a^4 + 5*a^3 + 5/2*a^2 - 21/2*a)*q^17 + a*q^18 + (a^5 - a^4 - 7*a^3 + 4*a^2 + 10*a - 1)*q^19 + (1/2*a^5 - 1/2*a^4 - 4*a^3 + 7/2*a^2 + 9/2*a - 3)*q^20 + (-1/2*a^5 + 1/2*a^4 + 3*a^3 - 5/2*a^2 - 5/2*a + 2)*q^21 + (-3/2*a^5 + 3/2*a^4 + 11*a^3 - 17/2*a^2 - 29/2*a + 3)*q^22 + (a^5 - 3/2*a^4 - 11/2*a^3 + 6*a^2 + 9/2*a + 3/2)*q^23 + (a^3 - 4*a)*q^24 + (a^5 - 3/2*a^4 - 17/2*a^3 + 9*a^2 + 31/2*a - 13/2)*q^25 + (1/2*a^5 + 1/2*a^4 - 4*a^3 - 5/2*a^2 + 7/2*a)*q^26 + q^27 + (-3/2*a^5 + 1/2*a^4 + 10*a^3 - 3/2*a^2 - 25/2*a - 1)*q^28 + (-2*a^5 + 4*a^4 + 12*a^3 - 20*a^2 - 12*a + 12)*q^29 + (a^5 - 3/2*a^4 - 13/2*a^3 + 6*a^2 + 19/2*a - 3/2)*q^30 + (5/2*a^5 - 9/2*a^4 - 15*a^3 + 47/2*a^2 + 27/2*a - 13)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^5 + 3/2*a^4 + 13/2*a^3 - 7*a^2 - 19/2*a + 9/2)*q^33 + (-2*a^5 + 5/2*a^4 + 23/2*a^3 - 10*a^2 - 19/2*a + 3/2)*q^34 + (a^5 - a^4 - 7*a^3 + 4*a^2 + 10*a)*q^35 + (a^2 - 2)*q^36 + (-a^5 + 1/2*a^4 + 13/2*a^3 - 19/2*a - 11/2)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-1/4*a^6 + 1/4*a^5 + 11/4*a^4 - 5/2*a^3 - 31/4*a^2 + 25/4*a + 13/4)*q^5 - a*q^6 + (1/2*a^6 - 7*a^4 + a^3 + 26*a^2 - 7*a - 27/2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (1/4*a^6 - 3/4*a^5 - 11/4*a^4 + 6*a^3 + 33/4*a^2 - 33/4*a - 19/4)*q^10 + (-3/4*a^6 + 1/4*a^5 + 41/4*a^4 - 4*a^3 - 151/4*a^2 + 67/4*a + 93/4)*q^11 + (-a^2 + 2)*q^12 + (-1/2*a^6 + 1/2*a^5 + 7*a^4 - 11/2*a^3 - 55/2*a^2 + 15*a + 21)*q^13 + (3/2*a^4 - 3/2*a^3 - 11*a^2 + 19/2*a + 19/2)*q^14 + (1/4*a^6 - 1/4*a^5 - 11/4*a^4 + 5/2*a^3 + 31/4*a^2 - 25/4*a - 13/4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 - 1/2*a^5 - 27/2*a^4 + 6*a^3 + 97/2*a^2 - 39/2*a - 28)*q^17 + a*q^18 + (-1/2*a^6 + 1/2*a^5 + 11/2*a^4 - 4*a^3 - 33/2*a^2 + 11/2*a + 27/2)*q^19 + (-1/4*a^6 + 1/4*a^5 + 3/4*a^4 - 1/2*a^3 + 21/4*a^2 - 23/4*a - 7/4)*q^20 + (-1/2*a^6 + 7*a^4 - a^3 - 26*a^2 + 7*a + 27/2)*q^21 + (1/4*a^6 - 1/4*a^5 - 19/4*a^4 + 7/2*a^3 + 91/4*a^2 - 45/4*a - 57/4)*q^22 + (a^6 - a^5 - 27/2*a^4 + 21/2*a^3 + 50*a^2 - 55/2*a - 63/2)*q^23 + (-a^3 + 4*a)*q^24 + (a^6 - a^5 - 25/2*a^4 + 21/2*a^3 + 43*a^2 - 55/2*a - 53/2)*q^25 + (1/2*a^6 - 6*a^4 + 19*a^2 - 2*a - 19/2)*q^26 - q^27 + (-a^6 + 3/2*a^5 + 25/2*a^4 - 13*a^3 - 85/2*a^2 + 47/2*a + 27)*q^28 - 2*a*q^29 + (-1/4*a^6 + 3/4*a^5 + 11/4*a^4 - 6*a^3 - 33/4*a^2 + 33/4*a + 19/4)*q^30 + (-3/4*a^6 + 3/4*a^5 + 41/4*a^4 - 17/2*a^3 - 153/4*a^2 + 87/4*a + 107/4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (3/4*a^6 - 1/4*a^5 - 41/4*a^4 + 4*a^3 + 151/4*a^2 - 67/4*a - 93/4)*q^33 + (-1/2*a^6 + 1/2*a^5 + 7*a^4 - 13/2*a^3 - 55/2*a^2 + 18*a + 19)*q^34 + (-5/4*a^6 + 3/4*a^5 + 69/4*a^4 - 21/2*a^3 - 257/4*a^2 + 139/4*a + 157/4)*q^35 + (a^2 - 2)*q^36 + (1/4*a^6 - 3/4*a^5 - 11/4*a^4 + 7*a^3 + 33/4*a^2 - 53/4*a - 19/4)*q^37 + O(q^38)
*]> ;  // time = 48.751 seconds




J[322] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 322, 322, 322, 322, 322, 322, 322, 161, 161, 161, 161, 46, 23, 14 ], new_dimensions := [ 1, 1, 1, 1, 2, 2, 3, 1, 2, 3, 5, 1, 2, 1 ], dimensions := [ 1, 1, 1, 1, 2, 2, 3, 2, 4, 6, 10, 2, 8, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 0, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 5, 1, 11, 1, 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 0, 1, 1, 361, 1, 7, 1, 1, 1, 1, 1, 1, 25, 1, 1, 0, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 25, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 361, 1, 25, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0 ], ap_traces := [
[ -1, 2, 0, 1, 4, 0, 6, -6, -1, 10, 4, -2 ],
[ -1, 0, -2, 1, -4, 4, -8, -2, 1, 2, -6, -10 ],
[ 1, -2, -2, -1, -2, -4, -6, 0, 1, -2, 4, 0 ],
[ 1, 2, -2, 1, 6, -4, -2, 4, 1, -10, -8, -8 ],
[ -2, -2, -2, -2, 0, -4, -10, 0, -2, -4, 2, 12 ],
[ 2, -2, 2, 2, 0, 4, 2, -4, 2, 16, -10, 8 ],
[ 3, 2, 4, -3, -4, 2, 8, 0, -3, -10, -2, -10 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 + 2*x - 4,
x^2 + 2*x - 2,
x^3 - 2*x^2 - 6*x + 8
], atkin_lehners := [
[ 1, -1, 1 ],
[ 1, -1, -1 ],
[ -1, 1, -1 ],
[ -1, -1, -1 ],
[ 1, 1, 1 ],
[ -1, -1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 7, 1, 1 ],
[ 1, 3, 1 ],
[ 5, 1, 1 ],
[ 1, 1, 1 ],
[ 5, 1, 1 ],
[ 11, 11, 1 ],
[ 11, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 5, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 11, 11, 1 ],
[ 11, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 11, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 1, 0, 0, 1, 0, 1, 11 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 0, 1/121, 1 ], eigenvalues := [*
[ -1, 2, 0, 1, 4, 0, 6, -6, -1, 10, 4, -2 ],
[ -1, 0, -2, 1, -4, 4, -8, -2, 1, 2, -6, -10 ],
[ 1, -2, -2, -1, -2, -4, -6, 0, 1, -2, 4, 0 ],
[ 1, 2, -2, 1, 6, -4, -2, 4, 1, -10, -8, -8 ],
[
-1,
a,
-a - 2,
-1,
0,
-2*a - 4,
a - 4,
2*a + 2,
-1,
-2,
a + 2,
6
],
[
1,
a,
a + 2,
1,
-2*a - 2,
-2*a,
-a,
-2,
1,
8,
3*a - 2,
-2*a + 2
],
[
1,
a,
-a + 2,
-1,
-a^2 + 4,
-a^2 + 6,
a^2 - a - 2,
a^2 - 2*a - 4,
-1,
a^2 + 2*a - 10,
-a^2 + a + 4,
-2*a^2 + 2*a + 6
]
*], q_expansions := [*
q - q^2 + 2*q^3 + q^4 - 2*q^6 + q^7 - q^8 + q^9 + 4*q^11 + 2*q^12 - q^14 + q^16 + 6*q^17 - q^18 - 6*q^19 + 2*q^21 - 4*q^22 - q^23 - 2*q^24 - 5*q^25 - 4*q^27 + q^28 + 10*q^29 + 4*q^31 - q^32 + 8*q^33 - 6*q^34 + q^36 - 2*q^37 + O(q^38),
q - q^2 + q^4 - 2*q^5 + q^7 - q^8 - 3*q^9 + 2*q^10 - 4*q^11 + 4*q^13 - q^14 + q^16 - 8*q^17 + 3*q^18 - 2*q^19 - 2*q^20 + 4*q^22 + q^23 - q^25 - 4*q^26 + q^28 + 2*q^29 - 6*q^31 - q^32 + 8*q^34 - 2*q^35 - 3*q^36 - 10*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 2*q^5 - 2*q^6 - q^7 + q^8 + q^9 - 2*q^10 - 2*q^11 - 2*q^12 - 4*q^13 - q^14 + 4*q^15 + q^16 - 6*q^17 + q^18 - 2*q^20 + 2*q^21 - 2*q^22 + q^23 - 2*q^24 - q^25 - 4*q^26 + 4*q^27 - q^28 - 2*q^29 + 4*q^30 + 4*q^31 + q^32 + 4*q^33 - 6*q^34 + 2*q^35 + q^36 + O(q^38),
q + q^2 + 2*q^3 + q^4 - 2*q^5 + 2*q^6 + q^7 + q^8 + q^9 - 2*q^10 + 6*q^11 + 2*q^12 - 4*q^13 + q^14 - 4*q^15 + q^16 - 2*q^17 + q^18 + 4*q^19 - 2*q^20 + 2*q^21 + 6*q^22 + q^23 + 2*q^24 - q^25 - 4*q^26 - 4*q^27 + q^28 - 10*q^29 - 4*q^30 - 8*q^31 + q^32 + 12*q^33 - 2*q^34 - 2*q^35 + q^36 - 8*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a - 2)*q^5 - a*q^6 - q^7 - q^8 + (-2*a + 1)*q^9 + (a + 2)*q^10 + a*q^12 + (-2*a - 4)*q^13 + q^14 - 4*q^15 + q^16 + (a - 4)*q^17 + (2*a - 1)*q^18 + (2*a + 2)*q^19 + (-a - 2)*q^20 - a*q^21 - q^23 - a*q^24 + (2*a + 3)*q^25 + (2*a + 4)*q^26 + (2*a - 8)*q^27 - q^28 - 2*q^29 + 4*q^30 + (a + 2)*q^31 - q^32 + (-a + 4)*q^34 + (a + 2)*q^35 + (-2*a + 1)*q^36 + 6*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (a + 2)*q^5 + a*q^6 + q^7 + q^8 + (-2*a - 1)*q^9 + (a + 2)*q^10 + (-2*a - 2)*q^11 + a*q^12 - 2*a*q^13 + q^14 + 2*q^15 + q^16 - a*q^17 + (-2*a - 1)*q^18 - 2*q^19 + (a + 2)*q^20 + a*q^21 + (-2*a - 2)*q^22 + q^23 + a*q^24 + (2*a + 1)*q^25 - 2*a*q^26 - 4*q^27 + q^28 + 8*q^29 + 2*q^30 + (3*a - 2)*q^31 + q^32 + (2*a - 4)*q^33 - a*q^34 + (a + 2)*q^35 + (-2*a - 1)*q^36 + (-2*a + 2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a + 2)*q^5 + a*q^6 - q^7 + q^8 + (a^2 - 3)*q^9 + (-a + 2)*q^10 + (-a^2 + 4)*q^11 + a*q^12 + (-a^2 + 6)*q^13 - q^14 + (-a^2 + 2*a)*q^15 + q^16 + (a^2 - a - 2)*q^17 + (a^2 - 3)*q^18 + (a^2 - 2*a - 4)*q^19 + (-a + 2)*q^20 - a*q^21 + (-a^2 + 4)*q^22 - q^23 + a*q^24 + (a^2 - 4*a - 1)*q^25 + (-a^2 + 6)*q^26 + (2*a^2 - 8)*q^27 - q^28 + (a^2 + 2*a - 10)*q^29 + (-a^2 + 2*a)*q^30 + (-a^2 + a + 4)*q^31 + q^32 + (-2*a^2 - 2*a + 8)*q^33 + (a^2 - a - 2)*q^34 + (a - 2)*q^35 + (a^2 - 3)*q^36 + (-2*a^2 + 2*a + 6)*q^37 + O(q^38)
*]> ;  // time = 130.291 seconds




J[323] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 323, 323, 323, 323, 323, 323, 19, 17 ], new_dimensions := [ 1, 2, 4, 5, 6, 7, 1, 1 ], dimensions := [ 1, 2, 4, 5, 6, 7, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 7, 1, 5, 1, 1, 0, 1, 1, 17, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 3, 1, 1, 1, 0, 1, 1, 1, 1, 7, 17, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 7, 1, 3, 1, 0, 1, 1, 1, 3, 1, 1, 1, 1, 0 ], ap_traces := [
[ 0, 3, -2, 4, -2, 6, -1, 1, 0, -9, -9, 2 ],
[ -1, 1, 4, 2, -4, 4, -2, 2, 2, 9, -7, 14 ],
[ 0, -1, -7, -11, -2, -10, 4, 4, -3, -10, 1, -21 ],
[ -3, -3, -3, -5, 0, -20, -5, -5, 5, 6, -3, -19 ],
[ 2, -3, -1, 5, 2, 14, -6, 6, -1, -16, 9, 1 ],
[ 1, 3, 7, 1, 2, 20, 7, -7, -3, 10, 21, 21 ]
], hecke_fields := [
x - 1,
x^2 + x - 4,
x^4 - 6*x^2 - x + 7,
x^5 + 3*x^4 - 2*x^3 - 7*x^2 + 2*x + 1,
x^6 - 2*x^5 - 9*x^4 + 15*x^3 + 23*x^2 - 23*x - 21,
x^7 - x^6 - 10*x^5 + 9*x^4 + 26*x^3 - 19*x^2 - 12*x + 8
], atkin_lehners := [
[ 1, -1 ],
[ 1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 1, 1 ],
[ 7, 3 ],
[ 1, 1 ],
[ 9, 9 ],
[ 5, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 7, 3 ],
[ 1, 1 ],
[ 1, 9 ],
[ 5, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 9, 5 ], torsion_lower_bounds := [ 1, 1, 1, 1, 9, 5 ], l_ratios := [ 1, 1, 0, 0, 1/9, 1/5 ], analytic_sha_upper_bounds := [ 1, 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 0, 1, 1 ], eigenvalues := [*
[ 0, 3, -2, 4, -2, 6, -1, 1, 0, -9, -9, 2 ],
[
a,
a + 1,
2,
-2*a,
-2,
2,
-1,
1,
-2*a,
a + 5,
a - 3,
-2*a + 6
],
[
a,
a^3 - 2*a^2 - 4*a + 5,
-a^3 + a^2 + 3*a - 4,
-a^3 + 2*a^2 + 3*a - 8,
-2*a^3 + 4*a^2 + 7*a - 11,
-2*a^3 + a^2 + 7*a - 4,
1,
1,
3*a^3 - 8*a^2 - 9*a + 21,
2*a^3 - a^2 - 7*a - 1,
3*a^3 - 4*a^2 - 7*a + 10,
a^3 + 2*a^2 - 3*a - 12
],
[
a,
-a^3 - 2*a^2 + 2*a + 1,
a^4 + 3*a^3 - a^2 - 6*a - 1,
a^3 + 2*a^2 - a - 2,
-2*a^4 - 6*a^3 + 2*a^2 + 9*a - 1,
-a^2 - a - 2,
-1,
-1,
a^4 + 5*a^3 + 4*a^2 - 8*a - 4,
-3*a^4 - 10*a^3 + 5*a^2 + 24*a - 4,
a^3 - 2*a^2 - 9*a + 4,
4*a^4 + 11*a^3 - 8*a^2 - 21*a + 2
],
[
a,
1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 6*a - 1/2,
-a^4 + a^3 + 7*a^2 - 4*a - 9,
1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 7*a + 1/2,
1/2*a^5 - 1/2*a^4 - 5*a^3 + 5/2*a^2 + 11*a + 3/2,
-a^5 + a^4 + 8*a^3 - 4*a^2 - 13*a - 1,
-1,
1,
-1/2*a^5 - 1/2*a^4 + 4*a^3 + 11/2*a^2 - 8*a - 21/2,
a^4 - 9*a^2 + 12,
1/2*a^5 - 1/2*a^4 - 4*a^3 + 9/2*a^2 + 5*a - 11/2,
-a^3 + 3*a + 2
],
[
a,
1/2*a^6 - 1/2*a^5 - 5*a^4 + 7/2*a^3 + 13*a^2 - 7/2*a - 5,
a^6 - 10*a^4 + 26*a^2 + a - 10,
-a^3 + 5*a,
-a^6 + 11*a^4 + a^3 - 33*a^2 - 6*a + 18,
-a^2 - a + 6,
1,
-1,
-a^4 + a^3 + 6*a^2 - 4*a - 4,
3/2*a^6 - 1/2*a^5 - 15*a^4 + 7/2*a^3 + 39*a^2 - 5/2*a - 15,
-3/2*a^6 + 1/2*a^5 + 14*a^4 - 9/2*a^3 - 32*a^2 + 11/2*a + 13,
-3*a^6 + a^5 + 30*a^4 - 6*a^3 - 78*a^2 + 36
]
*], q_expansions := [*
q + 3*q^3 - 2*q^4 - 2*q^5 + 4*q^7 + 6*q^9 - 2*q^11 - 6*q^12 + 6*q^13 - 6*q^15 + 4*q^16 - q^17 + q^19 + 4*q^20 + 12*q^21 - q^25 + 9*q^27 - 8*q^28 - 9*q^29 - 9*q^31 - 6*q^33 - 8*q^35 - 12*q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + (-a + 2)*q^4 + 2*q^5 + 4*q^6 - 2*a*q^7 + (a - 4)*q^8 + (a + 2)*q^9 + 2*a*q^10 - 2*q^11 + (2*a - 2)*q^12 + 2*q^13 + (2*a - 8)*q^14 + (2*a + 2)*q^15 - 3*a*q^16 - q^17 + (a + 4)*q^18 + q^19 + (-2*a + 4)*q^20 - 8*q^21 - 2*a*q^22 - 2*a*q^23 - 4*a*q^24 - q^25 + 2*a*q^26 + (-a + 3)*q^27 + (-6*a + 8)*q^28 + (a + 5)*q^29 + 8*q^30 + (a - 3)*q^31 + (a - 4)*q^32 + (-2*a - 2)*q^33 - a*q^34 - 4*a*q^35 + a*q^36 + (-2*a + 6)*q^37 + O(q^38),
q + a*q^2 + (a^3 - 2*a^2 - 4*a + 5)*q^3 + (a^2 - 2)*q^4 + (-a^3 + a^2 + 3*a - 4)*q^5 + (-2*a^3 + 2*a^2 + 6*a - 7)*q^6 + (-a^3 + 2*a^2 + 3*a - 8)*q^7 + (a^3 - 4*a)*q^8 + (3*a^3 - 3*a^2 - 10*a + 8)*q^9 + (a^3 - 3*a^2 - 5*a + 7)*q^10 + (-2*a^3 + 4*a^2 + 7*a - 11)*q^11 + (-2*a^2 - a + 4)*q^12 + (-2*a^3 + a^2 + 7*a - 4)*q^13 + (2*a^3 - 3*a^2 - 9*a + 7)*q^14 + (-2*a^3 + 5*a^2 + 9*a - 13)*q^15 + (a - 3)*q^16 + q^17 + (-3*a^3 + 8*a^2 + 11*a - 21)*q^18 + q^19 + (-a^3 - a^2 + 2*a + 1)*q^20 + (-4*a^3 + 7*a^2 + 16*a - 19)*q^21 + (4*a^3 - 5*a^2 - 13*a + 14)*q^22 + (3*a^3 - 8*a^2 - 9*a + 21)*q^23 + (2*a^3 - 5*a^2 - 8*a + 14)*q^24 + (3*a^3 - 2*a^2 - 9*a + 4)*q^25 + (a^3 - 5*a^2 - 6*a + 14)*q^26 + (a^3 - 3*a^2 - 5*a + 11)*q^27 + (-a^3 - a^2 + 3*a + 2)*q^28 + (2*a^3 - a^2 - 7*a - 1)*q^29 + (5*a^3 - 3*a^2 - 15*a + 14)*q^30 + (3*a^3 - 4*a^2 - 7*a + 10)*q^31 + (-2*a^3 + a^2 + 5*a)*q^32 + (-5*a^3 + 6*a^2 + 18*a - 20)*q^33 + a*q^34 + (4*a^3 - 5*a^2 - 13*a + 18)*q^35 + (2*a^3 - a^2 - 4*a + 5)*q^36 + (a^3 + 2*a^2 - 3*a - 12)*q^37 + O(q^38),
q + a*q^2 + (-a^3 - 2*a^2 + 2*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^4 + 3*a^3 - a^2 - 6*a - 1)*q^5 + (-a^4 - 2*a^3 + 2*a^2 + a)*q^6 + (a^3 + 2*a^2 - a - 2)*q^7 + (a^3 - 4*a)*q^8 + (-a^4 - a^3 + 5*a^2 + a - 3)*q^9 + (a^3 + a^2 - 3*a - 1)*q^10 + (-2*a^4 - 6*a^3 + 2*a^2 + 9*a - 1)*q^11 + (a^4 + 2*a^3 - 2*a^2 - 2*a - 1)*q^12 + (-a^2 - a - 2)*q^13 + (a^4 + 2*a^3 - a^2 - 2*a)*q^14 + (a^4 + 4*a^3 + a^2 - 8*a - 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 - q^17 + (2*a^4 + 3*a^3 - 6*a^2 - a + 1)*q^18 - q^19 + (-a^4 - 5*a^3 - a^2 + 11*a + 2)*q^20 + (-a^2 - 2*a - 1)*q^21 + (-2*a^3 - 5*a^2 + 3*a + 2)*q^22 + (a^4 + 5*a^3 + 4*a^2 - 8*a - 4)*q^23 + (a^4 + 4*a^3 + a^2 - 5*a - 1)*q^24 + (-3*a^4 - 11*a^3 + 22*a + 1)*q^25 + (-a^3 - a^2 - 2*a)*q^26 + (2*a^4 + 5*a^3 - 3*a^2 - 5*a - 3)*q^27 + (-a^4 - a^3 + a^2 + 3)*q^28 + (-3*a^4 - 10*a^3 + 5*a^2 + 24*a - 4)*q^29 + (a^4 + 3*a^3 - a^2 - 4*a - 1)*q^30 + (a^3 - 2*a^2 - 9*a + 4)*q^31 + (-3*a^4 - 6*a^3 + 7*a^2 + 10*a - 1)*q^32 + (a^4 + a^3 - 2*a^2 + 7*a + 1)*q^33 - a*q^34 + (-2*a^4 - 6*a^3 + a^2 + 11*a + 2)*q^35 + (-a^4 + 3*a^2 - 5*a + 4)*q^36 + (4*a^4 + 11*a^3 - 8*a^2 - 21*a + 2)*q^37 + O(q^38),
q + a*q^2 + (1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 6*a - 1/2)*q^3 + (a^2 - 2)*q^4 + (-a^4 + a^3 + 7*a^2 - 4*a - 9)*q^5 + (1/2*a^5 + 1/2*a^4 - 5*a^3 - 11/2*a^2 + 11*a + 21/2)*q^6 + (1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 7*a + 1/2)*q^7 + (a^3 - 4*a)*q^8 + (-a^5 + 9*a^3 + 2*a^2 - 17*a - 8)*q^9 + (-a^5 + a^4 + 7*a^3 - 4*a^2 - 9*a)*q^10 + (1/2*a^5 - 1/2*a^4 - 5*a^3 + 5/2*a^2 + 11*a + 3/2)*q^11 + (1/2*a^5 + 1/2*a^4 - 5*a^3 - 11/2*a^2 + 10*a + 23/2)*q^12 + (-a^5 + a^4 + 8*a^3 - 4*a^2 - 13*a - 1)*q^13 + (1/2*a^5 + 1/2*a^4 - 5*a^3 - 9/2*a^2 + 12*a + 21/2)*q^14 + (a^5 - 8*a^3 - 4*a^2 + 12*a + 15)*q^15 + (a^4 - 6*a^2 + 4)*q^16 - q^17 + (-2*a^5 + 17*a^3 + 6*a^2 - 31*a - 21)*q^18 + q^19 + (-a^5 + 9*a^3 - 15*a - 3)*q^20 + (-a^2 + 5)*q^21 + (1/2*a^5 - 1/2*a^4 - 5*a^3 - 1/2*a^2 + 13*a + 21/2)*q^22 + (-1/2*a^5 - 1/2*a^4 + 4*a^3 + 11/2*a^2 - 8*a - 21/2)*q^23 + (1/2*a^5 - 3/2*a^4 - 3*a^3 + 19/2*a^2 + a - 21/2)*q^24 + (-a^5 + 9*a^3 + 3*a^2 - 20*a - 8)*q^25 + (-a^5 - a^4 + 11*a^3 + 10*a^2 - 24*a - 21)*q^26 + (a^5 + a^4 - 9*a^3 - 10*a^2 + 17*a + 16)*q^27 + (1/2*a^5 + 1/2*a^4 - 4*a^3 - 9/2*a^2 + 8*a + 19/2)*q^28 + (a^4 - 9*a^2 + 12)*q^29 + (2*a^5 + a^4 - 19*a^3 - 11*a^2 + 38*a + 21)*q^30 + (1/2*a^5 - 1/2*a^4 - 4*a^3 + 9/2*a^2 + 5*a - 11/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^4 - a^3 - 8*a^2 + 5*a + 15)*q^33 - a*q^34 + (-a^2 - a + 6)*q^35 + (-2*a^5 - a^4 + 18*a^3 + 11*a^2 - 33*a - 26)*q^36 + (-a^3 + 3*a + 2)*q^37 + O(q^38),
q + a*q^2 + (1/2*a^6 - 1/2*a^5 - 5*a^4 + 7/2*a^3 + 13*a^2 - 7/2*a - 5)*q^3 + (a^2 - 2)*q^4 + (a^6 - 10*a^4 + 26*a^2 + a - 10)*q^5 + (-a^4 + 6*a^2 + a - 4)*q^6 + (-a^3 + 5*a)*q^7 + (a^3 - 4*a)*q^8 + (-a^6 + 10*a^4 - 26*a^2 - 2*a + 12)*q^9 + (a^6 - 9*a^4 + 20*a^2 + 2*a - 8)*q^10 + (-a^6 + 11*a^4 + a^3 - 33*a^2 - 6*a + 18)*q^11 + (-a^6 + 10*a^4 - a^3 - 25*a^2 + 3*a + 10)*q^12 + (-a^2 - a + 6)*q^13 + (-a^4 + 5*a^2)*q^14 + (a^4 - 7*a^2 + 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + q^17 + (-a^6 + 9*a^4 - 21*a^2 + 8)*q^18 - q^19 + (-a^6 + a^5 + 11*a^4 - 6*a^3 - 31*a^2 + 2*a + 12)*q^20 + (a^6 - 11*a^4 - a^3 + 34*a^2 + 5*a - 20)*q^21 + (-a^6 + a^5 + 10*a^4 - 7*a^3 - 25*a^2 + 6*a + 8)*q^22 + (-a^4 + a^3 + 6*a^2 - 4*a - 4)*q^23 + (-a^6 + 10*a^4 + a^3 - 28*a^2 - 4*a + 16)*q^24 + (2*a^6 - 21*a^4 - a^3 + 58*a^2 + 8*a - 25)*q^25 + (-a^3 - a^2 + 6*a)*q^26 + (-1/2*a^6 + 1/2*a^5 + 5*a^4 - 7/2*a^3 - 12*a^2 + 5/2*a + 3)*q^27 + (-a^5 + 7*a^3 - 10*a)*q^28 + (3/2*a^6 - 1/2*a^5 - 15*a^4 + 7/2*a^3 + 39*a^2 - 5/2*a - 15)*q^29 + (a^5 - 7*a^3 + 6*a)*q^30 + (-3/2*a^6 + 1/2*a^5 + 14*a^4 - 9/2*a^3 - 32*a^2 + 11/2*a + 13)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2*a^6 - a^5 - 20*a^4 + 9*a^3 + 51*a^2 - 17*a - 18)*q^33 + a*q^34 + (3*a^6 - a^5 - 30*a^4 + 5*a^3 + 77*a^2 + 6*a - 32)*q^35 + (a^6 - a^5 - 11*a^4 + 5*a^3 + 33*a^2 - 16)*q^36 + (-3*a^6 + a^5 + 30*a^4 - 6*a^3 - 78*a^2 + 36)*q^37 + O(q^38)
*]> ;  // time = 48.319 seconds




J[326] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 326, 326, 326, 326, 326, 163, 163, 163 ], new_dimensions := [ 1, 1, 1, 5, 6, 1, 5, 7 ], dimensions := [ 1, 1, 1, 5, 6, 2, 10, 14 ], intersection_graph := [ 0, 1, 1, 1, 1, 3, 3, 1, 1, 0, 1, 17, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 5, 1, 17, 1, 0, 1, 1, 1, 611, 1, 1, 1, 1, 0, 3, 549, 1, 3, 1, 1, 1, 3, 0, 9, 1, 3, 1, 1, 1, 549, 9, 0, 1, 1, 3, 5, 611, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, -1, -1, 0, -5, 6, -6, -3, -1, -3, -2 ],
[ -1, -2, -3, -1, 0, 5, 0, 2, -3, 9, 5, 2 ],
[ 1, -2, -1, -3, -4, -1, 0, -2, -1, 3, -9, 6 ],
[ -5, 3, 9, 4, -1, 1, 2, 7, -4, 3, 16, 19 ],
[ 6, 5, 0, 5, 1, -4, 4, 7, -1, -14, 3, -9 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^5 - 3*x^4 - 8*x^3 + 27*x^2 - 5*x - 17,
x^6 - 5*x^5 + 29*x^3 - 25*x^2 - 35*x + 36
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 9, 1 ],
[ 9, 3 ],
[ 5, 1 ],
[ 611, 1 ],
[ 67527, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 3 ],
[ 5, 1 ],
[ 1, 1 ],
[ 67527, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 1, 41 ], torsion_lower_bounds := [ 1, 3, 1, 1, 41 ], l_ratios := [ 0, 1/3, 0, 1, 1647/41 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1, 1 ], eigenvalues := [*
[ -1, 0, -1, -1, 0, -5, 6, -6, -3, -1, -3, -2 ],
[ -1, -2, -3, -1, 0, 5, 0, 2, -3, 9, 5, 2 ],
[ 1, -2, -1, -3, -4, -1, 0, -2, -1, 3, -9, 6 ],
[
-1,
a,
-7/13*a^4 + 10/13*a^3 + 68/13*a^2 - 84/13*a - 32/13,
4/13*a^4 - 2/13*a^3 - 50/13*a^2 + 22/13*a + 100/13,
-3/13*a^4 - 5/13*a^3 + 31/13*a^2 + 42/13*a - 49/13,
6/13*a^4 - 3/13*a^3 - 62/13*a^2 + 33/13*a + 72/13,
8/13*a^4 - 4/13*a^3 - 74/13*a^2 + 18/13*a + 70/13,
10/13*a^4 - 18/13*a^3 - 99/13*a^2 + 120/13*a + 120/13,
14/13*a^4 - 20/13*a^3 - 136/13*a^2 + 142/13*a + 116/13,
-14/13*a^4 + 20/13*a^3 + 123/13*a^2 - 168/13*a - 38/13,
-4/13*a^4 + 2/13*a^3 + 50/13*a^2 - 22/13*a - 48/13,
-3/13*a^4 - 5/13*a^3 + 57/13*a^2 + 42/13*a - 127/13
],
[
1,
a,
a^5 - 2*a^4 - 6*a^3 + 9*a^2 + 7*a - 7,
-3*a^5 + 7*a^4 + 18*a^3 - 37*a^2 - 23*a + 41,
3*a^5 - 8*a^4 - 17*a^3 + 44*a^2 + 19*a - 48,
a^5 - 3*a^4 - 7*a^3 + 19*a^2 + 12*a - 23,
2*a^2 - 2*a - 6,
-2*a^5 + 4*a^4 + 14*a^3 - 23*a^2 - 22*a + 30,
3*a^5 - 5*a^4 - 20*a^3 + 23*a^2 + 27*a - 21,
-5*a^5 + 11*a^4 + 32*a^3 - 60*a^2 - 43*a + 65,
-a^5 + 5*a^4 + 2*a^3 - 27*a^2 + 3*a + 27,
-a^5 + 4*a^4 + 3*a^3 - 22*a^2 + 3*a + 22
]
*], q_expansions := [*
q - q^2 + q^4 - q^5 - q^7 - q^8 - 3*q^9 + q^10 - 5*q^13 + q^14 + q^16 + 6*q^17 + 3*q^18 - 6*q^19 - q^20 - 3*q^23 - 4*q^25 + 5*q^26 - q^28 - q^29 - 3*q^31 - q^32 - 6*q^34 + q^35 - 3*q^36 - 2*q^37 + O(q^38),
q - q^2 - 2*q^3 + q^4 - 3*q^5 + 2*q^6 - q^7 - q^8 + q^9 + 3*q^10 - 2*q^12 + 5*q^13 + q^14 + 6*q^15 + q^16 - q^18 + 2*q^19 - 3*q^20 + 2*q^21 - 3*q^23 + 2*q^24 + 4*q^25 - 5*q^26 + 4*q^27 - q^28 + 9*q^29 - 6*q^30 + 5*q^31 - q^32 + 3*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - q^5 - 2*q^6 - 3*q^7 + q^8 + q^9 - q^10 - 4*q^11 - 2*q^12 - q^13 - 3*q^14 + 2*q^15 + q^16 + q^18 - 2*q^19 - q^20 + 6*q^21 - 4*q^22 - q^23 - 2*q^24 - 4*q^25 - q^26 + 4*q^27 - 3*q^28 + 3*q^29 + 2*q^30 - 9*q^31 + q^32 + 8*q^33 + 3*q^35 + q^36 + 6*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-7/13*a^4 + 10/13*a^3 + 68/13*a^2 - 84/13*a - 32/13)*q^5 - a*q^6 + (4/13*a^4 - 2/13*a^3 - 50/13*a^2 + 22/13*a + 100/13)*q^7 - q^8 + (a^2 - 3)*q^9 + (7/13*a^4 - 10/13*a^3 - 68/13*a^2 + 84/13*a + 32/13)*q^10 + (-3/13*a^4 - 5/13*a^3 + 31/13*a^2 + 42/13*a - 49/13)*q^11 + a*q^12 + (6/13*a^4 - 3/13*a^3 - 62/13*a^2 + 33/13*a + 72/13)*q^13 + (-4/13*a^4 + 2/13*a^3 + 50/13*a^2 - 22/13*a - 100/13)*q^14 + (-11/13*a^4 + 12/13*a^3 + 105/13*a^2 - 67/13*a - 119/13)*q^15 + q^16 + (8/13*a^4 - 4/13*a^3 - 74/13*a^2 + 18/13*a + 70/13)*q^17 + (-a^2 + 3)*q^18 + (10/13*a^4 - 18/13*a^3 - 99/13*a^2 + 120/13*a + 120/13)*q^19 + (-7/13*a^4 + 10/13*a^3 + 68/13*a^2 - 84/13*a - 32/13)*q^20 + (10/13*a^4 - 18/13*a^3 - 86/13*a^2 + 120/13*a + 68/13)*q^21 + (3/13*a^4 + 5/13*a^3 - 31/13*a^2 - 42/13*a + 49/13)*q^22 + (14/13*a^4 - 20/13*a^3 - 136/13*a^2 + 142/13*a + 116/13)*q^23 - a*q^24 + (-16/13*a^4 + 21/13*a^3 + 148/13*a^2 - 179/13*a - 49/13)*q^25 + (-6/13*a^4 + 3/13*a^3 + 62/13*a^2 - 33/13*a - 72/13)*q^26 + (a^3 - 6*a)*q^27 + (4/13*a^4 - 2/13*a^3 - 50/13*a^2 + 22/13*a + 100/13)*q^28 + (-14/13*a^4 + 20/13*a^3 + 123/13*a^2 - 168/13*a - 38/13)*q^29 + (11/13*a^4 - 12/13*a^3 - 105/13*a^2 + 67/13*a + 119/13)*q^30 + (-4/13*a^4 + 2/13*a^3 + 50/13*a^2 - 22/13*a - 48/13)*q^31 - q^32 + (-14/13*a^4 + 7/13*a^3 + 123/13*a^2 - 64/13*a - 51/13)*q^33 + (-8/13*a^4 + 4/13*a^3 + 74/13*a^2 - 18/13*a - 70/13)*q^34 + (-8/13*a^4 + 30/13*a^3 + 48/13*a^2 - 226/13*a + 86/13)*q^35 + (a^2 - 3)*q^36 + (-3/13*a^4 - 5/13*a^3 + 57/13*a^2 + 42/13*a - 127/13)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (a^5 - 2*a^4 - 6*a^3 + 9*a^2 + 7*a - 7)*q^5 + a*q^6 + (-3*a^5 + 7*a^4 + 18*a^3 - 37*a^2 - 23*a + 41)*q^7 + q^8 + (a^2 - 3)*q^9 + (a^5 - 2*a^4 - 6*a^3 + 9*a^2 + 7*a - 7)*q^10 + (3*a^5 - 8*a^4 - 17*a^3 + 44*a^2 + 19*a - 48)*q^11 + a*q^12 + (a^5 - 3*a^4 - 7*a^3 + 19*a^2 + 12*a - 23)*q^13 + (-3*a^5 + 7*a^4 + 18*a^3 - 37*a^2 - 23*a + 41)*q^14 + (3*a^5 - 6*a^4 - 20*a^3 + 32*a^2 + 28*a - 36)*q^15 + q^16 + (2*a^2 - 2*a - 6)*q^17 + (a^2 - 3)*q^18 + (-2*a^5 + 4*a^4 + 14*a^3 - 23*a^2 - 22*a + 30)*q^19 + (a^5 - 2*a^4 - 6*a^3 + 9*a^2 + 7*a - 7)*q^20 + (-8*a^5 + 18*a^4 + 50*a^3 - 98*a^2 - 64*a + 108)*q^21 + (3*a^5 - 8*a^4 - 17*a^3 + 44*a^2 + 19*a - 48)*q^22 + (3*a^5 - 5*a^4 - 20*a^3 + 23*a^2 + 27*a - 21)*q^23 + a*q^24 + (-3*a^5 + 7*a^4 + 19*a^3 - 39*a^2 - 26*a + 44)*q^25 + (a^5 - 3*a^4 - 7*a^3 + 19*a^2 + 12*a - 23)*q^26 + (a^3 - 6*a)*q^27 + (-3*a^5 + 7*a^4 + 18*a^3 - 37*a^2 - 23*a + 41)*q^28 + (-5*a^5 + 11*a^4 + 32*a^3 - 60*a^2 - 43*a + 65)*q^29 + (3*a^5 - 6*a^4 - 20*a^3 + 32*a^2 + 28*a - 36)*q^30 + (-a^5 + 5*a^4 + 2*a^3 - 27*a^2 + 3*a + 27)*q^31 + q^32 + (7*a^5 - 17*a^4 - 43*a^3 + 94*a^2 + 57*a - 108)*q^33 + (2*a^2 - 2*a - 6)*q^34 + (3*a^5 - 7*a^4 - 18*a^3 + 35*a^2 + 23*a - 35)*q^35 + (a^2 - 3)*q^36 + (-a^5 + 4*a^4 + 3*a^3 - 22*a^2 + 3*a + 22)*q^37 + O(q^38)
*]> ;  // time = 72.73 seconds




J[327] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 327, 327, 327, 327, 109, 109, 109 ], new_dimensions := [ 1, 3, 6, 9, 1, 3, 4 ], dimensions := [ 1, 3, 6, 9, 2, 6, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 13, 1, 1, 1, 0, 1, 1, 1, 107, 1, 1, 1, 0, 1, 139, 1, 1, 1, 1, 1, 0, 1, 1, 1, 13, 1, 139, 1, 0, 1, 1, 1, 107, 1, 1, 1, 0 ], ap_traces := [
[ -1, 1, -1, -2, -1, -4, -4, -7, 1, 7, -2, -6 ],
[ -3, -3, -3, -2, -1, -2, -8, 5, -9, -7, 6, -12 ],
[ 4, -6, 5, -2, 7, 6, 14, -15, 9, 5, -14, 8 ],
[ 3, 9, 1, 6, -5, 6, 0, 13, -5, -3, 18, 16 ]
], hecke_fields := [
x - 1,
x^3 + 3*x^2 - x - 5,
x^6 - 4*x^5 - 2*x^4 + 20*x^3 - 8*x^2 - 16*x + 1,
x^9 - 3*x^8 - 11*x^7 + 35*x^6 + 34*x^5 - 122*x^4 - 29*x^3 + 127*x^2 + 9*x - 5
], atkin_lehners := [
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 13, 1 ],
[ 107, 1 ],
[ 7645, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 7645, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 55 ], torsion_lower_bounds := [ 1, 1, 1, 55 ], l_ratios := [ 0, 0, 1, 139/55 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[ -1, 1, -1, -2, -1, -4, -4, -7, 1, 7, -2, -6 ],
[
a,
-1,
-1,
-a^2 - 2*a + 1,
a^2 + a - 3,
-a^2 - 2*a + 1,
2*a^2 + 2*a - 8,
a^2 + a - 1,
a - 2,
a^2 + 2*a - 4,
4*a + 6,
-3*a^2 - 2*a + 5
],
[
a,
-1,
1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 5/2*a^2 + 19/2*a + 1/2,
-a^5 + 2*a^4 + 5*a^3 - 8*a^2 - 3*a + 1,
-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 5/2*a^2 - 19/2*a + 3/2,
a^5 - a^4 - 7*a^3 + 3*a^2 + 11*a + 3,
-a^4 + a^3 + 5*a^2 - 4*a + 1,
1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 1/2*a^2 + 23/2*a + 5/2,
-5/2*a^5 + 11/2*a^4 + 27/2*a^3 - 47/2*a^2 - 31/2*a + 17/2,
-3/2*a^5 + 11/2*a^4 + 7/2*a^3 - 47/2*a^2 + 15/2*a + 17/2,
-a^5 + 2*a^4 + 5*a^3 - 6*a^2 - 7*a - 5,
2*a^3 - 12*a
],
[
a,
1,
-1/6*a^8 - 1/6*a^7 + 8/3*a^6 + 7/3*a^5 - 40/3*a^4 - 10*a^3 + 125/6*a^2 + 85/6*a - 1/3,
-1/3*a^8 + 2/3*a^7 + 13/3*a^6 - 22/3*a^5 - 53/3*a^4 + 22*a^3 + 68/3*a^2 - 44/3*a + 1/3,
3*a^8 - 7/2*a^7 - 79/2*a^6 + 33*a^5 + 163*a^4 - 72*a^3 - 217*a^2 - 5/2*a + 23/2,
-4/3*a^8 + 5/3*a^7 + 52/3*a^6 - 46/3*a^5 - 212/3*a^4 + 30*a^3 + 278/3*a^2 + 31/3*a - 2/3,
-7/3*a^8 + 8/3*a^7 + 91/3*a^6 - 73/3*a^5 - 368/3*a^4 + 48*a^3 + 473/3*a^2 + 43/3*a - 11/3,
8/3*a^8 - 17/6*a^7 - 211/6*a^6 + 77/3*a^5 + 433/3*a^4 - 48*a^3 - 562/3*a^2 - 163/6*a + 35/6,
-a^8 + 3/2*a^7 + 25/2*a^6 - 16*a^5 - 47*a^4 + 48*a^3 + 53*a^2 - 69/2*a - 5/2,
-3/2*a^8 + 3/2*a^7 + 20*a^6 - 13*a^5 - 84*a^4 + 20*a^3 + 231/2*a^2 + 49/2*a - 9,
-11/3*a^8 + 13/3*a^7 + 143/3*a^6 - 122/3*a^5 - 577/3*a^4 + 88*a^3 + 736/3*a^2 + 11/3*a - 13/3,
-5/3*a^8 + 4/3*a^7 + 68/3*a^6 - 32/3*a^5 - 292/3*a^4 + 10*a^3 + 409/3*a^2 + 116/3*a - 22/3
]
*], q_expansions := [*
q - q^2 + q^3 - q^4 - q^5 - q^6 - 2*q^7 + 3*q^8 + q^9 + q^10 - q^11 - q^12 - 4*q^13 + 2*q^14 - q^15 - q^16 - 4*q^17 - q^18 - 7*q^19 + q^20 - 2*q^21 + q^22 + q^23 + 3*q^24 - 4*q^25 + 4*q^26 + q^27 + 2*q^28 + 7*q^29 + q^30 - 2*q^31 - 5*q^32 - q^33 + 4*q^34 + 2*q^35 - q^36 - 6*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 - q^5 - a*q^6 + (-a^2 - 2*a + 1)*q^7 + (-3*a^2 - 3*a + 5)*q^8 + q^9 - a*q^10 + (a^2 + a - 3)*q^11 + (-a^2 + 2)*q^12 + (-a^2 - 2*a + 1)*q^13 + (a^2 - 5)*q^14 + q^15 + (4*a^2 + 2*a - 11)*q^16 + (2*a^2 + 2*a - 8)*q^17 + a*q^18 + (a^2 + a - 1)*q^19 + (-a^2 + 2)*q^20 + (a^2 + 2*a - 1)*q^21 + (-2*a^2 - 2*a + 5)*q^22 + (a - 2)*q^23 + (3*a^2 + 3*a - 5)*q^24 - 4*q^25 + (a^2 - 5)*q^26 - q^27 + (-a^2 + 3)*q^28 + (a^2 + 2*a - 4)*q^29 + a*q^30 + (4*a + 6)*q^31 + (-4*a^2 - a + 10)*q^32 + (-a^2 - a + 3)*q^33 + (-4*a^2 - 6*a + 10)*q^34 + (a^2 + 2*a - 1)*q^35 + (a^2 - 2)*q^36 + (-3*a^2 - 2*a + 5)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 5/2*a^2 + 19/2*a + 1/2)*q^5 - a*q^6 + (-a^5 + 2*a^4 + 5*a^3 - 8*a^2 - 3*a + 1)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (3/2*a^5 - 7/2*a^4 - 15/2*a^3 + 27/2*a^2 + 17/2*a - 1/2)*q^10 + (-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 5/2*a^2 - 19/2*a + 3/2)*q^11 + (-a^2 + 2)*q^12 + (a^5 - a^4 - 7*a^3 + 3*a^2 + 11*a + 3)*q^13 + (-2*a^5 + 3*a^4 + 12*a^3 - 11*a^2 - 15*a + 1)*q^14 + (-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 5/2*a^2 - 19/2*a - 1/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 + a^3 + 5*a^2 - 4*a + 1)*q^17 + a*q^18 + (1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 1/2*a^2 + 23/2*a + 5/2)*q^19 + (3/2*a^5 - 7/2*a^4 - 15/2*a^3 + 31/2*a^2 + 9/2*a - 5/2)*q^20 + (a^5 - 2*a^4 - 5*a^3 + 8*a^2 + 3*a - 1)*q^21 + (-3/2*a^5 + 7/2*a^4 + 15/2*a^3 - 27/2*a^2 - 13/2*a + 1/2)*q^22 + (-5/2*a^5 + 11/2*a^4 + 27/2*a^3 - 47/2*a^2 - 31/2*a + 17/2)*q^23 + (-a^3 + 4*a)*q^24 + (5/2*a^5 - 13/2*a^4 - 25/2*a^3 + 57/2*a^2 + 19/2*a - 9/2)*q^25 + (3*a^5 - 5*a^4 - 17*a^3 + 19*a^2 + 19*a - 1)*q^26 - q^27 + (-3*a^5 + 4*a^4 + 19*a^3 - 15*a^2 - 25*a)*q^28 + (-3/2*a^5 + 11/2*a^4 + 7/2*a^3 - 47/2*a^2 + 15/2*a + 17/2)*q^29 + (-3/2*a^5 + 7/2*a^4 + 15/2*a^3 - 27/2*a^2 - 17/2*a + 1/2)*q^30 + (-a^5 + 2*a^4 + 5*a^3 - 6*a^2 - 7*a - 5)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 5/2*a^2 + 19/2*a - 3/2)*q^33 + (-a^5 + a^4 + 5*a^3 - 4*a^2 + a)*q^34 + (a^5 - 3*a^4 - 3*a^3 + 11*a^2 - 3*a + 1)*q^35 + (a^2 - 2)*q^36 + (2*a^3 - 12*a)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-1/6*a^8 - 1/6*a^7 + 8/3*a^6 + 7/3*a^5 - 40/3*a^4 - 10*a^3 + 125/6*a^2 + 85/6*a - 1/3)*q^5 + a*q^6 + (-1/3*a^8 + 2/3*a^7 + 13/3*a^6 - 22/3*a^5 - 53/3*a^4 + 22*a^3 + 68/3*a^2 - 44/3*a + 1/3)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-2/3*a^8 + 5/6*a^7 + 49/6*a^6 - 23/3*a^5 - 91/3*a^4 + 16*a^3 + 106/3*a^2 + 7/6*a - 5/6)*q^10 + (3*a^8 - 7/2*a^7 - 79/2*a^6 + 33*a^5 + 163*a^4 - 72*a^3 - 217*a^2 - 5/2*a + 23/2)*q^11 + (a^2 - 2)*q^12 + (-4/3*a^8 + 5/3*a^7 + 52/3*a^6 - 46/3*a^5 - 212/3*a^4 + 30*a^3 + 278/3*a^2 + 31/3*a - 2/3)*q^13 + (-1/3*a^8 + 2/3*a^7 + 13/3*a^6 - 19/3*a^5 - 56/3*a^4 + 13*a^3 + 83/3*a^2 + 10/3*a - 5/3)*q^14 + (-1/6*a^8 - 1/6*a^7 + 8/3*a^6 + 7/3*a^5 - 40/3*a^4 - 10*a^3 + 125/6*a^2 + 85/6*a - 1/3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-7/3*a^8 + 8/3*a^7 + 91/3*a^6 - 73/3*a^5 - 368/3*a^4 + 48*a^3 + 473/3*a^2 + 43/3*a - 11/3)*q^17 + a*q^18 + (8/3*a^8 - 17/6*a^7 - 211/6*a^6 + 77/3*a^5 + 433/3*a^4 - 48*a^3 - 562/3*a^2 - 163/6*a + 35/6)*q^19 + (-5/6*a^8 + 7/6*a^7 + 31/3*a^6 - 37/3*a^5 - 116/3*a^4 + 36*a^3 + 265/6*a^2 - 139/6*a - 8/3)*q^20 + (-1/3*a^8 + 2/3*a^7 + 13/3*a^6 - 22/3*a^5 - 53/3*a^4 + 22*a^3 + 68/3*a^2 - 44/3*a + 1/3)*q^21 + (11/2*a^8 - 13/2*a^7 - 72*a^6 + 61*a^5 + 294*a^4 - 130*a^3 - 767/2*a^2 - 31/2*a + 15)*q^22 + (-a^8 + 3/2*a^7 + 25/2*a^6 - 16*a^5 - 47*a^4 + 48*a^3 + 53*a^2 - 69/2*a - 5/2)*q^23 + (a^3 - 4*a)*q^24 + (-1/6*a^8 - 1/6*a^7 + 8/3*a^6 + 7/3*a^5 - 40/3*a^4 - 8*a^3 + 125/6*a^2 + 25/6*a + 2/3)*q^25 + (-7/3*a^8 + 8/3*a^7 + 94/3*a^6 - 76/3*a^5 - 398/3*a^4 + 54*a^3 + 539/3*a^2 + 34/3*a - 20/3)*q^26 + q^27 + (1/3*a^8 - 2/3*a^7 - 10/3*a^6 + 22/3*a^5 + 23/3*a^4 - 26*a^3 + 1/3*a^2 + 92/3*a - 7/3)*q^28 + (-3/2*a^8 + 3/2*a^7 + 20*a^6 - 13*a^5 - 84*a^4 + 20*a^3 + 231/2*a^2 + 49/2*a - 9)*q^29 + (-2/3*a^8 + 5/6*a^7 + 49/6*a^6 - 23/3*a^5 - 91/3*a^4 + 16*a^3 + 106/3*a^2 + 7/6*a - 5/6)*q^30 + (-11/3*a^8 + 13/3*a^7 + 143/3*a^6 - 122/3*a^5 - 577/3*a^4 + 88*a^3 + 736/3*a^2 + 11/3*a - 13/3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (3*a^8 - 7/2*a^7 - 79/2*a^6 + 33*a^5 + 163*a^4 - 72*a^3 - 217*a^2 - 5/2*a + 23/2)*q^33 + (-13/3*a^8 + 14/3*a^7 + 172/3*a^6 - 130/3*a^5 - 710/3*a^4 + 90*a^3 + 932/3*a^2 + 52/3*a - 35/3)*q^34 + (1/3*a^8 - 2/3*a^7 - 10/3*a^6 + 22/3*a^5 + 20/3*a^4 - 24*a^3 + 19/3*a^2 + 62/3*a - 22/3)*q^35 + (a^2 - 2)*q^36 + (-5/3*a^8 + 4/3*a^7 + 68/3*a^6 - 32/3*a^5 - 292/3*a^4 + 10*a^3 + 409/3*a^2 + 116/3*a - 22/3)*q^37 + O(q^38)
*]> ;  // time = 48.569 seconds




J[329] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 329, 329, 329, 329, 329, 329, 329, 47 ], new_dimensions := [ 1, 2, 3, 3, 3, 5, 6, 4 ], dimensions := [ 1, 2, 3, 3, 3, 5, 6, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 5, 1, 9, 1, 0, 1, 1, 1, 1, 13, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 37, 1, 19, 1, 1, 1, 1, 0, 1, 1, 83, 5, 1, 1, 37, 1, 0, 1, 31, 1, 13, 1, 1, 1, 1, 0, 1, 9, 1, 1, 19, 83, 31, 1, 0 ], ap_traces := [
[ -1, -1, 3, -1, 3, -6, 6, 8, 4, 2, 6, 9 ],
[ -2, 1, -3, 2, -7, 4, 4, 8, 8, -4, -2, 7 ],
[ -1, -2, -2, -3, -4, 1, 5, -4, -5, -6, -16, -12 ],
[ 1, 1, -1, -3, 1, -4, -10, 0, 10, -2, 18, -5 ],
[ -1, -4, 0, 3, 0, -11, -9, -10, 1, 6, -20, -4 ],
[ 1, 2, -4, -5, 4, 1, -3, -2, -7, 4, 10, 4 ],
[ 0, 3, 5, 6, 7, 5, -3, 0, 1, 6, 36, -13 ]
], hecke_fields := [
x - 1,
x^2 + x - 4,
x^3 + x^2 - 2*x - 1,
x^3 - x^2 - 5*x + 1,
x^3 + x^2 - 2*x - 1,
x^5 - x^4 - 11*x^3 + 12*x^2 + 28*x - 33,
x^6 - 12*x^4 + 5*x^3 + 36*x^2 - 29*x + 3
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 9, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 19, 1 ],
[ 83, 1 ],
[ 31, 1 ],
[ 3, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 83, 1 ],
[ 1, 1 ],
[ 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 3 ], l_ratios := [ 1, 1, 0, 1, 0, 1, 1/3 ], analytic_sha_upper_bounds := [ 1, 1, 0, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 1, 0, 1, 1 ], eigenvalues := [*
[ -1, -1, 3, -1, 3, -6, 6, 8, 4, 2, 6, 9 ],
[
-1,
a + 1,
a - 1,
1,
a - 3,
2,
2,
4,
4,
-2,
-2*a - 2,
3*a + 5
],
[
a,
-a^2 + 1,
-a - 1,
-1,
a^2 - 3,
a^2 - 2*a - 2,
3*a^2 + 4*a - 2,
2*a^2 + 5*a - 3,
-a^2 - 3*a - 1,
-4*a^2 + a + 5,
-5*a^2 - 3*a + 2,
-2*a^2 - 4*a - 2
],
[
a,
a^2 - a - 3,
1/2*a^2 - 2*a - 3/2,
-1,
-1/2*a^2 - a + 5/2,
-a - 1,
2*a - 4,
-a^2 + 2*a + 3,
-a^2 + 3*a + 6,
a^2 + 2*a - 5,
6,
2*a^2 - 9
],
[
a,
a^2 - 3,
-2*a^2 - a + 3,
1,
3*a^2 - 5,
-a^2 - 2,
-a^2 - 2*a - 2,
a - 3,
5*a^2 + 3*a - 7,
3*a + 3,
a^2 + a - 8,
2*a^2 + 8*a - 2
],
[
a,
-a^2 + 5,
a - 1,
-1,
-a^4 + 10*a^2 + a - 20,
a^3 - 2*a^2 - 6*a + 11,
-a^4 - a^3 + 9*a^2 + 5*a - 18,
a^4 + 2*a^3 - 11*a^2 - 12*a + 28,
-a^4 - a^3 + 9*a^2 + 6*a - 19,
a^4 + 2*a^3 - 9*a^2 - 12*a + 20,
a^4 - 10*a^2 - 2*a + 23,
-2*a^4 - 2*a^3 + 18*a^2 + 10*a - 34
],
[
a,
-a^3 + 6*a - 2,
1/2*a^5 + 1/2*a^4 - 9/2*a^3 - 2*a^2 + 10*a - 3/2,
1,
-1/2*a^5 - 1/2*a^4 + 9/2*a^3 + a^2 - 11*a + 15/2,
-a^5 - a^4 + 10*a^3 + 4*a^2 - 26*a + 8,
a^4 + a^3 - 7*a^2 - 3*a + 6,
-a^4 + 7*a^2 - 2*a - 4,
a^5 + 2*a^4 - 8*a^3 - 9*a^2 + 16*a - 6,
-a^4 - 2*a^3 + 5*a^2 + 8*a,
a^4 + 2*a^3 - 6*a^2 - 10*a + 11,
-a^5 - 2*a^4 + 10*a^3 + 10*a^2 - 29*a + 5
]
*], q_expansions := [*
q - q^2 - q^3 - q^4 + 3*q^5 + q^6 - q^7 + 3*q^8 - 2*q^9 - 3*q^10 + 3*q^11 + q^12 - 6*q^13 + q^14 - 3*q^15 - q^16 + 6*q^17 + 2*q^18 + 8*q^19 - 3*q^20 + q^21 - 3*q^22 + 4*q^23 - 3*q^24 + 4*q^25 + 6*q^26 + 5*q^27 + q^28 + 2*q^29 + 3*q^30 + 6*q^31 - 5*q^32 - 3*q^33 - 6*q^34 - 3*q^35 + 2*q^36 + 9*q^37 + O(q^38),
q - q^2 + (a + 1)*q^3 - q^4 + (a - 1)*q^5 + (-a - 1)*q^6 + q^7 + 3*q^8 + (a + 2)*q^9 + (-a + 1)*q^10 + (a - 3)*q^11 + (-a - 1)*q^12 + 2*q^13 - q^14 + (-a + 3)*q^15 - q^16 + 2*q^17 + (-a - 2)*q^18 + 4*q^19 + (-a + 1)*q^20 + (a + 1)*q^21 + (-a + 3)*q^22 + 4*q^23 + (3*a + 3)*q^24 - 3*a*q^25 - 2*q^26 + (-a + 3)*q^27 - q^28 - 2*q^29 + (a - 3)*q^30 + (-2*a - 2)*q^31 - 5*q^32 + (-3*a + 1)*q^33 - 2*q^34 + (a - 1)*q^35 + (-a - 2)*q^36 + (3*a + 5)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + 1)*q^3 + (a^2 - 2)*q^4 + (-a - 1)*q^5 + (a^2 - a - 1)*q^6 - q^7 + (-a^2 - 2*a + 1)*q^8 + (a^2 - a - 3)*q^9 + (-a^2 - a)*q^10 + (a^2 - 3)*q^11 + (a - 1)*q^12 + (a^2 - 2*a - 2)*q^13 - a*q^14 + a*q^15 + (-3*a^2 - a + 3)*q^16 + (3*a^2 + 4*a - 2)*q^17 + (-2*a^2 - a + 1)*q^18 + (2*a^2 + 5*a - 3)*q^19 + q^20 + (a^2 - 1)*q^21 + (-a^2 - a + 1)*q^22 + (-a^2 - 3*a - 1)*q^23 + (-a^2 + a + 2)*q^24 + (a^2 + 2*a - 4)*q^25 + (-3*a^2 + 1)*q^26 + (3*a^2 + 2*a - 4)*q^27 + (-a^2 + 2)*q^28 + (-4*a^2 + a + 5)*q^29 + a^2*q^30 + (-5*a^2 - 3*a + 2)*q^31 + (4*a^2 + a - 5)*q^32 + (a^2 + a - 2)*q^33 + (a^2 + 4*a + 3)*q^34 + (a + 1)*q^35 + (-a^2 - a + 4)*q^36 + (-2*a^2 - 4*a - 2)*q^37 + O(q^38),
q + a*q^2 + (a^2 - a - 3)*q^3 + (a^2 - 2)*q^4 + (1/2*a^2 - 2*a - 3/2)*q^5 + (2*a - 1)*q^6 - q^7 + (a^2 + a - 1)*q^8 + (-a^2 + 7)*q^9 + (-3/2*a^2 + a - 1/2)*q^10 + (-1/2*a^2 - a + 5/2)*q^11 + (a + 6)*q^12 + (-a - 1)*q^13 - a*q^14 + (-1/2*a^2 - 3*a + 13/2)*q^15 + (4*a + 3)*q^16 + (2*a - 4)*q^17 + (-a^2 + 2*a + 1)*q^18 + (-a^2 + 2*a + 3)*q^19 + (-3/2*a^2 - 4*a + 9/2)*q^20 + (-a^2 + a + 3)*q^21 + (-3/2*a^2 + 1/2)*q^22 + (-a^2 + 3*a + 6)*q^23 + (a^2 + 2*a + 2)*q^24 + (2*a^2 - 3*a - 1)*q^25 + (-a^2 - a)*q^26 + (2*a^2 - 3*a - 12)*q^27 + (-a^2 + 2)*q^28 + (a^2 + 2*a - 5)*q^29 + (-7/2*a^2 + 4*a + 1/2)*q^30 + 6*q^31 + (2*a^2 + a + 2)*q^32 + (3/2*a^2 - 4*a - 13/2)*q^33 + (2*a^2 - 4*a)*q^34 + (-1/2*a^2 + 2*a + 3/2)*q^35 + (3*a^2 - 4*a - 13)*q^36 + (2*a^2 - 9)*q^37 + O(q^38),
q + a*q^2 + (a^2 - 3)*q^3 + (a^2 - 2)*q^4 + (-2*a^2 - a + 3)*q^5 + (-a^2 - a + 1)*q^6 + q^7 + (-a^2 - 2*a + 1)*q^8 + (-3*a^2 - a + 5)*q^9 + (a^2 - a - 2)*q^10 + (3*a^2 - 5)*q^11 + (-2*a^2 - a + 5)*q^12 + (-a^2 - 2)*q^13 + a*q^14 + (4*a^2 + 3*a - 8)*q^15 + (-3*a^2 - a + 3)*q^16 + (-a^2 - 2*a - 2)*q^17 + (2*a^2 - a - 3)*q^18 + (a - 3)*q^19 + (2*a^2 + 2*a - 5)*q^20 + (a^2 - 3)*q^21 + (-3*a^2 + a + 3)*q^22 + (5*a^2 + 3*a - 7)*q^23 + (3*a^2 + 3*a - 4)*q^24 + (-3*a^2 - 2*a + 4)*q^25 + (a^2 - 4*a - 1)*q^26 + (3*a^2 + 4*a - 4)*q^27 + (a^2 - 2)*q^28 + (3*a + 3)*q^29 + (-a^2 + 4)*q^30 + (a^2 + a - 8)*q^31 + (4*a^2 + a - 5)*q^32 + (-5*a^2 - 3*a + 12)*q^33 + (-a^2 - 4*a - 1)*q^34 + (-2*a^2 - a + 3)*q^35 + (3*a^2 + 3*a - 8)*q^36 + (2*a^2 + 8*a - 2)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + 5)*q^3 + (a^2 - 2)*q^4 + (a - 1)*q^5 + (-a^3 + 5*a)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (a^4 - 10*a^2 + 22)*q^9 + (a^2 - a)*q^10 + (-a^4 + 10*a^2 + a - 20)*q^11 + (-a^4 + 7*a^2 - 10)*q^12 + (a^3 - 2*a^2 - 6*a + 11)*q^13 - a*q^14 + (-a^3 + a^2 + 5*a - 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 - a^3 + 9*a^2 + 5*a - 18)*q^17 + (a^4 + a^3 - 12*a^2 - 6*a + 33)*q^18 + (a^4 + 2*a^3 - 11*a^2 - 12*a + 28)*q^19 + (a^3 - a^2 - 2*a + 2)*q^20 + (a^2 - 5)*q^21 + (-a^4 - a^3 + 13*a^2 + 8*a - 33)*q^22 + (-a^4 - a^3 + 9*a^2 + 6*a - 19)*q^23 + (-a^4 - 2*a^3 + 12*a^2 + 8*a - 33)*q^24 + (a^2 - 2*a - 4)*q^25 + (a^4 - 2*a^3 - 6*a^2 + 11*a)*q^26 + (3*a^4 + a^3 - 29*a^2 - 5*a + 62)*q^27 + (-a^2 + 2)*q^28 + (a^4 + 2*a^3 - 9*a^2 - 12*a + 20)*q^29 + (-a^4 + a^3 + 5*a^2 - 5*a)*q^30 + (a^4 - 10*a^2 - 2*a + 23)*q^31 + (a^4 + 3*a^3 - 12*a^2 - 16*a + 33)*q^32 + (-3*a^4 - 2*a^3 + 30*a^2 + 10*a - 67)*q^33 + (-2*a^4 - 2*a^3 + 17*a^2 + 10*a - 33)*q^34 + (-a + 1)*q^35 + (-a^3 + 2*a^2 + 5*a - 11)*q^36 + (-2*a^4 - 2*a^3 + 18*a^2 + 10*a - 34)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 6*a - 2)*q^3 + (a^2 - 2)*q^4 + (1/2*a^5 + 1/2*a^4 - 9/2*a^3 - 2*a^2 + 10*a - 3/2)*q^5 + (-a^4 + 6*a^2 - 2*a)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (-a^3 + 5*a - 2)*q^9 + (1/2*a^5 + 3/2*a^4 - 9/2*a^3 - 8*a^2 + 13*a - 3/2)*q^10 + (-1/2*a^5 - 1/2*a^4 + 9/2*a^3 + a^2 - 11*a + 15/2)*q^11 + (-a^5 + 8*a^3 - 2*a^2 - 12*a + 4)*q^12 + (-a^5 - a^4 + 10*a^3 + 4*a^2 - 26*a + 8)*q^13 + a*q^14 + (1/2*a^5 + 1/2*a^4 - 11/2*a^3 - 3*a^2 + 16*a - 3/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 + a^3 - 7*a^2 - 3*a + 6)*q^17 + (-a^4 + 5*a^2 - 2*a)*q^18 + (-a^4 + 7*a^2 - 2*a - 4)*q^19 + (1/2*a^5 + 1/2*a^4 - 3/2*a^3 - a^2 - 7*a + 3/2)*q^20 + (-a^3 + 6*a - 2)*q^21 + (-1/2*a^5 - 3/2*a^4 + 7/2*a^3 + 7*a^2 - 7*a + 3/2)*q^22 + (a^5 + 2*a^4 - 8*a^3 - 9*a^2 + 16*a - 6)*q^23 + (-2*a^4 + 3*a^3 + 12*a^2 - 21*a + 3)*q^24 + (a^5 + a^4 - 10*a^3 - 4*a^2 + 26*a - 8)*q^25 + (-a^5 - 2*a^4 + 9*a^3 + 10*a^2 - 21*a + 3)*q^26 + (a^4 + 2*a^3 - 6*a^2 - 11*a + 7)*q^27 + (a^2 - 2)*q^28 + (-a^4 - 2*a^3 + 5*a^2 + 8*a)*q^29 + (1/2*a^5 + 1/2*a^4 - 11/2*a^3 - 2*a^2 + 13*a - 3/2)*q^30 + (a^4 + 2*a^3 - 6*a^2 - 10*a + 11)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^5 + 1/2*a^4 - 13/2*a^3 - a^2 + 22*a - 21/2)*q^33 + (a^5 + a^4 - 7*a^3 - 3*a^2 + 6*a)*q^34 + (1/2*a^5 + 1/2*a^4 - 9/2*a^3 - 2*a^2 + 10*a - 3/2)*q^35 + (-a^5 + 7*a^3 - 2*a^2 - 10*a + 4)*q^36 + (-a^5 - 2*a^4 + 10*a^3 + 10*a^2 - 29*a + 5)*q^37 + O(q^38)
*]> ;  // time = 47.721 seconds




J[330] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 330, 330, 330, 330, 330, 165, 165, 165, 110, 110, 110, 110, 66, 66, 66, 55, 55, 33, 30, 15, 11 ], new_dimensions := [ 1, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 4, 4, 6, 2, 2, 2, 4, 2, 2, 2, 4, 8, 4, 2, 4, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 1, 1, 25, 5, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 49, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 49, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 2401, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 81, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 25, 1, 1, 25, 1, 1, 1, 25, 1, 2401, 81, 1, 1, 0 ], ap_traces := [
[ -1, -1, -1, 0, 1, 2, -2, 8, 4, 2, 8, -2 ],
[ -1, -1, 1, -4, 1, -2, -2, -8, 0, 2, -8, -10 ],
[ 1, -1, -1, 4, -1, 2, 2, 4, -4, 6, 0, -10 ],
[ 1, -1, 1, 0, 1, 6, 2, -4, 0, -10, 0, 6 ],
[ 1, 1, 1, 0, -1, -2, 2, -4, 0, -2, 0, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, 1, -1 ],
[ 1, 1, -1, -1 ],
[ -1, 1, 1, 1 ],
[ -1, 1, -1, -1 ],
[ -1, -1, -1, 1 ]
], component_group_orders := [
[ 1, 5, 1, 1 ],
[ 1, 1, 1, 1 ],
[ 7, 5, 1, 1 ],
[ 1, 3, 1, 1 ],
[ 1, 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1, 1 ],
[ 1, 1, 1, 1 ],
[ 7, 1, 1, 1 ],
[ 1, 1, 1, 1 ],
[ 1, 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 1, 0, 7, 1, 1 ], analytic_sha_upper_bounds := [ 1, 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1, 1, 1 ], eigenvalues := [*
[ -1, -1, -1, 0, 1, 2, -2, 8, 4, 2, 8, -2 ],
[ -1, -1, 1, -4, 1, -2, -2, -8, 0, 2, -8, -10 ],
[ 1, -1, -1, 4, -1, 2, 2, 4, -4, 6, 0, -10 ],
[ 1, -1, 1, 0, 1, 6, 2, -4, 0, -10, 0, 6 ],
[ 1, 1, 1, 0, -1, -2, 2, -4, 0, -2, 0, -2 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - q^5 + q^6 - q^8 + q^9 + q^10 + q^11 - q^12 + 2*q^13 + q^15 + q^16 - 2*q^17 - q^18 + 8*q^19 - q^20 - q^22 + 4*q^23 + q^24 + q^25 - 2*q^26 - q^27 + 2*q^29 - q^30 + 8*q^31 - q^32 - q^33 + 2*q^34 + q^36 - 2*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + q^5 + q^6 - 4*q^7 - q^8 + q^9 - q^10 + q^11 - q^12 - 2*q^13 + 4*q^14 - q^15 + q^16 - 2*q^17 - q^18 - 8*q^19 + q^20 + 4*q^21 - q^22 + q^24 + q^25 + 2*q^26 - q^27 - 4*q^28 + 2*q^29 + q^30 - 8*q^31 - q^32 - q^33 + 2*q^34 - 4*q^35 + q^36 - 10*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - q^5 - q^6 + 4*q^7 + q^8 + q^9 - q^10 - q^11 - q^12 + 2*q^13 + 4*q^14 + q^15 + q^16 + 2*q^17 + q^18 + 4*q^19 - q^20 - 4*q^21 - q^22 - 4*q^23 - q^24 + q^25 + 2*q^26 - q^27 + 4*q^28 + 6*q^29 + q^30 + q^32 + q^33 + 2*q^34 - 4*q^35 + q^36 - 10*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + q^8 + q^9 + q^10 + q^11 - q^12 + 6*q^13 - q^15 + q^16 + 2*q^17 + q^18 - 4*q^19 + q^20 + q^22 - q^24 + q^25 + 6*q^26 - q^27 - 10*q^29 - q^30 + q^32 - q^33 + 2*q^34 + q^36 + 6*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^5 + q^6 + q^8 + q^9 + q^10 - q^11 + q^12 - 2*q^13 + q^15 + q^16 + 2*q^17 + q^18 - 4*q^19 + q^20 - q^22 + q^24 + q^25 - 2*q^26 + q^27 - 2*q^29 + q^30 + q^32 - q^33 + 2*q^34 + q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 625.69 seconds




J[331] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 331, 331, 331, 331 ], new_dimensions := [ 1, 3, 7, 16 ], dimensions := [ 1, 3, 7, 16 ], intersection_graph := [ 0, 1, 3, 1, 1, 0, 53, 1, 3, 53, 0, 1, 1, 1, 1, 0 ], ap_traces := [
[ -1, -2, 1, 2, 0, -4, 1, -3, -8, -10, 7, -8 ],
[ -2, -1, -6, 3, -7, -13, -3, 6, -2, -2, -14, 11 ],
[ -2, 0, -13, -8, -10, 5, -17, -19, 15, -24, 4, 2 ],
[ 3, -1, 20, 1, 9, 8, 19, 2, 5, 32, -1, 1 ]
], hecke_fields := [
x - 1,
x^3 + 2*x^2 - 4*x - 7,
x^7 + 2*x^6 - 6*x^5 - 8*x^4 + 11*x^3 + 3*x^2 - 5*x + 1,
x^16 - 3*x^15 - 19*x^14 + 60*x^13 + 136*x^12 - 465*x^11 - 448*x^10 + 1747*x^9 + 657*x^8 - 3241*x^7 - 375*x^6 + 2695*x^5 + 230*x^4 - 855*x^3 - 110*x^2 + 56*x + 8
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 55 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 55 ]
], torsion_upper_bounds := [ 1, 1, 1, 55 ], torsion_lower_bounds := [ 1, 1, 1, 55 ], l_ratios := [ 0, 0, 0, 1/55 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1 ], eigenvalues := [*
[ -1, -2, 1, 2, 0, -4, 1, -3, -8, -10, 7, -8 ],
[
a,
-a - 1,
-a^2 + 2,
a^2 - 3,
-a - 3,
-2*a^2 - a + 3,
2*a^2 - 9,
-a^2 + 6,
2*a^2 + 4*a - 6,
-2*a^2 - 2*a + 6,
a^2 + 4*a - 6,
-3*a^2 + 2*a + 17
],
[
a,
-a^6 - 3*a^5 + 4*a^4 + 13*a^3 - 4*a^2 - 9*a + 3,
4*a^6 + 10*a^5 - 19*a^4 - 42*a^3 + 23*a^2 + 25*a - 11,
-5*a^6 - 11*a^5 + 27*a^4 + 45*a^3 - 41*a^2 - 24*a + 13,
8*a^6 + 20*a^5 - 38*a^4 - 82*a^3 + 48*a^2 + 45*a - 20,
-7*a^6 - 17*a^5 + 34*a^4 + 70*a^3 - 42*a^2 - 38*a + 14,
-a^6 - 4*a^5 + 14*a^3 + 12*a^2 - a - 7,
-6*a^6 - 17*a^5 + 22*a^4 + 67*a^3 - 11*a^2 - 31*a + 2,
9*a^6 + 22*a^5 - 44*a^4 - 91*a^3 + 58*a^2 + 49*a - 21,
2*a^6 + 7*a^5 - 4*a^4 - 27*a^3 - 8*a^2 + 13*a - 1,
-11*a^6 - 27*a^5 + 55*a^4 + 113*a^3 - 77*a^2 - 65*a + 31,
2*a^6 + 7*a^5 - 3*a^4 - 26*a^3 - 16*a^2 + 6*a + 11
],
[
a,
-1069/10445*a^15 + 5881/10445*a^14 + 17079/10445*a^13 - 23704/2089*a^12 - 84578/10445*a^11 + 923333/10445*a^10 + 43752/10445*a^9 - 3472853/10445*a^8 + 749508/10445*a^7 + 6394904/10445*a^6 - 1779062/10445*a^5 - 5163977/10445*a^4 + 881194/10445*a^3 + 1507308/10445*a^2 - 64022/10445*a - 14094/2089,
-193/41780*a^15 + 3141/41780*a^14 + 8817/41780*a^13 - 34827/20890*a^12 - 31464/10445*a^11 + 604449/41780*a^10 + 402503/20890*a^9 - 2602543/41780*a^8 - 2497031/41780*a^7 + 1153919/8356*a^6 + 3522077/41780*a^5 - 6042977/41780*a^4 - 85673/2089*a^3 + 2150027/41780*a^2 + 44617/10445*a - 14807/10445,
-5839/10445*a^15 + 9898/10445*a^14 + 114836/10445*a^13 - 191702/10445*a^12 - 859383/10445*a^11 + 1427727/10445*a^10 + 3015533/10445*a^9 - 5069699/10445*a^8 - 4853023/10445*a^7 + 1713921/2089*a^6 + 2824461/10445*a^5 - 5994991/10445*a^4 - 56504/2089*a^3 + 1607476/10445*a^2 - 86331/10445*a - 91994/10445,
-3028/10445*a^15 + 5627/10445*a^14 + 58148/10445*a^13 - 21605/2089*a^12 - 419726/10445*a^11 + 793671/10445*a^10 + 1386534/10445*a^9 - 2758186/10445*a^8 - 1983964/10445*a^7 + 4488793/10445*a^6 + 864276/10445*a^5 - 2892759/10445*a^4 - 153317/10445*a^3 + 679861/10445*a^2 + 75441/10445*a - 4708/2089,
11711/20890*a^15 - 26481/20890*a^14 - 223473/20890*a^13 + 258476/10445*a^12 + 798976/10445*a^11 - 3881061/20890*a^10 - 2583287/10445*a^9 + 13914713/20890*a^8 + 6823439/20890*a^7 - 23859907/20890*a^6 - 249959/4178*a^5 + 17062757/20890*a^4 - 942881/10445*a^3 - 884743/4178*a^2 + 295971/10445*a + 126152/10445,
-1163/20890*a^15 - 2383/10445*a^14 + 2987/2089*a^13 + 101753/20890*a^12 - 150653/10445*a^11 - 169427/4178*a^10 + 303653/4178*a^9 + 3466543/20890*a^8 - 396958/2089*a^7 - 3587263/10445*a^6 + 2479577/10445*a^5 + 3404271/10445*a^4 - 2254001/20890*a^3 - 2106001/20890*a^2 + 304807/20890*a + 41803/10445,
-6259/41780*a^15 + 4297/8356*a^14 + 112473/41780*a^13 - 107181/10445*a^12 - 181532/10445*a^11 + 3317291/41780*a^10 + 464876/10445*a^9 - 2492457/8356*a^8 - 625319/41780*a^7 + 23200151/41780*a^6 - 4108631/41780*a^5 - 3899193/8356*a^4 + 2021913/20890*a^3 + 6198629/41780*a^2 - 99793/4178*a - 74482/10445,
2332/10445*a^15 + 3189/10445*a^14 - 10849/2089*a^13 - 69647/10445*a^12 + 500884/10445*a^11 + 118145/2089*a^10 - 467090/2089*a^9 - 2461587/10445*a^8 + 1148618/2089*a^7 + 5226699/10445*a^6 - 6978761/10445*a^5 - 5264758/10445*a^4 + 3388984/10445*a^3 + 2024199/10445*a^2 - 540218/10445*a - 148334/10445,
8807/20890*a^15 - 2953/4178*a^14 - 175709/20890*a^13 + 143826/10445*a^12 + 672947/10445*a^11 - 2163643/20890*a^10 - 2463261/10445*a^9 + 1563499/4178*a^8 + 8701507/20890*a^7 - 13635973/20890*a^6 - 6721027/20890*a^5 + 2012599/4178*a^4 + 1138871/10445*a^3 - 2636267/20890*a^2 - 20260/2089*a + 78272/10445,
-3206/10445*a^15 + 2533/20890*a^14 + 136337/20890*a^13 - 7403/4178*a^12 - 570112/10445*a^11 + 81712/10445*a^10 + 4752891/20890*a^9 - 9247/10445*a^8 - 10289071/20890*a^7 - 1564493/20890*a^6 + 10877949/20890*a^5 + 3457649/20890*a^4 - 4630483/20890*a^3 - 961108/10445*a^2 + 455799/20890*a + 18789/2089,
1789/2089*a^15 - 14424/10445*a^14 - 174664/10445*a^13 + 274689/10445*a^12 + 258721/2089*a^11 - 1996708/10445*a^10 - 4469182/10445*a^9 + 6817782/10445*a^8 + 7022272/10445*a^7 - 10685442/10445*a^6 - 3974896/10445*a^5 + 6155623/10445*a^4 + 595163/10445*a^3 - 1044086/10445*a^2 + 25213/10445*a + 5818/10445
]
*], q_expansions := [*
q - q^2 - 2*q^3 - q^4 + q^5 + 2*q^6 + 2*q^7 + 3*q^8 + q^9 - q^10 + 2*q^12 - 4*q^13 - 2*q^14 - 2*q^15 - q^16 + q^17 - q^18 - 3*q^19 - q^20 - 4*q^21 - 8*q^23 - 6*q^24 - 4*q^25 + 4*q^26 + 4*q^27 - 2*q^28 - 10*q^29 + 2*q^30 + 7*q^31 - 5*q^32 - q^34 + 2*q^35 - q^36 - 8*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (a^2 - 2)*q^4 + (-a^2 + 2)*q^5 + (-a^2 - a)*q^6 + (a^2 - 3)*q^7 + (-2*a^2 + 7)*q^8 + (a^2 + 2*a - 2)*q^9 + (2*a^2 - 2*a - 7)*q^10 + (-a - 3)*q^11 + (a^2 - 2*a - 5)*q^12 + (-2*a^2 - a + 3)*q^13 + (-2*a^2 + a + 7)*q^14 + (-a^2 + 2*a + 5)*q^15 + (2*a^2 - a - 10)*q^16 + (2*a^2 - 9)*q^17 + (2*a + 7)*q^18 + (-a^2 + 6)*q^19 + (-4*a^2 + a + 10)*q^20 + (a^2 - a - 4)*q^21 + (-a^2 - 3*a)*q^22 + (2*a^2 + 4*a - 6)*q^23 + (-2*a^2 + a + 7)*q^24 + (4*a^2 - a - 15)*q^25 + (3*a^2 - 5*a - 14)*q^26 + (-a^2 - a - 2)*q^27 + (3*a^2 - a - 8)*q^28 + (-2*a^2 - 2*a + 6)*q^29 + (4*a^2 + a - 7)*q^30 + (a^2 + 4*a - 6)*q^31 + (-a^2 - 2*a)*q^32 + (a^2 + 4*a + 3)*q^33 + (-4*a^2 - a + 14)*q^34 + (-3*a^2 + a + 8)*q^35 + (3*a + 4)*q^36 + (-3*a^2 + 2*a + 17)*q^37 + O(q^38),
q + a*q^2 + (-a^6 - 3*a^5 + 4*a^4 + 13*a^3 - 4*a^2 - 9*a + 3)*q^3 + (a^2 - 2)*q^4 + (4*a^6 + 10*a^5 - 19*a^4 - 42*a^3 + 23*a^2 + 25*a - 11)*q^5 + (-a^6 - 2*a^5 + 5*a^4 + 7*a^3 - 6*a^2 - 2*a + 1)*q^6 + (-5*a^6 - 11*a^5 + 27*a^4 + 45*a^3 - 41*a^2 - 24*a + 13)*q^7 + (a^3 - 4*a)*q^8 + (a^6 + 2*a^5 - 6*a^4 - 7*a^3 + 11*a^2 - 2*a - 3)*q^9 + (2*a^6 + 5*a^5 - 10*a^4 - 21*a^3 + 13*a^2 + 9*a - 4)*q^10 + (8*a^6 + 20*a^5 - 38*a^4 - 82*a^3 + 48*a^2 + 45*a - 20)*q^11 + (2*a^6 + 5*a^5 - 9*a^4 - 21*a^3 + 9*a^2 + 14*a - 5)*q^12 + (-7*a^6 - 17*a^5 + 34*a^4 + 70*a^3 - 42*a^2 - 38*a + 14)*q^13 + (-a^6 - 3*a^5 + 5*a^4 + 14*a^3 - 9*a^2 - 12*a + 5)*q^14 + (-a^6 - a^5 + 7*a^4 + 2*a^3 - 11*a^2 + 6*a - 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^6 - 4*a^5 + 14*a^3 + 12*a^2 - a - 7)*q^17 + (a^4 - 5*a^2 + 2*a - 1)*q^18 + (-6*a^6 - 17*a^5 + 22*a^4 + 67*a^3 - 11*a^2 - 31*a + 2)*q^19 + (-7*a^6 - 18*a^5 + 33*a^4 + 75*a^3 - 43*a^2 - 44*a + 20)*q^20 + (a^6 + 4*a^5 - a^4 - 18*a^3 - 8*a^2 + 19*a - 3)*q^21 + (4*a^6 + 10*a^5 - 18*a^4 - 40*a^3 + 21*a^2 + 20*a - 8)*q^22 + (9*a^6 + 22*a^5 - 44*a^4 - 91*a^3 + 58*a^2 + 49*a - 21)*q^23 + (3*a^6 + 7*a^5 - 15*a^4 - 27*a^3 + 20*a^2 + 9*a - 4)*q^24 + (-4*a^6 - 10*a^5 + 20*a^4 + 45*a^3 - 26*a^2 - 33*a + 14)*q^25 + (-3*a^6 - 8*a^5 + 14*a^4 + 35*a^3 - 17*a^2 - 21*a + 7)*q^26 + (8*a^6 + 19*a^5 - 39*a^4 - 75*a^3 + 50*a^2 + 33*a - 14)*q^27 + (9*a^6 + 21*a^5 - 48*a^4 - 88*a^3 + 73*a^2 + 48*a - 25)*q^28 + (2*a^6 + 7*a^5 - 4*a^4 - 27*a^3 - 8*a^2 + 13*a - 1)*q^29 + (a^6 + a^5 - 6*a^4 + 9*a^2 - 7*a + 1)*q^30 + (-11*a^6 - 27*a^5 + 55*a^4 + 113*a^3 - 77*a^2 - 65*a + 31)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^6 - 2*a^5 + 5*a^4 + 7*a^3 - 6*a^2 - 2*a - 1)*q^33 + (-2*a^6 - 6*a^5 + 6*a^4 + 23*a^3 + 2*a^2 - 12*a + 1)*q^34 + (3*a^6 + 3*a^5 - 24*a^4 - 9*a^3 + 54*a^2 - 4*a - 14)*q^35 + (-2*a^6 - 3*a^5 + 12*a^4 + 9*a^3 - 20*a^2 + 3*a + 6)*q^36 + (2*a^6 + 7*a^5 - 3*a^4 - 26*a^3 - 16*a^2 + 6*a + 11)*q^37 + O(q^38),
q + a*q^2 + (-1069/10445*a^15 + 5881/10445*a^14 + 17079/10445*a^13 - 23704/2089*a^12 - 84578/10445*a^11 + 923333/10445*a^10 + 43752/10445*a^9 - 3472853/10445*a^8 + 749508/10445*a^7 + 6394904/10445*a^6 - 1779062/10445*a^5 - 5163977/10445*a^4 + 881194/10445*a^3 + 1507308/10445*a^2 - 64022/10445*a - 14094/2089)*q^3 + (a^2 - 2)*q^4 + (-193/41780*a^15 + 3141/41780*a^14 + 8817/41780*a^13 - 34827/20890*a^12 - 31464/10445*a^11 + 604449/41780*a^10 + 402503/20890*a^9 - 2602543/41780*a^8 - 2497031/41780*a^7 + 1153919/8356*a^6 + 3522077/41780*a^5 - 6042977/41780*a^4 - 85673/2089*a^3 + 2150027/41780*a^2 + 44617/10445*a - 14807/10445)*q^5 + (2674/10445*a^15 - 3232/10445*a^14 - 10876/2089*a^13 + 60806/10445*a^12 + 426248/10445*a^11 - 87032/2089*a^10 - 321062/2089*a^9 + 1451841/10445*a^8 + 586055/2089*a^7 - 2179937/10445*a^6 - 2283022/10445*a^5 + 1127064/10445*a^4 + 593313/10445*a^3 - 181612/10445*a^2 - 10606/10445*a + 8552/10445)*q^6 + (-5839/10445*a^15 + 9898/10445*a^14 + 114836/10445*a^13 - 191702/10445*a^12 - 859383/10445*a^11 + 1427727/10445*a^10 + 3015533/10445*a^9 - 5069699/10445*a^8 - 4853023/10445*a^7 + 1713921/2089*a^6 + 2824461/10445*a^5 - 5994991/10445*a^4 - 56504/2089*a^3 + 1607476/10445*a^2 - 86331/10445*a - 91994/10445)*q^7 + (a^3 - 4*a)*q^8 + (1988/10445*a^15 - 719/2089*a^14 - 39926/10445*a^13 + 70023/10445*a^12 + 310006/10445*a^11 - 525127/10445*a^10 - 1165718/10445*a^9 + 377466/2089*a^8 + 2172098/10445*a^7 - 3284252/10445*a^6 - 1856308/10445*a^5 + 500081/2089*a^4 + 672948/10445*a^3 - 801488/10445*a^2 - 10528/2089*a + 84701/10445)*q^9 + (1281/20890*a^15 + 515/4178*a^14 - 29037/20890*a^13 - 24902/10445*a^12 + 128676/10445*a^11 + 359271/20890*a^10 - 566343/10445*a^9 - 237023/4178*a^8 + 2572041/20890*a^7 + 1724851/20890*a^6 - 2761421/20890*a^5 - 166907/4178*a^4 + 496253/10445*a^3 + 78619/20890*a^2 - 2421/2089*a + 386/10445)*q^10 + (-3028/10445*a^15 + 5627/10445*a^14 + 58148/10445*a^13 - 21605/2089*a^12 - 419726/10445*a^11 + 793671/10445*a^10 + 1386534/10445*a^9 - 2758186/10445*a^8 - 1983964/10445*a^7 + 4488793/10445*a^6 + 864276/10445*a^5 - 2892759/10445*a^4 - 153317/10445*a^3 + 679861/10445*a^2 + 75441/10445*a - 4708/2089)*q^11 + (6928/10445*a^15 - 15336/10445*a^14 - 133792/10445*a^13 + 299624/10445*a^12 + 977406/10445*a^11 - 2254024/10445*a^10 - 3307141/10445*a^9 + 8119163/10445*a^8 + 4987481/10445*a^7 - 2814016/2089*a^6 - 2521242/10445*a^5 + 10306247/10445*a^4 + 68454/2089*a^3 - 2731082/10445*a^2 - 13148/10445*a + 119548/10445)*q^12 + (11711/20890*a^15 - 26481/20890*a^14 - 223473/20890*a^13 + 258476/10445*a^12 + 798976/10445*a^11 - 3881061/20890*a^10 - 2583287/10445*a^9 + 13914713/20890*a^8 + 6823439/20890*a^7 - 23859907/20890*a^6 - 249959/4178*a^5 + 17062757/20890*a^4 - 942881/10445*a^3 - 884743/4178*a^2 + 295971/10445*a + 126152/10445)*q^13 + (-7619/10445*a^15 + 779/2089*a^14 + 158638/10445*a^13 - 65279/10445*a^12 - 1287408/10445*a^11 + 399661/10445*a^10 + 5131034/10445*a^9 - 203360/2089*a^8 - 10354594/10445*a^7 + 634836/10445*a^6 + 9741114/10445*a^5 + 212090/2089*a^4 - 3384869/10445*a^3 - 728621/10445*a^2 + 46998/2089*a + 46712/10445)*q^14 + (19/20890*a^15 + 7419/20890*a^14 - 7319/20890*a^13 - 15024/2089*a^12 + 65239/10445*a^11 + 1168437/20890*a^10 - 451136/10445*a^9 - 4344267/20890*a^8 + 2915607/20890*a^7 + 7766491/20890*a^6 - 4179063/20890*a^5 - 5828803/20890*a^4 + 909453/10445*a^3 + 1369117/20890*a^2 - 34264/10445*a + 2566/2089)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1163/20890*a^15 - 2383/10445*a^14 + 2987/2089*a^13 + 101753/20890*a^12 - 150653/10445*a^11 - 169427/4178*a^10 + 303653/4178*a^9 + 3466543/20890*a^8 - 396958/2089*a^7 - 3587263/10445*a^6 + 2479577/10445*a^5 + 3404271/10445*a^4 - 2254001/20890*a^3 - 2106001/20890*a^2 + 304807/20890*a + 41803/10445)*q^17 + (2369/10445*a^15 - 2154/10445*a^14 - 49257/10445*a^13 + 39638/10445*a^12 + 399293/10445*a^11 - 275094/10445*a^10 - 1585706/10445*a^9 + 865982/10445*a^8 + 3158856/10445*a^7 - 1110808/10445*a^6 - 571451/2089*a^5 + 215708/10445*a^4 + 898252/10445*a^3 + 33208/2089*a^2 - 26627/10445*a - 15904/10445)*q^18 + (-6259/41780*a^15 + 4297/8356*a^14 + 112473/41780*a^13 - 107181/10445*a^12 - 181532/10445*a^11 + 3317291/41780*a^10 + 464876/10445*a^9 - 2492457/8356*a^8 - 625319/41780*a^7 + 23200151/41780*a^6 - 4108631/41780*a^5 - 3899193/8356*a^4 + 2021913/20890*a^3 + 6198629/41780*a^2 - 99793/4178*a - 74482/10445)*q^19 + (6611/20890*a^15 - 7839/20890*a^14 - 135481/20890*a^13 + 15279/2089*a^12 + 540396/10445*a^11 - 1163247/20890*a^10 - 2114014/10445*a^9 + 4332967/20890*a^8 + 8373603/20890*a^7 - 8050641/20890*a^6 - 7808907/20890*a^5 + 6740853/20890*a^4 + 1443667/10445*a^3 - 2033327/20890*a^2 - 124716/10445*a + 4898/2089)*q^20 + (-468/2089*a^15 - 339/2089*a^14 + 10080/2089*a^13 + 8176/2089*a^12 - 84887/2089*a^11 - 75939/2089*a^10 + 352554/2089*a^9 + 347203/2089*a^8 - 741957/2089*a^7 - 818000/2089*a^6 + 705878/2089*a^5 + 927895/2089*a^4 - 178848/2089*a^3 - 390330/2089*a^2 - 35802/2089*a + 31596/2089)*q^21 + (-3457/10445*a^15 + 616/10445*a^14 + 14731/2089*a^13 - 7918/10445*a^12 - 614349/10445*a^11 + 5998/2089*a^10 + 506346/2089*a^9 + 5432/10445*a^8 - 1064991/2089*a^7 - 271224/10445*a^6 + 5267701/10445*a^5 + 543123/10445*a^4 - 1909079/10445*a^3 - 257639/10445*a^2 + 146028/10445*a + 24224/10445)*q^22 + (2332/10445*a^15 + 3189/10445*a^14 - 10849/2089*a^13 - 69647/10445*a^12 + 500884/10445*a^11 + 118145/2089*a^10 - 467090/2089*a^9 - 2461587/10445*a^8 + 1148618/2089*a^7 + 5226699/10445*a^6 - 6978761/10445*a^5 - 5264758/10445*a^4 + 3388984/10445*a^3 + 2024199/10445*a^2 - 540218/10445*a - 148334/10445)*q^23 + (20/2089*a^15 + 4304/10445*a^14 - 7296/10445*a^13 - 86414/10445*a^12 + 23000/2089*a^11 + 666923/10445*a^10 - 773433/10445*a^9 - 2467897/10445*a^8 + 2523018/10445*a^7 + 4436632/10445*a^6 - 3798669/10445*a^5 - 3505298/10445*a^4 + 2005732/10445*a^3 + 1112156/10445*a^2 - 247208/10445*a - 72528/10445)*q^24 + (-2183/41780*a^15 - 2291/41780*a^14 + 13421/8356*a^13 + 10677/10445*a^12 - 196234/10445*a^11 - 58709/8356*a^10 + 224447/2089*a^9 + 845783/41780*a^8 - 2624627/8356*a^7 - 615541/41780*a^6 + 18137889/41780*a^5 - 1079553/41780*a^4 - 4449373/20890*a^3 + 903109/41780*a^2 + 431961/20890*a - 24151/10445)*q^25 + (4326/10445*a^15 - 482/10445*a^14 - 92854/10445*a^13 + 2628/10445*a^12 + 782277/10445*a^11 + 39977/10445*a^10 - 3272202/10445*a^9 - 435344/10445*a^8 + 7047722/10445*a^7 + 314183/2089*a^6 - 7249194/10445*a^5 - 2289646/10445*a^4 + 558919/2089*a^3 + 940076/10445*a^2 - 201756/10445*a - 46844/10445)*q^26 + (-4282/10445*a^15 + 8977/10445*a^14 + 83711/10445*a^13 - 179694/10445*a^12 - 623049/10445*a^11 + 1402252/10445*a^10 + 2179183/10445*a^9 - 5348441/10445*a^8 - 3527473/10445*a^7 + 10197999/10445*a^6 + 435060/2089*a^5 - 8880719/10445*a^4 - 411586/10445*a^3 + 592640/2089*a^2 + 8756/10445*a - 196308/10445)*q^27 + (-7284/10445*a^15 - 5919/10445*a^14 + 162189/10445*a^13 + 26436/2089*a^12 - 1424408/10445*a^11 - 1137732/10445*a^10 + 6262527/10445*a^9 + 4790487/10445*a^8 - 14352297/10445*a^7 - 10255221/10445*a^6 + 15944733/10445*a^5 + 10357483/10445*a^4 - 6677826/10445*a^3 - 3818052/10445*a^2 + 646038/10445*a + 48988/2089)*q^28 + (8807/20890*a^15 - 2953/4178*a^14 - 175709/20890*a^13 + 143826/10445*a^12 + 672947/10445*a^11 - 2163643/20890*a^10 - 2463261/10445*a^9 + 1563499/4178*a^8 + 8701507/20890*a^7 - 13635973/20890*a^6 - 6721027/20890*a^5 + 2012599/4178*a^4 + 1138871/10445*a^3 - 2636267/20890*a^2 - 20260/2089*a + 78272/10445)*q^29 + (3738/10445*a^15 - 3479/10445*a^14 - 15138/2089*a^13 + 63947/10445*a^12 + 588636/10445*a^11 - 89376/2089*a^10 - 437746/2089*a^9 + 1451562/10445*a^8 + 782807/2089*a^7 - 2085969/10445*a^6 - 2940004/10445*a^5 + 907268/10445*a^4 + 692681/10445*a^3 - 33219/10445*a^2 + 12298/10445*a - 76/10445)*q^30 + (-3206/10445*a^15 + 2533/20890*a^14 + 136337/20890*a^13 - 7403/4178*a^12 - 570112/10445*a^11 + 81712/10445*a^10 + 4752891/20890*a^9 - 9247/10445*a^8 - 10289071/20890*a^7 - 1564493/20890*a^6 + 10877949/20890*a^5 + 3457649/20890*a^4 - 4630483/20890*a^3 - 961108/10445*a^2 + 455799/20890*a + 18789/2089)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2598/10445*a^15 - 5751/10445*a^14 - 50172/10445*a^13 + 112359/10445*a^12 + 363916/10445*a^11 - 845259/10445*a^10 - 1194481/10445*a^9 + 3048603/10445*a^8 + 1579151/10445*a^7 - 1063612/2089*a^6 - 133367/10445*a^5 + 4020212/10445*a^4 - 156595/2089*a^3 - 1267002/10445*a^2 + 230082/10445*a + 123168/10445)*q^33 + (-1651/4178*a^15 + 7773/20890*a^14 + 171533/20890*a^13 - 71569/10445*a^12 - 138793/2089*a^11 + 997241/20890*a^10 + 2749152/10445*a^9 - 3205489/20890*a^8 - 10943809/20890*a^7 + 4523029/20890*a^6 + 9942827/20890*a^5 - 1986511/20890*a^4 - 1550183/10445*a^3 + 176877/20890*a^2 + 74367/10445*a + 4652/10445)*q^34 + (-4226/10445*a^15 + 4786/10445*a^14 + 85558/10445*a^13 - 89042/10445*a^12 - 667277/10445*a^11 + 626946/10445*a^10 + 2498769/10445*a^9 - 2032553/10445*a^8 - 4514259/10445*a^7 + 2855272/10445*a^6 + 669215/2089*a^5 - 1121647/10445*a^4 - 517293/10445*a^3 - 7364/2089*a^2 - 160347/10445*a + 16096/10445)*q^35 + (977/10445*a^15 + 2944/10445*a^14 - 4530/2089*a^13 - 62937/10445*a^12 + 206479/10445*a^11 + 105172/2089*a^10 - 188245/2089*a^9 - 2172237/10445*a^8 + 444585/2089*a^7 + 4599624/10445*a^6 - 2456131/10445*a^5 - 4647428/10445*a^4 + 845639/10445*a^3 + 1836939/10445*a^2 - 43288/10445*a - 188354/10445)*q^36 + (1789/2089*a^15 - 14424/10445*a^14 - 174664/10445*a^13 + 274689/10445*a^12 + 258721/2089*a^11 - 1996708/10445*a^10 - 4469182/10445*a^9 + 6817782/10445*a^8 + 7022272/10445*a^7 - 10685442/10445*a^6 - 3974896/10445*a^5 + 6155623/10445*a^4 + 595163/10445*a^3 - 1044086/10445*a^2 + 25213/10445*a + 5818/10445)*q^37 + O(q^38)
*]> ;  // time = 6.399 seconds




J[334] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 334, 334, 334, 334, 334, 334, 167, 167 ], new_dimensions := [ 1, 2, 2, 2, 3, 3, 2, 12 ], dimensions := [ 1, 2, 2, 2, 3, 3, 4, 24 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 7, 1, 1, 63, 1, 1, 1, 0, 1, 1, 1, 99, 1, 1, 7, 1, 0, 1, 1, 791, 1, 1, 1, 1, 1, 0, 11, 1, 1, 5, 1, 1, 1, 11, 0, 1, 1, 1, 63, 99, 791, 1, 1, 0 ], ap_traces := [
[ 1, 0, 3, 1, 0, -2, -2, 2, 2, -4, 1, -3 ],
[ -2, -1, -2, 0, -5, 0, -5, 0, -4, -12, -4, 3 ],
[ -2, 0, 2, -6, 0, 8, 4, 4, 12, 8, -10, -6 ],
[ 2, -3, -4, -6, -9, 2, 1, -2, 0, -16, 2, -3 ],
[ -3, -1, 0, 0, 11, -10, 9, -4, -10, 18, 4, 1 ],
[ 3, 1, -3, 3, 7, 2, 3, -4, 4, 4, -5, -4 ]
], hecke_fields := [
x - 1,
x^2 + x - 1,
x^2 - 8,
x^2 + 3*x + 1,
x^3 + x^2 - 5*x - 4,
x^3 - x^2 - 7*x + 8
], atkin_lehners := [
[ -1, 1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 5, 1 ],
[ 63, 1 ],
[ 99, 1 ],
[ 791, 1 ],
[ 77, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 99, 1 ],
[ 1, 1 ],
[ 77, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 7 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 7 ], l_ratios := [ 1, 0, 1, 0, 1, 11/7 ], analytic_sha_upper_bounds := [ 1, 0, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1, 0, 1, 1 ], eigenvalues := [*
[ 1, 0, 3, 1, 0, -2, -2, 2, 2, -4, 1, -3 ],
[
-1,
a,
-1,
-2*a - 1,
-a - 3,
-2*a - 1,
3*a - 1,
2*a + 1,
2*a - 1,
-2*a - 7,
6*a + 1,
9*a + 6
],
[
-1,
a,
-1/2*a + 1,
-3,
a,
a + 4,
a + 2,
-2*a + 2,
-a + 6,
-a + 4,
-a - 5,
-3/2*a - 3
],
[
1,
a,
-2*a - 5,
-3,
a - 3,
4*a + 7,
-5*a - 7,
4*a + 5,
2*a + 3,
2*a - 5,
-4*a - 5,
-3*a - 6
],
[
-1,
a,
-a^2 + a + 4,
-a^2 + a + 4,
a^2,
-a^2 - a,
-a^2 - 2*a + 6,
a^2 + 3*a - 4,
-a^2 - a,
-a^2 + a + 10,
-3*a^2 - a + 12,
-a
],
[
1,
a,
-1,
1,
-a^2 - 2*a + 8,
-a^2 - a + 6,
-a^2 + 6,
a^2 - a - 6,
3*a^2 + a - 14,
a^2 + a - 4,
-2*a^2 - 2*a + 9,
a^2 + 2*a - 7
]
*], q_expansions := [*
q + q^2 + q^4 + 3*q^5 + q^7 + q^8 - 3*q^9 + 3*q^10 - 2*q^13 + q^14 + q^16 - 2*q^17 - 3*q^18 + 2*q^19 + 3*q^20 + 2*q^23 + 4*q^25 - 2*q^26 + q^28 - 4*q^29 + q^31 + q^32 - 2*q^34 + 3*q^35 - 3*q^36 - 3*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - q^5 - a*q^6 + (-2*a - 1)*q^7 - q^8 + (-a - 2)*q^9 + q^10 + (-a - 3)*q^11 + a*q^12 + (-2*a - 1)*q^13 + (2*a + 1)*q^14 - a*q^15 + q^16 + (3*a - 1)*q^17 + (a + 2)*q^18 + (2*a + 1)*q^19 - q^20 + (a - 2)*q^21 + (a + 3)*q^22 + (2*a - 1)*q^23 - a*q^24 - 4*q^25 + (2*a + 1)*q^26 + (-4*a - 1)*q^27 + (-2*a - 1)*q^28 + (-2*a - 7)*q^29 + a*q^30 + (6*a + 1)*q^31 - q^32 + (-2*a - 1)*q^33 + (-3*a + 1)*q^34 + (2*a + 1)*q^35 + (-a - 2)*q^36 + (9*a + 6)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-1/2*a + 1)*q^5 - a*q^6 - 3*q^7 - q^8 + 5*q^9 + (1/2*a - 1)*q^10 + a*q^11 + a*q^12 + (a + 4)*q^13 + 3*q^14 + (a - 4)*q^15 + q^16 + (a + 2)*q^17 - 5*q^18 + (-2*a + 2)*q^19 + (-1/2*a + 1)*q^20 - 3*a*q^21 - a*q^22 + (-a + 6)*q^23 - a*q^24 + (-a - 2)*q^25 + (-a - 4)*q^26 + 2*a*q^27 - 3*q^28 + (-a + 4)*q^29 + (-a + 4)*q^30 + (-a - 5)*q^31 - q^32 + 8*q^33 + (-a - 2)*q^34 + (3/2*a - 3)*q^35 + 5*q^36 + (-3/2*a - 3)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-2*a - 5)*q^5 + a*q^6 - 3*q^7 + q^8 + (-3*a - 4)*q^9 + (-2*a - 5)*q^10 + (a - 3)*q^11 + a*q^12 + (4*a + 7)*q^13 - 3*q^14 + (a + 2)*q^15 + q^16 + (-5*a - 7)*q^17 + (-3*a - 4)*q^18 + (4*a + 5)*q^19 + (-2*a - 5)*q^20 - 3*a*q^21 + (a - 3)*q^22 + (2*a + 3)*q^23 + a*q^24 + (8*a + 16)*q^25 + (4*a + 7)*q^26 + (2*a + 3)*q^27 - 3*q^28 + (2*a - 5)*q^29 + (a + 2)*q^30 + (-4*a - 5)*q^31 + q^32 + (-6*a - 1)*q^33 + (-5*a - 7)*q^34 + (6*a + 15)*q^35 + (-3*a - 4)*q^36 + (-3*a - 6)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a^2 + a + 4)*q^5 - a*q^6 + (-a^2 + a + 4)*q^7 - q^8 + (a^2 - 3)*q^9 + (a^2 - a - 4)*q^10 + a^2*q^11 + a*q^12 + (-a^2 - a)*q^13 + (a^2 - a - 4)*q^14 + (2*a^2 - a - 4)*q^15 + q^16 + (-a^2 - 2*a + 6)*q^17 + (-a^2 + 3)*q^18 + (a^2 + 3*a - 4)*q^19 + (-a^2 + a + 4)*q^20 + (2*a^2 - a - 4)*q^21 - a^2*q^22 + (-a^2 - a)*q^23 - a*q^24 + (a^2 - 3*a - 1)*q^25 + (a^2 + a)*q^26 + (-a^2 - a + 4)*q^27 + (-a^2 + a + 4)*q^28 + (-a^2 + a + 10)*q^29 + (-2*a^2 + a + 4)*q^30 + (-3*a^2 - a + 12)*q^31 - q^32 + (-a^2 + 5*a + 4)*q^33 + (a^2 + 2*a - 6)*q^34 + (a^2 - 3*a + 4)*q^35 + (a^2 - 3)*q^36 - a*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - q^5 + a*q^6 + q^7 + q^8 + (a^2 - 3)*q^9 - q^10 + (-a^2 - 2*a + 8)*q^11 + a*q^12 + (-a^2 - a + 6)*q^13 + q^14 - a*q^15 + q^16 + (-a^2 + 6)*q^17 + (a^2 - 3)*q^18 + (a^2 - a - 6)*q^19 - q^20 + a*q^21 + (-a^2 - 2*a + 8)*q^22 + (3*a^2 + a - 14)*q^23 + a*q^24 - 4*q^25 + (-a^2 - a + 6)*q^26 + (a^2 + a - 8)*q^27 + q^28 + (a^2 + a - 4)*q^29 - a*q^30 + (-2*a^2 - 2*a + 9)*q^31 + q^32 + (-3*a^2 + a + 8)*q^33 + (-a^2 + 6)*q^34 - q^35 + (a^2 - 3)*q^36 + (a^2 + 2*a - 7)*q^37 + O(q^38)
*]> ;  // time = 71.439 seconds




J[335] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 335, 335, 335, 335, 335, 67, 67, 67 ], new_dimensions := [ 1, 2, 2, 7, 11, 1, 2, 2 ], dimensions := [ 1, 2, 2, 7, 11, 2, 4, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 9, 1, 1, 1, 0, 179, 1, 1, 1, 1, 1, 1, 179, 0, 1, 1, 1, 59, 1, 1, 1, 1, 0, 1, 81, 1, 1, 1, 1, 1, 1, 0, 1, 25, 1, 9, 1, 1, 81, 1, 0, 1, 1, 1, 1, 59, 1, 25, 1, 0 ], ap_traces := [
[ 0, 0, 1, -2, -2, -2, -3, -1, -1, -9, 0, -3 ],
[ 0, 0, -2, -4, 0, -4, -6, -2, -6, 6, 4, -10 ],
[ 1, 0, -2, 0, -6, 12, -2, -4, 2, -10, 12, -6 ],
[ 2, 4, -7, 10, 6, 4, 17, 3, 5, -1, 0, 15 ],
[ 0, 0, 11, 4, 6, 4, 2, 10, -10, 26, -8, 12 ]
], hecke_fields := [
x - 1,
x^2 - 2,
x^2 - x - 1,
x^7 - 2*x^6 - 12*x^5 + 21*x^4 + 42*x^3 - 52*x^2 - 39*x - 6,
x^11 - 18*x^9 + 2*x^8 + 114*x^7 - 24*x^6 - 306*x^5 + 86*x^4 + 332*x^3 - 109*x^2 - 114*x + 46
], atkin_lehners := [
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 9, 1 ],
[ 1, 1 ],
[ 177, 3 ],
[ 1377, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 3 ],
[ 1377, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 17 ], torsion_lower_bounds := [ 1, 1, 1, 3, 17 ], l_ratios := [ 0, 0, 1, 1/3, 81/17 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1, 1 ], eigenvalues := [*
[ 0, 0, 1, -2, -2, -2, -3, -1, -1, -9, 0, -3 ],
[
a,
-a,
-1,
-2,
a,
-2,
a - 3,
-1,
-a - 3,
-2*a + 3,
3*a + 2,
3*a - 5
],
[
a,
2*a - 1,
-1,
2*a - 1,
2*a - 4,
6,
-6*a + 2,
4*a - 4,
-2*a + 2,
-4*a - 3,
-4*a + 8,
2*a - 4
],
[
a,
-2*a^6 + a^5 + 23*a^4 - 8*a^3 - 66*a^2 + 12*a + 10,
-1,
2*a^6 + 2*a^5 - 23*a^4 - 26*a^3 + 61*a^2 + 81*a + 20,
-2*a^5 + 22*a^3 + 2*a^2 - 58*a - 12,
3*a^6 - 4*a^5 - 34*a^4 + 39*a^3 + 100*a^2 - 90*a - 34,
-3*a^6 + 4*a^5 + 34*a^4 - 41*a^3 - 100*a^2 + 100*a + 39,
2*a^3 - 12*a - 1,
a^6 - 4*a^5 - 12*a^4 + 45*a^3 + 42*a^2 - 122*a - 39,
3*a^6 - 5*a^5 - 33*a^4 + 51*a^3 + 96*a^2 - 124*a - 45,
-2*a^6 + 10*a^5 + 22*a^4 - 108*a^3 - 74*a^2 + 282*a + 86,
7*a^6 - 8*a^5 - 80*a^4 + 79*a^3 + 236*a^2 - 186*a - 73
],
[
a,
43/5261*a^10 - 84/5261*a^9 - 1344/5261*a^8 + 1488/5261*a^7 + 13496/5261*a^6 - 9411/5261*a^5 - 54847/5261*a^4 + 24218/5261*a^3 + 84666/5261*a^2 - 17145/5261*a - 28424/5261,
1,
2136/5261*a^10 + 966/5261*a^9 - 37154/5261*a^8 - 11851/5261*a^7 + 223588/5261*a^6 + 42464/5261*a^5 - 550354/5261*a^4 - 52284/5261*a^3 + 499421/5261*a^2 + 31446/5261*a - 115048/5261,
-1271/5261*a^10 + 770/5261*a^9 + 22842/5261*a^8 - 13640/5261*a^7 - 141250/5261*a^6 + 78376/5261*a^5 + 351072/5261*a^4 - 160620/5261*a^3 - 307876/5261*a^2 + 86139/5261*a + 57128/5261,
1936/5261*a^10 + 1112/5261*a^9 - 34818/5261*a^8 - 16692/5261*a^7 + 219421/5261*a^6 + 85502/5261*a^5 - 576654/5261*a^4 - 176549/5261*a^3 + 579238/5261*a^2 + 109722/5261*a - 156334/5261,
-1169/5261*a^10 - 41/5261*a^9 + 20388/5261*a^8 - 2280/5261*a^7 - 123184/5261*a^6 + 27912/5261*a^5 + 306614/5261*a^4 - 76990/5261*a^3 - 293500/5261*a^2 + 41799/5261*a + 82077/5261,
1666/5261*a^10 + 783/5261*a^9 - 29560/5261*a^8 - 10864/5261*a^7 + 184597/5261*a^6 + 52588/5261*a^5 - 491156/5261*a^4 - 119399/5261*a^3 + 529424/5261*a^2 + 107018/5261*a - 153673/5261,
-769/5261*a^10 - 333/5261*a^9 + 15716/5261*a^8 + 7402/5261*a^7 - 114850/5261*a^6 - 58164/5261*a^5 + 359214/5261*a^4 + 182062/5261*a^3 - 453134/5261*a^2 - 177885/5261*a + 164649/5261,
-436/5261*a^10 - 2207/5261*a^9 + 6776/5261*a^8 + 34586/5261*a^7 - 38230/5261*a^6 - 176803/5261*a^5 + 105757/5261*a^4 + 327278/5261*a^3 - 149340/5261*a^2 - 160170/5261*a + 87187/5261,
1977/5261*a^10 + 1766/5261*a^9 - 34876/5261*a^8 - 26774/5261*a^7 + 214304/5261*a^6 + 136602/5261*a^5 - 547588/5261*a^4 - 276418/5261*a^3 + 549118/5261*a^2 + 171433/5261*a - 178542/5261,
-1793/5261*a^10 - 1269/5261*a^9 + 32306/5261*a^8 + 17970/5261*a^7 - 206472/5261*a^6 - 84866/5261*a^5 + 561262/5261*a^4 + 170832/5261*a^3 - 594982/5261*a^2 - 144961/5261*a + 180119/5261
]
*], q_expansions := [*
q - 2*q^4 + q^5 - 2*q^7 - 3*q^9 - 2*q^11 - 2*q^13 + 4*q^16 - 3*q^17 - q^19 - 2*q^20 - q^23 + q^25 + 4*q^28 - 9*q^29 - 2*q^35 + 6*q^36 - 3*q^37 + O(q^38),
q + a*q^2 - a*q^3 - q^5 - 2*q^6 - 2*q^7 - 2*a*q^8 - q^9 - a*q^10 + a*q^11 - 2*q^13 - 2*a*q^14 + a*q^15 - 4*q^16 + (a - 3)*q^17 - a*q^18 - q^19 + 2*a*q^21 + 2*q^22 + (-a - 3)*q^23 + 4*q^24 + q^25 - 2*a*q^26 + 4*a*q^27 + (-2*a + 3)*q^29 + 2*q^30 + (3*a + 2)*q^31 - 2*q^33 + (-3*a + 2)*q^34 + 2*q^35 + (3*a - 5)*q^37 + O(q^38),
q + a*q^2 + (2*a - 1)*q^3 + (a - 1)*q^4 - q^5 + (a + 2)*q^6 + (2*a - 1)*q^7 + (-2*a + 1)*q^8 + 2*q^9 - a*q^10 + (2*a - 4)*q^11 + (-a + 3)*q^12 + 6*q^13 + (a + 2)*q^14 + (-2*a + 1)*q^15 - 3*a*q^16 + (-6*a + 2)*q^17 + 2*a*q^18 + (4*a - 4)*q^19 + (-a + 1)*q^20 + 5*q^21 + (-2*a + 2)*q^22 + (-2*a + 2)*q^23 - 5*q^24 + q^25 + 6*a*q^26 + (-2*a + 1)*q^27 + (-a + 3)*q^28 + (-4*a - 3)*q^29 + (-a - 2)*q^30 + (-4*a + 8)*q^31 + (a - 5)*q^32 + (-6*a + 8)*q^33 + (-4*a - 6)*q^34 + (-2*a + 1)*q^35 + (2*a - 2)*q^36 + (2*a - 4)*q^37 + O(q^38),
q + a*q^2 + (-2*a^6 + a^5 + 23*a^4 - 8*a^3 - 66*a^2 + 12*a + 10)*q^3 + (a^2 - 2)*q^4 - q^5 + (-3*a^6 - a^5 + 34*a^4 + 18*a^3 - 92*a^2 - 68*a - 12)*q^6 + (2*a^6 + 2*a^5 - 23*a^4 - 26*a^3 + 61*a^2 + 81*a + 20)*q^7 + (a^3 - 4*a)*q^8 + (3*a^5 - 36*a^3 - 5*a^2 + 105*a + 31)*q^9 - a*q^10 + (-2*a^5 + 22*a^3 + 2*a^2 - 58*a - 12)*q^11 + (-3*a^6 - 4*a^5 + 35*a^4 + 50*a^3 - 92*a^2 - 153*a - 38)*q^12 + (3*a^6 - 4*a^5 - 34*a^4 + 39*a^3 + 100*a^2 - 90*a - 34)*q^13 + (6*a^6 + a^5 - 68*a^4 - 23*a^3 + 185*a^2 + 98*a + 12)*q^14 + (2*a^6 - a^5 - 23*a^4 + 8*a^3 + 66*a^2 - 12*a - 10)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3*a^6 + 4*a^5 + 34*a^4 - 41*a^3 - 100*a^2 + 100*a + 39)*q^17 + (3*a^6 - 36*a^4 - 5*a^3 + 105*a^2 + 31*a)*q^18 + (2*a^3 - 12*a - 1)*q^19 + (-a^2 + 2)*q^20 + (-3*a^6 + 4*a^5 + 35*a^4 - 39*a^3 - 107*a^2 + 87*a + 38)*q^21 + (-2*a^6 + 22*a^4 + 2*a^3 - 58*a^2 - 12*a)*q^22 + (a^6 - 4*a^5 - 12*a^4 + 45*a^3 + 42*a^2 - 122*a - 39)*q^23 + (-4*a^6 + a^5 + 45*a^4 - 2*a^3 - 125*a^2 - 19*a + 6)*q^24 + q^25 + (2*a^6 + 2*a^5 - 24*a^4 - 26*a^3 + 66*a^2 + 83*a + 18)*q^26 + (-3*a^6 - a^5 + 35*a^4 + 17*a^3 - 98*a^2 - 66*a - 8)*q^27 + (9*a^6 - 103*a^4 - 15*a^3 + 288*a^2 + 84*a - 4)*q^28 + (3*a^6 - 5*a^5 - 33*a^4 + 51*a^3 + 96*a^2 - 124*a - 45)*q^29 + (3*a^6 + a^5 - 34*a^4 - 18*a^3 + 92*a^2 + 68*a + 12)*q^30 + (-2*a^6 + 10*a^5 + 22*a^4 - 108*a^3 - 74*a^2 + 282*a + 86)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-6*a^6 + 4*a^5 + 68*a^4 - 34*a^3 - 194*a^2 + 62*a + 36)*q^33 + (-2*a^6 - 2*a^5 + 22*a^4 + 26*a^3 - 56*a^2 - 78*a - 18)*q^34 + (-2*a^6 - 2*a^5 + 23*a^4 + 26*a^3 - 61*a^2 - 81*a - 20)*q^35 + (6*a^6 - 6*a^5 - 68*a^4 + 51*a^3 + 197*a^2 - 93*a - 44)*q^36 + (7*a^6 - 8*a^5 - 80*a^4 + 79*a^3 + 236*a^2 - 186*a - 73)*q^37 + O(q^38),
q + a*q^2 + (43/5261*a^10 - 84/5261*a^9 - 1344/5261*a^8 + 1488/5261*a^7 + 13496/5261*a^6 - 9411/5261*a^5 - 54847/5261*a^4 + 24218/5261*a^3 + 84666/5261*a^2 - 17145/5261*a - 28424/5261)*q^3 + (a^2 - 2)*q^4 + q^5 + (-84/5261*a^10 - 570/5261*a^9 + 1402/5261*a^8 + 8594/5261*a^7 - 8379/5261*a^6 - 41689/5261*a^5 + 20520/5261*a^4 + 70390/5261*a^3 - 12458/5261*a^2 - 23522/5261*a - 1978/5261)*q^6 + (2136/5261*a^10 + 966/5261*a^9 - 37154/5261*a^8 - 11851/5261*a^7 + 223588/5261*a^6 + 42464/5261*a^5 - 550354/5261*a^4 - 52284/5261*a^3 + 499421/5261*a^2 + 31446/5261*a - 115048/5261)*q^7 + (a^3 - 4*a)*q^8 + (-2405/5261*a^10 - 1664/5261*a^9 + 41769/5261*a^8 + 23464/5261*a^7 - 251736/5261*a^6 - 108264/5261*a^5 + 628092/5261*a^4 + 195152/5261*a^3 - 607584/5261*a^2 - 115666/5261*a + 188255/5261)*q^9 + a*q^10 + (-1271/5261*a^10 + 770/5261*a^9 + 22842/5261*a^8 - 13640/5261*a^7 - 141250/5261*a^6 + 78376/5261*a^5 + 351072/5261*a^4 - 160620/5261*a^3 - 307876/5261*a^2 + 86139/5261*a + 57128/5261)*q^11 + (-656/5261*a^10 + 58/5261*a^9 + 11450/5261*a^8 - 1779/5261*a^7 - 70697/5261*a^6 + 13638/5261*a^5 + 187308/5261*a^4 - 33006/5261*a^3 - 202010/5261*a^2 + 22736/5261*a + 60712/5261)*q^12 + (1936/5261*a^10 + 1112/5261*a^9 - 34818/5261*a^8 - 16692/5261*a^7 + 219421/5261*a^6 + 85502/5261*a^5 - 576654/5261*a^4 - 176549/5261*a^3 + 579238/5261*a^2 + 109722/5261*a - 156334/5261)*q^13 + (966/5261*a^10 + 1294/5261*a^9 - 16123/5261*a^8 - 19916/5261*a^7 + 93728/5261*a^6 + 103262/5261*a^5 - 235980/5261*a^4 - 209731/5261*a^3 + 264270/5261*a^2 + 128456/5261*a - 98256/5261)*q^14 + (43/5261*a^10 - 84/5261*a^9 - 1344/5261*a^8 + 1488/5261*a^7 + 13496/5261*a^6 - 9411/5261*a^5 - 54847/5261*a^4 + 24218/5261*a^3 + 84666/5261*a^2 - 17145/5261*a - 28424/5261)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1169/5261*a^10 - 41/5261*a^9 + 20388/5261*a^8 - 2280/5261*a^7 - 123184/5261*a^6 + 27912/5261*a^5 + 306614/5261*a^4 - 76990/5261*a^3 - 293500/5261*a^2 + 41799/5261*a + 82077/5261)*q^17 + (-1664/5261*a^10 - 1521/5261*a^9 + 28274/5261*a^8 + 22434/5261*a^7 - 165984/5261*a^6 - 107838/5261*a^5 + 401982/5261*a^4 + 190876/5261*a^3 - 377811/5261*a^2 - 85915/5261*a + 110630/5261)*q^18 + (1666/5261*a^10 + 783/5261*a^9 - 29560/5261*a^8 - 10864/5261*a^7 + 184597/5261*a^6 + 52588/5261*a^5 - 491156/5261*a^4 - 119399/5261*a^3 + 529424/5261*a^2 + 107018/5261*a - 153673/5261)*q^19 + (a^2 - 2)*q^20 + (-1904/5261*a^10 - 2398/5261*a^9 + 35286/5261*a^8 + 38721/5261*a^7 - 237273/5261*a^6 - 211918/5261*a^5 + 707126/5261*a^4 + 457377/5261*a^3 - 883889/5261*a^2 - 319218/5261*a + 330450/5261)*q^21 + (770/5261*a^10 - 36/5261*a^9 - 11098/5261*a^8 + 3644/5261*a^7 + 47872/5261*a^6 - 37854/5261*a^5 - 51314/5261*a^4 + 114096/5261*a^3 - 52400/5261*a^2 - 87766/5261*a + 58466/5261)*q^22 + (-769/5261*a^10 - 333/5261*a^9 + 15716/5261*a^8 + 7402/5261*a^7 - 114850/5261*a^6 - 58164/5261*a^5 + 359214/5261*a^4 + 182062/5261*a^3 - 453134/5261*a^2 - 177885/5261*a + 164649/5261)*q^23 + (226/5261*a^10 + 782/5261*a^9 - 3271/5261*a^8 - 13101/5261*a^7 + 14652/5261*a^6 + 69950/5261*a^5 - 17630/5261*a^4 - 124998/5261*a^3 - 23852/5261*a^2 + 32972/5261*a + 34132/5261)*q^24 + q^25 + (1112/5261*a^10 + 30/5261*a^9 - 20564/5261*a^8 - 1283/5261*a^7 + 131966/5261*a^6 + 15762/5261*a^5 - 343045/5261*a^4 - 63514/5261*a^3 + 320746/5261*a^2 + 64370/5261*a - 89056/5261)*q^26 + (3334/5261*a^10 + 828/5261*a^9 - 60406/5261*a^8 - 10158/5261*a^7 + 387807/5261*a^6 + 44665/5261*a^5 - 1066225/5261*a^4 - 114711/5261*a^3 + 1184156/5261*a^2 + 145702/5261*a - 366172/5261)*q^27 + (-2978/5261*a^10 - 667/5261*a^9 + 52460/5261*a^8 + 7306/5261*a^7 - 320730/5261*a^6 - 25312/5261*a^5 + 807901/5261*a^4 + 48126/5261*a^3 - 765092/5261*a^2 - 51024/5261*a + 185660/5261)*q^28 + (-436/5261*a^10 - 2207/5261*a^9 + 6776/5261*a^8 + 34586/5261*a^7 - 38230/5261*a^6 - 176803/5261*a^5 + 105757/5261*a^4 + 327278/5261*a^3 - 149340/5261*a^2 - 160170/5261*a + 87187/5261)*q^29 + (-84/5261*a^10 - 570/5261*a^9 + 1402/5261*a^8 + 8594/5261*a^7 - 8379/5261*a^6 - 41689/5261*a^5 + 20520/5261*a^4 + 70390/5261*a^3 - 12458/5261*a^2 - 23522/5261*a - 1978/5261)*q^30 + (1977/5261*a^10 + 1766/5261*a^9 - 34876/5261*a^8 - 26774/5261*a^7 + 214304/5261*a^6 + 136602/5261*a^5 - 547588/5261*a^4 - 276418/5261*a^3 + 549118/5261*a^2 + 171433/5261*a - 178542/5261)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2642/5261*a^10 + 3648/5261*a^9 - 46852/5261*a^8 - 57106/5261*a^7 + 297736/5261*a^6 + 300480/5261*a^5 - 836302/5261*a^4 - 618848/5261*a^3 + 1020398/5261*a^2 + 388338/5261*a - 414534/5261)*q^33 + (-41/5261*a^10 - 654/5261*a^9 + 58/5261*a^8 + 10082/5261*a^7 - 144/5261*a^6 - 51100/5261*a^5 + 23544/5261*a^4 + 94608/5261*a^3 - 85622/5261*a^2 - 51189/5261*a + 53774/5261)*q^34 + (2136/5261*a^10 + 966/5261*a^9 - 37154/5261*a^8 - 11851/5261*a^7 + 223588/5261*a^6 + 42464/5261*a^5 - 550354/5261*a^4 - 52284/5261*a^3 + 499421/5261*a^2 + 31446/5261*a - 115048/5261)*q^35 + (3289/5261*a^10 + 1650/5261*a^9 - 57776/5261*a^8 - 23216/5261*a^7 + 355698/5261*a^6 + 109326/5261*a^5 - 922204/5261*a^4 - 215667/5261*a^3 + 947877/5261*a^2 + 152266/5261*a - 299966/5261)*q^36 + (-1793/5261*a^10 - 1269/5261*a^9 + 32306/5261*a^8 + 17970/5261*a^7 - 206472/5261*a^6 - 84866/5261*a^5 + 561262/5261*a^4 + 170832/5261*a^3 - 594982/5261*a^2 - 144961/5261*a + 180119/5261)*q^37 + O(q^38)
*]> ;  // time = 47.28 seconds




J[337] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 337, 337 ], new_dimensions := [ 12, 15 ], dimensions := [ 12, 15 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -6, -11, -10, -13, -7, -6, -19, 1, -41, -7, -11, -5 ],
[ 3, 9, 10, 7, 9, -4, 15, 1, 45, 1, 11, -11 ]
], hecke_fields := [
x^12 + 6*x^11 + x^10 - 54*x^9 - 76*x^8 + 135*x^7 + 289*x^6 - 97*x^5 - 392*x^4 - 28*x^3 + 201*x^2 + 36*x - 27,
x^15 - 3*x^14 - 18*x^13 + 56*x^12 + 123*x^11 - 402*x^10 - 400*x^9 + 1395*x^8 + 643*x^7 - 2406*x^6 - 496*x^5 + 1843*x^4 + 200*x^3 - 388*x^2 - 69*x + 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 7 ]
], tamagawa_numbers := [
[ 1 ],
[ 7 ]
], torsion_upper_bounds := [ 1, 7 ], torsion_lower_bounds := [ 1, 7 ], l_ratios := [ 0, 1/7 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-41/27*a^11 - 23/3*a^10 + 148/27*a^9 + 679/9*a^8 + 1208/27*a^7 - 2122/9*a^6 - 5621/27*a^5 + 8552/27*a^4 + 7303/27*a^3 - 5185/27*a^2 - 316/3*a + 124/3,
76/27*a^11 + 40/3*a^10 - 356/27*a^9 - 1184/9*a^8 - 1393/27*a^7 + 3701/9*a^6 + 7618/27*a^5 - 14677/27*a^4 - 9914/27*a^3 + 8360/27*a^2 + 422/3*a - 182/3,
-49/27*a^11 - 22/3*a^10 + 356/27*a^9 + 671/9*a^8 - 362/27*a^7 - 2189/9*a^6 - 976/27*a^5 + 8845/27*a^4 + 1571/27*a^3 - 4607/27*a^2 - 68/3*a + 68/3,
2*a^11 + 26/3*a^10 - 13*a^9 - 268/3*a^8 - 3*a^7 + 895/3*a^6 + 107*a^5 - 1243/3*a^4 - 473/3*a^3 + 683/3*a^2 + 187/3*a - 37,
-5/3*a^11 - 22/3*a^10 + 31/3*a^9 + 224/3*a^8 + 20/3*a^7 - 731/3*a^6 - 293/3*a^5 + 976/3*a^4 + 401/3*a^3 - 491/3*a^2 - 146/3*a + 19,
29/27*a^11 + 14/3*a^10 - 187/27*a^9 - 439/9*a^8 - 107/27*a^7 + 1504/9*a^6 + 2018/27*a^5 - 6560/27*a^4 - 3319/27*a^3 + 4027/27*a^2 + 178/3*a - 94/3,
56/27*a^11 + 25/3*a^10 - 430/27*a^9 - 784/9*a^8 + 595/27*a^7 + 2677/9*a^6 + 830/27*a^5 - 11375/27*a^4 - 1960/27*a^3 + 6016/27*a^2 + 119/3*a - 82/3,
-65/27*a^11 - 31/3*a^10 + 421/27*a^9 + 946/9*a^8 + 62/27*a^7 - 3100/9*a^6 - 3161/27*a^5 + 12734/27*a^4 + 4678/27*a^3 - 6925/27*a^2 - 221/3*a + 109/3,
-20/27*a^11 - 2*a^10 + 223/27*a^9 + 175/9*a^8 - 982/27*a^7 - 502/9*a^6 + 2473/27*a^5 + 1304/27*a^4 - 3062/27*a^3 + 410/27*a^2 + 42*a - 53/3,
-43/9*a^11 - 68/3*a^10 + 209/9*a^9 + 227*a^8 + 739/9*a^7 - 729*a^6 - 4300/9*a^5 + 8977/9*a^4 + 5831/9*a^3 - 5249/9*a^2 - 790/3*a + 112,
-25/27*a^11 - 8/3*a^10 + 299/27*a^9 + 269/9*a^8 - 1376/27*a^7 - 1004/9*a^6 + 3314/27*a^5 + 4528/27*a^4 - 3877/27*a^3 - 2300/27*a^2 + 155/3*a + 20/3
],
[
a,
-1949/1618*a^14 + 1320/809*a^13 + 19977/809*a^12 - 22552/809*a^11 - 322023/1618*a^10 + 281379/1618*a^9 + 1285759/1618*a^8 - 383962/809*a^7 - 2607215/1618*a^6 + 826791/1618*a^5 + 2373167/1618*a^4 - 68300/809*a^3 - 287702/809*a^2 - 35427/809*a + 4591/1618,
971/1618*a^14 - 954/809*a^13 - 9264/809*a^12 + 16549/809*a^11 + 137225/1618*a^10 - 212741/1618*a^9 - 498023/1618*a^8 + 309926/809*a^7 + 915105/1618*a^6 - 797805/1618*a^5 - 761279/1618*a^4 + 176743/809*a^3 + 85396/809*a^2 - 10937/809*a - 3535/1618,
849/1618*a^14 - 685/809*a^13 - 8280/809*a^12 + 11507/809*a^11 + 125879/1618*a^10 - 139611/1618*a^9 - 470549/1618*a^8 + 180836/809*a^7 + 890021/1618*a^6 - 342519/1618*a^5 - 750325/1618*a^4 - 655/809*a^3 + 74829/809*a^2 + 24406/809*a + 7347/1618,
6103/3236*a^14 - 4299/1618*a^13 - 30978/809*a^12 + 36187/809*a^11 + 989877/3236*a^10 - 882049/3236*a^9 - 3925325/3236*a^8 + 575536/809*a^7 + 7937621/3236*a^6 - 2195013/3236*a^5 - 7252033/3236*a^4 - 12097/809*a^3 + 444324/809*a^2 + 86502/809*a + 9625/3236,
797/809*a^14 - 1207/809*a^13 - 16066/809*a^12 + 20440/809*a^11 + 127515/809*a^10 - 126146/809*a^9 - 503042/809*a^8 + 339199/809*a^7 + 1014207/809*a^6 - 356190/809*a^5 - 927323/809*a^4 + 52978/809*a^3 + 229839/809*a^2 + 28557/809*a + 142/809,
297/809*a^14 - 262/809*a^13 - 6462/809*a^12 + 4589/809*a^11 + 55127/809*a^10 - 29346/809*a^9 - 231190/809*a^8 + 81729/809*a^7 + 484013/809*a^6 - 86129/809*a^5 - 437957/809*a^4 - 221/809*a^3 + 89565/809*a^2 + 21112/809*a + 2553/809,
4399/3236*a^14 - 3433/1618*a^13 - 22077/809*a^12 + 29662/809*a^11 + 695493/3236*a^10 - 757317/3236*a^9 - 2709089/3236*a^8 + 543180/809*a^7 + 5356125/3236*a^6 - 2677477/3236*a^5 - 4752777/3236*a^4 + 248195/809*a^3 + 280212/809*a^2 + 2867/809*a - 18751/3236,
-843/3236*a^14 + 1189/1618*a^13 + 3519/809*a^12 - 10331/809*a^11 - 86489/3236*a^10 + 268213/3236*a^9 + 242333/3236*a^8 - 200875/809*a^7 - 326413/3236*a^6 + 1115229/3236*a^5 + 238737/3236*a^4 - 155353/809*a^3 - 30245/809*a^2 + 21947/809*a + 25751/3236,
-4577/1618*a^14 + 3043/809*a^13 + 47022/809*a^12 - 51190/809*a^11 - 760587/1618*a^10 + 620917/1618*a^9 + 3052801/1618*a^8 - 797474/809*a^7 - 6243287/1618*a^6 + 1420385/1618*a^5 + 5772927/1618*a^4 + 115904/809*a^3 - 730440/809*a^2 - 157784/809*a + 1711/1618,
-4961/3236*a^14 + 3147/1618*a^13 + 25232/809*a^12 - 25493/809*a^11 - 809243/3236*a^10 + 579087/3236*a^9 + 3227683/3236*a^8 - 319249/809*a^7 - 6582287/3236*a^6 + 505327/3236*a^5 + 6089839/3236*a^4 + 305414/809*a^3 - 382354/809*a^2 - 128732/809*a - 14779/3236,
177/809*a^14 - 197/809*a^13 - 3704/809*a^12 + 2694/809*a^11 + 31023/809*a^10 - 9350/809*a^9 - 133359/809*a^8 - 14689/809*a^7 + 310524/809*a^6 + 126765/809*a^5 - 365619/809*a^4 - 176698/809*a^3 + 164014/809*a^2 + 34858/809*a - 8971/809
]
*], q_expansions := [*
q + a*q^2 + (-41/27*a^11 - 23/3*a^10 + 148/27*a^9 + 679/9*a^8 + 1208/27*a^7 - 2122/9*a^6 - 5621/27*a^5 + 8552/27*a^4 + 7303/27*a^3 - 5185/27*a^2 - 316/3*a + 124/3)*q^3 + (a^2 - 2)*q^4 + (76/27*a^11 + 40/3*a^10 - 356/27*a^9 - 1184/9*a^8 - 1393/27*a^7 + 3701/9*a^6 + 7618/27*a^5 - 14677/27*a^4 - 9914/27*a^3 + 8360/27*a^2 + 422/3*a - 182/3)*q^5 + (13/9*a^11 + 7*a^10 - 59/9*a^9 - 212/3*a^8 - 277/9*a^7 + 692/3*a^6 + 1525/9*a^5 - 2923/9*a^4 - 2111/9*a^3 + 1799/9*a^2 + 96*a - 41)*q^6 + (-49/27*a^11 - 22/3*a^10 + 356/27*a^9 + 671/9*a^8 - 362/27*a^7 - 2189/9*a^6 - 976/27*a^5 + 8845/27*a^4 + 1571/27*a^3 - 4607/27*a^2 - 68/3*a + 68/3)*q^7 + (a^3 - 4*a)*q^8 + (11/9*a^11 + 19/3*a^10 - 34/9*a^9 - 62*a^8 - 377/9*a^7 + 193*a^6 + 1649/9*a^5 - 2363/9*a^4 - 2080/9*a^3 + 1492/9*a^2 + 254/3*a - 37)*q^9 + (-32/9*a^11 - 16*a^10 + 184/9*a^9 + 487/3*a^8 + 281/9*a^7 - 1594/3*a^6 - 2435/9*a^5 + 6626/9*a^4 + 3496/9*a^3 - 3826/9*a^2 - 162*a + 76)*q^10 + (2*a^11 + 26/3*a^10 - 13*a^9 - 268/3*a^8 - 3*a^7 + 895/3*a^6 + 107*a^5 - 1243/3*a^4 - 473/3*a^3 + 683/3*a^2 + 187/3*a - 37)*q^11 + (37/27*a^11 + 22/3*a^10 - 98/27*a^9 - 647/9*a^8 - 1453/27*a^7 + 2012/9*a^6 + 6256/27*a^5 - 8149/27*a^4 - 8117/27*a^3 + 5123/27*a^2 + 353/3*a - 131/3)*q^12 + (-5/3*a^11 - 22/3*a^10 + 31/3*a^9 + 224/3*a^8 + 20/3*a^7 - 731/3*a^6 - 293/3*a^5 + 976/3*a^4 + 401/3*a^3 - 491/3*a^2 - 146/3*a + 19)*q^13 + (32/9*a^11 + 15*a^10 - 211/9*a^9 - 454/3*a^8 + 16/9*a^7 + 1465/3*a^6 + 1364/9*a^5 - 5879/9*a^4 - 1993/9*a^3 + 3079/9*a^2 + 88*a - 49)*q^14 + (-a^11 - 14/3*a^10 + 5*a^9 + 139/3*a^8 + 15*a^7 - 442/3*a^6 - 89*a^5 + 610/3*a^4 + 347/3*a^3 - 371/3*a^2 - 127/3*a + 21)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (29/27*a^11 + 14/3*a^10 - 187/27*a^9 - 439/9*a^8 - 107/27*a^7 + 1504/9*a^6 + 2018/27*a^5 - 6560/27*a^4 - 3319/27*a^3 + 4027/27*a^2 + 178/3*a - 94/3)*q^17 + (-a^11 - 5*a^10 + 4*a^9 + 51*a^8 + 28*a^7 - 170*a^6 - 144*a^5 + 248*a^4 + 200*a^3 - 161*a^2 - 81*a + 33)*q^18 + (56/27*a^11 + 25/3*a^10 - 430/27*a^9 - 784/9*a^8 + 595/27*a^7 + 2677/9*a^6 + 830/27*a^5 - 11375/27*a^4 - 1960/27*a^3 + 6016/27*a^2 + 119/3*a - 82/3)*q^19 + (-8/27*a^11 - 8/3*a^10 - 89/27*a^9 + 217/9*a^8 + 1400/27*a^7 - 589/9*a^6 - 4670/27*a^5 + 2210/27*a^4 + 5662/27*a^3 - 1798/27*a^2 - 232/3*a + 76/3)*q^20 + (67/27*a^11 + 12*a^10 - 284/27*a^9 - 1061/9*a^8 - 1546/27*a^7 + 3299/9*a^6 + 7825/27*a^5 - 13138/27*a^4 - 10292/27*a^3 + 7847/27*a^2 + 151*a - 191/3)*q^21 + (-10/3*a^11 - 15*a^10 + 56/3*a^9 + 149*a^8 + 85/3*a^7 - 471*a^6 - 661/3*a^5 + 1879/3*a^4 + 851/3*a^3 - 1019/3*a^2 - 109*a + 54)*q^22 + (-65/27*a^11 - 31/3*a^10 + 421/27*a^9 + 946/9*a^8 + 62/27*a^7 - 3100/9*a^6 - 3161/27*a^5 + 12734/27*a^4 + 4678/27*a^3 - 6925/27*a^2 - 221/3*a + 109/3)*q^23 + (-34/9*a^11 - 19*a^10 + 137/9*a^9 + 575/3*a^8 + 901/9*a^7 - 1877/3*a^6 - 4570/9*a^5 + 7975/9*a^4 + 6275/9*a^3 - 5018/9*a^2 - 285*a + 119)*q^24 + (16/9*a^11 + 22/3*a^10 - 119/9*a^9 - 232/3*a^8 + 125/9*a^7 + 808/3*a^6 + 412/9*a^5 - 3589/9*a^4 - 824/9*a^3 + 2123/9*a^2 + 140/3*a - 37)*q^25 + (8/3*a^11 + 12*a^10 - 46/3*a^9 - 120*a^8 - 56/3*a^7 + 384*a^6 + 491/3*a^5 - 1559/3*a^4 - 631/3*a^3 + 859/3*a^2 + 79*a - 45)*q^26 + (-22/27*a^11 - 5*a^10 + 5/27*a^9 + 458/9*a^8 + 1501/27*a^7 - 1553/9*a^6 - 6268/27*a^5 + 7396/27*a^4 + 8744/27*a^3 - 5813/27*a^2 - 133*a + 167/3)*q^27 + (-73/27*a^11 - 37/3*a^10 + 386/27*a^9 + 1106/9*a^8 + 949/27*a^7 - 3506/9*a^6 - 6373/27*a^5 + 13963/27*a^4 + 8783/27*a^3 - 7706/27*a^2 - 395/3*a + 152/3)*q^28 + (-20/27*a^11 - 2*a^10 + 223/27*a^9 + 175/9*a^8 - 982/27*a^7 - 502/9*a^6 + 2473/27*a^5 + 1304/27*a^4 - 3062/27*a^3 + 410/27*a^2 + 42*a - 53/3)*q^29 + (4/3*a^11 + 6*a^10 - 23/3*a^9 - 61*a^8 - 37/3*a^7 + 200*a^6 + 319/3*a^5 - 829/3*a^4 - 455/3*a^3 + 476/3*a^2 + 57*a - 27)*q^30 + (-43/9*a^11 - 68/3*a^10 + 209/9*a^9 + 227*a^8 + 739/9*a^7 - 729*a^6 - 4300/9*a^5 + 8977/9*a^4 + 5831/9*a^3 - 5249/9*a^2 - 790/3*a + 112)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (4/9*a^11 + 5/3*a^10 - 23/9*a^9 - 12*a^8 + 29/9*a^7 + 12*a^6 - 221/9*a^5 + 278/9*a^4 + 637/9*a^3 - 481/9*a^2 - 125/3*a + 18)*q^33 + (-16/9*a^11 - 8*a^10 + 83/9*a^9 + 233/3*a^8 + 199/9*a^7 - 707/3*a^6 - 1249/9*a^5 + 2683/9*a^4 + 1613/9*a^3 - 1409/9*a^2 - 70*a + 29)*q^34 + (-161/27*a^11 - 28*a^10 + 784/27*a^9 + 2491/9*a^8 + 2633/27*a^7 - 7804/9*a^6 - 15056/27*a^5 + 30893/27*a^4 + 19666/27*a^3 - 17314/27*a^2 - 283*a + 364/3)*q^35 + (-13/9*a^11 - 23/3*a^10 + 41/9*a^9 + 76*a^8 + 439/9*a^7 - 241*a^6 - 1939/9*a^5 + 2998/9*a^4 + 2459/9*a^3 - 1904/9*a^2 - 301/3*a + 47)*q^36 + (-25/27*a^11 - 8/3*a^10 + 299/27*a^9 + 269/9*a^8 - 1376/27*a^7 - 1004/9*a^6 + 3314/27*a^5 + 4528/27*a^4 - 3877/27*a^3 - 2300/27*a^2 + 155/3*a + 20/3)*q^37 + O(q^38),
q + a*q^2 + (-1949/1618*a^14 + 1320/809*a^13 + 19977/809*a^12 - 22552/809*a^11 - 322023/1618*a^10 + 281379/1618*a^9 + 1285759/1618*a^8 - 383962/809*a^7 - 2607215/1618*a^6 + 826791/1618*a^5 + 2373167/1618*a^4 - 68300/809*a^3 - 287702/809*a^2 - 35427/809*a + 4591/1618)*q^3 + (a^2 - 2)*q^4 + (971/1618*a^14 - 954/809*a^13 - 9264/809*a^12 + 16549/809*a^11 + 137225/1618*a^10 - 212741/1618*a^9 - 498023/1618*a^8 + 309926/809*a^7 + 915105/1618*a^6 - 797805/1618*a^5 - 761279/1618*a^4 + 176743/809*a^3 + 85396/809*a^2 - 10937/809*a - 3535/1618)*q^5 + (-3207/1618*a^14 + 2436/809*a^13 + 32020/809*a^12 - 41148/809*a^11 - 502119/1618*a^10 + 506159/1618*a^9 + 1950931/1618*a^8 - 677004/809*a^7 - 3862503/1618*a^6 + 1406463/1618*a^5 + 3455407/1618*a^4 - 92802/809*a^3 - 413533/809*a^2 - 64945/809*a + 1949/1618)*q^6 + (849/1618*a^14 - 685/809*a^13 - 8280/809*a^12 + 11507/809*a^11 + 125879/1618*a^10 - 139611/1618*a^9 - 470549/1618*a^8 + 180836/809*a^7 + 890021/1618*a^6 - 342519/1618*a^5 - 750325/1618*a^4 - 655/809*a^3 + 74829/809*a^2 + 24406/809*a + 7347/1618)*q^7 + (a^3 - 4*a)*q^8 + (-606/809*a^14 + 935/809*a^13 + 12229/809*a^12 - 16244/809*a^11 - 96808/809*a^10 + 104054/809*a^9 + 379209/809*a^8 - 298333/809*a^7 - 754729/809*a^6 + 362952/809*a^5 + 673455/809*a^4 - 125369/809*a^3 - 154777/809*a^2 - 3959/809*a + 1508/809)*q^9 + (1005/1618*a^14 - 525/809*a^13 - 10639/809*a^12 + 8896/809*a^11 + 177601/1618*a^10 - 109623/1618*a^9 - 734693/1618*a^8 + 145376/809*a^7 + 1538421/1618*a^6 - 279663/1618*a^5 - 1436067/1618*a^4 - 11704/809*a^3 + 177437/809*a^2 + 31732/809*a - 971/1618)*q^10 + (6103/3236*a^14 - 4299/1618*a^13 - 30978/809*a^12 + 36187/809*a^11 + 989877/3236*a^10 - 882049/3236*a^9 - 3925325/3236*a^8 + 575536/809*a^7 + 7937621/3236*a^6 - 2195013/3236*a^5 - 7252033/3236*a^4 - 12097/809*a^3 + 444324/809*a^2 + 86502/809*a + 9625/3236)*q^11 + (-851/1618*a^14 + 517/809*a^13 + 8694/809*a^12 - 8725/809*a^11 - 139009/1618*a^10 + 105373/1618*a^9 + 548239/1618*a^8 - 132277/809*a^7 - 1095149/1618*a^6 + 211153/1618*a^5 + 978563/1618*a^4 + 43767/809*a^3 - 111699/809*a^2 - 38813/809*a - 5975/1618)*q^12 + (797/809*a^14 - 1207/809*a^13 - 16066/809*a^12 + 20440/809*a^11 + 127515/809*a^10 - 126146/809*a^9 - 503042/809*a^8 + 339199/809*a^7 + 1014207/809*a^6 - 356190/809*a^5 - 927323/809*a^4 + 52978/809*a^3 + 229839/809*a^2 + 28557/809*a + 142/809)*q^13 + (1177/1618*a^14 - 639/809*a^13 - 12265/809*a^12 + 10726/809*a^11 + 201687/1618*a^10 - 130949/1618*a^9 - 822683/1618*a^8 + 172057/809*a^7 + 1700175/1618*a^6 - 329221/1618*a^5 - 1566017/1618*a^4 - 10071/809*a^3 + 189112/809*a^2 + 32964/809*a - 849/1618)*q^14 + (-163/809*a^14 + 122/809*a^13 + 3571/809*a^12 - 2001/809*a^11 - 30530/809*a^10 + 11170/809*a^9 + 127514/809*a^8 - 21982/809*a^7 - 262872/809*a^6 - 3259/809*a^5 + 225771/809*a^4 + 44777/809*a^3 - 29682/809*a^2 - 20039/809*a - 3869/809)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (297/809*a^14 - 262/809*a^13 - 6462/809*a^12 + 4589/809*a^11 + 55127/809*a^10 - 29346/809*a^9 - 231190/809*a^8 + 81729/809*a^7 + 484013/809*a^6 - 86129/809*a^5 - 437957/809*a^4 - 221/809*a^3 + 89565/809*a^2 + 21112/809*a + 2553/809)*q^17 + (-883/809*a^14 + 1321/809*a^13 + 17692/809*a^12 - 22270/809*a^11 - 139558/809*a^10 + 136809/809*a^9 + 547037/809*a^8 - 365071/809*a^7 - 1095084/809*a^6 + 372879/809*a^5 + 991489/809*a^4 - 33577/809*a^3 - 239087/809*a^2 - 40306/809*a + 606/809)*q^18 + (4399/3236*a^14 - 3433/1618*a^13 - 22077/809*a^12 + 29662/809*a^11 + 695493/3236*a^10 - 757317/3236*a^9 - 2709089/3236*a^8 + 543180/809*a^7 + 5356125/3236*a^6 - 2677477/3236*a^5 - 4752777/3236*a^4 + 248195/809*a^3 + 280212/809*a^2 + 2867/809*a - 18751/3236)*q^19 + (23/1618*a^14 + 314/809*a^13 - 716/809*a^12 - 6105/809*a^11 + 19937/1618*a^10 + 92789/1618*a^9 - 115177/1618*a^8 - 173749/809*a^7 + 308157/1618*a^6 + 658023/1618*a^5 - 353065/1618*a^4 - 276549/809*a^3 + 55910/809*a^2 + 56061/809*a + 6065/1618)*q^20 + (-2009/809*a^14 + 3077/809*a^13 + 40524/809*a^12 - 52928/809*a^11 - 321131/809*a^10 + 335063/809*a^9 + 1260651/809*a^8 - 945573/809*a^7 - 2517193/809*a^6 + 1119308/809*a^5 + 2264525/809*a^4 - 349829/809*a^3 - 549101/809*a^2 - 35666/809*a + 9346/809)*q^21 + (9711/3236*a^14 - 7029/1618*a^13 - 49255/809*a^12 + 59802/809*a^11 + 1571357/3236*a^10 - 1484125/3236*a^9 - 6211541/3236*a^8 + 1003348/809*a^7 + 12488805/3236*a^6 - 4224945/3236*a^5 - 11296217/3236*a^4 + 139174/809*a^3 + 678493/809*a^2 + 107683/809*a - 6103/3236)*q^22 + (-843/3236*a^14 + 1189/1618*a^13 + 3519/809*a^12 - 10331/809*a^11 - 86489/3236*a^10 + 268213/3236*a^9 + 242333/3236*a^8 - 200875/809*a^7 - 326413/3236*a^6 + 1115229/3236*a^5 + 238737/3236*a^4 - 155353/809*a^3 - 30245/809*a^2 + 21947/809*a + 25751/3236)*q^23 + (4895/1618*a^14 - 3837/809*a^13 - 48937/809*a^12 + 65128/809*a^11 + 767509/1618*a^10 - 804479/1618*a^9 - 2979271/1618*a^8 + 1080030/809*a^7 + 5888653/1618*a^6 - 2256459/1618*a^5 - 5254887/1618*a^4 + 159005/809*a^3 + 623159/809*a^2 + 97543/809*a - 3047/1618)*q^24 + (352/809*a^14 - 730/809*a^13 - 6580/809*a^12 + 12570/809*a^11 + 47298/809*a^10 - 79635/809*a^9 - 164758/809*a^8 + 225495/809*a^7 + 288098/809*a^6 - 272628/809*a^5 - 228749/809*a^4 + 100114/809*a^3 + 49611/809*a^2 - 1166/809*a + 419/809)*q^25 + (1184/809*a^14 - 1720/809*a^13 - 24192/809*a^12 + 29484/809*a^11 + 194248/809*a^10 - 184242/809*a^9 - 772616/809*a^8 + 501736/809*a^7 + 1561392/809*a^6 - 532011/809*a^5 - 1415893/809*a^4 + 70439/809*a^3 + 337793/809*a^2 + 55135/809*a - 797/809)*q^26 + (-3451/809*a^14 + 5139/809*a^13 + 69594/809*a^12 - 87093/809*a^11 - 551508/809*a^10 + 536732/809*a^9 + 2166870/809*a^8 - 1433508/809*a^7 - 4336587/809*a^6 + 1464349/809*a^5 + 3912557/809*a^4 - 133927/809*a^3 - 934863/809*a^2 - 168116/809*a + 252/809)*q^27 + (555/1618*a^14 - 302/809*a^13 - 5670/809*a^12 + 5444/809*a^11 + 90447/1618*a^10 - 72661/1618*a^9 - 356703/1618*a^8 + 110010/809*a^7 + 722599/1618*a^6 - 297187/1618*a^5 - 688703/1618*a^4 + 72722/809*a^3 + 111644/809*a^2 - 8630/809*a - 15871/1618)*q^28 + (-4577/1618*a^14 + 3043/809*a^13 + 47022/809*a^12 - 51190/809*a^11 - 760587/1618*a^10 + 620917/1618*a^9 + 3052801/1618*a^8 - 797474/809*a^7 - 6243287/1618*a^6 + 1420385/1618*a^5 + 5772927/1618*a^4 + 115904/809*a^3 - 730440/809*a^2 - 157784/809*a + 1711/1618)*q^29 + (-367/809*a^14 + 637/809*a^13 + 7127/809*a^12 - 10481/809*a^11 - 54356/809*a^10 + 62314/809*a^9 + 205403/809*a^8 - 158063/809*a^7 - 395437/809*a^6 + 144923/809*a^5 + 345186/809*a^4 + 2918/809*a^3 - 83283/809*a^2 - 15116/809*a + 163/809)*q^30 + (-4961/3236*a^14 + 3147/1618*a^13 + 25232/809*a^12 - 25493/809*a^11 - 809243/3236*a^10 + 579087/3236*a^9 + 3227683/3236*a^8 - 319249/809*a^7 - 6582287/3236*a^6 + 505327/3236*a^5 + 6089839/3236*a^4 + 305414/809*a^3 - 382354/809*a^2 - 128732/809*a - 14779/3236)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1420/809*a^14 - 1713/809*a^13 - 29670/809*a^12 + 29031/809*a^11 + 244511/809*a^10 - 178641/809*a^9 - 999777/809*a^8 + 471364/809*a^7 + 2071695/809*a^6 - 443891/809*a^5 - 1907430/809*a^4 - 57022/809*a^3 + 441061/809*a^2 + 111590/809*a + 6388/809)*q^33 + (629/809*a^14 - 1116/809*a^13 - 12043/809*a^12 + 18596/809*a^11 + 90048/809*a^10 - 112390/809*a^9 - 332586/809*a^8 + 293042/809*a^7 + 628453/809*a^6 - 290645/809*a^5 - 547592/809*a^4 + 30165/809*a^3 + 136348/809*a^2 + 23046/809*a - 297/809)*q^34 + (1005/809*a^14 - 1859/809*a^13 - 19660/809*a^12 + 32354/809*a^11 + 150095/809*a^10 - 208321/809*a^9 - 564803/809*a^8 + 606262/809*a^7 + 1081336/809*a^6 - 774771/809*a^5 - 943386/809*a^4 + 338215/809*a^3 + 235142/809*a^2 - 30380/809*a - 9061/809)*q^35 + (-116/809*a^14 - 72/809*a^13 + 2720/809*a^12 + 1539/809*a^11 - 24541/809*a^10 - 14271/809*a^9 + 108296/809*a^8 + 69351/809*a^7 - 242161/809*a^6 - 172383/809*a^5 + 246882/809*a^4 + 188251/809*a^3 - 73356/809*a^2 - 52403/809*a - 2133/809)*q^36 + (177/809*a^14 - 197/809*a^13 - 3704/809*a^12 + 2694/809*a^11 + 31023/809*a^10 - 9350/809*a^9 - 133359/809*a^8 - 14689/809*a^7 + 310524/809*a^6 + 126765/809*a^5 - 365619/809*a^4 - 176698/809*a^3 + 164014/809*a^2 + 34858/809*a - 8971/809)*q^37 + O(q^38)
*]> ;  // time = 5.951 seconds




J[339] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 339, 339, 339, 339, 339, 339, 339, 339, 113, 113, 113, 113 ], new_dimensions := [ 1, 1, 1, 2, 2, 2, 5, 5, 1, 2, 3, 3 ], dimensions := [ 1, 1, 1, 2, 2, 2, 5, 5, 2, 4, 6, 6 ], intersection_graph := [ 0, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 7, 1, 7, 1, 1, 1, 0, 1, 71, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 13, 1, 1, 13, 1, 1, 1, 1, 1, 71, 1, 0, 1, 1, 11, 1, 11, 1, 1, 1, 1, 1, 13, 1, 0, 1, 1, 13, 1, 3, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 9, 1, 1, 3, 1, 1, 1, 11, 1, 1, 0, 1, 121, 1, 1, 1, 7, 1, 13, 1, 13, 1, 1, 0, 1, 3, 9, 1, 1, 1, 1, 11, 1, 9, 121, 1, 0 ], ap_traces := [
[ 2, -1, 2, 3, -6, 5, 3, 0, 3, -3, -7, 2 ],
[ 0, 1, -1, -3, -4, -2, -2, -2, 1, -7, 8, 4 ],
[ -2, 1, -3, 1, -2, -2, -2, 0, -5, -5, -4, -4 ],
[ 0, -2, -2, -2, 0, -8, 4, -8, 6, -14, 4, -8 ],
[ -2, -2, 2, 6, 4, 10, -6, 0, -6, 4, 14, -8 ],
[ 4, 2, 3, -1, -2, -6, -6, 6, 5, 2, 0, -2 ],
[ 1, -5, -2, -5, 4, -3, -1, 8, -11, 22, 7, 12 ],
[ 0, 5, 3, -3, 2, 8, 16, -12, 7, 27, -10, 2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 - 2,
x^2 + 2*x - 1,
x^2 + 2*x - 16,
x^5 - x^4 - 10*x^3 + 6*x^2 + 22*x + 4,
x^5 - 7*x^3 - 4*x^2 + 6*x + 2
], atkin_lehners := [
[ 1, -1 ],
[ -1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 9, 1 ],
[ 9, 1 ],
[ 3, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 13, 1 ],
[ 121, 1 ],
[ 247, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 9, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 13, 1 ],
[ 1, 1 ],
[ 247, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 1, 19 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 19 ], l_ratios := [ 1, 0, 0, 0, 1, 13, 1, 13/19 ], analytic_sha_upper_bounds := [ 1, 0, 0, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 0, 1, 1, 1, 1 ], eigenvalues := [*
[ 2, -1, 2, 3, -6, 5, 3, 0, 3, -3, -7, 2 ],
[ 0, 1, -1, -3, -4, -2, -2, -2, 1, -7, 8, 4 ],
[ -2, 1, -3, 1, -2, -2, -2, 0, -5, -5, -4, -4 ],
[
a,
-1,
-a - 1,
-1,
-a,
-2*a - 4,
4*a + 2,
3*a - 4,
-3*a + 3,
a - 7,
2,
2*a - 4
],
[
a,
-1,
-2*a - 1,
3,
2*a + 4,
5,
2*a - 1,
0,
2*a - 1,
-4*a - 2,
7,
2*a - 2
],
[
2,
1,
-1/2*a + 1,
1/2*a,
a,
-3,
-3,
-a + 2,
3/2*a + 4,
-2*a - 1,
-a - 1,
a
],
[
a,
-1,
-a^3 - a^2 + 7*a + 5,
1/2*a^4 + 1/2*a^3 - 3*a^2 - 3*a - 2,
-a^3 + 7*a + 2,
-1/2*a^4 + 1/2*a^3 + 3*a^2 - 3*a - 1,
-1/2*a^4 - 1/2*a^3 + 2*a^2 + 3*a + 5,
a^4 + a^3 - 7*a^2 - 7*a + 4,
1/2*a^4 - 3/2*a^3 - 4*a^2 + 8*a + 4,
a^3 + a^2 - 7*a - 1,
-1/2*a^4 + 1/2*a^3 + 3*a^2 - 3*a + 1,
a^4 - a^3 - 8*a^2 + 4*a + 12
],
[
a,
1,
-a^4 + a^3 + 5*a^2 - a - 1,
-a^4 + 2*a^3 + 3*a^2 - 4*a + 1,
2*a^4 - 3*a^3 - 10*a^2 + 5*a + 6,
-2*a^3 + 3*a^2 + 8*a - 2,
-a^4 + 2*a^3 + 4*a^2 - 4*a + 2,
3*a^4 - 3*a^3 - 17*a^2 + a + 8,
a^3 - 7*a - 1,
2*a^4 - a^3 - 11*a^2 - 5*a + 9,
2*a^4 - 2*a^3 - 11*a^2 + 4,
-2*a^3 + 4*a^2 + 8*a - 6
]
*], q_expansions := [*
q + 2*q^2 - q^3 + 2*q^4 + 2*q^5 - 2*q^6 + 3*q^7 + q^9 + 4*q^10 - 6*q^11 - 2*q^12 + 5*q^13 + 6*q^14 - 2*q^15 - 4*q^16 + 3*q^17 + 2*q^18 + 4*q^20 - 3*q^21 - 12*q^22 + 3*q^23 - q^25 + 10*q^26 - q^27 + 6*q^28 - 3*q^29 - 4*q^30 - 7*q^31 - 8*q^32 + 6*q^33 + 6*q^34 + 6*q^35 + 2*q^36 + 2*q^37 + O(q^38),
q + q^3 - 2*q^4 - q^5 - 3*q^7 + q^9 - 4*q^11 - 2*q^12 - 2*q^13 - q^15 + 4*q^16 - 2*q^17 - 2*q^19 + 2*q^20 - 3*q^21 + q^23 - 4*q^25 + q^27 + 6*q^28 - 7*q^29 + 8*q^31 - 4*q^33 + 3*q^35 - 2*q^36 + 4*q^37 + O(q^38),
q - 2*q^2 + q^3 + 2*q^4 - 3*q^5 - 2*q^6 + q^7 + q^9 + 6*q^10 - 2*q^11 + 2*q^12 - 2*q^13 - 2*q^14 - 3*q^15 - 4*q^16 - 2*q^17 - 2*q^18 - 6*q^20 + q^21 + 4*q^22 - 5*q^23 + 4*q^25 + 4*q^26 + q^27 + 2*q^28 - 5*q^29 + 6*q^30 - 4*q^31 + 8*q^32 - 2*q^33 + 4*q^34 - 3*q^35 + 2*q^36 - 4*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a - 1)*q^5 - a*q^6 - q^7 - 2*a*q^8 + q^9 + (-a - 2)*q^10 - a*q^11 + (-2*a - 4)*q^13 - a*q^14 + (a + 1)*q^15 - 4*q^16 + (4*a + 2)*q^17 + a*q^18 + (3*a - 4)*q^19 + q^21 - 2*q^22 + (-3*a + 3)*q^23 + 2*a*q^24 + (2*a - 2)*q^25 + (-4*a - 4)*q^26 - q^27 + (a - 7)*q^29 + (a + 2)*q^30 + 2*q^31 + a*q^33 + (2*a + 8)*q^34 + (a + 1)*q^35 + (2*a - 4)*q^37 + O(q^38),
q + a*q^2 - q^3 + (-2*a - 1)*q^4 + (-2*a - 1)*q^5 - a*q^6 + 3*q^7 + (a - 2)*q^8 + q^9 + (3*a - 2)*q^10 + (2*a + 4)*q^11 + (2*a + 1)*q^12 + 5*q^13 + 3*a*q^14 + (2*a + 1)*q^15 + 3*q^16 + (2*a - 1)*q^17 + a*q^18 + (-4*a + 5)*q^20 - 3*q^21 + 2*q^22 + (2*a - 1)*q^23 + (-a + 2)*q^24 - 4*a*q^25 + 5*a*q^26 - q^27 + (-6*a - 3)*q^28 + (-4*a - 2)*q^29 + (-3*a + 2)*q^30 + 7*q^31 + (a + 4)*q^32 + (-2*a - 4)*q^33 + (-5*a + 2)*q^34 + (-6*a - 3)*q^35 + (-2*a - 1)*q^36 + (2*a - 2)*q^37 + O(q^38),
q + 2*q^2 + q^3 + 2*q^4 + (-1/2*a + 1)*q^5 + 2*q^6 + 1/2*a*q^7 + q^9 + (-a + 2)*q^10 + a*q^11 + 2*q^12 - 3*q^13 + a*q^14 + (-1/2*a + 1)*q^15 - 4*q^16 - 3*q^17 + 2*q^18 + (-a + 2)*q^19 + (-a + 2)*q^20 + 1/2*a*q^21 + 2*a*q^22 + (3/2*a + 4)*q^23 - 3/2*a*q^25 - 6*q^26 + q^27 + a*q^28 + (-2*a - 1)*q^29 + (-a + 2)*q^30 + (-a - 1)*q^31 - 8*q^32 + a*q^33 - 6*q^34 + (a - 4)*q^35 + 2*q^36 + a*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^3 - a^2 + 7*a + 5)*q^5 - a*q^6 + (1/2*a^4 + 1/2*a^3 - 3*a^2 - 3*a - 2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^4 - a^3 + 7*a^2 + 5*a)*q^10 + (-a^3 + 7*a + 2)*q^11 + (-a^2 + 2)*q^12 + (-1/2*a^4 + 1/2*a^3 + 3*a^2 - 3*a - 1)*q^13 + (a^4 + 2*a^3 - 6*a^2 - 13*a - 2)*q^14 + (a^3 + a^2 - 7*a - 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^4 - 1/2*a^3 + 2*a^2 + 3*a + 5)*q^17 + a*q^18 + (a^4 + a^3 - 7*a^2 - 7*a + 4)*q^19 + (-2*a^4 - a^3 + 13*a^2 + 8*a - 6)*q^20 + (-1/2*a^4 - 1/2*a^3 + 3*a^2 + 3*a + 2)*q^21 + (-a^4 + 7*a^2 + 2*a)*q^22 + (1/2*a^4 - 3/2*a^3 - 4*a^2 + 8*a + 4)*q^23 + (-a^3 + 4*a)*q^24 + (-a^2 + 8)*q^25 + (-2*a^3 + 10*a + 2)*q^26 - q^27 + (2*a^4 + 3*a^3 - 13*a^2 - 18*a)*q^28 + (a^3 + a^2 - 7*a - 1)*q^29 + (a^4 + a^3 - 7*a^2 - 5*a)*q^30 + (-1/2*a^4 + 1/2*a^3 + 3*a^2 - 3*a + 1)*q^31 + (a^4 + 2*a^3 - 6*a^2 - 10*a - 4)*q^32 + (a^3 - 7*a - 2)*q^33 + (-a^4 - 3*a^3 + 6*a^2 + 16*a + 2)*q^34 + (-1/2*a^4 + 3/2*a^3 + 4*a^2 - 12*a - 8)*q^35 + (a^2 - 2)*q^36 + (a^4 - a^3 - 8*a^2 + 4*a + 12)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^4 + a^3 + 5*a^2 - a - 1)*q^5 + a*q^6 + (-a^4 + 2*a^3 + 3*a^2 - 4*a + 1)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (a^4 - 2*a^3 - 5*a^2 + 5*a + 2)*q^10 + (2*a^4 - 3*a^3 - 10*a^2 + 5*a + 6)*q^11 + (a^2 - 2)*q^12 + (-2*a^3 + 3*a^2 + 8*a - 2)*q^13 + (2*a^4 - 4*a^3 - 8*a^2 + 7*a + 2)*q^14 + (-a^4 + a^3 + 5*a^2 - a - 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 + 2*a^3 + 4*a^2 - 4*a + 2)*q^17 + a*q^18 + (3*a^4 - 3*a^3 - 17*a^2 + a + 8)*q^19 + (-a^2 - 2*a)*q^20 + (-a^4 + 2*a^3 + 3*a^2 - 4*a + 1)*q^21 + (-3*a^4 + 4*a^3 + 13*a^2 - 6*a - 4)*q^22 + (a^3 - 7*a - 1)*q^23 + (a^3 - 4*a)*q^24 + (-3*a^4 + 4*a^3 + 15*a^2 - 6*a - 8)*q^25 + (-2*a^4 + 3*a^3 + 8*a^2 - 2*a)*q^26 + q^27 + (-2*a^4 + 2*a^3 + 9*a^2 - 2*a - 6)*q^28 + (2*a^4 - a^3 - 11*a^2 - 5*a + 9)*q^29 + (a^4 - 2*a^3 - 5*a^2 + 5*a + 2)*q^30 + (2*a^4 - 2*a^3 - 11*a^2 + 4)*q^31 + (-a^3 + 4*a^2 + 6*a - 2)*q^32 + (2*a^4 - 3*a^3 - 10*a^2 + 5*a + 6)*q^33 + (2*a^4 - 3*a^3 - 8*a^2 + 8*a + 2)*q^34 + (-2*a^4 + 3*a^3 + 10*a^2 - 5*a - 3)*q^35 + (a^2 - 2)*q^36 + (-2*a^3 + 4*a^2 + 8*a - 6)*q^37 + O(q^38)
*]> ;  // time = 60.879 seconds




J[341] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 341, 341, 341, 341, 31, 11 ], new_dimensions := [ 2, 4, 8, 11, 2, 1 ], dimensions := [ 2, 4, 8, 11, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 5, 5, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 49, 1, 1, 1, 1, 0, 1, 39, 5, 1, 49, 1, 0, 5, 5, 1, 1, 39, 5, 0 ], ap_traces := [
[ 1, -2, -3, 1, 2, -2, -4, -10, -2, 0, 2, -4 ],
[ -2, -2, -1, -5, -4, -6, 0, -14, 0, -10, -4, 2 ],
[ 1, 4, -5, 7, -8, 8, 0, 16, 4, 8, 8, 8 ],
[ 1, 4, 3, 5, 11, -2, -10, 24, 2, -12, -11, -12 ]
], hecke_fields := [
x^2 - x - 1,
x^4 + 8*x^3 - 37*x^2 - 122*x + 331,
x^8 - x^7 - 14*x^6 + 11*x^5 + 60*x^4 - 31*x^3 - 74*x^2 + 5*x + 3,
x^11 - x^10 - 20*x^9 + 20*x^8 + 141*x^7 - 135*x^6 - 421*x^5 + 347*x^4 + 530*x^3 - 288*x^2 - 239*x + 17
], atkin_lehners := [
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 147, 3 ],
[ 1, 39 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 3 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 5, 1, 3, 1 ], torsion_lower_bounds := [ 1, 1, 3, 1 ], l_ratios := [ 0, 0, 1/3, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
a,
-1,
-a - 1,
-3*a + 2,
1,
4*a - 3,
2*a - 3,
2*a - 6,
2*a - 2,
0,
1,
-2*a - 1
],
[
-1/106*a^3 - 15/106*a^2 - 15/106*a + 88/53,
1/318*a^3 + 5/106*a^2 + 121/318*a - 88/159,
1/53*a^3 + 37/318*a^2 - 281/318*a - 367/318,
-7/318*a^3 - 26/159*a^2 + 80/159*a - 31/106,
-1,
-1/318*a^3 - 5/106*a^2 - 121/318*a - 230/159,
-5/106*a^3 - 119/318*a^2 + 199/318*a + 313/159,
1/318*a^3 + 5/106*a^2 + 121/318*a - 565/159,
4/159*a^3 + 20/53*a^2 + 166/159*a - 704/159,
-3/53*a^3 - 82/159*a^2 + 236/159*a + 577/159,
-1,
11/106*a^3 + 283/318*a^2 - 671/318*a - 1208/159
],
[
a,
1/4*a^7 - 1/4*a^6 - 13/4*a^5 + 5/2*a^4 + 51/4*a^3 - 25/4*a^2 - 55/4*a + 1,
-1/2*a^4 + 1/2*a^3 + 3*a^2 - 5/2*a - 3/2,
-1/4*a^6 + 1/4*a^5 + 9/4*a^4 - 3/2*a^3 - 19/4*a^2 + 1/4*a + 11/4,
-1,
1/2*a^5 - 1/2*a^4 - 5*a^3 + 5/2*a^2 + 23/2*a + 2,
-1/4*a^6 - 1/4*a^5 + 11/4*a^4 + 7/2*a^3 - 29/4*a^2 - 41/4*a + 3/4,
1/4*a^6 + 1/4*a^5 - 11/4*a^4 - 5/2*a^3 + 25/4*a^2 + 21/4*a + 17/4,
-1/4*a^7 + 1/4*a^6 + 13/4*a^5 - 3*a^4 - 45/4*a^3 + 37/4*a^2 + 25/4*a - 3/2,
-1/2*a^7 + 1/2*a^6 + 7*a^5 - 11/2*a^4 - 59/2*a^3 + 16*a^2 + 32*a - 3,
1,
-1/2*a^7 + 7*a^5 - 1/2*a^4 - 59/2*a^3 + 4*a^2 + 35*a + 1/2
],
[
a,
-7/88*a^10 + 1/44*a^9 + 3/2*a^8 - 15/44*a^7 - 867/88*a^6 + 67/44*a^5 + 2301/88*a^4 - 69/44*a^3 - 1029/44*a^2 - 17/11*a + 171/88,
-1/88*a^10 - 3/44*a^9 + 1/4*a^8 + 45/44*a^7 - 171/88*a^6 - 201/44*a^5 + 555/88*a^4 + 229/44*a^3 - 167/22*a^2 + 47/22*a + 191/88,
13/88*a^10 + 3/22*a^9 - 11/4*a^8 - 28/11*a^7 + 1563/88*a^6 + 721/44*a^5 - 4091/88*a^4 - 933/22*a^3 + 464/11*a^2 + 1627/44*a - 107/88,
1,
3/88*a^10 + 9/44*a^9 - 3/4*a^8 - 157/44*a^7 + 513/88*a^6 + 933/44*a^5 - 1621/88*a^4 - 2183/44*a^3 + 201/11*a^2 + 827/22*a + 219/88,
-1/8*a^10 + 9/4*a^8 - 107/8*a^6 - 1/4*a^5 + 227/8*a^4 + 5/2*a^3 - 14*a^2 - 17/4*a - 25/8,
19/88*a^10 + 1/22*a^9 - 17/4*a^8 - 15/22*a^7 + 2545/88*a^6 + 167/44*a^5 - 6937/88*a^4 - 128/11*a^3 + 822/11*a^2 + 645/44*a - 549/88,
-23/88*a^10 - 3/44*a^9 + 5*a^8 + 45/44*a^7 - 2899/88*a^6 - 267/44*a^5 + 7661/88*a^4 + 889/44*a^3 - 3645/44*a^2 - 279/11*a + 983/88,
1/88*a^10 + 3/44*a^9 - 1/4*a^8 - 45/44*a^7 + 127/88*a^6 + 201/44*a^5 - 71/88*a^4 - 251/44*a^3 - 141/22*a^2 + 15/11*a + 161/88,
-1,
-3/44*a^10 + 1/11*a^9 + 3/2*a^8 - 41/22*a^7 - 491/44*a^6 + 133/11*a^5 + 1401/44*a^4 - 567/22*a^3 - 617/22*a^2 + 108/11*a - 43/44
]
*], q_expansions := [*
q + a*q^2 - q^3 + (a - 1)*q^4 + (-a - 1)*q^5 - a*q^6 + (-3*a + 2)*q^7 + (-2*a + 1)*q^8 - 2*q^9 + (-2*a - 1)*q^10 + q^11 + (-a + 1)*q^12 + (4*a - 3)*q^13 + (-a - 3)*q^14 + (a + 1)*q^15 - 3*a*q^16 + (2*a - 3)*q^17 - 2*a*q^18 + (2*a - 6)*q^19 - a*q^20 + (3*a - 2)*q^21 + a*q^22 + (2*a - 2)*q^23 + (2*a - 1)*q^24 + (3*a - 3)*q^25 + (a + 4)*q^26 + 5*q^27 + (2*a - 5)*q^28 + (2*a + 1)*q^30 + q^31 + (a - 5)*q^32 - q^33 + (-a + 2)*q^34 + (4*a + 1)*q^35 + (-2*a + 2)*q^36 + (-2*a - 1)*q^37 + O(q^38),
q + (-1/106*a^3 - 15/106*a^2 - 15/106*a + 88/53)*q^2 + (1/318*a^3 + 5/106*a^2 + 121/318*a - 88/159)*q^3 + (1/106*a^3 + 15/106*a^2 + 15/106*a - 141/53)*q^4 + (1/53*a^3 + 37/318*a^2 - 281/318*a - 367/318)*q^5 + (-4/159*a^3 - 67/318*a^2 + 13/106*a + 401/318)*q^6 + (-7/318*a^3 - 26/159*a^2 + 80/159*a - 31/106)*q^7 + (1/53*a^3 + 15/53*a^2 + 15/53*a - 229/53)*q^8 + (5/318*a^3 + 25/106*a^2 - 31/318*a - 599/159)*q^9 + (5/159*a^3 + 97/318*a^2 - 115/318*a - 251/106)*q^10 - q^11 + (7/318*a^3 + 26/159*a^2 - 80/159*a - 75/106)*q^12 + (-1/318*a^3 - 5/106*a^2 - 121/318*a - 230/159)*q^13 + (2/159*a^3 + 10/53*a^2 + 83/159*a - 352/159)*q^14 + (-7/318*a^3 - 26/159*a^2 + 80/159*a - 137/106)*q^15 + (-3/106*a^3 - 45/106*a^2 - 45/106*a + 264/53)*q^16 + (-5/106*a^3 - 119/318*a^2 + 199/318*a + 313/159)*q^17 + (5/318*a^3 + 11/159*a^2 - 14/53*a - 509/318)*q^18 + (1/318*a^3 + 5/106*a^2 + 121/318*a - 565/159)*q^19 + (-8/159*a^3 - 67/159*a^2 + 66/53*a + 560/159)*q^20 + (-1/6*a^2 - 7/6*a + 19/6)*q^21 + (1/106*a^3 + 15/106*a^2 + 15/106*a - 88/53)*q^22 + (4/159*a^3 + 20/53*a^2 + 166/159*a - 704/159)*q^23 + (5/106*a^3 + 119/318*a^2 - 199/318*a - 313/159)*q^24 + (1/318*a^3 - 19/159*a^2 - 125/159*a + 277/106)*q^25 + (7/159*a^3 + 157/318*a^2 + 17/106*a - 1457/318)*q^26 + (7/318*a^3 - 1/318*a^2 - 177/106*a + 73/159)*q^27 + (1/106*a^3 - 4/159*a^2 - 163/159*a + 797/318)*q^28 + (-3/53*a^3 - 82/159*a^2 + 236/159*a + 577/159)*q^29 + (7/318*a^3 + 35/106*a^2 + 211/318*a - 616/159)*q^30 - q^31 + (-1/106*a^3 - 15/106*a^2 - 15/106*a + 353/53)*q^32 + (-1/318*a^3 - 5/106*a^2 - 121/318*a + 88/159)*q^33 + (5/159*a^3 + 97/318*a^2 + 203/318*a - 251/106)*q^34 + (-1/53*a^3 + 8/159*a^2 + 326/159*a - 638/159)*q^35 + (-5/159*a^3 - 97/318*a^2 + 115/318*a + 569/106)*q^36 + (11/106*a^3 + 283/318*a^2 - 671/318*a - 1208/159)*q^37 + O(q^38),
q + a*q^2 + (1/4*a^7 - 1/4*a^6 - 13/4*a^5 + 5/2*a^4 + 51/4*a^3 - 25/4*a^2 - 55/4*a + 1)*q^3 + (a^2 - 2)*q^4 + (-1/2*a^4 + 1/2*a^3 + 3*a^2 - 5/2*a - 3/2)*q^5 + (1/4*a^6 - 1/4*a^5 - 9/4*a^4 + 3/2*a^3 + 19/4*a^2 - 1/4*a - 3/4)*q^6 + (-1/4*a^6 + 1/4*a^5 + 9/4*a^4 - 3/2*a^3 - 19/4*a^2 + 1/4*a + 11/4)*q^7 + (a^3 - 4*a)*q^8 + (1/4*a^7 - 1/4*a^6 - 13/4*a^5 + 3*a^4 + 49/4*a^3 - 41/4*a^2 - 45/4*a + 11/2)*q^9 + (-1/2*a^5 + 1/2*a^4 + 3*a^3 - 5/2*a^2 - 3/2*a)*q^10 - q^11 + (-1/4*a^7 + 1/4*a^6 + 17/4*a^5 - 7/2*a^4 - 83/4*a^3 + 49/4*a^2 + 107/4*a - 2)*q^12 + (1/2*a^5 - 1/2*a^4 - 5*a^3 + 5/2*a^2 + 23/2*a + 2)*q^13 + (-1/4*a^7 + 1/4*a^6 + 9/4*a^5 - 3/2*a^4 - 19/4*a^3 + 1/4*a^2 + 11/4*a)*q^14 + (-1/4*a^7 + 1/4*a^6 + 13/4*a^5 - 5/2*a^4 - 55/4*a^3 + 25/4*a^2 + 75/4*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/4*a^6 - 1/4*a^5 + 11/4*a^4 + 7/2*a^3 - 29/4*a^2 - 41/4*a + 3/4)*q^17 + (1/4*a^6 + 1/4*a^5 - 11/4*a^4 - 5/2*a^3 + 29/4*a^2 + 17/4*a - 3/4)*q^18 + (1/4*a^6 + 1/4*a^5 - 11/4*a^4 - 5/2*a^3 + 25/4*a^2 + 21/4*a + 17/4)*q^19 + (-1/2*a^6 + 1/2*a^5 + 4*a^4 - 7/2*a^3 - 15/2*a^2 + 5*a + 3)*q^20 + (1/2*a^7 - 3/4*a^6 - 27/4*a^5 + 31/4*a^4 + 28*a^3 - 79/4*a^2 - 139/4*a + 11/4)*q^21 - a*q^22 + (-1/4*a^7 + 1/4*a^6 + 13/4*a^5 - 3*a^4 - 45/4*a^3 + 37/4*a^2 + 25/4*a - 3/2)*q^23 + (1/4*a^6 - 1/4*a^5 - 5/4*a^4 + 3/2*a^3 - 5/4*a^2 - 1/4*a + 9/4)*q^24 + (-1/4*a^7 + 3/4*a^6 + 11/4*a^5 - 7*a^4 - 35/4*a^3 + 63/4*a^2 + 25/4*a - 7/2)*q^25 + (1/2*a^6 - 1/2*a^5 - 5*a^4 + 5/2*a^3 + 23/2*a^2 + 2*a)*q^26 + (1/4*a^7 - 1/4*a^6 - 17/4*a^5 + 4*a^4 + 85/4*a^3 - 65/4*a^2 - 117/4*a + 17/2)*q^27 + (-3/4*a^6 + 3/4*a^5 + 23/4*a^4 - 9/2*a^3 - 25/4*a^2 + 3/4*a - 19/4)*q^28 + (-1/2*a^7 + 1/2*a^6 + 7*a^5 - 11/2*a^4 - 59/2*a^3 + 16*a^2 + 32*a - 3)*q^29 + (-1/4*a^6 + 1/4*a^5 + 5/4*a^4 - 3/2*a^3 + 1/4*a^2 + 5/4*a + 3/4)*q^30 + q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-1/4*a^7 + 1/4*a^6 + 13/4*a^5 - 5/2*a^4 - 51/4*a^3 + 25/4*a^2 + 55/4*a - 1)*q^33 + (-1/4*a^7 - 1/4*a^6 + 11/4*a^5 + 7/2*a^4 - 29/4*a^3 - 41/4*a^2 + 3/4*a)*q^34 + (1/4*a^6 - 1/4*a^5 - 9/4*a^4 + 5/2*a^3 + 23/4*a^2 - 25/4*a - 15/4)*q^35 + (-1/4*a^7 + 3/4*a^6 + 15/4*a^5 - 17/2*a^4 - 69/4*a^3 + 99/4*a^2 + 87/4*a - 11)*q^36 + (-1/2*a^7 + 7*a^5 - 1/2*a^4 - 59/2*a^3 + 4*a^2 + 35*a + 1/2)*q^37 + O(q^38),
q + a*q^2 + (-7/88*a^10 + 1/44*a^9 + 3/2*a^8 - 15/44*a^7 - 867/88*a^6 + 67/44*a^5 + 2301/88*a^4 - 69/44*a^3 - 1029/44*a^2 - 17/11*a + 171/88)*q^3 + (a^2 - 2)*q^4 + (-1/88*a^10 - 3/44*a^9 + 1/4*a^8 + 45/44*a^7 - 171/88*a^6 - 201/44*a^5 + 555/88*a^4 + 229/44*a^3 - 167/22*a^2 + 47/22*a + 191/88)*q^5 + (-5/88*a^10 - 1/11*a^9 + 5/4*a^8 + 15/11*a^7 - 811/88*a^6 - 323/44*a^5 + 2291/88*a^4 + 413/22*a^3 - 269/11*a^2 - 751/44*a + 119/88)*q^6 + (13/88*a^10 + 3/22*a^9 - 11/4*a^8 - 28/11*a^7 + 1563/88*a^6 + 721/44*a^5 - 4091/88*a^4 - 933/22*a^3 + 464/11*a^2 + 1627/44*a - 107/88)*q^7 + (a^3 - 4*a)*q^8 + (-9/88*a^10 - 5/44*a^9 + 2*a^8 + 97/44*a^7 - 1209/88*a^6 - 643/44*a^5 + 3411/88*a^4 + 1665/44*a^3 - 1653/44*a^2 - 699/22*a + 201/88)*q^9 + (-7/88*a^10 + 1/44*a^9 + 5/4*a^8 - 15/44*a^7 - 537/88*a^6 + 67/44*a^5 + 805/88*a^4 - 69/44*a^3 - 25/22*a^2 - 6/11*a + 17/88)*q^10 + q^11 + (1/88*a^10 + 3/44*a^9 - 1/2*a^8 - 23/44*a^7 + 413/88*a^6 - 41/44*a^5 - 1215/88*a^4 + 387/44*a^3 + 587/44*a^2 - 201/22*a - 257/88)*q^12 + (3/88*a^10 + 9/44*a^9 - 3/4*a^8 - 157/44*a^7 + 513/88*a^6 + 933/44*a^5 - 1621/88*a^4 - 2183/44*a^3 + 201/11*a^2 + 827/22*a + 219/88)*q^13 + (25/88*a^10 + 9/44*a^9 - 11/2*a^8 - 135/44*a^7 + 3197/88*a^6 + 691/44*a^5 - 8243/88*a^4 - 1589/44*a^3 + 3499/44*a^2 + 375/11*a - 221/88)*q^14 + (-5/44*a^10 - 2/11*a^9 + 9/4*a^8 + 71/22*a^7 - 345/22*a^6 - 211/11*a^5 + 1983/44*a^4 + 969/22*a^3 - 2031/44*a^2 - 381/11*a + 71/11)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/8*a^10 + 9/4*a^8 - 107/8*a^6 - 1/4*a^5 + 227/8*a^4 + 5/2*a^3 - 14*a^2 - 17/4*a - 25/8)*q^17 + (-19/88*a^10 - 1/22*a^9 + 17/4*a^8 + 15/22*a^7 - 2501/88*a^6 - 189/44*a^5 + 6453/88*a^4 + 183/11*a^3 - 1347/22*a^2 - 975/44*a + 153/88)*q^18 + (19/88*a^10 + 1/22*a^9 - 17/4*a^8 - 15/22*a^7 + 2545/88*a^6 + 167/44*a^5 - 6937/88*a^4 - 128/11*a^3 + 822/11*a^2 + 645/44*a - 549/88)*q^19 + (-3/88*a^10 - 9/44*a^9 + 3/4*a^8 + 135/44*a^7 - 469/88*a^6 - 669/44*a^5 + 1181/88*a^4 + 1347/44*a^3 - 91/11*a^2 - 254/11*a - 263/88)*q^20 + (27/88*a^10 + 1/11*a^9 - 23/4*a^8 - 15/11*a^7 + 3209/88*a^6 + 301/44*a^5 - 7813/88*a^4 - 325/22*a^3 + 742/11*a^2 + 509/44*a + 123/88)*q^21 + a*q^22 + (-23/88*a^10 - 3/44*a^9 + 5*a^8 + 45/44*a^7 - 2899/88*a^6 - 267/44*a^5 + 7661/88*a^4 + 889/44*a^3 - 3645/44*a^2 - 279/11*a + 983/88)*q^23 + (17/88*a^10 - 1/11*a^9 - 13/4*a^8 + 4/11*a^7 + 1675/88*a^6 + 249/44*a^5 - 4155/88*a^4 - 665/22*a^3 + 947/22*a^2 + 1493/44*a - 255/88)*q^24 + (9/88*a^10 + 5/44*a^9 - 2*a^8 - 97/44*a^7 + 1209/88*a^6 + 643/44*a^5 - 3455/88*a^4 - 1643/44*a^3 + 1829/44*a^2 + 300/11*a - 157/88)*q^25 + (21/88*a^10 - 3/44*a^9 - 17/4*a^8 + 45/44*a^7 + 2271/88*a^6 - 179/44*a^5 - 5407/88*a^4 + 9/44*a^3 + 1043/22*a^2 + 117/11*a - 51/88)*q^26 + (-2/11*a^10 - 1/11*a^9 + 13/4*a^8 + 41/22*a^7 - 873/44*a^6 - 277/22*a^5 + 1043/22*a^4 + 344/11*a^3 - 1505/44*a^2 - 251/11*a - 155/44)*q^27 + (17/88*a^10 - 1/11*a^9 - 13/4*a^8 + 15/11*a^7 + 1631/88*a^6 - 301/44*a^5 - 3671/88*a^4 + 303/22*a^3 + 347/11*a^2 - 377/44*a - 211/88)*q^28 + (1/88*a^10 + 3/44*a^9 - 1/4*a^8 - 45/44*a^7 + 127/88*a^6 + 201/44*a^5 - 71/88*a^4 - 251/44*a^3 - 141/22*a^2 + 15/11*a + 161/88)*q^29 + (-13/44*a^10 - 1/44*a^9 + 11/2*a^8 + 15/44*a^7 - 1519/44*a^6 - 61/22*a^5 + 3673/44*a^4 + 619/44*a^3 - 741/11*a^2 - 911/44*a + 85/44)*q^30 - q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-7/88*a^10 + 1/44*a^9 + 3/2*a^8 - 15/44*a^7 - 867/88*a^6 + 67/44*a^5 + 2301/88*a^4 - 69/44*a^3 - 1029/44*a^2 - 17/11*a + 171/88)*q^33 + (-1/8*a^10 - 1/4*a^9 + 5/2*a^8 + 17/4*a^7 - 137/8*a^6 - 97/4*a^5 + 367/8*a^4 + 209/4*a^3 - 161/4*a^2 - 33*a + 17/8)*q^34 + (2/11*a^10 - 7/44*a^9 - 7/2*a^8 + 127/44*a^7 + 254/11*a^6 - 361/22*a^5 - 1307/22*a^4 + 1231/44*a^3 + 522/11*a^2 - 173/44*a + 36/11)*q^35 + (-5/88*a^10 + 7/44*a^9 + a^8 - 105/44*a^7 - 525/88*a^6 + 513/44*a^5 + 1235/88*a^4 - 989/44*a^3 - 405/44*a^2 + 301/22*a - 79/88)*q^36 + (-3/44*a^10 + 1/11*a^9 + 3/2*a^8 - 41/22*a^7 - 491/44*a^6 + 133/11*a^5 + 1401/44*a^4 - 567/22*a^3 - 617/22*a^2 + 108/11*a - 43/44)*q^37 + O(q^38)
*]> ;  // time = 49.05 seconds




J[345] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 345, 345, 345, 345, 345, 345, 345, 345, 345, 345, 115, 115, 115, 69, 69, 23, 15 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 2, 4, 1, 2, 2, 1 ], dimensions := [ 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 2, 4, 8, 2, 4, 8, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 5, 1, 1, 5, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 11, 1, 3, 1, 1, 5, 5, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 25, 1, 1, 1, 5, 1, 1, 1, 9, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 0, 121, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 25, 1, 1, 1, 121, 0, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 0, -1, -1, 1, 4, 0, 5, 0, 1, 5, 3, -5 ],
[ 2, -1, 1, 3, 2, -2, 5, -2, -1, -5, 3, -7 ],
[ 1, 1, -1, 4, 4, 6, -2, -4, -1, -10, -8, 2 ],
[ -1, 1, -1, 4, -4, -2, 6, 8, -1, 6, 8, 6 ],
[ 0, 1, -1, -3, -4, 0, -3, -8, 1, 9, -5, -9 ],
[ -2, 1, 1, -5, -2, -6, 1, 2, -1, -1, -5, -7 ],
[ 0, -2, -2, -2, -8, 4, 2, -4, -2, -10, -14, 6 ],
[ -2, -2, 2, -6, -2, 2, -8, -10, 2, -4, -6, 10 ],
[ 0, 2, -2, -2, 0, 4, -6, 4, -2, 6, 10, -2 ],
[ -1, 3, 3, 6, -2, 4, -2, 2, 3, -6, 2, 0 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 2,
x^2 + 2*x - 2,
x^2 - 6,
x^3 + x^2 - 4*x - 2
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, 1, 1 ],
[ -1, 1, -1 ],
[ -1, -1, 1 ],
[ 1, 1, 1 ],
[ 1, -1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 5, 1 ],
[ 1, 1, 3 ],
[ 5, 3, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 9, 1, 1 ],
[ 1, 11, 3 ],
[ 15, 1, 1 ],
[ 11, 11, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 5, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 1, 11, 3 ],
[ 15, 1, 1 ],
[ 11, 11, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1, 3, 11 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1, 3, 1 ], l_ratios := [ 1, 1, 5, 1, 0, 0, 0, 0, 5/3, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 0, 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1, 0, 0, 0, 0, 1, 1/121 ], eigenvalues := [*
[ 0, -1, -1, 1, 4, 0, 5, 0, 1, 5, 3, -5 ],
[ 2, -1, 1, 3, 2, -2, 5, -2, -1, -5, 3, -7 ],
[ 1, 1, -1, 4, 4, 6, -2, -4, -1, -10, -8, 2 ],
[ -1, 1, -1, 4, -4, -2, 6, 8, -1, 6, 8, 6 ],
[ 0, 1, -1, -3, -4, 0, -3, -8, 1, 9, -5, -9 ],
[ -2, 1, 1, -5, -2, -6, 1, 2, -1, -1, -5, -7 ],
[
a,
-1,
-1,
-2*a - 1,
-a - 4,
-a + 2,
5*a + 1,
3*a - 2,
-1,
-a - 5,
-2*a - 7,
3
],
[
a,
-1,
1,
-3,
a,
-3*a - 2,
-a - 5,
-a - 6,
1,
a - 1,
4*a + 1,
4*a + 9
],
[
a,
1,
-1,
-1,
-a,
-a + 2,
a - 3,
-a + 2,
-1,
-3*a + 3,
2*a + 5,
-2*a - 1
],
[
a,
1,
1,
a^2 - 1,
-a^2 - a + 2,
-a^2 - a + 4,
-a - 1,
-a^2 + a + 4,
1,
3*a - 1,
-a^2 - 2*a + 3,
-a^2 + 3
]
*], q_expansions := [*
q - q^3 - 2*q^4 - q^5 + q^7 + q^9 + 4*q^11 + 2*q^12 + q^15 + 4*q^16 + 5*q^17 + 2*q^20 - q^21 + q^23 + q^25 - q^27 - 2*q^28 + 5*q^29 + 3*q^31 - 4*q^33 - q^35 - 2*q^36 - 5*q^37 + O(q^38),
q + 2*q^2 - q^3 + 2*q^4 + q^5 - 2*q^6 + 3*q^7 + q^9 + 2*q^10 + 2*q^11 - 2*q^12 - 2*q^13 + 6*q^14 - q^15 - 4*q^16 + 5*q^17 + 2*q^18 - 2*q^19 + 2*q^20 - 3*q^21 + 4*q^22 - q^23 + q^25 - 4*q^26 - q^27 + 6*q^28 - 5*q^29 - 2*q^30 + 3*q^31 - 8*q^32 - 2*q^33 + 10*q^34 + 3*q^35 + 2*q^36 - 7*q^37 + O(q^38),
q + q^2 + q^3 - q^4 - q^5 + q^6 + 4*q^7 - 3*q^8 + q^9 - q^10 + 4*q^11 - q^12 + 6*q^13 + 4*q^14 - q^15 - q^16 - 2*q^17 + q^18 - 4*q^19 + q^20 + 4*q^21 + 4*q^22 - q^23 - 3*q^24 + q^25 + 6*q^26 + q^27 - 4*q^28 - 10*q^29 - q^30 - 8*q^31 + 5*q^32 + 4*q^33 - 2*q^34 - 4*q^35 - q^36 + 2*q^37 + O(q^38),
q - q^2 + q^3 - q^4 - q^5 - q^6 + 4*q^7 + 3*q^8 + q^9 + q^10 - 4*q^11 - q^12 - 2*q^13 - 4*q^14 - q^15 - q^16 + 6*q^17 - q^18 + 8*q^19 + q^20 + 4*q^21 + 4*q^22 - q^23 + 3*q^24 + q^25 + 2*q^26 + q^27 - 4*q^28 + 6*q^29 + q^30 + 8*q^31 - 5*q^32 - 4*q^33 - 6*q^34 - 4*q^35 - q^36 + 6*q^37 + O(q^38),
q + q^3 - 2*q^4 - q^5 - 3*q^7 + q^9 - 4*q^11 - 2*q^12 - q^15 + 4*q^16 - 3*q^17 - 8*q^19 + 2*q^20 - 3*q^21 + q^23 + q^25 + q^27 + 6*q^28 + 9*q^29 - 5*q^31 - 4*q^33 + 3*q^35 - 2*q^36 - 9*q^37 + O(q^38),
q - 2*q^2 + q^3 + 2*q^4 + q^5 - 2*q^6 - 5*q^7 + q^9 - 2*q^10 - 2*q^11 + 2*q^12 - 6*q^13 + 10*q^14 + q^15 - 4*q^16 + q^17 - 2*q^18 + 2*q^19 + 2*q^20 - 5*q^21 + 4*q^22 - q^23 + q^25 + 12*q^26 + q^27 - 10*q^28 - q^29 - 2*q^30 - 5*q^31 + 8*q^32 - 2*q^33 - 2*q^34 - 5*q^35 + 2*q^36 - 7*q^37 + O(q^38),
q + a*q^2 - q^3 - q^5 - a*q^6 + (-2*a - 1)*q^7 - 2*a*q^8 + q^9 - a*q^10 + (-a - 4)*q^11 + (-a + 2)*q^13 + (-a - 4)*q^14 + q^15 - 4*q^16 + (5*a + 1)*q^17 + a*q^18 + (3*a - 2)*q^19 + (2*a + 1)*q^21 + (-4*a - 2)*q^22 - q^23 + 2*a*q^24 + q^25 + (2*a - 2)*q^26 - q^27 + (-a - 5)*q^29 + a*q^30 + (-2*a - 7)*q^31 + (a + 4)*q^33 + (a + 10)*q^34 + (2*a + 1)*q^35 + 3*q^37 + O(q^38),
q + a*q^2 - q^3 - 2*a*q^4 + q^5 - a*q^6 - 3*q^7 + (2*a - 4)*q^8 + q^9 + a*q^10 + a*q^11 + 2*a*q^12 + (-3*a - 2)*q^13 - 3*a*q^14 - q^15 + (-4*a + 4)*q^16 + (-a - 5)*q^17 + a*q^18 + (-a - 6)*q^19 - 2*a*q^20 + 3*q^21 + (-2*a + 2)*q^22 + q^23 + (-2*a + 4)*q^24 + q^25 + (4*a - 6)*q^26 - q^27 + 6*a*q^28 + (a - 1)*q^29 - a*q^30 + (4*a + 1)*q^31 + 8*a*q^32 - a*q^33 + (-3*a - 2)*q^34 - 3*q^35 - 2*a*q^36 + (4*a + 9)*q^37 + O(q^38),
q + a*q^2 + q^3 + 4*q^4 - q^5 + a*q^6 - q^7 + 2*a*q^8 + q^9 - a*q^10 - a*q^11 + 4*q^12 + (-a + 2)*q^13 - a*q^14 - q^15 + 4*q^16 + (a - 3)*q^17 + a*q^18 + (-a + 2)*q^19 - 4*q^20 - q^21 - 6*q^22 - q^23 + 2*a*q^24 + q^25 + (2*a - 6)*q^26 + q^27 - 4*q^28 + (-3*a + 3)*q^29 - a*q^30 + (2*a + 5)*q^31 - a*q^33 + (-3*a + 6)*q^34 + q^35 + 4*q^36 + (-2*a - 1)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + q^5 + a*q^6 + (a^2 - 1)*q^7 + (-a^2 + 2)*q^8 + q^9 + a*q^10 + (-a^2 - a + 2)*q^11 + (a^2 - 2)*q^12 + (-a^2 - a + 4)*q^13 + (-a^2 + 3*a + 2)*q^14 + q^15 + (-a^2 - 2*a + 2)*q^16 + (-a - 1)*q^17 + a*q^18 + (-a^2 + a + 4)*q^19 + (a^2 - 2)*q^20 + (a^2 - 1)*q^21 + (-2*a - 2)*q^22 + q^23 + (-a^2 + 2)*q^24 + q^25 - 2*q^26 + q^27 + (2*a^2 - 2*a)*q^28 + (3*a - 1)*q^29 + a*q^30 + (-a^2 - 2*a + 3)*q^31 + (a^2 - 2*a - 6)*q^32 + (-a^2 - a + 2)*q^33 + (-a^2 - a)*q^34 + (a^2 - 1)*q^35 + (a^2 - 2)*q^36 + (-a^2 + 3)*q^37 + O(q^38)
*]> ;  // time = 113.771 seconds




J[346] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 346, 346, 346, 346, 346, 173, 173 ], new_dimensions := [ 1, 1, 3, 4, 5, 4, 10 ], dimensions := [ 1, 1, 3, 4, 5, 8, 20 ], intersection_graph := [ 0, 1, 1, 1, 7, 1, 1, 1, 0, 1, 1, 1, 1, 7, 1, 1, 0, 1, 1, 1, 469, 1, 1, 1, 0, 1, 31, 1, 7, 1, 1, 1, 0, 79, 1, 1, 1, 1, 31, 79, 0, 1, 1, 7, 469, 1, 1, 1, 0 ], ap_traces := [
[ 1, 1, -1, 4, 4, -6, -4, 5, 5, 8, -7, -2 ],
[ 1, -1, -3, -2, -4, 0, -2, 7, -3, -4, -7, -4 ],
[ -3, 1, 0, -3, 12, 0, 2, 1, 9, 10, 5, -6 ],
[ -4, -2, -5, -1, -13, 3, -6, -12, -1, -21, -3, 7 ],
[ 5, -3, 5, -2, 5, 9, 6, -5, -2, 5, -8, 7 ]
], hecke_fields := [
x - 1,
x - 1,
x^3 - x^2 - 6*x + 4,
x^4 + 2*x^3 - 5*x^2 - 5*x - 1,
x^5 + 3*x^4 - 8*x^3 - 21*x^2 + 18*x + 28
], atkin_lehners := [
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 7, 1 ],
[ 469, 1 ],
[ 31, 1 ],
[ 2291, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 2291, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 29 ], torsion_lower_bounds := [ 1, 1, 1, 1, 29 ], l_ratios := [ 1, 0, 1, 0, 79/29 ], analytic_sha_upper_bounds := [ 1, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1, 0, 1 ], eigenvalues := [*
[ 1, 1, -1, 4, 4, -6, -4, 5, 5, 8, -7, -2 ],
[ 1, -1, -3, -2, -4, 0, -2, 7, -3, -4, -7, -4 ],
[
-1,
a,
-1/2*a^2 + 1/2*a + 2,
-1/2*a^2 + 1/2*a + 1,
4,
-a^2 + a + 4,
a^2 + a - 4,
2*a^2 - a - 8,
-a^2 - 2*a + 8,
-a^2 - a + 8,
-a^2 + 6,
-2
],
[
-1,
a,
-3*a^3 - 5*a^2 + 16*a + 7,
5*a^3 + 8*a^2 - 29*a - 14,
3*a^3 + 4*a^2 - 18*a - 9,
-3*a^3 - 4*a^2 + 17*a + 6,
-2*a^3 - 4*a^2 + 10*a + 6,
-2*a^3 - 3*a^2 + 12*a + 2,
-3*a^3 - 3*a^2 + 20*a + 3,
-a^3 - a^2 + 9*a - 3,
7*a^3 + 11*a^2 - 36*a - 17,
-5*a^3 - 9*a^2 + 25*a + 17
],
[
1,
a,
-1/2*a^4 - 1/2*a^3 + 3*a^2 + 1/2*a,
1/2*a^4 + 1/2*a^3 - 4*a^2 - 3/2*a + 5,
a^2 - 4,
a^3 + 2*a^2 - 5*a - 4,
a^4 + a^3 - 8*a^2 - 3*a + 12,
-a^4 - a^3 + 7*a^2 + a - 8,
2*a^3 + 4*a^2 - 10*a - 12,
-2*a^3 - 4*a^2 + 9*a + 12,
-2*a^3 - 4*a^2 + 10*a + 10,
-a^4 - a^3 + 8*a^2 + 2*a - 10
]
*], q_expansions := [*
q + q^2 + q^3 + q^4 - q^5 + q^6 + 4*q^7 + q^8 - 2*q^9 - q^10 + 4*q^11 + q^12 - 6*q^13 + 4*q^14 - q^15 + q^16 - 4*q^17 - 2*q^18 + 5*q^19 - q^20 + 4*q^21 + 4*q^22 + 5*q^23 + q^24 - 4*q^25 - 6*q^26 - 5*q^27 + 4*q^28 + 8*q^29 - q^30 - 7*q^31 + q^32 + 4*q^33 - 4*q^34 - 4*q^35 - 2*q^36 - 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 3*q^5 - q^6 - 2*q^7 + q^8 - 2*q^9 - 3*q^10 - 4*q^11 - q^12 - 2*q^14 + 3*q^15 + q^16 - 2*q^17 - 2*q^18 + 7*q^19 - 3*q^20 + 2*q^21 - 4*q^22 - 3*q^23 - q^24 + 4*q^25 + 5*q^27 - 2*q^28 - 4*q^29 + 3*q^30 - 7*q^31 + q^32 + 4*q^33 - 2*q^34 + 6*q^35 - 2*q^36 - 4*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-1/2*a^2 + 1/2*a + 2)*q^5 - a*q^6 + (-1/2*a^2 + 1/2*a + 1)*q^7 - q^8 + (a^2 - 3)*q^9 + (1/2*a^2 - 1/2*a - 2)*q^10 + 4*q^11 + a*q^12 + (-a^2 + a + 4)*q^13 + (1/2*a^2 - 1/2*a - 1)*q^14 + (-a + 2)*q^15 + q^16 + (a^2 + a - 4)*q^17 + (-a^2 + 3)*q^18 + (2*a^2 - a - 8)*q^19 + (-1/2*a^2 + 1/2*a + 2)*q^20 + (-2*a + 2)*q^21 - 4*q^22 + (-a^2 - 2*a + 8)*q^23 - a*q^24 + (-1/2*a^2 - 1/2*a)*q^25 + (a^2 - a - 4)*q^26 + (a^2 - 4)*q^27 + (-1/2*a^2 + 1/2*a + 1)*q^28 + (-a^2 - a + 8)*q^29 + (a - 2)*q^30 + (-a^2 + 6)*q^31 - q^32 + 4*a*q^33 + (-a^2 - a + 4)*q^34 + (-a + 3)*q^35 + (a^2 - 3)*q^36 - 2*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-3*a^3 - 5*a^2 + 16*a + 7)*q^5 - a*q^6 + (5*a^3 + 8*a^2 - 29*a - 14)*q^7 - q^8 + (a^2 - 3)*q^9 + (3*a^3 + 5*a^2 - 16*a - 7)*q^10 + (3*a^3 + 4*a^2 - 18*a - 9)*q^11 + a*q^12 + (-3*a^3 - 4*a^2 + 17*a + 6)*q^13 + (-5*a^3 - 8*a^2 + 29*a + 14)*q^14 + (a^3 + a^2 - 8*a - 3)*q^15 + q^16 + (-2*a^3 - 4*a^2 + 10*a + 6)*q^17 + (-a^2 + 3)*q^18 + (-2*a^3 - 3*a^2 + 12*a + 2)*q^19 + (-3*a^3 - 5*a^2 + 16*a + 7)*q^20 + (-2*a^3 - 4*a^2 + 11*a + 5)*q^21 + (-3*a^3 - 4*a^2 + 18*a + 9)*q^22 + (-3*a^3 - 3*a^2 + 20*a + 3)*q^23 - a*q^24 + (3*a^3 + 5*a^2 - 14*a - 6)*q^25 + (3*a^3 + 4*a^2 - 17*a - 6)*q^26 + (a^3 - 6*a)*q^27 + (5*a^3 + 8*a^2 - 29*a - 14)*q^28 + (-a^3 - a^2 + 9*a - 3)*q^29 + (-a^3 - a^2 + 8*a + 3)*q^30 + (7*a^3 + 11*a^2 - 36*a - 17)*q^31 - q^32 + (-2*a^3 - 3*a^2 + 6*a + 3)*q^33 + (2*a^3 + 4*a^2 - 10*a - 6)*q^34 + (2*a^2 + 4*a - 8)*q^35 + (a^2 - 3)*q^36 + (-5*a^3 - 9*a^2 + 25*a + 17)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-1/2*a^4 - 1/2*a^3 + 3*a^2 + 1/2*a)*q^5 + a*q^6 + (1/2*a^4 + 1/2*a^3 - 4*a^2 - 3/2*a + 5)*q^7 + q^8 + (a^2 - 3)*q^9 + (-1/2*a^4 - 1/2*a^3 + 3*a^2 + 1/2*a)*q^10 + (a^2 - 4)*q^11 + a*q^12 + (a^3 + 2*a^2 - 5*a - 4)*q^13 + (1/2*a^4 + 1/2*a^3 - 4*a^2 - 3/2*a + 5)*q^14 + (a^4 - a^3 - 10*a^2 + 9*a + 14)*q^15 + q^16 + (a^4 + a^3 - 8*a^2 - 3*a + 12)*q^17 + (a^2 - 3)*q^18 + (-a^4 - a^3 + 7*a^2 + a - 8)*q^19 + (-1/2*a^4 - 1/2*a^3 + 3*a^2 + 1/2*a)*q^20 + (-a^4 + 9*a^2 - 4*a - 14)*q^21 + (a^2 - 4)*q^22 + (2*a^3 + 4*a^2 - 10*a - 12)*q^23 + a*q^24 + (-1/2*a^4 - 3/2*a^3 + 2*a^2 + 9/2*a + 2)*q^25 + (a^3 + 2*a^2 - 5*a - 4)*q^26 + (a^3 - 6*a)*q^27 + (1/2*a^4 + 1/2*a^3 - 4*a^2 - 3/2*a + 5)*q^28 + (-2*a^3 - 4*a^2 + 9*a + 12)*q^29 + (a^4 - a^3 - 10*a^2 + 9*a + 14)*q^30 + (-2*a^3 - 4*a^2 + 10*a + 10)*q^31 + q^32 + (a^3 - 4*a)*q^33 + (a^4 + a^3 - 8*a^2 - 3*a + 12)*q^34 + (a^4 + 2*a^3 - 7*a^2 - 7*a + 7)*q^35 + (a^2 - 3)*q^36 + (-a^4 - a^3 + 8*a^2 + 2*a - 10)*q^37 + O(q^38)
*]> ;  // time = 77.18 seconds




J[347] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 347, 347, 347, 347 ], new_dimensions := [ 1, 2, 7, 19 ], dimensions := [ 1, 2, 7, 19 ], intersection_graph := [ 0, 1, 7, 1, 1, 0, 19, 1, 7, 19, 0, 1, 1, 1, 1, 0 ], ap_traces := [
[ -2, 1, 0, -2, -3, -2, 4, -4, 4, -9, 8, -12 ],
[ 2, -1, -2, -4, 3, -7, -2, 6, -10, 3, -1, 10 ],
[ -2, -7, -8, -5, 2, -22, -9, -11, 2, 3, -11, -40 ],
[ 0, 7, 10, 9, 0, 39, 11, 5, 0, 7, 14, 50 ]
], hecke_fields := [
x - 1,
x^2 - 5*x - 5,
x^7 + 2*x^6 - 7*x^5 - 15*x^4 + 6*x^3 + 22*x^2 + 9*x + 1,
x^19 - 30*x^17 + x^16 + 374*x^15 - 21*x^14 - 2509*x^13 + 166*x^12 + 9794*x^11 - 586*x^10 - 22435*x^9 + 749*x^8 + 28885*x^7 + 329*x^6 - 18752*x^5 - 878*x^4 + 4788*x^3 - 64*x^2 - 352*x + 32
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 173 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 173 ]
], torsion_upper_bounds := [ 1, 1, 1, 173 ], torsion_lower_bounds := [ 1, 1, 1, 173 ], l_ratios := [ 0, 0, 0, 1/173 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1 ], eigenvalues := [*
[ -2, 1, 0, -2, -3, -2, 4, -4, 4, -9, 8, -12 ],
[
1,
-1/3*a + 1/3,
2/3*a - 8/3,
-2,
1/3*a + 2/3,
-1/3*a - 8/3,
-2*a + 4,
-2/3*a + 14/3,
-2/3*a - 10/3,
a - 1,
7/3*a - 19/3,
2/3*a + 10/3
],
[
a,
-a^6 - 3*a^5 + 7*a^4 + 23*a^3 - 7*a^2 - 35*a - 8,
-a^6 - a^5 + 8*a^4 + 7*a^3 - 13*a^2 - 10*a - 1,
7*a^6 + 13*a^5 - 52*a^4 - 98*a^3 + 64*a^2 + 147*a + 31,
a^6 + a^5 - 8*a^4 - 7*a^3 + 14*a^2 + 8*a - 3,
-7*a^6 - 12*a^5 + 52*a^4 + 89*a^3 - 65*a^2 - 130*a - 30,
9*a^6 + 17*a^5 - 66*a^4 - 128*a^3 + 78*a^2 + 192*a + 41,
-9*a^6 - 15*a^5 + 68*a^4 + 113*a^3 - 89*a^2 - 171*a - 36,
-11*a^6 - 17*a^5 + 82*a^4 + 126*a^3 - 103*a^2 - 184*a - 40,
-9*a^6 - 16*a^5 + 66*a^4 + 120*a^3 - 79*a^2 - 181*a - 38,
-7*a^6 - 11*a^5 + 52*a^4 + 83*a^3 - 64*a^2 - 125*a - 30,
3*a^6 + 7*a^5 - 22*a^4 - 53*a^3 + 25*a^2 + 79*a + 13
],
[
a,
2368973/4704816*a^18 + 1050541/1176204*a^17 - 31607009/2352408*a^16 - 36697577/1568272*a^15 + 339797849/2352408*a^14 + 1165084067/4704816*a^13 - 3751578757/4704816*a^12 - 1061167243/784136*a^11 + 5581476023/2352408*a^10 + 3170767733/784136*a^9 - 16906363175/4704816*a^8 - 10048243833/1568272*a^7 + 10241331209/4704816*a^6 + 22186663277/4704816*a^5 - 7109191/98017*a^4 - 2643825137/2352408*a^3 - 39417161/1176204*a^2 + 13783403/196034*a - 855884/294051,
-980543/1176204*a^18 - 1785727/1176204*a^17 + 6561631/294051*a^16 + 15589663/392068*a^15 - 283700599/1176204*a^14 - 494801387/1176204*a^13 + 790733963/588102*a^12 + 901585957/392068*a^11 - 1199040037/294051*a^10 - 674954441/98017*a^9 + 7585353371/1176204*a^8 + 2155488049/196034*a^7 - 1318656575/294051*a^6 - 4877268607/588102*a^5 + 327508265/392068*a^4 + 1268626007/588102*a^3 - 77888231/588102*a^2 - 14544684/98017*a + 4691882/294051,
254717/392068*a^18 + 110486/98017*a^17 - 3410281/196034*a^16 - 11527033/392068*a^15 + 18437081/98017*a^14 + 121308673/392068*a^13 - 411259833/392068*a^12 - 329234001/196034*a^11 + 311975523/98017*a^10 + 976357683/196034*a^9 - 1974765875/392068*a^8 - 3073671159/392068*a^7 + 1370183785/392068*a^6 + 2261308991/392068*a^5 - 60115173/98017*a^4 - 137696806/98017*a^3 + 6349214/98017*a^2 + 8587867/98017*a - 682804/98017,
522269/4704816*a^18 + 671615/2352408*a^17 - 6584189/2352408*a^16 - 11725677/1568272*a^15 + 32694409/1176204*a^14 + 371742047/4704816*a^13 - 639471631/4704816*a^12 - 168802541/392068*a^11 + 764712737/2352408*a^10 + 1002908423/784136*a^9 - 1284114683/4704816*a^8 - 3135543555/1568272*a^7 - 968651485/4704816*a^6 + 6656149319/4704816*a^5 + 288043943/784136*a^4 - 676439837/2352408*a^3 - 30767191/588102*a^2 + 1105024/98017*a + 534685/294051,
642419/4704816*a^18 + 434591/2352408*a^17 - 8711789/2352408*a^16 - 7419763/1568272*a^15 + 24019073/588102*a^14 + 229515917/4704816*a^13 - 1107152677/4704816*a^12 - 101525541/392068*a^11 + 1781542433/2352408*a^10 + 588817265/784136*a^9 - 6350978021/4704816*a^8 - 1824770561/1568272*a^7 + 5887629269/4704816*a^6 + 4077327977/4704816*a^5 - 443678627/784136*a^4 - 559454345/2352408*a^3 + 42697672/294051*a^2 + 4280313/196034*a - 2624813/294051,
-1498825/784136*a^18 - 338257/98017*a^17 + 20033323/392068*a^16 + 70906555/784136*a^15 - 216116265/392068*a^14 - 750681383/784136*a^13 + 2402147597/784136*a^12 + 2053493701/392068*a^11 - 3624129799/392068*a^10 - 6154392763/392068*a^9 + 11350532611/784136*a^8 + 19657542371/784136*a^7 - 7681463365/784136*a^6 - 14785685709/784136*a^5 + 151360905/98017*a^4 + 1897351113/392068*a^3 - 39234841/196034*a^2 - 32586531/98017*a + 3020132/98017,
885827/2352408*a^18 + 645773/1176204*a^17 - 12083705/1176204*a^16 - 11100075/784136*a^15 + 67088227/588102*a^14 + 345952373/2352408*a^13 - 1556862025/2352408*a^12 - 77162807/98017*a^11 + 2515379201/1176204*a^10 + 903435069/392068*a^9 - 8900138933/2352408*a^8 - 2828110589/784136*a^7 + 7858218881/2352408*a^6 + 6390223949/2352408*a^5 - 484112597/392068*a^4 - 881852441/1176204*a^3 + 54226883/294051*a^2 + 5216536/98017*a - 2163100/294051,
1633939/2352408*a^18 + 1387231/1176204*a^17 - 22102117/1176204*a^16 - 24276151/784136*a^15 + 121167269/588102*a^14 + 773091889/2352408*a^13 - 2756723237/2352408*a^12 - 353929127/196034*a^11 + 4310944543/1176204*a^10 + 2136084749/392068*a^9 - 14389040821/2352408*a^8 - 6910605289/784136*a^7 + 11276922925/2352408*a^6 + 16048723549/2352408*a^5 - 523837543/392068*a^4 - 2238258211/1176204*a^3 + 53348137/294051*a^2 + 13933767/98017*a - 2191166/294051,
-103549/98017*a^18 - 1582691/784136*a^17 + 10993967/392068*a^16 + 20740781/392068*a^15 - 234989867/784136*a^14 - 54916076/98017*a^13 + 1288844691/784136*a^12 + 2405153509/784136*a^11 - 476214844/98017*a^10 - 3608361961/392068*a^9 + 2869994205/392068*a^8 + 11548481693/784136*a^7 - 3492293489/784136*a^6 - 8715714161/784136*a^5 + 184015687/784136*a^4 + 1126014055/392068*a^3 + 4623933/392068*a^2 - 19454680/98017*a + 1042728/98017,
-1381283/4704816*a^18 - 1049771/2352408*a^17 + 18742649/2352408*a^16 + 18129915/1568272*a^15 - 25803286/294051*a^14 - 568069157/4704816*a^13 + 2365173301/4704816*a^12 + 254992049/392068*a^11 - 3745660505/2352408*a^10 - 1504251917/784136*a^9 + 12813708581/4704816*a^8 + 4757379401/1568272*a^7 - 10612637621/4704816*a^6 - 10929534929/4704816*a^5 + 571544015/784136*a^4 + 1597943177/2352408*a^3 - 62284679/588102*a^2 - 14333625/196034*a + 2401052/294051,
-5198741/2352408*a^18 - 4467947/1176204*a^17 + 69848393/1176204*a^16 + 78016097/784136*a^15 - 189648692/294051*a^14 - 2476258475/2352408*a^13 + 8510674255/2352408*a^12 + 1127823451/196034*a^11 - 13025013023/1176204*a^10 - 6749660287/392068*a^9 + 41875368971/2352408*a^8 + 21510548411/784136*a^7 - 30292526291/2352408*a^6 - 48406564283/2352408*a^5 + 1118317889/392068*a^4 + 6203522903/1176204*a^3 - 140150756/294051*a^2 - 36708983/98017*a + 13391446/294051
]
*], q_expansions := [*
q - 2*q^2 + q^3 + 2*q^4 - 2*q^6 - 2*q^7 - 2*q^9 - 3*q^11 + 2*q^12 - 2*q^13 + 4*q^14 - 4*q^16 + 4*q^17 + 4*q^18 - 4*q^19 - 2*q^21 + 6*q^22 + 4*q^23 - 5*q^25 + 4*q^26 - 5*q^27 - 4*q^28 - 9*q^29 + 8*q^31 + 8*q^32 - 3*q^33 - 8*q^34 - 4*q^36 - 12*q^37 + O(q^38),
q + q^2 + (-1/3*a + 1/3)*q^3 - q^4 + (2/3*a - 8/3)*q^5 + (-1/3*a + 1/3)*q^6 - 2*q^7 - 3*q^8 + (1/3*a - 7/3)*q^9 + (2/3*a - 8/3)*q^10 + (1/3*a + 2/3)*q^11 + (1/3*a - 1/3)*q^12 + (-1/3*a - 8/3)*q^13 - 2*q^14 - 2*q^15 - q^16 + (-2*a + 4)*q^17 + (1/3*a - 7/3)*q^18 + (-2/3*a + 14/3)*q^19 + (-2/3*a + 8/3)*q^20 + (2/3*a - 2/3)*q^21 + (1/3*a + 2/3)*q^22 + (-2/3*a - 10/3)*q^23 + (a - 1)*q^24 + (-4/3*a + 13/3)*q^25 + (-1/3*a - 8/3)*q^26 + (4/3*a - 7/3)*q^27 + 2*q^28 + (a - 1)*q^29 - 2*q^30 + (7/3*a - 19/3)*q^31 + 5*q^32 + (-2/3*a - 1/3)*q^33 + (-2*a + 4)*q^34 + (-4/3*a + 16/3)*q^35 + (-1/3*a + 7/3)*q^36 + (2/3*a + 10/3)*q^37 + O(q^38),
q + a*q^2 + (-a^6 - 3*a^5 + 7*a^4 + 23*a^3 - 7*a^2 - 35*a - 8)*q^3 + (a^2 - 2)*q^4 + (-a^6 - a^5 + 8*a^4 + 7*a^3 - 13*a^2 - 10*a - 1)*q^5 + (-a^6 + 8*a^4 - a^3 - 13*a^2 + a + 1)*q^6 + (7*a^6 + 13*a^5 - 52*a^4 - 98*a^3 + 64*a^2 + 147*a + 31)*q^7 + (a^3 - 4*a)*q^8 + (a^5 - 7*a^3 + a^2 + 8*a)*q^9 + (a^6 + a^5 - 8*a^4 - 7*a^3 + 12*a^2 + 8*a + 1)*q^10 + (a^6 + a^5 - 8*a^4 - 7*a^3 + 14*a^2 + 8*a - 3)*q^11 + (4*a^6 + 7*a^5 - 30*a^4 - 53*a^3 + 37*a^2 + 80*a + 17)*q^12 + (-7*a^6 - 12*a^5 + 52*a^4 + 89*a^3 - 65*a^2 - 130*a - 30)*q^13 + (-a^6 - 3*a^5 + 7*a^4 + 22*a^3 - 7*a^2 - 32*a - 7)*q^14 + (-4*a^6 - 4*a^5 + 31*a^4 + 29*a^3 - 44*a^2 - 41*a - 7)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (9*a^6 + 17*a^5 - 66*a^4 - 128*a^3 + 78*a^2 + 192*a + 41)*q^17 + (a^6 - 7*a^4 + a^3 + 8*a^2)*q^18 + (-9*a^6 - 15*a^5 + 68*a^4 + 113*a^3 - 89*a^2 - 171*a - 36)*q^19 + (a^6 + a^5 - 8*a^4 - 8*a^3 + 12*a^2 + 12*a + 1)*q^20 + (-a^5 + 8*a^3 + 2*a^2 - 11*a - 7)*q^21 + (-a^6 - a^5 + 8*a^4 + 8*a^3 - 14*a^2 - 12*a - 1)*q^22 + (-11*a^6 - 17*a^5 + 82*a^4 + 126*a^3 - 103*a^2 - 184*a - 40)*q^23 + (a^6 - 2*a^5 - 9*a^4 + 15*a^3 + 18*a^2 - 21*a - 6)*q^24 + (3*a^6 + 2*a^5 - 24*a^4 - 13*a^3 + 39*a^2 + 17*a - 3)*q^25 + (2*a^6 + 3*a^5 - 16*a^4 - 23*a^3 + 24*a^2 + 33*a + 7)*q^26 + (12*a^6 + 18*a^5 - 90*a^4 - 136*a^3 + 115*a^2 + 209*a + 43)*q^27 + (-15*a^6 - 26*a^5 + 111*a^4 + 195*a^3 - 138*a^2 - 292*a - 61)*q^28 + (-9*a^6 - 16*a^5 + 66*a^4 + 120*a^3 - 79*a^2 - 181*a - 38)*q^29 + (4*a^6 + 3*a^5 - 31*a^4 - 20*a^3 + 47*a^2 + 29*a + 4)*q^30 + (-7*a^6 - 11*a^5 + 52*a^4 + 83*a^3 - 64*a^2 - 125*a - 30)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (12*a^6 + 17*a^5 - 91*a^4 - 126*a^3 + 121*a^2 + 189*a + 38)*q^33 + (-a^6 - 3*a^5 + 7*a^4 + 24*a^3 - 6*a^2 - 40*a - 9)*q^34 + (6*a^6 + 9*a^5 - 45*a^4 - 66*a^3 + 59*a^2 + 97*a + 19)*q^35 + (-2*a^6 - 2*a^5 + 16*a^4 + 16*a^3 - 24*a^2 - 25*a - 1)*q^36 + (3*a^6 + 7*a^5 - 22*a^4 - 53*a^3 + 25*a^2 + 79*a + 13)*q^37 + O(q^38),
q + a*q^2 + (2368973/4704816*a^18 + 1050541/1176204*a^17 - 31607009/2352408*a^16 - 36697577/1568272*a^15 + 339797849/2352408*a^14 + 1165084067/4704816*a^13 - 3751578757/4704816*a^12 - 1061167243/784136*a^11 + 5581476023/2352408*a^10 + 3170767733/784136*a^9 - 16906363175/4704816*a^8 - 10048243833/1568272*a^7 + 10241331209/4704816*a^6 + 22186663277/4704816*a^5 - 7109191/98017*a^4 - 2643825137/2352408*a^3 - 39417161/1176204*a^2 + 13783403/196034*a - 855884/294051)*q^3 + (a^2 - 2)*q^4 + (-980543/1176204*a^18 - 1785727/1176204*a^17 + 6561631/294051*a^16 + 15589663/392068*a^15 - 283700599/1176204*a^14 - 494801387/1176204*a^13 + 790733963/588102*a^12 + 901585957/392068*a^11 - 1199040037/294051*a^10 - 674954441/98017*a^9 + 7585353371/1176204*a^8 + 2155488049/196034*a^7 - 1318656575/294051*a^6 - 4877268607/588102*a^5 + 327508265/392068*a^4 + 1268626007/588102*a^3 - 77888231/588102*a^2 - 14544684/98017*a + 4691882/294051)*q^5 + (1050541/1176204*a^18 + 1963793/1176204*a^17 - 14057713/588102*a^16 - 17200017/392068*a^15 + 303708125/1176204*a^14 + 548043625/1176204*a^13 - 422515811/294051*a^12 - 1003230793/392068*a^11 + 1275801536/294051*a^10 + 755032210/98017*a^9 - 7979773069/1176204*a^8 - 2424435579/196034*a^7 + 2675908895/588102*a^6 + 2755108783/294051*a^5 - 267307665/392068*a^4 - 1437538921/588102*a^3 + 60301993/588102*a^2 + 17087174/98017*a - 4737946/294051)*q^6 + (254717/392068*a^18 + 110486/98017*a^17 - 3410281/196034*a^16 - 11527033/392068*a^15 + 18437081/98017*a^14 + 121308673/392068*a^13 - 411259833/392068*a^12 - 329234001/196034*a^11 + 311975523/98017*a^10 + 976357683/196034*a^9 - 1974765875/392068*a^8 - 3073671159/392068*a^7 + 1370183785/392068*a^6 + 2261308991/392068*a^5 - 60115173/98017*a^4 - 137696806/98017*a^3 + 6349214/98017*a^2 + 8587867/98017*a - 682804/98017)*q^7 + (a^3 - 4*a)*q^8 + (189277/2352408*a^18 + 21952/294051*a^17 - 1291487/588102*a^16 - 1504961/784136*a^15 + 28612399/1176204*a^14 + 47038261/2352408*a^13 - 330007517/2352408*a^12 - 10623638/98017*a^11 + 131848978/294051*a^10 + 128308163/392068*a^9 - 1830843091/2352408*a^8 - 430859777/784136*a^7 + 1550203843/2352408*a^6 + 1139927455/2352408*a^5 - 79777799/392068*a^4 - 114867929/588102*a^3 + 489083/588102*a^2 + 5196691/196034*a + 675919/294051)*q^9 + (-1785727/1176204*a^18 - 1584883/588102*a^17 + 11937383/294051*a^16 + 27674161/392068*a^15 - 257696395/588102*a^14 - 878714461/1176204*a^13 + 2867528009/1176204*a^12 + 801212999/196034*a^11 - 4337025745/588102*a^10 - 2402188139/196034*a^9 + 13667355001/1176204*a^8 + 7682786085/392068*a^7 - 9431938567/1176204*a^6 - 17404617541/1176204*a^5 + 139694605/98017*a^4 + 2269531711/588102*a^3 - 59322740/294051*a^2 - 27198634/98017*a + 7844344/294051)*q^10 + (522269/4704816*a^18 + 671615/2352408*a^17 - 6584189/2352408*a^16 - 11725677/1568272*a^15 + 32694409/1176204*a^14 + 371742047/4704816*a^13 - 639471631/4704816*a^12 - 168802541/392068*a^11 + 764712737/2352408*a^10 + 1002908423/784136*a^9 - 1284114683/4704816*a^8 - 3135543555/1568272*a^7 - 968651485/4704816*a^6 + 6656149319/4704816*a^5 + 288043943/784136*a^4 - 676439837/2352408*a^3 - 30767191/588102*a^2 + 1105024/98017*a + 534685/294051)*q^11 + (1558613/2352408*a^18 + 649861/588102*a^17 - 21043583/1176204*a^16 - 22765229/784136*a^15 + 230307137/1176204*a^14 + 726404183/2352408*a^13 - 2616585613/2352408*a^12 - 667430227/392068*a^11 + 4094527523/1176204*a^10 + 2025603689/392068*a^9 - 13760574191/2352408*a^8 - 6613795497/784136*a^7 + 11108283077/2352408*a^6 + 15608980397/2352408*a^5 - 148506855/98017*a^4 - 2265561185/1176204*a^3 + 175557517/588102*a^2 + 15453151/98017*a - 6692560/294051)*q^12 + (642419/4704816*a^18 + 434591/2352408*a^17 - 8711789/2352408*a^16 - 7419763/1568272*a^15 + 24019073/588102*a^14 + 229515917/4704816*a^13 - 1107152677/4704816*a^12 - 101525541/392068*a^11 + 1781542433/2352408*a^10 + 588817265/784136*a^9 - 6350978021/4704816*a^8 - 1824770561/1568272*a^7 + 5887629269/4704816*a^6 + 4077327977/4704816*a^5 - 443678627/784136*a^4 - 559454345/2352408*a^3 + 42697672/294051*a^2 + 4280313/196034*a - 2624813/294051)*q^13 + (110486/98017*a^18 + 205237/98017*a^17 - 5890875/196034*a^16 - 10757917/196034*a^15 + 63328865/196034*a^14 + 56956280/98017*a^13 - 175187756/98017*a^12 - 623398103/196034*a^11 + 525494882/98017*a^10 + 934952505/98017*a^9 - 816113548/98017*a^8 - 1496829190/98017*a^7 + 1088753549/196034*a^6 + 1133998123/98017*a^5 - 163572849/196034*a^4 - 298547035/98017*a^3 + 12663339/98017*a^2 + 21732292/98017*a - 2037736/98017)*q^14 + (-2746715/1176204*a^18 - 4786099/1176204*a^17 + 36908357/588102*a^16 + 41788957/392068*a^15 - 802092829/1176204*a^14 - 1326727187/1176204*a^13 + 2252324789/588102*a^12 + 2418741747/392068*a^11 - 3455705497/294051*a^10 - 1812644212/98017*a^9 + 22341864815/1176204*a^8 + 5802652713/196034*a^7 - 8191213567/588102*a^6 - 13217075509/588102*a^5 + 1263400635/392068*a^4 + 3524270795/588102*a^3 - 301770695/588102*a^2 - 43933130/98017*a + 14552384/294051)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1498825/784136*a^18 - 338257/98017*a^17 + 20033323/392068*a^16 + 70906555/784136*a^15 - 216116265/392068*a^14 - 750681383/784136*a^13 + 2402147597/784136*a^12 + 2053493701/392068*a^11 - 3624129799/392068*a^10 - 6154392763/392068*a^9 + 11350532611/784136*a^8 + 19657542371/784136*a^7 - 7681463365/784136*a^6 - 14785685709/784136*a^5 + 151360905/98017*a^4 + 1897351113/392068*a^3 - 39234841/196034*a^2 - 32586531/98017*a + 3020132/98017)*q^17 + (21952/294051*a^18 + 256181/1176204*a^17 - 588020/294051*a^16 - 565200/98017*a^15 + 25506539/1176204*a^14 + 36222119/588102*a^13 - 143193647/1176204*a^12 - 133164519/392068*a^11 + 220191325/588102*a^10 + 201298867/196034*a^9 - 358586951/588102*a^8 - 652843717/392068*a^7 + 538827661/1176204*a^6 + 1535327755/1176204*a^5 - 48881085/392068*a^4 - 113037743/294051*a^3 + 18618505/588102*a^2 + 3001369/98017*a - 757108/294051)*q^18 + (885827/2352408*a^18 + 645773/1176204*a^17 - 12083705/1176204*a^16 - 11100075/784136*a^15 + 67088227/588102*a^14 + 345952373/2352408*a^13 - 1556862025/2352408*a^12 - 77162807/98017*a^11 + 2515379201/1176204*a^10 + 903435069/392068*a^9 - 8900138933/2352408*a^8 - 2828110589/784136*a^7 + 7858218881/2352408*a^6 + 6390223949/2352408*a^5 - 484112597/392068*a^4 - 881852441/1176204*a^3 + 54226883/294051*a^2 + 5216536/98017*a - 2163100/294051)*q^19 + (-302170/294051*a^18 - 562706/294051*a^17 + 16157581/588102*a^16 + 9821855/196034*a^15 - 174406765/588102*a^14 - 155814565/294051*a^13 + 485193206/294051*a^12 + 567640501/196034*a^11 - 1466811140/294051*a^10 - 849710305/98017*a^9 + 2303790259/294051*a^8 + 1356910770/98017*a^7 - 3133930379/588102*a^6 - 3075135754/294051*a^5 + 167690921/196034*a^4 + 809566472/294051*a^3 - 32279303/294051*a^2 - 20677176/98017*a + 4902052/294051)*q^20 + (4564103/1176204*a^18 + 8228713/1176204*a^17 - 30565609/294051*a^16 - 71965089/392068*a^15 + 1322429599/1176204*a^14 + 2289058193/1176204*a^13 - 1843817644/294051*a^12 - 4181992695/392068*a^11 + 11183942351/588102*a^10 + 3140943604/98017*a^9 - 35335595891/1176204*a^8 - 5035611077/98017*a^7 + 12216736951/588102*a^6 + 22915088665/588102*a^5 - 1451718595/392068*a^4 - 3020804743/294051*a^3 + 318770897/588102*a^2 + 73704080/98017*a - 20177318/294051)*q^21 + (671615/2352408*a^18 + 624923/1176204*a^17 - 8924825/1176204*a^16 - 10758495/784136*a^15 + 23919356/294051*a^14 + 335450645/2352408*a^13 - 1056163573/2352408*a^12 - 149403213/196034*a^11 + 1580875043/1176204*a^10 + 869415861/392068*a^9 - 4898905073/2352408*a^8 - 2675731925/784136*a^7 + 3242161409/2352408*a^6 + 5760925973/2352408*a^5 - 74527291/392068*a^4 - 686690375/1176204*a^3 + 5404148/294051*a^2 + 4008201/98017*a - 1044538/294051)*q^22 + (1633939/2352408*a^18 + 1387231/1176204*a^17 - 22102117/1176204*a^16 - 24276151/784136*a^15 + 121167269/588102*a^14 + 773091889/2352408*a^13 - 2756723237/2352408*a^12 - 353929127/196034*a^11 + 4310944543/1176204*a^10 + 2136084749/392068*a^9 - 14389040821/2352408*a^8 - 6910605289/784136*a^7 + 11276922925/2352408*a^6 + 16048723549/2352408*a^5 - 523837543/392068*a^4 - 2238258211/1176204*a^3 + 53348137/294051*a^2 + 13933767/98017*a - 2191166/294051)*q^23 + (-66780/98017*a^18 - 265329/196034*a^17 + 3550617/196034*a^16 + 3503884/98017*a^15 - 37974787/196034*a^14 - 37425004/98017*a^13 + 104039244/98017*a^12 + 206782035/98017*a^11 - 306077301/98017*a^10 - 626443234/98017*a^9 + 454596027/98017*a^8 + 2022850039/196034*a^7 - 262961435/98017*a^6 - 767449753/98017*a^5 + 1876326/98017*a^4 + 197495933/98017*a^3 - 491212/98017*a^2 - 13545544/98017*a + 1080480/98017)*q^24 + (745457/1176204*a^18 + 338326/294051*a^17 - 10007741/588102*a^16 - 11889149/392068*a^15 + 108523577/588102*a^14 + 380113055/1176204*a^13 - 1214141509/1176204*a^12 - 349255909/196034*a^11 + 1848751319/588102*a^10 + 1056216163/196034*a^9 - 5883964235/1176204*a^8 - 3411225605/392068*a^7 + 4148394833/1176204*a^6 + 7814854985/1176204*a^5 - 68700261/98017*a^4 - 1033021763/588102*a^3 + 36768148/294051*a^2 + 11986540/98017*a - 4221551/294051)*q^25 + (434591/2352408*a^18 + 115562/294051*a^17 - 5725427/1176204*a^16 - 8018687/784136*a^15 + 60751679/1176204*a^14 + 252338297/2352408*a^13 - 662474023/2352408*a^12 - 227397235/392068*a^11 + 977340281/1176204*a^10 + 671807687/392068*a^9 - 2977741757/2352408*a^8 - 2111440591/784136*a^7 + 1932986063/2352408*a^6 + 4692284663/2352408*a^5 - 23119367/196034*a^4 - 598184855/1176204*a^3 + 17980291/588102*a^2 + 3836135/98017*a - 1284838/294051)*q^26 + (843367/1176204*a^18 + 3112927/2352408*a^17 - 22453307/1176204*a^16 - 6811169/196034*a^15 + 481151659/2352408*a^14 + 433488007/1176204*a^13 - 2642437393/2352408*a^12 - 1583463303/784136*a^11 + 974569193/294051*a^10 + 2373706243/392068*a^9 - 2904261203/588102*a^8 - 7560839177/784136*a^7 + 6699216935/2352408*a^6 + 16852638191/2352408*a^5 + 45021083/784136*a^4 - 2055851471/1176204*a^3 - 94988395/1176204*a^2 + 9978199/98017*a - 811747/294051)*q^27 + (155757/196034*a^18 + 296341/196034*a^17 - 4158327/196034*a^16 - 3893815/98017*a^15 + 22402324/98017*a^14 + 82734563/196034*a^13 - 124409811/98017*a^12 - 227371001/98017*a^11 + 375746255/98017*a^10 + 686282179/98017*a^9 - 1184400533/196034*a^8 - 1110175756/98017*a^7 + 825112673/196034*a^6 + 859392552/98017*a^5 - 81309981/98017*a^4 - 240950017/98017*a^3 + 16104968/98017*a^2 + 19677602/98017*a - 2169944/98017)*q^28 + (-103549/98017*a^18 - 1582691/784136*a^17 + 10993967/392068*a^16 + 20740781/392068*a^15 - 234989867/784136*a^14 - 54916076/98017*a^13 + 1288844691/784136*a^12 + 2405153509/784136*a^11 - 476214844/98017*a^10 - 3608361961/392068*a^9 + 2869994205/392068*a^8 + 11548481693/784136*a^7 - 3492293489/784136*a^6 - 8715714161/784136*a^5 + 184015687/784136*a^4 + 1126014055/392068*a^3 + 4623933/392068*a^2 - 19454680/98017*a + 1042728/98017)*q^29 + (-4786099/1176204*a^18 - 2146184/294051*a^17 + 64056793/588102*a^16 + 75059527/392068*a^15 - 692204101/588102*a^14 - 2386858357/1176204*a^13 + 7712179931/1176204*a^12 + 2179750787/196034*a^11 - 11680652767/588102*a^10 - 6546781035/196034*a^9 + 36873205813/1176204*a^8 + 20985478547/392068*a^7 - 25530481783/1176204*a^6 - 47716197775/1176204*a^5 + 386410485/98017*a^4 + 6273865015/588102*a^3 - 175746830/294051*a^2 - 75719512/98017*a + 21973720/294051)*q^30 + (-1381283/4704816*a^18 - 1049771/2352408*a^17 + 18742649/2352408*a^16 + 18129915/1568272*a^15 - 25803286/294051*a^14 - 568069157/4704816*a^13 + 2365173301/4704816*a^12 + 254992049/392068*a^11 - 3745660505/2352408*a^10 - 1504251917/784136*a^9 + 12813708581/4704816*a^8 + 4757379401/1568272*a^7 - 10612637621/4704816*a^6 - 10929534929/4704816*a^5 + 571544015/784136*a^4 + 1597943177/2352408*a^3 - 62284679/588102*a^2 - 14333625/196034*a + 2401052/294051)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (4564787/2352408*a^18 + 4277081/1176204*a^17 - 30459331/588102*a^16 - 74866343/784136*a^15 + 163942103/294051*a^14 + 2383322363/2352408*a^13 - 7265311585/2352408*a^12 - 2179097809/392068*a^11 + 2725495739/294051*a^10 + 6552075641/392068*a^9 - 33785054753/2352408*a^8 - 21012190929/784136*a^7 + 22236219335/2352408*a^6 + 47691481031/2352408*a^5 - 248422573/196034*a^4 - 1554494912/294051*a^3 + 102992665/588102*a^2 + 75765157/196034*a - 8796535/294051)*q^33 + (-338257/98017*a^18 - 612263/98017*a^17 + 18101345/196034*a^16 + 32082005/196034*a^15 - 195539177/196034*a^14 - 169800541/98017*a^13 + 544474044/98017*a^12 + 1857808113/196034*a^11 - 1648387122/98017*a^10 - 2784450783/98017*a^9 + 2597520287/98017*a^8 + 4451512095/98017*a^7 - 3573143071/196034*a^6 - 3361884895/98017*a^5 + 619683469/196034*a^4 + 877429342/98017*a^3 - 44577131/98017*a^2 - 62928168/98017*a + 5995300/98017)*q^34 + (-519359/1176204*a^18 - 308195/588102*a^17 + 7127369/588102*a^16 + 5313511/392068*a^15 - 39780817/294051*a^14 - 166229165/1176204*a^13 + 927039253/1176204*a^12 + 74413368/98017*a^11 - 1501716551/588102*a^10 - 435919521/196034*a^9 + 5317926545/1176204*a^8 + 1352316205/392068*a^7 - 4699457537/1176204*a^6 - 2937976409/1176204*a^5 + 292540229/196034*a^4 + 352152359/588102*a^3 - 67105906/294051*a^2 - 3070678/98017*a + 2004776/294051)*q^35 + (16726/294051*a^18 + 26636/294051*a^17 - 426065/294051*a^16 - 469795/196034*a^15 + 4265852/294051*a^14 + 7519591/294051*a^13 - 21015542/294051*a^12 - 27440265/196034*a^11 + 102228433/588102*a^10 + 40245800/98017*a^9 - 48364063/294051*a^8 - 58743924/98017*a^7 - 10941230/294051*a^6 + 180002453/588102*a^5 + 17268541/196034*a^4 + 38142011/588102*a^3 + 9919952/294051*a^2 - 2873359/98017*a - 2054302/294051)*q^36 + (-5198741/2352408*a^18 - 4467947/1176204*a^17 + 69848393/1176204*a^16 + 78016097/784136*a^15 - 189648692/294051*a^14 - 2476258475/2352408*a^13 + 8510674255/2352408*a^12 + 1127823451/196034*a^11 - 13025013023/1176204*a^10 - 6749660287/392068*a^9 + 41875368971/2352408*a^8 + 21510548411/784136*a^7 - 30292526291/2352408*a^6 - 48406564283/2352408*a^5 + 1118317889/392068*a^4 + 6203522903/1176204*a^3 - 140150756/294051*a^2 - 36708983/98017*a + 13391446/294051)*q^37 + O(q^38)
*]> ;  // time = 7.7 seconds




J[349] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 349, 349 ], new_dimensions := [ 11, 17 ], dimensions := [ 11, 17 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -5, -6, -9, -3, -31, -4, -1, -17, -24, -17, -10, -1 ],
[ 5, 6, 5, 1, 39, -6, 1, 7, 8, 9, -2, -7 ]
], hecke_fields := [
x^11 + 5*x^10 - x^9 - 35*x^8 - 24*x^7 + 80*x^6 + 66*x^5 - 77*x^4 - 56*x^3 + 31*x^2 + 15*x - 4,
x^17 - 5*x^16 - 14*x^15 + 102*x^14 + 26*x^13 - 792*x^12 + 474*x^11 + 2887*x^10 - 3021*x^9 - 4835*x^8 + 6673*x^7 + 2880*x^6 - 5373*x^5 - 164*x^4 + 1075*x^3 + 75*x^2 - 41*x - 4
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 29 ]
], tamagawa_numbers := [
[ 1 ],
[ 29 ]
], torsion_upper_bounds := [ 1, 29 ], torsion_lower_bounds := [ 1, 29 ], l_ratios := [ 0, 1/29 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-3/2*a^10 - 13/2*a^9 + 5*a^8 + 91/2*a^7 + 7*a^6 - 205/2*a^5 - 35/2*a^4 + 181/2*a^3 - 11/2*a^2 - 51/2*a + 7,
1/2*a^9 + 3*a^8 + 2*a^7 - 33/2*a^6 - 49/2*a^5 + 22*a^4 + 87/2*a^3 - 7*a^2 - 39/2*a,
5/2*a^10 + 21/2*a^9 - 11*a^8 - 159/2*a^7 + 2*a^6 + 401/2*a^5 + 27/2*a^4 - 399/2*a^3 + 27/2*a^2 + 125/2*a - 14,
-2*a^10 - 9*a^9 + 6*a^8 + 64*a^7 + 15*a^6 - 148*a^5 - 39*a^4 + 135*a^3 + 10*a^2 - 40*a + 2,
1/2*a^10 + 3*a^9 + 3*a^8 - 29/2*a^7 - 65/2*a^6 + 10*a^5 + 133/2*a^4 + 11*a^3 - 93/2*a^2 - 5*a + 8,
1/2*a^10 + a^9 - 7*a^8 - 27/2*a^7 + 61/2*a^6 + 53*a^5 - 99/2*a^4 - 66*a^3 + 53/2*a^2 + 19*a - 3,
-7/2*a^9 - 18*a^8 + 229/2*a^6 + 183/2*a^5 - 217*a^4 - 369/2*a^3 + 149*a^2 + 169/2*a - 31,
-5/2*a^10 - 12*a^9 + 3*a^8 + 157/2*a^7 + 95/2*a^6 - 157*a^5 - 207/2*a^4 + 118*a^3 + 97/2*a^2 - 26*a - 3,
5/2*a^9 + 12*a^8 - a^7 - 145/2*a^6 - 115/2*a^5 + 123*a^4 + 227/2*a^3 - 73*a^2 - 95/2*a + 13,
a^10 + 6*a^9 + 4*a^8 - 36*a^7 - 58*a^6 + 57*a^5 + 135*a^4 - 19*a^3 - 97*a^2 - 6*a + 15,
5*a^10 + 20*a^9 - 27*a^8 - 158*a^7 + 40*a^6 + 427*a^5 - 54*a^4 - 467*a^3 + 88*a^2 + 164*a - 37
],
[
a,
715008/3463583*a^16 - 3971843/3463583*a^15 - 16588569/6927166*a^14 + 158865051/6927166*a^13 - 16523199/3463583*a^12 - 1193366371/6927166*a^11 + 1225665635/6927166*a^10 + 2040760680/3463583*a^9 - 6331983519/6927166*a^8 - 2910324614/3463583*a^7 + 12956859425/6927166*a^6 + 677682467/3463583*a^5 - 9771397341/6927166*a^4 + 1891397865/6927166*a^3 + 1628902717/6927166*a^2 - 173708857/6927166*a - 26729619/3463583,
954477/13854332*a^16 - 3024095/6927166*a^15 - 4718181/6927166*a^14 + 61112781/6927166*a^13 - 14161207/3463583*a^12 - 233310948/3463583*a^11 + 551154783/6927166*a^10 + 3290717187/13854332*a^9 - 2682361823/6927166*a^8 - 5084510469/13854332*a^7 + 2729699073/3463583*a^6 + 1087579147/6927166*a^5 - 8563127797/13854332*a^4 + 550576315/13854332*a^3 + 869328429/6927166*a^2 + 84175177/13854332*a - 15215169/3463583,
2905513/6927166*a^16 - 27261015/13854332*a^15 - 86394221/13854332*a^14 + 554333223/13854332*a^13 + 258068317/13854332*a^12 - 4278239417/13854332*a^11 + 1871113733/13854332*a^10 + 15393324859/13854332*a^9 - 6994671029/6927166*a^8 - 12444132529/6927166*a^7 + 31554547335/13854332*a^6 + 12622965207/13854332*a^5 - 24549976441/13854332*a^4 + 466327327/3463583*a^3 + 4093560537/13854332*a^2 - 260015547/13854332*a - 28163165/3463583,
1694339/13854332*a^16 - 6118499/13854332*a^15 - 31509881/13854332*a^14 + 126344463/13854332*a^13 + 207627961/13854332*a^12 - 999938265/13854332*a^11 - 523641917/13854332*a^10 + 941303368/3463583*a^9 + 19400320/3463583*a^8 - 6714025959/13854332*a^7 + 1333064643/13854332*a^6 + 4674545327/13854332*a^5 - 193589442/3463583*a^4 - 580301749/13854332*a^3 - 446523973/13854332*a^2 - 3306351/6927166*a + 17995286/3463583,
-307079/6927166*a^16 + 1424408/3463583*a^15 - 1232279/6927166*a^14 - 26858856/3463583*a^13 + 53251971/3463583*a^12 + 361410325/6927166*a^11 - 526373679/3463583*a^10 - 945585989/6927166*a^9 + 4338299075/6927166*a^8 + 95570172/3463583*a^7 - 4039539605/3463583*a^6 + 1360511433/3463583*a^5 + 2862527382/3463583*a^4 - 2663083419/6927166*a^3 - 763538811/6927166*a^2 + 225157233/6927166*a + 6941920/3463583,
2698673/6927166*a^16 - 28026303/13854332*a^15 - 70719525/13854332*a^14 + 566848915/13854332*a^13 + 41370511/13854332*a^12 - 4340118953/13854332*a^11 + 3328381171/13854332*a^10 + 15411437581/13854332*a^9 - 4780564465/3463583*a^8 - 6063387545/3463583*a^7 + 40761786819/13854332*a^6 + 11134012511/13854332*a^5 - 31818363241/13854332*a^4 + 661217942/3463583*a^3 + 5784664491/13854332*a^2 - 242863527/13854332*a - 37906728/3463583,
1722393/6927166*a^16 - 5062420/3463583*a^15 - 9056650/3463583*a^14 + 202075449/6927166*a^13 - 39350519/3463583*a^12 - 756500511/3463583*a^11 + 1787578417/6927166*a^10 + 5145409169/6927166*a^9 - 4406909975/3463583*a^8 - 3625533762/3463583*a^7 + 17740728377/6927166*a^6 + 788880719/3463583*a^5 - 13201772377/6927166*a^4 + 1149770855/3463583*a^3 + 1002861002/3463583*a^2 - 60560322/3463583*a - 13432199/3463583,
156980/3463583*a^16 + 98840/3463583*a^15 - 10910929/6927166*a^14 + 179770/3463583*a^13 + 70797455/3463583*a^12 - 58578045/6927166*a^11 - 446773604/3463583*a^10 + 293662381/3463583*a^9 + 2887694239/6927166*a^8 - 2389701929/6927166*a^7 - 2214032209/3463583*a^6 + 2149811799/3463583*a^5 + 2269192643/6927166*a^4 - 1395873813/3463583*a^3 + 276497241/6927166*a^2 + 119625054/3463583*a - 17507217/3463583,
1673905/6927166*a^16 - 20021703/13854332*a^15 - 34790195/13854332*a^14 + 400465941/13854332*a^13 - 162675785/13854332*a^12 - 3005182683/13854332*a^11 + 3567509397/13854332*a^10 + 10233474217/13854332*a^9 - 8801373433/6927166*a^8 - 3581659405/3463583*a^7 + 35818086437/13854332*a^6 + 2481613975/13854332*a^5 - 27659653187/13854332*a^4 + 2917526599/6927166*a^3 + 5154324181/13854332*a^2 - 876661761/13854332*a - 45978824/3463583,
-147529/3463583*a^16 - 637205/6927166*a^15 + 10695599/6927166*a^14 + 11943727/6927166*a^13 - 144759819/6927166*a^12 - 80093589/6927166*a^11 + 965194573/6927166*a^10 + 216690843/6927166*a^9 - 1702731057/3463583*a^8 - 68268776/3463583*a^7 + 6195175011/6927166*a^6 - 198161953/6927166*a^5 - 5075046499/6927166*a^4 - 30972968/3463583*a^3 + 1310289645/6927166*a^2 + 217300797/6927166*a - 15699373/3463583,
-6279271/13854332*a^16 + 35105987/13854332*a^15 + 73144699/13854332*a^14 - 703433505/13854332*a^13 + 137265359/13854332*a^12 + 5300866217/13854332*a^11 - 5301014985/13854332*a^10 - 9123276643/6927166*a^9 + 6843001421/3463583*a^8 + 26518624041/13854332*a^7 - 55608358727/13854332*a^6 - 7524469695/13854332*a^5 + 20408629339/6927166*a^4 - 7005914249/13854332*a^3 - 5619508281/13854332*a^2 + 189779269/6927166*a + 11877959/3463583
]
*], q_expansions := [*
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46497940699/13854332*a^6 - 15421947665/13854332*a^5 + 9010847602/3463583*a^4 - 2144598935/13854332*a^3 - 6392923987/13854332*a^2 + 146057591/6927166*a + 55242131/3463583)*q^25 + (1313421/6927166*a^16 - 5531385/6927166*a^15 - 11197827/3463583*a^14 + 57243998/3463583*a^13 + 118203757/6927166*a^12 - 453595956/3463583*a^11 - 29524458/3463583*a^10 + 1705306708/3463583*a^9 - 1293586621/6927166*a^8 - 6029941043/6927166*a^7 + 1802705193/3463583*a^6 + 4075119297/6927166*a^5 - 2713444375/6927166*a^4 - 216714443/3463583*a^3 + 124094079/3463583*a^2 + 1293601/6927166*a - 614158/3463583)*q^26 + (547063/6927166*a^16 - 2895974/3463583*a^15 + 3189319/6927166*a^14 + 114160211/6927166*a^13 - 106211839/3463583*a^12 - 837427529/6927166*a^11 + 2082399623/6927166*a^10 + 2738512187/6927166*a^9 - 8687004369/6927166*a^8 - 3470480999/6927166*a^7 + 16744861955/6927166*a^6 - 22128185/3463583*a^5 - 6528474313/3463583*a^4 + 826042130/3463583*a^3 + 2682557887/6927166*a^2 - 29815098/3463583*a - 36194395/3463583)*q^27 + (-3845667/6927166*a^16 + 41248211/13854332*a^15 + 96770353/13854332*a^14 - 831220261/13854332*a^13 + 21489855/13854332*a^12 + 6322961121/13854332*a^11 - 5356069983/13854332*a^10 - 22158582651/13854332*a^9 + 14715400489/6927166*a^8 + 8422902762/3463583*a^7 - 61603479613/13854332*a^6 - 12787832947/13854332*a^5 + 47240895329/13854332*a^4 - 3177567369/6927166*a^3 - 8196080293/13854332*a^2 + 616833913/13854332*a + 58120445/3463583)*q^28 + (1673905/6927166*a^16 - 20021703/13854332*a^15 - 34790195/13854332*a^14 + 400465941/13854332*a^13 - 162675785/13854332*a^12 - 3005182683/13854332*a^11 + 3567509397/13854332*a^10 + 10233474217/13854332*a^9 - 8801373433/6927166*a^8 - 3581659405/3463583*a^7 + 35818086437/13854332*a^6 + 2481613975/13854332*a^5 - 27659653187/13854332*a^4 + 2917526599/6927166*a^3 + 5154324181/13854332*a^2 - 876661761/13854332*a - 45978824/3463583)*q^29 + (-385625/3463583*a^16 + 1113141/6927166*a^15 + 19349009/6927166*a^14 - 12684177/3463583*a^13 - 196819349/6927166*a^12 + 231577079/6927166*a^11 + 519313732/3463583*a^10 - 1077992377/6927166*a^9 - 1503943407/3463583*a^8 + 2680160367/6927166*a^7 + 2303351691/3463583*a^6 - 3346668351/6927166*a^5 - 3200511213/6927166*a^4 + 1653737621/6927166*a^3 + 649387987/6927166*a^2 - 53553963/3463583*a - 12229852/3463583)*q^30 + (-147529/3463583*a^16 - 637205/6927166*a^15 + 10695599/6927166*a^14 + 11943727/6927166*a^13 - 144759819/6927166*a^12 - 80093589/6927166*a^11 + 965194573/6927166*a^10 + 216690843/6927166*a^9 - 1702731057/3463583*a^8 - 68268776/3463583*a^7 + 6195175011/6927166*a^6 - 198161953/6927166*a^5 - 5075046499/6927166*a^4 - 30972968/3463583*a^3 + 1310289645/6927166*a^2 + 217300797/6927166*a - 15699373/3463583)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (8102349/6927166*a^16 - 20588041/3463583*a^15 - 108827237/6927166*a^14 + 415715848/3463583*a^13 + 59764596/3463583*a^12 - 6346223805/6927166*a^11 + 2256560089/3463583*a^10 + 22384167811/6927166*a^9 - 26701234777/6927166*a^8 - 17282861197/3463583*a^7 + 28481115024/3463583*a^6 + 7112107119/3463583*a^5 - 21803614831/3463583*a^4 + 5600046787/6927166*a^3 + 7256026981/6927166*a^2 - 605360155/6927166*a - 116193166/3463583)*q^33 + (-1039573/13854332*a^16 + 4843319/13854332*a^15 + 16319623/13854332*a^14 - 98960485/13854332*a^13 - 65420921/13854332*a^12 + 770039167/13854332*a^11 - 170700321/13854332*a^10 - 1408437797/6927166*a^9 + 921308865/6927166*a^8 + 4745296961/13854332*a^7 - 4410343969/13854332*a^6 - 2818423183/13854332*a^5 + 882509128/3463583*a^4 - 17482459/13854332*a^3 - 647664477/13854332*a^2 + 34832137/6927166*a + 5397346/3463583)*q^34 + (-4955897/6927166*a^16 + 53522659/13854332*a^15 + 123431877/13854332*a^14 - 1079528765/13854332*a^13 + 56383651/13854332*a^12 + 8223969505/13854332*a^11 - 7152276383/13854332*a^10 - 28905093419/13854332*a^9 + 19488055831/6927166*a^8 + 11075708641/3463583*a^7 - 81508528657/13854332*a^6 - 17713157335/13854332*a^5 + 62627795385/13854332*a^4 - 3685860561/6927166*a^3 - 10898521001/13854332*a^2 + 743797797/13854332*a + 87207433/3463583)*q^35 + (1173981/6927166*a^16 - 3407501/6927166*a^15 - 24157873/6927166*a^14 + 36436494/3463583*a^13 + 188407685/6927166*a^12 - 610046509/6927166*a^11 - 338306606/3463583*a^10 + 1263999272/3463583*a^9 + 504170683/3463583*a^8 - 2699823840/3463583*a^7 - 19966918/3463583*a^6 + 5618660441/6927166*a^5 - 578050196/3463583*a^4 - 1210511595/3463583*a^3 + 749073807/6927166*a^2 + 236260979/6927166*a - 27294414/3463583)*q^36 + (-6279271/13854332*a^16 + 35105987/13854332*a^15 + 73144699/13854332*a^14 - 703433505/13854332*a^13 + 137265359/13854332*a^12 + 5300866217/13854332*a^11 - 5301014985/13854332*a^10 - 9123276643/6927166*a^9 + 6843001421/3463583*a^8 + 26518624041/13854332*a^7 - 55608358727/13854332*a^6 - 7524469695/13854332*a^5 + 20408629339/6927166*a^4 - 7005914249/13854332*a^3 - 5619508281/13854332*a^2 + 189779269/6927166*a + 11877959/3463583)*q^37 + O(q^38)
*]> ;  // time = 6.3 seconds




J[353] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 353, 353, 353, 353 ], new_dimensions := [ 1, 3, 11, 14 ], dimensions := [ 1, 3, 11, 14 ], intersection_graph := [ 0, 1, 1, 3, 1, 0, 1, 127, 1, 1, 0, 1, 3, 127, 1, 0 ], ap_traces := [
[ -1, 2, 2, -2, 4, 2, 2, 0, 4, 2, 2, 2 ],
[ 1, 3, 2, 2, 3, 11, -14, 4, -11, 7, -10, 13 ],
[ -5, -5, -4, -25, -4, -13, -2, -18, -19, 6, -18, -17 ],
[ 4, -2, -4, 29, -7, 2, 8, 14, 16, -9, 28, 8 ]
], hecke_fields := [
x - 1,
x^3 - x^2 - 6*x + 4,
x^11 + 5*x^10 - x^9 - 36*x^8 - 28*x^7 + 82*x^6 + 87*x^5 - 65*x^4 - 71*x^3 + 21*x^2 + 14*x - 4,
x^14 - 4*x^13 - 14*x^12 + 71*x^11 + 47*x^10 - 452*x^9 + 101*x^8 + 1251*x^7 - 740*x^6 - 1488*x^5 + 1096*x^4 + 600*x^3 - 410*x^2 - 42*x - 1
], atkin_lehners := [
[ -1 ],
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 11 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 11 ]
], torsion_upper_bounds := [ 1, 1, 1, 11 ], torsion_lower_bounds := [ 1, 1, 1, 11 ], l_ratios := [ 1, 1, 0, 1/11 ], analytic_sha_upper_bounds := [ 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 1 ], eigenvalues := [*
[ -1, 2, 2, -2, 4, 2, 2, 0, 4, 2, 2, 2 ],
[
a,
-1/2*a^2 + 1/2*a + 3,
-a + 1,
-a + 1,
1/2*a^2 - 1/2*a - 1,
-1/2*a^2 - 1/2*a + 6,
a - 5,
a + 1,
-1/2*a^2 - 3/2*a - 1,
3/2*a^2 - 1/2*a - 4,
-a - 3,
5/2*a^2 - 3/2*a - 6
],
[
a,
-5/2*a^10 - 21/2*a^9 + 19/2*a^8 + 77*a^7 + 15*a^6 - 177*a^5 - 153/2*a^4 + 259/2*a^3 + 99/2*a^2 - 39/2*a - 3,
3*a^10 + 14*a^9 - 6*a^8 - 99*a^7 - 58*a^6 + 213*a^5 + 186*a^4 - 132*a^3 - 134*a^2 + 8*a + 17,
-2*a^9 - 8*a^8 + 9*a^7 + 59*a^6 + a^5 - 137*a^4 - 34*a^3 + 103*a^2 + 18*a - 19,
5/2*a^10 + 25/2*a^9 - 1/2*a^8 - 83*a^7 - 80*a^6 + 156*a^5 + 445/2*a^4 - 117/2*a^3 - 305/2*a^2 - 29/2*a + 19,
5/2*a^10 + 23/2*a^9 - 11/2*a^8 - 82*a^7 - 46*a^6 + 178*a^5 + 303/2*a^4 - 223/2*a^3 - 215/2*a^2 + 17/2*a + 12,
-5*a^10 - 26*a^9 - a^8 + 175*a^7 + 176*a^6 - 338*a^5 - 486*a^4 + 139*a^3 + 343*a^2 + 31*a - 49,
-a^10 - 8*a^9 - 12*a^8 + 47*a^7 + 125*a^6 - 59*a^5 - 314*a^4 - 43*a^3 + 241*a^2 + 53*a - 43,
-7/2*a^10 - 39/2*a^9 - 13/2*a^8 + 128*a^7 + 167*a^6 - 237*a^5 - 895/2*a^4 + 169/2*a^3 + 655/2*a^2 + 57/2*a - 49,
1/2*a^10 + 7/2*a^9 + 5/2*a^8 - 25*a^7 - 37*a^6 + 55*a^5 + 193/2*a^4 - 73/2*a^3 - 133/2*a^2 + 7/2*a + 4,
2*a^10 + 13*a^9 + 12*a^8 - 78*a^7 - 153*a^6 + 112*a^5 + 379*a^4 + 25*a^3 - 271*a^2 - 50*a + 41,
-17/2*a^10 - 81/2*a^9 + 27/2*a^8 + 284*a^7 + 190*a^6 - 602*a^5 - 1163/2*a^4 + 731/2*a^3 + 809/2*a^2 - 61/2*a - 48
],
[
a,
1/8*a^13 - 7/8*a^12 - 9/8*a^11 + 65/4*a^10 - 55/8*a^9 - 855/8*a^8 + 405/4*a^7 + 2405/8*a^6 - 2763/8*a^5 - 2871/8*a^4 + 3453/8*a^3 + 1145/8*a^2 - 1245/8*a - 75/8,
7/4*a^13 - 25/4*a^12 - 103/4*a^11 + 221/2*a^10 + 415/4*a^9 - 2793/4*a^8 + 89/2*a^7 + 7619/4*a^6 - 3777/4*a^5 - 8801/4*a^4 + 6115/4*a^3 + 3263/4*a^2 - 2347/4*a - 121/4,
3/8*a^13 - 13/8*a^12 - 39/8*a^11 + 113/4*a^10 + 99/8*a^9 - 1409/8*a^8 + 253/4*a^7 + 3815/8*a^6 - 2637/8*a^5 - 4409/8*a^4 + 3663/8*a^3 + 1667/8*a^2 - 1371/8*a - 53/8,
-1/2*a^13 + 3/2*a^12 + 15/2*a^11 - 25*a^10 - 71/2*a^9 + 299/2*a^8 + 41*a^7 - 777/2*a^6 + 191/2*a^5 + 853/2*a^4 - 443/2*a^3 - 293/2*a^2 + 191/2*a + 9/2,
5/4*a^13 - 15/4*a^12 - 81/4*a^11 + 135/2*a^10 + 417/4*a^9 - 1735/4*a^8 - 287/2*a^7 + 4805/4*a^6 - 927/4*a^5 - 5623/4*a^4 + 2489/4*a^3 + 2093/4*a^2 - 1073/4*a - 59/4,
-1/2*a^12 + a^11 + 17/2*a^10 - 33/2*a^9 - 52*a^8 + 195/2*a^7 + 277/2*a^6 - 250*a^5 - 309/2*a^4 + 271*a^3 + 101/2*a^2 - 90*a + 1/2,
11/4*a^13 - 39/4*a^12 - 163/4*a^11 + 173*a^10 + 669/4*a^9 - 4393/4*a^8 + 49*a^7 + 12061/4*a^6 - 5777/4*a^5 - 14059/4*a^4 + 9519/4*a^3 + 5281/4*a^2 - 3703/4*a - 183/4,
3/4*a^13 - 17/4*a^12 - 31/4*a^11 + 149/2*a^10 - 41/4*a^9 - 1881/4*a^8 + 693/2*a^7 + 5191/4*a^6 - 5029/4*a^5 - 6165/4*a^4 + 6355/4*a^3 + 2427/4*a^2 - 2251/4*a - 117/4,
3/2*a^13 - 33/4*a^12 - 16*a^11 + 581/4*a^10 - 59/4*a^9 - 1835/2*a^8 + 2693/4*a^7 + 10073/4*a^6 - 4993/2*a^5 - 11805/4*a^4 + 3200*a^3 + 4521/4*a^2 - 2311/2*a - 211/4,
7/8*a^13 - 25/8*a^12 - 107/8*a^11 + 229/4*a^10 + 447/8*a^9 - 2973/8*a^8 + 85/4*a^7 + 8219/8*a^6 - 4081/8*a^5 - 9429/8*a^4 + 6651/8*a^3 + 3271/8*a^2 - 2543/8*a - 65/8,
-7/4*a^13 + 27/4*a^12 + 99/4*a^11 - 119*a^10 - 349/4*a^9 + 3001/4*a^8 - 142*a^7 - 8173/4*a^6 + 4777/4*a^5 + 9419/4*a^4 - 7207/4*a^3 - 3465/4*a^2 + 2743/4*a + 123/4
]
*], q_expansions := [*
q - q^2 + 2*q^3 - q^4 + 2*q^5 - 2*q^6 - 2*q^7 + 3*q^8 + q^9 - 2*q^10 + 4*q^11 - 2*q^12 + 2*q^13 + 2*q^14 + 4*q^15 - q^16 + 2*q^17 - q^18 - 2*q^20 - 4*q^21 - 4*q^22 + 4*q^23 + 6*q^24 - q^25 - 2*q^26 - 4*q^27 + 2*q^28 + 2*q^29 - 4*q^30 + 2*q^31 - 5*q^32 + 8*q^33 - 2*q^34 - 4*q^35 - q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^2 + 1/2*a + 3)*q^3 + (a^2 - 2)*q^4 + (-a + 1)*q^5 + 2*q^6 + (-a + 1)*q^7 + (a^2 + 2*a - 4)*q^8 + (-3/2*a^2 + 1/2*a + 7)*q^9 + (-a^2 + a)*q^10 + (1/2*a^2 - 1/2*a - 1)*q^11 + (a^2 + a - 6)*q^12 + (-1/2*a^2 - 1/2*a + 6)*q^13 + (-a^2 + a)*q^14 + (-1/2*a^2 + 1/2*a + 1)*q^15 + (a^2 + 2*a)*q^16 + (a - 5)*q^17 + (-a^2 - 2*a + 6)*q^18 + (a + 1)*q^19 + (-4*a + 2)*q^20 + (-1/2*a^2 + 1/2*a + 1)*q^21 + (2*a - 2)*q^22 + (-1/2*a^2 - 3/2*a - 1)*q^23 + (2*a^2 - 8)*q^24 + (a^2 - 2*a - 4)*q^25 + (-a^2 + 3*a + 2)*q^26 + (-2*a^2 - a + 13)*q^27 + (-4*a + 2)*q^28 + (3/2*a^2 - 1/2*a - 4)*q^29 + (-2*a + 2)*q^30 + (-a - 3)*q^31 + (a^2 + 2*a + 4)*q^32 + (1/2*a^2 + 1/2*a - 4)*q^33 + (a^2 - 5*a)*q^34 + (a^2 - 2*a + 1)*q^35 + (-a - 10)*q^36 + (5/2*a^2 - 3/2*a - 6)*q^37 + O(q^38),
q + a*q^2 + (-5/2*a^10 - 21/2*a^9 + 19/2*a^8 + 77*a^7 + 15*a^6 - 177*a^5 - 153/2*a^4 + 259/2*a^3 + 99/2*a^2 - 39/2*a - 3)*q^3 + (a^2 - 2)*q^4 + (3*a^10 + 14*a^9 - 6*a^8 - 99*a^7 - 58*a^6 + 213*a^5 + 186*a^4 - 132*a^3 - 134*a^2 + 8*a + 17)*q^5 + (2*a^10 + 7*a^9 - 13*a^8 - 55*a^7 + 28*a^6 + 141*a^5 - 33*a^4 - 128*a^3 + 33*a^2 + 32*a - 10)*q^6 + (-2*a^9 - 8*a^8 + 9*a^7 + 59*a^6 + a^5 - 137*a^4 - 34*a^3 + 103*a^2 + 18*a - 19)*q^7 + (a^3 - 4*a)*q^8 + (1/2*a^10 + 5/2*a^9 - 1/2*a^8 - 18*a^7 - 13*a^6 + 42*a^5 + 73/2*a^4 - 69/2*a^3 - 41/2*a^2 + 13/2*a - 1)*q^9 + (-a^10 - 3*a^9 + 9*a^8 + 26*a^7 - 33*a^6 - 75*a^5 + 63*a^4 + 79*a^3 - 55*a^2 - 25*a + 12)*q^10 + (5/2*a^10 + 25/2*a^9 - 1/2*a^8 - 83*a^7 - 80*a^6 + 156*a^5 + 445/2*a^4 - 117/2*a^3 - 305/2*a^2 - 29/2*a + 19)*q^11 + (2*a^10 + 10*a^9 - 2*a^8 - 70*a^7 - 53*a^6 + 147*a^5 + 155*a^4 - 84*a^3 - 109*a^2 + a + 14)*q^12 + (5/2*a^10 + 23/2*a^9 - 11/2*a^8 - 82*a^7 - 46*a^6 + 178*a^5 + 303/2*a^4 - 223/2*a^3 - 215/2*a^2 + 17/2*a + 12)*q^13 + (-2*a^10 - 8*a^9 + 9*a^8 + 59*a^7 + a^6 - 137*a^5 - 34*a^4 + 103*a^3 + 18*a^2 - 19*a)*q^14 + (1/2*a^10 - 1/2*a^9 - 25/2*a^8 - 4*a^7 + 75*a^6 + 38*a^5 - 329/2*a^4 - 143/2*a^3 + 245/2*a^2 + 61/2*a - 23)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-5*a^10 - 26*a^9 - a^8 + 175*a^7 + 176*a^6 - 338*a^5 - 486*a^4 + 139*a^3 + 343*a^2 + 31*a - 49)*q^17 + (a^7 + a^6 - 7*a^5 - 2*a^4 + 15*a^3 - 4*a^2 - 8*a + 2)*q^18 + (-a^10 - 8*a^9 - 12*a^8 + 47*a^7 + 125*a^6 - 59*a^5 - 314*a^4 - 43*a^3 + 241*a^2 + 53*a - 43)*q^19 + (-4*a^10 - 20*a^9 + 2*a^8 + 137*a^7 + 123*a^6 - 276*a^5 - 358*a^4 + 138*a^3 + 264*a^2 + 10*a - 38)*q^20 + (11/2*a^10 + 49/2*a^9 - 29/2*a^8 - 174*a^7 - 81*a^6 + 377*a^5 + 569/2*a^4 - 475/2*a^3 - 411/2*a^2 + 37/2*a + 25)*q^21 + (2*a^9 + 7*a^8 - 10*a^7 - 49*a^6 + 5*a^5 + 104*a^4 + 25*a^3 - 67*a^2 - 16*a + 10)*q^22 + (-7/2*a^10 - 39/2*a^9 - 13/2*a^8 + 128*a^7 + 167*a^6 - 237*a^5 - 895/2*a^4 + 169/2*a^3 + 655/2*a^2 + 57/2*a - 49)*q^23 + (-4*a^10 - 14*a^9 + 28*a^8 + 113*a^7 - 73*a^6 - 301*a^5 + 112*a^4 + 289*a^3 - 107*a^2 - 78*a + 28)*q^24 + (2*a^10 + 16*a^9 + 23*a^8 - 95*a^7 - 238*a^6 + 130*a^5 + 585*a^4 + 46*a^3 - 430*a^2 - 68*a + 68)*q^25 + (-a^10 - 3*a^9 + 8*a^8 + 24*a^7 - 27*a^6 - 66*a^5 + 51*a^4 + 70*a^3 - 44*a^2 - 23*a + 10)*q^26 + (-2*a^10 - 2*a^9 + 34*a^8 + 34*a^7 - 186*a^6 - 157*a^5 + 409*a^4 + 248*a^3 - 325*a^2 - 104*a + 61)*q^27 + (2*a^10 + 11*a^9 + 3*a^8 - 73*a^7 - 91*a^6 + 138*a^5 + 247*a^4 - 56*a^3 - 183*a^2 - 8*a + 30)*q^28 + (1/2*a^10 + 7/2*a^9 + 5/2*a^8 - 25*a^7 - 37*a^6 + 55*a^5 + 193/2*a^4 - 73/2*a^3 - 133/2*a^2 + 7/2*a + 4)*q^29 + (-3*a^10 - 12*a^9 + 14*a^8 + 89*a^7 - 3*a^6 - 208*a^5 - 39*a^4 + 158*a^3 + 20*a^2 - 30*a + 2)*q^30 + (2*a^10 + 13*a^9 + 12*a^8 - 78*a^7 - 153*a^6 + 112*a^5 + 379*a^4 + 25*a^3 - 271*a^2 - 50*a + 41)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (11/2*a^10 + 49/2*a^9 - 31/2*a^8 - 175*a^7 - 71*a^6 + 383*a^5 + 499/2*a^4 - 497/2*a^3 - 321/2*a^2 + 51/2*a + 14)*q^33 + (-a^10 - 6*a^9 - 5*a^8 + 36*a^7 + 72*a^6 - 51*a^5 - 186*a^4 - 12*a^3 + 136*a^2 + 21*a - 20)*q^34 + (-11*a^10 - 53*a^9 + 15*a^8 + 370*a^7 + 266*a^6 - 775*a^5 - 812*a^4 + 442*a^3 + 597*a^2 - 6*a - 83)*q^35 + (-a^10 - 5*a^9 + 2*a^8 + 37*a^7 + 19*a^6 - 86*a^5 - 58*a^4 + 65*a^3 + 33*a^2 - 11*a + 2)*q^36 + (-17/2*a^10 - 81/2*a^9 + 27/2*a^8 + 284*a^7 + 190*a^6 - 602*a^5 - 1163/2*a^4 + 731/2*a^3 + 809/2*a^2 - 61/2*a - 48)*q^37 + O(q^38),
q + a*q^2 + (1/8*a^13 - 7/8*a^12 - 9/8*a^11 + 65/4*a^10 - 55/8*a^9 - 855/8*a^8 + 405/4*a^7 + 2405/8*a^6 - 2763/8*a^5 - 2871/8*a^4 + 3453/8*a^3 + 1145/8*a^2 - 1245/8*a - 75/8)*q^3 + (a^2 - 2)*q^4 + (7/4*a^13 - 25/4*a^12 - 103/4*a^11 + 221/2*a^10 + 415/4*a^9 - 2793/4*a^8 + 89/2*a^7 + 7619/4*a^6 - 3777/4*a^5 - 8801/4*a^4 + 6115/4*a^3 + 3263/4*a^2 - 2347/4*a - 121/4)*q^5 + (-3/8*a^13 + 5/8*a^12 + 59/8*a^11 - 51/4*a^10 - 403/8*a^9 + 709/8*a^8 + 577/4*a^7 - 2023/8*a^6 - 1383/8*a^5 + 2357/8*a^4 + 545/8*a^3 - 835/8*a^2 - 33/8*a + 1/8)*q^6 + (3/8*a^13 - 13/8*a^12 - 39/8*a^11 + 113/4*a^10 + 99/8*a^9 - 1409/8*a^8 + 253/4*a^7 + 3815/8*a^6 - 2637/8*a^5 - 4409/8*a^4 + 3663/8*a^3 + 1667/8*a^2 - 1371/8*a - 53/8)*q^7 + (a^3 - 4*a)*q^8 + (-7/4*a^13 + 6*a^12 + 105/4*a^11 - 423/4*a^10 - 227/2*a^9 + 2669/4*a^8 + 81/4*a^7 - 3643/2*a^6 + 3081/4*a^5 + 2107*a^4 - 5377/4*a^3 - 1559/2*a^2 + 2131/4*a + 55/2)*q^9 + (3/4*a^13 - 5/4*a^12 - 55/4*a^11 + 43/2*a^10 + 371/4*a^9 - 529/4*a^8 - 569/2*a^7 + 1403/4*a^6 + 1615/4*a^5 - 1557/4*a^4 - 937/4*a^3 + 523/4*a^2 + 173/4*a + 7/4)*q^10 + (-1/2*a^13 + 3/2*a^12 + 15/2*a^11 - 25*a^10 - 71/2*a^9 + 299/2*a^8 + 41*a^7 - 777/2*a^6 + 191/2*a^5 + 853/2*a^4 - 443/2*a^3 - 293/2*a^2 + 191/2*a + 9/2)*q^11 + (-9/8*a^13 + 31/8*a^12 + 129/8*a^11 - 261/4*a^10 - 537/8*a^9 + 3167/8*a^8 + 55/4*a^7 - 8413/8*a^6 + 3419/8*a^5 + 9575/8*a^4 - 5941/8*a^3 - 3553/8*a^2 + 2365/8*a + 147/8)*q^12 + (5/4*a^13 - 15/4*a^12 - 81/4*a^11 + 135/2*a^10 + 417/4*a^9 - 1735/4*a^8 - 287/2*a^7 + 4805/4*a^6 - 927/4*a^5 - 5623/4*a^4 + 2489/4*a^3 + 2093/4*a^2 - 1073/4*a - 59/4)*q^13 + (-1/8*a^13 + 3/8*a^12 + 13/8*a^11 - 21/4*a^10 - 53/8*a^9 + 203/8*a^8 + 31/4*a^7 - 417/8*a^6 + 55/8*a^5 + 375/8*a^4 - 133/8*a^3 - 141/8*a^2 + 73/8*a + 3/8)*q^14 + (-9/4*a^13 + 41/4*a^12 + 117/4*a^11 - 183*a^10 - 255/4*a^9 + 4679/4*a^8 - 503*a^7 - 12955/4*a^6 + 9719/4*a^5 + 15277/4*a^4 - 13381/4*a^3 - 5867/4*a^2 + 4925/4*a + 261/4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^12 + a^11 + 17/2*a^10 - 33/2*a^9 - 52*a^8 + 195/2*a^7 + 277/2*a^6 - 250*a^5 - 309/2*a^4 + 271*a^3 + 101/2*a^2 - 90*a + 1/2)*q^17 + (-a^13 + 7/4*a^12 + 37/2*a^11 - 125/4*a^10 - 495/4*a^9 + 197*a^8 + 1471/4*a^7 - 2099/4*a^6 - 497*a^5 + 2295/4*a^4 + 541/2*a^3 - 739/4*a^2 - 46*a - 7/4)*q^18 + (11/4*a^13 - 39/4*a^12 - 163/4*a^11 + 173*a^10 + 669/4*a^9 - 4393/4*a^8 + 49*a^7 + 12061/4*a^6 - 5777/4*a^5 - 14059/4*a^4 + 9519/4*a^3 + 5281/4*a^2 - 3703/4*a - 183/4)*q^19 + (-7/4*a^13 + 37/4*a^12 + 79/4*a^11 - 327/2*a^10 - 3/4*a^9 + 4145/4*a^8 - 1353/2*a^7 - 11403/4*a^6 + 10461/4*a^5 + 13377/4*a^4 - 13507/4*a^3 - 5123/4*a^2 + 4827/4*a + 245/4)*q^20 + (-1/2*a^13 + 5/4*a^12 + 8*a^11 - 81/4*a^10 - 181/4*a^9 + 237/2*a^8 + 423/4*a^7 - 1221/4*a^6 - 159/2*a^5 + 1329/4*a^4 - 28*a^3 - 417/4*a^2 + 45/2*a - 5/4)*q^21 + (-1/2*a^13 + 1/2*a^12 + 21/2*a^11 - 12*a^10 - 153/2*a^9 + 183/2*a^8 + 237*a^7 - 549/2*a^6 - 635/2*a^5 + 653/2*a^4 + 307/2*a^3 - 219/2*a^2 - 33/2*a - 1/2)*q^22 + (3/4*a^13 - 17/4*a^12 - 31/4*a^11 + 149/2*a^10 - 41/4*a^9 - 1881/4*a^8 + 693/2*a^7 + 5191/4*a^6 - 5029/4*a^5 - 6165/4*a^4 + 6355/4*a^3 + 2427/4*a^2 - 2251/4*a - 117/4)*q^23 + (1/8*a^13 - 7/8*a^12 - 1/8*a^11 + 45/4*a^10 - 95/8*a^9 - 399/8*a^8 + 269/4*a^7 + 805/8*a^6 - 1051/8*a^5 - 791/8*a^4 + 757/8*a^3 + 345/8*a^2 - 165/8*a - 11/8)*q^24 + (-3*a^13 + 12*a^12 + 42*a^11 - 213*a^10 - 140*a^9 + 1353*a^8 - 314*a^7 - 3718*a^6 + 2256*a^5 + 4337*a^4 - 3329*a^3 - 1632*a^2 + 1240*a + 68)*q^25 + (5/4*a^13 - 11/4*a^12 - 85/4*a^11 + 91/2*a^10 + 525/4*a^9 - 1079/4*a^8 - 725/2*a^7 + 2773/4*a^6 + 1817/4*a^5 - 2991/4*a^4 - 907/4*a^3 + 977/4*a^2 + 151/4*a + 5/4)*q^26 + (5/4*a^13 - 23/4*a^12 - 63/4*a^11 + 101*a^10 + 121/4*a^9 - 2545/4*a^8 + 293*a^7 + 6957/4*a^6 - 5401/4*a^5 - 8085/4*a^4 + 7305/4*a^3 + 3025/4*a^2 - 2651/4*a - 125/4)*q^27 + (-7/8*a^13 + 25/8*a^12 + 107/8*a^11 - 229/4*a^10 - 447/8*a^9 + 2981/8*a^8 - 89/4*a^7 - 8315/8*a^6 + 4161/8*a^5 + 9781/8*a^4 - 6867/8*a^3 - 3671/8*a^2 + 2703/8*a + 105/8)*q^28 + (3/2*a^13 - 33/4*a^12 - 16*a^11 + 581/4*a^10 - 59/4*a^9 - 1835/2*a^8 + 2693/4*a^7 + 10073/4*a^6 - 4993/2*a^5 - 11805/4*a^4 + 3200*a^3 + 4521/4*a^2 - 2311/2*a - 211/4)*q^29 + (5/4*a^13 - 9/4*a^12 - 93/4*a^11 + 42*a^10 + 611/4*a^9 - 1103/4*a^8 - 424*a^7 + 3059/4*a^6 + 1885/4*a^5 - 3517/4*a^4 - 467/4*a^3 + 1235/4*a^2 - 117/4*a - 9/4)*q^30 + (7/8*a^13 - 25/8*a^12 - 107/8*a^11 + 229/4*a^10 + 447/8*a^9 - 2973/8*a^8 + 85/4*a^7 + 8219/8*a^6 - 4081/8*a^5 - 9429/8*a^4 + 6651/8*a^3 + 3271/8*a^2 - 2543/8*a - 65/8)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^13 - 3/2*a^12 - 15/2*a^11 + 25*a^10 + 71/2*a^9 - 301/2*a^8 - 38*a^7 + 795/2*a^6 - 249/2*a^5 - 889/2*a^4 + 583/2*a^3 + 305/2*a^2 - 267/2*a - 13/2)*q^33 + (-1/2*a^13 + a^12 + 17/2*a^11 - 33/2*a^10 - 52*a^9 + 195/2*a^8 + 277/2*a^7 - 250*a^6 - 309/2*a^5 + 271*a^4 + 101/2*a^3 - 90*a^2 + 1/2*a)*q^34 + (11/4*a^13 - 39/4*a^12 - 163/4*a^11 + 173*a^10 + 665/4*a^9 - 4381/4*a^8 + 58*a^7 + 11937/4*a^6 - 5841/4*a^5 - 13707/4*a^4 + 9475/4*a^3 + 4993/4*a^2 - 3603/4*a - 175/4)*q^35 + (5/4*a^13 - 15/2*a^12 - 51/4*a^11 + 539/4*a^10 - 28*a^9 - 3463/4*a^8 + 2743/4*a^7 + 2406*a^6 - 9819/4*a^5 - 5695/2*a^4 + 12415/4*a^3 + 1103*a^2 - 4437/4*a - 56)*q^36 + (-7/4*a^13 + 27/4*a^12 + 99/4*a^11 - 119*a^10 - 349/4*a^9 + 3001/4*a^8 - 142*a^7 - 8173/4*a^6 + 4777/4*a^5 + 9419/4*a^4 - 7207/4*a^3 - 3465/4*a^2 + 2743/4*a + 123/4)*q^37 + O(q^38)
*]> ;  // time = 7.479 seconds




J[354] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 354, 354, 354, 354, 354, 354, 354, 354, 177, 177, 177, 177, 118, 118, 118, 118, 59 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 3, 1, 1, 1, 1, 5 ], dimensions := [ 1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 4, 6, 2, 2, 2, 2, 20 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 11, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 11, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 19, 1, 1, 1, 1, 1, 29, 5, 1, 1, 1, 11, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 0, 1, 1, 1, 1, 1, 961, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 52441, 3, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 361, 1, 1, 1, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 1, 1, 1, 1, 1, 1, 1, 1, 29, 1, 1, 961, 52441, 1, 361, 1, 1, 0 ], ap_traces := [
[ -1, -1, 0, -1, -5, 1, 1, 0, -6, -10, -8, 9 ],
[ -1, -1, 2, 0, 4, -6, 2, 4, 8, 2, 8, 2 ],
[ -1, 1, 0, -1, 3, 5, -3, 8, -6, 6, 8, 5 ],
[ 1, -1, 0, 0, 4, 4, 6, -4, -4, 0, 2, -8 ],
[ 1, -1, 4, 0, -4, 0, -2, 4, 4, 4, -10, -4 ],
[ 1, -1, -4, -1, -3, -1, -7, -4, 2, -2, 0, 7 ],
[ -2, 2, 2, 8, -4, -2, 0, -4, 4, -10, -2, -2 ],
[ 3, 3, 2, -1, 1, 1, -3, 0, -10, -8, -2, 9 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 2*x - 10,
x^3 - 2*x^2 - 6*x + 8
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, 1, 1 ],
[ -1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 5, 3, 1 ],
[ 1, 3, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 11, 9, 1 ],
[ 7, 1, 1 ],
[ 11, 5, 1 ],
[ 551, 29, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 11, 1, 1 ],
[ 7, 1, 1 ],
[ 1, 5, 1 ],
[ 551, 29, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 1, 1, 1, 29 ], torsion_lower_bounds := [ 1, 1, 3, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 1/3, 1, 11, 0, 5, 19 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 1, 0, 1, 1/841 ], eigenvalues := [*
[ -1, -1, 0, -1, -5, 1, 1, 0, -6, -10, -8, 9 ],
[ -1, -1, 2, 0, 4, -6, 2, 4, 8, 2, 8, 2 ],
[ -1, 1, 0, -1, 3, 5, -3, 8, -6, 6, 8, 5 ],
[ 1, -1, 0, 0, 4, 4, 6, -4, -4, 0, 2, -8 ],
[ 1, -1, 4, 0, -4, 0, -2, 4, 4, 4, -10, -4 ],
[ 1, -1, -4, -1, -3, -1, -7, -4, 2, -2, 0, 7 ],
[
-1,
1,
a,
4,
-2,
-a,
-2*a + 2,
-2,
-2*a + 4,
-a - 4,
a - 2,
-a
],
[
1,
1,
a,
-1/2*a^2 - a + 3,
3/2*a^2 - a - 7,
-1/2*a^2 + 3,
-1/2*a^2 + a + 1,
a^2 - 2*a - 4,
-a^2 + 2,
-a^2 + a + 2,
-a^2 + a + 4,
-1/2*a^2 + 4*a + 3
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + q^6 - q^7 - q^8 + q^9 - 5*q^11 - q^12 + q^13 + q^14 + q^16 + q^17 - q^18 + q^21 + 5*q^22 - 6*q^23 + q^24 - 5*q^25 - q^26 - q^27 - q^28 - 10*q^29 - 8*q^31 - q^32 + 5*q^33 - q^34 + q^36 + 9*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + 2*q^5 + q^6 - q^8 + q^9 - 2*q^10 + 4*q^11 - q^12 - 6*q^13 - 2*q^15 + q^16 + 2*q^17 - q^18 + 4*q^19 + 2*q^20 - 4*q^22 + 8*q^23 + q^24 - q^25 + 6*q^26 - q^27 + 2*q^29 + 2*q^30 + 8*q^31 - q^32 - 4*q^33 - 2*q^34 + q^36 + 2*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - q^6 - q^7 - q^8 + q^9 + 3*q^11 + q^12 + 5*q^13 + q^14 + q^16 - 3*q^17 - q^18 + 8*q^19 - q^21 - 3*q^22 - 6*q^23 - q^24 - 5*q^25 - 5*q^26 + q^27 - q^28 + 6*q^29 + 8*q^31 - q^32 + 3*q^33 + 3*q^34 + q^36 + 5*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - q^6 + q^8 + q^9 + 4*q^11 - q^12 + 4*q^13 + q^16 + 6*q^17 + q^18 - 4*q^19 + 4*q^22 - 4*q^23 - q^24 - 5*q^25 + 4*q^26 - q^27 + 2*q^31 + q^32 - 4*q^33 + 6*q^34 + q^36 - 8*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + 4*q^5 - q^6 + q^8 + q^9 + 4*q^10 - 4*q^11 - q^12 - 4*q^15 + q^16 - 2*q^17 + q^18 + 4*q^19 + 4*q^20 - 4*q^22 + 4*q^23 - q^24 + 11*q^25 - q^27 + 4*q^29 - 4*q^30 - 10*q^31 + q^32 + 4*q^33 - 2*q^34 + q^36 - 4*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 4*q^5 - q^6 - q^7 + q^8 + q^9 - 4*q^10 - 3*q^11 - q^12 - q^13 - q^14 + 4*q^15 + q^16 - 7*q^17 + q^18 - 4*q^19 - 4*q^20 + q^21 - 3*q^22 + 2*q^23 - q^24 + 11*q^25 - q^26 - q^27 - q^28 - 2*q^29 + 4*q^30 + q^32 + 3*q^33 - 7*q^34 + 4*q^35 + q^36 + 7*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + a*q^5 - q^6 + 4*q^7 - q^8 + q^9 - a*q^10 - 2*q^11 + q^12 - a*q^13 - 4*q^14 + a*q^15 + q^16 + (-2*a + 2)*q^17 - q^18 - 2*q^19 + a*q^20 + 4*q^21 + 2*q^22 + (-2*a + 4)*q^23 - q^24 + (2*a + 5)*q^25 + a*q^26 + q^27 + 4*q^28 + (-a - 4)*q^29 - a*q^30 + (a - 2)*q^31 - q^32 - 2*q^33 + (2*a - 2)*q^34 + 4*a*q^35 + q^36 - a*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + a*q^5 + q^6 + (-1/2*a^2 - a + 3)*q^7 + q^8 + q^9 + a*q^10 + (3/2*a^2 - a - 7)*q^11 + q^12 + (-1/2*a^2 + 3)*q^13 + (-1/2*a^2 - a + 3)*q^14 + a*q^15 + q^16 + (-1/2*a^2 + a + 1)*q^17 + q^18 + (a^2 - 2*a - 4)*q^19 + a*q^20 + (-1/2*a^2 - a + 3)*q^21 + (3/2*a^2 - a - 7)*q^22 + (-a^2 + 2)*q^23 + q^24 + (a^2 - 5)*q^25 + (-1/2*a^2 + 3)*q^26 + q^27 + (-1/2*a^2 - a + 3)*q^28 + (-a^2 + a + 2)*q^29 + a*q^30 + (-a^2 + a + 4)*q^31 + q^32 + (3/2*a^2 - a - 7)*q^33 + (-1/2*a^2 + a + 1)*q^34 + (-2*a^2 + 4)*q^35 + q^36 + (-1/2*a^2 + 4*a + 3)*q^37 + O(q^38)
*]> ;  // time = 233.28 seconds




J[355] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 355, 355, 355, 355, 355, 71, 71 ], new_dimensions := [ 1, 4, 4, 6, 8, 3, 3 ], dimensions := [ 1, 4, 4, 6, 8, 6, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 61, 7, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 103, 359, 1, 1, 61, 1, 103, 0, 81, 1, 1, 7, 1, 359, 81, 0 ], ap_traces := [
[ 0, -2, 1, -1, 0, 5, 6, -1, 0, -3, 2, 8 ],
[ -2, -1, -4, 1, -9, -2, -5, -7, -4, -19, -6, 12 ],
[ -4, -3, 4, -5, -1, -14, -13, 1, -6, -27, 8, -14 ],
[ 3, 3, 6, 6, 3, 5, 9, -8, 4, 20, -12, -4 ],
[ 4, -1, -8, -5, 7, -4, 5, -1, 14, 35, -4, 4 ]
], hecke_fields := [
x - 1,
x^4 + 2*x^3 - 2*x^2 - 3*x + 1,
x^4 + 4*x^3 + 2*x^2 - 5*x - 3,
x^6 - 3*x^5 - 6*x^4 + 21*x^3 + 4*x^2 - 35*x + 16,
x^8 - 4*x^7 - 5*x^6 + 31*x^5 - 3*x^4 - 57*x^3 + 5*x^2 + 32*x + 8
], atkin_lehners := [
[ -1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 3, 1 ],
[ 1, 1 ],
[ 427, 1 ],
[ 1, 1 ],
[ 36977, 1 ]
], tamagawa_numbers := [
[ 3, 1 ],
[ 1, 1 ],
[ 427, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 3, 1, 7, 1, 1 ], torsion_lower_bounds := [ 3, 1, 1, 1, 1 ], l_ratios := [ 1/3, 0, 0, 1, 1 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 1 ], eigenvalues := [*
[ 0, -2, 1, -1, 0, 5, 6, -1, 0, -3, 2, 8 ],
[
a,
-a^3 - a^2 + 2*a,
-1,
a^3 - 4*a + 1,
a^3 + a^2 - a - 2,
2*a^3 + 5*a^2 - 2*a - 6,
-a^3 - 4*a^2 + 4,
-3*a^3 - 5*a^2 + 4*a + 2,
5*a^2 + 4*a - 9,
-a^3 - 2*a^2 + 3*a - 2,
4*a^3 + 8*a^2 - 3*a - 8,
-2*a^3 - 3*a^2 + a + 4
],
[
a,
-a^3 - 3*a^2 + 2,
1,
a^3 + 4*a^2 + 2*a - 5,
a^3 + a^2 - 5*a - 2,
2*a^3 + 5*a^2 - 4*a - 10,
-3*a^3 - 8*a^2 + 2*a + 4,
3*a^3 + 9*a^2 - 2*a - 10,
-2*a^3 - 7*a^2 + 2*a + 9,
-a^3 - 4*a^2 - a - 2,
-4*a^3 - 8*a^2 + 9*a + 10,
-2*a^3 - 5*a^2 + 3*a + 2
],
[
a,
-a^3 + a^2 + 4*a - 2,
1,
a^3 - 2*a^2 - 4*a + 7,
-a^5 + 2*a^4 + 7*a^3 - 12*a^2 - 12*a + 16,
a^4 - 2*a^3 - 3*a^2 + 7*a - 3,
a^5 - 2*a^4 - 7*a^3 + 11*a^2 + 11*a - 10,
-a^5 + a^4 + 9*a^3 - 8*a^2 - 20*a + 15,
-a^5 + a^4 + 10*a^3 - 8*a^2 - 24*a + 16,
a^5 - a^4 - 7*a^3 + 5*a^2 + 9*a - 3,
a^5 - 2*a^4 - 8*a^3 + 11*a^2 + 18*a - 14,
-2*a^4 + 2*a^3 + 11*a^2 - 7*a - 8
],
[
a,
a^7 - 3*a^6 - 6*a^5 + 21*a^4 + 3*a^3 - 28*a^2 + 2*a + 6,
-1,
-1/2*a^7 - a^6 + 15/2*a^5 + 17/2*a^4 - 61/2*a^3 - 35/2*a^2 + 61/2*a + 13,
-a^7 + 12*a^5 + a^4 - 42*a^3 - 5*a^2 + 39*a + 12,
3/2*a^7 - 3*a^6 - 21/2*a^5 + 39/2*a^4 + 25/2*a^3 - 45/2*a^2 - 5/2*a + 5,
a^7 - 3*a^6 - 5*a^5 + 21*a^4 - 5*a^3 - 30*a^2 + 13*a + 12,
-a^7 + 4*a^6 + 4*a^5 - 30*a^4 + 12*a^3 + 49*a^2 - 23*a - 19,
a^7 - 3*a^6 - 7*a^5 + 22*a^4 + 10*a^3 - 33*a^2 - 6*a + 10,
a^7 + a^6 - 13*a^5 - 10*a^4 + 47*a^3 + 26*a^2 - 41*a - 17,
-a^6 + 2*a^5 + 6*a^4 - 11*a^3 - a^2 + 3*a - 6,
a^6 - a^5 - 8*a^4 + 5*a^3 + 15*a^2 - 2*a - 8
]
*], q_expansions := [*
q - 2*q^3 - 2*q^4 + q^5 - q^7 + q^9 + 4*q^12 + 5*q^13 - 2*q^15 + 4*q^16 + 6*q^17 - q^19 - 2*q^20 + 2*q^21 + q^25 + 4*q^27 + 2*q^28 - 3*q^29 + 2*q^31 - q^35 - 2*q^36 + 8*q^37 + O(q^38),
q + a*q^2 + (-a^3 - a^2 + 2*a)*q^3 + (a^2 - 2)*q^4 - q^5 + (a^3 - 3*a + 1)*q^6 + (a^3 - 4*a + 1)*q^7 + (a^3 - 4*a)*q^8 + (a^3 + a^2 - 3*a - 2)*q^9 - a*q^10 + (a^3 + a^2 - a - 2)*q^11 + (a^2 - 1)*q^12 + (2*a^3 + 5*a^2 - 2*a - 6)*q^13 + (-2*a^3 - 2*a^2 + 4*a - 1)*q^14 + (a^3 + a^2 - 2*a)*q^15 + (-2*a^3 - 4*a^2 + 3*a + 3)*q^16 + (-a^3 - 4*a^2 + 4)*q^17 + (-a^3 - a^2 + a - 1)*q^18 + (-3*a^3 - 5*a^2 + 4*a + 2)*q^19 + (-a^2 + 2)*q^20 + (-2*a^3 - a^2 + 7*a - 2)*q^21 + (-a^3 + a^2 + a - 1)*q^22 + (5*a^2 + 4*a - 9)*q^23 + (-a^3 + 5*a - 2)*q^24 + q^25 + (a^3 + 2*a^2 - 2)*q^26 + (3*a^3 + 4*a^2 - 4*a - 2)*q^27 + a*q^28 + (-a^3 - 2*a^2 + 3*a - 2)*q^29 + (-a^3 + 3*a - 1)*q^30 + (4*a^3 + 8*a^2 - 3*a - 8)*q^31 + (-2*a^3 - a^2 + 5*a + 2)*q^32 + (2*a^3 + a^2 - 4*a)*q^33 + (-2*a^3 - 2*a^2 + a + 1)*q^34 + (-a^3 + 4*a - 1)*q^35 + (-a^3 - 3*a^2 + 2*a + 5)*q^36 + (-2*a^3 - 3*a^2 + a + 4)*q^37 + O(q^38),
q + a*q^2 + (-a^3 - 3*a^2 + 2)*q^3 + (a^2 - 2)*q^4 + q^5 + (a^3 + 2*a^2 - 3*a - 3)*q^6 + (a^3 + 4*a^2 + 2*a - 5)*q^7 + (a^3 - 4*a)*q^8 + (a^3 + 3*a^2 + a - 2)*q^9 + a*q^10 + (a^3 + a^2 - 5*a - 2)*q^11 + (a^2 + 2*a - 1)*q^12 + (2*a^3 + 5*a^2 - 4*a - 10)*q^13 + 3*q^14 + (-a^3 - 3*a^2 + 2)*q^15 + (-4*a^3 - 8*a^2 + 5*a + 7)*q^16 + (-3*a^3 - 8*a^2 + 2*a + 4)*q^17 + (-a^3 - a^2 + 3*a + 3)*q^18 + (3*a^3 + 9*a^2 - 2*a - 10)*q^19 + (a^2 - 2)*q^20 + (2*a^3 + 5*a^2 - 5*a - 10)*q^21 + (-3*a^3 - 7*a^2 + 3*a + 3)*q^22 + (-2*a^3 - 7*a^2 + 2*a + 9)*q^23 + (-a^3 - 2*a^2 + 5*a + 6)*q^24 + q^25 + (-3*a^3 - 8*a^2 + 6)*q^26 + (3*a^3 + 8*a^2 - 4*a - 10)*q^27 + (-2*a^3 - 8*a^2 - a + 10)*q^28 + (-a^3 - 4*a^2 - a - 2)*q^29 + (a^3 + 2*a^2 - 3*a - 3)*q^30 + (-4*a^3 - 8*a^2 + 9*a + 10)*q^31 + (6*a^3 + 13*a^2 - 5*a - 12)*q^32 + (-2*a^3 - 3*a^2 + 10*a + 8)*q^33 + (4*a^3 + 8*a^2 - 11*a - 9)*q^34 + (a^3 + 4*a^2 + 2*a - 5)*q^35 + (a^3 - a^2 - 4*a + 1)*q^36 + (-2*a^3 - 5*a^2 + 3*a + 2)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + a^2 + 4*a - 2)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^4 + a^3 + 4*a^2 - 2*a)*q^6 + (a^3 - 2*a^2 - 4*a + 7)*q^7 + (a^3 - 4*a)*q^8 + (a^5 - a^4 - 9*a^3 + 8*a^2 + 19*a - 15)*q^9 + a*q^10 + (-a^5 + 2*a^4 + 7*a^3 - 12*a^2 - 12*a + 16)*q^11 + (-a^5 + a^4 + 6*a^3 - 4*a^2 - 8*a + 4)*q^12 + (a^4 - 2*a^3 - 3*a^2 + 7*a - 3)*q^13 + (a^4 - 2*a^3 - 4*a^2 + 7*a)*q^14 + (-a^3 + a^2 + 4*a - 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^5 - 2*a^4 - 7*a^3 + 11*a^2 + 11*a - 10)*q^17 + (2*a^5 - 3*a^4 - 13*a^3 + 15*a^2 + 20*a - 16)*q^18 + (-a^5 + a^4 + 9*a^3 - 8*a^2 - 20*a + 15)*q^19 + (a^2 - 2)*q^20 + (-a^2 + a + 2)*q^21 + (-a^5 + a^4 + 9*a^3 - 8*a^2 - 19*a + 16)*q^22 + (-a^5 + a^4 + 10*a^3 - 8*a^2 - 24*a + 16)*q^23 + (-2*a^5 + 2*a^4 + 15*a^3 - 12*a^2 - 27*a + 16)*q^24 + q^25 + (a^5 - 2*a^4 - 3*a^3 + 7*a^2 - 3*a)*q^26 + (a^5 - 2*a^4 - 7*a^3 + 11*a^2 + 11*a - 12)*q^27 + (a^5 - 2*a^4 - 6*a^3 + 11*a^2 + 8*a - 14)*q^28 + (a^5 - a^4 - 7*a^3 + 5*a^2 + 9*a - 3)*q^29 + (-a^4 + a^3 + 4*a^2 - 2*a)*q^30 + (a^5 - 2*a^4 - 8*a^3 + 11*a^2 + 18*a - 14)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^5 + 2*a^4 + 8*a^3 - 12*a^2 - 17*a + 16)*q^33 + (a^5 - a^4 - 10*a^3 + 7*a^2 + 25*a - 16)*q^34 + (a^3 - 2*a^2 - 4*a + 7)*q^35 + (a^5 + a^4 - 9*a^3 - 4*a^2 + 16*a - 2)*q^36 + (-2*a^4 + 2*a^3 + 11*a^2 - 7*a - 8)*q^37 + O(q^38),
q + a*q^2 + (a^7 - 3*a^6 - 6*a^5 + 21*a^4 + 3*a^3 - 28*a^2 + 2*a + 6)*q^3 + (a^2 - 2)*q^4 - q^5 + (a^7 - a^6 - 10*a^5 + 6*a^4 + 29*a^3 - 3*a^2 - 26*a - 8)*q^6 + (-1/2*a^7 - a^6 + 15/2*a^5 + 17/2*a^4 - 61/2*a^3 - 35/2*a^2 + 61/2*a + 13)*q^7 + (a^3 - 4*a)*q^8 + (a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 8*a^2 - 8*a + 1)*q^9 - a*q^10 + (-a^7 + 12*a^5 + a^4 - 42*a^3 - 5*a^2 + 39*a + 12)*q^11 + (a^7 + a^6 - 13*a^5 - 10*a^4 + 48*a^3 + 25*a^2 - 44*a - 20)*q^12 + (3/2*a^7 - 3*a^6 - 21/2*a^5 + 39/2*a^4 + 25/2*a^3 - 45/2*a^2 - 5/2*a + 5)*q^13 + (-3*a^7 + 5*a^6 + 24*a^5 - 32*a^4 - 46*a^3 + 33*a^2 + 29*a + 4)*q^14 + (-a^7 + 3*a^6 + 6*a^5 - 21*a^4 - 3*a^3 + 28*a^2 - 2*a - 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^7 - 3*a^6 - 5*a^5 + 21*a^4 - 5*a^3 - 30*a^2 + 13*a + 12)*q^17 + (a^7 - 2*a^6 - 7*a^5 + 12*a^4 + 8*a^3 - 8*a^2 + a)*q^18 + (-a^7 + 4*a^6 + 4*a^5 - 30*a^4 + 12*a^3 + 49*a^2 - 23*a - 19)*q^19 + (-a^2 + 2)*q^20 + (-a^7 + 3*a^6 + 4*a^5 - 19*a^4 + 12*a^3 + 18*a^2 - 23*a - 2)*q^21 + (-4*a^7 + 7*a^6 + 32*a^5 - 45*a^4 - 62*a^3 + 44*a^2 + 44*a + 8)*q^22 + (a^7 - 3*a^6 - 7*a^5 + 22*a^4 + 10*a^3 - 33*a^2 - 6*a + 10)*q^23 + (3*a^7 - 6*a^6 - 21*a^5 + 39*a^4 + 24*a^3 - 43*a^2 + 8)*q^24 + q^25 + (3*a^7 - 3*a^6 - 27*a^5 + 17*a^4 + 63*a^3 - 10*a^2 - 43*a - 12)*q^26 + (-3*a^6 + 4*a^5 + 24*a^4 - 24*a^3 - 41*a^2 + 20*a + 12)*q^27 + (-6*a^7 + 11*a^6 + 46*a^5 - 72*a^4 - 77*a^3 + 79*a^2 + 39*a - 2)*q^28 + (a^7 + a^6 - 13*a^5 - 10*a^4 + 47*a^3 + 26*a^2 - 41*a - 17)*q^29 + (-a^7 + a^6 + 10*a^5 - 6*a^4 - 29*a^3 + 3*a^2 + 26*a + 8)*q^30 + (-a^6 + 2*a^5 + 6*a^4 - 11*a^3 - a^2 + 3*a - 6)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^7 + 4*a^6 + 2*a^5 - 27*a^4 + 27*a^3 + 33*a^2 - 46*a - 16)*q^33 + (a^7 - 10*a^5 - 2*a^4 + 27*a^3 + 8*a^2 - 20*a - 8)*q^34 + (1/2*a^7 + a^6 - 15/2*a^5 - 17/2*a^4 + 61/2*a^3 + 35/2*a^2 - 61/2*a - 13)*q^35 + (2*a^7 - 4*a^6 - 15*a^5 + 25*a^4 + 25*a^3 - 20*a^2 - 16*a - 10)*q^36 + (a^6 - a^5 - 8*a^4 + 5*a^3 + 15*a^2 - 2*a - 8)*q^37 + O(q^38)
*]> ;  // time = 54.8 seconds




J[357] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 357, 357, 357, 357, 357, 357, 357, 357, 119, 119, 51, 51, 21, 17 ], new_dimensions := [ 1, 1, 1, 1, 2, 2, 3, 4, 4, 5, 1, 2, 1, 1 ], dimensions := [ 1, 1, 1, 1, 2, 2, 3, 4, 8, 10, 2, 4, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 17, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 47, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 223, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 223, 0, 1, 3, 1, 1, 1, 17, 1, 1, 1, 1, 47, 1, 1, 1, 0, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 0 ], ap_traces := [
[ 0, -1, 1, -1, 3, 3, 1, 3, 7, -6, 10, 4 ],
[ 0, -1, 1, 1, -5, -5, 1, -5, -1, -6, -6, 4 ],
[ 2, 1, 1, -1, 1, 1, -1, 1, -3, -2, 0, -6 ],
[ -2, 1, -3, 1, -3, 1, -1, -7, 1, -10, 4, -10 ],
[ 0, -2, -2, -2, 2, -6, -2, -10, -2, 8, 0, -8 ],
[ -2, 2, -4, -2, -10, -4, 2, -4, -6, 8, -6, 6 ],
[ 1, 3, 2, 3, 6, -2, 3, -4, 6, 6, -14, -4 ],
[ 2, -4, -2, 4, 2, 2, -4, 10, 6, -4, -4, 0 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 2,
x^2 + 2*x - 2,
x^3 - x^2 - 4*x + 2,
x^4 - 2*x^3 - 5*x^2 + 8*x + 2
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, -1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, 1 ],
[ 1, 1, 1 ],
[ -1, 1, -1 ],
[ -1, -1, -1 ],
[ 1, -1, 1 ]
], component_group_orders := [
[ 17, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 3 ],
[ 7, 1, 1 ],
[ 1, 1, 1 ],
[ 47, 1, 3 ],
[ 1, 1, 1 ],
[ 223, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 7, 1, 1 ],
[ 1, 1, 1 ],
[ 47, 1, 3 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 1, 0, 1, 0, 0, 0, 1, 1 ], analytic_sha_upper_bounds := [ 1, 0, 1, 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1, 0, 0, 0, 1, 1 ], eigenvalues := [*
[ 0, -1, 1, -1, 3, 3, 1, 3, 7, -6, 10, 4 ],
[ 0, -1, 1, 1, -5, -5, 1, -5, -1, -6, -6, 4 ],
[ 2, 1, 1, -1, 1, 1, -1, 1, -3, -2, 0, -6 ],
[ -2, 1, -3, 1, -3, 1, -1, -7, 1, -10, 4, -10 ],
[
a,
-1,
-a - 1,
-1,
1,
-a - 3,
-1,
-a - 5,
2*a - 1,
-2*a + 4,
7*a,
3*a - 4
],
[
a,
1,
-a - 3,
-1,
-5,
3*a + 1,
1,
-3*a - 5,
-3,
4,
-a - 4,
a + 4
],
[
a,
1,
-a + 1,
1,
-a^2 + 5,
-2*a^2 + a + 5,
1,
-a - 1,
a^2 - 1,
2*a^2 - 4,
-a^2 + a - 2,
3*a^2 - a - 10
],
[
a,
-1,
-a^3 + a^2 + 5*a - 3,
1,
-a^2 + 2*a + 3,
a^3 - a^2 - 5*a + 3,
-1,
-a^3 + a^2 + 3*a + 1,
-2*a^3 + a^2 + 8*a + 1,
-2*a,
a^3 + 2*a^2 - 7*a - 8,
a^3 - 7*a
]
*], q_expansions := [*
q - q^3 - 2*q^4 + q^5 - q^7 + q^9 + 3*q^11 + 2*q^12 + 3*q^13 - q^15 + 4*q^16 + q^17 + 3*q^19 - 2*q^20 + q^21 + 7*q^23 - 4*q^25 - q^27 + 2*q^28 - 6*q^29 + 10*q^31 - 3*q^33 - q^35 - 2*q^36 + 4*q^37 + O(q^38),
q - q^3 - 2*q^4 + q^5 + q^7 + q^9 - 5*q^11 + 2*q^12 - 5*q^13 - q^15 + 4*q^16 + q^17 - 5*q^19 - 2*q^20 - q^21 - q^23 - 4*q^25 - q^27 - 2*q^28 - 6*q^29 - 6*q^31 + 5*q^33 + q^35 - 2*q^36 + 4*q^37 + O(q^38),
q + 2*q^2 + q^3 + 2*q^4 + q^5 + 2*q^6 - q^7 + q^9 + 2*q^10 + q^11 + 2*q^12 + q^13 - 2*q^14 + q^15 - 4*q^16 - q^17 + 2*q^18 + q^19 + 2*q^20 - q^21 + 2*q^22 - 3*q^23 - 4*q^25 + 2*q^26 + q^27 - 2*q^28 - 2*q^29 + 2*q^30 - 8*q^32 + q^33 - 2*q^34 - q^35 + 2*q^36 - 6*q^37 + O(q^38),
q - 2*q^2 + q^3 + 2*q^4 - 3*q^5 - 2*q^6 + q^7 + q^9 + 6*q^10 - 3*q^11 + 2*q^12 + q^13 - 2*q^14 - 3*q^15 - 4*q^16 - q^17 - 2*q^18 - 7*q^19 - 6*q^20 + q^21 + 6*q^22 + q^23 + 4*q^25 - 2*q^26 + q^27 + 2*q^28 - 10*q^29 + 6*q^30 + 4*q^31 + 8*q^32 - 3*q^33 + 2*q^34 - 3*q^35 + 2*q^36 - 10*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a - 1)*q^5 - a*q^6 - q^7 - 2*a*q^8 + q^9 + (-a - 2)*q^10 + q^11 + (-a - 3)*q^13 - a*q^14 + (a + 1)*q^15 - 4*q^16 - q^17 + a*q^18 + (-a - 5)*q^19 + q^21 + a*q^22 + (2*a - 1)*q^23 + 2*a*q^24 + (2*a - 2)*q^25 + (-3*a - 2)*q^26 - q^27 + (-2*a + 4)*q^29 + (a + 2)*q^30 + 7*a*q^31 - q^33 - a*q^34 + (a + 1)*q^35 + (3*a - 4)*q^37 + O(q^38),
q + a*q^2 + q^3 - 2*a*q^4 + (-a - 3)*q^5 + a*q^6 - q^7 + (2*a - 4)*q^8 + q^9 + (-a - 2)*q^10 - 5*q^11 - 2*a*q^12 + (3*a + 1)*q^13 - a*q^14 + (-a - 3)*q^15 + (-4*a + 4)*q^16 + q^17 + a*q^18 + (-3*a - 5)*q^19 + (2*a + 4)*q^20 - q^21 - 5*a*q^22 - 3*q^23 + (2*a - 4)*q^24 + (4*a + 6)*q^25 + (-5*a + 6)*q^26 + q^27 + 2*a*q^28 + 4*q^29 + (-a - 2)*q^30 + (-a - 4)*q^31 + 8*a*q^32 - 5*q^33 + a*q^34 + (a + 3)*q^35 - 2*a*q^36 + (a + 4)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a + 1)*q^5 + a*q^6 + q^7 + (a^2 - 2)*q^8 + q^9 + (-a^2 + a)*q^10 + (-a^2 + 5)*q^11 + (a^2 - 2)*q^12 + (-2*a^2 + a + 5)*q^13 + a*q^14 + (-a + 1)*q^15 + (-a^2 + 2*a + 2)*q^16 + q^17 + a*q^18 + (-a - 1)*q^19 - 2*a*q^20 + q^21 + (-a^2 + a + 2)*q^22 + (a^2 - 1)*q^23 + (a^2 - 2)*q^24 + (a^2 - 2*a - 4)*q^25 + (-a^2 - 3*a + 4)*q^26 + q^27 + (a^2 - 2)*q^28 + (2*a^2 - 4)*q^29 + (-a^2 + a)*q^30 + (-a^2 + a - 2)*q^31 + (-a^2 - 2*a + 6)*q^32 + (-a^2 + 5)*q^33 + a*q^34 + (-a + 1)*q^35 + (a^2 - 2)*q^36 + (3*a^2 - a - 10)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^3 + a^2 + 5*a - 3)*q^5 - a*q^6 + q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^3 + 5*a + 2)*q^10 + (-a^2 + 2*a + 3)*q^11 + (-a^2 + 2)*q^12 + (a^3 - a^2 - 5*a + 3)*q^13 + a*q^14 + (a^3 - a^2 - 5*a + 3)*q^15 + (2*a^3 - a^2 - 8*a + 2)*q^16 - q^17 + a*q^18 + (-a^3 + a^2 + 3*a + 1)*q^19 + (-2*a^2 + 8)*q^20 - q^21 + (-a^3 + 2*a^2 + 3*a)*q^22 + (-2*a^3 + a^2 + 8*a + 1)*q^23 + (-a^3 + 4*a)*q^24 + (-3*a^2 + 2*a + 12)*q^25 + (a^3 - 5*a - 2)*q^26 - q^27 + (a^2 - 2)*q^28 - 2*a*q^29 + (a^3 - 5*a - 2)*q^30 + (a^3 + 2*a^2 - 7*a - 8)*q^31 + (a^3 + 2*a^2 - 6*a - 4)*q^32 + (a^2 - 2*a - 3)*q^33 - a*q^34 + (-a^3 + a^2 + 5*a - 3)*q^35 + (a^2 - 2)*q^36 + (a^3 - 7*a)*q^37 + O(q^38)
*]> ;  // time = 113.52 seconds




J[358] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 358, 358, 358, 358, 358, 358, 358, 179, 179, 179 ], new_dimensions := [ 1, 1, 2, 2, 2, 2, 4, 1, 3, 11 ], dimensions := [ 1, 1, 2, 2, 2, 2, 4, 2, 6, 22 ], intersection_graph := [ 0, 1, 3, 1, 1, 1, 1, 1, 1, 17, 1, 0, 1, 11, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 5, 1, 17, 1, 11, 1, 0, 11, 1, 1, 1, 29, 1, 1, 1, 1, 11, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 79, 1, 1, 1, 1, 1, 1, 0, 1, 13, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 81, 1, 1, 1, 29, 1, 1, 13, 1, 0, 1, 17, 1, 17, 1, 1, 79, 1, 81, 1, 0 ], ap_traces := [
[ -1, 2, 0, -2, 5, 6, 3, -2, 2, 2, 5, -1 ],
[ 1, -2, 0, 2, 3, 2, 3, 2, 6, -6, 5, -7 ],
[ -2, 1, 6, 2, -2, -3, 0, -7, 1, 4, -8, 13 ],
[ 2, 3, 1, 4, -2, -11, 5, -3, -2, -5, 5, -6 ],
[ 2, 3, 2, -4, 4, 3, -4, 5, -7, 0, -6, 1 ],
[ 2, -3, -4, -6, 0, -3, -8, -9, -3, 6, 4, 7 ],
[ -4, -2, -7, 0, -4, -8, -15, 4, -9, -7, 3, -7 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - x - 5,
x^2 - 3*x + 1,
x^2 - 3*x + 1,
x^2 + 3*x + 1,
x^4 + 2*x^3 - 7*x^2 - 8*x - 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, 1 ]
], component_group_orders := [
[ 17, 1 ],
[ 3, 1 ],
[ 85, 1 ],
[ 29, 1 ],
[ 5, 1 ],
[ 79, 1 ],
[ 13, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 29, 1 ],
[ 5, 1 ],
[ 79, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 1, 5, 1, 1 ], torsion_lower_bounds := [ 1, 3, 1, 1, 5, 1, 1 ], l_ratios := [ 1, 1/3, 1, 29, 1/5, 0, 0 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 1, 0, 0 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1, 1, 0, 0 ], eigenvalues := [*
[ -1, 2, 0, -2, 5, 6, 3, -2, 2, 2, 5, -1 ],
[ 1, -2, 0, 2, 3, 2, 3, 2, 6, -6, 5, -7 ],
[
-1,
a,
3,
1,
-1,
-a - 1,
-2*a + 1,
-a - 3,
-a + 1,
-2*a + 3,
-2*a - 3,
-a + 7
],
[
1,
a,
-3*a + 5,
2,
2*a - 4,
a - 7,
3*a - 2,
-a,
-2*a + 2,
a - 4,
-7*a + 13,
-2*a
],
[
1,
a,
1,
-2*a + 1,
-2*a + 5,
-a + 3,
-2*a + 1,
a + 1,
5*a - 11,
-6*a + 9,
4*a - 9,
-3*a + 5
],
[
1,
a,
-2*a - 5,
-3,
2*a + 3,
3*a + 3,
-2*a - 7,
-3*a - 9,
3*a + 3,
3,
6*a + 11,
-7*a - 7
],
[
-1,
a,
1/2*a^3 + 1/2*a^2 - 9/2*a - 3,
-a^3 - 3/2*a^2 + 13/2*a + 7/2,
a^3 + 3/2*a^2 - 17/2*a - 11/2,
-a^3 - 2*a^2 + 7*a + 4,
-1/2*a^3 - a^2 + 4*a - 1/2,
2*a^3 + 7/2*a^2 - 27/2*a - 17/2,
-1/2*a^3 + 4*a - 7/2,
-1/2*a^3 + 7*a - 3/2,
-1/2*a^3 - 1/2*a^2 + 5/2*a + 1,
1/2*a^3 + 2*a^2 - 2*a - 17/2
]
*], q_expansions := [*
q - q^2 + 2*q^3 + q^4 - 2*q^6 - 2*q^7 - q^8 + q^9 + 5*q^11 + 2*q^12 + 6*q^13 + 2*q^14 + q^16 + 3*q^17 - q^18 - 2*q^19 - 4*q^21 - 5*q^22 + 2*q^23 - 2*q^24 - 5*q^25 - 6*q^26 - 4*q^27 - 2*q^28 + 2*q^29 + 5*q^31 - q^32 + 10*q^33 - 3*q^34 + q^36 - q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 2*q^6 + 2*q^7 + q^8 + q^9 + 3*q^11 - 2*q^12 + 2*q^13 + 2*q^14 + q^16 + 3*q^17 + q^18 + 2*q^19 - 4*q^21 + 3*q^22 + 6*q^23 - 2*q^24 - 5*q^25 + 2*q^26 + 4*q^27 + 2*q^28 - 6*q^29 + 5*q^31 + q^32 - 6*q^33 + 3*q^34 + q^36 - 7*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + 3*q^5 - a*q^6 + q^7 - q^8 + (a + 2)*q^9 - 3*q^10 - q^11 + a*q^12 + (-a - 1)*q^13 - q^14 + 3*a*q^15 + q^16 + (-2*a + 1)*q^17 + (-a - 2)*q^18 + (-a - 3)*q^19 + 3*q^20 + a*q^21 + q^22 + (-a + 1)*q^23 - a*q^24 + 4*q^25 + (a + 1)*q^26 + 5*q^27 + q^28 + (-2*a + 3)*q^29 - 3*a*q^30 + (-2*a - 3)*q^31 - q^32 - a*q^33 + (2*a - 1)*q^34 + 3*q^35 + (a + 2)*q^36 + (-a + 7)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-3*a + 5)*q^5 + a*q^6 + 2*q^7 + q^8 + (3*a - 4)*q^9 + (-3*a + 5)*q^10 + (2*a - 4)*q^11 + a*q^12 + (a - 7)*q^13 + 2*q^14 + (-4*a + 3)*q^15 + q^16 + (3*a - 2)*q^17 + (3*a - 4)*q^18 - a*q^19 + (-3*a + 5)*q^20 + 2*a*q^21 + (2*a - 4)*q^22 + (-2*a + 2)*q^23 + a*q^24 + (-3*a + 11)*q^25 + (a - 7)*q^26 + (2*a - 3)*q^27 + 2*q^28 + (a - 4)*q^29 + (-4*a + 3)*q^30 + (-7*a + 13)*q^31 + q^32 + (2*a - 2)*q^33 + (3*a - 2)*q^34 + (-6*a + 10)*q^35 + (3*a - 4)*q^36 - 2*a*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + q^5 + a*q^6 + (-2*a + 1)*q^7 + q^8 + (3*a - 4)*q^9 + q^10 + (-2*a + 5)*q^11 + a*q^12 + (-a + 3)*q^13 + (-2*a + 1)*q^14 + a*q^15 + q^16 + (-2*a + 1)*q^17 + (3*a - 4)*q^18 + (a + 1)*q^19 + q^20 + (-5*a + 2)*q^21 + (-2*a + 5)*q^22 + (5*a - 11)*q^23 + a*q^24 - 4*q^25 + (-a + 3)*q^26 + (2*a - 3)*q^27 + (-2*a + 1)*q^28 + (-6*a + 9)*q^29 + a*q^30 + (4*a - 9)*q^31 + q^32 + (-a + 2)*q^33 + (-2*a + 1)*q^34 + (-2*a + 1)*q^35 + (3*a - 4)*q^36 + (-3*a + 5)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-2*a - 5)*q^5 + a*q^6 - 3*q^7 + q^8 + (-3*a - 4)*q^9 + (-2*a - 5)*q^10 + (2*a + 3)*q^11 + a*q^12 + (3*a + 3)*q^13 - 3*q^14 + (a + 2)*q^15 + q^16 + (-2*a - 7)*q^17 + (-3*a - 4)*q^18 + (-3*a - 9)*q^19 + (-2*a - 5)*q^20 - 3*a*q^21 + (2*a + 3)*q^22 + (3*a + 3)*q^23 + a*q^24 + (8*a + 16)*q^25 + (3*a + 3)*q^26 + (2*a + 3)*q^27 - 3*q^28 + 3*q^29 + (a + 2)*q^30 + (6*a + 11)*q^31 + q^32 + (-3*a - 2)*q^33 + (-2*a - 7)*q^34 + (6*a + 15)*q^35 + (-3*a - 4)*q^36 + (-7*a - 7)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (1/2*a^3 + 1/2*a^2 - 9/2*a - 3)*q^5 - a*q^6 + (-a^3 - 3/2*a^2 + 13/2*a + 7/2)*q^7 - q^8 + (a^2 - 3)*q^9 + (-1/2*a^3 - 1/2*a^2 + 9/2*a + 3)*q^10 + (a^3 + 3/2*a^2 - 17/2*a - 11/2)*q^11 + a*q^12 + (-a^3 - 2*a^2 + 7*a + 4)*q^13 + (a^3 + 3/2*a^2 - 13/2*a - 7/2)*q^14 + (-1/2*a^3 - a^2 + a + 1/2)*q^15 + q^16 + (-1/2*a^3 - a^2 + 4*a - 1/2)*q^17 + (-a^2 + 3)*q^18 + (2*a^3 + 7/2*a^2 - 27/2*a - 17/2)*q^19 + (1/2*a^3 + 1/2*a^2 - 9/2*a - 3)*q^20 + (1/2*a^3 - 1/2*a^2 - 9/2*a - 1)*q^21 + (-a^3 - 3/2*a^2 + 17/2*a + 11/2)*q^22 + (-1/2*a^3 + 4*a - 7/2)*q^23 - a*q^24 + (-1/2*a^3 + 7*a + 3/2)*q^25 + (a^3 + 2*a^2 - 7*a - 4)*q^26 + (a^3 - 6*a)*q^27 + (-a^3 - 3/2*a^2 + 13/2*a + 7/2)*q^28 + (-1/2*a^3 + 7*a - 3/2)*q^29 + (1/2*a^3 + a^2 - a - 1/2)*q^30 + (-1/2*a^3 - 1/2*a^2 + 5/2*a + 1)*q^31 - q^32 + (-1/2*a^3 - 3/2*a^2 + 5/2*a + 1)*q^33 + (1/2*a^3 + a^2 - 4*a + 1/2)*q^34 + (a^3 + 5/2*a^2 - 7/2*a - 13/2)*q^35 + (a^2 - 3)*q^36 + (1/2*a^3 + 2*a^2 - 2*a - 17/2)*q^37 + O(q^38)
*]> ;  // time = 84.38 seconds




J[359] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 359, 359, 359, 359 ], new_dimensions := [ 1, 1, 4, 24 ], dimensions := [ 1, 1, 4, 24 ], intersection_graph := [ 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0 ], ap_traces := [
[ 1, -2, 1, 1, -2, -6, -3, -1, 0, -4, -1, 7 ],
[ -1, 0, 1, -1, -2, 0, -3, 1, -6, -6, 1, -9 ],
[ -2, -1, -6, -3, 1, -5, 1, -13, 6, 13, -19, -9 ],
[ 1, 5, 6, 5, 1, 19, 5, 25, -8, 1, 41, 23 ]
], hecke_fields := [
x - 1,
x - 1,
x^4 + 2*x^3 - 3*x^2 - 5*x + 1,
x^24 - x^23 - 39*x^22 + 38*x^21 + 658*x^20 - 619*x^19 - 6300*x^18 + 5654*x^17 + 37740*x^16 - 31780*x^15 - 147096*x^14 + 113400*x^13 + 376092*x^12 - 255412*x^11 - 621508*x^10 + 349080*x^9 + 638532*x^8 - 266744*x^7 - 378124*x^6 + 98609*x^5 + 110695*x^4 - 14509*x^3 - 11972*x^2 + 780*x + 381
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 179 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 179 ]
], torsion_upper_bounds := [ 1, 1, 1, 179 ], torsion_lower_bounds := [ 1, 1, 1, 179 ], l_ratios := [ 0, 0, 0, 1/179 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1 ], eigenvalues := [*
[ 1, -2, 1, 1, -2, -6, -3, -1, 0, -4, -1, 7 ],
[ -1, 0, 1, -1, -2, 0, -3, 1, -6, -6, 1, -9 ],
[
a,
-a^3 - a^2 + 3*a + 1,
-a - 2,
a^3 + a^2 - 3*a - 2,
a^3 + a^2 - 3*a - 1,
a^3 - 3*a,
-a^3 + a^2 + 4*a - 3,
-a^3 + 4*a - 4,
-2*a^2 - 3*a + 5,
a^3 + 2*a^2 + 1,
-a^3 - 3*a^2 + 2*a + 1,
-3*a^3 - 3*a^2 + 8*a + 1
],
[
a,
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*]> ;  // time = 10.519 seconds




J[362] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 362, 362, 362, 362, 362, 362, 181, 181 ], new_dimensions := [ 1, 1, 2, 2, 5, 5, 5, 9 ], dimensions := [ 1, 1, 2, 2, 5, 5, 10, 18 ], intersection_graph := [ 0, 1, 5, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 7, 5, 1, 0, 1, 1, 1, 29, 1, 1, 1, 1, 0, 1, 17, 23, 1, 1, 1, 1, 1, 0, 1, 1, 2391, 1, 1, 1, 17, 1, 0, 17, 1, 1, 1, 29, 23, 1, 17, 0, 1, 1, 7, 1, 1, 2391, 1, 1, 0 ], ap_traces := [
[ -1, -1, 2, -4, -1, 4, -6, -2, -3, 4, -11, -12 ],
[ 1, -1, -2, -4, -1, -4, 2, 6, -1, -8, -1, 0 ],
[ -2, -2, -1, -3, -2, -7, 8, -9, -1, 3, 3, -9 ],
[ 2, 2, 4, 0, -10, 8, 4, 0, -14, 0, 6, 0 ],
[ -5, 4, 0, 5, 4, 10, 0, 4, 0, -10, 12, 22 ],
[ 5, 0, -1, 6, 4, -5, 0, 1, 15, 5, -9, 21 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + 2*x - 4,
x^2 - 2*x - 1,
x^5 - 4*x^4 - 2*x^3 + 17*x^2 - x - 17,
x^5 - 13*x^3 + 3*x^2 + 38*x - 28
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 7, 1 ],
[ 29, 1 ],
[ 161, 1 ],
[ 7173, 3 ],
[ 221, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 161, 1 ],
[ 1, 3 ],
[ 221, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 7, 3, 13 ], torsion_lower_bounds := [ 1, 1, 1, 7, 3, 13 ], l_ratios := [ 0, 0, 0, 23/7, 1/3, 17/13 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1, 1 ], eigenvalues := [*
[ -1, -1, 2, -4, -1, 4, -6, -2, -3, 4, -11, -12 ],
[ 1, -1, -2, -4, -1, -4, 2, 6, -1, -8, -1, 0 ],
[
-1,
a,
-1/2*a - 1,
-1/2*a - 2,
-a - 2,
-1/2*a - 4,
4,
-1/2*a - 5,
7/2*a + 3,
5/2*a + 4,
1/2*a + 2,
-1/2*a - 5
],
[
1,
a,
-a + 3,
-2*a + 2,
a - 6,
a + 3,
3*a - 1,
-5*a + 5,
a - 8,
-4*a + 4,
5*a - 2,
a - 1
],
[
-1,
a,
a^4 - 3*a^3 - 3*a^2 + 8*a + 3,
-a^3 + 2*a^2 + 3*a - 2,
a^3 - 3*a^2 - 2*a + 7,
-a^4 + 3*a^3 + 3*a^2 - 8*a - 1,
-a^4 + 3*a^3 + 3*a^2 - 8*a - 3,
-a^4 + a^3 + 11*a^2 - 6*a - 21,
-a^3 + 5*a^2 - 2*a - 11,
-2*a^3 + 4*a^2 + 6*a - 8,
a^4 - 3*a^3 - 4*a^2 + 6*a + 11,
a^4 - a^3 - 7*a^2 + 15
],
[
1,
a,
-1/2*a^4 + 9/2*a^2 + 1/2*a - 5,
1/2*a^4 - 9/2*a^2 - 1/2*a + 6,
-a^2 - a + 6,
1/2*a^4 + a^3 - 13/2*a^2 - 19/2*a + 16,
-2*a,
1/2*a^4 - 9/2*a^2 - 1/2*a + 5,
-1/2*a^4 + 11/2*a^2 + 3/2*a - 7,
-1/2*a^4 - a^3 + 13/2*a^2 + 15/2*a - 16,
1/2*a^4 + a^3 - 11/2*a^2 - 15/2*a + 10,
-1/2*a^4 - 2*a^3 + 17/2*a^2 + 33/2*a - 25
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + 2*q^5 + q^6 - 4*q^7 - q^8 - 2*q^9 - 2*q^10 - q^11 - q^12 + 4*q^13 + 4*q^14 - 2*q^15 + q^16 - 6*q^17 + 2*q^18 - 2*q^19 + 2*q^20 + 4*q^21 + q^22 - 3*q^23 + q^24 - q^25 - 4*q^26 + 5*q^27 - 4*q^28 + 4*q^29 + 2*q^30 - 11*q^31 - q^32 + q^33 + 6*q^34 - 8*q^35 - 2*q^36 - 12*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 2*q^5 - q^6 - 4*q^7 + q^8 - 2*q^9 - 2*q^10 - q^11 - q^12 - 4*q^13 - 4*q^14 + 2*q^15 + q^16 + 2*q^17 - 2*q^18 + 6*q^19 - 2*q^20 + 4*q^21 - q^22 - q^23 - q^24 - q^25 - 4*q^26 + 5*q^27 - 4*q^28 - 8*q^29 + 2*q^30 - q^31 + q^32 + q^33 + 2*q^34 + 8*q^35 - 2*q^36 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-1/2*a - 1)*q^5 - a*q^6 + (-1/2*a - 2)*q^7 - q^8 + (-2*a + 1)*q^9 + (1/2*a + 1)*q^10 + (-a - 2)*q^11 + a*q^12 + (-1/2*a - 4)*q^13 + (1/2*a + 2)*q^14 - 2*q^15 + q^16 + 4*q^17 + (2*a - 1)*q^18 + (-1/2*a - 5)*q^19 + (-1/2*a - 1)*q^20 + (-a - 2)*q^21 + (a + 2)*q^22 + (7/2*a + 3)*q^23 - a*q^24 + (1/2*a - 3)*q^25 + (1/2*a + 4)*q^26 + (2*a - 8)*q^27 + (-1/2*a - 2)*q^28 + (5/2*a + 4)*q^29 + 2*q^30 + (1/2*a + 2)*q^31 - q^32 - 4*q^33 - 4*q^34 + (a + 3)*q^35 + (-2*a + 1)*q^36 + (-1/2*a - 5)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a + 3)*q^5 + a*q^6 + (-2*a + 2)*q^7 + q^8 + (2*a - 2)*q^9 + (-a + 3)*q^10 + (a - 6)*q^11 + a*q^12 + (a + 3)*q^13 + (-2*a + 2)*q^14 + (a - 1)*q^15 + q^16 + (3*a - 1)*q^17 + (2*a - 2)*q^18 + (-5*a + 5)*q^19 + (-a + 3)*q^20 + (-2*a - 2)*q^21 + (a - 6)*q^22 + (a - 8)*q^23 + a*q^24 + (-4*a + 5)*q^25 + (a + 3)*q^26 + (-a + 2)*q^27 + (-2*a + 2)*q^28 + (-4*a + 4)*q^29 + (a - 1)*q^30 + (5*a - 2)*q^31 + q^32 + (-4*a + 1)*q^33 + (3*a - 1)*q^34 + (-4*a + 8)*q^35 + (2*a - 2)*q^36 + (a - 1)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (a^4 - 3*a^3 - 3*a^2 + 8*a + 3)*q^5 - a*q^6 + (-a^3 + 2*a^2 + 3*a - 2)*q^7 - q^8 + (a^2 - 3)*q^9 + (-a^4 + 3*a^3 + 3*a^2 - 8*a - 3)*q^10 + (a^3 - 3*a^2 - 2*a + 7)*q^11 + a*q^12 + (-a^4 + 3*a^3 + 3*a^2 - 8*a - 1)*q^13 + (a^3 - 2*a^2 - 3*a + 2)*q^14 + (a^4 - a^3 - 9*a^2 + 4*a + 17)*q^15 + q^16 + (-a^4 + 3*a^3 + 3*a^2 - 8*a - 3)*q^17 + (-a^2 + 3)*q^18 + (-a^4 + a^3 + 11*a^2 - 6*a - 21)*q^19 + (a^4 - 3*a^3 - 3*a^2 + 8*a + 3)*q^20 + (-a^4 + 2*a^3 + 3*a^2 - 2*a)*q^21 + (-a^3 + 3*a^2 + 2*a - 7)*q^22 + (-a^3 + 5*a^2 - 2*a - 11)*q^23 - a*q^24 + (2*a^3 - 8*a^2 - 2*a + 21)*q^25 + (a^4 - 3*a^3 - 3*a^2 + 8*a + 1)*q^26 + (a^3 - 6*a)*q^27 + (-a^3 + 2*a^2 + 3*a - 2)*q^28 + (-2*a^3 + 4*a^2 + 6*a - 8)*q^29 + (-a^4 + a^3 + 9*a^2 - 4*a - 17)*q^30 + (a^4 - 3*a^3 - 4*a^2 + 6*a + 11)*q^31 - q^32 + (a^4 - 3*a^3 - 2*a^2 + 7*a)*q^33 + (a^4 - 3*a^3 - 3*a^2 + 8*a + 3)*q^34 + (2*a^4 - 4*a^3 - 14*a^2 + 12*a + 28)*q^35 + (a^2 - 3)*q^36 + (a^4 - a^3 - 7*a^2 + 15)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-1/2*a^4 + 9/2*a^2 + 1/2*a - 5)*q^5 + a*q^6 + (1/2*a^4 - 9/2*a^2 - 1/2*a + 6)*q^7 + q^8 + (a^2 - 3)*q^9 + (-1/2*a^4 + 9/2*a^2 + 1/2*a - 5)*q^10 + (-a^2 - a + 6)*q^11 + a*q^12 + (1/2*a^4 + a^3 - 13/2*a^2 - 19/2*a + 16)*q^13 + (1/2*a^4 - 9/2*a^2 - 1/2*a + 6)*q^14 + (-2*a^3 + 2*a^2 + 14*a - 14)*q^15 + q^16 - 2*a*q^17 + (a^2 - 3)*q^18 + (1/2*a^4 - 9/2*a^2 - 1/2*a + 5)*q^19 + (-1/2*a^4 + 9/2*a^2 + 1/2*a - 5)*q^20 + (2*a^3 - 2*a^2 - 13*a + 14)*q^21 + (-a^2 - a + 6)*q^22 + (-1/2*a^4 + 11/2*a^2 + 3/2*a - 7)*q^23 + a*q^24 + (-1/2*a^4 - a^3 + 13/2*a^2 + 15/2*a - 15)*q^25 + (1/2*a^4 + a^3 - 13/2*a^2 - 19/2*a + 16)*q^26 + (a^3 - 6*a)*q^27 + (1/2*a^4 - 9/2*a^2 - 1/2*a + 6)*q^28 + (-1/2*a^4 - a^3 + 13/2*a^2 + 15/2*a - 16)*q^29 + (-2*a^3 + 2*a^2 + 14*a - 14)*q^30 + (1/2*a^4 + a^3 - 11/2*a^2 - 15/2*a + 10)*q^31 + q^32 + (-a^3 - a^2 + 6*a)*q^33 - 2*a*q^34 + (a^3 - 2*a^2 - 7*a + 5)*q^35 + (a^2 - 3)*q^36 + (-1/2*a^4 - 2*a^3 + 17/2*a^2 + 33/2*a - 25)*q^37 + O(q^38)
*]> ;  // time = 85.65 seconds




J[365] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 365, 365, 365, 365, 365, 73, 73, 73 ], new_dimensions := [ 2, 3, 5, 7, 8, 1, 2, 2 ], dimensions := [ 2, 3, 5, 7, 8, 2, 4, 4 ], intersection_graph := [ 0, 1, 1, 75, 1, 1, 11, 1, 1, 0, 1, 1, 1, 1, 1, 13, 1, 1, 0, 1, 1, 1, 19, 1, 75, 1, 1, 0, 1, 1, 5, 1, 1, 1, 1, 1, 0, 1, 1, 27, 1, 1, 1, 1, 1, 0, 1, 9, 11, 1, 19, 5, 1, 1, 0, 1, 1, 13, 1, 1, 27, 9, 1, 0 ], ap_traces := [
[ 0, 4, 2, 6, -6, 0, 0, 4, -4, -8, 14, 16 ],
[ -1, -4, 3, -1, -9, -1, 3, -15, -1, -11, -21, 4 ],
[ -1, -6, -5, -5, 3, -9, -5, -15, -3, 3, -7, -6 ],
[ -1, 2, 7, -3, 15, 5, -5, 13, -5, -3, 11, -26 ],
[ 2, 8, -8, 7, -7, 11, 5, 21, 5, -3, 3, 18 ]
], hecke_fields := [
x^2 - 3,
x^3 + x^2 - 2*x - 1,
x^5 + x^4 - 5*x^3 - 4*x^2 + 4*x + 1,
x^7 + x^6 - 12*x^5 - 9*x^4 + 39*x^3 + 19*x^2 - 16*x - 3,
x^8 - 2*x^7 - 11*x^6 + 19*x^5 + 36*x^4 - 46*x^3 - 41*x^2 + 25*x + 3
], atkin_lehners := [
[ -1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 11, 1 ],
[ 13, 1 ],
[ 19, 1 ],
[ 185, 1 ],
[ 81, 3 ]
], tamagawa_numbers := [
[ 11, 1 ],
[ 13, 1 ],
[ 1, 1 ],
[ 185, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 1, 1, 1, 37, 3 ], torsion_lower_bounds := [ 1, 1, 1, 37, 3 ], l_ratios := [ 11, 0, 0, 5/37, 1/3 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 1 ], eigenvalues := [*
[
a,
2,
1,
-a + 3,
-a - 3,
2*a,
-2*a,
-2*a + 2,
4*a - 2,
-2*a - 4,
a + 7,
8
],
[
a,
a^2 - 3,
1,
-3*a^2 - 2*a + 4,
-3,
3*a^2 + a - 5,
a^2 + 2*a,
2*a^2 + a - 8,
-2*a^2 - 3*a + 2,
-a^2 - 2,
a^2 + 2*a - 8,
-3*a^2 + 2*a + 7
],
[
a,
-a^2 + 1,
-1,
a^3 - 4*a - 1,
-2*a^4 - a^3 + 9*a^2 + 2*a - 4,
-a^3 + 3*a - 2,
3*a^4 + a^3 - 13*a^2 - 5*a + 4,
-2*a^4 - a^3 + 9*a^2 + 5*a - 7,
-3*a^3 + a^2 + 11*a - 3,
-a^4 + a^3 + 5*a^2 - a - 2,
2*a^4 + a^3 - 10*a^2 - 4*a + 5,
-2*a^3 + a^2 + 10*a - 3
],
[
a,
-1/2*a^5 - 1/2*a^4 + 5/2*a^3 + 2*a^2 + 2*a + 1/2,
1,
a^5 + 2*a^4 - 6*a^3 - 11*a^2 + 3*a + 3,
-1/2*a^5 - 3/2*a^4 + 5/2*a^3 + 8*a^2 + a + 3/2,
-1/2*a^6 - 1/2*a^5 + 13/2*a^4 + 4*a^3 - 22*a^2 - 11/2*a + 6,
1/2*a^6 + 1/2*a^5 - 9/2*a^4 - 3*a^3 + 9*a^2 + 5/2*a,
a^3 + a^2 - 5*a - 1,
1/2*a^5 + 1/2*a^4 - 5/2*a^3 - 3*a^2 - 3*a + 5/2,
-a^6 - 2*a^5 + 9*a^4 + 14*a^3 - 21*a^2 - 16*a + 5,
1/2*a^5 + 3/2*a^4 - 3/2*a^3 - 8*a^2 - 9*a + 5/2,
a^5 - a^4 - 7*a^3 + 7*a^2 + 2*a - 4
],
[
a,
-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 3*a^2 - 8*a + 5/2,
-1,
1/2*a^7 - 1/2*a^6 - 5*a^5 + 7/2*a^4 + 23/2*a^3 - 9/2*a^2 - 3*a + 7/2,
-1/4*a^7 + 5/4*a^6 + 3/2*a^5 - 45/4*a^4 - 1/4*a^3 + 87/4*a^2 + a - 15/4,
1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 3*a^3 + 8*a^2 - 5/2*a + 2,
-3/4*a^7 + 5/4*a^6 + 15/2*a^5 - 43/4*a^4 - 77/4*a^3 + 85/4*a^2 + 27/2*a - 27/4,
a^3 - a^2 - 5*a + 5,
-1/4*a^7 - 3/4*a^6 + 7/2*a^5 + 31/4*a^4 - 49/4*a^3 - 69/4*a^2 + 5*a + 9/4,
1/2*a^7 - 3/2*a^6 - 4*a^5 + 25/2*a^4 + 11/2*a^3 - 41/2*a^2 + 3/2,
-1/2*a^7 + 1/2*a^6 + 11/2*a^5 - 4*a^4 - 16*a^3 + 17/2*a^2 + 11*a - 7,
a^5 - a^4 - 9*a^3 + 7*a^2 + 16*a - 4
]
*], q_expansions := [*
q + a*q^2 + 2*q^3 + q^4 + q^5 + 2*a*q^6 + (-a + 3)*q^7 - a*q^8 + q^9 + a*q^10 + (-a - 3)*q^11 + 2*q^12 + 2*a*q^13 + (3*a - 3)*q^14 + 2*q^15 - 5*q^16 - 2*a*q^17 + a*q^18 + (-2*a + 2)*q^19 + q^20 + (-2*a + 6)*q^21 + (-3*a - 3)*q^22 + (4*a - 2)*q^23 - 2*a*q^24 + q^25 + 6*q^26 - 4*q^27 + (-a + 3)*q^28 + (-2*a - 4)*q^29 + 2*a*q^30 + (a + 7)*q^31 - 3*a*q^32 + (-2*a - 6)*q^33 - 6*q^34 + (-a + 3)*q^35 + q^36 + 8*q^37 + O(q^38),
q + a*q^2 + (a^2 - 3)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^2 - a + 1)*q^6 + (-3*a^2 - 2*a + 4)*q^7 + (-a^2 - 2*a + 1)*q^8 + (-3*a^2 - a + 5)*q^9 + a*q^10 - 3*q^11 + (-2*a^2 - a + 5)*q^12 + (3*a^2 + a - 5)*q^13 + (a^2 - 2*a - 3)*q^14 + (a^2 - 3)*q^15 + (-3*a^2 - a + 3)*q^16 + (a^2 + 2*a)*q^17 + (2*a^2 - a - 3)*q^18 + (2*a^2 + a - 8)*q^19 + (a^2 - 2)*q^20 + (6*a^2 + 5*a - 11)*q^21 - 3*a*q^22 + (-2*a^2 - 3*a + 2)*q^23 + (3*a^2 + 3*a - 4)*q^24 + q^25 + (-2*a^2 + a + 3)*q^26 + (3*a^2 + 4*a - 4)*q^27 + (3*a^2 + 3*a - 7)*q^28 + (-a^2 - 2)*q^29 + (-a^2 - a + 1)*q^30 + (a^2 + 2*a - 8)*q^31 + (4*a^2 + a - 5)*q^32 + (-3*a^2 + 9)*q^33 + (a^2 + 2*a + 1)*q^34 + (-3*a^2 - 2*a + 4)*q^35 + (3*a^2 + 3*a - 8)*q^36 + (-3*a^2 + 2*a + 7)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + 1)*q^3 + (a^2 - 2)*q^4 - q^5 + (-a^3 + a)*q^6 + (a^3 - 4*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (a^4 - 2*a^2 - 2)*q^9 - a*q^10 + (-2*a^4 - a^3 + 9*a^2 + 2*a - 4)*q^11 + (-a^4 + 3*a^2 - 2)*q^12 + (-a^3 + 3*a - 2)*q^13 + (a^4 - 4*a^2 - a)*q^14 + (a^2 - 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (3*a^4 + a^3 - 13*a^2 - 5*a + 4)*q^17 + (-a^4 + 3*a^3 + 4*a^2 - 6*a - 1)*q^18 + (-2*a^4 - a^3 + 9*a^2 + 5*a - 7)*q^19 + (-a^2 + 2)*q^20 + (a^4 - 3*a^2)*q^21 + (a^4 - a^3 - 6*a^2 + 4*a + 2)*q^22 + (-3*a^3 + a^2 + 11*a - 3)*q^23 + (a^4 - 4*a^2 + 1)*q^24 + q^25 + (-a^4 + 3*a^2 - 2*a)*q^26 + (-3*a^4 + a^3 + 11*a^2 - 3*a - 6)*q^27 + (-a^4 - a^3 + 3*a^2 + 4*a + 1)*q^28 + (-a^4 + a^3 + 5*a^2 - a - 2)*q^29 + (a^3 - a)*q^30 + (2*a^4 + a^3 - 10*a^2 - 4*a + 5)*q^31 + (-a^4 - 3*a^3 + 4*a^2 + 8*a - 1)*q^32 + (a^2 + 4*a - 3)*q^33 + (-2*a^4 + 2*a^3 + 7*a^2 - 8*a - 3)*q^34 + (-a^3 + 4*a + 1)*q^35 + (2*a^4 - a^3 - 6*a^2 + 3*a + 5)*q^36 + (-2*a^3 + a^2 + 10*a - 3)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^5 - 1/2*a^4 + 5/2*a^3 + 2*a^2 + 2*a + 1/2)*q^3 + (a^2 - 2)*q^4 + q^5 + (-1/2*a^6 - 1/2*a^5 + 5/2*a^4 + 2*a^3 + 2*a^2 + 1/2*a)*q^6 + (a^5 + 2*a^4 - 6*a^3 - 11*a^2 + 3*a + 3)*q^7 + (a^3 - 4*a)*q^8 + (1/2*a^6 + 1/2*a^5 - 9/2*a^4 - 4*a^3 + 10*a^2 + 15/2*a - 2)*q^9 + a*q^10 + (-1/2*a^5 - 3/2*a^4 + 5/2*a^3 + 8*a^2 + a + 3/2)*q^11 + (-5/2*a^5 - 3/2*a^4 + 33/2*a^3 + 6*a^2 - 12*a - 5/2)*q^12 + (-1/2*a^6 - 1/2*a^5 + 13/2*a^4 + 4*a^3 - 22*a^2 - 11/2*a + 6)*q^13 + (a^6 + 2*a^5 - 6*a^4 - 11*a^3 + 3*a^2 + 3*a)*q^14 + (-1/2*a^5 - 1/2*a^4 + 5/2*a^3 + 2*a^2 + 2*a + 1/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/2*a^6 + 1/2*a^5 - 9/2*a^4 - 3*a^3 + 9*a^2 + 5/2*a)*q^17 + (3/2*a^5 + 1/2*a^4 - 19/2*a^3 - 2*a^2 + 6*a + 3/2)*q^18 + (a^3 + a^2 - 5*a - 1)*q^19 + (a^2 - 2)*q^20 + (-a^4 + 5*a^2 - 2*a)*q^21 + (-1/2*a^6 - 3/2*a^5 + 5/2*a^4 + 8*a^3 + a^2 + 3/2*a)*q^22 + (1/2*a^5 + 1/2*a^4 - 5/2*a^3 - 3*a^2 - 3*a + 5/2)*q^23 + (-3/2*a^6 - 1/2*a^5 + 23/2*a^4 + 2*a^3 - 16*a^2 - 7/2*a)*q^24 + q^25 + (1/2*a^5 - 1/2*a^4 - 5/2*a^3 + 4*a^2 - 2*a - 3/2)*q^26 + (a^6 + a^5 - 8*a^4 - 6*a^3 + 14*a^2 + 4*a - 1)*q^27 + (a^6 + 4*a^5 - 6*a^4 - 24*a^3 + 6*a^2 + 10*a - 3)*q^28 + (-a^6 - 2*a^5 + 9*a^4 + 14*a^3 - 21*a^2 - 16*a + 5)*q^29 + (-1/2*a^6 - 1/2*a^5 + 5/2*a^4 + 2*a^3 + 2*a^2 + 1/2*a)*q^30 + (1/2*a^5 + 3/2*a^4 - 3/2*a^3 - 8*a^2 - 9*a + 5/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^4 - 3*a^3 + 5*a^2 + 17*a + 3)*q^33 + (3/2*a^5 + 3/2*a^4 - 21/2*a^3 - 7*a^2 + 8*a + 3/2)*q^34 + (a^5 + 2*a^4 - 6*a^3 - 11*a^2 + 3*a + 3)*q^35 + (1/2*a^6 - 1/2*a^5 - 1/2*a^4 + 6*a^3 - 14*a^2 - 27/2*a + 4)*q^36 + (a^5 - a^4 - 7*a^3 + 7*a^2 + 2*a - 4)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 3*a^2 - 8*a + 5/2)*q^3 + (a^2 - 2)*q^4 - q^5 + (-1/2*a^6 + 1/2*a^5 + 9/2*a^4 - 3*a^3 - 8*a^2 + 5/2*a)*q^6 + (1/2*a^7 - 1/2*a^6 - 5*a^5 + 7/2*a^4 + 23/2*a^3 - 9/2*a^2 - 3*a + 7/2)*q^7 + (a^3 - 4*a)*q^8 + (-1/4*a^7 - 1/4*a^6 + 5/2*a^5 + 15/4*a^4 - 19/4*a^3 - 53/4*a^2 - 5/2*a + 31/4)*q^9 - a*q^10 + (-1/4*a^7 + 5/4*a^6 + 3/2*a^5 - 45/4*a^4 - 1/4*a^3 + 87/4*a^2 + a - 15/4)*q^11 + (-1/2*a^7 + 1/2*a^6 + 11/2*a^5 - 4*a^4 - 17*a^3 + 17/2*a^2 + 16*a - 5)*q^12 + (1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 3*a^3 + 8*a^2 - 5/2*a + 2)*q^13 + (1/2*a^7 + 1/2*a^6 - 6*a^5 - 13/2*a^4 + 37/2*a^3 + 35/2*a^2 - 9*a - 3/2)*q^14 + (1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 3*a^2 + 8*a - 5/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3/4*a^7 + 5/4*a^6 + 15/2*a^5 - 43/4*a^4 - 77/4*a^3 + 85/4*a^2 + 27/2*a - 27/4)*q^17 + (-3/4*a^7 - 1/4*a^6 + 17/2*a^5 + 17/4*a^4 - 99/4*a^3 - 51/4*a^2 + 14*a + 3/4)*q^18 + (a^3 - a^2 - 5*a + 5)*q^19 + (-a^2 + 2)*q^20 + (3/2*a^7 - 3/2*a^6 - 16*a^5 + 23/2*a^4 + 89/2*a^3 - 39/2*a^2 - 30*a + 19/2)*q^21 + (3/4*a^7 - 5/4*a^6 - 13/2*a^5 + 35/4*a^4 + 41/4*a^3 - 37/4*a^2 + 5/2*a + 3/4)*q^22 + (-1/4*a^7 - 3/4*a^6 + 7/2*a^5 + 31/4*a^4 - 49/4*a^3 - 69/4*a^2 + 5*a + 9/4)*q^23 + (-1/2*a^7 + a^6 + 9/2*a^5 - 8*a^4 - 17/2*a^3 + 23/2*a^2 + 5/2*a + 3/2)*q^24 + q^25 + (1/2*a^7 - 1/2*a^6 - 9/2*a^5 + 3*a^4 + 8*a^3 - 5/2*a^2 + 2*a)*q^26 + (-1/4*a^7 - 7/4*a^6 + 4*a^5 + 73/4*a^4 - 55/4*a^3 - 181/4*a^2 + 2*a + 67/4)*q^27 + (1/2*a^7 + 1/2*a^6 - 6*a^5 - 13/2*a^4 + 35/2*a^3 + 41/2*a^2 - 8*a - 17/2)*q^28 + (1/2*a^7 - 3/2*a^6 - 4*a^5 + 25/2*a^4 + 11/2*a^3 - 41/2*a^2 + 3/2)*q^29 + (1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 3*a^3 + 8*a^2 - 5/2*a)*q^30 + (-1/2*a^7 + 1/2*a^6 + 11/2*a^5 - 4*a^4 - 16*a^3 + 17/2*a^2 + 11*a - 7)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/4*a^7 + 3/4*a^6 - 3*a^5 - 37/4*a^4 + 35/4*a^3 + 113/4*a^2 - 5*a - 51/4)*q^33 + (-1/4*a^7 - 3/4*a^6 + 7/2*a^5 + 31/4*a^4 - 53/4*a^3 - 69/4*a^2 + 12*a + 9/4)*q^34 + (-1/2*a^7 + 1/2*a^6 + 5*a^5 - 7/2*a^4 - 23/2*a^3 + 9/2*a^2 + 3*a - 7/2)*q^35 + (-5/4*a^7 + 3/4*a^6 + 27/2*a^5 - 21/4*a^4 - 151/4*a^3 + 39/4*a^2 + 49/2*a - 53/4)*q^36 + (a^5 - a^4 - 9*a^3 + 7*a^2 + 16*a - 4)*q^37 + O(q^38)
*]> ;  // time = 57.699 seconds




J[366] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 366, 366, 366, 366, 366, 366, 366, 366, 183, 183, 183, 122, 122, 122, 61, 61 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 6, 1, 2, 3, 1, 3 ], dimensions := [ 1, 1, 1, 1, 1, 1, 1, 2, 4, 6, 12, 2, 4, 6, 4, 12 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 19, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 7, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 5, 13, 1, 1, 1, 1, 1, 1, 0, 1, 13, 1, 1, 17, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 13, 1, 0, 1, 1, 1, 1, 1, 361, 1, 19, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 31, 9, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 17, 1, 1, 1, 1, 0, 1, 1, 169, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 31, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 361, 1, 1, 169, 1, 1, 0 ], ap_traces := [
[ -1, -1, -2, 4, -4, -2, 6, 4, 8, 10, 4, 6 ],
[ -1, 1, 1, -2, 6, 0, 3, 0, -1, 6, 0, 3 ],
[ -1, 1, -3, -1, -3, -1, -6, -4, 3, 0, -4, 8 ],
[ 1, -1, -1, 2, 2, 4, 1, 4, -3, -2, 4, -1 ],
[ 1, -1, -3, -3, -1, -5, 2, -8, 5, 0, -4, 4 ],
[ 1, 1, 1, 1, -1, -5, 2, 0, -3, 8, 4, -4 ],
[ 1, 1, 1, -2, 2, 4, -7, 0, 9, -10, -8, -7 ],
[ -2, -2, 0, -3, 3, 7, -3, 8, -10, -2, 8, 5 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 17
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ 1, -1, -1 ],
[ -1, 1, 1 ],
[ -1, 1, -1 ],
[ -1, -1, -1 ],
[ -1, -1, -1 ],
[ 1, 1, -1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 19, 3, 1 ],
[ 1, 3, 1 ],
[ 7, 13, 1 ],
[ 5, 1, 1 ],
[ 1, 1, 1 ],
[ 5, 5, 1 ],
[ 13, 17, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 3, 1 ],
[ 7, 1, 1 ],
[ 5, 1, 1 ],
[ 1, 1, 1 ],
[ 5, 5, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 1, 1, 5, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 1, 3, 0, 7, 0, 1, 1, 1 ], analytic_sha_upper_bounds := [ 1, 1, 0, 1, 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 1, 0, 1, 1/25, 1 ], eigenvalues := [*
[ -1, -1, -2, 4, -4, -2, 6, 4, 8, 10, 4, 6 ],
[ -1, 1, 1, -2, 6, 0, 3, 0, -1, 6, 0, 3 ],
[ -1, 1, -3, -1, -3, -1, -6, -4, 3, 0, -4, 8 ],
[ 1, -1, -1, 2, 2, 4, 1, 4, -3, -2, 4, -1 ],
[ 1, -1, -3, -3, -1, -5, 2, -8, 5, 0, -4, 4 ],
[ 1, 1, 1, 1, -1, -5, 2, 0, -3, 8, 4, -4 ],
[ 1, 1, 1, -2, 2, 4, -7, 0, 9, -10, -8, -7 ],
[
-1,
-1,
a,
1/2*a - 3/2,
-1/2*a + 3/2,
-1/2*a + 7/2,
-1/2*a - 3/2,
4,
-5,
a - 1,
4,
3/2*a + 5/2
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - 2*q^5 + q^6 + 4*q^7 - q^8 + q^9 + 2*q^10 - 4*q^11 - q^12 - 2*q^13 - 4*q^14 + 2*q^15 + q^16 + 6*q^17 - q^18 + 4*q^19 - 2*q^20 - 4*q^21 + 4*q^22 + 8*q^23 + q^24 - q^25 + 2*q^26 - q^27 + 4*q^28 + 10*q^29 - 2*q^30 + 4*q^31 - q^32 + 4*q^33 - 6*q^34 - 8*q^35 + q^36 + 6*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + q^5 - q^6 - 2*q^7 - q^8 + q^9 - q^10 + 6*q^11 + q^12 + 2*q^14 + q^15 + q^16 + 3*q^17 - q^18 + q^20 - 2*q^21 - 6*q^22 - q^23 - q^24 - 4*q^25 + q^27 - 2*q^28 + 6*q^29 - q^30 - q^32 + 6*q^33 - 3*q^34 - 2*q^35 + q^36 + 3*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - 3*q^5 - q^6 - q^7 - q^8 + q^9 + 3*q^10 - 3*q^11 + q^12 - q^13 + q^14 - 3*q^15 + q^16 - 6*q^17 - q^18 - 4*q^19 - 3*q^20 - q^21 + 3*q^22 + 3*q^23 - q^24 + 4*q^25 + q^26 + q^27 - q^28 + 3*q^30 - 4*q^31 - q^32 - 3*q^33 + 6*q^34 + 3*q^35 + q^36 + 8*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - q^5 - q^6 + 2*q^7 + q^8 + q^9 - q^10 + 2*q^11 - q^12 + 4*q^13 + 2*q^14 + q^15 + q^16 + q^17 + q^18 + 4*q^19 - q^20 - 2*q^21 + 2*q^22 - 3*q^23 - q^24 - 4*q^25 + 4*q^26 - q^27 + 2*q^28 - 2*q^29 + q^30 + 4*q^31 + q^32 - 2*q^33 + q^34 - 2*q^35 + q^36 - q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 3*q^5 - q^6 - 3*q^7 + q^8 + q^9 - 3*q^10 - q^11 - q^12 - 5*q^13 - 3*q^14 + 3*q^15 + q^16 + 2*q^17 + q^18 - 8*q^19 - 3*q^20 + 3*q^21 - q^22 + 5*q^23 - q^24 + 4*q^25 - 5*q^26 - q^27 - 3*q^28 + 3*q^30 - 4*q^31 + q^32 + q^33 + 2*q^34 + 9*q^35 + q^36 + 4*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^5 + q^6 + q^7 + q^8 + q^9 + q^10 - q^11 + q^12 - 5*q^13 + q^14 + q^15 + q^16 + 2*q^17 + q^18 + q^20 + q^21 - q^22 - 3*q^23 + q^24 - 4*q^25 - 5*q^26 + q^27 + q^28 + 8*q^29 + q^30 + 4*q^31 + q^32 - q^33 + 2*q^34 + q^35 + q^36 - 4*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^5 + q^6 - 2*q^7 + q^8 + q^9 + q^10 + 2*q^11 + q^12 + 4*q^13 - 2*q^14 + q^15 + q^16 - 7*q^17 + q^18 + q^20 - 2*q^21 + 2*q^22 + 9*q^23 + q^24 - 4*q^25 + 4*q^26 + q^27 - 2*q^28 - 10*q^29 + q^30 - 8*q^31 + q^32 + 2*q^33 - 7*q^34 - 2*q^35 + q^36 - 7*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + a*q^5 + q^6 + (1/2*a - 3/2)*q^7 - q^8 + q^9 - a*q^10 + (-1/2*a + 3/2)*q^11 - q^12 + (-1/2*a + 7/2)*q^13 + (-1/2*a + 3/2)*q^14 - a*q^15 + q^16 + (-1/2*a - 3/2)*q^17 - q^18 + 4*q^19 + a*q^20 + (-1/2*a + 3/2)*q^21 + (1/2*a - 3/2)*q^22 - 5*q^23 + q^24 + 12*q^25 + (1/2*a - 7/2)*q^26 - q^27 + (1/2*a - 3/2)*q^28 + (a - 1)*q^29 + a*q^30 + 4*q^31 - q^32 + (1/2*a - 3/2)*q^33 + (1/2*a + 3/2)*q^34 + (-3/2*a + 17/2)*q^35 + q^36 + (3/2*a + 5/2)*q^37 + O(q^38)
*]> ;  // time = 238.53 seconds




J[367] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 367, 367 ], new_dimensions := [ 11, 19 ], dimensions := [ 11, 19 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -8, -6, -8, -7, -10, -5, -32, 3, -15, -26, 3, -10 ],
[ 9, 4, 6, 1, 4, 5, 40, -3, 21, 28, -13, 8 ]
], hecke_fields := [
x^11 + 8*x^10 + 16*x^9 - 26*x^8 - 121*x^7 - 61*x^6 + 197*x^5 + 212*x^4 - 66*x^3 - 132*x^2 - 12*x + 13,
x^19 - 9*x^18 + 11*x^17 + 123*x^16 - 372*x^15 - 469*x^14 + 2884*x^13 - 550*x^12 - 10042*x^11 + 8029*x^10 + 17059*x^9 - 20350*x^8 - 12836*x^7 + 20779*x^6 + 2682*x^5 - 7739*x^4 + 63*x^3 + 899*x^2 - 27*x - 29
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 61 ]
], tamagawa_numbers := [
[ 1 ],
[ 61 ]
], torsion_upper_bounds := [ 1, 61 ], torsion_lower_bounds := [ 1, 61 ], l_ratios := [ 0, 1/61 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-8*a^10 - 54*a^9 - 61*a^8 + 282*a^7 + 616*a^6 - 269*a^5 - 1230*a^4 - 177*a^3 + 729*a^2 + 149*a - 83,
24*a^10 + 162*a^9 + 181*a^8 - 852*a^7 - 1836*a^6 + 844*a^5 + 3668*a^4 + 472*a^3 - 2173*a^2 - 426*a + 246,
-17*a^10 - 114*a^9 - 124*a^8 + 605*a^7 + 1275*a^6 - 627*a^5 - 2555*a^4 - 279*a^3 + 1515*a^2 + 278*a - 171,
19*a^10 + 127*a^9 + 138*a^8 - 671*a^7 - 1419*a^6 + 680*a^5 + 2837*a^4 + 340*a^3 - 1673*a^2 - 321*a + 184,
-11*a^10 - 75*a^9 - 86*a^8 + 393*a^7 + 861*a^6 - 383*a^5 - 1716*a^4 - 227*a^3 + 1013*a^2 + 196*a - 114,
-6*a^10 - 40*a^9 - 43*a^8 + 211*a^7 + 441*a^6 - 214*a^5 - 871*a^4 - 104*a^3 + 505*a^2 + 101*a - 60,
29*a^10 + 196*a^9 + 220*a^8 - 1031*a^7 - 2231*a^6 + 1023*a^5 + 4474*a^4 + 564*a^3 - 2674*a^2 - 508*a + 307,
12*a^10 + 79*a^9 + 81*a^8 - 424*a^7 - 859*a^6 + 460*a^5 + 1730*a^4 + 163*a^3 - 1028*a^2 - 189*a + 116,
44*a^10 + 296*a^9 + 327*a^8 - 1561*a^7 - 3335*a^6 + 1569*a^5 + 6669*a^4 + 815*a^3 - 3956*a^2 - 755*a + 449,
-71*a^10 - 477*a^9 - 526*a^8 + 2515*a^7 + 5375*a^6 - 2518*a^5 - 10765*a^4 - 1354*a^3 + 6401*a^2 + 1255*a - 733,
-72*a^10 - 483*a^9 - 530*a^8 + 2548*a^7 + 5422*a^6 - 2565*a^5 - 10838*a^4 - 1323*a^3 + 6416*a^2 + 1231*a - 726
],
[
a,
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]
*], q_expansions := [*
q + a*q^2 + (-8*a^10 - 54*a^9 - 61*a^8 + 282*a^7 + 616*a^6 - 269*a^5 - 1230*a^4 - 177*a^3 + 729*a^2 + 149*a - 83)*q^3 + (a^2 - 2)*q^4 + (24*a^10 + 162*a^9 + 181*a^8 - 852*a^7 - 1836*a^6 + 844*a^5 + 3668*a^4 + 472*a^3 - 2173*a^2 - 426*a + 246)*q^5 + (10*a^10 + 67*a^9 + 74*a^8 - 352*a^7 - 757*a^6 + 346*a^5 + 1519*a^4 + 201*a^3 - 907*a^2 - 179*a + 104)*q^6 + (-17*a^10 - 114*a^9 - 124*a^8 + 605*a^7 + 1275*a^6 - 627*a^5 - 2555*a^4 - 279*a^3 + 1515*a^2 + 278*a - 171)*q^7 + (a^3 - 4*a)*q^8 + (-22*a^10 - 148*a^9 - 163*a^8 + 782*a^7 + 1665*a^6 - 792*a^5 - 3331*a^4 - 402*a^3 + 1975*a^2 + 381*a - 225)*q^9 + (-30*a^10 - 203*a^9 - 228*a^8 + 1068*a^7 + 2308*a^6 - 1060*a^5 - 4616*a^4 - 589*a^3 + 2742*a^2 + 534*a - 312)*q^10 + (19*a^10 + 127*a^9 + 138*a^8 - 671*a^7 - 1419*a^6 + 680*a^5 + 2837*a^4 + 340*a^3 - 1673*a^2 - 321*a + 184)*q^11 + (3*a^10 + 22*a^9 + 30*a^8 - 111*a^7 - 276*a^6 + 87*a^5 + 541*a^4 + 107*a^3 - 317*a^2 - 74*a + 36)*q^12 + (-11*a^10 - 75*a^9 - 86*a^8 + 393*a^7 + 861*a^6 - 383*a^5 - 1716*a^4 - 227*a^3 + 1013*a^2 + 196*a - 114)*q^13 + (22*a^10 + 148*a^9 + 163*a^8 - 782*a^7 - 1664*a^6 + 794*a^5 + 3325*a^4 + 393*a^3 - 1966*a^2 - 375*a + 221)*q^14 + (27*a^10 + 182*a^9 + 203*a^8 - 957*a^7 - 2063*a^6 + 946*a^5 + 4129*a^4 + 537*a^3 - 2454*a^2 - 483*a + 278)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-6*a^10 - 40*a^9 - 43*a^8 + 211*a^7 + 441*a^6 - 214*a^5 - 871*a^4 - 104*a^3 + 505*a^2 + 101*a - 60)*q^17 + (28*a^10 + 189*a^9 + 210*a^8 - 997*a^7 - 2134*a^6 + 1003*a^5 + 4262*a^4 + 523*a^3 - 2523*a^2 - 489*a + 286)*q^18 + (29*a^10 + 196*a^9 + 220*a^8 - 1031*a^7 - 2231*a^6 + 1023*a^5 + 4474*a^4 + 564*a^3 - 2674*a^2 - 508*a + 307)*q^19 + (-11*a^10 - 72*a^9 - 74*a^8 + 382*a^7 + 782*a^6 - 394*a^5 - 1565*a^4 - 182*a^3 + 920*a^2 + 180*a - 102)*q^20 + (12*a^10 + 80*a^9 + 86*a^8 - 424*a^7 - 889*a^6 + 436*a^5 + 1779*a^4 + 203*a^3 - 1049*a^2 - 197*a + 114)*q^21 + (-25*a^10 - 166*a^9 - 177*a^8 + 880*a^7 + 1839*a^6 - 906*a^5 - 3688*a^4 - 419*a^3 + 2187*a^2 + 412*a - 247)*q^22 + (12*a^10 + 79*a^9 + 81*a^8 - 424*a^7 - 859*a^6 + 460*a^5 + 1730*a^4 + 163*a^3 - 1028*a^2 - 189*a + 116)*q^23 + (-22*a^10 - 152*a^9 - 181*a^8 + 791*a^7 + 1784*a^6 - 742*a^5 - 3567*a^4 - 521*a^3 + 2136*a^2 + 430*a - 247)*q^24 + (-7*a^10 - 48*a^9 - 57*a^8 + 248*a^7 + 564*a^6 - 222*a^5 - 1129*a^4 - 186*a^3 + 678*a^2 + 143*a - 82)*q^25 + (13*a^10 + 90*a^9 + 107*a^8 - 470*a^7 - 1054*a^6 + 451*a^5 + 2105*a^4 + 287*a^3 - 1256*a^2 - 246*a + 143)*q^26 + (14*a^10 + 94*a^9 + 104*a^8 - 493*a^7 - 1058*a^6 + 480*a^5 + 2105*a^4 + 295*a^3 - 1235*a^2 - 259*a + 139)*q^27 + (6*a^10 + 39*a^9 + 38*a^8 - 212*a^7 - 414*a^6 + 245*a^5 + 839*a^4 + 44*a^3 - 501*a^2 - 71*a + 56)*q^28 + (44*a^10 + 296*a^9 + 327*a^8 - 1561*a^7 - 3335*a^6 + 1569*a^5 + 6669*a^4 + 815*a^3 - 3956*a^2 - 755*a + 449)*q^29 + (-34*a^10 - 229*a^9 - 255*a^8 + 1204*a^7 + 2593*a^6 - 1190*a^5 - 5187*a^4 - 672*a^3 + 3081*a^2 + 602*a - 351)*q^30 + (-71*a^10 - 477*a^9 - 526*a^8 + 2515*a^7 + 5375*a^6 - 2518*a^5 - 10765*a^4 - 1354*a^3 + 6401*a^2 + 1255*a - 733)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (7*a^10 + 47*a^9 + 52*a^8 - 246*a^7 - 528*a^6 + 236*a^5 + 1047*a^4 + 159*a^3 - 611*a^2 - 141*a + 68)*q^33 + (8*a^10 + 53*a^9 + 55*a^8 - 285*a^7 - 580*a^6 + 311*a^5 + 1168*a^4 + 109*a^3 - 691*a^2 - 132*a + 78)*q^34 + (-74*a^10 - 498*a^9 - 551*a^8 + 2625*a^7 + 5616*a^6 - 2629*a^5 - 11228*a^4 - 1400*a^3 + 6651*a^2 + 1295*a - 752)*q^35 + (9*a^10 + 58*a^9 + 57*a^8 - 310*a^7 - 619*a^6 + 330*a^5 + 1249*a^4 + 129*a^3 - 743*a^2 - 140*a + 86)*q^36 + (-72*a^10 - 483*a^9 - 530*a^8 + 2548*a^7 + 5422*a^6 - 2565*a^5 - 10838*a^4 - 1323*a^3 + 6416*a^2 + 1231*a - 726)*q^37 + O(q^38),
q + a*q^2 + (6827828/23610721*a^18 - 49682236/23610721*a^17 - 6832536/23610721*a^16 + 803001118/23610721*a^15 - 1171782712/23610721*a^14 - 4794282730/23610721*a^13 + 10991047449/23610721*a^12 + 12384298965/23610721*a^11 - 42478188938/23610721*a^10 - 9593322662/23610721*a^9 + 80448498286/23610721*a^8 - 13480943176/23610721*a^7 - 72276385698/23610721*a^6 + 24824130950/23610721*a^5 + 25244646700/23610721*a^4 - 151658173/387061*a^3 - 3069626859/23610721*a^2 + 818237984/23610721*a + 127146744/23610721)*q^3 + (a^2 - 2)*q^4 + (-1297203/23610721*a^18 + 14414733/23610721*a^17 - 31674448/23610721*a^16 - 177259634/23610721*a^15 + 783001630/23610721*a^14 + 404568652/23610721*a^13 - 5772832937/23610721*a^12 + 3265357555/23610721*a^11 + 19924295543/23610721*a^10 - 21018429365/23610721*a^9 - 34798304039/23610721*a^8 + 47067197132/23610721*a^7 + 29544729494/23610721*a^6 - 45508663466/23610721*a^5 - 10825879428/23610721*a^4 + 257534213/387061*a^3 + 2047419967/23610721*a^2 - 1129150019/23610721*a - 90300556/23610721)*q^5 + (11768216/23610721*a^18 - 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2530134065/23610721*a - 926645599/23610721)*q^37 + O(q^38)
*]> ;  // time = 7.329 seconds




J[370] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 370, 370, 370, 370, 370, 370, 370, 185, 185, 185, 185, 185, 74, 74, 37, 37 ], new_dimensions := [ 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 5, 5, 2, 2, 1, 1 ], dimensions := [ 1, 1, 1, 1, 2, 2, 3, 2, 2, 2, 10, 10, 4, 4, 4, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 9, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 5, 1, 1, 1, 1, 31, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 9, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 27, 1, 1, 9, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 19, 1, 1, 1, 9, 1, 1, 13, 1, 1, 1, 1, 1, 27, 1, 0, 1, 1, 9, 1, 1, 1, 1, 1, 1, 31, 1, 1, 1, 1, 19, 1, 0, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 0, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 9, 1, 9, 1, 1, 0 ], ap_traces := [
[ -1, 0, -1, 0, -4, 2, -2, -4, 0, -6, -4, -1 ],
[ -1, -2, -1, -1, 3, -4, 3, 2, 6, 3, 5, 1 ],
[ -1, 2, 1, 1, 3, 0, 3, -6, 2, -3, 3, -1 ],
[ 1, -2, 1, 2, 0, 2, 6, 2, 0, 6, -10, 1 ],
[ -2, -2, 2, -6, -4, -4, 4, 2, -16, -4, -2, 2 ],
[ 2, 4, 2, -3, -1, 2, -5, -4, 2, -1, -11, 2 ],
[ 3, 0, -3, -1, 11, 0, 1, 0, -2, -5, 3, -3 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 + 2*x - 2,
x^2 - 13*x - 32,
x^3 - 10*x + 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ],
[ 1, -1, -1 ],
[ -1, -1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 3, 3, 3 ],
[ 11, 1, 1 ],
[ 3, 3, 1 ],
[ 3, 13, 1 ],
[ 3, 1, 1 ],
[ 5, 31, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 3 ],
[ 1, 1, 1 ],
[ 3, 3, 1 ],
[ 1, 13, 1 ],
[ 3, 1, 1 ],
[ 5, 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 3, 1, 1, 1 ], torsion_lower_bounds := [ 1, 3, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1/3, 1, 1, 0, 3, 5 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1/9, 0, 1, 1 ], eigenvalues := [*
[ -1, 0, -1, 0, -4, 2, -2, -4, 0, -6, -4, -1 ],
[ -1, -2, -1, -1, 3, -4, 3, 2, 6, 3, 5, 1 ],
[ -1, 2, 1, 1, 3, 0, 3, -6, 2, -3, 3, -1 ],
[ 1, -2, 1, 2, 0, 2, 6, 2, 0, 6, -10, 1 ],
[
-1,
a,
1,
-a - 4,
-2*a - 4,
-2*a - 4,
2*a + 4,
3*a + 4,
-8,
4*a + 2,
a,
1
],
[
1,
2,
1,
-1/3*a + 2/3,
1/3*a - 8/3,
2/3*a - 10/3,
1/3*a - 14/3,
-2,
-2/3*a + 16/3,
-a + 6,
-1/3*a - 10/3,
1
],
[
1,
a,
-1,
-1/2*a^2 + 3,
-1/2*a^2 - a + 7,
-2*a,
1/2*a^2 + a - 3,
a,
-a^2 - 2*a + 6,
1/2*a^2 - a - 5,
3/2*a^2 - 9,
-1
]
*], q_expansions := [*
q - q^2 + q^4 - q^5 - q^8 - 3*q^9 + q^10 - 4*q^11 + 2*q^13 + q^16 - 2*q^17 + 3*q^18 - 4*q^19 - q^20 + 4*q^22 + q^25 - 2*q^26 - 6*q^29 - 4*q^31 - q^32 + 2*q^34 - 3*q^36 - q^37 + O(q^38),
q - q^2 - 2*q^3 + q^4 - q^5 + 2*q^6 - q^7 - q^8 + q^9 + q^10 + 3*q^11 - 2*q^12 - 4*q^13 + q^14 + 2*q^15 + q^16 + 3*q^17 - q^18 + 2*q^19 - q^20 + 2*q^21 - 3*q^22 + 6*q^23 + 2*q^24 + q^25 + 4*q^26 + 4*q^27 - q^28 + 3*q^29 - 2*q^30 + 5*q^31 - q^32 - 6*q^33 - 3*q^34 + q^35 + q^36 + q^37 + O(q^38),
q - q^2 + 2*q^3 + q^4 + q^5 - 2*q^6 + q^7 - q^8 + q^9 - q^10 + 3*q^11 + 2*q^12 - q^14 + 2*q^15 + q^16 + 3*q^17 - q^18 - 6*q^19 + q^20 + 2*q^21 - 3*q^22 + 2*q^23 - 2*q^24 + q^25 - 4*q^27 + q^28 - 3*q^29 - 2*q^30 + 3*q^31 - q^32 + 6*q^33 - 3*q^34 + q^35 + q^36 - q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 + q^5 - 2*q^6 + 2*q^7 + q^8 + q^9 + q^10 - 2*q^12 + 2*q^13 + 2*q^14 - 2*q^15 + q^16 + 6*q^17 + q^18 + 2*q^19 + q^20 - 4*q^21 - 2*q^24 + q^25 + 2*q^26 + 4*q^27 + 2*q^28 + 6*q^29 - 2*q^30 - 10*q^31 + q^32 + 6*q^34 + 2*q^35 + q^36 + q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + q^5 - a*q^6 + (-a - 4)*q^7 - q^8 + (-2*a - 1)*q^9 - q^10 + (-2*a - 4)*q^11 + a*q^12 + (-2*a - 4)*q^13 + (a + 4)*q^14 + a*q^15 + q^16 + (2*a + 4)*q^17 + (2*a + 1)*q^18 + (3*a + 4)*q^19 + q^20 + (-2*a - 2)*q^21 + (2*a + 4)*q^22 - 8*q^23 - a*q^24 + q^25 + (2*a + 4)*q^26 - 4*q^27 + (-a - 4)*q^28 + (4*a + 2)*q^29 - a*q^30 + a*q^31 - q^32 - 4*q^33 + (-2*a - 4)*q^34 + (-a - 4)*q^35 + (-2*a - 1)*q^36 + q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 + q^5 + 2*q^6 + (-1/3*a + 2/3)*q^7 + q^8 + q^9 + q^10 + (1/3*a - 8/3)*q^11 + 2*q^12 + (2/3*a - 10/3)*q^13 + (-1/3*a + 2/3)*q^14 + 2*q^15 + q^16 + (1/3*a - 14/3)*q^17 + q^18 - 2*q^19 + q^20 + (-2/3*a + 4/3)*q^21 + (1/3*a - 8/3)*q^22 + (-2/3*a + 16/3)*q^23 + 2*q^24 + q^25 + (2/3*a - 10/3)*q^26 - 4*q^27 + (-1/3*a + 2/3)*q^28 + (-a + 6)*q^29 + 2*q^30 + (-1/3*a - 10/3)*q^31 + q^32 + (2/3*a - 16/3)*q^33 + (1/3*a - 14/3)*q^34 + (-1/3*a + 2/3)*q^35 + q^36 + q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - q^5 + a*q^6 + (-1/2*a^2 + 3)*q^7 + q^8 + (a^2 - 3)*q^9 - q^10 + (-1/2*a^2 - a + 7)*q^11 + a*q^12 - 2*a*q^13 + (-1/2*a^2 + 3)*q^14 - a*q^15 + q^16 + (1/2*a^2 + a - 3)*q^17 + (a^2 - 3)*q^18 + a*q^19 - q^20 + (-2*a + 2)*q^21 + (-1/2*a^2 - a + 7)*q^22 + (-a^2 - 2*a + 6)*q^23 + a*q^24 + q^25 - 2*a*q^26 + (4*a - 4)*q^27 + (-1/2*a^2 + 3)*q^28 + (1/2*a^2 - a - 5)*q^29 - a*q^30 + (3/2*a^2 - 9)*q^31 + q^32 + (-a^2 + 2*a + 2)*q^33 + (1/2*a^2 + a - 3)*q^34 + (1/2*a^2 - 3)*q^35 + (a^2 - 3)*q^36 - q^37 + O(q^38)
*]> ;  // time = 177.589 seconds




J[371] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 371, 371, 371, 371, 371, 371, 53, 53 ], new_dimensions := [ 1, 1, 2, 3, 9, 11, 1, 3 ], dimensions := [ 1, 1, 2, 3, 9, 11, 2, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 3, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 191, 1, 5, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 191, 1, 1, 0 ], ap_traces := [
[ 1, -1, 0, -1, 0, 1, -7, -7, 1, 9, 4, -3 ],
[ 2, 0, 3, 1, 3, -6, 6, -5, 4, 5, -11, 5 ],
[ -1, -1, -3, 2, 0, -3, 6, -8, -6, -2, -1, -17 ],
[ 0, 0, -5, -3, -4, -12, 3, -1, 1, -5, -21, -4 ],
[ 0, 3, 9, -9, 0, 13, 0, 10, -6, 8, 15, 21 ],
[ -1, -1, 2, 11, 5, 13, -6, 7, -2, 7, 22, 24 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + x - 1,
x^3 - 4*x - 1,
x^9 - 15*x^7 + x^6 + 74*x^5 - 9*x^4 - 132*x^3 + 24*x^2 + 64*x - 16,
x^11 + x^10 - 20*x^9 - 19*x^8 + 140*x^7 + 125*x^6 - 396*x^5 - 333*x^4 + 359*x^3 + 298*x^2 - 4*x - 24
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 1 ],
[ 5, 1 ],
[ 1, 1 ],
[ 191, 1 ],
[ 27, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 3, 1 ],
[ 5, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 27, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 27 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 27 ], l_ratios := [ 0, 3, 0, 0, 1, 1/27 ], analytic_sha_upper_bounds := [ 0, 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 0, 1, 1 ], eigenvalues := [*
[ 1, -1, 0, -1, 0, 1, -7, -7, 1, 9, 4, -3 ],
[ 2, 0, 3, 1, 3, -6, 6, -5, 4, 5, -11, 5 ],
[
a,
a,
-a - 2,
1,
-2*a - 1,
-a - 2,
3,
-2*a - 5,
4*a - 1,
-1,
3*a + 1,
a - 8
],
[
a,
-a,
-a^2 + 1,
-1,
a^2 - a - 4,
a - 4,
1,
-2*a^2 + 2*a + 5,
2*a^2 - 5,
2*a^2 - 2*a - 7,
-a - 7,
-2*a^2 - a + 4
],
[
a,
1/8*a^8 - 15/8*a^6 - 3/8*a^5 + 35/4*a^4 + 23/8*a^3 - 13*a^2 - 7/2*a + 4,
1/8*a^8 - 11/8*a^6 + 5/8*a^5 + 17/4*a^4 - 37/8*a^3 - 3*a^2 + 7*a,
-1,
-1/4*a^7 + 11/4*a^5 - 1/4*a^4 - 17/2*a^3 + 1/4*a^2 + 6*a + 2,
a^4 + a^3 - 7*a^2 - 5*a + 8,
-1/4*a^8 - 1/2*a^7 + 11/4*a^6 + 21/4*a^5 - 9*a^4 - 63/4*a^3 + 17/2*a^2 + 13*a,
-1/4*a^8 + 15/4*a^6 + 1/4*a^5 - 18*a^4 - 11/4*a^3 + 59/2*a^2 + 11/2*a - 10,
1/4*a^8 + 1/2*a^7 - 11/4*a^6 - 21/4*a^5 + 9*a^4 + 63/4*a^3 - 21/2*a^2 - 11*a + 6,
-1/4*a^8 - 1/2*a^7 + 11/4*a^6 + 21/4*a^5 - 10*a^4 - 67/4*a^3 + 33/2*a^2 + 16*a - 9,
-1/2*a^5 - 3/2*a^4 + 4*a^3 + 21/2*a^2 - 13/2*a - 8,
1/2*a^8 + 1/4*a^7 - 13/2*a^6 - 9/4*a^5 + 105/4*a^4 + 6*a^3 - 129/4*a^2 - 6*a + 6
],
[
a,
3/4*a^10 + 3/8*a^9 - 121/8*a^8 - 53/8*a^7 + 215/2*a^6 + 313/8*a^5 - 2513/8*a^4 - 715/8*a^3 + 315*a^2 + 127/2*a - 38,
-1/2*a^10 - 1/4*a^9 + 10*a^8 + 9/2*a^7 - 281/4*a^6 - 109/4*a^5 + 403/2*a^4 + 129/2*a^3 - 779/4*a^2 - 97/2*a + 21,
1,
3*a^10 + 3/2*a^9 - 243/4*a^8 - 107/4*a^7 + 1733/4*a^6 + 160*a^5 - 5065/4*a^4 - 1487/4*a^3 + 5027/4*a^2 + 271*a - 144,
-13/8*a^10 - 7/8*a^9 + 263/8*a^8 + 31/2*a^7 - 1875/8*a^6 - 735/8*a^5 + 5485/8*a^4 + 841/4*a^3 - 1365/2*a^2 - 148*a + 80,
-13/8*a^10 - 7/8*a^9 + 263/8*a^8 + 31/2*a^7 - 1875/8*a^6 - 735/8*a^5 + 5485/8*a^4 + 845/4*a^3 - 1365/2*a^2 - 155*a + 78,
7/4*a^10 + 7/8*a^9 - 283/8*a^8 - 123/8*a^7 + 1007/4*a^6 + 725/8*a^5 - 5871/8*a^4 - 1673/8*a^3 + 2899/4*a^2 + 156*a - 79,
-3/4*a^10 - 3/8*a^9 + 123/8*a^8 + 55/8*a^7 - 445/4*a^6 - 345/8*a^5 + 2647/8*a^4 + 865/8*a^3 - 1345/4*a^2 - 175/2*a + 39,
-13/8*a^10 - 7/8*a^9 + 263/8*a^8 + 31/2*a^7 - 1875/8*a^6 - 735/8*a^5 + 5493/8*a^4 + 841/4*a^3 - 1381/2*a^2 - 148*a + 87,
3/4*a^10 + 1/4*a^9 - 61/4*a^8 - 9/2*a^7 + 437/4*a^6 + 109/4*a^5 - 1283/4*a^4 - 129/2*a^3 + 321*a^2 + 93/2*a - 40,
-15/8*a^10 - 7/8*a^9 + 305/8*a^8 + 31/2*a^7 - 2187/8*a^6 - 735/8*a^5 + 6439/8*a^4 + 845/4*a^3 - 3231/4*a^2 - 155*a + 98
]
*], q_expansions := [*
q + q^2 - q^3 - q^4 - q^6 - q^7 - 3*q^8 - 2*q^9 + q^12 + q^13 - q^14 - q^16 - 7*q^17 - 2*q^18 - 7*q^19 + q^21 + q^23 + 3*q^24 - 5*q^25 + q^26 + 5*q^27 + q^28 + 9*q^29 + 4*q^31 + 5*q^32 - 7*q^34 + 2*q^36 - 3*q^37 + O(q^38),
q + 2*q^2 + 2*q^4 + 3*q^5 + q^7 - 3*q^9 + 6*q^10 + 3*q^11 - 6*q^13 + 2*q^14 - 4*q^16 + 6*q^17 - 6*q^18 - 5*q^19 + 6*q^20 + 6*q^22 + 4*q^23 + 4*q^25 - 12*q^26 + 2*q^28 + 5*q^29 - 11*q^31 - 8*q^32 + 12*q^34 + 3*q^35 - 6*q^36 + 5*q^37 + O(q^38),
q + a*q^2 + a*q^3 + (-a - 1)*q^4 + (-a - 2)*q^5 + (-a + 1)*q^6 + q^7 + (-2*a - 1)*q^8 + (-a - 2)*q^9 + (-a - 1)*q^10 + (-2*a - 1)*q^11 - q^12 + (-a - 2)*q^13 + a*q^14 + (-a - 1)*q^15 + 3*a*q^16 + 3*q^17 + (-a - 1)*q^18 + (-2*a - 5)*q^19 + (2*a + 3)*q^20 + a*q^21 + (a - 2)*q^22 + (4*a - 1)*q^23 + (a - 2)*q^24 + 3*a*q^25 + (-a - 1)*q^26 + (-4*a - 1)*q^27 + (-a - 1)*q^28 - q^29 - q^30 + (3*a + 1)*q^31 + (a + 5)*q^32 + (a - 2)*q^33 + 3*a*q^34 + (-a - 2)*q^35 + (2*a + 3)*q^36 + (a - 8)*q^37 + O(q^38),
q + a*q^2 - a*q^3 + (a^2 - 2)*q^4 + (-a^2 + 1)*q^5 - a^2*q^6 - q^7 + q^8 + (a^2 - 3)*q^9 + (-3*a - 1)*q^10 + (a^2 - a - 4)*q^11 + (-2*a - 1)*q^12 + (a - 4)*q^13 - a*q^14 + (3*a + 1)*q^15 + (-2*a^2 + a + 4)*q^16 + q^17 + (a + 1)*q^18 + (-2*a^2 + 2*a + 5)*q^19 + (-a^2 - a - 2)*q^20 + a*q^21 + (-a^2 + 1)*q^22 + (2*a^2 - 5)*q^23 - a*q^24 + (2*a^2 + a - 4)*q^25 + (a^2 - 4*a)*q^26 + (2*a - 1)*q^27 + (-a^2 + 2)*q^28 + (2*a^2 - 2*a - 7)*q^29 + (3*a^2 + a)*q^30 + (-a - 7)*q^31 + (a^2 - 4*a - 4)*q^32 + (a^2 - 1)*q^33 + a*q^34 + (a^2 - 1)*q^35 + (-a^2 + a + 6)*q^36 + (-2*a^2 - a + 4)*q^37 + O(q^38),
q + a*q^2 + (1/8*a^8 - 15/8*a^6 - 3/8*a^5 + 35/4*a^4 + 23/8*a^3 - 13*a^2 - 7/2*a + 4)*q^3 + (a^2 - 2)*q^4 + (1/8*a^8 - 11/8*a^6 + 5/8*a^5 + 17/4*a^4 - 37/8*a^3 - 3*a^2 + 7*a)*q^5 + (-1/2*a^6 - 1/2*a^5 + 4*a^4 + 7/2*a^3 - 13/2*a^2 - 4*a + 2)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-a^3 + 5*a + 1)*q^9 + (1/2*a^7 + 1/2*a^6 - 5*a^5 - 7/2*a^4 + 27/2*a^3 + 4*a^2 - 8*a + 2)*q^10 + (-1/4*a^7 + 11/4*a^5 - 1/4*a^4 - 17/2*a^3 + 1/4*a^2 + 6*a + 2)*q^11 + (-1/4*a^8 - 1/2*a^7 + 13/4*a^6 + 19/4*a^5 - 14*a^4 - 49/4*a^3 + 22*a^2 + 9*a - 8)*q^12 + (a^4 + a^3 - 7*a^2 - 5*a + 8)*q^13 - a*q^14 + (1/4*a^8 + 1/4*a^7 - 15/4*a^6 - 7/2*a^5 + 71/4*a^4 + 57/4*a^3 - 109/4*a^2 - 15*a + 9)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/4*a^8 - 1/2*a^7 + 11/4*a^6 + 21/4*a^5 - 9*a^4 - 63/4*a^3 + 17/2*a^2 + 13*a)*q^17 + (-a^4 + 5*a^2 + a)*q^18 + (-1/4*a^8 + 15/4*a^6 + 1/4*a^5 - 18*a^4 - 11/4*a^3 + 59/2*a^2 + 11/2*a - 10)*q^19 + (1/4*a^8 + 1/2*a^7 - 9/4*a^6 - 19/4*a^5 + 5*a^4 + 53/4*a^3 - 2*a^2 - 12*a)*q^20 + (-1/8*a^8 + 15/8*a^6 + 3/8*a^5 - 35/4*a^4 - 23/8*a^3 + 13*a^2 + 7/2*a - 4)*q^21 + (-1/4*a^8 + 11/4*a^6 - 1/4*a^5 - 17/2*a^4 + 1/4*a^3 + 6*a^2 + 2*a)*q^22 + (1/4*a^8 + 1/2*a^7 - 11/4*a^6 - 21/4*a^5 + 9*a^4 + 63/4*a^3 - 21/2*a^2 - 11*a + 6)*q^23 + (-1/2*a^8 - 1/2*a^7 + 6*a^6 + 11/2*a^5 - 45/2*a^4 - 18*a^3 + 28*a^2 + 16*a - 8)*q^24 + (1/4*a^7 + a^6 - 7/4*a^5 - 35/4*a^4 + 5/2*a^3 + 71/4*a^2 - 3*a - 3)*q^25 + (a^5 + a^4 - 7*a^3 - 5*a^2 + 8*a)*q^26 + (1/4*a^8 + 1/2*a^7 - 11/4*a^6 - 21/4*a^5 + 9*a^4 + 63/4*a^3 - 17/2*a^2 - 13*a + 2)*q^27 + (-a^2 + 2)*q^28 + (-1/4*a^8 - 1/2*a^7 + 11/4*a^6 + 21/4*a^5 - 10*a^4 - 67/4*a^3 + 33/2*a^2 + 16*a - 9)*q^29 + (1/4*a^8 - 15/4*a^6 - 3/4*a^5 + 33/2*a^4 + 23/4*a^3 - 21*a^2 - 7*a + 4)*q^30 + (-1/2*a^5 - 3/2*a^4 + 4*a^3 + 21/2*a^2 - 13/2*a - 8)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (3/8*a^8 + 1/2*a^7 - 41/8*a^6 - 41/8*a^5 + 95/4*a^4 + 121/8*a^3 - 40*a^2 - 29/2*a + 14)*q^33 + (-1/2*a^8 - a^7 + 11/2*a^6 + 19/2*a^5 - 18*a^4 - 49/2*a^3 + 19*a^2 + 16*a - 4)*q^34 + (-1/8*a^8 + 11/8*a^6 - 5/8*a^5 - 17/4*a^4 + 37/8*a^3 + 3*a^2 - 7*a)*q^35 + (-a^5 + 7*a^3 + a^2 - 10*a - 2)*q^36 + (1/2*a^8 + 1/4*a^7 - 13/2*a^6 - 9/4*a^5 + 105/4*a^4 + 6*a^3 - 129/4*a^2 - 6*a + 6)*q^37 + O(q^38),
q + a*q^2 + (3/4*a^10 + 3/8*a^9 - 121/8*a^8 - 53/8*a^7 + 215/2*a^6 + 313/8*a^5 - 2513/8*a^4 - 715/8*a^3 + 315*a^2 + 127/2*a - 38)*q^3 + (a^2 - 2)*q^4 + (-1/2*a^10 - 1/4*a^9 + 10*a^8 + 9/2*a^7 - 281/4*a^6 - 109/4*a^5 + 403/2*a^4 + 129/2*a^3 - 779/4*a^2 - 97/2*a + 21)*q^5 + (-3/8*a^10 - 1/8*a^9 + 61/8*a^8 + 5/2*a^7 - 437/8*a^6 - 137/8*a^5 + 1283/8*a^4 + 183/4*a^3 - 160*a^2 - 35*a + 18)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (1/8*a^10 + 1/8*a^9 - 21/8*a^8 - 9/4*a^7 + 155/8*a^6 + 109/8*a^5 - 467/8*a^4 - 63/2*a^3 + 119/2*a^2 + 21*a - 5)*q^9 + (1/4*a^10 - 5*a^8 - 1/4*a^7 + 141/4*a^6 + 7/2*a^5 - 102*a^4 - 61/4*a^3 + 201/2*a^2 + 19*a - 12)*q^10 + (3*a^10 + 3/2*a^9 - 243/4*a^8 - 107/4*a^7 + 1733/4*a^6 + 160*a^5 - 5065/4*a^4 - 1487/4*a^3 + 5027/4*a^2 + 271*a - 144)*q^11 + (-5/4*a^10 - 5/8*a^9 + 205/8*a^8 + 89/8*a^7 - 741/4*a^6 - 531/8*a^5 + 4393/8*a^4 + 1227/8*a^3 - 2213/4*a^2 - 221/2*a + 67)*q^12 + (-13/8*a^10 - 7/8*a^9 + 263/8*a^8 + 31/2*a^7 - 1875/8*a^6 - 735/8*a^5 + 5485/8*a^4 + 841/4*a^3 - 1365/2*a^2 - 148*a + 80)*q^13 + a*q^14 + (a^10 + 1/2*a^9 - 81/4*a^8 - 37/4*a^7 + 579/4*a^6 + 58*a^5 - 1703/4*a^4 - 569/4*a^3 + 1709/4*a^2 + 107*a - 45)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-13/8*a^10 - 7/8*a^9 + 263/8*a^8 + 31/2*a^7 - 1875/8*a^6 - 735/8*a^5 + 5485/8*a^4 + 845/4*a^3 - 1365/2*a^2 - 155*a + 78)*q^17 + (-1/8*a^9 + 1/8*a^8 + 15/8*a^7 - 2*a^6 - 71/8*a^5 + 81/8*a^4 + 117/8*a^3 - 65/4*a^2 - 9/2*a + 3)*q^18 + (7/4*a^10 + 7/8*a^9 - 283/8*a^8 - 123/8*a^7 + 1007/4*a^6 + 725/8*a^5 - 5871/8*a^4 - 1673/8*a^3 + 2899/4*a^2 + 156*a - 79)*q^19 + (3/4*a^10 + 1/2*a^9 - 31/2*a^8 - 35/4*a^7 + 451/4*a^6 + 103/2*a^5 - 335*a^4 - 473/4*a^3 + 334*a^2 + 86*a - 36)*q^20 + (3/4*a^10 + 3/8*a^9 - 121/8*a^8 - 53/8*a^7 + 215/2*a^6 + 313/8*a^5 - 2513/8*a^4 - 715/8*a^3 + 315*a^2 + 127/2*a - 38)*q^21 + (-3/2*a^10 - 3/4*a^9 + 121/4*a^8 + 53/4*a^7 - 215*a^6 - 313/4*a^5 + 2509/4*a^4 + 719/4*a^3 - 623*a^2 - 132*a + 72)*q^22 + (-3/4*a^10 - 3/8*a^9 + 123/8*a^8 + 55/8*a^7 - 445/4*a^6 - 345/8*a^5 + 2647/8*a^4 + 865/8*a^3 - 1345/4*a^2 - 175/2*a + 39)*q^23 + (11/8*a^10 + 7/8*a^9 - 223/8*a^8 - 61/4*a^7 + 1593/8*a^6 + 707/8*a^5 - 4669/8*a^4 - 196*a^3 + 582*a^2 + 132*a - 66)*q^24 + (-5/4*a^10 - 1/2*a^9 + 101/4*a^8 + 9*a^7 - 359/2*a^6 - 109/2*a^5 + 2089/4*a^4 + 129*a^3 - 2059/4*a^2 - 97*a + 61)*q^25 + (3/4*a^10 + 3/8*a^9 - 123/8*a^8 - 55/8*a^7 + 445/4*a^6 + 337/8*a^5 - 2647/8*a^4 - 793/8*a^3 + 1345/4*a^2 + 147/2*a - 39)*q^26 + (-11/4*a^10 - 11/8*a^9 + 447/8*a^8 + 195/8*a^7 - 1599/4*a^6 - 1161/8*a^5 + 9371/8*a^4 + 2701/8*a^3 - 4659/4*a^2 - 503/2*a + 133)*q^27 + (a^2 - 2)*q^28 + (-13/8*a^10 - 7/8*a^9 + 263/8*a^8 + 31/2*a^7 - 1875/8*a^6 - 735/8*a^5 + 5493/8*a^4 + 841/4*a^3 - 1381/2*a^2 - 148*a + 87)*q^29 + (-1/2*a^10 - 1/4*a^9 + 39/4*a^8 + 19/4*a^7 - 67*a^6 - 119/4*a^5 + 763/4*a^4 + 273/4*a^3 - 191*a^2 - 41*a + 24)*q^30 + (3/4*a^10 + 1/4*a^9 - 61/4*a^8 - 9/2*a^7 + 437/4*a^6 + 109/4*a^5 - 1283/4*a^4 - 129/2*a^3 + 321*a^2 + 93/2*a - 40)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^10 + 1/4*a^9 - 10*a^8 - 4*a^7 + 281/4*a^6 + 81/4*a^5 - 403/2*a^4 - 73/2*a^3 + 775/4*a^2 + 20*a - 21)*q^33 + (3/4*a^10 + 3/8*a^9 - 123/8*a^8 - 55/8*a^7 + 445/4*a^6 + 337/8*a^5 - 2639/8*a^4 - 793/8*a^3 + 1317/4*a^2 + 143/2*a - 39)*q^34 + (-1/2*a^10 - 1/4*a^9 + 10*a^8 + 9/2*a^7 - 281/4*a^6 - 109/4*a^5 + 403/2*a^4 + 129/2*a^3 - 779/4*a^2 - 97/2*a + 21)*q^35 + (-3/8*a^10 - 1/8*a^9 + 57/8*a^8 + 5/2*a^7 - 381/8*a^6 - 137/8*a^5 + 1051/8*a^4 + 187/4*a^3 - 247/2*a^2 - 39*a + 10)*q^36 + (-15/8*a^10 - 7/8*a^9 + 305/8*a^8 + 31/2*a^7 - 2187/8*a^6 - 735/8*a^5 + 6439/8*a^4 + 845/4*a^3 - 3231/4*a^2 - 155*a + 98)*q^37 + O(q^38)
*]> ;  // time = 60.931 seconds




J[373] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 373, 373, 373 ], new_dimensions := [ 1, 12, 17 ], dimensions := [ 1, 12, 17 ], intersection_graph := [ 0, 11, 1, 11, 0, 1, 1, 1, 0 ], ap_traces := [
[ -2, 1, 2, -4, -6, -1, -1, 6, -4, 2, -3, 5 ],
[ -4, -15, -11, -1, -8, -10, -21, -11, -24, -7, -3, -8 ],
[ 4, 14, 9, 3, 16, -1, 16, 5, 32, -7, -6, -13 ]
], hecke_fields := [
x - 1,
x^12 + 4*x^11 - 8*x^10 - 43*x^9 + 14*x^8 + 161*x^7 + 17*x^6 - 260*x^5 - 53*x^4 + 177*x^3 + 18*x^2 - 42*x + 7,
x^17 - 4*x^16 - 18*x^15 + 85*x^14 + 111*x^13 - 713*x^12 - 211*x^11 + 3017*x^10 - 469*x^9 - 6832*x^8 + 2513*x^7 + 8146*x^6 - 3634*x^5 - 4743*x^4 + 2092*x^3 + 1142*x^2 - 417*x - 62
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 31 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 31 ]
], torsion_upper_bounds := [ 1, 1, 31 ], torsion_lower_bounds := [ 1, 1, 31 ], l_ratios := [ 0, 0, 1/31 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[ -2, 1, 2, -4, -6, -1, -1, 6, -4, 2, -3, 5 ],
[
a,
-183/839*a^11 - 627/839*a^10 + 1810/839*a^9 + 6913/839*a^8 - 5772/839*a^7 - 26330/839*a^6 + 5697/839*a^5 + 41863/839*a^4 + 3312/839*a^3 - 26479/839*a^2 - 5280/839*a + 3976/839,
580/839*a^11 + 2111/839*a^10 - 5081/839*a^9 - 22286/839*a^8 + 12352/839*a^7 + 80296/839*a^6 - 1895/839*a^5 - 119660/839*a^4 - 23756/839*a^3 + 67656/839*a^2 + 16982/839*a - 9704/839,
-810/839*a^11 - 2789/839*a^10 + 7255/839*a^9 + 27999/839*a^8 - 20693/839*a^7 - 92638/839*a^6 + 22768/839*a^5 + 119028/839*a^4 - 6893/839*a^3 - 49642/839*a^2 - 745/839*a + 1864/839,
1369/839*a^11 + 4663/839*a^10 - 12816/839*a^9 - 47965/839*a^8 + 40305/839*a^7 + 164796/839*a^6 - 56744/839*a^5 - 223651/839*a^4 + 41188/839*a^3 + 101083/839*a^2 - 18447/839*a - 4441/839,
-818/839*a^11 - 2280/839*a^10 + 9709/839*a^9 + 25367/839*a^8 - 43337/839*a^7 - 95898/839*a^6 + 91650/839*a^5 + 142695/839*a^4 - 89933/839*a^3 - 66007/839*a^2 + 32818/839*a - 3771/839,
-181/839*a^11 - 964/839*a^10 + 777/839*a^9 + 10088/839*a^8 + 3245/839*a^7 - 37261/839*a^6 - 16977/839*a^5 + 61326/839*a^4 + 18199/839*a^3 - 41475/839*a^2 - 4232/839*a + 4336/839,
-384/839*a^11 - 1577/839*a^10 + 2849/839*a^9 + 17133/839*a^8 - 1246/839*a^7 - 63351/839*a^6 - 29528/839*a^5 + 93978/839*a^4 + 64772/839*a^3 - 49717/839*a^2 - 30899/839*a + 7229/839,
463/839*a^11 + 2109/839*a^10 - 2961/839*a^9 - 23024/839*a^8 - 2933/839*a^7 + 85895/839*a^6 + 47576/839*a^5 - 128532/839*a^4 - 87108/839*a^3 + 67328/839*a^2 + 39574/839*a - 13145/839,
514/839*a^11 + 2325/839*a^10 - 2874/839*a^9 - 23025/839*a^8 - 3305/839*a^7 + 76893/839*a^6 + 35714/839*a^5 - 108358/839*a^4 - 55255/839*a^3 + 63319/839*a^2 + 26865/839*a - 12355/839,
-62/839*a^11 - 1299/839*a^10 - 2376/839*a^9 + 14840/839*a^8 + 30064/839*a^7 - 62181/839*a^6 - 112614/839*a^5 + 118187/839*a^4 + 159363/839*a^3 - 93898/839*a^2 - 70243/839*a + 23239/839,
-675/839*a^11 - 4142/839*a^10 + 33/839*a^9 + 41371/839*a^8 + 45541/839*a^7 - 141242/839*a^6 - 200565/839*a^5 + 211616/839*a^4 + 296995/839*a^3 - 147362/839*a^2 - 136399/839*a + 43783/839
],
[
a,
10962/1330649*a^16 - 265741/2661298*a^15 + 489372/1330649*a^14 + 1557461/2661298*a^13 - 18088447/2661298*a^12 + 9973416/1330649*a^11 + 48773751/1330649*a^10 - 202067069/2661298*a^9 - 192189119/2661298*a^8 + 319203756/1330649*a^7 + 73893629/2661298*a^6 - 846614357/2661298*a^5 + 115213101/2661298*a^4 + 459872889/2661298*a^3 - 28306907/1330649*a^2 - 81401149/2661298*a - 814958/1330649,
-407799/2661298*a^16 + 748889/1330649*a^15 + 7168899/2661298*a^14 - 29547049/2661298*a^13 - 22986124/1330649*a^12 + 113930640/1330649*a^11 + 128101461/2661298*a^10 - 879317883/2661298*a^9 - 61910858/1330649*a^8 + 1795836473/2661298*a^7 - 63296739/2661298*a^6 - 1875483221/2661298*a^5 + 130028319/2661298*a^4 + 442512119/1330649*a^3 - 10590271/2661298*a^2 - 71735682/1330649*a - 5909922/1330649,
-132782/1330649*a^16 + 1533075/2661298*a^15 + 1209121/1330649*a^14 - 26739099/2661298*a^13 + 7723523/2661298*a^12 + 88186848/1330649*a^11 - 74026625/1330649*a^10 - 567955415/2661298*a^9 + 576995227/2661298*a^8 + 485531762/1330649*a^7 - 939553863/2661298*a^6 - 883437933/2661298*a^5 + 632351857/2661298*a^4 + 372074013/2661298*a^3 - 56650959/1330649*a^2 - 44855475/2661298*a - 4821929/1330649,
149313/1330649*a^16 - 3344217/5322596*a^15 - 2625427/2661298*a^14 + 56732533/5322596*a^13 - 19121565/5322596*a^12 - 89565281/1330649*a^11 + 82372259/1330649*a^10 + 1078781059/5322596*a^9 - 1219660959/5322596*a^8 - 839607101/2661298*a^7 + 1854259197/5322596*a^6 + 1379889043/5322596*a^5 - 1125253243/5322596*a^4 - 562428377/5322596*a^3 + 80147103/2661298*a^2 + 102871355/5322596*a + 15162753/2661298,
1070361/5322596*a^16 - 1496987/1330649*a^15 - 7913485/5322596*a^14 + 95474451/5322596*a^13 - 27696311/2661298*a^12 - 134826293/1330649*a^11 + 685775097/5322596*a^10 + 1306878505/5322596*a^9 - 581664567/1330649*a^8 - 1263561145/5322596*a^7 + 3337708399/5322596*a^6 + 201908005/5322596*a^5 - 2028216973/5322596*a^4 + 62692706/1330649*a^3 + 375128761/5322596*a^2 - 19459385/1330649*a + 5626240/1330649,
-1026627/5322596*a^16 + 1238917/1330649*a^15 + 12090187/5322596*a^14 - 84158317/5322596*a^13 - 12835953/2661298*a^12 + 134146067/1330649*a^11 - 137455367/5322596*a^10 - 1673422987/5322596*a^9 + 143576392/1330649*a^8 + 2871108483/5322596*a^7 - 492874097/5322596*a^6 - 2883720219/5322596*a^5 - 225312925/5322596*a^4 + 385000459/1330649*a^3 + 299275065/5322596*a^2 - 73689362/1330649*a - 11265322/1330649,
-248099/2661298*a^16 + 3020885/5322596*a^15 + 242822/1330649*a^14 - 40202911/5322596*a^13 + 61833429/5322596*a^12 + 36522830/1330649*a^11 - 227099411/2661298*a^10 + 44543259/5322596*a^9 + 1088956571/5322596*a^8 - 261950122/1330649*a^7 - 811727211/5322596*a^6 + 1556097975/5322596*a^5 - 81734267/5322596*a^4 - 612988099/5322596*a^3 + 27401212/1330649*a^2 + 20350393/5322596*a + 11925175/2661298,
1696/1330649*a^16 + 691009/5322596*a^15 - 2650437/2661298*a^14 - 1563449/5322596*a^13 + 83609253/5322596*a^12 - 23355454/1330649*a^11 - 118593896/1330649*a^10 + 780180601/5322596*a^9 + 1183729735/5322596*a^8 - 1189674189/2661298*a^7 - 1304550385/5322596*a^6 + 3168599157/5322596*a^5 + 583409763/5322596*a^4 - 1760227615/5322596*a^3 - 58018341/2661298*a^2 + 296904393/5322596*a + 13765403/2661298,
839505/5322596*a^16 - 2247449/2661298*a^15 - 5599085/5322596*a^14 + 68146869/5322596*a^13 - 14084924/1330649*a^12 - 84635162/1330649*a^11 + 646582913/5322596*a^10 + 505332711/5322596*a^9 - 1145950323/2661298*a^8 + 691756715/5322596*a^7 + 3703093521/5322596*a^6 - 2646032297/5322596*a^5 - 2917587011/5322596*a^4 + 1169815455/2661298*a^3 + 1037630465/5322596*a^2 - 304293369/2661298*a - 25229106/1330649,
246659/1330649*a^16 - 4607227/2661298*a^15 + 2334236/1330649*a^14 + 66563229/2661298*a^13 - 165354215/2661298*a^12 - 150930386/1330649*a^11 + 591537016/1330649*a^10 + 333471359/2661298*a^9 - 3583452345/2661298*a^8 + 417442072/1330649*a^7 + 5141212095/2661298*a^6 - 2118472337/2661298*a^5 - 3477410365/2661298*a^4 + 1475405891/2661298*a^3 + 496903094/1330649*a^2 - 332823657/2661298*a - 35833166/1330649,
289677/5322596*a^16 - 865303/2661298*a^15 - 70849/5322596*a^14 + 23470021/5322596*a^13 - 13231898/1330649*a^12 - 20828959/1330649*a^11 + 454903129/5322596*a^10 - 100577801/5322596*a^9 - 795571893/2661298*a^8 + 1127286131/5322596*a^7 + 2760059809/5322596*a^6 - 2233181077/5322596*a^5 - 2400828903/5322596*a^4 + 845842163/2661298*a^3 + 847064281/5322596*a^2 - 221091959/2661298*a - 14629829/1330649
]
*], q_expansions := [*
q - 2*q^2 + q^3 + 2*q^4 + 2*q^5 - 2*q^6 - 4*q^7 - 2*q^9 - 4*q^10 - 6*q^11 + 2*q^12 - q^13 + 8*q^14 + 2*q^15 - 4*q^16 - q^17 + 4*q^18 + 6*q^19 + 4*q^20 - 4*q^21 + 12*q^22 - 4*q^23 - q^25 + 2*q^26 - 5*q^27 - 8*q^28 + 2*q^29 - 4*q^30 - 3*q^31 + 8*q^32 - 6*q^33 + 2*q^34 - 8*q^35 - 4*q^36 + 5*q^37 + O(q^38),
q + a*q^2 + (-183/839*a^11 - 627/839*a^10 + 1810/839*a^9 + 6913/839*a^8 - 5772/839*a^7 - 26330/839*a^6 + 5697/839*a^5 + 41863/839*a^4 + 3312/839*a^3 - 26479/839*a^2 - 5280/839*a + 3976/839)*q^3 + (a^2 - 2)*q^4 + (580/839*a^11 + 2111/839*a^10 - 5081/839*a^9 - 22286/839*a^8 + 12352/839*a^7 + 80296/839*a^6 - 1895/839*a^5 - 119660/839*a^4 - 23756/839*a^3 + 67656/839*a^2 + 16982/839*a - 9704/839)*q^5 + (105/839*a^11 + 346/839*a^10 - 956/839*a^9 - 3210/839*a^8 + 3133/839*a^7 + 8808/839*a^6 - 5717/839*a^5 - 6387/839*a^4 + 5912/839*a^3 - 1986/839*a^2 - 3710/839*a + 1281/839)*q^6 + (-810/839*a^11 - 2789/839*a^10 + 7255/839*a^9 + 27999/839*a^8 - 20693/839*a^7 - 92638/839*a^6 + 22768/839*a^5 + 119028/839*a^4 - 6893/839*a^3 - 49642/839*a^2 - 745/839*a + 1864/839)*q^7 + (a^3 - 4*a)*q^8 + (-30/839*a^11 - 818/839*a^10 - 2124/839*a^9 + 7749/839*a^8 + 23316/839*a^7 - 24810/839*a^6 - 77712/839*a^5 + 35265/839*a^4 + 93837/839*a^3 - 22565/839*a^2 - 31661/839*a + 7185/839)*q^9 + (-209/839*a^11 - 441/839*a^10 + 2654/839*a^9 + 4232/839*a^8 - 13084/839*a^7 - 11755/839*a^6 + 31140/839*a^5 + 6984/839*a^4 - 35004/839*a^3 + 6542/839*a^2 + 14656/839*a - 4060/839)*q^10 + (1369/839*a^11 + 4663/839*a^10 - 12816/839*a^9 - 47965/839*a^8 + 40305/839*a^7 + 164796/839*a^6 - 56744/839*a^5 - 223651/839*a^4 + 41188/839*a^3 + 101083/839*a^2 - 18447/839*a - 4441/839)*q^11 + (292/839*a^11 + 1138/839*a^10 - 2315/839*a^9 - 12163/839*a^8 + 3447/839*a^7 + 45158/839*a^6 + 9519/839*a^5 - 72249/839*a^4 - 27195/839*a^3 + 47358/839*a^2 + 16251/839*a - 8687/839)*q^12 + (-818/839*a^11 - 2280/839*a^10 + 9709/839*a^9 + 25367/839*a^8 - 43337/839*a^7 - 95898/839*a^6 + 91650/839*a^5 + 142695/839*a^4 - 89933/839*a^3 - 66007/839*a^2 + 32818/839*a - 3771/839)*q^13 + (451/839*a^11 + 775/839*a^10 - 6831/839*a^9 - 9353/839*a^8 + 37772/839*a^7 + 36538/839*a^6 - 91572/839*a^5 - 49823/839*a^4 + 93728/839*a^3 + 13835/839*a^2 - 32156/839*a + 5670/839)*q^14 + (-108/839*a^11 + 579/839*a^10 + 3764/839*a^9 - 6167/839*a^8 - 31341/839*a^7 + 23949/839*a^6 + 98458/839*a^5 - 42524/839*a^4 - 120113/839*a^3 + 34548/839*a^2 + 43249/839*a - 14406/839)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-181/839*a^11 - 964/839*a^10 + 777/839*a^9 + 10088/839*a^8 + 3245/839*a^7 - 37261/839*a^6 - 16977/839*a^5 + 61326/839*a^4 + 18199/839*a^3 - 41475/839*a^2 - 4232/839*a + 4336/839)*q^17 + (-698/839*a^11 - 2364/839*a^10 + 6459/839*a^9 + 23736/839*a^8 - 19980/839*a^7 - 77202/839*a^6 + 27465/839*a^5 + 92247/839*a^4 - 17255/839*a^3 - 31121/839*a^2 + 5925/839*a + 210/839)*q^18 + (-384/839*a^11 - 1577/839*a^10 + 2849/839*a^9 + 17133/839*a^8 - 1246/839*a^7 - 63351/839*a^6 - 29528/839*a^5 + 93978/839*a^4 + 64772/839*a^3 - 49717/839*a^2 - 30899/839*a + 7229/839)*q^19 + (-765/839*a^11 - 3240/839*a^10 + 5407/839*a^9 + 34414/839*a^8 - 2810/839*a^7 - 125899/839*a^6 - 43566/839*a^5 + 193239/839*a^4 + 91047/839*a^3 - 116894/839*a^2 - 46802/839*a + 20871/839)*q^20 + (1405/839*a^11 + 4470/839*a^10 - 13791/839*a^9 - 45350/839*a^8 + 47396/839*a^7 + 151779/839*a^6 - 74741/839*a^5 - 196332/839*a^4 + 54098/839*a^3 + 81177/839*a^2 - 17202/839*a - 2156/839)*q^21 + (-813/839*a^11 - 1864/839*a^10 + 10902/839*a^9 + 21139/839*a^8 - 55613/839*a^7 - 80017/839*a^6 + 132289/839*a^5 + 113745/839*a^4 - 141230/839*a^3 - 43089/839*a^2 + 53057/839*a - 9583/839)*q^22 + (463/839*a^11 + 2109/839*a^10 - 2961/839*a^9 - 23024/839*a^8 - 2933/839*a^7 + 85895/839*a^6 + 47576/839*a^5 - 128532/839*a^4 - 87108/839*a^3 + 67328/839*a^2 + 39574/839*a - 13145/839)*q^23 + (-240/839*a^11 - 671/839*a^10 + 2305/839*a^9 + 5779/839*a^8 - 8120/839*a^7 - 13061/839*a^6 + 15105/839*a^5 + 1055/839*a^4 - 16150/839*a^3 + 14967/839*a^2 + 10997/839*a - 4606/839)*q^24 + (-216/839*a^11 - 1359/839*a^10 - 23/839*a^9 + 13675/839*a^8 + 14506/839*a^7 - 47748/839*a^6 - 61496/839*a^5 + 74362/839*a^4 + 84467/839*a^3 - 50042/839*a^2 - 31801/839*a + 11460/839)*q^25 + (992/839*a^11 + 3165/839*a^10 - 9807/839*a^9 - 31885/839*a^8 + 35800/839*a^7 + 105556/839*a^6 - 69985/839*a^5 - 133287/839*a^4 + 78779/839*a^3 + 47542/839*a^2 - 38127/839*a + 5726/839)*q^26 + (36/839*a^11 + 1485/839*a^10 + 4059/839*a^9 - 15004/839*a^8 - 44927/839*a^7 + 53264/839*a^6 + 157354/839*a^5 - 86785/839*a^4 - 205230/839*a^3 + 66511/839*a^2 + 78433/839*a - 24563/839)*q^27 + (591/839*a^11 + 2355/839*a^10 - 4470/839*a^9 - 24540/839*a^8 + 5313/839*a^7 + 86037/839*a^6 + 21901/839*a^5 - 120425/839*a^4 - 52206/839*a^3 + 59010/839*a^2 + 26102/839*a - 6885/839)*q^28 + (514/839*a^11 + 2325/839*a^10 - 2874/839*a^9 - 23025/839*a^8 - 3305/839*a^7 + 76893/839*a^6 + 35714/839*a^5 - 108358/839*a^4 - 55255/839*a^3 + 63319/839*a^2 + 26865/839*a - 12355/839)*q^29 + (1011/839*a^11 + 2900/839*a^10 - 10811/839*a^9 - 29829/839*a^8 + 41337/839*a^7 + 100294/839*a^6 - 70604/839*a^5 - 125837/839*a^4 + 53664/839*a^3 + 45193/839*a^2 - 18942/839*a + 756/839)*q^30 + (-62/839*a^11 - 1299/839*a^10 - 2376/839*a^9 + 14840/839*a^8 + 30064/839*a^7 - 62181/839*a^6 - 112614/839*a^5 + 118187/839*a^4 + 159363/839*a^3 - 93898/839*a^2 - 70243/839*a + 23239/839)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-838/839*a^11 - 2266/839*a^10 + 9132/839*a^9 + 21304/839*a^8 - 39539/839*a^7 - 59581/839*a^6 + 92699/839*a^5 + 42033/839*a^4 - 113792/839*a^3 + 26901/839*a^2 + 57576/839*a - 19117/839)*q^33 + (-240/839*a^11 - 671/839*a^10 + 2305/839*a^9 + 5779/839*a^8 - 8120/839*a^7 - 13900/839*a^6 + 14266/839*a^5 + 8606/839*a^4 - 9438/839*a^3 - 974/839*a^2 - 3266/839*a + 1267/839)*q^34 + (-1113/839*a^11 - 4171/839*a^10 + 9798/839*a^9 + 45772/839*a^8 - 21296/839*a^7 - 171224/839*a^6 - 15581/839*a^5 + 257484/839*a^4 + 80634/839*a^3 - 139533/839*a^2 - 43735/839*a + 19478/839)*q^35 + (488/839*a^11 + 2511/839*a^10 - 2030/839*a^9 - 25706/839*a^8 - 11456/839*a^7 + 88951/839*a^6 + 66191/839*a^5 - 124779/839*a^4 - 95249/839*a^3 + 63619/839*a^2 + 34216/839*a - 9484/839)*q^36 + (-675/839*a^11 - 4142/839*a^10 + 33/839*a^9 + 41371/839*a^8 + 45541/839*a^7 - 141242/839*a^6 - 200565/839*a^5 + 211616/839*a^4 + 296995/839*a^3 - 147362/839*a^2 - 136399/839*a + 43783/839)*q^37 + O(q^38),
q + a*q^2 + (10962/1330649*a^16 - 265741/2661298*a^15 + 489372/1330649*a^14 + 1557461/2661298*a^13 - 18088447/2661298*a^12 + 9973416/1330649*a^11 + 48773751/1330649*a^10 - 202067069/2661298*a^9 - 192189119/2661298*a^8 + 319203756/1330649*a^7 + 73893629/2661298*a^6 - 846614357/2661298*a^5 + 115213101/2661298*a^4 + 459872889/2661298*a^3 - 28306907/1330649*a^2 - 81401149/2661298*a - 814958/1330649)*q^3 + (a^2 - 2)*q^4 + (-407799/2661298*a^16 + 748889/1330649*a^15 + 7168899/2661298*a^14 - 29547049/2661298*a^13 - 22986124/1330649*a^12 + 113930640/1330649*a^11 + 128101461/2661298*a^10 - 879317883/2661298*a^9 - 61910858/1330649*a^8 + 1795836473/2661298*a^7 - 63296739/2661298*a^6 - 1875483221/2661298*a^5 + 130028319/2661298*a^4 + 442512119/1330649*a^3 - 10590271/2661298*a^2 - 71735682/1330649*a - 5909922/1330649)*q^5 + (-178045/2661298*a^16 + 686688/1330649*a^15 - 306079/2661298*a^14 - 20522011/2661298*a^13 + 17789322/1330649*a^12 + 51086733/1330649*a^11 - 268211777/2661298*a^10 - 181906763/2661298*a^9 + 394096140/1330649*a^8 + 18798617/2661298*a^7 - 1025207261/2661298*a^6 + 194884917/2661298*a^5 + 563858421/2661298*a^4 - 51239411/1330649*a^3 - 106438357/2661298*a^2 + 3756196/1330649*a + 679644/1330649)*q^6 + (-132782/1330649*a^16 + 1533075/2661298*a^15 + 1209121/1330649*a^14 - 26739099/2661298*a^13 + 7723523/2661298*a^12 + 88186848/1330649*a^11 - 74026625/1330649*a^10 - 567955415/2661298*a^9 + 576995227/2661298*a^8 + 485531762/1330649*a^7 - 939553863/2661298*a^6 - 883437933/2661298*a^5 + 632351857/2661298*a^4 + 372074013/2661298*a^3 - 56650959/1330649*a^2 - 44855475/2661298*a - 4821929/1330649)*q^7 + (a^3 - 4*a)*q^8 + (97328/1330649*a^16 - 163458/1330649*a^15 - 2971047/1330649*a^14 + 5773779/1330649*a^13 + 32515571/1330649*a^12 - 68093721/1330649*a^11 - 168320551/1330649*a^10 + 366444172/1330649*a^9 + 452371749/1330649*a^8 - 981951236/1330649*a^7 - 658898456/1330649*a^6 + 1302958442/1330649*a^5 + 524720063/1330649*a^4 - 777681658/1330649*a^3 - 197972620/1330649*a^2 + 160335736/1330649*a + 24798398/1330649)*q^9 + (-66709/1330649*a^16 - 171483/2661298*a^15 + 2557933/1330649*a^14 - 706559/2661298*a^13 - 62899407/2661298*a^12 + 21027936/1330649*a^11 + 175505850/1330649*a^10 - 315079447/2661298*a^9 - 990246295/2661298*a^8 + 480751074/1330649*a^7 + 1446447433/2661298*a^6 - 1351913247/2661298*a^5 - 1049166419/2661298*a^4 + 842525237/2661298*a^3 + 161117547/1330649*a^2 - 181872027/2661298*a - 12641769/1330649)*q^10 + (149313/1330649*a^16 - 3344217/5322596*a^15 - 2625427/2661298*a^14 + 56732533/5322596*a^13 - 19121565/5322596*a^12 - 89565281/1330649*a^11 + 82372259/1330649*a^10 + 1078781059/5322596*a^9 - 1219660959/5322596*a^8 - 839607101/2661298*a^7 + 1854259197/5322596*a^6 + 1379889043/5322596*a^5 - 1125253243/5322596*a^4 - 562428377/5322596*a^3 + 80147103/2661298*a^2 + 102871355/5322596*a + 15162753/2661298)*q^11 + (308674/1330649*a^16 - 2979407/2661298*a^15 - 3672837/1330649*a^14 + 52226717/2661298*a^13 + 11404275/2661298*a^12 - 172836468/1330649*a^11 + 80079999/1330649*a^10 + 1108823313/2661298*a^9 - 813226585/2661298*a^8 - 927297600/1330649*a^7 + 1497452229/2661298*a^6 + 1610071605/2661298*a^5 - 1177372459/2661298*a^4 - 653713995/2661298*a^3 + 162033705/1330649*a^2 + 89916821/2661298*a - 3889479/1330649)*q^12 + (1070361/5322596*a^16 - 1496987/1330649*a^15 - 7913485/5322596*a^14 + 95474451/5322596*a^13 - 27696311/2661298*a^12 - 134826293/1330649*a^11 + 685775097/5322596*a^10 + 1306878505/5322596*a^9 - 581664567/1330649*a^8 - 1263561145/5322596*a^7 + 3337708399/5322596*a^6 + 201908005/5322596*a^5 - 2028216973/5322596*a^4 + 62692706/1330649*a^3 + 375128761/5322596*a^2 - 19459385/1330649*a + 5626240/1330649)*q^13 + (470819/2661298*a^16 - 1180955/1330649*a^15 - 4166159/2661298*a^14 + 37201127/2661298*a^13 - 6486718/1330649*a^12 - 102043627/1330649*a^11 + 233251173/2661298*a^10 + 452445711/2661298*a^9 - 421634862/1330649*a^8 - 272191531/2661298*a^7 + 1279846411/2661298*a^6 - 332707719/2661298*a^5 - 887496039/2661298*a^4 + 221128985/1330649*a^3 + 258418613/2661298*a^2 - 60192023/1330649*a - 8232484/1330649)*q^14 + (136132/1330649*a^16 - 815640/1330649*a^15 - 450689/1330649*a^14 + 11547343/1330649*a^13 - 14802344/1330649*a^12 - 50799185/1330649*a^11 + 120279030/1330649*a^10 + 55578417/1330649*a^9 - 326474719/1330649*a^8 + 100079230/1330649*a^7 + 341011348/1330649*a^6 - 189269256/1330649*a^5 - 107046699/1330649*a^4 + 44388957/1330649*a^3 - 7641963/1330649*a^2 + 8286286/1330649*a + 5875364/1330649)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1026627/5322596*a^16 + 1238917/1330649*a^15 + 12090187/5322596*a^14 - 84158317/5322596*a^13 - 12835953/2661298*a^12 + 134146067/1330649*a^11 - 137455367/5322596*a^10 - 1673422987/5322596*a^9 + 143576392/1330649*a^8 + 2871108483/5322596*a^7 - 492874097/5322596*a^6 - 2883720219/5322596*a^5 - 225312925/5322596*a^4 + 385000459/1330649*a^3 + 299275065/5322596*a^2 - 73689362/1330649*a - 11265322/1330649)*q^17 + (225854/1330649*a^16 - 1219143/1330649*a^15 - 2499101/1330649*a^14 + 21712163/1330649*a^13 + 1301143/1330649*a^12 - 147784343/1330649*a^11 + 72805596/1330649*a^10 + 498018581/1330649*a^9 - 317006340/1330649*a^8 - 903483720/1330649*a^7 + 510124554/1330649*a^6 + 878410015/1330649*a^5 - 316054954/1330649*a^4 - 401582796/1330649*a^3 + 49187160/1330649*a^2 + 65384174/1330649*a + 6034336/1330649)*q^18 + (-248099/2661298*a^16 + 3020885/5322596*a^15 + 242822/1330649*a^14 - 40202911/5322596*a^13 + 61833429/5322596*a^12 + 36522830/1330649*a^11 - 227099411/2661298*a^10 + 44543259/5322596*a^9 + 1088956571/5322596*a^8 - 261950122/1330649*a^7 - 811727211/5322596*a^6 + 1556097975/5322596*a^5 - 81734267/5322596*a^4 - 612988099/5322596*a^3 + 27401212/1330649*a^2 + 20350393/5322596*a + 11925175/2661298)*q^19 + (110443/2661298*a^16 - 140607/1330649*a^15 - 3703827/2661298*a^14 + 11004089/2661298*a^13 + 19436667/1330649*a^12 - 66431029/1330649*a^11 - 168760263/2661298*a^10 + 705816429/2661298*a^9 + 148816902/1330649*a^8 - 1809946079/2661298*a^7 - 138496741/2661298*a^6 + 2216959011/2661298*a^5 - 50332975/2661298*a^4 - 584351463/1330649*a^3 - 8328129/2661298*a^2 + 103011942/1330649*a + 7683886/1330649)*q^20 + (266740/1330649*a^16 - 1129271/1330649*a^15 - 3390495/1330649*a^14 + 18614423/1330649*a^13 + 10751025/1330649*a^12 - 112013802/1330649*a^11 + 11992172/1330649*a^10 + 310451971/1330649*a^9 - 92154944/1330649*a^8 - 420435862/1330649*a^7 + 90760133/1330649*a^6 + 280509229/1330649*a^5 + 487361/1330649*a^4 - 87822883/1330649*a^3 + 6892598/1330649*a^2 + 9399867/1330649*a - 7002758/1330649)*q^21 + (-955209/5322596*a^16 + 2749841/2661298*a^15 + 5966113/5322596*a^14 - 85416537/5322596*a^13 + 16894888/1330649*a^12 + 113877302/1330649*a^11 - 723128225/5322596*a^10 - 939549771/5322596*a^9 + 1200605731/2661298*a^8 + 353364921/5322596*a^7 - 3485325749/5322596*a^6 + 1045160525/5322596*a^5 + 2270337859/5322596*a^4 - 544578489/2661298*a^3 - 579190429/5322596*a^2 + 139689795/2661298*a + 9257406/1330649)*q^22 + (1696/1330649*a^16 + 691009/5322596*a^15 - 2650437/2661298*a^14 - 1563449/5322596*a^13 + 83609253/5322596*a^12 - 23355454/1330649*a^11 - 118593896/1330649*a^10 + 780180601/5322596*a^9 + 1183729735/5322596*a^8 - 1189674189/2661298*a^7 - 1304550385/5322596*a^6 + 3168599157/5322596*a^5 + 583409763/5322596*a^4 - 1760227615/5322596*a^3 - 58018341/2661298*a^2 + 296904393/5322596*a + 13765403/2661298)*q^23 + (-153925/2661298*a^16 + 509919/1330649*a^15 + 364295/2661298*a^14 - 16077331/2661298*a^13 + 11669450/1330649*a^12 + 43036747/1330649*a^11 - 217292049/2661298*a^10 - 159876847/2661298*a^9 + 393370888/1330649*a^8 - 91540529/2661298*a^7 - 1368430681/2661298*a^6 + 676300339/2661298*a^5 + 1146650727/2661298*a^4 - 381233481/1330649*a^3 - 402217881/2661298*a^2 + 117315187/1330649*a + 17778500/1330649)*q^24 + (-461171/1330649*a^16 + 1954365/1330649*a^15 + 6563347/1330649*a^14 - 35423255/1330649*a^13 - 25987076/1330649*a^12 + 244486110/1330649*a^11 - 17011749/1330649*a^10 - 819675152/1330649*a^9 + 333583215/1330649*a^8 + 1406478627/1330649*a^7 - 767779067/1330649*a^6 - 1174231015/1330649*a^5 + 659410018/1330649*a^4 + 394193497/1330649*a^3 - 171278217/1330649*a^2 - 31213009/1330649*a - 4718951/1330649)*q^25 + (-426626/1330649*a^16 + 11353013/5322596*a^15 + 2246883/2661298*a^14 - 174202693/5322596*a^13 + 223862221/5322596*a^12 + 227905317/1330649*a^11 - 480600158/1330649*a^10 - 1824658959/5322596*a^9 + 6049145207/5322596*a^8 + 323945603/2661298*a^7 - 8517252701/5322596*a^6 + 1861474901/5322596*a^5 + 5327493047/5322596*a^4 - 1864066451/5322596*a^3 - 650094901/2661298*a^2 + 468845497/5322596*a + 33181191/2661298)*q^26 + (-182630/1330649*a^16 + 1097988/1330649*a^15 + 355941/1330649*a^14 - 15236652/1330649*a^13 + 25741900/1330649*a^12 + 60871239/1330649*a^11 - 214567283/1330649*a^10 - 6912528/1330649*a^9 + 669089153/1330649*a^8 - 417396943/1330649*a^7 - 955593107/1330649*a^6 + 801551801/1330649*a^5 + 639456613/1330649*a^4 - 495416792/1330649*a^3 - 171996340/1330649*a^2 + 93281465/1330649*a + 13035313/1330649)*q^27 + (26247/1330649*a^16 + 1242433/2661298*a^15 - 3827486/1330649*a^14 - 11756147/2661298*a^13 + 116159647/2661298*a^12 - 10076705/1330649*a^11 - 335954356/1330649*a^10 + 513455217/2661298*a^9 + 1790453423/2661298*a^8 - 922724392/1330649*a^7 - 2288891567/2661298*a^6 + 2590336073/2661298*a^5 + 1410648773/2661298*a^4 - 1470682761/2661298*a^3 - 215727754/1330649*a^2 + 269577505/2661298*a + 24239247/1330649)*q^28 + (839505/5322596*a^16 - 2247449/2661298*a^15 - 5599085/5322596*a^14 + 68146869/5322596*a^13 - 14084924/1330649*a^12 - 84635162/1330649*a^11 + 646582913/5322596*a^10 + 505332711/5322596*a^9 - 1145950323/2661298*a^8 + 691756715/5322596*a^7 + 3703093521/5322596*a^6 - 2646032297/5322596*a^5 - 2917587011/5322596*a^4 + 1169815455/2661298*a^3 + 1037630465/5322596*a^2 - 304293369/2661298*a - 25229106/1330649)*q^29 + (-271112/1330649*a^16 + 1999687/1330649*a^15 - 23877/1330649*a^14 - 29912996/1330649*a^13 + 46262931/1330649*a^12 + 149002882/1330649*a^11 - 355131827/1330649*a^10 - 262628811/1330649*a^9 + 1030133054/1330649*a^8 - 1088368/1330649*a^7 - 1298200528/1330649*a^6 + 387656989/1330649*a^5 + 690063033/1330649*a^4 - 292430107/1330649*a^3 - 147176458/1330649*a^2 + 62642408/1330649*a + 8440184/1330649)*q^30 + (246659/1330649*a^16 - 4607227/2661298*a^15 + 2334236/1330649*a^14 + 66563229/2661298*a^13 - 165354215/2661298*a^12 - 150930386/1330649*a^11 + 591537016/1330649*a^10 + 333471359/2661298*a^9 - 3583452345/2661298*a^8 + 417442072/1330649*a^7 + 5141212095/2661298*a^6 - 2118472337/2661298*a^5 - 3477410365/2661298*a^4 + 1475405891/2661298*a^3 + 496903094/1330649*a^2 - 332823657/2661298*a - 35833166/1330649)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (93531/1330649*a^16 - 1214587/2661298*a^15 + 139819/1330649*a^14 + 16616065/2661298*a^13 - 40291597/2661298*a^12 - 29066581/1330649*a^11 + 167830781/1330649*a^10 - 100404029/2661298*a^9 - 1150969411/2661298*a^8 + 503624266/1330649*a^7 + 1908833411/2661298*a^6 - 2155539181/2661298*a^5 - 1519991987/2661298*a^4 + 1810003879/2661298*a^3 + 247494314/1330649*a^2 - 485266435/2661298*a - 18021081/1330649)*q^33 + (212290/1330649*a^16 - 6389099/5322596*a^15 + 1552489/2661298*a^14 + 88283691/5322596*a^13 - 195400783/5322596*a^12 - 88518416/1330649*a^11 + 355977668/1330649*a^10 + 92817505/5322596*a^9 - 4142807181/5322596*a^8 + 1043519777/2661298*a^7 + 5479183323/5322596*a^6 - 3956075443/5322596*a^5 - 3329290025/5322596*a^4 + 2446978749/5322596*a^3 + 438825293/2661298*a^2 - 473164747/5322596*a - 31825437/2661298)*q^34 + (-702028/1330649*a^16 + 3167998/1330649*a^15 + 9500457/1330649*a^14 - 57179196/1330649*a^13 - 32818550/1330649*a^12 + 395315850/1330649*a^11 - 51708559/1330649*a^10 - 1350826131/1330649*a^9 + 500755077/1330649*a^8 + 2460559942/1330649*a^7 - 951536761/1330649*a^6 - 2364349446/1330649*a^5 + 619095340/1330649*a^4 + 1059897586/1330649*a^3 - 69043306/1330649*a^2 - 163735913/1330649*a - 21550382/1330649)*q^35 + (-510383/1330649*a^16 + 1893187/1330649*a^15 + 8456667/1330649*a^14 - 35316209/1330649*a^13 - 51781583/1330649*a^12 + 256648232/1330649*a^11 + 153258165/1330649*a^10 - 943969158/1330649*a^9 - 265192690/1330649*a^8 + 1906455924/1330649*a^7 + 356400243/1330649*a^6 - 2101218402/1330649*a^5 - 379797400/1330649*a^4 + 1132063908/1330649*a^3 + 203404146/1330649*a^2 - 220456018/1330649*a - 35593848/1330649)*q^36 + (289677/5322596*a^16 - 865303/2661298*a^15 - 70849/5322596*a^14 + 23470021/5322596*a^13 - 13231898/1330649*a^12 - 20828959/1330649*a^11 + 454903129/5322596*a^10 - 100577801/5322596*a^9 - 795571893/2661298*a^8 + 1127286131/5322596*a^7 + 2760059809/5322596*a^6 - 2233181077/5322596*a^5 - 2400828903/5322596*a^4 + 845842163/2661298*a^3 + 847064281/5322596*a^2 - 221091959/2661298*a - 14629829/1330649)*q^37 + O(q^38)
*]> ;  // time = 7.891 seconds




J[374] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 374, 374, 374, 374, 374, 187, 187, 187, 187, 187, 187, 34, 17, 11 ], new_dimensions := [ 1, 3, 3, 4, 4, 1, 1, 2, 2, 3, 4, 1, 1, 1 ], dimensions := [ 1, 3, 3, 4, 4, 2, 2, 4, 4, 6, 8, 2, 4, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 25, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 37, 1, 9, 1, 1, 1, 1, 1, 0, 1, 1, 3, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 13, 1, 1, 1, 1, 5, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 25, 1, 9, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 25, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 0, 1, 1, 1, 9, 1, 5, 1, 37, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 25, 1, 1, 1, 25, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 9, 1, 1, 1, 0, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, 0, -2, -1, -2, -1, -4, 6, -4, -2, -4 ],
[ -3, -1, -1, 1, -3, 11, 3, 3, -8, 8, 14, -1 ],
[ 3, 3, -1, 7, -3, -3, -3, 5, 4, -4, 2, -9 ],
[ -4, 1, 5, 1, 4, -3, -4, 7, 6, 4, 4, 25 ],
[ 4, 1, -1, 1, 4, -1, 4, 1, 8, -10, -2, -1 ]
], hecke_fields := [
x - 1,
x^3 + x^2 - 6*x - 5,
x^3 - 3*x^2 - 2*x + 7,
x^4 - x^3 - 10*x^2 + 9*x + 16,
x^4 - x^3 - 10*x^2 + 13*x - 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ -1, 1, 1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 5, 1, 1 ],
[ 125, 1, 3 ],
[ 111, 9, 1 ],
[ 75, 3, 1 ],
[ 65, 1, 5 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 3 ],
[ 111, 1, 1 ],
[ 1, 3, 1 ],
[ 65, 1, 5 ]
], torsion_upper_bounds := [ 1, 3, 3, 3, 5 ], torsion_lower_bounds := [ 1, 3, 3, 3, 1 ], l_ratios := [ 0, 1/3, 37/3, 1/3, 13 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 1/25 ], eigenvalues := [*
[ -1, 0, 0, -2, -1, -2, -1, -4, 6, -4, -2, -4 ],
[
-1,
a,
-a^2 + 4,
-a^2 + a + 5,
-1,
a + 4,
1,
a^2 + a - 3,
2*a - 2,
-2*a + 2,
-2*a + 4,
-a^2 - 3*a + 3
],
[
1,
a,
-a^2 + 4,
a^2 - a - 1,
-1,
-a,
-1,
-a^2 - a + 7,
4*a^2 - 6*a - 10,
-4*a^2 + 6*a + 10,
-4*a^2 + 2*a + 16,
3*a^2 - 3*a - 13
],
[
-1,
a,
a^2 - 4,
-a^3 - 2*a^2 + 7*a + 10,
1,
2*a^3 + 2*a^2 - 13*a - 10,
-1,
-a^3 - 2*a^2 + 5*a + 12,
-2*a + 2,
2*a^3 + 2*a^2 - 14*a - 8,
-2*a^3 - 2*a^2 + 14*a + 10,
-a^3 - 2*a^2 + 7*a + 16
],
[
1,
a,
2*a^3 - a^2 - 20*a + 14,
-a^3 + 9*a - 4,
1,
-6*a^3 + 2*a^2 + 61*a - 38,
1,
-3*a^3 + 2*a^2 + 31*a - 24,
6*a^3 - 2*a^2 - 62*a + 40,
-2*a - 2,
-2*a,
-3*a^3 + 31*a - 14
]
*], q_expansions := [*
q - q^2 + q^4 - 2*q^7 - q^8 - 3*q^9 - q^11 - 2*q^13 + 2*q^14 + q^16 - q^17 + 3*q^18 - 4*q^19 + q^22 + 6*q^23 - 5*q^25 + 2*q^26 - 2*q^28 - 4*q^29 - 2*q^31 - q^32 + q^34 - 3*q^36 - 4*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a^2 + 4)*q^5 - a*q^6 + (-a^2 + a + 5)*q^7 - q^8 + (a^2 - 3)*q^9 + (a^2 - 4)*q^10 - q^11 + a*q^12 + (a + 4)*q^13 + (a^2 - a - 5)*q^14 + (a^2 - 2*a - 5)*q^15 + q^16 + q^17 + (-a^2 + 3)*q^18 + (a^2 + a - 3)*q^19 + (-a^2 + 4)*q^20 + (2*a^2 - a - 5)*q^21 + q^22 + (2*a - 2)*q^23 - a*q^24 + (-a^2 - a + 6)*q^25 + (-a - 4)*q^26 + (-a^2 + 5)*q^27 + (-a^2 + a + 5)*q^28 + (-2*a + 2)*q^29 + (-a^2 + 2*a + 5)*q^30 + (-2*a + 4)*q^31 - q^32 - a*q^33 - q^34 + (-a^2 - 3*a + 10)*q^35 + (a^2 - 3)*q^36 + (-a^2 - 3*a + 3)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a^2 + 4)*q^5 + a*q^6 + (a^2 - a - 1)*q^7 + q^8 + (a^2 - 3)*q^9 + (-a^2 + 4)*q^10 - q^11 + a*q^12 - a*q^13 + (a^2 - a - 1)*q^14 + (-3*a^2 + 2*a + 7)*q^15 + q^16 - q^17 + (a^2 - 3)*q^18 + (-a^2 - a + 7)*q^19 + (-a^2 + 4)*q^20 + (2*a^2 + a - 7)*q^21 - q^22 + (4*a^2 - 6*a - 10)*q^23 + a*q^24 + (3*a^2 - a - 10)*q^25 - a*q^26 + (3*a^2 - 4*a - 7)*q^27 + (a^2 - a - 1)*q^28 + (-4*a^2 + 6*a + 10)*q^29 + (-3*a^2 + 2*a + 7)*q^30 + (-4*a^2 + 2*a + 16)*q^31 + q^32 - a*q^33 - q^34 + (-3*a^2 - a + 10)*q^35 + (a^2 - 3)*q^36 + (3*a^2 - 3*a - 13)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (a^2 - 4)*q^5 - a*q^6 + (-a^3 - 2*a^2 + 7*a + 10)*q^7 - q^8 + (a^2 - 3)*q^9 + (-a^2 + 4)*q^10 + q^11 + a*q^12 + (2*a^3 + 2*a^2 - 13*a - 10)*q^13 + (a^3 + 2*a^2 - 7*a - 10)*q^14 + (a^3 - 4*a)*q^15 + q^16 - q^17 + (-a^2 + 3)*q^18 + (-a^3 - 2*a^2 + 5*a + 12)*q^19 + (a^2 - 4)*q^20 + (-3*a^3 - 3*a^2 + 19*a + 16)*q^21 - q^22 + (-2*a + 2)*q^23 - a*q^24 + (a^3 + 2*a^2 - 9*a - 5)*q^25 + (-2*a^3 - 2*a^2 + 13*a + 10)*q^26 + (a^3 - 6*a)*q^27 + (-a^3 - 2*a^2 + 7*a + 10)*q^28 + (2*a^3 + 2*a^2 - 14*a - 8)*q^29 + (-a^3 + 4*a)*q^30 + (-2*a^3 - 2*a^2 + 14*a + 10)*q^31 - q^32 + a*q^33 + q^34 + (-2*a^3 - 3*a^2 + 15*a + 8)*q^35 + (a^2 - 3)*q^36 + (-a^3 - 2*a^2 + 7*a + 16)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (2*a^3 - a^2 - 20*a + 14)*q^5 + a*q^6 + (-a^3 + 9*a - 4)*q^7 + q^8 + (a^2 - 3)*q^9 + (2*a^3 - a^2 - 20*a + 14)*q^10 + q^11 + a*q^12 + (-6*a^3 + 2*a^2 + 61*a - 38)*q^13 + (-a^3 + 9*a - 4)*q^14 + (a^3 - 12*a + 8)*q^15 + q^16 + q^17 + (a^2 - 3)*q^18 + (-3*a^3 + 2*a^2 + 31*a - 24)*q^19 + (2*a^3 - a^2 - 20*a + 14)*q^20 + (-a^3 - a^2 + 9*a - 4)*q^21 + q^22 + (6*a^3 - 2*a^2 - 62*a + 40)*q^23 + a*q^24 + (5*a^3 - 2*a^2 - 53*a + 35)*q^25 + (-6*a^3 + 2*a^2 + 61*a - 38)*q^26 + (a^3 - 6*a)*q^27 + (-a^3 + 9*a - 4)*q^28 + (-2*a - 2)*q^29 + (a^3 - 12*a + 8)*q^30 - 2*a*q^31 + q^32 + a*q^33 + q^34 + (2*a^3 - a^2 - 19*a + 12)*q^35 + (a^2 - 3)*q^36 + (-3*a^3 + 31*a - 14)*q^37 + O(q^38)
*]> ;  // time = 171.24 seconds




J[377] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 377, 377, 377, 377, 377, 377, 29 ], new_dimensions := [ 1, 2, 5, 5, 7, 9, 2 ], dimensions := [ 1, 2, 5, 5, 7, 9, 4 ], intersection_graph := [ 0, 1, 1, 7, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 7, 1, 1, 0, 1, 1, 31, 1, 3, 1, 1, 0, 1, 161, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 31, 161, 1, 0 ], ap_traces := [
[ 1, 0, -2, 0, -4, 1, 2, -4, 8, 1, -8, 2 ],
[ 0, 2, 0, 6, 4, -2, -8, 0, 4, 2, 8, 4 ],
[ -1, -4, -2, -11, 3, -5, -2, 0, -11, -5, -3, -3 ],
[ -3, -4, 2, -15, -7, 5, -2, -14, -15, 5, -15, -23 ],
[ 3, 2, -2, 7, -3, -7, 14, -12, 5, 7, -3, 9 ],
[ 1, 0, 2, 17, 3, 9, -2, 14, 13, -9, 13, 17 ]
], hecke_fields := [
x - 1,
x^2 - 3,
x^5 + x^4 - 5*x^3 - 3*x^2 + 6*x + 1,
x^5 + 3*x^4 - 3*x^3 - 13*x^2 - 8*x - 1,
x^7 - 3*x^6 - 8*x^5 + 26*x^4 + 9*x^3 - 36*x^2 - 14*x + 3,
x^9 - x^8 - 13*x^7 + 13*x^6 + 51*x^5 - 50*x^4 - 59*x^3 + 45*x^2 + 20*x - 3
], atkin_lehners := [
[ -1, -1 ],
[ 1, -1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 31, 1 ],
[ 161, 7 ],
[ 15, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 31, 1 ],
[ 1, 7 ],
[ 15, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 7, 15 ], torsion_lower_bounds := [ 1, 1, 1, 1, 7, 15 ], l_ratios := [ 0, 1, 0, 0, 1/7, 1/15 ], analytic_sha_upper_bounds := [ 0, 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 0, 1, 1 ], eigenvalues := [*
[ 1, 0, -2, 0, -4, 1, 2, -4, 8, 1, -8, 2 ],
[
a,
a + 1,
-2*a,
a + 3,
2,
-1,
-2*a - 4,
-2*a,
2*a + 2,
1,
-2*a + 4,
-4*a + 2
],
[
a,
a^3 - 3*a,
-a^3 - 2*a^2 + 2*a + 3,
-a^4 - a^3 + 4*a^2 + 2*a - 5,
a^3 + 3*a^2 - 2*a - 5,
-1,
2*a^4 + a^3 - 5*a^2 - 2,
3*a^4 + 3*a^3 - 11*a^2 - 7*a + 6,
-2*a^4 - a^3 + 6*a^2 - a - 3,
-1,
a^2 + 4*a - 2,
-2*a^4 - 5*a^3 + 4*a^2 + 12*a
],
[
a,
-2*a^4 - 5*a^3 + 8*a^2 + 21*a + 6,
2*a^4 + 5*a^3 - 8*a^2 - 22*a - 7,
a^4 + 3*a^3 - 4*a^2 - 14*a - 7,
-a^3 - a^2 + 4*a + 1,
1,
-2*a^4 - 3*a^3 + 11*a^2 + 12*a - 2,
a^4 + 3*a^3 - 3*a^2 - 11*a - 8,
-a^3 + 5*a - 3,
1,
-a^2,
2*a^4 + 3*a^3 - 12*a^2 - 12*a
],
[
a,
-a^6 + 2*a^5 + 8*a^4 - 15*a^3 - 7*a^2 + 8*a + 1,
-a^6 + 2*a^5 + 8*a^4 - 15*a^3 - 7*a^2 + 9*a,
4*a^6 - 3*a^5 - 40*a^4 + 16*a^3 + 83*a^2 + 28*a - 6,
-5*a^6 + 5*a^5 + 49*a^4 - 32*a^3 - 97*a^2 - 13*a + 11,
-1,
3*a^6 - 2*a^5 - 30*a^4 + 9*a^3 + 62*a^2 + 29*a - 1,
4*a^6 - 4*a^5 - 39*a^4 + 25*a^3 + 75*a^2 + 15*a - 6,
-6*a^6 + 5*a^5 + 59*a^4 - 28*a^3 - 117*a^2 - 39*a + 8,
1,
4*a^6 - 5*a^5 - 37*a^4 + 33*a^3 + 62*a^2 + 8*a - 5,
5*a^6 - 3*a^5 - 51*a^4 + 12*a^3 + 110*a^2 + 51*a - 4
],
[
a,
3/4*a^8 - 37/4*a^6 + 133/4*a^4 - 1/4*a^3 - 31*a^2 - 17/4*a + 7/4,
1/2*a^8 - 13/2*a^6 + 51/2*a^4 - 1/2*a^3 - 29*a^2 - 1/2*a + 9/2,
-1/4*a^8 - 1/2*a^7 + 13/4*a^6 + 6*a^5 - 51/4*a^4 - 83/4*a^3 + 15*a^2 + 75/4*a + 5/4,
-1/2*a^8 + 13/2*a^6 - a^5 - 49/2*a^4 + 15/2*a^3 + 23*a^2 - 11/2*a - 3/2,
1,
-1/2*a^8 + 13/2*a^6 - 51/2*a^4 + 1/2*a^3 + 28*a^2 + 1/2*a - 3/2,
-a^4 + a^3 + 7*a^2 - 5*a - 4,
-1/2*a^8 + 11/2*a^6 + a^5 - 33/2*a^4 - 13/2*a^3 + 9*a^2 + 17/2*a + 15/2,
-1,
a^5 - a^4 - 7*a^3 + 4*a^2 + 6*a + 5,
-3/2*a^8 + 39/2*a^6 - a^5 - 151/2*a^4 + 17/2*a^3 + 82*a^2 - 9/2*a - 23/2
]
*], q_expansions := [*
q + q^2 - q^4 - 2*q^5 - 3*q^8 - 3*q^9 - 2*q^10 - 4*q^11 + q^13 - q^16 + 2*q^17 - 3*q^18 - 4*q^19 + 2*q^20 - 4*q^22 + 8*q^23 - q^25 + q^26 + q^29 - 8*q^31 + 5*q^32 + 2*q^34 + 3*q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + q^4 - 2*a*q^5 + (a + 3)*q^6 + (a + 3)*q^7 - a*q^8 + (2*a + 1)*q^9 - 6*q^10 + 2*q^11 + (a + 1)*q^12 - q^13 + (3*a + 3)*q^14 + (-2*a - 6)*q^15 - 5*q^16 + (-2*a - 4)*q^17 + (a + 6)*q^18 - 2*a*q^19 - 2*a*q^20 + (4*a + 6)*q^21 + 2*a*q^22 + (2*a + 2)*q^23 + (-a - 3)*q^24 + 7*q^25 - a*q^26 + 4*q^27 + (a + 3)*q^28 + q^29 + (-6*a - 6)*q^30 + (-2*a + 4)*q^31 - 3*a*q^32 + (2*a + 2)*q^33 + (-4*a - 6)*q^34 + (-6*a - 6)*q^35 + (2*a + 1)*q^36 + (-4*a + 2)*q^37 + O(q^38),
q + a*q^2 + (a^3 - 3*a)*q^3 + (a^2 - 2)*q^4 + (-a^3 - 2*a^2 + 2*a + 3)*q^5 + (a^4 - 3*a^2)*q^6 + (-a^4 - a^3 + 4*a^2 + 2*a - 5)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^3 + 5*a - 2)*q^9 + (-a^4 - 2*a^3 + 2*a^2 + 3*a)*q^10 + (a^3 + 3*a^2 - 2*a - 5)*q^11 + (-a^4 + 3*a^2 - 1)*q^12 - q^13 + (-a^3 - a^2 + a + 1)*q^14 + (a^4 + a^3 - 3*a^2 - 2*a + 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^4 + a^3 - 5*a^2 - 2)*q^17 + (-2*a^4 + 5*a^2 - 2*a)*q^18 + (3*a^4 + 3*a^3 - 11*a^2 - 7*a + 6)*q^19 + (-a^4 - a^3 + 4*a^2 + 2*a - 5)*q^20 + (-a^3 + a^2 + 3*a - 2)*q^21 + (a^4 + 3*a^3 - 2*a^2 - 5*a)*q^22 + (-2*a^4 - a^3 + 6*a^2 - a - 3)*q^23 + (-a^4 - 2*a^3 + 3*a^2 + 5*a + 1)*q^24 + (2*a^4 + 4*a^3 - 5*a^2 - 7*a + 1)*q^25 - a*q^26 + (-a^4 - a^3 + 3*a^2 + 5*a - 2)*q^27 + (a^4 + a^3 - 7*a^2 - 3*a + 10)*q^28 - q^29 + (2*a^3 + a^2 - 5*a - 1)*q^30 + (a^2 + 4*a - 2)*q^31 + (-a^4 - 3*a^3 + 3*a^2 + 6*a - 1)*q^32 + (-2*a^4 - a^3 + 6*a^2 + 2*a - 2)*q^33 + (-a^4 + 5*a^3 + 6*a^2 - 14*a - 2)*q^34 + (-a^4 + a^3 + 10*a^2 - 14)*q^35 + (2*a^4 - a^3 - 8*a^2 + 2*a + 6)*q^36 + (-2*a^4 - 5*a^3 + 4*a^2 + 12*a)*q^37 + O(q^38),
q + a*q^2 + (-2*a^4 - 5*a^3 + 8*a^2 + 21*a + 6)*q^3 + (a^2 - 2)*q^4 + (2*a^4 + 5*a^3 - 8*a^2 - 22*a - 7)*q^5 + (a^4 + 2*a^3 - 5*a^2 - 10*a - 2)*q^6 + (a^4 + 3*a^3 - 4*a^2 - 14*a - 7)*q^7 + (a^3 - 4*a)*q^8 + (2*a^4 + 4*a^3 - 10*a^2 - 15*a + 2)*q^9 + (-a^4 - 2*a^3 + 4*a^2 + 9*a + 2)*q^10 + (-a^3 - a^2 + 4*a + 1)*q^11 + (3*a^4 + 8*a^3 - 13*a^2 - 36*a - 11)*q^12 + q^13 + (-a^3 - a^2 + a + 1)*q^14 + (-a^4 - a^3 + 7*a^2 + 4*a - 9)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-2*a^4 - 3*a^3 + 11*a^2 + 12*a - 2)*q^17 + (-2*a^4 - 4*a^3 + 11*a^2 + 18*a + 2)*q^18 + (a^4 + 3*a^3 - 3*a^2 - 11*a - 8)*q^19 + (-3*a^4 - 9*a^3 + 12*a^2 + 38*a + 13)*q^20 + (4*a^4 + 11*a^3 - 13*a^2 - 45*a - 20)*q^21 + (-a^4 - a^3 + 4*a^2 + a)*q^22 + (-a^3 + 5*a - 3)*q^23 + (-3*a^4 - 8*a^3 + 13*a^2 + 33*a + 7)*q^24 + (-2*a^3 - 3*a^2 + 9*a + 9)*q^25 + a*q^26 + (-5*a^4 - 13*a^3 + 21*a^2 + 55*a + 12)*q^27 + (-3*a^4 - 7*a^3 + 9*a^2 + 29*a + 14)*q^28 + q^29 + (2*a^4 + 4*a^3 - 9*a^2 - 17*a - 1)*q^30 - a^2*q^31 + (-3*a^4 - 5*a^3 + 13*a^2 + 20*a + 1)*q^32 + (2*a^4 + 5*a^3 - 8*a^2 - 18*a - 2)*q^33 + (3*a^4 + 5*a^3 - 14*a^2 - 18*a - 2)*q^34 + (-5*a^4 - 13*a^3 + 18*a^2 + 58*a + 26)*q^35 + (-2*a^4 - 3*a^3 + 12*a^2 + 16*a - 6)*q^36 + (2*a^4 + 3*a^3 - 12*a^2 - 12*a)*q^37 + O(q^38),
q + a*q^2 + (-a^6 + 2*a^5 + 8*a^4 - 15*a^3 - 7*a^2 + 8*a + 1)*q^3 + (a^2 - 2)*q^4 + (-a^6 + 2*a^5 + 8*a^4 - 15*a^3 - 7*a^2 + 9*a)*q^5 + (-a^6 + 11*a^4 + 2*a^3 - 28*a^2 - 13*a + 3)*q^6 + (4*a^6 - 3*a^5 - 40*a^4 + 16*a^3 + 83*a^2 + 28*a - 6)*q^7 + (a^3 - 4*a)*q^8 + (-a^6 + 2*a^5 + 8*a^4 - 14*a^3 - 7*a^2 + 2*a + 1)*q^9 + (-a^6 + 11*a^4 + 2*a^3 - 27*a^2 - 14*a + 3)*q^10 + (-5*a^6 + 5*a^5 + 49*a^4 - 32*a^3 - 97*a^2 - 13*a + 11)*q^11 + (-a^6 - a^5 + 12*a^4 + 11*a^3 - 35*a^2 - 27*a + 1)*q^12 - q^13 + (9*a^6 - 8*a^5 - 88*a^4 + 47*a^3 + 172*a^2 + 50*a - 12)*q^14 + (-a^6 + 11*a^4 + 3*a^3 - 28*a^2 - 19*a + 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (3*a^6 - 2*a^5 - 30*a^4 + 9*a^3 + 62*a^2 + 29*a - 1)*q^17 + (-a^6 + 12*a^4 + 2*a^3 - 34*a^2 - 13*a + 3)*q^18 + (4*a^6 - 4*a^5 - 39*a^4 + 25*a^3 + 75*a^2 + 15*a - 6)*q^19 + (-a^6 - a^5 + 12*a^4 + 12*a^3 - 36*a^2 - 29*a + 3)*q^20 + (2*a^6 - a^5 - 21*a^4 + 4*a^3 + 48*a^2 + 17*a - 3)*q^21 + (-10*a^6 + 9*a^5 + 98*a^4 - 52*a^3 - 193*a^2 - 59*a + 15)*q^22 + (-6*a^6 + 5*a^5 + 59*a^4 - 28*a^3 - 117*a^2 - 39*a + 8)*q^23 + (-2*a^6 + 4*a^5 + 15*a^4 - 30*a^3 - 7*a^2 + 13*a - 3)*q^24 + (-a^6 - 2*a^5 + 14*a^4 + 20*a^3 - 48*a^2 - 42*a + 4)*q^25 - a*q^26 + (2*a^6 - 23*a^4 - 3*a^3 + 63*a^2 + 17*a - 8)*q^27 + (11*a^6 - 10*a^5 - 107*a^4 + 59*a^3 + 208*a^2 + 58*a - 15)*q^28 + q^29 + (-3*a^6 + 3*a^5 + 29*a^4 - 19*a^3 - 55*a^2 - 8*a + 3)*q^30 + (4*a^6 - 5*a^5 - 37*a^4 + 33*a^3 + 62*a^2 + 8*a - 5)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^6 - 3*a^5 + 17*a^4 + 26*a^3 - 72*a^2 - 33*a + 20)*q^33 + (7*a^6 - 6*a^5 - 69*a^4 + 35*a^3 + 137*a^2 + 41*a - 9)*q^34 + (7*a^6 - 6*a^5 - 69*a^4 + 35*a^3 + 137*a^2 + 39*a - 9)*q^35 + (-a^6 + 12*a^4 + 3*a^3 - 35*a^2 - 15*a + 1)*q^36 + (5*a^6 - 3*a^5 - 51*a^4 + 12*a^3 + 110*a^2 + 51*a - 4)*q^37 + O(q^38),
q + a*q^2 + (3/4*a^8 - 37/4*a^6 + 133/4*a^4 - 1/4*a^3 - 31*a^2 - 17/4*a + 7/4)*q^3 + (a^2 - 2)*q^4 + (1/2*a^8 - 13/2*a^6 + 51/2*a^4 - 1/2*a^3 - 29*a^2 - 1/2*a + 9/2)*q^5 + (3/4*a^8 + 1/2*a^7 - 39/4*a^6 - 5*a^5 + 149/4*a^4 + 53/4*a^3 - 38*a^2 - 53/4*a + 9/4)*q^6 + (-1/4*a^8 - 1/2*a^7 + 13/4*a^6 + 6*a^5 - 51/4*a^4 - 83/4*a^3 + 15*a^2 + 75/4*a + 5/4)*q^7 + (a^3 - 4*a)*q^8 + (-1/2*a^8 + 13/2*a^6 - 51/2*a^4 - 1/2*a^3 + 29*a^2 + 11/2*a - 7/2)*q^9 + (1/2*a^8 - 13/2*a^6 + 49/2*a^4 + 1/2*a^3 - 23*a^2 - 11/2*a + 3/2)*q^10 + (-1/2*a^8 + 13/2*a^6 - a^5 - 49/2*a^4 + 15/2*a^3 + 23*a^2 - 11/2*a - 3/2)*q^11 + (-1/4*a^8 + 15/4*a^6 - a^5 - 63/4*a^4 + 27/4*a^3 + 15*a^2 - 17/4*a - 5/4)*q^12 + q^13 + (-3/4*a^8 + 37/4*a^6 - 133/4*a^4 + 1/4*a^3 + 30*a^2 + 25/4*a - 3/4)*q^14 + (-1/2*a^8 + 13/2*a^6 - 49/2*a^4 - 3/2*a^3 + 22*a^2 + 21/2*a + 3/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^8 + 13/2*a^6 - 51/2*a^4 + 1/2*a^3 + 28*a^2 + 1/2*a - 3/2)*q^17 + (-1/2*a^8 + 13/2*a^6 - 51/2*a^4 - 1/2*a^3 + 28*a^2 + 13/2*a - 3/2)*q^18 + (-a^4 + a^3 + 7*a^2 - 5*a - 4)*q^19 + (-1/2*a^8 + 13/2*a^6 - a^5 - 51/2*a^4 + 15/2*a^3 + 30*a^2 - 15/2*a - 15/2)*q^20 + (3/2*a^8 - 37/2*a^6 - a^5 + 135/2*a^4 + 15/2*a^3 - 68*a^2 - 43/2*a + 13/2)*q^21 + (-1/2*a^8 + 11/2*a^6 + a^5 - 35/2*a^4 - 13/2*a^3 + 17*a^2 + 17/2*a - 3/2)*q^22 + (-1/2*a^8 + 11/2*a^6 + a^5 - 33/2*a^4 - 13/2*a^3 + 9*a^2 + 17/2*a + 15/2)*q^23 + (-7/4*a^8 - 1/2*a^7 + 87/4*a^6 + 7*a^5 - 321/4*a^4 - 105/4*a^3 + 83*a^2 + 121/4*a - 21/4)*q^24 + (-a^7 + 12*a^5 - 41*a^3 + 34*a + 7)*q^25 + a*q^26 + (3/2*a^8 + a^7 - 39/2*a^6 - 12*a^5 + 151/2*a^4 + 83/2*a^3 - 81*a^2 - 91/2*a + 5/2)*q^27 + (-1/4*a^8 + 1/2*a^7 + 13/4*a^6 - 7*a^5 - 47/4*a^4 + 109/4*a^3 + 10*a^2 - 93/4*a - 19/4)*q^28 - q^29 + (-1/2*a^8 + 13/2*a^6 + a^5 - 53/2*a^4 - 15/2*a^3 + 33*a^2 + 23/2*a - 3/2)*q^30 + (a^5 - a^4 - 7*a^3 + 4*a^2 + 6*a + 5)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^8 - 13/2*a^6 + a^5 + 49/2*a^4 - 15/2*a^3 - 22*a^2 + 7/2*a - 3/2)*q^33 + (-1/2*a^8 + 13/2*a^6 - 49/2*a^4 - 3/2*a^3 + 23*a^2 + 17/2*a - 3/2)*q^34 + (3/2*a^8 - 39/2*a^6 + 155/2*a^4 - 3/2*a^3 - 93*a^2 - 3/2*a + 33/2)*q^35 + (1/2*a^8 - 13/2*a^6 + 51/2*a^4 - 1/2*a^3 - 29*a^2 - 5/2*a + 11/2)*q^36 + (-3/2*a^8 + 39/2*a^6 - a^5 - 151/2*a^4 + 17/2*a^3 + 82*a^2 - 9/2*a - 23/2)*q^37 + O(q^38)
*]> ;  // time = 58.929 seconds




J[379] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 379, 379 ], new_dimensions := [ 13, 18 ], dimensions := [ 13, 18 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -5, -5, -20, -3, -20, -11, -20, -12, 2, -41, -12, -1 ],
[ 3, 1, 22, 1, 10, 9, 14, 2, 12, 47, 0, 5 ]
], hecke_fields := [
x^13 + 5*x^12 - 5*x^11 - 56*x^10 - 27*x^9 + 210*x^8 + 184*x^7 - 347*x^6 - 346*x^5 + 252*x^4 + 246*x^3 - 60*x^2 - 48*x - 1,
x^18 - 3*x^17 - 22*x^16 + 69*x^15 + 190*x^14 - 638*x^13 - 807*x^12 + 3041*x^11 + 1680*x^10 - 7967*x^9 - 1220*x^8 + 11334*x^7 - 1006*x^6 - 8079*x^5 + 1938*x^4 + 2287*x^3 - 752*x^2 - 68*x + 24
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 63 ]
], tamagawa_numbers := [
[ 1 ],
[ 63 ]
], torsion_upper_bounds := [ 1, 63 ], torsion_lower_bounds := [ 1, 63 ], l_ratios := [ 0, 1/63 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-2*a^12 - 5*a^11 + 23*a^10 + 54*a^9 - 91*a^8 - 187*a^7 + 164*a^6 + 262*a^5 - 121*a^4 - 154*a^3 + 20*a^2 + 33*a + 2,
a^12 + a^11 - 12*a^10 - a^9 + 52*a^8 - 62*a^7 - 105*a^6 + 246*a^5 + 67*a^4 - 255*a^3 + 4*a^2 + 46*a + 1,
4*a^12 + 13*a^11 - 46*a^10 - 162*a^9 + 180*a^8 + 704*a^7 - 321*a^6 - 1330*a^5 + 286*a^4 + 1020*a^3 - 99*a^2 - 203*a - 8,
-3*a^11 - 4*a^10 + 42*a^9 + 39*a^8 - 213*a^7 - 103*a^6 + 478*a^5 + 49*a^4 - 413*a^3 + 38*a^2 + 83*a - 3,
9*a^12 + 31*a^11 - 85*a^10 - 341*a^9 + 229*a^8 + 1234*a^7 - 239*a^6 - 1902*a^5 + 145*a^4 + 1200*a^3 - 77*a^2 - 200*a - 8,
2*a^12 - 41*a^10 - 15*a^9 + 270*a^8 + 139*a^7 - 693*a^6 - 354*a^5 + 688*a^4 + 322*a^3 - 204*a^2 - 74*a + 4,
8*a^12 + 25*a^11 - 82*a^10 - 275*a^9 + 268*a^8 + 992*a^7 - 399*a^6 - 1512*a^5 + 296*a^4 + 956*a^3 - 94*a^2 - 172*a - 4,
-18*a^12 - 57*a^11 + 196*a^10 + 667*a^9 - 710*a^8 - 2654*a^7 + 1188*a^6 + 4558*a^5 - 1009*a^4 - 3205*a^3 + 352*a^2 + 588*a + 17,
2*a^12 + 10*a^11 - 17*a^10 - 127*a^9 + 29*a^8 + 568*a^7 + 19*a^6 - 1111*a^5 - 6*a^4 + 848*a^3 - 45*a^2 - 140*a - 6,
a^12 + 10*a^11 + 2*a^10 - 122*a^9 - 86*a^8 + 525*a^7 + 271*a^6 - 1020*a^5 - 158*a^4 + 782*a^3 - 81*a^2 - 133*a + 5,
-16*a^12 - 45*a^11 + 186*a^10 + 524*a^9 - 752*a^8 - 2064*a^7 + 1429*a^6 + 3478*a^5 - 1292*a^4 - 2409*a^3 + 440*a^2 + 448*a - 2
],
[
a,
239646933/1793175190*a^17 - 484282877/1793175190*a^16 - 2918698602/896587595*a^15 + 10920077991/1793175190*a^14 + 29192188967/896587595*a^13 - 49015280444/896587595*a^12 - 309792337413/1793175190*a^11 + 446493548451/1793175190*a^10 + 468794375957/896587595*a^9 - 217714639577/358635038*a^8 - 160785930047/179317519*a^7 + 690161150041/896587595*a^6 + 143607053551/179317519*a^5 - 825796553337/1793175190*a^4 - 265893375512/896587595*a^3 + 37055169135/358635038*a^2 + 15664352337/896587595*a - 3492196834/896587595,
-587362301/3586350380*a^17 + 1362705089/3586350380*a^16 + 3490982682/896587595*a^15 - 31159994897/3586350380*a^14 - 33784895822/896587595*a^13 + 142584136593/1793175190*a^12 + 685645325291/3586350380*a^11 - 1335062480207/3586350380*a^10 - 975760111749/1793175190*a^9 + 678126786911/717270076*a^8 + 306882475889/358635038*a^7 - 2287907721217/1793175190*a^6 - 239276091071/358635038*a^5 + 2998847142899/3586350380*a^4 + 164405587057/896587595*a^3 - 149169579219/717270076*a^2 + 15788512921/1793175190*a + 5934308694/896587595,
345660171/1793175190*a^17 - 702742249/1793175190*a^16 - 4120088259/896587595*a^15 + 15812721467/1793175190*a^14 + 40042452629/896587595*a^13 - 70877456353/896587595*a^12 - 409354057071/1793175190*a^11 + 645708072847/1793175190*a^10 + 591085357224/896587595*a^9 - 315794194981/358635038*a^8 - 191825947930/179317519*a^7 + 1008875577592/896587595*a^6 + 161672018357/179317519*a^5 - 1220808555709/1793175190*a^4 - 287618713729/896587595*a^3 + 54423378047/358635038*a^2 + 20699218389/896587595*a - 4083266708/896587595,
-132736008/896587595*a^17 + 285175122/896587595*a^16 + 3108067204/896587595*a^15 - 6410410811/896587595*a^14 - 29427805654/896587595*a^13 + 57409574768/896587595*a^12 + 144807378128/896587595*a^11 - 261431891741/896587595*a^10 - 395843560339/896587595*a^9 + 128154480581/179317519*a^8 + 118727431138/179317519*a^7 - 826932759102/896587595*a^6 - 88759808824/179317519*a^5 + 515880487037/896587595*a^4 + 120250963559/896587595*a^3 - 25509324900/179317519*a^2 + 6461272046/896587595*a + 6332734098/896587595,
-30264879/896587595*a^17 - 6594934/896587595*a^16 + 870582572/896587595*a^15 + 230342647/896587595*a^14 - 10275736617/896587595*a^13 - 3222650196/896587595*a^12 + 63928825349/896587595*a^11 + 23296598632/896587595*a^10 - 223604548322/896587595*a^9 - 18609033847/179317519*a^8 + 86531089630/179317519*a^7 + 202344819449/896587595*a^6 - 84643457170/179317519*a^5 - 218774233984/896587595*a^4 + 171397060597/896587595*a^3 + 18772501151/179317519*a^2 - 16314528032/896587595*a - 4256662976/896587595,
-146108351/1793175190*a^17 + 188501929/1793175190*a^16 + 1902055069/896587595*a^15 - 4234622807/1793175190*a^14 - 20457998569/896587595*a^13 + 18794361623/896587595*a^12 + 234317317701/1793175190*a^11 - 167104337257/1793175190*a^10 - 382507571479/896587595*a^9 + 77843282301/358635038*a^8 + 140657995989/179317519*a^7 - 228547137492/896587595*a^6 - 133208557571/179317519*a^5 + 248528372249/1793175190*a^4 + 259457039619/896587595*a^3 - 10282825013/358635038*a^2 - 16700513004/896587595*a + 1407321288/896587595,
-1215443849/3586350380*a^17 + 2971233491/3586350380*a^16 + 14065403371/1793175190*a^15 - 67400410513/3586350380*a^14 - 131468921151/1793175190*a^13 + 305526007287/1793175190*a^12 + 1275988558639/3586350380*a^11 - 2829570734333/3586350380*a^10 - 859217509588/896587595*a^9 + 1419520582587/717270076*a^8 + 253438402568/179317519*a^7 - 4727174421043/1793175190*a^6 - 369366545749/358635038*a^5 + 6133620725511/3586350380*a^4 + 470202125351/1793175190*a^3 - 310148437835/717270076*a^2 + 12431252557/896587595*a + 15343011526/896587595,
115785587/1793175190*a^17 - 150281454/896587595*a^16 - 2724939751/1793175190*a^15 + 7075049449/1793175190*a^14 + 25839434521/1793175190*a^13 - 33741137556/896587595*a^12 - 126130776057/1793175190*a^11 + 167901325767/896587595*a^10 + 334306657081/1793175190*a^9 - 187154837807/358635038*a^8 - 92213140217/358635038*a^7 + 728555824754/896587595*a^6 + 27957857002/179317519*a^5 - 1184384230793/1793175190*a^4 - 45057693931/1793175190*a^3 + 81568779161/358635038*a^2 + 2164441221/1793175190*a - 11293820916/896587595,
450912671/1793175190*a^17 - 847968909/1793175190*a^16 - 5438739019/896587595*a^15 + 18988582387/1793175190*a^14 + 53546899699/896587595*a^13 - 84442615363/896587595*a^12 - 554699129301/1793175190*a^11 + 759238528537/1793175190*a^10 + 810609799579/896587595*a^9 - 363075256387/358635038*a^8 - 265250685508/179317519*a^7 + 1115363540672/896587595*a^6 + 223770953014/179317519*a^5 - 1261743695469/1793175190*a^4 - 391531916199/896587595*a^3 + 49912205679/358635038*a^2 + 19969891994/896587595*a - 1163329128/896587595,
-52266898/896587595*a^17 + 118302427/896587595*a^16 + 1262178604/896587595*a^15 - 2892916041/896587595*a^14 - 12385475839/896587595*a^13 + 29018965298/896587595*a^12 + 63514804458/896587595*a^11 - 154100141271/896587595*a^10 - 181938517514/896587595*a^9 + 93014975393/179317519*a^8 + 57302867160/179317519*a^7 - 790969930422/896587595*a^6 - 44152113450/179317519*a^5 + 695269872242/896587595*a^4 + 49931606239/896587595*a^3 - 50065116590/179317519*a^2 + 12664934346/896587595*a + 13003623058/896587595,
-265074377/3586350380*a^17 + 421693023/3586350380*a^16 + 3249233053/1793175190*a^15 - 9403941449/3586350380*a^14 - 32679086213/1793175190*a^13 + 41612690571/1793175190*a^12 + 347824662647/3586350380*a^11 - 372418636609/3586350380*a^10 - 262208179254/896587595*a^9 + 178506107155/717270076*a^8 + 88189022021/179317519*a^7 - 568700676419/1793175190*a^6 - 148945815165/358635038*a^5 + 752530222303/3586350380*a^4 + 240231261623/1793175190*a^3 - 44422247507/717270076*a^2 - 3133776184/896587595*a + 2401780438/896587595
]
*], q_expansions := [*
q + a*q^2 + (-2*a^12 - 5*a^11 + 23*a^10 + 54*a^9 - 91*a^8 - 187*a^7 + 164*a^6 + 262*a^5 - 121*a^4 - 154*a^3 + 20*a^2 + 33*a + 2)*q^3 + (a^2 - 2)*q^4 + (a^12 + a^11 - 12*a^10 - a^9 + 52*a^8 - 62*a^7 - 105*a^6 + 246*a^5 + 67*a^4 - 255*a^3 + 4*a^2 + 46*a + 1)*q^5 + (5*a^12 + 13*a^11 - 58*a^10 - 145*a^9 + 233*a^8 + 532*a^7 - 432*a^6 - 813*a^5 + 350*a^4 + 512*a^3 - 87*a^2 - 94*a - 2)*q^6 + (4*a^12 + 13*a^11 - 46*a^10 - 162*a^9 + 180*a^8 + 704*a^7 - 321*a^6 - 1330*a^5 + 286*a^4 + 1020*a^3 - 99*a^2 - 203*a - 8)*q^7 + (a^3 - 4*a)*q^8 + (-8*a^12 - 22*a^11 + 91*a^10 + 247*a^9 - 357*a^8 - 917*a^7 + 659*a^6 + 1428*a^5 - 565*a^4 - 909*a^3 + 170*a^2 + 158*a + 2)*q^9 + (-4*a^12 - 7*a^11 + 55*a^10 + 79*a^9 - 272*a^8 - 289*a^7 + 593*a^6 + 413*a^5 - 507*a^4 - 242*a^3 + 106*a^2 + 49*a + 1)*q^10 + (-3*a^11 - 4*a^10 + 42*a^9 + 39*a^8 - 213*a^7 - 103*a^6 + 478*a^5 + 49*a^4 - 413*a^3 + 38*a^2 + 83*a - 3)*q^11 + (-8*a^12 - 23*a^11 + 89*a^10 + 260*a^9 - 336*a^8 - 978*a^7 + 594*a^6 + 1556*a^5 - 506*a^4 - 1009*a^3 + 166*a^2 + 172*a + 1)*q^12 + (9*a^12 + 31*a^11 - 85*a^10 - 341*a^9 + 229*a^8 + 1234*a^7 - 239*a^6 - 1902*a^5 + 145*a^4 + 1200*a^3 - 77*a^2 - 200*a - 8)*q^13 + (-7*a^12 - 26*a^11 + 62*a^10 + 288*a^9 - 136*a^8 - 1057*a^7 + 58*a^6 + 1670*a^5 + 12*a^4 - 1083*a^3 + 37*a^2 + 184*a + 4)*q^14 + (5*a^12 + 13*a^11 - 58*a^10 - 145*a^9 + 234*a^8 + 533*a^7 - 443*a^6 - 820*a^5 + 385*a^4 + 522*a^3 - 117*a^2 - 97*a - 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^12 - 41*a^10 - 15*a^9 + 270*a^8 + 139*a^7 - 693*a^6 - 354*a^5 + 688*a^4 + 322*a^3 - 204*a^2 - 74*a + 4)*q^17 + (18*a^12 + 51*a^11 - 201*a^10 - 573*a^9 + 763*a^8 + 2131*a^7 - 1348*a^6 - 3333*a^5 + 1107*a^4 + 2138*a^3 - 322*a^2 - 382*a - 8)*q^18 + (8*a^12 + 25*a^11 - 82*a^10 - 275*a^9 + 268*a^8 + 992*a^7 - 399*a^6 - 1512*a^5 + 296*a^4 + 956*a^3 - 94*a^2 - 172*a - 4)*q^19 + (11*a^12 + 33*a^11 - 121*a^10 - 378*a^9 + 447*a^8 + 1453*a^7 - 765*a^6 - 2383*a^5 + 632*a^4 + 1600*a^3 - 199*a^2 - 283*a - 6)*q^20 + (8*a^12 + 23*a^11 - 88*a^10 - 256*a^9 + 328*a^8 + 938*a^7 - 579*a^6 - 1440*a^5 + 494*a^4 + 900*a^3 - 156*a^2 - 152*a - 8)*q^21 + (-3*a^12 - 4*a^11 + 42*a^10 + 39*a^9 - 213*a^8 - 103*a^7 + 478*a^6 + 49*a^5 - 413*a^4 + 38*a^3 + 83*a^2 - 3*a)*q^22 + (-18*a^12 - 57*a^11 + 196*a^10 + 667*a^9 - 710*a^8 - 2654*a^7 + 1188*a^6 + 4558*a^5 - 1009*a^4 - 3205*a^3 + 352*a^2 + 588*a + 17)*q^23 + (7*a^12 + 23*a^11 - 72*a^10 - 262*a^9 + 236*a^8 + 1002*a^7 - 356*a^6 - 1648*a^5 + 307*a^4 + 1110*a^3 - 134*a^2 - 195*a - 4)*q^24 + (-16*a^12 - 51*a^11 + 158*a^10 + 551*a^9 - 477*a^8 - 1924*a^7 + 631*a^6 + 2791*a^5 - 439*a^4 - 1651*a^3 + 170*a^2 + 284*a + 1)*q^25 + (-14*a^12 - 40*a^11 + 163*a^10 + 472*a^9 - 656*a^8 - 1895*a^7 + 1221*a^6 + 3259*a^5 - 1068*a^4 - 2291*a^3 + 340*a^2 + 424*a + 9)*q^26 + (-7*a^12 - 24*a^11 + 73*a^10 + 284*a^9 - 243*a^8 - 1152*a^7 + 364*a^6 + 2033*a^5 - 315*a^4 - 1459*a^3 + 145*a^2 + 265*a)*q^27 + (a^12 + a^11 - 12*a^10 - a^9 + 53*a^8 - 62*a^7 - 117*a^6 + 250*a^5 + 109*a^4 - 281*a^3 - 38*a^2 + 74*a + 9)*q^28 + (2*a^12 + 10*a^11 - 17*a^10 - 127*a^9 + 29*a^8 + 568*a^7 + 19*a^6 - 1111*a^5 - 6*a^4 + 848*a^3 - 45*a^2 - 140*a - 6)*q^29 + (-12*a^12 - 33*a^11 + 135*a^10 + 369*a^9 - 517*a^8 - 1363*a^7 + 915*a^6 + 2115*a^5 - 738*a^4 - 1347*a^3 + 203*a^2 + 238*a + 5)*q^30 + (a^12 + 10*a^11 + 2*a^10 - 122*a^9 - 86*a^8 + 525*a^7 + 271*a^6 - 1020*a^5 - 158*a^4 + 782*a^3 - 81*a^2 - 133*a + 5)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (16*a^12 + 48*a^11 - 171*a^10 - 537*a^9 + 599*a^8 + 1989*a^7 - 947*a^6 - 3120*a^5 + 685*a^4 + 2022*a^3 - 166*a^2 - 368*a - 14)*q^33 + (-10*a^12 - 31*a^11 + 97*a^10 + 324*a^9 - 281*a^8 - 1061*a^7 + 340*a^6 + 1380*a^5 - 182*a^4 - 696*a^3 + 46*a^2 + 100*a + 2)*q^34 + (2*a^12 + 15*a^11 + 7*a^10 - 147*a^9 - 206*a^8 + 427*a^7 + 700*a^6 - 471*a^5 - 743*a^4 + 156*a^3 + 191*a^2 + 7*a)*q^35 + (-23*a^12 - 67*a^11 + 253*a^10 + 755*a^9 - 935*a^8 - 2826*a^7 + 1595*a^6 + 4479*a^5 - 1268*a^4 - 2932*a^3 + 358*a^2 + 540*a + 14)*q^36 + (-16*a^12 - 45*a^11 + 186*a^10 + 524*a^9 - 752*a^8 - 2064*a^7 + 1429*a^6 + 3478*a^5 - 1292*a^4 - 2409*a^3 + 440*a^2 + 448*a - 2)*q^37 + O(q^38),
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22232538811/896587595*a^14 - 111900181534/896587595*a^13 + 199497573808/896587595*a^12 + 566720635483/896587595*a^11 - 909548631686/896587595*a^10 - 1613218519454/896587595*a^9 + 444884971836/179317519*a^8 + 511645883867/179317519*a^7 - 2834700306622/896587595*a^6 - 413736919446/179317519*a^5 + 1695379273422/896587595*a^4 + 659752365624/896587595*a^3 - 73158314668/179317519*a^2 - 16719581624/896587595*a + 9837343728/896587595)*q^24 + (-525006043/896587595*a^17 + 2273009009/1793175190*a^16 + 25066613053/1793175190*a^15 - 25853707956/896587595*a^14 - 243990818953/1793175190*a^13 + 235079850638/896587595*a^12 + 624325979138/896587595*a^11 - 2182896201297/1793175190*a^10 - 3604467126423/1793175190*a^9 + 548361248777/179317519*a^8 + 1162930716189/358635038*a^7 - 3647541049567/896587595*a^6 - 478327719334/179317519*a^5 + 2349837587447/896587595*a^4 + 1538594164153/1793175190*a^3 - 115464482607/179317519*a^2 - 29908109313/1793175190*a + 19089711203/896587595)*q^25 + (-97389571/896587595*a^17 + 204755234/896587595*a^16 + 2318619298/896587595*a^15 - 4525409607/896587595*a^14 - 22531642998/896587595*a^13 + 39505067996/896587595*a^12 + 115332095671/896587595*a^11 - 172759551602/896587595*a^10 - 334165460228/896587595*a^9 + 79146459154/179317519*a^8 + 109073391607/179317519*a^7 - 453663754124/896587595*a^6 - 92656838285/179317519*a^5 + 230050396099/896587595*a^4 + 163078284028/896587595*a^3 - 7814743408/179317519*a^2 - 6314674748/896587595*a + 726357096/896587595)*q^26 + (731227612/896587595*a^17 - 1546094238/896587595*a^16 - 17409080126/896587595*a^15 + 34998226559/896587595*a^14 + 168778915621/896587595*a^13 - 316230149722/896587595*a^12 - 858795346442/896587595*a^11 + 1456286406554/896587595*a^10 + 2459515229316/896587595*a^9 - 723867467173/179317519*a^8 - 785611727659/179317519*a^7 + 4748560024048/896587595*a^6 + 639424978077/179317519*a^5 - 3012166694033/896587595*a^4 - 1019993953351/896587595*a^3 + 147503297067/179317519*a^2 + 16854198666/896587595*a - 23894078332/896587595)*q^27 + (-162129153/896587595*a^17 + 360447987/896587595*a^16 + 3913692794/896587595*a^15 - 8177218351/896587595*a^14 - 38666048579/896587595*a^13 + 73897798648/896587595*a^12 + 201875590243/896587595*a^11 - 339016410881/896587595*a^10 - 599009625144/896587595*a^9 + 166575140896/179317519*a^8 + 201271679002/179317519*a^7 - 1063739325492/896587595*a^6 - 177825627114/179317519*a^5 + 637727717472/896587595*a^4 + 343703415259/896587595*a^3 - 27754824773/179317519*a^2 - 34182257854/896587595*a + 4155674248/896587595)*q^28 + (450912671/1793175190*a^17 - 847968909/1793175190*a^16 - 5438739019/896587595*a^15 + 18988582387/1793175190*a^14 + 53546899699/896587595*a^13 - 84442615363/896587595*a^12 - 554699129301/1793175190*a^11 + 759238528537/1793175190*a^10 + 810609799579/896587595*a^9 - 363075256387/358635038*a^8 - 265250685508/179317519*a^7 + 1115363540672/896587595*a^6 + 223770953014/179317519*a^5 - 1261743695469/1793175190*a^4 - 391531916199/896587595*a^3 + 49912205679/358635038*a^2 + 19969891994/896587595*a - 1163329128/896587595)*q^29 + (276764003/896587595*a^17 - 600305417/896587595*a^16 - 6538902114/896587595*a^15 + 13566931281/896587595*a^14 + 62768293069/896587595*a^13 - 122210467763/896587595*a^12 - 315483025473/896587595*a^11 + 559495414416/896587595*a^10 + 891180925074/896587595*a^9 - 274829460366/179317519*a^8 - 281416528203/179317519*a^7 + 1757006013412/896587595*a^6 + 229345128023/179317519*a^5 - 1048676619657/896587595*a^4 - 381472739229/896587595*a^3 + 44312731546/179317519*a^2 + 14657633254/896587595*a - 6841649388/896587595)*q^30 + (-52266898/896587595*a^17 + 118302427/896587595*a^16 + 1262178604/896587595*a^15 - 2892916041/896587595*a^14 - 12385475839/896587595*a^13 + 29018965298/896587595*a^12 + 63514804458/896587595*a^11 - 154100141271/896587595*a^10 - 181938517514/896587595*a^9 + 93014975393/179317519*a^8 + 57302867160/179317519*a^7 - 790969930422/896587595*a^6 - 44152113450/179317519*a^5 + 695269872242/896587595*a^4 + 49931606239/896587595*a^3 - 50065116590/179317519*a^2 + 12664934346/896587595*a + 13003623058/896587595)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (89365994/896587595*a^17 - 175966471/896587595*a^16 - 2132056652/896587595*a^15 + 3914057368/896587595*a^14 + 20778071677/896587595*a^13 - 34360523499/896587595*a^12 - 106968538479/896587595*a^11 + 150455981053/896587595*a^10 + 314038629182/896587595*a^9 - 67994281372/179317519*a^8 - 105570614351/179317519*a^7 + 364485492161/896587595*a^6 + 95580161964/179317519*a^5 - 134766530941/896587595*a^4 - 195938862477/896587595*a^3 - 2065059889/179317519*a^2 + 19330272042/896587595*a + 1433720436/896587595)*q^33 + (-124911562/896587595*a^17 + 294863208/896587595*a^16 + 2923426706/896587595*a^15 - 6577705224/896587595*a^14 - 27814202346/896587595*a^13 + 58203939222/896587595*a^12 + 138605579067/896587595*a^11 - 259776556639/896587595*a^10 - 387414410456/896587595*a^9 + 122832777167/179317519*a^8 + 119889777525/179317519*a^7 - 739535288408/896587595*a^6 - 93188099548/179317519*a^5 + 401036031738/896587595*a^4 + 141367836836/896587595*a^3 - 14327450596/179317519*a^2 - 3560362646/896587595*a + 1753300212/896587595)*q^34 + (58559104/179317519*a^17 - 117631389/179317519*a^16 - 1392746355/179317519*a^15 + 2627861347/179317519*a^14 + 13490638992/179317519*a^13 - 23313483077/179317519*a^12 - 68626183001/179317519*a^11 + 104522845689/179317519*a^10 + 196824734348/179317519*a^9 - 248993860384/179317519*a^8 - 316185342463/179317519*a^7 + 303133526648/179317519*a^6 + 261898828413/179317519*a^5 - 164817263761/179317519*a^4 - 88453353685/179317519*a^3 + 26321755263/179317519*a^2 + 3481263315/179317519*a + 437189304/179317519)*q^35 + (29951406/896587595*a^17 - 51876254/896587595*a^16 - 694404023/896587595*a^15 + 1157637007/896587595*a^14 + 6479975473/896587595*a^13 - 10251379371/896587595*a^12 - 31461219386/896587595*a^11 + 45695286397/896587595*a^10 + 86856593513/896587595*a^9 - 21314599796/179317519*a^8 - 28778853002/179317519*a^7 + 119360679019/896587595*a^6 + 30249616959/179317519*a^5 - 42030635114/896587595*a^4 - 97688900978/896587595*a^3 - 2271466109/179317519*a^2 + 26596539468/896587595*a + 228954554/896587595)*q^36 + (-265074377/3586350380*a^17 + 421693023/3586350380*a^16 + 3249233053/1793175190*a^15 - 9403941449/3586350380*a^14 - 32679086213/1793175190*a^13 + 41612690571/1793175190*a^12 + 347824662647/3586350380*a^11 - 372418636609/3586350380*a^10 - 262208179254/896587595*a^9 + 178506107155/717270076*a^8 + 88189022021/179317519*a^7 - 568700676419/1793175190*a^6 - 148945815165/358635038*a^5 + 752530222303/3586350380*a^4 + 240231261623/1793175190*a^3 - 44422247507/717270076*a^2 - 3133776184/896587595*a + 2401780438/896587595)*q^37 + O(q^38)
*]> ;  // time = 7.799 seconds




J[381] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 381, 381, 381, 381, 381, 127, 127 ], new_dimensions := [ 1, 1, 5, 5, 9, 3, 7 ], dimensions := [ 1, 1, 5, 5, 9, 6, 14 ], intersection_graph := [ 0, 1, 1, 1, 11, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 0, 1, 1, 19, 1, 1, 1, 1, 0, 1, 1, 647, 11, 1, 1, 1, 0, 109, 1, 1, 1, 19, 1, 109, 0, 1, 1, 5, 1, 647, 1, 1, 0 ], ap_traces := [
[ 2, 1, 3, -4, 6, -7, -2, 0, 1, 9, -5, -3 ],
[ 0, 1, -1, -2, -4, -3, 0, -4, -3, 5, -5, 5 ],
[ -1, -5, -5, 0, -16, 3, -6, -8, -9, -17, -9, -1 ],
[ 2, -5, 1, 0, 14, -5, 4, 4, 15, 9, 3, -5 ],
[ -2, 9, -4, 10, 8, 14, -6, 12, -4, -8, 4, 22 ]
], hecke_fields := [
x - 1,
x - 1,
x^5 + x^4 - 5*x^3 - 3*x^2 + 5*x + 2,
x^5 - 2*x^4 - 6*x^3 + 10*x^2 + 5*x - 4,
x^9 + 2*x^8 - 14*x^7 - 26*x^6 + 59*x^5 + 99*x^4 - 66*x^3 - 102*x^2 - 24*x - 1
], atkin_lehners := [
[ -1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 5, 1 ],
[ 19, 1 ],
[ 647, 1 ],
[ 109, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 5, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 109, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 1, 0, 0, 1, 109 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 1 ], eigenvalues := [*
[ 2, 1, 3, -4, 6, -7, -2, 0, 1, 9, -5, -3 ],
[ 0, 1, -1, -2, -4, -3, 0, -4, -3, 5, -5, 5 ],
[
a,
-1,
-a^4 - a^3 + 3*a^2 + a - 1,
2*a^4 + 2*a^3 - 8*a^2 - 4*a + 4,
-a^3 - a^2 + 2*a - 2,
-a^4 + 6*a^2 - a - 5,
-a^4 - 2*a^3 + 4*a^2 + 5*a - 4,
-a^4 + 2*a^3 + 8*a^2 - 7*a - 10,
a^4 - a^3 - 5*a^2 + 5*a + 1,
-a^4 - a^3 + 5*a^2 + 5*a - 7,
2*a^4 - a^3 - 13*a^2 + 6*a + 11,
-2*a^4 - 3*a^3 + 5*a^2 + 4*a + 1
],
[
a,
-1,
1/2*a^4 - a^3 - 5/2*a^2 + 4*a + 1,
-1/2*a^3 + 7/2*a,
-1/2*a^4 + 7/2*a^2,
-1/2*a^3 + 7/2*a - 1,
-a^4 + a^3 + 5*a^2 - 3*a,
a^4 - a^3 - 7*a^2 + 3*a + 8,
a^4 - a^3 - 6*a^2 + 3*a + 7,
1/2*a^4 + a^3 - 9/2*a^2 - 5*a + 7,
a^4 - a^3 - 4*a^2 + a - 1,
-3/2*a^3 + 2*a^2 + 9/2*a - 5
],
[
a,
1,
1/6*a^8 + 1/2*a^7 - 7/3*a^6 - 20/3*a^5 + 29/3*a^4 + 157/6*a^3 - 59/6*a^2 - 85/3*a - 16/3,
-3/4*a^8 - 5/4*a^7 + 43/4*a^6 + 65/4*a^5 - 95/2*a^4 - 247/4*a^3 + 247/4*a^2 + 251/4*a + 31/4,
5/12*a^8 + 3/4*a^7 - 73/12*a^6 - 113/12*a^5 + 169/6*a^4 + 401/12*a^3 - 499/12*a^2 - 349/12*a + 17/12,
1/3*a^8 + 1/2*a^7 - 31/6*a^6 - 19/3*a^5 + 76/3*a^4 + 67/3*a^3 - 235/6*a^2 - 109/6*a + 13/3,
2/3*a^8 + a^7 - 28/3*a^6 - 38/3*a^5 + 119/3*a^4 + 140/3*a^3 - 145/3*a^2 - 139/3*a - 16/3,
2/3*a^8 + a^7 - 28/3*a^6 - 38/3*a^5 + 119/3*a^4 + 140/3*a^3 - 145/3*a^2 - 139/3*a - 10/3,
-a^8 - 2*a^7 + 14*a^6 + 25*a^5 - 60*a^4 - 89*a^3 + 74*a^2 + 80*a + 11,
-5/4*a^8 - 9/4*a^7 + 73/4*a^6 + 117/4*a^5 - 165/2*a^4 - 445/4*a^3 + 439/4*a^2 + 453/4*a + 43/4,
a^8 + 2*a^7 - 14*a^6 - 26*a^5 + 59*a^4 + 99*a^3 - 68*a^2 - 103*a - 14,
-1/2*a^8 - a^7 + 7*a^6 + 25/2*a^5 - 30*a^4 - 87/2*a^3 + 39*a^2 + 35*a + 3/2
]
*], q_expansions := [*
q + 2*q^2 + q^3 + 2*q^4 + 3*q^5 + 2*q^6 - 4*q^7 + q^9 + 6*q^10 + 6*q^11 + 2*q^12 - 7*q^13 - 8*q^14 + 3*q^15 - 4*q^16 - 2*q^17 + 2*q^18 + 6*q^20 - 4*q^21 + 12*q^22 + q^23 + 4*q^25 - 14*q^26 + q^27 - 8*q^28 + 9*q^29 + 6*q^30 - 5*q^31 - 8*q^32 + 6*q^33 - 4*q^34 - 12*q^35 + 2*q^36 - 3*q^37 + O(q^38),
q + q^3 - 2*q^4 - q^5 - 2*q^7 + q^9 - 4*q^11 - 2*q^12 - 3*q^13 - q^15 + 4*q^16 - 4*q^19 + 2*q^20 - 2*q^21 - 3*q^23 - 4*q^25 + q^27 + 4*q^28 + 5*q^29 - 5*q^31 - 4*q^33 + 2*q^35 - 2*q^36 + 5*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^4 - a^3 + 3*a^2 + a - 1)*q^5 - a*q^6 + (2*a^4 + 2*a^3 - 8*a^2 - 4*a + 4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-2*a^3 - 2*a^2 + 4*a + 2)*q^10 + (-a^3 - a^2 + 2*a - 2)*q^11 + (-a^2 + 2)*q^12 + (-a^4 + 6*a^2 - a - 5)*q^13 + (2*a^3 + 2*a^2 - 6*a - 4)*q^14 + (a^4 + a^3 - 3*a^2 - a + 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 - 2*a^3 + 4*a^2 + 5*a - 4)*q^17 + a*q^18 + (-a^4 + 2*a^3 + 8*a^2 - 7*a - 10)*q^19 + (-2*a^2 + 2)*q^20 + (-2*a^4 - 2*a^3 + 8*a^2 + 4*a - 4)*q^21 + (-a^4 - a^3 + 2*a^2 - 2*a)*q^22 + (a^4 - a^3 - 5*a^2 + 5*a + 1)*q^23 + (-a^3 + 4*a)*q^24 + (a^4 + 3*a^3 + a^2 - 5*a - 6)*q^25 + (a^4 + a^3 - 4*a^2 + 2)*q^26 - q^27 + (-2*a^4 - 2*a^3 + 10*a^2 + 4*a - 8)*q^28 + (-a^4 - a^3 + 5*a^2 + 5*a - 7)*q^29 + (2*a^3 + 2*a^2 - 4*a - 2)*q^30 + (2*a^4 - a^3 - 13*a^2 + 6*a + 11)*q^31 + (-a^4 - 3*a^3 + 3*a^2 + 7*a - 2)*q^32 + (a^3 + a^2 - 2*a + 2)*q^33 + (-a^4 - a^3 + 2*a^2 + a + 2)*q^34 - 4*q^35 + (a^2 - 2)*q^36 + (-2*a^4 - 3*a^3 + 5*a^2 + 4*a + 1)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (1/2*a^4 - a^3 - 5/2*a^2 + 4*a + 1)*q^5 - a*q^6 + (-1/2*a^3 + 7/2*a)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (1/2*a^3 - a^2 - 3/2*a + 2)*q^10 + (-1/2*a^4 + 7/2*a^2)*q^11 + (-a^2 + 2)*q^12 + (-1/2*a^3 + 7/2*a - 1)*q^13 + (-1/2*a^4 + 7/2*a^2)*q^14 + (-1/2*a^4 + a^3 + 5/2*a^2 - 4*a - 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 + a^3 + 5*a^2 - 3*a)*q^17 + a*q^18 + (a^4 - a^3 - 7*a^2 + 3*a + 8)*q^19 + (-1/2*a^4 + a^3 + 7/2*a^2 - 6*a - 2)*q^20 + (1/2*a^3 - 7/2*a)*q^21 + (-a^4 + 1/2*a^3 + 5*a^2 + 5/2*a - 2)*q^22 + (a^4 - a^3 - 6*a^2 + 3*a + 7)*q^23 + (-a^3 + 4*a)*q^24 + (1/2*a^3 - a^2 - 7/2*a + 2)*q^25 + (-1/2*a^4 + 7/2*a^2 - a)*q^26 - q^27 + (-a^4 + 3/2*a^3 + 5*a^2 - 9/2*a - 2)*q^28 + (1/2*a^4 + a^3 - 9/2*a^2 - 5*a + 7)*q^29 + (-1/2*a^3 + a^2 + 3/2*a - 2)*q^30 + (a^4 - a^3 - 4*a^2 + a - 1)*q^31 + (2*a^4 - 2*a^3 - 10*a^2 + 7*a + 4)*q^32 + (1/2*a^4 - 7/2*a^2)*q^33 + (-a^4 - a^3 + 7*a^2 + 5*a - 4)*q^34 + (a^3 - 2*a^2 - 4*a + 6)*q^35 + (a^2 - 2)*q^36 + (-3/2*a^3 + 2*a^2 + 9/2*a - 5)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (1/6*a^8 + 1/2*a^7 - 7/3*a^6 - 20/3*a^5 + 29/3*a^4 + 157/6*a^3 - 59/6*a^2 - 85/3*a - 16/3)*q^5 + a*q^6 + (-3/4*a^8 - 5/4*a^7 + 43/4*a^6 + 65/4*a^5 - 95/2*a^4 - 247/4*a^3 + 247/4*a^2 + 251/4*a + 31/4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (1/6*a^8 - 7/3*a^6 - 1/6*a^5 + 29/3*a^4 + 7/6*a^3 - 34/3*a^2 - 4/3*a + 1/6)*q^10 + (5/12*a^8 + 3/4*a^7 - 73/12*a^6 - 113/12*a^5 + 169/6*a^4 + 401/12*a^3 - 499/12*a^2 - 349/12*a + 17/12)*q^11 + (a^2 - 2)*q^12 + (1/3*a^8 + 1/2*a^7 - 31/6*a^6 - 19/3*a^5 + 76/3*a^4 + 67/3*a^3 - 235/6*a^2 - 109/6*a + 13/3)*q^13 + (1/4*a^8 + 1/4*a^7 - 13/4*a^6 - 13/4*a^5 + 25/2*a^4 + 49/4*a^3 - 55/4*a^2 - 41/4*a - 3/4)*q^14 + (1/6*a^8 + 1/2*a^7 - 7/3*a^6 - 20/3*a^5 + 29/3*a^4 + 157/6*a^3 - 59/6*a^2 - 85/3*a - 16/3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2/3*a^8 + a^7 - 28/3*a^6 - 38/3*a^5 + 119/3*a^4 + 140/3*a^3 - 145/3*a^2 - 139/3*a - 16/3)*q^17 + a*q^18 + (2/3*a^8 + a^7 - 28/3*a^6 - 38/3*a^5 + 119/3*a^4 + 140/3*a^3 - 145/3*a^2 - 139/3*a - 10/3)*q^19 + (-2/3*a^8 - a^7 + 53/6*a^6 + 79/6*a^5 - 104/3*a^4 - 158/3*a^3 + 106/3*a^2 + 365/6*a + 65/6)*q^20 + (-3/4*a^8 - 5/4*a^7 + 43/4*a^6 + 65/4*a^5 - 95/2*a^4 - 247/4*a^3 + 247/4*a^2 + 251/4*a + 31/4)*q^21 + (-1/12*a^8 - 1/4*a^7 + 17/12*a^6 + 43/12*a^5 - 47/6*a^4 - 169/12*a^3 + 161/12*a^2 + 137/12*a + 5/12)*q^22 + (-a^8 - 2*a^7 + 14*a^6 + 25*a^5 - 60*a^4 - 89*a^3 + 74*a^2 + 80*a + 11)*q^23 + (a^3 - 4*a)*q^24 + (-19/12*a^8 - 11/4*a^7 + 275/12*a^6 + 421/12*a^5 - 611/6*a^4 - 1543/12*a^3 + 1571/12*a^2 + 1451/12*a + 191/12)*q^25 + (-1/6*a^8 - 1/2*a^7 + 7/3*a^6 + 17/3*a^5 - 32/3*a^4 - 103/6*a^3 + 95/6*a^2 + 37/3*a + 1/3)*q^26 + q^27 + (5/4*a^8 + 11/4*a^7 - 73/4*a^6 - 139/4*a^5 + 165/2*a^4 + 505/4*a^3 - 433/4*a^2 - 481/4*a - 61/4)*q^28 + (-5/4*a^8 - 9/4*a^7 + 73/4*a^6 + 117/4*a^5 - 165/2*a^4 - 445/4*a^3 + 439/4*a^2 + 453/4*a + 43/4)*q^29 + (1/6*a^8 - 7/3*a^6 - 1/6*a^5 + 29/3*a^4 + 7/6*a^3 - 34/3*a^2 - 4/3*a + 1/6)*q^30 + (a^8 + 2*a^7 - 14*a^6 - 26*a^5 + 59*a^4 + 99*a^3 - 68*a^2 - 103*a - 14)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (5/12*a^8 + 3/4*a^7 - 73/12*a^6 - 113/12*a^5 + 169/6*a^4 + 401/12*a^3 - 499/12*a^2 - 349/12*a + 17/12)*q^33 + (-1/3*a^8 + 14/3*a^6 + 1/3*a^5 - 58/3*a^4 - 13/3*a^3 + 65/3*a^2 + 32/3*a + 2/3)*q^34 + (3/4*a^8 + 7/4*a^7 - 41/4*a^6 - 93/4*a^5 + 83/2*a^4 + 363/4*a^3 - 165/4*a^2 - 389/4*a - 91/4)*q^35 + (a^2 - 2)*q^36 + (-1/2*a^8 - a^7 + 7*a^6 + 25/2*a^5 - 30*a^4 - 87/2*a^3 + 39*a^2 + 35*a + 3/2)*q^37 + O(q^38)
*]> ;  // time = 63.04 seconds




J[382] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 382, 382, 382, 382, 191, 191 ], new_dimensions := [ 3, 3, 4, 5, 2, 14 ], dimensions := [ 3, 3, 4, 5, 4, 28 ], intersection_graph := [ 0, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 967, 1, 1, 0, 1, 11, 1, 1, 1, 1, 0, 1, 69047, 5, 1, 11, 1, 0, 1, 1, 967, 1, 69047, 1, 0 ], ap_traces := [
[ -3, -1, -4, -1, -3, -3, -13, 1, -5, -5, 2, -2 ],
[ 3, -5, -6, -5, -3, -11, -9, -9, -1, 1, -4, 12 ],
[ 4, 3, 4, 1, 3, -1, -3, 3, 7, -5, 4, -4 ],
[ -5, 3, 8, 1, 5, 1, 11, -13, 15, 1, -10, 6 ]
], hecke_fields := [
x^3 + x^2 - 4*x + 1,
x^3 + 5*x^2 + 6*x + 1,
x^4 - 3*x^3 - 2*x^2 + 9*x - 4,
x^5 - 3*x^4 - 8*x^3 + 25*x^2 + 8*x - 32
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 5, 1 ],
[ 967, 1 ],
[ 11, 1 ],
[ 69047, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 967, 1 ],
[ 11, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1 ], l_ratios := [ 0, 0, 11, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
-1,
a,
-a^2 - 2*a + 1,
a^2 + a - 3,
a^2 - 4,
-1,
a - 4,
-2*a^2 - 4*a + 5,
-3*a^2 - 4*a + 6,
4*a^2 + 8*a - 11,
a + 1,
a^2 + 2*a - 3
],
[
1,
a,
a^2 + 2*a - 3,
-3*a^2 - 11*a - 7,
3*a^2 + 12*a + 6,
-2*a^2 - 6*a - 5,
2*a^2 + 7*a,
2*a^2 + 10*a + 5,
-3*a^2 - 10*a - 4,
6*a^2 + 22*a + 11,
2*a^2 + 3*a - 5,
-3*a^2 - 6*a + 7
],
[
1,
a,
a^3 - 2*a^2 - 4*a + 6,
-a^3 + 2*a^2 + 3*a - 4,
-a^2 + 4,
-a^3 + a^2 + 4*a - 2,
-2*a^3 + 4*a^2 + 7*a - 10,
a^3 - a^2 - 6*a + 4,
a^2 - 2*a,
-3*a^3 + 7*a^2 + 10*a - 18,
3*a^3 - 5*a^2 - 11*a + 12,
3*a^3 - 4*a^2 - 10*a + 6
],
[
-1,
a,
1/2*a^4 - 1/2*a^3 - 4*a^2 + 5/2*a + 6,
1/3*a^4 - 2/3*a^3 - 10/3*a^2 + 4*a + 20/3,
-7/12*a^4 + 5/12*a^3 + 13/3*a^2 - 5/4*a - 8/3,
-1/6*a^4 + 5/6*a^3 + 5/3*a^2 - 11/2*a - 10/3,
-7/6*a^4 + 5/6*a^3 + 32/3*a^2 - 11/2*a - 40/3,
-17/12*a^4 + 7/12*a^3 + 41/3*a^2 - 11/4*a - 76/3,
-1/3*a^4 - 1/3*a^3 + 7/3*a^2 + a + 10/3,
7/12*a^4 + 7/12*a^3 - 19/3*a^2 - 19/4*a + 38/3,
1/2*a^4 - 1/2*a^3 - 5*a^2 + 3/2*a + 8,
-3/4*a^4 + 5/4*a^3 + 6*a^2 - 27/4*a - 6
]
*], q_expansions := [*
q - q^2 + a*q^3 + q^4 + (-a^2 - 2*a + 1)*q^5 - a*q^6 + (a^2 + a - 3)*q^7 - q^8 + (a^2 - 3)*q^9 + (a^2 + 2*a - 1)*q^10 + (a^2 - 4)*q^11 + a*q^12 - q^13 + (-a^2 - a + 3)*q^14 + (-a^2 - 3*a + 1)*q^15 + q^16 + (a - 4)*q^17 + (-a^2 + 3)*q^18 + (-2*a^2 - 4*a + 5)*q^19 + (-a^2 - 2*a + 1)*q^20 + (a - 1)*q^21 + (-a^2 + 4)*q^22 + (-3*a^2 - 4*a + 6)*q^23 - a*q^24 + (3*a^2 + 7*a - 7)*q^25 + q^26 + (-a^2 - 2*a - 1)*q^27 + (a^2 + a - 3)*q^28 + (4*a^2 + 8*a - 11)*q^29 + (a^2 + 3*a - 1)*q^30 + (a + 1)*q^31 - q^32 + (-a^2 - 1)*q^33 + (-a + 4)*q^34 - q^35 + (a^2 - 3)*q^36 + (a^2 + 2*a - 3)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (a^2 + 2*a - 3)*q^5 + a*q^6 + (-3*a^2 - 11*a - 7)*q^7 + q^8 + (a^2 - 3)*q^9 + (a^2 + 2*a - 3)*q^10 + (3*a^2 + 12*a + 6)*q^11 + a*q^12 + (-2*a^2 - 6*a - 5)*q^13 + (-3*a^2 - 11*a - 7)*q^14 + (-3*a^2 - 9*a - 1)*q^15 + q^16 + (2*a^2 + 7*a)*q^17 + (a^2 - 3)*q^18 + (2*a^2 + 10*a + 5)*q^19 + (a^2 + 2*a - 3)*q^20 + (4*a^2 + 11*a + 3)*q^21 + (3*a^2 + 12*a + 6)*q^22 + (-3*a^2 - 10*a - 4)*q^23 + a*q^24 + (-3*a^2 - 7*a + 5)*q^25 + (-2*a^2 - 6*a - 5)*q^26 + (-5*a^2 - 12*a - 1)*q^27 + (-3*a^2 - 11*a - 7)*q^28 + (6*a^2 + 22*a + 11)*q^29 + (-3*a^2 - 9*a - 1)*q^30 + (2*a^2 + 3*a - 5)*q^31 + q^32 + (-3*a^2 - 12*a - 3)*q^33 + (2*a^2 + 7*a)*q^34 + (8*a^2 + 34*a + 23)*q^35 + (a^2 - 3)*q^36 + (-3*a^2 - 6*a + 7)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (a^3 - 2*a^2 - 4*a + 6)*q^5 + a*q^6 + (-a^3 + 2*a^2 + 3*a - 4)*q^7 + q^8 + (a^2 - 3)*q^9 + (a^3 - 2*a^2 - 4*a + 6)*q^10 + (-a^2 + 4)*q^11 + a*q^12 + (-a^3 + a^2 + 4*a - 2)*q^13 + (-a^3 + 2*a^2 + 3*a - 4)*q^14 + (a^3 - 2*a^2 - 3*a + 4)*q^15 + q^16 + (-2*a^3 + 4*a^2 + 7*a - 10)*q^17 + (a^2 - 3)*q^18 + (a^3 - a^2 - 6*a + 4)*q^19 + (a^3 - 2*a^2 - 4*a + 6)*q^20 + (-a^3 + a^2 + 5*a - 4)*q^21 + (-a^2 + 4)*q^22 + (a^2 - 2*a)*q^23 + a*q^24 + (2*a^3 - 5*a^2 - 7*a + 11)*q^25 + (-a^3 + a^2 + 4*a - 2)*q^26 + (a^3 - 6*a)*q^27 + (-a^3 + 2*a^2 + 3*a - 4)*q^28 + (-3*a^3 + 7*a^2 + 10*a - 18)*q^29 + (a^3 - 2*a^2 - 3*a + 4)*q^30 + (3*a^3 - 5*a^2 - 11*a + 12)*q^31 + q^32 + (-a^3 + 4*a)*q^33 + (-2*a^3 + 4*a^2 + 7*a - 10)*q^34 + (-a^3 + 3*a^2 + 2*a - 8)*q^35 + (a^2 - 3)*q^36 + (3*a^3 - 4*a^2 - 10*a + 6)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (1/2*a^4 - 1/2*a^3 - 4*a^2 + 5/2*a + 6)*q^5 - a*q^6 + (1/3*a^4 - 2/3*a^3 - 10/3*a^2 + 4*a + 20/3)*q^7 - q^8 + (a^2 - 3)*q^9 + (-1/2*a^4 + 1/2*a^3 + 4*a^2 - 5/2*a - 6)*q^10 + (-7/12*a^4 + 5/12*a^3 + 13/3*a^2 - 5/4*a - 8/3)*q^11 + a*q^12 + (-1/6*a^4 + 5/6*a^3 + 5/3*a^2 - 11/2*a - 10/3)*q^13 + (-1/3*a^4 + 2/3*a^3 + 10/3*a^2 - 4*a - 20/3)*q^14 + (a^4 - 10*a^2 + 2*a + 16)*q^15 + q^16 + (-7/6*a^4 + 5/6*a^3 + 32/3*a^2 - 11/2*a - 40/3)*q^17 + (-a^2 + 3)*q^18 + (-17/12*a^4 + 7/12*a^3 + 41/3*a^2 - 11/4*a - 76/3)*q^19 + (1/2*a^4 - 1/2*a^3 - 4*a^2 + 5/2*a + 6)*q^20 + (1/3*a^4 - 2/3*a^3 - 13/3*a^2 + 4*a + 32/3)*q^21 + (7/12*a^4 - 5/12*a^3 - 13/3*a^2 + 5/4*a + 8/3)*q^22 + (-1/3*a^4 - 1/3*a^3 + 7/3*a^2 + a + 10/3)*q^23 - a*q^24 + (a^4 - a^3 - 7*a^2 + 4*a + 7)*q^25 + (1/6*a^4 - 5/6*a^3 - 5/3*a^2 + 11/2*a + 10/3)*q^26 + (a^3 - 6*a)*q^27 + (1/3*a^4 - 2/3*a^3 - 10/3*a^2 + 4*a + 20/3)*q^28 + (7/12*a^4 + 7/12*a^3 - 19/3*a^2 - 19/4*a + 38/3)*q^29 + (-a^4 + 10*a^2 - 2*a - 16)*q^30 + (1/2*a^4 - 1/2*a^3 - 5*a^2 + 3/2*a + 8)*q^31 - q^32 + (-4/3*a^4 - 1/3*a^3 + 40/3*a^2 + 2*a - 56/3)*q^33 + (7/6*a^4 - 5/6*a^3 - 32/3*a^2 + 11/2*a + 40/3)*q^34 + (-a^3 - a^2 + 6*a + 8)*q^35 + (a^2 - 3)*q^36 + (-3/4*a^4 + 5/4*a^3 + 6*a^2 - 27/4*a - 6)*q^37 + O(q^38)
*]> ;  // time = 90.9 seconds




J[383] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 383, 383, 383 ], new_dimensions := [ 2, 6, 24 ], dimensions := [ 2, 6, 24 ], intersection_graph := [ 0, 11, 1, 11, 0, 1, 1, 1, 0 ], ap_traces := [
[ -1, -3, 1, -4, 5, 0, -10, -1, -1, -2, 10, -13 ],
[ -3, 1, -4, -7, -7, -18, 0, -6, 0, -2, -14, -6 ],
[ 5, 2, 3, 17, 0, 28, 16, 13, 7, -2, 0, 35 ]
], hecke_fields := [
x^2 + x - 1,
x^6 + 3*x^5 - 3*x^4 - 12*x^3 - x^2 + 8*x + 3,
x^24 - 5*x^23 - 26*x^22 + 160*x^21 + 244*x^20 - 2173*x^19 - 711*x^18 + 16368*x^17 - 4007*x^16 - 75111*x^15 + 42025*x^14 + 217575*x^13 - 160547*x^12 - 399209*x^11 + 331301*x^10 + 452295*x^9 - 388291*x^8 - 296126*x^7 + 247918*x^6 + 96139*x^5 - 75925*x^4 - 9553*x^3 + 8302*x^2 - 342*x - 49
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 191 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 191 ]
], torsion_upper_bounds := [ 1, 1, 191 ], torsion_lower_bounds := [ 1, 1, 191 ], l_ratios := [ 0, 0, 1/191 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[
a,
a - 1,
a + 1,
-2*a - 3,
-a + 2,
0,
-2*a - 6,
-a - 1,
a,
-2*a - 2,
4*a + 7,
3*a - 5
],
[
a,
a^5 + 2*a^4 - 5*a^3 - 8*a^2 + 5*a + 5,
-a^5 - 2*a^4 + 5*a^3 + 8*a^2 - 6*a - 6,
-a^5 - 2*a^4 + 5*a^3 + 7*a^2 - 6*a - 4,
a^5 + 3*a^4 - 4*a^3 - 12*a^2 + 4*a + 5,
-2*a^5 - 5*a^4 + 8*a^3 + 18*a^2 - 7*a - 11,
-2*a^5 - 5*a^4 + 8*a^3 + 19*a^2 - 6*a - 10,
2*a^5 + 5*a^4 - 9*a^3 - 18*a^2 + 13*a + 7,
-3*a^5 - 9*a^4 + 11*a^3 + 36*a^2 - 9*a - 20,
6*a^5 + 13*a^4 - 29*a^3 - 51*a^2 + 32*a + 29,
a^5 + 2*a^4 - 4*a^3 - 6*a^2 + 2*a - 1,
8*a^5 + 20*a^4 - 32*a^3 - 75*a^2 + 27*a + 38
],
[
a,
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*], q_expansions := [*
q + a*q^2 + (a - 1)*q^3 + (-a - 1)*q^4 + (a + 1)*q^5 + (-2*a + 1)*q^6 + (-2*a - 3)*q^7 + (-2*a - 1)*q^8 + (-3*a - 1)*q^9 + q^10 + (-a + 2)*q^11 + a*q^12 + (-a - 2)*q^14 - a*q^15 + 3*a*q^16 + (-2*a - 6)*q^17 + (2*a - 3)*q^18 + (-a - 1)*q^19 + (-a - 2)*q^20 + (a + 1)*q^21 + (3*a - 1)*q^22 + a*q^23 + (3*a - 1)*q^24 + (a - 3)*q^25 + (2*a + 1)*q^27 + (3*a + 5)*q^28 + (-2*a - 2)*q^29 + (a - 1)*q^30 + (4*a + 7)*q^31 + (a + 5)*q^32 + (4*a - 3)*q^33 + (-4*a - 2)*q^34 + (-3*a - 5)*q^35 + (a + 4)*q^36 + (3*a - 5)*q^37 + O(q^38),
q + a*q^2 + (a^5 + 2*a^4 - 5*a^3 - 8*a^2 + 5*a + 5)*q^3 + (a^2 - 2)*q^4 + (-a^5 - 2*a^4 + 5*a^3 + 8*a^2 - 6*a - 6)*q^5 + (-a^5 - 2*a^4 + 4*a^3 + 6*a^2 - 3*a - 3)*q^6 + (-a^5 - 2*a^4 + 5*a^3 + 7*a^2 - 6*a - 4)*q^7 + (a^3 - 4*a)*q^8 + (a^5 + 2*a^4 - 4*a^3 - 6*a^2 + 3*a + 1)*q^9 + (a^5 + 2*a^4 - 4*a^3 - 7*a^2 + 2*a + 3)*q^10 + (a^5 + 3*a^4 - 4*a^3 - 12*a^2 + 4*a + 5)*q^11 + (-a^5 - 3*a^4 + 4*a^3 + 12*a^2 - 5*a - 7)*q^12 + (-2*a^5 - 5*a^4 + 8*a^3 + 18*a^2 - 7*a - 11)*q^13 + (a^5 + 2*a^4 - 5*a^3 - 7*a^2 + 4*a + 3)*q^14 + (-a^5 - 2*a^4 + 5*a^3 + 8*a^2 - 5*a - 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-2*a^5 - 5*a^4 + 8*a^3 + 19*a^2 - 6*a - 10)*q^17 + (-a^5 - a^4 + 6*a^3 + 4*a^2 - 7*a - 3)*q^18 + (2*a^5 + 5*a^4 - 9*a^3 - 18*a^2 + 13*a + 7)*q^19 + (a^5 + 3*a^4 - 5*a^3 - 13*a^2 + 7*a + 9)*q^20 + (a^4 + a^3 - 4*a^2 + 1)*q^21 + (-a^4 + 5*a^2 - 3*a - 3)*q^22 + (-3*a^5 - 9*a^4 + 11*a^3 + 36*a^2 - 9*a - 20)*q^23 + (2*a^5 + 5*a^4 - 8*a^3 - 18*a^2 + 7*a + 9)*q^24 + (a^5 + 2*a^4 - 6*a^3 - 9*a^2 + 9*a + 4)*q^25 + (a^5 + 2*a^4 - 6*a^3 - 9*a^2 + 5*a + 6)*q^26 + (-4*a^5 - 9*a^4 + 19*a^3 + 36*a^2 - 21*a - 22)*q^27 + (a^5 + 2*a^4 - 5*a^3 - 9*a^2 + 7*a + 5)*q^28 + (6*a^5 + 13*a^4 - 29*a^3 - 51*a^2 + 32*a + 29)*q^29 + (a^5 + 2*a^4 - 4*a^3 - 6*a^2 + 2*a + 3)*q^30 + (a^5 + 2*a^4 - 4*a^3 - 6*a^2 + 2*a - 1)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^5 - a^4 + 6*a^3 + 3*a^2 - 6*a - 2)*q^33 + (a^5 + 2*a^4 - 5*a^3 - 8*a^2 + 6*a + 6)*q^34 + (-a^4 - a^3 + 4*a^2 + 2*a)*q^35 + (-a^4 + 4*a^2 - a + 1)*q^36 + (8*a^5 + 20*a^4 - 32*a^3 - 75*a^2 + 27*a + 38)*q^37 + O(q^38),
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*]> ;  // time = 10.339 seconds




J[385] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 385, 385, 385, 385, 385, 385, 385, 385, 77, 77, 77, 77, 55, 55, 35, 35, 11 ], new_dimensions := [ 1, 1, 2, 2, 3, 3, 3, 4, 1, 1, 1, 2, 1, 2, 1, 2, 1 ], dimensions := [ 1, 1, 2, 2, 3, 3, 3, 4, 2, 2, 2, 4, 2, 4, 2, 4, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 25, 5, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 0, 7, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 5, 1, 1, 7, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 25, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 9, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 49, 1, 1, 1, 3, 1, 5, 1, 1, 1, 1, 9, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 9, 1, 1, 1, 49, 1, 1, 0 ], ap_traces := [
[ -1, 0, 1, -1, 1, -6, 6, -4, -8, -10, -4, 6 ],
[ -1, -2, 1, 1, -1, 4, -4, -8, 0, -6, -6, -6 ],
[ 2, 0, -2, -2, 2, 4, -4, 0, 12, 4, -12, 8 ],
[ 0, 2, -2, 2, -2, -2, 6, -8, 12, 0, 10, -8 ],
[ -3, -2, -3, -3, -3, 2, 0, 6, -10, -10, -10, -16 ],
[ -3, -4, -3, 3, 3, -8, -14, 2, -6, 2, -4, 8 ],
[ 1, 0, 3, 3, 3, 0, 6, 10, 2, 2, 8, -12 ],
[ 2, 2, 4, -4, -4, -8, -6, 6, 14, -4, 10, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2*x - 1,
x^2 - 3,
x^3 + 3*x^2 - x - 5,
x^3 + 3*x^2 - x - 5,
x^3 - x^2 - 3*x + 1,
x^4 - 2*x^3 - 6*x^2 + 8*x + 7
], atkin_lehners := [
[ -1, 1, -1 ],
[ -1, -1, 1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ 1, 1, 1 ],
[ 1, -1, -1 ],
[ -1, -1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 9, 1 ],
[ 1, 3, 1 ],
[ 5, 1, 1 ],
[ 1, 25, 5 ],
[ 5, 5, 1 ],
[ 7, 1, 19 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 1, 25, 5 ],
[ 5, 5, 1 ],
[ 7, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 1, 1, 5, 1 ], torsion_lower_bounds := [ 1, 1, 1, 3, 1, 1, 1, 1 ], l_ratios := [ 0, 0, 1, 1/3, 0, 0, 1, 7 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1, 0, 0, 1/25, 1 ], eigenvalues := [*
[ -1, 0, 1, -1, 1, -6, 6, -4, -8, -10, -4, 6 ],
[ -1, -2, 1, 1, -1, 4, -4, -8, 0, -6, -6, -6 ],
[
a,
a - 1,
-1,
-1,
1,
-a + 3,
-a - 1,
0,
-2*a + 8,
2*a,
-3*a - 3,
2*a + 2
],
[
a,
a + 1,
-1,
1,
-1,
a - 1,
-3*a + 3,
-4,
6,
-2*a,
-a + 5,
-4*a - 4
],
[
a,
-a^2 - a + 2,
-1,
-1,
-1,
a^2 - a - 4,
3*a^2 + 3*a - 8,
2*a + 4,
a^2 + 2*a - 5,
-2*a^2 - 4*a,
-2*a^2 - 3*a + 1,
a^2 + 4*a - 5
],
[
a,
a^2 + a - 4,
-1,
1,
1,
-a^2 - a,
-a^2 - a - 2,
-2*a^2 - 6*a + 2,
3*a^2 + 2*a - 11,
-2*a^2 + 8,
4*a^2 + 7*a - 9,
-5*a^2 - 4*a + 17
],
[
a,
a^2 - a - 2,
1,
1,
1,
a^2 - a - 2,
-a^2 + a + 4,
-2*a^2 + 8,
-a^2 + 3,
-4*a + 2,
-2*a^2 + a + 7,
a^2 + 2*a - 7
],
[
a,
-a^2 + a + 4,
1,
-1,
-1,
a^3 - 2*a^2 - 4*a + 3,
-a^2 + a + 2,
-a^3 + a^2 + 3*a + 1,
a^3 - 7*a + 2,
-2*a^3 + 2*a^2 + 10*a - 4,
3*a + 1,
-a^3 + 5*a + 2
]
*], q_expansions := [*
q - q^2 - q^4 + q^5 - q^7 + 3*q^8 - 3*q^9 - q^10 + q^11 - 6*q^13 + q^14 - q^16 + 6*q^17 + 3*q^18 - 4*q^19 - q^20 - q^22 - 8*q^23 + q^25 + 6*q^26 + q^28 - 10*q^29 - 4*q^31 - 5*q^32 - 6*q^34 - q^35 + 3*q^36 + 6*q^37 + O(q^38),
q - q^2 - 2*q^3 - q^4 + q^5 + 2*q^6 + q^7 + 3*q^8 + q^9 - q^10 - q^11 + 2*q^12 + 4*q^13 - q^14 - 2*q^15 - q^16 - 4*q^17 - q^18 - 8*q^19 - q^20 - 2*q^21 + q^22 - 6*q^24 + q^25 - 4*q^26 + 4*q^27 - q^28 - 6*q^29 + 2*q^30 - 6*q^31 - 5*q^32 + 2*q^33 + 4*q^34 + q^35 - q^36 - 6*q^37 + O(q^38),
q + a*q^2 + (a - 1)*q^3 + (2*a - 1)*q^4 - q^5 + (a + 1)*q^6 - q^7 + (a + 2)*q^8 - q^9 - a*q^10 + q^11 + (a + 3)*q^12 + (-a + 3)*q^13 - a*q^14 + (-a + 1)*q^15 + 3*q^16 + (-a - 1)*q^17 - a*q^18 + (-2*a + 1)*q^20 + (-a + 1)*q^21 + a*q^22 + (-2*a + 8)*q^23 + (3*a - 1)*q^24 + q^25 + (a - 1)*q^26 + (-4*a + 4)*q^27 + (-2*a + 1)*q^28 + 2*a*q^29 + (-a - 1)*q^30 + (-3*a - 3)*q^31 + (a - 4)*q^32 + (a - 1)*q^33 + (-3*a - 1)*q^34 + q^35 + (-2*a + 1)*q^36 + (2*a + 2)*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + q^4 - q^5 + (a + 3)*q^6 + q^7 - a*q^8 + (2*a + 1)*q^9 - a*q^10 - q^11 + (a + 1)*q^12 + (a - 1)*q^13 + a*q^14 + (-a - 1)*q^15 - 5*q^16 + (-3*a + 3)*q^17 + (a + 6)*q^18 - 4*q^19 - q^20 + (a + 1)*q^21 - a*q^22 + 6*q^23 + (-a - 3)*q^24 + q^25 + (-a + 3)*q^26 + 4*q^27 + q^28 - 2*a*q^29 + (-a - 3)*q^30 + (-a + 5)*q^31 - 3*a*q^32 + (-a - 1)*q^33 + (3*a - 9)*q^34 - q^35 + (2*a + 1)*q^36 + (-4*a - 4)*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 2)*q^3 + (a^2 - 2)*q^4 - q^5 + (2*a^2 + a - 5)*q^6 - q^7 + (-3*a^2 - 3*a + 5)*q^8 + (a^2 - 4)*q^9 - a*q^10 - q^11 + (-3*a^2 - a + 6)*q^12 + (a^2 - a - 4)*q^13 - a*q^14 + (a^2 + a - 2)*q^15 + (4*a^2 + 2*a - 11)*q^16 + (3*a^2 + 3*a - 8)*q^17 + (-3*a^2 - 3*a + 5)*q^18 + (2*a + 4)*q^19 + (-a^2 + 2)*q^20 + (a^2 + a - 2)*q^21 - a*q^22 + (a^2 + 2*a - 5)*q^23 + (4*a^2 + a - 5)*q^24 + q^25 + (-4*a^2 - 3*a + 5)*q^26 + (2*a^2 + 4*a - 4)*q^27 + (-a^2 + 2)*q^28 + (-2*a^2 - 4*a)*q^29 + (-2*a^2 - a + 5)*q^30 + (-2*a^2 - 3*a + 1)*q^31 + (-4*a^2 - a + 10)*q^32 + (a^2 + a - 2)*q^33 + (-6*a^2 - 5*a + 15)*q^34 + q^35 + (4*a^2 + 2*a - 7)*q^36 + (a^2 + 4*a - 5)*q^37 + O(q^38),
q + a*q^2 + (a^2 + a - 4)*q^3 + (a^2 - 2)*q^4 - q^5 + (-2*a^2 - 3*a + 5)*q^6 + q^7 + (-3*a^2 - 3*a + 5)*q^8 + (-3*a^2 - 4*a + 8)*q^9 - a*q^10 + q^11 + (a^2 + a - 2)*q^12 + (-a^2 - a)*q^13 + a*q^14 + (-a^2 - a + 4)*q^15 + (4*a^2 + 2*a - 11)*q^16 + (-a^2 - a - 2)*q^17 + (5*a^2 + 5*a - 15)*q^18 + (-2*a^2 - 6*a + 2)*q^19 + (-a^2 + 2)*q^20 + (a^2 + a - 4)*q^21 + a*q^22 + (3*a^2 + 2*a - 11)*q^23 + (2*a^2 + 5*a - 5)*q^24 + q^25 + (2*a^2 - a - 5)*q^26 + (4*a^2 + 8*a - 10)*q^27 + (a^2 - 2)*q^28 + (-2*a^2 + 8)*q^29 + (2*a^2 + 3*a - 5)*q^30 + (4*a^2 + 7*a - 9)*q^31 + (-4*a^2 - a + 10)*q^32 + (a^2 + a - 4)*q^33 + (2*a^2 - 3*a - 5)*q^34 - q^35 + (-4*a^2 - 2*a + 9)*q^36 + (-5*a^2 - 4*a + 17)*q^37 + O(q^38),
q + a*q^2 + (a^2 - a - 2)*q^3 + (a^2 - 2)*q^4 + q^5 + (a - 1)*q^6 + q^7 + (a^2 - a - 1)*q^8 + (-a^2 + 2)*q^9 + a*q^10 + q^11 + (-a^2 + a + 4)*q^12 + (a^2 - a - 2)*q^13 + a*q^14 + (a^2 - a - 2)*q^15 + (-2*a^2 + 2*a + 3)*q^16 + (-a^2 + a + 4)*q^17 + (-a^2 - a + 1)*q^18 + (-2*a^2 + 8)*q^19 + (a^2 - 2)*q^20 + (a^2 - a - 2)*q^21 + a*q^22 + (-a^2 + 3)*q^23 + (-a + 3)*q^24 + q^25 + (a - 1)*q^26 + (-2*a^2 + 2*a + 2)*q^27 + (a^2 - 2)*q^28 + (-4*a + 2)*q^29 + (a - 1)*q^30 + (-2*a^2 + a + 7)*q^31 + (-2*a^2 - a + 4)*q^32 + (a^2 - a - 2)*q^33 + (a + 1)*q^34 + q^35 + (-2*a - 3)*q^36 + (a^2 + 2*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + a + 4)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^3 + a^2 + 4*a)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-a^2 + 6)*q^9 + a*q^10 - q^11 + (-a^3 + 6*a - 1)*q^12 + (a^3 - 2*a^2 - 4*a + 3)*q^13 - a*q^14 + (-a^2 + a + 4)*q^15 + (2*a^3 - 8*a - 3)*q^16 + (-a^2 + a + 2)*q^17 + (-a^3 + 6*a)*q^18 + (-a^3 + a^2 + 3*a + 1)*q^19 + (a^2 - 2)*q^20 + (a^2 - a - 4)*q^21 - a*q^22 + (a^3 - 7*a + 2)*q^23 + (-2*a^2 - a + 7)*q^24 + q^25 + (2*a^2 - 5*a - 7)*q^26 + (a^3 - a^2 - 5*a + 5)*q^27 + (-a^2 + 2)*q^28 + (-2*a^3 + 2*a^2 + 10*a - 4)*q^29 + (-a^3 + a^2 + 4*a)*q^30 + (3*a + 1)*q^31 + (2*a^3 + 4*a^2 - 11*a - 14)*q^32 + (a^2 - a - 4)*q^33 + (-a^3 + a^2 + 2*a)*q^34 - q^35 + (-2*a^3 + 2*a^2 + 8*a - 5)*q^36 + (-a^3 + 5*a + 2)*q^37 + O(q^38)
*]> ;  // time = 123.269 seconds




J[386] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 386, 386, 386, 386, 193, 193, 193 ], new_dimensions := [ 2, 2, 6, 7, 2, 5, 8 ], dimensions := [ 2, 2, 6, 7, 4, 10, 16 ], intersection_graph := [ 0, 1, 1, 1, 1, 29, 1, 1, 0, 1, 1, 1, 1, 31, 1, 1, 0, 1, 1, 1, 1355, 1, 1, 1, 0, 19, 229, 1, 1, 1, 1, 19, 0, 121, 1, 29, 1, 1, 229, 121, 0, 1, 1, 31, 1355, 1, 1, 1, 0 ], ap_traces := [
[ -2, -1, 1, -4, -4, -3, 6, -6, -2, -8, -14, 1 ],
[ 2, -3, -5, -2, -2, -7, -6, -10, 8, 0, -6, 1 ],
[ -6, 1, -5, 8, -2, 9, -2, 18, 6, 0, 18, 7 ],
[ 7, 3, 5, 2, 2, 5, 8, 4, -8, 0, -6, -1 ]
], hecke_fields := [
x^2 + x - 1,
x^2 + 3*x + 1,
x^6 - x^5 - 12*x^4 + 7*x^3 + 40*x^2 - 13*x - 37,
x^7 - 3*x^6 - 10*x^5 + 33*x^4 + 14*x^3 - 91*x^2 + 45*x + 16
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 29, 1 ],
[ 31, 1 ],
[ 4065, 3 ],
[ 422047, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 31, 1 ],
[ 1, 3 ],
[ 422047, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 97 ], torsion_lower_bounds := [ 1, 1, 3, 97 ], l_ratios := [ 0, 0, 1/3, 4351/97 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
-1,
a,
-a,
-2,
-2,
-3*a - 3,
-2*a + 2,
2*a - 2,
6*a + 2,
4*a - 2,
-2*a - 8,
9*a + 5
],
[
1,
a,
-a - 4,
-2*a - 4,
2*a + 2,
3*a + 1,
2*a,
-2*a - 8,
-4*a - 2,
4*a + 6,
6*a + 6,
3*a + 5
],
[
-1,
a,
-1/2*a^5 + 11/2*a^3 + 2*a^2 - 23/2*a - 6,
a^4 - a^3 - 9*a^2 + 4*a + 16,
-a^4 + a^3 + 8*a^2 - 3*a - 11,
1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 1/2*a^2 + 17/2*a + 13/2,
a^4 - 2*a^3 - 8*a^2 + 9*a + 12,
a^2 - a - 1,
a^5 - 10*a^3 - 7*a^2 + 18*a + 22,
-a^5 + a^4 + 9*a^3 - 2*a^2 - 16*a - 6,
-a^5 - a^4 + 11*a^3 + 14*a^2 - 24*a - 24,
-1/2*a^5 - 1/2*a^4 + 11/2*a^3 + 13/2*a^2 - 21/2*a - 21/2
],
[
1,
a,
-3*a^6 + 9/2*a^5 + 37*a^4 - 89/2*a^3 - 110*a^2 + 229/2*a + 36,
4*a^6 - 6*a^5 - 49*a^4 + 59*a^3 + 143*a^2 - 152*a - 40,
3*a^6 - 5*a^5 - 37*a^4 + 50*a^3 + 112*a^2 - 126*a - 38,
-7/2*a^6 + 6*a^5 + 85/2*a^4 - 60*a^3 - 249/2*a^2 + 150*a + 36,
-4*a^6 + 6*a^5 + 49*a^4 - 58*a^3 - 144*a^2 + 145*a + 46,
7*a^6 - 11*a^5 - 86*a^4 + 109*a^3 + 255*a^2 - 278*a - 78,
2*a^6 - 3*a^5 - 24*a^4 + 28*a^3 + 69*a^2 - 68*a - 24,
a^6 - 2*a^5 - 12*a^4 + 20*a^3 + 35*a^2 - 49*a - 8,
6*a^6 - 9*a^5 - 73*a^4 + 87*a^3 + 212*a^2 - 220*a - 64,
-15/2*a^6 + 12*a^5 + 183/2*a^4 - 117*a^3 - 543/2*a^2 + 290*a + 92
]
*], q_expansions := [*
q - q^2 + a*q^3 + q^4 - a*q^5 - a*q^6 - 2*q^7 - q^8 + (-a - 2)*q^9 + a*q^10 - 2*q^11 + a*q^12 + (-3*a - 3)*q^13 + 2*q^14 + (a - 1)*q^15 + q^16 + (-2*a + 2)*q^17 + (a + 2)*q^18 + (2*a - 2)*q^19 - a*q^20 - 2*a*q^21 + 2*q^22 + (6*a + 2)*q^23 - a*q^24 + (-a - 4)*q^25 + (3*a + 3)*q^26 + (-4*a - 1)*q^27 - 2*q^28 + (4*a - 2)*q^29 + (-a + 1)*q^30 + (-2*a - 8)*q^31 - q^32 - 2*a*q^33 + (2*a - 2)*q^34 + 2*a*q^35 + (-a - 2)*q^36 + (9*a + 5)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a - 4)*q^5 + a*q^6 + (-2*a - 4)*q^7 + q^8 + (-3*a - 4)*q^9 + (-a - 4)*q^10 + (2*a + 2)*q^11 + a*q^12 + (3*a + 1)*q^13 + (-2*a - 4)*q^14 + (-a + 1)*q^15 + q^16 + 2*a*q^17 + (-3*a - 4)*q^18 + (-2*a - 8)*q^19 + (-a - 4)*q^20 + (2*a + 2)*q^21 + (2*a + 2)*q^22 + (-4*a - 2)*q^23 + a*q^24 + (5*a + 10)*q^25 + (3*a + 1)*q^26 + (2*a + 3)*q^27 + (-2*a - 4)*q^28 + (4*a + 6)*q^29 + (-a + 1)*q^30 + (6*a + 6)*q^31 + q^32 + (-4*a - 2)*q^33 + 2*a*q^34 + (6*a + 14)*q^35 + (-3*a - 4)*q^36 + (3*a + 5)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-1/2*a^5 + 11/2*a^3 + 2*a^2 - 23/2*a - 6)*q^5 - a*q^6 + (a^4 - a^3 - 9*a^2 + 4*a + 16)*q^7 - q^8 + (a^2 - 3)*q^9 + (1/2*a^5 - 11/2*a^3 - 2*a^2 + 23/2*a + 6)*q^10 + (-a^4 + a^3 + 8*a^2 - 3*a - 11)*q^11 + a*q^12 + (1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 1/2*a^2 + 17/2*a + 13/2)*q^13 + (-a^4 + a^3 + 9*a^2 - 4*a - 16)*q^14 + (-1/2*a^5 - 1/2*a^4 + 11/2*a^3 + 17/2*a^2 - 25/2*a - 37/2)*q^15 + q^16 + (a^4 - 2*a^3 - 8*a^2 + 9*a + 12)*q^17 + (-a^2 + 3)*q^18 + (a^2 - a - 1)*q^19 + (-1/2*a^5 + 11/2*a^3 + 2*a^2 - 23/2*a - 6)*q^20 + (a^5 - a^4 - 9*a^3 + 4*a^2 + 16*a)*q^21 + (a^4 - a^3 - 8*a^2 + 3*a + 11)*q^22 + (a^5 - 10*a^3 - 7*a^2 + 18*a + 22)*q^23 - a*q^24 + (a^5 + a^4 - 12*a^3 - 14*a^2 + 27*a + 31)*q^25 + (-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 1/2*a^2 - 17/2*a - 13/2)*q^26 + (a^3 - 6*a)*q^27 + (a^4 - a^3 - 9*a^2 + 4*a + 16)*q^28 + (-a^5 + a^4 + 9*a^3 - 2*a^2 - 16*a - 6)*q^29 + (1/2*a^5 + 1/2*a^4 - 11/2*a^3 - 17/2*a^2 + 25/2*a + 37/2)*q^30 + (-a^5 - a^4 + 11*a^3 + 14*a^2 - 24*a - 24)*q^31 - q^32 + (-a^5 + a^4 + 8*a^3 - 3*a^2 - 11*a)*q^33 + (-a^4 + 2*a^3 + 8*a^2 - 9*a - 12)*q^34 + (-a^5 - a^4 + 13*a^3 + 12*a^2 - 34*a - 22)*q^35 + (a^2 - 3)*q^36 + (-1/2*a^5 - 1/2*a^4 + 11/2*a^3 + 13/2*a^2 - 21/2*a - 21/2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-3*a^6 + 9/2*a^5 + 37*a^4 - 89/2*a^3 - 110*a^2 + 229/2*a + 36)*q^5 + a*q^6 + (4*a^6 - 6*a^5 - 49*a^4 + 59*a^3 + 143*a^2 - 152*a - 40)*q^7 + q^8 + (a^2 - 3)*q^9 + (-3*a^6 + 9/2*a^5 + 37*a^4 - 89/2*a^3 - 110*a^2 + 229/2*a + 36)*q^10 + (3*a^6 - 5*a^5 - 37*a^4 + 50*a^3 + 112*a^2 - 126*a - 38)*q^11 + a*q^12 + (-7/2*a^6 + 6*a^5 + 85/2*a^4 - 60*a^3 - 249/2*a^2 + 150*a + 36)*q^13 + (4*a^6 - 6*a^5 - 49*a^4 + 59*a^3 + 143*a^2 - 152*a - 40)*q^14 + (-9/2*a^6 + 7*a^5 + 109/2*a^4 - 68*a^3 - 317/2*a^2 + 171*a + 48)*q^15 + q^16 + (-4*a^6 + 6*a^5 + 49*a^4 - 58*a^3 - 144*a^2 + 145*a + 46)*q^17 + (a^2 - 3)*q^18 + (7*a^6 - 11*a^5 - 86*a^4 + 109*a^3 + 255*a^2 - 278*a - 78)*q^19 + (-3*a^6 + 9/2*a^5 + 37*a^4 - 89/2*a^3 - 110*a^2 + 229/2*a + 36)*q^20 + (6*a^6 - 9*a^5 - 73*a^4 + 87*a^3 + 212*a^2 - 220*a - 64)*q^21 + (3*a^6 - 5*a^5 - 37*a^4 + 50*a^3 + 112*a^2 - 126*a - 38)*q^22 + (2*a^6 - 3*a^5 - 24*a^4 + 28*a^3 + 69*a^2 - 68*a - 24)*q^23 + a*q^24 + (-2*a^6 + 3*a^5 + 25*a^4 - 30*a^3 - 76*a^2 + 77*a + 27)*q^25 + (-7/2*a^6 + 6*a^5 + 85/2*a^4 - 60*a^3 - 249/2*a^2 + 150*a + 36)*q^26 + (a^3 - 6*a)*q^27 + (4*a^6 - 6*a^5 - 49*a^4 + 59*a^3 + 143*a^2 - 152*a - 40)*q^28 + (a^6 - 2*a^5 - 12*a^4 + 20*a^3 + 35*a^2 - 49*a - 8)*q^29 + (-9/2*a^6 + 7*a^5 + 109/2*a^4 - 68*a^3 - 317/2*a^2 + 171*a + 48)*q^30 + (6*a^6 - 9*a^5 - 73*a^4 + 87*a^3 + 212*a^2 - 220*a - 64)*q^31 + q^32 + (4*a^6 - 7*a^5 - 49*a^4 + 70*a^3 + 147*a^2 - 173*a - 48)*q^33 + (-4*a^6 + 6*a^5 + 49*a^4 - 58*a^3 - 144*a^2 + 145*a + 46)*q^34 + (-2*a^6 + 3*a^5 + 25*a^4 - 29*a^3 - 78*a^2 + 72*a + 32)*q^35 + (a^2 - 3)*q^36 + (-15/2*a^6 + 12*a^5 + 183/2*a^4 - 117*a^3 - 543/2*a^2 + 290*a + 92)*q^37 + O(q^38)
*]> ;  // time = 107.2 seconds




J[389] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 389, 389, 389, 389, 389 ], new_dimensions := [ 1, 2, 3, 6, 20 ], dimensions := [ 1, 2, 3, 6, 20 ], intersection_graph := [ 0, 1, 1, 1, 5, 1, 0, 1, 9, 1, 1, 1, 0, 31, 1, 1, 9, 31, 0, 1, 5, 1, 1, 1, 0 ], ap_traces := [
[ -2, -2, -3, -5, -4, -3, -6, 5, -4, -6, 4, -8 ],
[ 0, -4, -2, -2, -4, 2, 8, -2, 4, 8, -16, 4 ],
[ 0, 0, -5, -3, -4, -9, 2, -9, -6, -2, 2, 2 ],
[ -3, -5, 3, -4, -2, -5, -16, -33, 5, -14, -14, -3 ],
[ 3, 11, 1, 12, 10, 17, 2, 51, 3, 0, 36, 9 ]
], hecke_fields := [
x - 1,
x^2 - 2,
x^3 - 4*x - 2,
x^6 + 3*x^5 - 2*x^4 - 8*x^3 + 2*x^2 + 4*x - 1,
x^20 - 3*x^19 - 29*x^18 + 91*x^17 + 338*x^16 - 1130*x^15 - 2023*x^14 + 7432*x^13 + 6558*x^12 - 28021*x^11 - 10909*x^10 + 61267*x^9 + 6954*x^8 - 74752*x^7 + 1407*x^6 + 46330*x^5 - 1087*x^4 - 12558*x^3 - 942*x^2 + 960*x + 148
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ 97 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ 97 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 97 ], torsion_lower_bounds := [ 1, 1, 1, 1, 97 ], l_ratios := [ 0, 0, 0, 0, 25/97 ], analytic_sha_upper_bounds := [ 0, 0, 0, 0, 25 ], analytic_sha_lower_bounds := [ 0, 0, 0, 0, 25 ], eigenvalues := [*
[ -2, -2, -3, -5, -4, -3, -6, 5, -4, -6, 4, -8 ],
[
a,
a - 2,
-1,
-2*a - 1,
-2,
2*a + 1,
-2*a + 4,
2*a - 1,
-a + 2,
2*a + 4,
a - 8,
-2*a + 2
],
[
a,
-a,
-a^2 + 1,
-1,
a^2 - 4,
-3,
a^2 - 2*a - 2,
-3*a^2 + 2*a + 5,
3*a - 2,
2*a^2 - 4*a - 6,
4*a^2 - 5*a - 10,
-2*a^2 + 6*a + 6
],
[
a,
a^5 + 3*a^4 - 2*a^3 - 8*a^2 + a + 2,
-a^5 - 2*a^4 + 4*a^3 + 6*a^2 - 4*a - 2,
-2*a^5 - 8*a^4 - 2*a^3 + 17*a^2 + 7*a - 6,
2*a^5 + 5*a^4 - 4*a^3 - 11*a^2 + 3,
2*a^4 + 5*a^3 - 5*a^2 - 11*a + 3,
a^3 + 5*a^2 + 2*a - 9,
a^5 + 3*a^4 - a^3 - 6*a^2 - 4,
a^5 + a^4 - 8*a^3 - 7*a^2 + 8*a + 3,
-4*a^5 - 14*a^4 - a^3 + 25*a^2 + 8*a - 5,
3*a^5 + 11*a^4 + a^3 - 23*a^2 - 4*a + 6,
5*a^5 + 18*a^4 + a^3 - 36*a^2 - 9*a + 8
],
[
a,
-20146763/1097385680*a^19 + 20466323/219477136*a^18 + 119884773/274346420*a^17 - 753611053/274346420*a^16 - 381358355/109738568*a^15 + 3611475535/109738568*a^14 + 6349339639/1097385680*a^13 - 56878934241/274346420*a^12 + 71555185319/1097385680*a^11 + 163330998525/219477136*a^10 - 223188336749/548692840*a^9 - 169878973265/109738568*a^8 + 265944624817/274346420*a^7 + 199655892261/109738568*a^6 - 1167579836501/1097385680*a^5 - 619178000979/548692840*a^4 + 261766056911/548692840*a^3 + 4410485304/13717321*a^2 - 14646077211/274346420*a - 1604641167/68586605,
252247073/1097385680*a^19 - 89195955/109738568*a^18 - 6876716517/1097385680*a^17 + 13248231811/548692840*a^16 + 3639338697/54869284*a^15 - 32041245347/109738568*a^14 - 367946611589/1097385680*a^13 + 2037515640679/1097385680*a^12 + 816602908511/1097385680*a^11 - 368120881159/54869284*a^10 - 19595857657/1097385680*a^9 + 763403091515/54869284*a^8 - 403904463001/137173210*a^7 - 1743458092745/109738568*a^6 + 5304122556631/1097385680*a^5 + 9907751136883/1097385680*a^4 - 704659646193/274346420*a^3 - 236814032039/109738568*a^2 + 88326575941/274346420*a + 37821733103/274346420,
-39775309/274346420*a^19 + 6458830/13717321*a^18 + 564024213/137173210*a^17 - 3911580261/274346420*a^16 - 2533437265/54869284*a^15 + 9687600453/54869284*a^14 + 17684386693/68586605*a^13 - 158547430721/137173210*a^12 - 196249673593/274346420*a^11 + 237151369759/54869284*a^10 + 47009341559/68586605*a^9 - 127672839145/13717321*a^8 + 263943432849/274346420*a^7 + 302422095641/27434642*a^6 - 354882792659/137173210*a^5 - 1763634812489/274346420*a^4 + 214619964123/137173210*a^3 + 42696419019/27434642*a^2 - 13851314508/68586605*a - 6725054004/68586605,
2980761/27434642*a^19 - 40519427/109738568*a^18 - 324413157/109738568*a^17 + 599348931/54869284*a^16 + 1712230339/54869284*a^15 - 3604639961/27434642*a^14 - 2154216098/13717321*a^13 + 91078987557/109738568*a^12 + 18913069911/54869284*a^11 - 326505305885/109738568*a^10 + 1008925971/109738568*a^9 + 83920016323/13717321*a^8 - 77512727581/54869284*a^7 - 380562335831/54869284*a^6 + 125733598661/54869284*a^5 + 432237324953/109738568*a^4 - 66332195991/54869284*a^3 - 52749441099/54869284*a^2 + 2005234461/13717321*a + 1799373559/27434642,
-439672887/1097385680*a^19 + 75006137/54869284*a^18 + 12101299333/1097385680*a^17 - 22321474039/548692840*a^16 - 1625891079/13717321*a^15 + 54100172827/109738568*a^14 + 676736498991/1097385680*a^13 - 3448581869471/1097385680*a^12 - 1621748439689/1097385680*a^11 + 1249216368921/109738568*a^10 + 633899235433/1097385680*a^9 - 1297751833749/54869284*a^8 + 291323290537/68586605*a^7 + 2963292254483/109738568*a^6 - 8441184290969/1097385680*a^5 - 16753315901627/1097385680*a^4 + 572725946281/137173210*a^3 + 396656876947/109738568*a^2 - 139835925059/274346420*a - 62765065187/274346420,
-96200111/1097385680*a^19 + 7624809/27434642*a^18 + 2853118449/1097385680*a^17 - 4795763297/548692840*a^16 - 423432401/13717321*a^15 + 12411754799/109738568*a^14 + 203135935283/1097385680*a^13 - 853928410103/1097385680*a^12 - 622919458457/1097385680*a^11 + 336738706757/109738568*a^10 + 754599107669/1097385680*a^9 - 190842523479/27434642*a^8 + 33571717731/68586605*a^7 + 941835927157/109738568*a^6 - 2104972582597/1097385680*a^5 - 5575654493331/1097385680*a^4 + 83865827689/68586605*a^3 + 132711500843/109738568*a^2 - 43295694207/274346420*a - 19899224791/274346420,
82111709/274346420*a^19 - 13758531/13717321*a^18 - 1155056903/137173210*a^17 + 4165768503/137173210*a^16 + 1279191001/13717321*a^15 - 5157845168/13717321*a^14 - 139030839677/274346420*a^13 + 675125041837/274346420*a^12 + 179943620499/137173210*a^11 - 504618055349/54869284*a^10 - 224371009951/274346420*a^9 + 1085232917573/54869284*a^8 - 873645627239/274346420*a^7 - 1281612267983/54869284*a^6 + 900297300599/137173210*a^5 + 928578480591/68586605*a^4 - 256083272659/68586605*a^3 - 44584612267/13717321*a^2 + 31755395838/68586605*a + 14279975219/68586605,
361528801/548692840*a^19 - 469329025/219477136*a^18 - 20607647913/1097385680*a^17 + 35719791819/548692840*a^16 + 23258962967/109738568*a^15 - 44515496167/54869284*a^14 - 651844514603/548692840*a^13 + 5871304106201/1097385680*a^12 + 900582640591/274346420*a^11 - 4425959444819/219477136*a^10 - 3222387783273/1097385680*a^9 + 2400549885397/54869284*a^8 - 2937061857781/548692840*a^7 - 5714663430681/109738568*a^6 + 1836935375943/137173210*a^5 + 33289520944497/1097385680*a^4 - 4399252166429/548692840*a^3 - 800617114943/109738568*a^2 + 70700546851/68586605*a + 127452412027/274346420,
5506177/54869284*a^19 - 30186849/109738568*a^18 - 338631113/109738568*a^17 + 240627075/27434642*a^16 + 527539826/13717321*a^15 - 6319183801/54869284*a^14 - 3395655753/13717321*a^13 + 88231152703/109738568*a^12 + 47131691267/54869284*a^11 - 352513546207/109738568*a^10 - 160419763619/109738568*a^9 + 403196202045/54869284*a^8 + 34546356079/54869284*a^7 - 248987779583/27434642*a^6 + 30766716641/27434642*a^5 + 581192798143/109738568*a^4 - 53514563731/54869284*a^3 - 67136120597/54869284*a^2 + 1855170924/13717321*a + 2059393637/27434642,
21281459/137173210*a^19 - 126641469/219477136*a^18 - 4389199143/1097385680*a^17 + 9133854009/548692840*a^16 + 4238318731/109738568*a^15 - 2657576246/13717321*a^14 - 44543688079/274346420*a^13 + 1286098247731/1097385680*a^12 + 97651272727/548692840*a^11 - 872304044211/219477136*a^10 + 878256967417/1097385680*a^9 + 419553570571/54869284*a^8 - 1556791312041/548692840*a^7 - 888639623063/109738568*a^6 + 1823354529817/548692840*a^5 + 4830480473947/1097385680*a^4 - 812339073929/548692840*a^3 - 115485758833/109738568*a^2 + 23109909757/137173210*a + 19292002117/274346420,
-77763363/548692840*a^19 + 56391515/109738568*a^18 + 1025565821/274346420*a^17 - 4110700781/274346420*a^16 - 515942739/13717321*a^15 + 4853590653/27434642*a^14 + 95337883389/548692840*a^13 - 299456914927/274346420*a^12 - 165693969661/548692840*a^11 + 417338645439/109738568*a^10 - 22528280166/68586605*a^9 - 416158163661/54869284*a^8 + 550915685819/274346420*a^7 + 460980462593/54869284*a^6 - 1472859564331/548692840*a^5 - 1314351276119/274346420*a^4 + 357262105061/274346420*a^3 + 16340008413/13717321*a^2 - 21148069681/137173210*a - 5180700504/68586605
]
*], q_expansions := [*
q - 2*q^2 - 2*q^3 + 2*q^4 - 3*q^5 + 4*q^6 - 5*q^7 + q^9 + 6*q^10 - 4*q^11 - 4*q^12 - 3*q^13 + 10*q^14 + 6*q^15 - 4*q^16 - 6*q^17 - 2*q^18 + 5*q^19 - 6*q^20 + 10*q^21 + 8*q^22 - 4*q^23 + 4*q^25 + 6*q^26 + 4*q^27 - 10*q^28 - 6*q^29 - 12*q^30 + 4*q^31 + 8*q^32 + 8*q^33 + 12*q^34 + 15*q^35 + 2*q^36 - 8*q^37 + O(q^38),
q + a*q^2 + (a - 2)*q^3 - q^5 + (-2*a + 2)*q^6 + (-2*a - 1)*q^7 - 2*a*q^8 + (-4*a + 3)*q^9 - a*q^10 - 2*q^11 + (2*a + 1)*q^13 + (-a - 4)*q^14 + (-a + 2)*q^15 - 4*q^16 + (-2*a + 4)*q^17 + (3*a - 8)*q^18 + (2*a - 1)*q^19 + (3*a - 2)*q^21 - 2*a*q^22 + (-a + 2)*q^23 + (4*a - 4)*q^24 - 4*q^25 + (a + 4)*q^26 + (8*a - 8)*q^27 + (2*a + 4)*q^29 + (2*a - 2)*q^30 + (a - 8)*q^31 + (-2*a + 4)*q^33 + (4*a - 4)*q^34 + (2*a + 1)*q^35 + (-2*a + 2)*q^37 + O(q^38),
q + a*q^2 - a*q^3 + (a^2 - 2)*q^4 + (-a^2 + 1)*q^5 - a^2*q^6 - q^7 + 2*q^8 + (a^2 - 3)*q^9 + (-3*a - 2)*q^10 + (a^2 - 4)*q^11 + (-2*a - 2)*q^12 - 3*q^13 - a*q^14 + (3*a + 2)*q^15 + (-2*a^2 + 2*a + 4)*q^16 + (a^2 - 2*a - 2)*q^17 + (a + 2)*q^18 + (-3*a^2 + 2*a + 5)*q^19 + (-a^2 - 2*a - 2)*q^20 + a*q^21 + 2*q^22 + (3*a - 2)*q^23 - 2*a*q^24 + (2*a^2 + 2*a - 4)*q^25 - 3*a*q^26 + (2*a - 2)*q^27 + (-a^2 + 2)*q^28 + (2*a^2 - 4*a - 6)*q^29 + (3*a^2 + 2*a)*q^30 + (4*a^2 - 5*a - 10)*q^31 + (2*a^2 - 4*a - 8)*q^32 - 2*q^33 + (-2*a^2 + 2*a + 2)*q^34 + (a^2 - 1)*q^35 + (-a^2 + 2*a + 6)*q^36 + (-2*a^2 + 6*a + 6)*q^37 + O(q^38),
q + a*q^2 + (a^5 + 3*a^4 - 2*a^3 - 8*a^2 + a + 2)*q^3 + (a^2 - 2)*q^4 + (-a^5 - 2*a^4 + 4*a^3 + 6*a^2 - 4*a - 2)*q^5 + (-a^2 - 2*a + 1)*q^6 + (-2*a^5 - 8*a^4 - 2*a^3 + 17*a^2 + 7*a - 6)*q^7 + (a^3 - 4*a)*q^8 + (a^4 + 3*a^3 - a^2 - 4*a + 1)*q^9 + (a^5 + 2*a^4 - 2*a^3 - 2*a^2 + 2*a - 1)*q^10 + (2*a^5 + 5*a^4 - 4*a^3 - 11*a^2 + 3)*q^11 + (-2*a^5 - 6*a^4 + 3*a^3 + 14*a^2 - a - 4)*q^12 + (2*a^4 + 5*a^3 - 5*a^2 - 11*a + 3)*q^13 + (-2*a^5 - 6*a^4 + a^3 + 11*a^2 + 2*a - 2)*q^14 + (-a^5 - 5*a^4 - 4*a^3 + 10*a^2 + 8*a - 7)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^3 + 5*a^2 + 2*a - 9)*q^17 + (a^5 + 3*a^4 - a^3 - 4*a^2 + a)*q^18 + (a^5 + 3*a^4 - a^3 - 6*a^2 - 4)*q^19 + (a^5 + 4*a^4 - 2*a^3 - 12*a^2 + 3*a + 5)*q^20 + (2*a^4 + 7*a^3 + a^2 - 11*a - 3)*q^21 + (-a^5 + 5*a^3 - 4*a^2 - 5*a + 2)*q^22 + (a^5 + a^4 - 8*a^3 - 7*a^2 + 8*a + 3)*q^23 + (-a^4 - 2*a^3 + 5*a^2 + 8*a - 4)*q^24 + (a^5 + 5*a^4 + 3*a^3 - 11*a^2 - 7*a + 4)*q^25 + (2*a^5 + 5*a^4 - 5*a^3 - 11*a^2 + 3*a)*q^26 + (-3*a^5 - 11*a^4 + 25*a^2 + 5*a - 8)*q^27 + (4*a^5 + 13*a^4 - a^3 - 28*a^2 - 8*a + 10)*q^28 + (-4*a^5 - 14*a^4 - a^3 + 25*a^2 + 8*a - 5)*q^29 + (-2*a^5 - 6*a^4 + 2*a^3 + 10*a^2 - 3*a - 1)*q^30 + (3*a^5 + 11*a^4 + a^3 - 23*a^2 - 4*a + 6)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^4 + 2*a^3 - 2*a^2 + 4)*q^33 + (a^4 + 5*a^3 + 2*a^2 - 9*a)*q^34 + (4*a^5 + 12*a^4 - 6*a^3 - 30*a^2 + a + 10)*q^35 + (-a^4 - 2*a^3 + a^2 + 4*a - 1)*q^36 + (5*a^5 + 18*a^4 + a^3 - 36*a^2 - 9*a + 8)*q^37 + O(q^38),
q + a*q^2 + (-20146763/1097385680*a^19 + 20466323/219477136*a^18 + 119884773/274346420*a^17 - 753611053/274346420*a^16 - 381358355/109738568*a^15 + 3611475535/109738568*a^14 + 6349339639/1097385680*a^13 - 56878934241/274346420*a^12 + 71555185319/1097385680*a^11 + 163330998525/219477136*a^10 - 223188336749/548692840*a^9 - 169878973265/109738568*a^8 + 265944624817/274346420*a^7 + 199655892261/109738568*a^6 - 1167579836501/1097385680*a^5 - 619178000979/548692840*a^4 + 261766056911/548692840*a^3 + 4410485304/13717321*a^2 - 14646077211/274346420*a - 1604641167/68586605)*q^3 + (a^2 - 2)*q^4 + (252247073/1097385680*a^19 - 89195955/109738568*a^18 - 6876716517/1097385680*a^17 + 13248231811/548692840*a^16 + 3639338697/54869284*a^15 - 32041245347/109738568*a^14 - 367946611589/1097385680*a^13 + 2037515640679/1097385680*a^12 + 816602908511/1097385680*a^11 - 368120881159/54869284*a^10 - 19595857657/1097385680*a^9 + 763403091515/54869284*a^8 - 403904463001/137173210*a^7 - 1743458092745/109738568*a^6 + 5304122556631/1097385680*a^5 + 9907751136883/1097385680*a^4 - 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88893425141/219477136*a^12 - 5359015190/13717321*a^11 + 306114670915/219477136*a^10 + 154619760553/219477136*a^9 - 296902387811/109738568*a^8 - 75951654405/109738568*a^7 + 154412719695/54869284*a^6 + 39426236541/109738568*a^5 - 307048284081/219477136*a^4 - 10303754517/109738568*a^3 + 29275772663/109738568*a^2 - 24627919/27434642*a - 751425563/54869284)*q^24 + (-635686483/1097385680*a^19 + 196820225/109738568*a^18 + 18156678107/1097385680*a^17 - 29807635581/548692840*a^16 - 2574686584/13717321*a^15 + 73833684289/109738568*a^14 + 1168931834019/1097385680*a^13 - 4832768326629/1097385680*a^12 - 3347485802781/1097385680*a^11 + 451458813321/27434642*a^10 + 3627603145387/1097385680*a^9 - 1940486657197/54869284*a^8 + 809510353387/274346420*a^7 + 4574835704909/109738568*a^6 - 10556188679541/1097385680*a^5 - 26385989727993/1097385680*a^4 + 1643275812923/274346420*a^3 + 626324979245/109738568*a^2 - 215571712871/274346420*a - 98243883593/274346420)*q^25 + (181104079/1097385680*a^19 - 64921439/109738568*a^18 - 4632715361/1097385680*a^17 + 9269074743/548692840*a^16 + 1104284149/27434642*a^15 - 21272175141/109738568*a^14 - 180932973287/1097385680*a^13 + 1261626353257/1097385680*a^12 + 172089722583/1097385680*a^11 - 416249228885/109738568*a^10 + 982402092849/1097385680*a^9 + 771865790479/109738568*a^8 - 1616752552097/548692840*a^7 - 97782056737/13717321*a^6 + 3616728953083/1097385680*a^5 + 4103883142079/1097385680*a^4 - 388710836369/274346420*a^3 - 97351555979/109738568*a^2 + 42756427693/274346420*a + 16267896819/274346420)*q^26 + (-51367879/548692840*a^19 + 58310959/219477136*a^18 + 3085635187/1097385680*a^17 - 4614090841/548692840*a^16 - 3717871471/109738568*a^15 + 1503517850/13717321*a^14 + 113398279897/548692840*a^13 - 834207317399/1097385680*a^12 - 177455352779/274346420*a^11 + 663750577285/219477136*a^10 + 888290205147/1097385680*a^9 - 94956201103/13717321*a^8 + 290452157609/548692840*a^7 + 947674216705/109738568*a^6 - 152504692621/68586605*a^5 - 5694516402323/1097385680*a^4 + 798993579191/548692840*a^3 + 140465760845/109738568*a^2 - 13501942744/68586605*a - 22108636993/274346420)*q^27 + (41833551/137173210*a^19 - 52942165/54869284*a^18 - 1187819989/137173210*a^17 + 7985536143/274346420*a^16 + 5347545961/54869284*a^15 - 19686571601/54869284*a^14 - 150088492451/274346420*a^13 + 160200481164/68586605*a^12 + 211326787837/137173210*a^11 - 238059563223/27434642*a^10 - 109763745882/68586605*a^9 + 254467452190/13717321*a^8 - 445331083157/274346420*a^7 - 598314655625/27434642*a^6 + 1349153657909/274346420*a^5 + 3465443166297/274346420*a^4 - 206912176017/68586605*a^3 - 83336496579/27434642*a^2 + 26810153929/68586605*a + 13085633107/68586605)*q^28 + (5506177/54869284*a^19 - 30186849/109738568*a^18 - 338631113/109738568*a^17 + 240627075/27434642*a^16 + 527539826/13717321*a^15 - 6319183801/54869284*a^14 - 3395655753/13717321*a^13 + 88231152703/109738568*a^12 + 47131691267/54869284*a^11 - 352513546207/109738568*a^10 - 160419763619/109738568*a^9 + 403196202045/54869284*a^8 + 34546356079/54869284*a^7 - 248987779583/27434642*a^6 + 30766716641/27434642*a^5 + 581192798143/109738568*a^4 - 53514563731/54869284*a^3 - 67136120597/54869284*a^2 + 1855170924/13717321*a + 2059393637/27434642)*q^29 + (56297417/548692840*a^19 - 10652503/27434642*a^18 - 1499018293/548692840*a^17 + 3132008009/274346420*a^16 + 1526534081/54869284*a^15 - 1868697591/13717321*a^14 - 71584212321/548692840*a^13 + 467196480241/548692840*a^12 + 126005819039/548692840*a^11 - 165134245395/54869284*a^10 + 150404954767/548692840*a^9 + 333320208717/54869284*a^8 - 462493208351/274346420*a^7 - 184600374441/27434642*a^6 + 1279085682299/548692840*a^5 + 2038218499707/548692840*a^4 - 156358423307/137173210*a^3 - 47338120899/54869284*a^2 + 18280558129/137173210*a + 7529682447/137173210)*q^30 + (21281459/137173210*a^19 - 126641469/219477136*a^18 - 4389199143/1097385680*a^17 + 9133854009/548692840*a^16 + 4238318731/109738568*a^15 - 2657576246/13717321*a^14 - 44543688079/274346420*a^13 + 1286098247731/1097385680*a^12 + 97651272727/548692840*a^11 - 872304044211/219477136*a^10 + 878256967417/1097385680*a^9 + 419553570571/54869284*a^8 - 1556791312041/548692840*a^7 - 888639623063/109738568*a^6 + 1823354529817/548692840*a^5 + 4830480473947/1097385680*a^4 - 812339073929/548692840*a^3 - 115485758833/109738568*a^2 + 23109909757/137173210*a + 19292002117/274346420)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-135100019/548692840*a^19 + 86743633/109738568*a^18 + 968304149/137173210*a^17 - 6618845933/274346420*a^16 - 1103209894/13717321*a^15 + 4137363849/13717321*a^14 + 251585917217/548692840*a^13 - 273906558943/137173210*a^12 - 723039439613/548692840*a^11 + 829845108481/109738568*a^10 + 389120140943/274346420*a^9 - 905380694239/54869284*a^8 + 372913505137/274346420*a^7 + 1085213544149/54869284*a^6 - 2373604580183/548692840*a^5 - 1593268119611/137173210*a^4 + 736389526043/274346420*a^3 + 77003165387/27434642*a^2 - 48464750593/137173210*a - 12327300737/68586605)*q^33 + (16392027/1097385680*a^19 + 6331523/109738568*a^18 - 837316493/1097385680*a^17 - 679477281/548692840*a^16 + 192642782/13717321*a^15 + 852311073/109738568*a^14 - 138969185151/1097385680*a^13 + 7960869481/1097385680*a^12 + 671763757239/1097385680*a^11 - 29484790323/109738568*a^10 - 1739808738523/1097385680*a^9 + 120612305559/109738568*a^8 + 1113604287049/548692840*a^7 - 98480951321/54869284*a^6 - 1118703350701/1097385680*a^5 + 1237283722367/1097385680*a^4 + 29758503623/274346420*a^3 - 26380328139/109738568*a^2 + 3188801849/274346420*a + 3559404107/274346420)*q^34 + (-14369373/274346420*a^19 + 1358861/54869284*a^18 + 282668501/137173210*a^17 - 504569217/274346420*a^16 - 1764987935/54869284*a^15 + 2142378883/54869284*a^14 + 35106865047/137173210*a^13 - 104573645679/274346420*a^12 - 75376683279/68586605*a^11 + 107080112145/54869284*a^10 + 669207511447/274346420*a^9 - 293658968605/54869284*a^8 - 154627101228/68586605*a^7 + 409530623313/54869284*a^6 - 11619417331/274346420*a^5 - 1258684348283/274346420*a^4 + 49062503473/68586605*a^3 + 28822779369/27434642*a^2 - 7160639541/68586605*a - 4282919658/68586605)*q^35 + (-245720121/1097385680*a^19 + 166802647/219477136*a^18 + 865027753/137173210*a^17 - 12625954717/548692840*a^16 - 959632656/13717321*a^15 + 3908162360/13717321*a^14 + 418576532143/1097385680*a^13 - 511521360957/274346420*a^12 - 1092874279807/1097385680*a^11 + 1529047253939/219477136*a^10 + 363945756427/548692840*a^9 - 1643367473955/109738568*a^8 + 1251169955203/548692840*a^7 + 1938339068977/109738568*a^6 - 5272011428577/1097385680*a^5 - 2799101924639/274346420*a^4 + 1503862752617/548692840*a^3 + 132849825097/54869284*a^2 - 91503978607/274346420*a - 20807021483/137173210)*q^36 + (-77763363/548692840*a^19 + 56391515/109738568*a^18 + 1025565821/274346420*a^17 - 4110700781/274346420*a^16 - 515942739/13717321*a^15 + 4853590653/27434642*a^14 + 95337883389/548692840*a^13 - 299456914927/274346420*a^12 - 165693969661/548692840*a^11 + 417338645439/109738568*a^10 - 22528280166/68586605*a^9 - 416158163661/54869284*a^8 + 550915685819/274346420*a^7 + 460980462593/54869284*a^6 - 1472859564331/548692840*a^5 - 1314351276119/274346420*a^4 + 357262105061/274346420*a^3 + 16340008413/13717321*a^2 - 21148069681/137173210*a - 5180700504/68586605)*q^37 + O(q^38)
*]> ;  // time = 9.49 seconds




J[390] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 390, 390, 390, 390, 390, 390, 390, 390, 195, 195, 195, 195, 195, 130, 130, 130, 78, 65, 65, 65, 39, 39, 30, 26, 26, 15 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 4, 8, 8, 4, 8, 2, 4, 4, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 7, 1, 1, 7, 1, 1, 5, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 49, 1, 1, 1, 1, 1, 9, 1, 1, 5, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 49, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 9, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 121, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 121, 1, 1, 1, 1, 1, 0, 1, 1, 1, 3, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 49, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 49, 1, 1, 49, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 49, 1, 1, 1, 1, 1, 1, 1, 1, 1, 49, 1, 0, 1, 1, 49, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 25, 1, 9, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1, 49, 1, 49, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ -1, -1, -1, 0, 0, -1, -6, 0, -4, -10, 0, -6 ],
[ -1, -1, 1, -2, 4, -1, 4, -2, 2, 8, 4, 6 ],
[ -1, 1, -1, 4, 0, -1, -2, 4, 8, 2, -8, 2 ],
[ -1, 1, 1, 2, 0, 1, 0, 2, -6, 0, 8, 2 ],
[ 1, -1, -1, 2, 4, -1, 8, -6, 6, -4, 0, -2 ],
[ 1, -1, 1, 0, 4, 1, -6, 4, 8, 6, -8, -10 ],
[ 1, 1, -1, 2, 0, 1, 0, 2, -6, 0, -4, 2 ],
[ 2, 2, 2, 0, 0, -2, -4, 0, 0, -12, 8, -12 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 8
], atkin_lehners := [
[ 1, 1, 1, 1 ],
[ 1, 1, -1, 1 ],
[ 1, -1, 1, 1 ],
[ 1, -1, -1, -1 ],
[ -1, 1, 1, 1 ],
[ -1, 1, -1, -1 ],
[ -1, -1, 1, -1 ],
[ -1, -1, -1, 1 ]
], component_group_orders := [
[ 1, 1, 1, 1 ],
[ 5, 1, 1, 1 ],
[ 5, 1, 1, 1 ],
[ 5, 9, 3, 1 ],
[ 1, 3, 1, 1 ],
[ 1, 1, 1, 1 ],
[ 3, 3, 1, 1 ],
[ 7, 7, 7, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1, 1 ],
[ 1, 1, 1, 1 ],
[ 1, 1, 1, 1 ],
[ 1, 9, 3, 1 ],
[ 1, 1, 1, 1 ],
[ 1, 1, 1, 1 ],
[ 3, 3, 1, 1 ],
[ 7, 7, 7, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 1, 1, 3, 7 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 1, 3, 1, 1, 1, 7 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1/9, 1, 1, 1/9, 1/49 ], eigenvalues := [*
[ -1, -1, -1, 0, 0, -1, -6, 0, -4, -10, 0, -6 ],
[ -1, -1, 1, -2, 4, -1, 4, -2, 2, 8, 4, 6 ],
[ -1, 1, -1, 4, 0, -1, -2, 4, 8, 2, -8, 2 ],
[ -1, 1, 1, 2, 0, 1, 0, 2, -6, 0, 8, 2 ],
[ 1, -1, -1, 2, 4, -1, 8, -6, 6, -4, 0, -2 ],
[ 1, -1, 1, 0, 4, 1, -6, 4, 8, 6, -8, -10 ],
[ 1, 1, -1, 2, 0, 1, 0, 2, -6, 0, -4, 2 ],
[
1,
1,
1,
a,
-2*a,
-1,
-a - 2,
-a,
3*a,
a - 6,
4,
2*a - 6
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - q^5 + q^6 - q^8 + q^9 + q^10 - q^12 - q^13 + q^15 + q^16 - 6*q^17 - q^18 - q^20 - 4*q^23 + q^24 + q^25 + q^26 - q^27 - 10*q^29 - q^30 - q^32 + 6*q^34 + q^36 - 6*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + q^5 + q^6 - 2*q^7 - q^8 + q^9 - q^10 + 4*q^11 - q^12 - q^13 + 2*q^14 - q^15 + q^16 + 4*q^17 - q^18 - 2*q^19 + q^20 + 2*q^21 - 4*q^22 + 2*q^23 + q^24 + q^25 + q^26 - q^27 - 2*q^28 + 8*q^29 + q^30 + 4*q^31 - q^32 - 4*q^33 - 4*q^34 - 2*q^35 + q^36 + 6*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - q^5 - q^6 + 4*q^7 - q^8 + q^9 + q^10 + q^12 - q^13 - 4*q^14 - q^15 + q^16 - 2*q^17 - q^18 + 4*q^19 - q^20 + 4*q^21 + 8*q^23 - q^24 + q^25 + q^26 + q^27 + 4*q^28 + 2*q^29 + q^30 - 8*q^31 - q^32 + 2*q^34 - 4*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + q^5 - q^6 + 2*q^7 - q^8 + q^9 - q^10 + q^12 + q^13 - 2*q^14 + q^15 + q^16 - q^18 + 2*q^19 + q^20 + 2*q^21 - 6*q^23 - q^24 + q^25 - q^26 + q^27 + 2*q^28 - q^30 + 8*q^31 - q^32 + 2*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - q^5 - q^6 + 2*q^7 + q^8 + q^9 - q^10 + 4*q^11 - q^12 - q^13 + 2*q^14 + q^15 + q^16 + 8*q^17 + q^18 - 6*q^19 - q^20 - 2*q^21 + 4*q^22 + 6*q^23 - q^24 + q^25 - q^26 - q^27 + 2*q^28 - 4*q^29 + q^30 + q^32 - 4*q^33 + 8*q^34 - 2*q^35 + q^36 - 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + q^8 + q^9 + q^10 + 4*q^11 - q^12 + q^13 - q^15 + q^16 - 6*q^17 + q^18 + 4*q^19 + q^20 + 4*q^22 + 8*q^23 - q^24 + q^25 + q^26 - q^27 + 6*q^29 - q^30 - 8*q^31 + q^32 - 4*q^33 - 6*q^34 + q^36 - 10*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - q^5 + q^6 + 2*q^7 + q^8 + q^9 - q^10 + q^12 + q^13 + 2*q^14 - q^15 + q^16 + q^18 + 2*q^19 - q^20 + 2*q^21 - 6*q^23 + q^24 + q^25 + q^26 + q^27 + 2*q^28 - q^30 - 4*q^31 + q^32 - 2*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^5 + q^6 + a*q^7 + q^8 + q^9 + q^10 - 2*a*q^11 + q^12 - q^13 + a*q^14 + q^15 + q^16 + (-a - 2)*q^17 + q^18 - a*q^19 + q^20 + a*q^21 - 2*a*q^22 + 3*a*q^23 + q^24 + q^25 - q^26 + q^27 + a*q^28 + (a - 6)*q^29 + q^30 + 4*q^31 + q^32 - 2*a*q^33 + (-a - 2)*q^34 + a*q^35 + q^36 + (2*a - 6)*q^37 + O(q^38)
*]> ;  // time = 779.62 seconds




J[391] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 391, 391, 391, 391, 391, 23, 17 ], new_dimensions := [ 2, 3, 3, 9, 12, 2, 1 ], dimensions := [ 2, 3, 3, 9, 12, 4, 2 ], intersection_graph := [ 0, 9, 1, 1, 1, 1, 1, 9, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 5, 1, 1, 1, 0, 1, 109, 1, 1, 1, 1, 1, 0, 1, 7, 1, 1, 5, 109, 1, 0, 1, 1, 1, 5, 1, 7, 1, 0 ], ap_traces := [
[ -1, 2, -2, -2, -8, -2, -2, 4, -2, -8, 6, 0 ],
[ -1, -6, -3, 1, 1, 1, -3, -2, -3, -12, -8, -5 ],
[ -1, 0, -1, -5, -3, -3, 3, -2, 3, -8, -8, 3 ],
[ 2, 2, 7, 3, 11, -9, -9, -4, 9, 24, -6, 15 ],
[ 4, 2, 5, -9, 11, 7, 12, 4, -12, 22, -4, -15 ]
], hecke_fields := [
x^2 + x - 1,
x^3 + x^2 - 4*x - 3,
x^3 + x^2 - 4*x + 1,
x^9 - 2*x^8 - 12*x^7 + 23*x^6 + 43*x^5 - 79*x^4 - 43*x^3 + 78*x^2 + 11*x - 21,
x^12 - 4*x^11 - 12*x^10 + 62*x^9 + 27*x^8 - 321*x^7 + 108*x^6 + 625*x^5 - 362*x^4 - 372*x^3 + 116*x^2 + 97*x + 13
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 5, 5 ],
[ 109, 3 ],
[ 1, 7 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 5, 5 ],
[ 1, 3 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 1 ], torsion_lower_bounds := [ 1, 1, 1, 3, 1 ], l_ratios := [ 0, 0, 0, 1/3, 1 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[
a,
1,
-2*a - 2,
2*a,
-4,
-1,
-1,
2,
-1,
-2*a - 5,
-4*a + 1,
8*a + 4
],
[
a,
-2,
-a^2 + 2,
-a,
-a^2 - a + 3,
2*a^2 - a - 6,
-1,
2*a^2 + 2*a - 6,
-1,
2*a^2 - 10,
2*a - 2,
-3*a^2 - a + 7
],
[
a,
0,
-a^2 - 2*a + 2,
-a - 2,
a^2 + 3*a - 3,
2*a^2 + 3*a - 6,
1,
-2*a^2 - 4*a + 4,
1,
2*a - 2,
4*a^2 + 8*a - 12,
3*a^2 + 3*a - 7
],
[
a,
-1/4*a^8 + 1/4*a^7 + 7/2*a^6 - 5/2*a^5 - 33/2*a^4 + 7*a^3 + 57/2*a^2 - 19/4*a - 47/4,
-1/4*a^8 + 1/4*a^7 + 13/4*a^6 - 11/4*a^5 - 55/4*a^4 + 35/4*a^3 + 85/4*a^2 - 13/2*a - 9,
-1/4*a^7 + 1/4*a^6 + 13/4*a^5 - 11/4*a^4 - 47/4*a^3 + 31/4*a^2 + 33/4*a - 5/2,
1/4*a^8 - 15/4*a^6 + 1/4*a^5 + 73/4*a^4 - 9/4*a^3 - 125/4*a^2 + 9/2*a + 57/4,
-a^8 + 3/2*a^7 + 12*a^6 - 16*a^5 - 43*a^4 + 47*a^3 + 43*a^2 - 26*a - 23/2,
-1,
1/2*a^8 - 1/4*a^7 - 27/4*a^6 + 9/4*a^5 + 117/4*a^4 - 19/4*a^3 - 177/4*a^2 + 3/4*a + 37/2,
1,
-3/4*a^8 + 3/4*a^7 + 37/4*a^6 - 31/4*a^5 - 131/4*a^4 + 83/4*a^3 + 105/4*a^2 - 7*a + 3/2,
1/2*a^8 - 1/4*a^7 - 27/4*a^6 + 9/4*a^5 + 117/4*a^4 - 19/4*a^3 - 169/4*a^2 - 5/4*a + 25/2,
3/4*a^8 - 1/2*a^7 - 39/4*a^6 + 17/4*a^5 + 161/4*a^4 - 29/4*a^3 - 221/4*a^2 - 5*a + 83/4
],
[
a,
-9/14*a^11 + 12/7*a^10 + 19/2*a^9 - 181/7*a^8 - 89/2*a^7 + 888/7*a^6 + 460/7*a^5 - 429/2*a^4 - 30/7*a^3 + 867/14*a^2 + 7*a + 9/14,
-1/14*a^11 - 9/14*a^10 + 3*a^9 + 141/14*a^8 - 69/2*a^7 - 368/7*a^6 + 1084/7*a^5 + 205/2*a^4 - 3677/14*a^3 - 443/7*a^2 + 201/2*a + 379/14,
3/14*a^11 - 1/14*a^10 - 9/2*a^9 + 9/7*a^8 + 35*a^7 - 58/7*a^6 - 851/7*a^5 + 43/2*a^4 + 2435/14*a^3 - 191/14*a^2 - 60*a - 82/7,
13/7*a^11 - 39/14*a^10 - 33*a^9 + 295/7*a^8 + 425/2*a^7 - 1464/7*a^6 - 4230/7*a^5 + 366*a^4 + 10195/14*a^3 - 795/7*a^2 - 256*a - 635/14,
15/7*a^11 - 40/7*a^10 - 32*a^9 + 608/7*a^8 + 153*a^7 - 3030/7*a^6 - 1678/7*a^5 + 764*a^4 + 303/7*a^3 - 2012/7*a^2 - 22*a + 97/7,
1,
-15/14*a^11 + 75/14*a^10 + 19/2*a^9 - 570/7*a^8 + 22*a^7 + 2838/7*a^6 - 2577/7*a^5 - 1433/2*a^4 + 11569/14*a^3 + 4161/14*a^2 - 279*a - 521/7,
-1,
-55/14*a^11 + 121/14*a^10 + 63*a^9 - 1835/14*a^8 - 693/2*a^7 + 4561/7*a^6 + 5384/7*a^5 - 2289/2*a^4 - 9259/14*a^3 + 2837/7*a^2 + 503/2*a + 391/14,
-89/14*a^11 + 221/14*a^10 + 195/2*a^9 - 1674/7*a^8 - 493*a^7 + 8296/7*a^6 + 6351/7*a^5 - 4127/2*a^4 - 6737/14*a^3 + 9913/14*a^2 + 209*a + 90/7,
a^11 - 11/2*a^10 - 8*a^9 + 84*a^8 - 67/2*a^7 - 422*a^6 + 408*a^5 + 762*a^4 - 1781/2*a^3 - 346*a^2 + 321*a + 175/2
]
*], q_expansions := [*
q + a*q^2 + q^3 + (-a - 1)*q^4 + (-2*a - 2)*q^5 + a*q^6 + 2*a*q^7 + (-2*a - 1)*q^8 - 2*q^9 - 2*q^10 - 4*q^11 + (-a - 1)*q^12 - q^13 + (-2*a + 2)*q^14 + (-2*a - 2)*q^15 + 3*a*q^16 - q^17 - 2*a*q^18 + 2*q^19 + (2*a + 4)*q^20 + 2*a*q^21 - 4*a*q^22 - q^23 + (-2*a - 1)*q^24 + (4*a + 3)*q^25 - a*q^26 - 5*q^27 - 2*q^28 + (-2*a - 5)*q^29 - 2*q^30 + (-4*a + 1)*q^31 + (a + 5)*q^32 - 4*q^33 - a*q^34 - 4*q^35 + (2*a + 2)*q^36 + (8*a + 4)*q^37 + O(q^38),
q + a*q^2 - 2*q^3 + (a^2 - 2)*q^4 + (-a^2 + 2)*q^5 - 2*a*q^6 - a*q^7 + (-a^2 + 3)*q^8 + q^9 + (a^2 - 2*a - 3)*q^10 + (-a^2 - a + 3)*q^11 + (-2*a^2 + 4)*q^12 + (2*a^2 - a - 6)*q^13 - a^2*q^14 + (2*a^2 - 4)*q^15 + (-a^2 - a + 1)*q^16 - q^17 + a*q^18 + (2*a^2 + 2*a - 6)*q^19 + (-a^2 + a - 1)*q^20 + 2*a*q^21 + (-a - 3)*q^22 - q^23 + (2*a^2 - 6)*q^24 + (a^2 - a - 4)*q^25 + (-3*a^2 + 2*a + 6)*q^26 + 4*q^27 + (a^2 - 2*a - 3)*q^28 + (2*a^2 - 10)*q^29 + (-2*a^2 + 4*a + 6)*q^30 + (2*a - 2)*q^31 + (2*a^2 - 3*a - 9)*q^32 + (2*a^2 + 2*a - 6)*q^33 - a*q^34 + (-a^2 + 2*a + 3)*q^35 + (a^2 - 2)*q^36 + (-3*a^2 - a + 7)*q^37 + O(q^38),
q + a*q^2 + (a^2 - 2)*q^4 + (-a^2 - 2*a + 2)*q^5 + (-a - 2)*q^7 + (-a^2 - 1)*q^8 - 3*q^9 + (-a^2 - 2*a + 1)*q^10 + (a^2 + 3*a - 3)*q^11 + (2*a^2 + 3*a - 6)*q^13 + (-a^2 - 2*a)*q^14 + (-a^2 - 5*a + 5)*q^16 + q^17 - 3*a*q^18 + (-2*a^2 - 4*a + 4)*q^19 + (a^2 + a - 3)*q^20 + (2*a^2 + a - 1)*q^22 + q^23 + (a^2 + 3*a - 4)*q^25 + (a^2 + 2*a - 2)*q^26 + (-a^2 - 2*a + 5)*q^28 + (2*a - 2)*q^29 + (4*a^2 + 8*a - 12)*q^31 + (-2*a^2 + a + 3)*q^32 + a*q^34 + (3*a^2 + 6*a - 5)*q^35 + (-3*a^2 + 6)*q^36 + (3*a^2 + 3*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-1/4*a^8 + 1/4*a^7 + 7/2*a^6 - 5/2*a^5 - 33/2*a^4 + 7*a^3 + 57/2*a^2 - 19/4*a - 47/4)*q^3 + (a^2 - 2)*q^4 + (-1/4*a^8 + 1/4*a^7 + 13/4*a^6 - 11/4*a^5 - 55/4*a^4 + 35/4*a^3 + 85/4*a^2 - 13/2*a - 9)*q^5 + (-1/4*a^8 + 1/2*a^7 + 13/4*a^6 - 23/4*a^5 - 51/4*a^4 + 71/4*a^3 + 59/4*a^2 - 9*a - 21/4)*q^6 + (-1/4*a^7 + 1/4*a^6 + 13/4*a^5 - 11/4*a^4 - 47/4*a^3 + 31/4*a^2 + 33/4*a - 5/2)*q^7 + (a^3 - 4*a)*q^8 + (1/2*a^8 - a^7 - 11/2*a^6 + 21/2*a^5 + 33/2*a^4 - 61/2*a^3 - 17/2*a^2 + 17*a + 5/2)*q^9 + (-1/4*a^8 + 1/4*a^7 + 3*a^6 - 3*a^5 - 11*a^4 + 21/2*a^3 + 13*a^2 - 25/4*a - 21/4)*q^10 + (1/4*a^8 - 15/4*a^6 + 1/4*a^5 + 73/4*a^4 - 9/4*a^3 - 125/4*a^2 + 9/2*a + 57/4)*q^11 + (1/2*a^8 - 1/4*a^7 - 7*a^6 + 3*a^5 + 31*a^4 - 10*a^3 - 93/2*a^2 + 7*a + 73/4)*q^12 + (-a^8 + 3/2*a^7 + 12*a^6 - 16*a^5 - 43*a^4 + 47*a^3 + 43*a^2 - 26*a - 23/2)*q^13 + (-1/4*a^8 + 1/4*a^7 + 13/4*a^6 - 11/4*a^5 - 47/4*a^4 + 31/4*a^3 + 33/4*a^2 - 5/2*a)*q^14 + (a^8 - 5/4*a^7 - 25/2*a^6 + 27/2*a^5 + 95/2*a^4 - 81/2*a^3 - 55*a^2 + 24*a + 87/4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 - q^17 + (1/2*a^7 - a^6 - 5*a^5 + 9*a^4 + 13*a^3 - 22*a^2 - 3*a + 21/2)*q^18 + (1/2*a^8 - 1/4*a^7 - 27/4*a^6 + 9/4*a^5 + 117/4*a^4 - 19/4*a^3 - 177/4*a^2 + 3/4*a + 37/2)*q^19 + (1/4*a^8 - 1/2*a^7 - 15/4*a^6 + 21/4*a^5 + 73/4*a^4 - 61/4*a^3 - 117/4*a^2 + 21/2*a + 51/4)*q^20 + (-5/4*a^8 + a^7 + 67/4*a^6 - 41/4*a^5 - 285/4*a^4 + 117/4*a^3 + 405/4*a^2 - 41/2*a - 145/4)*q^21 + (1/2*a^8 - 3/4*a^7 - 11/2*a^6 + 15/2*a^5 + 35/2*a^4 - 41/2*a^3 - 15*a^2 + 23/2*a + 21/4)*q^22 + q^23 + (5/4*a^8 - 2*a^7 - 15*a^6 + 21*a^5 + 55*a^4 - 121/2*a^3 - 123/2*a^2 + 123/4*a + 21)*q^24 + (a^8 - 3/2*a^7 - 13*a^6 + 16*a^5 + 53*a^4 - 47*a^3 - 69*a^2 + 29*a + 47/2)*q^25 + (-1/2*a^8 + 7*a^6 - 32*a^4 + 52*a^2 - 1/2*a - 21)*q^26 + (-1/2*a^7 + a^6 + 5*a^5 - 11*a^4 - 11*a^3 + 32*a^2 - 4*a - 25/2)*q^27 + (-1/4*a^8 + 3/4*a^7 + 5/2*a^6 - 15/2*a^5 - 13/2*a^4 + 21*a^3 + 3/2*a^2 - 55/4*a - 1/4)*q^28 + (-3/4*a^8 + 3/4*a^7 + 37/4*a^6 - 31/4*a^5 - 131/4*a^4 + 83/4*a^3 + 105/4*a^2 - 7*a + 3/2)*q^29 + (3/4*a^8 - 1/2*a^7 - 19/2*a^6 + 9/2*a^5 + 77/2*a^4 - 12*a^3 - 54*a^2 + 43/4*a + 21)*q^30 + (1/2*a^8 - 1/4*a^7 - 27/4*a^6 + 9/4*a^5 + 117/4*a^4 - 19/4*a^3 - 169/4*a^2 - 5/4*a + 25/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-3/2*a^8 + 5/2*a^7 + 73/4*a^6 - 107/4*a^5 - 271/4*a^4 + 313/4*a^3 + 313/4*a^2 - 167/4*a - 129/4)*q^33 - a*q^34 + (-a^8 + a^7 + 13*a^6 - 10*a^5 - 54*a^4 + 28*a^3 + 76*a^2 - 20*a - 30)*q^35 + (-1/2*a^8 + a^7 + 6*a^6 - 12*a^5 - 20*a^4 + 39*a^3 + 14*a^2 - 47/2*a - 5)*q^36 + (3/4*a^8 - 1/2*a^7 - 39/4*a^6 + 17/4*a^5 + 161/4*a^4 - 29/4*a^3 - 221/4*a^2 - 5*a + 83/4)*q^37 + O(q^38),
q + a*q^2 + (-9/14*a^11 + 12/7*a^10 + 19/2*a^9 - 181/7*a^8 - 89/2*a^7 + 888/7*a^6 + 460/7*a^5 - 429/2*a^4 - 30/7*a^3 + 867/14*a^2 + 7*a + 9/14)*q^3 + (a^2 - 2)*q^4 + (-1/14*a^11 - 9/14*a^10 + 3*a^9 + 141/14*a^8 - 69/2*a^7 - 368/7*a^6 + 1084/7*a^5 + 205/2*a^4 - 3677/14*a^3 - 443/7*a^2 + 201/2*a + 379/14)*q^5 + (-6/7*a^11 + 25/14*a^10 + 14*a^9 - 190/7*a^8 - 159/2*a^7 + 946/7*a^6 + 1311/7*a^5 - 237*a^4 - 2481/14*a^3 + 571/7*a^2 + 63*a + 117/14)*q^6 + (3/14*a^11 - 1/14*a^10 - 9/2*a^9 + 9/7*a^8 + 35*a^7 - 58/7*a^6 - 851/7*a^5 + 43/2*a^4 + 2435/14*a^3 - 191/14*a^2 - 60*a - 82/7)*q^7 + (a^3 - 4*a)*q^8 + (-4/7*a^11 + 13/7*a^10 + 8*a^9 - 199/7*a^8 - 33*a^7 + 1004/7*a^6 + 188/7*a^5 - 260*a^4 + 349/7*a^3 + 768/7*a^2 - 13*a - 52/7)*q^9 + (-13/14*a^11 + 15/7*a^10 + 29/2*a^9 - 228/7*a^8 - 151/2*a^7 + 1138/7*a^6 + 1030/7*a^5 - 577/2*a^4 - 629/7*a^3 + 1523/14*a^2 + 34*a + 13/14)*q^10 + (13/7*a^11 - 39/14*a^10 - 33*a^9 + 295/7*a^8 + 425/2*a^7 - 1464/7*a^6 - 4230/7*a^5 + 366*a^4 + 10195/14*a^3 - 795/7*a^2 - 256*a - 635/14)*q^11 + (-5/14*a^11 + 2/7*a^10 + 7*a^9 - 65/14*a^8 - 51*a^7 + 183/7*a^6 + 1171/7*a^5 - 117/2*a^4 - 1601/7*a^3 + 270/7*a^2 + 155/2*a + 69/7)*q^12 + (15/7*a^11 - 40/7*a^10 - 32*a^9 + 608/7*a^8 + 153*a^7 - 3030/7*a^6 - 1678/7*a^5 + 764*a^4 + 303/7*a^3 - 2012/7*a^2 - 22*a + 97/7)*q^13 + (11/14*a^11 - 27/14*a^10 - 12*a^9 + 409/14*a^8 + 121/2*a^7 - 1013/7*a^6 - 787/7*a^5 + 503/2*a^4 + 925/14*a^3 - 594/7*a^2 - 65/2*a - 39/14)*q^14 + (-1/2*a^11 - a^10 + 13*a^9 + 31/2*a^8 - 119*a^7 - 79*a^6 + 465*a^5 + 293/2*a^4 - 712*a^3 - 88*a^2 + 473/2*a + 57)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + q^17 + (-3/7*a^11 + 8/7*a^10 + 7*a^9 - 123/7*a^8 - 40*a^7 + 620/7*a^6 + 680/7*a^5 - 157*a^4 - 720/7*a^3 + 373/7*a^2 + 48*a + 52/7)*q^18 + (-15/14*a^11 + 75/14*a^10 + 19/2*a^9 - 570/7*a^8 + 22*a^7 + 2838/7*a^6 - 2577/7*a^5 - 1433/2*a^4 + 11569/14*a^3 + 4161/14*a^2 - 279*a - 521/7)*q^19 + (-10/7*a^11 + 65/14*a^10 + 19*a^9 - 494/7*a^8 - 133/2*a^7 + 2468/7*a^6 - 125/7*a^5 - 631*a^4 + 4041/14*a^3 + 1878/7*a^2 - 110*a - 589/14)*q^20 + (-12/7*a^11 + 57/14*a^10 + 27*a^9 - 436/7*a^8 - 287/2*a^7 + 2200/7*a^6 + 2069/7*a^5 - 571*a^4 - 2981/14*a^3 + 1660/7*a^2 + 77*a + 45/14)*q^21 + (65/14*a^11 - 75/7*a^10 - 73*a^9 + 2273/14*a^8 + 387*a^7 - 5634/7*a^6 - 5563/7*a^5 + 2801/2*a^4 + 4041/7*a^3 - 3300/7*a^2 - 451/2*a - 169/7)*q^22 - q^23 + (4/7*a^11 - 6/7*a^10 - 21/2*a^9 + 181/14*a^8 + 141/2*a^7 - 451/7*a^6 - 1469/7*a^5 + 116*a^4 + 1821/7*a^3 - 619/14*a^2 - 163/2*a - 169/14)*q^24 + (8/7*a^11 - 40/7*a^10 - 10*a^9 + 608/7*a^8 - 26*a^7 - 3030/7*a^6 + 2865/7*a^5 + 768*a^4 - 6466/7*a^3 - 2285/7*a^2 + 328*a + 643/7)*q^25 + (20/7*a^11 - 44/7*a^10 - 46*a^9 + 666/7*a^8 + 255*a^7 - 3298/7*a^6 - 4027/7*a^5 + 819*a^4 + 3568/7*a^3 - 1894/7*a^2 - 194*a - 195/7)*q^26 + (18/7*a^11 - 34/7*a^10 - 43*a^9 + 514/7*a^8 + 253*a^7 - 2544/7*a^6 - 4416/7*a^5 + 632*a^4 + 4572/7*a^3 - 1405/7*a^2 - 248*a - 319/7)*q^27 + (11/14*a^11 - 17/7*a^10 - 21/2*a^9 + 257/7*a^8 + 75/2*a^7 - 1265/7*a^6 + 25/7*a^5 + 615/2*a^4 - 983/7*a^3 - 1349/14*a^2 + 41*a + 185/14)*q^28 + (-55/14*a^11 + 121/14*a^10 + 63*a^9 - 1835/14*a^8 - 693/2*a^7 + 4561/7*a^6 + 5384/7*a^5 - 2289/2*a^4 - 9259/14*a^3 + 2837/7*a^2 + 503/2*a + 391/14)*q^29 + (-3*a^11 + 7*a^10 + 93/2*a^9 - 211/2*a^8 - 479/2*a^7 + 519*a^6 + 459*a^5 - 893*a^4 - 274*a^3 + 589/2*a^2 + 211/2*a + 13/2)*q^30 + (-89/14*a^11 + 221/14*a^10 + 195/2*a^9 - 1674/7*a^8 - 493*a^7 + 8296/7*a^6 + 6351/7*a^5 - 4127/2*a^4 - 6737/14*a^3 + 9913/14*a^2 + 209*a + 90/7)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (3/7*a^11 + 19/14*a^10 - 25/2*a^9 - 293/14*a^8 + 123*a^7 + 745/7*a^6 - 3550/7*a^5 - 198*a^4 + 11471/14*a^3 + 1627/14*a^2 - 623/2*a - 472/7)*q^33 + a*q^34 + (-2/7*a^11 + 3/7*a^10 + 5*a^9 - 47/7*a^8 - 31*a^7 + 250/7*a^6 + 563/7*a^5 - 75*a^4 - 522/7*a^3 + 384/7*a^2 - a - 47/7)*q^35 + (4/7*a^11 - 13/7*a^10 - 7*a^9 + 199/7*a^8 + 17*a^7 - 1004/7*a^6 + 400/7*a^5 + 262*a^4 - 1441/7*a^3 - 852/7*a^2 + 75*a + 143/7)*q^36 + (a^11 - 11/2*a^10 - 8*a^9 + 84*a^8 - 67/2*a^7 - 422*a^6 + 408*a^5 + 762*a^4 - 1781/2*a^3 - 346*a^2 + 321*a + 175/2)*q^37 + O(q^38)
*]> ;  // time = 62.73 seconds




J[393] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 393, 393, 393, 393, 393, 131, 131 ], new_dimensions := [ 2, 4, 4, 5, 6, 1, 10 ], dimensions := [ 2, 4, 4, 5, 6, 2, 20 ], intersection_graph := [ 0, 1, 1, 23, 1, 1, 23, 1, 0, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1931, 23, 1, 1, 0, 1, 1, 7613, 1, 1, 1, 1, 0, 5, 1, 1, 3, 1, 1, 5, 0, 1, 23, 1, 1931, 7613, 1, 1, 0 ], ap_traces := [
[ -2, -2, 0, 8, 2, 10, -6, -2, 8, -2, 2, 8 ],
[ -1, -4, 0, -8, 2, -9, -6, -7, -8, 10, -10, -10 ],
[ -3, 4, -8, -8, -4, -5, -10, -1, -18, -16, 0, 4 ],
[ 2, -5, -2, 4, -6, -3, 8, 15, 8, -22, 18, -8 ],
[ 1, 6, 8, 4, 6, -3, 4, -1, 14, 12, -2, -12 ]
], hecke_fields := [
x^2 + 2*x - 1,
x^4 + x^3 - 4*x^2 - 2*x + 3,
x^4 + 3*x^3 - 4*x - 1,
x^5 - 2*x^4 - 7*x^3 + 12*x^2 + 9*x - 9,
x^6 - x^5 - 7*x^4 + 5*x^3 + 13*x^2 - 4*x - 5
], atkin_lehners := [
[ 1, -1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 23, 1 ],
[ 3, 1 ],
[ 1931, 1 ],
[ 7613, 1 ],
[ 55, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1931, 1 ],
[ 1, 1 ],
[ 55, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 11 ], torsion_lower_bounds := [ 1, 1, 1, 1, 11 ], l_ratios := [ 1, 0, 0, 1, 5/11 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 1 ], eigenvalues := [*
[
a,
-1,
-2*a - 2,
4,
1,
5,
3*a,
a,
-2*a + 2,
3*a + 2,
a + 2,
4
],
[
a,
-1,
-a^3 - a^2 + 2*a + 1,
a^3 - 3*a - 1,
2*a^3 + a^2 - 7*a,
-2*a^3 - 2*a^2 + 5*a,
3*a^2 + a - 8,
3*a^2 + 2*a - 8,
a^3 + 2*a^2 - a - 5,
-a^3 - 2*a^2 + 3*a + 6,
-a^3 - 5*a^2 + 7,
2*a^3 + a^2 - 3*a - 2
],
[
a,
1,
-a^3 - 3*a^2 + 1,
a^3 + 2*a^2 - 3*a - 5,
3*a^2 + 5*a - 4,
4*a^3 + 8*a^2 - 5*a - 8,
-3*a^2 - 3*a + 2,
-6*a^3 - 11*a^2 + 8*a + 8,
-3*a^3 - 4*a^2 + 5*a - 3,
3*a^3 + 6*a^2 - 5*a - 10,
a^3 + a^2 + 2*a + 3,
2*a^3 - a^2 - 9*a + 4
],
[
a,
-1,
1/3*a^4 - 2/3*a^3 - 7/3*a^2 + 4*a + 2,
1/3*a^4 - 2/3*a^3 - 4/3*a^2 + 3*a,
-2/3*a^4 - 2/3*a^3 + 11/3*a^2 + 5*a - 2,
-a^4 + a^3 + 6*a^2 - 3*a - 5,
2/3*a^4 - 4/3*a^3 - 11/3*a^2 + 5*a + 4,
1/3*a^4 + 1/3*a^3 - 7/3*a^2 - 2*a + 5,
a^4 - 8*a^2 - a + 12,
-a^3 + 2*a^2 + 3*a - 10,
a^4 - 7*a^2 + 10,
a^2 - 3*a - 4
],
[
a,
1,
-a^4 + 5*a^2 - 2,
a^5 - a^4 - 5*a^3 + 4*a^2 + 4*a - 1,
a^4 - a^3 - 5*a^2 + 3*a + 5,
-a^5 + 2*a^4 + 5*a^3 - 10*a^2 - 4*a + 7,
a^5 + a^4 - 6*a^3 - 5*a^2 + 6*a + 4,
-a^5 + 5*a^3 - a^2 - 3*a + 3,
-a^5 + a^4 + 7*a^3 - 4*a^2 - 12*a + 3,
-a^4 + 2*a^3 + 2*a^2 - 7*a + 5,
-a^3 + 3*a^2 + 2*a - 7,
a^5 - 9*a^3 + a^2 + 18*a - 3
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-2*a - 1)*q^4 + (-2*a - 2)*q^5 - a*q^6 + 4*q^7 + (a - 2)*q^8 + q^9 + (2*a - 2)*q^10 + q^11 + (2*a + 1)*q^12 + 5*q^13 + 4*a*q^14 + (2*a + 2)*q^15 + 3*q^16 + 3*a*q^17 + a*q^18 + a*q^19 + (-2*a + 6)*q^20 - 4*q^21 + a*q^22 + (-2*a + 2)*q^23 + (-a + 2)*q^24 + 3*q^25 + 5*a*q^26 - q^27 + (-8*a - 4)*q^28 + (3*a + 2)*q^29 + (-2*a + 2)*q^30 + (a + 2)*q^31 + (a + 4)*q^32 - q^33 + (-6*a + 3)*q^34 + (-8*a - 8)*q^35 + (-2*a - 1)*q^36 + 4*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^3 - a^2 + 2*a + 1)*q^5 - a*q^6 + (a^3 - 3*a - 1)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-2*a^2 - a + 3)*q^10 + (2*a^3 + a^2 - 7*a)*q^11 + (-a^2 + 2)*q^12 + (-2*a^3 - 2*a^2 + 5*a)*q^13 + (-a^3 + a^2 + a - 3)*q^14 + (a^3 + a^2 - 2*a - 1)*q^15 + (-a^3 - 2*a^2 + 2*a + 1)*q^16 + (3*a^2 + a - 8)*q^17 + a*q^18 + (3*a^2 + 2*a - 8)*q^19 + (a^2 - a - 2)*q^20 + (-a^3 + 3*a + 1)*q^21 + (-a^3 + a^2 + 4*a - 6)*q^22 + (a^3 + 2*a^2 - a - 5)*q^23 + (-a^3 + 4*a)*q^24 + (a^2 + a - 4)*q^25 + (-3*a^2 - 4*a + 6)*q^26 - q^27 + (-3*a^2 + a + 5)*q^28 + (-a^3 - 2*a^2 + 3*a + 6)*q^29 + (2*a^2 + a - 3)*q^30 + (-a^3 - 5*a^2 + 7)*q^31 + (-3*a^3 - 2*a^2 + 7*a + 3)*q^32 + (-2*a^3 - a^2 + 7*a)*q^33 + (3*a^3 + a^2 - 8*a)*q^34 + (2*a^3 + 2*a^2 - 3*a - 4)*q^35 + (a^2 - 2)*q^36 + (2*a^3 + a^2 - 3*a - 2)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^3 - 3*a^2 + 1)*q^5 + a*q^6 + (a^3 + 2*a^2 - 3*a - 5)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-3*a - 1)*q^10 + (3*a^2 + 5*a - 4)*q^11 + (a^2 - 2)*q^12 + (4*a^3 + 8*a^2 - 5*a - 8)*q^13 + (-a^3 - 3*a^2 - a + 1)*q^14 + (-a^3 - 3*a^2 + 1)*q^15 + (-3*a^3 - 6*a^2 + 4*a + 5)*q^16 + (-3*a^2 - 3*a + 2)*q^17 + a*q^18 + (-6*a^3 - 11*a^2 + 8*a + 8)*q^19 + (2*a^3 + 3*a^2 - a - 2)*q^20 + (a^3 + 2*a^2 - 3*a - 5)*q^21 + (3*a^3 + 5*a^2 - 4*a)*q^22 + (-3*a^3 - 4*a^2 + 5*a - 3)*q^23 + (a^3 - 4*a)*q^24 + (2*a^3 + 7*a^2 + 3*a - 4)*q^25 + (-4*a^3 - 5*a^2 + 8*a + 4)*q^26 + q^27 + (-2*a^3 - 5*a^2 + 3*a + 9)*q^28 + (3*a^3 + 6*a^2 - 5*a - 10)*q^29 + (-3*a - 1)*q^30 + (a^3 + a^2 + 2*a + 3)*q^31 + (a^3 + 4*a^2 + a - 3)*q^32 + (3*a^2 + 5*a - 4)*q^33 + (-3*a^3 - 3*a^2 + 2*a)*q^34 + (2*a^3 + 8*a^2 + 7*a - 2)*q^35 + (a^2 - 2)*q^36 + (2*a^3 - a^2 - 9*a + 4)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (1/3*a^4 - 2/3*a^3 - 7/3*a^2 + 4*a + 2)*q^5 - a*q^6 + (1/3*a^4 - 2/3*a^3 - 4/3*a^2 + 3*a)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a + 3)*q^10 + (-2/3*a^4 - 2/3*a^3 + 11/3*a^2 + 5*a - 2)*q^11 + (-a^2 + 2)*q^12 + (-a^4 + a^3 + 6*a^2 - 3*a - 5)*q^13 + (a^3 - a^2 - 3*a + 3)*q^14 + (-1/3*a^4 + 2/3*a^3 + 7/3*a^2 - 4*a - 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2/3*a^4 - 4/3*a^3 - 11/3*a^2 + 5*a + 4)*q^17 + a*q^18 + (1/3*a^4 + 1/3*a^3 - 7/3*a^2 - 2*a + 5)*q^19 + (-2/3*a^4 + 4/3*a^3 + 11/3*a^2 - 5*a - 4)*q^20 + (-1/3*a^4 + 2/3*a^3 + 4/3*a^2 - 3*a)*q^21 + (-2*a^4 - a^3 + 13*a^2 + 4*a - 6)*q^22 + (a^4 - 8*a^2 - a + 12)*q^23 + (-a^3 + 4*a)*q^24 + (1/3*a^4 + 1/3*a^3 - 13/3*a^2 - 3*a + 11)*q^25 + (-a^4 - a^3 + 9*a^2 + 4*a - 9)*q^26 - q^27 + (1/3*a^4 + 1/3*a^3 - 1/3*a^2 - 3*a)*q^28 + (-a^3 + 2*a^2 + 3*a - 10)*q^29 + (a - 3)*q^30 + (a^4 - 7*a^2 + 10)*q^31 + (2*a^4 - a^3 - 12*a^2 + 3*a + 9)*q^32 + (2/3*a^4 + 2/3*a^3 - 11/3*a^2 - 5*a + 2)*q^33 + (a^3 - 3*a^2 - 2*a + 6)*q^34 + (-1/3*a^4 + 5/3*a^3 - 2/3*a^2 - 7*a + 9)*q^35 + (a^2 - 2)*q^36 + (a^2 - 3*a - 4)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^4 + 5*a^2 - 2)*q^5 + a*q^6 + (a^5 - a^4 - 5*a^3 + 4*a^2 + 4*a - 1)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^5 + 5*a^3 - 2*a)*q^10 + (a^4 - a^3 - 5*a^2 + 3*a + 5)*q^11 + (a^2 - 2)*q^12 + (-a^5 + 2*a^4 + 5*a^3 - 10*a^2 - 4*a + 7)*q^13 + (2*a^4 - a^3 - 9*a^2 + 3*a + 5)*q^14 + (-a^4 + 5*a^2 - 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^5 + a^4 - 6*a^3 - 5*a^2 + 6*a + 4)*q^17 + a*q^18 + (-a^5 + 5*a^3 - a^2 - 3*a + 3)*q^19 + (-a^5 + 5*a^3 + a^2 - 4*a - 1)*q^20 + (a^5 - a^4 - 5*a^3 + 4*a^2 + 4*a - 1)*q^21 + (a^5 - a^4 - 5*a^3 + 3*a^2 + 5*a)*q^22 + (-a^5 + a^4 + 7*a^3 - 4*a^2 - 12*a + 3)*q^23 + (a^3 - 4*a)*q^24 + (-3*a^4 + a^3 + 15*a^2 - 3*a - 11)*q^25 + (a^5 - 2*a^4 - 5*a^3 + 9*a^2 + 3*a - 5)*q^26 + q^27 + (a^4 + a^3 - 5*a^2 - 3*a + 2)*q^28 + (-a^4 + 2*a^3 + 2*a^2 - 7*a + 5)*q^29 + (-a^5 + 5*a^3 - 2*a)*q^30 + (-a^3 + 3*a^2 + 2*a - 7)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^4 - a^3 - 5*a^2 + 3*a + 5)*q^33 + (2*a^5 + a^4 - 10*a^3 - 7*a^2 + 8*a + 5)*q^34 + (2*a^5 - 3*a^4 - 9*a^3 + 12*a^2 + 3*a - 3)*q^35 + (a^2 - 2)*q^36 + (a^5 - 9*a^3 + a^2 + 18*a - 3)*q^37 + O(q^38)
*]> ;  // time = 68.041 seconds




J[394] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 394, 394, 394, 394, 394, 394, 197, 197, 197 ], new_dimensions := [ 2, 2, 2, 2, 4, 4, 1, 5, 10 ], dimensions := [ 2, 2, 2, 2, 4, 4, 2, 10, 20 ], intersection_graph := [ 0, 5, 5, 1, 1, 1, 5, 25, 1, 5, 0, 5, 1, 1, 1, 5, 5, 1, 5, 5, 0, 1, 1, 1, 5, 5, 1, 1, 1, 1, 0, 1, 1, 1, 1, 31, 1, 1, 1, 1, 0, 1, 1, 109, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1087, 5, 5, 5, 1, 1, 1, 0, 25, 1, 25, 5, 5, 1, 109, 1, 25, 0, 1, 1, 1, 1, 31, 1, 1087, 1, 1, 0 ], ap_traces := [
[ 2, 0, 3, 4, 2, 3, 4, -9, 4, -16, -7, 4 ],
[ 2, 0, 5, -6, 3, 6, -1, 4, -11, 9, 0, 9 ],
[ 2, -1, 0, 4, -3, -2, 6, 4, 6, 15, 7, -17 ],
[ 2, -2, -5, -4, -5, -2, -5, 2, -3, -1, -2, -5 ],
[ -4, -3, -5, 2, -8, 4, -9, -12, -5, -20, -11, 4 ],
[ -4, 2, 2, 0, 11, -5, 9, 5, 9, 7, -7, -17 ]
], hecke_fields := [
x^2 + 3*x - 5,
x^2 - 5,
x^2 + x - 5,
x^2 + 17*x + 61,
x^4 + 3*x^3 - 2*x^2 - 7*x + 1,
x^4 + 2*x^3 - 41*x^2 + 94*x - 52
], atkin_lehners := [
[ -1, 1 ],
[ -1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 25, 1 ],
[ 55, 1 ],
[ 15, 1 ],
[ 31, 1 ],
[ 109, 1 ],
[ 1087, 1 ]
], tamagawa_numbers := [
[ 25, 1 ],
[ 55, 1 ],
[ 15, 1 ],
[ 31, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 11, 3, 1, 1, 1 ], torsion_lower_bounds := [ 1, 11, 3, 1, 1, 1 ], l_ratios := [ 25, 5/11, 5/3, 0, 0, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1, 0, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 0, 0, 1 ], eigenvalues := [*
[
1,
0,
-a,
2,
2*a + 4,
a + 3,
2,
a - 3,
2,
-8,
-a - 5,
2
],
[
1,
a,
-1/2*a + 5/2,
-3,
-3/2*a + 3/2,
3,
1/2*a - 1/2,
-a + 2,
1/2*a - 11/2,
-1/2*a + 9/2,
-3*a,
3/2*a + 9/2
],
[
1,
a,
0,
2,
a - 1,
-2*a - 2,
-2*a + 2,
2,
-2*a + 2,
-a + 7,
3*a + 5,
a - 8
],
[
1,
-1,
1/3*a + 1/3,
-2/3*a - 23/3,
1/3*a + 1/3,
-4/3*a - 37/3,
5/3*a + 35/3,
4/3*a + 37/3,
5/3*a + 38/3,
-7/3*a - 61/3,
-4/3*a - 37/3,
1/3*a + 1/3
],
[
-1,
a,
1/2*a^3 - 3*a - 1/2,
-a^3 - a^2 + 3*a,
1/2*a^3 + 2*a^2 - 11/2,
a^3 + a^2 - 5*a,
-1/2*a^3 - 2*a^2 - a + 1/2,
-2*a^3 - 5*a^2 + 5*a + 5,
3/2*a^3 + 5*a^2 - 17/2,
-3/2*a^3 - 4*a^2 + 2*a + 1/2,
a^3 + 3*a^2 + 2*a - 5,
-1/2*a^3 + 3*a^2 + 7*a - 13/2
],
[
-1,
-2/13*a^3 - 11/13*a^2 + 50/13*a,
-1/13*a^3 - 11/26*a^2 + 37/26*a,
3/13*a^3 + 10/13*a^2 - 114/13*a + 10,
-1/26*a^3 + 1/26*a^2 + 32/13*a - 2,
-1/2*a^3 - 2*a^2 + 33/2*a - 17,
5/26*a^3 + 21/26*a^2 - 69/13*a + 8,
-19/26*a^3 - 36/13*a^2 + 631/26*a - 25,
-9/26*a^3 - 43/26*a^2 + 119/13*a - 4,
15/26*a^3 + 63/26*a^2 - 233/13*a + 18,
9/26*a^3 + 28/13*a^2 - 173/26*a - 5,
15/26*a^3 + 63/26*a^2 - 233/13*a + 12
]
*], q_expansions := [*
q + q^2 + q^4 - a*q^5 + 2*q^7 + q^8 - 3*q^9 - a*q^10 + (2*a + 4)*q^11 + (a + 3)*q^13 + 2*q^14 + q^16 + 2*q^17 - 3*q^18 + (a - 3)*q^19 - a*q^20 + (2*a + 4)*q^22 + 2*q^23 - 3*a*q^25 + (a + 3)*q^26 + 2*q^28 - 8*q^29 + (-a - 5)*q^31 + q^32 + 2*q^34 - 2*a*q^35 - 3*q^36 + 2*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-1/2*a + 5/2)*q^5 + a*q^6 - 3*q^7 + q^8 + 2*q^9 + (-1/2*a + 5/2)*q^10 + (-3/2*a + 3/2)*q^11 + a*q^12 + 3*q^13 - 3*q^14 + (5/2*a - 5/2)*q^15 + q^16 + (1/2*a - 1/2)*q^17 + 2*q^18 + (-a + 2)*q^19 + (-1/2*a + 5/2)*q^20 - 3*a*q^21 + (-3/2*a + 3/2)*q^22 + (1/2*a - 11/2)*q^23 + a*q^24 + (-5/2*a + 5/2)*q^25 + 3*q^26 - a*q^27 - 3*q^28 + (-1/2*a + 9/2)*q^29 + (5/2*a - 5/2)*q^30 - 3*a*q^31 + q^32 + (3/2*a - 15/2)*q^33 + (1/2*a - 1/2)*q^34 + (3/2*a - 15/2)*q^35 + 2*q^36 + (3/2*a + 9/2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + a*q^6 + 2*q^7 + q^8 + (-a + 2)*q^9 + (a - 1)*q^11 + a*q^12 + (-2*a - 2)*q^13 + 2*q^14 + q^16 + (-2*a + 2)*q^17 + (-a + 2)*q^18 + 2*q^19 + 2*a*q^21 + (a - 1)*q^22 + (-2*a + 2)*q^23 + a*q^24 - 5*q^25 + (-2*a - 2)*q^26 - 5*q^27 + 2*q^28 + (-a + 7)*q^29 + (3*a + 5)*q^31 + q^32 + (-2*a + 5)*q^33 + (-2*a + 2)*q^34 + (-a + 2)*q^36 + (a - 8)*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + (1/3*a + 1/3)*q^5 - q^6 + (-2/3*a - 23/3)*q^7 + q^8 - 2*q^9 + (1/3*a + 1/3)*q^10 + (1/3*a + 1/3)*q^11 - q^12 + (-4/3*a - 37/3)*q^13 + (-2/3*a - 23/3)*q^14 + (-1/3*a - 1/3)*q^15 + q^16 + (5/3*a + 35/3)*q^17 - 2*q^18 + (4/3*a + 37/3)*q^19 + (1/3*a + 1/3)*q^20 + (2/3*a + 23/3)*q^21 + (1/3*a + 1/3)*q^22 + (5/3*a + 38/3)*q^23 - q^24 + (-5/3*a - 35/3)*q^25 + (-4/3*a - 37/3)*q^26 + 5*q^27 + (-2/3*a - 23/3)*q^28 + (-7/3*a - 61/3)*q^29 + (-1/3*a - 1/3)*q^30 + (-4/3*a - 37/3)*q^31 + q^32 + (-1/3*a - 1/3)*q^33 + (5/3*a + 35/3)*q^34 + (a + 11)*q^35 - 2*q^36 + (1/3*a + 1/3)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (1/2*a^3 - 3*a - 1/2)*q^5 - a*q^6 + (-a^3 - a^2 + 3*a)*q^7 - q^8 + (a^2 - 3)*q^9 + (-1/2*a^3 + 3*a + 1/2)*q^10 + (1/2*a^3 + 2*a^2 - 11/2)*q^11 + a*q^12 + (a^3 + a^2 - 5*a)*q^13 + (a^3 + a^2 - 3*a)*q^14 + (-3/2*a^3 - 2*a^2 + 3*a - 1/2)*q^15 + q^16 + (-1/2*a^3 - 2*a^2 - a + 1/2)*q^17 + (-a^2 + 3)*q^18 + (-2*a^3 - 5*a^2 + 5*a + 5)*q^19 + (1/2*a^3 - 3*a - 1/2)*q^20 + (2*a^3 + a^2 - 7*a + 1)*q^21 + (-1/2*a^3 - 2*a^2 + 11/2)*q^22 + (3/2*a^3 + 5*a^2 - 17/2)*q^23 - a*q^24 + (1/2*a^3 + 3*a^2 + 2*a - 9/2)*q^25 + (-a^3 - a^2 + 5*a)*q^26 + (a^3 - 6*a)*q^27 + (-a^3 - a^2 + 3*a)*q^28 + (-3/2*a^3 - 4*a^2 + 2*a + 1/2)*q^29 + (3/2*a^3 + 2*a^2 - 3*a + 1/2)*q^30 + (a^3 + 3*a^2 + 2*a - 5)*q^31 - q^32 + (1/2*a^3 + a^2 - 2*a - 1/2)*q^33 + (1/2*a^3 + 2*a^2 + a - 1/2)*q^34 + (1/2*a^3 + a - 1/2)*q^35 + (a^2 - 3)*q^36 + (-1/2*a^3 + 3*a^2 + 7*a - 13/2)*q^37 + O(q^38),
q - q^2 + (-2/13*a^3 - 11/13*a^2 + 50/13*a)*q^3 + q^4 + (-1/13*a^3 - 11/26*a^2 + 37/26*a)*q^5 + (2/13*a^3 + 11/13*a^2 - 50/13*a)*q^6 + (3/13*a^3 + 10/13*a^2 - 114/13*a + 10)*q^7 - q^8 + (-2/13*a^3 - 11/13*a^2 + 50/13*a + 1)*q^9 + (1/13*a^3 + 11/26*a^2 - 37/26*a)*q^10 + (-1/26*a^3 + 1/26*a^2 + 32/13*a - 2)*q^11 + (-2/13*a^3 - 11/13*a^2 + 50/13*a)*q^12 + (-1/2*a^3 - 2*a^2 + 33/2*a - 17)*q^13 + (-3/13*a^3 - 10/13*a^2 + 114/13*a - 10)*q^14 + (5/26*a^3 + 21/26*a^2 - 69/13*a + 6)*q^15 + q^16 + (5/26*a^3 + 21/26*a^2 - 69/13*a + 8)*q^17 + (2/13*a^3 + 11/13*a^2 - 50/13*a - 1)*q^18 + (-19/26*a^3 - 36/13*a^2 + 631/26*a - 25)*q^19 + (-1/13*a^3 - 11/26*a^2 + 37/26*a)*q^20 + (a^3 + 4*a^2 - 32*a + 32)*q^21 + (1/26*a^3 - 1/26*a^2 - 32/13*a + 2)*q^22 + (-9/26*a^3 - 43/26*a^2 + 119/13*a - 4)*q^23 + (2/13*a^3 + 11/13*a^2 - 50/13*a)*q^24 + (3/13*a^3 + 33/26*a^2 - 163/26*a)*q^25 + (1/2*a^3 + 2*a^2 - 33/2*a + 17)*q^26 + (2/13*a^3 + 11/13*a^2 - 50/13*a + 4)*q^27 + (3/13*a^3 + 10/13*a^2 - 114/13*a + 10)*q^28 + (15/26*a^3 + 63/26*a^2 - 233/13*a + 18)*q^29 + (-5/26*a^3 - 21/26*a^2 + 69/13*a - 6)*q^30 + (9/26*a^3 + 28/13*a^2 - 173/26*a - 5)*q^31 - q^32 + (-23/26*a^3 - 107/26*a^2 + 333/13*a - 18)*q^33 + (-5/26*a^3 - 21/26*a^2 + 69/13*a - 8)*q^34 + (9/26*a^3 + 43/26*a^2 - 132/13*a + 10)*q^35 + (-2/13*a^3 - 11/13*a^2 + 50/13*a + 1)*q^36 + (15/26*a^3 + 63/26*a^2 - 233/13*a + 12)*q^37 + O(q^38)
*]> ;  // time = 100.91 seconds




J[395] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 395, 395, 395, 395, 395, 395, 395, 395, 79, 79 ], new_dimensions := [ 1, 1, 1, 3, 3, 3, 4, 11, 1, 5 ], dimensions := [ 1, 1, 1, 3, 3, 3, 4, 11, 2, 10 ], intersection_graph := [ 0, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 17, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 3, 3, 1, 1, 0, 1, 9, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 97, 3, 1, 17, 1, 9, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 17399, 1, 3, 1, 3, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 97, 1, 17399, 1, 0 ], ap_traces := [
[ -1, 0, 1, -4, 4, 6, 6, -4, 0, 6, 0, 10 ],
[ -1, 2, 1, 2, 4, -6, 0, 4, 8, -6, 8, 4 ],
[ -2, -1, 1, 3, -3, 4, -2, 0, 4, 0, 7, 3 ],
[ 0, 0, -3, -3, -6, -6, 6, -9, 6, -9, 3, -24 ],
[ 6, 1, 3, 3, 3, 0, 0, 4, 4, 0, -11, 15 ],
[ -2, -2, 3, -3, 2, -10, -12, -1, -12, 5, -5, -18 ],
[ 1, 2, 4, 3, -6, 8, 12, -5, -16, 1, -5, -2 ],
[ 0, -2, -11, 7, 6, 14, -16, 11, -6, 5, 15, 38 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^3 - 3*x + 1,
x^3 - 8*x^2 + 48,
x^3 + 2*x^2 - x - 1,
x^4 - x^3 - 7*x^2 + 6*x - 1,
x^11 - 21*x^9 + x^8 + 159*x^7 - 18*x^6 - 511*x^5 + 105*x^4 + 604*x^3 - 208*x^2 - 128*x + 48
], atkin_lehners := [
[ -1, 1 ],
[ -1, 1 ],
[ -1, 1 ],
[ 1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 1 ],
[ 5, 1 ],
[ 3, 1 ],
[ 3, 1 ],
[ 97, 1 ],
[ 1, 1 ],
[ 52197, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 3, 1 ],
[ 5, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 97, 1 ],
[ 1, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 1, 1, 5, 1, 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 5, 1, 1, 1, 1, 3 ], l_ratios := [ 1, 3, 1/5, 0, 3, 0, 1, 1/3 ], analytic_sha_upper_bounds := [ 1, 1, 1, 0, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 0, 1, 0, 1, 1 ], eigenvalues := [*
[ -1, 0, 1, -4, 4, 6, 6, -4, 0, 6, 0, 10 ],
[ -1, 2, 1, 2, 4, -6, 0, 4, 8, -6, 8, 4 ],
[ -2, -1, 1, 3, -3, 4, -2, 0, 4, 0, 7, 3 ],
[
a,
-a^2 - a + 2,
-1,
2*a^2 + a - 5,
a^2 - a - 4,
-a^2 - a,
-a + 2,
-2*a^2 + a + 1,
-2*a^2 - a + 6,
-a^2 + a - 1,
-3*a^2 - a + 7,
2*a^2 + a - 12
],
[
2,
1/2*a - 1,
1,
-1/4*a^2 + 1/2*a + 5,
1/4*a^2 - 2*a + 1,
0,
1/4*a^2 - 2*a,
-1/2*a^2 + 3*a + 4,
1/2*a^2 - 2*a - 4,
0,
-1/2*a^2 + 3*a - 1,
1/4*a^2 - 1/2*a + 1
],
[
a,
a^2 + a - 2,
1,
-2*a^2 - 3*a + 1,
-a^2 - a + 2,
-a^2 - a - 2,
2*a^2 + 3*a - 6,
4*a^2 + 5*a - 5,
2*a^2 + 3*a - 6,
-a^2 - 7*a - 1,
-5*a^2 - 5*a + 5,
4*a^2 + 9*a - 8
],
[
a,
2*a^3 - a^2 - 15*a + 6,
1,
-a + 1,
2*a^3 - a^2 - 15*a + 4,
-a^2 - a + 6,
-3*a^3 + 2*a^2 + 22*a - 7,
-2*a^3 + 15*a - 3,
-a^3 + 8*a - 5,
a^3 - a^2 - 4*a + 4,
-a^3 + a^2 + 8*a - 6,
-5*a^3 + 4*a^2 + 34*a - 19
],
[
a,
1/32*a^10 + 1/16*a^9 - 25/32*a^8 - 33/32*a^7 + 221/32*a^6 + 11/2*a^5 - 823/32*a^4 - 317/32*a^3 + 569/16*a^2 + 25/8*a - 35/4,
-1,
7/32*a^10 + 1/16*a^9 - 143/32*a^8 - 43/32*a^7 + 1055/32*a^6 + 75/8*a^5 - 3305/32*a^4 - 727/32*a^3 + 1889/16*a^2 + 71/8*a - 91/4,
-1/16*a^10 + 17/16*a^8 - 1/16*a^7 - 99/16*a^6 + 7/8*a^5 + 243/16*a^4 - 57/16*a^3 - 35/2*a^2 + 17/4*a + 6,
1/8*a^10 + 1/4*a^9 - 21/8*a^8 - 33/8*a^7 + 157/8*a^6 + 45/2*a^5 - 491/8*a^4 - 353/8*a^3 + 277/4*a^2 + 39/2*a - 13,
1/8*a^10 + 1/8*a^9 - 19/8*a^8 - 2*a^7 + 16*a^6 + 79/8*a^5 - 363/8*a^4 - 14*a^3 + 381/8*a^2 - 5/2*a - 15/2,
1/16*a^10 + 1/8*a^9 - 25/16*a^8 - 33/16*a^7 + 221/16*a^6 + 11*a^5 - 807/16*a^4 - 301/16*a^3 + 513/8*a^2 - 3/4*a - 23/2,
-1/8*a^10 + 17/8*a^8 - 1/8*a^7 - 99/8*a^6 + 7/4*a^5 + 235/8*a^4 - 57/8*a^3 - 28*a^2 + 17/2*a + 6,
-1/8*a^10 - 1/4*a^9 + 21/8*a^8 + 33/8*a^7 - 157/8*a^6 - 45/2*a^5 + 491/8*a^4 + 361/8*a^3 - 277/4*a^2 - 53/2*a + 15,
3/16*a^10 + 1/8*a^9 - 67/16*a^8 - 31/16*a^7 + 531/16*a^6 + 39/4*a^5 - 1749/16*a^4 - 259/16*a^3 + 1017/8*a^2 - 1/4*a - 41/2,
-1/32*a^10 + 1/16*a^9 + 25/32*a^8 - 19/32*a^7 - 217/32*a^6 - 1/8*a^5 + 751/32*a^4 + 289/32*a^3 - 415/16*a^2 - 49/8*a + 29/4
]
*], q_expansions := [*
q - q^2 - q^4 + q^5 - 4*q^7 + 3*q^8 - 3*q^9 - q^10 + 4*q^11 + 6*q^13 + 4*q^14 - q^16 + 6*q^17 + 3*q^18 - 4*q^19 - q^20 - 4*q^22 + q^25 - 6*q^26 + 4*q^28 + 6*q^29 - 5*q^32 - 6*q^34 - 4*q^35 + 3*q^36 + 10*q^37 + O(q^38),
q - q^2 + 2*q^3 - q^4 + q^5 - 2*q^6 + 2*q^7 + 3*q^8 + q^9 - q^10 + 4*q^11 - 2*q^12 - 6*q^13 - 2*q^14 + 2*q^15 - q^16 - q^18 + 4*q^19 - q^20 + 4*q^21 - 4*q^22 + 8*q^23 + 6*q^24 + q^25 + 6*q^26 - 4*q^27 - 2*q^28 - 6*q^29 - 2*q^30 + 8*q^31 - 5*q^32 + 8*q^33 + 2*q^35 - q^36 + 4*q^37 + O(q^38),
q - 2*q^2 - q^3 + 2*q^4 + q^5 + 2*q^6 + 3*q^7 - 2*q^9 - 2*q^10 - 3*q^11 - 2*q^12 + 4*q^13 - 6*q^14 - q^15 - 4*q^16 - 2*q^17 + 4*q^18 + 2*q^20 - 3*q^21 + 6*q^22 + 4*q^23 + q^25 - 8*q^26 + 5*q^27 + 6*q^28 + 2*q^30 + 7*q^31 + 8*q^32 + 3*q^33 + 4*q^34 + 3*q^35 - 4*q^36 + 3*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 2)*q^3 + (a^2 - 2)*q^4 - q^5 + (-a^2 - a + 1)*q^6 + (2*a^2 + a - 5)*q^7 + (-a - 1)*q^8 + (a - 1)*q^9 - a*q^10 + (a^2 - a - 4)*q^11 + (a^2 - 3)*q^12 + (-a^2 - a)*q^13 + (a^2 + a - 2)*q^14 + (a^2 + a - 2)*q^15 + (-3*a^2 - a + 4)*q^16 + (-a + 2)*q^17 + (a^2 - a)*q^18 + (-2*a^2 + a + 1)*q^19 + (-a^2 + 2)*q^20 + (2*a^2 - 7)*q^21 + (-a^2 - a - 1)*q^22 + (-2*a^2 - a + 6)*q^23 + (2*a^2 + 2*a - 3)*q^24 + q^25 + (-a^2 - 3*a + 1)*q^26 + (3*a^2 + 3*a - 7)*q^27 + (-3*a^2 - a + 9)*q^28 + (-a^2 + a - 1)*q^29 + (a^2 + a - 1)*q^30 + (-3*a^2 - a + 7)*q^31 + (-a^2 - 3*a + 5)*q^32 + (4*a^2 + 3*a - 8)*q^33 + (-a^2 + 2*a)*q^34 + (-2*a^2 - a + 5)*q^35 + (-a^2 + a + 1)*q^36 + (2*a^2 + a - 12)*q^37 + O(q^38),
q + 2*q^2 + (1/2*a - 1)*q^3 + 2*q^4 + q^5 + (a - 2)*q^6 + (-1/4*a^2 + 1/2*a + 5)*q^7 + (1/4*a^2 - a - 2)*q^9 + 2*q^10 + (1/4*a^2 - 2*a + 1)*q^11 + (a - 2)*q^12 + (-1/2*a^2 + a + 10)*q^14 + (1/2*a - 1)*q^15 - 4*q^16 + (1/4*a^2 - 2*a)*q^17 + (1/2*a^2 - 2*a - 4)*q^18 + (-1/2*a^2 + 3*a + 4)*q^19 + 2*q^20 + (-1/2*a^2 + 2*a + 1)*q^21 + (1/2*a^2 - 4*a + 2)*q^22 + (1/2*a^2 - 2*a - 4)*q^23 + q^25 + (1/4*a^2 - 3/2*a - 1)*q^27 + (-1/2*a^2 + a + 10)*q^28 + (a - 2)*q^30 + (-1/2*a^2 + 3*a - 1)*q^31 - 8*q^32 + (-1/4*a^2 + 5/2*a - 7)*q^33 + (1/2*a^2 - 4*a)*q^34 + (-1/4*a^2 + 1/2*a + 5)*q^35 + (1/2*a^2 - 2*a - 4)*q^36 + (1/4*a^2 - 1/2*a + 1)*q^37 + O(q^38),
q + a*q^2 + (a^2 + a - 2)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^2 - a + 1)*q^6 + (-2*a^2 - 3*a + 1)*q^7 + (-2*a^2 - 3*a + 1)*q^8 + (-2*a^2 - 3*a + 1)*q^9 + a*q^10 + (-a^2 - a + 2)*q^11 + (-a^2 - 2*a + 3)*q^12 + (-a^2 - a - 2)*q^13 + (a^2 - a - 2)*q^14 + (a^2 + a - 2)*q^15 + (-a^2 - a + 2)*q^16 + (2*a^2 + 3*a - 6)*q^17 + (a^2 - a - 2)*q^18 + (4*a^2 + 5*a - 5)*q^19 + (a^2 - 2)*q^20 + (2*a^2 + 4*a - 3)*q^21 + (a^2 + a - 1)*q^22 + (2*a^2 + 3*a - 6)*q^23 + (2*a^2 + 4*a - 3)*q^24 + q^25 + (a^2 - 3*a - 1)*q^26 + (-a^2 + a + 3)*q^27 + (a^2 + 5*a - 1)*q^28 + (-a^2 - 7*a - 1)*q^29 + (-a^2 - a + 1)*q^30 + (-5*a^2 - 5*a + 5)*q^31 + (5*a^2 + 7*a - 3)*q^32 + (2*a^2 + 3*a - 4)*q^33 + (-a^2 - 4*a + 2)*q^34 + (-2*a^2 - 3*a + 1)*q^35 + (a^2 + 5*a - 1)*q^36 + (4*a^2 + 9*a - 8)*q^37 + O(q^38),
q + a*q^2 + (2*a^3 - a^2 - 15*a + 6)*q^3 + (a^2 - 2)*q^4 + q^5 + (a^3 - a^2 - 6*a + 2)*q^6 + (-a + 1)*q^7 + (a^3 - 4*a)*q^8 + (-a^3 + 6*a + 2)*q^9 + a*q^10 + (2*a^3 - a^2 - 15*a + 4)*q^11 + (-4*a^3 + 3*a^2 + 26*a - 11)*q^12 + (-a^2 - a + 6)*q^13 + (-a^2 + a)*q^14 + (2*a^3 - a^2 - 15*a + 6)*q^15 + (a^3 + a^2 - 6*a + 5)*q^16 + (-3*a^3 + 2*a^2 + 22*a - 7)*q^17 + (-a^3 - a^2 + 8*a - 1)*q^18 + (-2*a^3 + 15*a - 3)*q^19 + (a^2 - 2)*q^20 + (a^3 - 9*a + 4)*q^21 + (a^3 - a^2 - 8*a + 2)*q^22 + (-a^3 + 8*a - 5)*q^23 + (-3*a^3 + 25*a - 8)*q^24 + q^25 + (-a^3 - a^2 + 6*a)*q^26 + (3*a^3 - a^2 - 22*a + 6)*q^27 + (-a^3 + a^2 + 2*a - 2)*q^28 + (a^3 - a^2 - 4*a + 4)*q^29 + (a^3 - a^2 - 6*a + 2)*q^30 + (-a^3 + a^2 + 8*a - 6)*q^31 + (a^2 + 7*a + 1)*q^32 + (-5*a^3 + 2*a^2 + 36*a - 7)*q^33 + (-a^3 + a^2 + 11*a - 3)*q^34 + (-a + 1)*q^35 + (a^2 - 7*a - 5)*q^36 + (-5*a^3 + 4*a^2 + 34*a - 19)*q^37 + O(q^38),
q + a*q^2 + (1/32*a^10 + 1/16*a^9 - 25/32*a^8 - 33/32*a^7 + 221/32*a^6 + 11/2*a^5 - 823/32*a^4 - 317/32*a^3 + 569/16*a^2 + 25/8*a - 35/4)*q^3 + (a^2 - 2)*q^4 - q^5 + (1/16*a^10 - 1/8*a^9 - 17/16*a^8 + 31/16*a^7 + 97/16*a^6 - 39/4*a^5 - 211/16*a^4 + 267/16*a^3 + 77/8*a^2 - 19/4*a - 3/2)*q^6 + (7/32*a^10 + 1/16*a^9 - 143/32*a^8 - 43/32*a^7 + 1055/32*a^6 + 75/8*a^5 - 3305/32*a^4 - 727/32*a^3 + 1889/16*a^2 + 71/8*a - 91/4)*q^7 + (a^3 - 4*a)*q^8 + (-1/4*a^10 - 1/8*a^9 + 21/4*a^8 + 19/8*a^7 - 315/8*a^6 - 119/8*a^5 + 123*a^4 + 257/8*a^3 - 1081/8*a^2 - 17/2*a + 53/2)*q^9 - a*q^10 + (-1/16*a^10 + 17/16*a^8 - 1/16*a^7 - 99/16*a^6 + 7/8*a^5 + 243/16*a^4 - 57/16*a^3 - 35/2*a^2 + 17/4*a + 6)*q^11 + (-3/16*a^10 + 1/8*a^9 + 55/16*a^8 - 29/16*a^7 - 359/16*a^6 + 31/4*a^5 + 985/16*a^4 - 133/16*a^3 - 503/8*a^2 + 1/4*a + 29/2)*q^12 + (1/8*a^10 + 1/4*a^9 - 21/8*a^8 - 33/8*a^7 + 157/8*a^6 + 45/2*a^5 - 491/8*a^4 - 353/8*a^3 + 277/4*a^2 + 39/2*a - 13)*q^13 + (1/16*a^10 + 1/8*a^9 - 25/16*a^8 - 29/16*a^7 + 213/16*a^6 + 17/2*a^5 - 731/16*a^4 - 225/16*a^3 + 435/8*a^2 + 21/4*a - 21/2)*q^14 + (-1/32*a^10 - 1/16*a^9 + 25/32*a^8 + 33/32*a^7 - 221/32*a^6 - 11/2*a^5 + 823/32*a^4 + 317/32*a^3 - 569/16*a^2 - 25/8*a + 35/4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/8*a^10 + 1/8*a^9 - 19/8*a^8 - 2*a^7 + 16*a^6 + 79/8*a^5 - 363/8*a^4 - 14*a^3 + 381/8*a^2 - 5/2*a - 15/2)*q^17 + (-1/8*a^10 + 21/8*a^8 + 3/8*a^7 - 155/8*a^6 - 19/4*a^5 + 467/8*a^4 + 127/8*a^3 - 121/2*a^2 - 11/2*a + 12)*q^18 + (1/16*a^10 + 1/8*a^9 - 25/16*a^8 - 33/16*a^7 + 221/16*a^6 + 11*a^5 - 807/16*a^4 - 301/16*a^3 + 513/8*a^2 - 3/4*a - 23/2)*q^19 + (-a^2 + 2)*q^20 + (-3/8*a^10 - 1/4*a^9 + 63/8*a^8 + 35/8*a^7 - 475/8*a^6 - 25*a^5 + 1501/8*a^4 + 387/8*a^3 - 843/4*a^2 - 21/2*a + 44)*q^21 + (-1/4*a^9 + 15/4*a^7 - 1/4*a^6 - 67/4*a^5 + 3*a^4 + 81/4*a^3 - 35/4*a^2 - 2*a + 3)*q^22 + (-1/8*a^10 + 17/8*a^8 - 1/8*a^7 - 99/8*a^6 + 7/4*a^5 + 235/8*a^4 - 57/8*a^3 - 28*a^2 + 17/2*a + 6)*q^23 + (-1/4*a^9 + 1/2*a^8 + 7/2*a^7 - 31/4*a^6 - 59/4*a^5 + 151/4*a^4 + 17*a^3 - 58*a^2 + 12)*q^24 + q^25 + (1/4*a^10 - 17/4*a^8 - 1/4*a^7 + 99/4*a^6 + 5/2*a^5 - 229/4*a^4 - 25/4*a^3 + 91/2*a^2 + 3*a - 6)*q^26 + (9/32*a^10 - 1/16*a^9 - 185/32*a^8 + 27/32*a^7 + 1377/32*a^6 - 29/8*a^5 - 4383/32*a^4 + 191/32*a^3 + 2583/16*a^2 - 55/8*a - 125/4)*q^27 + (-5/16*a^10 - 3/8*a^9 + 113/16*a^8 + 97/16*a^7 - 901/16*a^6 - 65/2*a^5 + 2975/16*a^4 + 993/16*a^3 - 1743/8*a^2 - 81/4*a + 85/2)*q^28 + (-1/8*a^10 - 1/4*a^9 + 21/8*a^8 + 33/8*a^7 - 157/8*a^6 - 45/2*a^5 + 491/8*a^4 + 361/8*a^3 - 277/4*a^2 - 53/2*a + 15)*q^29 + (-1/16*a^10 + 1/8*a^9 + 17/16*a^8 - 31/16*a^7 - 97/16*a^6 + 39/4*a^5 + 211/16*a^4 - 267/16*a^3 - 77/8*a^2 + 19/4*a + 3/2)*q^30 + (3/16*a^10 + 1/8*a^9 - 67/16*a^8 - 31/16*a^7 + 531/16*a^6 + 39/4*a^5 - 1749/16*a^4 - 259/16*a^3 + 1017/8*a^2 - 1/4*a - 41/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (11/32*a^10 + 1/16*a^9 - 235/32*a^8 - 39/32*a^7 + 1787/32*a^6 + 67/8*a^5 - 5645/32*a^4 - 667/32*a^3 + 3161/16*a^2 + 27/8*a - 171/4)*q^33 + (1/8*a^10 + 1/4*a^9 - 17/8*a^8 - 31/8*a^7 + 97/8*a^6 + 37/2*a^5 - 217/8*a^4 - 223/8*a^3 + 47/2*a^2 + 17/2*a - 6)*q^34 + (-7/32*a^10 - 1/16*a^9 + 143/32*a^8 + 43/32*a^7 - 1055/32*a^6 - 75/8*a^5 + 3305/32*a^4 + 727/32*a^3 - 1889/16*a^2 - 71/8*a + 91/4)*q^35 + (1/2*a^10 + 1/4*a^9 - 10*a^8 - 17/4*a^7 + 287/4*a^6 + 97/4*a^5 - 217*a^4 - 197/4*a^3 + 955/4*a^2 + 13*a - 47)*q^36 + (-1/32*a^10 + 1/16*a^9 + 25/32*a^8 - 19/32*a^7 - 217/32*a^6 - 1/8*a^5 + 751/32*a^4 + 289/32*a^3 - 415/16*a^2 - 49/8*a + 29/4)*q^37 + O(q^38)
*]> ;  // time = 69.391 seconds




J[397] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 397, 397, 397, 397, 397 ], new_dimensions := [ 2, 2, 5, 10, 13 ], dimensions := [ 2, 2, 5, 10, 13 ], intersection_graph := [ 0, 1, 1, 1, 31, 1, 0, 1, 23, 1, 1, 1, 0, 761, 1, 1, 23, 761, 0, 1, 31, 1, 1, 1, 0 ], ap_traces := [
[ -2, 0, -4, 6, 0, -8, -8, 8, 0, -14, 0, -6 ],
[ 2, 4, 0, -2, 4, 4, -4, 0, 8, -6, -12, -2 ],
[ 0, 5, -2, 1, 6, 2, 20, -9, 1, 7, 20, -3 ],
[ 7, 0, 7, 10, 15, -7, -3, 16, 11, 13, -16, 4 ],
[ -7, -11, -5, -17, -31, 1, -3, -17, -36, -2, 0, -5 ]
], hecke_fields := [
x^2 + 2*x - 1,
x^2 - 2*x - 1,
x^5 - 6*x^3 + x^2 + 7*x - 1,
x^10 - 7*x^9 + 8*x^8 + 43*x^7 - 105*x^6 - 26*x^5 + 234*x^4 - 119*x^3 - 82*x^2 + 47*x + 3,
x^13 + 7*x^12 + 5*x^11 - 63*x^10 - 124*x^9 + 157*x^8 + 526*x^7 + 2*x^6 - 794*x^5 - 328*x^4 + 408*x^3 + 203*x^2 - 66*x - 23
], atkin_lehners := [
[ 1 ],
[ -1 ],
[ -1 ],
[ -1 ],
[ 1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 11 ],
[ 3 ],
[ 1 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 11 ],
[ 3 ],
[ 1 ]
], torsion_upper_bounds := [ 1, 1, 11, 3, 1 ], torsion_lower_bounds := [ 1, 1, 11, 3, 1 ], l_ratios := [ 0, 1, 1/11, 1/3, 0 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 0 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 0 ], eigenvalues := [*
[
a,
0,
-2,
a + 4,
-2*a - 2,
-2*a - 6,
2*a - 2,
-2*a + 2,
-2*a - 2,
-7,
2*a + 2,
2*a - 1
],
[
a,
-a + 3,
a - 1,
-2*a + 1,
a + 1,
3*a - 1,
-3*a + 1,
-2*a + 2,
4,
-3,
3*a - 9,
-4*a + 3
],
[
a,
a + 1,
-a^3 + 4*a - 1,
-a^3 - a^2 + 3*a + 2,
a^4 + a^3 - 5*a^2 - 4*a + 5,
a^4 - 6*a^2 + a + 6,
a^4 + 2*a^3 - 4*a^2 - 7*a + 6,
2*a^3 + a^2 - 6*a - 3,
-a^4 - 3*a^3 + 3*a^2 + 9*a,
-a^4 - a^3 + 4*a^2 + a,
2*a^4 - 9*a^2 + 3*a + 8,
-a^4 - 2*a^3 + 5*a^2 + 4*a - 5
],
[
a,
23/11*a^9 - 107/11*a^8 - 72/11*a^7 + 841/11*a^6 - 38*a^5 - 1753/11*a^4 + 1294/11*a^3 + 699/11*a^2 - 37*a - 52/11,
-57/11*a^9 + 280/11*a^8 + 122/11*a^7 - 2166/11*a^6 + 135*a^5 + 4342/11*a^4 - 4161/11*a^3 - 1409/11*a^2 + 125*a + 60/11,
a^9 - 5*a^8 - 2*a^7 + 39*a^6 - 27*a^5 - 81*a^4 + 75*a^3 + 35*a^2 - 26*a - 4,
35/11*a^9 - 170/11*a^8 - 89/11*a^7 + 1330/11*a^6 - 72*a^5 - 2736/11*a^4 + 2269/11*a^3 + 1002/11*a^2 - 63*a - 27/11,
5/11*a^9 - 29/11*a^8 + 3/11*a^7 + 223/11*a^6 - 22*a^5 - 438/11*a^4 + 607/11*a^3 + 118/11*a^2 - 20*a + 4/11,
-38/11*a^9 + 183/11*a^8 + 96/11*a^7 - 1422/11*a^6 + 79*a^5 + 2880/11*a^4 - 2510/11*a^3 - 976/11*a^2 + 75*a + 18/11,
-36/11*a^9 + 178/11*a^8 + 73/11*a^7 - 1368/11*a^6 + 87*a^5 + 2696/11*a^4 - 2628/11*a^3 - 788/11*a^2 + 77*a + 46/11,
16/11*a^9 - 84/11*a^8 - 8/11*a^7 + 630/11*a^6 - 58*a^5 - 1164/11*a^4 + 1685/11*a^3 + 195/11*a^2 - 58*a + 48/11,
74/11*a^9 - 361/11*a^8 - 169/11*a^7 + 2812/11*a^6 - 169*a^5 - 5763/11*a^4 + 5325/11*a^3 + 2193/11*a^2 - 169*a - 174/11,
-81/11*a^9 + 395/11*a^8 + 189/11*a^7 - 3067/11*a^6 + 179*a^5 + 6209/11*a^4 - 5528/11*a^3 - 2136/11*a^2 + 151*a + 76/11,
-12/11*a^9 + 63/11*a^8 + 6/11*a^7 - 478/11*a^6 + 44*a^5 + 939/11*a^4 - 1294/11*a^3 - 369/11*a^2 + 45*a + 85/11
],
[
a,
-356/1325*a^12 - 372/265*a^11 + 358/265*a^10 + 20873/1325*a^9 + 7163/1325*a^8 - 83228/1325*a^7 - 10893/265*a^6 + 141118/1325*a^5 + 90693/1325*a^4 - 99828/1325*a^3 - 42657/1325*a^2 + 25211/1325*a + 3304/1325,
-181/265*a^12 - 207/53*a^11 + 65/53*a^10 + 10433/265*a^9 + 9023/265*a^8 - 35473/265*a^7 - 8923/53*a^6 + 45208/265*a^5 + 67048/265*a^4 - 17133/265*a^3 - 29932/265*a^2 + 2046/265*a + 2719/265,
804/1325*a^12 + 858/265*a^11 - 612/265*a^10 - 44907/1325*a^9 - 22817/1325*a^8 + 163102/1325*a^7 + 26727/265*a^6 - 238237/1325*a^5 - 200387/1325*a^4 + 129027/1325*a^3 + 81063/1325*a^2 - 26224/1325*a - 8236/1325,
1136/1325*a^12 + 1327/265*a^11 - 398/265*a^10 - 68988/1325*a^9 - 59853/1325*a^8 + 247493/1325*a^7 + 60423/265*a^6 - 357708/1325*a^5 - 470183/1325*a^4 + 202518/1325*a^3 + 225817/1325*a^2 - 51641/1325*a - 23674/1325,
-496/1325*a^12 - 557/265*a^11 + 338/265*a^10 + 30868/1325*a^9 + 19508/1325*a^8 - 121273/1325*a^7 - 23228/265*a^6 + 205338/1325*a^5 + 198013/1325*a^4 - 157398/1325*a^3 - 105837/1325*a^2 + 52276/1325*a + 8489/1325,
-1552/1325*a^12 - 1854/265*a^11 + 331/265*a^10 + 95091/1325*a^9 + 95021/1325*a^8 - 324501/1325*a^7 - 92351/265*a^6 + 401231/1325*a^5 + 695456/1325*a^4 - 133001/1325*a^3 - 308044/1325*a^2 + 16712/1325*a + 25793/1325,
-487/1325*a^12 - 494/265*a^11 + 521/265*a^10 + 26771/1325*a^9 + 4376/1325*a^8 - 108956/1325*a^7 - 9486/265*a^6 + 205336/1325*a^5 + 92761/1325*a^4 - 175181/1325*a^3 - 60814/1325*a^2 + 52022/1325*a + 4758/1325,
-3/1325*a^12 - 21/265*a^11 - 61/265*a^10 + 924/1325*a^9 + 3719/1325*a^8 + 311/1325*a^7 - 2019/265*a^6 - 16341/1325*a^5 - 4666/1325*a^4 + 33311/1325*a^3 + 25184/1325*a^2 - 16257/1325*a - 8473/1325,
3082/1325*a^12 + 3554/265*a^11 - 1286/265*a^10 - 186056/1325*a^9 - 155261/1325*a^8 + 666741/1325*a^7 + 161416/265*a^6 - 936871/1325*a^5 - 1277171/1325*a^4 + 464791/1325*a^3 + 625429/1325*a^2 - 82417/1325*a - 62488/1325,
4713/1325*a^12 + 5431/265*a^11 - 1954/265*a^10 - 282954/1325*a^9 - 233824/1325*a^8 + 1011319/1325*a^7 + 240949/265*a^6 - 1428514/1325*a^5 - 1882439/1325*a^4 + 745269/1325*a^3 + 897461/1325*a^2 - 170553/1325*a - 85992/1325,
-254/265*a^12 - 294/53*a^11 + 100/53*a^10 + 15162/265*a^9 + 12157/265*a^8 - 54582/265*a^7 - 12260/53*a^6 + 80322/265*a^5 + 94577/265*a^4 - 45202/265*a^3 - 44023/265*a^2 + 9259/265*a + 3331/265
]
*], q_expansions := [*
q + a*q^2 + (-2*a - 1)*q^4 - 2*q^5 + (a + 4)*q^7 + (a - 2)*q^8 - 3*q^9 - 2*a*q^10 + (-2*a - 2)*q^11 + (-2*a - 6)*q^13 + (2*a + 1)*q^14 + 3*q^16 + (2*a - 2)*q^17 - 3*a*q^18 + (-2*a + 2)*q^19 + (4*a + 2)*q^20 + (2*a - 2)*q^22 + (-2*a - 2)*q^23 - q^25 + (-2*a - 2)*q^26 + (-5*a - 6)*q^28 - 7*q^29 + (2*a + 2)*q^31 + (a + 4)*q^32 + (-6*a + 2)*q^34 + (-2*a - 8)*q^35 + (6*a + 3)*q^36 + (2*a - 1)*q^37 + O(q^38),
q + a*q^2 + (-a + 3)*q^3 + (2*a - 1)*q^4 + (a - 1)*q^5 + (a - 1)*q^6 + (-2*a + 1)*q^7 + (a + 2)*q^8 + (-4*a + 7)*q^9 + (a + 1)*q^10 + (a + 1)*q^11 + (3*a - 5)*q^12 + (3*a - 1)*q^13 + (-3*a - 2)*q^14 + (2*a - 4)*q^15 + 3*q^16 + (-3*a + 1)*q^17 + (-a - 4)*q^18 + (-2*a + 2)*q^19 + (a + 3)*q^20 + (-3*a + 5)*q^21 + (3*a + 1)*q^22 + 4*q^23 + (-a + 5)*q^24 - 3*q^25 + (5*a + 3)*q^26 + (-8*a + 16)*q^27 + (-4*a - 5)*q^28 - 3*q^29 + 2*q^30 + (3*a - 9)*q^31 + (a - 4)*q^32 + 2*q^33 + (-5*a - 3)*q^34 + (-a - 3)*q^35 + (2*a - 15)*q^36 + (-4*a + 3)*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + (a^2 - 2)*q^4 + (-a^3 + 4*a - 1)*q^5 + (a^2 + a)*q^6 + (-a^3 - a^2 + 3*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (a^2 + 2*a - 2)*q^9 + (-a^4 + 4*a^2 - a)*q^10 + (a^4 + a^3 - 5*a^2 - 4*a + 5)*q^11 + (a^3 + a^2 - 2*a - 2)*q^12 + (a^4 - 6*a^2 + a + 6)*q^13 + (-a^4 - a^3 + 3*a^2 + 2*a)*q^14 + (-a^4 - a^3 + 4*a^2 + 3*a - 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 + 2*a^3 - 4*a^2 - 7*a + 6)*q^17 + (a^3 + 2*a^2 - 2*a)*q^18 + (2*a^3 + a^2 - 6*a - 3)*q^19 + (-a + 1)*q^20 + (-a^4 - 2*a^3 + 2*a^2 + 5*a + 2)*q^21 + (a^4 + a^3 - 5*a^2 - 2*a + 1)*q^22 + (-a^4 - 3*a^3 + 3*a^2 + 9*a)*q^23 + (a^4 + a^3 - 4*a^2 - 4*a)*q^24 + (-2*a^4 + a^3 + 9*a^2 - 7*a - 4)*q^25 + (-a + 1)*q^26 + (a^3 + 3*a^2 - 3*a - 5)*q^27 + (-a^4 - a^3 + 5*a^2 + a - 5)*q^28 + (-a^4 - a^3 + 4*a^2 + a)*q^29 + (-a^4 - 2*a^3 + 4*a^2 + 6*a - 1)*q^30 + (2*a^4 - 9*a^2 + 3*a + 8)*q^31 + (-2*a^3 - a^2 + 5*a + 1)*q^32 + (2*a^4 + 2*a^3 - 10*a^2 - 6*a + 6)*q^33 + (2*a^4 + 2*a^3 - 8*a^2 - a + 1)*q^34 + (-a^4 + 5*a^2 - a - 1)*q^35 + (a^4 + 2*a^3 - 4*a^2 - 4*a + 4)*q^36 + (-a^4 - 2*a^3 + 5*a^2 + 4*a - 5)*q^37 + O(q^38),
q + a*q^2 + (23/11*a^9 - 107/11*a^8 - 72/11*a^7 + 841/11*a^6 - 38*a^5 - 1753/11*a^4 + 1294/11*a^3 + 699/11*a^2 - 37*a - 52/11)*q^3 + (a^2 - 2)*q^4 + (-57/11*a^9 + 280/11*a^8 + 122/11*a^7 - 2166/11*a^6 + 135*a^5 + 4342/11*a^4 - 4161/11*a^3 - 1409/11*a^2 + 125*a + 60/11)*q^5 + (54/11*a^9 - 256/11*a^8 - 148/11*a^7 + 1997/11*a^6 - 105*a^5 - 4088/11*a^4 + 3436/11*a^3 + 1479/11*a^2 - 103*a - 69/11)*q^6 + (a^9 - 5*a^8 - 2*a^7 + 39*a^6 - 27*a^5 - 81*a^4 + 75*a^3 + 35*a^2 - 26*a - 4)*q^7 + (a^3 - 4*a)*q^8 + (26/11*a^9 - 131/11*a^8 - 46/11*a^7 + 1010/11*a^6 - 68*a^5 - 2007/11*a^4 + 2019/11*a^3 + 618/11*a^2 - 58*a - 10/11)*q^9 + (-119/11*a^9 + 578/11*a^8 + 285/11*a^7 - 4500/11*a^6 + 260*a^5 + 9177/11*a^4 - 8192/11*a^3 - 3299/11*a^2 + 249*a + 171/11)*q^10 + (35/11*a^9 - 170/11*a^8 - 89/11*a^7 + 1330/11*a^6 - 72*a^5 - 2736/11*a^4 + 2269/11*a^3 + 1002/11*a^2 - 63*a - 27/11)*q^11 + (76/11*a^9 - 366/11*a^8 - 181/11*a^7 + 2833/11*a^6 - 168*a^5 - 5694/11*a^4 + 5317/11*a^3 + 1897/11*a^2 - 163*a - 58/11)*q^12 + (5/11*a^9 - 29/11*a^8 + 3/11*a^7 + 223/11*a^6 - 22*a^5 - 438/11*a^4 + 607/11*a^3 + 118/11*a^2 - 20*a + 4/11)*q^13 + (2*a^9 - 10*a^8 - 4*a^7 + 78*a^6 - 55*a^5 - 159*a^4 + 154*a^3 + 56*a^2 - 51*a - 3)*q^14 + (-38/11*a^9 + 183/11*a^8 + 96/11*a^7 - 1433/11*a^6 + 81*a^5 + 2968/11*a^4 - 2642/11*a^3 - 1174/11*a^2 + 87*a + 117/11)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-38/11*a^9 + 183/11*a^8 + 96/11*a^7 - 1422/11*a^6 + 79*a^5 + 2880/11*a^4 - 2510/11*a^3 - 976/11*a^2 + 75*a + 18/11)*q^17 + (51/11*a^9 - 254/11*a^8 - 108/11*a^7 + 1982/11*a^6 - 121*a^5 - 4065/11*a^4 + 3712/11*a^3 + 1494/11*a^2 - 112*a - 78/11)*q^18 + (-36/11*a^9 + 178/11*a^8 + 73/11*a^7 - 1368/11*a^6 + 87*a^5 + 2696/11*a^4 - 2628/11*a^3 - 788/11*a^2 + 77*a + 46/11)*q^19 + (-141/11*a^9 + 677/11*a^8 + 373/11*a^7 - 5303/11*a^6 + 283*a^5 + 10970/11*a^4 - 9138/11*a^3 - 4201/11*a^2 + 274*a + 237/11)*q^20 + (62/11*a^9 - 298/11*a^8 - 152/11*a^7 + 2301/11*a^6 - 132*a^5 - 4593/11*a^4 + 4163/11*a^3 + 1450/11*a^2 - 126*a - 23/11)*q^21 + (75/11*a^9 - 369/11*a^8 - 175/11*a^7 + 2883/11*a^6 - 166*a^5 - 5921/11*a^4 + 5167/11*a^3 + 2177/11*a^2 - 152*a - 105/11)*q^22 + (16/11*a^9 - 84/11*a^8 - 8/11*a^7 + 630/11*a^6 - 58*a^5 - 1164/11*a^4 + 1685/11*a^3 + 195/11*a^2 - 58*a + 48/11)*q^23 + (58/11*a^9 - 277/11*a^8 - 139/11*a^7 + 2138/11*a^6 - 128*a^5 - 4291/11*a^4 + 4069/11*a^3 + 1481/11*a^2 - 124*a - 90/11)*q^24 + (-7/11*a^9 + 45/11*a^8 - 24/11*a^7 - 332/11*a^6 + 45*a^5 + 589/11*a^4 - 1171/11*a^3 - 64/11*a^2 + 38*a + 23/11)*q^25 + (6/11*a^9 - 37/11*a^8 + 8/11*a^7 + 283/11*a^6 - 28*a^5 - 563/11*a^4 + 713/11*a^3 + 190/11*a^2 - 21*a - 15/11)*q^26 + (-5*a^9 + 24*a^8 + 13*a^7 - 187*a^6 + 111*a^5 + 382*a^4 - 320*a^3 - 138*a^2 + 98*a + 7)*q^27 + (2*a^9 - 10*a^8 - 4*a^7 + 77*a^6 - 53*a^5 - 152*a^4 + 144*a^3 + 43*a^2 - 45*a + 2)*q^28 + (74/11*a^9 - 361/11*a^8 - 169/11*a^7 + 2812/11*a^6 - 169*a^5 - 5763/11*a^4 + 5325/11*a^3 + 2193/11*a^2 - 169*a - 174/11)*q^29 + (-83/11*a^9 + 400/11*a^8 + 201/11*a^7 - 3099/11*a^6 + 180*a^5 + 6250/11*a^4 - 5696/11*a^3 - 2159/11*a^2 + 173*a + 114/11)*q^30 + (-81/11*a^9 + 395/11*a^8 + 189/11*a^7 - 3067/11*a^6 + 179*a^5 + 6209/11*a^4 - 5528/11*a^3 - 2136/11*a^2 + 151*a + 76/11)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (86/11*a^9 - 402/11*a^8 - 263/11*a^7 + 3158/11*a^6 - 147*a^5 - 6570/11*a^4 + 4969/11*a^3 + 2573/11*a^2 - 142*a - 138/11)*q^33 + (-83/11*a^9 + 400/11*a^8 + 212/11*a^7 - 3121/11*a^6 + 172*a^5 + 6382/11*a^4 - 5498/11*a^3 - 2291/11*a^2 + 164*a + 114/11)*q^34 + (-124/11*a^9 + 596/11*a^8 + 326/11*a^7 - 4668/11*a^6 + 251*a^5 + 9637/11*a^4 - 8095/11*a^3 - 3626/11*a^2 + 239*a + 222/11)*q^35 + (51/11*a^9 - 254/11*a^8 - 119/11*a^7 + 2004/11*a^6 - 113*a^5 - 4208/11*a^4 + 3525/11*a^3 + 1714/11*a^2 - 109*a - 133/11)*q^36 + (-12/11*a^9 + 63/11*a^8 + 6/11*a^7 - 478/11*a^6 + 44*a^5 + 939/11*a^4 - 1294/11*a^3 - 369/11*a^2 + 45*a + 85/11)*q^37 + O(q^38),
q + a*q^2 + (-356/1325*a^12 - 372/265*a^11 + 358/265*a^10 + 20873/1325*a^9 + 7163/1325*a^8 - 83228/1325*a^7 - 10893/265*a^6 + 141118/1325*a^5 + 90693/1325*a^4 - 99828/1325*a^3 - 42657/1325*a^2 + 25211/1325*a + 3304/1325)*q^3 + (a^2 - 2)*q^4 + (-181/265*a^12 - 207/53*a^11 + 65/53*a^10 + 10433/265*a^9 + 9023/265*a^8 - 35473/265*a^7 - 8923/53*a^6 + 45208/265*a^5 + 67048/265*a^4 - 17133/265*a^3 - 29932/265*a^2 + 2046/265*a + 2719/265)*q^5 + (632/1325*a^12 + 714/265*a^11 - 311/265*a^10 - 36981/1325*a^9 - 27336/1325*a^8 + 132791/1325*a^7 + 28366/265*a^6 - 191971/1325*a^5 - 216596/1325*a^4 + 102591/1325*a^3 + 97479/1325*a^2 - 20192/1325*a - 8188/1325)*q^6 + (804/1325*a^12 + 858/265*a^11 - 612/265*a^10 - 44907/1325*a^9 - 22817/1325*a^8 + 163102/1325*a^7 + 26727/265*a^6 - 238237/1325*a^5 - 200387/1325*a^4 + 129027/1325*a^3 + 81063/1325*a^2 - 26224/1325*a - 8236/1325)*q^7 + (a^3 - 4*a)*q^8 + (306/265*a^12 + 340/53*a^11 - 191/53*a^10 - 18193/265*a^9 - 12313/265*a^8 + 67123/265*a^7 + 13813/53*a^6 - 99178/265*a^5 - 108923/265*a^4 + 55758/265*a^3 + 49432/265*a^2 - 13141/265*a - 3629/265)*q^9 + (232/265*a^12 + 246/53*a^11 - 194/53*a^10 - 13421/265*a^9 - 7056/265*a^8 + 50591/265*a^7 + 9114/53*a^6 - 76666/265*a^5 - 76501/265*a^4 + 43916/265*a^3 + 38789/265*a^2 - 9227/265*a - 4163/265)*q^10 + (1136/1325*a^12 + 1327/265*a^11 - 398/265*a^10 - 68988/1325*a^9 - 59853/1325*a^8 + 247493/1325*a^7 + 60423/265*a^6 - 357708/1325*a^5 - 470183/1325*a^4 + 202518/1325*a^3 + 225817/1325*a^2 - 51641/1325*a - 23674/1325)*q^11 + (-142/1325*a^12 - 199/265*a^11 - 149/265*a^10 + 9286/1325*a^9 + 19241/1325*a^8 - 24146/1325*a^7 - 16861/265*a^6 + 2976/1325*a^5 + 128501/1325*a^4 + 39279/1325*a^3 - 63174/1325*a^2 - 16898/1325*a + 7928/1325)*q^12 + (-496/1325*a^12 - 557/265*a^11 + 338/265*a^10 + 30868/1325*a^9 + 19508/1325*a^8 - 121273/1325*a^7 - 23228/265*a^6 + 205338/1325*a^5 + 198013/1325*a^4 - 157398/1325*a^3 - 105837/1325*a^2 + 52276/1325*a + 8489/1325)*q^13 + (-1338/1325*a^12 - 1416/265*a^11 + 1149/265*a^10 + 76879/1325*a^9 + 36874/1325*a^8 - 289269/1325*a^7 - 47969/265*a^6 + 437989/1325*a^5 + 392739/1325*a^4 - 246969/1325*a^3 - 189436/1325*a^2 + 44828/1325*a + 18492/1325)*q^14 + (388/265*a^12 + 437/53*a^11 - 202/53*a^10 - 22779/265*a^9 - 16534/265*a^8 + 82384/265*a^7 + 17642/53*a^6 - 120249/265*a^5 - 140739/265*a^4 + 66309/265*a^3 + 71711/265*a^2 - 13983/265*a - 9032/265)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1552/1325*a^12 - 1854/265*a^11 + 331/265*a^10 + 95091/1325*a^9 + 95021/1325*a^8 - 324501/1325*a^7 - 92351/265*a^6 + 401231/1325*a^5 + 695456/1325*a^4 - 133001/1325*a^3 - 308044/1325*a^2 + 16712/1325*a + 25793/1325)*q^17 + (-442/265*a^12 - 497/53*a^11 + 217/53*a^10 + 25631/265*a^9 + 19081/265*a^8 - 91891/265*a^7 - 19958/53*a^6 + 134041/265*a^5 + 156126/265*a^4 - 75416/265*a^3 - 75259/265*a^2 + 16567/265*a + 7038/265)*q^18 + (-487/1325*a^12 - 494/265*a^11 + 521/265*a^10 + 26771/1325*a^9 + 4376/1325*a^8 - 108956/1325*a^7 - 9486/265*a^6 + 205336/1325*a^5 + 92761/1325*a^4 - 175181/1325*a^3 - 60814/1325*a^2 + 52022/1325*a + 4758/1325)*q^19 + (-32/265*a^12 - 12/53*a^11 + 109/53*a^10 + 846/265*a^9 - 3879/265*a^8 - 5516/265*a^7 + 2420/53*a^6 + 17291/265*a^5 - 14084/265*a^4 - 21601/265*a^3 + 3541/265*a^2 + 7057/265*a - 102/265)*q^20 + (-3932/1325*a^12 - 4469/265*a^11 + 1846/265*a^10 + 231881/1325*a^9 + 179011/1325*a^8 - 828166/1325*a^7 - 186506/265*a^6 + 1173646/1325*a^5 + 1454596/1325*a^4 - 609516/1325*a^3 - 689129/1325*a^2 + 130992/1325*a + 60938/1325)*q^21 + (-1317/1325*a^12 - 1534/265*a^11 + 516/265*a^10 + 81011/1325*a^9 + 69141/1325*a^8 - 295421/1325*a^7 - 71996/265*a^6 + 431801/1325*a^5 + 575126/1325*a^4 - 237671/1325*a^3 - 282249/1325*a^2 + 51302/1325*a + 26128/1325)*q^22 + (-3/1325*a^12 - 21/265*a^11 - 61/265*a^10 + 924/1325*a^9 + 3719/1325*a^8 + 311/1325*a^7 - 2019/265*a^6 - 16341/1325*a^5 - 4666/1325*a^4 + 33311/1325*a^3 + 25184/1325*a^2 - 16257/1325*a - 8473/1325)*q^23 + (-253/265*a^12 - 287/53*a^11 + 138/53*a^10 + 15119/265*a^9 + 10564/265*a^8 - 55039/265*a^7 - 11216/53*a^6 + 79939/265*a^5 + 85179/265*a^4 - 42084/265*a^3 - 36606/265*a^2 + 7788/265*a + 2622/265)*q^24 + (58/53*a^12 + 334/53*a^11 - 110/53*a^10 - 3395/53*a^9 - 2771/53*a^8 + 11866/53*a^7 + 13698/53*a^6 - 16331/53*a^5 - 20437/53*a^4 + 7799/53*a^3 + 8730/53*a^2 - 1260/53*a - 577/53)*q^25 + (687/1325*a^12 + 834/265*a^11 - 76/265*a^10 - 41996/1325*a^9 - 43401/1325*a^8 + 144756/1325*a^7 + 41266/265*a^6 - 195811/1325*a^5 - 320086/1325*a^4 + 96531/1325*a^3 + 152964/1325*a^2 - 24247/1325*a - 11408/1325)*q^26 + (-671/1325*a^12 - 722/265*a^11 + 578/265*a^10 + 41043/1325*a^9 + 24008/1325*a^8 - 156573/1325*a^7 - 31028/265*a^6 + 228638/1325*a^5 + 250013/1325*a^4 - 120048/1325*a^3 - 100012/1325*a^2 + 32776/1325*a - 2586/1325)*q^27 + (678/1325*a^12 + 771/265*a^11 - 259/265*a^10 - 39224/1325*a^9 - 33569/1325*a^8 + 137739/1325*a^7 + 34679/265*a^6 - 193159/1325*a^5 - 285059/1325*a^4 + 98414/1325*a^3 + 154316/1325*a^2 - 17368/1325*a - 14302/1325)*q^28 + (3082/1325*a^12 + 3554/265*a^11 - 1286/265*a^10 - 186056/1325*a^9 - 155261/1325*a^8 + 666741/1325*a^7 + 161416/265*a^6 - 936871/1325*a^5 - 1277171/1325*a^4 + 464791/1325*a^3 + 625429/1325*a^2 - 82417/1325*a - 62488/1325)*q^29 + (-531/265*a^12 - 590/53*a^11 + 333/53*a^10 + 31578/265*a^9 + 21468/265*a^8 - 115878/265*a^7 - 24205/53*a^6 + 167333/265*a^5 + 193573/265*a^4 - 86593/265*a^3 - 92747/265*a^2 + 16576/265*a + 8924/265)*q^30 + (4713/1325*a^12 + 5431/265*a^11 - 1954/265*a^10 - 282954/1325*a^9 - 233824/1325*a^8 + 1011319/1325*a^7 + 240949/265*a^6 - 1428514/1325*a^5 - 1882439/1325*a^4 + 745269/1325*a^3 + 897461/1325*a^2 - 170553/1325*a - 85992/1325)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (937/1325*a^12 + 994/265*a^11 - 911/265*a^10 - 56721/1325*a^9 - 24276/1325*a^8 + 226606/1325*a^7 + 35676/265*a^6 - 375036/1325*a^5 - 317711/1325*a^4 + 251956/1325*a^3 + 174739/1325*a^2 - 63397/1325*a - 21708/1325)*q^33 + (1594/1325*a^12 + 1883/265*a^11 - 537/265*a^10 - 97427/1325*a^9 - 80837/1325*a^8 + 354597/1325*a^7 + 80867/265*a^6 - 536832/1325*a^5 - 642057/1325*a^4 + 325172/1325*a^3 + 331768/1325*a^2 - 76639/1325*a - 35696/1325)*q^34 + (-459/265*a^12 - 510/53*a^11 + 313/53*a^10 + 27687/265*a^9 + 17012/265*a^8 - 105587/265*a^7 - 20004/53*a^6 + 167052/265*a^5 + 167492/265*a^4 - 105102/265*a^3 - 89518/265*a^2 + 23554/265*a + 10346/265)*q^35 + (-3/265*a^12 - 21/53*a^11 - 61/53*a^10 + 659/265*a^9 + 2129/265*a^8 - 1544/265*a^7 - 641/53*a^6 + 3534/265*a^5 - 2546/265*a^4 - 6439/265*a^3 + 7429/265*a^2 + 4148/265*a - 2908/265)*q^36 + (-254/265*a^12 - 294/53*a^11 + 100/53*a^10 + 15162/265*a^9 + 12157/265*a^8 - 54582/265*a^7 - 12260/53*a^6 + 80322/265*a^5 + 94577/265*a^4 - 45202/265*a^3 - 44023/265*a^2 + 9259/265*a + 3331/265)*q^37 + O(q^38)
*]> ;  // time = 9.089 seconds




J[398] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 398, 398, 398, 398, 398, 199, 199, 199 ], new_dimensions := [ 1, 2, 2, 6, 6, 2, 4, 10 ], dimensions := [ 1, 2, 2, 6, 6, 4, 8, 20 ], intersection_graph := [ 0, 1, 1, 11, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 11, 1, 1, 1, 0, 1, 1, 11, 1, 9, 11, 1, 1, 0, 1, 1, 1, 40149, 1, 1, 1, 1, 0, 1, 149, 1, 5, 1, 11, 1, 1, 0, 1, 5041, 1, 11, 1, 1, 149, 1, 0, 1, 1, 1, 9, 40149, 1, 5041, 1, 0 ], ap_traces := [
[ -1, 2, -2, 0, 2, 6, 6, 6, 0, -6, 8, -8 ],
[ -2, -1, 0, -3, 1, -6, -2, -4, -1, 2, 3, -19 ],
[ 2, -3, -2, -7, -7, -4, 4, 0, -3, -6, -5, -9 ],
[ -6, 1, 4, 11, -7, -2, 2, -2, 1, -2, 9, 33 ],
[ 6, 3, 2, 7, 5, 0, -4, 2, 7, -2, -3, 7 ]
], hecke_fields := [
x - 1,
x^2 + x - 1,
x^2 + 3*x + 1,
x^6 - x^5 - 14*x^4 + 5*x^3 + 54*x^2 + 9*x - 27,
x^6 - 3*x^5 - 6*x^4 + 21*x^3 + 2*x^2 - 21*x - 5
], atkin_lehners := [
[ 1, -1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 11, 1 ],
[ 99, 1 ],
[ 120447, 3 ],
[ 3725, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 99, 1 ],
[ 1, 3 ],
[ 3725, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 25 ], torsion_lower_bounds := [ 1, 1, 1, 3, 25 ], l_ratios := [ 1, 0, 0, 1/3, 149/25 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 1 ], eigenvalues := [*
[ -1, 2, -2, 0, 2, 6, 6, 6, 0, -6, 8, -8 ],
[
-1,
a,
0,
-a - 2,
-3*a - 1,
-2*a - 4,
2*a,
4*a,
-a - 1,
6*a + 4,
a + 2,
a - 9
],
[
1,
a,
-2*a - 4,
a - 2,
-a - 5,
-2,
4*a + 8,
0,
7*a + 9,
-2*a - 6,
-5*a - 10,
-3*a - 9
],
[
-1,
a,
1/3*a^5 - a^4 - 3*a^3 + 7*a^2 + 23/3*a - 5,
1/9*a^5 - 1/9*a^4 - 5/9*a^3 - 4/9*a^2 - a + 4,
-1/3*a^4 + 1/3*a^3 + 5/3*a^2 + 1/3*a + 1,
1/3*a^4 - 4/3*a^3 - 5/3*a^2 + 20/3*a + 1,
1/9*a^5 - 7/9*a^4 + 1/9*a^3 + 53/9*a^2 - 13/3*a - 7,
-1/9*a^5 + 4/9*a^4 + 11/9*a^3 - 38/9*a^2 - 13/3*a + 6,
-5/9*a^5 + 14/9*a^4 + 43/9*a^3 - 97/9*a^2 - 11*a + 10,
1/9*a^5 + 2/9*a^4 - 17/9*a^3 - 28/9*a^2 + 17/3*a + 8,
a^2 - 2*a - 3,
-5/9*a^5 + 14/9*a^4 + 34/9*a^3 - 88/9*a^2 - 4*a + 14
],
[
1,
a,
a^5 - a^4 - 7*a^3 + 5*a^2 + 7*a + 3,
-a^5 + a^4 + 7*a^3 - 6*a^2 - 7*a + 2,
-a^4 + a^3 + 7*a^2 - 7*a - 5,
-2*a^5 + 3*a^4 + 14*a^3 - 17*a^2 - 14*a + 1,
a^5 - a^4 - 9*a^3 + 5*a^2 + 17*a + 3,
-a^5 + 2*a^4 + 7*a^3 - 12*a^2 - 7*a + 4,
a^5 - 2*a^4 - 5*a^3 + 13*a^2 - 5*a - 6,
a^5 - 2*a^4 - 7*a^3 + 12*a^2 + 7*a - 4,
2*a^5 - 18*a^3 - 3*a^2 + 36*a + 15,
a^5 - 2*a^4 - 8*a^3 + 12*a^2 + 12*a - 2
]
*], q_expansions := [*
q - q^2 + 2*q^3 + q^4 - 2*q^5 - 2*q^6 - q^8 + q^9 + 2*q^10 + 2*q^11 + 2*q^12 + 6*q^13 - 4*q^15 + q^16 + 6*q^17 - q^18 + 6*q^19 - 2*q^20 - 2*q^22 - 2*q^24 - q^25 - 6*q^26 - 4*q^27 - 6*q^29 + 4*q^30 + 8*q^31 - q^32 + 4*q^33 - 6*q^34 + q^36 - 8*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - a*q^6 + (-a - 2)*q^7 - q^8 + (-a - 2)*q^9 + (-3*a - 1)*q^11 + a*q^12 + (-2*a - 4)*q^13 + (a + 2)*q^14 + q^16 + 2*a*q^17 + (a + 2)*q^18 + 4*a*q^19 + (-a - 1)*q^21 + (3*a + 1)*q^22 + (-a - 1)*q^23 - a*q^24 - 5*q^25 + (2*a + 4)*q^26 + (-4*a - 1)*q^27 + (-a - 2)*q^28 + (6*a + 4)*q^29 + (a + 2)*q^31 - q^32 + (2*a - 3)*q^33 - 2*a*q^34 + (-a - 2)*q^36 + (a - 9)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-2*a - 4)*q^5 + a*q^6 + (a - 2)*q^7 + q^8 + (-3*a - 4)*q^9 + (-2*a - 4)*q^10 + (-a - 5)*q^11 + a*q^12 - 2*q^13 + (a - 2)*q^14 + (2*a + 2)*q^15 + q^16 + (4*a + 8)*q^17 + (-3*a - 4)*q^18 + (-2*a - 4)*q^20 + (-5*a - 1)*q^21 + (-a - 5)*q^22 + (7*a + 9)*q^23 + a*q^24 + (4*a + 7)*q^25 - 2*q^26 + (2*a + 3)*q^27 + (a - 2)*q^28 + (-2*a - 6)*q^29 + (2*a + 2)*q^30 + (-5*a - 10)*q^31 + q^32 + (-2*a + 1)*q^33 + (4*a + 8)*q^34 + (6*a + 10)*q^35 + (-3*a - 4)*q^36 + (-3*a - 9)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (1/3*a^5 - a^4 - 3*a^3 + 7*a^2 + 23/3*a - 5)*q^5 - a*q^6 + (1/9*a^5 - 1/9*a^4 - 5/9*a^3 - 4/9*a^2 - a + 4)*q^7 - q^8 + (a^2 - 3)*q^9 + (-1/3*a^5 + a^4 + 3*a^3 - 7*a^2 - 23/3*a + 5)*q^10 + (-1/3*a^4 + 1/3*a^3 + 5/3*a^2 + 1/3*a + 1)*q^11 + a*q^12 + (1/3*a^4 - 4/3*a^3 - 5/3*a^2 + 20/3*a + 1)*q^13 + (-1/9*a^5 + 1/9*a^4 + 5/9*a^3 + 4/9*a^2 + a - 4)*q^14 + (-2/3*a^5 + 5/3*a^4 + 16/3*a^3 - 31/3*a^2 - 8*a + 9)*q^15 + q^16 + (1/9*a^5 - 7/9*a^4 + 1/9*a^3 + 53/9*a^2 - 13/3*a - 7)*q^17 + (-a^2 + 3)*q^18 + (-1/9*a^5 + 4/9*a^4 + 11/9*a^3 - 38/9*a^2 - 13/3*a + 6)*q^19 + (1/3*a^5 - a^4 - 3*a^3 + 7*a^2 + 23/3*a - 5)*q^20 + (a^4 - a^3 - 7*a^2 + 3*a + 3)*q^21 + (1/3*a^4 - 1/3*a^3 - 5/3*a^2 - 1/3*a - 1)*q^22 + (-5/9*a^5 + 14/9*a^4 + 43/9*a^3 - 97/9*a^2 - 11*a + 10)*q^23 - a*q^24 + (2/9*a^5 - 14/9*a^4 + 2/9*a^3 + 88/9*a^2 - 20/3*a - 1)*q^25 + (-1/3*a^4 + 4/3*a^3 + 5/3*a^2 - 20/3*a - 1)*q^26 + (a^3 - 6*a)*q^27 + (1/9*a^5 - 1/9*a^4 - 5/9*a^3 - 4/9*a^2 - a + 4)*q^28 + (1/9*a^5 + 2/9*a^4 - 17/9*a^3 - 28/9*a^2 + 17/3*a + 8)*q^29 + (2/3*a^5 - 5/3*a^4 - 16/3*a^3 + 31/3*a^2 + 8*a - 9)*q^30 + (a^2 - 2*a - 3)*q^31 - q^32 + (-1/3*a^5 + 1/3*a^4 + 5/3*a^3 + 1/3*a^2 + a)*q^33 + (-1/9*a^5 + 7/9*a^4 - 1/9*a^3 - 53/9*a^2 + 13/3*a + 7)*q^34 + (10/9*a^5 - 19/9*a^4 - 104/9*a^3 + 131/9*a^2 + 28*a - 15)*q^35 + (a^2 - 3)*q^36 + (-5/9*a^5 + 14/9*a^4 + 34/9*a^3 - 88/9*a^2 - 4*a + 14)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (a^5 - a^4 - 7*a^3 + 5*a^2 + 7*a + 3)*q^5 + a*q^6 + (-a^5 + a^4 + 7*a^3 - 6*a^2 - 7*a + 2)*q^7 + q^8 + (a^2 - 3)*q^9 + (a^5 - a^4 - 7*a^3 + 5*a^2 + 7*a + 3)*q^10 + (-a^4 + a^3 + 7*a^2 - 7*a - 5)*q^11 + a*q^12 + (-2*a^5 + 3*a^4 + 14*a^3 - 17*a^2 - 14*a + 1)*q^13 + (-a^5 + a^4 + 7*a^3 - 6*a^2 - 7*a + 2)*q^14 + (2*a^5 - a^4 - 16*a^3 + 5*a^2 + 24*a + 5)*q^15 + q^16 + (a^5 - a^4 - 9*a^3 + 5*a^2 + 17*a + 3)*q^17 + (a^2 - 3)*q^18 + (-a^5 + 2*a^4 + 7*a^3 - 12*a^2 - 7*a + 4)*q^19 + (a^5 - a^4 - 7*a^3 + 5*a^2 + 7*a + 3)*q^20 + (-2*a^5 + a^4 + 15*a^3 - 5*a^2 - 19*a - 5)*q^21 + (-a^4 + a^3 + 7*a^2 - 7*a - 5)*q^22 + (a^5 - 2*a^4 - 5*a^3 + 13*a^2 - 5*a - 6)*q^23 + a*q^24 + (-2*a^5 + 18*a^3 + 2*a^2 - 36*a - 11)*q^25 + (-2*a^5 + 3*a^4 + 14*a^3 - 17*a^2 - 14*a + 1)*q^26 + (a^3 - 6*a)*q^27 + (-a^5 + a^4 + 7*a^3 - 6*a^2 - 7*a + 2)*q^28 + (a^5 - 2*a^4 - 7*a^3 + 12*a^2 + 7*a - 4)*q^29 + (2*a^5 - a^4 - 16*a^3 + 5*a^2 + 24*a + 5)*q^30 + (2*a^5 - 18*a^3 - 3*a^2 + 36*a + 15)*q^31 + q^32 + (-a^5 + a^4 + 7*a^3 - 7*a^2 - 5*a)*q^33 + (a^5 - a^4 - 9*a^3 + 5*a^2 + 17*a + 3)*q^34 + (2*a^5 - a^4 - 16*a^3 + 3*a^2 + 24*a + 11)*q^35 + (a^2 - 3)*q^36 + (a^5 - 2*a^4 - 8*a^3 + 12*a^2 + 12*a - 2)*q^37 + O(q^38)
*]> ;  // time = 102.12 seconds




J[399] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 399, 399, 399, 399, 399, 399, 399, 133, 133, 133, 133, 57, 57, 57, 21, 19 ], new_dimensions := [ 1, 1, 1, 3, 3, 5, 5, 2, 2, 2, 3, 1, 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 3, 3, 5, 5, 4, 4, 4, 6, 2, 2, 2, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 7, 1, 0, 1, 1, 29, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 29, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 27, 1, 1, 1, 1, 1, 3, 5, 1, 1, 1, 29, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 29, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 1, 27, 1, 1, 0, 1, 1, 1, 1, 1, 9, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 49, 3, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 5, 1, 1, 1, 9, 0, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 9, 49, 1, 1, 1, 1, 0 ], ap_traces := [
[ 1, -1, 0, -1, -2, -4, -4, -1, 2, -2, 0, 6 ],
[ -1, -1, 0, 1, -2, 0, -4, 1, -6, -6, 0, -2 ],
[ -1, 1, 4, -1, -2, 4, 0, -1, -6, 10, 0, 6 ],
[ 1, -3, 4, -3, 0, 6, 8, 3, -4, 20, 8, -10 ],
[ 1, 3, 0, -3, 4, 2, 12, -3, -8, -8, -8, -2 ],
[ 3, -5, 4, 5, 8, -6, 12, -5, 12, 4, -8, 2 ],
[ 1, 5, -2, 5, -2, 8, -2, 5, 2, 0, 8, 2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^3 - x^2 - 3*x + 1,
x^3 - x^2 - 7*x + 9,
x^5 - 3*x^4 - 4*x^3 + 14*x^2 - 3*x - 1,
x^5 - x^4 - 8*x^3 + 6*x^2 + 13*x - 3
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, -1, -1 ],
[ -1, 1, 1 ],
[ 1, 1, -1 ],
[ -1, 1, 1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 5, 3, 1 ],
[ 3, 1, 1 ],
[ 1, 1, 3 ],
[ 13, 1, 1 ],
[ 29, 11, 1 ],
[ 29, 13, 1 ],
[ 243, 3, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 29, 1, 1 ],
[ 1, 13, 1 ],
[ 243, 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 9 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 0, 1, 1, 29, 13, 9 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1, 1, 1, 1/81 ], eigenvalues := [*
[ 1, -1, 0, -1, -2, -4, -4, -1, 2, -2, 0, 6 ],
[ -1, -1, 0, 1, -2, 0, -4, 1, -6, -6, 0, -2 ],
[ -1, 1, 4, -1, -2, 4, 0, -1, -6, 10, 0, 6 ],
[
a,
-1,
a^2 - 1,
-1,
-2*a^2 + 2*a + 4,
-2*a^2 + 2*a + 6,
-a^2 + 5,
1,
2*a^2 - 6*a - 4,
a^2 - 2*a + 5,
4*a^2 - 2*a - 6,
-4*a - 2
],
[
a,
1,
-a^2 + 5,
-1,
-2*a^2 - 2*a + 12,
2*a^2 + 2*a - 10,
a^2 - 1,
-1,
-2*a^2 - 2*a + 8,
a^2 - 2*a - 7,
-2*a - 2,
4*a^2 + 4*a - 22
],
[
a,
-1,
a^4 - 3*a^3 - 4*a^2 + 13*a - 1,
1,
-2*a^4 + 4*a^3 + 10*a^2 - 18*a + 2,
a^4 - 4*a^3 - 4*a^2 + 20*a - 3,
a^4 - a^3 - 6*a^2 + 3*a + 5,
-1,
-2*a^2 + 2*a + 8,
-a^4 + 3*a^3 + 6*a^2 - 15*a - 3,
-a^4 + 4*a^3 + 2*a^2 - 20*a + 7,
-2*a^3 + 2*a^2 + 10*a - 4
],
[
a,
1,
-a^3 + 5*a,
1,
a^4 - 6*a^2 + 3,
-2*a + 2,
a^3 - 2*a^2 - 5*a + 6,
1,
-a^4 + 6*a^2 - 3,
-a^4 - a^3 + 6*a^2 + 5*a - 3,
a^4 - 6*a^2 + 5,
-2*a^3 - 2*a^2 + 10*a + 8
]
*], q_expansions := [*
q + q^2 - q^3 - q^4 - q^6 - q^7 - 3*q^8 + q^9 - 2*q^11 + q^12 - 4*q^13 - q^14 - q^16 - 4*q^17 + q^18 - q^19 + q^21 - 2*q^22 + 2*q^23 + 3*q^24 - 5*q^25 - 4*q^26 - q^27 + q^28 - 2*q^29 + 5*q^32 + 2*q^33 - 4*q^34 - q^36 + 6*q^37 + O(q^38),
q - q^2 - q^3 - q^4 + q^6 + q^7 + 3*q^8 + q^9 - 2*q^11 + q^12 - q^14 - q^16 - 4*q^17 - q^18 + q^19 - q^21 + 2*q^22 - 6*q^23 - 3*q^24 - 5*q^25 - q^27 - q^28 - 6*q^29 - 5*q^32 + 2*q^33 + 4*q^34 - q^36 - 2*q^37 + O(q^38),
q - q^2 + q^3 - q^4 + 4*q^5 - q^6 - q^7 + 3*q^8 + q^9 - 4*q^10 - 2*q^11 - q^12 + 4*q^13 + q^14 + 4*q^15 - q^16 - q^18 - q^19 - 4*q^20 - q^21 + 2*q^22 - 6*q^23 + 3*q^24 + 11*q^25 - 4*q^26 + q^27 + q^28 + 10*q^29 - 4*q^30 - 5*q^32 - 2*q^33 - 4*q^35 - q^36 + 6*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (a^2 - 1)*q^5 - a*q^6 - q^7 + (a^2 - a - 1)*q^8 + q^9 + (a^2 + 2*a - 1)*q^10 + (-2*a^2 + 2*a + 4)*q^11 + (-a^2 + 2)*q^12 + (-2*a^2 + 2*a + 6)*q^13 - a*q^14 + (-a^2 + 1)*q^15 + (-2*a^2 + 2*a + 3)*q^16 + (-a^2 + 5)*q^17 + a*q^18 + q^19 + (a^2 + 2*a + 1)*q^20 + q^21 + (-2*a + 2)*q^22 + (2*a^2 - 6*a - 4)*q^23 + (-a^2 + a + 1)*q^24 + (2*a^2 + 2*a - 5)*q^25 + 2*q^26 - q^27 + (-a^2 + 2)*q^28 + (a^2 - 2*a + 5)*q^29 + (-a^2 - 2*a + 1)*q^30 + (4*a^2 - 2*a - 6)*q^31 + (-2*a^2 - a + 4)*q^32 + (2*a^2 - 2*a - 4)*q^33 + (-a^2 + 2*a + 1)*q^34 + (-a^2 + 1)*q^35 + (a^2 - 2)*q^36 + (-4*a - 2)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^2 + 5)*q^5 + a*q^6 - q^7 + (a^2 + 3*a - 9)*q^8 + q^9 + (-a^2 - 2*a + 9)*q^10 + (-2*a^2 - 2*a + 12)*q^11 + (a^2 - 2)*q^12 + (2*a^2 + 2*a - 10)*q^13 - a*q^14 + (-a^2 + 5)*q^15 + (2*a^2 - 2*a - 5)*q^16 + (a^2 - 1)*q^17 + a*q^18 - q^19 + (-a^2 + 2*a - 1)*q^20 - q^21 + (-4*a^2 - 2*a + 18)*q^22 + (-2*a^2 - 2*a + 8)*q^23 + (a^2 + 3*a - 9)*q^24 + (-2*a^2 - 2*a + 11)*q^25 + (4*a^2 + 4*a - 18)*q^26 + q^27 + (-a^2 + 2)*q^28 + (a^2 - 2*a - 7)*q^29 + (-a^2 - 2*a + 9)*q^30 + (-2*a - 2)*q^31 + (-2*a^2 + 3*a)*q^32 + (-2*a^2 - 2*a + 12)*q^33 + (a^2 + 6*a - 9)*q^34 + (a^2 - 5)*q^35 + (a^2 - 2)*q^36 + (4*a^2 + 4*a - 22)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (a^4 - 3*a^3 - 4*a^2 + 13*a - 1)*q^5 - a*q^6 + q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^2 + 2*a + 1)*q^10 + (-2*a^4 + 4*a^3 + 10*a^2 - 18*a + 2)*q^11 + (-a^2 + 2)*q^12 + (a^4 - 4*a^3 - 4*a^2 + 20*a - 3)*q^13 + a*q^14 + (-a^4 + 3*a^3 + 4*a^2 - 13*a + 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 - a^3 - 6*a^2 + 3*a + 5)*q^17 + a*q^18 - q^19 + (-2*a^4 + 5*a^3 + 10*a^2 - 25*a + 2)*q^20 - q^21 + (-2*a^4 + 2*a^3 + 10*a^2 - 4*a - 2)*q^22 + (-2*a^2 + 2*a + 8)*q^23 + (-a^3 + 4*a)*q^24 + (a^4 - 2*a^3 - 6*a^2 + 6*a + 8)*q^25 + (-a^4 + 6*a^2 + 1)*q^26 - q^27 + (a^2 - 2)*q^28 + (-a^4 + 3*a^3 + 6*a^2 - 15*a - 3)*q^29 + (a^2 - 2*a - 1)*q^30 + (-a^4 + 4*a^3 + 2*a^2 - 20*a + 7)*q^31 + (3*a^4 - 4*a^3 - 14*a^2 + 15*a + 1)*q^32 + (2*a^4 - 4*a^3 - 10*a^2 + 18*a - 2)*q^33 + (2*a^4 - 2*a^3 - 11*a^2 + 8*a + 1)*q^34 + (a^4 - 3*a^3 - 4*a^2 + 13*a - 1)*q^35 + (a^2 - 2)*q^36 + (-2*a^3 + 2*a^2 + 10*a - 4)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^3 + 5*a)*q^5 + a*q^6 + q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^4 + 5*a^2)*q^10 + (a^4 - 6*a^2 + 3)*q^11 + (a^2 - 2)*q^12 + (-2*a + 2)*q^13 + a*q^14 + (-a^3 + 5*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^3 - 2*a^2 - 5*a + 6)*q^17 + a*q^18 + q^19 + (-a^4 - a^3 + 6*a^2 + 3*a - 3)*q^20 + q^21 + (a^4 + 2*a^3 - 6*a^2 - 10*a + 3)*q^22 + (-a^4 + 6*a^2 - 3)*q^23 + (a^3 - 4*a)*q^24 + (-a^4 + 2*a^3 + 6*a^2 - 10*a - 2)*q^25 + (-2*a^2 + 2*a)*q^26 + q^27 + (a^2 - 2)*q^28 + (-a^4 - a^3 + 6*a^2 + 5*a - 3)*q^29 + (-a^4 + 5*a^2)*q^30 + (a^4 - 6*a^2 + 5)*q^31 + (a^4 - 6*a^2 - a + 3)*q^32 + (a^4 - 6*a^2 + 3)*q^33 + (a^4 - 2*a^3 - 5*a^2 + 6*a)*q^34 + (-a^3 + 5*a)*q^35 + (a^2 - 2)*q^36 + (-2*a^3 - 2*a^2 + 10*a + 8)*q^37 + O(q^38)
*]> ;  // time = 137.029 seconds




J[401] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 401, 401 ], new_dimensions := [ 12, 21 ], dimensions := [ 12, 21 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -3, -5, -7, -20, -11, -11, 1, -34, -7, -6, -52, 3 ],
[ 0, 3, 3, 24, 1, 9, -1, 38, 3, -4, 70, 3 ]
], hecke_fields := [
x^12 + 3*x^11 - 10*x^10 - 34*x^9 + 29*x^8 + 129*x^7 - 24*x^6 - 203*x^5 + x^4 + 130*x^3 - 5*x^2 - 22*x + 4,
x^21 - 35*x^19 + 521*x^17 + 2*x^16 - 4305*x^15 - 51*x^14 + 21617*x^13 + 519*x^12 - 67876*x^11 - 2749*x^10 + 132085*x^9 + 8292*x^8 - 152221*x^7 - 14353*x^6 + 93934*x^5 + 12831*x^4 - 24699*x^3 - 4111*x^2 + 1058*x - 44
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 25 ]
], tamagawa_numbers := [
[ 1 ],
[ 25 ]
], torsion_upper_bounds := [ 1, 25 ], torsion_lower_bounds := [ 1, 25 ], l_ratios := [ 0, 1/25 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-2*a^11 - 4*a^10 + 21*a^9 + 43*a^8 - 66*a^7 - 151*a^6 + 63*a^5 + 211*a^4 + 5*a^3 - 114*a^2 - 17*a + 13,
11/2*a^11 + 23/2*a^10 - 60*a^9 - 124*a^8 + 417/2*a^7 + 863/2*a^6 - 274*a^5 - 1151/2*a^4 + 231/2*a^3 + 265*a^2 + 25/2*a - 23,
-2*a^11 - 4*a^10 + 23*a^9 + 43*a^8 - 89*a^7 - 147*a^6 + 145*a^5 + 183*a^4 - 94*a^3 - 64*a^2 + 5*a + 1,
-11/2*a^11 - 11/2*a^10 + 70*a^9 + 53*a^8 - 629/2*a^7 - 289/2*a^6 + 630*a^5 + 151/2*a^4 - 1093/2*a^3 + 101*a^2 + 253/2*a - 36,
11/2*a^11 + 15/2*a^10 - 65*a^9 - 76*a^8 + 521/2*a^7 + 473/2*a^6 - 446*a^5 - 487/2*a^4 + 643/2*a^3 + 41*a^2 - 111/2*a + 7,
1/2*a^11 - 9/2*a^10 - 12*a^9 + 54*a^8 + 171/2*a^7 - 435/2*a^6 - 239*a^5 + 733/2*a^4 + 521/2*a^3 - 251*a^2 - 167/2*a + 39,
13/2*a^11 + 13/2*a^10 - 84*a^9 - 66*a^8 + 767/2*a^7 + 409/2*a^6 - 773*a^5 - 379/2*a^4 + 1313/2*a^3 - 27*a^2 - 283/2*a + 26,
-5*a^11 - 10*a^10 + 54*a^9 + 107*a^8 - 183*a^7 - 369*a^6 + 226*a^5 + 487*a^4 - 80*a^3 - 220*a^2 - 13*a + 13,
-3*a^11 - 13*a^10 + 24*a^9 + 149*a^8 - 23*a^7 - 571*a^6 - 150*a^5 + 899*a^4 + 297*a^3 - 551*a^2 - 129*a + 71,
3*a^11 + 10*a^10 - 28*a^9 - 110*a^8 + 67*a^7 + 393*a^6 - 7*a^5 - 552*a^4 - 90*a^3 + 289*a^2 + 58*a - 37,
-13/2*a^11 - 13/2*a^10 + 84*a^9 + 62*a^8 - 777/2*a^7 - 325/2*a^6 + 817*a^5 + 115/2*a^4 - 1521/2*a^3 + 160*a^2 + 399/2*a - 50
],
[
a,
-18286877149/2056085485264*a^20 - 11127199047/2056085485264*a^19 + 83946583113/257010685658*a^18 + 82268698561/514021371316*a^17 - 10577086239965/2056085485264*a^16 - 4006759400165/2056085485264*a^15 + 5820872970774/128505342829*a^14 + 26143714096043/2056085485264*a^13 - 31289587591503/128505342829*a^12 - 100786701349185/2056085485264*a^11 + 1682873453689943/2056085485264*a^10 + 122664373913815/1028042742632*a^9 - 3480210083621745/2056085485264*a^8 - 413112998448921/2056085485264*a^7 + 2090208291142399/1028042742632*a^6 + 521232062879477/2056085485264*a^5 - 2588114268141401/2056085485264*a^4 - 216362373657685/1028042742632*a^3 + 634884906799859/2056085485264*a^2 + 70645897189647/1028042742632*a - 3293700981999/514021371316,
-722413535/128505342829*a^20 + 4850669160/128505342829*a^19 + 17729132132/128505342829*a^18 - 616176543847/514021371316*a^17 - 545133209029/514021371316*a^16 + 4061635213501/257010685658*a^15 - 81942846175/257010685658*a^14 - 28814567024775/257010685658*a^13 + 6461969206283/128505342829*a^12 + 59717775138331/128505342829*a^11 - 160937518187779/514021371316*a^10 - 294890352574975/257010685658*a^9 + 459977117780719/514021371316*a^8 + 853299070638225/514021371316*a^7 - 673509990918971/514021371316*a^6 - 695729399878955/514021371316*a^5 + 119791311761006/128505342829*a^4 + 302525984112977/514021371316*a^3 - 68216128320123/257010685658*a^2 - 28194703453239/257010685658*a + 1197867446729/128505342829,
11788227381/1028042742632*a^20 - 17556105935/1028042742632*a^19 - 175917004357/514021371316*a^18 + 277765645839/514021371316*a^17 + 4221110609895/1028042742632*a^16 - 7240673316675/1028042742632*a^15 - 3198938144554/128505342829*a^14 + 50222989912785/1028042742632*a^13 + 39080024046237/514021371316*a^12 - 200432877759707/1028042742632*a^11 - 80842481868219/1028042742632*a^10 + 116739845694491/257010685658*a^9 - 158230419832287/1028042742632*a^8 - 623823499506267/1028042742632*a^7 + 63600503938346/128505342829*a^6 + 471363605727771/1028042742632*a^5 - 464992827043603/1028042742632*a^4 - 26823439523891/128505342829*a^3 + 139429229628541/1028042742632*a^2 + 26480698676661/514021371316*a - 286007594119/257010685658,
-65872818475/1028042742632*a^20 + 24504892221/1028042742632*a^19 + 275445436750/128505342829*a^18 - 94128553210/128505342829*a^17 - 31019594825691/1028042742632*a^16 + 9424250012195/1028042742632*a^15 + 29901763784562/128505342829*a^14 - 61663707257231/1028042742632*a^13 - 551547004674839/514021371316*a^12 + 225232260705723/1028042742632*a^11 + 3120061386536981/1028042742632*a^10 - 112655572100787/257010685658*a^9 - 5350818255511181/1028042742632*a^8 + 422995988582409/1028042742632*a^7 + 1328612115857249/257010685658*a^6 - 25831277280967/1028042742632*a^5 - 2767570136776731/1028042742632*a^4 - 58048134220281/257010685658*a^3 + 593287325531071/1028042742632*a^2 + 53353117310705/514021371316*a - 2788481204299/257010685658,
5922142461/514021371316*a^20 - 4388103687/257010685658*a^19 - 190854757593/514021371316*a^18 + 282772054063/514021371316*a^17 + 1293881759277/257010685658*a^16 - 3745952572257/514021371316*a^15 - 9667642818631/257010685658*a^14 + 26267034142439/514021371316*a^13 + 88028827271723/514021371316*a^12 - 104417140872075/514021371316*a^11 - 256484825359039/514021371316*a^10 + 232486914297775/514021371316*a^9 + 489257916738043/514021371316*a^8 - 261224184161481/514021371316*a^7 - 601810751729847/514021371316*a^6 + 96962568271683/514021371316*a^5 + 430021502626571/514021371316*a^4 + 37497517466363/514021371316*a^3 - 129911109286611/514021371316*a^2 - 5918147205798/128505342829*a + 1164757232946/128505342829,
9354331725/514021371316*a^20 - 14630632579/257010685658*a^19 - 310472433251/514021371316*a^18 + 924337350471/514021371316*a^17 + 2174339827069/257010685658*a^16 - 12071288087343/514021371316*a^15 - 16829994603905/257010685658*a^14 + 84138714162195/514021371316*a^13 + 158852143543987/514021371316*a^12 - 336903298269333/514021371316*a^11 - 476779687011101/514021371316*a^10 + 774501168309915/514021371316*a^9 + 918273560798407/514021371316*a^8 - 955172014800243/514021371316*a^7 - 1100406271074901/514021371316*a^6 + 514435743408067/514021371316*a^5 + 736483474702639/514021371316*a^4 - 25844651336335/514021371316*a^3 - 199670719820553/514021371316*a^2 - 10578582540277/128505342829*a + 732906735340/128505342829,
19560055923/2056085485264*a^20 + 83428578419/2056085485264*a^19 - 44235265769/128505342829*a^18 - 666022272627/514021371316*a^17 + 10907735035495/2056085485264*a^16 + 35393334158353/2056085485264*a^15 - 23255725275895/514021371316*a^14 - 253344758111913/2056085485264*a^13 + 238602075943719/1028042742632*a^12 + 1057357625768757/2056085485264*a^11 - 1500286864381305/2056085485264*a^10 - 650532718677195/514021371316*a^9 + 2826906311914709/2056085485264*a^8 + 3646499843568451/2056085485264*a^7 - 748824329814221/514021371316*a^6 - 2681091340987393/2056085485264*a^5 + 1576536932169655/2056085485264*a^4 + 222169433006333/514021371316*a^3 - 335443937810391/2056085485264*a^2 - 44606561166255/1028042742632*a + 4645881872331/514021371316,
41890165043/2056085485264*a^20 - 117493570401/2056085485264*a^19 - 379820873039/514021371316*a^18 + 234914130250/128505342829*a^17 + 23531499422459/2056085485264*a^16 - 49972006570527/2056085485264*a^15 - 50909461062953/514021371316*a^14 + 357104005194783/2056085485264*a^13 + 540493577391165/1028042742632*a^12 - 1479551537157843/2056085485264*a^11 - 3629795412271505/2056085485264*a^10 + 445143419319317/257010685658*a^9 + 7638436761590461/2056085485264*a^8 - 4659598358491357/2056085485264*a^7 - 598715874427860/128505342829*a^6 + 2656081010713183/2056085485264*a^5 + 6397840212256703/2056085485264*a^4 - 141713838695/128505342829*a^3 - 1742131333927103/2056085485264*a^2 - 172394469464539/1028042742632*a + 10917703709407/514021371316,
33237272127/2056085485264*a^20 + 12515858277/2056085485264*a^19 - 523071738485/1028042742632*a^18 - 247005367077/1028042742632*a^17 + 13502207952929/2056085485264*a^16 + 8119184198997/2056085485264*a^15 - 22843759265753/514021371316*a^14 - 71738574102713/2056085485264*a^13 + 85145284094723/514021371316*a^12 + 366951354705153/2056085485264*a^11 - 646173453920921/2056085485264*a^10 - 545065981708513/1028042742632*a^9 + 357080894122149/2056085485264*a^8 + 1786004506344087/2056085485264*a^7 + 318288949584957/1028042742632*a^6 - 1404655951930429/2056085485264*a^5 - 948906923145845/2056085485264*a^4 + 166279465202455/1028042742632*a^3 + 308014940862725/2056085485264*a^2 + 21392607749449/1028042742632*a + 1772840173967/514021371316,
-9279772743/1028042742632*a^20 + 34558546045/1028042742632*a^19 + 161233419919/514021371316*a^18 - 277999796259/257010685658*a^17 - 4807633299301/1028042742632*a^16 + 14818488721359/1028042742632*a^15 + 5058241944549/128505342829*a^14 - 105562595883047/1028042742632*a^13 - 106365525442013/514021371316*a^12 + 432106560242233/1028042742632*a^11 + 725775751307935/1028042742632*a^10 - 505249343259197/514021371316*a^9 - 1598675703214837/1028042742632*a^8 + 1235692800963433/1028042742632*a^7 + 269851349872658/128505342829*a^6 - 564658722354737/1028042742632*a^5 - 1587503694005337/1028042742632*a^4 - 69526365361707/514021371316*a^3 + 480574859157299/1028042742632*a^2 + 61585977613059/514021371316*a - 2818881017317/257010685658,
48972673319/1028042742632*a^20 + 64766312769/1028042742632*a^19 - 857503239253/514021371316*a^18 - 1062063046557/514021371316*a^17 + 25481381831101/1028042742632*a^16 + 29222577001601/1028042742632*a^15 - 26164127151164/128505342829*a^14 - 219054802866929/1028042742632*a^13 + 129783040936358/128505342829*a^12 + 972784954543949/1028042742632*a^11 - 3190696828517025/1028042742632*a^10 - 1304870375013637/514021371316*a^9 + 6000704847254093/1028042742632*a^8 + 4152097043677227/1028042742632*a^7 - 3288274030738325/514021371316*a^6 - 3726805797057009/1028042742632*a^5 + 3776590249450851/1028042742632*a^4 + 855525292345967/514021371316*a^3 - 890920662328779/1028042742632*a^2 - 154017421800297/514021371316*a + 6288346886539/257010685658
]
*], q_expansions := [*
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24490020703/514021371316*a^18 - 1252235477289/514021371316*a^17 + 2103383411935/2056085485264*a^16 + 67341904882677/2056085485264*a^15 - 5507192513787/514021371316*a^14 - 488414884550029/2056085485264*a^13 + 62289493696655/1028042742632*a^12 + 2068658771146093/2056085485264*a^11 - 381631448676241/2056085485264*a^10 - 646837854748879/257010685658*a^9 + 572855201368073/2056085485264*a^8 + 7368890606005255/2056085485264*a^7 - 62988186948729/514021371316*a^6 - 5440750435128857/2056085485264*a^5 - 225478681142249/2056085485264*a^4 + 210595340583441/257010685658*a^3 + 154984767184077/2056085485264*a^2 - 45683296949039/1028042742632*a + 1100551939223/514021371316)*q^30 + (-9279772743/1028042742632*a^20 + 34558546045/1028042742632*a^19 + 161233419919/514021371316*a^18 - 277999796259/257010685658*a^17 - 4807633299301/1028042742632*a^16 + 14818488721359/1028042742632*a^15 + 5058241944549/128505342829*a^14 - 105562595883047/1028042742632*a^13 - 106365525442013/514021371316*a^12 + 432106560242233/1028042742632*a^11 + 725775751307935/1028042742632*a^10 - 505249343259197/514021371316*a^9 - 1598675703214837/1028042742632*a^8 + 1235692800963433/1028042742632*a^7 + 269851349872658/128505342829*a^6 - 564658722354737/1028042742632*a^5 - 1587503694005337/1028042742632*a^4 - 69526365361707/514021371316*a^3 + 480574859157299/1028042742632*a^2 + 61585977613059/514021371316*a - 2818881017317/257010685658)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-1347603101/257010685658*a^20 - 16365371459/514021371316*a^19 + 118369407559/514021371316*a^18 + 524923555201/514021371316*a^17 - 2175356043441/514021371316*a^16 - 3516333754701/257010685658*a^15 + 10920198797217/257010685658*a^14 + 12796696286068/128505342829*a^13 - 130993547013769/514021371316*a^12 - 110445612160593/257010685658*a^11 + 120478377845742/128505342829*a^10 + 580676039700667/514021371316*a^9 - 537361198482565/257010685658*a^8 - 230925540768000/128505342829*a^7 + 1383436693821555/514021371316*a^6 + 428757008072853/257010685658*a^5 - 462555041302805/257010685658*a^4 - 424258575536853/514021371316*a^3 + 62154248516187/128505342829*a^2 + 41507904623199/257010685658*a - 1143395782262/128505342829)*q^33 + (-14630632579/257010685658*a^20 + 4232294281/128505342829*a^19 + 924337350471/514021371316*a^18 - 524927174587/514021371316*a^17 - 12089996750793/514021371316*a^16 + 6610408868315/514021371316*a^15 + 42307892540085/257010685658*a^14 - 21680222677669/257010685658*a^13 - 85439549108652/128505342829*a^12 + 158154933154999/514021371316*a^11 + 200054056555485/128505342829*a^10 - 158646672549109/257010685658*a^9 - 1032738133463943/514021371316*a^8 + 80879864609081/128505342829*a^7 + 162174616664248/128505342829*a^6 - 142206321553511/514021371316*a^5 - 72935040849905/257010685658*a^4 + 15685959727611/257010685658*a^3 - 3858672439633/514021371316*a^2 - 3482628011845/257010685658*a + 102897648975/128505342829)*q^34 + (46992828407/1028042742632*a^20 + 72097226751/1028042742632*a^19 - 858594234225/514021371316*a^18 - 1150314868903/514021371316*a^17 + 26737716973537/1028042742632*a^16 + 30603257162807/1028042742632*a^15 - 57764091896421/257010685658*a^14 - 220348406082853/1028042742632*a^13 + 604737004528709/514021371316*a^12 + 934436496704983/1028042742632*a^11 - 3930310180977837/1028042742632*a^10 - 597130710918339/257010685658*a^9 + 7819941202005459/1028042742632*a^8 + 3652425594305831/1028042742632*a^7 - 1131121549579156/128505342829*a^6 - 3280207874136299/1028042742632*a^5 + 5463503164559567/1028042742632*a^4 + 420109234710719/257010685658*a^3 - 1349234478791725/1028042742632*a^2 - 195866518418523/514021371316*a + 8283666914047/257010685658)*q^35 + (46438565055/2056085485264*a^20 + 40840782901/2056085485264*a^19 - 849903952519/1028042742632*a^18 - 676157375153/1028042742632*a^17 + 26557990905613/2056085485264*a^16 + 18793939564693/2056085485264*a^15 - 57746323096283/514021371316*a^14 - 142815320454017/2056085485264*a^13 + 305683153388947/514021371316*a^12 + 648916964329005/2056085485264*a^11 - 4046531070727293/2056085485264*a^10 - 908666549555735/1028042742632*a^9 + 8279779100520837/2056085485264*a^8 + 3138556426566511/2056085485264*a^7 - 4990640475945667/1028042742632*a^6 - 3272166487074569/2056085485264*a^5 + 6375466297178087/2056085485264*a^4 + 959107640529617/1028042742632*a^3 - 1678821125020419/2056085485264*a^2 - 238839788813159/1028042742632*a + 10627987606115/514021371316)*q^36 + (48972673319/1028042742632*a^20 + 64766312769/1028042742632*a^19 - 857503239253/514021371316*a^18 - 1062063046557/514021371316*a^17 + 25481381831101/1028042742632*a^16 + 29222577001601/1028042742632*a^15 - 26164127151164/128505342829*a^14 - 219054802866929/1028042742632*a^13 + 129783040936358/128505342829*a^12 + 972784954543949/1028042742632*a^11 - 3190696828517025/1028042742632*a^10 - 1304870375013637/514021371316*a^9 + 6000704847254093/1028042742632*a^8 + 4152097043677227/1028042742632*a^7 - 3288274030738325/514021371316*a^6 - 3726805797057009/1028042742632*a^5 + 3776590249450851/1028042742632*a^4 + 855525292345967/514021371316*a^3 - 890920662328779/1028042742632*a^2 - 154017421800297/514021371316*a + 6288346886539/257010685658)*q^37 + O(q^38)
*]> ;  // time = 8.671 seconds




J[402] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 402, 402, 402, 402, 402, 402, 402, 201, 201, 201, 201, 201, 134, 134, 67, 67, 67 ], new_dimensions := [ 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 3, 5, 3, 3, 1, 2, 2 ], dimensions := [ 1, 1, 1, 1, 2, 2, 3, 2, 2, 2, 6, 10, 6, 6, 4, 8, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 23, 1, 37, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 1, 37, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1, 1, 1, 5, 1, 9, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 361, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 17, 1, 841, 1, 1, 1, 9, 1, 37, 1, 1, 1, 1, 1, 1, 1, 0, 1, 25, 1, 25, 1, 1, 1, 3, 1, 37, 1, 1, 1, 1, 1, 17, 1, 0, 1, 361, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 25, 1, 0, 1, 625, 1, 1, 1, 1, 1, 1, 1, 25, 1, 1, 1, 841, 1, 361, 1, 0, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 361, 1, 25, 1, 625, 1, 0 ], ap_traces := [
[ -1, -1, 1, -3, 0, -4, 2, -2, -3, 0, -9, -3 ],
[ -1, 1, 2, 0, 4, -2, 2, -4, 4, -2, 0, 6 ],
[ -1, 1, -3, -1, 0, -4, -6, 2, -9, 0, 5, -7 ],
[ 1, -1, 2, 2, -4, 0, 6, 4, -6, 8, 2, -2 ],
[ -2, -2, 0, 6, -4, -2, 0, 4, 14, -2, 10, -4 ],
[ 2, -2, 1, -1, 8, 8, -4, -2, 9, -8, -7, 15 ],
[ 3, 3, 3, 1, 0, -6, -2, -6, 3, 6, -13, -7 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 12,
x^2 - x - 10,
x^3 - 3*x^2 - 4*x + 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ 1, -1, -1 ],
[ -1, 1, 1 ],
[ 1, 1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 9, 1 ],
[ 1, 3, 1 ],
[ 23, 37, 1 ],
[ 5, 37, 1 ],
[ 11, 11, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 9, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 5, 1, 1 ],
[ 11, 11, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 1, 1, 11 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 0, 1, 1, 5, 1 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1, 1, 1, 1/121 ], eigenvalues := [*
[ -1, -1, 1, -3, 0, -4, 2, -2, -3, 0, -9, -3 ],
[ -1, 1, 2, 0, 4, -2, 2, -4, 4, -2, 0, 6 ],
[ -1, 1, -3, -1, 0, -4, -6, 2, -9, 0, 5, -7 ],
[ 1, -1, 2, 2, -4, 0, 6, 4, -6, 8, 2, -2 ],
[
-1,
-1,
a,
1/2*a + 3,
-2,
-1/2*a - 1,
-a,
2,
1/2*a + 7,
-5/2*a - 1,
3/2*a + 5,
-2
],
[
1,
-1,
a,
-a,
4,
4,
-2,
-2*a,
a + 4,
-4,
a - 4,
-a + 8
],
[
1,
1,
a,
1/2*a^2 - 3/2*a - 1,
-2*a + 2,
-3/2*a^2 + 7/2*a + 3,
-a^2 + a + 4,
-2,
3/2*a^2 - 9/2*a - 3,
3/2*a^2 - 7/2*a - 3,
-1/2*a^2 + 3/2*a - 3,
a^2 + 2*a - 10
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + q^5 + q^6 - 3*q^7 - q^8 + q^9 - q^10 - q^12 - 4*q^13 + 3*q^14 - q^15 + q^16 + 2*q^17 - q^18 - 2*q^19 + q^20 + 3*q^21 - 3*q^23 + q^24 - 4*q^25 + 4*q^26 - q^27 - 3*q^28 + q^30 - 9*q^31 - q^32 - 2*q^34 - 3*q^35 + q^36 - 3*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + 2*q^5 - q^6 - q^8 + q^9 - 2*q^10 + 4*q^11 + q^12 - 2*q^13 + 2*q^15 + q^16 + 2*q^17 - q^18 - 4*q^19 + 2*q^20 - 4*q^22 + 4*q^23 - q^24 - q^25 + 2*q^26 + q^27 - 2*q^29 - 2*q^30 - q^32 + 4*q^33 - 2*q^34 + q^36 + 6*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - 3*q^5 - q^6 - q^7 - q^8 + q^9 + 3*q^10 + q^12 - 4*q^13 + q^14 - 3*q^15 + q^16 - 6*q^17 - q^18 + 2*q^19 - 3*q^20 - q^21 - 9*q^23 - q^24 + 4*q^25 + 4*q^26 + q^27 - q^28 + 3*q^30 + 5*q^31 - q^32 + 6*q^34 + 3*q^35 + q^36 - 7*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + 2*q^5 - q^6 + 2*q^7 + q^8 + q^9 + 2*q^10 - 4*q^11 - q^12 + 2*q^14 - 2*q^15 + q^16 + 6*q^17 + q^18 + 4*q^19 + 2*q^20 - 2*q^21 - 4*q^22 - 6*q^23 - q^24 - q^25 - q^27 + 2*q^28 + 8*q^29 - 2*q^30 + 2*q^31 + q^32 + 4*q^33 + 6*q^34 + 4*q^35 + q^36 - 2*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + a*q^5 + q^6 + (1/2*a + 3)*q^7 - q^8 + q^9 - a*q^10 - 2*q^11 - q^12 + (-1/2*a - 1)*q^13 + (-1/2*a - 3)*q^14 - a*q^15 + q^16 - a*q^17 - q^18 + 2*q^19 + a*q^20 + (-1/2*a - 3)*q^21 + 2*q^22 + (1/2*a + 7)*q^23 + q^24 + 7*q^25 + (1/2*a + 1)*q^26 - q^27 + (1/2*a + 3)*q^28 + (-5/2*a - 1)*q^29 + a*q^30 + (3/2*a + 5)*q^31 - q^32 + 2*q^33 + a*q^34 + (3*a + 6)*q^35 + q^36 - 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + a*q^5 - q^6 - a*q^7 + q^8 + q^9 + a*q^10 + 4*q^11 - q^12 + 4*q^13 - a*q^14 - a*q^15 + q^16 - 2*q^17 + q^18 - 2*a*q^19 + a*q^20 + a*q^21 + 4*q^22 + (a + 4)*q^23 - q^24 + (a + 5)*q^25 + 4*q^26 - q^27 - a*q^28 - 4*q^29 - a*q^30 + (a - 4)*q^31 + q^32 - 4*q^33 - 2*q^34 + (-a - 10)*q^35 + q^36 + (-a + 8)*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + a*q^5 + q^6 + (1/2*a^2 - 3/2*a - 1)*q^7 + q^8 + q^9 + a*q^10 + (-2*a + 2)*q^11 + q^12 + (-3/2*a^2 + 7/2*a + 3)*q^13 + (1/2*a^2 - 3/2*a - 1)*q^14 + a*q^15 + q^16 + (-a^2 + a + 4)*q^17 + q^18 - 2*q^19 + a*q^20 + (1/2*a^2 - 3/2*a - 1)*q^21 + (-2*a + 2)*q^22 + (3/2*a^2 - 9/2*a - 3)*q^23 + q^24 + (a^2 - 5)*q^25 + (-3/2*a^2 + 7/2*a + 3)*q^26 + q^27 + (1/2*a^2 - 3/2*a - 1)*q^28 + (3/2*a^2 - 7/2*a - 3)*q^29 + a*q^30 + (-1/2*a^2 + 3/2*a - 3)*q^31 + q^32 + (-2*a + 2)*q^33 + (-a^2 + a + 4)*q^34 + (a - 2)*q^35 + q^36 + (a^2 + 2*a - 10)*q^37 + O(q^38)
*]> ;  // time = 273.98 seconds




J[403] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 403, 403, 403, 403, 403, 31 ], new_dimensions := [ 2, 6, 7, 8, 8, 2 ], dimensions := [ 2, 6, 7, 8, 8, 4 ], intersection_graph := [ 0, 1, 1, 1, 181, 1, 1, 0, 1, 1, 1, 11, 1, 1, 0, 1, 1, 41, 1, 1, 1, 0, 1, 1, 181, 1, 1, 1, 0, 1, 1, 11, 41, 1, 1, 0 ], ap_traces := [
[ 3, -4, 0, 2, 0, 2, 6, 2, -6, 6, -2, -6 ],
[ -2, -5, -9, 0, -5, 6, -23, 7, -18, -18, 6, -13 ],
[ 2, 5, 11, 4, 8, -7, 7, 1, 6, -2, 7, 28 ],
[ -5, -3, -15, -4, -5, -8, -11, -9, 0, -12, -8, -9 ],
[ -1, 7, 11, -2, -2, 8, 7, -5, 14, 12, -8, 2 ]
], hecke_fields := [
x^2 - 3*x + 1,
x^6 + 2*x^5 - 7*x^4 - 13*x^3 + 6*x^2 + 7*x - 3,
x^7 - 2*x^6 - 9*x^5 + 17*x^4 + 20*x^3 - 37*x^2 + x + 4,
x^8 + 5*x^7 - 30*x^5 - 24*x^4 + 54*x^3 + 54*x^2 - 28*x - 29,
x^8 + x^7 - 11*x^6 - 10*x^5 + 37*x^4 + 33*x^3 - 36*x^2 - 33*x - 4
], atkin_lehners := [
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 11, 1 ],
[ 41, 7 ],
[ 1, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 11, 1 ],
[ 1, 7 ],
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 7, 1, 1 ], torsion_lower_bounds := [ 1, 1, 7, 1, 1 ], l_ratios := [ 1, 0, 1/7, 0, 1 ], analytic_sha_upper_bounds := [ 1, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1, 0, 1 ], eigenvalues := [*
[
a,
-2,
2*a - 3,
1,
-4*a + 6,
1,
-2*a + 6,
1,
2*a - 6,
2*a,
-1,
-6*a + 6
],
[
a,
-a^5 - 3*a^4 + 5*a^3 + 19*a^2 + 6*a - 8,
3*a^5 + 8*a^4 - 17*a^3 - 51*a^2 - 8*a + 18,
-2*a^5 - 5*a^4 + 12*a^3 + 31*a^2 - 10,
5*a^5 + 12*a^4 - 29*a^3 - 75*a^2 - 8*a + 24,
1,
-3*a^5 - 8*a^4 + 17*a^3 + 51*a^2 + 6*a - 24,
-12*a^5 - 29*a^4 + 69*a^3 + 184*a^2 + 23*a - 67,
4*a^5 + 11*a^4 - 22*a^3 - 71*a^2 - 13*a + 27,
8*a^5 + 20*a^4 - 46*a^3 - 127*a^2 - 14*a + 45,
1,
-3*a^4 - 3*a^3 + 20*a^2 + 17*a - 13
],
[
a,
a^5 - 3*a^4 - 3*a^3 + 13*a^2 - 6*a,
-a^5 + 2*a^4 + 5*a^3 - 9*a^2 - 2*a + 4,
a^4 - 2*a^3 - 5*a^2 + 8*a + 2,
-a^6 + 3*a^5 + 3*a^4 - 14*a^3 + 7*a^2 + 5*a - 1,
-1,
-a^5 + 4*a^4 + a^3 - 17*a^2 + 14*a,
-a^6 + 4*a^5 + 2*a^4 - 20*a^3 + 10*a^2 + 10*a,
-a^6 + 4*a^5 + 2*a^4 - 19*a^3 + 9*a^2 + 4*a + 4,
a^6 - 4*a^5 + a^4 + 13*a^3 - 23*a^2 + 19*a - 2,
1,
-2*a^5 + 5*a^4 + 9*a^3 - 22*a^2 - a + 7
],
[
a,
-a^7 - 3*a^6 + 6*a^5 + 19*a^4 - 12*a^3 - 36*a^2 + 8*a + 19,
-a^5 - 2*a^4 + 5*a^3 + 7*a^2 - 6*a - 6,
a^4 + 2*a^3 - 3*a^2 - 4*a,
2*a^7 + 7*a^6 - 9*a^5 - 43*a^4 + 8*a^3 + 77*a^2 + a - 37,
-1,
-a^6 - a^5 + 9*a^4 + 4*a^3 - 25*a^2 - a + 17,
-a^6 - 4*a^5 + 16*a^3 + 14*a^2 - 14*a - 16,
a^7 + 4*a^6 - 3*a^5 - 22*a^4 - 2*a^3 + 32*a^2 + 8*a - 11,
-a^7 - 2*a^6 + 7*a^5 + 11*a^4 - 14*a^3 - 12*a^2 + 7*a - 5,
-1,
2*a^7 + 8*a^6 - 6*a^5 - 45*a^4 - a^3 + 74*a^2 + 5*a - 33
],
[
a,
-a^5 - a^4 + 7*a^3 + 5*a^2 - 10*a - 4,
-a^7 + 10*a^5 - a^4 - 29*a^3 + 25*a + 8,
2*a^6 + 2*a^5 - 15*a^4 - 10*a^3 + 25*a^2 + 10*a - 2,
a^6 + a^5 - 7*a^4 - 4*a^3 + 11*a^2 + a - 3,
1,
a^7 - 10*a^5 + a^4 + 27*a^3 - 2*a^2 - 17*a,
-a^7 - a^6 + 9*a^5 + 7*a^4 - 22*a^3 - 15*a^2 + 13*a + 8,
a^7 - a^6 - 11*a^5 + 9*a^4 + 35*a^3 - 16*a^2 - 33*a,
-a^7 - a^6 + 7*a^5 + 4*a^4 - 9*a^3 - 6*a - 2,
-1,
-2*a^6 - 2*a^5 + 15*a^4 + 9*a^3 - 26*a^2 - 5*a + 5
]
*], q_expansions := [*
q + a*q^2 - 2*q^3 + (3*a - 3)*q^4 + (2*a - 3)*q^5 - 2*a*q^6 + q^7 + (4*a - 3)*q^8 + q^9 + (3*a - 2)*q^10 + (-4*a + 6)*q^11 + (-6*a + 6)*q^12 + q^13 + a*q^14 + (-4*a + 6)*q^15 + (3*a + 2)*q^16 + (-2*a + 6)*q^17 + a*q^18 + q^19 + (3*a + 3)*q^20 - 2*q^21 + (-6*a + 4)*q^22 + (2*a - 6)*q^23 + (-8*a + 6)*q^24 + a*q^26 + 4*q^27 + (3*a - 3)*q^28 + 2*a*q^29 + (-6*a + 4)*q^30 - q^31 + (3*a + 3)*q^32 + (8*a - 12)*q^33 + 2*q^34 + (2*a - 3)*q^35 + (3*a - 3)*q^36 + (-6*a + 6)*q^37 + O(q^38),
q + a*q^2 + (-a^5 - 3*a^4 + 5*a^3 + 19*a^2 + 6*a - 8)*q^3 + (a^2 - 2)*q^4 + (3*a^5 + 8*a^4 - 17*a^3 - 51*a^2 - 8*a + 18)*q^5 + (-a^5 - 2*a^4 + 6*a^3 + 12*a^2 - a - 3)*q^6 + (-2*a^5 - 5*a^4 + 12*a^3 + 31*a^2 - 10)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^5 - 4*a^4 + 13*a^3 + 25*a^2 - 4*a - 8)*q^9 + (2*a^5 + 4*a^4 - 12*a^3 - 26*a^2 - 3*a + 9)*q^10 + (5*a^5 + 12*a^4 - 29*a^3 - 75*a^2 - 8*a + 24)*q^11 + (2*a^5 + 5*a^4 - 11*a^3 - 33*a^2 - 8*a + 13)*q^12 + q^13 + (-a^5 - 2*a^4 + 5*a^3 + 12*a^2 + 4*a - 6)*q^14 + (3*a^5 + 8*a^4 - 16*a^3 - 50*a^2 - 11*a + 18)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3*a^5 - 8*a^4 + 17*a^3 + 51*a^2 + 6*a - 24)*q^17 + (-a^4 - a^3 + 8*a^2 + 6*a - 6)*q^18 + (-12*a^5 - 29*a^4 + 69*a^3 + 184*a^2 + 23*a - 67)*q^19 + (-6*a^5 - 14*a^4 + 34*a^3 + 87*a^2 + 11*a - 30)*q^20 + (a^5 + a^4 - 8*a^3 - 4*a^2 + 13*a - 4)*q^21 + (2*a^5 + 6*a^4 - 10*a^3 - 38*a^2 - 11*a + 15)*q^22 + (4*a^5 + 11*a^4 - 22*a^3 - 71*a^2 - 13*a + 27)*q^23 + (3*a^5 + 7*a^4 - 19*a^3 - 44*a^2 + a + 12)*q^24 + (-7*a^5 - 19*a^4 + 39*a^3 + 122*a^2 + 23*a - 47)*q^25 + a*q^26 + (6*a^5 + 15*a^4 - 35*a^3 - 94*a^2 - 9*a + 31)*q^27 + (4*a^5 + 8*a^4 - 25*a^3 - 52*a^2 + a + 17)*q^28 + (8*a^5 + 20*a^4 - 46*a^3 - 127*a^2 - 14*a + 45)*q^29 + (2*a^5 + 5*a^4 - 11*a^3 - 29*a^2 - 3*a + 9)*q^30 + q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (5*a^5 + 14*a^4 - 26*a^3 - 90*a^2 - 27*a + 36)*q^33 + (-2*a^5 - 4*a^4 + 12*a^3 + 24*a^2 - 3*a - 9)*q^34 + (a^4 + a^3 - 5*a^2 - a)*q^35 + (3*a^5 + 7*a^4 - 18*a^3 - 44*a^2 + 2*a + 16)*q^36 + (-3*a^4 - 3*a^3 + 20*a^2 + 17*a - 13)*q^37 + O(q^38),
q + a*q^2 + (a^5 - 3*a^4 - 3*a^3 + 13*a^2 - 6*a)*q^3 + (a^2 - 2)*q^4 + (-a^5 + 2*a^4 + 5*a^3 - 9*a^2 - 2*a + 4)*q^5 + (a^6 - 3*a^5 - 3*a^4 + 13*a^3 - 6*a^2)*q^6 + (a^4 - 2*a^3 - 5*a^2 + 8*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 11*a^2 - 15*a + 1)*q^9 + (-a^6 + 2*a^5 + 5*a^4 - 9*a^3 - 2*a^2 + 4*a)*q^10 + (-a^6 + 3*a^5 + 3*a^4 - 14*a^3 + 7*a^2 + 5*a - 1)*q^11 + (-a^6 + 4*a^5 + 2*a^4 - 20*a^3 + 11*a^2 + 11*a - 4)*q^12 - q^13 + (a^5 - 2*a^4 - 5*a^3 + 8*a^2 + 2*a)*q^14 + (a^5 - 4*a^4 + 16*a^2 - 19*a + 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^5 + 4*a^4 + a^3 - 17*a^2 + 14*a)*q^17 + (2*a^5 - 5*a^4 - 9*a^3 + 22*a^2 - 4)*q^18 + (-a^6 + 4*a^5 + 2*a^4 - 20*a^3 + 10*a^2 + 10*a)*q^19 + (-2*a^5 + 4*a^4 + 8*a^3 - 15*a^2 + 5*a - 4)*q^20 + (a^5 - 3*a^4 - 4*a^3 + 14*a^2 - a - 4)*q^21 + (a^6 - 6*a^5 + 3*a^4 + 27*a^3 - 32*a^2 + 4)*q^22 + (-a^6 + 4*a^5 + 2*a^4 - 19*a^3 + 9*a^2 + 4*a + 4)*q^23 + (-a^5 + 3*a^4 + 5*a^3 - 14*a^2 - 3*a + 4)*q^24 + (-3*a^5 + 5*a^4 + 17*a^3 - 22*a^2 - 13*a + 7)*q^25 - a*q^26 + (a^6 - 4*a^5 - 2*a^4 + 20*a^3 - 12*a^2 - 10*a + 8)*q^27 + (a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 12*a^2 - 16*a - 4)*q^28 + (a^6 - 4*a^5 + a^4 + 13*a^3 - 23*a^2 + 19*a - 2)*q^29 + (a^6 - 4*a^5 + 16*a^3 - 19*a^2 + 4*a)*q^30 + q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^5 - 2*a^4 - 6*a^3 + 10*a^2 + 5*a - 4)*q^33 + (-a^6 + 4*a^5 + a^4 - 17*a^3 + 14*a^2)*q^34 + (3*a^4 - 5*a^3 - 15*a^2 + 19*a + 4)*q^35 + (-a^5 + 5*a^4 - 2*a^3 - 22*a^2 + 26*a - 2)*q^36 + (-2*a^5 + 5*a^4 + 9*a^3 - 22*a^2 - a + 7)*q^37 + O(q^38),
q + a*q^2 + (-a^7 - 3*a^6 + 6*a^5 + 19*a^4 - 12*a^3 - 36*a^2 + 8*a + 19)*q^3 + (a^2 - 2)*q^4 + (-a^5 - 2*a^4 + 5*a^3 + 7*a^2 - 6*a - 6)*q^5 + (2*a^7 + 6*a^6 - 11*a^5 - 36*a^4 + 18*a^3 + 62*a^2 - 9*a - 29)*q^6 + (a^4 + 2*a^3 - 3*a^2 - 4*a)*q^7 + (a^3 - 4*a)*q^8 + (a^7 + 3*a^6 - 5*a^5 - 18*a^4 + 6*a^3 + 34*a^2 - 2*a - 19)*q^9 + (-a^6 - 2*a^5 + 5*a^4 + 7*a^3 - 6*a^2 - 6*a)*q^10 + (2*a^7 + 7*a^6 - 9*a^5 - 43*a^4 + 8*a^3 + 77*a^2 + a - 37)*q^11 + (-2*a^7 - 5*a^6 + 12*a^5 + 28*a^4 - 22*a^3 - 45*a^2 + 11*a + 20)*q^12 - q^13 + (a^5 + 2*a^4 - 3*a^3 - 4*a^2)*q^14 + (2*a^7 + 5*a^6 - 13*a^5 - 29*a^4 + 29*a^3 + 50*a^2 - 20*a - 27)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^6 - a^5 + 9*a^4 + 4*a^3 - 25*a^2 - a + 17)*q^17 + (-2*a^7 - 5*a^6 + 12*a^5 + 30*a^4 - 20*a^3 - 56*a^2 + 9*a + 29)*q^18 + (-a^6 - 4*a^5 + 16*a^3 + 14*a^2 - 14*a - 16)*q^19 + (-a^7 - 2*a^6 + 7*a^5 + 11*a^4 - 16*a^3 - 20*a^2 + 12*a + 12)*q^20 + (a^7 + 3*a^6 - 8*a^5 - 23*a^4 + 21*a^3 + 49*a^2 - 17*a - 29)*q^21 + (-3*a^7 - 9*a^6 + 17*a^5 + 56*a^4 - 31*a^3 - 107*a^2 + 19*a + 58)*q^22 + (a^7 + 4*a^6 - 3*a^5 - 22*a^4 - 2*a^3 + 32*a^2 + 8*a - 11)*q^23 + (a^7 - 10*a^5 + 2*a^4 + 27*a^3 - 5*a^2 - 18*a)*q^24 + (a^7 + 3*a^6 - 2*a^5 - 11*a^4 - 8*a^3 + 7*a^2 + 15*a + 2)*q^25 - a*q^26 + (-2*a^7 - 6*a^6 + 10*a^5 + 33*a^4 - 13*a^3 - 48*a^2 + 3*a + 17)*q^27 + (a^6 + 2*a^5 - 5*a^4 - 8*a^3 + 6*a^2 + 8*a)*q^28 + (-a^7 - 2*a^6 + 7*a^5 + 11*a^4 - 14*a^3 - 12*a^2 + 7*a - 5)*q^29 + (-5*a^7 - 13*a^6 + 31*a^5 + 77*a^4 - 58*a^3 - 128*a^2 + 29*a + 58)*q^30 - q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-2*a^7 - 7*a^6 + 11*a^5 + 47*a^4 - 19*a^3 - 94*a^2 + 16*a + 51)*q^33 + (-a^7 - a^6 + 9*a^5 + 4*a^4 - 25*a^3 - a^2 + 17*a)*q^34 + (-a^7 - 3*a^6 + 7*a^5 + 19*a^4 - 22*a^3 - 40*a^2 + 23*a + 29)*q^35 + (3*a^7 + 6*a^6 - 20*a^5 - 32*a^4 + 40*a^3 + 49*a^2 - 23*a - 20)*q^36 + (2*a^7 + 8*a^6 - 6*a^5 - 45*a^4 - a^3 + 74*a^2 + 5*a - 33)*q^37 + O(q^38),
q + a*q^2 + (-a^5 - a^4 + 7*a^3 + 5*a^2 - 10*a - 4)*q^3 + (a^2 - 2)*q^4 + (-a^7 + 10*a^5 - a^4 - 29*a^3 + 25*a + 8)*q^5 + (-a^6 - a^5 + 7*a^4 + 5*a^3 - 10*a^2 - 4*a)*q^6 + (2*a^6 + 2*a^5 - 15*a^4 - 10*a^3 + 25*a^2 + 10*a - 2)*q^7 + (a^3 - 4*a)*q^8 + (-a^6 - 2*a^5 + 7*a^4 + 12*a^3 - 11*a^2 - 15*a + 1)*q^9 + (a^7 - a^6 - 11*a^5 + 8*a^4 + 33*a^3 - 11*a^2 - 25*a - 4)*q^10 + (a^6 + a^5 - 7*a^4 - 4*a^3 + 11*a^2 + a - 3)*q^11 + (-a^7 - a^6 + 9*a^5 + 7*a^4 - 24*a^3 - 14*a^2 + 20*a + 8)*q^12 + q^13 + (2*a^7 + 2*a^6 - 15*a^5 - 10*a^4 + 25*a^3 + 10*a^2 - 2*a)*q^14 + (-a^5 - 2*a^4 + 6*a^3 + 12*a^2 - 7*a - 12)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^7 - 10*a^5 + a^4 + 27*a^3 - 2*a^2 - 17*a)*q^17 + (-a^7 - 2*a^6 + 7*a^5 + 12*a^4 - 11*a^3 - 15*a^2 + a)*q^18 + (-a^7 - a^6 + 9*a^5 + 7*a^4 - 22*a^3 - 15*a^2 + 13*a + 8)*q^19 + (-2*a^5 - 2*a^4 + 14*a^3 + 11*a^2 - 21*a - 12)*q^20 + (a^7 + 2*a^6 - 6*a^5 - 12*a^4 + 4*a^3 + 13*a^2 + 8*a + 8)*q^21 + (a^7 + a^6 - 7*a^5 - 4*a^4 + 11*a^3 + a^2 - 3*a)*q^22 + (a^7 - a^6 - 11*a^5 + 9*a^4 + 35*a^3 - 16*a^2 - 33*a)*q^23 + (-a^5 - a^4 + 9*a^3 + 4*a^2 - 17*a - 4)*q^24 + (-2*a^7 + 21*a^5 - a^4 - 65*a^3 - 6*a^2 + 59*a + 23)*q^25 + a*q^26 + (a^7 - a^6 - 11*a^5 + 9*a^4 + 34*a^3 - 15*a^2 - 31*a - 4)*q^27 + (3*a^6 + 6*a^5 - 19*a^4 - 36*a^3 + 20*a^2 + 46*a + 12)*q^28 + (-a^7 - a^6 + 7*a^5 + 4*a^4 - 9*a^3 - 6*a - 2)*q^29 + (-a^6 - 2*a^5 + 6*a^4 + 12*a^3 - 7*a^2 - 12*a)*q^30 - q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^5 + 2*a^4 - 6*a^3 - 10*a^2 + 5*a + 8)*q^33 + (-a^7 + a^6 + 11*a^5 - 10*a^4 - 35*a^3 + 19*a^2 + 33*a + 4)*q^34 + (2*a^6 + 2*a^5 - 17*a^4 - 11*a^3 + 37*a^2 + 11*a - 12)*q^35 + (-a^7 - 2*a^6 + 6*a^5 + 12*a^4 - 6*a^3 - 13*a^2 - 3*a - 6)*q^36 + (-2*a^6 - 2*a^5 + 15*a^4 + 9*a^3 - 26*a^2 - 5*a + 5)*q^37 + O(q^38)
*]> ;  // time = 61.38 seconds




J[406] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 406, 406, 406, 406, 406, 406, 406, 203, 203, 203, 203, 203, 203, 203, 58, 58, 29, 14 ], new_dimensions := [ 1, 1, 1, 1, 2, 3, 4, 1, 1, 1, 2, 2, 3, 5, 1, 1, 2, 1 ], dimensions := [ 1, 1, 1, 1, 2, 3, 4, 2, 2, 2, 4, 4, 6, 10, 2, 2, 8, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 81, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1, 81, 0, 1, 1, 1, 1, 49, 1, 5, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 3, 3, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 49, 1, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, 0, -1, -4, 0, -4, 4, 0, -1, -6, -2 ],
[ -1, 2, 2, 1, 4, -2, -4, 2, 0, -1, -2, 2 ],
[ -1, 1, -3, 1, -3, -1, 0, -4, -6, 1, 5, 2 ],
[ 1, -1, -3, -1, -1, -1, -4, -4, -2, 1, -1, 6 ],
[ 2, 4, 2, -2, 0, -2, -2, 0, -4, -2, 6, -8 ],
[ -3, 1, 5, -3, 1, 7, 8, -8, 6, 3, 5, 10 ],
[ 4, 1, -1, 4, 7, -7, 0, 2, 6, 4, -7, -12 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 + 2*x - 26,
x^3 - x^2 - 8*x + 4,
x^4 - x^3 - 10*x^2 + 4*x + 8
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ 1, -1, -1 ],
[ -1, 1, -1 ],
[ -1, 1, 1 ],
[ 1, 1, -1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 5, 3, 1 ],
[ 1, 5, 1 ],
[ 1, 1, 3 ],
[ 1, 1, 1 ],
[ 13, 3, 1 ],
[ 25, 1, 1 ],
[ 7, 7, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 5, 1 ],
[ 1, 1, 3 ],
[ 1, 1, 1 ],
[ 13, 1, 1 ],
[ 1, 1, 1 ],
[ 7, 7, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 1, 1, 7 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 5, 0, 0, 13, 1, 1 ], analytic_sha_upper_bounds := [ 0, 1, 0, 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 0, 1, 1, 1/49 ], eigenvalues := [*
[ -1, 0, 0, -1, -4, 0, -4, 4, 0, -1, -6, -2 ],
[ -1, 2, 2, 1, 4, -2, -4, 2, 0, -1, -2, 2 ],
[ -1, 1, -3, 1, -3, -1, 0, -4, -6, 1, 5, 2 ],
[ 1, -1, -3, -1, -1, -1, -4, -4, -2, 1, -1, 6 ],
[
1,
2,
-1/3*a + 2/3,
-1,
2/3*a + 2/3,
1/3*a - 2/3,
a,
2/3*a + 2/3,
-4/3*a - 10/3,
-1,
-a + 2,
-4
],
[
-1,
a,
1/2*a^2 - 1/2*a - 1,
-1,
-a^2 + 6,
-1/2*a^2 + 1/2*a + 5,
-1/2*a^2 + 3/2*a + 5,
-2*a - 2,
-a^2 - a + 8,
1,
-1/2*a^2 - 3/2*a + 5,
a^2 - a - 2
],
[
1,
a,
1/4*a^3 - 3/4*a^2 - 2*a + 3,
1,
-a + 2,
-3/4*a^3 + 1/4*a^2 + 6*a - 1,
-1/4*a^3 + 3/4*a^2 + a - 3,
1/2*a^3 - 1/2*a^2 - 5*a + 2,
-1/2*a^3 + 1/2*a^2 + 5*a,
1,
1/4*a^3 + 1/4*a^2 - 5*a - 3,
1/2*a^3 - 1/2*a^2 - 3*a - 2
]
*], q_expansions := [*
q - q^2 + q^4 - q^7 - q^8 - 3*q^9 - 4*q^11 + q^14 + q^16 - 4*q^17 + 3*q^18 + 4*q^19 + 4*q^22 - 5*q^25 - q^28 - q^29 - 6*q^31 - q^32 + 4*q^34 - 3*q^36 - 2*q^37 + O(q^38),
q - q^2 + 2*q^3 + q^4 + 2*q^5 - 2*q^6 + q^7 - q^8 + q^9 - 2*q^10 + 4*q^11 + 2*q^12 - 2*q^13 - q^14 + 4*q^15 + q^16 - 4*q^17 - q^18 + 2*q^19 + 2*q^20 + 2*q^21 - 4*q^22 - 2*q^24 - q^25 + 2*q^26 - 4*q^27 + q^28 - q^29 - 4*q^30 - 2*q^31 - q^32 + 8*q^33 + 4*q^34 + 2*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - 3*q^5 - q^6 + q^7 - q^8 - 2*q^9 + 3*q^10 - 3*q^11 + q^12 - q^13 - q^14 - 3*q^15 + q^16 + 2*q^18 - 4*q^19 - 3*q^20 + q^21 + 3*q^22 - 6*q^23 - q^24 + 4*q^25 + q^26 - 5*q^27 + q^28 + q^29 + 3*q^30 + 5*q^31 - q^32 - 3*q^33 - 3*q^35 - 2*q^36 + 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 3*q^5 - q^6 - q^7 + q^8 - 2*q^9 - 3*q^10 - q^11 - q^12 - q^13 - q^14 + 3*q^15 + q^16 - 4*q^17 - 2*q^18 - 4*q^19 - 3*q^20 + q^21 - q^22 - 2*q^23 - q^24 + 4*q^25 - q^26 + 5*q^27 - q^28 + q^29 + 3*q^30 - q^31 + q^32 + q^33 - 4*q^34 + 3*q^35 - 2*q^36 + 6*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 + (-1/3*a + 2/3)*q^5 + 2*q^6 - q^7 + q^8 + q^9 + (-1/3*a + 2/3)*q^10 + (2/3*a + 2/3)*q^11 + 2*q^12 + (1/3*a - 2/3)*q^13 - q^14 + (-2/3*a + 4/3)*q^15 + q^16 + a*q^17 + q^18 + (2/3*a + 2/3)*q^19 + (-1/3*a + 2/3)*q^20 - 2*q^21 + (2/3*a + 2/3)*q^22 + (-4/3*a - 10/3)*q^23 + 2*q^24 + (-2/3*a - 5/3)*q^25 + (1/3*a - 2/3)*q^26 - 4*q^27 - q^28 - q^29 + (-2/3*a + 4/3)*q^30 + (-a + 2)*q^31 + q^32 + (4/3*a + 4/3)*q^33 + a*q^34 + (1/3*a - 2/3)*q^35 + q^36 - 4*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (1/2*a^2 - 1/2*a - 1)*q^5 - a*q^6 - q^7 - q^8 + (a^2 - 3)*q^9 + (-1/2*a^2 + 1/2*a + 1)*q^10 + (-a^2 + 6)*q^11 + a*q^12 + (-1/2*a^2 + 1/2*a + 5)*q^13 + q^14 + (3*a - 2)*q^15 + q^16 + (-1/2*a^2 + 3/2*a + 5)*q^17 + (-a^2 + 3)*q^18 + (-2*a - 2)*q^19 + (1/2*a^2 - 1/2*a - 1)*q^20 - a*q^21 + (a^2 - 6)*q^22 + (-a^2 - a + 8)*q^23 - a*q^24 + (a^2 - 2*a - 3)*q^25 + (1/2*a^2 - 1/2*a - 5)*q^26 + (a^2 + 2*a - 4)*q^27 - q^28 + q^29 + (-3*a + 2)*q^30 + (-1/2*a^2 - 3/2*a + 5)*q^31 - q^32 + (-a^2 - 2*a + 4)*q^33 + (1/2*a^2 - 3/2*a - 5)*q^34 + (-1/2*a^2 + 1/2*a + 1)*q^35 + (a^2 - 3)*q^36 + (a^2 - a - 2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (1/4*a^3 - 3/4*a^2 - 2*a + 3)*q^5 + a*q^6 + q^7 + q^8 + (a^2 - 3)*q^9 + (1/4*a^3 - 3/4*a^2 - 2*a + 3)*q^10 + (-a + 2)*q^11 + a*q^12 + (-3/4*a^3 + 1/4*a^2 + 6*a - 1)*q^13 + q^14 + (-1/2*a^3 + 1/2*a^2 + 2*a - 2)*q^15 + q^16 + (-1/4*a^3 + 3/4*a^2 + a - 3)*q^17 + (a^2 - 3)*q^18 + (1/2*a^3 - 1/2*a^2 - 5*a + 2)*q^19 + (1/4*a^3 - 3/4*a^2 - 2*a + 3)*q^20 + a*q^21 + (-a + 2)*q^22 + (-1/2*a^3 + 1/2*a^2 + 5*a)*q^23 + a*q^24 + (a^3 - a^2 - 9*a + 5)*q^25 + (-3/4*a^3 + 1/4*a^2 + 6*a - 1)*q^26 + (a^3 - 6*a)*q^27 + q^28 + q^29 + (-1/2*a^3 + 1/2*a^2 + 2*a - 2)*q^30 + (1/4*a^3 + 1/4*a^2 - 5*a - 3)*q^31 + q^32 + (-a^2 + 2*a)*q^33 + (-1/4*a^3 + 3/4*a^2 + a - 3)*q^34 + (1/4*a^3 - 3/4*a^2 - 2*a + 3)*q^35 + (a^2 - 3)*q^36 + (1/2*a^3 - 1/2*a^2 - 3*a - 2)*q^37 + O(q^38)
*]> ;  // time = 198.92 seconds




J[407] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 407, 407, 407, 407, 37, 37, 11 ], new_dimensions := [ 4, 4, 11, 12, 1, 1, 1 ], dimensions := [ 4, 4, 11, 12, 2, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 7, 1, 1, 1, 0, 1, 1, 1, 3, 7, 1, 1, 0, 1, 1, 15, 1, 1, 1, 1, 0, 17, 1, 41, 7, 1, 1, 17, 0, 1, 1, 1, 3, 15, 1, 1, 0, 1, 1, 7, 1, 41, 1, 1, 0 ], ap_traces := [
[ -1, 0, 1, -7, -4, -10, -9, -6, -4, 1, 6, -4 ],
[ 1, -4, -5, -1, 4, -12, -13, -2, -6, 1, -8, 4 ],
[ 2, 0, 1, 9, -11, 22, 19, 14, -14, 13, 12, 11 ],
[ 1, 8, 5, 7, 12, 14, 9, -2, 8, -17, -10, -12 ]
], hecke_fields := [
x^4 + x^3 - 4*x^2 + 1,
x^4 - x^3 - 4*x^2 + 2*x + 3,
x^11 - 2*x^10 - 16*x^9 + 32*x^8 + 89*x^7 - 179*x^6 - 201*x^5 + 407*x^4 + 168*x^3 - 333*x^2 - 51*x + 75,
x^12 - x^11 - 18*x^10 + 18*x^9 + 111*x^8 - 104*x^7 - 274*x^6 + 212*x^5 + 255*x^4 - 129*x^3 - 78*x^2 + 4*x + 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 7, 1 ],
[ 3, 7 ],
[ 45, 3 ],
[ 323, 41 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 3, 7 ],
[ 1, 3 ],
[ 323, 1 ]
], torsion_upper_bounds := [ 1, 3, 3, 19 ], torsion_lower_bounds := [ 1, 1, 3, 19 ], l_ratios := [ 0, 0, 1/3, 17/19 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
a,
a^3 + a^2 - 4*a,
-a^3 - a^2 + 3*a,
-2*a^3 - 3*a^2 + 6*a,
-1,
a^3 + a^2 - 2*a - 2,
a^3 + 3*a^2 - a - 6,
3*a^3 + 6*a^2 - 7*a - 7,
-a^3 + 5*a - 3,
a^3 - 6*a + 2,
3*a^3 + 2*a^2 - 11*a + 4,
-1
],
[
a,
-a^3 + a^2 + 2*a - 2,
a^3 - a^2 - 3*a,
-a^2 + 2,
1,
-a^3 + a^2 + 2*a - 4,
-a^3 - a^2 + 3*a,
3*a^3 - 4*a^2 - 7*a + 5,
-a^3 + 4*a^2 + a - 9,
-3*a^3 + 4*a^2 + 10*a - 6,
a^3 + a - 4,
1
],
[
a,
10/59*a^10 - 1/59*a^9 - 156/59*a^8 + 831/59*a^6 + 78/59*a^5 - 1732/59*a^4 - 330/59*a^3 + 1171/59*a^2 + 305/59*a - 196/59,
-83/59*a^10 + 26/59*a^9 + 1342/59*a^8 - 6*a^7 - 7564/59*a^6 + 1630/59*a^5 + 17420/59*a^4 - 2512/59*a^3 - 14457/59*a^2 + 448/59*a + 3090/59,
61/59*a^10 - 12/59*a^9 - 987/59*a^8 + 3*a^7 + 5547/59*a^6 - 893/59*a^5 - 12701/59*a^4 + 1409/59*a^3 + 10512/59*a^2 - 57/59*a - 2234/59,
-1,
100/59*a^10 - 10/59*a^9 - 1619/59*a^8 + 2*a^7 + 9136/59*a^6 - 459/59*a^5 - 21096/59*a^4 + 181/59*a^3 + 17610/59*a^2 + 1044/59*a - 3671/59,
-1/59*a^10 + 6/59*a^9 - 8/59*a^8 - 2*a^7 + 265/59*a^6 + 771/59*a^5 - 1467/59*a^4 - 1855/59*a^3 + 2532/59*a^2 + 1238/59*a - 771/59,
-148/59*a^10 + 3/59*a^9 + 2415/59*a^8 - 13762/59*a^6 - 175/59*a^5 + 32218/59*a^4 + 1167/59*a^3 - 27526/59*a^2 - 1977/59*a + 6193/59,
161/59*a^10 - 22/59*a^9 - 2606/59*a^8 + 5*a^7 + 14683/59*a^6 - 1411/59*a^5 - 33797/59*a^4 + 2121/59*a^3 + 28122/59*a^2 - 75/59*a - 6141/59,
-161/59*a^10 + 22/59*a^9 + 2606/59*a^8 - 5*a^7 - 14683/59*a^6 + 1352/59*a^5 + 33797/59*a^4 - 1590/59*a^3 - 28122/59*a^2 - 987/59*a + 6141/59,
202/59*a^10 - 32/59*a^9 - 3281/59*a^8 + 7*a^7 + 18627/59*a^6 - 1811/59*a^5 - 43565/59*a^4 + 2243/59*a^3 + 37531/59*a^2 + 615/59*a - 8396/59,
1
],
[
a,
-370/249*a^11 + 52/249*a^10 + 6619/249*a^9 - 934/249*a^8 - 40324/249*a^7 + 1087/83*a^6 + 94670/249*a^5 + 5092/249*a^4 - 67508/249*a^3 - 10735/249*a^2 + 3599/249*a - 66/83,
142/249*a^11 + 11/249*a^10 - 2512/249*a^9 - 188/249*a^8 + 15010/249*a^7 + 704/83*a^6 - 33614/249*a^5 - 10396/249*a^4 + 19526/249*a^3 + 11563/249*a^2 + 2806/249*a - 164/83,
-239/249*a^11 + 113/249*a^10 + 4256/249*a^9 - 2135/249*a^8 - 25856/249*a^7 + 4078/83*a^6 + 61468/249*a^5 - 22588/249*a^4 - 49207/249*a^3 + 12121/249*a^2 + 8362/249*a - 153/83,
1,
350/249*a^11 + 18/83*a^10 - 6250/249*a^9 - 285/83*a^8 + 38086/249*a^7 + 6716/249*a^6 - 89371/249*a^5 - 8440/83*a^4 + 61757/249*a^3 + 7256/83*a^2 - 320/249*a + 1199/249,
157/83*a^11 + 85/249*a^10 - 8470/249*a^9 - 1498/249*a^8 + 52099/249*a^7 + 12004/249*a^6 - 41344/83*a^5 - 43526/249*a^4 + 88595/249*a^3 + 39143/249*a^2 - 3587/249*a - 512/249,
-92/83*a^11 + 56/83*a^10 + 1631/83*a^9 - 1025/83*a^8 - 9830/83*a^7 + 5772/83*a^6 + 23147/83*a^5 - 10580/83*a^4 - 18885/83*a^3 + 5384/83*a^2 + 4227/83*a - 143/83,
295/249*a^11 + 55/249*a^10 - 1752/83*a^9 - 940/249*a^8 + 10630/83*a^7 + 7406/249*a^6 - 74114/249*a^5 - 27080/249*a^4 + 16469/83*a^3 + 25445/249*a^2 + 582/83*a - 634/249,
395/249*a^11 + 63/83*a^10 - 7018/249*a^9 - 1122/83*a^8 + 42250/249*a^7 + 23174/249*a^6 - 95131/249*a^5 - 22900/83*a^4 + 51602/249*a^3 + 19005/83*a^2 + 13654/249*a - 1240/249,
-733/249*a^11 + 14/83*a^10 + 13196/249*a^9 - 277/83*a^8 - 81284/249*a^7 + 926/249*a^6 + 194918/249*a^5 + 6900/83*a^4 - 146611/249*a^3 - 8946/83*a^2 + 13234/249*a - 211/249,
-1
]
*], q_expansions := [*
q + a*q^2 + (a^3 + a^2 - 4*a)*q^3 + (a^2 - 2)*q^4 + (-a^3 - a^2 + 3*a)*q^5 - q^6 + (-2*a^3 - 3*a^2 + 6*a)*q^7 + (a^3 - 4*a)*q^8 + (-a^2 - a + 1)*q^9 + (-a^2 + 1)*q^10 - q^11 + (-2*a^3 - 2*a^2 + 7*a)*q^12 + (a^3 + a^2 - 2*a - 2)*q^13 + (-a^3 - 2*a^2 + 2)*q^14 + (a^2 + a - 3)*q^15 + (-a^3 - 2*a^2 + 3)*q^16 + (a^3 + 3*a^2 - a - 6)*q^17 + (-a^3 - a^2 + a)*q^18 + (3*a^3 + 6*a^2 - 7*a - 7)*q^19 + (a^3 + 2*a^2 - 5*a)*q^20 + (2*a^2 + 3*a - 6)*q^21 - a*q^22 + (-a^3 + 5*a - 3)*q^23 + (-a^2 + 4)*q^24 + (-a - 3)*q^25 + (2*a^2 - 2*a - 1)*q^26 + (-2*a^3 - 2*a^2 + 9*a + 1)*q^27 + (3*a^3 + 2*a^2 - 10*a + 1)*q^28 + (a^3 - 6*a + 2)*q^29 + (a^3 + a^2 - 3*a)*q^30 + (3*a^3 + 2*a^2 - 11*a + 4)*q^31 + (-3*a^3 - 4*a^2 + 11*a + 1)*q^32 + (-a^3 - a^2 + 4*a)*q^33 + (2*a^3 + 3*a^2 - 6*a - 1)*q^34 + (a^3 - 3*a + 4)*q^35 + (-a^2 + 2*a - 1)*q^36 - q^37 + O(q^38),
q + a*q^2 + (-a^3 + a^2 + 2*a - 2)*q^3 + (a^2 - 2)*q^4 + (a^3 - a^2 - 3*a)*q^5 + (-2*a^2 + 3)*q^6 + (-a^2 + 2)*q^7 + (a^3 - 4*a)*q^8 + (2*a^3 - a^2 - 5*a + 1)*q^9 + (a^2 - 2*a - 3)*q^10 + q^11 + (-2*a^2 - a + 4)*q^12 + (-a^3 + a^2 + 2*a - 4)*q^13 + (-a^3 + 2*a)*q^14 + (a^2 + a - 3)*q^15 + (a^3 - 2*a^2 - 2*a + 1)*q^16 + (-a^3 - a^2 + 3*a)*q^17 + (a^3 + 3*a^2 - 3*a - 6)*q^18 + (3*a^3 - 4*a^2 - 7*a + 5)*q^19 + (-a^3 + 3*a)*q^20 + (2*a^2 + a - 4)*q^21 + a*q^22 + (-a^3 + 4*a^2 + a - 9)*q^23 + (-2*a^3 + 3*a^2 + 4*a - 6)*q^24 + (-2*a^3 + 7*a + 1)*q^25 + (-2*a^2 - 2*a + 3)*q^26 + (-2*a^2 + a + 1)*q^27 + (-a^3 + 2*a - 1)*q^28 + (-3*a^3 + 4*a^2 + 10*a - 6)*q^29 + (a^3 + a^2 - 3*a)*q^30 + (a^3 + a - 4)*q^31 + (-3*a^3 + 2*a^2 + 7*a - 3)*q^32 + (-a^3 + a^2 + 2*a - 2)*q^33 + (-2*a^3 - a^2 + 2*a + 3)*q^34 + (a^3 - 3*a)*q^35 + (3*a^2 + 2*a - 5)*q^36 + q^37 + O(q^38),
q + a*q^2 + (10/59*a^10 - 1/59*a^9 - 156/59*a^8 + 831/59*a^6 + 78/59*a^5 - 1732/59*a^4 - 330/59*a^3 + 1171/59*a^2 + 305/59*a - 196/59)*q^3 + (a^2 - 2)*q^4 + (-83/59*a^10 + 26/59*a^9 + 1342/59*a^8 - 6*a^7 - 7564/59*a^6 + 1630/59*a^5 + 17420/59*a^4 - 2512/59*a^3 - 14457/59*a^2 + 448/59*a + 3090/59)*q^5 + (19/59*a^10 + 4/59*a^9 - 320/59*a^8 - a^7 + 1868/59*a^6 + 278/59*a^5 - 4400/59*a^4 - 509/59*a^3 + 3635/59*a^2 + 314/59*a - 750/59)*q^6 + (61/59*a^10 - 12/59*a^9 - 987/59*a^8 + 3*a^7 + 5547/59*a^6 - 893/59*a^5 - 12701/59*a^4 + 1409/59*a^3 + 10512/59*a^2 - 57/59*a - 2234/59)*q^7 + (a^3 - 4*a)*q^8 + (31/59*a^10 - 9/59*a^9 - 519/59*a^8 + 2*a^7 + 3054/59*a^6 - 478/59*a^5 - 7446/59*a^4 + 452/59*a^3 + 6763/59*a^2 + 385/59*a - 1528/59)*q^9 + (-140/59*a^10 + 14/59*a^9 + 2302/59*a^8 - 3*a^7 - 13227/59*a^6 + 737/59*a^5 + 31269/59*a^4 - 513/59*a^3 - 27191/59*a^2 - 1143/59*a + 6225/59)*q^10 - q^11 + (22/59*a^10 - 14/59*a^9 - 355/59*a^8 + 3*a^7 + 2017/59*a^6 - 737/59*a^5 - 4778/59*a^4 + 1103/59*a^3 + 4299/59*a^2 - 391/59*a - 1033/59)*q^12 + (100/59*a^10 - 10/59*a^9 - 1619/59*a^8 + 2*a^7 + 9136/59*a^6 - 459/59*a^5 - 21096/59*a^4 + 181/59*a^3 + 17610/59*a^2 + 1044/59*a - 3671/59)*q^13 + (110/59*a^10 - 11/59*a^9 - 1775/59*a^8 + 2*a^7 + 10026/59*a^6 - 440/59*a^5 - 23418/59*a^4 + 264/59*a^3 + 20256/59*a^2 + 877/59*a - 4575/59)*q^14 + (-48/59*a^10 - 7/59*a^9 + 796/59*a^8 + 2*a^7 - 4626/59*a^6 - 634/59*a^5 + 11122/59*a^4 + 1348/59*a^3 - 10034/59*a^2 - 815/59*a + 2640/59)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/59*a^10 + 6/59*a^9 - 8/59*a^8 - 2*a^7 + 265/59*a^6 + 771/59*a^5 - 1467/59*a^4 - 1855/59*a^3 + 2532/59*a^2 + 1238/59*a - 771/59)*q^17 + (53/59*a^10 - 23/59*a^9 - 874/59*a^8 + 5*a^7 + 5071/59*a^6 - 1215/59*a^5 - 12165/59*a^4 + 1555/59*a^3 + 10708/59*a^2 + 53/59*a - 2325/59)*q^18 + (-148/59*a^10 + 3/59*a^9 + 2415/59*a^8 - 13762/59*a^6 - 175/59*a^5 + 32218/59*a^4 + 1167/59*a^3 - 27526/59*a^2 - 1977/59*a + 6193/59)*q^19 + (-100/59*a^10 + 10/59*a^9 + 1619/59*a^8 - a^7 - 9195/59*a^6 - 131/59*a^5 + 21627/59*a^4 + 1353/59*a^3 - 18849/59*a^2 - 1811/59*a + 4320/59)*q^20 + (108/59*a^10 + 1/59*a^9 - 1732/59*a^8 - a^7 + 9671/59*a^6 + 453/59*a^5 - 22163/59*a^4 - 1381/59*a^3 + 18653/59*a^2 + 1288/59*a - 4229/59)*q^21 - a*q^22 + (161/59*a^10 - 22/59*a^9 - 2606/59*a^8 + 5*a^7 + 14683/59*a^6 - 1411/59*a^5 - 33797/59*a^4 + 2121/59*a^3 + 28122/59*a^2 - 75/59*a - 6141/59)*q^23 + (-8/59*a^10 - 11/59*a^9 + 113/59*a^8 + 3*a^7 - 535/59*a^6 - 912/59*a^5 + 949/59*a^4 + 1621/59*a^3 - 335/59*a^2 - 539/59*a - 150/59)*q^24 + (-170/59*a^10 + 17/59*a^9 + 2770/59*a^8 - 3*a^7 - 15779/59*a^6 + 503/59*a^5 + 37055/59*a^4 + 477/59*a^3 - 32179/59*a^2 - 2058/59*a + 7580/59)*q^25 + (190/59*a^10 - 19/59*a^9 - 3082/59*a^8 + 4*a^7 + 17441/59*a^6 - 996/59*a^5 - 40519/59*a^4 + 810/59*a^3 + 34344/59*a^2 + 1429/59*a - 7500/59)*q^26 + (-71/59*a^10 + 13/59*a^9 + 1143/59*a^8 - 3*a^7 - 6437/59*a^6 + 815/59*a^5 + 15023/59*a^4 - 961/59*a^3 - 13158/59*a^2 - 720/59*a + 3020/59)*q^27 + (87/59*a^10 + 9/59*a^9 - 1428/59*a^8 - 2*a^7 + 8156/59*a^6 + 478/59*a^5 - 19104/59*a^4 - 1042/59*a^3 + 16483/59*a^2 + 1149/59*a - 3782/59)*q^28 + (-161/59*a^10 + 22/59*a^9 + 2606/59*a^8 - 5*a^7 - 14683/59*a^6 + 1352/59*a^5 + 33797/59*a^4 - 1590/59*a^3 - 28122/59*a^2 - 987/59*a + 6141/59)*q^29 + (-103/59*a^10 + 28/59*a^9 + 1654/59*a^8 - 6*a^7 - 9226/59*a^6 + 1474/59*a^5 + 20884/59*a^4 - 1970/59*a^3 - 16799/59*a^2 + 192/59*a + 3600/59)*q^30 + (202/59*a^10 - 32/59*a^9 - 3281/59*a^8 + 7*a^7 + 18627/59*a^6 - 1811/59*a^5 - 43565/59*a^4 + 2243/59*a^3 + 37531/59*a^2 + 615/59*a - 8396/59)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-10/59*a^10 + 1/59*a^9 + 156/59*a^8 - 831/59*a^6 - 78/59*a^5 + 1732/59*a^4 + 330/59*a^3 - 1171/59*a^2 - 305/59*a + 196/59)*q^33 + (4/59*a^10 - 24/59*a^9 - 86/59*a^8 + 6*a^7 + 592/59*a^6 - 1668/59*a^5 - 1448/59*a^4 + 2700/59*a^3 + 905/59*a^2 - 822/59*a + 75/59)*q^34 + (-202/59*a^10 + 32/59*a^9 + 3281/59*a^8 - 7*a^7 - 18627/59*a^6 + 1811/59*a^5 + 43565/59*a^4 - 2243/59*a^3 - 37413/59*a^2 - 733/59*a + 8160/59)*q^35 + (21/59*a^10 - 8/59*a^9 - 363/59*a^8 + 2*a^7 + 2164/59*a^6 - 556/59*a^5 - 5124/59*a^4 + 900/59*a^3 + 4176/59*a^2 - 392/59*a - 919/59)*q^36 + q^37 + O(q^38),
q + a*q^2 + (-370/249*a^11 + 52/249*a^10 + 6619/249*a^9 - 934/249*a^8 - 40324/249*a^7 + 1087/83*a^6 + 94670/249*a^5 + 5092/249*a^4 - 67508/249*a^3 - 10735/249*a^2 + 3599/249*a - 66/83)*q^3 + (a^2 - 2)*q^4 + (142/249*a^11 + 11/249*a^10 - 2512/249*a^9 - 188/249*a^8 + 15010/249*a^7 + 704/83*a^6 - 33614/249*a^5 - 10396/249*a^4 + 19526/249*a^3 + 11563/249*a^2 + 2806/249*a - 164/83)*q^5 + (-106/83*a^11 - 41/249*a^10 + 5726/249*a^9 + 746/249*a^8 - 35219/249*a^7 - 6710/249*a^6 + 27844/83*a^5 + 26842/249*a^4 - 58465/249*a^3 - 25261/249*a^2 + 1282/249*a + 370/249)*q^6 + (-239/249*a^11 + 113/249*a^10 + 4256/249*a^9 - 2135/249*a^8 - 25856/249*a^7 + 4078/83*a^6 + 61468/249*a^5 - 22588/249*a^4 - 49207/249*a^3 + 12121/249*a^2 + 8362/249*a - 153/83)*q^7 + (a^3 - 4*a)*q^8 + (10/83*a^11 + 7/249*a^10 - 595/249*a^9 - 97/249*a^8 + 4270/249*a^7 + 514/249*a^6 - 4434/83*a^5 - 1364/249*a^4 + 16802/249*a^3 + 1337/249*a^2 - 6371/249*a + 34/249)*q^9 + (51/83*a^11 + 44/249*a^10 - 2744/249*a^9 - 752/249*a^8 + 16880/249*a^7 + 5294/249*a^6 - 13500/83*a^5 - 16684/249*a^4 + 29881/249*a^3 + 13882/249*a^2 - 1060/249*a - 142/249)*q^10 + q^11 + (127/83*a^11 - 34/83*a^10 - 2256/83*a^9 + 649/83*a^8 + 13622/83*a^7 - 3374/83*a^6 - 31694/83*a^5 + 4147/83*a^4 + 22911/83*a^3 - 684/83*a^2 - 1852/83*a + 238/83)*q^12 + (350/249*a^11 + 18/83*a^10 - 6250/249*a^9 - 285/83*a^8 + 38086/249*a^7 + 6716/249*a^6 - 89371/249*a^5 - 8440/83*a^4 + 61757/249*a^3 + 7256/83*a^2 - 320/249*a + 1199/249)*q^13 + (-42/83*a^11 - 46/249*a^10 + 2167/249*a^9 + 673/249*a^8 - 12622/249*a^7 - 4018/249*a^6 + 9360/83*a^5 + 11738/249*a^4 - 18710/249*a^3 - 10280/249*a^2 + 497/249*a + 239/249)*q^14 + (-614/249*a^11 - 116/83*a^10 + 11071/249*a^9 + 2058/83*a^8 - 68524/249*a^7 - 41252/249*a^6 + 164248/249*a^5 + 38824/83*a^4 - 113816/249*a^3 - 30788/83*a^2 - 2761/249*a + 2104/249)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (157/83*a^11 + 85/249*a^10 - 8470/249*a^9 - 1498/249*a^8 + 52099/249*a^7 + 12004/249*a^6 - 41344/83*a^5 - 43526/249*a^4 + 88595/249*a^3 + 39143/249*a^2 - 3587/249*a - 512/249)*q^17 + (37/249*a^11 - 55/249*a^10 - 637/249*a^9 + 940/249*a^8 + 3634/249*a^7 - 1694/83*a^6 - 7724/249*a^5 + 9152/249*a^4 + 5207/249*a^3 - 4031/249*a^2 - 86/249*a - 10/83)*q^18 + (-92/83*a^11 + 56/83*a^10 + 1631/83*a^9 - 1025/83*a^8 - 9830/83*a^7 + 5772/83*a^6 + 23147/83*a^5 - 10580/83*a^4 - 18885/83*a^3 + 5384/83*a^2 + 4227/83*a - 143/83)*q^19 + (-29/83*a^11 - 4/83*a^10 + 506/83*a^9 + 91/83*a^8 - 2938/83*a^7 - 934/83*a^6 + 6036/83*a^5 + 3886/83*a^4 - 1811/83*a^3 - 4084/83*a^2 - 2122/83*a + 277/83)*q^20 + (53/83*a^11 - 104/249*a^10 - 2863/249*a^9 + 1868/249*a^8 + 17734/249*a^7 - 10340/249*a^6 - 14752/83*a^5 + 18700/249*a^4 + 41807/249*a^3 - 10402/249*a^2 - 12593/249*a + 1558/249)*q^21 + a*q^22 + (295/249*a^11 + 55/249*a^10 - 1752/83*a^9 - 940/249*a^8 + 10630/83*a^7 + 7406/249*a^6 - 74114/249*a^5 - 27080/249*a^4 + 16469/83*a^3 + 25445/249*a^2 + 582/83*a - 634/249)*q^23 + (305/83*a^11 + 172/249*a^10 - 16363/249*a^9 - 2917/249*a^8 + 99940/249*a^7 + 22732/249*a^6 - 78465/83*a^5 - 82106/249*a^4 + 164027/249*a^3 + 74684/249*a^2 - 3374/249*a - 1121/249)*q^24 + (829/249*a^11 + 80/249*a^10 - 14851/249*a^9 - 1322/249*a^8 + 90964/249*a^7 + 4290/83*a^6 - 216170/249*a^5 - 57634/249*a^4 + 158147/249*a^3 + 58108/249*a^2 - 11759/249*a - 325/83)*q^25 + (404/249*a^11 + 50/249*a^10 - 2385/83*a^9 - 764/249*a^8 + 14372/83*a^7 + 6529/249*a^6 - 99520/249*a^5 - 27493/249*a^4 + 22306/83*a^3 + 26980/249*a^2 - 67/83*a - 350/249)*q^26 + (-285/83*a^11 + 91/249*a^10 + 15173/249*a^9 - 1759/249*a^8 - 91400/249*a^7 + 5686/249*a^6 + 70178/83*a^5 + 15634/249*a^4 - 143371/249*a^3 - 29431/249*a^2 + 3331/249*a + 691/249)*q^27 + (102/83*a^11 - 109/83*a^10 - 1857/83*a^9 + 1878/83*a^8 + 11530/83*a^7 - 10304/83*a^6 - 28162/83*a^5 + 19532/83*a^4 + 23960/83*a^3 - 11191/83*a^2 - 5327/83*a + 348/83)*q^28 + (395/249*a^11 + 63/83*a^10 - 7018/249*a^9 - 1122/83*a^8 + 42250/249*a^7 + 23174/249*a^6 - 95131/249*a^5 - 22900/83*a^4 + 51602/249*a^3 + 19005/83*a^2 + 13654/249*a - 1240/249)*q^29 + (-962/249*a^11 + 19/249*a^10 + 5742/83*a^9 - 370/249*a^8 - 35036/83*a^7 - 3988/249*a^6 + 246640/249*a^5 + 42754/249*a^4 - 57190/83*a^3 - 50653/249*a^2 + 1520/83*a + 614/249)*q^30 + (-733/249*a^11 + 14/83*a^10 + 13196/249*a^9 - 277/83*a^8 - 81284/249*a^7 + 926/249*a^6 + 194918/249*a^5 + 6900/83*a^4 - 146611/249*a^3 - 8946/83*a^2 + 13234/249*a - 211/249)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-370/249*a^11 + 52/249*a^10 + 6619/249*a^9 - 934/249*a^8 - 40324/249*a^7 + 1087/83*a^6 + 94670/249*a^5 + 5092/249*a^4 - 67508/249*a^3 - 10735/249*a^2 + 3599/249*a - 66/83)*q^33 + (556/249*a^11 + 8/249*a^10 - 9976/249*a^9 - 182/249*a^8 + 60988/249*a^7 + 1674/83*a^6 - 143378/249*a^5 - 31510/249*a^4 + 99902/249*a^3 + 33151/249*a^2 - 2396/249*a - 157/83)*q^34 + (35/249*a^11 - 476/249*a^10 - 542/249*a^9 + 8339/249*a^8 + 2132/249*a^7 - 16354/83*a^6 - 994/249*a^5 + 108688/249*a^4 + 3445/249*a^3 - 71494/249*a^2 - 9826/249*a + 917/83)*q^35 + (-26/83*a^11 + 5/83*a^10 + 488/83*a^9 - 93/83*a^8 - 3258/83*a^7 + 462/83*a^6 + 9304/83*a^5 - 500/83*a^4 - 10954/83*a^3 + 42/83*a^2 + 4188/83*a - 35/83)*q^36 - q^37 + O(q^38)
*]> ;  // time = 71.851 seconds




J[409] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 409, 409 ], new_dimensions := [ 13, 20 ], dimensions := [ 13, 20 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -6, -3, -10, -9, -26, -3, -8, -15, -31, -12, -24, 0 ],
[ 5, 1, 8, 5, 30, -7, 6, 1, 37, 12, 10, -4 ]
], hecke_fields := [
x^13 + 6*x^12 + 2*x^11 - 47*x^10 - 64*x^9 + 117*x^8 + 226*x^7 - 94*x^6 - 278*x^5 + 9*x^4 + 134*x^3 + 15*x^2 - 22*x - 4,
x^20 - 5*x^19 - 19*x^18 + 126*x^17 + 100*x^16 - 1283*x^15 + 247*x^14 + 6767*x^13 - 4554*x^12 - 19689*x^11 + 18771*x^10 + 31011*x^9 - 35515*x^8 - 23548*x^7 + 31466*x^6 + 5354*x^5 - 10552*x^4 + 1129*x^3 + 523*x^2 - 54*x - 4
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 17 ]
], tamagawa_numbers := [
[ 1 ],
[ 17 ]
], torsion_upper_bounds := [ 1, 17 ], torsion_lower_bounds := [ 1, 17 ], l_ratios := [ 0, 1/17 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
1/2*a^12 + 2*a^11 - 5*a^10 - 51/2*a^9 + 14*a^8 + 237/2*a^7 + a^6 - 241*a^5 - 45*a^4 + 397/2*a^3 + 34*a^2 - 97/2*a - 7,
3*a^12 + 19*a^11 + 14*a^10 - 128*a^9 - 237*a^8 + 208*a^7 + 696*a^6 + 102*a^5 - 617*a^4 - 284*a^3 + 134*a^2 + 91*a + 9,
-11/2*a^12 - 33*a^11 - 14*a^10 + 483/2*a^9 + 349*a^8 - 1029/2*a^7 - 1088*a^6 + 219*a^5 + 1021*a^4 + 277/2*a^3 - 245*a^2 - 141/2*a - 9,
a^12 + 6*a^11 + 2*a^10 - 46*a^9 - 60*a^8 + 111*a^7 + 191*a^6 - 90*a^5 - 180*a^4 + 31*a^3 + 42*a^2 - 7*a - 1,
5/2*a^12 + 17*a^11 + 18*a^10 - 213/2*a^9 - 246*a^8 + 243/2*a^7 + 697*a^6 + 265*a^5 - 602*a^4 - 855/2*a^3 + 118*a^2 + 263/2*a + 14,
-1/2*a^12 - 3*a^11 + 55/2*a^9 + 26*a^8 - 189/2*a^7 - 111*a^6 + 152*a^5 + 170*a^4 - 229/2*a^3 - 96*a^2 + 65/2*a + 14,
-7*a^12 - 44*a^11 - 29*a^10 + 305*a^9 + 525*a^8 - 555*a^7 - 1557*a^6 - 33*a^5 + 1383*a^4 + 462*a^3 - 285*a^2 - 160*a - 27,
8*a^12 + 45*a^11 + a^10 - 365*a^9 - 371*a^8 + 987*a^7 + 1317*a^6 - 1038*a^5 - 1437*a^4 + 478*a^3 + 491*a^2 - 78*a - 37,
-a^12 + 2*a^11 + 45*a^10 + 62*a^9 - 288*a^8 - 585*a^7 + 575*a^6 + 1597*a^5 - 219*a^4 - 1483*a^3 - 161*a^2 + 391*a + 75,
5/2*a^12 + 16*a^11 + 12*a^10 - 217/2*a^9 - 199*a^8 + 369/2*a^7 + 580*a^6 + 56*a^5 - 499*a^4 - 435/2*a^3 + 76*a^2 + 155/2*a + 17,
-a^12 - 12*a^11 - 37*a^10 + 36*a^9 + 324*a^8 + 233*a^7 - 796*a^6 - 1026*a^5 + 556*a^4 + 1069*a^3 - 14*a^2 - 293*a - 47
],
[
a,
5906164375/162850891556*a^19 - 15774159671/81425445778*a^18 - 107686582751/162850891556*a^17 + 798722115271/162850891556*a^16 + 481520956263/162850891556*a^15 - 2050473493008/40712722889*a^14 + 2498437987155/162850891556*a^13 + 21972471737353/81425445778*a^12 - 7959712712957/40712722889*a^11 - 131831067667341/162850891556*a^10 + 30712236161176/40712722889*a^9 + 221211978185803/162850891556*a^8 - 55611571523398/40712722889*a^7 - 48608103951096/40712722889*a^6 + 46652982992112/40712722889*a^5 + 17979458538027/40712722889*a^4 - 28038937609583/81425445778*a^3 - 2326223684821/162850891556*a^2 + 443586426186/40712722889*a - 44065152976/40712722889,
-2560786107/162850891556*a^19 + 9076732659/162850891556*a^18 + 60298895933/162850891556*a^17 - 229379147681/162850891556*a^16 - 275927126505/81425445778*a^15 + 2347011223577/162850891556*a^14 + 597961855763/40712722889*a^13 - 3120181347050/40712722889*a^12 - 4248976214165/162850891556*a^11 + 36854713614423/162850891556*a^10 - 613197361755/40712722889*a^9 - 59975401748255/162850891556*a^8 + 21817021655123/162850891556*a^7 + 12621195418983/40712722889*a^6 - 32869974381839/162850891556*a^5 - 9941198174579/81425445778*a^4 + 19691957684943/162850891556*a^3 + 4110537282939/162850891556*a^2 - 1895999523577/81425445778*a - 33987898180/40712722889,
25967484603/162850891556*a^19 - 57287577643/81425445778*a^18 - 136636999142/40712722889*a^17 + 2908280870845/162850891556*a^16 + 3943405627137/162850891556*a^15 - 29902354806501/162850891556*a^14 - 1852661628937/40712722889*a^13 + 159894514950179/162850891556*a^12 - 11094767296944/40712722889*a^11 - 237527794880135/81425445778*a^10 + 133859388171295/81425445778*a^9 + 775451110931723/162850891556*a^8 - 140433841924434/40712722889*a^7 - 635389645330641/162850891556*a^6 + 128860831319787/40712722889*a^5 + 194732099068897/162850891556*a^4 - 42558736550317/40712722889*a^3 + 1528087372629/81425445778*a^2 + 3059320582297/81425445778*a - 14140300195/40712722889,
10914238563/325701783112*a^19 - 29673377197/162850891556*a^18 - 205434567225/325701783112*a^17 + 1520932471077/325701783112*a^16 + 1066479838551/325701783112*a^15 - 7946023085995/162850891556*a^14 + 2622590359827/325701783112*a^13 + 43689523869755/162850891556*a^12 - 23469433898305/162850891556*a^11 - 272921271717275/325701783112*a^10 + 93548041203723/162850891556*a^9 + 489467605119575/325701783112*a^8 - 42211064794523/40712722889*a^7 - 242484222571247/162850891556*a^6 + 140271650291825/162850891556*a^5 + 117544975345383/162850891556*a^4 - 11034497100645/40712722889*a^3 - 39745436607747/325701783112*a^2 + 3899677406031/162850891556*a + 435370372621/81425445778,
32049403425/162850891556*a^19 - 33909880642/40712722889*a^18 - 692164300671/162850891556*a^17 + 3439765523177/162850891556*a^16 + 5339890532871/162850891556*a^15 - 8839357204006/40712722889*a^14 - 14317952707495/162850891556*a^13 + 47328312802098/40712722889*a^12 - 12602053520053/81425445778*a^11 - 565386893447353/162850891556*a^10 + 59039918075223/40712722889*a^9 + 937073342406945/162850891556*a^8 - 264395441890469/81425445778*a^7 - 401484825414553/81425445778*a^6 + 247631367575193/81425445778*a^5 + 145072020213637/81425445778*a^4 - 41882994058594/40712722889*a^3 - 20644361846253/162850891556*a^2 + 1932254681161/40712722889*a + 157473499787/40712722889,
30128947659/162850891556*a^19 - 134862255993/162850891556*a^18 - 157849172126/40712722889*a^17 + 3431412588733/162850891556*a^16 + 1126932777902/40712722889*a^15 - 17707174872785/81425445778*a^14 - 7932753034815/162850891556*a^13 + 190559920917919/162850891556*a^12 - 54777944057259/162850891556*a^11 - 286255787588921/81425445778*a^10 + 79723298760756/40712722889*a^9 + 954989470968277/162850891556*a^8 - 660500969665581/162850891556*a^7 - 821387907366689/162850891556*a^6 + 597485171753503/162850891556*a^5 + 292676591523933/162850891556*a^4 - 192628332924385/162850891556*a^3 - 4158484987447/40712722889*a^2 + 3531120947733/81425445778*a + 177202893806/40712722889,
-69407407613/325701783112*a^19 + 42206358748/40712722889*a^18 + 1355988548009/325701783112*a^17 - 8541171808379/325701783112*a^16 - 7859892462299/325701783112*a^15 + 43715965600403/162850891556*a^14 - 8069814523501/325701783112*a^13 - 58083995650478/40712722889*a^12 + 33790925469385/40712722889*a^11 + 1367616837473615/325701783112*a^10 - 588895388849991/162850891556*a^9 - 2195022474299657/325701783112*a^8 + 1141145222465073/162850891556*a^7 + 216417464744711/40712722889*a^6 - 256267048161562/40712722889*a^5 - 114825203078279/81425445778*a^4 + 344492233514139/162850891556*a^3 - 46515508608545/325701783112*a^2 - 15859451546583/162850891556*a + 328577054011/81425445778,
2702449149/81425445778*a^19 - 16418677867/81425445778*a^18 - 36200646061/81425445778*a^17 + 394649390085/81425445778*a^16 - 55709305939/40712722889*a^15 - 3734237057153/81425445778*a^14 + 2278645267171/40712722889*a^13 + 8691653179460/40712722889*a^12 - 32899379721745/81425445778*a^11 - 39435061913259/81425445778*a^10 + 55666725277550/40712722889*a^9 + 29785633210691/81425445778*a^8 - 194597748563943/81425445778*a^7 + 16509387882073/40712722889*a^6 + 167397018736807/81425445778*a^5 - 31742681792598/40712722889*a^4 - 56062437951145/81425445778*a^3 + 24249976778507/81425445778*a^2 + 802572620517/40712722889*a - 195103923399/40712722889,
14512196427/162850891556*a^19 - 18410075138/40712722889*a^18 - 281035536009/162850891556*a^17 + 1878934883909/162850891556*a^16 + 1589983271265/162850891556*a^15 - 4871740618877/40712722889*a^14 + 2116149316033/162850891556*a^13 + 52844006232209/81425445778*a^12 - 14496486831873/40712722889*a^11 - 321347300980551/162850891556*a^10 + 123602061398325/81425445778*a^9 + 545110347063599/162850891556*a^8 - 235285585948725/81425445778*a^7 - 239173760339207/81425445778*a^6 + 103335079624302/40712722889*a^5 + 85681684660725/81425445778*a^4 - 67854947526543/81425445778*a^3 - 5330028183415/162850891556*a^2 + 3896325901615/81425445778*a - 67947930598/40712722889,
-26458908317/81425445778*a^19 + 254486088635/162850891556*a^18 + 261687753028/40712722889*a^17 - 3219916352591/81425445778*a^16 - 6371295474007/162850891556*a^15 + 66021049412473/162850891556*a^14 - 1578534207471/162850891556*a^13 - 176145454743653/81425445778*a^12 + 176885704380449/162850891556*a^11 + 261756557447589/40712722889*a^10 - 396372526181893/81425445778*a^9 - 860583107308653/81425445778*a^8 + 1530316984769795/162850891556*a^7 + 361875362825407/40712722889*a^6 - 1354214195555301/162850891556*a^5 - 243885490191163/81425445778*a^4 + 447157413450181/162850891556*a^3 + 2902236731998/40712722889*a^2 - 11463926001181/81425445778*a + 106139367935/40712722889,
-5397312033/40712722889*a^19 + 31399802613/81425445778*a^18 + 274980358861/81425445778*a^17 - 399098112689/40712722889*a^16 - 2841865318175/81425445778*a^15 + 4092579982368/40712722889*a^14 + 7650203258043/40712722889*a^13 - 43284030898093/81425445778*a^12 - 45743586456007/81425445778*a^11 + 124873733224881/81425445778*a^10 + 36967624058132/40712722889*a^9 - 94742206080042/40712722889*a^8 - 53296574302883/81425445778*a^7 + 126753356813161/81425445778*a^6 - 2733734296809/81425445778*a^5 - 12118726544137/81425445778*a^4 + 19835588953783/81425445778*a^3 - 10229858583045/81425445778*a^2 - 1240426816483/40712722889*a + 264853066907/40712722889
]
*], q_expansions := [*
q + a*q^2 + (1/2*a^12 + 2*a^11 - 5*a^10 - 51/2*a^9 + 14*a^8 + 237/2*a^7 + a^6 - 241*a^5 - 45*a^4 + 397/2*a^3 + 34*a^2 - 97/2*a - 7)*q^3 + (a^2 - 2)*q^4 + (3*a^12 + 19*a^11 + 14*a^10 - 128*a^9 - 237*a^8 + 208*a^7 + 696*a^6 + 102*a^5 - 617*a^4 - 284*a^3 + 134*a^2 + 91*a + 9)*q^5 + (-a^12 - 6*a^11 - 2*a^10 + 46*a^9 + 60*a^8 - 112*a^7 - 194*a^6 + 94*a^5 + 194*a^4 - 33*a^3 - 56*a^2 + 4*a + 2)*q^6 + (-11/2*a^12 - 33*a^11 - 14*a^10 + 483/2*a^9 + 349*a^8 - 1029/2*a^7 - 1088*a^6 + 219*a^5 + 1021*a^4 + 277/2*a^3 - 245*a^2 - 141/2*a - 9)*q^7 + (a^3 - 4*a)*q^8 + (-5/2*a^12 - 14*a^11 + 229/2*a^9 + 115*a^8 - 629/2*a^7 - 417*a^6 + 342*a^5 + 470*a^4 - 331/2*a^3 - 168*a^2 + 55/2*a + 13)*q^9 + (a^12 + 8*a^11 + 13*a^10 - 45*a^9 - 143*a^8 + 18*a^7 + 384*a^6 + 217*a^5 - 311*a^4 - 268*a^3 + 46*a^2 + 75*a + 12)*q^10 + (a^12 + 6*a^11 + 2*a^10 - 46*a^9 - 60*a^8 + 111*a^7 + 191*a^6 - 90*a^5 - 180*a^4 + 31*a^3 + 42*a^2 - 7*a - 1)*q^11 + (-a^12 - 4*a^11 + 9*a^10 + 47*a^9 - 23*a^8 - 205*a^7 - 2*a^6 + 398*a^5 + 66*a^4 - 319*a^3 - 49*a^2 + 77*a + 10)*q^12 + (5/2*a^12 + 17*a^11 + 18*a^10 - 213/2*a^9 - 246*a^8 + 243/2*a^7 + 697*a^6 + 265*a^5 - 602*a^4 - 855/2*a^3 + 118*a^2 + 263/2*a + 14)*q^13 + (-3*a^11 - 17*a^10 - 3*a^9 + 129*a^8 + 155*a^7 - 298*a^6 - 508*a^5 + 188*a^4 + 492*a^3 + 12*a^2 - 130*a - 22)*q^14 + (3/2*a^12 + 10*a^11 + 10*a^10 - 127/2*a^9 - 143*a^8 + 155/2*a^7 + 415*a^6 + 141*a^5 - 377*a^4 - 469/2*a^3 + 89*a^2 + 139/2*a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^12 - 3*a^11 + 55/2*a^9 + 26*a^8 - 189/2*a^7 - 111*a^6 + 152*a^5 + 170*a^4 - 229/2*a^3 - 96*a^2 + 65/2*a + 14)*q^17 + (a^12 + 5*a^11 - 3*a^10 - 45*a^9 - 22*a^8 + 148*a^7 + 107*a^6 - 225*a^5 - 143*a^4 + 167*a^3 + 65*a^2 - 42*a - 10)*q^18 + (-7*a^12 - 44*a^11 - 29*a^10 + 305*a^9 + 525*a^8 - 555*a^7 - 1557*a^6 - 33*a^5 + 1383*a^4 + 462*a^3 - 285*a^2 - 160*a - 27)*q^19 + (-4*a^12 - 27*a^11 - 26*a^10 + 177*a^9 + 375*a^8 - 258*a^7 - 1081*a^6 - 237*a^5 + 957*a^4 + 480*a^3 - 208*a^2 - 148*a - 14)*q^20 + (9/2*a^12 + 23*a^11 - 13*a^10 - 419/2*a^9 - 107*a^8 + 1379/2*a^7 + 511*a^6 - 1014*a^5 - 676*a^4 + 1365/2*a^3 + 306*a^2 - 299/2*a - 46)*q^21 + (a^10 + 4*a^9 - 6*a^8 - 35*a^7 + 4*a^6 + 98*a^5 + 22*a^4 - 92*a^3 - 22*a^2 + 21*a + 4)*q^22 + (8*a^12 + 45*a^11 + a^10 - 365*a^9 - 371*a^8 + 987*a^7 + 1317*a^6 - 1038*a^5 - 1437*a^4 + 478*a^3 + 491*a^2 - 78*a - 37)*q^23 + (4*a^12 + 23*a^11 + 4*a^10 - 179*a^9 - 208*a^8 + 448*a^7 + 692*a^6 - 400*a^5 - 698*a^4 + 151*a^3 + 204*a^2 - 20*a - 8)*q^24 + (-4*a^12 - 26*a^11 - 22*a^10 + 172*a^9 + 343*a^8 - 259*a^7 - 999*a^6 - 207*a^5 + 887*a^4 + 449*a^3 - 192*a^2 - 136*a - 16)*q^25 + (2*a^12 + 13*a^11 + 11*a^10 - 86*a^9 - 171*a^8 + 132*a^7 + 500*a^6 + 93*a^5 - 450*a^4 - 217*a^3 + 94*a^2 + 69*a + 10)*q^26 + (-a^12 - 2*a^11 + 21*a^10 + 52*a^9 - 111*a^8 - 331*a^7 + 187*a^6 + 792*a^5 - 18*a^4 - 693*a^3 - 98*a^2 + 175*a + 33)*q^27 + (8*a^12 + 49*a^11 + 25*a^10 - 354*a^9 - 543*a^8 + 731*a^7 + 1668*a^6 - 250*a^5 - 1550*a^4 - 265*a^3 + 360*a^2 + 119*a + 18)*q^28 + (-a^12 + 2*a^11 + 45*a^10 + 62*a^9 - 288*a^8 - 585*a^7 + 575*a^6 + 1597*a^5 - 219*a^4 - 1483*a^3 - 161*a^2 + 391*a + 75)*q^29 + (a^12 + 7*a^11 + 7*a^10 - 47*a^9 - 98*a^8 + 76*a^7 + 282*a^6 + 40*a^5 - 248*a^4 - 112*a^3 + 47*a^2 + 36*a + 6)*q^30 + (5/2*a^12 + 16*a^11 + 12*a^10 - 217/2*a^9 - 199*a^8 + 369/2*a^7 + 580*a^6 + 56*a^5 - 499*a^4 - 435/2*a^3 + 76*a^2 + 155/2*a + 17)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^12 + 6*a^11 + 20*a^10 - 23/2*a^9 - 167*a^8 - 329/2*a^7 + 382*a^6 + 625*a^5 - 210*a^4 - 1237/2*a^3 - 44*a^2 + 321/2*a + 33)*q^33 + (a^11 + 4*a^10 - 6*a^9 - 36*a^8 + 2*a^7 + 105*a^6 + 31*a^5 - 110*a^4 - 29*a^3 + 40*a^2 + 3*a - 2)*q^34 + (-3/2*a^12 - 10*a^11 - 10*a^10 + 127/2*a^9 + 143*a^8 - 157/2*a^7 - 419*a^6 - 139*a^5 + 398*a^4 + 485/2*a^3 - 116*a^2 - 157/2*a + 1)*q^35 + (4*a^12 + 23*a^11 + 2*a^10 - 187*a^9 - 199*a^8 + 510*a^7 + 703*a^6 - 549*a^5 - 782*a^4 + 262*a^3 + 279*a^2 - 43*a - 22)*q^36 + (-a^12 - 12*a^11 - 37*a^10 + 36*a^9 + 324*a^8 + 233*a^7 - 796*a^6 - 1026*a^5 + 556*a^4 + 1069*a^3 - 14*a^2 - 293*a - 47)*q^37 + O(q^38),
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229716963217777/81425445778*a^9 - 173407339861485/40712722889*a^8 + 412682181159657/81425445778*a^7 + 291310379783463/81425445778*a^6 - 175056078891148/40712722889*a^5 - 96173228577751/81425445778*a^4 + 54920643204018/40712722889*a^3 - 12435868499/81425445778*a^2 - 4047091842687/81425445778*a + 42588698996/40712722889)*q^21 + (-4775561579/325701783112*a^19 + 241995684/40712722889*a^18 + 145738412139/325701783112*a^17 - 24944017749/325701783112*a^16 - 1889078095661/325701783112*a^15 - 36613282617/162850891556*a^14 + 13522395383689/325701783112*a^13 + 691143654823/81425445778*a^12 - 7253853581296/40712722889*a^11 - 17775089658627/325701783112*a^10 + 75503076521191/162850891556*a^9 + 49930664208761/325701783112*a^8 - 113979977730485/162850891556*a^7 - 15721032509927/81425445778*a^6 + 22081889678058/40712722889*a^5 + 3361383563952/40712722889*a^4 - 26033805972687/162850891556*a^3 + 2091208043613/325701783112*a^2 + 1165425186443/162850891556*a + 10914238563/81425445778)*q^22 + (2702449149/81425445778*a^19 - 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80857971430109/81425445778*a^5 - 41324806509473/81425445778*a^4 + 10862187403835/40712722889*a^3 + 8079276108409/162850891556*a^2 - 439417091573/81425445778*a - 29181604461/40712722889)*q^24 + (5175041569/162850891556*a^19 - 59092761047/162850891556*a^18 + 4486366917/81425445778*a^17 + 1469755676113/162850891556*a^16 - 554904932465/40712722889*a^15 - 3670202317756/40712722889*a^14 + 29562969210827/162850891556*a^13 + 75130197375513/162850891556*a^12 - 175523860667167/162850891556*a^11 - 51860237997622/40712722889*a^10 + 275092403602849/81425445778*a^9 + 293210523973167/162850891556*a^8 - 923863481119499/162850891556*a^7 - 159563173957013/162850891556*a^6 + 767933337828043/162850891556*a^5 - 37700086843179/162850891556*a^4 - 244659254936669/162850891556*a^3 + 24211164429811/81425445778*a^2 + 2213997822857/40712722889*a - 122006983988/40712722889)*q^25 + (24607494557/162850891556*a^19 - 20806408899/40712722889*a^18 - 598459308373/162850891556*a^17 + 2134950190371/162850891556*a^16 + 5761955778251/162850891556*a^15 - 11117077676735/81425445778*a^14 - 27565061768583/162850891556*a^13 + 30187219039336/40712722889*a^12 + 16408452646868/40712722889*a^11 - 365439679389783/162850891556*a^10 - 28405353602865/81425445778*a^9 + 609443678857937/162850891556*a^8 - 24135149488603/81425445778*a^7 - 128300948255166/40712722889*a^6 + 29637883622456/40712722889*a^5 + 42663332176556/40712722889*a^4 - 28414069156539/81425445778*a^3 - 9032819266631/162850891556*a^2 + 1180280892049/81425445778*a + 32049403425/40712722889)*q^26 + (19911278983/81425445778*a^19 - 45671574323/40712722889*a^18 - 414491660813/81425445778*a^17 + 2339140746615/81425445778*a^16 + 2902090131711/81425445778*a^15 - 12186235865063/40712722889*a^14 - 4354686225805/81425445778*a^13 + 66519256317106/40712722889*a^12 - 20839207287372/40712722889*a^11 - 408627922967627/81425445778*a^10 + 114941489068953/40712722889*a^9 + 706124754350779/81425445778*a^8 - 236570858795132/40712722889*a^7 - 322664228467642/40712722889*a^6 + 214188133830886/40712722889*a^5 + 130456529027950/40712722889*a^4 - 68477902122897/40712722889*a^3 - 25458126573445/81425445778*a^2 + 2253711415428/40712722889*a + 362807141915/40712722889)*q^27 + (-7197354918/40712722889*a^19 + 77755604145/81425445778*a^18 + 516707426119/162850891556*a^17 - 1964430287721/81425445778*a^16 - 532484242664/40712722889*a^15 + 40207476125617/162850891556*a^14 - 14581616996361/162850891556*a^13 - 214066448074295/162850891556*a^12 + 84770025275755/81425445778*a^11 + 633796597887571/162850891556*a^10 - 324117944625695/81425445778*a^9 - 258192525341802/40712722889*a^8 + 590608535319557/81425445778*a^7 + 846238960805003/162850891556*a^6 - 504413440324887/81425445778*a^5 - 254677864432915/162850891556*a^4 + 78944109713430/40712722889*a^3 - 12748832545001/162850891556*a^2 - 5654624966705/81425445778*a + 43542868119/40712722889)*q^28 + (14512196427/162850891556*a^19 - 18410075138/40712722889*a^18 - 281035536009/162850891556*a^17 + 1878934883909/162850891556*a^16 + 1589983271265/162850891556*a^15 - 4871740618877/40712722889*a^14 + 2116149316033/162850891556*a^13 + 52844006232209/81425445778*a^12 - 14496486831873/40712722889*a^11 - 321347300980551/162850891556*a^10 + 123602061398325/81425445778*a^9 + 545110347063599/162850891556*a^8 - 235285585948725/81425445778*a^7 - 239173760339207/81425445778*a^6 + 103335079624302/40712722889*a^5 + 85681684660725/81425445778*a^4 - 67854947526543/81425445778*a^3 - 5330028183415/162850891556*a^2 + 3896325901615/81425445778*a - 67947930598/40712722889)*q^29 + (-20025076487/162850891556*a^19 + 35156768677/81425445778*a^18 + 479906462983/162850891556*a^17 - 1798543464669/162850891556*a^16 - 4533698880431/162850891556*a^15 + 4675752464395/40712722889*a^14 + 21100270857447/162850891556*a^13 - 25416590416973/40712722889*a^12 - 23856972139611/81425445778*a^11 + 309267560395037/162850891556*a^10 + 16735055066043/81425445778*a^9 - 522490368843107/162850891556*a^8 + 13408082942088/40712722889*a^7 + 113333335100608/40712722889*a^6 - 51874210613407/81425445778*a^5 - 40710375813842/40712722889*a^4 + 11914002924964/40712722889*a^3 + 11932682157261/162850891556*a^2 - 754712782641/81425445778*a - 24323179875/40712722889)*q^30 + (-26458908317/81425445778*a^19 + 254486088635/162850891556*a^18 + 261687753028/40712722889*a^17 - 3219916352591/81425445778*a^16 - 6371295474007/162850891556*a^15 + 66021049412473/162850891556*a^14 - 1578534207471/162850891556*a^13 - 176145454743653/81425445778*a^12 + 176885704380449/162850891556*a^11 + 261756557447589/40712722889*a^10 - 396372526181893/81425445778*a^9 - 860583107308653/81425445778*a^8 + 1530316984769795/162850891556*a^7 + 361875362825407/40712722889*a^6 - 1354214195555301/162850891556*a^5 - 243885490191163/81425445778*a^4 + 447157413450181/162850891556*a^3 + 2902236731998/40712722889*a^2 - 11463926001181/81425445778*a + 106139367935/40712722889)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-976473108/40712722889*a^19 + 1068932607/81425445778*a^18 + 66098880205/81425445778*a^17 - 33812595903/81425445778*a^16 - 931465515819/81425445778*a^15 + 218783631619/40712722889*a^14 + 7079947153961/81425445778*a^13 - 1501110977876/40712722889*a^12 - 15696462880956/40712722889*a^11 + 11852176119587/81425445778*a^10 + 81829762873353/81425445778*a^9 - 13745951727011/40712722889*a^8 - 119421375838353/81425445778*a^7 + 37217527203895/81425445778*a^6 + 42558362379571/40712722889*a^5 - 28720765301435/81425445778*a^4 - 10046933768496/40712722889*a^3 + 10972363386231/81425445778*a^2 - 79934887453/81425445778*a - 272319935125/40712722889)*q^33 + (7891241151/81425445778*a^19 - 58946682983/162850891556*a^18 - 364834816301/162850891556*a^17 + 373709086427/40712722889*a^16 + 3241090100927/162850891556*a^15 - 3843650776647/40712722889*a^14 - 6661333945267/81425445778*a^13 + 82429283581827/162850891556*a^12 + 20697275280209/162850891556*a^11 - 246657281464065/162850891556*a^10 + 5165168778757/40712722889*a^9 + 102382151610951/40712722889*a^8 - 111911447892557/162850891556*a^7 - 350552295284591/162850891556*a^6 + 131366205757647/162850891556*a^5 + 125292322773383/162850891556*a^4 - 50649521856799/162850891556*a^3 - 8695197730191/162850891556*a^2 + 1167887374405/81425445778*a + 30128947659/40712722889)*q^34 + (-20023311847/325701783112*a^19 + 78898392313/162850891556*a^18 + 238463189591/325701783112*a^17 - 4071177284193/325701783112*a^16 + 1621776230769/325701783112*a^15 + 5367199800360/40712722889*a^14 - 42414561863389/325701783112*a^13 - 59787264010217/81425445778*a^12 + 146205633667859/162850891556*a^11 + 760040303769465/325701783112*a^10 - 487023340419631/162850891556*a^9 - 1392572613791075/325701783112*a^8 + 209923757002770/40712722889*a^7 + 175983569405642/40712722889*a^6 - 702680874419995/162850891556*a^5 - 85016840448297/40712722889*a^4 + 56500799323606/40712722889*a^3 + 98291765533033/325701783112*a^2 - 15952942234735/162850891556*a - 539387775963/81425445778)*q^35 + (11236075800/40712722889*a^19 - 55670801855/40712722889*a^18 - 220838316421/40712722889*a^17 + 1417189838387/40712722889*a^16 + 1311888314186/40712722889*a^15 - 14640056753089/40712722889*a^14 + 803516731644/40712722889*a^13 + 78912549734312/40712722889*a^12 - 40259488908032/40712722889*a^11 - 237836716002129/40712722889*a^10 + 176489685281918/40712722889*a^9 + 399047642280338/40712722889*a^8 - 336669379027612/40712722889*a^7 - 346785114432697/40712722889*a^6 + 291957533683022/40712722889*a^5 + 125428800092749/40712722889*a^4 - 90684616631118/40712722889*a^3 - 6658750944191/40712722889*a^2 + 2938571935489/40712722889*a + 183528780366/40712722889)*q^36 + (-5397312033/40712722889*a^19 + 31399802613/81425445778*a^18 + 274980358861/81425445778*a^17 - 399098112689/40712722889*a^16 - 2841865318175/81425445778*a^15 + 4092579982368/40712722889*a^14 + 7650203258043/40712722889*a^13 - 43284030898093/81425445778*a^12 - 45743586456007/81425445778*a^11 + 124873733224881/81425445778*a^10 + 36967624058132/40712722889*a^9 - 94742206080042/40712722889*a^8 - 53296574302883/81425445778*a^7 + 126753356813161/81425445778*a^6 - 2733734296809/81425445778*a^5 - 12118726544137/81425445778*a^4 + 19835588953783/81425445778*a^3 - 10229858583045/81425445778*a^2 - 1240426816483/40712722889*a + 264853066907/40712722889)*q^37 + O(q^38)
*]> ;  // time = 9.091 seconds




J[410] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 410, 410, 410, 410, 410, 410, 410, 410, 410, 205, 205, 205, 205, 205, 205, 205, 82, 82, 41 ], new_dimensions := [ 1, 1, 1, 1, 2, 2, 2, 2, 3, 1, 1, 1, 2, 2, 3, 3, 1, 2, 3 ], dimensions := [ 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 4, 4, 6, 6, 2, 4, 12 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 11, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 11, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 9, 1, 0, 1, 1, 1, 1, 169, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 961, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 169, 961, 1, 1, 1, 0 ], ap_traces := [
[ -1, -2, 1, 2, 0, -4, 0, 8, 0, 6, 8, 2 ],
[ -1, 0, 1, -2, -6, -2, 8, -6, 0, -8, 0, -6 ],
[ 1, -2, -1, -2, 2, -6, -6, -2, -4, -6, 0, 10 ],
[ 1, 0, 1, 4, 0, -2, 2, 0, 0, -2, 0, 6 ],
[ -2, -2, -2, -2, 2, -8, 0, -10, 4, 12, -12, -4 ],
[ -2, 2, -2, 4, 0, 4, 6, 4, 0, -6, 4, 16 ],
[ -2, 4, 2, 2, 2, 8, -6, 2, 0, 2, 0, -12 ],
[ 2, 0, 2, -4, 0, 8, 4, 0, -12, 8, 0, 0 ],
[ 3, 0, -3, 6, -4, 8, -2, 8, 4, -12, 8, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 + 2*x - 4,
x^2 - 2*x - 2,
x^2 - 6*x - 8,
x^2 - 6,
x^3 - 8*x + 4
], atkin_lehners := [
[ 1, -1, 1 ],
[ 1, -1, -1 ],
[ -1, 1, -1 ],
[ -1, -1, -1 ],
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 1, 3, 1 ],
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 5, 1, 1 ],
[ 13, 1, 3 ],
[ 1, 1, 1 ],
[ 15, 5, 1 ],
[ 33, 7, 1 ]
], tamagawa_numbers := [
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 3 ],
[ 1, 1, 1 ],
[ 15, 5, 1 ],
[ 33, 1, 1 ]
], torsion_upper_bounds := [ 3, 1, 1, 1, 1, 3, 1, 5, 3 ], torsion_lower_bounds := [ 3, 1, 1, 1, 1, 3, 1, 1, 3 ], l_ratios := [ 1/3, 0, 0, 3, 0, 1/3, 1, 3, 11/3 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 0, 1, 1, 1/25, 1 ], eigenvalues := [*
[ -1, -2, 1, 2, 0, -4, 0, 8, 0, 6, 8, 2 ],
[ -1, 0, 1, -2, -6, -2, 8, -6, 0, -8, 0, -6 ],
[ 1, -2, -1, -2, 2, -6, -6, -2, -4, -6, 0, 10 ],
[ 1, 0, 1, 4, 0, -2, 2, 0, 0, -2, 0, 6 ],
[
-1,
a,
-1,
-a - 2,
-a,
-4,
-2*a - 2,
a - 4,
2*a + 4,
2*a + 8,
2*a - 4,
-2
],
[
-1,
a,
-1,
2,
0,
-2*a + 4,
a + 2,
2*a,
-2*a + 2,
-3*a,
-2*a + 4,
8
],
[
-1,
2,
1,
a - 2,
-a + 4,
4,
-a,
-a + 4,
0,
a - 2,
0,
-6
],
[
1,
a,
1,
-2,
-2*a,
4,
-a + 2,
0,
-6,
-a + 4,
-2*a,
2*a
],
[
1,
a,
-1,
2,
-a^2 + 4,
-a^2 - 2*a + 8,
a^2 - a - 6,
-a^2 - 2*a + 8,
a^2 - 4,
a - 4,
2*a^2 + 2*a - 8,
a^2 - 2*a - 6
]
*], q_expansions := [*
q - q^2 - 2*q^3 + q^4 + q^5 + 2*q^6 + 2*q^7 - q^8 + q^9 - q^10 - 2*q^12 - 4*q^13 - 2*q^14 - 2*q^15 + q^16 - q^18 + 8*q^19 + q^20 - 4*q^21 + 2*q^24 + q^25 + 4*q^26 + 4*q^27 + 2*q^28 + 6*q^29 + 2*q^30 + 8*q^31 - q^32 + 2*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 + q^4 + q^5 - 2*q^7 - q^8 - 3*q^9 - q^10 - 6*q^11 - 2*q^13 + 2*q^14 + q^16 + 8*q^17 + 3*q^18 - 6*q^19 + q^20 + 6*q^22 + q^25 + 2*q^26 - 2*q^28 - 8*q^29 - q^32 - 8*q^34 - 2*q^35 - 3*q^36 - 6*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - q^5 - 2*q^6 - 2*q^7 + q^8 + q^9 - q^10 + 2*q^11 - 2*q^12 - 6*q^13 - 2*q^14 + 2*q^15 + q^16 - 6*q^17 + q^18 - 2*q^19 - q^20 + 4*q^21 + 2*q^22 - 4*q^23 - 2*q^24 + q^25 - 6*q^26 + 4*q^27 - 2*q^28 - 6*q^29 + 2*q^30 + q^32 - 4*q^33 - 6*q^34 + 2*q^35 + q^36 + 10*q^37 + O(q^38),
q + q^2 + q^4 + q^5 + 4*q^7 + q^8 - 3*q^9 + q^10 - 2*q^13 + 4*q^14 + q^16 + 2*q^17 - 3*q^18 + q^20 + q^25 - 2*q^26 + 4*q^28 - 2*q^29 + q^32 + 2*q^34 + 4*q^35 - 3*q^36 + 6*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - q^5 - a*q^6 + (-a - 2)*q^7 - q^8 + (-2*a + 1)*q^9 + q^10 - a*q^11 + a*q^12 - 4*q^13 + (a + 2)*q^14 - a*q^15 + q^16 + (-2*a - 2)*q^17 + (2*a - 1)*q^18 + (a - 4)*q^19 - q^20 - 4*q^21 + a*q^22 + (2*a + 4)*q^23 - a*q^24 + q^25 + 4*q^26 + (2*a - 8)*q^27 + (-a - 2)*q^28 + (2*a + 8)*q^29 + a*q^30 + (2*a - 4)*q^31 - q^32 + (2*a - 4)*q^33 + (2*a + 2)*q^34 + (a + 2)*q^35 + (-2*a + 1)*q^36 - 2*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - q^5 - a*q^6 + 2*q^7 - q^8 + (2*a - 1)*q^9 + q^10 + a*q^12 + (-2*a + 4)*q^13 - 2*q^14 - a*q^15 + q^16 + (a + 2)*q^17 + (-2*a + 1)*q^18 + 2*a*q^19 - q^20 + 2*a*q^21 + (-2*a + 2)*q^23 - a*q^24 + q^25 + (2*a - 4)*q^26 + 4*q^27 + 2*q^28 - 3*a*q^29 + a*q^30 + (-2*a + 4)*q^31 - q^32 + (-a - 2)*q^34 - 2*q^35 + (2*a - 1)*q^36 + 8*q^37 + O(q^38),
q - q^2 + 2*q^3 + q^4 + q^5 - 2*q^6 + (a - 2)*q^7 - q^8 + q^9 - q^10 + (-a + 4)*q^11 + 2*q^12 + 4*q^13 + (-a + 2)*q^14 + 2*q^15 + q^16 - a*q^17 - q^18 + (-a + 4)*q^19 + q^20 + (2*a - 4)*q^21 + (a - 4)*q^22 - 2*q^24 + q^25 - 4*q^26 - 4*q^27 + (a - 2)*q^28 + (a - 2)*q^29 - 2*q^30 - q^32 + (-2*a + 8)*q^33 + a*q^34 + (a - 2)*q^35 + q^36 - 6*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + q^5 + a*q^6 - 2*q^7 + q^8 + 3*q^9 + q^10 - 2*a*q^11 + a*q^12 + 4*q^13 - 2*q^14 + a*q^15 + q^16 + (-a + 2)*q^17 + 3*q^18 + q^20 - 2*a*q^21 - 2*a*q^22 - 6*q^23 + a*q^24 + q^25 + 4*q^26 - 2*q^28 + (-a + 4)*q^29 + a*q^30 - 2*a*q^31 + q^32 - 12*q^33 + (-a + 2)*q^34 - 2*q^35 + 3*q^36 + 2*a*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - q^5 + a*q^6 + 2*q^7 + q^8 + (a^2 - 3)*q^9 - q^10 + (-a^2 + 4)*q^11 + a*q^12 + (-a^2 - 2*a + 8)*q^13 + 2*q^14 - a*q^15 + q^16 + (a^2 - a - 6)*q^17 + (a^2 - 3)*q^18 + (-a^2 - 2*a + 8)*q^19 - q^20 + 2*a*q^21 + (-a^2 + 4)*q^22 + (a^2 - 4)*q^23 + a*q^24 + q^25 + (-a^2 - 2*a + 8)*q^26 + (2*a - 4)*q^27 + 2*q^28 + (a - 4)*q^29 - a*q^30 + (2*a^2 + 2*a - 8)*q^31 + q^32 + (-4*a + 4)*q^33 + (a^2 - a - 6)*q^34 - 2*q^35 + (a^2 - 3)*q^36 + (a^2 - 2*a - 6)*q^37 + O(q^38)
*]> ;  // time = 221.33 seconds




J[411] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 411, 411, 411, 411, 411, 137, 137 ], new_dimensions := [ 3, 3, 3, 5, 9, 4, 7 ], dimensions := [ 3, 3, 3, 5, 9, 8, 14 ], intersection_graph := [ 0, 1, 1, 1, 1, 29, 1, 1, 0, 1, 47, 1, 31, 1, 1, 1, 0, 1, 1, 1, 71, 1, 47, 1, 0, 1, 19, 1, 1, 1, 1, 1, 0, 1, 7753, 29, 31, 1, 19, 1, 0, 1, 1, 1, 71, 1, 7753, 1, 0 ], ap_traces := [
[ 1, -3, -2, -3, -3, -11, 4, -3, 5, -22, -3, -9 ],
[ 6, 3, 2, 0, 4, 2, 0, -4, -4, 0, -8, -4 ],
[ -3, 3, -6, -3, -9, -3, -6, -3, -3, -12, 3, -9 ],
[ -1, 5, 6, -1, 1, -1, 4, -5, 13, 22, -3, 1 ],
[ 0, -9, 6, 7, 7, 7, 0, 11, -3, 22, 15, 27 ]
], hecke_fields := [
x^3 - x^2 - 2*x + 1,
x^3 - 39*x - 65,
x^3 + 3*x^2 - 3,
x^5 + x^4 - 7*x^3 - 10*x^2 + 1,
x^9 - 16*x^7 + x^6 + 82*x^5 - 9*x^4 - 141*x^3 + 18*x^2 + 52*x + 8
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 29, 1 ],
[ 31, 1 ],
[ 71, 1 ],
[ 437, 1 ],
[ 7753, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 31, 1 ],
[ 71, 1 ],
[ 437, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 23, 1 ], torsion_lower_bounds := [ 1, 1, 1, 23, 1 ], l_ratios := [ 0, 31, 0, 19/23, 1 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1, 1 ], eigenvalues := [*
[
a,
-1,
-a^2 + 1,
-a^2 - a + 1,
a^2 - 2*a - 2,
a - 4,
3*a^2 - 2*a - 3,
4*a^2 + a - 8,
a^2 + 3*a - 1,
-a^2 + a - 6,
-7*a^2 + 5*a + 9,
5*a^2 - 7*a - 9
],
[
2,
1,
-1/3*a + 2/3,
-1/9*a^2 + 7/9*a + 26/9,
2/9*a^2 - 2/9*a - 40/9,
2/9*a^2 - 8/9*a - 46/9,
-4/9*a^2 + 10/9*a + 104/9,
1/9*a^2 - 10/9*a - 38/9,
1/9*a^2 + 8/9*a - 38/9,
1/9*a^2 + 2/9*a - 26/9,
-4/9*a^2 + 4/9*a + 80/9,
-4/9*a^2 + 7/9*a + 92/9
],
[
a,
1,
-a^2 - 2*a - 1,
a^2 + a - 3,
a^2 + 2*a - 4,
-2*a^2 - 3*a + 2,
3*a^2 + 4*a - 7,
-2*a^2 - a + 4,
a^2 - a - 5,
a^2 + a - 6,
-a^2 - 3*a + 1,
-a^2 - a - 1
],
[
a,
1,
-a^4 - a^3 + 7*a^2 + 9*a + 1,
-a^4 + 6*a^2 + 4*a,
a^4 + a^3 - 7*a^2 - 11*a,
2*a^4 - a^3 - 13*a^2 - 3*a + 5,
2*a^4 - 13*a^2 - 10*a + 3,
-a^4 + 2*a^3 + 5*a^2 - 6*a - 3,
-a^4 + 2*a^3 + 4*a^2 - 4*a + 4,
-a^3 + 2*a^2 + 5*a + 1,
2*a^4 + a^3 - 12*a^2 - 15*a - 4,
a^4 - 6*a^2 - 4*a
],
[
a,
-1,
-1/8*a^8 + 2*a^6 - 5/8*a^5 - 43/4*a^4 + 45/8*a^3 + 165/8*a^2 - 41/4*a - 6,
3/16*a^8 - 1/8*a^7 - 11/4*a^6 + 35/16*a^5 + 51/4*a^4 - 179/16*a^3 - 309/16*a^2 + 63/4*a + 21/4,
1/8*a^8 + 1/4*a^7 - 3/2*a^6 - 23/8*a^5 + 11/2*a^4 + 71/8*a^3 - 55/8*a^2 - 9/2*a + 3/2,
-3/8*a^8 - 1/4*a^7 + 11/2*a^6 + 21/8*a^5 - 25*a^4 - 53/8*a^3 + 273/8*a^2 - 7/2,
-1/4*a^8 + 4*a^6 - 1/4*a^5 - 41/2*a^4 + 9/4*a^3 + 137/4*a^2 - 9/2*a - 8,
3/16*a^8 + 1/8*a^7 - 11/4*a^6 - 13/16*a^5 + 13*a^4 - 11/16*a^3 - 345/16*a^2 + 9/2*a + 39/4,
1/16*a^8 - 1/8*a^7 - 5/4*a^6 + 17/16*a^5 + 15/2*a^4 - 25/16*a^3 - 235/16*a^2 + 25/4,
5/16*a^8 - 1/8*a^7 - 21/4*a^6 + 21/16*a^5 + 27*a^4 - 77/16*a^3 - 671/16*a^2 + 19/2*a + 49/4,
a^3 - 7*a + 2,
-1/8*a^8 + 2*a^6 + 3/8*a^5 - 39/4*a^4 - 19/8*a^3 + 109/8*a^2 - 5/4*a + 2
]
*], q_expansions := [*
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 + 1)*q^5 - a*q^6 + (-a^2 - a + 1)*q^7 + (a^2 - 2*a - 1)*q^8 + q^9 + (-a^2 - a + 1)*q^10 + (a^2 - 2*a - 2)*q^11 + (-a^2 + 2)*q^12 + (a - 4)*q^13 + (-2*a^2 - a + 1)*q^14 + (a^2 - 1)*q^15 + (-3*a^2 + a + 3)*q^16 + (3*a^2 - 2*a - 3)*q^17 + a*q^18 + (4*a^2 + a - 8)*q^19 + (-a - 1)*q^20 + (a^2 + a - 1)*q^21 + (-a^2 - 1)*q^22 + (a^2 + 3*a - 1)*q^23 + (-a^2 + 2*a + 1)*q^24 + (a^2 + a - 5)*q^25 + (a^2 - 4*a)*q^26 - q^27 + (-a^2 - a)*q^28 + (-a^2 + a - 6)*q^29 + (a^2 + a - 1)*q^30 + (-7*a^2 + 5*a + 9)*q^31 + (-4*a^2 + a + 5)*q^32 + (-a^2 + 2*a + 2)*q^33 + (a^2 + 3*a - 3)*q^34 + (2*a^2 + 2*a - 1)*q^35 + (a^2 - 2)*q^36 + (5*a^2 - 7*a - 9)*q^37 + O(q^38),
q + 2*q^2 + q^3 + 2*q^4 + (-1/3*a + 2/3)*q^5 + 2*q^6 + (-1/9*a^2 + 7/9*a + 26/9)*q^7 + q^9 + (-2/3*a + 4/3)*q^10 + (2/9*a^2 - 2/9*a - 40/9)*q^11 + 2*q^12 + (2/9*a^2 - 8/9*a - 46/9)*q^13 + (-2/9*a^2 + 14/9*a + 52/9)*q^14 + (-1/3*a + 2/3)*q^15 - 4*q^16 + (-4/9*a^2 + 10/9*a + 104/9)*q^17 + 2*q^18 + (1/9*a^2 - 10/9*a - 38/9)*q^19 + (-2/3*a + 4/3)*q^20 + (-1/9*a^2 + 7/9*a + 26/9)*q^21 + (4/9*a^2 - 4/9*a - 80/9)*q^22 + (1/9*a^2 + 8/9*a - 38/9)*q^23 + (1/9*a^2 - 4/9*a - 41/9)*q^25 + (4/9*a^2 - 16/9*a - 92/9)*q^26 + q^27 + (-2/9*a^2 + 14/9*a + 52/9)*q^28 + (1/9*a^2 + 2/9*a - 26/9)*q^29 + (-2/3*a + 4/3)*q^30 + (-4/9*a^2 + 4/9*a + 80/9)*q^31 - 8*q^32 + (2/9*a^2 - 2/9*a - 40/9)*q^33 + (-8/9*a^2 + 20/9*a + 208/9)*q^34 + (-1/3*a^2 + a + 13/3)*q^35 + 2*q^36 + (-4/9*a^2 + 7/9*a + 92/9)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^2 - 2*a - 1)*q^5 + a*q^6 + (a^2 + a - 3)*q^7 + (-3*a^2 - 4*a + 3)*q^8 + q^9 + (a^2 - a - 3)*q^10 + (a^2 + 2*a - 4)*q^11 + (a^2 - 2)*q^12 + (-2*a^2 - 3*a + 2)*q^13 + (-2*a^2 - 3*a + 3)*q^14 + (-a^2 - 2*a - 1)*q^15 + (3*a^2 + 3*a - 5)*q^16 + (3*a^2 + 4*a - 7)*q^17 + a*q^18 + (-2*a^2 - a + 4)*q^19 + (-2*a^2 + a + 5)*q^20 + (a^2 + a - 3)*q^21 + (-a^2 - 4*a + 3)*q^22 + (a^2 - a - 5)*q^23 + (-3*a^2 - 4*a + 3)*q^24 + (3*a^2 + 7*a - 1)*q^25 + (3*a^2 + 2*a - 6)*q^26 + q^27 + (a^2 + a)*q^28 + (a^2 + a - 6)*q^29 + (a^2 - a - 3)*q^30 + (-a^2 - 3*a + 1)*q^31 + (3*a + 3)*q^32 + (a^2 + 2*a - 4)*q^33 + (-5*a^2 - 7*a + 9)*q^34 + (2*a + 3)*q^35 + (a^2 - 2)*q^36 + (-a^2 - a - 1)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^4 - a^3 + 7*a^2 + 9*a + 1)*q^5 + a*q^6 + (-a^4 + 6*a^2 + 4*a)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^2 + a + 1)*q^10 + (a^4 + a^3 - 7*a^2 - 11*a)*q^11 + (a^2 - 2)*q^12 + (2*a^4 - a^3 - 13*a^2 - 3*a + 5)*q^13 + (a^4 - a^3 - 6*a^2 + 1)*q^14 + (-a^4 - a^3 + 7*a^2 + 9*a + 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^4 - 13*a^2 - 10*a + 3)*q^17 + a*q^18 + (-a^4 + 2*a^3 + 5*a^2 - 6*a - 3)*q^19 + (2*a^4 + a^3 - 13*a^2 - 17*a - 2)*q^20 + (-a^4 + 6*a^2 + 4*a)*q^21 + (-a^2 - 1)*q^22 + (-a^4 + 2*a^3 + 4*a^2 - 4*a + 4)*q^23 + (a^3 - 4*a)*q^24 + (-2*a^4 - 3*a^3 + 14*a^2 + 25*a + 4)*q^25 + (-3*a^4 + a^3 + 17*a^2 + 5*a - 2)*q^26 + q^27 + (a^3 - 2*a^2 - 7*a - 1)*q^28 + (-a^3 + 2*a^2 + 5*a + 1)*q^29 + (-a^2 + a + 1)*q^30 + (2*a^4 + a^3 - 12*a^2 - 15*a - 4)*q^31 + (-a^4 - a^3 + 10*a^2 + 12*a - 1)*q^32 + (a^4 + a^3 - 7*a^2 - 11*a)*q^33 + (-2*a^4 + a^3 + 10*a^2 + 3*a - 2)*q^34 + (-2*a^4 + 12*a^2 + 10*a + 3)*q^35 + (a^2 - 2)*q^36 + (a^4 - 6*a^2 - 4*a)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-1/8*a^8 + 2*a^6 - 5/8*a^5 - 43/4*a^4 + 45/8*a^3 + 165/8*a^2 - 41/4*a - 6)*q^5 - a*q^6 + (3/16*a^8 - 1/8*a^7 - 11/4*a^6 + 35/16*a^5 + 51/4*a^4 - 179/16*a^3 - 309/16*a^2 + 63/4*a + 21/4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-1/2*a^6 - 1/2*a^5 + 9/2*a^4 + 3*a^3 - 8*a^2 + 1/2*a + 1)*q^10 + (1/8*a^8 + 1/4*a^7 - 3/2*a^6 - 23/8*a^5 + 11/2*a^4 + 71/8*a^3 - 55/8*a^2 - 9/2*a + 3/2)*q^11 + (-a^2 + 2)*q^12 + (-3/8*a^8 - 1/4*a^7 + 11/2*a^6 + 21/8*a^5 - 25*a^4 - 53/8*a^3 + 273/8*a^2 - 7/2)*q^13 + (-1/8*a^8 + 1/4*a^7 + 2*a^6 - 21/8*a^5 - 19/2*a^4 + 57/8*a^3 + 99/8*a^2 - 9/2*a - 3/2)*q^14 + (1/8*a^8 - 2*a^6 + 5/8*a^5 + 43/4*a^4 - 45/8*a^3 - 165/8*a^2 + 41/4*a + 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/4*a^8 + 4*a^6 - 1/4*a^5 - 41/2*a^4 + 9/4*a^3 + 137/4*a^2 - 9/2*a - 8)*q^17 + a*q^18 + (3/16*a^8 + 1/8*a^7 - 11/4*a^6 - 13/16*a^5 + 13*a^4 - 11/16*a^3 - 345/16*a^2 + 9/2*a + 39/4)*q^19 + (1/4*a^8 - 1/2*a^7 - 9/2*a^6 + 23/4*a^5 + 49/2*a^4 - 77/4*a^3 - 163/4*a^2 + 43/2*a + 12)*q^20 + (-3/16*a^8 + 1/8*a^7 + 11/4*a^6 - 35/16*a^5 - 51/4*a^4 + 179/16*a^3 + 309/16*a^2 - 63/4*a - 21/4)*q^21 + (1/4*a^8 + 1/2*a^7 - 3*a^6 - 19/4*a^5 + 10*a^4 + 43/4*a^3 - 27/4*a^2 - 5*a - 1)*q^22 + (1/16*a^8 - 1/8*a^7 - 5/4*a^6 + 17/16*a^5 + 15/2*a^4 - 25/16*a^3 - 235/16*a^2 + 25/4)*q^23 + (-a^3 + 4*a)*q^24 + (7/16*a^8 + 1/8*a^7 - 27/4*a^6 - 25/16*a^5 + 63/2*a^4 + 81/16*a^3 - 669/16*a^2 + 35/4)*q^25 + (-1/4*a^8 - 1/2*a^7 + 3*a^6 + 23/4*a^5 - 10*a^4 - 75/4*a^3 + 27/4*a^2 + 16*a + 3)*q^26 - q^27 + (-1/8*a^8 + 1/4*a^7 + 3*a^6 - 29/8*a^5 - 39/2*a^4 + 137/8*a^3 + 291/8*a^2 - 53/2*a - 19/2)*q^28 + (5/16*a^8 - 1/8*a^7 - 21/4*a^6 + 21/16*a^5 + 27*a^4 - 77/16*a^3 - 671/16*a^2 + 19/2*a + 49/4)*q^29 + (1/2*a^6 + 1/2*a^5 - 9/2*a^4 - 3*a^3 + 8*a^2 - 1/2*a - 1)*q^30 + (a^3 - 7*a + 2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-1/8*a^8 - 1/4*a^7 + 3/2*a^6 + 23/8*a^5 - 11/2*a^4 - 71/8*a^3 + 55/8*a^2 + 9/2*a - 3/2)*q^33 + (-a^3 + 5*a + 2)*q^34 + (3/16*a^8 - 1/8*a^7 - 11/4*a^6 + 35/16*a^5 + 47/4*a^4 - 179/16*a^3 - 181/16*a^2 + 55/4*a - 15/4)*q^35 + (a^2 - 2)*q^36 + (-1/8*a^8 + 2*a^6 + 3/8*a^5 - 39/4*a^4 - 19/8*a^3 + 109/8*a^2 - 5/4*a + 2)*q^37 + O(q^38)
*]> ;  // time = 82.831 seconds




J[413] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 413, 413, 413, 413, 413, 413, 59 ], new_dimensions := [ 2, 3, 5, 5, 5, 9, 5 ], dimensions := [ 2, 3, 5, 5, 5, 9, 10 ], intersection_graph := [ 0, 1, 1, 11, 1, 1, 19, 1, 0, 1, 73, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 11, 73, 1, 0, 1, 1, 227, 1, 1, 1, 1, 0, 1, 661, 1, 1, 1, 1, 1, 0, 1, 19, 7, 1, 227, 661, 1, 0 ], ap_traces := [
[ 0, -1, 2, -2, -5, 1, -12, -3, 15, 1, 10, 16 ],
[ -3, 3, 0, -3, 3, -3, 6, 1, 1, 11, -2, -2 ],
[ -2, -5, 1, -5, -7, -3, -1, 0, -5, -6, -12, -18 ],
[ 4, 7, -3, -5, 9, -1, 11, 4, -1, -6, -8, -10 ],
[ 0, -7, -5, 5, 1, -17, -3, -20, -5, -2, -4, -8 ],
[ 0, 7, 3, 9, 3, 13, 1, 14, 7, -20, 16, 4 ]
], hecke_fields := [
x^2 - 5,
x^3 - 3*x^2 - 13*x + 23,
x^5 + 2*x^4 - 3*x^3 - 5*x^2 + x + 1,
x^5 - 4*x^4 - 3*x^3 + 29*x^2 - 35*x + 11,
x^5 - 5*x^3 - x^2 + 5*x + 1,
x^9 - 13*x^7 + x^6 + 54*x^5 - 7*x^4 - 75*x^3 + 9*x^2 + 17*x - 3
], atkin_lehners := [
[ 1, -1 ],
[ 1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 19, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 227, 1 ],
[ 661, 1 ],
[ 15, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 661, 1 ],
[ 15, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 15 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 15 ], l_ratios := [ 1, 1, 0, 1, 0, 1/15 ], analytic_sha_upper_bounds := [ 1, 1, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 1, 0, 1 ], eigenvalues := [*
[
a,
1/2*a - 1/2,
a + 1,
-1,
1/2*a - 5/2,
-3/2*a + 1/2,
-6,
1/2*a - 3/2,
-1/2*a + 15/2,
7/2*a + 1/2,
-a + 5,
8
],
[
-1,
1/2*a + 1/2,
a - 1,
-1,
1/2*a + 1/2,
-3/4*a^2 + 1/2*a + 29/4,
2,
-1/4*a^2 - 1/2*a + 15/4,
-1/4*a^2 + 3/2*a + 7/4,
-1/2*a^2 - 1/2*a + 10,
-a^2 + a + 10,
1/2*a^2 - 2*a - 9/2
],
[
a,
-a^3 - a^2 + 3*a,
a^4 + 2*a^3 - 3*a^2 - 5*a + 1,
-1,
a^4 + a^3 - 4*a^2 - 3*a,
a^4 + 3*a^3 - 2*a^2 - 6*a,
-3*a^4 - 4*a^3 + 12*a^2 + 8*a - 7,
-3*a^4 - 4*a^3 + 10*a^2 + 5*a - 4,
-2*a^4 - 6*a^3 + 3*a^2 + 15*a + 1,
2*a^4 + 4*a^3 - 3*a^2 - 6*a - 4,
-2*a^4 - 3*a^3 + 8*a^2 + 7*a - 7,
2*a^4 + a^3 - 11*a^2 - a + 5
],
[
a,
-a^3 + a^2 + 7*a - 6,
a^4 - 2*a^3 - 7*a^2 + 15*a - 5,
-1,
a^4 - a^3 - 8*a^2 + 9*a + 4,
a^4 - 3*a^3 - 6*a^2 + 22*a - 12,
a^4 - 8*a^2 + 9,
a^4 - 4*a^3 - 6*a^2 + 29*a - 14,
-4*a^4 + 10*a^3 + 25*a^2 - 77*a + 39,
-2*a^4 + 4*a^3 + 13*a^2 - 30*a + 12,
-4*a^4 + 9*a^3 + 26*a^2 - 71*a + 31,
a^3 - a^2 - 9*a + 7
],
[
a,
a^3 - a^2 - 3*a,
-a^4 + 3*a^2 + a - 1,
1,
3*a^4 - 3*a^3 - 10*a^2 + 5*a + 4,
-a^4 + a^3 + 4*a^2 - 4*a - 6,
-3*a^4 + 4*a^3 + 12*a^2 - 10*a - 9,
a^4 - 4*a^2 + a - 2,
3*a^2 - a - 7,
2*a^4 - 4*a^3 - 7*a^2 + 10*a + 4,
4*a^4 - 3*a^3 - 16*a^2 + 5*a + 9,
-4*a^4 - a^3 + 17*a^2 + 7*a - 11
],
[
a,
-3/8*a^8 + 1/8*a^7 + 5*a^6 - 11/8*a^5 - 169/8*a^4 + 7/2*a^3 + 229/8*a^2 + 3/4*a - 25/8,
-1/4*a^8 - 1/4*a^7 + 3*a^6 + 11/4*a^5 - 47/4*a^4 - 9*a^3 + 67/4*a^2 + 17/2*a - 15/4,
1,
1/8*a^8 + 1/8*a^7 - 2*a^6 - 15/8*a^5 + 79/8*a^4 + 17/2*a^3 - 119/8*a^2 - 47/4*a + 15/8,
-3/8*a^8 - 3/8*a^7 + 4*a^6 + 29/8*a^5 - 93/8*a^4 - 19/2*a^3 + 53/8*a^2 + 25/4*a + 19/8,
1/2*a^8 + 1/2*a^7 - 6*a^6 - 11/2*a^5 + 45/2*a^4 + 18*a^3 - 55/2*a^2 - 17*a + 9/2,
5/8*a^8 + 1/8*a^7 - 8*a^6 - 11/8*a^5 + 263/8*a^4 + 13/2*a^3 - 363/8*a^2 - 57/4*a + 79/8,
-3/8*a^8 - 3/8*a^7 + 5*a^6 + 29/8*a^5 - 173/8*a^4 - 19/2*a^3 + 245/8*a^2 + 25/4*a - 21/8,
5/8*a^8 + 1/8*a^7 - 7*a^6 - 3/8*a^5 + 183/8*a^4 - 7/2*a^3 - 163/8*a^2 + 35/4*a - 9/8,
1/4*a^8 + 1/4*a^7 - 3*a^6 - 7/4*a^5 + 43/4*a^4 + a^3 - 43/4*a^2 + 9/2*a + 11/4,
a^8 + a^7 - 12*a^6 - 9*a^5 + 45*a^4 + 21*a^3 - 54*a^2 - 13*a + 8
]
*], q_expansions := [*
q + a*q^2 + (1/2*a - 1/2)*q^3 + 3*q^4 + (a + 1)*q^5 + (-1/2*a + 5/2)*q^6 - q^7 + a*q^8 + (-1/2*a - 3/2)*q^9 + (a + 5)*q^10 + (1/2*a - 5/2)*q^11 + (3/2*a - 3/2)*q^12 + (-3/2*a + 1/2)*q^13 - a*q^14 + 2*q^15 - q^16 - 6*q^17 + (-3/2*a - 5/2)*q^18 + (1/2*a - 3/2)*q^19 + (3*a + 3)*q^20 + (-1/2*a + 1/2)*q^21 + (-5/2*a + 5/2)*q^22 + (-1/2*a + 15/2)*q^23 + (-1/2*a + 5/2)*q^24 + (2*a + 1)*q^25 + (1/2*a - 15/2)*q^26 + (-2*a + 1)*q^27 - 3*q^28 + (7/2*a + 1/2)*q^29 + 2*a*q^30 + (-a + 5)*q^31 - 3*a*q^32 + (-3/2*a + 5/2)*q^33 - 6*a*q^34 + (-a - 1)*q^35 + (-3/2*a - 9/2)*q^36 + 8*q^37 + O(q^38),
q - q^2 + (1/2*a + 1/2)*q^3 - q^4 + (a - 1)*q^5 + (-1/2*a - 1/2)*q^6 - q^7 + 3*q^8 + (1/4*a^2 + 1/2*a - 11/4)*q^9 + (-a + 1)*q^10 + (1/2*a + 1/2)*q^11 + (-1/2*a - 1/2)*q^12 + (-3/4*a^2 + 1/2*a + 29/4)*q^13 + q^14 + (1/2*a^2 - 1/2)*q^15 - q^16 + 2*q^17 + (-1/4*a^2 - 1/2*a + 11/4)*q^18 + (-1/4*a^2 - 1/2*a + 15/4)*q^19 + (-a + 1)*q^20 + (-1/2*a - 1/2)*q^21 + (-1/2*a - 1/2)*q^22 + (-1/4*a^2 + 3/2*a + 7/4)*q^23 + (3/2*a + 3/2)*q^24 + (a^2 - 2*a - 4)*q^25 + (3/4*a^2 - 1/2*a - 29/4)*q^26 + (3/4*a^2 - a - 23/4)*q^27 + q^28 + (-1/2*a^2 - 1/2*a + 10)*q^29 + (-1/2*a^2 + 1/2)*q^30 + (-a^2 + a + 10)*q^31 - 5*q^32 + (1/4*a^2 + 1/2*a + 1/4)*q^33 - 2*q^34 + (-a + 1)*q^35 + (-1/4*a^2 - 1/2*a + 11/4)*q^36 + (1/2*a^2 - 2*a - 9/2)*q^37 + O(q^38),
q + a*q^2 + (-a^3 - a^2 + 3*a)*q^3 + (a^2 - 2)*q^4 + (a^4 + 2*a^3 - 3*a^2 - 5*a + 1)*q^5 + (-a^4 - a^3 + 3*a^2)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-2*a^4 - a^3 + 8*a^2 - a - 3)*q^9 - q^10 + (a^4 + a^3 - 4*a^2 - 3*a)*q^11 + (a^4 + 2*a^3 - 3*a^2 - 5*a + 1)*q^12 + (a^4 + 3*a^3 - 2*a^2 - 6*a)*q^13 - a*q^14 + (a^2 + a - 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3*a^4 - 4*a^3 + 12*a^2 + 8*a - 7)*q^17 + (3*a^4 + 2*a^3 - 11*a^2 - a + 2)*q^18 + (-3*a^4 - 4*a^3 + 10*a^2 + 5*a - 4)*q^19 + (-2*a^4 - 4*a^3 + 6*a^2 + 9*a - 2)*q^20 + (a^3 + a^2 - 3*a)*q^21 + (-a^4 - a^3 + 2*a^2 - a - 1)*q^22 + (-2*a^4 - 6*a^3 + 3*a^2 + 15*a + 1)*q^23 + (2*a^4 + 2*a^3 - 6*a^2 - 1)*q^24 + (a^4 + a^3 - 5*a^2 - 2*a + 1)*q^25 + (a^4 + a^3 - a^2 - a - 1)*q^26 + (7*a^4 + 9*a^3 - 23*a^2 - 12*a + 5)*q^27 + (-a^2 + 2)*q^28 + (2*a^4 + 4*a^3 - 3*a^2 - 6*a - 4)*q^29 + (a^3 + a^2 - 3*a)*q^30 + (-2*a^4 - 3*a^3 + 8*a^2 + 7*a - 7)*q^31 + (-2*a^4 - 5*a^3 + 5*a^2 + 11*a - 1)*q^32 + (-a^4 + a^3 + 7*a^2 - 3*a - 3)*q^33 + (2*a^4 + 3*a^3 - 7*a^2 - 4*a + 3)*q^34 + (-a^4 - 2*a^3 + 3*a^2 + 5*a - 1)*q^35 + (-2*a^2 + a + 3)*q^36 + (2*a^4 + a^3 - 11*a^2 - a + 5)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + a^2 + 7*a - 6)*q^3 + (a^2 - 2)*q^4 + (a^4 - 2*a^3 - 7*a^2 + 15*a - 5)*q^5 + (-a^4 + a^3 + 7*a^2 - 6*a)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-2*a^4 + 3*a^3 + 14*a^2 - 25*a + 11)*q^9 + (2*a^4 - 4*a^3 - 14*a^2 + 30*a - 11)*q^10 + (a^4 - a^3 - 8*a^2 + 9*a + 4)*q^11 + (-3*a^4 + 6*a^3 + 21*a^2 - 49*a + 23)*q^12 + (a^4 - 3*a^3 - 6*a^2 + 22*a - 12)*q^13 - a*q^14 + (4*a^4 - 8*a^3 - 27*a^2 + 61*a - 25)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 - 8*a^2 + 9)*q^17 + (-5*a^4 + 8*a^3 + 33*a^2 - 59*a + 22)*q^18 + (a^4 - 4*a^3 - 6*a^2 + 29*a - 14)*q^19 + (2*a^4 - 4*a^3 - 14*a^2 + 29*a - 12)*q^20 + (a^3 - a^2 - 7*a + 6)*q^21 + (3*a^4 - 5*a^3 - 20*a^2 + 39*a - 11)*q^22 + (-4*a^4 + 10*a^3 + 25*a^2 - 77*a + 39)*q^23 + (-4*a^4 + 10*a^3 + 24*a^2 - 70*a + 33)*q^24 + (-3*a^4 + 5*a^3 + 21*a^2 - 38*a + 9)*q^25 + (a^4 - 3*a^3 - 7*a^2 + 23*a - 11)*q^26 + (-5*a^4 + 9*a^3 + 35*a^2 - 72*a + 29)*q^27 + (-a^2 + 2)*q^28 + (-2*a^4 + 4*a^3 + 13*a^2 - 30*a + 12)*q^29 + (8*a^4 - 15*a^3 - 55*a^2 + 115*a - 44)*q^30 + (-4*a^4 + 9*a^3 + 26*a^2 - 71*a + 31)*q^31 + (4*a^4 - 5*a^3 - 29*a^2 + 47*a - 11)*q^32 + (5*a^4 - 13*a^3 - 31*a^2 + 101*a - 57)*q^33 + (4*a^4 - 5*a^3 - 29*a^2 + 44*a - 11)*q^34 + (-a^4 + 2*a^3 + 7*a^2 - 15*a + 5)*q^35 + (-8*a^4 + 12*a^3 + 58*a^2 - 103*a + 33)*q^36 + (a^3 - a^2 - 9*a + 7)*q^37 + O(q^38),
q + a*q^2 + (a^3 - a^2 - 3*a)*q^3 + (a^2 - 2)*q^4 + (-a^4 + 3*a^2 + a - 1)*q^5 + (a^4 - a^3 - 3*a^2)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (-3*a^3 + 2*a^2 + 9*a - 1)*q^9 + (-2*a^3 + 4*a + 1)*q^10 + (3*a^4 - 3*a^3 - 10*a^2 + 5*a + 4)*q^11 + (-a^4 + 3*a^2 + a - 1)*q^12 + (-a^4 + a^3 + 4*a^2 - 4*a - 6)*q^13 + a*q^14 + (2*a^4 - 5*a^2 - 3*a - 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3*a^4 + 4*a^3 + 12*a^2 - 10*a - 9)*q^17 + (-3*a^4 + 2*a^3 + 9*a^2 - a)*q^18 + (a^4 - 4*a^2 + a - 2)*q^19 + (-2*a^2 - a + 2)*q^20 + (a^3 - a^2 - 3*a)*q^21 + (-3*a^4 + 5*a^3 + 8*a^2 - 11*a - 3)*q^22 + (3*a^2 - a - 7)*q^23 + (-2*a^4 + 6*a^2 + 4*a + 1)*q^24 + (a^4 - a^3 - a^2 + 4*a - 3)*q^25 + (a^4 - a^3 - 5*a^2 - a + 1)*q^26 + (a^4 + 3*a^3 - 3*a^2 - 10*a - 5)*q^27 + (a^2 - 2)*q^28 + (2*a^4 - 4*a^3 - 7*a^2 + 10*a + 4)*q^29 + (5*a^3 - a^2 - 11*a - 2)*q^30 + (4*a^4 - 3*a^3 - 16*a^2 + 5*a + 9)*q^31 + (-3*a^3 + a^2 + 7*a - 1)*q^32 + (-3*a^4 + 3*a^3 + 7*a^2 - a + 1)*q^33 + (4*a^4 - 3*a^3 - 13*a^2 + 6*a + 3)*q^34 + (-a^4 + 3*a^2 + a - 1)*q^35 + (2*a^4 - 8*a^2 - 3*a + 5)*q^36 + (-4*a^4 - a^3 + 17*a^2 + 7*a - 11)*q^37 + O(q^38),
q + a*q^2 + (-3/8*a^8 + 1/8*a^7 + 5*a^6 - 11/8*a^5 - 169/8*a^4 + 7/2*a^3 + 229/8*a^2 + 3/4*a - 25/8)*q^3 + (a^2 - 2)*q^4 + (-1/4*a^8 - 1/4*a^7 + 3*a^6 + 11/4*a^5 - 47/4*a^4 - 9*a^3 + 67/4*a^2 + 17/2*a - 15/4)*q^5 + (1/8*a^8 + 1/8*a^7 - a^6 - 7/8*a^5 + 7/8*a^4 + 1/2*a^3 + 33/8*a^2 + 13/4*a - 9/8)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (-3/8*a^8 + 1/8*a^7 + 5*a^6 - 11/8*a^5 - 169/8*a^4 + 7/2*a^3 + 221/8*a^2 + 3/4*a - 1/8)*q^9 + (-1/4*a^8 - 1/4*a^7 + 3*a^6 + 7/4*a^5 - 43/4*a^4 - 2*a^3 + 43/4*a^2 + 1/2*a - 3/4)*q^10 + (1/8*a^8 + 1/8*a^7 - 2*a^6 - 15/8*a^5 + 79/8*a^4 + 17/2*a^3 - 119/8*a^2 - 47/4*a + 15/8)*q^11 + (7/8*a^8 + 3/8*a^7 - 11*a^6 - 25/8*a^5 + 349/8*a^4 + 13/2*a^3 - 441/8*a^2 - 19/4*a + 53/8)*q^12 + (-3/8*a^8 - 3/8*a^7 + 4*a^6 + 29/8*a^5 - 93/8*a^4 - 19/2*a^3 + 53/8*a^2 + 25/4*a + 19/8)*q^13 + a*q^14 + (a^5 - 9*a^3 + 18*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/2*a^8 + 1/2*a^7 - 6*a^6 - 11/2*a^5 + 45/2*a^4 + 18*a^3 - 55/2*a^2 - 17*a + 9/2)*q^17 + (1/8*a^8 + 1/8*a^7 - a^6 - 7/8*a^5 + 7/8*a^4 - 1/2*a^3 + 33/8*a^2 + 25/4*a - 9/8)*q^18 + (5/8*a^8 + 1/8*a^7 - 8*a^6 - 11/8*a^5 + 263/8*a^4 + 13/2*a^3 - 363/8*a^2 - 57/4*a + 79/8)*q^19 + (1/4*a^8 + 1/4*a^7 - 4*a^6 - 11/4*a^5 + 79/4*a^4 + 10*a^3 - 123/4*a^2 - 27/2*a + 27/4)*q^20 + (-3/8*a^8 + 1/8*a^7 + 5*a^6 - 11/8*a^5 - 169/8*a^4 + 7/2*a^3 + 229/8*a^2 + 3/4*a - 25/8)*q^21 + (1/8*a^8 - 3/8*a^7 - 2*a^6 + 25/8*a^5 + 75/8*a^4 - 11/2*a^3 - 103/8*a^2 - 1/4*a + 3/8)*q^22 + (-3/8*a^8 - 3/8*a^7 + 5*a^6 + 29/8*a^5 - 173/8*a^4 - 19/2*a^3 + 245/8*a^2 + 25/4*a - 21/8)*q^23 + (1/8*a^8 + 1/8*a^7 - 2*a^6 - 15/8*a^5 + 87/8*a^4 + 19/2*a^3 - 167/8*a^2 - 59/4*a + 39/8)*q^24 + (-1/2*a^8 - 1/2*a^7 + 6*a^6 + 9/2*a^5 - 45/2*a^4 - 10*a^3 + 55/2*a^2 + 2*a - 7/2)*q^25 + (-3/8*a^8 - 7/8*a^7 + 4*a^6 + 69/8*a^5 - 97/8*a^4 - 43/2*a^3 + 77/8*a^2 + 35/4*a - 9/8)*q^26 + (-1/2*a^8 - 1/2*a^7 + 6*a^6 + 9/2*a^5 - 45/2*a^4 - 10*a^3 + 51/2*a^2 + 4*a + 5/2)*q^27 + (a^2 - 2)*q^28 + (5/8*a^8 + 1/8*a^7 - 7*a^6 - 3/8*a^5 + 183/8*a^4 - 7/2*a^3 - 163/8*a^2 + 35/4*a - 9/8)*q^29 + (a^6 - 9*a^4 + 18*a^2)*q^30 + (1/4*a^8 + 1/4*a^7 - 3*a^6 - 7/4*a^5 + 43/4*a^4 + a^3 - 43/4*a^2 + 9/2*a + 11/4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (9/8*a^8 + 9/8*a^7 - 14*a^6 - 95/8*a^5 + 439/8*a^4 + 75/2*a^3 - 559/8*a^2 - 155/4*a + 87/8)*q^33 + (1/2*a^8 + 1/2*a^7 - 6*a^6 - 9/2*a^5 + 43/2*a^4 + 10*a^3 - 43/2*a^2 - 4*a + 3/2)*q^34 + (-1/4*a^8 - 1/4*a^7 + 3*a^6 + 11/4*a^5 - 47/4*a^4 - 9*a^3 + 67/4*a^2 + 17/2*a - 15/4)*q^35 + (7/8*a^8 + 3/8*a^7 - 11*a^6 - 25/8*a^5 + 341/8*a^4 + 13/2*a^3 - 401/8*a^2 - 19/4*a + 5/8)*q^36 + (a^8 + a^7 - 12*a^6 - 9*a^5 + 45*a^4 + 21*a^3 - 54*a^2 - 13*a + 8)*q^37 + O(q^38)
*]> ;  // time = 70.279 seconds




J[415] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 415, 415, 415, 415, 415, 83, 83 ], new_dimensions := [ 1, 2, 6, 7, 11, 1, 6 ], dimensions := [ 1, 2, 6, 7, 11, 2, 12 ], intersection_graph := [ 0, 1, 1, 1, 7, 1, 1, 1, 0, 1, 1, 1, 1, 11, 1, 1, 0, 1, 1, 1, 1069, 1, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 11, 1069, 1, 1, 1, 0 ], ap_traces := [
[ 1, 3, 1, 1, 3, -6, -7, 2, 4, -7, 5, -7 ],
[ -1, -1, 2, 0, -4, -3, -7, -4, -6, -8, -5, -5 ],
[ 2, 3, -6, 0, 4, 7, 21, 2, 8, 10, -13, 1 ],
[ -3, -5, -7, -6, -2, -5, -25, 6, -9, -2, 1, -13 ],
[ 0, 0, 11, -3, -1, 1, 28, -2, 1, 21, 4, -10 ]
], hecke_fields := [
x - 1,
x^2 + x - 1,
x^6 - 2*x^5 - 5*x^4 + 9*x^3 + 5*x^2 - 6*x - 1,
x^7 + 3*x^6 - 6*x^5 - 19*x^4 + 9*x^3 + 28*x^2 - 4*x - 8,
x^11 - 20*x^9 - x^8 + 146*x^7 + 15*x^6 - 464*x^5 - 76*x^4 + 567*x^3 + 136*x^2 - 100*x - 8
], atkin_lehners := [
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 11, 1 ],
[ 1069, 1 ],
[ 1, 1 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 11, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 7 ], torsion_lower_bounds := [ 1, 1, 1, 1, 7 ], l_ratios := [ 1, 0, 1, 0, 1/7 ], analytic_sha_upper_bounds := [ 1, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1, 0, 1 ], eigenvalues := [*
[ 1, 3, 1, 1, 3, -6, -7, 2, 4, -7, 5, -7 ],
[
a,
-a - 1,
1,
2*a + 1,
-2,
-a - 2,
-a - 4,
-2*a - 3,
-4*a - 5,
2*a - 3,
3*a - 1,
-3*a - 4
],
[
a,
-a^4 + a^3 + 5*a^2 - 3*a - 3,
-1,
a^5 - a^4 - 5*a^3 + 3*a^2 + 5*a,
2*a^5 - 3*a^4 - 10*a^3 + 12*a^2 + 9*a - 4,
-a^3 + a^2 + 2*a,
-a^5 + 2*a^4 + 4*a^3 - 8*a^2 - 2*a + 7,
a^5 - 3*a^4 - 3*a^3 + 11*a^2 - a - 2,
a^5 - a^4 - 5*a^3 + 3*a^2 + 3*a + 2,
-2*a^5 + 3*a^4 + 10*a^3 - 12*a^2 - 11*a + 7,
a^5 + a^4 - 6*a^3 - 4*a^2 + 5*a - 2,
-3*a^5 + 4*a^4 + 14*a^3 - 16*a^2 - 8*a + 7
],
[
a,
-1/4*a^6 - 1/4*a^5 + 2*a^4 + 3/4*a^3 - 19/4*a^2 + 1/2*a + 2,
-1,
-1/4*a^6 - 3/4*a^5 + 3/2*a^4 + 19/4*a^3 - 9/4*a^2 - 7*a,
a^6 + 5/2*a^5 - 11/2*a^4 - 13*a^3 + 11/2*a^2 + 21/2*a,
-a^5 - 2*a^4 + 5*a^3 + 8*a^2 - 4*a - 4,
-1/4*a^6 - 3/4*a^5 + 3/2*a^4 + 15/4*a^3 - 9/4*a^2 - 2*a - 4,
-1/2*a^6 - 3/2*a^5 + 2*a^4 + 15/2*a^3 + 5/2*a^2 - 4*a - 6,
1/2*a^6 + 1/2*a^5 - 4*a^4 - 5/2*a^3 + 17/2*a^2 + 4*a - 5,
3/4*a^6 + 15/4*a^5 - 2*a^4 - 85/4*a^3 - 15/4*a^2 + 41/2*a + 4,
-1/2*a^5 - 7/2*a^4 + a^3 + 37/2*a^2 - 1/2*a - 12,
1/2*a^6 + 2*a^5 - 1/2*a^4 - 21/2*a^3 - 9*a^2 + 17/2*a + 6
],
[
a,
-a^10 - 7/4*a^9 + 65/4*a^8 + 119/4*a^7 - 83*a^6 - 164*a^5 + 483/4*a^4 + 1195/4*a^3 + 213/4*a^2 - 93/2*a - 6,
1,
1/4*a^9 - 1/4*a^8 - 15/4*a^7 + 7/2*a^6 + 18*a^5 - 61/4*a^4 - 115/4*a^3 + 83/4*a^2 + 7*a - 4,
3/4*a^10 + 9/4*a^9 - 51/4*a^8 - 37*a^7 + 137/2*a^6 + 789/4*a^5 - 425/4*a^4 - 1401/4*a^3 - 91/2*a^2 + 133/2*a + 6,
-a^3 - a^2 + 6*a + 4,
3/2*a^10 + 11/4*a^9 - 99/4*a^8 - 187/4*a^7 + 261/2*a^6 + 517/2*a^5 - 847/4*a^4 - 1913/4*a^3 - 117/4*a^2 + 96*a + 4,
a^10 + 5/2*a^9 - 33/2*a^8 - 83/2*a^7 + 85*a^6 + 223*a^5 - 237/2*a^4 - 791/2*a^3 - 165/2*a^2 + 62*a + 10,
-3/2*a^10 - 4*a^9 + 25*a^8 + 133/2*a^7 - 131*a^6 - 719/2*a^5 + 194*a^4 + 651*a^3 + 193/2*a^2 - 132*a - 9,
a^10 + 13/4*a^9 - 67/4*a^8 - 213/4*a^7 + 87*a^6 + 282*a^5 - 473/4*a^4 - 1965/4*a^3 - 395/4*a^2 + 143/2*a + 8,
13/4*a^10 + 19/4*a^9 - 213/4*a^8 - 82*a^7 + 557/2*a^6 + 1835/4*a^5 - 1791/4*a^4 - 3387/4*a^3 - 121/2*a^2 + 263/2*a + 6,
-7/4*a^10 - 11/4*a^9 + 113/4*a^8 + 95/2*a^7 - 287/2*a^6 - 1065/4*a^5 + 839/4*a^4 + 1979/4*a^3 + 81*a^2 - 171/2*a - 8
]
*], q_expansions := [*
q + q^2 + 3*q^3 - q^4 + q^5 + 3*q^6 + q^7 - 3*q^8 + 6*q^9 + q^10 + 3*q^11 - 3*q^12 - 6*q^13 + q^14 + 3*q^15 - q^16 - 7*q^17 + 6*q^18 + 2*q^19 - q^20 + 3*q^21 + 3*q^22 + 4*q^23 - 9*q^24 + q^25 - 6*q^26 + 9*q^27 - q^28 - 7*q^29 + 3*q^30 + 5*q^31 + 5*q^32 + 9*q^33 - 7*q^34 + q^35 - 6*q^36 - 7*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (-a - 1)*q^4 + q^5 - q^6 + (2*a + 1)*q^7 + (-2*a - 1)*q^8 + (a - 1)*q^9 + a*q^10 - 2*q^11 + (a + 2)*q^12 + (-a - 2)*q^13 + (-a + 2)*q^14 + (-a - 1)*q^15 + 3*a*q^16 + (-a - 4)*q^17 + (-2*a + 1)*q^18 + (-2*a - 3)*q^19 + (-a - 1)*q^20 + (-a - 3)*q^21 - 2*a*q^22 + (-4*a - 5)*q^23 + (a + 3)*q^24 + q^25 + (-a - 1)*q^26 + (4*a + 3)*q^27 + (-a - 3)*q^28 + (2*a - 3)*q^29 - q^30 + (3*a - 1)*q^31 + (a + 5)*q^32 + (2*a + 2)*q^33 + (-3*a - 1)*q^34 + (2*a + 1)*q^35 + a*q^36 + (-3*a - 4)*q^37 + O(q^38),
q + a*q^2 + (-a^4 + a^3 + 5*a^2 - 3*a - 3)*q^3 + (a^2 - 2)*q^4 - q^5 + (-a^5 + a^4 + 5*a^3 - 3*a^2 - 3*a)*q^6 + (a^5 - a^4 - 5*a^3 + 3*a^2 + 5*a)*q^7 + (a^3 - 4*a)*q^8 + (-a^5 + 6*a^3 - 6*a + 2)*q^9 - a*q^10 + (2*a^5 - 3*a^4 - 10*a^3 + 12*a^2 + 9*a - 4)*q^11 + (-a^5 + 2*a^4 + 4*a^3 - 8*a^2 + 5)*q^12 + (-a^3 + a^2 + 2*a)*q^13 + (a^5 - 6*a^3 + 6*a + 1)*q^14 + (a^4 - a^3 - 5*a^2 + 3*a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^5 + 2*a^4 + 4*a^3 - 8*a^2 - 2*a + 7)*q^17 + (-2*a^5 + a^4 + 9*a^3 - a^2 - 4*a - 1)*q^18 + (a^5 - 3*a^4 - 3*a^3 + 11*a^2 - a - 2)*q^19 + (-a^2 + 2)*q^20 + (a^4 + a^3 - 5*a^2 - 5*a + 1)*q^21 + (a^5 - 6*a^3 - a^2 + 8*a + 2)*q^22 + (a^5 - a^4 - 5*a^3 + 3*a^2 + 3*a + 2)*q^23 + (2*a^5 - 3*a^4 - 9*a^3 + 11*a^2 + 5*a - 1)*q^24 + q^25 + (-a^4 + a^3 + 2*a^2)*q^26 + (-a^5 - a^4 + 5*a^3 + 5*a^2 - a)*q^27 + (a^4 + a^3 - 5*a^2 - 3*a + 1)*q^28 + (-2*a^5 + 3*a^4 + 10*a^3 - 12*a^2 - 11*a + 7)*q^29 + (a^5 - a^4 - 5*a^3 + 3*a^2 + 3*a)*q^30 + (a^5 + a^4 - 6*a^3 - 4*a^2 + 5*a - 2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-2*a^5 + 4*a^4 + 12*a^3 - 18*a^2 - 18*a + 10)*q^33 + (-a^4 + a^3 + 3*a^2 + a - 1)*q^34 + (-a^5 + a^4 + 5*a^3 - 3*a^2 - 5*a)*q^35 + (-a^5 - a^4 + 5*a^3 + 6*a^2 - a - 6)*q^36 + (-3*a^5 + 4*a^4 + 14*a^3 - 16*a^2 - 8*a + 7)*q^37 + O(q^38),
q + a*q^2 + (-1/4*a^6 - 1/4*a^5 + 2*a^4 + 3/4*a^3 - 19/4*a^2 + 1/2*a + 2)*q^3 + (a^2 - 2)*q^4 - q^5 + (1/2*a^6 + 1/2*a^5 - 4*a^4 - 5/2*a^3 + 15/2*a^2 + a - 2)*q^6 + (-1/4*a^6 - 3/4*a^5 + 3/2*a^4 + 19/4*a^3 - 9/4*a^2 - 7*a)*q^7 + (a^3 - 4*a)*q^8 + (1/2*a^6 + a^5 - 7/2*a^4 - 9/2*a^3 + 8*a^2 + 3/2*a - 5)*q^9 - a*q^10 + (a^6 + 5/2*a^5 - 11/2*a^4 - 13*a^3 + 11/2*a^2 + 21/2*a)*q^11 + (-1/2*a^6 - 1/2*a^5 + 3*a^4 + 3/2*a^3 - 7/2*a^2 - a)*q^12 + (-a^5 - 2*a^4 + 5*a^3 + 8*a^2 - 4*a - 4)*q^13 + (-a - 2)*q^14 + (1/4*a^6 + 1/4*a^5 - 2*a^4 - 3/4*a^3 + 19/4*a^2 - 1/2*a - 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/4*a^6 - 3/4*a^5 + 3/2*a^4 + 15/4*a^3 - 9/4*a^2 - 2*a - 4)*q^17 + (-1/2*a^6 - 1/2*a^5 + 5*a^4 + 7/2*a^3 - 25/2*a^2 - 3*a + 4)*q^18 + (-1/2*a^6 - 3/2*a^5 + 2*a^4 + 15/2*a^3 + 5/2*a^2 - 4*a - 6)*q^19 + (-a^2 + 2)*q^20 + (-1/4*a^6 - 3/4*a^5 + 3/2*a^4 + 19/4*a^3 - 5/4*a^2 - 5*a - 1)*q^21 + (-1/2*a^6 + 1/2*a^5 + 6*a^4 - 7/2*a^3 - 35/2*a^2 + 4*a + 8)*q^22 + (1/2*a^6 + 1/2*a^5 - 4*a^4 - 5/2*a^3 + 17/2*a^2 + 4*a - 5)*q^23 + (-a^5 + 6*a^3 - 2*a^2 - 4*a)*q^24 + q^25 + (-a^6 - 2*a^5 + 5*a^4 + 8*a^3 - 4*a^2 - 4*a)*q^26 + (-1/4*a^6 - 5/4*a^5 + a^4 + 27/4*a^3 - 3/4*a^2 - 9/2*a - 3)*q^27 + (1/2*a^6 + 3/2*a^5 - 3*a^4 - 19/2*a^3 + 7/2*a^2 + 12*a)*q^28 + (3/4*a^6 + 15/4*a^5 - 2*a^4 - 85/4*a^3 - 15/4*a^2 + 41/2*a + 4)*q^29 + (-1/2*a^6 - 1/2*a^5 + 4*a^4 + 5/2*a^3 - 15/2*a^2 - a + 2)*q^30 + (-1/2*a^5 - 7/2*a^4 + a^3 + 37/2*a^2 - 1/2*a - 12)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-1/4*a^6 - 1/4*a^5 + 3*a^4 + 3/4*a^3 - 43/4*a^2 + 9/2*a + 5)*q^33 + (-a^4 + 5*a^2 - 5*a - 2)*q^34 + (1/4*a^6 + 3/4*a^5 - 3/2*a^4 - 19/4*a^3 + 9/4*a^2 + 7*a)*q^35 + (a^4 + a^3 - 5*a^2 - a + 6)*q^36 + (1/2*a^6 + 2*a^5 - 1/2*a^4 - 21/2*a^3 - 9*a^2 + 17/2*a + 6)*q^37 + O(q^38),
q + a*q^2 + (-a^10 - 7/4*a^9 + 65/4*a^8 + 119/4*a^7 - 83*a^6 - 164*a^5 + 483/4*a^4 + 1195/4*a^3 + 213/4*a^2 - 93/2*a - 6)*q^3 + (a^2 - 2)*q^4 + q^5 + (-7/4*a^10 - 15/4*a^9 + 115/4*a^8 + 63*a^7 - 149*a^6 - 1373/4*a^5 + 891/4*a^4 + 2481/4*a^3 + 179/2*a^2 - 106*a - 8)*q^6 + (1/4*a^9 - 1/4*a^8 - 15/4*a^7 + 7/2*a^6 + 18*a^5 - 61/4*a^4 - 115/4*a^3 + 83/4*a^2 + 7*a - 4)*q^7 + (a^3 - 4*a)*q^8 + (7/4*a^10 + 11/4*a^9 - 113/4*a^8 - 95/2*a^7 + 287/2*a^6 + 1065/4*a^5 - 839/4*a^4 - 1979/4*a^3 - 81*a^2 + 167/2*a + 9)*q^9 + a*q^10 + (3/4*a^10 + 9/4*a^9 - 51/4*a^8 - 37*a^7 + 137/2*a^6 + 789/4*a^5 - 425/4*a^4 - 1401/4*a^3 - 91/2*a^2 + 133/2*a + 6)*q^11 + (-7/4*a^10 - 11/4*a^9 + 115/4*a^8 + 47*a^7 - 151*a^6 - 1045/4*a^5 + 983/4*a^4 + 1937/4*a^3 + 51/2*a^2 - 90*a - 2)*q^12 + (-a^3 - a^2 + 6*a + 4)*q^13 + (1/4*a^10 - 1/4*a^9 - 15/4*a^8 + 7/2*a^7 + 18*a^6 - 61/4*a^5 - 115/4*a^4 + 83/4*a^3 + 7*a^2 - 4*a)*q^14 + (-a^10 - 7/4*a^9 + 65/4*a^8 + 119/4*a^7 - 83*a^6 - 164*a^5 + 483/4*a^4 + 1195/4*a^3 + 213/4*a^2 - 93/2*a - 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (3/2*a^10 + 11/4*a^9 - 99/4*a^8 - 187/4*a^7 + 261/2*a^6 + 517/2*a^5 - 847/4*a^4 - 1913/4*a^3 - 117/4*a^2 + 96*a + 4)*q^17 + (11/4*a^10 + 27/4*a^9 - 183/4*a^8 - 112*a^7 + 240*a^6 + 2409/4*a^5 - 1447/4*a^4 - 4293/4*a^3 - 309/2*a^2 + 184*a + 14)*q^18 + (a^10 + 5/2*a^9 - 33/2*a^8 - 83/2*a^7 + 85*a^6 + 223*a^5 - 237/2*a^4 - 791/2*a^3 - 165/2*a^2 + 62*a + 10)*q^19 + (a^2 - 2)*q^20 + (-3/2*a^10 - 13/4*a^9 + 101/4*a^8 + 217/4*a^7 - 273/2*a^6 - 587/2*a^5 + 921/4*a^4 + 2111/4*a^3 + 87/4*a^2 - 99*a + 3)*q^21 + (9/4*a^10 + 9/4*a^9 - 145/4*a^8 - 41*a^7 + 186*a^6 + 967/4*a^5 - 1173/4*a^4 - 1883/4*a^3 - 71/2*a^2 + 81*a + 6)*q^22 + (-3/2*a^10 - 4*a^9 + 25*a^8 + 133/2*a^7 - 131*a^6 - 719/2*a^5 + 194*a^4 + 651*a^3 + 193/2*a^2 - 132*a - 9)*q^23 + (3/4*a^10 + 5/4*a^9 - 49/4*a^8 - 43/2*a^7 + 63*a^6 + 481/4*a^5 - 377/4*a^4 - 891/4*a^3 - 31*a^2 + 35*a + 2)*q^24 + q^25 + (-a^4 - a^3 + 6*a^2 + 4*a)*q^26 + (-5/2*a^10 - 13/4*a^9 + 163/4*a^8 + 227/4*a^7 - 212*a^6 - 643/2*a^5 + 1361/4*a^4 + 2417/4*a^3 + 157/4*a^2 - 219/2*a - 7)*q^27 + (-1/4*a^10 + 3/4*a^9 + 17/4*a^8 - 11*a^7 - 26*a^6 + 205/4*a^5 + 281/4*a^4 - 309/4*a^3 - 159/2*a^2 + 11*a + 10)*q^28 + (a^10 + 13/4*a^9 - 67/4*a^8 - 213/4*a^7 + 87*a^6 + 282*a^5 - 473/4*a^4 - 1965/4*a^3 - 395/4*a^2 + 143/2*a + 8)*q^29 + (-7/4*a^10 - 15/4*a^9 + 115/4*a^8 + 63*a^7 - 149*a^6 - 1373/4*a^5 + 891/4*a^4 + 2481/4*a^3 + 179/2*a^2 - 106*a - 8)*q^30 + (13/4*a^10 + 19/4*a^9 - 213/4*a^8 - 82*a^7 + 557/2*a^6 + 1835/4*a^5 - 1791/4*a^4 - 3387/4*a^3 - 121/2*a^2 + 263/2*a + 6)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (3/2*a^10 + 3/4*a^9 - 97/4*a^8 - 61/4*a^7 + 127*a^6 + 197/2*a^5 - 879/4*a^4 - 835/4*a^3 + 125/4*a^2 + 91/2*a + 1)*q^33 + (11/4*a^10 + 21/4*a^9 - 181/4*a^8 - 177/2*a^7 + 236*a^6 + 1937/4*a^5 - 1457/4*a^4 - 3519/4*a^3 - 108*a^2 + 154*a + 12)*q^34 + (1/4*a^9 - 1/4*a^8 - 15/4*a^7 + 7/2*a^6 + 18*a^5 - 61/4*a^4 - 115/4*a^3 + 83/4*a^2 + 7*a - 4)*q^35 + (13/4*a^10 + 15/4*a^9 - 211/4*a^8 - 133/2*a^7 + 274*a^6 + 1527/4*a^5 - 1779/4*a^4 - 2897/4*a^3 - 28*a^2 + 122*a + 4)*q^36 + (-7/4*a^10 - 11/4*a^9 + 113/4*a^8 + 95/2*a^7 - 287/2*a^6 - 1065/4*a^5 + 839/4*a^4 + 1979/4*a^3 + 81*a^2 - 171/2*a - 8)*q^37 + O(q^38)
*]> ;  // time = 71.1 seconds




J[417] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 417, 417, 417, 417, 417, 417, 139, 139, 139 ], new_dimensions := [ 1, 2, 3, 3, 7, 7, 1, 3, 7 ], dimensions := [ 1, 2, 3, 3, 7, 7, 2, 6, 14 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 3, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 19, 1, 1, 0, 1, 1, 1, 1, 1, 37, 1, 1, 1, 0, 1, 173, 1, 13, 1, 1, 1, 1, 1, 0, 1, 1, 29, 1, 1, 1, 1, 173, 1, 0, 1, 7, 1, 3, 1, 1, 1, 1, 1, 0, 1, 9, 1, 1, 1, 13, 29, 7, 1, 0, 1, 3, 19, 37, 1, 1, 1, 9, 1, 0 ], ap_traces := [
[ 1, -1, 2, 0, 5, 5, -3, 7, 2, 0, -6, -7 ],
[ -1, 2, -2, -7, 0, -6, -5, 2, -4, 4, -3, -9 ],
[ 0, -3, 2, 5, 3, -5, 12, -3, 16, 0, 11, -8 ],
[ 0, 3, 4, 5, 4, 4, -11, 8, -6, -14, -3, 17 ],
[ -3, -7, -4, -9, -4, -4, -15, -2, -22, -12, -9, 4 ],
[ 0, 7, -4, 6, -4, 4, 12, 0, 18, 0, 18, 3 ]
], hecke_fields := [
x - 1,
x^2 + x - 1,
x^3 - 4*x - 1,
x^3 - 4*x - 1,
x^7 + 3*x^6 - 6*x^5 - 19*x^4 + 9*x^3 + 30*x^2 - 8,
x^7 - 14*x^5 + 2*x^4 + 57*x^3 - 14*x^2 - 56*x + 8
], atkin_lehners := [
[ 1, -1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 9, 1 ],
[ 19, 1 ],
[ 37, 1 ],
[ 91, 1 ],
[ 29, 1 ],
[ 35, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 19, 1 ],
[ 1, 1 ],
[ 91, 1 ],
[ 1, 1 ],
[ 35, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 7, 1, 5 ], torsion_lower_bounds := [ 1, 1, 1, 7, 1, 5 ], l_ratios := [ 1, 0, 1, 13/7, 0, 7/5 ], analytic_sha_upper_bounds := [ 1, 0, 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1, 1, 0, 1 ], eigenvalues := [*
[ 1, -1, 2, 0, 5, 5, -3, 7, 2, 0, -6, -7 ],
[
a,
1,
-1,
-a - 4,
-2*a - 1,
2*a - 2,
-3*a - 4,
4*a + 3,
2*a - 1,
4*a + 4,
-3*a - 3,
-a - 5
],
[
a,
-1,
a^2 - a - 2,
a^2 - 1,
1,
-a^2 + a + 1,
a + 4,
-1,
-a^2 - a + 8,
0,
-2*a^2 - a + 9,
-a^2 + 2*a
],
[
a,
1,
-a^2 - a + 4,
a^2 - 1,
-a^2 + a + 4,
2*a^2 - 4,
-a^2 - 1,
a^2 - a,
-3*a^2 + a + 6,
2*a^2 - 2*a - 10,
-3*a - 1,
-2*a^2 + a + 11
],
[
a,
-1,
1/2*a^6 + a^5 - 7/2*a^4 - 11/2*a^3 + 6*a^2 + 11/2*a - 1,
-3/4*a^6 - 7/4*a^5 + 5*a^4 + 37/4*a^3 - 41/4*a^2 - 10*a + 3,
-1/4*a^6 + 1/4*a^5 + 7/2*a^4 - 1/4*a^3 - 37/4*a^2 - 3/2*a + 2,
1/4*a^6 - 1/4*a^5 - 9/2*a^4 + 1/4*a^3 + 65/4*a^2 - 1/2*a - 10,
1/2*a^6 + 3/2*a^5 - 2*a^4 - 17/2*a^3 - 1/2*a^2 + 12*a,
a^4 + 2*a^3 - 3*a^2 - 6*a - 2,
-a^4 + 7*a^2 - 2*a - 10,
-3/4*a^6 - 7/4*a^5 + 4*a^4 + 25/4*a^3 - 29/4*a^2 + a + 3,
1/2*a^6 + a^5 - 9/2*a^4 - 13/2*a^3 + 13*a^2 + 21/2*a - 9,
-a^6 - 3*a^5 + 7*a^4 + 19*a^3 - 15*a^2 - 22*a + 7
],
[
a,
1,
-1/2*a^3 + 7/2*a - 1,
1/4*a^6 - 5/2*a^4 + 21/4*a^2 + 1,
-1/4*a^6 - 1/2*a^5 + 3*a^4 + 4*a^3 - 39/4*a^2 - 11/2*a + 4,
-1/4*a^6 + 5/2*a^4 - 1/2*a^3 - 25/4*a^2 + 3/2*a + 4,
1/2*a^4 - 7/2*a^2 + 4,
1/2*a^5 - 7/2*a^3 + 2*a + 2,
-a^4 + 7*a^2 - 2*a - 2,
1/4*a^6 - 5/2*a^4 + a^3 + 21/4*a^2 - 5*a + 1,
1/2*a^3 - 3/2*a + 3,
1/2*a^5 + a^4 - 7/2*a^3 - 6*a^2 + 2*a + 3
]
*], q_expansions := [*
q + q^2 - q^3 - q^4 + 2*q^5 - q^6 - 3*q^8 + q^9 + 2*q^10 + 5*q^11 + q^12 + 5*q^13 - 2*q^15 - q^16 - 3*q^17 + q^18 + 7*q^19 - 2*q^20 + 5*q^22 + 2*q^23 + 3*q^24 - q^25 + 5*q^26 - q^27 - 2*q^30 - 6*q^31 + 5*q^32 - 5*q^33 - 3*q^34 - q^36 - 7*q^37 + O(q^38),
q + a*q^2 + q^3 + (-a - 1)*q^4 - q^5 + a*q^6 + (-a - 4)*q^7 + (-2*a - 1)*q^8 + q^9 - a*q^10 + (-2*a - 1)*q^11 + (-a - 1)*q^12 + (2*a - 2)*q^13 + (-3*a - 1)*q^14 - q^15 + 3*a*q^16 + (-3*a - 4)*q^17 + a*q^18 + (4*a + 3)*q^19 + (a + 1)*q^20 + (-a - 4)*q^21 + (a - 2)*q^22 + (2*a - 1)*q^23 + (-2*a - 1)*q^24 - 4*q^25 + (-4*a + 2)*q^26 + q^27 + (4*a + 5)*q^28 + (4*a + 4)*q^29 - a*q^30 + (-3*a - 3)*q^31 + (a + 5)*q^32 + (-2*a - 1)*q^33 + (-a - 3)*q^34 + (a + 4)*q^35 + (-a - 1)*q^36 + (-a - 5)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (a^2 - a - 2)*q^5 - a*q^6 + (a^2 - 1)*q^7 + q^8 + q^9 + (-a^2 + 2*a + 1)*q^10 + q^11 + (-a^2 + 2)*q^12 + (-a^2 + a + 1)*q^13 + (3*a + 1)*q^14 + (-a^2 + a + 2)*q^15 + (-2*a^2 + a + 4)*q^16 + (a + 4)*q^17 + a*q^18 - q^19 + (-a + 3)*q^20 + (-a^2 + 1)*q^21 + a*q^22 + (-a^2 - a + 8)*q^23 - q^24 + (a^2 - 3*a - 3)*q^25 + (a^2 - 3*a - 1)*q^26 - q^27 + (a^2 + a + 2)*q^28 + (a^2 - 2*a - 1)*q^30 + (-2*a^2 - a + 9)*q^31 + (a^2 - 4*a - 4)*q^32 - q^33 + (a^2 + 4*a)*q^34 + (a^2 - 2*a + 1)*q^35 + (a^2 - 2)*q^36 + (-a^2 + 2*a)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^2 - a + 4)*q^5 + a*q^6 + (a^2 - 1)*q^7 + q^8 + q^9 + (-a^2 - 1)*q^10 + (-a^2 + a + 4)*q^11 + (a^2 - 2)*q^12 + (2*a^2 - 4)*q^13 + (3*a + 1)*q^14 + (-a^2 - a + 4)*q^15 + (-2*a^2 + a + 4)*q^16 + (-a^2 - 1)*q^17 + a*q^18 + (a^2 - a)*q^19 + (2*a^2 - 3*a - 9)*q^20 + (a^2 - 1)*q^21 + (a^2 - 1)*q^22 + (-3*a^2 + a + 6)*q^23 + q^24 + (-3*a^2 + a + 13)*q^25 + (4*a + 2)*q^26 + q^27 + (a^2 + a + 2)*q^28 + (2*a^2 - 2*a - 10)*q^29 + (-a^2 - 1)*q^30 + (-3*a - 1)*q^31 + (a^2 - 4*a - 4)*q^32 + (-a^2 + a + 4)*q^33 + (-5*a - 1)*q^34 + (a^2 - 4*a - 5)*q^35 + (a^2 - 2)*q^36 + (-2*a^2 + a + 11)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (1/2*a^6 + a^5 - 7/2*a^4 - 11/2*a^3 + 6*a^2 + 11/2*a - 1)*q^5 - a*q^6 + (-3/4*a^6 - 7/4*a^5 + 5*a^4 + 37/4*a^3 - 41/4*a^2 - 10*a + 3)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-1/2*a^6 - 1/2*a^5 + 4*a^4 + 3/2*a^3 - 19/2*a^2 - a + 4)*q^10 + (-1/4*a^6 + 1/4*a^5 + 7/2*a^4 - 1/4*a^3 - 37/4*a^2 - 3/2*a + 2)*q^11 + (-a^2 + 2)*q^12 + (1/4*a^6 - 1/4*a^5 - 9/2*a^4 + 1/4*a^3 + 65/4*a^2 - 1/2*a - 10)*q^13 + (1/2*a^6 + 1/2*a^5 - 5*a^4 - 7/2*a^3 + 25/2*a^2 + 3*a - 6)*q^14 + (-1/2*a^6 - a^5 + 7/2*a^4 + 11/2*a^3 - 6*a^2 - 11/2*a + 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/2*a^6 + 3/2*a^5 - 2*a^4 - 17/2*a^3 - 1/2*a^2 + 12*a)*q^17 + a*q^18 + (a^4 + 2*a^3 - 3*a^2 - 6*a - 2)*q^19 + (-a^5 - a^4 + 6*a^3 + 2*a^2 - 7*a - 2)*q^20 + (3/4*a^6 + 7/4*a^5 - 5*a^4 - 37/4*a^3 + 41/4*a^2 + 10*a - 3)*q^21 + (a^6 + 2*a^5 - 5*a^4 - 7*a^3 + 6*a^2 + 2*a - 2)*q^22 + (-a^4 + 7*a^2 - 2*a - 10)*q^23 + (-a^3 + 4*a)*q^24 + (1/4*a^6 + 5/4*a^5 - a^4 - 27/4*a^3 + 11/4*a^2 + 7*a - 2)*q^25 + (-a^6 - 3*a^5 + 5*a^4 + 14*a^3 - 8*a^2 - 10*a + 2)*q^26 - q^27 + (1/2*a^6 + 3/2*a^5 - 4*a^4 - 21/2*a^3 + 17/2*a^2 + 14*a - 2)*q^28 + (-3/4*a^6 - 7/4*a^5 + 4*a^4 + 25/4*a^3 - 29/4*a^2 + a + 3)*q^29 + (1/2*a^6 + 1/2*a^5 - 4*a^4 - 3/2*a^3 + 19/2*a^2 + a - 4)*q^30 + (1/2*a^6 + a^5 - 9/2*a^4 - 13/2*a^3 + 13*a^2 + 21/2*a - 9)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/4*a^6 - 1/4*a^5 - 7/2*a^4 + 1/4*a^3 + 37/4*a^2 + 3/2*a - 2)*q^33 + (a^5 + a^4 - 5*a^3 - 3*a^2 + 4)*q^34 + (-1/2*a^6 - a^5 + 9/2*a^4 + 15/2*a^3 - 8*a^2 - 15/2*a - 4)*q^35 + (a^2 - 2)*q^36 + (-a^6 - 3*a^5 + 7*a^4 + 19*a^3 - 15*a^2 - 22*a + 7)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-1/2*a^3 + 7/2*a - 1)*q^5 + a*q^6 + (1/4*a^6 - 5/2*a^4 + 21/4*a^2 + 1)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-1/2*a^4 + 7/2*a^2 - a)*q^10 + (-1/4*a^6 - 1/2*a^5 + 3*a^4 + 4*a^3 - 39/4*a^2 - 11/2*a + 4)*q^11 + (a^2 - 2)*q^12 + (-1/4*a^6 + 5/2*a^4 - 1/2*a^3 - 25/4*a^2 + 3/2*a + 4)*q^13 + (a^5 - 1/2*a^4 - 9*a^3 + 7/2*a^2 + 15*a - 2)*q^14 + (-1/2*a^3 + 7/2*a - 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/2*a^4 - 7/2*a^2 + 4)*q^17 + a*q^18 + (1/2*a^5 - 7/2*a^3 + 2*a + 2)*q^19 + (-1/2*a^5 + 9/2*a^3 - a^2 - 7*a + 2)*q^20 + (1/4*a^6 - 5/2*a^4 + 21/4*a^2 + 1)*q^21 + (-1/2*a^6 - 1/2*a^5 + 9/2*a^4 + 9/2*a^3 - 9*a^2 - 10*a + 2)*q^22 + (-a^4 + 7*a^2 - 2*a - 2)*q^23 + (a^3 - 4*a)*q^24 + (1/4*a^6 - 7/2*a^4 + a^3 + 49/4*a^2 - 7*a - 4)*q^25 + (-a^5 + 8*a^3 - 2*a^2 - 10*a + 2)*q^26 + q^27 + (1/2*a^6 - 1/2*a^5 - 4*a^4 + 7/2*a^3 + 9/2*a^2 - 2*a - 2)*q^28 + (1/4*a^6 - 5/2*a^4 + a^3 + 21/4*a^2 - 5*a + 1)*q^29 + (-1/2*a^4 + 7/2*a^2 - a)*q^30 + (1/2*a^3 - 3/2*a + 3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-1/4*a^6 - 1/2*a^5 + 3*a^4 + 4*a^3 - 39/4*a^2 - 11/2*a + 4)*q^33 + (1/2*a^5 - 7/2*a^3 + 4*a)*q^34 + (a^5 - 21/2*a^3 + a^2 + 49/2*a - 4)*q^35 + (a^2 - 2)*q^36 + (1/2*a^5 + a^4 - 7/2*a^3 - 6*a^2 + 2*a + 3)*q^37 + O(q^38)
*]> ;  // time = 77.04 seconds




J[418] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 418, 418, 418, 418, 418, 418, 418, 418, 209, 209, 209, 209, 38, 38, 19, 11 ], new_dimensions := [ 1, 1, 1, 2, 2, 2, 3, 3, 1, 2, 5, 7, 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 2, 2, 2, 3, 3, 2, 4, 10, 14, 2, 2, 4, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 43, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 5, 7, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 3, 5, 1, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 7, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 0, 1, 1, 1, 3, 1, 9, 1, 1, 1, 1, 1, 1, 1, 7, 7, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 43, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 25, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 225, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 3, 0, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 5, 1, 1, 0, 1, 5, 1, 1, 1, 1, 3, 3, 1, 1, 9, 1, 1, 225, 9, 1, 0, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 25, 1, 1, 5, 1, 0 ], ap_traces := [
[ 1, -1, -2, -3, -1, 1, -7, 1, -5, 1, 10, -6 ],
[ 1, 0, 2, 2, 1, -2, 6, 1, -8, -6, 6, 8 ],
[ 1, 3, -2, 1, 1, -7, -3, 1, 3, 1, 2, -6 ],
[ -2, 1, 4, 3, 2, -3, 3, -2, 7, 1, 4, -2 ],
[ -2, -3, -1, -1, 2, -3, -2, 2, -10, -13, -3, -4 ],
[ 2, -1, 3, -5, 2, 7, -6, 2, 6, 9, -17, 16 ],
[ -3, 0, -3, -6, -3, 0, -9, -3, -15, 6, -3, -6 ],
[ 3, 1, 5, 1, -3, 5, 4, -3, 2, 7, -3, -14 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 - x - 4,
x^2 + 3*x - 1,
x^2 + x - 5,
x^3 - 6*x - 3,
x^3 - x^2 - 5*x + 4
], atkin_lehners := [
[ -1, 1, -1 ],
[ -1, -1, -1 ],
[ -1, -1, -1 ],
[ 1, -1, 1 ],
[ 1, -1, -1 ],
[ -1, -1, -1 ],
[ 1, 1, 1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 13, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 43, 1, 1 ],
[ 3, 3, 1 ],
[ 45, 3, 5 ],
[ 7, 1, 1 ],
[ 7, 7, 1 ]
], tamagawa_numbers := [
[ 13, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 45, 3, 5 ],
[ 1, 1, 1 ],
[ 7, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 3, 15, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 1, 1, 0, 3, 0, 7 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 0, 1/225, 0, 1 ], eigenvalues := [*
[ 1, -1, -2, -3, -1, 1, -7, 1, -5, 1, 10, -6 ],
[ 1, 0, 2, 2, 1, -2, 6, 1, -8, -6, 6, 8 ],
[ 1, 3, -2, 1, 1, -7, -3, 1, 3, 1, 2, -6 ],
[
-1,
a,
2,
-a + 2,
1,
a - 2,
-a + 2,
-1,
-a + 4,
-3*a + 2,
2,
-2*a
],
[
-1,
a,
-a - 2,
a + 1,
1,
-a - 3,
-2*a - 4,
1,
2*a - 2,
-a - 8,
-a - 3,
4*a + 4
],
[
1,
a,
a + 2,
-a - 3,
1,
-a + 3,
-2*a - 4,
1,
-2*a + 2,
-a + 4,
-a - 9,
8
],
[
-1,
a,
-a^2 + 3,
a^2 - 2*a - 6,
-1,
a^2 - 2*a - 4,
-a^2 + a + 1,
-1,
-a^2 + a - 1,
2*a^2 - a - 6,
3*a - 1,
-2*a^2 + 2*a + 6
],
[
1,
a,
-a + 2,
-a^2 + 4,
-1,
a^2 - 2,
2*a^2 - 6,
-1,
-2*a^2 + 8,
-2*a^2 - a + 10,
a^2 - 2*a - 4,
-2*a^2 + 2*a + 2
]
*], q_expansions := [*
q + q^2 - q^3 + q^4 - 2*q^5 - q^6 - 3*q^7 + q^8 - 2*q^9 - 2*q^10 - q^11 - q^12 + q^13 - 3*q^14 + 2*q^15 + q^16 - 7*q^17 - 2*q^18 + q^19 - 2*q^20 + 3*q^21 - q^22 - 5*q^23 - q^24 - q^25 + q^26 + 5*q^27 - 3*q^28 + q^29 + 2*q^30 + 10*q^31 + q^32 + q^33 - 7*q^34 + 6*q^35 - 2*q^36 - 6*q^37 + O(q^38),
q + q^2 + q^4 + 2*q^5 + 2*q^7 + q^8 - 3*q^9 + 2*q^10 + q^11 - 2*q^13 + 2*q^14 + q^16 + 6*q^17 - 3*q^18 + q^19 + 2*q^20 + q^22 - 8*q^23 - q^25 - 2*q^26 + 2*q^28 - 6*q^29 + 6*q^31 + q^32 + 6*q^34 + 4*q^35 - 3*q^36 + 8*q^37 + O(q^38),
q + q^2 + 3*q^3 + q^4 - 2*q^5 + 3*q^6 + q^7 + q^8 + 6*q^9 - 2*q^10 + q^11 + 3*q^12 - 7*q^13 + q^14 - 6*q^15 + q^16 - 3*q^17 + 6*q^18 + q^19 - 2*q^20 + 3*q^21 + q^22 + 3*q^23 + 3*q^24 - q^25 - 7*q^26 + 9*q^27 + q^28 + q^29 - 6*q^30 + 2*q^31 + q^32 + 3*q^33 - 3*q^34 - 2*q^35 + 6*q^36 - 6*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + 2*q^5 - a*q^6 + (-a + 2)*q^7 - q^8 + (a + 1)*q^9 - 2*q^10 + q^11 + a*q^12 + (a - 2)*q^13 + (a - 2)*q^14 + 2*a*q^15 + q^16 + (-a + 2)*q^17 + (-a - 1)*q^18 - q^19 + 2*q^20 + (a - 4)*q^21 - q^22 + (-a + 4)*q^23 - a*q^24 - q^25 + (-a + 2)*q^26 + (-a + 4)*q^27 + (-a + 2)*q^28 + (-3*a + 2)*q^29 - 2*a*q^30 + 2*q^31 - q^32 + a*q^33 + (a - 2)*q^34 + (-2*a + 4)*q^35 + (a + 1)*q^36 - 2*a*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a - 2)*q^5 - a*q^6 + (a + 1)*q^7 - q^8 + (-3*a - 2)*q^9 + (a + 2)*q^10 + q^11 + a*q^12 + (-a - 3)*q^13 + (-a - 1)*q^14 + (a - 1)*q^15 + q^16 + (-2*a - 4)*q^17 + (3*a + 2)*q^18 + q^19 + (-a - 2)*q^20 + (-2*a + 1)*q^21 - q^22 + (2*a - 2)*q^23 - a*q^24 + a*q^25 + (a + 3)*q^26 + (4*a - 3)*q^27 + (a + 1)*q^28 + (-a - 8)*q^29 + (-a + 1)*q^30 + (-a - 3)*q^31 - q^32 + a*q^33 + (2*a + 4)*q^34 - 3*q^35 + (-3*a - 2)*q^36 + (4*a + 4)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (a + 2)*q^5 + a*q^6 + (-a - 3)*q^7 + q^8 + (-a + 2)*q^9 + (a + 2)*q^10 + q^11 + a*q^12 + (-a + 3)*q^13 + (-a - 3)*q^14 + (a + 5)*q^15 + q^16 + (-2*a - 4)*q^17 + (-a + 2)*q^18 + q^19 + (a + 2)*q^20 + (-2*a - 5)*q^21 + q^22 + (-2*a + 2)*q^23 + a*q^24 + (3*a + 4)*q^25 + (-a + 3)*q^26 - 5*q^27 + (-a - 3)*q^28 + (-a + 4)*q^29 + (a + 5)*q^30 + (-a - 9)*q^31 + q^32 + a*q^33 + (-2*a - 4)*q^34 + (-4*a - 11)*q^35 + (-a + 2)*q^36 + 8*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a^2 + 3)*q^5 - a*q^6 + (a^2 - 2*a - 6)*q^7 - q^8 + (a^2 - 3)*q^9 + (a^2 - 3)*q^10 - q^11 + a*q^12 + (a^2 - 2*a - 4)*q^13 + (-a^2 + 2*a + 6)*q^14 + (-3*a - 3)*q^15 + q^16 + (-a^2 + a + 1)*q^17 + (-a^2 + 3)*q^18 - q^19 + (-a^2 + 3)*q^20 + (-2*a^2 + 3)*q^21 + q^22 + (-a^2 + a - 1)*q^23 - a*q^24 + (3*a + 4)*q^25 + (-a^2 + 2*a + 4)*q^26 + 3*q^27 + (a^2 - 2*a - 6)*q^28 + (2*a^2 - a - 6)*q^29 + (3*a + 3)*q^30 + (3*a - 1)*q^31 - q^32 - a*q^33 + (a^2 - a - 1)*q^34 + (3*a^2 + 3*a - 12)*q^35 + (a^2 - 3)*q^36 + (-2*a^2 + 2*a + 6)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a + 2)*q^5 + a*q^6 + (-a^2 + 4)*q^7 + q^8 + (a^2 - 3)*q^9 + (-a + 2)*q^10 - q^11 + a*q^12 + (a^2 - 2)*q^13 + (-a^2 + 4)*q^14 + (-a^2 + 2*a)*q^15 + q^16 + (2*a^2 - 6)*q^17 + (a^2 - 3)*q^18 - q^19 + (-a + 2)*q^20 + (-a^2 - a + 4)*q^21 - q^22 + (-2*a^2 + 8)*q^23 + a*q^24 + (a^2 - 4*a - 1)*q^25 + (a^2 - 2)*q^26 + (a^2 - a - 4)*q^27 + (-a^2 + 4)*q^28 + (-2*a^2 - a + 10)*q^29 + (-a^2 + 2*a)*q^30 + (a^2 - 2*a - 4)*q^31 + q^32 - a*q^33 + (2*a^2 - 6)*q^34 + (-a^2 + a + 4)*q^35 + (a^2 - 3)*q^36 + (-2*a^2 + 2*a + 2)*q^37 + O(q^38)
*]> ;  // time = 203.651 seconds




J[419] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 419, 419 ], new_dimensions := [ 9, 26 ], dimensions := [ 9, 26 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -2, -4, -5, -7, -6, -19, 0, -10, -3, -20, -11, -25 ],
[ 2, 2, 5, 7, 4, 27, 2, 8, -1, 46, 17, 45 ]
], hecke_fields := [
x^9 + 2*x^8 - 7*x^7 - 13*x^6 + 15*x^5 + 25*x^4 - 9*x^3 - 15*x^2 - x + 1,
x^26 - 2*x^25 - 43*x^24 + 85*x^23 + 807*x^22 - 1571*x^21 - 8689*x^20 + 16575*x^19 + 59362*x^18 - 110217*x^17 - 268789*x^16 + 481513*x^15 + 817911*x^14 - 1398615*x^13 - 1658267*x^12 + 2674771*x^11 + 2166607*x^10 - 3262315*x^9 - 1701132*x^8 + 2384864*x^7 + 697992*x^6 - 932912*x^5 - 104448*x^4 + 158080*x^3 - 4736*x^2 - 6656*x + 512
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 209 ]
], tamagawa_numbers := [
[ 1 ],
[ 209 ]
], torsion_upper_bounds := [ 1, 209 ], torsion_lower_bounds := [ 1, 209 ], l_ratios := [ 0, 1/209 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
a^8 + a^7 - 8*a^6 - 5*a^5 + 21*a^4 + 5*a^3 - 19*a^2 + 3,
a^8 + 2*a^7 - 7*a^6 - 13*a^5 + 15*a^4 + 24*a^3 - 10*a^2 - 12*a,
-2*a^8 - 3*a^7 + 15*a^6 + 17*a^5 - 37*a^4 - 24*a^3 + 32*a^2 + 6*a - 6,
a^5 - 5*a^3 + a^2 + 4*a - 1,
2*a^8 + 3*a^7 - 16*a^6 - 18*a^5 + 42*a^4 + 29*a^3 - 36*a^2 - 13*a + 2,
-3*a^8 - 4*a^7 + 24*a^6 + 25*a^5 - 61*a^4 - 43*a^3 + 50*a^2 + 20*a - 7,
-a^8 + 11*a^6 + a^5 - 36*a^4 - 5*a^3 + 34*a^2 + 8*a - 4,
-a^8 - a^7 + 7*a^6 + 4*a^5 - 14*a^4 - a^3 + 6*a^2 - 3*a - 1,
a^8 + a^7 - 6*a^6 - 4*a^5 + 7*a^4 + a^3 + 7*a^2 + 3*a - 7,
3*a^8 + 3*a^7 - 27*a^6 - 21*a^5 + 79*a^4 + 44*a^3 - 77*a^2 - 27*a + 10,
a^8 - 9*a^6 + a^5 + 24*a^4 - 7*a^3 - 18*a^2 + 12*a - 1
],
[
a,
11600552657805477/618506107859120384*a^25 - 1445919658165295/309253053929560192*a^24 - 489898657622267755/618506107859120384*a^23 + 107914954606597717/618506107859120384*a^22 + 8985089110311196755/618506107859120384*a^21 - 1677761853489598063/618506107859120384*a^20 - 93908850339439447893/618506107859120384*a^19 + 13918818822044869947/618506107859120384*a^18 + 308521474664772454481/309253053929560192*a^17 - 64913077960712591713/618506107859120384*a^16 - 2653463884228242370997/618506107859120384*a^15 + 158054791007502082829/618506107859120384*a^14 + 7542124894930787266803/618506107859120384*a^13 - 114826826055616751971/618506107859120384*a^12 - 13997662661670064334423/618506107859120384*a^11 - 303774076907980503369/618506107859120384*a^10 + 16402726266989189697963/618506107859120384*a^9 + 721388016885671188593/618506107859120384*a^8 - 2858156076211631583195/154626526964780096*a^7 - 131421687286070081665/154626526964780096*a^6 + 133526089632281764867/19328315870597512*a^5 + 3114222442535169313/19328315870597512*a^4 - 5479963010523513969/4832078967649378*a^3 + 347436269895930943/9664157935298756*a^2 + 115195871402394161/2416039483824689*a - 9403602456845085/2416039483824689,
-15339110851698681/618506107859120384*a^25 + 1659882976959243/154626526964780096*a^24 + 647804819296844439/618506107859120384*a^23 - 261094882733415019/618506107859120384*a^22 - 11883707853507702469/618506107859120384*a^21 + 4379051822405265577/618506107859120384*a^20 + 124269331201630752739/618506107859120384*a^19 - 40851748330058436361/618506107859120384*a^18 - 204353554500038141865/154626526964780096*a^17 + 232298733292163357085/618506107859120384*a^16 + 3522271328534996747539/618506107859120384*a^15 - 833773198676597351211/618506107859120384*a^14 - 10047619638821988328637/618506107859120384*a^13 + 1911697358637588946733/618506107859120384*a^12 + 18759839398286226300949/618506107859120384*a^11 - 2833518240599129473281/618506107859120384*a^10 - 22190495513779505976209/618506107859120384*a^9 + 2802903817103605614913/618506107859120384*a^8 + 7838747736618934727003/309253053929560192*a^7 - 7422528181590734491/2416039483824689*a^6 - 745747450776653745449/77313263482390048*a^5 + 51094395904343293019/38656631741195024*a^4 + 31404172083373982729/19328315870597512*a^3 - 2622227156419926079/9664157935298756*a^2 - 358926392933727053/4832078967649378*a + 23150340870738341/2416039483824689,
-8863839496337407/309253053929560192*a^25 - 891227784723507/38656631741195024*a^24 + 385167517531066755/309253053929560192*a^23 + 296011659624924835/309253053929560192*a^22 - 7296357727589355205/309253053929560192*a^21 - 5316969070158088675/309253053929560192*a^20 + 79079629987114027495/309253053929560192*a^19 + 54137797970389542119/309253053929560192*a^18 - 270475397670112461457/154626526964780096*a^17 - 343712030514259712015/309253053929560192*a^16 + 2430211827232656201389/309253053929560192*a^15 + 1408518450537328044749/309253053929560192*a^14 - 7233604422337648843241/309253053929560192*a^13 - 3723633221392188900391/309253053929560192*a^12 + 14065380090305185317589/309253053929560192*a^11 + 6154287517520404208367/309253053929560192*a^10 - 17214441168598886170513/309253053929560192*a^9 - 5932646140944618265895/309253053929560192*a^8 + 3097908679538199990775/77313263482390048*a^7 + 1463080099193828555373/154626526964780096*a^6 - 580251204341804069003/38656631741195024*a^5 - 67739723955687955103/38656631741195024*a^4 + 45087263596456571019/19328315870597512*a^3 - 420740139153670539/9664157935298756*a^2 - 422904240001996079/4832078967649378*a + 20162886288801526/2416039483824689,
2624951423839507/309253053929560192*a^25 + 864714761109041/77313263482390048*a^24 - 115190386680000141/309253053929560192*a^23 - 141931181194005311/309253053929560192*a^22 + 2206926087781757503/309253053929560192*a^21 + 2515920062426191125/309253053929560192*a^20 - 24231593512952764345/309253053929560192*a^19 - 25245059275215458725/309253053929560192*a^18 + 42057341458042821857/77313263482390048*a^17 + 157823923829239306385/309253053929560192*a^16 - 768596413957611044153/309253053929560192*a^15 - 637436787342126079951/309253053929560192*a^14 + 2332253342452014421831/309253053929560192*a^13 + 1668307758579552752553/309253053929560192*a^12 - 4638386215069439223647/309253053929560192*a^11 - 2761098638629791825261/309253053929560192*a^10 + 5836044142774413189363/309253053929560192*a^9 + 2733789611335979463661/309253053929560192*a^8 - 2179139808976009405541/154626526964780096*a^7 - 11464838695214791855/2416039483824689*a^6 + 216225308932095586355/38656631741195024*a^5 + 22175334591203582665/19328315870597512*a^4 - 2384269020723186934/2416039483824689*a^3 - 168604006548282602/2416039483824689*a^2 + 144988979787663183/2416039483824689*a + 2533241512306150/2416039483824689,
18286899019576087/618506107859120384*a^25 - 5894344397986029/309253053929560192*a^24 - 766111264106621881/618506107859120384*a^23 + 471168870486082791/618506107859120384*a^22 + 13922639055892491201/618506107859120384*a^21 - 8069778480182433605/618506107859120384*a^20 - 144001763638989605479/618506107859120384*a^19 + 77397866044694049257/618506107859120384*a^18 + 467579448862133101323/309253053929560192*a^17 - 456656313606355035067/618506107859120384*a^16 - 3970050046577309300871/618506107859120384*a^15 + 1719687671324427722719/618506107859120384*a^14 + 11130371603133618637169/618506107859120384*a^13 - 4174582169576353238401/618506107859120384*a^12 - 20361915844234980816541/618506107859120384*a^11 + 6503610407720369451005/618506107859120384*a^10 + 23492863605680564906457/618506107859120384*a^9 - 6410159455082569400069/618506107859120384*a^8 - 4015981862327647639385/154626526964780096*a^7 + 965970510415925839073/154626526964780096*a^6 + 364245782918146239653/38656631741195024*a^5 - 41070925522691941949/19328315870597512*a^4 - 14040041850842425621/9664157935298756*a^3 + 1609898669988803781/4832078967649378*a^2 + 120809385477014950/2416039483824689*a - 20763481876800285/2416039483824689,
-9452065314873201/309253053929560192*a^25 + 569808323358243/154626526964780096*a^24 + 403334789788890787/309253053929560192*a^23 - 41526874078466881/309253053929560192*a^22 - 7491566561964566371/309253053929560192*a^21 + 623800518564105935/309253053929560192*a^20 + 79524390043194009893/309253053929560192*a^19 - 4908978635890839331/309253053929560192*a^18 - 266341658225461798347/154626526964780096*a^17 + 21056295622004569393/309253053929560192*a^16 + 2346602429988253206817/309253053929560192*a^15 - 45169471823807203565/309253053929560192*a^14 - 6877117319855274668643/309253053929560192*a^13 + 35824022697376113459/309253053929560192*a^12 + 13276630541977197198879/309253053929560192*a^11 - 42177179955584271871/309253053929560192*a^10 - 16382280786694921546019/309253053929560192*a^9 + 302910843731533481607/309253053929560192*a^8 + 764172038113645304419/19328315870597512*a^7 - 4952251742929815629/2416039483824689*a^6 - 626264687981311231349/38656631741195024*a^5 + 3759431168880174677/2416039483824689*a^4 + 7339515286718525658/2416039483824689*a^3 - 1988234325440504521/4832078967649378*a^2 - 388905248750884814/2416039483824689*a + 45540379097120744/2416039483824689,
-25393254810891759/309253053929560192*a^25 - 3041399972389495/154626526964780096*a^24 + 1085390644728523277/309253053929560192*a^23 + 266758956152745225/309253053929560192*a^22 - 20186052923794734741/309253053929560192*a^21 - 5096342249122415191/309253053929560192*a^20 + 214373256731097884019/309253053929560192*a^19 + 55583263415901127051/309253053929560192*a^18 - 717121244323166467809/154626526964780096*a^17 - 380110916451324653025/309253053929560192*a^16 + 6292099717272352700071/309253053929560192*a^15 + 1681697238852161604581/309253053929560192*a^14 - 18270317143985779596309/309253053929560192*a^13 - 4786935594043997250859/309253053929560192*a^12 + 34647043681260543233721/309253053929560192*a^11 + 8442758483294117538455/309253053929560192*a^10 - 41393002037736227935285/309253053929560192*a^9 - 8545186374596961334719/309253053929560192*a^8 + 3648283620175782594325/38656631741195024*a^7 + 67221230426802773909/4832078967649378*a^6 - 1351272974277776802267/38656631741195024*a^5 - 45716940443506545803/19328315870597512*a^4 + 26423312776526565267/4832078967649378*a^3 - 472839460313177852/2416039483824689*a^2 - 522030965267204306/2416039483824689*a + 45580231439791752/2416039483824689,
-2558841842108261/154626526964780096*a^25 - 4409568375306127/154626526964780096*a^24 + 28912322350853323/38656631741195024*a^23 + 2805962348895829/2416039483824689*a^22 - 2285256228690932977/154626526964780096*a^21 - 3149700732293670429/154626526964780096*a^20 + 25909323659093759761/154626526964780096*a^19 + 31133925954963975081/154626526964780096*a^18 - 23236778008763873855/19328315870597512*a^17 - 47636438661404718111/38656631741195024*a^16 + 219529049124898831311/38656631741195024*a^15 + 746548872918122285453/154626526964780096*a^14 - 2755183189896665951463/154626526964780096*a^13 - 1868556244211686049869/154626526964780096*a^12 + 5663744465467580011047/154626526964780096*a^11 + 2885177144106761857731/154626526964780096*a^10 - 7356334349617622597347/154626526964780096*a^9 - 2533640325967535251555/154626526964780096*a^8 + 176424820035076364909/4832078967649378*a^7 + 1059232063151933495967/154626526964780096*a^6 - 282982611182841518911/19328315870597512*a^5 - 6783269681089184067/9664157935298756*a^4 + 5849252779116850044/2416039483824689*a^3 - 1842809530593762597/9664157935298756*a^2 - 198747817175734094/2416039483824689*a + 30273790865496723/2416039483824689,
65656112147742251/618506107859120384*a^25 + 10375673337710817/309253053929560192*a^24 - 2822201815919056525/618506107859120384*a^23 - 889738846283759921/618506107859120384*a^22 + 52829778649655403793/618506107859120384*a^21 + 16580584390992559387/618506107859120384*a^20 - 565290592996993899079/618506107859120384*a^19 - 176003797134111449551/618506107859120384*a^18 + 1907651598612382911725/309253053929560192*a^17 + 1169513158714447418457/618506107859120384*a^16 - 16910200049446342903263/618506107859120384*a^15 - 5023204878143048616145/618506107859120384*a^14 + 49699208942178544544289/618506107859120384*a^13 + 13876135324370740718991/618506107859120384*a^12 - 95628933217123903268853/618506107859120384*a^11 - 23721691283881082684499/618506107859120384*a^10 + 116330913436966558970129/618506107859120384*a^9 + 23130896872620346280571/618506107859120384*a^8 - 655972931017878638773/4832078967649378*a^7 - 2736289406989009382227/154626526964780096*a^6 + 1003756215693545203703/19328315870597512*a^5 + 46884857350281933033/19328315870597512*a^4 - 164879743763169148121/19328315870597512*a^3 + 2020854318529102097/4832078967649378*a^2 + 1684992635394927047/4832078967649378*a - 65625674033591298/2416039483824689,
-26855390630130931/309253053929560192*a^25 - 533455301792255/77313263482390048*a^24 + 1144733303407208417/309253053929560192*a^23 + 105449559218637135/309253053929560192*a^22 - 21225401377224350915/309253053929560192*a^21 - 2255305416999625273/309253053929560192*a^20 + 224679623386828522029/309253053929560192*a^19 + 27330958990851922817/309253053929560192*a^18 - 46817760895882357965/9664157935298756*a^17 - 205517504119654892437/309253053929560192*a^16 + 6551496564010627398377/309253053929560192*a^15 + 985617139899510956323/309253053929560192*a^14 - 18973299300077098464483/309253053929560192*a^13 - 2985029578250747169917/309253053929560192*a^12 + 35930229022446316685459/309253053929560192*a^11 + 5466820783003066708265/309253053929560192*a^10 - 42970065561628294111223/309253053929560192*a^9 - 5546252251761476835161/309253053929560192*a^8 + 15235408572403679212959/154626526964780096*a^7 + 652680677828681825793/77313263482390048*a^6 - 1433121154936485846251/38656631741195024*a^5 - 17678119118850968543/19328315870597512*a^4 + 29172263575227468901/4832078967649378*a^3 - 1512651843443052025/4832078967649378*a^2 - 633886799502314386/2416039483824689*a + 52139113121572668/2416039483824689,
60166597258267563/618506107859120384*a^25 + 395202586687591/309253053929560192*a^24 - 2553718586362508837/618506107859120384*a^23 - 86806555389895861/618506107859120384*a^22 + 47105944308862011325/618506107859120384*a^21 + 2716344467727527855/618506107859120384*a^20 - 495496902460019074459/618506107859120384*a^19 - 41692333847033391467/618506107859120384*a^18 + 1639237469889937743455/309253053929560192*a^17 + 368855559684931024225/618506107859120384*a^16 - 14199923132204739221211/618506107859120384*a^15 - 1994140228784523803197/618506107859120384*a^14 + 40632030070040651491213/618506107859120384*a^13 + 6650769065691434446803/618506107859120384*a^12 - 75774357815327124704825/618506107859120384*a^11 - 13338659558194553388999/618506107859120384*a^10 + 88818415847738160513733/618506107859120384*a^9 + 15135974931914865805055/618506107859120384*a^8 - 15323199192292792654229/154626526964780096*a^7 - 2176311555648773641323/154626526964780096*a^6 + 1384975414788801864911/38656631741195024*a^5 + 123406275944681811165/38656631741195024*a^4 - 104780231032893912089/19328315870597512*a^3 - 366815333206146175/9664157935298756*a^2 + 474670583379550183/2416039483824689*a - 14700746571043152/2416039483824689
]
*], q_expansions := [*
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65625674033591298/2416039483824689)*q^29 + (-493706202855639/2416039483824689*a^25 - 1249329899517157/154626526964780096*a^24 + 168363913799445763/19328315870597512*a^23 + 74840337472830907/154626526964780096*a^22 - 24974800814550306283/154626526964780096*a^21 - 1835381893596710981/154626526964780096*a^20 + 264373871640348742009/154626526964780096*a^19 + 24620136872756738227/154626526964780096*a^18 - 1762911465975487506393/154626526964780096*a^17 - 24987580944849625835/19328315870597512*a^16 + 7709898099440866119681/154626526964780096*a^15 + 1016614677761417931075/154626526964780096*a^14 - 22332570781736553493323/154626526964780096*a^13 - 3223623585679892177773/154626526964780096*a^12 + 42308518975168225731533/154626526964780096*a^11 + 6133739174388374608261/154626526964780096*a^10 - 50632028954206634987481/154626526964780096*a^9 - 6454870366015699854889/154626526964780096*a^8 + 35938197115652430492465/154626526964780096*a^7 + 1590901020291412715105/77313263482390048*a^6 - 1691292316439845285063/19328315870597512*a^5 - 6156748639263193727/2416039483824689*a^4 + 34225913082233334324/2416039483824689*a^3 - 3420620151308531957/4832078967649378*a^2 - 1409531355619838085/2416039483824689*a + 112221737272315038/2416039483824689)*q^30 + (-26855390630130931/309253053929560192*a^25 - 533455301792255/77313263482390048*a^24 + 1144733303407208417/309253053929560192*a^23 + 105449559218637135/309253053929560192*a^22 - 21225401377224350915/309253053929560192*a^21 - 2255305416999625273/309253053929560192*a^20 + 224679623386828522029/309253053929560192*a^19 + 27330958990851922817/309253053929560192*a^18 - 46817760895882357965/9664157935298756*a^17 - 205517504119654892437/309253053929560192*a^16 + 6551496564010627398377/309253053929560192*a^15 + 985617139899510956323/309253053929560192*a^14 - 18973299300077098464483/309253053929560192*a^13 - 2985029578250747169917/309253053929560192*a^12 + 35930229022446316685459/309253053929560192*a^11 + 5466820783003066708265/309253053929560192*a^10 - 42970065561628294111223/309253053929560192*a^9 - 5546252251761476835161/309253053929560192*a^8 + 15235408572403679212959/154626526964780096*a^7 + 652680677828681825793/77313263482390048*a^6 - 1433121154936485846251/38656631741195024*a^5 - 17678119118850968543/19328315870597512*a^4 + 29172263575227468901/4832078967649378*a^3 - 1512651843443052025/4832078967649378*a^2 - 633886799502314386/2416039483824689*a + 52139113121572668/2416039483824689)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-20390552747667151/309253053929560192*a^25 - 2688727866722189/154626526964780096*a^24 + 872480185673282833/309253053929560192*a^23 + 235681798792339965/309253053929560192*a^22 - 16243781375925653029/309253053929560192*a^21 - 4497473943914384295/309253053929560192*a^20 + 172687082654587744499/309253053929560192*a^19 + 48968361957173842443/309253053929560192*a^18 - 578220511094385240461/154626526964780096*a^17 - 334177552132990224557/309253053929560192*a^16 + 5077272687541396462947/309253053929560192*a^15 + 1475394781071502348773/309253053929560192*a^14 - 14750618774432557533669/309253053929560192*a^13 - 4193178711234340309851/309253053929560192*a^12 + 27982753571085884734985/309253053929560192*a^11 + 7392302105444059235999/309253053929560192*a^10 - 33458124703751200211221/309253053929560192*a^9 - 7488963319126512406631/309253053929560192*a^8 + 2958959895275077504895/38656631741195024*a^7 + 943011980700630167065/77313263482390048*a^6 - 138740322917818904105/4832078967649378*a^5 - 39309251917252504811/19328315870597512*a^4 + 11338147376213643907/2416039483824689*a^3 - 920913891472089469/4832078967649378*a^2 - 534503425515501723/2416039483824689*a + 39373447826032280/2416039483824689)*q^33 + (-4441128495757479/77313263482390048*a^25 - 388002343832107/38656631741195024*a^24 + 190474669421438801/77313263482390048*a^23 + 34062536784526709/77313263482390048*a^22 - 3556348522775423209/77313263482390048*a^21 - 651151369434808399/77313263482390048*a^20 + 37939750989533116811/77313263482390048*a^19 + 7102546192644840267/77313263482390048*a^18 - 127590248398421878153/38656631741195024*a^17 - 48502188482799904193/77313263482390048*a^16 + 1126530713534183107387/77313263482390048*a^15 + 213457718474495008617/77313263482390048*a^14 - 3295994076916001475789/77313263482390048*a^13 - 599354362880410300947/77313263482390048*a^12 + 6309983253593280610025/77313263482390048*a^11 + 1024157522241639963247/77313263482390048*a^10 - 7633175903489758309677/77313263482390048*a^9 - 963114540850638323207/77313263482390048*a^8 + 684625064749835788411/9664157935298756*a^7 + 49604639669015170675/9664157935298756*a^6 - 521046122963270333291/19328315870597512*a^5 - 373370010218006358/2416039483824689*a^4 + 21358367002296301949/4832078967649378*a^3 - 738631665401193251/2416039483824689*a^2 - 445967017276285708/2416039483824689*a + 37808261259492804/2416039483824689)*q^34 + (-45553220834854219/618506107859120384*a^25 - 10566028062091491/309253053929560192*a^24 + 1984957473996816053/618506107859120384*a^23 + 865543008306795213/618506107859120384*a^22 - 37735225417083478549/618506107859120384*a^21 - 15291526292392860167/618506107859120384*a^20 + 410887117715180636083/618506107859120384*a^19 + 152530766246439715251/618506107859120384*a^18 - 1414190856289528096795/309253053929560192*a^17 - 942920182623387950337/618506107859120384*a^16 + 12817753615876076808995/618506107859120384*a^15 + 3722869182733515367829/618506107859120384*a^14 - 38631711953568940551285/618506107859120384*a^13 - 9289927298023332662603/618506107859120384*a^12 + 76506964597837651500145/618506107859120384*a^11 + 13854423591910915774463/618506107859120384*a^10 - 96254093493747348156349/618506107859120384*a^9 - 10676437472896530569239/618506107859120384*a^8 + 18080629238531783177739/154626526964780096*a^7 + 599516373356538496015/154626526964780096*a^6 - 909237883006996923729/19328315870597512*a^5 + 77317922711321258839/38656631741195024*a^4 + 160429577151879031249/19328315870597512*a^3 - 4270113288726630523/4832078967649378*a^2 - 920217464976453435/2416039483824689*a + 92100701987037652/2416039483824689)*q^35 + (13222857030407459/77313263482390048*a^25 + 1605154588758789/77313263482390048*a^24 - 565762270540260491/77313263482390048*a^23 - 37193755554879517/38656631741195024*a^22 + 329233633152618574/2416039483824689*a^21 + 46918596737408410/2416039483824689*a^20 - 14009016519086727717/9664157935298756*a^19 - 8638813946542801337/38656631741195024*a^18 + 751511619630106095495/77313263482390048*a^17 + 124226485641960318919/77313263482390048*a^16 - 1653781580716177520921/38656631741195024*a^15 - 71747564325225109657/9664157935298756*a^14 + 2412448401377960031881/19328315870597512*a^13 + 422013957029354545055/19328315870597512*a^12 - 9215733511051280676441/38656631741195024*a^11 - 756385188156540396983/19328315870597512*a^10 + 11133817722275160461309/38656631741195024*a^9 + 94561179154120859330/2416039483824689*a^8 - 15983976505551618546089/77313263482390048*a^7 - 176763195295183586359/9664157935298756*a^6 + 381259741453206644077/4832078967649378*a^5 + 9839567714961317803/4832078967649378*a^4 - 125560375247082064309/9664157935298756*a^3 + 1473832479983964826/2416039483824689*a^2 + 1314065991779451727/2416039483824689*a - 89935926490824584/2416039483824689)*q^36 + (60166597258267563/618506107859120384*a^25 + 395202586687591/309253053929560192*a^24 - 2553718586362508837/618506107859120384*a^23 - 86806555389895861/618506107859120384*a^22 + 47105944308862011325/618506107859120384*a^21 + 2716344467727527855/618506107859120384*a^20 - 495496902460019074459/618506107859120384*a^19 - 41692333847033391467/618506107859120384*a^18 + 1639237469889937743455/309253053929560192*a^17 + 368855559684931024225/618506107859120384*a^16 - 14199923132204739221211/618506107859120384*a^15 - 1994140228784523803197/618506107859120384*a^14 + 40632030070040651491213/618506107859120384*a^13 + 6650769065691434446803/618506107859120384*a^12 - 75774357815327124704825/618506107859120384*a^11 - 13338659558194553388999/618506107859120384*a^10 + 88818415847738160513733/618506107859120384*a^9 + 15135974931914865805055/618506107859120384*a^8 - 15323199192292792654229/154626526964780096*a^7 - 2176311555648773641323/154626526964780096*a^6 + 1384975414788801864911/38656631741195024*a^5 + 123406275944681811165/38656631741195024*a^4 - 104780231032893912089/19328315870597512*a^3 - 366815333206146175/9664157935298756*a^2 + 474670583379550183/2416039483824689*a - 14700746571043152/2416039483824689)*q^37 + O(q^38)
*]> ;  // time = 11.961 seconds




J[421] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 421, 421 ], new_dimensions := [ 15, 19 ], dimensions := [ 15, 19 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -6, -9, -11, -5, -33, -8, -14, -30, 1, -21, -15, -7 ],
[ 4, 7, 7, 3, 31, -2, 16, 24, 13, 9, 9, -25 ]
], hecke_fields := [
x^15 + 6*x^14 - 2*x^13 - 71*x^12 - 74*x^11 + 296*x^10 + 488*x^9 - 494*x^8 - 1157*x^7 + 205*x^6 + 1137*x^5 + 203*x^4 - 374*x^3 - 127*x^2 + 3*x + 3,
x^19 - 4*x^18 - 20*x^17 + 93*x^16 + 145*x^15 - 874*x^14 - 402*x^13 + 4263*x^12 - 159*x^11 - 11551*x^10 + 3133*x^9 + 17375*x^8 - 5935*x^7 - 14018*x^6 + 4016*x^5 + 5896*x^4 - 1088*x^3 - 1185*x^2 + 101*x + 89
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 35 ]
], tamagawa_numbers := [
[ 1 ],
[ 35 ]
], torsion_upper_bounds := [ 1, 35 ], torsion_lower_bounds := [ 1, 35 ], l_ratios := [ 0, 1/35 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-25193/24617*a^14 - 139169/24617*a^13 + 111469/24617*a^12 + 1714563/24617*a^11 + 1101947/24617*a^10 - 7699217/24617*a^9 - 8792218/24617*a^8 + 15213141/24617*a^7 + 21912927/24617*a^6 - 12318890/24617*a^5 - 22124776/24617*a^4 + 1991679/24617*a^3 + 7618866/24617*a^2 + 844015/24617*a - 229186/24617,
22400/24617*a^14 + 122208/24617*a^13 - 106252/24617*a^12 - 1516251/24617*a^11 - 900656/24617*a^10 + 6884713/24617*a^9 + 7511320/24617*a^8 - 13885777/24617*a^7 - 18990607/24617*a^6 + 11807197/24617*a^5 + 19349004/24617*a^4 - 2528241/24617*a^3 - 6727668/24617*a^2 - 555389/24617*a + 212047/24617,
-9732/24617*a^14 - 52251/24617*a^13 + 49908/24617*a^12 + 654805/24617*a^11 + 351986/24617*a^10 - 3026606/24617*a^9 - 3132051/24617*a^8 + 6356091/24617*a^7 + 8147248/24617*a^6 - 6082602/24617*a^5 - 8594613/24617*a^4 + 2265940/24617*a^3 + 3152696/24617*a^2 - 229332/24617*a - 135633/24617,
15431/24617*a^14 + 87106/24617*a^13 - 62166/24617*a^12 - 1066618/24617*a^11 - 729237/24617*a^10 + 4759078/24617*a^9 + 5469436/24617*a^8 - 9377862/24617*a^7 - 13019022/24617*a^6 + 7761488/24617*a^5 + 12265003/24617*a^4 - 1665986/24617*a^3 - 3686252/24617*a^2 - 271133/24617*a - 1979/24617,
20552/24617*a^14 + 123942/24617*a^13 - 45052/24617*a^12 - 1495721/24617*a^11 - 1499873/24617*a^10 + 6485166/24617*a^9 + 10133695/24617*a^8 - 11956949/24617*a^7 - 24682389/24617*a^6 + 8005410/24617*a^5 + 25309884/24617*a^4 + 535357/24617*a^3 - 9036331/24617*a^2 - 1313376/24617*a + 200892/24617,
-22369/24617*a^14 - 143737/24617*a^13 + 12512/24617*a^12 + 1712070/24617*a^11 + 2095321/24617*a^10 - 7260440/24617*a^9 - 13200156/24617*a^8 + 12769687/24617*a^7 + 31439211/24617*a^6 - 7278221/24617*a^5 - 31704107/24617*a^4 - 2007574/24617*a^3 + 11119222/24617*a^2 + 1615379/24617*a - 339807/24617,
-44034/24617*a^14 - 245934/24617*a^13 + 170512/24617*a^12 + 2977902/24617*a^11 + 2217452/24617*a^10 - 12977225/24617*a^9 - 16641683/24617*a^8 + 24202052/24617*a^7 + 40814214/24617*a^6 - 17016384/24617*a^5 - 40931907/24617*a^4 + 361281/24617*a^3 + 14001439/24617*a^2 + 2037806/24617*a - 402233/24617,
38328/24617*a^14 + 212764/24617*a^13 - 162498/24617*a^12 - 2608718/24617*a^11 - 1756591/24617*a^10 + 11644851/24617*a^9 + 13710835/24617*a^8 - 22892062/24617*a^7 - 34026157/24617*a^6 + 18745886/24617*a^5 + 34553847/24617*a^4 - 3878121/24617*a^3 - 12348815/24617*a^2 - 590313/24617*a + 478167/24617,
50847/24617*a^14 + 311554/24617*a^13 - 94659/24617*a^12 - 3758611/24617*a^11 - 3915675/24617*a^10 + 16335309/24617*a^9 + 25977848/24617*a^8 - 30527054/24617*a^7 - 62823259/24617*a^6 + 22075756/24617*a^5 + 64133950/24617*a^4 - 1731884/24617*a^3 - 23124562/24617*a^2 - 1803712/24617*a + 789075/24617,
-33461/24617*a^14 - 195671/24617*a^13 + 117050/24617*a^12 + 2433349/24617*a^11 + 1885158/24617*a^10 - 11134701/24617*a^9 - 13802561/24617*a^8 + 22938972/24617*a^7 + 33916419/24617*a^6 - 20752676/24617*a^5 - 34066929/24617*a^4 + 5992804/24617*a^3 + 11660581/24617*a^2 + 253185/24617*a - 375164/24617,
29281/24617*a^14 + 164426/24617*a^13 - 119290/24617*a^12 - 2027035/24617*a^11 - 1434697/24617*a^10 + 9109718/24617*a^9 + 11105865/24617*a^8 - 18060362/24617*a^7 - 27890693/24617*a^6 + 15009554/24617*a^5 + 28753034/24617*a^4 - 3503675/24617*a^3 - 10182630/24617*a^2 - 198186/24617*a + 382169/24617
],
[
a,
1430551/9117529*a^18 - 2454755/9117529*a^17 - 38550465/9117529*a^16 + 61521646/9117529*a^15 + 433188182/9117529*a^14 - 634476014/9117529*a^13 - 2625122576/9117529*a^12 + 3471841595/9117529*a^11 + 9256149754/9117529*a^10 - 10815766925/9117529*a^9 - 19082230913/9117529*a^8 + 19034855015/9117529*a^7 + 21961332366/9117529*a^6 - 17464171573/9117529*a^5 - 12883617829/9117529*a^4 + 6876539232/9117529*a^3 + 3602610333/9117529*a^2 - 873971523/9117529*a - 365040381/9117529,
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*], q_expansions := [*
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405042452/9117529)*q^36 + (-3651234/9117529*a^18 + 15382618/9117529*a^17 + 65763326/9117529*a^16 - 342756981/9117529*a^15 - 366430291/9117529*a^14 + 3026591132/9117529*a^13 + 8666401/9117529*a^12 - 13398920115/9117529*a^11 + 7208238367/9117529*a^10 + 30835742346/9117529*a^9 - 27497442139/9117529*a^8 - 34087739411/9117529*a^7 + 41638952128/9117529*a^6 + 13940693999/9117529*a^5 - 26126412945/9117529*a^4 - 1054174331/9117529*a^3 + 6918871923/9117529*a^2 - 237982061/9117529*a - 668912884/9117529)*q^37 + O(q^38)
*]> ;  // time = 9.37 seconds




J[422] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 422, 422, 422, 422, 422, 422, 211, 211, 211, 211 ], new_dimensions := [ 1, 2, 3, 3, 3, 6, 2, 3, 3, 9 ], dimensions := [ 1, 2, 3, 3, 3, 6, 4, 6, 6, 18 ], intersection_graph := [ 0, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 29, 1, 1, 11, 1, 1, 19, 3, 1, 0, 1, 1, 1, 1, 7, 7, 1, 1, 29, 1, 0, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 0, 1, 1, 1, 1, 223, 1, 1, 1, 1, 1, 0, 1, 1, 41, 1, 1, 11, 1, 1, 1, 1, 0, 1, 1, 1681, 1, 1, 7, 1, 1, 1, 1, 0, 49, 1, 1, 1, 7, 1, 1, 41, 1, 49, 0, 1, 1, 19, 1, 23, 223, 1, 1681, 1, 1, 0 ], ap_traces := [
[ -1, 0, 1, -2, -3, -7, 4, 7, -6, -6, 2, -7 ],
[ -2, 3, 2, 8, 2, 0, -4, 0, 0, -7, 6, 0 ],
[ -3, -1, -5, -5, 9, -11, -7, -14, 9, 2, -7, -12 ],
[ -3, -1, 1, 1, -5, 11, 5, 10, -1, 14, 1, 20 ],
[ 3, -5, -3, -9, -5, -7, -7, -4, -7, 10, -7, -6 ],
[ 6, 4, -2, 7, 4, 8, 1, 11, -3, -9, 1, -5 ]
], hecke_fields := [
x - 1,
x^2 - 3*x + 1,
x^3 + x^2 - 8*x - 3,
x^3 + x^2 - 6*x - 5,
x^3 + 5*x^2 + 6*x + 1,
x^6 - 4*x^5 - 4*x^4 + 28*x^3 - 15*x^2 - 33*x + 28
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 209, 1 ],
[ 49, 1 ],
[ 69, 3 ],
[ 223, 1 ],
[ 2173, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 3 ],
[ 223, 1 ],
[ 2173, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 1, 53 ], torsion_lower_bounds := [ 1, 1, 1, 3, 1, 53 ], l_ratios := [ 0, 1, 0, 1/3, 0, 41/53 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1, 0, 1 ], eigenvalues := [*
[ -1, 0, 1, -2, -3, -7, 4, 7, -6, -6, 2, -7 ],
[
-1,
a,
-2*a + 4,
4,
-2*a + 4,
0,
-2,
4*a - 6,
4*a - 6,
a - 5,
-2*a + 6,
-4*a + 6
],
[
-1,
a,
-1/3*a^2 - 2/3*a,
-a - 2,
1/3*a^2 - 1/3*a + 1,
-2/3*a^2 - 1/3*a,
2/3*a^2 + 1/3*a - 6,
-a - 5,
3,
-5/3*a^2 - 1/3*a + 10,
a^2 + 3*a - 7,
1/3*a^2 - 1/3*a - 6
],
[
-1,
a,
a^2 - 4,
-a,
-a^2 + a + 3,
a + 4,
a + 2,
-a + 3,
-2*a - 1,
a^2 - a,
-a^2 + a + 5,
a^2 - a + 2
],
[
1,
a,
a^2 + 2*a - 2,
-2*a^2 - 7*a - 6,
-3*a^2 - 11*a - 7,
2*a^2 + 9*a + 4,
2*a^2 + 9*a + 4,
4*a^2 + 13*a + 3,
4*a^2 + 16*a + 7,
-3*a^2 - 5*a + 8,
-a^2 - 3*a - 3,
-5*a^2 - 19*a - 12
],
[
1,
a,
-4*a^5 + 10*a^4 + 31*a^3 - 66*a^2 - 38*a + 77,
3*a^5 - 7*a^4 - 24*a^3 + 45*a^2 + 31*a - 50,
2*a^5 - 6*a^4 - 14*a^3 + 41*a^2 + 13*a - 47,
6*a^5 - 15*a^4 - 46*a^3 + 97*a^2 + 54*a - 107,
a^5 - 3*a^4 - 8*a^3 + 23*a^2 + 11*a - 32,
-3*a^5 + 8*a^4 + 23*a^3 - 53*a^2 - 30*a + 63,
a^5 - 3*a^4 - 7*a^3 + 20*a^2 + 6*a - 22,
-5*a^5 + 13*a^4 + 38*a^3 - 86*a^2 - 45*a + 98,
-3*a^5 + 8*a^4 + 22*a^3 - 53*a^2 - 24*a + 62,
-7*a^5 + 19*a^4 + 53*a^3 - 129*a^2 - 63*a + 153
]
*], q_expansions := [*
q - q^2 + q^4 + q^5 - 2*q^7 - q^8 - 3*q^9 - q^10 - 3*q^11 - 7*q^13 + 2*q^14 + q^16 + 4*q^17 + 3*q^18 + 7*q^19 + q^20 + 3*q^22 - 6*q^23 - 4*q^25 + 7*q^26 - 2*q^28 - 6*q^29 + 2*q^31 - q^32 - 4*q^34 - 2*q^35 - 3*q^36 - 7*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-2*a + 4)*q^5 - a*q^6 + 4*q^7 - q^8 + (3*a - 4)*q^9 + (2*a - 4)*q^10 + (-2*a + 4)*q^11 + a*q^12 - 4*q^14 + (-2*a + 2)*q^15 + q^16 - 2*q^17 + (-3*a + 4)*q^18 + (4*a - 6)*q^19 + (-2*a + 4)*q^20 + 4*a*q^21 + (2*a - 4)*q^22 + (4*a - 6)*q^23 - a*q^24 + (-4*a + 7)*q^25 + (2*a - 3)*q^27 + 4*q^28 + (a - 5)*q^29 + (2*a - 2)*q^30 + (-2*a + 6)*q^31 - q^32 + (-2*a + 2)*q^33 + 2*q^34 + (-8*a + 16)*q^35 + (3*a - 4)*q^36 + (-4*a + 6)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-1/3*a^2 - 2/3*a)*q^5 - a*q^6 + (-a - 2)*q^7 - q^8 + (a^2 - 3)*q^9 + (1/3*a^2 + 2/3*a)*q^10 + (1/3*a^2 - 1/3*a + 1)*q^11 + a*q^12 + (-2/3*a^2 - 1/3*a)*q^13 + (a + 2)*q^14 + (-1/3*a^2 - 8/3*a - 1)*q^15 + q^16 + (2/3*a^2 + 1/3*a - 6)*q^17 + (-a^2 + 3)*q^18 + (-a - 5)*q^19 + (-1/3*a^2 - 2/3*a)*q^20 + (-a^2 - 2*a)*q^21 + (-1/3*a^2 + 1/3*a - 1)*q^22 + 3*q^23 - a*q^24 + (a^2 + 3*a - 4)*q^25 + (2/3*a^2 + 1/3*a)*q^26 + (-a^2 + 2*a + 3)*q^27 + (-a - 2)*q^28 + (-5/3*a^2 - 1/3*a + 10)*q^29 + (1/3*a^2 + 8/3*a + 1)*q^30 + (a^2 + 3*a - 7)*q^31 - q^32 + (-2/3*a^2 + 11/3*a + 1)*q^33 + (-2/3*a^2 - 1/3*a + 6)*q^34 + (a^2 + 4*a + 1)*q^35 + (a^2 - 3)*q^36 + (1/3*a^2 - 1/3*a - 6)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (a^2 - 4)*q^5 - a*q^6 - a*q^7 - q^8 + (a^2 - 3)*q^9 + (-a^2 + 4)*q^10 + (-a^2 + a + 3)*q^11 + a*q^12 + (a + 4)*q^13 + a*q^14 + (-a^2 + 2*a + 5)*q^15 + q^16 + (a + 2)*q^17 + (-a^2 + 3)*q^18 + (-a + 3)*q^19 + (a^2 - 4)*q^20 - a^2*q^21 + (a^2 - a - 3)*q^22 + (-2*a - 1)*q^23 - a*q^24 + (-a^2 - a + 6)*q^25 + (-a - 4)*q^26 + (-a^2 + 5)*q^27 - a*q^28 + (a^2 - a)*q^29 + (a^2 - 2*a - 5)*q^30 + (-a^2 + a + 5)*q^31 - q^32 + (2*a^2 - 3*a - 5)*q^33 + (-a - 2)*q^34 + (a^2 - 2*a - 5)*q^35 + (a^2 - 3)*q^36 + (a^2 - a + 2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (a^2 + 2*a - 2)*q^5 + a*q^6 + (-2*a^2 - 7*a - 6)*q^7 + q^8 + (a^2 - 3)*q^9 + (a^2 + 2*a - 2)*q^10 + (-3*a^2 - 11*a - 7)*q^11 + a*q^12 + (2*a^2 + 9*a + 4)*q^13 + (-2*a^2 - 7*a - 6)*q^14 + (-3*a^2 - 8*a - 1)*q^15 + q^16 + (2*a^2 + 9*a + 4)*q^17 + (a^2 - 3)*q^18 + (4*a^2 + 13*a + 3)*q^19 + (a^2 + 2*a - 2)*q^20 + (3*a^2 + 6*a + 2)*q^21 + (-3*a^2 - 11*a - 7)*q^22 + (4*a^2 + 16*a + 7)*q^23 + a*q^24 + (-a^2 - 3*a)*q^25 + (2*a^2 + 9*a + 4)*q^26 + (-5*a^2 - 12*a - 1)*q^27 + (-2*a^2 - 7*a - 6)*q^28 + (-3*a^2 - 5*a + 8)*q^29 + (-3*a^2 - 8*a - 1)*q^30 + (-a^2 - 3*a - 3)*q^31 + q^32 + (4*a^2 + 11*a + 3)*q^33 + (2*a^2 + 9*a + 4)*q^34 + (a^2 + 10*a + 13)*q^35 + (a^2 - 3)*q^36 + (-5*a^2 - 19*a - 12)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-4*a^5 + 10*a^4 + 31*a^3 - 66*a^2 - 38*a + 77)*q^5 + a*q^6 + (3*a^5 - 7*a^4 - 24*a^3 + 45*a^2 + 31*a - 50)*q^7 + q^8 + (a^2 - 3)*q^9 + (-4*a^5 + 10*a^4 + 31*a^3 - 66*a^2 - 38*a + 77)*q^10 + (2*a^5 - 6*a^4 - 14*a^3 + 41*a^2 + 13*a - 47)*q^11 + a*q^12 + (6*a^5 - 15*a^4 - 46*a^3 + 97*a^2 + 54*a - 107)*q^13 + (3*a^5 - 7*a^4 - 24*a^3 + 45*a^2 + 31*a - 50)*q^14 + (-6*a^5 + 15*a^4 + 46*a^3 - 98*a^2 - 55*a + 112)*q^15 + q^16 + (a^5 - 3*a^4 - 8*a^3 + 23*a^2 + 11*a - 32)*q^17 + (a^2 - 3)*q^18 + (-3*a^5 + 8*a^4 + 23*a^3 - 53*a^2 - 30*a + 63)*q^19 + (-4*a^5 + 10*a^4 + 31*a^3 - 66*a^2 - 38*a + 77)*q^20 + (5*a^5 - 12*a^4 - 39*a^3 + 76*a^2 + 49*a - 84)*q^21 + (2*a^5 - 6*a^4 - 14*a^3 + 41*a^2 + 13*a - 47)*q^22 + (a^5 - 3*a^4 - 7*a^3 + 20*a^2 + 6*a - 22)*q^23 + a*q^24 + (8*a^5 - 20*a^4 - 62*a^3 + 131*a^2 + 77*a - 152)*q^25 + (6*a^5 - 15*a^4 - 46*a^3 + 97*a^2 + 54*a - 107)*q^26 + (a^3 - 6*a)*q^27 + (3*a^5 - 7*a^4 - 24*a^3 + 45*a^2 + 31*a - 50)*q^28 + (-5*a^5 + 13*a^4 + 38*a^3 - 86*a^2 - 45*a + 98)*q^29 + (-6*a^5 + 15*a^4 + 46*a^3 - 98*a^2 - 55*a + 112)*q^30 + (-3*a^5 + 8*a^4 + 22*a^3 - 53*a^2 - 24*a + 62)*q^31 + q^32 + (2*a^5 - 6*a^4 - 15*a^3 + 43*a^2 + 19*a - 56)*q^33 + (a^5 - 3*a^4 - 8*a^3 + 23*a^2 + 11*a - 32)*q^34 + (-12*a^5 + 31*a^4 + 92*a^3 - 206*a^2 - 111*a + 238)*q^35 + (a^2 - 3)*q^36 + (-7*a^5 + 19*a^4 + 53*a^3 - 129*a^2 - 63*a + 153)*q^37 + O(q^38)
*]> ;  // time = 113.719 seconds




J[426] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 426, 426, 426, 426, 426, 426, 426, 213, 213, 213, 213, 213, 142, 142, 142, 142, 142, 71, 71 ], new_dimensions := [ 1, 1, 1, 2, 2, 3, 3, 1, 2, 2, 2, 4, 1, 1, 1, 1, 1, 3, 3 ], dimensions := [ 1, 1, 1, 2, 2, 3, 3, 2, 4, 4, 4, 8, 2, 2, 2, 2, 2, 12, 12 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 31, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 11, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 19, 1, 1, 1, 1, 1, 7, 1, 7, 1, 1, 1, 1, 1, 1, 1, 0, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 11, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 9, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 81, 25, 1, 1, 1, 31, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 361, 3721, 3, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 9, 1, 1, 9, 9, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 1, 1, 81, 81, 1, 1, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 9, 9, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 81, 361, 1, 9, 81, 1, 9, 0, 6561, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 25, 3721, 1, 9, 81, 1, 9, 6561, 0 ], ap_traces := [
[ -1, -1, -2, 2, -2, 0, 0, -4, -4, -6, -2, -6 ],
[ -1, 1, 3, -1, 3, 2, -6, 5, -6, -9, 11, -4 ],
[ 1, 1, 1, 3, -3, -6, -2, 5, -6, 5, 7, 8 ],
[ -2, -2, 2, -2, 10, -8, 0, 2, 12, 6, 2, -16 ],
[ -2, 2, -3, 5, -1, 4, 6, 5, 2, 5, -3, 6 ],
[ 3, -3, 4, 2, 2, 2, 10, -2, 4, 8, -2, -2 ],
[ 3, 3, 1, -1, 3, 8, -6, -7, 6, -11, -13, -4 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 - 2*x - 7,
x^2 + 3*x - 2,
x^3 - 4*x^2 - 3*x + 10,
x^3 - x^2 - 12*x + 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 5, 3, 1 ],
[ 9, 15, 1 ],
[ 5, 5, 1 ],
[ 31, 7, 1 ],
[ 1, 1, 1 ],
[ 11, 5, 1 ],
[ 133, 49, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 15, 1 ],
[ 5, 5, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 11, 1, 1 ],
[ 133, 49, 1 ]
], torsion_upper_bounds := [ 1, 3, 5, 1, 1, 1, 7 ], torsion_lower_bounds := [ 1, 3, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 5/3, 1, 1, 1, 11, 133 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1/25, 1, 1, 1, 1/49 ], eigenvalues := [*
[ -1, -1, -2, 2, -2, 0, 0, -4, -4, -6, -2, -6 ],
[ -1, 1, 3, -1, 3, 2, -6, 5, -6, -9, 11, -4 ],
[ 1, 1, 1, 3, -3, -6, -2, 5, -6, 5, 7, 8 ],
[
-1,
-1,
a,
3/2*a - 5/2,
-1/2*a + 11/2,
-a - 3,
-a + 1,
1,
-a + 7,
2*a + 1,
-5/2*a + 7/2,
-a - 7
],
[
-1,
1,
a,
a + 4,
-a - 2,
2,
-2*a,
-3*a - 2,
2*a + 4,
a + 4,
a,
2*a + 6
],
[
1,
-1,
a,
1/2*a^2 - 3/2*a - 1,
-1/2*a^2 - 1/2*a + 5,
-a^2 + 3*a + 4,
a^2 - 3*a,
-a^2 + 2*a + 4,
a^2 - 3*a - 2,
-a^2 + 10,
1/2*a^2 + 1/2*a - 5,
a^2 - 3*a - 4
],
[
1,
1,
a,
-a,
1/2*a^2 - 1/2*a - 3,
-1/2*a^2 - 1/2*a + 7,
-a^2 + a + 6,
-a - 2,
a^2 - a - 6,
a - 4,
-a - 4,
2*a - 2
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - 2*q^5 + q^6 + 2*q^7 - q^8 + q^9 + 2*q^10 - 2*q^11 - q^12 - 2*q^14 + 2*q^15 + q^16 - q^18 - 4*q^19 - 2*q^20 - 2*q^21 + 2*q^22 - 4*q^23 + q^24 - q^25 - q^27 + 2*q^28 - 6*q^29 - 2*q^30 - 2*q^31 - q^32 + 2*q^33 - 4*q^35 + q^36 - 6*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + 3*q^5 - q^6 - q^7 - q^8 + q^9 - 3*q^10 + 3*q^11 + q^12 + 2*q^13 + q^14 + 3*q^15 + q^16 - 6*q^17 - q^18 + 5*q^19 + 3*q^20 - q^21 - 3*q^22 - 6*q^23 - q^24 + 4*q^25 - 2*q^26 + q^27 - q^28 - 9*q^29 - 3*q^30 + 11*q^31 - q^32 + 3*q^33 + 6*q^34 - 3*q^35 + q^36 - 4*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^5 + q^6 + 3*q^7 + q^8 + q^9 + q^10 - 3*q^11 + q^12 - 6*q^13 + 3*q^14 + q^15 + q^16 - 2*q^17 + q^18 + 5*q^19 + q^20 + 3*q^21 - 3*q^22 - 6*q^23 + q^24 - 4*q^25 - 6*q^26 + q^27 + 3*q^28 + 5*q^29 + q^30 + 7*q^31 + q^32 - 3*q^33 - 2*q^34 + 3*q^35 + q^36 + 8*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + a*q^5 + q^6 + (3/2*a - 5/2)*q^7 - q^8 + q^9 - a*q^10 + (-1/2*a + 11/2)*q^11 - q^12 + (-a - 3)*q^13 + (-3/2*a + 5/2)*q^14 - a*q^15 + q^16 + (-a + 1)*q^17 - q^18 + q^19 + a*q^20 + (-3/2*a + 5/2)*q^21 + (1/2*a - 11/2)*q^22 + (-a + 7)*q^23 + q^24 + (2*a + 2)*q^25 + (a + 3)*q^26 - q^27 + (3/2*a - 5/2)*q^28 + (2*a + 1)*q^29 + a*q^30 + (-5/2*a + 7/2)*q^31 - q^32 + (1/2*a - 11/2)*q^33 + (a - 1)*q^34 + (1/2*a + 21/2)*q^35 + q^36 + (-a - 7)*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + a*q^5 - q^6 + (a + 4)*q^7 - q^8 + q^9 - a*q^10 + (-a - 2)*q^11 + q^12 + 2*q^13 + (-a - 4)*q^14 + a*q^15 + q^16 - 2*a*q^17 - q^18 + (-3*a - 2)*q^19 + a*q^20 + (a + 4)*q^21 + (a + 2)*q^22 + (2*a + 4)*q^23 - q^24 + (-3*a - 3)*q^25 - 2*q^26 + q^27 + (a + 4)*q^28 + (a + 4)*q^29 - a*q^30 + a*q^31 - q^32 + (-a - 2)*q^33 + 2*a*q^34 + (a + 2)*q^35 + q^36 + (2*a + 6)*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + a*q^5 - q^6 + (1/2*a^2 - 3/2*a - 1)*q^7 + q^8 + q^9 + a*q^10 + (-1/2*a^2 - 1/2*a + 5)*q^11 - q^12 + (-a^2 + 3*a + 4)*q^13 + (1/2*a^2 - 3/2*a - 1)*q^14 - a*q^15 + q^16 + (a^2 - 3*a)*q^17 + q^18 + (-a^2 + 2*a + 4)*q^19 + a*q^20 + (-1/2*a^2 + 3/2*a + 1)*q^21 + (-1/2*a^2 - 1/2*a + 5)*q^22 + (a^2 - 3*a - 2)*q^23 - q^24 + (a^2 - 5)*q^25 + (-a^2 + 3*a + 4)*q^26 - q^27 + (1/2*a^2 - 3/2*a - 1)*q^28 + (-a^2 + 10)*q^29 - a*q^30 + (1/2*a^2 + 1/2*a - 5)*q^31 + q^32 + (1/2*a^2 + 1/2*a - 5)*q^33 + (a^2 - 3*a)*q^34 + (1/2*a^2 + 1/2*a - 5)*q^35 + q^36 + (a^2 - 3*a - 4)*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + a*q^5 + q^6 - a*q^7 + q^8 + q^9 + a*q^10 + (1/2*a^2 - 1/2*a - 3)*q^11 + q^12 + (-1/2*a^2 - 1/2*a + 7)*q^13 - a*q^14 + a*q^15 + q^16 + (-a^2 + a + 6)*q^17 + q^18 + (-a - 2)*q^19 + a*q^20 - a*q^21 + (1/2*a^2 - 1/2*a - 3)*q^22 + (a^2 - a - 6)*q^23 + q^24 + (a^2 - 5)*q^25 + (-1/2*a^2 - 1/2*a + 7)*q^26 + q^27 - a*q^28 + (a - 4)*q^29 + a*q^30 + (-a - 4)*q^31 + q^32 + (1/2*a^2 - 1/2*a - 3)*q^33 + (-a^2 + a + 6)*q^34 - a^2*q^35 + q^36 + (2*a - 2)*q^37 + O(q^38)
*]> ;  // time = 296.07 seconds




J[427] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 427, 427, 427, 427, 427, 427, 427, 61, 61 ], new_dimensions := [ 1, 1, 1, 6, 6, 7, 9, 1, 3 ], dimensions := [ 1, 1, 1, 6, 6, 7, 9, 2, 6 ], intersection_graph := [ 0, 1, 1, 3, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 11, 1, 1, 1, 1, 1, 0, 1, 7, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 7, 1, 0, 1, 1, 1, 139, 1, 11, 1, 1, 1, 0, 1, 7, 1, 1, 1, 1, 1, 1, 1, 0, 1, 313, 3, 1, 1, 3, 1, 7, 1, 0, 1, 1, 1, 1, 1, 139, 1, 313, 1, 0 ], ap_traces := [
[ -1, 1, 0, -1, -5, 4, -5, -7, 9, -6, 0, 2 ],
[ 0, 2, 4, 1, -2, 2, 5, -8, -6, 2, 1, 4 ],
[ 1, 1, -4, 1, -3, -4, 5, 1, 7, -10, -8, 10 ],
[ -5, 0, -5, -6, -6, -13, -11, 10, -18, -14, 6, -15 ],
[ -5, -8, -9, 6, 0, -5, -17, -10, -10, -2, 6, -15 ],
[ 4, 1, 7, 7, 1, 5, 12, 9, 9, 10, 2, 3 ],
[ 5, -1, 9, -9, 3, 13, 9, 1, 1, 18, -7, 13 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^6 + 5*x^5 + 2*x^4 - 18*x^3 - 12*x^2 + 18*x + 5,
x^6 + 5*x^5 + 2*x^4 - 22*x^3 - 30*x^2 + 9,
x^7 - 4*x^6 - 3*x^5 + 26*x^4 - 12*x^3 - 38*x^2 + 23*x + 11,
x^9 - 5*x^8 - 3*x^7 + 45*x^6 - 32*x^5 - 108*x^4 + 123*x^3 + 30*x^2 - 43*x + 4
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 139, 1 ],
[ 217, 1 ],
[ 313, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 139, 1 ],
[ 217, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 3, 31, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 31, 1 ], l_ratios := [ 0, 1, 0, 0, 0, 7/31, 1 ], analytic_sha_upper_bounds := [ 0, 1, 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 0, 0, 1, 1 ], eigenvalues := [*
[ -1, 1, 0, -1, -5, 4, -5, -7, 9, -6, 0, 2 ],
[ 0, 2, 4, 1, -2, 2, 5, -8, -6, 2, 1, 4 ],
[ 1, 1, -4, 1, -3, -4, 5, 1, 7, -10, -8, 10 ],
[
a,
a^5 + 3*a^4 - 3*a^3 - 9*a^2 + 4*a + 3,
-a^5 - 3*a^4 + 2*a^3 + 7*a^2 - 2*a - 2,
-1,
-a^5 - 3*a^4 + 3*a^3 + 9*a^2 - 4*a - 4,
-a^5 - 2*a^4 + 8*a^3 + 12*a^2 - 14*a - 10,
-a^4 - 4*a^3 - a^2 + 9*a + 2,
-a^5 - a^4 + 10*a^3 + 7*a^2 - 21*a - 1,
-2*a^4 - 6*a^3 + 3*a^2 + 11*a - 5,
a^5 + 6*a^4 + 6*a^3 - 14*a^2 - 13*a + 5,
a^5 + 2*a^4 - 4*a^3 - 2*a^2 + 9*a - 3,
2*a^4 + 4*a^3 - 5*a^2 - 6*a - 3
],
[
a,
-1/3*a^5 - 5/3*a^4 + 1/3*a^3 + 25/3*a^2 + 4*a - 5,
a^5 + 3*a^4 - 4*a^3 - 15*a^2 - 2*a + 6,
1,
-5/3*a^5 - 13/3*a^4 + 23/3*a^3 + 59/3*a^2 - 2*a - 6,
-a^5 - 4*a^4 + 2*a^3 + 20*a^2 + 10*a - 10,
2*a^5 + 7*a^4 - 6*a^3 - 33*a^2 - 13*a + 6,
a^5 + 3*a^4 - 4*a^3 - 15*a^2 - 3*a + 5,
2/3*a^5 + 10/3*a^4 - 2/3*a^3 - 47/3*a^2 - 7*a + 3,
-1/3*a^5 - 2/3*a^4 + 4/3*a^3 + 10/3*a^2 + a - 3,
5*a^5 + 16*a^4 - 16*a^3 - 74*a^2 - 25*a + 23,
-2*a^5 - 6*a^4 + 8*a^3 + 27*a^2 + 4*a - 7
],
[
a,
-2*a^6 + 5*a^5 + 13*a^4 - 31*a^3 - 21*a^2 + 38*a + 13,
a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 13*a^2 - 14*a - 7,
1,
-a^6 + 2*a^5 + 7*a^4 - 13*a^3 - 13*a^2 + 18*a + 9,
a^6 - 4*a^5 - 6*a^4 + 26*a^3 + 10*a^2 - 34*a - 9,
4*a^6 - 10*a^5 - 27*a^4 + 64*a^3 + 47*a^2 - 83*a - 28,
a^5 - a^4 - 6*a^3 + 3*a^2 + 7*a + 3,
-a^2 - a + 5,
a^6 - 2*a^5 - 6*a^4 + 12*a^3 + 6*a^2 - 15*a + 2,
3*a^6 - 6*a^5 - 20*a^4 + 36*a^3 + 30*a^2 - 41*a - 10,
4*a^6 - 8*a^5 - 28*a^4 + 50*a^3 + 51*a^2 - 66*a - 29
],
[
a,
-5/16*a^8 + 9/8*a^7 + 37/16*a^6 - 85/8*a^5 - 15/8*a^4 + 217/8*a^3 - 161/16*a^2 - 161/16*a + 7/4,
1/8*a^8 - 1/4*a^7 - 9/8*a^6 + 5/4*a^5 + 15/4*a^4 + 3/4*a^3 - 43/8*a^2 - 43/8*a + 5/2,
-1,
-1/16*a^8 + 5/8*a^7 - 15/16*a^6 - 41/8*a^5 + 93/8*a^4 + 85/8*a^3 - 461/16*a^2 - 13/16*a + 27/4,
1/8*a^8 - 1/4*a^7 - 9/8*a^6 + 5/4*a^5 + 19/4*a^4 - 5/4*a^3 - 83/8*a^2 + 21/8*a + 9/2,
-5/16*a^8 + 9/8*a^7 + 37/16*a^6 - 77/8*a^5 - 31/8*a^4 + 177/8*a^3 - 33/16*a^2 - 145/16*a + 11/4,
-5/16*a^8 + 9/8*a^7 + 37/16*a^6 - 85/8*a^5 - 15/8*a^4 + 225/8*a^3 - 193/16*a^2 - 241/16*a + 31/4,
1/16*a^8 - 5/8*a^7 - 1/16*a^6 + 57/8*a^5 - 37/8*a^4 - 173/8*a^3 + 269/16*a^2 + 189/16*a - 11/4,
a^8 - 4*a^7 - 6*a^6 + 36*a^5 - 4*a^4 - 88*a^3 + 53*a^2 + 32*a - 14,
-3/4*a^8 + 5/2*a^7 + 23/4*a^6 - 45/2*a^5 - 17/2*a^4 + 115/2*a^3 - 47/4*a^2 - 127/4*a + 4,
-1/2*a^8 + 2*a^7 + 5/2*a^6 - 16*a^5 + 3*a^4 + 33*a^3 - 43/2*a^2 - 11/2*a + 10
]
*], q_expansions := [*
q - q^2 + q^3 - q^4 - q^6 - q^7 + 3*q^8 - 2*q^9 - 5*q^11 - q^12 + 4*q^13 + q^14 - q^16 - 5*q^17 + 2*q^18 - 7*q^19 - q^21 + 5*q^22 + 9*q^23 + 3*q^24 - 5*q^25 - 4*q^26 - 5*q^27 + q^28 - 6*q^29 - 5*q^32 - 5*q^33 + 5*q^34 + 2*q^36 + 2*q^37 + O(q^38),
q + 2*q^3 - 2*q^4 + 4*q^5 + q^7 + q^9 - 2*q^11 - 4*q^12 + 2*q^13 + 8*q^15 + 4*q^16 + 5*q^17 - 8*q^19 - 8*q^20 + 2*q^21 - 6*q^23 + 11*q^25 - 4*q^27 - 2*q^28 + 2*q^29 + q^31 - 4*q^33 + 4*q^35 - 2*q^36 + 4*q^37 + O(q^38),
q + q^2 + q^3 - q^4 - 4*q^5 + q^6 + q^7 - 3*q^8 - 2*q^9 - 4*q^10 - 3*q^11 - q^12 - 4*q^13 + q^14 - 4*q^15 - q^16 + 5*q^17 - 2*q^18 + q^19 + 4*q^20 + q^21 - 3*q^22 + 7*q^23 - 3*q^24 + 11*q^25 - 4*q^26 - 5*q^27 - q^28 - 10*q^29 - 4*q^30 - 8*q^31 + 5*q^32 - 3*q^33 + 5*q^34 - 4*q^35 + 2*q^36 + 10*q^37 + O(q^38),
q + a*q^2 + (a^5 + 3*a^4 - 3*a^3 - 9*a^2 + 4*a + 3)*q^3 + (a^2 - 2)*q^4 + (-a^5 - 3*a^4 + 2*a^3 + 7*a^2 - 2*a - 2)*q^5 + (-2*a^5 - 5*a^4 + 9*a^3 + 16*a^2 - 15*a - 5)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (a^5 + 2*a^4 - 5*a^3 - 6*a^2 + 6*a + 1)*q^9 + (2*a^5 + 4*a^4 - 11*a^3 - 14*a^2 + 16*a + 5)*q^10 + (-a^5 - 3*a^4 + 3*a^3 + 9*a^2 - 4*a - 4)*q^11 + (3*a^5 + 7*a^4 - 14*a^3 - 21*a^2 + 23*a + 4)*q^12 + (-a^5 - 2*a^4 + 8*a^3 + 12*a^2 - 14*a - 10)*q^13 - a*q^14 + (-2*a^5 - 5*a^4 + 9*a^3 + 16*a^2 - 14*a - 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 - 4*a^3 - a^2 + 9*a + 2)*q^17 + (-3*a^5 - 7*a^4 + 12*a^3 + 18*a^2 - 17*a - 5)*q^18 + (-a^5 - a^4 + 10*a^3 + 7*a^2 - 21*a - 1)*q^19 + (-4*a^5 - 9*a^4 + 18*a^3 + 26*a^2 - 27*a - 6)*q^20 + (-a^5 - 3*a^4 + 3*a^3 + 9*a^2 - 4*a - 3)*q^21 + (2*a^5 + 5*a^4 - 9*a^3 - 16*a^2 + 14*a + 5)*q^22 + (-2*a^4 - 6*a^3 + 3*a^2 + 11*a - 5)*q^23 + (-4*a^5 - 10*a^4 + 15*a^3 + 27*a^2 - 20*a - 5)*q^24 + (2*a^5 + 6*a^4 - 5*a^3 - 14*a^2 + 8*a - 1)*q^25 + (3*a^5 + 10*a^4 - 6*a^3 - 26*a^2 + 8*a + 5)*q^26 + (a^5 + a^4 - 9*a^3 - 4*a^2 + 18*a - 1)*q^27 + (-a^2 + 2)*q^28 + (a^5 + 6*a^4 + 6*a^3 - 14*a^2 - 13*a + 5)*q^29 + (5*a^5 + 13*a^4 - 20*a^3 - 38*a^2 + 30*a + 10)*q^30 + (a^5 + 2*a^4 - 4*a^3 - 2*a^2 + 9*a - 3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-2*a^5 - 5*a^4 + 8*a^3 + 15*a^2 - 10*a - 7)*q^33 + (-a^5 - 4*a^4 - a^3 + 9*a^2 + 2*a)*q^34 + (a^5 + 3*a^4 - 2*a^3 - 7*a^2 + 2*a + 2)*q^35 + (6*a^5 + 14*a^4 - 26*a^3 - 41*a^2 + 37*a + 13)*q^36 + (2*a^4 + 4*a^3 - 5*a^2 - 6*a - 3)*q^37 + O(q^38),
q + a*q^2 + (-1/3*a^5 - 5/3*a^4 + 1/3*a^3 + 25/3*a^2 + 4*a - 5)*q^3 + (a^2 - 2)*q^4 + (a^5 + 3*a^4 - 4*a^3 - 15*a^2 - 2*a + 6)*q^5 + (a^4 + a^3 - 6*a^2 - 5*a + 3)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (1/3*a^5 + 8/3*a^4 + 5/3*a^3 - 40/3*a^2 - 12*a + 7)*q^9 + (-2*a^5 - 6*a^4 + 7*a^3 + 28*a^2 + 6*a - 9)*q^10 + (-5/3*a^5 - 13/3*a^4 + 23/3*a^3 + 59/3*a^2 - 2*a - 6)*q^11 + (5/3*a^5 + 13/3*a^4 - 20/3*a^3 - 65/3*a^2 - 5*a + 10)*q^12 + (-a^5 - 4*a^4 + 2*a^3 + 20*a^2 + 10*a - 10)*q^13 + a*q^14 + (a^4 + a^3 - 4*a^2 - 2*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^5 + 7*a^4 - 6*a^3 - 33*a^2 - 13*a + 6)*q^17 + (a^5 + a^4 - 6*a^3 - 2*a^2 + 7*a - 3)*q^18 + (a^5 + 3*a^4 - 4*a^3 - 15*a^2 - 3*a + 5)*q^19 + (2*a^5 + 5*a^4 - 8*a^3 - 24*a^2 - 5*a + 6)*q^20 + (-1/3*a^5 - 5/3*a^4 + 1/3*a^3 + 25/3*a^2 + 4*a - 5)*q^21 + (4*a^5 + 11*a^4 - 17*a^3 - 52*a^2 - 6*a + 15)*q^22 + (2/3*a^5 + 10/3*a^4 - 2/3*a^3 - 47/3*a^2 - 7*a + 3)*q^23 + (-4*a^5 - 12*a^4 + 13*a^3 + 57*a^2 + 20*a - 21)*q^24 + (-4*a^5 - 12*a^4 + 15*a^3 + 58*a^2 + 12*a - 23)*q^25 + (a^5 + 4*a^4 - 2*a^3 - 20*a^2 - 10*a + 9)*q^26 + (-a^5 - 5*a^4 - a^3 + 24*a^2 + 24*a - 11)*q^27 + (a^2 - 2)*q^28 + (-1/3*a^5 - 2/3*a^4 + 4/3*a^3 + 10/3*a^2 + a - 3)*q^29 + (a^5 + a^4 - 4*a^3 - 2*a^2)*q^30 + (5*a^5 + 16*a^4 - 16*a^3 - 74*a^2 - 25*a + 23)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-8/3*a^5 - 31/3*a^4 + 20/3*a^3 + 155/3*a^2 + 24*a - 21)*q^33 + (-3*a^5 - 10*a^4 + 11*a^3 + 47*a^2 + 6*a - 18)*q^34 + (a^5 + 3*a^4 - 4*a^3 - 15*a^2 - 2*a + 6)*q^35 + (-14/3*a^5 - 40/3*a^4 + 50/3*a^3 + 191/3*a^2 + 21*a - 23)*q^36 + (-2*a^5 - 6*a^4 + 8*a^3 + 27*a^2 + 4*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-2*a^6 + 5*a^5 + 13*a^4 - 31*a^3 - 21*a^2 + 38*a + 13)*q^3 + (a^2 - 2)*q^4 + (a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 13*a^2 - 14*a - 7)*q^5 + (-3*a^6 + 7*a^5 + 21*a^4 - 45*a^3 - 38*a^2 + 59*a + 22)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (a^6 - 2*a^5 - 8*a^4 + 13*a^3 + 18*a^2 - 18*a - 10)*q^9 + (2*a^6 - 4*a^5 - 14*a^4 + 25*a^3 + 24*a^2 - 30*a - 11)*q^10 + (-a^6 + 2*a^5 + 7*a^4 - 13*a^3 - 13*a^2 + 18*a + 9)*q^11 + (-a^6 + 2*a^5 + 7*a^4 - 12*a^3 - 13*a^2 + 15*a + 7)*q^12 + (a^6 - 4*a^5 - 6*a^4 + 26*a^3 + 10*a^2 - 34*a - 9)*q^13 + a*q^14 + (-4*a^6 + 10*a^5 + 27*a^4 - 63*a^3 - 48*a^2 + 80*a + 30)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (4*a^6 - 10*a^5 - 27*a^4 + 64*a^3 + 47*a^2 - 83*a - 28)*q^17 + (2*a^6 - 5*a^5 - 13*a^4 + 30*a^3 + 20*a^2 - 33*a - 11)*q^18 + (a^5 - a^4 - 6*a^3 + 3*a^2 + 7*a + 3)*q^19 + (2*a^6 - 4*a^5 - 13*a^4 + 24*a^3 + 20*a^2 - 29*a - 8)*q^20 + (-2*a^6 + 5*a^5 + 13*a^4 - 31*a^3 - 21*a^2 + 38*a + 13)*q^21 + (-2*a^6 + 4*a^5 + 13*a^4 - 25*a^3 - 20*a^2 + 32*a + 11)*q^22 + (-a^2 - a + 5)*q^23 + (4*a^6 - 10*a^5 - 28*a^4 + 65*a^3 + 53*a^2 - 88*a - 33)*q^24 + (3*a^6 - 7*a^5 - 20*a^4 + 43*a^3 + 34*a^2 - 52*a - 22)*q^25 + (-3*a^5 + 22*a^3 + 4*a^2 - 32*a - 11)*q^26 + (a^6 - 2*a^5 - 7*a^4 + 13*a^3 + 12*a^2 - 20*a - 4)*q^27 + (a^2 - 2)*q^28 + (a^6 - 2*a^5 - 6*a^4 + 12*a^3 + 6*a^2 - 15*a + 2)*q^29 + (-6*a^6 + 15*a^5 + 41*a^4 - 96*a^3 - 72*a^2 + 122*a + 44)*q^30 + (3*a^6 - 6*a^5 - 20*a^4 + 36*a^3 + 30*a^2 - 41*a - 10)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-4*a^6 + 10*a^5 + 27*a^4 - 64*a^3 - 47*a^2 + 84*a + 29)*q^33 + (6*a^6 - 15*a^5 - 40*a^4 + 95*a^3 + 69*a^2 - 120*a - 44)*q^34 + (a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 13*a^2 - 14*a - 7)*q^35 + (a^6 - 3*a^5 - 6*a^4 + 18*a^3 + 7*a^2 - 21*a - 2)*q^36 + (4*a^6 - 8*a^5 - 28*a^4 + 50*a^3 + 51*a^2 - 66*a - 29)*q^37 + O(q^38),
q + a*q^2 + (-5/16*a^8 + 9/8*a^7 + 37/16*a^6 - 85/8*a^5 - 15/8*a^4 + 217/8*a^3 - 161/16*a^2 - 161/16*a + 7/4)*q^3 + (a^2 - 2)*q^4 + (1/8*a^8 - 1/4*a^7 - 9/8*a^6 + 5/4*a^5 + 15/4*a^4 + 3/4*a^3 - 43/8*a^2 - 43/8*a + 5/2)*q^5 + (-7/16*a^8 + 11/8*a^7 + 55/16*a^6 - 95/8*a^5 - 53/8*a^4 + 227/8*a^3 - 11/16*a^2 - 187/16*a + 5/4)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (1/16*a^8 - 5/8*a^7 + 15/16*a^6 + 41/8*a^5 - 85/8*a^4 - 101/8*a^3 + 381/16*a^2 + 141/16*a - 15/4)*q^9 + (3/8*a^8 - 3/4*a^7 - 35/8*a^6 + 31/4*a^5 + 57/4*a^4 - 83/4*a^3 - 73/8*a^2 + 63/8*a - 1/2)*q^10 + (-1/16*a^8 + 5/8*a^7 - 15/16*a^6 - 41/8*a^5 + 93/8*a^4 + 85/8*a^3 - 461/16*a^2 - 13/16*a + 27/4)*q^11 + (-3/16*a^8 - 1/8*a^7 + 51/16*a^6 + 5/8*a^5 - 121/8*a^4 - 9/8*a^3 + 345/16*a^2 + 41/16*a - 7/4)*q^12 + (1/8*a^8 - 1/4*a^7 - 9/8*a^6 + 5/4*a^5 + 19/4*a^4 - 5/4*a^3 - 83/8*a^2 + 21/8*a + 9/2)*q^13 - a*q^14 + (a^4 - 3*a^3 - 4*a^2 + 12*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-5/16*a^8 + 9/8*a^7 + 37/16*a^6 - 77/8*a^5 - 31/8*a^4 + 177/8*a^3 - 33/16*a^2 - 145/16*a + 11/4)*q^17 + (-5/16*a^8 + 9/8*a^7 + 37/16*a^6 - 69/8*a^5 - 47/8*a^4 + 129/8*a^3 + 111/16*a^2 - 17/16*a - 1/4)*q^18 + (-5/16*a^8 + 9/8*a^7 + 37/16*a^6 - 85/8*a^5 - 15/8*a^4 + 225/8*a^3 - 193/16*a^2 - 241/16*a + 31/4)*q^19 + (7/8*a^8 - 11/4*a^7 - 55/8*a^6 + 95/4*a^5 + 49/4*a^4 - 227/4*a^3 + 59/8*a^2 + 211/8*a - 13/2)*q^20 + (5/16*a^8 - 9/8*a^7 - 37/16*a^6 + 85/8*a^5 + 15/8*a^4 - 217/8*a^3 + 161/16*a^2 + 161/16*a - 7/4)*q^21 + (5/16*a^8 - 9/8*a^7 - 37/16*a^6 + 77/8*a^5 + 31/8*a^4 - 169/8*a^3 + 17/16*a^2 + 65/16*a + 1/4)*q^22 + (1/16*a^8 - 5/8*a^7 - 1/16*a^6 + 57/8*a^5 - 37/8*a^4 - 173/8*a^3 + 269/16*a^2 + 189/16*a - 11/4)*q^23 + (-3/16*a^8 - 1/8*a^7 + 35/16*a^6 + 21/8*a^5 - 65/8*a^4 - 97/8*a^3 + 153/16*a^2 + 217/16*a - 7/4)*q^24 + (3/4*a^8 - 5/2*a^7 - 23/4*a^6 + 43/2*a^5 + 17/2*a^4 - 93/2*a^3 + 47/4*a^2 + 19/4*a - 2)*q^25 + (3/8*a^8 - 3/4*a^7 - 35/8*a^6 + 35/4*a^5 + 49/4*a^4 - 103/4*a^3 - 9/8*a^2 + 79/8*a - 1/2)*q^26 + (-3/16*a^8 + 7/8*a^7 + 19/16*a^6 - 67/8*a^5 - 9/8*a^4 + 191/8*a^3 - 23/16*a^2 - 279/16*a - 7/4)*q^27 + (-a^2 + 2)*q^28 + (a^8 - 4*a^7 - 6*a^6 + 36*a^5 - 4*a^4 - 88*a^3 + 53*a^2 + 32*a - 14)*q^29 + (a^5 - 3*a^4 - 4*a^3 + 12*a^2)*q^30 + (-3/4*a^8 + 5/2*a^7 + 23/4*a^6 - 45/2*a^5 - 17/2*a^4 + 115/2*a^3 - 47/4*a^2 - 127/4*a + 4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (5/16*a^8 - 9/8*a^7 - 37/16*a^6 + 77/8*a^5 + 31/8*a^4 - 161/8*a^3 + 1/16*a^2 - 31/16*a + 17/4)*q^33 + (-7/16*a^8 + 11/8*a^7 + 71/16*a^6 - 111/8*a^5 - 93/8*a^4 + 291/8*a^3 + 5/16*a^2 - 171/16*a + 5/4)*q^34 + (-1/8*a^8 + 1/4*a^7 + 9/8*a^6 - 5/4*a^5 - 15/4*a^4 - 3/4*a^3 + 43/8*a^2 + 43/8*a - 5/2)*q^35 + (-9/16*a^8 + 21/8*a^7 + 57/16*a^6 - 209/8*a^5 + 29/8*a^4 + 565/8*a^3 - 629/16*a^2 - 501/16*a + 35/4)*q^36 + (-1/2*a^8 + 2*a^7 + 5/2*a^6 - 16*a^5 + 3*a^4 + 33*a^3 - 43/2*a^2 - 11/2*a + 10)*q^37 + O(q^38)
*]> ;  // time = 77.329 seconds




J[429] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 429, 429, 429, 429, 429, 429, 429, 429, 143, 143, 143, 39, 39, 33, 11 ], new_dimensions := [ 1, 1, 2, 2, 3, 3, 3, 4, 1, 4, 6, 1, 2, 1, 1 ], dimensions := [ 1, 1, 2, 2, 3, 3, 3, 4, 2, 8, 12, 2, 4, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 23, 1, 1, 7, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 129, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 379, 1, 1, 1, 1, 1, 1, 3, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23, 129, 1, 1, 1, 1, 0, 1, 1, 7, 3, 81, 1, 1, 1, 1, 1, 1, 1, 379, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 7, 1, 25, 1, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 0, 9, 1, 1, 1, 1, 3, 1, 5, 1, 1, 81, 1, 1, 1, 9, 0 ], ap_traces := [
[ -1, -1, 0, 0, 1, 1, -4, -8, 0, 4, -6, -6 ],
[ -1, 1, -2, 0, -1, 1, -6, -4, -8, -10, 0, 6 ],
[ 0, -2, -2, -4, -2, -2, 10, -8, -4, 2, -6, -4 ],
[ -2, 2, -4, -4, 2, -2, -8, -12, 4, 0, 0, 4 ],
[ -1, -3, -2, 2, 3, -3, -2, 10, -12, 12, 16, 0 ],
[ 3, 3, 4, -2, -3, -3, 0, 2, 4, 2, 14, 0 ],
[ 1, 3, 0, -2, 3, 3, 8, 6, 8, 2, -6, -12 ],
[ -2, -4, 0, 2, -4, 4, -8, 18, 0, -10, 12, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 3,
x^2 + 2*x - 1,
x^3 + x^2 - 5*x - 3,
x^3 - 3*x^2 - x + 5,
x^3 - x^2 - 3*x + 1,
x^4 + 2*x^3 - 6*x^2 - 12*x - 1
], atkin_lehners := [
[ 1, -1, -1 ],
[ -1, 1, -1 ],
[ 1, 1, 1 ],
[ -1, -1, 1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ],
[ 1, 1, -1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 23, 7, 1 ],
[ 129, 1, 3 ],
[ 5, 25, 1 ],
[ 5, 1, 5 ],
[ 379, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 23, 7, 1 ],
[ 1, 1, 1 ],
[ 5, 1, 1 ],
[ 5, 1, 5 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 5, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 0, 0, 0, 1, 5, 1, 1 ], analytic_sha_upper_bounds := [ 0, 0, 0, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 0, 1, 1, 1/25, 1 ], eigenvalues := [*
[ -1, -1, 0, 0, 1, 1, -4, -8, 0, 4, -6, -6 ],
[ -1, 1, -2, 0, -1, 1, -6, -4, -8, -10, 0, 6 ],
[
a,
-1,
-a - 1,
-2,
-1,
-1,
-a + 5,
-2*a - 4,
-2,
3*a + 1,
3*a - 3,
-2
],
[
a,
1,
a - 1,
-2*a - 4,
1,
-1,
-a - 5,
-6,
-2*a,
3*a + 3,
3*a + 3,
4*a + 6
],
[
a,
-1,
a^2 + a - 4,
a^2 - 3,
1,
-1,
-a - 1,
-a^2 + 7,
a^2 + 2*a - 7,
2*a^2 + a - 3,
a^2 + a + 2,
-2*a^2 - 4*a + 6
],
[
a,
1,
-a^2 + a + 4,
-a^2 + 3,
-1,
-1,
-a + 1,
a^2 - 3,
-a^2 - 2*a + 7,
4*a^2 - 7*a - 7,
a^2 - a + 2,
-4*a + 4
],
[
a,
1,
-a^2 + a + 2,
-a^2 + 2*a + 1,
1,
1,
2*a^2 - 3*a - 1,
-a^2 - 2*a + 5,
a^2 - 2*a + 1,
-2*a^2 + a + 5,
a^2 - a - 4,
-2*a^2 + 2*a
],
[
a,
-1,
a^3 - 6*a - 1,
a^3 - 5*a,
-1,
1,
-a^3 - a^2 + 8*a + 4,
a^3 - 5*a + 4,
-a^2 - 2*a + 3,
-2*a^3 - 2*a^2 + 11*a + 7,
-a^3 - 2*a^2 + 4*a + 11,
a^3 - a^2 - 5*a + 3
]
*], q_expansions := [*
q - q^2 - q^3 - q^4 + q^6 + 3*q^8 + q^9 + q^11 + q^12 + q^13 - q^16 - 4*q^17 - q^18 - 8*q^19 - q^22 - 3*q^24 - 5*q^25 - q^26 - q^27 + 4*q^29 - 6*q^31 - 5*q^32 - q^33 + 4*q^34 - q^36 - 6*q^37 + O(q^38),
q - q^2 + q^3 - q^4 - 2*q^5 - q^6 + 3*q^8 + q^9 + 2*q^10 - q^11 - q^12 + q^13 - 2*q^15 - q^16 - 6*q^17 - q^18 - 4*q^19 + 2*q^20 + q^22 - 8*q^23 + 3*q^24 - q^25 - q^26 + q^27 - 10*q^29 + 2*q^30 - 5*q^32 - q^33 + 6*q^34 - q^36 + 6*q^37 + O(q^38),
q + a*q^2 - q^3 + q^4 + (-a - 1)*q^5 - a*q^6 - 2*q^7 - a*q^8 + q^9 + (-a - 3)*q^10 - q^11 - q^12 - q^13 - 2*a*q^14 + (a + 1)*q^15 - 5*q^16 + (-a + 5)*q^17 + a*q^18 + (-2*a - 4)*q^19 + (-a - 1)*q^20 + 2*q^21 - a*q^22 - 2*q^23 + a*q^24 + (2*a - 1)*q^25 - a*q^26 - q^27 - 2*q^28 + (3*a + 1)*q^29 + (a + 3)*q^30 + (3*a - 3)*q^31 - 3*a*q^32 + q^33 + (5*a - 3)*q^34 + (2*a + 2)*q^35 + q^36 - 2*q^37 + O(q^38),
q + a*q^2 + q^3 + (-2*a - 1)*q^4 + (a - 1)*q^5 + a*q^6 + (-2*a - 4)*q^7 + (a - 2)*q^8 + q^9 + (-3*a + 1)*q^10 + q^11 + (-2*a - 1)*q^12 - q^13 - 2*q^14 + (a - 1)*q^15 + 3*q^16 + (-a - 5)*q^17 + a*q^18 - 6*q^19 + (5*a - 1)*q^20 + (-2*a - 4)*q^21 + a*q^22 - 2*a*q^23 + (a - 2)*q^24 + (-4*a - 3)*q^25 - a*q^26 + q^27 + (2*a + 8)*q^28 + (3*a + 3)*q^29 + (-3*a + 1)*q^30 + (3*a + 3)*q^31 + (a + 4)*q^32 + q^33 + (-3*a - 1)*q^34 + (2*a + 2)*q^35 + (-2*a - 1)*q^36 + (4*a + 6)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (a^2 + a - 4)*q^5 - a*q^6 + (a^2 - 3)*q^7 + (-a^2 + a + 3)*q^8 + q^9 + (a + 3)*q^10 + q^11 + (-a^2 + 2)*q^12 - q^13 + (-a^2 + 2*a + 3)*q^14 + (-a^2 - a + 4)*q^15 + (-2*a + 1)*q^16 + (-a - 1)*q^17 + a*q^18 + (-a^2 + 7)*q^19 + (-a^2 + a + 8)*q^20 + (-a^2 + 3)*q^21 + a*q^22 + (a^2 + 2*a - 7)*q^23 + (a^2 - a - 3)*q^24 + (-3*a^2 + 14)*q^25 - a*q^26 - q^27 + (a^2 - 2*a + 3)*q^28 + (2*a^2 + a - 3)*q^29 + (-a - 3)*q^30 + (a^2 + a + 2)*q^31 + (-a - 6)*q^32 - q^33 + (-a^2 - a)*q^34 + (-2*a^2 + 12)*q^35 + (a^2 - 2)*q^36 + (-2*a^2 - 4*a + 6)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^2 + a + 4)*q^5 + a*q^6 + (-a^2 + 3)*q^7 + (3*a^2 - 3*a - 5)*q^8 + q^9 + (-2*a^2 + 3*a + 5)*q^10 - q^11 + (a^2 - 2)*q^12 - q^13 + (-3*a^2 + 2*a + 5)*q^14 + (-a^2 + a + 4)*q^15 + (4*a^2 - 2*a - 11)*q^16 + (-a + 1)*q^17 + a*q^18 + (a^2 - 3)*q^19 + (-a^2 + a + 2)*q^20 + (-a^2 + 3)*q^21 - a*q^22 + (-a^2 - 2*a + 7)*q^23 + (3*a^2 - 3*a - 5)*q^24 + (-3*a^2 + 4*a + 6)*q^25 - a*q^26 + q^27 + (-5*a^2 + 2*a + 9)*q^28 + (4*a^2 - 7*a - 7)*q^29 + (-2*a^2 + 3*a + 5)*q^30 + (a^2 - a + 2)*q^31 + (4*a^2 - a - 10)*q^32 - q^33 + (-a^2 + a)*q^34 + 2*q^35 + (a^2 - 2)*q^36 + (-4*a + 4)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^2 + a + 2)*q^5 + a*q^6 + (-a^2 + 2*a + 1)*q^7 + (a^2 - a - 1)*q^8 + q^9 + (-a + 1)*q^10 + q^11 + (a^2 - 2)*q^12 + q^13 + (a^2 - 2*a + 1)*q^14 + (-a^2 + a + 2)*q^15 + (-2*a^2 + 2*a + 3)*q^16 + (2*a^2 - 3*a - 1)*q^17 + a*q^18 + (-a^2 - 2*a + 5)*q^19 + (a^2 - a - 4)*q^20 + (-a^2 + 2*a + 1)*q^21 + a*q^22 + (a^2 - 2*a + 1)*q^23 + (a^2 - a - 1)*q^24 - a^2*q^25 + a*q^26 + q^27 + (a^2 - 3)*q^28 + (-2*a^2 + a + 5)*q^29 + (-a + 1)*q^30 + (a^2 - a - 4)*q^31 + (-2*a^2 - a + 4)*q^32 + q^33 + (-a^2 + 5*a - 2)*q^34 + (-2*a + 4)*q^35 + (a^2 - 2)*q^36 + (-2*a^2 + 2*a)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (a^3 - 6*a - 1)*q^5 - a*q^6 + (a^3 - 5*a)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-2*a^3 + 11*a + 1)*q^10 - q^11 + (-a^2 + 2)*q^12 + q^13 + (-2*a^3 + a^2 + 12*a + 1)*q^14 + (-a^3 + 6*a + 1)*q^15 + (-2*a^3 + 12*a + 5)*q^16 + (-a^3 - a^2 + 8*a + 4)*q^17 + a*q^18 + (a^3 - 5*a + 4)*q^19 + (2*a^3 - a^2 - 11*a)*q^20 + (-a^3 + 5*a)*q^21 - a*q^22 + (-a^2 - 2*a + 3)*q^23 + (-a^3 + 4*a)*q^24 + (2*a^3 + a^2 - 14*a - 6)*q^25 + a*q^26 - q^27 + (3*a^3 - 13*a - 2)*q^28 + (-2*a^3 - 2*a^2 + 11*a + 7)*q^29 + (2*a^3 - 11*a - 1)*q^30 + (-a^3 - 2*a^2 + 4*a + 11)*q^31 + (2*a^3 - 11*a - 2)*q^32 + q^33 + (a^3 + 2*a^2 - 8*a - 1)*q^34 + (a^3 + a^2 - 9*a - 1)*q^35 + (a^2 - 2)*q^36 + (a^3 - a^2 - 5*a + 3)*q^37 + O(q^38)
*]> ;  // time = 153.49 seconds




J[430] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 430, 430, 430, 430, 430, 430, 430, 430, 215, 215, 215, 215, 86, 86, 43, 43 ], new_dimensions := [ 1, 1, 1, 1, 2, 2, 2, 3, 1, 3, 5, 6, 2, 2, 1, 2 ], dimensions := [ 1, 1, 1, 1, 2, 2, 2, 3, 2, 6, 10, 12, 4, 4, 4, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 5, 1, 1, 5, 5, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 59, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 223, 17, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 0, 2401, 1, 1, 11, 1, 1, 1, 1, 1, 5, 59, 1, 1, 1, 1, 2401, 0, 1, 1, 5, 25, 1, 1, 1, 9, 1, 1, 1, 1, 223, 1, 1, 1, 0, 3, 1, 1, 961, 1, 5, 1, 1, 1, 1, 1, 17, 1, 1, 1, 3, 0, 1, 1, 49, 1, 1, 1, 5, 1, 19, 1, 1, 1, 11, 5, 1, 1, 0, 25, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 25, 1, 1, 25, 0, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 961, 49, 1, 1, 0 ], ap_traces := [
[ -1, 0, -1, 1, -4, -1, 0, 1, -4, -5, -9, 4 ],
[ -1, 0, 1, -3, 0, -3, -4, -1, 0, -3, 7, -8 ],
[ 1, -2, -1, -1, -6, 5, -6, -7, -6, -3, 5, 2 ],
[ 1, -2, 1, -5, -2, -5, 2, 3, -6, -1, -11, -10 ],
[ -2, 2, 2, 2, 2, 2, 10, -6, 6, 16, -16, -2 ],
[ 2, 0, -2, 2, 4, -2, 0, 2, 4, 14, -6, -4 ],
[ 2, 0, 2, 2, 4, 2, 0, -2, 4, -6, 2, -4 ],
[ -3, -2, -3, -6, 6, -4, 8, 2, 14, 6, 0, -8 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 2*x - 2,
x^2 - 6,
x^2 - 2,
x^3 + 2*x^2 - 6*x - 8
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, -1, -1 ],
[ -1, 1, -1 ],
[ -1, -1, 1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ],
[ 1, 1, -1 ]
], component_group_orders := [
[ 3, 1, 1 ],
[ 1, 5, 1 ],
[ 9, 1, 1 ],
[ 15, 5, 1 ],
[ 177, 1, 1 ],
[ 3, 19, 1 ],
[ 7, 7, 1 ],
[ 223, 17, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 5, 1 ],
[ 9, 1, 1 ],
[ 15, 5, 1 ],
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 7, 7, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 1, 1, 7, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 0, 0, 0, 1, 3, 1, 1 ], analytic_sha_upper_bounds := [ 0, 0, 0, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 0, 1, 1, 1/49, 1 ], eigenvalues := [*
[ -1, 0, -1, 1, -4, -1, 0, 1, -4, -5, -9, 4 ],
[ -1, 0, 1, -3, 0, -3, -4, -1, 0, -3, 7, -8 ],
[ 1, -2, -1, -1, -6, 5, -6, -7, -6, -3, 5, 2 ],
[ 1, -2, 1, -5, -2, -5, 2, 3, -6, -1, -11, -10 ],
[
-1,
a,
1,
-2*a + 3,
-a + 2,
2*a - 1,
a + 4,
2*a - 5,
-3*a + 6,
-a + 9,
-a - 7,
-3*a + 2
],
[
1,
a,
-1,
1,
-a + 2,
-1,
-a,
-2*a + 1,
a + 2,
-a + 7,
-a - 3,
-a - 2
],
[
1,
a,
1,
1,
-a + 2,
-2*a + 1,
a,
-1,
-5*a + 2,
3*a - 3,
-a + 1,
3*a - 2
],
[
-1,
a,
-1,
1/2*a^2 + a - 4,
-a^2 + a + 8,
-3/2*a^2 - a + 6,
a^2 + a - 2,
-1/2*a^2 + a + 4,
a^2 + a,
-1/2*a^2 - 4*a + 2,
3/2*a^2 - 8,
-2*a^2 - 3*a + 6
]
*], q_expansions := [*
q - q^2 + q^4 - q^5 + q^7 - q^8 - 3*q^9 + q^10 - 4*q^11 - q^13 - q^14 + q^16 + 3*q^18 + q^19 - q^20 + 4*q^22 - 4*q^23 + q^25 + q^26 + q^28 - 5*q^29 - 9*q^31 - q^32 - q^35 - 3*q^36 + 4*q^37 + O(q^38),
q - q^2 + q^4 + q^5 - 3*q^7 - q^8 - 3*q^9 - q^10 - 3*q^13 + 3*q^14 + q^16 - 4*q^17 + 3*q^18 - q^19 + q^20 + q^25 + 3*q^26 - 3*q^28 - 3*q^29 + 7*q^31 - q^32 + 4*q^34 - 3*q^35 - 3*q^36 - 8*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - q^5 - 2*q^6 - q^7 + q^8 + q^9 - q^10 - 6*q^11 - 2*q^12 + 5*q^13 - q^14 + 2*q^15 + q^16 - 6*q^17 + q^18 - 7*q^19 - q^20 + 2*q^21 - 6*q^22 - 6*q^23 - 2*q^24 + q^25 + 5*q^26 + 4*q^27 - q^28 - 3*q^29 + 2*q^30 + 5*q^31 + q^32 + 12*q^33 - 6*q^34 + q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 + q^5 - 2*q^6 - 5*q^7 + q^8 + q^9 + q^10 - 2*q^11 - 2*q^12 - 5*q^13 - 5*q^14 - 2*q^15 + q^16 + 2*q^17 + q^18 + 3*q^19 + q^20 + 10*q^21 - 2*q^22 - 6*q^23 - 2*q^24 + q^25 - 5*q^26 + 4*q^27 - 5*q^28 - q^29 - 2*q^30 - 11*q^31 + q^32 + 4*q^33 + 2*q^34 - 5*q^35 + q^36 - 10*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + q^5 - a*q^6 + (-2*a + 3)*q^7 - q^8 + (2*a - 1)*q^9 - q^10 + (-a + 2)*q^11 + a*q^12 + (2*a - 1)*q^13 + (2*a - 3)*q^14 + a*q^15 + q^16 + (a + 4)*q^17 + (-2*a + 1)*q^18 + (2*a - 5)*q^19 + q^20 + (-a - 4)*q^21 + (a - 2)*q^22 + (-3*a + 6)*q^23 - a*q^24 + q^25 + (-2*a + 1)*q^26 + 4*q^27 + (-2*a + 3)*q^28 + (-a + 9)*q^29 - a*q^30 + (-a - 7)*q^31 - q^32 - 2*q^33 + (-a - 4)*q^34 + (-2*a + 3)*q^35 + (2*a - 1)*q^36 + (-3*a + 2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - q^5 + a*q^6 + q^7 + q^8 + 3*q^9 - q^10 + (-a + 2)*q^11 + a*q^12 - q^13 + q^14 - a*q^15 + q^16 - a*q^17 + 3*q^18 + (-2*a + 1)*q^19 - q^20 + a*q^21 + (-a + 2)*q^22 + (a + 2)*q^23 + a*q^24 + q^25 - q^26 + q^28 + (-a + 7)*q^29 - a*q^30 + (-a - 3)*q^31 + q^32 + (2*a - 6)*q^33 - a*q^34 - q^35 + 3*q^36 + (-a - 2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + q^5 + a*q^6 + q^7 + q^8 - q^9 + q^10 + (-a + 2)*q^11 + a*q^12 + (-2*a + 1)*q^13 + q^14 + a*q^15 + q^16 + a*q^17 - q^18 - q^19 + q^20 + a*q^21 + (-a + 2)*q^22 + (-5*a + 2)*q^23 + a*q^24 + q^25 + (-2*a + 1)*q^26 - 4*a*q^27 + q^28 + (3*a - 3)*q^29 + a*q^30 + (-a + 1)*q^31 + q^32 + (2*a - 2)*q^33 + a*q^34 + q^35 - q^36 + (3*a - 2)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - q^5 - a*q^6 + (1/2*a^2 + a - 4)*q^7 - q^8 + (a^2 - 3)*q^9 + q^10 + (-a^2 + a + 8)*q^11 + a*q^12 + (-3/2*a^2 - a + 6)*q^13 + (-1/2*a^2 - a + 4)*q^14 - a*q^15 + q^16 + (a^2 + a - 2)*q^17 + (-a^2 + 3)*q^18 + (-1/2*a^2 + a + 4)*q^19 - q^20 + (-a + 4)*q^21 + (a^2 - a - 8)*q^22 + (a^2 + a)*q^23 - a*q^24 + q^25 + (3/2*a^2 + a - 6)*q^26 + (-2*a^2 + 8)*q^27 + (1/2*a^2 + a - 4)*q^28 + (-1/2*a^2 - 4*a + 2)*q^29 + a*q^30 + (3/2*a^2 - 8)*q^31 - q^32 + (3*a^2 + 2*a - 8)*q^33 + (-a^2 - a + 2)*q^34 + (-1/2*a^2 - a + 4)*q^35 + (a^2 - 3)*q^36 + (-2*a^2 - 3*a + 6)*q^37 + O(q^38)
*]> ;  // time = 210.709 seconds




J[431] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 431, 431, 431, 431, 431, 431 ], new_dimensions := [ 1, 1, 3, 3, 4, 24 ], dimensions := [ 1, 1, 3, 3, 4, 24 ], intersection_graph := [ 0, 1, 5, 1, 1, 1, 1, 0, 1, 5, 1, 1, 5, 1, 0, 1, 19, 1, 1, 5, 1, 0, 1, 6947, 1, 1, 19, 1, 0, 1, 1, 1, 1, 6947, 1, 0 ], ap_traces := [
[ -1, 1, 1, -2, -5, -2, -2, 5, -1, -3, -4, 4 ],
[ -1, 3, -3, 2, 1, -2, 6, 7, 1, -7, 4, 4 ],
[ 1, -1, -3, -6, 0, -6, -6, -11, -1, 5, 6, -10 ],
[ 0, 1, 1, 0, -12, 8, -2, -1, 5, -3, 4, 12 ],
[ -1, -3, -5, 2, 1, -5, 2, -6, 4, -5, -25, -1 ],
[ 1, 1, 13, 8, 15, 11, 6, 18, -8, 17, 37, 7 ]
], hecke_fields := [
x - 1,
x - 1,
x^3 - x^2 - 4*x + 3,
x^3 - 5*x + 1,
x^4 + x^3 - 3*x^2 - x + 1,
x^24 - x^23 - 40*x^22 + 40*x^21 + 692*x^20 - 687*x^19 - 6790*x^18 + 6631*x^17 + 41657*x^16 - 39533*x^15 - 166175*x^14 + 150668*x^13 + 434546*x^12 - 367120*x^11 - 733353*x^10 + 555013*x^9 + 766426*x^8 - 486022*x^7 - 458392*x^6 + 216189*x^5 + 133642*x^4 - 39443*x^3 - 11021*x^2 + 2767*x + 13
], atkin_lehners := [
[ 1 ],
[ -1 ],
[ 1 ],
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ 215 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ 215 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 215 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 215 ], l_ratios := [ 0, 1, 0, 1, 0, 1/215 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1, 0, 1 ], eigenvalues := [*
[ -1, 1, 1, -2, -5, -2, -2, 5, -1, -3, -4, 4 ],
[ -1, 3, -3, 2, 1, -2, 6, 7, 1, -7, 4, 4 ],
[
a,
-a,
-a^2 + 2,
-2,
0,
-2,
-2,
a - 4,
a^2 - a - 3,
3*a^2 - a - 7,
-2*a^2 + 8,
2*a - 4
],
[
a,
a^2 - 3,
a^2 + a - 3,
-2*a,
-4,
2*a^2 - 4,
-2*a^2 - 2*a + 6,
-a^2 + 3,
2*a^2 + a - 5,
a - 1,
-2*a^2 + 2*a + 8,
4
],
[
a,
-a^3 - a^2 + 3*a,
a^3 + a^2 - 3*a - 2,
-a^2 - a + 2,
-a^3 - 2*a^2 + 2,
2*a^3 + 3*a^2 - 4*a - 4,
-a^3 + 2*a^2 + 3*a - 4,
a^3 + 3*a^2 - 5,
2*a^3 + 4*a^2 - 2*a - 3,
-a^2 + 2*a + 1,
a^3 + a^2 - 3*a - 7,
-5*a^3 - 8*a^2 + 8*a + 7
],
[
a,
7935096512256799/3739222839496792400*a^23 + 810620141708163/3739222839496792400*a^22 - 173528413706803033/1869611419748396200*a^21 - 23895258075624573/3739222839496792400*a^20 + 3321529293701165417/1869611419748396200*a^19 + 252660572416622679/3739222839496792400*a^18 - 73061583647644979333/3739222839496792400*a^17 - 75898348765588621/373922283949679240*a^16 + 509534382412117002413/3739222839496792400*a^15 - 3325298853080540599/1869611419748396200*a^14 - 1172645596977846012287/1869611419748396200*a^13 + 903232533678644389/46740285493709905*a^12 + 3592287897607973222257/1869611419748396200*a^11 - 146985643477082908299/1869611419748396200*a^10 - 14402977230229462788321/3739222839496792400*a^9 + 590485552799907048989/3739222839496792400*a^8 + 9016487276459122122203/1869611419748396200*a^7 - 20629371559270104601/149568913579871696*a^6 - 6400831287872758553179/1869611419748396200*a^5 + 27385716846365639607/3739222839496792400*a^4 + 4165925951152361601299/3739222839496792400*a^3 + 1735042892911132546/46740285493709905*a^2 - 321943156993297734389/3739222839496792400*a + 5458880528184681463/1869611419748396200,
-3001918608458321/1869611419748396200*a^23 - 12759708706795807/1869611419748396200*a^22 + 287562107923492403/3739222839496792400*a^21 + 501204055954295587/1869611419748396200*a^20 - 1502875401940431783/934805709874198100*a^19 - 16932298038253081847/3739222839496792400*a^18 + 71928844431916175609/3739222839496792400*a^17 + 16082743684625791651/373922283949679240*a^16 - 543060246362583052439/3739222839496792400*a^15 - 942558898465922137941/3739222839496792400*a^14 + 672495179452626345253/934805709874198100*a^13 + 43971863404446227282/46740285493709905*a^12 - 4402363403637250822151/1869611419748396200*a^11 - 4160062215272089935323/1869611419748396200*a^10 + 9344614349012167227349/1869611419748396200*a^9 + 749898640478464070373/233701427468549525*a^8 - 24465019598760262751343/3739222839496792400*a^7 - 194198287645854433175/74784456789935848*a^6 + 4449007914580759656591/934805709874198100*a^5 + 3820952747901107923889/3739222839496792400*a^4 - 5722288875361777878787/3739222839496792400*a^3 - 65155149072801915771/373922283949679240*a^2 + 432741984388948972677/3739222839496792400*a + 13141980820492227997/3739222839496792400,
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-29447136684089627/934805709874198100*a^23 + 26242082770678841/934805709874198100*a^22 + 2345774219566058361/1869611419748396200*a^21 - 1051490124684271081/934805709874198100*a^20 - 20179765126407933267/934805709874198100*a^19 + 36108015743634470311/1869611419748396200*a^18 + 393111367649484952283/1869611419748396200*a^17 - 34742062422939077753/186961141974839620*a^16 - 2387382828795524287593/1869611419748396200*a^15 + 2055713742392103141083/1869611419748396200*a^14 + 1173424114548608289668/233701427468549525*a^13 - 385990220104677040989/93480570987419810*a^12 - 12021016151207630045487/934805709874198100*a^11 + 9147877141766781032099/934805709874198100*a^10 + 19678938479459677643163/934805709874198100*a^9 - 3277892713557832986098/233701427468549525*a^8 - 39351539612496011857941/1869611419748396200*a^7 + 410660936171269500743/37392228394967924*a^6 + 11056654390522333660009/934805709874198100*a^5 - 6880564126349736047357/1869611419748396200*a^4 - 5916477909164850037369/1869611419748396200*a^3 + 40484263614205801513/186961141974839620*a^2 + 354268671653852247999/1869611419748396200*a - 6811392445559260811/1869611419748396200,
281324527852433579/3739222839496792400*a^23 - 487863155509851437/3739222839496792400*a^22 - 5433285670939605743/1869611419748396200*a^21 + 19248787131524483207/3739222839496792400*a^20 + 89738988857424479177/1869611419748396200*a^19 - 325624394582622090381/3739222839496792400*a^18 - 1653790237158210929973/3739222839496792400*a^17 + 308769485432725196897/373922283949679240*a^16 + 9293556051720599052513/3739222839496792400*a^15 - 9002463445374763282479/1869611419748396200*a^14 - 16316138267871312663867/1869611419748396200*a^13 + 832613639603157873633/46740285493709905*a^12 + 35047728827772297694077/1869611419748396200*a^11 - 77715498527294256512019/1869611419748396200*a^10 - 84686031783071407416061/3739222839496792400*a^9 + 219319594061300561909349/3739222839496792400*a^8 + 21934623940625771095853/1869611419748396200*a^7 - 6786257730990343557381/149568913579871696*a^6 + 2203243439578220729541/1869611419748396200*a^5 + 57801766203859116535267/3739222839496792400*a^4 - 8469578900572476561741/3739222839496792400*a^3 - 250495123848414801967/186961141974839620*a^2 + 1186889311028330763071/3739222839496792400*a - 11938862166570034437/1869611419748396200,
-300064858386950083/3739222839496792400*a^23 + 257215934031731507/1869611419748396200*a^22 + 1451537093226821259/467402854937099050*a^21 - 20306849741568284399/3739222839496792400*a^20 - 192347237029403583093/3739222839496792400*a^19 + 21482896856541313792/233701427468549525*a^18 + 1780425538563949674841/3739222839496792400*a^17 - 652354038136722868957/747844567899358480*a^16 - 5039977423176476678693/1869611419748396200*a^15 + 2379806836396731606627/467402854937099050*a^14 + 17927715416585691893119/1869611419748396200*a^13 - 7052637928883114100471/373922283949679240*a^12 - 9868618492719564725531/467402854937099050*a^11 + 82447215071084262345723/1869611419748396200*a^10 + 100848043033609128682127/3739222839496792400*a^9 - 116706853360008662737209/1869611419748396200*a^8 - 15687653704087081535383/934805709874198100*a^7 + 7265311263152485767021/149568913579871696*a^6 + 8538491663870001558411/3739222839496792400*a^5 - 3921068259642160526754/233701427468549525*a^4 + 4182140668683639313737/3739222839496792400*a^3 + 1138982061306427044877/747844567899358480*a^2 - 407401473617555930651/1869611419748396200*a - 1564918695811353343/934805709874198100,
123746154424603511/3739222839496792400*a^23 - 97855527515094349/1869611419748396200*a^22 - 2404341430872620187/1869611419748396200*a^21 + 7711085975715111123/3739222839496792400*a^20 + 80159023387407028921/3739222839496792400*a^19 - 65107715382203920407/1869611419748396200*a^18 - 749468325999438460527/3739222839496792400*a^17 + 49285578935300719769/149568913579871696*a^16 + 1078399864190620442613/934805709874198100*a^15 - 3583924832897931718611/1869611419748396200*a^14 - 7892325194318492176963/1869611419748396200*a^13 + 2645588380913185401099/373922283949679240*a^12 + 9153704654540844335169/934805709874198100*a^11 - 30817801415303532257681/1869611419748396200*a^10 - 52025429995054248404179/3739222839496792400*a^9 + 43509053521505799356793/1869611419748396200*a^8 + 21052772641180506610437/1869611419748396200*a^7 - 2707275799135844042433/149568913579871696*a^6 - 17252733288009915874887/3739222839496792400*a^5 + 11697403526580336482429/1869611419748396200*a^4 + 3258795554522567368601/3739222839496792400*a^3 - 402924597960333272653/747844567899358480*a^2 - 3900764045610082361/233701427468549525*a + 11266173076706579377/1869611419748396200,
-74331153196484057/1869611419748396200*a^23 + 44537224295419579/467402854937099050*a^22 + 2777371083381009163/1869611419748396200*a^21 - 7044560108709693211/1869611419748396200*a^20 - 43739839388714993087/1869611419748396200*a^19 + 119531173679220216603/1869611419748396200*a^18 + 46867496194078608693/233701427468549525*a^17 - 227571779188582385349/373922283949679240*a^16 - 1869277202179051591509/1869611419748396200*a^15 + 6667135146830276236339/1869611419748396200*a^14 + 2605311599599147538191/934805709874198100*a^13 - 2480927900756682671271/186961141974839620*a^12 - 2955728078598767556151/934805709874198100*a^11 + 7287587723976778978883/233701427468549525*a^10 - 7052400762745517024247/1869611419748396200*a^9 - 41505022280194972582601/934805709874198100*a^8 + 29958506931988938703917/1869611419748396200*a^7 + 2606580722914642385861/74784456789935848*a^6 - 33258467339853242066131/1869611419748396200*a^5 - 23144871264411291503801/1869611419748396200*a^4 + 1624991049349791126046/233701427468549525*a^3 + 512938210700342034217/373922283949679240*a^2 - 1125454309693886680273/1869611419748396200*a + 2019438237556022657/1869611419748396200,
-43549720290049949/373922283949679240*a^23 + 14170601039249629/93480570987419810*a^22 + 1698395884000162021/373922283949679240*a^21 - 2243193097444878423/373922283949679240*a^20 - 5686220275637555403/74784456789935848*a^19 + 38039190792584214067/373922283949679240*a^18 + 6677061224741748195/9348057098741981*a^17 - 361340669636851249047/373922283949679240*a^16 - 1544722186951023311289/373922283949679240*a^15 + 2109225810354888259703/373922283949679240*a^14 + 2837925217338127515403/186961141974839620*a^13 - 3902180574523987762189/186961141974839620*a^12 - 6590029525449853899589/186961141974839620*a^11 + 909713427720337832197/18696114197483962*a^10 + 18581957497928840094309/373922283949679240*a^9 - 12803406123747742303913/186961141974839620*a^8 - 14544555135823176402433/373922283949679240*a^7 + 3938055775625319006653/74784456789935848*a^6 + 5306581768390794512833/373922283949679240*a^5 - 1318129829562537309073/74784456789935848*a^4 - 175319470729785918039/93480570987419810*a^3 + 518123240683760203003/373922283949679240*a^2 - 9347559174541960237/373922283949679240*a - 361238798587682663/373922283949679240
]
*], q_expansions := [*
q - q^2 + q^3 - q^4 + q^5 - q^6 - 2*q^7 + 3*q^8 - 2*q^9 - q^10 - 5*q^11 - q^12 - 2*q^13 + 2*q^14 + q^15 - q^16 - 2*q^17 + 2*q^18 + 5*q^19 - q^20 - 2*q^21 + 5*q^22 - q^23 + 3*q^24 - 4*q^25 + 2*q^26 - 5*q^27 + 2*q^28 - 3*q^29 - q^30 - 4*q^31 - 5*q^32 - 5*q^33 + 2*q^34 - 2*q^35 + 2*q^36 + 4*q^37 + O(q^38),
q - q^2 + 3*q^3 - q^4 - 3*q^5 - 3*q^6 + 2*q^7 + 3*q^8 + 6*q^9 + 3*q^10 + q^11 - 3*q^12 - 2*q^13 - 2*q^14 - 9*q^15 - q^16 + 6*q^17 - 6*q^18 + 7*q^19 + 3*q^20 + 6*q^21 - q^22 + q^23 + 9*q^24 + 4*q^25 + 2*q^26 + 9*q^27 - 2*q^28 - 7*q^29 + 9*q^30 + 4*q^31 - 5*q^32 + 3*q^33 - 6*q^34 - 6*q^35 - 6*q^36 + 4*q^37 + O(q^38),
q + a*q^2 - a*q^3 + (a^2 - 2)*q^4 + (-a^2 + 2)*q^5 - a^2*q^6 - 2*q^7 + (a^2 - 3)*q^8 + (a^2 - 3)*q^9 + (-a^2 - 2*a + 3)*q^10 + (-a^2 - 2*a + 3)*q^12 - 2*q^13 - 2*a*q^14 + (a^2 + 2*a - 3)*q^15 + (-a^2 + a + 1)*q^16 - 2*q^17 + (a^2 + a - 3)*q^18 + (a - 4)*q^19 + (-a^2 - a - 1)*q^20 + 2*a*q^21 + (a^2 - a - 3)*q^23 + (-a^2 - a + 3)*q^24 + (a^2 + a - 4)*q^25 - 2*a*q^26 + (-a^2 + 2*a + 3)*q^27 + (-2*a^2 + 4)*q^28 + (3*a^2 - a - 7)*q^29 + (3*a^2 + a - 3)*q^30 + (-2*a^2 + 8)*q^31 + (-2*a^2 - 3*a + 9)*q^32 - 2*a*q^34 + (2*a^2 - 4)*q^35 + (a + 3)*q^36 + (2*a - 4)*q^37 + O(q^38),
q + a*q^2 + (a^2 - 3)*q^3 + (a^2 - 2)*q^4 + (a^2 + a - 3)*q^5 + (2*a - 1)*q^6 - 2*a*q^7 + (a - 1)*q^8 + (-a^2 - a + 6)*q^9 + (a^2 + 2*a - 1)*q^10 - 4*q^11 + (-a + 6)*q^12 + (2*a^2 - 4)*q^13 - 2*a^2*q^14 + (-a^2 + a + 8)*q^15 + (-a^2 - a + 4)*q^16 + (-2*a^2 - 2*a + 6)*q^17 + (-a^2 + a + 1)*q^18 + (-a^2 + 3)*q^19 + (2*a + 5)*q^20 + (-4*a + 2)*q^21 - 4*a*q^22 + (2*a^2 + a - 5)*q^23 + (-a^2 + 2*a + 2)*q^24 + (3*a + 2)*q^25 + (6*a - 2)*q^26 + (a^2 - a - 8)*q^27 + (-6*a + 2)*q^28 + (a - 1)*q^29 + (a^2 + 3*a + 1)*q^30 + (-2*a^2 + 2*a + 8)*q^31 + (-a^2 - 3*a + 3)*q^32 + (-4*a^2 + 12)*q^33 + (-2*a^2 - 4*a + 2)*q^34 + (-2*a^2 - 4*a + 2)*q^35 + (3*a^2 - 2*a - 11)*q^36 + 4*q^37 + O(q^38),
q + a*q^2 + (-a^3 - a^2 + 3*a)*q^3 + (a^2 - 2)*q^4 + (a^3 + a^2 - 3*a - 2)*q^5 + (-a + 1)*q^6 + (-a^2 - a + 2)*q^7 + (a^3 - 4*a)*q^8 + (a^3 - 4*a)*q^9 + (-a - 1)*q^10 + (-a^3 - 2*a^2 + 2)*q^11 + (2*a^3 + a^2 - 5*a)*q^12 + (2*a^3 + 3*a^2 - 4*a - 4)*q^13 + (-a^3 - a^2 + 2*a)*q^14 + (a^3 + 2*a^2 - 2*a - 3)*q^15 + (-a^3 - 3*a^2 + a + 3)*q^16 + (-a^3 + 2*a^2 + 3*a - 4)*q^17 + (-a^3 - a^2 + a - 1)*q^18 + (a^3 + 3*a^2 - 5)*q^19 + (-2*a^3 - 3*a^2 + 5*a + 4)*q^20 + (-2*a^3 - a^2 + 6*a - 1)*q^21 + (-a^3 - 3*a^2 + a + 1)*q^22 + (2*a^3 + 4*a^2 - 2*a - 3)*q^23 + (-a^3 + a^2 + 4*a - 4)*q^24 + (-3*a^3 - 4*a^2 + 8*a + 2)*q^25 + (a^3 + 2*a^2 - 2*a - 2)*q^26 + (2*a^3 + 4*a^2 - 5*a - 4)*q^27 + (a^2 + a - 3)*q^28 + (-a^2 + 2*a + 1)*q^29 + (a^3 + a^2 - 2*a - 1)*q^30 + (a^3 + a^2 - 3*a - 7)*q^31 + (-4*a^3 - 2*a^2 + 10*a + 1)*q^32 + (-a^3 - a^2 + 4*a)*q^33 + (3*a^3 - 5*a + 1)*q^34 + (2*a^3 + 3*a^2 - 4*a - 3)*q^35 + (-2*a^3 - 2*a^2 + 6*a + 1)*q^36 + (-5*a^3 - 8*a^2 + 8*a + 7)*q^37 + O(q^38),
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8*a^3 + 12*a)*q^32 + (-202363206342934401/3739222839496792400*a^23 + 341538862180487893/3739222839496792400*a^22 + 3940885913954632017/1869611419748396200*a^21 - 13454619639506038693/3739222839496792400*a^20 - 8228230555667981571/233701427468549525*a^19 + 227257436953688589549/3739222839496792400*a^18 + 1232448929146593632907/3739222839496792400*a^17 - 5379650321444014824/9348057098741981*a^16 - 7089690044005215055157/3739222839496792400*a^15 + 6266846994230541958101/1869611419748396200*a^14 + 12914693566716390861433/1869611419748396200*a^13 - 2317443989172870154167/186961141974839620*a^12 - 29573999786567441605233/1869611419748396200*a^11 + 54141859337637149279721/1869611419748396200*a^10 + 81350189265367197825139/3739222839496792400*a^9 - 153540685489492950074301/3739222839496792400*a^8 - 30279505522162937595967/1869611419748396200*a^7 + 4817463345997036733647/149568913579871696*a^6 + 1218533516023727250737/233701427468549525*a^5 - 42723935741430834832203/3739222839496792400*a^4 - 1799868793059812098341/3739222839496792400*a^3 + 431047486536563275009/373922283949679240*a^2 - 139086992195789609459/3739222839496792400*a - 27990618684829554857/1869611419748396200)*q^33 + (-1602526956705393/467402854937099050*a^23 - 9996715161111799/1869611419748396200*a^22 + 126395342679313999/934805709874198100*a^21 + 197653458982088617/934805709874198100*a^20 - 4352350060304677187/1869611419748396200*a^19 - 6780748520452182377/1869611419748396200*a^18 + 5388412809375731968/233701427468549525*a^17 + 13195183380543779257/373922283949679240*a^16 - 272553566672127307299/1869611419748396200*a^15 - 199681480284160608053/934805709874198100*a^14 + 288419494435822755473/467402854937099050*a^13 + 155023861263356201771/186961141974839620*a^12 - 1662755677696202832141/934805709874198100*a^11 - 479051887306875646542/233701427468549525*a^10 + 3231972818215304205759/934805709874198100*a^9 + 5786562747984141068263/1869611419748396200*a^8 - 4045432861192871175219/934805709874198100*a^7 - 97667099534835145591/37392228394967924*a^6 + 5851729938843568695649/1869611419748396200*a^5 + 1954270572305361825699/1869611419748396200*a^4 - 239765523539879537549/233701427468549525*a^3 - 58961023027370262067/373922283949679240*a^2 + 156149061964192735007/1869611419748396200*a + 382812776893165151/934805709874198100)*q^34 + (59436053696067801/934805709874198100*a^23 - 141635018763579653/934805709874198100*a^22 - 4513769194241118843/1869611419748396200*a^21 + 5583295537280518533/934805709874198100*a^20 + 36350864978435801301/934805709874198100*a^19 - 188903994410579988803/1869611419748396200*a^18 - 644652497677955976299/1869611419748396200*a^17 + 89656560295662165973/93480570987419810*a^16 + 3402802112972609215969/1869611419748396200*a^15 - 10479639911441566167979/1869611419748396200*a^14 - 2666960437140567228273/467402854937099050*a^13 + 1945710974803415383991/93480570987419810*a^12 + 8913495975608044105101/934805709874198100*a^11 - 45662686507362738111097/934805709874198100*a^10 - 3842596285387152060559/934805709874198100*a^9 + 16251989541359938837939/233701427468549525*a^8 - 21893478960572486633097/1869611419748396200*a^7 - 2044308094649007998025/37392228394967924*a^6 + 16794804393524492384233/934805709874198100*a^5 + 36351707796349138250421/1869611419748396200*a^4 - 14348674245840360514483/1869611419748396200*a^3 - 97959170556055092808/46740285493709905*a^2 + 1354724403071655151873/1869611419748396200*a + 16711794643293346763/1869611419748396200)*q^35 + (-56769664834122497/3739222839496792400*a^23 + 34804719901022653/1869611419748396200*a^22 + 1118206044880004599/1869611419748396200*a^21 - 2784734406300922961/3739222839496792400*a^20 - 37977663026336854807/3739222839496792400*a^19 + 23870558435090345059/1869611419748396200*a^18 + 364126879934453913109/3739222839496792400*a^17 - 91745617802760136411/747844567899358480*a^16 - 271157905949357489393/467402854937099050*a^15 + 1355967265594683711697/1869611419748396200*a^14 + 4164907232762412864191/1869611419748396200*a^13 - 203763356087157294871/74784456789935848*a^12 - 5178111282280286328253/934805709874198100*a^11 + 12116990661242071716527/1869611419748396200*a^10 + 32682144683740661455953/3739222839496792400*a^9 - 17575567576999514184901/1869611419748396200*a^8 - 15634382465658776490039/1869611419748396200*a^7 + 1140317925055766986479/149568913579871696*a^6 + 16851855033103980737549/3739222839496792400*a^5 - 5381449783317310188693/1869611419748396200*a^4 - 4540009858546309283107/3739222839496792400*a^3 + 51752860821864859555/149568913579871696*a^2 + 80104317537123366053/934805709874198100*a - 29217454151335920269/1869611419748396200)*q^36 + (-43549720290049949/373922283949679240*a^23 + 14170601039249629/93480570987419810*a^22 + 1698395884000162021/373922283949679240*a^21 - 2243193097444878423/373922283949679240*a^20 - 5686220275637555403/74784456789935848*a^19 + 38039190792584214067/373922283949679240*a^18 + 6677061224741748195/9348057098741981*a^17 - 361340669636851249047/373922283949679240*a^16 - 1544722186951023311289/373922283949679240*a^15 + 2109225810354888259703/373922283949679240*a^14 + 2837925217338127515403/186961141974839620*a^13 - 3902180574523987762189/186961141974839620*a^12 - 6590029525449853899589/186961141974839620*a^11 + 909713427720337832197/18696114197483962*a^10 + 18581957497928840094309/373922283949679240*a^9 - 12803406123747742303913/186961141974839620*a^8 - 14544555135823176402433/373922283949679240*a^7 + 3938055775625319006653/74784456789935848*a^6 + 5306581768390794512833/373922283949679240*a^5 - 1318129829562537309073/74784456789935848*a^4 - 175319470729785918039/93480570987419810*a^3 + 518123240683760203003/373922283949679240*a^2 - 9347559174541960237/373922283949679240*a - 361238798587682663/373922283949679240)*q^37 + O(q^38)
*]> ;  // time = 17.36 seconds




J[433] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 433, 433, 433, 433 ], new_dimensions := [ 1, 3, 15, 16 ], dimensions := [ 1, 3, 15, 16 ], intersection_graph := [ 0, 1, 1, 7, 1, 0, 1, 111, 1, 1, 0, 1, 7, 111, 1, 0 ], ap_traces := [
[ -1, -2, -4, -3, -4, -5, -3, -4, 8, 2, -9, -3 ],
[ 3, 0, 0, 7, 6, 5, -1, -6, 6, 6, -13, -1 ],
[ -10, -8, -5, -15, -14, -9, -25, -1, -45, -10, -3, -9 ],
[ 7, 6, 7, 7, 12, -3, 17, 9, 47, 10, 17, -7 ]
], hecke_fields := [
x - 1,
x^3 - 3*x^2 - 69*x - 37,
x^15 + 10*x^14 + 29*x^13 - 22*x^12 - 251*x^11 - 272*x^10 + 583*x^9 + 1252*x^8 - 186*x^7 - 1821*x^6 - 675*x^5 + 899*x^4 + 482*x^3 - 93*x^2 - 27*x - 1,
x^16 - 7*x^15 - 5*x^14 + 129*x^13 - 125*x^12 - 929*x^11 + 1471*x^10 + 3333*x^9 - 6394*x^8 - 6443*x^7 + 13118*x^6 + 7162*x^5 - 12217*x^4 - 4691*x^3 + 3598*x^2 + 1114*x - 3
], atkin_lehners := [
[ -1 ],
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 9 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 9 ]
], torsion_upper_bounds := [ 1, 1, 1, 9 ], torsion_lower_bounds := [ 1, 1, 1, 9 ], l_ratios := [ 0, 1, 0, 49/9 ], analytic_sha_upper_bounds := [ 0, 1, 0, 49 ], analytic_sha_lower_bounds := [ 0, 1, 0, 49 ], eigenvalues := [*
[ -1, -2, -4, -3, -4, -5, -3, -4, 8, 2, -9, -3 ],
[
1,
-1/3*a + 1/3,
-1/3*a + 1/3,
-1/18*a^2 + 1/9*a + 89/18,
1/3*a + 5/3,
-1/9*a^2 + 8/9*a + 56/9,
-1/9*a^2 + 5/9*a + 41/9,
-1/3*a - 5/3,
1/3*a + 5/3,
-2/3*a + 8/3,
1/18*a^2 + 2/9*a - 131/18,
2/9*a^2 - 13/9*a - 88/9
],
[
a,
7/2*a^14 + 30*a^13 + 59*a^12 - 158*a^11 - 1291/2*a^10 - 46*a^9 + 2030*a^8 + 1468*a^7 - 2510*a^6 - 5207/2*a^5 + 2113/2*a^4 + 1328*a^3 - 137/2*a^2 - 153/2*a - 6,
-11/2*a^14 - 95/2*a^13 - 95*a^12 + 248*a^11 + 2073/2*a^10 + 189/2*a^9 - 3276*a^8 - 2403*a^7 + 4121*a^6 + 8483/2*a^5 - 1864*a^4 - 4315/2*a^3 + 429/2*a^2 + 106*a + 13/2,
31/4*a^14 + 267/4*a^13 + 263/2*a^12 - 358*a^11 - 5825/4*a^10 - 227/4*a^9 + 9379/2*a^8 + 6327/2*a^7 - 6135*a^6 - 22843/4*a^5 + 6209/2*a^4 + 11653/4*a^3 - 2129/4*a^2 - 243/2*a - 9/4,
7/2*a^14 + 31*a^13 + 67*a^12 - 146*a^11 - 1397/2*a^10 - 197*a^9 + 2115*a^8 + 1987*a^7 - 2435*a^6 - 6677/2*a^5 + 1613/2*a^4 + 1740*a^3 + 103/2*a^2 - 281/2*a - 11,
2*a^14 + 17*a^13 + 32*a^12 - 97*a^11 - 369*a^10 + 32*a^9 + 1244*a^8 + 677*a^7 - 1780*a^6 - 1306*a^5 + 1114*a^4 + 662*a^3 - 297*a^2 + 5*a + 3,
-21/2*a^14 - 90*a^13 - 176*a^12 + 482*a^11 + 3895/2*a^10 + 81*a^9 - 6233*a^8 - 4278*a^7 + 8027*a^6 + 15465/2*a^5 - 7745/2*a^4 - 3989*a^3 + 1133/2*a^2 + 409/2*a + 4,
-8*a^14 - 139/2*a^13 - 141*a^12 + 359*a^11 + 1532*a^10 + 351/2*a^9 - 4842*a^8 - 3650*a^7 + 6101*a^6 + 6423*a^5 - 5545/2*a^4 - 6609/2*a^3 + 328*a^2 + 373/2*a + 7/2,
-a^14 - 17/2*a^13 - 17*a^12 + 42*a^11 + 181*a^10 + 73/2*a^9 - 543*a^8 - 486*a^7 + 597*a^6 + 824*a^5 - 303/2*a^4 - 835/2*a^3 - 37*a^2 + 67/2*a - 3/2,
-15/2*a^14 - 127/2*a^13 - 119*a^12 + 357*a^11 + 2705/2*a^10 - 179/2*a^9 - 4439*a^8 - 2557*a^7 + 6002*a^6 + 9625/2*a^5 - 3277*a^4 - 4841/2*a^3 + 1307/2*a^2 + 50*a - 1/2,
-1/4*a^14 + 1/4*a^13 + 29/2*a^12 + 39*a^11 - 297/4*a^10 - 1385/4*a^9 + 29/2*a^8 + 2159/2*a^7 + 507*a^6 - 5751/4*a^5 - 906*a^4 + 3003/4*a^3 + 1695/4*a^2 - 103*a - 59/4,
-7/2*a^14 - 30*a^13 - 59*a^12 + 159*a^11 + 1299/2*a^10 + 38*a^9 - 2072*a^8 - 1450*a^7 + 2669*a^6 + 5207/2*a^5 - 2625/2*a^4 - 1360*a^3 + 441/2*a^2 + 181/2*a - 5
],
[
a,
3364/49429*a^15 - 28373/98858*a^14 - 107815/98858*a^13 + 258788/49429*a^12 + 350948/49429*a^11 - 3787471/98858*a^10 - 2600707/98858*a^9 + 7085854/49429*a^8 + 3337167/49429*a^7 - 14044214/49429*a^6 - 12055899/98858*a^5 + 13153828/49429*a^4 + 12276925/98858*a^3 - 7391141/98858*a^2 - 1965284/49429*a - 162529/98858,
7937/49429*a^15 - 80035/98858*a^14 - 239229/98858*a^13 + 793664/49429*a^12 + 600510/49429*a^11 - 12594013/98858*a^10 - 2013751/98858*a^9 + 25390228/49429*a^8 + 503083/49429*a^7 - 54050496/49429*a^6 - 10121395/98858*a^5 + 54992077/49429*a^4 + 28175043/98858*a^3 - 33332341/98858*a^2 - 5344871/49429*a - 82767/98858,
13927/49429*a^15 - 65146/49429*a^14 - 451983/98858*a^13 + 1307187/49429*a^12 + 1299411/49429*a^11 - 10432928/49429*a^10 - 6129257/98858*a^9 + 41960809/49429*a^8 + 3228040/49429*a^7 - 88189139/49429*a^6 - 7409068/49429*a^5 + 176059573/98858*a^4 + 34422491/98858*a^3 - 26963958/49429*a^2 - 13190897/98858*a + 179455/98858,
-68823/98858*a^15 + 319749/98858*a^14 + 555916/49429*a^13 - 3177931/49429*a^12 - 6425979/98858*a^11 + 50230627/98858*a^10 + 7934153/49429*a^9 - 99992803/49429*a^8 - 10277701/49429*a^7 + 416113753/98858*a^6 + 23198686/49429*a^5 - 411857973/98858*a^4 - 91203129/98858*a^3 + 63067083/49429*a^2 + 34013857/98858*a - 95214/49429,
-182691/197716*a^15 + 213527/49429*a^14 + 2938339/197716*a^13 - 8509457/98858*a^12 - 16723251/197716*a^11 + 67437849/98858*a^10 + 39072321/197716*a^9 - 134692546/49429*a^8 - 21136039/98858*a^7 + 1125412803/197716*a^6 + 102144287/197716*a^5 - 1117812989/197716*a^4 - 57707857/49429*a^3 + 340584749/197716*a^2 + 87448217/197716*a - 555115/197716,
43733/197716*a^15 - 104421/98858*a^14 - 734087/197716*a^13 + 2182945/98858*a^12 + 4283369/197716*a^11 - 9060544/49429*a^10 - 9511945/197716*a^9 + 37852911/49429*a^8 + 3067465/98858*a^7 - 330347305/197716*a^6 - 17025899/197716*a^5 + 342265579/197716*a^4 + 29652905/98858*a^3 - 108729889/197716*a^2 - 24124475/197716*a + 1553055/197716,
-15745/49429*a^15 + 68919/49429*a^14 + 269921/49429*a^13 - 1384684/49429*a^12 - 1745622/49429*a^11 + 11068873/49429*a^10 + 5467284/49429*a^9 - 44565234/49429*a^8 - 10328817/49429*a^7 + 93553252/49429*a^6 + 18237915/49429*a^5 - 92921144/49429*a^4 - 24485211/49429*a^3 + 28542368/49429*a^2 + 8313550/49429*a + 120653/49429,
40653/49429*a^15 - 184451/49429*a^14 - 668744/49429*a^13 + 3665810/49429*a^12 + 3993317/49429*a^11 - 28877289/49429*a^10 - 10592931/49429*a^9 + 114092589/49429*a^8 + 15449149/49429*a^7 - 234202178/49429*a^6 - 30283345/49429*a^5 + 227210030/49429*a^4 + 51818148/49429*a^3 - 67683176/49429*a^2 - 18797898/49429*a + 35034/49429,
-68265/98858*a^15 + 168594/49429*a^14 + 1022737/98858*a^13 - 3289121/49429*a^12 - 5195223/98858*a^11 + 25707277/49429*a^10 + 9493749/98858*a^9 - 102350616/49429*a^8 - 3416775/49429*a^7 + 431431277/98858*a^6 + 39945447/98858*a^5 - 435485439/98858*a^4 - 52753976/49429*a^3 + 132362749/98858*a^2 + 40136677/98858*a + 321753/98858,
133499/98858*a^15 - 317716/49429*a^14 - 1051866/49429*a^13 + 6301174/49429*a^12 + 11556873/98858*a^11 - 49789143/49429*a^10 - 12456539/49429*a^9 + 198841570/49429*a^8 + 11417524/49429*a^7 - 833693139/98858*a^6 - 71222143/98858*a^5 + 417238377/49429*a^4 + 177882947/98858*a^3 - 256907871/98858*a^2 - 34264061/49429*a + 509501/49429,
52165/197716*a^15 - 137423/98858*a^14 - 674431/197716*a^13 + 2600727/98858*a^12 + 1989469/197716*a^11 - 9783468/49429*a^10 + 7013315/197716*a^9 + 37245108/49429*a^8 - 22518647/98858*a^7 - 299718017/197716*a^6 + 58260161/197716*a^5 + 290897251/197716*a^4 + 4557819/98858*a^3 - 84688417/197716*a^2 - 12929043/197716*a + 395459/197716
]
*], q_expansions := [*
q - q^2 - 2*q^3 - q^4 - 4*q^5 + 2*q^6 - 3*q^7 + 3*q^8 + q^9 + 4*q^10 - 4*q^11 + 2*q^12 - 5*q^13 + 3*q^14 + 8*q^15 - q^16 - 3*q^17 - q^18 - 4*q^19 + 4*q^20 + 6*q^21 + 4*q^22 + 8*q^23 - 6*q^24 + 11*q^25 + 5*q^26 + 4*q^27 + 3*q^28 + 2*q^29 - 8*q^30 - 9*q^31 - 5*q^32 + 8*q^33 + 3*q^34 + 12*q^35 - q^36 - 3*q^37 + O(q^38),
q + q^2 + (-1/3*a + 1/3)*q^3 - q^4 + (-1/3*a + 1/3)*q^5 + (-1/3*a + 1/3)*q^6 + (-1/18*a^2 + 1/9*a + 89/18)*q^7 - 3*q^8 + (1/9*a^2 - 2/9*a - 26/9)*q^9 + (-1/3*a + 1/3)*q^10 + (1/3*a + 5/3)*q^11 + (1/3*a - 1/3)*q^12 + (-1/9*a^2 + 8/9*a + 56/9)*q^13 + (-1/18*a^2 + 1/9*a + 89/18)*q^14 + (1/9*a^2 - 2/9*a + 1/9)*q^15 - q^16 + (-1/9*a^2 + 5/9*a + 41/9)*q^17 + (1/9*a^2 - 2/9*a - 26/9)*q^18 + (-1/3*a - 5/3)*q^19 + (1/3*a - 1/3)*q^20 + (-1/3*a + 7/3)*q^21 + (1/3*a + 5/3)*q^22 + (1/3*a + 5/3)*q^23 + (a - 1)*q^24 + (1/9*a^2 - 2/9*a - 44/9)*q^25 + (-1/9*a^2 + 8/9*a + 56/9)*q^26 + (-2/3*a - 10/3)*q^27 + (1/18*a^2 - 1/9*a - 89/18)*q^28 + (-2/3*a + 8/3)*q^29 + (1/9*a^2 - 2/9*a + 1/9)*q^30 + (1/18*a^2 + 2/9*a - 131/18)*q^31 + 5*q^32 + (-1/9*a^2 - 4/9*a + 5/9)*q^33 + (-1/9*a^2 + 5/9*a + 41/9)*q^34 + (-1/3*a + 7/3)*q^35 + (-1/9*a^2 + 2/9*a + 26/9)*q^36 + (2/9*a^2 - 13/9*a - 88/9)*q^37 + O(q^38),
q + a*q^2 + (7/2*a^14 + 30*a^13 + 59*a^12 - 158*a^11 - 1291/2*a^10 - 46*a^9 + 2030*a^8 + 1468*a^7 - 2510*a^6 - 5207/2*a^5 + 2113/2*a^4 + 1328*a^3 - 137/2*a^2 - 153/2*a - 6)*q^3 + (a^2 - 2)*q^4 + (-11/2*a^14 - 95/2*a^13 - 95*a^12 + 248*a^11 + 2073/2*a^10 + 189/2*a^9 - 3276*a^8 - 2403*a^7 + 4121*a^6 + 8483/2*a^5 - 1864*a^4 - 4315/2*a^3 + 429/2*a^2 + 106*a + 13/2)*q^5 + (-5*a^14 - 85/2*a^13 - 81*a^12 + 233*a^11 + 906*a^10 - 21/2*a^9 - 2914*a^8 - 1859*a^7 + 3770*a^6 + 3419*a^5 - 3637/2*a^4 - 3511/2*a^3 + 249*a^2 + 177/2*a + 7/2)*q^6 + (31/4*a^14 + 267/4*a^13 + 263/2*a^12 - 358*a^11 - 5825/4*a^10 - 227/4*a^9 + 9379/2*a^8 + 6327/2*a^7 - 6135*a^6 - 22843/4*a^5 + 6209/2*a^4 + 11653/4*a^3 - 2129/4*a^2 - 243/2*a - 9/4)*q^7 + (a^3 - 4*a)*q^8 + (-11*a^14 - 95*a^13 - 190*a^12 + 496*a^11 + 2073*a^10 + 190*a^9 - 6549*a^8 - 4815*a^7 + 8216*a^6 + 8515*a^5 - 3655*a^4 - 4371*a^3 + 364*a^2 + 252*a + 15)*q^9 + (15/2*a^14 + 129/2*a^13 + 127*a^12 - 344*a^11 - 2803/2*a^10 - 139/2*a^9 + 4483*a^8 + 3098*a^7 - 5774*a^6 - 11153/2*a^5 + 2787*a^4 + 5731/2*a^3 - 811/2*a^2 - 142*a - 11/2)*q^10 + (7/2*a^14 + 31*a^13 + 67*a^12 - 146*a^11 - 1397/2*a^10 - 197*a^9 + 2115*a^8 + 1987*a^7 - 2435*a^6 - 6677/2*a^5 + 1613/2*a^4 + 1740*a^3 + 103/2*a^2 - 281/2*a - 11)*q^11 + (1/2*a^14 + 4*a^13 + 5*a^12 - 33*a^11 - 159/2*a^10 + 93*a^9 + 341*a^8 - 96*a^7 - 666*a^6 + 27/2*a^5 + 1253/2*a^4 + 3*a^3 - 479/2*a^2 + 43/2*a + 7)*q^12 + (2*a^14 + 17*a^13 + 32*a^12 - 97*a^11 - 369*a^10 + 32*a^9 + 1244*a^8 + 677*a^7 - 1780*a^6 - 1306*a^5 + 1114*a^4 + 662*a^3 - 297*a^2 + 5*a + 3)*q^13 + (-43/4*a^14 - 373/4*a^13 - 375/2*a^12 + 489*a^11 + 8205/4*a^10 + 685/4*a^9 - 13079/2*a^8 - 9387/2*a^7 + 8402*a^6 + 33343/4*a^5 - 4054*a^4 - 17071/4*a^3 + 2397/4*a^2 + 207*a + 31/4)*q^14 + (13/2*a^14 + 113/2*a^13 + 115*a^12 - 290*a^11 - 2491/2*a^10 - 317/2*a^9 + 3918*a^8 + 3015*a^7 - 4881*a^6 - 10569/2*a^5 + 2131*a^4 + 5459/2*a^3 - 387/2*a^2 - 171*a - 27/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-21/2*a^14 - 90*a^13 - 176*a^12 + 482*a^11 + 3895/2*a^10 + 81*a^9 - 6233*a^8 - 4278*a^7 + 8027*a^6 + 15465/2*a^5 - 7745/2*a^4 - 3989*a^3 + 1133/2*a^2 + 409/2*a + 4)*q^17 + (15*a^14 + 129*a^13 + 254*a^12 - 688*a^11 - 2802*a^10 - 136*a^9 + 8957*a^8 + 6170*a^7 - 11516*a^6 - 11080*a^5 + 5518*a^4 + 5666*a^3 - 771*a^2 - 282*a - 11)*q^18 + (-8*a^14 - 139/2*a^13 - 141*a^12 + 359*a^11 + 1532*a^10 + 351/2*a^9 - 4842*a^8 - 3650*a^7 + 6101*a^6 + 6423*a^5 - 5545/2*a^4 - 6609/2*a^3 + 328*a^2 + 373/2*a + 7/2)*q^19 + (1/2*a^14 + 9/2*a^13 + 11*a^12 - 15*a^11 - 205/2*a^10 - 157/2*a^9 + 260*a^8 + 427*a^7 - 161*a^6 - 1267/2*a^5 - 149*a^4 + 589/2*a^3 + 253/2*a^2 - 15*a - 11/2)*q^20 + (-22*a^14 - 187*a^13 - 357*a^12 + 1024*a^11 + 3996*a^10 - 31*a^9 - 12883*a^8 - 8246*a^7 + 16784*a^6 + 15160*a^5 - 8305*a^4 - 7780*a^3 + 1276*a^2 + 365*a + 8)*q^21 + (-4*a^14 - 69/2*a^13 - 69*a^12 + 180*a^11 + 755*a^10 + 149/2*a^9 - 2395*a^8 - 1784*a^7 + 3035*a^6 + 3169*a^5 - 2813/2*a^4 - 3271/2*a^3 + 185*a^2 + 167/2*a + 7/2)*q^22 + (-a^14 - 17/2*a^13 - 17*a^12 + 42*a^11 + 181*a^10 + 73/2*a^9 - 543*a^8 - 486*a^7 + 597*a^6 + 824*a^5 - 303/2*a^4 - 835/2*a^3 - 37*a^2 + 67/2*a - 3/2)*q^23 + (9*a^14 + 151/2*a^13 + 140*a^12 - 420*a^11 - 1583*a^10 + 141/2*a^9 + 5106*a^8 + 3145*a^7 - 6616*a^6 - 5874*a^5 + 6381/2*a^4 + 6061/2*a^3 - 430*a^2 - 313/2*a - 13/2)*q^24 + (5*a^14 + 42*a^13 + 78*a^12 - 234*a^11 - 882*a^10 + 45*a^9 + 2852*a^8 + 1717*a^7 - 3729*a^6 - 3185*a^5 + 1865*a^4 + 1589*a^3 - 299*a^2 - 44*a - 1)*q^25 + (-3*a^14 - 26*a^13 - 53*a^12 + 133*a^11 + 576*a^10 + 78*a^9 - 1827*a^8 - 1408*a^7 + 2336*a^6 + 2464*a^5 - 1136*a^4 - 1261*a^3 + 191*a^2 + 57*a + 2)*q^26 + (31*a^14 + 265*a^13 + 515*a^12 - 1425*a^11 - 5709*a^10 - 181*a^9 + 18268*a^8 + 12383*a^7 - 23479*a^6 - 22413*a^5 + 11210*a^4 + 11512*a^3 - 1533*a^2 - 585*a - 27)*q^27 + (-5/4*a^14 - 37/4*a^13 - 21/2*a^12 + 69*a^11 + 639/4*a^10 - 635/4*a^9 - 1227/2*a^8 + 151/2*a^7 + 1030*a^6 + 445/4*a^5 - 1625/2*a^4 - 183/4*a^3 + 1087/4*a^2 - 79/2*a - 25/4)*q^28 + (-15/2*a^14 - 127/2*a^13 - 119*a^12 + 357*a^11 + 2705/2*a^10 - 179/2*a^9 - 4439*a^8 - 2557*a^7 + 6002*a^6 + 9625/2*a^5 - 3277*a^4 - 4841/2*a^3 + 1307/2*a^2 + 50*a - 1/2)*q^29 + (-17/2*a^14 - 147/2*a^13 - 147*a^12 + 386*a^11 + 3219/2*a^10 + 257/2*a^9 - 5123*a^8 - 3672*a^7 + 6552*a^6 + 13037/2*a^5 - 3114*a^4 - 6653/2*a^3 + 867/2*a^2 + 162*a + 13/2)*q^30 + (-1/4*a^14 + 1/4*a^13 + 29/2*a^12 + 39*a^11 - 297/4*a^10 - 1385/4*a^9 + 29/2*a^8 + 2159/2*a^7 + 507*a^6 - 5751/4*a^5 - 906*a^4 + 3003/4*a^3 + 1695/4*a^2 - 103*a - 59/4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (5*a^14 + 41*a^13 + 69*a^12 - 253*a^11 - 836*a^10 + 246*a^9 + 2874*a^8 + 1094*a^7 - 4178*a^6 - 2428*a^5 + 2626*a^4 + 1283*a^3 - 663*a^2 - 27*a + 13)*q^33 + (15*a^14 + 257/2*a^13 + 251*a^12 - 688*a^11 - 2775*a^10 - 223/2*a^9 + 8868*a^8 + 6074*a^7 - 11388*a^6 - 10960*a^5 + 10901/2*a^4 + 11255/2*a^3 - 772*a^2 - 559/2*a - 21/2)*q^34 + (-3/2*a^14 - 14*a^13 - 34*a^12 + 57*a^11 + 679/2*a^10 + 170*a^9 - 1000*a^8 - 1160*a^7 + 1083*a^6 + 3725/2*a^5 - 505/2*a^4 - 955*a^3 - 187/2*a^2 + 151/2*a + 8)*q^35 + (a^14 + 9*a^13 + 22*a^12 - 29*a^11 - 202*a^10 - 168*a^9 + 488*a^8 + 904*a^7 - 197*a^6 - 1387*a^5 - 509*a^4 + 741*a^3 + 385*a^2 - 110*a - 15)*q^36 + (-7/2*a^14 - 30*a^13 - 59*a^12 + 159*a^11 + 1299/2*a^10 + 38*a^9 - 2072*a^8 - 1450*a^7 + 2669*a^6 + 5207/2*a^5 - 2625/2*a^4 - 1360*a^3 + 441/2*a^2 + 181/2*a - 5)*q^37 + O(q^38),
q + a*q^2 + (3364/49429*a^15 - 28373/98858*a^14 - 107815/98858*a^13 + 258788/49429*a^12 + 350948/49429*a^11 - 3787471/98858*a^10 - 2600707/98858*a^9 + 7085854/49429*a^8 + 3337167/49429*a^7 - 14044214/49429*a^6 - 12055899/98858*a^5 + 13153828/49429*a^4 + 12276925/98858*a^3 - 7391141/98858*a^2 - 1965284/49429*a - 162529/98858)*q^3 + (a^2 - 2)*q^4 + (7937/49429*a^15 - 80035/98858*a^14 - 239229/98858*a^13 + 793664/49429*a^12 + 600510/49429*a^11 - 12594013/98858*a^10 - 2013751/98858*a^9 + 25390228/49429*a^8 + 503083/49429*a^7 - 54050496/49429*a^6 - 10121395/98858*a^5 + 54992077/49429*a^4 + 28175043/98858*a^3 - 33332341/98858*a^2 - 5344871/49429*a - 82767/98858)*q^5 + (18723/98858*a^15 - 74175/98858*a^14 - 175168/49429*a^13 + 771448/49429*a^12 + 2462841/98858*a^11 - 12497595/98858*a^10 - 4126358/49429*a^9 + 24846583/49429*a^8 + 7630038/49429*a^7 - 100313803/98858*a^6 - 10939140/49429*a^5 + 94472901/98858*a^4 + 24169907/98858*a^3 - 14068956/49429*a^2 - 7657521/98858*a + 10092/49429)*q^6 + (13927/49429*a^15 - 65146/49429*a^14 - 451983/98858*a^13 + 1307187/49429*a^12 + 1299411/49429*a^11 - 10432928/49429*a^10 - 6129257/98858*a^9 + 41960809/49429*a^8 + 3228040/49429*a^7 - 88189139/49429*a^6 - 7409068/49429*a^5 + 176059573/98858*a^4 + 34422491/98858*a^3 - 26963958/49429*a^2 - 13190897/98858*a + 179455/98858)*q^7 + (a^3 - 4*a)*q^8 + (-22098/49429*a^15 + 109809/49429*a^14 + 325567/49429*a^13 - 2143126/49429*a^12 - 1524728/49429*a^11 + 16652001/49429*a^10 + 1586550/49429*a^9 - 65414973/49429*a^8 + 4054909/49429*a^7 + 135192714/49429*a^6 + 368237/49429*a^5 - 133959445/49429*a^4 - 22606887/49429*a^3 + 40605968/49429*a^2 + 10070272/49429*a - 23957/49429)*q^9 + (31083/98858*a^15 - 159859/98858*a^14 - 230209/49429*a^13 + 1592635/49429*a^12 + 2152933/98858*a^11 - 25364405/98858*a^10 - 1063793/49429*a^9 + 51252261/49429*a^8 - 2912405/49429*a^7 - 218356527/98858*a^6 - 1852717/49429*a^5 + 222107701/98858*a^4 + 41132593/98858*a^3 - 33902197/49429*a^2 - 17766403/98858*a + 23811/49429)*q^10 + (-68823/98858*a^15 + 319749/98858*a^14 + 555916/49429*a^13 - 3177931/49429*a^12 - 6425979/98858*a^11 + 50230627/98858*a^10 + 7934153/49429*a^9 - 99992803/49429*a^8 - 10277701/49429*a^7 + 416113753/98858*a^6 + 23198686/49429*a^5 - 411857973/98858*a^4 - 91203129/98858*a^3 + 63067083/49429*a^2 + 34013857/98858*a - 95214/49429)*q^11 + (21715/49429*a^15 - 199975/98858*a^14 - 656741/98858*a^13 + 1884032/49429*a^12 + 1746140/49429*a^11 - 28219307/98858*a^10 - 7509179/98858*a^9 + 53315761/49429*a^8 + 3484909/49429*a^7 - 105654869/49429*a^6 - 15509427/98858*a^5 + 100146743/49429*a^4 + 35137831/98858*a^3 - 60240593/98858*a^2 - 6488051/49429*a + 381227/98858)*q^12 + (-182691/197716*a^15 + 213527/49429*a^14 + 2938339/197716*a^13 - 8509457/98858*a^12 - 16723251/197716*a^11 + 67437849/98858*a^10 + 39072321/197716*a^9 - 134692546/49429*a^8 - 21136039/98858*a^7 + 1125412803/197716*a^6 + 102144287/197716*a^5 - 1117812989/197716*a^4 - 57707857/49429*a^3 + 340584749/197716*a^2 + 87448217/197716*a - 555115/197716)*q^13 + (32343/49429*a^15 - 312713/98858*a^14 - 489396/49429*a^13 + 3040286/49429*a^12 + 2505255/49429*a^11 - 47102491/98858*a^10 - 4457882/49429*a^9 + 92277278/49429*a^8 + 1542522/49429*a^7 - 190103454/49429*a^6 - 23430775/98858*a^5 + 374714809/98858*a^4 + 38367599/49429*a^3 - 113409589/98858*a^2 - 30849901/98858*a + 41781/49429)*q^14 + (8168/49429*a^15 - 45554/49429*a^14 - 98565/49429*a^13 + 846170/49429*a^12 + 271318/49429*a^11 - 6368676/49429*a^10 + 752313/49429*a^9 + 24945379/49429*a^8 - 3688878/49429*a^7 - 53242761/49429*a^6 - 584116/49429*a^5 + 55857183/49429*a^4 + 12901781/49429*a^3 - 18099924/49429*a^2 - 5795029/49429*a + 113247/49429)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (43733/197716*a^15 - 104421/98858*a^14 - 734087/197716*a^13 + 2182945/98858*a^12 + 4283369/197716*a^11 - 9060544/49429*a^10 - 9511945/197716*a^9 + 37852911/49429*a^8 + 3067465/98858*a^7 - 330347305/197716*a^6 - 17025899/197716*a^5 + 342265579/197716*a^4 + 29652905/98858*a^3 - 108729889/197716*a^2 - 24124475/197716*a + 1553055/197716)*q^17 + (-44877/49429*a^15 + 215077/49429*a^14 + 707516/49429*a^13 - 4286978/49429*a^12 - 3877041/49429*a^11 + 34092708/49429*a^10 + 8237661/49429*a^9 - 137239703/49429*a^8 - 7184700/49429*a^7 + 290249801/49429*a^6 + 24306431/49429*a^5 - 292578153/49429*a^4 - 63055750/49429*a^3 + 89578876/49429*a^2 + 24593215/49429*a - 66294/49429)*q^18 + (-15745/49429*a^15 + 68919/49429*a^14 + 269921/49429*a^13 - 1384684/49429*a^12 - 1745622/49429*a^11 + 11068873/49429*a^10 + 5467284/49429*a^9 - 44565234/49429*a^8 - 10328817/49429*a^7 + 93553252/49429*a^6 + 18237915/49429*a^5 - 92921144/49429*a^4 - 24485211/49429*a^3 + 28542368/49429*a^2 + 8313550/49429*a + 120653/49429)*q^19 + (12987/49429*a^15 - 144933/98858*a^14 - 345979/98858*a^13 + 1431826/49429*a^12 + 554831/49429*a^11 - 22662653/98858*a^10 + 2932385/98858*a^9 + 45679490/49429*a^8 - 10050545/49429*a^7 - 97625122/49429*a^6 + 19734045/98858*a^5 + 100452648/49429*a^4 + 21655873/98858*a^3 - 62938355/98858*a^2 - 6599678/49429*a + 258783/98858)*q^20 + (47817/98858*a^15 - 231619/98858*a^14 - 354613/49429*a^13 + 2221486/49429*a^12 + 3578735/98858*a^11 - 34137611/98858*a^10 - 3220954/49429*a^9 + 66829250/49429*a^8 + 1477954/49429*a^7 - 277165565/98858*a^6 - 8584835/49429*a^5 + 275414063/98858*a^4 + 53424165/98858*a^3 - 41663919/49429*a^2 - 21263511/98858*a - 97240/49429)*q^21 + (-81006/49429*a^15 + 767717/98858*a^14 + 2522305/98858*a^13 - 7514427/49429*a^12 - 6852970/49429*a^11 + 117106939/98858*a^10 + 29401453/98858*a^9 - 230304832/49429*a^8 - 13656418/49429*a^7 + 474608743/49429*a^6 + 81052353/98858*a^5 - 466006860/49429*a^4 - 196714527/98858*a^3 + 281639011/98858*a^2 + 38239197/49429*a - 206469/98858)*q^22 + (40653/49429*a^15 - 184451/49429*a^14 - 668744/49429*a^13 + 3665810/49429*a^12 + 3993317/49429*a^11 - 28877289/49429*a^10 - 10592931/49429*a^9 + 114092589/49429*a^8 + 15449149/49429*a^7 - 234202178/49429*a^6 - 30283345/49429*a^5 + 227210030/49429*a^4 + 51818148/49429*a^3 - 67683176/49429*a^2 - 18797898/49429*a + 35034/49429)*q^23 + (66589/98858*a^15 - 291241/98858*a^14 - 566867/49429*a^13 + 2917619/49429*a^12 + 7201481/98858*a^11 - 46399519/98858*a^10 - 10807618/49429*a^9 + 92637453/49429*a^8 + 18994800/49429*a^7 - 384596561/98858*a^6 - 33497807/49429*a^5 + 376776339/98858*a^4 + 95149723/98858*a^3 - 56480709/49429*a^2 - 32684751/98858*a + 44961/49429)*q^24 + (68653/49429*a^15 - 320810/49429*a^14 - 1087523/49429*a^13 + 6309518/49429*a^12 + 6099915/49429*a^11 - 49349573/49429*a^10 - 14205980/49429*a^9 + 194559962/49429*a^8 + 16700007/49429*a^7 - 401108526/49429*a^6 - 42167919/49429*a^5 + 392951415/49429*a^4 + 88841897/49429*a^3 - 117484075/49429*a^2 - 33187212/49429*a - 94766/49429)*q^25 + (-424729/197716*a^15 + 506221/49429*a^14 + 6548225/197716*a^13 - 19779813/98858*a^12 - 34844241/197716*a^11 + 153905391/98858*a^10 + 70138919/197716*a^9 - 302599583/49429*a^8 - 25832655/98858*a^7 + 2498684825/197716*a^6 + 190619953/197716*a^5 - 2462767375/197716*a^4 - 129104683/49429*a^3 + 744770435/197716*a^2 + 202962659/197716*a - 548073/197716)*q^26 + (-60747/49429*a^15 + 296300/49429*a^14 + 912445/49429*a^13 - 5772613/49429*a^12 - 4562724/49429*a^11 + 44826650/49429*a^10 + 7248303/49429*a^9 - 176184802/49429*a^8 + 1038399/49429*a^7 + 364374960/49429*a^6 + 16667037/49429*a^5 - 360570337/49429*a^4 - 71482721/49429*a^3 + 108819881/49429*a^2 + 29957158/49429*a + 173215/49429)*q^27 + (84381/98858*a^15 - 197389/49429*a^14 - 679978/49429*a^13 + 3933756/49429*a^12 + 7793159/98858*a^11 - 31168579/49429*a^10 - 9392684/49429*a^9 + 124422046/49429*a^8 + 11826415/49429*a^7 - 519225167/98858*a^6 - 58930051/98858*a^5 + 257442457/49429*a^4 + 121187455/98858*a^3 - 155734297/98858*a^2 - 22797424/49429*a - 82426/49429)*q^28 + (-68265/98858*a^15 + 168594/49429*a^14 + 1022737/98858*a^13 - 3289121/49429*a^12 - 5195223/98858*a^11 + 25707277/49429*a^10 + 9493749/98858*a^9 - 102350616/49429*a^8 - 3416775/49429*a^7 + 431431277/98858*a^6 + 39945447/98858*a^5 - 435485439/98858*a^4 - 52753976/49429*a^3 + 132362749/98858*a^2 + 40136677/98858*a + 321753/98858)*q^29 + (11622/49429*a^15 - 57725/49429*a^14 - 207502/49429*a^13 + 1292318/49429*a^12 + 1219396/49429*a^11 - 11262815/49429*a^10 - 2278565/49429*a^9 + 48537314/49429*a^8 - 616337/49429*a^7 - 107731940/49429*a^6 - 2642033/49429*a^5 + 112690237/49429*a^4 + 20216164/49429*a^3 - 35183493/49429*a^2 - 8985905/49429*a + 24504/49429)*q^30 + (133499/98858*a^15 - 317716/49429*a^14 - 1051866/49429*a^13 + 6301174/49429*a^12 + 11556873/98858*a^11 - 49789143/49429*a^10 - 12456539/49429*a^9 + 198841570/49429*a^8 + 11417524/49429*a^7 - 833693139/98858*a^6 - 71222143/98858*a^5 + 417238377/49429*a^4 + 177882947/98858*a^3 - 256907871/98858*a^2 - 34264061/49429*a + 509501/49429)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (61573/49429*a^15 - 298123/49429*a^14 - 927048/49429*a^13 + 5789607/49429*a^12 + 4682750/49429*a^11 - 44793838/49429*a^10 - 7822511/49429*a^9 + 175304110/49429*a^8 + 330168/49429*a^7 - 360799183/49429*a^6 - 17107741/49429*a^5 + 355491485/49429*a^4 + 68700207/49429*a^3 - 107856384/49429*a^2 - 28777820/49429*a + 164016/49429)*q^33 + (97289/197716*a^15 - 257711/98858*a^14 - 1275667/197716*a^13 + 4874997/98858*a^12 + 4385781/197716*a^11 - 18460797/49429*a^10 + 5649555/197716*a^9 + 71440933/49429*a^8 - 24287793/98858*a^7 - 590715393/197716*a^6 + 29049833/197716*a^5 + 593591871/197716*a^4 + 48210807/98858*a^3 - 181475809/197716*a^2 - 47165507/197716*a + 131199/197716)*q^34 + (-3943/98858*a^15 + 15225/98858*a^14 + 25609/49429*a^13 - 105968/49429*a^12 - 271117/98858*a^11 + 1021885/98858*a^10 + 506412/49429*a^9 - 933476/49429*a^8 - 1634596/49429*a^7 + 378781/98858*a^6 + 3093184/49429*a^5 + 2041491/98858*a^4 - 4932375/98858*a^3 - 396991/49429*a^2 + 1522787/98858*a - 83187/49429)*q^35 + (-54866/49429*a^15 + 263513/49429*a^14 + 851021/49429*a^13 - 5200414/49429*a^12 - 4548569/49429*a^11 + 40947726/49429*a^10 + 9162238/49429*a^9 - 163298292/49429*a^8 - 7002528/49429*a^7 + 342617489/49429*a^6 + 28094447/49429*a^5 - 343399169/49429*a^4 - 75725357/49429*a^3 + 104848725/49429*a^2 + 29786140/49429*a - 86717/49429)*q^36 + (52165/197716*a^15 - 137423/98858*a^14 - 674431/197716*a^13 + 2600727/98858*a^12 + 1989469/197716*a^11 - 9783468/49429*a^10 + 7013315/197716*a^9 + 37245108/49429*a^8 - 22518647/98858*a^7 - 299718017/197716*a^6 + 58260161/197716*a^5 + 290897251/197716*a^4 + 4557819/98858*a^3 - 84688417/197716*a^2 - 12929043/197716*a + 395459/197716)*q^37 + O(q^38)
*]> ;  // time = 10.74 seconds




J[434] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 434, 434, 434, 434, 434, 434, 434, 434, 434, 217, 217, 217, 217, 62, 62, 31, 14 ], new_dimensions := [ 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 1, 2, 2, 1 ], dimensions := [ 1, 1, 1, 1, 1, 2, 2, 3, 3, 6, 6, 8, 10, 2, 4, 8, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 17, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 0, 1, 1, 17, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 61, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 17, 1, 1, 1, 1, 5, 1, 3, 1, 3, 1, 1, 1, 17, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 17, 1, 0, 1, 1, 1, 3, 361, 3, 1, 1, 1, 5, 1, 17, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 61, 1, 1, 1, 1, 0, 1, 1, 961, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 1, 1, 3, 1, 1, 1, 0, 121, 3, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 361, 1, 961, 1, 121, 0, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 0 ], ap_traces := [
[ -1, 0, 0, -1, -2, -2, 2, -6, 0, 8, -1, -8 ],
[ 1, 2, 2, -1, -6, 4, 2, -4, -4, 0, -1, 8 ],
[ 1, -3, -3, -1, 4, 4, 2, 6, -9, 5, -1, -2 ],
[ 1, -2, -2, 1, -2, -4, -2, -8, 0, 0, -1, -8 ],
[ 1, 1, 3, 1, 0, -4, -6, 2, -3, 3, 1, 2 ],
[ -2, 2, -2, 2, 0, 8, 0, 4, -6, 10, -2, -8 ],
[ 2, 1, 3, -2, 8, -6, 4, -6, 7, 3, -2, -4 ],
[ -3, -2, -2, -3, 2, 2, -10, 18, 14, 2, 3, 16 ],
[ 3, 1, -1, 3, -4, 12, 6, 10, -7, -9, 3, -14 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 2*x - 1,
x^2 - x - 4,
x^3 + 2*x^2 - 5*x - 8,
x^3 - x^2 - 8*x + 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ -1, 1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, 1 ],
[ -1, -1, -1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ 1, 1, -1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 5, 1, 1 ],
[ 9, 1, 1 ],
[ 17, 1, 7 ],
[ 17, 1, 1 ],
[ 61, 25, 1 ],
[ 85, 5, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 5, 1, 1 ],
[ 9, 1, 1 ],
[ 1, 1, 1 ],
[ 17, 1, 1 ],
[ 1, 1, 1 ],
[ 85, 5, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 3, 1, 1, 1, 5 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 3, 0, 1, 1, 17, 1, 17 ], analytic_sha_upper_bounds := [ 0, 1, 1, 0, 1, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 0, 1/9, 1, 1, 1, 1/25 ], eigenvalues := [*
[ -1, 0, 0, -1, -2, -2, 2, -6, 0, 8, -1, -8 ],
[ 1, 2, 2, -1, -6, 4, 2, -4, -4, 0, -1, 8 ],
[ 1, -3, -3, -1, 4, 4, 2, 6, -9, 5, -1, -2 ],
[ 1, -2, -2, 1, -2, -4, -2, -8, 0, 0, -1, -8 ],
[ 1, 1, 3, 1, 0, -4, -6, 2, -3, 3, 1, 2 ],
[
-1,
a,
2*a - 3,
1,
0,
-2*a + 6,
-2*a + 2,
2,
-a - 2,
-a + 6,
-1,
-2*a - 2
],
[
1,
a,
-a + 2,
-1,
4,
-2*a - 2,
2,
2*a - 4,
-a + 4,
-a + 2,
-1,
-2
],
[
-1,
a,
-a^2 + 4,
-1,
-2*a^2 + 10,
2*a + 2,
2*a - 2,
6,
2*a^2 + a - 4,
-2*a^2 - 3*a + 8,
1,
-2*a^2 + 2*a + 16
],
[
1,
a,
-a,
1,
-a^2 + a + 4,
4,
-a^2 - a + 8,
a^2 - a - 2,
-a - 2,
a^2 - 2*a - 8,
1,
-2*a - 4
]
*], q_expansions := [*
q - q^2 + q^4 - q^7 - q^8 - 3*q^9 - 2*q^11 - 2*q^13 + q^14 + q^16 + 2*q^17 + 3*q^18 - 6*q^19 + 2*q^22 - 5*q^25 + 2*q^26 - q^28 + 8*q^29 - q^31 - q^32 - 2*q^34 - 3*q^36 - 8*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 + 2*q^5 + 2*q^6 - q^7 + q^8 + q^9 + 2*q^10 - 6*q^11 + 2*q^12 + 4*q^13 - q^14 + 4*q^15 + q^16 + 2*q^17 + q^18 - 4*q^19 + 2*q^20 - 2*q^21 - 6*q^22 - 4*q^23 + 2*q^24 - q^25 + 4*q^26 - 4*q^27 - q^28 + 4*q^30 - q^31 + q^32 - 12*q^33 + 2*q^34 - 2*q^35 + q^36 + 8*q^37 + O(q^38),
q + q^2 - 3*q^3 + q^4 - 3*q^5 - 3*q^6 - q^7 + q^8 + 6*q^9 - 3*q^10 + 4*q^11 - 3*q^12 + 4*q^13 - q^14 + 9*q^15 + q^16 + 2*q^17 + 6*q^18 + 6*q^19 - 3*q^20 + 3*q^21 + 4*q^22 - 9*q^23 - 3*q^24 + 4*q^25 + 4*q^26 - 9*q^27 - q^28 + 5*q^29 + 9*q^30 - q^31 + q^32 - 12*q^33 + 2*q^34 + 3*q^35 + 6*q^36 - 2*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 2*q^5 - 2*q^6 + q^7 + q^8 + q^9 - 2*q^10 - 2*q^11 - 2*q^12 - 4*q^13 + q^14 + 4*q^15 + q^16 - 2*q^17 + q^18 - 8*q^19 - 2*q^20 - 2*q^21 - 2*q^22 - 2*q^24 - q^25 - 4*q^26 + 4*q^27 + q^28 + 4*q^30 - q^31 + q^32 + 4*q^33 - 2*q^34 - 2*q^35 + q^36 - 8*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + 3*q^5 + q^6 + q^7 + q^8 - 2*q^9 + 3*q^10 + q^12 - 4*q^13 + q^14 + 3*q^15 + q^16 - 6*q^17 - 2*q^18 + 2*q^19 + 3*q^20 + q^21 - 3*q^23 + q^24 + 4*q^25 - 4*q^26 - 5*q^27 + q^28 + 3*q^29 + 3*q^30 + q^31 + q^32 - 6*q^34 + 3*q^35 - 2*q^36 + 2*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (2*a - 3)*q^5 - a*q^6 + q^7 - q^8 + (2*a - 2)*q^9 + (-2*a + 3)*q^10 + a*q^12 + (-2*a + 6)*q^13 - q^14 + (a + 2)*q^15 + q^16 + (-2*a + 2)*q^17 + (-2*a + 2)*q^18 + 2*q^19 + (2*a - 3)*q^20 + a*q^21 + (-a - 2)*q^23 - a*q^24 + (-4*a + 8)*q^25 + (2*a - 6)*q^26 + (-a + 2)*q^27 + q^28 + (-a + 6)*q^29 + (-a - 2)*q^30 - q^31 - q^32 + (2*a - 2)*q^34 + (2*a - 3)*q^35 + (2*a - 2)*q^36 + (-2*a - 2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a + 2)*q^5 + a*q^6 - q^7 + q^8 + (a + 1)*q^9 + (-a + 2)*q^10 + 4*q^11 + a*q^12 + (-2*a - 2)*q^13 - q^14 + (a - 4)*q^15 + q^16 + 2*q^17 + (a + 1)*q^18 + (2*a - 4)*q^19 + (-a + 2)*q^20 - a*q^21 + 4*q^22 + (-a + 4)*q^23 + a*q^24 + (-3*a + 3)*q^25 + (-2*a - 2)*q^26 + (-a + 4)*q^27 - q^28 + (-a + 2)*q^29 + (a - 4)*q^30 - q^31 + q^32 + 4*a*q^33 + 2*q^34 + (a - 2)*q^35 + (a + 1)*q^36 - 2*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a^2 + 4)*q^5 - a*q^6 - q^7 - q^8 + (a^2 - 3)*q^9 + (a^2 - 4)*q^10 + (-2*a^2 + 10)*q^11 + a*q^12 + (2*a + 2)*q^13 + q^14 + (2*a^2 - a - 8)*q^15 + q^16 + (2*a - 2)*q^17 + (-a^2 + 3)*q^18 + 6*q^19 + (-a^2 + 4)*q^20 - a*q^21 + (2*a^2 - 10)*q^22 + (2*a^2 + a - 4)*q^23 - a*q^24 + (a^2 - 2*a - 5)*q^25 + (-2*a - 2)*q^26 + (-2*a^2 - a + 8)*q^27 - q^28 + (-2*a^2 - 3*a + 8)*q^29 + (-2*a^2 + a + 8)*q^30 + q^31 - q^32 + (4*a^2 - 16)*q^33 + (-2*a + 2)*q^34 + (a^2 - 4)*q^35 + (a^2 - 3)*q^36 + (-2*a^2 + 2*a + 16)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - a*q^5 + a*q^6 + q^7 + q^8 + (a^2 - 3)*q^9 - a*q^10 + (-a^2 + a + 4)*q^11 + a*q^12 + 4*q^13 + q^14 - a^2*q^15 + q^16 + (-a^2 - a + 8)*q^17 + (a^2 - 3)*q^18 + (a^2 - a - 2)*q^19 - a*q^20 + a*q^21 + (-a^2 + a + 4)*q^22 + (-a - 2)*q^23 + a*q^24 + (a^2 - 5)*q^25 + 4*q^26 + (a^2 + 2*a - 4)*q^27 + q^28 + (a^2 - 2*a - 8)*q^29 - a^2*q^30 + q^31 + q^32 + (-4*a + 4)*q^33 + (-a^2 - a + 8)*q^34 - a*q^35 + (a^2 - 3)*q^36 + (-2*a - 4)*q^37 + O(q^38)
*]> ;  // time = 221.36 seconds




J[435] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 435, 435, 435, 435, 435, 435, 435, 435, 435, 435, 145, 145, 145, 145, 87, 87, 29, 15 ], new_dimensions := [ 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 1, 2, 3, 3, 2, 3, 2, 1 ], dimensions := [ 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 2, 4, 6, 6, 4, 6, 8, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 7, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 17, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 1, 1, 17, 0, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 19, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 0, 1, 1, 1, 1, 49, 1, 5, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 625, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 0, 5, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 5, 0, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 529, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 49, 625, 1, 1, 529, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 0, -1, -1, -2, 1, 6, 4, -2, 3, 1, -4, -3 ],
[ 0, 1, -1, 2, 3, 2, 0, 2, 3, -1, 8, -1 ],
[ 1, 1, 1, 4, -4, 6, 6, -4, -4, 1, -8, 2 ],
[ -1, 1, 1, -4, 0, 6, 2, 8, -4, 1, 4, 6 ],
[ 0, 2, -2, 4, -4, 4, 0, 4, -4, -2, -4, 8 ],
[ -1, 2, -2, -6, -2, -8, -2, 2, 0, 2, -16, -16 ],
[ 1, 2, 2, 2, -7, -4, -6, 2, 9, 2, 8, 9 ],
[ -1, 2, 2, 2, 10, 0, -6, -2, -8, 2, 8, -8 ],
[ 1, -3, 3, -4, 9, 6, 2, -4, 1, -3, 0, 13 ],
[ -3, -4, -4, 2, -2, -8, -10, -2, -12, -4, -4, -16 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 5,
x^2 + x - 1,
x^2 - x - 4,
x^2 + x - 5,
x^3 - x^2 - 5*x + 4,
x^4 + 3*x^3 - 2*x^2 - 7*x + 1
], atkin_lehners := [
[ 1, 1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ],
[ -1, -1, -1 ],
[ -1, 1, 1 ],
[ -1, 1, -1 ],
[ -1, -1, -1 ],
[ -1, -1, -1 ],
[ 1, -1, 1 ],
[ 1, 1, 1 ]
], component_group_orders := [
[ 5, 7, 1 ],
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 11, 1 ],
[ 19, 1, 1 ],
[ 9, 1, 1 ],
[ 7, 7, 1 ],
[ 19, 1, 7 ],
[ 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 19, 1, 1 ],
[ 9, 1, 1 ],
[ 7, 7, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 1, 1, 1, 1, 7, 1, 1 ], torsion_lower_bounds := [ 1, 3, 1, 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 1, 1/3, 1, 1, 1, 0, 9, 1, 1, 0 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 1, 0, 1, 1, 1, 0 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1, 1, 0, 1, 1/49, 1, 0 ], eigenvalues := [*
[ 0, -1, -1, -2, 1, 6, 4, -2, 3, 1, -4, -3 ],
[ 0, 1, -1, 2, 3, 2, 0, 2, 3, -1, 8, -1 ],
[ 1, 1, 1, 4, -4, 6, 6, -4, -4, 1, -8, 2 ],
[ -1, 1, 1, -4, 0, 6, 2, 8, -4, 1, 4, 6 ],
[
a,
1,
-1,
2,
-2,
2,
-2*a,
2,
-2,
-1,
-2,
-2*a + 4
],
[
a,
1,
-1,
-3,
-4*a - 3,
-2*a - 5,
4*a + 1,
6*a + 4,
0,
1,
-8,
-8
],
[
a,
1,
1,
-2*a + 2,
-a - 3,
-2,
2*a - 4,
-2*a + 2,
-a + 5,
1,
4,
3*a + 3
],
[
a,
1,
1,
1,
5,
-2*a - 1,
-3,
2*a,
-4,
1,
4,
-4
],
[
a,
-1,
1,
-a^2 + a + 2,
3,
a^2 + a - 2,
-a^2 + a + 4,
-2*a^2 + 6,
-a^2 - 3*a + 5,
-1,
0,
-a^2 - 3*a + 9
],
[
a,
-1,
-1,
-a^3 - 3*a^2 + a + 5,
a^3 + 3*a^2 - a - 5,
a^3 + a^2 - 5*a - 3,
-a^3 - a^2 + 3*a - 3,
2*a^3 + 4*a^2 - 6*a - 6,
-2*a^3 - 2*a^2 + 6*a - 4,
-1,
2*a^3 + 2*a^2 - 6*a,
2*a^2 + 6*a - 6
]
*], q_expansions := [*
q - q^3 - 2*q^4 - q^5 - 2*q^7 + q^9 + q^11 + 2*q^12 + 6*q^13 + q^15 + 4*q^16 + 4*q^17 - 2*q^19 + 2*q^20 + 2*q^21 + 3*q^23 + q^25 - q^27 + 4*q^28 + q^29 - 4*q^31 - q^33 + 2*q^35 - 2*q^36 - 3*q^37 + O(q^38),
q + q^3 - 2*q^4 - q^5 + 2*q^7 + q^9 + 3*q^11 - 2*q^12 + 2*q^13 - q^15 + 4*q^16 + 2*q^19 + 2*q^20 + 2*q^21 + 3*q^23 + q^25 + q^27 - 4*q^28 - q^29 + 8*q^31 + 3*q^33 - 2*q^35 - 2*q^36 - q^37 + O(q^38),
q + q^2 + q^3 - q^4 + q^5 + q^6 + 4*q^7 - 3*q^8 + q^9 + q^10 - 4*q^11 - q^12 + 6*q^13 + 4*q^14 + q^15 - q^16 + 6*q^17 + q^18 - 4*q^19 - q^20 + 4*q^21 - 4*q^22 - 4*q^23 - 3*q^24 + q^25 + 6*q^26 + q^27 - 4*q^28 + q^29 + q^30 - 8*q^31 + 5*q^32 - 4*q^33 + 6*q^34 + 4*q^35 - q^36 + 2*q^37 + O(q^38),
q - q^2 + q^3 - q^4 + q^5 - q^6 - 4*q^7 + 3*q^8 + q^9 - q^10 - q^12 + 6*q^13 + 4*q^14 + q^15 - q^16 + 2*q^17 - q^18 + 8*q^19 - q^20 - 4*q^21 - 4*q^23 + 3*q^24 + q^25 - 6*q^26 + q^27 + 4*q^28 + q^29 - q^30 + 4*q^31 - 5*q^32 - 2*q^34 - 4*q^35 - q^36 + 6*q^37 + O(q^38),
q + a*q^2 + q^3 + 3*q^4 - q^5 + a*q^6 + 2*q^7 + a*q^8 + q^9 - a*q^10 - 2*q^11 + 3*q^12 + 2*q^13 + 2*a*q^14 - q^15 - q^16 - 2*a*q^17 + a*q^18 + 2*q^19 - 3*q^20 + 2*q^21 - 2*a*q^22 - 2*q^23 + a*q^24 + q^25 + 2*a*q^26 + q^27 + 6*q^28 - q^29 - a*q^30 - 2*q^31 - 3*a*q^32 - 2*q^33 - 10*q^34 - 2*q^35 + 3*q^36 + (-2*a + 4)*q^37 + O(q^38),
q + a*q^2 + q^3 + (-a - 1)*q^4 - q^5 + a*q^6 - 3*q^7 + (-2*a - 1)*q^8 + q^9 - a*q^10 + (-4*a - 3)*q^11 + (-a - 1)*q^12 + (-2*a - 5)*q^13 - 3*a*q^14 - q^15 + 3*a*q^16 + (4*a + 1)*q^17 + a*q^18 + (6*a + 4)*q^19 + (a + 1)*q^20 - 3*q^21 + (a - 4)*q^22 + (-2*a - 1)*q^24 + q^25 + (-3*a - 2)*q^26 + q^27 + (3*a + 3)*q^28 + q^29 - a*q^30 - 8*q^31 + (a + 5)*q^32 + (-4*a - 3)*q^33 + (-3*a + 4)*q^34 + 3*q^35 + (-a - 1)*q^36 - 8*q^37 + O(q^38),
q + a*q^2 + q^3 + (a + 2)*q^4 + q^5 + a*q^6 + (-2*a + 2)*q^7 + (a + 4)*q^8 + q^9 + a*q^10 + (-a - 3)*q^11 + (a + 2)*q^12 - 2*q^13 - 8*q^14 + q^15 + 3*a*q^16 + (2*a - 4)*q^17 + a*q^18 + (-2*a + 2)*q^19 + (a + 2)*q^20 + (-2*a + 2)*q^21 + (-4*a - 4)*q^22 + (-a + 5)*q^23 + (a + 4)*q^24 + q^25 - 2*a*q^26 + q^27 + (-4*a - 4)*q^28 + q^29 + a*q^30 + 4*q^31 + (a + 4)*q^32 + (-a - 3)*q^33 + (-2*a + 8)*q^34 + (-2*a + 2)*q^35 + (a + 2)*q^36 + (3*a + 3)*q^37 + O(q^38),
q + a*q^2 + q^3 + (-a + 3)*q^4 + q^5 + a*q^6 + q^7 + (2*a - 5)*q^8 + q^9 + a*q^10 + 5*q^11 + (-a + 3)*q^12 + (-2*a - 1)*q^13 + a*q^14 + q^15 + (-5*a + 4)*q^16 - 3*q^17 + a*q^18 + 2*a*q^19 + (-a + 3)*q^20 + q^21 + 5*a*q^22 - 4*q^23 + (2*a - 5)*q^24 + q^25 + (a - 10)*q^26 + q^27 + (-a + 3)*q^28 + q^29 + a*q^30 + 4*q^31 + (5*a - 15)*q^32 + 5*q^33 - 3*a*q^34 + q^35 + (-a + 3)*q^36 - 4*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + q^5 - a*q^6 + (-a^2 + a + 2)*q^7 + (a^2 + a - 4)*q^8 + q^9 + a*q^10 + 3*q^11 + (-a^2 + 2)*q^12 + (a^2 + a - 2)*q^13 + (-3*a + 4)*q^14 - q^15 + a*q^16 + (-a^2 + a + 4)*q^17 + a*q^18 + (-2*a^2 + 6)*q^19 + (a^2 - 2)*q^20 + (a^2 - a - 2)*q^21 + 3*a*q^22 + (-a^2 - 3*a + 5)*q^23 + (-a^2 - a + 4)*q^24 + q^25 + (2*a^2 + 3*a - 4)*q^26 - q^27 + (-a^2 + 2*a - 4)*q^28 - q^29 - a*q^30 + (-a^2 - 2*a + 8)*q^32 - 3*q^33 + (-a + 4)*q^34 + (-a^2 + a + 2)*q^35 + (a^2 - 2)*q^36 + (-a^2 - 3*a + 9)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 - q^5 - a*q^6 + (-a^3 - 3*a^2 + a + 5)*q^7 + (a^3 - 4*a)*q^8 + q^9 - a*q^10 + (a^3 + 3*a^2 - a - 5)*q^11 + (-a^2 + 2)*q^12 + (a^3 + a^2 - 5*a - 3)*q^13 + (-a^2 - 2*a + 1)*q^14 + q^15 + (-3*a^3 - 4*a^2 + 7*a + 3)*q^16 + (-a^3 - a^2 + 3*a - 3)*q^17 + a*q^18 + (2*a^3 + 4*a^2 - 6*a - 6)*q^19 + (-a^2 + 2)*q^20 + (a^3 + 3*a^2 - a - 5)*q^21 + (a^2 + 2*a - 1)*q^22 + (-2*a^3 - 2*a^2 + 6*a - 4)*q^23 + (-a^3 + 4*a)*q^24 + q^25 + (-2*a^3 - 3*a^2 + 4*a - 1)*q^26 - q^27 + (a^3 + 4*a^2 - a - 10)*q^28 - q^29 + a*q^30 + (2*a^3 + 2*a^2 - 6*a)*q^31 + (3*a^3 + a^2 - 10*a + 3)*q^32 + (-a^3 - 3*a^2 + a + 5)*q^33 + (2*a^3 + a^2 - 10*a + 1)*q^34 + (a^3 + 3*a^2 - a - 5)*q^35 + (a^2 - 2)*q^36 + (2*a^2 + 6*a - 6)*q^37 + O(q^38)
*]> ;  // time = 172.879 seconds




J[437] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 437, 437, 437, 437, 437, 437, 437, 437, 23, 19 ], new_dimensions := [ 1, 1, 2, 2, 2, 5, 8, 12, 2, 1 ], dimensions := [ 1, 1, 2, 2, 2, 5, 8, 12, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 11, 1, 1, 1, 1, 1, 5, 1, 0, 9, 1, 1, 1, 11, 1, 1, 1, 1, 9, 0, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 0, 1, 81, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 11, 1, 1, 81, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0 ], ap_traces := [
[ 2, 2, 1, -3, 5, -2, 3, -1, 1, 4, -4, -8 ],
[ 0, 2, -1, -5, -1, 0, -7, 1, 1, 6, 4, 2 ],
[ -2, -3, 2, 1, -5, 0, 2, -2, -2, -10, -15, -9 ],
[ 0, -1, -2, -5, -7, 0, 6, 2, 2, 2, -7, -21 ],
[ 0, -4, -2, -2, 2, 0, -6, 2, 2, -4, 8, 0 ],
[ -1, -4, -1, -9, -1, -10, 5, -5, -5, 10, -4, -14 ],
[ 0, 5, 2, 9, 7, 8, -10, -8, 8, -8, 13, 27 ],
[ 2, 7, -1, 14, 4, 2, 9, 12, -12, 2, 17, 9 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - x - 1,
x^2 - 5,
x^2 - 2,
x^5 + x^4 - 7*x^3 - 2*x^2 + 12*x - 4,
x^8 - 13*x^6 + 47*x^4 - 2*x^3 - 37*x^2 - 2*x + 2,
x^12 - 2*x^11 - 19*x^10 + 35*x^9 + 137*x^8 - 219*x^7 - 483*x^6 + 605*x^5 + 866*x^4 - 707*x^3 - 682*x^2 + 236*x + 96
], atkin_lehners := [
[ 1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 11, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 81, 5 ],
[ 3, 9 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 11, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 5 ],
[ 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 5, 3 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 5, 3 ], l_ratios := [ 1, 0, 0, 0, 0, 0, 1/5, 1/3 ], analytic_sha_upper_bounds := [ 1, 0, 0, 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 0, 0, 0, 1, 1 ], eigenvalues := [*
[ 2, 2, 1, -3, 5, -2, 3, -1, 1, 4, -4, -8 ],
[ 0, 2, -1, -5, -1, 0, -7, 1, 1, 6, 4, 2 ],
[
-1,
-a - 1,
-2*a + 2,
3*a - 1,
3*a - 4,
-4*a + 2,
2*a,
-1,
-1,
2*a - 6,
a - 8,
a - 5
],
[
a,
-1/2*a - 1/2,
-a - 1,
-1/2*a - 5/2,
-1/2*a - 7/2,
2*a,
a + 3,
1,
1,
a + 1,
-5/2*a - 7/2,
-1/2*a - 21/2
],
[
a,
a - 2,
-a - 1,
a - 1,
a + 1,
-4*a,
a - 3,
1,
1,
-5*a - 2,
2*a + 4,
a
],
[
a,
-a^2 - a + 2,
a^2 + a - 3,
-a^2 - a + 1,
-a^4 - a^3 + 6*a^2 + a - 7,
-a^4 - 2*a^3 + 5*a^2 + 6*a - 8,
2*a^4 + 2*a^3 - 11*a^2 - 5*a + 11,
-1,
-1,
-a^4 - 3*a^3 + 2*a^2 + 7*a + 2,
2*a^4 + 5*a^3 - 8*a^2 - 14*a + 8,
-2*a^4 - 5*a^3 + 9*a^2 + 17*a - 14
],
[
a,
-3/10*a^7 + 1/10*a^6 + 37/10*a^5 - 9/10*a^4 - 64/5*a^3 + 11/5*a^2 + 51/5*a + 6/5,
1/10*a^7 + 3/10*a^6 - 7/5*a^5 - 16/5*a^4 + 51/10*a^3 + 81/10*a^2 - 17/5*a - 12/5,
-1/2*a^7 + 13/2*a^5 - 1/2*a^4 - 23*a^3 + 9/2*a^2 + 16*a,
-1/5*a^7 - 1/10*a^6 + 23/10*a^5 + 19/10*a^4 - 67/10*a^3 - 41/5*a^2 + 14/5*a + 29/5,
3/10*a^7 - 1/10*a^6 - 21/5*a^5 + 7/5*a^4 + 163/10*a^3 - 47/10*a^2 - 66/5*a - 1/5,
3/10*a^7 - 1/10*a^6 - 21/5*a^5 + 7/5*a^4 + 173/10*a^3 - 57/10*a^2 - 91/5*a + 4/5,
-1,
1,
-3/10*a^7 + 1/10*a^6 + 21/5*a^5 - 12/5*a^4 - 153/10*a^3 + 117/10*a^2 + 31/5*a - 19/5,
1/10*a^7 + 3/10*a^6 - 19/10*a^5 - 27/10*a^4 + 48/5*a^3 + 23/5*a^2 - 62/5*a + 8/5,
-6/5*a^7 + 2/5*a^6 + 153/10*a^5 - 51/10*a^4 - 527/10*a^3 + 203/10*a^2 + 159/5*a - 21/5
],
[
a,
-47/244*a^11 + 91/244*a^10 + 391/122*a^9 - 23/4*a^8 - 1137/61*a^7 + 117/4*a^6 + 5647/122*a^5 - 13993/244*a^4 - 10833/244*a^3 + 2207/61*a^2 + 299/61*a - 140/61,
-6/61*a^11 + 22/61*a^10 + 175/122*a^9 - 6*a^8 - 395/61*a^7 + 69/2*a^6 + 1099/122*a^5 - 5044/61*a^4 + 120/61*a^3 + 9121/122*a^2 - 408/61*a - 675/61,
5/244*a^11 + 63/244*a^10 - 50/61*a^9 - 17/4*a^8 + 1105/122*a^7 + 97/4*a^6 - 2327/61*a^5 - 14239/244*a^4 + 14601/244*a^3 + 3311/61*a^2 - 1379/61*a - 355/61,
7/122*a^11 + 15/122*a^10 - 79/61*a^9 - 5/2*a^8 + 1325/122*a^7 + 37/2*a^6 - 4967/122*a^5 - 3605/61*a^4 + 7607/122*a^3 + 8623/122*a^2 - 1348/61*a - 567/61,
-13/122*a^11 + 7/122*a^10 + 215/122*a^9 - 1/2*a^8 - 616/61*a^7 - a^6 + 2985/122*a^5 + 1861/122*a^4 - 2973/122*a^3 - 3605/122*a^2 + 473/61*a + 626/61,
13/122*a^11 - 7/122*a^10 - 215/122*a^9 + 1/2*a^8 + 616/61*a^7 + a^6 - 2985/122*a^5 - 1861/122*a^4 + 2851/122*a^3 + 3483/122*a^2 - 168/61*a - 321/61,
1,
-1,
8/61*a^11 + 43/122*a^10 - 198/61*a^9 - 6*a^8 + 3473/122*a^7 + 73/2*a^6 - 6487/61*a^5 - 5983/61*a^4 + 19383/122*a^3 + 6465/61*a^2 - 3787/61*a - 930/61,
1/122*a^11 - 85/122*a^10 + 41/61*a^9 + 12*a^8 - 694/61*a^7 - 73*a^6 + 6959/122*a^5 + 23187/122*a^4 - 6232/61*a^3 - 11571/61*a^2 + 2840/61*a + 1688/61,
1/4*a^11 - 5/4*a^10 - 3*a^9 + 81/4*a^8 + 7*a^7 - 449/4*a^6 + 21*a^5 + 1027/4*a^4 - 313/4*a^3 - 437/2*a^2 + 50*a + 26
]
*], q_expansions := [*
q + 2*q^2 + 2*q^3 + 2*q^4 + q^5 + 4*q^6 - 3*q^7 + q^9 + 2*q^10 + 5*q^11 + 4*q^12 - 2*q^13 - 6*q^14 + 2*q^15 - 4*q^16 + 3*q^17 + 2*q^18 - q^19 + 2*q^20 - 6*q^21 + 10*q^22 + q^23 - 4*q^25 - 4*q^26 - 4*q^27 - 6*q^28 + 4*q^29 + 4*q^30 - 4*q^31 - 8*q^32 + 10*q^33 + 6*q^34 - 3*q^35 + 2*q^36 - 8*q^37 + O(q^38),
q + 2*q^3 - 2*q^4 - q^5 - 5*q^7 + q^9 - q^11 - 4*q^12 - 2*q^15 + 4*q^16 - 7*q^17 + q^19 + 2*q^20 - 10*q^21 + q^23 - 4*q^25 - 4*q^27 + 10*q^28 + 6*q^29 + 4*q^31 - 2*q^33 + 5*q^35 - 2*q^36 + 2*q^37 + O(q^38),
q - q^2 + (-a - 1)*q^3 - q^4 + (-2*a + 2)*q^5 + (a + 1)*q^6 + (3*a - 1)*q^7 + 3*q^8 + (3*a - 1)*q^9 + (2*a - 2)*q^10 + (3*a - 4)*q^11 + (a + 1)*q^12 + (-4*a + 2)*q^13 + (-3*a + 1)*q^14 + 2*a*q^15 - q^16 + 2*a*q^17 + (-3*a + 1)*q^18 - q^19 + (2*a - 2)*q^20 + (-5*a - 2)*q^21 + (-3*a + 4)*q^22 - q^23 + (-3*a - 3)*q^24 + (-4*a + 3)*q^25 + (4*a - 2)*q^26 + (-2*a + 1)*q^27 + (-3*a + 1)*q^28 + (2*a - 6)*q^29 - 2*a*q^30 + (a - 8)*q^31 - 5*q^32 + (-2*a + 1)*q^33 - 2*a*q^34 + (2*a - 8)*q^35 + (-3*a + 1)*q^36 + (a - 5)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a - 1/2)*q^3 + 3*q^4 + (-a - 1)*q^5 + (-1/2*a - 5/2)*q^6 + (-1/2*a - 5/2)*q^7 + a*q^8 + (1/2*a - 3/2)*q^9 + (-a - 5)*q^10 + (-1/2*a - 7/2)*q^11 + (-3/2*a - 3/2)*q^12 + 2*a*q^13 + (-5/2*a - 5/2)*q^14 + (a + 3)*q^15 - q^16 + (a + 3)*q^17 + (-3/2*a + 5/2)*q^18 + q^19 + (-3*a - 3)*q^20 + (3/2*a + 5/2)*q^21 + (-7/2*a - 5/2)*q^22 + q^23 + (-1/2*a - 5/2)*q^24 + (2*a + 1)*q^25 + 10*q^26 + (2*a + 1)*q^27 + (-3/2*a - 15/2)*q^28 + (a + 1)*q^29 + (3*a + 5)*q^30 + (-5/2*a - 7/2)*q^31 - 3*a*q^32 + (2*a + 3)*q^33 + (3*a + 5)*q^34 + (3*a + 5)*q^35 + (3/2*a - 9/2)*q^36 + (-1/2*a - 21/2)*q^37 + O(q^38),
q + a*q^2 + (a - 2)*q^3 + (-a - 1)*q^5 + (-2*a + 2)*q^6 + (a - 1)*q^7 - 2*a*q^8 + (-4*a + 3)*q^9 + (-a - 2)*q^10 + (a + 1)*q^11 - 4*a*q^13 + (-a + 2)*q^14 + a*q^15 - 4*q^16 + (a - 3)*q^17 + (3*a - 8)*q^18 + q^19 + (-3*a + 4)*q^21 + (a + 2)*q^22 + q^23 + (4*a - 4)*q^24 + (2*a - 2)*q^25 - 8*q^26 + (8*a - 8)*q^27 + (-5*a - 2)*q^29 + 2*q^30 + (2*a + 4)*q^31 - a*q^33 + (-3*a + 2)*q^34 - q^35 + a*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 2)*q^3 + (a^2 - 2)*q^4 + (a^2 + a - 3)*q^5 + (-a^3 - a^2 + 2*a)*q^6 + (-a^2 - a + 1)*q^7 + (a^3 - 4*a)*q^8 + (a^4 + 2*a^3 - 3*a^2 - 4*a + 1)*q^9 + (a^3 + a^2 - 3*a)*q^10 + (-a^4 - a^3 + 6*a^2 + a - 7)*q^11 + (-a^4 - a^3 + 4*a^2 + 2*a - 4)*q^12 + (-a^4 - 2*a^3 + 5*a^2 + 6*a - 8)*q^13 + (-a^3 - a^2 + a)*q^14 + (-a^4 - 2*a^3 + 4*a^2 + 5*a - 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^4 + 2*a^3 - 11*a^2 - 5*a + 11)*q^17 + (a^4 + 4*a^3 - 2*a^2 - 11*a + 4)*q^18 - q^19 + (a^4 + a^3 - 5*a^2 - 2*a + 6)*q^20 + (a^4 + 2*a^3 - 2*a^2 - 3*a + 2)*q^21 + (-a^3 - a^2 + 5*a - 4)*q^22 - q^23 + (-a^3 + 2*a^2 + 4*a - 4)*q^24 + (a^4 + 2*a^3 - 5*a^2 - 6*a + 4)*q^25 + (-a^4 - 2*a^3 + 4*a^2 + 4*a - 4)*q^26 + (-2*a^4 - 5*a^3 + 8*a^2 + 14*a - 12)*q^27 + (-a^4 - a^3 + 3*a^2 + 2*a - 2)*q^28 + (-a^4 - 3*a^3 + 2*a^2 + 7*a + 2)*q^29 + (-a^4 - 3*a^3 + 3*a^2 + 6*a - 4)*q^30 + (2*a^4 + 5*a^3 - 8*a^2 - 14*a + 8)*q^31 + (-a^4 - a^3 + 2*a^2 + 4)*q^32 + (-a^4 + 8*a^2 + a - 10)*q^33 + (3*a^3 - a^2 - 13*a + 8)*q^34 + (-a^4 - 2*a^3 + 3*a^2 + 4*a - 3)*q^35 + (a^4 + a^3 - 3*a^2 + 2)*q^36 + (-2*a^4 - 5*a^3 + 9*a^2 + 17*a - 14)*q^37 + O(q^38),
q + a*q^2 + (-3/10*a^7 + 1/10*a^6 + 37/10*a^5 - 9/10*a^4 - 64/5*a^3 + 11/5*a^2 + 51/5*a + 6/5)*q^3 + (a^2 - 2)*q^4 + (1/10*a^7 + 3/10*a^6 - 7/5*a^5 - 16/5*a^4 + 51/10*a^3 + 81/10*a^2 - 17/5*a - 12/5)*q^5 + (1/10*a^7 - 1/5*a^6 - 9/10*a^5 + 13/10*a^4 + 8/5*a^3 - 9/10*a^2 + 3/5*a + 3/5)*q^6 + (-1/2*a^7 + 13/2*a^5 - 1/2*a^4 - 23*a^3 + 9/2*a^2 + 16*a)*q^7 + (a^3 - 4*a)*q^8 + (-1/2*a^7 + 13/2*a^5 + 1/2*a^4 - 24*a^3 - 5/2*a^2 + 21*a + 4)*q^9 + (3/10*a^7 - 1/10*a^6 - 16/5*a^5 + 2/5*a^4 + 83/10*a^3 + 3/10*a^2 - 11/5*a - 1/5)*q^10 + (-1/5*a^7 - 1/10*a^6 + 23/10*a^5 + 19/10*a^4 - 67/10*a^3 - 41/5*a^2 + 14/5*a + 29/5)*q^11 + (2/5*a^7 + 1/5*a^6 - 61/10*a^5 - 13/10*a^4 + 249/10*a^3 - 1/10*a^2 - 98/5*a - 13/5)*q^12 + (3/10*a^7 - 1/10*a^6 - 21/5*a^5 + 7/5*a^4 + 163/10*a^3 - 47/10*a^2 - 66/5*a - 1/5)*q^13 + (-1/2*a^5 + 1/2*a^4 + 7/2*a^3 - 5/2*a^2 - a + 1)*q^14 + (4/5*a^7 + 2/5*a^6 - 51/5*a^5 - 23/5*a^4 + 174/5*a^3 + 59/5*a^2 - 111/5*a - 26/5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (3/10*a^7 - 1/10*a^6 - 21/5*a^5 + 7/5*a^4 + 173/10*a^3 - 57/10*a^2 - 91/5*a + 4/5)*q^17 + (1/2*a^5 - 1/2*a^4 - 7/2*a^3 + 5/2*a^2 + 3*a + 1)*q^18 - q^19 + (-3/10*a^7 + 1/10*a^6 + 16/5*a^5 + 3/5*a^4 - 93/10*a^3 - 73/10*a^2 + 36/5*a + 21/5)*q^20 + (-2/5*a^7 - 1/5*a^6 + 51/10*a^5 + 23/10*a^4 - 179/10*a^3 - 69/10*a^2 + 73/5*a + 43/5)*q^21 + (-1/10*a^7 - 3/10*a^6 + 19/10*a^5 + 27/10*a^4 - 43/5*a^3 - 23/5*a^2 + 27/5*a + 2/5)*q^22 + q^23 + (-1/2*a^6 + 1/2*a^5 + 7/2*a^4 - 5/2*a^3 - 3*a^2 - 3*a - 2)*q^24 + (-1/5*a^7 + 2/5*a^6 + 14/5*a^5 - 23/5*a^4 - 61/5*a^3 + 64/5*a^2 + 74/5*a - 6/5)*q^25 + (-1/10*a^7 - 3/10*a^6 + 7/5*a^5 + 11/5*a^4 - 41/10*a^3 - 21/10*a^2 + 2/5*a - 3/5)*q^26 + (-1/2*a^7 - 1/2*a^6 + 7*a^5 + 6*a^4 - 55/2*a^3 - 37/2*a^2 + 24*a + 13)*q^27 + (a^7 - 1/2*a^6 - 25/2*a^5 + 9/2*a^4 + 87/2*a^3 - 10*a^2 - 31*a)*q^28 + (-3/10*a^7 + 1/10*a^6 + 21/5*a^5 - 12/5*a^4 - 153/10*a^3 + 117/10*a^2 + 31/5*a - 19/5)*q^29 + (2/5*a^7 + 1/5*a^6 - 23/5*a^5 - 14/5*a^4 + 67/5*a^3 + 37/5*a^2 - 18/5*a - 8/5)*q^30 + (1/10*a^7 + 3/10*a^6 - 19/10*a^5 - 27/10*a^4 + 48/5*a^3 + 23/5*a^2 - 62/5*a + 8/5)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-9/5*a^7 - 2/5*a^6 + 116/5*a^5 + 23/5*a^4 - 409/5*a^3 - 49/5*a^2 + 281/5*a + 46/5)*q^33 + (-1/10*a^7 - 3/10*a^6 + 7/5*a^5 + 16/5*a^4 - 51/10*a^3 - 71/10*a^2 + 7/5*a - 3/5)*q^34 + (4/5*a^7 + 2/5*a^6 - 51/5*a^5 - 23/5*a^4 + 179/5*a^3 + 54/5*a^2 - 136/5*a - 21/5)*q^35 + (a^7 + 1/2*a^6 - 27/2*a^5 - 9/2*a^4 + 101/2*a^3 + 8*a^2 - 41*a - 8)*q^36 + (-6/5*a^7 + 2/5*a^6 + 153/10*a^5 - 51/10*a^4 - 527/10*a^3 + 203/10*a^2 + 159/5*a - 21/5)*q^37 + O(q^38),
q + a*q^2 + (-47/244*a^11 + 91/244*a^10 + 391/122*a^9 - 23/4*a^8 - 1137/61*a^7 + 117/4*a^6 + 5647/122*a^5 - 13993/244*a^4 - 10833/244*a^3 + 2207/61*a^2 + 299/61*a - 140/61)*q^3 + (a^2 - 2)*q^4 + (-6/61*a^11 + 22/61*a^10 + 175/122*a^9 - 6*a^8 - 395/61*a^7 + 69/2*a^6 + 1099/122*a^5 - 5044/61*a^4 + 120/61*a^3 + 9121/122*a^2 - 408/61*a - 675/61)*q^5 + (-3/244*a^11 - 111/244*a^10 + 121/122*a^9 + 31/4*a^8 - 789/61*a^7 - 187/4*a^6 + 7221/122*a^5 + 29869/244*a^4 - 24401/244*a^3 - 15429/122*a^2 + 2633/61*a + 1128/61)*q^6 + (5/244*a^11 + 63/244*a^10 - 50/61*a^9 - 17/4*a^8 + 1105/122*a^7 + 97/4*a^6 - 2327/61*a^5 - 14239/244*a^4 + 14601/244*a^3 + 3311/61*a^2 - 1379/61*a - 355/61)*q^7 + (a^3 - 4*a)*q^8 + (-14/61*a^11 + 31/61*a^10 + 449/122*a^9 - 8*a^8 - 2433/122*a^7 + 85/2*a^6 + 2614/61*a^5 - 11237/122*a^4 - 1733/61*a^3 + 4592/61*a^2 - 342/61*a - 599/61)*q^9 + (10/61*a^11 - 53/122*a^10 - 156/61*a^9 + 7*a^8 + 1581/122*a^7 - 77/2*a^6 - 1414/61*a^5 + 5316/61*a^4 + 637/122*a^3 - 4500/61*a^2 + 741/61*a + 576/61)*q^10 + (7/122*a^11 + 15/122*a^10 - 79/61*a^9 - 5/2*a^8 + 1325/122*a^7 + 37/2*a^6 - 4967/122*a^5 - 3605/61*a^4 + 7607/122*a^3 + 8623/122*a^2 - 1348/61*a - 567/61)*q^11 + (-23/244*a^11 + 3/244*a^10 + 108/61*a^9 + 1/4*a^8 - 742/61*a^7 - 21/4*a^6 + 2274/61*a^5 + 6183/244*a^4 - 11313/244*a^3 - 4585/122*a^2 + 707/61*a + 352/61)*q^12 + (-13/122*a^11 + 7/122*a^10 + 215/122*a^9 - 1/2*a^8 - 616/61*a^7 - a^6 + 2985/122*a^5 + 1861/122*a^4 - 2973/122*a^3 - 3605/122*a^2 + 473/61*a + 626/61)*q^13 + (73/244*a^11 - 105/244*a^10 - 303/61*a^9 + 25/4*a^8 + 1753/61*a^7 - 113/4*a^6 - 4316/61*a^5 + 10271/244*a^4 + 16779/244*a^3 - 1053/122*a^2 - 650/61*a - 120/61)*q^14 + (-1/122*a^11 + 12/61*a^10 - 21/122*a^9 - 7/2*a^8 + 473/122*a^7 + 45/2*a^6 - 2567/122*a^5 - 7815/122*a^4 + 2450/61*a^3 + 8685/122*a^2 - 1254/61*a - 468/61)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (13/122*a^11 - 7/122*a^10 - 215/122*a^9 + 1/2*a^8 + 616/61*a^7 + a^6 - 2985/122*a^5 - 1861/122*a^4 + 2851/122*a^3 + 3483/122*a^2 - 168/61*a - 321/61)*q^17 + (3/61*a^11 - 83/122*a^10 + 2/61*a^9 + 23/2*a^8 - 947/122*a^7 - 68*a^6 + 5703/122*a^5 + 10391/61*a^4 - 5306/61*a^3 - 9890/61*a^2 + 2705/61*a + 1344/61)*q^18 + q^19 + (11/122*a^11 - 10/61*a^10 - 98/61*a^9 + 5/2*a^8 + 1263/122*a^7 - 13*a^6 - 1833/61*a^5 + 3493/122*a^4 + 2330/61*a^3 - 1560/61*a^2 - 968/61*a + 390/61)*q^20 + (3/122*a^11 - 11/122*a^10 - 59/122*a^9 + 2*a^8 + 175/61*a^7 - 31/2*a^6 - 206/61*a^5 + 5999/122*a^4 - 762/61*a^3 - 6779/122*a^2 + 1078/61*a + 428/61)*q^21 + (29/122*a^11 - 25/122*a^10 - 275/61*a^9 + 3*a^8 + 1895/61*a^7 - 13*a^6 - 11445/122*a^5 + 1545/122*a^4 + 6786/61*a^3 + 1039/61*a^2 - 1393/61*a - 336/61)*q^22 - q^23 + (-37/244*a^11 + 217/244*a^10 + 191/122*a^9 - 59/4*a^8 - 3/122*a^7 + 341/4*a^6 - 4393/122*a^5 - 51133/244*a^4 + 23371/244*a^3 + 24429/122*a^2 - 3557/61*a - 1704/61)*q^24 + (8/61*a^11 - 9/61*a^10 - 137/61*a^9 + 2*a^8 + 852/61*a^7 - 8*a^6 - 2461/61*a^5 + 605/61*a^4 + 3378/61*a^3 - 245/61*a^2 - 1774/61*a + 412/61)*q^25 + (-19/122*a^11 - 16/61*a^10 + 197/61*a^9 + 9/2*a^8 - 2969/122*a^7 - 27*a^6 + 4863/61*a^5 + 8285/122*a^4 - 6398/61*a^3 - 3960/61*a^2 + 2160/61*a + 624/61)*q^26 + (-81/244*a^11 + 53/244*a^10 + 383/61*a^9 - 11/4*a^8 - 2637/61*a^7 + 31/4*a^6 + 15993/122*a^5 + 2849/244*a^4 - 38213/244*a^3 - 6053/122*a^2 + 1795/61*a + 688/61)*q^27 + (31/244*a^11 + 49/244*a^10 - 315/122*a^9 - 15/4*a^8 + 2337/122*a^7 + 101/4*a^6 - 7639/122*a^5 - 17961/244*a^4 + 20303/244*a^3 + 10349/122*a^2 - 1669/61*a - 1042/61)*q^28 + (8/61*a^11 + 43/122*a^10 - 198/61*a^9 - 6*a^8 + 3473/122*a^7 + 73/2*a^6 - 6487/61*a^5 - 5983/61*a^4 + 19383/122*a^3 + 6465/61*a^2 - 3787/61*a - 930/61)*q^29 + (11/61*a^11 - 20/61*a^10 - 196/61*a^9 + 5*a^8 + 1263/61*a^7 - 25*a^6 - 3605/61*a^5 + 2883/61*a^4 + 3989/61*a^3 - 1595/61*a^2 - 350/61*a + 48/61)*q^30 + (1/122*a^11 - 85/122*a^10 + 41/61*a^9 + 12*a^8 - 694/61*a^7 - 73*a^6 + 6959/122*a^5 + 23187/122*a^4 - 6232/61*a^3 - 11571/61*a^2 + 2840/61*a + 1688/61)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (53/244*a^11 - 113/244*a^10 - 389/122*a^9 + 27/4*a^8 + 885/61*a^7 - 125/4*a^6 - 1230/61*a^5 + 13059/244*a^4 - 1243/244*a^3 - 2028/61*a^2 + 779/61*a + 324/61)*q^33 + (19/122*a^11 + 16/61*a^10 - 197/61*a^9 - 9/2*a^8 + 2969/122*a^7 + 27*a^6 - 4863/61*a^5 - 8407/122*a^4 + 6337/61*a^3 + 4265/61*a^2 - 1855/61*a - 624/61)*q^34 + (17/61*a^11 - 42/61*a^10 - 253/61*a^9 + 11*a^8 + 1170/61*a^7 - 60*a^6 - 1562/61*a^5 + 8232/61*a^4 - 1194/61*a^3 - 6674/61*a^2 + 2498/61*a + 357/61)*q^35 + (-15/122*a^11 - 3/61*a^10 + 295/122*a^9 + 3/2*a^8 - 1058/61*a^7 - 29/2*a^6 + 3348/61*a^5 + 3333/61*a^4 - 4303/61*a^3 - 4433/61*a^2 + 1320/61*a + 910/61)*q^36 + (1/4*a^11 - 5/4*a^10 - 3*a^9 + 81/4*a^8 + 7*a^7 - 449/4*a^6 + 21*a^5 + 1027/4*a^4 - 313/4*a^3 - 437/2*a^2 + 50*a + 26)*q^37 + O(q^38)
*]> ;  // time = 79.29 seconds




J[438] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 438, 438, 438, 438, 438, 438, 438, 438, 438, 219, 219, 219, 219, 219, 146, 146, 73, 73, 73 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 4, 6, 3, 4, 1, 2, 2 ], dimensions := [ 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 8, 12, 6, 8, 4, 8, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 23, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 5, 1, 1, 1, 1, 29, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 9, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 289, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 37, 1, 841, 1, 1, 1, 3, 1, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 81, 1, 1, 1, 1, 1, 1, 1, 1, 29, 1, 1, 1, 1, 37, 1, 0, 1, 361, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 81, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 1, 1, 1, 841, 1, 361, 1, 0, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 9, 289, 1, 81, 1, 81, 1, 0 ], ap_traces := [
[ -1, -1, 0, -2, 4, -6, 0, -4, 0, -4, 2, -10 ],
[ -1, 1, 2, -2, 2, 4, 4, -4, 0, 6, -2, -6 ],
[ -1, 1, 0, -4, -6, -4, -6, 8, 0, 0, 8, 2 ],
[ -1, 1, -4, 0, 2, 0, -6, -8, -8, -4, -4, 2 ],
[ 1, -1, -2, -4, 0, -2, -6, -4, 0, 6, -4, 6 ],
[ 1, 1, 0, 2, 0, -4, 6, -4, 0, 0, 2, 2 ],
[ 1, 1, 0, -2, 4, 4, -2, 4, 0, 0, -10, -6 ],
[ -2, -2, 0, 0, -4, 8, 4, 0, 0, 0, 8, 20 ],
[ 2, -2, -2, 4, 2, 6, 4, 8, 0, -10, 8, -8 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 8,
x^2 + 2*x - 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ 1, -1, -1 ],
[ 1, -1, -1 ],
[ -1, 1, -1 ],
[ -1, -1, -1 ],
[ -1, -1, -1 ],
[ 1, 1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 7, 1, 1 ],
[ 3, 3, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 9, 3, 1 ],
[ 1, 1, 1 ],
[ 23, 7, 1 ],
[ 5, 29, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 9, 3, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 5, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 1, 3, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 0, 0, 0, 3, 1, 1, 5 ], analytic_sha_upper_bounds := [ 0, 1, 0, 0, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 0, 0, 1/9, 1, 1, 1 ], eigenvalues := [*
[ -1, -1, 0, -2, 4, -6, 0, -4, 0, -4, 2, -10 ],
[ -1, 1, 2, -2, 2, 4, 4, -4, 0, 6, -2, -6 ],
[ -1, 1, 0, -4, -6, -4, -6, 8, 0, 0, 8, 2 ],
[ -1, 1, -4, 0, 2, 0, -6, -8, -8, -4, -4, 2 ],
[ 1, -1, -2, -4, 0, -2, -6, -4, 0, 6, -4, 6 ],
[ 1, 1, 0, 2, 0, -4, 6, -4, 0, 0, 2, 2 ],
[ 1, 1, 0, -2, 4, 4, -2, 4, 0, 0, -10, -6 ],
[
-1,
-1,
a,
a,
-2,
-a + 4,
2,
0,
-2*a,
a,
a + 4,
10
],
[
1,
-1,
a,
2,
-a,
-a + 2,
-2*a,
4,
4*a + 4,
a - 4,
2*a + 6,
2*a - 2
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + q^6 - 2*q^7 - q^8 + q^9 + 4*q^11 - q^12 - 6*q^13 + 2*q^14 + q^16 - q^18 - 4*q^19 + 2*q^21 - 4*q^22 + q^24 - 5*q^25 + 6*q^26 - q^27 - 2*q^28 - 4*q^29 + 2*q^31 - q^32 - 4*q^33 + q^36 - 10*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + 2*q^5 - q^6 - 2*q^7 - q^8 + q^9 - 2*q^10 + 2*q^11 + q^12 + 4*q^13 + 2*q^14 + 2*q^15 + q^16 + 4*q^17 - q^18 - 4*q^19 + 2*q^20 - 2*q^21 - 2*q^22 - q^24 - q^25 - 4*q^26 + q^27 - 2*q^28 + 6*q^29 - 2*q^30 - 2*q^31 - q^32 + 2*q^33 - 4*q^34 - 4*q^35 + q^36 - 6*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - q^6 - 4*q^7 - q^8 + q^9 - 6*q^11 + q^12 - 4*q^13 + 4*q^14 + q^16 - 6*q^17 - q^18 + 8*q^19 - 4*q^21 + 6*q^22 - q^24 - 5*q^25 + 4*q^26 + q^27 - 4*q^28 + 8*q^31 - q^32 - 6*q^33 + 6*q^34 + q^36 + 2*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - 4*q^5 - q^6 - q^8 + q^9 + 4*q^10 + 2*q^11 + q^12 - 4*q^15 + q^16 - 6*q^17 - q^18 - 8*q^19 - 4*q^20 - 2*q^22 - 8*q^23 - q^24 + 11*q^25 + q^27 - 4*q^29 + 4*q^30 - 4*q^31 - q^32 + 2*q^33 + 6*q^34 + q^36 + 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 2*q^5 - q^6 - 4*q^7 + q^8 + q^9 - 2*q^10 - q^12 - 2*q^13 - 4*q^14 + 2*q^15 + q^16 - 6*q^17 + q^18 - 4*q^19 - 2*q^20 + 4*q^21 - q^24 - q^25 - 2*q^26 - q^27 - 4*q^28 + 6*q^29 + 2*q^30 - 4*q^31 + q^32 - 6*q^34 + 8*q^35 + q^36 + 6*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^6 + 2*q^7 + q^8 + q^9 + q^12 - 4*q^13 + 2*q^14 + q^16 + 6*q^17 + q^18 - 4*q^19 + 2*q^21 + q^24 - 5*q^25 - 4*q^26 + q^27 + 2*q^28 + 2*q^31 + q^32 + 6*q^34 + q^36 + 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^6 - 2*q^7 + q^8 + q^9 + 4*q^11 + q^12 + 4*q^13 - 2*q^14 + q^16 - 2*q^17 + q^18 + 4*q^19 - 2*q^21 + 4*q^22 + q^24 - 5*q^25 + 4*q^26 + q^27 - 2*q^28 - 10*q^31 + q^32 + 4*q^33 - 2*q^34 + q^36 - 6*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + a*q^5 + q^6 + a*q^7 - q^8 + q^9 - a*q^10 - 2*q^11 - q^12 + (-a + 4)*q^13 - a*q^14 - a*q^15 + q^16 + 2*q^17 - q^18 + a*q^20 - a*q^21 + 2*q^22 - 2*a*q^23 + q^24 + 3*q^25 + (a - 4)*q^26 - q^27 + a*q^28 + a*q^29 + a*q^30 + (a + 4)*q^31 - q^32 + 2*q^33 - 2*q^34 + 8*q^35 + q^36 + 10*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + a*q^5 - q^6 + 2*q^7 + q^8 + q^9 + a*q^10 - a*q^11 - q^12 + (-a + 2)*q^13 + 2*q^14 - a*q^15 + q^16 - 2*a*q^17 + q^18 + 4*q^19 + a*q^20 - 2*q^21 - a*q^22 + (4*a + 4)*q^23 - q^24 + (-2*a - 1)*q^25 + (-a + 2)*q^26 - q^27 + 2*q^28 + (a - 4)*q^29 - a*q^30 + (2*a + 6)*q^31 + q^32 + a*q^33 - 2*a*q^34 + 2*a*q^35 + q^36 + (2*a - 2)*q^37 + O(q^38)
*]> ;  // time = 351.06 seconds




J[439] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 439, 439, 439 ], new_dimensions := [ 2, 9, 25 ], dimensions := [ 2, 9, 25 ], intersection_graph := [ 0, 31, 1, 31, 0, 1, 1, 1, 0 ], ap_traces := [
[ -2, 1, 1, -4, 2, -3, -4, -10, -1, -7, 3, 0 ],
[ -1, -4, -12, 0, -18, 2, -19, 9, -13, -26, -10, -2 ],
[ 4, 3, 15, 0, 24, 1, 25, -1, 26, 49, -11, 4 ]
], hecke_fields := [
x^2 + x - 1,
x^9 + x^8 - 12*x^7 - 6*x^6 + 49*x^5 - x^4 - 72*x^3 + 30*x^2 + 18*x - 9,
x^25 - 4*x^24 - 31*x^23 + 138*x^22 + 389*x^21 - 2034*x^20 - 2453*x^19 + 16766*x^18 + 7126*x^17 - 84887*x^16 + 1717*x^15 + 272618*x^14 - 79978*x^13 - 552928*x^12 + 255108*x^11 + 682589*x^10 - 376568*x^9 - 476301*x^8 + 270078*x^7 + 167567*x^6 - 81530*x^5 - 24739*x^4 + 6834*x^3 + 740*x^2 - 187*x + 5
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 73 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 73 ]
], torsion_upper_bounds := [ 1, 1, 73 ], torsion_lower_bounds := [ 1, 1, 73 ], l_ratios := [ 0, 0, 1/73 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[
-1,
a + 1,
-a,
-2,
-2*a,
-3*a - 3,
4*a,
2*a - 4,
-3*a - 2,
-a - 4,
3*a + 3,
8*a + 4
],
[
a,
1/9*a^8 + 1/9*a^7 - 5/3*a^6 - a^5 + 76/9*a^4 + 17/9*a^3 - 46/3*a^2 + 2/3*a + 5,
-7/9*a^8 - 10/9*a^7 + 28/3*a^6 + 9*a^5 - 343/9*a^4 - 158/9*a^3 + 167/3*a^2 + 10/3*a - 16,
1/3*a^8 + 2/3*a^7 - 11/3*a^6 - 6*a^5 + 40/3*a^4 + 15*a^3 - 52/3*a^2 - 10*a + 5,
8/9*a^8 + 14/9*a^7 - 29/3*a^6 - 12*a^5 + 320/9*a^4 + 187/9*a^3 - 142/3*a^2 - 2/3*a + 8,
4/3*a^8 + 5/3*a^7 - 47/3*a^6 - 13*a^5 + 187/3*a^4 + 24*a^3 - 268/3*a^2 - 4*a + 24,
-28/9*a^8 - 49/9*a^7 + 100/3*a^6 + 43*a^5 - 1093/9*a^4 - 740/9*a^3 + 500/3*a^2 + 58/3*a - 46,
-2/3*a^8 - 2/3*a^7 + 9*a^6 + 6*a^5 - 119/3*a^4 - 37/3*a^3 + 59*a^2 - a - 14,
-7/9*a^8 - 10/9*a^7 + 28/3*a^6 + 10*a^5 - 334/9*a^4 - 221/9*a^3 + 155/3*a^2 + 40/3*a - 16,
-38/9*a^8 - 71/9*a^7 + 128/3*a^6 + 61*a^5 - 1304/9*a^4 - 1021/9*a^3 + 562/3*a^2 + 80/3*a - 47,
-a^8 - 8/3*a^7 + 25/3*a^6 + 21*a^5 - 21*a^4 - 125/3*a^3 + 65/3*a^2 + 18*a - 8,
13/3*a^8 + 25/3*a^7 - 45*a^6 - 66*a^5 + 472/3*a^4 + 380/3*a^3 - 205*a^2 - 31*a + 47
],
[
a,
-4701618266782388979/28439477794057307596*a^24 + 11170291270990503687/28439477794057307596*a^23 + 80691352900513829125/14219738897028653798*a^22 - 95756906909083668938/7109869448514326899*a^21 - 2360014104287415004231/28439477794057307596*a^20 + 5603526973553122914217/28439477794057307596*a^19 + 9606353419503600675959/14219738897028653798*a^18 - 11443242660642603218230/7109869448514326899*a^17 - 47657446939209209379161/14219738897028653798*a^16 + 229252186441017254442939/28439477794057307596*a^15 + 147814175331208886241791/14219738897028653798*a^14 - 181746471101382290275787/7109869448514326899*a^13 - 281339988371005892185739/14219738897028653798*a^12 + 726870045488517750893127/14219738897028653798*a^11 + 305723654765418162524595/14219738897028653798*a^10 - 1768345960680669148360317/28439477794057307596*a^9 - 315741691603864767432427/28439477794057307596*a^8 + 608059283868001121353591/14219738897028653798*a^7 + 9358948221177614751930/7109869448514326899*a^6 - 419149212373168286417085/28439477794057307596*a^5 + 11708709882927074613999/28439477794057307596*a^4 + 29556806794776585249309/14219738897028653798*a^3 - 137000895117974247488/7109869448514326899*a^2 - 540274369868061400757/7109869448514326899*a + 76528473298370282193/28439477794057307596,
1647367022276221005/28439477794057307596*a^24 + 52969329716665563/28439477794057307596*a^23 - 31872281549317535945/14219738897028653798*a^22 - 1642972826875068120/7109869448514326899*a^21 + 1072871156604689252509/28439477794057307596*a^20 + 183875091502160176397/28439477794057307596*a^19 - 5155563190781254517255/14219738897028653798*a^18 - 604373366542309006201/7109869448514326899*a^17 + 31201776691348939943627/14219738897028653798*a^16 + 18077597347358541178579/28439477794057307596*a^15 - 123554336497637077062051/14219738897028653798*a^14 - 20667802391969160715848/7109869448514326899*a^13 + 321832665686801890019843/14219738897028653798*a^12 + 118077274906464419327349/14219738897028653798*a^11 - 539702315085517771538619/14219738897028653798*a^10 - 416229740572805534350269/28439477794057307596*a^9 + 1105702149650154520677205/28439477794057307596*a^8 + 216973001423995103443715/14219738897028653798*a^7 - 156181140411469097098958/7109869448514326899*a^6 - 246739270965029172348165/28439477794057307596*a^5 + 156220049353768141791119/28439477794057307596*a^4 + 31071838535063740568881/14219738897028653798*a^3 - 2021446512334916558334/7109869448514326899*a^2 - 625462724675585184804/7109869448514326899*a + 208500022795250045061/28439477794057307596,
760866391961395702/7109869448514326899*a^24 - 352947250668737963/7109869448514326899*a^23 - 28911603799610402491/7109869448514326899*a^22 + 10718205292913323729/7109869448514326899*a^21 + 477014484506977132871/7109869448514326899*a^20 - 131199993891360344735/7109869448514326899*a^19 - 4486054275057122572442/7109869448514326899*a^18 + 805170713552169373211/7109869448514326899*a^17 + 26516169424210896070583/7109869448514326899*a^16 - 2312555926413511583715/7109869448514326899*a^15 - 102331510399834199995606/7109869448514326899*a^14 + 196576008060484108694/7109869448514326899*a^13 + 259143820675389522123340/7109869448514326899*a^12 + 18748155772308558490129/7109869448514326899*a^11 - 421333352861918615161012/7109869448514326899*a^10 - 55490566740836759100524/7109869448514326899*a^9 + 417334664371244123502005/7109869448514326899*a^8 + 72629202470138982951061/7109869448514326899*a^7 - 227656793838545820646001/7109869448514326899*a^6 - 46079118638285359685507/7109869448514326899*a^5 + 54716583394085341357436/7109869448514326899*a^4 + 11925384749079586124000/7109869448514326899*a^3 - 2504671078478899488351/7109869448514326899*a^2 - 290182666330441546285/7109869448514326899*a + 27543920540087016679/7109869448514326899,
-5363965716272303177/42659216691085961394*a^24 + 8362916483887599729/14219738897028653798*a^23 + 81748757523398717794/21329608345542980697*a^22 - 435835051599899278496/21329608345542980697*a^21 - 2000599468066668784445/42659216691085961394*a^20 + 12956295889723099186417/42659216691085961394*a^19 + 6034729371051101100070/21329608345542980697*a^18 - 53936227689685691545243/21329608345542980697*a^17 - 15507685734981108378935/21329608345542980697*a^16 + 184218068452856337363945/14219738897028653798*a^15 - 17555249143191892565851/21329608345542980697*a^14 - 299904365681798076441792/7109869448514326899*a^13 + 236105536692116579700907/21329608345542980697*a^12 + 1853525264223744210576209/21329608345542980697*a^11 - 681188847885915118289719/21329608345542980697*a^10 - 1551579332027340548981117/14219738897028653798*a^9 + 1882255392142895617760359/42659216691085961394*a^8 + 1651410310945964679198761/21329608345542980697*a^7 - 626708241731951246677726/21329608345542980697*a^6 - 392000575123645713296741/14219738897028653798*a^5 + 330147732666917122472443/42659216691085961394*a^4 + 28701110130063012328168/7109869448514326899*a^3 - 2554082151194212341587/7109869448514326899*a^2 - 2529139964115426826100/21329608345542980697*a + 271668394370923929241/42659216691085961394,
6613357520299680839/28439477794057307596*a^24 - 9833442203461204495/28439477794057307596*a^23 - 117724620440653710961/14219738897028653798*a^22 + 81677913144810050904/7109869448514326899*a^21 + 3605600648398840021523/28439477794057307596*a^20 - 4588604515291107442053/28439477794057307596*a^19 - 15567967436961357261281/14219738897028653798*a^18 + 8879652626901733178740/7109869448514326899*a^17 + 83422143063537676010267/14219738897028653798*a^16 - 165338046129390363918831/28439477794057307596*a^15 - 287221865668277214026127/14219738897028653798*a^14 + 118096010348039284701203/7109869448514326899*a^13 + 635206950910049520286659/14219738897028653798*a^12 - 402309916886326694754431/14219738897028653798*a^11 - 875767943170837703868969/14219738897028653798*a^10 + 736337225586306308313841/28439477794057307596*a^9 + 1414777578604531766824739/28439477794057307596*a^8 - 123575013100995224756511/14219738897028653798*a^7 - 150688435350637604164938/7109869448514326899*a^6 - 71569823462051688820691/28439477794057307596*a^5 + 103916136653166581564709/28439477794057307596*a^4 + 24902518212364000960745/14219738897028653798*a^3 + 356843772345627785988/7109869448514326899*a^2 - 448726188893907291986/7109869448514326899*a - 8209749510389125421/28439477794057307596,
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-16441519854744563083/42659216691085961394*a^24 + 14381517914108135189/14219738897028653798*a^23 + 278799044946870083159/21329608345542980697*a^22 - 739708053352219355722/21329608345542980697*a^21 - 8035110503946902825767/42659216691085961394*a^20 + 21641321043120297891707/42659216691085961394*a^19 + 32119125275505345531323/21329608345542980697*a^18 - 88358092163500789615001/21329608345542980697*a^17 - 155755821941291572264429/21329608345542980697*a^16 + 294712117334307009487007/14219738897028653798*a^15 + 468925876589723455988521/21329608345542980697*a^14 - 465994669624135085237934/7109869448514326899*a^13 - 855679204781292212696338/21329608345542980697*a^12 + 2776810079325478895298217/21329608345542980697*a^11 + 866090726246811383837581/21329608345542980697*a^10 - 2216359281285977326563203/14219738897028653798*a^9 - 745929656009476236767503/42659216691085961394*a^8 + 2202475680938340162009103/21329608345542980697*a^7 - 15189321267448575183176/21329608345542980697*a^6 - 463805626849345367720371/14219738897028653798*a^5 + 77981788350304116192269/42659216691085961394*a^4 + 26764068351715408723490/7109869448514326899*a^3 - 1451283717574755785675/7109869448514326899*a^2 - 2657560225216137074050/21329608345542980697*a + 338902884625858451003/42659216691085961394,
25848687140928756451/85318433382171922788*a^24 - 24364415944961985457/28439477794057307596*a^23 - 436483070407482868409/42659216691085961394*a^22 + 630273842958837261329/21329608345542980697*a^21 + 12503073704081570091307/85318433382171922788*a^20 - 37126456471939471571513/85318433382171922788*a^19 - 49526427209849720889455/42659216691085961394*a^18 + 76360612155502746684547/21329608345542980697*a^17 + 236816238205267637743735/42659216691085961394*a^16 - 513606090875917097322373/28439477794057307596*a^15 - 696687017571381993486205/42659216691085961394*a^14 + 409650967072789196692176/7109869448514326899*a^13 + 1218316906313479995998593/42659216691085961394*a^12 - 4926383973508978851001885/42659216691085961394*a^11 - 1116537300556016226189937/42659216691085961394*a^10 + 3965396417132526347731003/28439477794057307596*a^9 + 611696931550668056134771/85318433382171922788*a^8 - 3965644690288120607256889/42659216691085961394*a^7 + 100930232625142222096216/21329608345542980697*a^6 + 837450385080713827548351/28439477794057307596*a^5 - 236927147073333333497003/85318433382171922788*a^4 - 48578490777026413507765/14219738897028653798*a^3 + 2504367637668869775638/7109869448514326899*a^2 + 2788478138166839271155/21329608345542980697*a - 731968057841014772897/85318433382171922788,
2888753937435278861/28439477794057307596*a^24 - 12251810475830564245/28439477794057307596*a^23 - 46532694311881645169/14219738897028653798*a^22 + 107179735380357584473/7109869448514326899*a^21 + 1250623325730043552277/28439477794057307596*a^20 - 6427287912365049186343/28439477794057307596*a^19 - 4527363290683358784783/14219738897028653798*a^18 + 13517660202156898063010/7109869448514326899*a^17 + 18877914113675554267589/14219738897028653798*a^16 - 280551650648327544163277/28439477794057307596*a^15 - 43728909912292405203695/14219738897028653798*a^14 + 232017659365027491469673/7109869448514326899*a^13 + 42724769074766250766995/14219738897028653798*a^12 - 975866514045192766962679/14219738897028653798*a^11 + 26326417162275778592453/14219738897028653798*a^10 + 2521122499553455160332063/28439477794057307596*a^9 - 193906422827734494599819/28439477794057307596*a^8 - 932629855772416244498193/14219738897028653798*a^7 + 33957520661586228078316/7109869448514326899*a^6 + 707423992677216165891475/28439477794057307596*a^5 - 16340175250207384961165/28439477794057307596*a^4 - 56351155449788959122511/14219738897028653798*a^3 - 1408342826614511129942/7109869448514326899*a^2 + 934743309353279817749/7109869448514326899*a + 93928686030339005/28439477794057307596,
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-4807743770711237899/7109869448514326899*a^24 + 12339799105364806957/7109869448514326899*a^23 + 162589984426930786007/7109869448514326899*a^22 - 422926478082532771952/7109869448514326899*a^21 - 2329566435264630374831/7109869448514326899*a^20 + 6184090383852013597081/7109869448514326899*a^19 + 18418422507265733475338/7109869448514326899*a^18 - 50491128700173883426365/7109869448514326899*a^17 - 87413166236121738269481/7109869448514326899*a^16 + 252798696170752617520476/7109869448514326899*a^15 + 251916753945748894557738/7109869448514326899*a^14 - 801713369488228787066202/7109869448514326899*a^13 - 416195273681386785475032/7109869448514326899*a^12 + 1604897780934514059689234/7109869448514326899*a^11 + 311522432831718242737884/7109869448514326899*a^10 - 1959193523751459080470483/7109869448514326899*a^9 + 43344713993686863057459/7109869448514326899*a^8 + 1360985683660449730091925/7109869448514326899*a^7 - 187145811394559561167420/7109869448514326899*a^6 - 481912868447467390328705/7109869448514326899*a^5 + 68311947055809694575121/7109869448514326899*a^4 + 71930057379853880856122/7109869448514326899*a^3 - 2071172179704211141453/7109869448514326899*a^2 - 2071787854343502916043/7109869448514326899*a + 79921880488941165950/7109869448514326899
]
*], q_expansions := [*
q - q^2 + (a + 1)*q^3 - q^4 - a*q^5 + (-a - 1)*q^6 - 2*q^7 + 3*q^8 + (a - 1)*q^9 + a*q^10 - 2*a*q^11 + (-a - 1)*q^12 + (-3*a - 3)*q^13 + 2*q^14 - q^15 - q^16 + 4*a*q^17 + (-a + 1)*q^18 + (2*a - 4)*q^19 + a*q^20 + (-2*a - 2)*q^21 + 2*a*q^22 + (-3*a - 2)*q^23 + (3*a + 3)*q^24 + (-a - 4)*q^25 + (3*a + 3)*q^26 + (-4*a - 3)*q^27 + 2*q^28 + (-a - 4)*q^29 + q^30 + (3*a + 3)*q^31 - 5*q^32 - 2*q^33 - 4*a*q^34 + 2*a*q^35 + (-a + 1)*q^36 + (8*a + 4)*q^37 + O(q^38),
q + a*q^2 + (1/9*a^8 + 1/9*a^7 - 5/3*a^6 - a^5 + 76/9*a^4 + 17/9*a^3 - 46/3*a^2 + 2/3*a + 5)*q^3 + (a^2 - 2)*q^4 + (-7/9*a^8 - 10/9*a^7 + 28/3*a^6 + 9*a^5 - 343/9*a^4 - 158/9*a^3 + 167/3*a^2 + 10/3*a - 16)*q^5 + (-1/3*a^7 - 1/3*a^6 + 3*a^5 + 2*a^4 - 22/3*a^3 - 8/3*a^2 + 3*a + 1)*q^6 + (1/3*a^8 + 2/3*a^7 - 11/3*a^6 - 6*a^5 + 40/3*a^4 + 15*a^3 - 52/3*a^2 - 10*a + 5)*q^7 + (a^3 - 4*a)*q^8 + (4/3*a^8 + 7/3*a^7 - 14*a^6 - 18*a^5 + 148/3*a^4 + 98/3*a^3 - 64*a^2 - 6*a + 14)*q^9 + (-1/3*a^8 + 13/3*a^6 - 55/3*a^4 - 1/3*a^3 + 80/3*a^2 - 2*a - 7)*q^10 + (8/9*a^8 + 14/9*a^7 - 29/3*a^6 - 12*a^5 + 320/9*a^4 + 187/9*a^3 - 142/3*a^2 - 2/3*a + 8)*q^11 + (-5/9*a^8 - 5/9*a^7 + 19/3*a^6 + 4*a^5 - 218/9*a^4 - 58/9*a^3 + 101/3*a^2 - 1/3*a - 10)*q^12 + (4/3*a^8 + 5/3*a^7 - 47/3*a^6 - 13*a^5 + 187/3*a^4 + 24*a^3 - 268/3*a^2 - 4*a + 24)*q^13 + (1/3*a^8 + 1/3*a^7 - 4*a^6 - 3*a^5 + 46/3*a^4 + 20/3*a^3 - 20*a^2 - a + 3)*q^14 + (-2*a^8 - 11/3*a^7 + 64/3*a^6 + 29*a^5 - 78*a^4 - 164/3*a^3 + 329/3*a^2 + 10*a - 30)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-28/9*a^8 - 49/9*a^7 + 100/3*a^6 + 43*a^5 - 1093/9*a^4 - 740/9*a^3 + 500/3*a^2 + 58/3*a - 46)*q^17 + (a^8 + 2*a^7 - 10*a^6 - 16*a^5 + 34*a^4 + 32*a^3 - 46*a^2 - 10*a + 12)*q^18 + (-2/3*a^8 - 2/3*a^7 + 9*a^6 + 6*a^5 - 119/3*a^4 - 37/3*a^3 + 59*a^2 - a - 14)*q^19 + (17/9*a^8 + 23/9*a^7 - 62/3*a^6 - 20*a^5 + 680/9*a^4 + 340/9*a^3 - 310/3*a^2 - 23/3*a + 29)*q^20 + (-2/3*a^8 - 2/3*a^7 + 8*a^6 + 5*a^5 - 95/3*a^4 - 22/3*a^3 + 44*a^2 - 3*a - 12)*q^21 + (2/3*a^8 + a^7 - 20/3*a^6 - 8*a^5 + 65/3*a^4 + 50/3*a^3 - 82/3*a^2 - 8*a + 8)*q^22 + (-7/9*a^8 - 10/9*a^7 + 28/3*a^6 + 10*a^5 - 334/9*a^4 - 221/9*a^3 + 155/3*a^2 + 40/3*a - 16)*q^23 + (1/3*a^7 + 4/3*a^6 - 3*a^5 - 11*a^4 + 25/3*a^3 + 65/3*a^2 - 6*a - 7)*q^24 + (7/3*a^8 + 11/3*a^7 - 80/3*a^6 - 29*a^5 + 313/3*a^4 + 54*a^3 - 448/3*a^2 - 7*a + 38)*q^25 + (1/3*a^8 + 1/3*a^7 - 5*a^6 - 3*a^5 + 76/3*a^4 + 20/3*a^3 - 44*a^2 + 12)*q^26 + (-4/9*a^8 - 7/9*a^7 + 16/3*a^6 + 6*a^5 - 205/9*a^4 - 89/9*a^3 + 113/3*a^2 + 1/3*a - 13)*q^27 + (-2/3*a^8 - 4/3*a^7 + 19/3*a^6 + 11*a^5 - 59/3*a^4 - 26*a^3 + 71/3*a^2 + 17*a - 7)*q^28 + (-38/9*a^8 - 71/9*a^7 + 128/3*a^6 + 61*a^5 - 1304/9*a^4 - 1021/9*a^3 + 562/3*a^2 + 80/3*a - 47)*q^29 + (-5/3*a^8 - 8/3*a^7 + 17*a^6 + 20*a^5 - 170/3*a^4 - 103/3*a^3 + 70*a^2 + 6*a - 18)*q^30 + (-a^8 - 8/3*a^7 + 25/3*a^6 + 21*a^5 - 21*a^4 - 125/3*a^3 + 65/3*a^2 + 18*a - 8)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^2 + a - 2)*q^33 + (-7/3*a^8 - 4*a^7 + 73/3*a^6 + 31*a^5 - 256/3*a^4 - 172/3*a^3 + 338/3*a^2 + 10*a - 28)*q^34 + (10/3*a^8 + 16/3*a^7 - 36*a^6 - 41*a^5 + 397/3*a^4 + 221/3*a^3 - 182*a^2 - 8*a + 45)*q^35 + (-5/3*a^8 - 8/3*a^7 + 18*a^6 + 21*a^5 - 197/3*a^4 - 118/3*a^3 + 88*a^2 + 6*a - 19)*q^36 + (13/3*a^8 + 25/3*a^7 - 45*a^6 - 66*a^5 + 472/3*a^4 + 380/3*a^3 - 205*a^2 - 31*a + 47)*q^37 + O(q^38),
q + a*q^2 + (-4701618266782388979/28439477794057307596*a^24 + 11170291270990503687/28439477794057307596*a^23 + 80691352900513829125/14219738897028653798*a^22 - 95756906909083668938/7109869448514326899*a^21 - 2360014104287415004231/28439477794057307596*a^20 + 5603526973553122914217/28439477794057307596*a^19 + 9606353419503600675959/14219738897028653798*a^18 - 11443242660642603218230/7109869448514326899*a^17 - 47657446939209209379161/14219738897028653798*a^16 + 229252186441017254442939/28439477794057307596*a^15 + 147814175331208886241791/14219738897028653798*a^14 - 181746471101382290275787/7109869448514326899*a^13 - 281339988371005892185739/14219738897028653798*a^12 + 726870045488517750893127/14219738897028653798*a^11 + 305723654765418162524595/14219738897028653798*a^10 - 1768345960680669148360317/28439477794057307596*a^9 - 315741691603864767432427/28439477794057307596*a^8 + 608059283868001121353591/14219738897028653798*a^7 + 9358948221177614751930/7109869448514326899*a^6 - 419149212373168286417085/28439477794057307596*a^5 + 11708709882927074613999/28439477794057307596*a^4 + 29556806794776585249309/14219738897028653798*a^3 - 137000895117974247488/7109869448514326899*a^2 - 540274369868061400757/7109869448514326899*a + 76528473298370282193/28439477794057307596)*q^3 + (a^2 - 2)*q^4 + (1647367022276221005/28439477794057307596*a^24 + 52969329716665563/28439477794057307596*a^23 - 31872281549317535945/14219738897028653798*a^22 - 1642972826875068120/7109869448514326899*a^21 + 1072871156604689252509/28439477794057307596*a^20 + 183875091502160176397/28439477794057307596*a^19 - 5155563190781254517255/14219738897028653798*a^18 - 604373366542309006201/7109869448514326899*a^17 + 31201776691348939943627/14219738897028653798*a^16 + 18077597347358541178579/28439477794057307596*a^15 - 123554336497637077062051/14219738897028653798*a^14 - 20667802391969160715848/7109869448514326899*a^13 + 321832665686801890019843/14219738897028653798*a^12 + 118077274906464419327349/14219738897028653798*a^11 - 539702315085517771538619/14219738897028653798*a^10 - 416229740572805534350269/28439477794057307596*a^9 + 1105702149650154520677205/28439477794057307596*a^8 + 216973001423995103443715/14219738897028653798*a^7 - 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17991865357688189174/7109869448514326899*a^21 - 901185068473834429590/7109869448514326899*a^20 + 225500447875482725733/7109869448514326899*a^19 + 8712821044874030713798/7109869448514326899*a^18 - 1416870568844872312573/7109869448514326899*a^17 - 53171582571888274520432/7109869448514326899*a^16 + 4072110254158861058561/7109869448514326899*a^15 + 212947205336420960312100/7109869448514326899*a^14 + 1234070089301804211730/7109869448514326899*a^13 - 562965448308145956655214/7109869448514326899*a^12 - 46458221720813847064858/7109869448514326899*a^11 + 961511944318473314434266/7109869448514326899*a^10 + 146195426934042281463867/7109869448514326899*a^9 - 1004656341474289980519787/7109869448514326899*a^8 - 215026755280555289785701/7109869448514326899*a^7 + 575293378657982347350254/7109869448514326899*a^6 + 155810233082125301074192/7109869448514326899*a^5 - 140730372527412319554841/7109869448514326899*a^4 - 46022227692220349567962/7109869448514326899*a^3 + 4616972680886049160901/7109869448514326899*a^2 + 1656173165411407901570/7109869448514326899*a - 50124171681048919807/7109869448514326899)*q^33 + (-1482937001871665502/7109869448514326899*a^24 + 3726402610011522286/7109869448514326899*a^23 + 51115614480337244030/7109869448514326899*a^22 - 128322050644708963304/7109869448514326899*a^21 - 752604493177921252895/7109869448514326899*a^20 + 1885680316020953299862/7109869448514326899*a^19 + 6196070616617018990371/7109869448514326899*a^18 - 15469245101932600012710/7109869448514326899*a^17 - 31328684062065252864436/7109869448514326899*a^16 + 77730166944607417614394/7109869448514326899*a^15 + 100477129875640474247832/7109869448514326899*a^14 - 246628861654872615991566/7109869448514326899*a^13 - 203621812567815385441168/7109869448514326899*a^12 + 490332829816473692180444/7109869448514326899*a^11 + 251896352913125715962896/7109869448514326899*a^10 - 584367561314162076737004/7109869448514326899*a^9 - 178516645597292154962544/7109869448514326899*a^8 + 380047882460187365169316/7109869448514326899*a^7 + 67443606783140980134980/7109869448514326899*a^6 - 113032168373309929477087/7109869448514326899*a^5 - 12436870656757664428728/7109869448514326899*a^4 + 10393879904887898818255/7109869448514326899*a^3 + 430980666285843464666/7109869448514326899*a^2 - 256378754052185761618/7109869448514326899*a + 7503468611132816290/7109869448514326899)*q^34 + (-2998674322071677661/14219738897028653798*a^24 + 5965061437410122531/14219738897028653798*a^23 + 51464508230892932875/7109869448514326899*a^22 - 100205497665340201370/7109869448514326899*a^21 - 1502906093782053073205/14219738897028653798*a^20 + 2856381252124933841401/14219738897028653798*a^19 + 6089495399990908650389/7109869448514326899*a^18 - 11276286094147897342947/7109869448514326899*a^17 - 29884731245153727598940/7109869448514326899*a^16 + 107932860462796092442865/14219738897028653798*a^15 + 90463711924304253143821/7109869448514326899*a^14 - 160649800412545571155989/7109869448514326899*a^13 - 162582113542105069496515/7109869448514326899*a^12 + 292600176862202781272045/7109869448514326899*a^11 + 150135528416512054610172/7109869448514326899*a^10 - 611127056086674460031671/14219738897028653798*a^9 - 62116249628079730977967/14219738897028653798*a^8 + 155828337170224165671915/7109869448514326899*a^7 - 46557306351796258433630/7109869448514326899*a^6 - 42787320516291328176713/14219738897028653798*a^5 + 55211282485381201696671/14219738897028653798*a^4 - 5013670803998496161253/7109869448514326899*a^3 - 4035981989469675147856/7109869448514326899*a^2 + 442961273430748386971/7109869448514326899*a + 120832404578839309803/14219738897028653798)*q^35 + (-38923373796838822799/28439477794057307596*a^24 + 99128881120698720915/28439477794057307596*a^23 + 660255618946589217379/14219738897028653798*a^22 - 848881915616741382558/7109869448514326899*a^21 - 19015068546802477152511/28439477794057307596*a^20 + 49605010103975192295205/28439477794057307596*a^19 + 75788561772611026462289/14219738897028653798*a^18 - 101101660956043806707008/7109869448514326899*a^17 - 364819087112027917962219/14219738897028653798*a^16 + 2019592719939860576419343/28439477794057307596*a^15 + 1079821244991832879248169/14219738897028653798*a^14 - 1593811000123673121753594/7109869448514326899*a^13 - 1892237749199328832669693/14219738897028653798*a^12 + 6325298099159085154840877/14219738897028653798*a^11 + 1706706760246547125944613/14219738897028653798*a^10 - 15173849966214508747270557/28439477794057307596*a^9 - 770472730835053258331667/28439477794057307596*a^8 + 5076573159782298666493399/14219738897028653798*a^7 - 198531463710743408131727/7109869448514326899*a^6 - 3309366993888192608678481/28439477794057307596*a^5 + 385562925399419627521031/28439477794057307596*a^4 + 207260086864955049390565/14219738897028653798*a^3 - 5919308041823390394882/7109869448514326899*a^2 - 2804677564903719064799/7109869448514326899*a + 531028516953051473393/28439477794057307596)*q^36 + (-4807743770711237899/7109869448514326899*a^24 + 12339799105364806957/7109869448514326899*a^23 + 162589984426930786007/7109869448514326899*a^22 - 422926478082532771952/7109869448514326899*a^21 - 2329566435264630374831/7109869448514326899*a^20 + 6184090383852013597081/7109869448514326899*a^19 + 18418422507265733475338/7109869448514326899*a^18 - 50491128700173883426365/7109869448514326899*a^17 - 87413166236121738269481/7109869448514326899*a^16 + 252798696170752617520476/7109869448514326899*a^15 + 251916753945748894557738/7109869448514326899*a^14 - 801713369488228787066202/7109869448514326899*a^13 - 416195273681386785475032/7109869448514326899*a^12 + 1604897780934514059689234/7109869448514326899*a^11 + 311522432831718242737884/7109869448514326899*a^10 - 1959193523751459080470483/7109869448514326899*a^9 + 43344713993686863057459/7109869448514326899*a^8 + 1360985683660449730091925/7109869448514326899*a^7 - 187145811394559561167420/7109869448514326899*a^6 - 481912868447467390328705/7109869448514326899*a^5 + 68311947055809694575121/7109869448514326899*a^4 + 71930057379853880856122/7109869448514326899*a^3 - 2071172179704211141453/7109869448514326899*a^2 - 2071787854343502916043/7109869448514326899*a + 79921880488941165950/7109869448514326899)*q^37 + O(q^38)
*]> ;  // time = 12.629 seconds




J[442] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 442, 442, 442, 442, 442, 442, 442, 442, 442, 221, 221, 221, 221, 221, 221, 221, 34, 26, 26, 17 ], new_dimensions := [ 1, 1, 1, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 2, 3, 6, 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 2, 2, 3, 3, 2, 2, 4, 4, 4, 6, 12, 2, 2, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 25, 1, 1, 1, 1, 1, 9, 1, 1, 1, 11, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 25, 1, 25, 0, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 5, 7, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 3, 1, 5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ -1, 2, 2, 2, 2, -1, 1, -4, -2, 2, -2, 2 ],
[ 1, 0, 2, 4, -2, -1, -1, 0, 2, 8, -8, -6 ],
[ 1, 2, -2, 2, 4, -1, -1, -4, 8, -8, 10, -10 ],
[ 1, 2, 4, -4, -2, -1, -1, -4, -4, -8, 4, 8 ],
[ 1, 0, -4, -2, -2, -1, 1, 0, -4, 2, -2, 0 ],
[ -2, 2, 4, -2, 2, 2, -2, 4, 10, -8, 2, -4 ],
[ -2, -4, 0, 0, -4, 2, 2, 4, -8, -16, -8, -8 ],
[ -3, -2, -4, 0, -2, -3, -3, -12, -12, 4, 8, 4 ],
[ 3, 2, 4, 0, -4, 3, 3, -4, 2, 10, -4, 4 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 2*x - 4,
x^2 + 4*x + 2,
x^3 + 2*x^2 - 4*x - 4,
x^3 - 2*x^2 - 6*x + 8
], atkin_lehners := [
[ 1, 1, -1 ],
[ -1, 1, 1 ],
[ -1, 1, 1 ],
[ -1, 1, 1 ],
[ -1, 1, -1 ],
[ 1, -1, 1 ],
[ 1, -1, -1 ],
[ 1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 1, 1, 3 ],
[ 1, 1, 1 ],
[ 11, 1, 5 ],
[ 1, 1, 3 ],
[ 11, 1, 5 ],
[ 7, 1, 7 ],
[ 5, 1, 1 ],
[ 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 11, 1, 1 ],
[ 1, 1, 3 ],
[ 1, 1, 1 ],
[ 1, 1, 7 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 1, 1, 1, 11, 0, 1, 0, 0, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 0, 1, 0, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1, 0, 1, 0, 0, 1 ], eigenvalues := [*
[ -1, 2, 2, 2, 2, -1, 1, -4, -2, 2, -2, 2 ],
[ 1, 0, 2, 4, -2, -1, -1, 0, 2, 8, -8, -6 ],
[ 1, 2, -2, 2, 4, -1, -1, -4, 8, -8, 10, -10 ],
[ 1, 2, 4, -4, -2, -1, -1, -4, -4, -8, 4, 8 ],
[ 1, 0, -4, -2, -2, -1, 1, 0, -4, 2, -2, 0 ],
[
-1,
a,
2,
-a,
-a + 2,
1,
-1,
2*a,
-a + 6,
-4,
-3*a + 4,
-4*a + 2
],
[
-1,
a,
-a - 2,
2*a + 4,
-2*a - 6,
1,
1,
2,
-a - 6,
-8,
-4,
-a - 6
],
[
-1,
a,
-a^2 - a + 2,
a^2 - 4,
-2*a - 2,
-1,
-1,
-a^2,
a^2 + 3*a - 6,
-a^2 - 2*a + 4,
a^2 + 2*a,
a^2 + a - 2
],
[
1,
a,
-a + 2,
0,
-a^2 + 4,
1,
1,
-a^2 + 4,
a^2 - a - 4,
a^2 - 2,
-2*a,
-a + 2
]
*], q_expansions := [*
q - q^2 + 2*q^3 + q^4 + 2*q^5 - 2*q^6 + 2*q^7 - q^8 + q^9 - 2*q^10 + 2*q^11 + 2*q^12 - q^13 - 2*q^14 + 4*q^15 + q^16 + q^17 - q^18 - 4*q^19 + 2*q^20 + 4*q^21 - 2*q^22 - 2*q^23 - 2*q^24 - q^25 + q^26 - 4*q^27 + 2*q^28 + 2*q^29 - 4*q^30 - 2*q^31 - q^32 + 4*q^33 - q^34 + 4*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 + q^4 + 2*q^5 + 4*q^7 + q^8 - 3*q^9 + 2*q^10 - 2*q^11 - q^13 + 4*q^14 + q^16 - q^17 - 3*q^18 + 2*q^20 - 2*q^22 + 2*q^23 - q^25 - q^26 + 4*q^28 + 8*q^29 - 8*q^31 + q^32 - q^34 + 8*q^35 - 3*q^36 - 6*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 - 2*q^5 + 2*q^6 + 2*q^7 + q^8 + q^9 - 2*q^10 + 4*q^11 + 2*q^12 - q^13 + 2*q^14 - 4*q^15 + q^16 - q^17 + q^18 - 4*q^19 - 2*q^20 + 4*q^21 + 4*q^22 + 8*q^23 + 2*q^24 - q^25 - q^26 - 4*q^27 + 2*q^28 - 8*q^29 - 4*q^30 + 10*q^31 + q^32 + 8*q^33 - q^34 - 4*q^35 + q^36 - 10*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 + 4*q^5 + 2*q^6 - 4*q^7 + q^8 + q^9 + 4*q^10 - 2*q^11 + 2*q^12 - q^13 - 4*q^14 + 8*q^15 + q^16 - q^17 + q^18 - 4*q^19 + 4*q^20 - 8*q^21 - 2*q^22 - 4*q^23 + 2*q^24 + 11*q^25 - q^26 - 4*q^27 - 4*q^28 - 8*q^29 + 8*q^30 + 4*q^31 + q^32 - 4*q^33 - q^34 - 16*q^35 + q^36 + 8*q^37 + O(q^38),
q + q^2 + q^4 - 4*q^5 - 2*q^7 + q^8 - 3*q^9 - 4*q^10 - 2*q^11 - q^13 - 2*q^14 + q^16 + q^17 - 3*q^18 - 4*q^20 - 2*q^22 - 4*q^23 + 11*q^25 - q^26 - 2*q^28 + 2*q^29 - 2*q^31 + q^32 + q^34 + 8*q^35 - 3*q^36 + O(q^38),
q - q^2 + a*q^3 + q^4 + 2*q^5 - a*q^6 - a*q^7 - q^8 + (2*a + 1)*q^9 - 2*q^10 + (-a + 2)*q^11 + a*q^12 + q^13 + a*q^14 + 2*a*q^15 + q^16 - q^17 + (-2*a - 1)*q^18 + 2*a*q^19 + 2*q^20 + (-2*a - 4)*q^21 + (a - 2)*q^22 + (-a + 6)*q^23 - a*q^24 - q^25 - q^26 + (2*a + 8)*q^27 - a*q^28 - 4*q^29 - 2*a*q^30 + (-3*a + 4)*q^31 - q^32 - 4*q^33 + q^34 - 2*a*q^35 + (2*a + 1)*q^36 + (-4*a + 2)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a - 2)*q^5 - a*q^6 + (2*a + 4)*q^7 - q^8 + (-4*a - 5)*q^9 + (a + 2)*q^10 + (-2*a - 6)*q^11 + a*q^12 + q^13 + (-2*a - 4)*q^14 + (2*a + 2)*q^15 + q^16 + q^17 + (4*a + 5)*q^18 + 2*q^19 + (-a - 2)*q^20 + (-4*a - 4)*q^21 + (2*a + 6)*q^22 + (-a - 6)*q^23 - a*q^24 - 3*q^25 - q^26 + (8*a + 8)*q^27 + (2*a + 4)*q^28 - 8*q^29 + (-2*a - 2)*q^30 - 4*q^31 - q^32 + (2*a + 4)*q^33 - q^34 - 4*q^35 + (-4*a - 5)*q^36 + (-a - 6)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a^2 - a + 2)*q^5 - a*q^6 + (a^2 - 4)*q^7 - q^8 + (a^2 - 3)*q^9 + (a^2 + a - 2)*q^10 + (-2*a - 2)*q^11 + a*q^12 - q^13 + (-a^2 + 4)*q^14 + (a^2 - 2*a - 4)*q^15 + q^16 - q^17 + (-a^2 + 3)*q^18 - a^2*q^19 + (-a^2 - a + 2)*q^20 + (-2*a^2 + 4)*q^21 + (2*a + 2)*q^22 + (a^2 + 3*a - 6)*q^23 - a*q^24 + (a^2 - 1)*q^25 + q^26 + (-2*a^2 - 2*a + 4)*q^27 + (a^2 - 4)*q^28 + (-a^2 - 2*a + 4)*q^29 + (-a^2 + 2*a + 4)*q^30 + (a^2 + 2*a)*q^31 - q^32 + (-2*a^2 - 2*a)*q^33 + q^34 + (4*a - 4)*q^35 + (a^2 - 3)*q^36 + (a^2 + a - 2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a + 2)*q^5 + a*q^6 + q^8 + (a^2 - 3)*q^9 + (-a + 2)*q^10 + (-a^2 + 4)*q^11 + a*q^12 + q^13 + (-a^2 + 2*a)*q^15 + q^16 + q^17 + (a^2 - 3)*q^18 + (-a^2 + 4)*q^19 + (-a + 2)*q^20 + (-a^2 + 4)*q^22 + (a^2 - a - 4)*q^23 + a*q^24 + (a^2 - 4*a - 1)*q^25 + q^26 + (2*a^2 - 8)*q^27 + (a^2 - 2)*q^29 + (-a^2 + 2*a)*q^30 - 2*a*q^31 + q^32 + (-2*a^2 - 2*a + 8)*q^33 + q^34 + (a^2 - 3)*q^36 + (-a + 2)*q^37 + O(q^38)
*]> ;  // time = 232.15 seconds




J[443] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 443, 443, 443, 443, 443 ], new_dimensions := [ 1, 1, 1, 12, 22 ], dimensions := [ 1, 1, 1, 12, 22 ], intersection_graph := [ 0, 1, 1, 3, 1, 1, 0, 1, 7, 1, 1, 1, 0, 1, 31, 3, 7, 1, 0, 1, 1, 1, 31, 1, 0 ], ap_traces := [
[ 0, 1, -2, 2, -2, -3, -2, -8, 6, -4, -10, 7 ],
[ -1, -2, 0, 1, 3, 3, -5, -7, -3, 0, 7, -3 ],
[ 1, -2, 4, -1, 5, 3, 3, -1, 3, 4, -7, -3 ],
[ -3, -7, -7, -16, -2, -42, -5, 0, -6, -5, 1, -46 ],
[ 1, 8, 3, 12, -8, 49, 15, 16, -10, 3, 13, 51 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^12 + 3*x^11 - 13*x^10 - 39*x^9 + 64*x^8 + 181*x^7 - 159*x^6 - 357*x^5 + 226*x^4 + 264*x^3 - 156*x^2 - 20*x + 6,
x^22 - x^21 - 35*x^20 + 33*x^19 + 523*x^18 - 456*x^17 - 4360*x^16 + 3428*x^15 + 22226*x^14 - 15227*x^13 - 71363*x^12 + 40569*x^11 + 143034*x^10 - 62774*x^9 - 170342*x^8 + 51992*x^7 + 107186*x^6 - 20952*x^5 - 26926*x^4 + 5536*x^3 + 1736*x^2 - 512*x + 32
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ 221 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ 221 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 221 ], torsion_lower_bounds := [ 1, 1, 1, 1, 221 ], l_ratios := [ 0, 0, 1, 0, 1/221 ], analytic_sha_upper_bounds := [ 0, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 0, 1 ], eigenvalues := [*
[ 0, 1, -2, 2, -2, -3, -2, -8, 6, -4, -10, 7 ],
[ -1, -2, 0, 1, 3, 3, -5, -7, -3, 0, 7, -3 ],
[ 1, -2, 4, -1, 5, 3, 3, -1, 3, 4, -7, -3 ],
[
a,
-953/3391*a^11 - 2407/3391*a^10 + 12118/3391*a^9 + 28943/3391*a^8 - 54989/3391*a^7 - 118907/3391*a^6 + 107898/3391*a^5 + 192792/3391*a^4 - 89082/3391*a^3 - 106533/3391*a^2 + 22942/3391*a + 7855/3391,
1928/10173*a^11 + 5446/10173*a^10 - 7892/3391*a^9 - 22794/3391*a^8 + 101843/10173*a^7 + 100645/3391*a^6 - 64436/3391*a^5 - 184296/3391*a^4 + 197453/10173*a^3 + 360922/10173*a^2 - 126538/10173*a - 5494/3391,
2606/10173*a^11 + 10126/10173*a^10 - 8613/3391*a^9 - 41834/3391*a^8 + 70319/10173*a^7 + 182256/3391*a^6 - 4206/3391*a^5 - 331390/3391*a^4 - 88522/10173*a^3 + 670810/10173*a^2 - 16183/10173*a - 19590/3391,
-2324/10173*a^11 - 6649/10173*a^10 + 7923/3391*a^9 + 24732/3391*a^8 - 67316/10173*a^7 - 92015/3391*a^6 + 4110/3391*a^5 + 130128/3391*a^4 + 116590/10173*a^3 - 173890/10173*a^2 - 59543/10173*a - 3438/3391,
-1705/10173*a^11 - 8288/10173*a^10 + 4749/3391*a^9 + 34907/3391*a^8 - 15523/10173*a^7 - 153681/3391*a^6 - 34989/3391*a^5 + 273166/3391*a^4 + 202298/10173*a^3 - 485564/10173*a^2 - 26056/10173*a - 8315/3391,
-1439/10173*a^11 - 3421/10173*a^10 + 7417/3391*a^9 + 17164/3391*a^8 - 126830/10173*a^7 - 92754/3391*a^6 + 110517/3391*a^5 + 210185/3391*a^4 - 402674/10173*a^3 - 504637/10173*a^2 + 188080/10173*a + 10872/3391,
1660/10173*a^11 + 3296/10173*a^10 - 7597/3391*a^9 - 12337/3391*a^8 + 114934/10173*a^7 + 41988/3391*a^6 - 89164/3391*a^5 - 35786/3391*a^4 + 296029/10173*a^3 - 64720/10173*a^2 - 118784/10173*a + 14082/3391,
5849/10173*a^11 + 14506/10173*a^10 - 23330/3391*a^9 - 55393/3391*a^8 + 282881/10173*a^7 + 211205/3391*a^6 - 144341/3391*a^5 - 302722/3391*a^4 + 163049/10173*a^3 + 424012/10173*a^2 + 99749/10173*a - 26696/3391,
-3020/10173*a^11 - 7222/10173*a^10 + 11574/3391*a^9 + 25672/3391*a^8 - 126242/10173*a^7 - 81985/3391*a^6 + 44101/3391*a^5 + 60202/3391*a^4 + 56623/10173*a^3 + 162848/10173*a^2 - 75239/10173*a - 30440/3391,
-553/3391*a^11 - 3247/3391*a^10 + 4420/3391*a^9 + 43108/3391*a^8 - 4987/3391*a^7 - 205891/3391*a^6 - 18699/3391*a^5 + 425374/3391*a^4 - 7495/3391*a^3 - 343442/3391*a^2 + 90779/3391*a + 29270/3391,
-7957/10173*a^11 - 19574/10173*a^10 + 33394/3391*a^9 + 76910/3391*a^8 - 455038/10173*a^7 - 311010/3391*a^6 + 308981/3391*a^5 + 504013/3391*a^4 - 869752/10173*a^3 - 849740/10173*a^2 + 312134/10173*a - 2389/3391
],
[
a,
24331639715/276511903884*a^21 - 8125806695/122894179504*a^20 - 3412458404095/1106047615536*a^19 + 2389711908563/1106047615536*a^18 + 51138378435019/1106047615536*a^17 - 32431419686159/1106047615536*a^16 - 214033136471141/553023807768*a^15 + 4926713915392/23042658657*a^14 + 548510219486683/276511903884*a^13 - 166235001605939/184341269256*a^12 - 7092131576110951/1106047615536*a^11 + 2420044653883823/1106047615536*a^10 + 14322072309976415/1106047615536*a^9 - 771797422040513/276511903884*a^8 - 2861400783481183/184341269256*a^7 + 748307574118151/553023807768*a^6 + 2701481312105405/276511903884*a^5 + 88077002352901/553023807768*a^4 - 221305411235065/92170634628*a^3 + 2558974223989/553023807768*a^2 + 15160229436083/92170634628*a - 2044922361293/138255951942,
-4487692457/553023807768*a^21 + 464915797/92170634628*a^20 + 17265814817/69127975971*a^19 - 58814741377/276511903884*a^18 - 447258475993/138255951942*a^17 + 1990589437673/553023807768*a^16 + 6368715278051/276511903884*a^15 - 497959835343/15361772438*a^14 - 27419742322367/276511903884*a^13 + 10498224082397/61447089752*a^12 + 18621638832281/69127975971*a^11 - 149378130661807/276511903884*a^10 - 260756674651403/553023807768*a^9 + 277082845647397/276511903884*a^8 + 24477554211125/46085317314*a^7 - 280269013911485/276511903884*a^6 - 98494826092843/276511903884*a^5 + 134782019264321/276511903884*a^4 + 3280809564745/30723544876*a^3 - 27800586430795/276511903884*a^2 - 684082799419/46085317314*a + 369225624443/69127975971,
-77378520413/1106047615536*a^21 + 11248192515/122894179504*a^20 + 2786326409257/1106047615536*a^19 - 3235313679647/1106047615536*a^18 - 42837539306137/1106047615536*a^17 + 21602664606733/553023807768*a^16 + 22968487627630/69127975971*a^15 - 26030166998233/92170634628*a^14 - 964027086846113/553023807768*a^13 + 440416402259833/368682538512*a^12 + 6368731241805277/1106047615536*a^11 - 3284291651518895/1106047615536*a^10 - 3277415486212031/276511903884*a^9 + 2261376132136177/553023807768*a^8 + 2659389515200819/184341269256*a^7 - 729926036929771/276511903884*a^6 - 5065503313809637/553023807768*a^5 + 144727804023313/276511903884*a^4 + 412422490650353/184341269256*a^3 - 40909468337813/276511903884*a^2 - 6718151258917/46085317314*a + 1360277665744/69127975971,
22030898407/276511903884*a^21 - 22355967073/184341269256*a^20 - 1602149670475/553023807768*a^19 + 2133015121595/553023807768*a^18 + 24838378447063/553023807768*a^17 - 28390101913589/553023807768*a^16 - 107299333802765/276511903884*a^15 + 8542868734255/23042658657*a^14 + 141583156365272/69127975971*a^13 - 72468197810867/46085317314*a^12 - 3761550886522039/553023807768*a^11 + 2183765319954767/553023807768*a^10 + 7787958126000041/553023807768*a^9 - 772557788684753/138255951942*a^8 - 1593947275306051/92170634628*a^7 + 1077979190630885/276511903884*a^6 + 774143588048455/69127975971*a^5 - 286253750311157/276511903884*a^4 - 67097718790501/23042658657*a^3 + 68665841942827/276511903884*a^2 + 3442866847655/15361772438*a - 1993849215107/69127975971,
-28106337295/737365077024*a^21 + 1790239187/245788359008*a^20 + 952185112427/737365077024*a^19 - 190843830589/737365077024*a^18 - 13706797493867/737365077024*a^17 + 1392565355075/368682538512*a^16 + 13664759825365/92170634628*a^15 - 1838677236247/61447089752*a^14 - 263987050082995/368682538512*a^13 + 35189455123363/245788359008*a^12 + 1585535871843647/737365077024*a^11 - 322273338485437/737365077024*a^10 - 732378231481303/184341269256*a^9 + 323065131836135/368682538512*a^8 + 532566927912329/122894179504*a^7 - 209230094037173/184341269256*a^6 - 961664330793791/368682538512*a^5 + 153056014419467/184341269256*a^4 + 97746233271315/122894179504*a^3 - 40755672026287/184341269256*a^2 - 2256745894127/30723544876*a + 376488821731/23042658657,
-184730416735/553023807768*a^21 + 2970771027/15361772438*a^20 + 1606832864495/138255951942*a^19 - 1766895502019/276511903884*a^18 - 23884705688453/138255951942*a^17 + 48308129073523/553023807768*a^16 + 99087424664059/69127975971*a^15 - 14722512766432/23042658657*a^14 - 2011480604792599/276511903884*a^13 + 495494412401261/184341269256*a^12 + 6428035752534421/276511903884*a^11 - 1781190829595273/276511903884*a^10 - 25609437570600349/553023807768*a^9 + 547608872895077/69127975971*a^8 + 1257697137294668/23042658657*a^7 - 904241581362559/276511903884*a^6 - 9293189186137943/276511903884*a^5 - 280292174684543/276511903884*a^4 + 736991822131795/92170634628*a^3 + 6333960798037/276511903884*a^2 - 12194932406789/23042658657*a + 3291493747678/69127975971,
7303311105/61447089752*a^21 + 14576458/23042658657*a^20 - 370061358029/92170634628*a^19 + 2577698432/23042658657*a^18 + 1776216758601/30723544876*a^17 - 522448076357/184341269256*a^16 - 42694246113701/92170634628*a^15 + 1228140760147/46085317314*a^14 + 208337956593377/92170634628*a^13 - 21933863295427/184341269256*a^12 - 636571552546919/92170634628*a^11 + 10835532522751/46085317314*a^10 + 802741492178233/61447089752*a^9 - 3697767687389/92170634628*a^8 - 111570420537581/7680886219*a^7 - 15409116636869/30723544876*a^6 + 779161228227629/92170634628*a^5 + 15536651889861/30723544876*a^4 - 184677539047787/92170634628*a^3 - 1777855487693/92170634628*a^2 + 6696514337983/46085317314*a - 221092595977/23042658657,
124062045775/553023807768*a^21 - 28105623923/184341269256*a^20 - 4328756627543/553023807768*a^19 + 2759569427881/553023807768*a^18 + 64501513552631/553023807768*a^17 - 18754723003085/276511903884*a^16 - 134056867263557/138255951942*a^15 + 22848440342635/46085317314*a^14 + 1362548576791999/276511903884*a^13 - 387466726716091/184341269256*a^12 - 8714456684729639/553023807768*a^11 + 2855888145050833/553023807768*a^10 + 2169991924254206/69127975971*a^9 - 1887616161343853/276511903884*a^8 - 3410391324500561/92170634628*a^7 + 532316295879419/138255951942*a^6 + 6318601928645915/276511903884*a^5 - 39180937928387/138255951942*a^4 - 510363018926531/92170634628*a^3 + 23589995439223/138255951942*a^2 + 2815070284467/7680886219*a - 2590479494044/69127975971,
-19687019897/368682538512*a^21 + 3813715383/122894179504*a^20 + 685975236451/368682538512*a^19 - 374850311417/368682538512*a^18 - 10210094100523/368682538512*a^17 + 634096740079/46085317314*a^16 + 21202737604435/92170634628*a^15 - 3052243188701/30723544876*a^14 - 215399007377105/184341269256*a^13 + 50446049312905/122894179504*a^12 + 1377312208331071/368682538512*a^11 - 352474453994129/368682538512*a^10 - 1371180455516209/184341269256*a^9 + 204380368844869/184341269256*a^8 + 537338819879421/61447089752*a^7 - 16193607014009/46085317314*a^6 - 985382146382221/184341269256*a^5 - 5304764952878/23042658657*a^4 + 77116410856601/61447089752*a^3 - 332669001655/46085317314*a^2 - 734184411535/7680886219*a + 304299932611/23042658657,
-56729238653/184341269256*a^21 + 19250031749/61447089752*a^20 + 2015724670693/184341269256*a^19 - 1858655082371/184341269256*a^18 - 30600643270141/184341269256*a^17 + 12464396317987/92170634628*a^16 + 32422513352546/23042658657*a^15 - 15028238776255/15361772438*a^14 - 672731078716757/92170634628*a^13 + 252893250552225/61447089752*a^12 + 4397678760703153/184341269256*a^11 - 1853842226488019/184341269256*a^10 - 1120819456295038/23042658657*a^9 + 1219399947630025/92170634628*a^8 + 1803876516165511/30723544876*a^7 - 338740777144057/46085317314*a^6 - 3410851515540241/92170634628*a^5 + 15806280328999/46085317314*a^4 + 275471525401189/30723544876*a^3 - 10174738166003/46085317314*a^2 - 4612941266422/7680886219*a + 1416432776348/23042658657,
-22810511171/138255951942*a^21 + 17969006199/122894179504*a^20 + 6432538363571/1106047615536*a^19 - 5200615152895/1106047615536*a^18 - 96816602595431/1106047615536*a^17 + 69529541228239/1106047615536*a^16 + 406471509653227/553023807768*a^15 - 10413564078764/23042658657*a^14 - 1043229030489485/276511903884*a^13 + 346709808308485/184341269256*a^12 + 13480705599653063/1106047615536*a^11 - 4987788087259075/1106047615536*a^10 - 27136415687949199/1106047615536*a^9 + 789349770110267/138255951942*a^8 + 5387970963743051/184341269256*a^7 - 1555428734101543/553023807768*a^6 - 5039864738087521/276511903884*a^5 - 119551218922889/553023807768*a^4 + 407854831722077/92170634628*a^3 - 12304780097513/553023807768*a^2 - 26875508337877/92170634628*a + 4231520364529/138255951942
]
*], q_expansions := [*
q + q^3 - 2*q^4 - 2*q^5 + 2*q^7 - 2*q^9 - 2*q^11 - 2*q^12 - 3*q^13 - 2*q^15 + 4*q^16 - 2*q^17 - 8*q^19 + 4*q^20 + 2*q^21 + 6*q^23 - q^25 - 5*q^27 - 4*q^28 - 4*q^29 - 10*q^31 - 2*q^33 - 4*q^35 + 4*q^36 + 7*q^37 + O(q^38),
q - q^2 - 2*q^3 - q^4 + 2*q^6 + q^7 + 3*q^8 + q^9 + 3*q^11 + 2*q^12 + 3*q^13 - q^14 - q^16 - 5*q^17 - q^18 - 7*q^19 - 2*q^21 - 3*q^22 - 3*q^23 - 6*q^24 - 5*q^25 - 3*q^26 + 4*q^27 - q^28 + 7*q^31 - 5*q^32 - 6*q^33 + 5*q^34 - q^36 - 3*q^37 + O(q^38),
q + q^2 - 2*q^3 - q^4 + 4*q^5 - 2*q^6 - q^7 - 3*q^8 + q^9 + 4*q^10 + 5*q^11 + 2*q^12 + 3*q^13 - q^14 - 8*q^15 - q^16 + 3*q^17 + q^18 - q^19 - 4*q^20 + 2*q^21 + 5*q^22 + 3*q^23 + 6*q^24 + 11*q^25 + 3*q^26 + 4*q^27 + q^28 + 4*q^29 - 8*q^30 - 7*q^31 + 5*q^32 - 10*q^33 + 3*q^34 - 4*q^35 - q^36 - 3*q^37 + O(q^38),
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3153481354875217/276511903884*a^5 + 298518938290309/138255951942*a^4 + 92870995320263/30723544876*a^3 - 66968313178235/138255951942*a^2 - 5308343291909/23042658657*a + 2762505242744/69127975971)*q^35 + (-45883573267/122894179504*a^21 + 131770933831/368682538512*a^20 + 4872083904517/368682538512*a^19 - 4244773009075/368682538512*a^18 - 24551843486111/122894179504*a^17 + 28486452328357/184341269256*a^16 + 77688215838755/46085317314*a^15 - 103119064612135/92170634628*a^14 - 1603959931459241/184341269256*a^13 + 1737601940143519/368682538512*a^12 + 10428336073598281/368682538512*a^11 - 4258905219734995/368682538512*a^10 - 1761630247039007/30723544876*a^9 + 2825516822071493/184341269256*a^8 + 4228666101557647/61447089752*a^7 - 270594363957901/30723544876*a^6 - 7964622256257665/184341269256*a^5 + 23619919687291/30723544876*a^4 + 1938837569526479/184341269256*a^3 - 32916530272325/92170634628*a^2 - 32638647580061/46085317314*a + 1714869603902/23042658657)*q^36 + (-22810511171/138255951942*a^21 + 17969006199/122894179504*a^20 + 6432538363571/1106047615536*a^19 - 5200615152895/1106047615536*a^18 - 96816602595431/1106047615536*a^17 + 69529541228239/1106047615536*a^16 + 406471509653227/553023807768*a^15 - 10413564078764/23042658657*a^14 - 1043229030489485/276511903884*a^13 + 346709808308485/184341269256*a^12 + 13480705599653063/1106047615536*a^11 - 4987788087259075/1106047615536*a^10 - 27136415687949199/1106047615536*a^9 + 789349770110267/138255951942*a^8 + 5387970963743051/184341269256*a^7 - 1555428734101543/553023807768*a^6 - 5039864738087521/276511903884*a^5 - 119551218922889/553023807768*a^4 + 407854831722077/92170634628*a^3 - 12304780097513/553023807768*a^2 - 26875508337877/92170634628*a + 4231520364529/138255951942)*q^37 + O(q^38)
*]> ;  // time = 14.87 seconds




J[445] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 445, 445, 445, 445, 445, 445, 445, 89, 89, 89 ], new_dimensions := [ 2, 2, 2, 4, 4, 7, 8, 1, 1, 5 ], dimensions := [ 2, 2, 2, 4, 4, 7, 8, 2, 2, 10 ], intersection_graph := [ 0, 1, 1, 11, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 0, 1, 7, 1, 1, 1, 1, 1, 11, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 13, 7, 1, 0, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 521, 1, 1, 1, 1, 1, 1, 0, 1, 1, 4121, 5, 1, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 25, 1, 1, 1, 1, 1, 521, 4121, 1, 25, 0 ], ap_traces := [
[ -2, -2, -2, 2, -4, 4, -4, -10, -6, 0, 2, -4 ],
[ 0, 2, 2, -2, 0, 4, 0, -2, 6, 0, -2, -8 ],
[ 2, 0, 2, 0, 8, 4, 8, 4, -8, -12, 4, 4 ],
[ 1, -2, -4, 2, -14, -5, -3, -1, -3, -10, -11, 3 ],
[ 1, 4, 4, 12, 2, -7, 1, -1, 13, 14, -11, -5 ],
[ -4, -8, 7, -16, -10, -7, -13, -7, -13, -4, 1, -5 ],
[ 1, 6, -8, -6, 14, -7, 17, 17, -1, 10, 1, -11 ]
], hecke_fields := [
x^2 + 6*x - 11,
x^2 - 3,
x^2 - 2*x - 1,
x^4 - x^3 - 5*x^2 + 7*x - 1,
x^4 - x^3 - 5*x^2 + 5*x + 1,
x^7 + 4*x^6 - 3*x^5 - 24*x^4 - 8*x^3 + 29*x^2 + 6*x - 9,
x^8 - x^7 - 11*x^6 + 9*x^5 + 34*x^4 - 19*x^3 - 27*x^2 + 11*x - 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ -1, 1 ],
[ 1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ]
], component_group_orders := [
[ 5, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 35, 1 ],
[ 521, 1 ],
[ 4121, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 35, 1 ],
[ 521, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 1, 5, 1, 1 ], torsion_lower_bounds := [ 1, 3, 1, 1, 5, 1, 1 ], l_ratios := [ 0, 1/3, 1, 0, 7/5, 0, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 0, 1, 0, 1 ], eigenvalues := [*
[
-1,
1/2*a + 1/2,
-1,
-1/2*a - 1/2,
a + 1,
-a - 1,
-2,
-1/2*a - 13/2,
-1/2*a - 9/2,
-a - 3,
1/2*a + 5/2,
a + 1
],
[
a,
a + 1,
1,
-a - 1,
0,
2,
0,
a - 1,
-a + 3,
-2*a,
-3*a - 1,
-2*a - 4
],
[
a,
-a + 1,
1,
a - 1,
4,
-2*a + 4,
2*a + 2,
-3*a + 5,
-3*a - 1,
-2*a - 4,
a + 1,
-4*a + 6
],
[
a,
a^3 - 5*a + 2,
-1,
-4*a^3 - 2*a^2 + 16*a - 3,
-a^3 + 5*a - 6,
5*a^3 + 3*a^2 - 21*a + 2,
a^3 + 3*a^2 - 3*a - 7,
6*a^3 + a^2 - 26*a + 11,
-3*a^3 - 3*a^2 + 11*a + 1,
5*a^3 + 2*a^2 - 19*a + 3,
-7*a^3 - 2*a^2 + 28*a - 13,
2*a^3 + 3*a^2 - 4*a - 4
],
[
a,
a^3 - 5*a + 2,
1,
3,
-a^3 + 3*a,
-a^3 - a^2 + 5*a,
-a^3 + a^2 + 3*a - 3,
-2*a^3 + a^2 + 10*a - 5,
-a^3 - a^2 + 5*a + 5,
a^3 - 2*a^2 - a + 9,
3*a^3 - 2*a^2 - 12*a + 5,
3*a^2 + 2*a - 10
],
[
a,
2/3*a^6 + 5/3*a^5 - 4*a^4 - 9*a^3 + 14/3*a^2 + 19/3*a - 3,
1,
-1/3*a^6 - 4/3*a^5 + a^4 + 7*a^3 + 5/3*a^2 - 14/3*a - 2,
-1/3*a^6 - 1/3*a^5 + 4*a^4 + 3*a^3 - 40/3*a^2 - 20/3*a + 7,
-5/3*a^6 - 17/3*a^5 + 5*a^4 + 28*a^3 + 40/3*a^2 - 37/3*a - 10,
-1/3*a^6 + 5/3*a^5 + 8*a^4 - 9*a^3 - 97/3*a^2 + 16/3*a + 14,
a^5 + 2*a^4 - 6*a^3 - 9*a^2 + 4*a,
5/3*a^6 + 14/3*a^5 - 8*a^4 - 23*a^3 + 11/3*a^2 + 34/3*a - 5,
a^6 + 3*a^5 - 3*a^4 - 14*a^3 - 9*a^2 + 5*a + 7,
2/3*a^6 + 2/3*a^5 - 8*a^4 - 5*a^3 + 80/3*a^2 + 28/3*a - 15,
-2*a^5 - 5*a^4 + 11*a^3 + 24*a^2 - 11*a - 11
],
[
a,
a^7 - 1/2*a^6 - 23/2*a^5 + 4*a^4 + 38*a^3 - 6*a^2 - 65/2*a + 9/2,
-1,
3*a^7 - 5/2*a^6 - 67/2*a^5 + 21*a^4 + 106*a^3 - 37*a^2 - 173/2*a + 33/2,
-a^3 + 5*a + 2,
a^7 - a^6 - 12*a^5 + 9*a^4 + 42*a^3 - 19*a^2 - 39*a + 9,
4*a^7 - 3*a^6 - 45*a^5 + 26*a^4 + 145*a^3 - 49*a^2 - 126*a + 26,
-3/2*a^7 + 3/2*a^6 + 17*a^5 - 13*a^4 - 55*a^3 + 49/2*a^2 + 91/2*a - 8,
-2*a^7 + 3/2*a^6 + 43/2*a^5 - 12*a^4 - 64*a^3 + 18*a^2 + 95/2*a - 15/2,
7*a^7 - 6*a^6 - 77*a^5 + 51*a^4 + 238*a^3 - 90*a^2 - 192*a + 37,
-9/2*a^7 + 7/2*a^6 + 51*a^5 - 29*a^4 - 164*a^3 + 97/2*a^2 + 271/2*a - 22,
-a^7 + a^6 + 12*a^5 - 9*a^4 - 43*a^3 + 19*a^2 + 44*a - 11
]
*], q_expansions := [*
q - q^2 + (1/2*a + 1/2)*q^3 - q^4 - q^5 + (-1/2*a - 1/2)*q^6 + (-1/2*a - 1/2)*q^7 + 3*q^8 - a*q^9 + q^10 + (a + 1)*q^11 + (-1/2*a - 1/2)*q^12 + (-a - 1)*q^13 + (1/2*a + 1/2)*q^14 + (-1/2*a - 1/2)*q^15 - q^16 - 2*q^17 + a*q^18 + (-1/2*a - 13/2)*q^19 + q^20 + (a - 3)*q^21 + (-a - 1)*q^22 + (-1/2*a - 9/2)*q^23 + (3/2*a + 3/2)*q^24 + q^25 + (a + 1)*q^26 + (a - 7)*q^27 + (1/2*a + 1/2)*q^28 + (-a - 3)*q^29 + (1/2*a + 1/2)*q^30 + (1/2*a + 5/2)*q^31 - 5*q^32 + (-2*a + 6)*q^33 + 2*q^34 + (1/2*a + 1/2)*q^35 + a*q^36 + (a + 1)*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + q^4 + q^5 + (a + 3)*q^6 + (-a - 1)*q^7 - a*q^8 + (2*a + 1)*q^9 + a*q^10 + (a + 1)*q^12 + 2*q^13 + (-a - 3)*q^14 + (a + 1)*q^15 - 5*q^16 + (a + 6)*q^18 + (a - 1)*q^19 + q^20 + (-2*a - 4)*q^21 + (-a + 3)*q^23 + (-a - 3)*q^24 + q^25 + 2*a*q^26 + 4*q^27 + (-a - 1)*q^28 - 2*a*q^29 + (a + 3)*q^30 + (-3*a - 1)*q^31 - 3*a*q^32 + (-a - 1)*q^35 + (2*a + 1)*q^36 + (-2*a - 4)*q^37 + O(q^38),
q + a*q^2 + (-a + 1)*q^3 + (2*a - 1)*q^4 + q^5 + (-a - 1)*q^6 + (a - 1)*q^7 + (a + 2)*q^8 - q^9 + a*q^10 + 4*q^11 + (-a - 3)*q^12 + (-2*a + 4)*q^13 + (a + 1)*q^14 + (-a + 1)*q^15 + 3*q^16 + (2*a + 2)*q^17 - a*q^18 + (-3*a + 5)*q^19 + (2*a - 1)*q^20 - 2*q^21 + 4*a*q^22 + (-3*a - 1)*q^23 + (-3*a + 1)*q^24 + q^25 - 2*q^26 + (4*a - 4)*q^27 + (a + 3)*q^28 + (-2*a - 4)*q^29 + (-a - 1)*q^30 + (a + 1)*q^31 + (a - 4)*q^32 + (-4*a + 4)*q^33 + (6*a + 2)*q^34 + (a - 1)*q^35 + (-2*a + 1)*q^36 + (-4*a + 6)*q^37 + O(q^38),
q + a*q^2 + (a^3 - 5*a + 2)*q^3 + (a^2 - 2)*q^4 - q^5 + (a^3 - 5*a + 1)*q^6 + (-4*a^3 - 2*a^2 + 16*a - 3)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^3 - a^2 + 9*a - 3)*q^9 - a*q^10 + (-a^3 + 5*a - 6)*q^11 + (-a^3 + 4*a - 3)*q^12 + (5*a^3 + 3*a^2 - 21*a + 2)*q^13 + (-6*a^3 - 4*a^2 + 25*a - 4)*q^14 + (-a^3 + 5*a - 2)*q^15 + (a^3 - a^2 - 7*a + 5)*q^16 + (a^3 + 3*a^2 - 3*a - 7)*q^17 + (-3*a^3 - a^2 + 11*a - 2)*q^18 + (6*a^3 + a^2 - 26*a + 11)*q^19 + (-a^2 + 2)*q^20 + (7*a^3 + 4*a^2 - 29*a + 4)*q^21 + (-a^3 + a - 1)*q^22 + (-3*a^3 - 3*a^2 + 11*a + 1)*q^23 + (-3*a^3 - a^2 + 14*a - 3)*q^24 + q^25 + (8*a^3 + 4*a^2 - 33*a + 5)*q^26 + (2*a^2 + 3*a - 6)*q^27 + (-2*a^3 - a^2 + 6*a)*q^28 + (5*a^3 + 2*a^2 - 19*a + 3)*q^29 + (-a^3 + 5*a - 1)*q^30 + (-7*a^3 - 2*a^2 + 28*a - 13)*q^31 + (-2*a^3 - 2*a^2 + 6*a + 1)*q^32 + (-2*a^3 + a^2 + 11*a - 8)*q^33 + (4*a^3 + 2*a^2 - 14*a + 1)*q^34 + (4*a^3 + 2*a^2 - 16*a + 3)*q^35 + (-2*a^2 + a + 3)*q^36 + (2*a^3 + 3*a^2 - 4*a - 4)*q^37 + O(q^38),
q + a*q^2 + (a^3 - 5*a + 2)*q^3 + (a^2 - 2)*q^4 + q^5 + (a^3 - 3*a - 1)*q^6 + 3*q^7 + (a^3 - 4*a)*q^8 + (-a^2 - a + 5)*q^9 + a*q^10 + (-a^3 + 3*a)*q^11 + (-a^3 + 2*a^2 + 4*a - 5)*q^12 + (-a^3 - a^2 + 5*a)*q^13 + 3*a*q^14 + (a^3 - 5*a + 2)*q^15 + (a^3 - a^2 - 5*a + 3)*q^16 + (-a^3 + a^2 + 3*a - 3)*q^17 + (-a^3 - a^2 + 5*a)*q^18 + (-2*a^3 + a^2 + 10*a - 5)*q^19 + (a^2 - 2)*q^20 + (3*a^3 - 15*a + 6)*q^21 + (-a^3 - 2*a^2 + 5*a + 1)*q^22 + (-a^3 - a^2 + 5*a + 5)*q^23 + (-a^3 - a^2 + 6*a + 3)*q^24 + q^25 + (-2*a^3 + 5*a + 1)*q^26 + (-2*a^2 - a + 6)*q^27 + (3*a^2 - 6)*q^28 + (a^3 - 2*a^2 - a + 9)*q^29 + (a^3 - 3*a - 1)*q^30 + (3*a^3 - 2*a^2 - 12*a + 5)*q^31 + (-2*a^3 + 6*a - 1)*q^32 + (a^2 - 3*a - 2)*q^33 + (-2*a^2 + 2*a + 1)*q^34 + 3*q^35 + (-2*a^3 + 2*a^2 + 7*a - 9)*q^36 + (3*a^2 + 2*a - 10)*q^37 + O(q^38),
q + a*q^2 + (2/3*a^6 + 5/3*a^5 - 4*a^4 - 9*a^3 + 14/3*a^2 + 19/3*a - 3)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^6 - 2*a^5 + 7*a^4 + 10*a^3 - 13*a^2 - 7*a + 6)*q^6 + (-1/3*a^6 - 4/3*a^5 + a^4 + 7*a^3 + 5/3*a^2 - 14/3*a - 2)*q^7 + (a^3 - 4*a)*q^8 + (-2/3*a^6 - 5/3*a^5 + 4*a^4 + 10*a^3 - 11/3*a^2 - 31/3*a + 2)*q^9 + a*q^10 + (-1/3*a^6 - 1/3*a^5 + 4*a^4 + 3*a^3 - 40/3*a^2 - 20/3*a + 7)*q^11 + (2/3*a^6 + 2/3*a^5 - 6*a^4 - 3*a^3 + 38/3*a^2 - 2/3*a - 3)*q^12 + (-5/3*a^6 - 17/3*a^5 + 5*a^4 + 28*a^3 + 40/3*a^2 - 37/3*a - 10)*q^13 + (-a^4 - a^3 + 5*a^2 - 3)*q^14 + (2/3*a^6 + 5/3*a^5 - 4*a^4 - 9*a^3 + 14/3*a^2 + 19/3*a - 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/3*a^6 + 5/3*a^5 + 8*a^4 - 9*a^3 - 97/3*a^2 + 16/3*a + 14)*q^17 + (a^6 + 2*a^5 - 6*a^4 - 9*a^3 + 9*a^2 + 6*a - 6)*q^18 + (a^5 + 2*a^4 - 6*a^3 - 9*a^2 + 4*a)*q^19 + (a^2 - 2)*q^20 + (-2*a^6 - 4*a^5 + 14*a^4 + 21*a^3 - 22*a^2 - 11*a + 8)*q^21 + (a^6 + 3*a^5 - 5*a^4 - 16*a^3 + 3*a^2 + 9*a - 3)*q^22 + (5/3*a^6 + 14/3*a^5 - 8*a^4 - 23*a^3 + 11/3*a^2 + 34/3*a - 5)*q^23 + (-a^4 - 2*a^3 + 6*a^2 + 7*a - 6)*q^24 + q^25 + (a^6 - 12*a^4 + 36*a^2 - 15)*q^26 + (-a^5 - 3*a^4 + 3*a^3 + 13*a^2 + 4*a - 8)*q^27 + (2/3*a^6 + 5/3*a^5 - 3*a^4 - 9*a^3 - 10/3*a^2 + 19/3*a + 4)*q^28 + (a^6 + 3*a^5 - 3*a^4 - 14*a^3 - 9*a^2 + 5*a + 7)*q^29 + (-a^6 - 2*a^5 + 7*a^4 + 10*a^3 - 13*a^2 - 7*a + 6)*q^30 + (2/3*a^6 + 2/3*a^5 - 8*a^4 - 5*a^3 + 80/3*a^2 + 28/3*a - 15)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^6 - 2*a^5 + 6*a^4 + 8*a^3 - 5*a^2 + 6*a - 4)*q^33 + (3*a^6 + 7*a^5 - 17*a^4 - 35*a^3 + 15*a^2 + 16*a - 3)*q^34 + (-1/3*a^6 - 4/3*a^5 + a^4 + 7*a^3 + 5/3*a^2 - 14/3*a - 2)*q^35 + (-2/3*a^6 + 1/3*a^5 + 7*a^4 - 3*a^3 - 47/3*a^2 + 26/3*a + 5)*q^36 + (-2*a^5 - 5*a^4 + 11*a^3 + 24*a^2 - 11*a - 11)*q^37 + O(q^38),
q + a*q^2 + (a^7 - 1/2*a^6 - 23/2*a^5 + 4*a^4 + 38*a^3 - 6*a^2 - 65/2*a + 9/2)*q^3 + (a^2 - 2)*q^4 - q^5 + (1/2*a^7 - 1/2*a^6 - 5*a^5 + 4*a^4 + 13*a^3 - 11/2*a^2 - 13/2*a + 1)*q^6 + (3*a^7 - 5/2*a^6 - 67/2*a^5 + 21*a^4 + 106*a^3 - 37*a^2 - 173/2*a + 33/2)*q^7 + (a^3 - 4*a)*q^8 + (-3*a^7 + 3*a^6 + 33*a^5 - 26*a^4 - 102*a^3 + 48*a^2 + 82*a - 16)*q^9 - a*q^10 + (-a^3 + 5*a + 2)*q^11 + (-2*a^7 + 3/2*a^6 + 45/2*a^5 - 12*a^4 - 72*a^3 + 19*a^2 + 121/2*a - 17/2)*q^12 + (a^7 - a^6 - 12*a^5 + 9*a^4 + 42*a^3 - 19*a^2 - 39*a + 9)*q^13 + (1/2*a^7 - 1/2*a^6 - 6*a^5 + 4*a^4 + 20*a^3 - 11/2*a^2 - 33/2*a + 3)*q^14 + (-a^7 + 1/2*a^6 + 23/2*a^5 - 4*a^4 - 38*a^3 + 6*a^2 + 65/2*a - 9/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (4*a^7 - 3*a^6 - 45*a^5 + 26*a^4 + 145*a^3 - 49*a^2 - 126*a + 26)*q^17 + (a^5 - 9*a^3 + a^2 + 17*a - 3)*q^18 + (-3/2*a^7 + 3/2*a^6 + 17*a^5 - 13*a^4 - 55*a^3 + 49/2*a^2 + 91/2*a - 8)*q^19 + (-a^2 + 2)*q^20 + (-4*a^7 + 3*a^6 + 45*a^5 - 26*a^4 - 145*a^3 + 48*a^2 + 126*a - 21)*q^21 + (-a^4 + 5*a^2 + 2*a)*q^22 + (-2*a^7 + 3/2*a^6 + 43/2*a^5 - 12*a^4 - 64*a^3 + 18*a^2 + 95/2*a - 15/2)*q^23 + (-3/2*a^7 + 3/2*a^6 + 16*a^5 - 12*a^4 - 45*a^3 + 35/2*a^2 + 53/2*a - 4)*q^24 + q^25 + (-a^6 + 8*a^4 - 12*a^2 - 2*a + 1)*q^26 + (a^7 - 12*a^5 - a^4 + 43*a^3 + 4*a^2 - 44*a + 9)*q^27 + (-6*a^7 + 9/2*a^6 + 133/2*a^5 - 39*a^4 - 208*a^3 + 71*a^2 + 341/2*a - 65/2)*q^28 + (7*a^7 - 6*a^6 - 77*a^5 + 51*a^4 + 238*a^3 - 90*a^2 - 192*a + 37)*q^29 + (-1/2*a^7 + 1/2*a^6 + 5*a^5 - 4*a^4 - 13*a^3 + 11/2*a^2 + 13/2*a - 1)*q^30 + (-9/2*a^7 + 7/2*a^6 + 51*a^5 - 29*a^4 - 164*a^3 + 97/2*a^2 + 271/2*a - 22)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (4*a^7 - 3*a^6 - 44*a^5 + 24*a^4 + 134*a^3 - 35*a^2 - 98*a + 14)*q^33 + (a^7 - a^6 - 10*a^5 + 9*a^4 + 27*a^3 - 18*a^2 - 18*a + 4)*q^34 + (-3*a^7 + 5/2*a^6 + 67/2*a^5 - 21*a^4 - 106*a^3 + 37*a^2 + 173/2*a - 33/2)*q^35 + (6*a^7 - 5*a^6 - 66*a^5 + 43*a^4 + 205*a^3 - 79*a^2 - 167*a + 32)*q^36 + (-a^7 + a^6 + 12*a^5 - 9*a^4 - 43*a^3 + 19*a^2 + 44*a - 11)*q^37 + O(q^38)
*]> ;  // time = 91.251 seconds




J[446] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 446, 446, 446, 446, 446, 446, 223, 223, 223 ], new_dimensions := [ 1, 1, 1, 1, 7, 8, 2, 4, 12 ], dimensions := [ 1, 1, 1, 1, 7, 8, 4, 8, 24 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 11, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 7, 1, 1, 3, 1, 0, 1, 7, 63, 1, 1, 11, 1, 1, 1, 0, 1, 1, 359353, 1, 1, 1, 1, 7, 1, 0, 49, 1, 3, 1, 3, 1, 63, 1, 49, 0, 1, 1, 1, 1, 7, 1, 359353, 1, 1, 0 ], ap_traces := [
[ -1, -1, 0, 0, 1, -2, 1, -4, 1, -3, -10, -3 ],
[ -1, -3, -4, -4, -5, -6, 1, 0, -5, -3, 2, 5 ],
[ 1, 2, 0, 0, -2, 4, -2, 8, -8, -6, 8, -6 ],
[ 1, -1, -2, -2, -3, 0, 1, -6, -3, 5, 2, -7 ],
[ 7, 1, 2, 6, 9, -2, -7, -2, 15, 9, -2, 5 ],
[ -8, 4, 4, 4, 2, 10, 8, 16, -4, 8, 12, 16 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^7 - x^6 - 14*x^5 + 12*x^4 + 50*x^3 - 36*x^2 - 38*x + 18,
x^8 - 4*x^7 - 12*x^6 + 54*x^5 + 34*x^4 - 204*x^3 + 6*x^2 + 160*x + 34
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 3, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 7, 1 ],
[ 3087, 1 ],
[ 1078059, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 7, 1 ],
[ 3087, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 7, 3 ], torsion_lower_bounds := [ 1, 1, 1, 1, 7, 3 ], l_ratios := [ 0, 0, 3, 0, 63, 121/3 ], analytic_sha_upper_bounds := [ 0, 0, 1, 0, 1, 121 ], analytic_sha_lower_bounds := [ 0, 0, 1, 0, 1, 121 ], eigenvalues := [*
[ -1, -1, 0, 0, 1, -2, 1, -4, 1, -3, -10, -3 ],
[ -1, -3, -4, -4, -5, -6, 1, 0, -5, -3, 2, 5 ],
[ 1, 2, 0, 0, -2, 4, -2, 8, -8, -6, 8, -6 ],
[ 1, -1, -2, -2, -3, 0, 1, -6, -3, 5, 2, -7 ],
[
1,
a,
-6/239*a^6 + 37/239*a^5 + 92/239*a^4 - 388/239*a^3 - 526/239*a^2 + 703/239*a + 858/239,
-41/239*a^6 - 26/239*a^5 + 549/239*a^4 + 376/239*a^3 - 1762/239*a^2 - 972/239*a + 1322/239,
36/239*a^6 + 17/239*a^5 - 552/239*a^4 - 301/239*a^3 + 2200/239*a^2 + 801/239*a - 1324/239,
64/239*a^6 - 76/239*a^5 - 822/239*a^4 + 713/239*a^3 + 2424/239*a^2 - 1205/239*a - 1026/239,
42/239*a^6 - 20/239*a^5 - 644/239*a^4 + 326/239*a^3 + 2487/239*a^2 - 1336/239*a - 1704/239,
-2*a,
73/239*a^6 - 12/239*a^5 - 960/239*a^4 + 100/239*a^3 + 2974/239*a^2 - 228/239*a - 1118/239,
-95/239*a^6 + 68/239*a^5 + 1138/239*a^4 - 726/239*a^3 - 2672/239*a^2 + 1770/239*a + 440/239,
-43/239*a^6 + 66/239*a^5 + 500/239*a^4 - 550/239*a^3 - 1061/239*a^2 + 298/239*a - 304/239,
13/239*a^6 - 120/239*a^5 - 40/239*a^4 + 1478/239*a^3 - 374/239*a^2 - 3714/239*a + 292/239
],
[
-1,
a,
-1/33*a^7 + 19/33*a^5 + 2/33*a^4 - 116/33*a^3 + 2/33*a^2 + 221/33*a - 10/33,
4/33*a^6 - 2/33*a^5 - 25/11*a^4 + 46/33*a^3 + 114/11*a^2 - 212/33*a - 184/33,
2/33*a^7 - 2/11*a^6 - 35/33*a^5 + 92/33*a^4 + 163/33*a^3 - 32/3*a^2 - 91/33*a + 164/33,
-2/33*a^7 + 4/33*a^6 + 12/11*a^5 - 38/33*a^4 - 73/11*a^3 + 16/33*a^2 + 395/33*a + 86/11,
-7/33*a^6 + 20/33*a^5 + 30/11*a^4 - 196/33*a^3 - 117/11*a^2 + 404/33*a + 322/33,
8/33*a^7 - 2/3*a^6 - 36/11*a^5 + 248/33*a^4 + 148/11*a^3 - 676/33*a^2 - 470/33*a + 56/11,
-2/33*a^7 + 6/11*a^6 - 4/33*a^5 - 218/33*a^4 + 206/33*a^3 + 718/33*a^2 - 644/33*a - 452/33,
-2*a + 2,
-4/33*a^7 + 1/3*a^6 + 18/11*a^5 - 124/33*a^4 - 74/11*a^3 + 305/33*a^2 + 202/33*a + 60/11,
2/11*a^7 - 6/11*a^6 - 24/11*a^5 + 70/11*a^4 + 64/11*a^3 - 18*a^2 + 30/11*a + 54/11
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + q^6 - q^8 - 2*q^9 + q^11 - q^12 - 2*q^13 + q^16 + q^17 + 2*q^18 - 4*q^19 - q^22 + q^23 + q^24 - 5*q^25 + 2*q^26 + 5*q^27 - 3*q^29 - 10*q^31 - q^32 - q^33 - q^34 - 2*q^36 - 3*q^37 + O(q^38),
q - q^2 - 3*q^3 + q^4 - 4*q^5 + 3*q^6 - 4*q^7 - q^8 + 6*q^9 + 4*q^10 - 5*q^11 - 3*q^12 - 6*q^13 + 4*q^14 + 12*q^15 + q^16 + q^17 - 6*q^18 - 4*q^20 + 12*q^21 + 5*q^22 - 5*q^23 + 3*q^24 + 11*q^25 + 6*q^26 - 9*q^27 - 4*q^28 - 3*q^29 - 12*q^30 + 2*q^31 - q^32 + 15*q^33 - q^34 + 16*q^35 + 6*q^36 + 5*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 + 2*q^6 + q^8 + q^9 - 2*q^11 + 2*q^12 + 4*q^13 + q^16 - 2*q^17 + q^18 + 8*q^19 - 2*q^22 - 8*q^23 + 2*q^24 - 5*q^25 + 4*q^26 - 4*q^27 - 6*q^29 + 8*q^31 + q^32 - 4*q^33 - 2*q^34 + q^36 - 6*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 2*q^5 - q^6 - 2*q^7 + q^8 - 2*q^9 - 2*q^10 - 3*q^11 - q^12 - 2*q^14 + 2*q^15 + q^16 + q^17 - 2*q^18 - 6*q^19 - 2*q^20 + 2*q^21 - 3*q^22 - 3*q^23 - q^24 - q^25 + 5*q^27 - 2*q^28 + 5*q^29 + 2*q^30 + 2*q^31 + q^32 + 3*q^33 + q^34 + 4*q^35 - 2*q^36 - 7*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-6/239*a^6 + 37/239*a^5 + 92/239*a^4 - 388/239*a^3 - 526/239*a^2 + 703/239*a + 858/239)*q^5 + a*q^6 + (-41/239*a^6 - 26/239*a^5 + 549/239*a^4 + 376/239*a^3 - 1762/239*a^2 - 972/239*a + 1322/239)*q^7 + q^8 + (a^2 - 3)*q^9 + (-6/239*a^6 + 37/239*a^5 + 92/239*a^4 - 388/239*a^3 - 526/239*a^2 + 703/239*a + 858/239)*q^10 + (36/239*a^6 + 17/239*a^5 - 552/239*a^4 - 301/239*a^3 + 2200/239*a^2 + 801/239*a - 1324/239)*q^11 + a*q^12 + (64/239*a^6 - 76/239*a^5 - 822/239*a^4 + 713/239*a^3 + 2424/239*a^2 - 1205/239*a - 1026/239)*q^13 + (-41/239*a^6 - 26/239*a^5 + 549/239*a^4 + 376/239*a^3 - 1762/239*a^2 - 972/239*a + 1322/239)*q^14 + (31/239*a^6 + 8/239*a^5 - 316/239*a^4 - 226/239*a^3 + 487/239*a^2 + 630/239*a + 108/239)*q^15 + q^16 + (42/239*a^6 - 20/239*a^5 - 644/239*a^4 + 326/239*a^3 + 2487/239*a^2 - 1336/239*a - 1704/239)*q^17 + (a^2 - 3)*q^18 - 2*a*q^19 + (-6/239*a^6 + 37/239*a^5 + 92/239*a^4 - 388/239*a^3 - 526/239*a^2 + 703/239*a + 858/239)*q^20 + (-67/239*a^6 - 25/239*a^5 + 868/239*a^4 + 288/239*a^3 - 2448/239*a^2 - 236/239*a + 738/239)*q^21 + (36/239*a^6 + 17/239*a^5 - 552/239*a^4 - 301/239*a^3 + 2200/239*a^2 + 801/239*a - 1324/239)*q^22 + (73/239*a^6 - 12/239*a^5 - 960/239*a^4 + 100/239*a^3 + 2974/239*a^2 - 228/239*a - 1118/239)*q^23 + a*q^24 + (-115/239*a^6 + 32/239*a^5 + 1604/239*a^4 - 426/239*a^3 - 5461/239*a^2 + 1564/239*a + 3539/239)*q^25 + (64/239*a^6 - 76/239*a^5 - 822/239*a^4 + 713/239*a^3 + 2424/239*a^2 - 1205/239*a - 1026/239)*q^26 + (a^3 - 6*a)*q^27 + (-41/239*a^6 - 26/239*a^5 + 549/239*a^4 + 376/239*a^3 - 1762/239*a^2 - 972/239*a + 1322/239)*q^28 + (-95/239*a^6 + 68/239*a^5 + 1138/239*a^4 - 726/239*a^3 - 2672/239*a^2 + 1770/239*a + 440/239)*q^29 + (31/239*a^6 + 8/239*a^5 - 316/239*a^4 - 226/239*a^3 + 487/239*a^2 + 630/239*a + 108/239)*q^30 + (-43/239*a^6 + 66/239*a^5 + 500/239*a^4 - 550/239*a^3 - 1061/239*a^2 + 298/239*a - 304/239)*q^31 + q^32 + (53/239*a^6 - 48/239*a^5 - 733/239*a^4 + 400/239*a^3 + 2097/239*a^2 + 44/239*a - 648/239)*q^33 + (42/239*a^6 - 20/239*a^5 - 644/239*a^4 + 326/239*a^3 + 2487/239*a^2 - 1336/239*a - 1704/239)*q^34 + (-69/239*a^6 + 67/239*a^5 + 1058/239*a^4 - 638/239*a^3 - 4376/239*a^2 + 556/239*a + 3414/239)*q^35 + (a^2 - 3)*q^36 + (13/239*a^6 - 120/239*a^5 - 40/239*a^4 + 1478/239*a^3 - 374/239*a^2 - 3714/239*a + 292/239)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-1/33*a^7 + 19/33*a^5 + 2/33*a^4 - 116/33*a^3 + 2/33*a^2 + 221/33*a - 10/33)*q^5 - a*q^6 + (4/33*a^6 - 2/33*a^5 - 25/11*a^4 + 46/33*a^3 + 114/11*a^2 - 212/33*a - 184/33)*q^7 - q^8 + (a^2 - 3)*q^9 + (1/33*a^7 - 19/33*a^5 - 2/33*a^4 + 116/33*a^3 - 2/33*a^2 - 221/33*a + 10/33)*q^10 + (2/33*a^7 - 2/11*a^6 - 35/33*a^5 + 92/33*a^4 + 163/33*a^3 - 32/3*a^2 - 91/33*a + 164/33)*q^11 + a*q^12 + (-2/33*a^7 + 4/33*a^6 + 12/11*a^5 - 38/33*a^4 - 73/11*a^3 + 16/33*a^2 + 395/33*a + 86/11)*q^13 + (-4/33*a^6 + 2/33*a^5 + 25/11*a^4 - 46/33*a^3 - 114/11*a^2 + 212/33*a + 184/33)*q^14 + (-4/33*a^7 + 7/33*a^6 + 56/33*a^5 - 82/33*a^4 - 202/33*a^3 + 227/33*a^2 + 50/11*a + 34/33)*q^15 + q^16 + (-7/33*a^6 + 20/33*a^5 + 30/11*a^4 - 196/33*a^3 - 117/11*a^2 + 404/33*a + 322/33)*q^17 + (-a^2 + 3)*q^18 + (8/33*a^7 - 2/3*a^6 - 36/11*a^5 + 248/33*a^4 + 148/11*a^3 - 676/33*a^2 - 470/33*a + 56/11)*q^19 + (-1/33*a^7 + 19/33*a^5 + 2/33*a^4 - 116/33*a^3 + 2/33*a^2 + 221/33*a - 10/33)*q^20 + (4/33*a^7 - 2/33*a^6 - 25/11*a^5 + 46/33*a^4 + 114/11*a^3 - 212/33*a^2 - 184/33*a)*q^21 + (-2/33*a^7 + 2/11*a^6 + 35/33*a^5 - 92/33*a^4 - 163/33*a^3 + 32/3*a^2 + 91/33*a - 164/33)*q^22 + (-2/33*a^7 + 6/11*a^6 - 4/33*a^5 - 218/33*a^4 + 206/33*a^3 + 718/33*a^2 - 644/33*a - 452/33)*q^23 - a*q^24 + (-2/11*a^7 + 6/11*a^6 + 24/11*a^5 - 70/11*a^4 - 64/11*a^3 + 19*a^2 - 52/11*a - 43/11)*q^25 + (2/33*a^7 - 4/33*a^6 - 12/11*a^5 + 38/33*a^4 + 73/11*a^3 - 16/33*a^2 - 395/33*a - 86/11)*q^26 + (a^3 - 6*a)*q^27 + (4/33*a^6 - 2/33*a^5 - 25/11*a^4 + 46/33*a^3 + 114/11*a^2 - 212/33*a - 184/33)*q^28 + (-2*a + 2)*q^29 + (4/33*a^7 - 7/33*a^6 - 56/33*a^5 + 82/33*a^4 + 202/33*a^3 - 227/33*a^2 - 50/11*a - 34/33)*q^30 + (-4/33*a^7 + 1/3*a^6 + 18/11*a^5 - 124/33*a^4 - 74/11*a^3 + 305/33*a^2 + 202/33*a + 60/11)*q^31 - q^32 + (2/33*a^7 - 1/3*a^6 - 16/33*a^5 + 95/33*a^4 + 56/33*a^3 - 103/33*a^2 - 52/11*a - 68/33)*q^33 + (7/33*a^6 - 20/33*a^5 - 30/11*a^4 + 196/33*a^3 + 117/11*a^2 - 404/33*a - 322/33)*q^34 + (8/33*a^7 - 10/11*a^6 - 71/33*a^5 + 332/33*a^4 + 2/3*a^3 - 964/33*a^2 + 614/33*a + 404/33)*q^35 + (a^2 - 3)*q^36 + (2/11*a^7 - 6/11*a^6 - 24/11*a^5 + 70/11*a^4 + 64/11*a^3 - 18*a^2 + 30/11*a + 54/11)*q^37 + O(q^38)
*]> ;  // time = 123.941 seconds




J[447] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 447, 447, 447, 447, 149, 149 ], new_dimensions := [ 3, 3, 9, 10, 3, 9 ], dimensions := [ 3, 3, 9, 10, 6, 18 ], intersection_graph := [ 0, 1, 1, 1, 13, 1, 1, 0, 1, 1, 1, 219, 1, 1, 0, 1, 139, 1, 1, 1, 1, 0, 1, 408113, 13, 1, 139, 1, 0, 1, 1, 219, 1, 408113, 1, 0 ], ap_traces := [
[ -1, -3, 0, -3, 3, -8, -8, -3, -5, 4, -1, -17 ],
[ -3, 3, -6, -3, -9, 0, -6, -3, -3, -6, 3, -9 ],
[ 4, 9, 8, 1, 13, -2, 10, -11, 11, 0, -13, 1 ],
[ 3, -10, 4, 9, -7, 4, 10, 9, 9, 8, 15, 31 ]
], hecke_fields := [
x^3 + x^2 - 2*x - 1,
x^3 + 3*x^2 - 3,
x^9 - 4*x^8 - 6*x^7 + 37*x^6 - 3*x^5 - 101*x^4 + 49*x^3 + 72*x^2 - 21*x - 13,
x^10 - 3*x^9 - 12*x^8 + 37*x^7 + 44*x^6 - 142*x^5 - 50*x^4 + 181*x^3 - 5*x^2 - 30*x + 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 13, 1 ],
[ 219, 1 ],
[ 3475, 1 ],
[ 408113, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 219, 1 ],
[ 3475, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 25, 1 ], torsion_lower_bounds := [ 1, 1, 25, 1 ], l_ratios := [ 0, 0, 139/25, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
a,
-1,
0,
-2*a^2 - a + 2,
a^2 - a - 1,
2*a^2 - 6,
-2*a^2 - 2*a,
a^2 + 2*a - 2,
4*a^2 + a - 8,
-2*a^2 - 2*a + 4,
3*a^2 + a - 5,
a^2 + 4*a - 6
],
[
a,
1,
-2,
-a - 2,
-a^2 - 3*a - 3,
-2*a^2 - 2*a + 4,
2*a^2 + 4*a - 4,
a^2 + 2*a - 2,
4*a^2 + 9*a - 4,
4*a^2 + 4*a - 10,
-3*a^2 - 3*a + 7,
a^2 - 6
],
[
a,
1,
2*a^8 - 4*a^7 - 21*a^6 + 35*a^5 + 71*a^4 - 83*a^3 - 79*a^2 + 31*a + 19,
-4*a^8 + 9*a^7 + 39*a^6 - 77*a^5 - 120*a^4 + 178*a^3 + 117*a^2 - 63*a - 26,
-2*a^8 + 4*a^7 + 21*a^6 - 34*a^5 - 73*a^4 + 77*a^3 + 88*a^2 - 25*a - 19,
6*a^8 - 13*a^7 - 60*a^6 + 112*a^5 + 192*a^4 - 262*a^3 - 202*a^2 + 98*a + 49,
2*a^8 - 5*a^7 - 19*a^6 + 43*a^5 + 57*a^4 - 99*a^3 - 55*a^2 + 31*a + 16,
-3*a^8 + 6*a^7 + 31*a^6 - 52*a^5 - 102*a^4 + 120*a^3 + 108*a^2 - 36*a - 24,
-5*a^8 + 11*a^7 + 51*a^6 - 97*a^5 - 166*a^4 + 232*a^3 + 175*a^2 - 88*a - 40,
-9*a^8 + 20*a^7 + 89*a^6 - 175*a^5 - 273*a^4 + 415*a^3 + 253*a^2 - 152*a - 55,
-3*a^8 + 7*a^7 + 30*a^6 - 63*a^5 - 94*a^4 + 156*a^3 + 91*a^2 - 67*a - 21,
-a^8 + 2*a^7 + 11*a^6 - 20*a^5 - 36*a^4 + 54*a^3 + 34*a^2 - 24*a - 10
],
[
a,
-1,
-135/647*a^9 + 358/647*a^8 + 1898/647*a^7 - 4732/647*a^6 - 8776/647*a^5 + 19642/647*a^4 + 14058/647*a^3 - 26097/647*a^2 - 2602/647*a + 2962/647,
29/647*a^9 - 144/647*a^8 - 355/647*a^7 + 1860/647*a^6 + 1636/647*a^5 - 7579/647*a^4 - 4357/647*a^3 + 10667/647*a^2 + 5572/647*a - 1983/647,
-51/647*a^9 + 164/647*a^8 + 602/647*a^7 - 2334/647*a^6 - 2007/647*a^5 + 10986/647*a^4 + 1170/647*a^3 - 17666/647*a^2 + 2784/647*a + 2528/647,
270/647*a^9 - 716/647*a^8 - 3149/647*a^7 + 8170/647*a^6 + 11082/647*a^5 - 27638/647*a^4 - 12588/647*a^3 + 28902/647*a^2 + 1322/647*a - 1395/647,
-55/647*a^9 + 50/647*a^8 + 941/647*a^7 - 538/647*a^6 - 5780/647*a^5 + 1724/647*a^4 + 14354/647*a^3 - 2293/647*a^2 - 10166/647*a + 2333/647,
16/647*a^9 - 191/647*a^8 - 62/647*a^7 + 2521/647*a^6 - 436/647*a^5 - 10830/647*a^4 + 1612/647*a^3 + 16148/647*a^2 - 1254/647*a - 1808/647,
-253/647*a^9 + 877/647*a^8 + 2517/647*a^7 - 9980/647*a^6 - 5884/647*a^5 + 33681/647*a^4 - 1389/647*a^3 - 36169/647*a^2 + 10043/647*a + 5297/647,
181/647*a^9 - 341/647*a^8 - 2238/647*a^7 + 3488/647*a^6 + 9140/647*a^5 - 9532/647*a^4 - 15570/647*a^3 + 6205/647*a^2 + 9187/647*a + 898/647,
166/647*a^9 - 445/647*a^8 - 2099/647*a^7 + 5694/647*a^6 + 8093/647*a^5 - 22590/647*a^4 - 8832/647*a^3 + 28107/647*a^2 - 3467/647*a - 1289/647,
-42/647*a^9 + 97/647*a^8 + 648/647*a^7 - 1199/647*a^6 - 3708/647*a^5 + 4328/647*a^4 + 10326/647*a^3 - 3892/647*a^2 - 13692/647*a + 864/647
]
*], q_expansions := [*
q + a*q^2 - q^3 + (a^2 - 2)*q^4 - a*q^6 + (-2*a^2 - a + 2)*q^7 + (-a^2 - 2*a + 1)*q^8 + q^9 + (a^2 - a - 1)*q^11 + (-a^2 + 2)*q^12 + (2*a^2 - 6)*q^13 + (a^2 - 2*a - 2)*q^14 + (-3*a^2 - a + 3)*q^16 + (-2*a^2 - 2*a)*q^17 + a*q^18 + (a^2 + 2*a - 2)*q^19 + (2*a^2 + a - 2)*q^21 + (-2*a^2 + a + 1)*q^22 + (4*a^2 + a - 8)*q^23 + (a^2 + 2*a - 1)*q^24 - 5*q^25 + (-2*a^2 - 2*a + 2)*q^26 - q^27 + (a^2 + 2*a - 3)*q^28 + (-2*a^2 - 2*a + 4)*q^29 + (3*a^2 + a - 5)*q^31 + (4*a^2 + a - 5)*q^32 + (-a^2 + a + 1)*q^33 + (-4*a - 2)*q^34 + (a^2 - 2)*q^36 + (a^2 + 4*a - 6)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 - 2*q^5 + a*q^6 + (-a - 2)*q^7 + (-3*a^2 - 4*a + 3)*q^8 + q^9 - 2*a*q^10 + (-a^2 - 3*a - 3)*q^11 + (a^2 - 2)*q^12 + (-2*a^2 - 2*a + 4)*q^13 + (-a^2 - 2*a)*q^14 - 2*q^15 + (3*a^2 + 3*a - 5)*q^16 + (2*a^2 + 4*a - 4)*q^17 + a*q^18 + (a^2 + 2*a - 2)*q^19 + (-2*a^2 + 4)*q^20 + (-a - 2)*q^21 + (-3*a - 3)*q^22 + (4*a^2 + 9*a - 4)*q^23 + (-3*a^2 - 4*a + 3)*q^24 - q^25 + (4*a^2 + 4*a - 6)*q^26 + q^27 + (a^2 + 2*a + 1)*q^28 + (4*a^2 + 4*a - 10)*q^29 - 2*a*q^30 + (-3*a^2 - 3*a + 7)*q^31 + (3*a + 3)*q^32 + (-a^2 - 3*a - 3)*q^33 + (-2*a^2 - 4*a + 6)*q^34 + (2*a + 4)*q^35 + (a^2 - 2)*q^36 + (a^2 - 6)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (2*a^8 - 4*a^7 - 21*a^6 + 35*a^5 + 71*a^4 - 83*a^3 - 79*a^2 + 31*a + 19)*q^5 + a*q^6 + (-4*a^8 + 9*a^7 + 39*a^6 - 77*a^5 - 120*a^4 + 178*a^3 + 117*a^2 - 63*a - 26)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (4*a^8 - 9*a^7 - 39*a^6 + 77*a^5 + 119*a^4 - 177*a^3 - 113*a^2 + 61*a + 26)*q^10 + (-2*a^8 + 4*a^7 + 21*a^6 - 34*a^5 - 73*a^4 + 77*a^3 + 88*a^2 - 25*a - 19)*q^11 + (a^2 - 2)*q^12 + (6*a^8 - 13*a^7 - 60*a^6 + 112*a^5 + 192*a^4 - 262*a^3 - 202*a^2 + 98*a + 49)*q^13 + (-7*a^8 + 15*a^7 + 71*a^6 - 132*a^5 - 226*a^4 + 313*a^3 + 225*a^2 - 110*a - 52)*q^14 + (2*a^8 - 4*a^7 - 21*a^6 + 35*a^5 + 71*a^4 - 83*a^3 - 79*a^2 + 31*a + 19)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^8 - 5*a^7 - 19*a^6 + 43*a^5 + 57*a^4 - 99*a^3 - 55*a^2 + 31*a + 16)*q^17 + a*q^18 + (-3*a^8 + 6*a^7 + 31*a^6 - 52*a^5 - 102*a^4 + 120*a^3 + 108*a^2 - 36*a - 24)*q^19 + (3*a^8 - 7*a^7 - 29*a^6 + 61*a^5 + 85*a^4 - 143*a^3 - 69*a^2 + 48*a + 14)*q^20 + (-4*a^8 + 9*a^7 + 39*a^6 - 77*a^5 - 120*a^4 + 178*a^3 + 117*a^2 - 63*a - 26)*q^21 + (-4*a^8 + 9*a^7 + 40*a^6 - 79*a^5 - 125*a^4 + 186*a^3 + 119*a^2 - 61*a - 26)*q^22 + (-5*a^8 + 11*a^7 + 51*a^6 - 97*a^5 - 166*a^4 + 232*a^3 + 175*a^2 - 88*a - 40)*q^23 + (a^3 - 4*a)*q^24 + (12*a^8 - 26*a^7 - 120*a^6 + 226*a^5 + 376*a^4 - 528*a^3 - 366*a^2 + 178*a + 83)*q^25 + (11*a^8 - 24*a^7 - 110*a^6 + 210*a^5 + 344*a^4 - 496*a^3 - 334*a^2 + 175*a + 78)*q^26 + q^27 + (-5*a^8 + 11*a^7 + 49*a^6 - 93*a^5 - 154*a^4 + 212*a^3 + 160*a^2 - 73*a - 39)*q^28 + (-9*a^8 + 20*a^7 + 89*a^6 - 175*a^5 - 273*a^4 + 415*a^3 + 253*a^2 - 152*a - 55)*q^29 + (4*a^8 - 9*a^7 - 39*a^6 + 77*a^5 + 119*a^4 - 177*a^3 - 113*a^2 + 61*a + 26)*q^30 + (-3*a^8 + 7*a^7 + 30*a^6 - 63*a^5 - 94*a^4 + 156*a^3 + 91*a^2 - 67*a - 21)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-2*a^8 + 4*a^7 + 21*a^6 - 34*a^5 - 73*a^4 + 77*a^3 + 88*a^2 - 25*a - 19)*q^33 + (3*a^8 - 7*a^7 - 31*a^6 + 63*a^5 + 103*a^4 - 153*a^3 - 113*a^2 + 58*a + 26)*q^34 + (-12*a^8 + 27*a^7 + 117*a^6 - 231*a^5 - 359*a^4 + 533*a^3 + 347*a^2 - 187*a - 78)*q^35 + (a^2 - 2)*q^36 + (-a^8 + 2*a^7 + 11*a^6 - 20*a^5 - 36*a^4 + 54*a^3 + 34*a^2 - 24*a - 10)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-135/647*a^9 + 358/647*a^8 + 1898/647*a^7 - 4732/647*a^6 - 8776/647*a^5 + 19642/647*a^4 + 14058/647*a^3 - 26097/647*a^2 - 2602/647*a + 2962/647)*q^5 - a*q^6 + (29/647*a^9 - 144/647*a^8 - 355/647*a^7 + 1860/647*a^6 + 1636/647*a^5 - 7579/647*a^4 - 4357/647*a^3 + 10667/647*a^2 + 5572/647*a - 1983/647)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-47/647*a^9 + 278/647*a^8 + 263/647*a^7 - 2836/647*a^6 + 472/647*a^5 + 7308/647*a^4 - 1662/647*a^3 - 3277/647*a^2 - 1088/647*a + 135/647)*q^10 + (-51/647*a^9 + 164/647*a^8 + 602/647*a^7 - 2334/647*a^6 - 2007/647*a^5 + 10986/647*a^4 + 1170/647*a^3 - 17666/647*a^2 + 2784/647*a + 2528/647)*q^11 + (-a^2 + 2)*q^12 + (270/647*a^9 - 716/647*a^8 - 3149/647*a^7 + 8170/647*a^6 + 11082/647*a^5 - 27638/647*a^4 - 12588/647*a^3 + 28902/647*a^2 + 1322/647*a - 1395/647)*q^13 + (-57/647*a^9 - 7/647*a^8 + 787/647*a^7 + 360/647*a^6 - 3461/647*a^5 - 2907/647*a^4 + 5418/647*a^3 + 5717/647*a^2 - 1113/647*a - 29/647)*q^14 + (135/647*a^9 - 358/647*a^8 - 1898/647*a^7 + 4732/647*a^6 + 8776/647*a^5 - 19642/647*a^4 - 14058/647*a^3 + 26097/647*a^2 + 2602/647*a - 2962/647)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-55/647*a^9 + 50/647*a^8 + 941/647*a^7 - 538/647*a^6 - 5780/647*a^5 + 1724/647*a^4 + 14354/647*a^3 - 2293/647*a^2 - 10166/647*a + 2333/647)*q^17 + a*q^18 + (16/647*a^9 - 191/647*a^8 - 62/647*a^7 + 2521/647*a^6 - 436/647*a^5 - 10830/647*a^4 + 1612/647*a^3 + 16148/647*a^2 - 1254/647*a - 1808/647)*q^19 + (407/647*a^9 - 1017/647*a^8 - 4893/647*a^7 + 12004/647*a^6 + 18186/647*a^5 - 43296/647*a^4 - 22886/647*a^3 + 50871/647*a^2 + 3929/647*a - 5877/647)*q^20 + (-29/647*a^9 + 144/647*a^8 + 355/647*a^7 - 1860/647*a^6 - 1636/647*a^5 + 7579/647*a^4 + 4357/647*a^3 - 10667/647*a^2 - 5572/647*a + 1983/647)*q^21 + (11/647*a^9 - 10/647*a^8 - 447/647*a^7 + 237/647*a^6 + 3744/647*a^5 - 1380/647*a^4 - 8435/647*a^3 + 2529/647*a^2 + 998/647*a + 51/647)*q^22 + (-253/647*a^9 + 877/647*a^8 + 2517/647*a^7 - 9980/647*a^6 - 5884/647*a^5 + 33681/647*a^4 - 1389/647*a^3 - 36169/647*a^2 + 10043/647*a + 5297/647)*q^23 + (-a^3 + 4*a)*q^24 + (-350/647*a^9 + 1024/647*a^8 + 4106/647*a^7 - 12364/647*a^6 - 14078/647*a^5 + 45556/647*a^4 + 12292/647*a^3 - 54000/647*a^2 + 6242/647*a + 9141/647)*q^25 + (94/647*a^9 + 91/647*a^8 - 1820/647*a^7 - 798/647*a^6 + 10702/647*a^5 + 912/647*a^4 - 19968/647*a^3 + 2672/647*a^2 + 6705/647*a - 270/647)*q^26 - q^27 + (-236/647*a^9 + 391/647*a^8 + 3179/647*a^7 - 4673/647*a^6 - 14273/647*a^5 + 17726/647*a^4 + 24748/647*a^3 - 22732/647*a^2 - 12883/647*a + 4023/647)*q^28 + (181/647*a^9 - 341/647*a^8 - 2238/647*a^7 + 3488/647*a^6 + 9140/647*a^5 - 9532/647*a^4 - 15570/647*a^3 + 6205/647*a^2 + 9187/647*a + 898/647)*q^29 + (47/647*a^9 - 278/647*a^8 - 263/647*a^7 + 2836/647*a^6 - 472/647*a^5 - 7308/647*a^4 + 1662/647*a^3 + 3277/647*a^2 + 1088/647*a - 135/647)*q^30 + (166/647*a^9 - 445/647*a^8 - 2099/647*a^7 + 5694/647*a^6 + 8093/647*a^5 - 22590/647*a^4 - 8832/647*a^3 + 28107/647*a^2 - 3467/647*a - 1289/647)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (51/647*a^9 - 164/647*a^8 - 602/647*a^7 + 2334/647*a^6 + 2007/647*a^5 - 10986/647*a^4 - 1170/647*a^3 + 17666/647*a^2 - 2784/647*a - 2528/647)*q^33 + (-115/647*a^9 + 281/647*a^8 + 1497/647*a^7 - 3360/647*a^6 - 6086/647*a^5 + 11604/647*a^4 + 7662/647*a^3 - 10441/647*a^2 + 683/647*a + 55/647)*q^34 + (65/647*a^9 - 412/647*a^8 - 171/647*a^7 + 5106/647*a^6 - 3874/647*a^5 - 20624/647*a^4 + 17386/647*a^3 + 30825/647*a^2 - 16336/647*a - 7345/647)*q^35 + (a^2 - 2)*q^36 + (-42/647*a^9 + 97/647*a^8 + 648/647*a^7 - 1199/647*a^6 - 3708/647*a^5 + 4328/647*a^4 + 10326/647*a^3 - 3892/647*a^2 - 13692/647*a + 864/647)*q^37 + O(q^38)
*]> ;  // time = 85.67 seconds




J[449] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 449, 449 ], new_dimensions := [ 14, 23 ], dimensions := [ 14, 23 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -3, -5, -7, -22, -14, -10, -6, -39, -6, -3, -57, -4 ],
[ 0, 3, 3, 26, 6, 10, 0, 41, 2, -7, 73, 8 ]
], hecke_fields := [
x^14 + 3*x^13 - 13*x^12 - 42*x^11 + 59*x^10 + 214*x^9 - 117*x^8 - 503*x^7 + 109*x^6 + 576*x^5 - 50*x^4 - 309*x^3 + 14*x^2 + 62*x - 3,
x^23 - 38*x^21 + x^20 + 623*x^19 - 31*x^18 - 5771*x^17 + 398*x^16 + 33229*x^15 - 2753*x^14 - 123306*x^13 + 11230*x^12 + 296022*x^11 - 28009*x^10 - 450008*x^9 + 43215*x^8 + 412760*x^7 - 40559*x^6 - 210040*x^5 + 21311*x^4 + 50781*x^3 - 5664*x^2 - 3789*x + 621
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 7 ]
], tamagawa_numbers := [
[ 1 ],
[ 7 ]
], torsion_upper_bounds := [ 1, 7 ], torsion_lower_bounds := [ 1, 7 ], l_ratios := [ 0, 1/7 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
1367/581*a^13 + 2544/581*a^12 - 21440/581*a^11 - 35460/581*a^10 + 130273/581*a^9 + 25269/83*a^8 - 397316/581*a^7 - 387181/581*a^6 + 91749/83*a^5 + 359615/581*a^4 - 504323/581*a^3 - 105389/581*a^2 + 145130/581*a - 6416/581,
-689/581*a^13 - 1037/581*a^12 + 11692/581*a^11 + 15082/581*a^10 - 77477/581*a^9 - 11333/83*a^8 + 255690/581*a^7 + 183819/581*a^6 - 62325/83*a^5 - 177694/581*a^4 + 352434/581*a^3 + 49678/581*a^2 - 102958/581*a + 5809/581,
291/581*a^13 + 1035/581*a^12 - 3099/581*a^11 - 13492/581*a^10 + 8490/581*a^9 + 8691/83*a^8 + 3319/581*a^7 - 115074/581*a^6 - 4771/83*a^5 + 87935/581*a^4 + 28887/581*a^3 - 19559/581*a^2 - 5371/581*a - 1821/581,
-1275/581*a^13 - 2672/581*a^12 + 18861/581*a^11 + 36126/581*a^10 - 106601/581*a^9 - 24622/83*a^8 + 302097/581*a^7 + 354412/581*a^6 - 66075/83*a^5 - 303487/581*a^4 + 350578/581*a^3 + 81426/581*a^2 - 98052/581*a + 3684/581,
-1506/581*a^13 - 3260/581*a^12 + 21920/581*a^11 + 44015/581*a^10 - 121175/581*a^9 - 29968/83*a^8 + 335676/581*a^7 + 432049/581*a^6 - 72910/83*a^5 - 373914/581*a^4 + 397996/581*a^3 + 102307/581*a^2 - 118436/581*a + 5441/581,
948/581*a^13 + 1485/581*a^12 - 15738/581*a^11 - 20899/581*a^10 + 102110/581*a^9 + 15003/83*a^8 - 331157/581*a^7 - 228612/581*a^6 + 79370/83*a^5 + 202026/581*a^4 - 434544/581*a^3 - 46857/581*a^2 + 120038/581*a - 9610/581,
-2082/581*a^13 - 5692/581*a^12 + 28114/581*a^11 + 77585/581*a^10 - 138531/581*a^9 - 53614/83*a^8 + 328777/581*a^7 + 791909/581*a^6 - 61441/83*a^5 - 714083/581*a^4 + 303987/581*a^3 + 213485/581*a^2 - 86158/581*a + 2337/581,
-1523/581*a^13 - 4171/581*a^12 + 19801/581*a^11 + 55954/581*a^10 - 90285/581*a^9 - 37784/83*a^8 + 182741/581*a^7 + 540758/581*a^6 - 25734/83*a^5 - 469162/581*a^4 + 86312/581*a^3 + 132280/581*a^2 - 16581/581*a + 2864/581,
481/83*a^13 + 1081/83*a^12 - 7099/83*a^11 - 14870/83*a^10 + 40020/83*a^9 + 72776/83*a^8 - 113261/83*a^7 - 155314/83*a^6 + 174109/83*a^5 + 140140/83*a^4 - 134230/83*a^3 - 40328/83*a^2 + 39107/83*a - 1913/83,
2189/581*a^13 + 4659/581*a^12 - 33027/581*a^11 - 64521/581*a^10 + 191475/581*a^9 + 45573/83*a^8 - 557407/581*a^7 - 691547/581*a^6 + 124427/83*a^5 + 640377/581*a^4 - 667715/581*a^3 - 195576/581*a^2 + 185914/581*a - 6828/581,
492/581*a^13 + 2852/581*a^12 - 1490/581*a^11 - 36300/581*a^10 - 36642/581*a^9 + 22615/83*a^8 + 251668/581*a^7 - 289321/581*a^6 - 82271/83*a^5 + 228624/581*a^4 + 524026/581*a^3 - 79447/581*a^2 - 158320/581*a + 12722/581
],
[
a,
3587401463/505414861488*a^22 - 7650779429/336943240992*a^21 - 150864645115/505414861488*a^20 + 825392841079/1010829722976*a^19 + 5450047860893/1010829722976*a^18 - 6344315242307/505414861488*a^17 - 27696702887935/505414861488*a^16 + 108892865144615/1010829722976*a^15 + 6012670597195/17428098672*a^14 - 71421083468347/126353715372*a^13 - 470356381031857/336943240992*a^12 + 943155604067327/505414861488*a^11 + 1228712346186743/336943240992*a^10 - 1940384255679473/505414861488*a^9 - 3041227590875047/505414861488*a^8 + 43884038119555/9359534472*a^7 + 6017749368007493/1010829722976*a^6 - 1532894924053417/505414861488*a^5 - 809680458782215/252707430744*a^4 + 194797323522557/252707430744*a^3 + 86827452979241/112314413664*a^2 - 1239867085561/336943240992*a - 4509261066899/112314413664,
36207620017/1516244584464*a^22 - 392715416/31588428843*a^21 - 347942083499/379061146116*a^20 + 326631794837/758122292232*a^19 + 11567268044365/758122292232*a^18 - 9606455528161/1516244584464*a^17 - 108957607448593/758122292232*a^16 + 78030276152777/1516244584464*a^15 + 2760254289026/3267768501*a^14 - 381574682954333/1516244584464*a^13 - 812551049946659/252707430744*a^12 + 286698557455579/379061146116*a^11 + 4027851952874915/505414861488*a^10 - 1032782020658657/758122292232*a^9 - 9557529760524427/758122292232*a^8 + 75413531184863/56157206832*a^7 + 9196221796045171/758122292232*a^6 - 791176870326971/1516244584464*a^5 - 9824972033892583/1516244584464*a^4 - 24143673588209/189530573058*a^3 + 133443099270145/84235810248*a^2 + 55513767426557/505414861488*a - 15548291459519/168471620496,
-3203239213/379061146116*a^22 - 595819192/31588428843*a^21 + 131419749017/379061146116*a^20 + 135495968281/189530573058*a^19 - 578128330394/94765286529*a^18 - 2208746478799/189530573058*a^17 + 11406429012787/189530573058*a^16 + 10118781621100/94765286529*a^15 - 4772077428473/13071074004*a^14 - 57120718814416/94765286529*a^13 + 177572889554965/126353715372*a^12 + 204603006231941/94765286529*a^11 - 108026982272480/31588428843*a^10 - 1843832442646961/379061146116*a^9 + 1928985934508705/379061146116*a^8 + 46197173442761/7019650854*a^7 - 1647721213925357/379061146116*a^6 - 1835788779751429/379061146116*a^5 + 369514164098459/189530573058*a^4 + 151311038776075/94765286529*a^3 - 17053794357965/42117905124*a^2 - 4474501036763/31588428843*a + 1456347043919/42117905124,
1316367895/13071074004*a^22 + 143938909/4357024668*a^21 - 98901947617/26142148008*a^20 - 31767174607/26142148008*a^19 + 800451361073/13071074004*a^18 + 504571904809/26142148008*a^17 - 14614387602187/26142148008*a^16 - 4536403667465/26142148008*a^15 + 10335990602869/3267768501*a^14 + 12686579651077/13071074004*a^13 - 50010652113031/4357024668*a^12 - 91081664277415/26142148008*a^11 + 232891347633433/8714049336*a^10 + 104039493898811/13071074004*a^9 - 507807968945921/13071074004*a^8 - 1338455500426/121028463*a^7 + 217470996651883/6535537002*a^6 + 223508416742801/26142148008*a^5 - 398585214435515/26142148008*a^4 - 83332756026185/26142148008*a^3 + 9178192928377/2904683112*a^2 + 450488942858/1089256167*a - 550385323477/2904683112,
195233617/42117905124*a^22 - 414868283/14039301708*a^21 - 15796492285/84235810248*a^20 + 86437170467/84235810248*a^19 + 135808599155/42117905124*a^18 - 1277406335507/84235810248*a^17 - 2585591022709/84235810248*a^16 + 10490165145163/84235810248*a^15 + 256148401301/1452341556*a^14 - 6555531117833/10529476281*a^13 - 2189147016799/3509825427*a^12 + 164502933796967/84235810248*a^11 + 36917895584197/28078603416*a^10 - 40262902255258/10529476281*a^9 - 30931084418797/21058952562*a^8 + 21094288477639/4679767236*a^7 + 22239202918745/42117905124*a^6 - 248588646677557/84235810248*a^5 + 28578818562373/84235810248*a^4 + 74722840056937/84235810248*a^3 - 2281389091951/9359534472*a^2 - 1034343318067/14039301708*a + 227399339381/9359534472,
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*], q_expansions := [*
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1234/581*a^12 + 4323/581*a^11 + 15989/581*a^10 - 14282/581*a^9 - 10203/83*a^8 + 9732/581*a^7 + 132809/581*a^6 + 2417/83*a^5 - 97410/581*a^4 - 17161/581*a^3 + 16987/581*a^2 + 1571/581*a + 4128/581)*q^28 + (481/83*a^13 + 1081/83*a^12 - 7099/83*a^11 - 14870/83*a^10 + 40020/83*a^9 + 72776/83*a^8 - 113261/83*a^7 - 155314/83*a^6 + 174109/83*a^5 + 140140/83*a^4 - 134230/83*a^3 - 40328/83*a^2 + 39107/83*a - 1913/83)*q^29 + (-1195/581*a^13 - 2657/581*a^12 + 18033/581*a^11 + 36983/581*a^10 - 104836/581*a^9 - 26304/83*a^8 + 307332/581*a^7 + 402685/581*a^6 - 69404/83*a^5 - 375427/581*a^4 + 379693/581*a^3 + 112045/581*a^2 - 112057/581*a + 5148/581)*q^30 + (2189/581*a^13 + 4659/581*a^12 - 33027/581*a^11 - 64521/581*a^10 + 191475/581*a^9 + 45573/83*a^8 - 557407/581*a^7 - 691547/581*a^6 + 124427/83*a^5 + 640377/581*a^4 - 667715/581*a^3 - 195576/581*a^2 + 185914/581*a - 6828/581)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-5696/581*a^13 - 12107/581*a^12 + 85331/581*a^11 + 166385/581*a^10 - 490536/581*a^9 - 116194/83*a^8 + 1417910/581*a^7 + 1733630/581*a^6 - 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1626943790408075/168471620496*a^8 - 35579037640065/12479379296*a^7 + 477066277407757/84235810248*a^6 + 143646544573985/84235810248*a^5 - 113803125750763/168471620496*a^4 - 111585992184365/336943240992*a^3 - 14957163294263/37438137888*a^2 - 4707146494667/112314413664*a + 664538893579/18719068944)*q^24 + (-94491272219/505414861488*a^22 - 8247170425/84235810248*a^21 + 1780601829215/252707430744*a^20 + 427483613083/126353715372*a^19 - 7230322473923/63176857686*a^18 - 25368334175611/505414861488*a^17 + 265016072996423/252707430744*a^16 + 212238729944345/505414861488*a^15 - 51934195464797/8714049336*a^14 - 1105018962472739/505414861488*a^13 + 1832144701129843/84235810248*a^12 + 928881744690769/126353715372*a^11 - 8601113593324441/168471620496*a^10 - 503372489935993/31588428843*a^9 + 4748036480013113/63176857686*a^8 + 400721829668233/18719068944*a^7 - 16606276510542755/252707430744*a^6 - 8288438982263951/505414861488*a^5 + 15730164464014559/505414861488*a^4 + 791780984397779/126353715372*a^3 - 189538441900349/28078603416*a^2 - 149003820202231/168471620496*a + 23449632643171/56157206832)*q^25 + (-414868283/14039301708*a^22 - 106526377/9359534472*a^21 + 28682234411/28078603416*a^20 + 1181504647/3509825427*a^19 - 421767283751/28078603416*a^18 - 110734871765/28078603416*a^17 + 3444919728677/28078603416*a^16 + 78407148203/3509825427*a^15 - 295225819813/484113852*a^14 - 366047970631/7019650854*a^13 + 17790887417683/9359534472*a^12 - 1611068263519/28078603416*a^11 - 17287034515831/4679767236*a^10 + 4332420113557/7019650854*a^9 + 15117631295008/3509825427*a^8 - 2160941660525/1559922412*a^7 - 77583895377917/28078603416*a^6 + 36864185463911/28078603416*a^5 + 22133864277721/28078603416*a^4 - 13453606145771/28078603416*a^3 - 73971361019/1559922412*a^2 + 391786044895/9359534472*a - 4490373191/1559922412)*q^26 + (-11974855817/168471620496*a^22 - 9419112967/112314413664*a^21 + 437118705247/168471620496*a^20 + 945218127197/336943240992*a^19 - 13734278370425/336943240992*a^18 - 6687914994679/168471620496*a^17 + 60845632234435/168471620496*a^16 + 104537375435113/336943240992*a^15 - 11547812363263/5809366224*a^14 - 123625691594491/84235810248*a^13 + 792901493844469/112314413664*a^12 + 730480540674721/168471620496*a^11 - 1830022661846495/112314413664*a^10 - 1345580933334271/168471620496*a^9 + 4050398248659175/168471620496*a^8 + 41852685756061/4679767236*a^7 - 7322822789488649/336943240992*a^6 - 983604157932737/168471620496*a^5 + 465131624681891/42117905124*a^4 + 175918665255385/84235810248*a^3 - 98461368966205/37438137888*a^2 - 37684931072543/112314413664*a + 6258170199011/37438137888)*q^27 + (16103137349/379061146116*a^22 + 5600428277/126353715372*a^21 - 572584959607/379061146116*a^20 - 604432966933/379061146116*a^19 + 8730346431079/379061146116*a^18 + 4661665460993/189530573058*a^17 - 18682473301774/94765286529*a^16 - 80669934608237/379061146116*a^15 + 13615071113491/13071074004*a^14 + 214866588170029/189530573058*a^13 - 111103270997912/31588428843*a^12 - 726934476684359/189530573058*a^11 + 959963546766595/126353715372*a^10 + 3103259398350379/379061146116*a^9 - 3874544148797527/379061146116*a^8 - 37072590134543/3509825427*a^7 + 767918106112294/94765286529*a^6 + 2843335588423241/379061146116*a^5 - 329126770382906/94765286529*a^4 - 229812484221191/94765286529*a^3 + 7428936378298/10529476281*a^2 + 27428843137243/126353715372*a - 1209677898431/21058952562)*q^28 + (215348032747/1516244584464*a^22 + 21963707233/505414861488*a^21 - 8172241837535/1516244584464*a^20 - 299653783195/189530573058*a^19 + 133679107912181/1516244584464*a^18 + 4730958767707/189530573058*a^17 - 1233669105418181/1516244584464*a^16 - 340593154897603/1516244584464*a^15 + 30429045595351/6535537002*a^14 + 1923188103260689/1516244584464*a^13 - 8643089525344747/505414861488*a^12 - 7032207084781475/1516244584464*a^11 + 20398622740094621/505414861488*a^10 + 1030684044513533/94765286529*a^9 - 22606511390748707/379061146116*a^8 - 875725763056777/56157206832*a^7 + 79167938242187513/1516244584464*a^6 + 2367497478607739/189530573058*a^5 - 4680546785556305/189530573058*a^4 - 7382800050900223/1516244584464*a^3 + 112421887653421/21058952562*a^2 + 85503964111997/126353715372*a - 55203800446847/168471620496)*q^29 + (14415136289/1010829722976*a^22 - 14129147599/336943240992*a^21 - 412708202035/1010829722976*a^20 + 93464362541/63176857686*a^19 + 4503835719265/1010829722976*a^18 - 11326193727085/505414861488*a^17 - 20581277059309/1010829722976*a^16 + 192928621312039/1010829722976*a^15 - 5091140687/2178512334*a^14 - 1015762148746213/1010829722976*a^13 + 148559326827865/336943240992*a^12 + 3418602648491081/1010829722976*a^11 - 688991826113237/336943240992*a^10 - 1831073660682635/252707430744*a^9 + 141791322914437/31588428843*a^8 + 354971649470353/37438137888*a^7 - 5297648608647011/1010829722976*a^6 - 3489288761304743/505414861488*a^5 + 1600105588804721/505414861488*a^4 + 2362081865348749/1010829722976*a^3 - 12038537804815/14039301708*a^2 - 40839592368475/168471620496*a + 7798336481171/112314413664)*q^30 + (-112071112939/1516244584464*a^22 - 3912787691/252707430744*a^21 + 4279881245573/1516244584464*a^20 + 820983678863/1516244584464*a^19 - 8814960458293/189530573058*a^18 - 3121941934445/379061146116*a^17 + 656471937396011/1516244584464*a^16 + 27284840436889/379061146116*a^15 - 65476148685727/26142148008*a^14 - 607378473001003/1516244584464*a^13 + 2358311208922511/252707430744*a^12 + 2233946330936921/1516244584464*a^11 - 709773249047462/31588428843*a^10 - 2698072087893457/758122292232*a^9 + 25912977574744333/758122292232*a^8 + 303521623662667/56157206832*a^7 - 11838504088614245/379061146116*a^6 - 453771493148938/94765286529*a^5 + 11878071131346077/758122292232*a^4 + 3391385990521963/1516244584464*a^3 - 608611769371835/168471620496*a^2 - 211693296901871/505414861488*a + 18769434509809/84235810248)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-93134877601/1516244584464*a^22 + 10421275963/252707430744*a^21 + 3523336606835/1516244584464*a^20 - 1957650689995/1516244584464*a^19 - 14380077329339/379061146116*a^18 + 3134243645801/189530573058*a^17 + 530318735984693/1516244584464*a^16 - 41691569193527/379061146116*a^15 - 52291917591757/26142148008*a^14 + 590216009403107/1516244584464*a^13 + 1853367559367531/252707430744*a^12 - 902384780793337/1516244584464*a^11 - 543354745501220/31588428843*a^10 - 248511689383723/758122292232*a^9 + 18944779184202613/758122292232*a^8 + 135455424073645/56157206832*a^7 - 7988530554517115/379061146116*a^6 - 1116546329459881/379061146116*a^5 + 7071369571836413/758122292232*a^4 + 2028496554479581/1516244584464*a^3 - 309936971362001/168471620496*a^2 - 95555259940445/505414861488*a + 8937636720655/84235810248)*q^33 + (10925722735/252707430744*a^22 + 11631059027/168471620496*a^21 - 95771790539/63176857686*a^20 - 1135829263759/505414861488*a^19 + 11463066922021/505414861488*a^18 + 1939864106033/63176857686*a^17 - 11962188926687/63176857686*a^16 - 115818922776467/505414861488*a^15 + 8443124818625/8714049336*a^14 + 128731679013767/126353715372*a^13 - 530346633281693/168471620496*a^12 - 349132103321155/126353715372*a^11 + 1099378166309353/168471620496*a^10 + 1139061764230391/252707430744*a^9 - 2146401433788143/252707430744*a^8 - 19818782708447/4679767236*a^7 + 3376285050524221/505414861488*a^6 + 68725032910175/31588428843*a^5 - 737989440255919/252707430744*a^4 - 151823145694213/252707430744*a^3 + 33756249881767/56157206832*a^2 + 13445182402003/168471620496*a - 2024062519681/56157206832)*q^34 + (11333746213/1516244584464*a^22 - 4602946877/126353715372*a^21 - 505014045665/1516244584464*a^20 + 1855106788339/1516244584464*a^19 + 4902899370097/758122292232*a^18 - 13158094115711/758122292232*a^17 - 108834211752911/1516244584464*a^16 + 51300498686213/379061146116*a^15 + 13125356579251/26142148008*a^14 - 957595845980339/1516244584464*a^13 - 290664460500031/126353715372*a^12 + 2720030887536151/1516244584464*a^11 + 877723667691785/126353715372*a^10 - 2264391298263725/758122292232*a^9 - 10270093202535445/758122292232*a^8 + 142531160108039/56157206832*a^7 + 12284468901813895/758122292232*a^6 - 389078445415393/758122292232*a^5 - 4066739950224247/379061146116*a^4 - 922607306575255/1516244584464*a^3 + 530857443371357/168471620496*a^2 + 148784144215631/505414861488*a - 17049971522617/84235810248)*q^35 + (14674419377/252707430744*a^22 + 1669192133/21058952562*a^21 - 1069649772773/505414861488*a^20 - 1328352304931/505414861488*a^19 + 4203206181065/126353715372*a^18 + 18619524837257/505414861488*a^17 - 149550593318297/505414861488*a^16 - 144108094187323/505414861488*a^15 + 14322317695669/8714049336*a^14 + 168949221099433/126353715372*a^13 - 500161679982065/84235810248*a^12 - 1986789414656453/505414861488*a^11 + 2374918644024815/168471620496*a^10 + 459269643290983/63176857686*a^9 - 1371718558362901/63176857686*a^8 - 77792481647249/9359534472*a^7 + 1315664143684033/63176857686*a^6 + 2870232644883859/505414861488*a^5 - 5744131969864771/505414861488*a^4 - 1092659583362311/505414861488*a^3 + 162015789673379/56157206832*a^2 + 3840465015038/10529476281*a - 10231685921345/56157206832)*q^36 + (66599443705/1516244584464*a^22 - 13257573929/505414861488*a^21 - 2574526100993/1516244584464*a^20 + 324837131287/379061146116*a^19 + 43082463302291/1516244584464*a^18 - 4398889049395/379061146116*a^17 - 408949332736295/1516244584464*a^16 + 126577130518847/1516244584464*a^15 + 20896242763787/13071074004*a^14 - 509118355145009/1516244584464*a^13 - 3102449774654593/505414861488*a^12 + 1054830267308143/1516244584464*a^11 + 7749331940177207/505414861488*a^10 - 142983882223921/379061146116*a^9 - 2310164722007744/94765286529*a^8 - 67117055668087/56157206832*a^7 + 35582586151682843/1516244584464*a^6 + 222400930816996/94765286529*a^5 - 4734423918267259/379061146116*a^4 - 2365318990302541/1516244584464*a^3 + 64035197193829/21058952562*a^2 + 44890163619545/126353715372*a - 31378939930961/168471620496)*q^37 + O(q^38)
*]> ;  // time = 11.789 seconds




J[451] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 451, 451, 451, 451, 451, 41, 11 ], new_dimensions := [ 1, 5, 5, 10, 12, 3, 1 ], dimensions := [ 1, 5, 5, 10, 12, 6, 2 ], intersection_graph := [ 0, 9, 1, 1, 1, 1, 1, 9, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 125, 5, 1, 1, 1, 0, 1, 1, 17, 1, 1, 1, 1, 0, 863, 1, 1, 1, 125, 1, 863, 0, 5, 1, 1, 5, 17, 1, 5, 0 ], ap_traces := [
[ 0, 1, -3, 4, -1, -6, 2, -8, -5, -8, 3, 7 ],
[ -2, -4, -4, -3, -5, 1, -9, 7, -3, -18, -1, -10 ],
[ -2, 0, -8, -5, 5, -5, 3, -11, -7, -24, -13, 2 ],
[ 4, 0, 6, 7, 10, 4, 9, 5, 7, 34, -23, -8 ],
[ 3, 1, 13, -7, -12, 0, 9, -13, 6, 42, 8, 9 ]
], hecke_fields := [
x - 1,
x^5 + 2*x^4 - 5*x^3 - 10*x^2 + 4*x + 9,
x^5 + 2*x^4 - 3*x^3 - 4*x^2 + 2*x + 1,
x^10 - 4*x^9 - 6*x^8 + 38*x^7 - 7*x^6 - 105*x^5 + 74*x^4 + 77*x^3 - 74*x^2 + 8,
x^12 - 3*x^11 - 16*x^10 + 48*x^9 + 93*x^8 - 270*x^7 - 251*x^6 + 633*x^5 + 359*x^4 - 582*x^3 - 248*x^2 + 136*x + 32
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 25, 1 ],
[ 7, 17 ],
[ 863, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 25, 1 ],
[ 7, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 5, 7, 1 ], torsion_lower_bounds := [ 1, 1, 1, 7, 1 ], l_ratios := [ 0, 0, 0, 1/7, 1 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ 0, 1, -3, 4, -1, -6, 2, -8, -5, -8, 3, 7 ],
[
a,
-a^4 - a^3 + 6*a^2 + 3*a - 8,
-2*a^4 - a^3 + 11*a^2 + 3*a - 12,
2*a^4 + a^3 - 12*a^2 - 4*a + 13,
-1,
3*a^4 + a^3 - 18*a^2 - 3*a + 21,
-3*a^4 + 19*a^2 - 25,
-3*a^4 - a^3 + 17*a^2 + 2*a - 17,
3*a^4 + 3*a^3 - 15*a^2 - 8*a + 13,
2*a^4 - a^3 - 12*a^2 + 4*a + 10,
6*a^4 + 3*a^3 - 35*a^2 - 9*a + 39,
a^4 - a^3 - 10*a^2 + 4*a + 16
],
[
a,
-a^4 - a^3 + 4*a^2 + a - 2,
-a^3 - 3*a^2 + a + 2,
2*a^4 + 3*a^3 - 6*a^2 - 4*a + 1,
1,
a^4 + 3*a^3 - 5*a - 3,
-a^4 - 4*a^3 + a^2 + 8*a - 1,
a^4 + 3*a^3 + a^2 - 2*a - 5,
-a^4 - 3*a^3 + a^2 + 6*a - 1,
-a^3 - 2*a^2 + 4*a - 2,
-4*a^4 - 9*a^3 + 7*a^2 + 13*a - 3,
-3*a^4 - 3*a^3 + 14*a^2 + 2*a - 10
],
[
a,
7/2*a^9 - 12*a^8 - 28*a^7 + 117*a^6 + 89/2*a^5 - 685/2*a^4 + 54*a^3 + 605/2*a^2 - 74*a - 44,
1/4*a^9 - a^8 - 3/2*a^7 + 19/2*a^6 - 7/4*a^5 - 105/4*a^4 + 35/2*a^3 + 81/4*a^2 - 27/2*a - 2,
5/2*a^9 - 17/2*a^8 - 20*a^7 + 83*a^6 + 63/2*a^5 - 244*a^4 + 79/2*a^3 + 437/2*a^2 - 105/2*a - 33,
1,
5/2*a^9 - 8*a^8 - 21*a^7 + 77*a^6 + 81/2*a^5 - 439/2*a^4 + 18*a^3 + 365/2*a^2 - 40*a - 23,
-3/4*a^9 + 3*a^8 + 11/2*a^7 - 61/2*a^6 - 19/4*a^5 + 383/4*a^4 - 49/2*a^3 - 383/4*a^2 + 47/2*a + 18,
-19/4*a^9 + 31/2*a^8 + 79/2*a^7 - 301/2*a^6 - 295/4*a^5 + 1749/4*a^4 - 40*a^3 - 1523/4*a^2 + 79*a + 55,
9/4*a^9 - 15/2*a^8 - 37/2*a^7 + 147/2*a^6 + 133/4*a^5 - 875/4*a^4 + 23*a^3 + 817/4*a^2 - 42*a - 35,
7/4*a^9 - 13/2*a^8 - 27/2*a^7 + 129/2*a^6 + 71/4*a^5 - 777/4*a^4 + 38*a^3 + 723/4*a^2 - 44*a - 25,
-7/2*a^9 + 23/2*a^8 + 29*a^7 - 112*a^6 - 107/2*a^5 + 327*a^4 - 61/2*a^3 - 575/2*a^2 + 115/2*a + 41,
-21/4*a^9 + 37/2*a^8 + 83/2*a^7 - 363/2*a^6 - 249/4*a^5 + 2147/4*a^4 - 91*a^3 - 1941/4*a^2 + 113*a + 77
],
[
a,
-11/232*a^11 - 15/232*a^10 + 27/29*a^9 + 36/29*a^8 - 1559/232*a^7 - 883/116*a^6 + 4841/232*a^5 + 3869/232*a^4 - 5605/232*a^3 - 1119/116*a^2 + 188/29*a - 31/29,
59/232*a^11 - 83/232*a^10 - 487/116*a^9 + 147/29*a^8 + 5599/232*a^7 - 1369/58*a^6 - 13121/232*a^5 + 9213/232*a^4 + 11403/232*a^3 - 1179/58*a^2 - 485/58*a + 103/29,
-7/232*a^11 + 1/232*a^10 + 37/58*a^9 + 1/58*a^8 - 1203/232*a^7 - 61/116*a^6 + 4557/232*a^5 + 353/232*a^4 - 7553/232*a^3 + 63/116*a^2 + 959/58*a - 54/29,
-1,
-49/232*a^11 + 123/232*a^10 + 86/29*a^9 - 214/29*a^8 - 3085/232*a^7 + 3923/116*a^6 + 4291/232*a^5 - 13073/232*a^4 + 489/232*a^3 + 3283/116*a^2 - 312/29*a - 30/29,
-1/29*a^11 + 71/116*a^10 - 19/116*a^9 - 277/29*a^8 + 172/29*a^7 + 5983/116*a^6 - 828/29*a^5 - 12927/116*a^4 + 4471/116*a^3 + 9787/116*a^2 - 441/58*a - 244/29,
21/232*a^11 - 61/232*a^10 - 135/116*a^9 + 229/58*a^8 + 825/232*a^7 - 1141/58*a^6 + 1061/232*a^5 + 8627/232*a^4 - 5703/232*a^3 - 823/29*a^2 + 519/29*a + 220/29,
-21/58*a^11 + 35/116*a^10 + 685/116*a^9 - 191/58*a^8 - 1927/58*a^7 + 921/116*a^6 + 2181/29*a^5 + 1277/116*a^4 - 7415/116*a^3 - 3797/116*a^2 + 418/29*a + 251/29,
-35/232*a^11 + 63/232*a^10 + 283/116*a^9 - 227/58*a^8 - 3231/232*a^7 + 540/29*a^6 + 7821/232*a^5 - 7225/232*a^4 - 7779/232*a^3 + 607/58*a^2 + 208/29*a + 136/29,
13/58*a^11 - 35/58*a^10 - 96/29*a^9 + 527/58*a^8 + 925/58*a^7 - 1345/29*a^6 - 1561/58*a^5 + 2682/29*a^4 + 387/29*a^3 - 1944/29*a^2 - 367/58*a + 281/29,
2/29*a^11 + 3/116*a^10 - 165/116*a^9 - 23/58*a^8 + 294/29*a^7 + 243/116*a^6 - 1647/58*a^5 - 507/116*a^4 + 2513/116*a^3 + 465/116*a^2 + 267/29*a - 5/29
]
*], q_expansions := [*
q + q^3 - 2*q^4 - 3*q^5 + 4*q^7 - 2*q^9 - q^11 - 2*q^12 - 6*q^13 - 3*q^15 + 4*q^16 + 2*q^17 - 8*q^19 + 6*q^20 + 4*q^21 - 5*q^23 + 4*q^25 - 5*q^27 - 8*q^28 - 8*q^29 + 3*q^31 - q^33 - 12*q^35 + 4*q^36 + 7*q^37 + O(q^38),
q + a*q^2 + (-a^4 - a^3 + 6*a^2 + 3*a - 8)*q^3 + (a^2 - 2)*q^4 + (-2*a^4 - a^3 + 11*a^2 + 3*a - 12)*q^5 + (a^4 + a^3 - 7*a^2 - 4*a + 9)*q^6 + (2*a^4 + a^3 - 12*a^2 - 4*a + 13)*q^7 + (a^3 - 4*a)*q^8 + (4*a^4 + 3*a^3 - 23*a^2 - 10*a + 25)*q^9 + (3*a^4 + a^3 - 17*a^2 - 4*a + 18)*q^10 - q^11 + (a^4 - 6*a^2 - a + 7)*q^12 + (3*a^4 + a^3 - 18*a^2 - 3*a + 21)*q^13 + (-3*a^4 - 2*a^3 + 16*a^2 + 5*a - 18)*q^14 + (2*a^4 + 2*a^3 - 12*a^2 - 6*a + 15)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3*a^4 + 19*a^2 - 25)*q^17 + (-5*a^4 - 3*a^3 + 30*a^2 + 9*a - 36)*q^18 + (-3*a^4 - a^3 + 17*a^2 + 2*a - 17)*q^19 + (-a^4 + 4*a^2 - 3)*q^20 + (-3*a^4 - 2*a^3 + 19*a^2 + 8*a - 23)*q^21 - a*q^22 + (3*a^4 + 3*a^3 - 15*a^2 - 8*a + 13)*q^23 + (-4*a^4 - 3*a^3 + 23*a^2 + 11*a - 27)*q^24 + (a^2 - a - 5)*q^25 + (-5*a^4 - 3*a^3 + 27*a^2 + 9*a - 27)*q^26 + (-5*a^4 - 3*a^3 + 29*a^2 + 12*a - 32)*q^27 + (-a^3 - a^2 + 2*a + 1)*q^28 + (2*a^4 - a^3 - 12*a^2 + 4*a + 10)*q^29 + (-2*a^4 - 2*a^3 + 14*a^2 + 7*a - 18)*q^30 + (6*a^4 + 3*a^3 - 35*a^2 - 9*a + 39)*q^31 + (-2*a^4 - 3*a^3 + 10*a^2 + 8*a - 9)*q^32 + (a^4 + a^3 - 6*a^2 - 3*a + 8)*q^33 + (6*a^4 + 4*a^3 - 30*a^2 - 13*a + 27)*q^34 + (a^2 + 2*a - 3)*q^35 + (-a^4 - a^3 + 5*a^2 + 4*a - 5)*q^36 + (a^4 - a^3 - 10*a^2 + 4*a + 16)*q^37 + O(q^38),
q + a*q^2 + (-a^4 - a^3 + 4*a^2 + a - 2)*q^3 + (a^2 - 2)*q^4 + (-a^3 - 3*a^2 + a + 2)*q^5 + (a^4 + a^3 - 3*a^2 + 1)*q^6 + (2*a^4 + 3*a^3 - 6*a^2 - 4*a + 1)*q^7 + (a^3 - 4*a)*q^8 + (a^3 + a^2 - 4*a - 1)*q^9 + (-a^4 - 3*a^3 + a^2 + 2*a)*q^10 + q^11 + (a^4 + 2*a^3 - 4*a^2 - 3*a + 3)*q^12 + (a^4 + 3*a^3 - 5*a - 3)*q^13 + (-a^4 + 4*a^2 - 3*a - 2)*q^14 + (-2*a^3 - 2*a^2 + 4*a - 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 - 4*a^3 + a^2 + 8*a - 1)*q^17 + (a^4 + a^3 - 4*a^2 - a)*q^18 + (a^4 + 3*a^3 + a^2 - 2*a - 5)*q^19 + (-a^4 + 4*a^2 - 3)*q^20 + (a^4 - 5*a^2 + 4*a - 1)*q^21 + a*q^22 + (-a^4 - 3*a^3 + a^2 + 6*a - 1)*q^23 + (-2*a^4 - 3*a^3 + 7*a^2 + a - 3)*q^24 + (2*a^4 + 6*a^3 + 3*a^2 - 5*a - 5)*q^25 + (a^4 + 3*a^3 - a^2 - 5*a - 1)*q^26 + (a^4 + a^3 - 5*a^2 - 4*a + 4)*q^27 + (-2*a^4 - 5*a^3 + 5*a^2 + 8*a - 1)*q^28 + (-a^3 - 2*a^2 + 4*a - 2)*q^29 + (-2*a^4 - 2*a^3 + 4*a^2 - a)*q^30 + (-4*a^4 - 9*a^3 + 7*a^2 + 13*a - 3)*q^31 + (-2*a^4 - 5*a^3 + 4*a^2 + 10*a - 1)*q^32 + (-a^4 - a^3 + 4*a^2 + a - 2)*q^33 + (-2*a^4 - 2*a^3 + 4*a^2 + a + 1)*q^34 + (4*a^3 + 5*a^2 - 8*a - 1)*q^35 + (-a^4 - 3*a^3 + a^2 + 6*a + 1)*q^36 + (-3*a^4 - 3*a^3 + 14*a^2 + 2*a - 10)*q^37 + O(q^38),
q + a*q^2 + (7/2*a^9 - 12*a^8 - 28*a^7 + 117*a^6 + 89/2*a^5 - 685/2*a^4 + 54*a^3 + 605/2*a^2 - 74*a - 44)*q^3 + (a^2 - 2)*q^4 + (1/4*a^9 - a^8 - 3/2*a^7 + 19/2*a^6 - 7/4*a^5 - 105/4*a^4 + 35/2*a^3 + 81/4*a^2 - 27/2*a - 2)*q^5 + (2*a^9 - 7*a^8 - 16*a^7 + 69*a^6 + 25*a^5 - 205*a^4 + 33*a^3 + 185*a^2 - 44*a - 28)*q^6 + (5/2*a^9 - 17/2*a^8 - 20*a^7 + 83*a^6 + 63/2*a^5 - 244*a^4 + 79/2*a^3 + 437/2*a^2 - 105/2*a - 33)*q^7 + (a^3 - 4*a)*q^8 + (a^9 - 3*a^8 - 9*a^7 + 29*a^6 + 22*a^5 - 83*a^4 - 10*a^3 + 69*a^2 - 2*a - 7)*q^9 + (-a^4 + a^3 + 5*a^2 - 2*a - 2)*q^10 + q^11 + (-6*a^9 + 20*a^8 + 49*a^7 - 195*a^6 - 84*a^5 + 570*a^4 - 77*a^3 - 501*a^2 + 120*a + 72)*q^12 + (5/2*a^9 - 8*a^8 - 21*a^7 + 77*a^6 + 81/2*a^5 - 439/2*a^4 + 18*a^3 + 365/2*a^2 - 40*a - 23)*q^13 + (3/2*a^9 - 5*a^8 - 12*a^7 + 49*a^6 + 37/2*a^5 - 291/2*a^4 + 26*a^3 + 265/2*a^2 - 33*a - 20)*q^14 + (-7*a^9 + 23*a^8 + 58*a^7 - 224*a^6 - 106*a^5 + 654*a^4 - 68*a^3 - 577*a^2 + 125*a + 88)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3/4*a^9 + 3*a^8 + 11/2*a^7 - 61/2*a^6 - 19/4*a^5 + 383/4*a^4 - 49/2*a^3 - 383/4*a^2 + 47/2*a + 18)*q^17 + (a^9 - 3*a^8 - 9*a^7 + 29*a^6 + 22*a^5 - 84*a^4 - 8*a^3 + 72*a^2 - 7*a - 8)*q^18 + (-19/4*a^9 + 31/2*a^8 + 79/2*a^7 - 301/2*a^6 - 295/4*a^5 + 1749/4*a^4 - 40*a^3 - 1523/4*a^2 + 79*a + 55)*q^19 + (-1/2*a^9 + 2*a^8 + 3*a^7 - 19*a^6 + 5/2*a^5 + 107/2*a^4 - 30*a^3 - 85/2*a^2 + 25*a + 4)*q^20 + (a^5 - a^4 - 7*a^3 + 3*a^2 + 10*a + 2)*q^21 + a*q^22 + (9/4*a^9 - 15/2*a^8 - 37/2*a^7 + 147/2*a^6 + 133/4*a^5 - 875/4*a^4 + 23*a^3 + 817/4*a^2 - 42*a - 35)*q^23 + (-8*a^9 + 27*a^8 + 65*a^7 - 264*a^6 - 110*a^5 + 777*a^4 - 105*a^3 - 694*a^2 + 160*a + 104)*q^24 + (-a^9 + 7/2*a^8 + 8*a^7 - 34*a^6 - 14*a^5 + 199/2*a^4 - 15/2*a^3 - 89*a^2 + 23/2*a + 16)*q^25 + (2*a^9 - 6*a^8 - 18*a^7 + 58*a^6 + 43*a^5 - 167*a^4 - 10*a^3 + 145*a^2 - 23*a - 20)*q^26 + (16*a^9 - 53*a^8 - 132*a^7 + 517*a^6 + 238*a^5 - 1515*a^4 + 166*a^3 + 1343*a^2 - 296*a - 200)*q^27 + (-4*a^9 + 14*a^8 + 32*a^7 - 137*a^6 - 51*a^5 + 403*a^4 - 62*a^3 - 359*a^2 + 85*a + 54)*q^28 + (7/4*a^9 - 13/2*a^8 - 27/2*a^7 + 129/2*a^6 + 71/4*a^5 - 777/4*a^4 + 38*a^3 + 723/4*a^2 - 44*a - 25)*q^29 + (-5*a^9 + 16*a^8 + 42*a^7 - 155*a^6 - 81*a^5 + 450*a^4 - 38*a^3 - 393*a^2 + 88*a + 56)*q^30 + (-7/2*a^9 + 23/2*a^8 + 29*a^7 - 112*a^6 - 107/2*a^5 + 327*a^4 - 61/2*a^3 - 575/2*a^2 + 115/2*a + 41)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (7/2*a^9 - 12*a^8 - 28*a^7 + 117*a^6 + 89/2*a^5 - 685/2*a^4 + 54*a^3 + 605/2*a^2 - 74*a - 44)*q^33 + (a^8 - 2*a^7 - 10*a^6 + 17*a^5 + 31*a^4 - 38*a^3 - 32*a^2 + 18*a + 6)*q^34 + (-23/4*a^9 + 19*a^8 + 95/2*a^7 - 369/2*a^6 - 347/4*a^5 + 2143/4*a^4 - 111/2*a^3 - 1859/4*a^2 + 211/2*a + 67)*q^35 + (-a^9 + 3*a^8 + 9*a^7 - 29*a^6 - 23*a^5 + 84*a^4 + 15*a^3 - 71*a^2 - 4*a + 6)*q^36 + (-21/4*a^9 + 37/2*a^8 + 83/2*a^7 - 363/2*a^6 - 249/4*a^5 + 2147/4*a^4 - 91*a^3 - 1941/4*a^2 + 113*a + 77)*q^37 + O(q^38),
q + a*q^2 + (-11/232*a^11 - 15/232*a^10 + 27/29*a^9 + 36/29*a^8 - 1559/232*a^7 - 883/116*a^6 + 4841/232*a^5 + 3869/232*a^4 - 5605/232*a^3 - 1119/116*a^2 + 188/29*a - 31/29)*q^3 + (a^2 - 2)*q^4 + (59/232*a^11 - 83/232*a^10 - 487/116*a^9 + 147/29*a^8 + 5599/232*a^7 - 1369/58*a^6 - 13121/232*a^5 + 9213/232*a^4 + 11403/232*a^3 - 1179/58*a^2 - 485/58*a + 103/29)*q^5 + (-6/29*a^11 + 5/29*a^10 + 102/29*a^9 - 67/29*a^8 - 592/29*a^7 + 260/29*a^6 + 1354/29*a^5 - 207/29*a^4 - 1080/29*a^3 - 153/29*a^2 + 156/29*a + 44/29)*q^6 + (-7/232*a^11 + 1/232*a^10 + 37/58*a^9 + 1/58*a^8 - 1203/232*a^7 - 61/116*a^6 + 4557/232*a^5 + 353/232*a^4 - 7553/232*a^3 + 63/116*a^2 + 959/58*a - 54/29)*q^7 + (a^3 - 4*a)*q^8 + (-3/232*a^11 - 99/232*a^10 + 49/58*a^9 + 197/29*a^8 - 2239/232*a^7 - 4285/116*a^6 + 8913/232*a^5 + 18297/232*a^4 - 11937/232*a^3 - 6817/116*a^2 + 452/29*a + 242/29)*q^9 + (47/116*a^11 - 15/116*a^10 - 207/29*a^9 + 14/29*a^8 + 5227/116*a^7 + 211/29*a^6 - 14067/116*a^5 - 4889/116*a^4 + 14811/116*a^3 + 3173/58*a^2 - 900/29*a - 236/29)*q^10 - q^11 + (-41/116*a^11 + 39/116*a^10 + 167/29*a^9 - 106/29*a^8 - 3881/116*a^7 + 579/58*a^6 + 9523/116*a^5 + 427/116*a^4 - 8975/116*a^3 - 1545/58*a^2 + 484/29*a + 254/29)*q^12 + (-49/232*a^11 + 123/232*a^10 + 86/29*a^9 - 214/29*a^8 - 3085/232*a^7 + 3923/116*a^6 + 4291/232*a^5 - 13073/232*a^4 + 489/232*a^3 + 3283/116*a^2 - 312/29*a - 30/29)*q^13 + (-5/58*a^11 + 9/58*a^10 + 85/58*a^9 - 69/29*a^8 - 503/58*a^7 + 350/29*a^6 + 598/29*a^5 - 630/29*a^4 - 987/58*a^3 + 525/58*a^2 + 65/29*a + 28/29)*q^14 + (41/232*a^11 - 39/232*a^10 - 167/58*a^9 + 53/29*a^8 + 3765/232*a^7 - 405/116*a^6 - 8595/232*a^5 - 3443/232*a^4 + 7235/232*a^3 + 4619/116*a^2 - 97/29*a - 359/29)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/29*a^11 + 71/116*a^10 - 19/116*a^9 - 277/29*a^8 + 172/29*a^7 + 5983/116*a^6 - 828/29*a^5 - 12927/116*a^4 + 4471/116*a^3 + 9787/116*a^2 - 441/58*a - 244/29)*q^17 + (-27/58*a^11 + 37/58*a^10 + 215/29*a^9 - 245/29*a^8 - 2345/58*a^7 + 1020/29*a^6 + 5049/58*a^5 - 2715/58*a^4 - 3845/58*a^3 + 359/29*a^2 + 293/29*a + 12/29)*q^18 + (21/232*a^11 - 61/232*a^10 - 135/116*a^9 + 229/58*a^8 + 825/232*a^7 - 1141/58*a^6 + 1061/232*a^5 + 8627/232*a^4 - 5703/232*a^3 - 823/29*a^2 + 519/29*a + 220/29)*q^19 + (67/116*a^11 + 7/116*a^10 - 613/58*a^9 - 80/29*a^8 + 7935/116*a^7 + 1603/58*a^6 - 21519/116*a^5 - 11275/116*a^4 + 22297/116*a^3 + 3193/29*a^2 - 1349/29*a - 582/29)*q^20 + (19/116*a^11 - 69/116*a^10 - 59/29*a^9 + 250/29*a^8 + 879/116*a^7 - 2519/58*a^6 - 885/116*a^5 + 10443/116*a^4 + 317/116*a^3 - 4173/58*a^2 - 312/29*a + 376/29)*q^21 - a*q^22 + (-21/58*a^11 + 35/116*a^10 + 685/116*a^9 - 191/58*a^8 - 1927/58*a^7 + 921/116*a^6 + 2181/29*a^5 + 1277/116*a^4 - 7415/116*a^3 - 3797/116*a^2 + 418/29*a + 251/29)*q^23 + (-9/29*a^11 - 7/29*a^10 + 182/29*a^9 + 117/29*a^8 - 1294/29*a^7 - 712/29*a^6 + 3887/29*a^5 + 1850/29*a^4 - 4578/29*a^3 - 1752/29*a^2 + 1336/29*a + 240/29)*q^24 + (1/4*a^11 - 1/4*a^10 - 9/2*a^9 + 7/2*a^8 + 117/4*a^7 - 16*a^6 - 331/4*a^5 + 105/4*a^4 + 391/4*a^3 - 14*a^2 - 71/2*a + 6)*q^25 + (-3/29*a^11 - 12/29*a^10 + 80/29*a^9 + 184/29*a^8 - 673/29*a^7 - 1001/29*a^6 + 2243/29*a^5 + 2260/29*a^4 - 2744/29*a^3 - 1831/29*a^2 + 803/29*a + 196/29)*q^26 + (19/232*a^11 - 69/232*a^10 - 59/58*a^9 + 125/29*a^8 + 647/232*a^7 - 2287/116*a^6 + 1319/232*a^5 + 6615/232*a^4 - 5367/232*a^3 - 751/116*a^2 + 366/29*a + 43/29)*q^27 + (-5/116*a^11 + 9/116*a^10 + 14/29*a^9 - 20/29*a^8 - 97/116*a^7 + 1/29*a^6 - 747/116*a^5 + 1263/116*a^4 + 2783/116*a^3 - 1173/58*a^2 - 591/29*a + 188/29)*q^28 + (-35/232*a^11 + 63/232*a^10 + 283/116*a^9 - 227/58*a^8 - 3231/232*a^7 + 540/29*a^6 + 7821/232*a^5 - 7225/232*a^4 - 7779/232*a^3 + 607/58*a^2 + 208/29*a + 136/29)*q^29 + (21/58*a^11 - 3/58*a^10 - 193/29*a^9 - 6/29*a^8 + 2565/58*a^7 + 212/29*a^6 - 7349/58*a^5 - 1871/58*a^4 + 8275/58*a^3 + 1174/29*a^2 - 1056/29*a - 164/29)*q^30 + (13/58*a^11 - 35/58*a^10 - 96/29*a^9 + 527/58*a^8 + 925/58*a^7 - 1345/29*a^6 - 1561/58*a^5 + 2682/29*a^4 + 387/29*a^3 - 1944/29*a^2 - 367/58*a + 281/29)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (11/232*a^11 + 15/232*a^10 - 27/29*a^9 - 36/29*a^8 + 1559/232*a^7 + 883/116*a^6 - 4841/232*a^5 - 3869/232*a^4 + 5605/232*a^3 + 1119/116*a^2 - 188/29*a + 31/29)*q^33 + (59/116*a^11 - 83/116*a^10 - 229/29*a^9 + 265/29*a^8 + 4903/116*a^7 - 1079/29*a^6 - 10395/116*a^5 + 5907/116*a^4 + 7459/116*a^3 - 937/58*a^2 - 108/29*a + 32/29)*q^34 + (-77/232*a^11 + 185/232*a^10 + 611/116*a^9 - 357/29*a^8 - 6737/232*a^7 + 1884/29*a^6 + 15559/232*a^5 - 31671/232*a^4 - 15745/232*a^3 + 3153/29*a^2 + 1211/58*a - 594/29)*q^35 + (-85/116*a^11 + 95/116*a^10 + 354/29*a^9 - 311/29*a^8 - 8261/116*a^7 + 2557/58*a^6 + 19839/116*a^5 - 6601/116*a^4 - 18055/116*a^3 + 707/58*a^2 + 944/29*a - 52/29)*q^36 + (2/29*a^11 + 3/116*a^10 - 165/116*a^9 - 23/58*a^8 + 294/29*a^7 + 243/116*a^6 - 1647/58*a^5 - 507/116*a^4 + 2513/116*a^3 + 465/116*a^2 + 267/29*a - 5/29)*q^37 + O(q^38)
*]> ;  // time = 81.699 seconds




J[453] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 453, 453, 453, 453, 453, 453, 453, 151, 151, 151 ], new_dimensions := [ 2, 2, 2, 2, 3, 5, 9, 3, 3, 6 ], dimensions := [ 2, 2, 2, 2, 3, 5, 9, 6, 6, 12 ], intersection_graph := [ 0, 11, 1, 1, 1, 1, 1, 1, 3, 23, 11, 0, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 0, 1, 1, 1, 491, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 0, 29, 1, 1, 1, 1, 1, 1, 1, 1, 29, 0, 1, 41, 1, 1, 1, 1, 491, 1, 1, 1, 0, 71, 1, 1, 1, 1, 1, 1, 1, 41, 71, 0, 1, 1, 3, 9, 1, 1, 1, 1, 1, 1, 0, 4489, 23, 1, 1, 19, 1, 1, 1, 1, 4489, 0 ], ap_traces := [
[ 0, -2, 4, 2, 4, 0, 0, 0, 12, 0, 12, 2 ],
[ 3, -2, -3, 2, 6, -2, 6, 0, 0, 9, -13, 5 ],
[ -3, 2, 3, -4, 6, 8, -2, 4, 10, -5, -5, 9 ],
[ -1, 2, -1, -6, -6, -2, 0, -8, -6, 9, -5, -3 ],
[ -1, -3, -3, 2, 1, -4, -19, 5, -16, -7, 5, 3 ],
[ -3, -5, -4, -6, -17, 4, 11, -5, -4, 0, -6, -24 ],
[ 6, 9, -2, 14, 2, -2, -2, 8, -8, 0, 16, 10 ]
], hecke_fields := [
x^2 - 3,
x^2 - 3*x + 1,
x^2 + 3*x + 1,
x^2 + x - 1,
x^3 + x^2 - 2*x - 1,
x^5 + 3*x^4 - 6*x^3 - 18*x^2 + 8*x + 19,
x^9 - 6*x^8 + 3*x^7 + 42*x^6 - 68*x^5 - 62*x^4 + 168*x^3 - 15*x^2 - 98*x + 31
], atkin_lehners := [
[ 1, -1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 69, 1 ],
[ 9, 1 ],
[ 19, 1 ],
[ 19, 1 ],
[ 1, 1 ],
[ 41, 1 ],
[ 71, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 19, 1 ],
[ 19, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 71, 1 ]
], torsion_upper_bounds := [ 1, 1, 19, 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 19, 1, 1, 1, 1 ], l_ratios := [ 1, 1, 1/19, 0, 0, 0, 71 ], analytic_sha_upper_bounds := [ 1, 1, 1, 0, 0, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 0, 0, 0, 1 ], eigenvalues := [*
[
a,
-1,
2,
1,
a + 2,
2*a,
0,
0,
-2*a + 6,
-2*a,
2*a + 6,
-4*a + 1
],
[
a,
-1,
a - 3,
1,
-2*a + 6,
-1,
-4*a + 9,
0,
2*a - 3,
-a + 6,
-3*a - 2,
-3*a + 7
],
[
a,
1,
a + 3,
-2*a - 5,
2*a + 6,
-2*a + 1,
-1,
4*a + 8,
5,
3*a + 2,
-5*a - 10,
-a + 3
],
[
a,
1,
-a - 1,
-3,
2*a - 2,
-1,
-2*a - 1,
-4,
-4*a - 5,
3*a + 6,
5*a,
-3*a - 3
],
[
a,
-1,
-2*a^2 - a + 2,
2*a^2 + 2*a - 2,
-a^2 - 3*a + 1,
-2*a - 2,
-a^2 - a - 5,
5*a^2 + 2*a - 6,
2*a^2 + 2*a - 8,
-a^2 + 2*a,
-2*a^2 + 3*a + 6,
-a^2 - 5*a + 1
],
[
a,
-1,
-a^4 - a^3 + 6*a^2 + 2*a - 6,
a^4 + a^3 - 7*a^2 - 4*a + 7,
a^4 - 7*a^2 + 2*a + 3,
-a^4 + a^3 + 9*a^2 - 6*a - 11,
2*a^4 + a^3 - 14*a^2 + 18,
-2*a^4 - 2*a^3 + 13*a^2 + 5*a - 15,
a^4 - a^3 - 9*a^2 + 6*a + 11,
-2*a^4 - a^3 + 15*a^2 - 20,
2*a^4 + 2*a^3 - 11*a^2 - 4*a + 5,
3*a - 3
],
[
a,
1,
2*a^8 - 7*a^7 - 12*a^6 + 56*a^5 + 5*a^4 - 123*a^3 + 38*a^2 + 74*a - 27,
-3/2*a^8 + 11/2*a^7 + 8*a^6 - 43*a^5 + 3*a^4 + 90*a^3 - 38*a^2 - 99/2*a + 47/2,
-15/2*a^8 + 55/2*a^7 + 42*a^6 - 218*a^5 - a^4 + 470*a^3 - 159*a^2 - 543/2*a + 195/2,
2*a^8 - 8*a^7 - 10*a^6 + 64*a^5 - 8*a^4 - 140*a^3 + 54*a^2 + 82*a - 26,
3*a^8 - 12*a^7 - 14*a^6 + 95*a^5 - 20*a^4 - 206*a^3 + 99*a^2 + 123*a - 50,
6*a^8 - 23*a^7 - 31*a^6 + 182*a^5 - 18*a^4 - 392*a^3 + 160*a^2 + 227*a - 87,
2*a^8 - 6*a^7 - 14*a^6 + 46*a^5 + 22*a^4 - 92*a^3 - 2*a^2 + 46*a - 6,
-2*a^8 + 9*a^7 + 7*a^6 - 72*a^5 + 32*a^4 + 158*a^3 - 104*a^2 - 95*a + 49,
2*a^8 - 7*a^7 - 12*a^6 + 56*a^5 + 5*a^4 - 121*a^3 + 36*a^2 + 66*a - 21,
-3/2*a^8 + 13/2*a^7 + 6*a^6 - 52*a^5 + 19*a^4 + 114*a^3 - 73*a^2 - 135/2*a + 81/2
]
*], q_expansions := [*
q + a*q^2 - q^3 + q^4 + 2*q^5 - a*q^6 + q^7 - a*q^8 + q^9 + 2*a*q^10 + (a + 2)*q^11 - q^12 + 2*a*q^13 + a*q^14 - 2*q^15 - 5*q^16 + a*q^18 + 2*q^20 - q^21 + (2*a + 3)*q^22 + (-2*a + 6)*q^23 + a*q^24 - q^25 + 6*q^26 - q^27 + q^28 - 2*a*q^29 - 2*a*q^30 + (2*a + 6)*q^31 - 3*a*q^32 + (-a - 2)*q^33 + 2*q^35 + q^36 + (-4*a + 1)*q^37 + O(q^38),
q + a*q^2 - q^3 + (3*a - 3)*q^4 + (a - 3)*q^5 - a*q^6 + q^7 + (4*a - 3)*q^8 + q^9 - q^10 + (-2*a + 6)*q^11 + (-3*a + 3)*q^12 - q^13 + a*q^14 + (-a + 3)*q^15 + (3*a + 2)*q^16 + (-4*a + 9)*q^17 + a*q^18 + (-3*a + 6)*q^20 - q^21 + 2*q^22 + (2*a - 3)*q^23 + (-4*a + 3)*q^24 + (-3*a + 3)*q^25 - a*q^26 - q^27 + (3*a - 3)*q^28 + (-a + 6)*q^29 + q^30 + (-3*a - 2)*q^31 + (3*a + 3)*q^32 + (2*a - 6)*q^33 + (-3*a + 4)*q^34 + (a - 3)*q^35 + (3*a - 3)*q^36 + (-3*a + 7)*q^37 + O(q^38),
q + a*q^2 + q^3 + (-3*a - 3)*q^4 + (a + 3)*q^5 + a*q^6 + (-2*a - 5)*q^7 + (4*a + 3)*q^8 + q^9 - q^10 + (2*a + 6)*q^11 + (-3*a - 3)*q^12 + (-2*a + 1)*q^13 + (a + 2)*q^14 + (a + 3)*q^15 + (-3*a + 2)*q^16 - q^17 + a*q^18 + (4*a + 8)*q^19 + (-3*a - 6)*q^20 + (-2*a - 5)*q^21 - 2*q^22 + 5*q^23 + (4*a + 3)*q^24 + (3*a + 3)*q^25 + (7*a + 2)*q^26 + q^27 + (3*a + 9)*q^28 + (3*a + 2)*q^29 - q^30 + (-5*a - 10)*q^31 + (3*a - 3)*q^32 + (2*a + 6)*q^33 - a*q^34 + (-5*a - 13)*q^35 + (-3*a - 3)*q^36 + (-a + 3)*q^37 + O(q^38),
q + a*q^2 + q^3 + (-a - 1)*q^4 + (-a - 1)*q^5 + a*q^6 - 3*q^7 + (-2*a - 1)*q^8 + q^9 - q^10 + (2*a - 2)*q^11 + (-a - 1)*q^12 - q^13 - 3*a*q^14 + (-a - 1)*q^15 + 3*a*q^16 + (-2*a - 1)*q^17 + a*q^18 - 4*q^19 + (a + 2)*q^20 - 3*q^21 + (-4*a + 2)*q^22 + (-4*a - 5)*q^23 + (-2*a - 1)*q^24 + (a - 3)*q^25 - a*q^26 + q^27 + (3*a + 3)*q^28 + (3*a + 6)*q^29 - q^30 + 5*a*q^31 + (a + 5)*q^32 + (2*a - 2)*q^33 + (a - 2)*q^34 + (3*a + 3)*q^35 + (-a - 1)*q^36 + (-3*a - 3)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-2*a^2 - a + 2)*q^5 - a*q^6 + (2*a^2 + 2*a - 2)*q^7 + (-a^2 - 2*a + 1)*q^8 + q^9 + (a^2 - 2*a - 2)*q^10 + (-a^2 - 3*a + 1)*q^11 + (-a^2 + 2)*q^12 + (-2*a - 2)*q^13 + (2*a + 2)*q^14 + (2*a^2 + a - 2)*q^15 + (-3*a^2 - a + 3)*q^16 + (-a^2 - a - 5)*q^17 + a*q^18 + (5*a^2 + 2*a - 6)*q^19 + (a^2 + 2*a - 3)*q^20 + (-2*a^2 - 2*a + 2)*q^21 + (-2*a^2 - a - 1)*q^22 + (2*a^2 + 2*a - 8)*q^23 + (a^2 + 2*a - 1)*q^24 + (a^2 - 1)*q^25 + (-2*a^2 - 2*a)*q^26 - q^27 + (-2*a^2 - 2*a + 4)*q^28 + (-a^2 + 2*a)*q^29 + (-a^2 + 2*a + 2)*q^30 + (-2*a^2 + 3*a + 6)*q^31 + (4*a^2 + a - 5)*q^32 + (a^2 + 3*a - 1)*q^33 + (-7*a - 1)*q^34 + (-2*a - 6)*q^35 + (a^2 - 2)*q^36 + (-a^2 - 5*a + 1)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^4 - a^3 + 6*a^2 + 2*a - 6)*q^5 - a*q^6 + (a^4 + a^3 - 7*a^2 - 4*a + 7)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (2*a^4 - 16*a^2 + 2*a + 19)*q^10 + (a^4 - 7*a^2 + 2*a + 3)*q^11 + (-a^2 + 2)*q^12 + (-a^4 + a^3 + 9*a^2 - 6*a - 11)*q^13 + (-2*a^4 - a^3 + 14*a^2 - a - 19)*q^14 + (a^4 + a^3 - 6*a^2 - 2*a + 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^4 + a^3 - 14*a^2 + 18)*q^17 + a*q^18 + (-2*a^4 - 2*a^3 + 13*a^2 + 5*a - 15)*q^19 + (-4*a^4 - 2*a^3 + 26*a^2 - a - 26)*q^20 + (-a^4 - a^3 + 7*a^2 + 4*a - 7)*q^21 + (-3*a^4 - a^3 + 20*a^2 - 5*a - 19)*q^22 + (a^4 - a^3 - 9*a^2 + 6*a + 11)*q^23 + (-a^3 + 4*a)*q^24 + (a^3 + 3*a^2 - 2*a - 7)*q^25 + (4*a^4 + 3*a^3 - 24*a^2 - 3*a + 19)*q^26 - q^27 + (3*a^4 - 23*a^2 + 5*a + 24)*q^28 + (-2*a^4 - a^3 + 15*a^2 - 20)*q^29 + (-2*a^4 + 16*a^2 - 2*a - 19)*q^30 + (2*a^4 + 2*a^3 - 11*a^2 - 4*a + 5)*q^31 + (-3*a^4 - 2*a^3 + 18*a^2 + 4*a - 19)*q^32 + (-a^4 + 7*a^2 - 2*a - 3)*q^33 + (-5*a^4 - 2*a^3 + 36*a^2 + 2*a - 38)*q^34 + (a^4 + 2*a^3 - 3*a^2 - 3*a - 4)*q^35 + (a^2 - 2)*q^36 + (3*a - 3)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (2*a^8 - 7*a^7 - 12*a^6 + 56*a^5 + 5*a^4 - 123*a^3 + 38*a^2 + 74*a - 27)*q^5 + a*q^6 + (-3/2*a^8 + 11/2*a^7 + 8*a^6 - 43*a^5 + 3*a^4 + 90*a^3 - 38*a^2 - 99/2*a + 47/2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (5*a^8 - 18*a^7 - 28*a^6 + 141*a^5 + a^4 - 298*a^3 + 104*a^2 + 169*a - 62)*q^10 + (-15/2*a^8 + 55/2*a^7 + 42*a^6 - 218*a^5 - a^4 + 470*a^3 - 159*a^2 - 543/2*a + 195/2)*q^11 + (a^2 - 2)*q^12 + (2*a^8 - 8*a^7 - 10*a^6 + 64*a^5 - 8*a^4 - 140*a^3 + 54*a^2 + 82*a - 26)*q^13 + (-7/2*a^8 + 25/2*a^7 + 20*a^6 - 99*a^5 - 3*a^4 + 214*a^3 - 72*a^2 - 247/2*a + 93/2)*q^14 + (2*a^8 - 7*a^7 - 12*a^6 + 56*a^5 + 5*a^4 - 123*a^3 + 38*a^2 + 74*a - 27)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (3*a^8 - 12*a^7 - 14*a^6 + 95*a^5 - 20*a^4 - 206*a^3 + 99*a^2 + 123*a - 50)*q^17 + a*q^18 + (6*a^8 - 23*a^7 - 31*a^6 + 182*a^5 - 18*a^4 - 392*a^3 + 160*a^2 + 227*a - 87)*q^19 + (8*a^8 - 29*a^7 - 45*a^6 + 229*a^5 + 2*a^4 - 490*a^3 + 168*a^2 + 280*a - 101)*q^20 + (-3/2*a^8 + 11/2*a^7 + 8*a^6 - 43*a^5 + 3*a^4 + 90*a^3 - 38*a^2 - 99/2*a + 47/2)*q^21 + (-35/2*a^8 + 129/2*a^7 + 97*a^6 - 511*a^5 + 5*a^4 + 1101*a^3 - 384*a^2 - 1275/2*a + 465/2)*q^22 + (2*a^8 - 6*a^7 - 14*a^6 + 46*a^5 + 22*a^4 - 92*a^3 - 2*a^2 + 46*a - 6)*q^23 + (a^3 - 4*a)*q^24 + (-12*a^8 + 45*a^7 + 65*a^6 - 358*a^5 + 14*a^4 + 780*a^3 - 280*a^2 - 465*a + 166)*q^25 + (4*a^8 - 16*a^7 - 20*a^6 + 128*a^5 - 16*a^4 - 282*a^3 + 112*a^2 + 170*a - 62)*q^26 + q^27 + (-11/2*a^8 + 39/2*a^7 + 32*a^6 - 155*a^5 - 9*a^4 + 336*a^3 - 100*a^2 - 395/2*a + 123/2)*q^28 + (-2*a^8 + 9*a^7 + 7*a^6 - 72*a^5 + 32*a^4 + 158*a^3 - 104*a^2 - 95*a + 49)*q^29 + (5*a^8 - 18*a^7 - 28*a^6 + 141*a^5 + a^4 - 298*a^3 + 104*a^2 + 169*a - 62)*q^30 + (2*a^8 - 7*a^7 - 12*a^6 + 56*a^5 + 5*a^4 - 121*a^3 + 36*a^2 + 66*a - 21)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-15/2*a^8 + 55/2*a^7 + 42*a^6 - 218*a^5 - a^4 + 470*a^3 - 159*a^2 - 543/2*a + 195/2)*q^33 + (6*a^8 - 23*a^7 - 31*a^6 + 184*a^5 - 20*a^4 - 405*a^3 + 168*a^2 + 244*a - 93)*q^34 + (9*a^8 - 33*a^7 - 50*a^6 + 262*a^5 - 4*a^4 - 566*a^3 + 206*a^2 + 327*a - 123)*q^35 + (a^2 - 2)*q^36 + (-3/2*a^8 + 13/2*a^7 + 6*a^6 - 52*a^5 + 19*a^4 + 114*a^3 - 73*a^2 - 135/2*a + 81/2)*q^37 + O(q^38)
*]> ;  // time = 86.921 seconds




J[454] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 454, 454, 454, 454, 227, 227, 227, 227, 227 ], new_dimensions := [ 2, 4, 5, 7, 2, 2, 2, 3, 10 ], dimensions := [ 2, 4, 5, 7, 4, 4, 4, 6, 20 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 19, 1, 0, 1, 1, 7, 1, 1, 7, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2957, 1, 1, 1, 0, 7, 1, 1, 41, 1, 1, 7, 1, 7, 0, 1, 1, 49, 1, 1, 1, 1, 1, 1, 0, 1, 1, 961, 1, 1, 1, 1, 1, 1, 0, 1, 4225, 1, 7, 1, 41, 49, 1, 1, 0, 1, 19, 1, 2957, 1, 1, 961, 4225, 1, 0 ], ap_traces := [
[ 2, -3, -2, -5, -9, 2, -6, -1, -3, -7, -2, 0 ],
[ -4, -2, -4, 2, -10, -4, -4, -2, -2, -22, 0, -8 ],
[ -5, -1, 3, -6, 7, 3, 8, 1, 6, 31, -4, 7 ],
[ 7, 4, -1, 5, 10, -5, -2, 0, 11, 16, -2, -23 ]
], hecke_fields := [
x^2 + 3*x + 1,
x^4 + 2*x^3 - 3*x^2 - 2*x + 1,
x^5 + x^4 - 11*x^3 - 8*x^2 + 28*x + 8,
x^7 - 4*x^6 - 9*x^5 + 48*x^4 - 11*x^3 - 92*x^2 + 28*x + 56
], atkin_lehners := [
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 19, 1 ],
[ 49, 1 ],
[ 2957, 1 ],
[ 5453, 1 ]
], tamagawa_numbers := [
[ 19, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 5453, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 19 ], torsion_lower_bounds := [ 1, 1, 1, 19 ], l_ratios := [ 0, 0, 1, 287/19 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
1,
a,
-2*a - 4,
a - 1,
a - 3,
-2*a - 2,
2*a,
3*a + 4,
-3*a - 6,
5*a + 4,
2*a + 2,
0
],
[
-1,
a,
-a^3 - 3*a^2 + a + 2,
a^3 + 3*a^2 - 2*a - 3,
a^3 + 2*a^2 - 3*a - 4,
3*a^3 + 6*a^2 - 8*a - 5,
-2*a^3 - 3*a^2 + 5*a - 1,
-2*a^3 - 4*a^2 + 5*a + 2,
-3*a^3 - 8*a^2 + 5*a + 7,
3*a^3 + 7*a^2 - 4*a - 10,
-3*a^2 - 5*a + 5,
-2*a^3 - 4*a^2 + 8*a + 2
],
[
-1,
a,
1/4*a^4 - 3/4*a^3 - 7/4*a^2 + 5*a + 1,
1/2*a^4 - 4*a^2 + 1/2*a + 3,
-a^2 + 6,
-1/4*a^4 - 3/4*a^3 + 9/4*a^2 + 11/2*a - 3,
1/2*a^4 + 1/2*a^3 - 7/2*a^2 - 2*a + 4,
-a^3 - a^2 + 6*a + 4,
-1/4*a^4 + 5/4*a^3 + 9/4*a^2 - 15/2*a - 1,
-a + 6,
3/2*a^4 - 3/2*a^3 - 23/2*a^2 + 9*a + 8,
-1/2*a^4 + a^3 + 2*a^2 - 15/2*a + 7
],
[
1,
a,
-1/4*a^6 + a^5 + 9/4*a^4 - 11*a^3 + 7/4*a^2 + 12*a + 1,
-3/2*a^6 + 7/2*a^5 + 39/2*a^4 - 81/2*a^3 - 105/2*a^2 + 123/2*a + 59,
2*a^6 - 5*a^5 - 26*a^4 + 58*a^3 + 70*a^2 - 90*a - 78,
5/4*a^6 - 7/2*a^5 - 57/4*a^4 + 79/2*a^3 + 85/4*a^2 - 103/2*a - 23,
5/2*a^6 - 7*a^5 - 59/2*a^4 + 79*a^3 + 109/2*a^2 - 104*a - 64,
3*a^6 - 7*a^5 - 39*a^4 + 81*a^3 + 105*a^2 - 124*a - 116,
-9/4*a^6 + 11/2*a^5 + 117/4*a^4 - 127/2*a^3 - 313/4*a^2 + 189/2*a + 89,
-6*a^6 + 15*a^5 + 76*a^4 - 172*a^3 - 187*a^2 + 249*a + 210,
-1/2*a^6 + 2*a^5 + 7/2*a^4 - 22*a^3 + 31/2*a^2 + 21*a - 16,
5/2*a^6 - 11/2*a^5 - 67/2*a^4 + 127/2*a^3 + 195/2*a^2 - 195/2*a - 107
]
*], q_expansions := [*
q + q^2 + a*q^3 + q^4 + (-2*a - 4)*q^5 + a*q^6 + (a - 1)*q^7 + q^8 + (-3*a - 4)*q^9 + (-2*a - 4)*q^10 + (a - 3)*q^11 + a*q^12 + (-2*a - 2)*q^13 + (a - 1)*q^14 + (2*a + 2)*q^15 + q^16 + 2*a*q^17 + (-3*a - 4)*q^18 + (3*a + 4)*q^19 + (-2*a - 4)*q^20 + (-4*a - 1)*q^21 + (a - 3)*q^22 + (-3*a - 6)*q^23 + a*q^24 + (4*a + 7)*q^25 + (-2*a - 2)*q^26 + (2*a + 3)*q^27 + (a - 1)*q^28 + (5*a + 4)*q^29 + (2*a + 2)*q^30 + (2*a + 2)*q^31 + q^32 + (-6*a - 1)*q^33 + 2*a*q^34 + (4*a + 6)*q^35 + (-3*a - 4)*q^36 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a^3 - 3*a^2 + a + 2)*q^5 - a*q^6 + (a^3 + 3*a^2 - 2*a - 3)*q^7 - q^8 + (a^2 - 3)*q^9 + (a^3 + 3*a^2 - a - 2)*q^10 + (a^3 + 2*a^2 - 3*a - 4)*q^11 + a*q^12 + (3*a^3 + 6*a^2 - 8*a - 5)*q^13 + (-a^3 - 3*a^2 + 2*a + 3)*q^14 + (-a^3 - 2*a^2 + 1)*q^15 + q^16 + (-2*a^3 - 3*a^2 + 5*a - 1)*q^17 + (-a^2 + 3)*q^18 + (-2*a^3 - 4*a^2 + 5*a + 2)*q^19 + (-a^3 - 3*a^2 + a + 2)*q^20 + (a^3 + a^2 - a - 1)*q^21 + (-a^3 - 2*a^2 + 3*a + 4)*q^22 + (-3*a^3 - 8*a^2 + 5*a + 7)*q^23 - a*q^24 + (2*a^2 + 4*a - 3)*q^25 + (-3*a^3 - 6*a^2 + 8*a + 5)*q^26 + (a^3 - 6*a)*q^27 + (a^3 + 3*a^2 - 2*a - 3)*q^28 + (3*a^3 + 7*a^2 - 4*a - 10)*q^29 + (a^3 + 2*a^2 - 1)*q^30 + (-3*a^2 - 5*a + 5)*q^31 - q^32 + (-2*a - 1)*q^33 + (2*a^3 + 3*a^2 - 5*a + 1)*q^34 + (2*a^3 + 3*a^2 - 5*a - 5)*q^35 + (a^2 - 3)*q^36 + (-2*a^3 - 4*a^2 + 8*a + 2)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (1/4*a^4 - 3/4*a^3 - 7/4*a^2 + 5*a + 1)*q^5 - a*q^6 + (1/2*a^4 - 4*a^2 + 1/2*a + 3)*q^7 - q^8 + (a^2 - 3)*q^9 + (-1/4*a^4 + 3/4*a^3 + 7/4*a^2 - 5*a - 1)*q^10 + (-a^2 + 6)*q^11 + a*q^12 + (-1/4*a^4 - 3/4*a^3 + 9/4*a^2 + 11/2*a - 3)*q^13 + (-1/2*a^4 + 4*a^2 - 1/2*a - 3)*q^14 + (-a^4 + a^3 + 7*a^2 - 6*a - 2)*q^15 + q^16 + (1/2*a^4 + 1/2*a^3 - 7/2*a^2 - 2*a + 4)*q^17 + (-a^2 + 3)*q^18 + (-a^3 - a^2 + 6*a + 4)*q^19 + (1/4*a^4 - 3/4*a^3 - 7/4*a^2 + 5*a + 1)*q^20 + (-1/2*a^4 + 3/2*a^3 + 9/2*a^2 - 11*a - 4)*q^21 + (a^2 - 6)*q^22 + (-1/4*a^4 + 5/4*a^3 + 9/4*a^2 - 15/2*a - 1)*q^23 - a*q^24 + (-1/4*a^4 - 3/4*a^3 + 9/4*a^2 + 7/2*a - 4)*q^25 + (1/4*a^4 + 3/4*a^3 - 9/4*a^2 - 11/2*a + 3)*q^26 + (a^3 - 6*a)*q^27 + (1/2*a^4 - 4*a^2 + 1/2*a + 3)*q^28 + (-a + 6)*q^29 + (a^4 - a^3 - 7*a^2 + 6*a + 2)*q^30 + (3/2*a^4 - 3/2*a^3 - 23/2*a^2 + 9*a + 8)*q^31 - q^32 + (-a^3 + 6*a)*q^33 + (-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 2*a - 4)*q^34 + (-3/4*a^4 + 9/4*a^3 + 25/4*a^2 - 16*a - 6)*q^35 + (a^2 - 3)*q^36 + (-1/2*a^4 + a^3 + 2*a^2 - 15/2*a + 7)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-1/4*a^6 + a^5 + 9/4*a^4 - 11*a^3 + 7/4*a^2 + 12*a + 1)*q^5 + a*q^6 + (-3/2*a^6 + 7/2*a^5 + 39/2*a^4 - 81/2*a^3 - 105/2*a^2 + 123/2*a + 59)*q^7 + q^8 + (a^2 - 3)*q^9 + (-1/4*a^6 + a^5 + 9/4*a^4 - 11*a^3 + 7/4*a^2 + 12*a + 1)*q^10 + (2*a^6 - 5*a^5 - 26*a^4 + 58*a^3 + 70*a^2 - 90*a - 78)*q^11 + a*q^12 + (5/4*a^6 - 7/2*a^5 - 57/4*a^4 + 79/2*a^3 + 85/4*a^2 - 103/2*a - 23)*q^13 + (-3/2*a^6 + 7/2*a^5 + 39/2*a^4 - 81/2*a^3 - 105/2*a^2 + 123/2*a + 59)*q^14 + (a^4 - a^3 - 11*a^2 + 8*a + 14)*q^15 + q^16 + (5/2*a^6 - 7*a^5 - 59/2*a^4 + 79*a^3 + 109/2*a^2 - 104*a - 64)*q^17 + (a^2 - 3)*q^18 + (3*a^6 - 7*a^5 - 39*a^4 + 81*a^3 + 105*a^2 - 124*a - 116)*q^19 + (-1/4*a^6 + a^5 + 9/4*a^4 - 11*a^3 + 7/4*a^2 + 12*a + 1)*q^20 + (-5/2*a^6 + 6*a^5 + 63/2*a^4 - 69*a^3 - 153/2*a^2 + 101*a + 84)*q^21 + (2*a^6 - 5*a^5 - 26*a^4 + 58*a^3 + 70*a^2 - 90*a - 78)*q^22 + (-9/4*a^6 + 11/2*a^5 + 117/4*a^4 - 127/2*a^3 - 313/4*a^2 + 189/2*a + 89)*q^23 + a*q^24 + (-5/4*a^6 + 7/2*a^5 + 53/4*a^4 - 77/2*a^3 - 41/4*a^2 + 83/2*a + 10)*q^25 + (5/4*a^6 - 7/2*a^5 - 57/4*a^4 + 79/2*a^3 + 85/4*a^2 - 103/2*a - 23)*q^26 + (a^3 - 6*a)*q^27 + (-3/2*a^6 + 7/2*a^5 + 39/2*a^4 - 81/2*a^3 - 105/2*a^2 + 123/2*a + 59)*q^28 + (-6*a^6 + 15*a^5 + 76*a^4 - 172*a^3 - 187*a^2 + 249*a + 210)*q^29 + (a^4 - a^3 - 11*a^2 + 8*a + 14)*q^30 + (-1/2*a^6 + 2*a^5 + 7/2*a^4 - 22*a^3 + 31/2*a^2 + 21*a - 16)*q^31 + q^32 + (3*a^6 - 8*a^5 - 38*a^4 + 92*a^3 + 94*a^2 - 134*a - 112)*q^33 + (5/2*a^6 - 7*a^5 - 59/2*a^4 + 79*a^3 + 109/2*a^2 - 104*a - 64)*q^34 + (-9/4*a^6 + 6*a^5 + 113/4*a^4 - 69*a^3 - 273/4*a^2 + 101*a + 80)*q^35 + (a^2 - 3)*q^36 + (5/2*a^6 - 11/2*a^5 - 67/2*a^4 + 127/2*a^3 + 195/2*a^2 - 195/2*a - 107)*q^37 + O(q^38)
*]> ;  // time = 125.1 seconds




J[455] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 455, 455, 455, 455, 455, 455, 91, 91, 91, 91, 65, 65, 65, 35, 35 ], new_dimensions := [ 1, 1, 4, 4, 6, 7, 1, 1, 2, 3, 1, 2, 2, 1, 2 ], dimensions := [ 1, 1, 4, 4, 6, 7, 2, 2, 4, 6, 2, 4, 4, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 67, 1, 25, 1, 1, 1, 1, 1, 1, 0, 1, 1, 9, 1, 1, 1, 1, 1, 23, 1, 67, 1, 1, 1, 1, 0, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 79, 1, 3, 1, 1, 19, 1, 3, 1, 1, 9, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 0, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 79, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 1, 67, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 23, 1, 1, 1, 1, 7, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 19, 1, 3, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 67, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 1, 0, -1, -1, 0, -1, -2, -4, 0, -2, 0, 2 ],
[ -1, 0, 1, -1, 0, 1, -6, 0, -4, -2, -4, -10 ],
[ -1, 0, -4, -4, 2, 4, 0, 18, -12, -2, 18, 4 ],
[ 3, 4, 4, -4, -2, -4, 16, 2, 0, -2, -2, 0 ],
[ 3, 0, 6, 6, -2, 6, 8, 6, 4, -14, -6, 20 ],
[ 0, 0, -7, 7, 6, -7, -2, 6, 4, 16, -6, -6 ]
], hecke_fields := [
x - 1,
x - 1,
x^4 + x^3 - 5*x^2 - 3*x + 1,
x^4 - 3*x^3 - x^2 + 5*x + 1,
x^6 - 3*x^5 - 6*x^4 + 20*x^3 + 6*x^2 - 31*x + 9,
x^7 - 15*x^5 + 2*x^4 + 66*x^3 - 17*x^2 - 72*x + 19
], atkin_lehners := [
[ 1, 1, 1 ],
[ -1, 1, -1 ],
[ 1, 1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ],
[ 1, -1, 1 ]
], component_group_orders := [
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 67, 25, 1 ],
[ 9, 23, 67 ],
[ 27, 1, 1 ],
[ 79, 3, 19 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 9, 1, 1 ],
[ 27, 1, 1 ],
[ 1, 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 3, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 0, 1, 9, 3, 3 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1, 1/9, 1 ], eigenvalues := [*
[ 1, 0, -1, -1, 0, -1, -2, -4, 0, -2, 0, 2 ],
[ -1, 0, 1, -1, 0, 1, -6, 0, -4, -2, -4, -10 ],
[
a,
a^3 + a^2 - 4*a - 2,
-1,
-1,
2*a^3 + 2*a^2 - 10*a - 4,
1,
a^3 - a^2 - 6*a + 3,
-a^3 - a^2 + 6*a + 7,
2*a^3 - 10*a - 2,
-a^3 - a^2 + 6*a + 2,
a^3 + a^2 - 6*a + 2,
a^3 + a^2 - 8*a - 2
],
[
a,
-a^3 + 3*a^2 - 2,
1,
-1,
-2*a^3 + 2*a^2 + 6*a,
-1,
-a^3 + a^2 + 2*a + 5,
a^3 + a^2 - 6*a - 3,
2*a^3 - 8*a^2 + 2*a + 10,
-a^3 + 3*a^2 - 2*a - 2,
3*a^3 - 5*a^2 - 6*a + 2,
5*a^3 - 11*a^2 - 8*a + 10
],
[
a,
-a^3 + a^2 + 4*a - 2,
1,
1,
-a^5 + 2*a^4 + 6*a^3 - 10*a^2 - 8*a + 9,
1,
a^5 - a^4 - 6*a^3 + 2*a^2 + 7*a + 3,
a^4 - 2*a^3 - 4*a^2 + 5*a + 2,
-a^5 + 2*a^4 + 6*a^3 - 8*a^2 - 8*a + 3,
-a^5 + 11*a^3 - 3*a^2 - 26*a + 9,
-2*a^4 + 3*a^3 + 9*a^2 - 8*a - 4,
a^5 - 2*a^4 - 7*a^3 + 11*a^2 + 10*a - 7
],
[
a,
-1/14*a^6 - 5/14*a^5 + 9/7*a^4 + 23/7*a^3 - 44/7*a^2 - 73/14*a + 71/14,
-1,
1,
3/14*a^6 + 1/14*a^5 - 13/7*a^4 - 6/7*a^3 + 13/7*a^2 + 51/14*a + 53/14,
-1,
1/7*a^6 - 2/7*a^5 - 11/7*a^4 + 10/7*a^3 + 32/7*a^2 + 24/7*a - 36/7,
5/14*a^6 - 3/14*a^5 - 24/7*a^4 + 18/7*a^3 + 45/7*a^2 - 97/14*a + 9/14,
-3/14*a^6 - 1/14*a^5 + 13/7*a^4 + 6/7*a^3 - 27/7*a^2 - 51/14*a + 87/14,
1/7*a^6 - 2/7*a^5 - 18/7*a^4 + 17/7*a^3 + 81/7*a^2 - 25/7*a - 36/7,
5/14*a^6 - 3/14*a^5 - 31/7*a^4 + 11/7*a^3 + 94/7*a^2 - 27/14*a - 75/14,
-1/7*a^6 + 2/7*a^5 + 4/7*a^4 - 17/7*a^3 + 31/7*a^2 + 25/7*a - 62/7
]
*], q_expansions := [*
q + q^2 - q^4 - q^5 - q^7 - 3*q^8 - 3*q^9 - q^10 - q^13 - q^14 - q^16 - 2*q^17 - 3*q^18 - 4*q^19 + q^20 + q^25 - q^26 + q^28 - 2*q^29 + 5*q^32 - 2*q^34 + q^35 + 3*q^36 + 2*q^37 + O(q^38),
q - q^2 - q^4 + q^5 - q^7 + 3*q^8 - 3*q^9 - q^10 + q^13 + q^14 - q^16 - 6*q^17 + 3*q^18 - q^20 - 4*q^23 + q^25 - q^26 + q^28 - 2*q^29 - 4*q^31 - 5*q^32 + 6*q^34 - q^35 + 3*q^36 - 10*q^37 + O(q^38),
q + a*q^2 + (a^3 + a^2 - 4*a - 2)*q^3 + (a^2 - 2)*q^4 - q^5 + (a^2 + a - 1)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-a^3 - a^2 + 6*a + 4)*q^9 - a*q^10 + (2*a^3 + 2*a^2 - 10*a - 4)*q^11 + (-a^3 - a^2 + 7*a + 4)*q^12 + q^13 - a*q^14 + (-a^3 - a^2 + 4*a + 2)*q^15 + (-a^3 - a^2 + 3*a + 3)*q^16 + (a^3 - a^2 - 6*a + 3)*q^17 + (a^2 + a + 1)*q^18 + (-a^3 - a^2 + 6*a + 7)*q^19 + (-a^2 + 2)*q^20 + (-a^3 - a^2 + 4*a + 2)*q^21 + (2*a - 2)*q^22 + (2*a^3 - 10*a - 2)*q^23 + (-a + 3)*q^24 + q^25 + a*q^26 + (2*a^2 - 7)*q^27 + (-a^2 + 2)*q^28 + (-a^3 - a^2 + 6*a + 2)*q^29 + (-a^2 - a + 1)*q^30 + (a^3 + a^2 - 6*a + 2)*q^31 + (-2*a^3 - 2*a^2 + 8*a + 1)*q^32 + (-2*a^3 - 4*a^2 + 10*a + 16)*q^33 + (-2*a^3 - a^2 + 6*a - 1)*q^34 + q^35 + (3*a^3 + 3*a^2 - 11*a - 8)*q^36 + (a^3 + a^2 - 8*a - 2)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 3*a^2 - 2)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^2 + 3*a + 1)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-a^3 + 3*a^2 - 2*a)*q^9 + a*q^10 + (-2*a^3 + 2*a^2 + 6*a)*q^11 + (a^3 - 3*a^2 + a + 4)*q^12 - q^13 - a*q^14 + (-a^3 + 3*a^2 - 2)*q^15 + (3*a^3 - 5*a^2 - 5*a + 3)*q^16 + (-a^3 + a^2 + 2*a + 5)*q^17 + (-3*a^2 + 5*a + 1)*q^18 + (a^3 + a^2 - 6*a - 3)*q^19 + (a^2 - 2)*q^20 + (a^3 - 3*a^2 + 2)*q^21 + (-4*a^3 + 4*a^2 + 10*a + 2)*q^22 + (2*a^3 - 8*a^2 + 2*a + 10)*q^23 + (4*a^2 - 7*a - 3)*q^24 + q^25 - a*q^26 + (2*a^2 - 8*a + 3)*q^27 + (-a^2 + 2)*q^28 + (-a^3 + 3*a^2 - 2*a - 2)*q^29 + (-a^2 + 3*a + 1)*q^30 + (3*a^3 - 5*a^2 - 6*a + 2)*q^31 + (2*a^3 - 2*a^2 - 4*a - 3)*q^32 + (-2*a^3 + 10*a + 4)*q^33 + (-2*a^3 + a^2 + 10*a + 1)*q^34 - q^35 + (-a^3 - a^2 + 5*a)*q^36 + (5*a^3 - 11*a^2 - 8*a + 10)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + a^2 + 4*a - 2)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^4 + a^3 + 4*a^2 - 2*a)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (a^5 - a^4 - 8*a^3 + 6*a^2 + 15*a - 8)*q^9 + a*q^10 + (-a^5 + 2*a^4 + 6*a^3 - 10*a^2 - 8*a + 9)*q^11 + (-a^5 + a^4 + 6*a^3 - 4*a^2 - 8*a + 4)*q^12 + q^13 + a*q^14 + (-a^3 + a^2 + 4*a - 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^5 - a^4 - 6*a^3 + 2*a^2 + 7*a + 3)*q^17 + (2*a^5 - 2*a^4 - 14*a^3 + 9*a^2 + 23*a - 9)*q^18 + (a^4 - 2*a^3 - 4*a^2 + 5*a + 2)*q^19 + (a^2 - 2)*q^20 + (-a^3 + a^2 + 4*a - 2)*q^21 + (-a^5 + 10*a^3 - 2*a^2 - 22*a + 9)*q^22 + (-a^5 + 2*a^4 + 6*a^3 - 8*a^2 - 8*a + 3)*q^23 + (-2*a^5 + 2*a^4 + 14*a^3 - 10*a^2 - 23*a + 9)*q^24 + q^25 + a*q^26 + (-a^4 + a^3 + 3*a^2 - 3*a + 4)*q^27 + (a^2 - 2)*q^28 + (-a^5 + 11*a^3 - 3*a^2 - 26*a + 9)*q^29 + (-a^4 + a^3 + 4*a^2 - 2*a)*q^30 + (-2*a^4 + 3*a^3 + 9*a^2 - 8*a - 4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2*a^3 - 10*a)*q^33 + (2*a^5 - 18*a^3 + a^2 + 34*a - 9)*q^34 + q^35 + (2*a^5 - 15*a^3 - a^2 + 23*a - 2)*q^36 + (a^5 - 2*a^4 - 7*a^3 + 11*a^2 + 10*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-1/14*a^6 - 5/14*a^5 + 9/7*a^4 + 23/7*a^3 - 44/7*a^2 - 73/14*a + 71/14)*q^3 + (a^2 - 2)*q^4 - q^5 + (-5/14*a^6 + 3/14*a^5 + 24/7*a^4 - 11/7*a^3 - 45/7*a^2 - 1/14*a + 19/14)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (-1/7*a^6 + 2/7*a^5 + 11/7*a^4 - 24/7*a^3 - 32/7*a^2 + 60/7*a + 43/7)*q^9 - a*q^10 + (3/14*a^6 + 1/14*a^5 - 13/7*a^4 - 6/7*a^3 + 13/7*a^2 + 51/14*a + 53/14)*q^11 + (5/14*a^6 - 17/14*a^5 - 24/7*a^4 + 74/7*a^3 + 45/7*a^2 - 195/14*a - 47/14)*q^12 - q^13 + a*q^14 + (1/14*a^6 + 5/14*a^5 - 9/7*a^4 - 23/7*a^3 + 44/7*a^2 + 73/14*a - 71/14)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/7*a^6 - 2/7*a^5 - 11/7*a^4 + 10/7*a^3 + 32/7*a^2 + 24/7*a - 36/7)*q^17 + (2/7*a^6 - 4/7*a^5 - 22/7*a^4 + 34/7*a^3 + 43/7*a^2 - 29/7*a + 19/7)*q^18 + (5/14*a^6 - 3/14*a^5 - 24/7*a^4 + 18/7*a^3 + 45/7*a^2 - 97/14*a + 9/14)*q^19 + (-a^2 + 2)*q^20 + (-1/14*a^6 - 5/14*a^5 + 9/7*a^4 + 23/7*a^3 - 44/7*a^2 - 73/14*a + 71/14)*q^21 + (1/14*a^6 + 19/14*a^5 - 9/7*a^4 - 86/7*a^3 + 51/7*a^2 + 269/14*a - 57/14)*q^22 + (-3/14*a^6 - 1/14*a^5 + 13/7*a^4 + 6/7*a^3 - 27/7*a^2 - 51/14*a + 87/14)*q^23 + (-1/2*a^6 + 3/2*a^5 + 3*a^4 - 14*a^3 + 5*a^2 + 45/2*a - 19/2)*q^24 + q^25 - a*q^26 + (-1/7*a^6 - 5/7*a^5 + 25/7*a^4 + 53/7*a^3 - 151/7*a^2 - 108/7*a + 155/7)*q^27 + (a^2 - 2)*q^28 + (1/7*a^6 - 2/7*a^5 - 18/7*a^4 + 17/7*a^3 + 81/7*a^2 - 25/7*a - 36/7)*q^29 + (5/14*a^6 - 3/14*a^5 - 24/7*a^4 + 11/7*a^3 + 45/7*a^2 + 1/14*a - 19/14)*q^30 + (5/14*a^6 - 3/14*a^5 - 31/7*a^4 + 11/7*a^3 + 94/7*a^2 - 27/14*a - 75/14)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-5/7*a^6 + 3/7*a^5 + 62/7*a^4 - 22/7*a^3 - 202/7*a^2 - 15/7*a + 131/7)*q^33 + (-2/7*a^6 + 4/7*a^5 + 8/7*a^4 - 34/7*a^3 + 41/7*a^2 + 36/7*a - 19/7)*q^34 - q^35 + (-2/7*a^6 + 4/7*a^5 + 8/7*a^4 - 41/7*a^3 + 69/7*a^2 + 43/7*a - 124/7)*q^36 + (-1/7*a^6 + 2/7*a^5 + 4/7*a^4 - 17/7*a^3 + 31/7*a^2 + 25/7*a - 62/7)*q^37 + O(q^38)
*]> ;  // time = 158.11 seconds




J[457] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 457, 457, 457 ], new_dimensions := [ 2, 15, 20 ], dimensions := [ 2, 15, 20 ], intersection_graph := [ 0, 31, 1, 31, 0, 1, 1, 1, 0 ], ap_traces := [
[ 1, 1, -4, -1, -10, 9, 0, -10, -5, -2, 2, 11 ],
[ -10, -12, -9, -15, 3, -22, -18, 0, -36, -6, -18, -15 ],
[ 6, 9, 11, 8, 9, 3, 12, 2, 41, 2, 22, -8 ]
], hecke_fields := [
x^2 - x - 1,
x^15 + 10*x^14 + 27*x^13 - 43*x^12 - 324*x^11 - 310*x^10 + 917*x^9 + 1910*x^8 - 330*x^7 - 3170*x^6 - 1281*x^5 + 1917*x^4 + 1110*x^3 - 506*x^2 - 232*x + 79,
x^20 - 6*x^19 - 12*x^18 + 130*x^17 - 25*x^16 - 1135*x^15 + 1068*x^14 + 5145*x^13 - 6910*x^12 - 12965*x^11 + 21043*x^10 + 17930*x^9 - 33307*x^8 - 12486*x^7 + 25549*x^6 + 3888*x^5 - 7077*x^4 - 927*x^3 + 255*x^2 + 6*x - 1
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 19 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 19 ]
], torsion_upper_bounds := [ 1, 1, 19 ], torsion_lower_bounds := [ 1, 1, 19 ], l_ratios := [ 0, 0, 1/19 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[
a,
-a + 1,
-2,
-a,
-5,
a + 4,
6*a - 3,
-2*a - 4,
-a - 2,
2*a - 2,
6*a - 2,
a + 5
],
[
a,
-22/3*a^14 - 176/3*a^13 - 248/3*a^12 + 1409/3*a^11 + 4334/3*a^10 - 488*a^9 - 17000/3*a^8 - 9601/3*a^7 + 24824/3*a^6 + 23065/3*a^5 - 14540/3*a^4 - 15932/3*a^3 + 4537/3*a^2 + 1170*a - 1043/3,
-8/3*a^14 - 79/3*a^13 - 184/3*a^12 + 502/3*a^11 + 2524/3*a^10 + 255*a^9 - 9145/3*a^8 - 9500/3*a^7 + 12118/3*a^6 + 18116/3*a^5 - 5953/3*a^4 - 11923/3*a^3 + 1877/3*a^2 + 878*a - 661/3,
5*a^14 + 51*a^13 + 123*a^12 - 326*a^11 - 1682*a^10 - 488*a^9 + 6221*a^8 + 6214*a^7 - 8724*a^6 - 12108*a^5 + 5002*a^4 + 8277*a^3 - 1832*a^2 - 1925*a + 546,
-7/3*a^14 - 77/3*a^13 - 206/3*a^12 + 455/3*a^11 + 2684/3*a^10 + 373*a^9 - 9638/3*a^8 - 10615/3*a^7 + 12791/3*a^6 + 19645/3*a^5 - 6359/3*a^4 - 12755/3*a^3 + 1999/3*a^2 + 921*a - 680/3,
11*a^14 + 85*a^13 + 105*a^12 - 706*a^11 - 1967*a^10 + 997*a^9 + 7813*a^8 + 3498*a^7 - 11471*a^6 - 9202*a^5 + 6665*a^4 + 6226*a^3 - 1917*a^2 - 1275*a + 375,
53/3*a^14 + 445/3*a^13 + 736/3*a^12 - 3337/3*a^11 - 11770/3*a^10 + 428*a^9 + 44569/3*a^8 + 32813/3*a^7 - 61669/3*a^6 - 70244/3*a^5 + 32200/3*a^4 + 46633/3*a^3 - 9203/3*a^2 - 3330*a + 2569/3,
50/3*a^14 + 421/3*a^13 + 706/3*a^12 - 3130/3*a^11 - 11221/3*a^10 + 298*a^9 + 42418/3*a^8 + 32393/3*a^7 - 58642/3*a^6 - 68993/3*a^5 + 30763/3*a^4 + 46282/3*a^3 - 9107/3*a^2 - 3370*a + 2623/3,
-32/3*a^14 - 280/3*a^13 - 511/3*a^12 + 2038/3*a^11 + 7852/3*a^10 - 24*a^9 - 29791/3*a^8 - 23765/3*a^7 + 42187/3*a^6 + 50105/3*a^5 - 23827/3*a^4 - 34381/3*a^3 + 7916/3*a^2 + 2608*a - 2209/3,
-88/3*a^14 - 707/3*a^13 - 1028/3*a^12 + 5546/3*a^11 + 17603/3*a^10 - 1552*a^9 - 68123/3*a^8 - 42907/3*a^7 + 97046/3*a^6 + 98737/3*a^5 - 53987/3*a^4 - 67268/3*a^3 + 16303/3*a^2 + 4894*a - 4091/3,
-34/3*a^14 - 296/3*a^13 - 533/3*a^12 + 2159/3*a^11 + 8192/3*a^10 - 64*a^9 - 30791/3*a^8 - 24244/3*a^7 + 42497/3*a^6 + 50329/3*a^5 - 22238/3*a^4 - 33188/3*a^3 + 6460/3*a^2 + 2364*a - 1826/3,
-4*a^14 - 25*a^13 - 3*a^12 + 251*a^11 + 346*a^10 - 773*a^9 - 1584*a^8 + 771*a^7 + 2506*a^6 - 127*a^5 - 1484*a^4 + 76*a^3 + 256*a^2 - 104*a + 28
],
[
a,
22455115672/70667500537*a^19 - 131066476891/70667500537*a^18 - 281638710286/70667500537*a^17 + 2827050388809/70667500537*a^16 - 236800773935/70667500537*a^15 - 24572680812432/70667500537*a^14 + 20468336976792/70667500537*a^13 + 111038976832369/70667500537*a^12 - 135310187190199/70667500537*a^11 - 280109875894214/70667500537*a^10 + 409957891106774/70667500537*a^9 + 392088569536235/70667500537*a^8 - 639579819395338/70667500537*a^7 - 284213051432448/70667500537*a^6 + 480311978754747/70667500537*a^5 + 97573129724064/70667500537*a^4 - 128240080396085/70667500537*a^3 - 22109590817361/70667500537*a^2 + 3261271772144/70667500537*a + 135908631555/70667500537,
14134866136/70667500537*a^19 - 90858404524/70667500537*a^18 - 150416122682/70667500537*a^17 + 1981953508303/70667500537*a^16 - 822666722358/70667500537*a^15 - 17445377937615/70667500537*a^14 + 19775891456742/70667500537*a^13 + 79838713829810/70667500537*a^12 - 122124432439636/70667500537*a^11 - 203410432641693/70667500537*a^10 + 368705087906845/70667500537*a^9 + 285096046890831/70667500537*a^8 - 583842989983930/70667500537*a^7 - 203149242580921/70667500537*a^6 + 447016306006133/70667500537*a^5 + 68504344846741/70667500537*a^4 - 120316903629571/70667500537*a^3 - 19243852222869/70667500537*a^2 + 2809965795401/70667500537*a + 195036968443/70667500537,
14206104584/70667500537*a^19 - 73929917660/70667500537*a^18 - 217625963104/70667500537*a^17 + 1623811314781/70667500537*a^16 + 718324474035/70667500537*a^15 - 14463092476282/70667500537*a^14 + 5200344860599/70667500537*a^13 + 67549212478312/70667500537*a^12 - 49344882750744/70667500537*a^11 - 178206976331195/70667500537*a^10 + 163692302662231/70667500537*a^9 + 265143660512813/70667500537*a^8 - 263282060201810/70667500537*a^7 - 208409915897199/70667500537*a^6 + 196702343066120/70667500537*a^5 + 76518886551657/70667500537*a^4 - 48490939532631/70667500537*a^3 - 14104399906234/70667500537*a^2 + 22202981870/70667500537*a + 63340582601/70667500537,
-24595468169/141335001074*a^19 + 113970680785/141335001074*a^18 + 445417497035/141335001074*a^17 - 2581228633099/141335001074*a^16 - 1366732334800/70667500537*a^15 + 23910472380145/141335001074*a^14 + 4112562606153/141335001074*a^13 - 58707296882270/70667500537*a^12 + 12376364403450/70667500537*a^11 + 330424742426235/141335001074*a^10 - 62086969654957/70667500537*a^9 - 267720899783620/70667500537*a^8 + 219725078787495/141335001074*a^7 + 473758827059255/141335001074*a^6 - 79935299288631/70667500537*a^5 - 102024360168682/70667500537*a^4 + 29709262547955/141335001074*a^3 + 19285855584398/70667500537*a^2 + 3216976978289/141335001074*a - 459481756199/141335001074,
-24627075324/70667500537*a^19 + 145423334846/70667500537*a^18 + 311309962668/70667500537*a^17 - 3174880687623/70667500537*a^16 + 257358757544/70667500537*a^15 + 28063877220520/70667500537*a^14 - 22994538360358/70667500537*a^13 - 129904014264785/70667500537*a^12 + 154174844812776/70667500537*a^11 + 339781738781552/70667500537*a^10 - 474770906826917/70667500537*a^9 - 504641225072251/70667500537*a^8 + 754617046141408/70667500537*a^7 + 408012228770064/70667500537*a^6 - 578079191407251/70667500537*a^5 - 172143607935413/70667500537*a^4 + 155940302389678/70667500537*a^3 + 42942236272783/70667500537*a^2 - 2174847959294/70667500537*a - 428737397425/70667500537,
-18501434527/70667500537*a^19 + 95576405501/70667500537*a^18 + 295003180320/70667500537*a^17 - 2155703961778/70667500537*a^16 - 1073727195632/70667500537*a^15 + 19780174831914/70667500537*a^14 - 6791485710640/70667500537*a^13 - 95282619280825/70667500537*a^12 + 71146184410520/70667500537*a^11 + 258443960121658/70667500537*a^10 - 250995674458021/70667500537*a^9 - 390668076051017/70667500537*a^8 + 428097942642417/70667500537*a^7 + 302368012827322/70667500537*a^6 - 340574823126910/70667500537*a^5 - 101449500549011/70667500537*a^4 + 93448978979824/70667500537*a^3 + 18443138250368/70667500537*a^2 - 3636265418188/70667500537*a - 232750663225/70667500537,
-25308571840/70667500537*a^19 + 137104352342/70667500537*a^18 + 359076772360/70667500537*a^17 - 2970171000597/70667500537*a^16 - 681563149974/70667500537*a^15 + 25991132302721/70667500537*a^14 - 14264171293602/70667500537*a^13 - 118704076796598/70667500537*a^12 + 109504428361468/70667500537*a^11 + 304584118011086/70667500537*a^10 - 343705974587218/70667500537*a^9 - 438097834562962/70667500537*a^8 + 540060371699547/70667500537*a^7 + 330663092817881/70667500537*a^6 - 403729196982328/70667500537*a^5 - 116400871163143/70667500537*a^4 + 106843386003666/70667500537*a^3 + 22057705374183/70667500537*a^2 - 2754458102371/70667500537*a - 85657254177/70667500537,
-66828478401/141335001074*a^19 + 431650691989/141335001074*a^18 + 674036720809/141335001074*a^17 - 9271663110759/141335001074*a^16 + 2245638125181/70667500537*a^15 + 80025136118317/141335001074*a^14 - 96618677324729/141335001074*a^13 - 178654473281685/70667500537*a^12 + 290162916842752/70667500537*a^11 + 882838098739135/141335001074*a^10 - 860052446392464/70667500537*a^9 - 595854208314799/70667500537*a^8 + 2689465340206701/141335001074*a^7 + 812906289819105/141335001074*a^6 - 1026111139673325/70667500537*a^5 - 133379375935520/70667500537*a^4 + 565206995085095/141335001074*a^3 + 38745066423842/70667500537*a^2 - 16406410349233/141335001074*a - 75215182709/141335001074,
17185596765/70667500537*a^19 - 84737526490/70667500537*a^18 - 284469323935/70667500537*a^17 + 1870506002513/70667500537*a^16 + 1388658751551/70667500537*a^15 - 16864095464638/70667500537*a^14 + 1102022517579/70667500537*a^13 + 80840868923215/70667500537*a^12 - 32615031055846/70667500537*a^11 - 224729852456439/70667500537*a^10 + 119480365786980/70667500537*a^9 + 370006259505670/70667500537*a^8 - 195046571902051/70667500537*a^7 - 351700140330880/70667500537*a^6 + 145124808874606/70667500537*a^5 + 177581051237823/70667500537*a^4 - 34805198253442/70667500537*a^3 - 38441592600047/70667500537*a^2 - 2929337065022/70667500537*a + 540267735402/70667500537,
-33089831567/141335001074*a^19 + 201093196679/141335001074*a^18 + 391673655943/141335001074*a^17 - 4365863118659/141335001074*a^16 + 471683110807/70667500537*a^15 + 38259972649885/141335001074*a^14 - 36373235992973/141335001074*a^13 - 87307009832151/70667500537*a^12 + 116846574034607/70667500537*a^11 + 445465108555543/141335001074*a^10 - 355625654228334/70667500537*a^9 - 315173342607157/70667500537*a^8 + 1129305589176249/141335001074*a^7 + 459383570675341/141335001074*a^6 - 436555768199840/70667500537*a^5 - 78024726348075/70667500537*a^4 + 246768118561351/141335001074*a^3 + 18047985018684/70667500537*a^2 - 10452096957281/141335001074*a - 1569322349/141335001074,
29279187028/70667500537*a^19 - 179663634232/70667500537*a^18 - 334276101795/70667500537*a^17 + 3891077285839/70667500537*a^16 - 1165199718243/70667500537*a^15 - 33866323647966/70667500537*a^14 + 35751842790564/70667500537*a^13 + 152104644055235/70667500537*a^12 - 226575846001678/70667500537*a^11 - 374433757055723/70667500537*a^10 + 689192463895933/70667500537*a^9 + 488054819611240/70667500537*a^8 - 1094591681507048/70667500537*a^7 - 286295945965726/70667500537*a^6 + 840844539413438/70667500537*a^5 + 45979544663994/70667500537*a^4 - 229930635056428/70667500537*a^3 - 11792551088345/70667500537*a^2 + 8321026131183/70667500537*a - 77043795460/70667500537
]
*], q_expansions := [*
q + a*q^2 + (-a + 1)*q^3 + (a - 1)*q^4 - 2*q^5 - q^6 - a*q^7 + (-2*a + 1)*q^8 + (-a - 1)*q^9 - 2*a*q^10 - 5*q^11 + (a - 2)*q^12 + (a + 4)*q^13 + (-a - 1)*q^14 + (2*a - 2)*q^15 - 3*a*q^16 + (6*a - 3)*q^17 + (-2*a - 1)*q^18 + (-2*a - 4)*q^19 + (-2*a + 2)*q^20 + q^21 - 5*a*q^22 + (-a - 2)*q^23 + (-a + 3)*q^24 - q^25 + (5*a + 1)*q^26 + (4*a - 3)*q^27 - q^28 + (2*a - 2)*q^29 + 2*q^30 + (6*a - 2)*q^31 + (a - 5)*q^32 + (5*a - 5)*q^33 + (3*a + 6)*q^34 + 2*a*q^35 - a*q^36 + (a + 5)*q^37 + O(q^38),
q + a*q^2 + (-22/3*a^14 - 176/3*a^13 - 248/3*a^12 + 1409/3*a^11 + 4334/3*a^10 - 488*a^9 - 17000/3*a^8 - 9601/3*a^7 + 24824/3*a^6 + 23065/3*a^5 - 14540/3*a^4 - 15932/3*a^3 + 4537/3*a^2 + 1170*a - 1043/3)*q^3 + (a^2 - 2)*q^4 + (-8/3*a^14 - 79/3*a^13 - 184/3*a^12 + 502/3*a^11 + 2524/3*a^10 + 255*a^9 - 9145/3*a^8 - 9500/3*a^7 + 12118/3*a^6 + 18116/3*a^5 - 5953/3*a^4 - 11923/3*a^3 + 1877/3*a^2 + 878*a - 661/3)*q^5 + (44/3*a^14 + 346/3*a^13 + 463/3*a^12 - 2794/3*a^11 - 8284/3*a^10 + 1058*a^9 + 32419/3*a^8 + 17564/3*a^7 - 46675/3*a^6 - 42722/3*a^5 + 26242/3*a^4 + 28957/3*a^3 - 7622/3*a^2 - 2049*a + 1738/3)*q^6 + (5*a^14 + 51*a^13 + 123*a^12 - 326*a^11 - 1682*a^10 - 488*a^9 + 6221*a^8 + 6214*a^7 - 8724*a^6 - 12108*a^5 + 5002*a^4 + 8277*a^3 - 1832*a^2 - 1925*a + 546)*q^7 + (a^3 - 4*a)*q^8 + (31/3*a^14 + 245/3*a^13 + 335/3*a^12 - 1961/3*a^11 - 5915/3*a^10 + 687*a^9 + 23006/3*a^8 + 13096/3*a^7 - 32771/3*a^6 - 31183/3*a^5 + 17993/3*a^4 + 21041/3*a^3 - 5134/3*a^2 - 1495*a + 1235/3)*q^9 + (1/3*a^14 + 32/3*a^13 + 158/3*a^12 - 68/3*a^11 - 1715/3*a^10 - 603*a^9 + 5780/3*a^8 + 9478/3*a^7 - 7244/3*a^6 - 16201/3*a^5 + 3413/3*a^4 + 10757/3*a^3 - 1414/3*a^2 - 839*a + 632/3)*q^10 + (-7/3*a^14 - 77/3*a^13 - 206/3*a^12 + 455/3*a^11 + 2684/3*a^10 + 373*a^9 - 9638/3*a^8 - 10615/3*a^7 + 12791/3*a^6 + 19645/3*a^5 - 6359/3*a^4 - 12755/3*a^3 + 1999/3*a^2 + 921*a - 680/3)*q^11 + (-50/3*a^14 - 373/3*a^13 - 406/3*a^12 + 3154/3*a^11 + 8146/3*a^10 - 1667*a^9 - 32476/3*a^8 - 12953/3*a^7 + 47110/3*a^6 + 36476/3*a^5 - 26311/3*a^4 - 24598/3*a^3 + 7043/3*a^2 + 1642*a - 1390/3)*q^12 + (11*a^14 + 85*a^13 + 105*a^12 - 706*a^11 - 1967*a^10 + 997*a^9 + 7813*a^8 + 3498*a^7 - 11471*a^6 - 9202*a^5 + 6665*a^4 + 6226*a^3 - 1917*a^2 - 1275*a + 375)*q^13 + (a^14 - 12*a^13 - 111*a^12 - 62*a^11 + 1062*a^10 + 1636*a^9 - 3336*a^8 - 7074*a^7 + 3742*a^6 + 11407*a^5 - 1308*a^4 - 7382*a^3 + 605*a^2 + 1706*a - 395)*q^14 + (-7/3*a^14 - 38/3*a^13 + 25/3*a^12 + 413/3*a^11 + 263/3*a^10 - 510*a^9 - 1427/3*a^8 + 2549/3*a^7 + 2051/3*a^6 - 2480/3*a^5 - 635/3*a^4 + 1741/3*a^3 - 374/3*a^2 - 183*a + 181/3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (53/3*a^14 + 445/3*a^13 + 736/3*a^12 - 3337/3*a^11 - 11770/3*a^10 + 428*a^9 + 44569/3*a^8 + 32813/3*a^7 - 61669/3*a^6 - 70244/3*a^5 + 32200/3*a^4 + 46633/3*a^3 - 9203/3*a^2 - 3330*a + 2569/3)*q^17 + (-65/3*a^14 - 502/3*a^13 - 628/3*a^12 + 4129/3*a^11 + 11671/3*a^10 - 1807*a^9 - 46114/3*a^8 - 22541/3*a^7 + 67087/3*a^6 + 57704/3*a^5 - 38386/3*a^4 - 39544/3*a^3 + 11201/3*a^2 + 2809*a - 2449/3)*q^18 + (50/3*a^14 + 421/3*a^13 + 706/3*a^12 - 3130/3*a^11 - 11221/3*a^10 + 298*a^9 + 42418/3*a^8 + 32393/3*a^7 - 58642/3*a^6 - 68993/3*a^5 + 30763/3*a^4 + 46282/3*a^3 - 9107/3*a^2 - 3370*a + 2623/3)*q^19 + (38/3*a^14 + 289/3*a^13 + 343/3*a^12 - 2395/3*a^11 - 6547/3*a^10 + 1111*a^9 + 25858/3*a^8 + 12086/3*a^7 - 37267/3*a^6 - 31538/3*a^5 + 20746/3*a^4 + 21322/3*a^3 - 5765/3*a^2 - 1468*a + 1243/3)*q^20 + (22/3*a^14 + 149/3*a^13 + 83/3*a^12 - 1406/3*a^11 - 2636/3*a^10 + 1192*a^9 + 11462/3*a^8 - 485/3*a^7 - 18251/3*a^6 - 6412/3*a^5 + 11822/3*a^4 + 5189/3*a^3 - 3358/3*a^2 - 357*a + 428/3)*q^21 + (-7/3*a^14 - 17/3*a^13 + 154/3*a^12 + 416/3*a^11 - 1051/3*a^10 - 1073*a^9 + 2755/3*a^8 + 10481/3*a^7 - 2545/3*a^6 - 15326/3*a^5 + 664/3*a^4 + 9769/3*a^3 - 779/3*a^2 - 768*a + 553/3)*q^22 + (-32/3*a^14 - 280/3*a^13 - 511/3*a^12 + 2038/3*a^11 + 7852/3*a^10 - 24*a^9 - 29791/3*a^8 - 23765/3*a^7 + 42187/3*a^6 + 50105/3*a^5 - 23827/3*a^4 - 34381/3*a^3 + 7916/3*a^2 + 2608*a - 2209/3)*q^23 + (13*a^14 + 84*a^13 + 26*a^12 - 822*a^11 - 1311*a^10 + 2342*a^9 + 5903*a^8 - 1506*a^7 - 9558*a^6 - 1639*a^5 + 6256*a^4 + 1543*a^3 - 1710*a^2 - 232*a + 158)*q^24 + (10/3*a^14 + 59/3*a^13 - 16/3*a^12 - 635/3*a^11 - 620/3*a^10 + 770*a^9 + 3134/3*a^8 - 3731/3*a^7 - 5177/3*a^6 + 3539/3*a^5 + 3059/3*a^4 - 2575/3*a^3 - 259/3*a^2 + 295*a - 235/3)*q^25 + (-25*a^14 - 192*a^13 - 233*a^12 + 1597*a^11 + 4407*a^10 - 2274*a^9 - 17512*a^8 - 7841*a^7 + 25668*a^6 + 20756*a^5 - 14861*a^4 - 14127*a^3 + 4291*a^2 + 2927*a - 869)*q^26 + (37/3*a^14 + 305/3*a^13 + 473/3*a^12 - 2369/3*a^11 - 7871/3*a^10 + 578*a^9 + 30545/3*a^8 + 19630/3*a^7 - 44282/3*a^6 - 44581/3*a^5 + 25847/3*a^4 + 30515/3*a^3 - 8281/3*a^2 - 2228*a + 1967/3)*q^27 + (-32*a^14 - 240*a^13 - 265*a^12 + 2038*a^11 + 5310*a^10 - 3277*a^9 - 21426*a^8 - 8356*a^7 + 32025*a^6 + 24189*a^5 - 19303*a^4 - 17059*a^3 + 5876*a^2 + 3687*a - 1171)*q^28 + (-88/3*a^14 - 707/3*a^13 - 1028/3*a^12 + 5546/3*a^11 + 17603/3*a^10 - 1552*a^9 - 68123/3*a^8 - 42907/3*a^7 + 97046/3*a^6 + 98737/3*a^5 - 53987/3*a^4 - 67268/3*a^3 + 16303/3*a^2 + 4894*a - 4091/3)*q^29 + (32/3*a^14 + 214/3*a^13 + 112/3*a^12 - 2005/3*a^11 - 3700/3*a^10 + 1664*a^9 + 15919/3*a^8 - 259/3*a^7 - 24670/3*a^6 - 9602/3*a^5 + 15160/3*a^4 + 7396/3*a^3 - 4091/3*a^2 - 481*a + 553/3)*q^30 + (-34/3*a^14 - 296/3*a^13 - 533/3*a^12 + 2159/3*a^11 + 8192/3*a^10 - 64*a^9 - 30791/3*a^8 - 24244/3*a^7 + 42497/3*a^6 + 50329/3*a^5 - 22238/3*a^4 - 33188/3*a^3 + 6460/3*a^2 + 2364*a - 1826/3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (20/3*a^14 + 145/3*a^13 + 139/3*a^12 - 1252/3*a^11 - 3016/3*a^10 + 740*a^9 + 12193/3*a^8 + 4067/3*a^7 - 17902/3*a^6 - 12815/3*a^5 + 10207/3*a^4 + 8773/3*a^3 - 2759/3*a^2 - 573*a + 493/3)*q^33 + (-85/3*a^14 - 695/3*a^13 - 1058/3*a^12 + 5402/3*a^11 + 17714/3*a^10 - 1344*a^9 - 68417/3*a^8 - 44179/3*a^7 + 97766/3*a^6 + 100093/3*a^5 - 54968/3*a^4 - 68033/3*a^3 + 16828/3*a^2 + 4955*a - 4187/3)*q^34 + (-31/3*a^14 - 215/3*a^13 - 143/3*a^12 + 2009/3*a^11 + 4022/3*a^10 - 1643*a^9 - 17450/3*a^8 - 244/3*a^7 + 28253/3*a^6 + 10936/3*a^5 - 19151/3*a^4 - 8783/3*a^3 + 5932/3*a^2 + 625*a - 824/3)*q^35 + (86/3*a^14 + 637/3*a^13 + 664/3*a^12 - 5467/3*a^11 - 13741/3*a^10 + 3123*a^9 + 55597/3*a^8 + 19445/3*a^7 - 82804/3*a^6 - 59285/3*a^5 + 49075/3*a^4 + 41269/3*a^3 - 14195/3*a^2 - 2853*a + 2665/3)*q^36 + (-4*a^14 - 25*a^13 - 3*a^12 + 251*a^11 + 346*a^10 - 773*a^9 - 1584*a^8 + 771*a^7 + 2506*a^6 - 127*a^5 - 1484*a^4 + 76*a^3 + 256*a^2 - 104*a + 28)*q^37 + O(q^38),
q + a*q^2 + (22455115672/70667500537*a^19 - 131066476891/70667500537*a^18 - 281638710286/70667500537*a^17 + 2827050388809/70667500537*a^16 - 236800773935/70667500537*a^15 - 24572680812432/70667500537*a^14 + 20468336976792/70667500537*a^13 + 111038976832369/70667500537*a^12 - 135310187190199/70667500537*a^11 - 280109875894214/70667500537*a^10 + 409957891106774/70667500537*a^9 + 392088569536235/70667500537*a^8 - 639579819395338/70667500537*a^7 - 284213051432448/70667500537*a^6 + 480311978754747/70667500537*a^5 + 97573129724064/70667500537*a^4 - 128240080396085/70667500537*a^3 - 22109590817361/70667500537*a^2 + 3261271772144/70667500537*a + 135908631555/70667500537)*q^3 + (a^2 - 2)*q^4 + (14134866136/70667500537*a^19 - 90858404524/70667500537*a^18 - 150416122682/70667500537*a^17 + 1981953508303/70667500537*a^16 - 822666722358/70667500537*a^15 - 17445377937615/70667500537*a^14 + 19775891456742/70667500537*a^13 + 79838713829810/70667500537*a^12 - 122124432439636/70667500537*a^11 - 203410432641693/70667500537*a^10 + 368705087906845/70667500537*a^9 + 285096046890831/70667500537*a^8 - 583842989983930/70667500537*a^7 - 203149242580921/70667500537*a^6 + 447016306006133/70667500537*a^5 + 68504344846741/70667500537*a^4 - 120316903629571/70667500537*a^3 - 19243852222869/70667500537*a^2 + 2809965795401/70667500537*a + 195036968443/70667500537)*q^5 + (3664217141/70667500537*a^19 - 12177322222/70667500537*a^18 - 92114648551/70667500537*a^17 + 324577117865/70667500537*a^16 + 913875475288/70667500537*a^15 - 3513726560904/70667500537*a^14 - 4492593300071/70667500537*a^13 + 19854662103321/70667500537*a^12 + 11020698793266/70667500537*a^11 - 62565107979122/70667500537*a^10 - 10531654462725/70667500537*a^9 + 108332718291966/70667500537*a^8 - 3838477151856/70667500537*a^7 - 93393771549181/70667500537*a^6 + 10267639991328/70667500537*a^5 + 30674773214659/70667500537*a^4 - 1293698589417/70667500537*a^3 - 2464782724216/70667500537*a^2 + 1177937523/70667500537*a + 22455115672/70667500537)*q^6 + (14206104584/70667500537*a^19 - 73929917660/70667500537*a^18 - 217625963104/70667500537*a^17 + 1623811314781/70667500537*a^16 + 718324474035/70667500537*a^15 - 14463092476282/70667500537*a^14 + 5200344860599/70667500537*a^13 + 67549212478312/70667500537*a^12 - 49344882750744/70667500537*a^11 - 178206976331195/70667500537*a^10 + 163692302662231/70667500537*a^9 + 265143660512813/70667500537*a^8 - 263282060201810/70667500537*a^7 - 208409915897199/70667500537*a^6 + 196702343066120/70667500537*a^5 + 76518886551657/70667500537*a^4 - 48490939532631/70667500537*a^3 - 14104399906234/70667500537*a^2 + 22202981870/70667500537*a + 63340582601/70667500537)*q^7 + (a^3 - 4*a)*q^8 + (24300825471/70667500537*a^19 - 133893133822/70667500537*a^18 - 337985653895/70667500537*a^17 + 2913593852405/70667500537*a^16 + 460534478084/70667500537*a^15 - 25632055472351/70667500537*a^14 + 15920355302300/70667500537*a^13 + 117808368415291/70667500537*a^12 - 118355307245425/70667500537*a^11 - 304771296294793/70667500537*a^10 + 373501176477836/70667500537*a^9 + 444521629868889/70667500537*a^8 - 596623194205738/70667500537*a^7 - 347904412792077/70667500537*a^6 + 456274106320933/70667500537*a^5 + 138049766292840/70667500537*a^4 - 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203761033397189/70667500537*a^10 - 82815453760662/70667500537*a^9 + 321097171953661/70667500537*a^8 + 97410611557579/70667500537*a^7 - 239894842664139/70667500537*a^6 - 79675910588325/70667500537*a^5 + 46865504994804/70667500537*a^4 + 33436512445543/70667500537*a^3 + 9396026959943/70667500537*a^2 + 119316910352/70667500537*a - 35957165828/70667500537)*q^35 + (-23506485161/70667500537*a^19 + 165214636867/70667500537*a^18 + 195489952129/70667500537*a^17 - 3580010792476/70667500537*a^16 + 2565919312644/70667500537*a^15 + 31322909615426/70667500537*a^14 - 43563622620995/70667500537*a^13 - 143017161576220/70667500537*a^12 + 253286253969293/70667500537*a^11 + 367690014462273/70667500537*a^10 - 747816867940533/70667500537*a^9 - 536780610132721/70667500537*a^8 + 1177389676857774/70667500537*a^7 + 435041918712550/70667500537*a^6 - 910590949562992/70667500537*a^5 - 201511668730509/70667500537*a^4 + 255247039197884/70667500537*a^3 + 61765062819927/70667500537*a^2 - 6024051073751/70667500537*a - 929073627526/70667500537)*q^36 + (29279187028/70667500537*a^19 - 179663634232/70667500537*a^18 - 334276101795/70667500537*a^17 + 3891077285839/70667500537*a^16 - 1165199718243/70667500537*a^15 - 33866323647966/70667500537*a^14 + 35751842790564/70667500537*a^13 + 152104644055235/70667500537*a^12 - 226575846001678/70667500537*a^11 - 374433757055723/70667500537*a^10 + 689192463895933/70667500537*a^9 + 488054819611240/70667500537*a^8 - 1094591681507048/70667500537*a^7 - 286295945965726/70667500537*a^6 + 840844539413438/70667500537*a^5 + 45979544663994/70667500537*a^4 - 229930635056428/70667500537*a^3 - 11792551088345/70667500537*a^2 + 8321026131183/70667500537*a - 77043795460/70667500537)*q^37 + O(q^38)
*]> ;  // time = 12.539 seconds




J[458] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 458, 458, 458, 458, 458, 229, 229, 229 ], new_dimensions := [ 1, 1, 2, 7, 9, 1, 6, 11 ], dimensions := [ 1, 1, 2, 7, 9, 2, 12, 22 ], intersection_graph := [ 0, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 5, 3, 1, 0, 1, 1, 1, 13, 1, 1, 1, 1, 0, 1, 1, 1, 18169, 1, 1, 1, 1, 0, 1, 43, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 13, 1, 43, 1, 0, 1, 1, 5, 1, 18169, 1, 1, 1, 0 ], ap_traces := [
[ -1, -3, 1, -2, 1, 2, 1, -1, -4, -2, -4, -6 ],
[ 1, -1, -1, -4, -1, -2, -3, 1, 2, -6, 8, -6 ],
[ -2, 0, 1, -3, -2, -8, -3, 0, -1, 6, -11, -3 ],
[ -7, 4, 1, 7, 6, 9, 0, 12, 11, -15, 1, 18 ],
[ 9, 2, 4, 6, -6, 11, 1, -6, 8, 5, 6, 3 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + 2*x - 12,
x^7 - 4*x^6 - 6*x^5 + 31*x^4 + 12*x^3 - 77*x^2 - 10*x + 59,
x^9 - 2*x^8 - 20*x^7 + 41*x^6 + 112*x^5 - 241*x^4 - 160*x^3 + 385*x^2 + 28*x - 112
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 5, 1 ],
[ 13, 1 ],
[ 54507, 3 ],
[ 4945, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 5, 1 ],
[ 1, 1 ],
[ 1, 3 ],
[ 4945, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 115 ], torsion_lower_bounds := [ 1, 1, 1, 3, 115 ], l_ratios := [ 0, 0, 0, 1/3, 43/115 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ -1, -3, 1, -2, 1, 2, 1, -1, -4, -2, -4, -6 ],
[ 1, -1, -1, -4, -1, -2, -3, 1, 2, -6, 8, -6 ],
[
-1,
0,
-1/2*a,
1/2*a - 1,
a,
-4,
1/2*a - 1,
-2*a - 2,
1/2*a,
-a + 2,
3/2*a - 4,
-3/2*a - 3
],
[
-1,
a,
a^6 - 5*a^5 + a^4 + 24*a^3 - 22*a^2 - 27*a + 31,
a^6 - 5*a^5 + 26*a^3 - 16*a^2 - 33*a + 23,
-a^5 + 4*a^4 + 3*a^3 - 20*a^2 - a + 24,
-a^6 + 6*a^5 - 4*a^4 - 30*a^3 + 37*a^2 + 38*a - 44,
a^6 - 7*a^5 + 7*a^4 + 37*a^3 - 58*a^2 - 48*a + 77,
-a^5 + 3*a^4 + 6*a^3 - 17*a^2 - 9*a + 23,
-2*a^6 + 10*a^5 - 55*a^3 + 40*a^2 + 73*a - 60,
a^6 - 5*a^5 - a^4 + 30*a^3 - 17*a^2 - 43*a + 29,
3*a^6 - 15*a^5 + a^4 + 80*a^3 - 67*a^2 - 101*a + 107,
2*a^6 - 12*a^5 + 8*a^4 + 60*a^3 - 78*a^2 - 74*a + 108
],
[
1,
a,
-737/145364*a^8 - 4313/72682*a^7 + 2682/36341*a^6 + 163547/145364*a^5 - 12038/36341*a^4 - 827039/145364*a^3 + 54071/36341*a^2 + 956203/145364*a - 16071/36341,
9607/145364*a^8 + 1685/72682*a^7 - 48570/36341*a^6 - 43925/145364*a^5 + 291336/36341*a^4 + 61617/145364*a^3 - 596202/36341*a^2 + 27859/145364*a + 362990/36341,
3537/72682*a^8 + 1271/36341*a^7 - 32942/36341*a^6 - 51465/72682*a^5 + 161896/36341*a^4 + 303949/72682*a^3 - 195820/36341*a^2 - 618113/72682*a + 39266/36341,
-7608/36341*a^8 + 3656/36341*a^7 + 153397/36341*a^6 - 75906/36341*a^5 - 890164/36341*a^4 + 435950/36341*a^3 + 1528695/36341*a^2 - 473202/36341*a - 503048/36341,
-9643/145364*a^8 - 4657/72682*a^7 + 50772/36341*a^6 + 157633/145364*a^5 - 318699/36341*a^4 - 657633/145364*a^3 + 627344/36341*a^2 + 601685/145364*a - 179358/36341,
1177/36341*a^8 + 4555/36341*a^7 - 21472/36341*a^6 - 79482/36341*a^5 + 101850/36341*a^4 + 334705/36341*a^3 - 131702/36341*a^2 - 280086/36341*a + 10454/36341,
2967/145364*a^8 + 2669/72682*a^7 - 17947/36341*a^6 - 116593/145364*a^5 + 138304/36341*a^4 + 751781/145364*a^3 - 343762/36341*a^2 - 1407269/145364*a + 116769/36341,
4539/72682*a^8 - 804/36341*a^7 - 46497/36341*a^6 + 30125/72682*a^5 + 267804/36341*a^4 - 114527/72682*a^3 - 378842/36341*a^2 - 187967/72682*a + 16792/36341,
18477/145364*a^8 - 943/72682*a^7 - 94458/36341*a^6 + 75697/145364*a^5 + 570634/36341*a^4 - 703805/145364*a^3 - 1101992/36341*a^2 + 1011921/145364*a + 491863/36341,
32345/145364*a^8 - 2823/72682*a^7 - 155329/36341*a^6 + 156625/145364*a^5 + 814853/36341*a^4 - 1216409/145364*a^3 - 1085863/36341*a^2 + 1449281/145364*a + 177556/36341
]
*], q_expansions := [*
q - q^2 - 3*q^3 + q^4 + q^5 + 3*q^6 - 2*q^7 - q^8 + 6*q^9 - q^10 + q^11 - 3*q^12 + 2*q^13 + 2*q^14 - 3*q^15 + q^16 + q^17 - 6*q^18 - q^19 + q^20 + 6*q^21 - q^22 - 4*q^23 + 3*q^24 - 4*q^25 - 2*q^26 - 9*q^27 - 2*q^28 - 2*q^29 + 3*q^30 - 4*q^31 - q^32 - 3*q^33 - q^34 - 2*q^35 + 6*q^36 - 6*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - q^5 - q^6 - 4*q^7 + q^8 - 2*q^9 - q^10 - q^11 - q^12 - 2*q^13 - 4*q^14 + q^15 + q^16 - 3*q^17 - 2*q^18 + q^19 - q^20 + 4*q^21 - q^22 + 2*q^23 - q^24 - 4*q^25 - 2*q^26 + 5*q^27 - 4*q^28 - 6*q^29 + q^30 + 8*q^31 + q^32 + q^33 - 3*q^34 + 4*q^35 - 2*q^36 - 6*q^37 + O(q^38),
q - q^2 + q^4 - 1/2*a*q^5 + (1/2*a - 1)*q^7 - q^8 - 3*q^9 + 1/2*a*q^10 + a*q^11 - 4*q^13 + (-1/2*a + 1)*q^14 + q^16 + (1/2*a - 1)*q^17 + 3*q^18 + (-2*a - 2)*q^19 - 1/2*a*q^20 - a*q^22 + 1/2*a*q^23 + (-1/2*a - 2)*q^25 + 4*q^26 + (1/2*a - 1)*q^28 + (-a + 2)*q^29 + (3/2*a - 4)*q^31 - q^32 + (-1/2*a + 1)*q^34 + (a - 3)*q^35 - 3*q^36 + (-3/2*a - 3)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (a^6 - 5*a^5 + a^4 + 24*a^3 - 22*a^2 - 27*a + 31)*q^5 - a*q^6 + (a^6 - 5*a^5 + 26*a^3 - 16*a^2 - 33*a + 23)*q^7 - q^8 + (a^2 - 3)*q^9 + (-a^6 + 5*a^5 - a^4 - 24*a^3 + 22*a^2 + 27*a - 31)*q^10 + (-a^5 + 4*a^4 + 3*a^3 - 20*a^2 - a + 24)*q^11 + a*q^12 + (-a^6 + 6*a^5 - 4*a^4 - 30*a^3 + 37*a^2 + 38*a - 44)*q^13 + (-a^6 + 5*a^5 - 26*a^3 + 16*a^2 + 33*a - 23)*q^14 + (-a^6 + 7*a^5 - 7*a^4 - 34*a^3 + 50*a^2 + 41*a - 59)*q^15 + q^16 + (a^6 - 7*a^5 + 7*a^4 + 37*a^3 - 58*a^2 - 48*a + 77)*q^17 + (-a^2 + 3)*q^18 + (-a^5 + 3*a^4 + 6*a^3 - 17*a^2 - 9*a + 23)*q^19 + (a^6 - 5*a^5 + a^4 + 24*a^3 - 22*a^2 - 27*a + 31)*q^20 + (-a^6 + 6*a^5 - 5*a^4 - 28*a^3 + 44*a^2 + 33*a - 59)*q^21 + (a^5 - 4*a^4 - 3*a^3 + 20*a^2 + a - 24)*q^22 + (-2*a^6 + 10*a^5 - 55*a^3 + 40*a^2 + 73*a - 60)*q^23 - a*q^24 + (-3*a^6 + 15*a^5 - a^4 - 80*a^3 + 68*a^2 + 99*a - 106)*q^25 + (a^6 - 6*a^5 + 4*a^4 + 30*a^3 - 37*a^2 - 38*a + 44)*q^26 + (a^3 - 6*a)*q^27 + (a^6 - 5*a^5 + 26*a^3 - 16*a^2 - 33*a + 23)*q^28 + (a^6 - 5*a^5 - a^4 + 30*a^3 - 17*a^2 - 43*a + 29)*q^29 + (a^6 - 7*a^5 + 7*a^4 + 34*a^3 - 50*a^2 - 41*a + 59)*q^30 + (3*a^6 - 15*a^5 + a^4 + 80*a^3 - 67*a^2 - 101*a + 107)*q^31 - q^32 + (-a^6 + 4*a^5 + 3*a^4 - 20*a^3 - a^2 + 24*a)*q^33 + (-a^6 + 7*a^5 - 7*a^4 - 37*a^3 + 58*a^2 + 48*a - 77)*q^34 + (2*a^5 - 6*a^4 - 14*a^3 + 40*a^2 + 20*a - 54)*q^35 + (a^2 - 3)*q^36 + (2*a^6 - 12*a^5 + 8*a^4 + 60*a^3 - 78*a^2 - 74*a + 108)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-737/145364*a^8 - 4313/72682*a^7 + 2682/36341*a^6 + 163547/145364*a^5 - 12038/36341*a^4 - 827039/145364*a^3 + 54071/36341*a^2 + 956203/145364*a - 16071/36341)*q^5 + a*q^6 + (9607/145364*a^8 + 1685/72682*a^7 - 48570/36341*a^6 - 43925/145364*a^5 + 291336/36341*a^4 + 61617/145364*a^3 - 596202/36341*a^2 + 27859/145364*a + 362990/36341)*q^7 + q^8 + (a^2 - 3)*q^9 + (-737/145364*a^8 - 4313/72682*a^7 + 2682/36341*a^6 + 163547/145364*a^5 - 12038/36341*a^4 - 827039/145364*a^3 + 54071/36341*a^2 + 956203/145364*a - 16071/36341)*q^10 + (3537/72682*a^8 + 1271/36341*a^7 - 32942/36341*a^6 - 51465/72682*a^5 + 161896/36341*a^4 + 303949/72682*a^3 - 195820/36341*a^2 - 618113/72682*a + 39266/36341)*q^11 + a*q^12 + (-7608/36341*a^8 + 3656/36341*a^7 + 153397/36341*a^6 - 75906/36341*a^5 - 890164/36341*a^4 + 435950/36341*a^3 + 1528695/36341*a^2 - 473202/36341*a - 503048/36341)*q^13 + (9607/145364*a^8 + 1685/72682*a^7 - 48570/36341*a^6 - 43925/145364*a^5 + 291336/36341*a^4 + 61617/145364*a^3 - 596202/36341*a^2 + 27859/145364*a + 362990/36341)*q^14 + (-2525/36341*a^8 - 1003/36341*a^7 + 48441/36341*a^6 + 8598/36341*a^5 - 251164/36341*a^4 + 24591/36341*a^3 + 309987/36341*a^2 - 10912/36341*a - 20636/36341)*q^15 + q^16 + (-9643/145364*a^8 - 4657/72682*a^7 + 50772/36341*a^6 + 157633/145364*a^5 - 318699/36341*a^4 - 657633/145364*a^3 + 627344/36341*a^2 + 601685/145364*a - 179358/36341)*q^17 + (a^2 - 3)*q^18 + (1177/36341*a^8 + 4555/36341*a^7 - 21472/36341*a^6 - 79482/36341*a^5 + 101850/36341*a^4 + 334705/36341*a^3 - 131702/36341*a^2 - 280086/36341*a + 10454/36341)*q^19 + (-737/145364*a^8 - 4313/72682*a^7 + 2682/36341*a^6 + 163547/145364*a^5 - 12038/36341*a^4 - 827039/145364*a^3 + 54071/36341*a^2 + 956203/145364*a - 16071/36341)*q^20 + (5646/36341*a^8 - 535/36341*a^7 - 109453/36341*a^6 + 22340/36341*a^5 + 594226/36341*a^4 - 211922/36341*a^3 - 917709/36341*a^2 + 295741/36341*a + 268996/36341)*q^21 + (3537/72682*a^8 + 1271/36341*a^7 - 32942/36341*a^6 - 51465/72682*a^5 + 161896/36341*a^4 + 303949/72682*a^3 - 195820/36341*a^2 - 618113/72682*a + 39266/36341)*q^22 + (2967/145364*a^8 + 2669/72682*a^7 - 17947/36341*a^6 - 116593/145364*a^5 + 138304/36341*a^4 + 751781/145364*a^3 - 343762/36341*a^2 - 1407269/145364*a + 116769/36341)*q^23 + a*q^24 + (-11009/145364*a^8 - 4367/72682*a^7 + 49530/36341*a^6 + 143603/145364*a^5 - 224345/36341*a^4 - 523663/145364*a^3 + 205968/36341*a^2 + 334731/145364*a + 73447/36341)*q^25 + (-7608/36341*a^8 + 3656/36341*a^7 + 153397/36341*a^6 - 75906/36341*a^5 - 890164/36341*a^4 + 435950/36341*a^3 + 1528695/36341*a^2 - 473202/36341*a - 503048/36341)*q^26 + (a^3 - 6*a)*q^27 + (9607/145364*a^8 + 1685/72682*a^7 - 48570/36341*a^6 - 43925/145364*a^5 + 291336/36341*a^4 + 61617/145364*a^3 - 596202/36341*a^2 + 27859/145364*a + 362990/36341)*q^28 + (4539/72682*a^8 - 804/36341*a^7 - 46497/36341*a^6 + 30125/72682*a^5 + 267804/36341*a^4 - 114527/72682*a^3 - 378842/36341*a^2 - 187967/72682*a + 16792/36341)*q^29 + (-2525/36341*a^8 - 1003/36341*a^7 + 48441/36341*a^6 + 8598/36341*a^5 - 251164/36341*a^4 + 24591/36341*a^3 + 309987/36341*a^2 - 10912/36341*a - 20636/36341)*q^30 + (18477/145364*a^8 - 943/72682*a^7 - 94458/36341*a^6 + 75697/145364*a^5 + 570634/36341*a^4 - 703805/145364*a^3 - 1101992/36341*a^2 + 1011921/145364*a + 491863/36341)*q^31 + q^32 + (4808/36341*a^8 + 2428/36341*a^7 - 98241/36341*a^6 - 36176/36341*a^5 + 578183/36341*a^4 + 87140/36341*a^3 - 989929/36341*a^2 - 10252/36341*a + 198072/36341)*q^33 + (-9643/145364*a^8 - 4657/72682*a^7 + 50772/36341*a^6 + 157633/145364*a^5 - 318699/36341*a^4 - 657633/145364*a^3 + 627344/36341*a^2 + 601685/145364*a - 179358/36341)*q^34 + (20135/72682*a^8 - 5392/36341*a^7 - 197926/36341*a^6 + 249583/72682*a^5 + 1093607/36341*a^4 - 1672619/72682*a^3 - 1700871/36341*a^2 + 2374771/72682*a + 475121/36341)*q^35 + (a^2 - 3)*q^36 + (32345/145364*a^8 - 2823/72682*a^7 - 155329/36341*a^6 + 156625/145364*a^5 + 814853/36341*a^4 - 1216409/145364*a^3 - 1085863/36341*a^2 + 1449281/145364*a + 177556/36341)*q^37 + O(q^38)
*]> ;  // time = 132.2 seconds




J[461] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 461, 461, 461, 461 ], new_dimensions := [ 2, 3, 7, 26 ], dimensions := [ 2, 3, 7, 26 ], intersection_graph := [ 0, 1, 19, 1, 1, 0, 97, 1, 19, 97, 0, 1, 1, 1, 1, 0 ], ap_traces := [
[ -1, -3, 0, -2, 0, -2, 9, -7, -6, -4, 0, -5 ],
[ -2, 0, -1, -3, -9, -4, 5, -7, 10, 0, -17, -2 ],
[ 0, -3, -4, -5, -7, 2, -15, -24, -10, 1, -13, -16 ],
[ 3, 8, 1, 10, 22, 6, -7, 50, -6, -5, 38, 19 ]
], hecke_fields := [
x^2 + x - 1,
x^3 + 2*x^2 - x - 1,
x^7 - 8*x^5 + x^4 + 18*x^3 - 2*x^2 - 12*x + 1,
x^26 - 3*x^25 - 41*x^24 + 126*x^23 + 726*x^22 - 2303*x^21 - 7266*x^20 + 24054*x^19 + 45144*x^18 - 158550*x^17 - 179824*x^16 + 687620*x^15 + 456511*x^14 - 1985932*x^13 - 703693*x^12 + 3785104*x^11 + 571532*x^10 - 4624305*x^9 - 111938*x^8 + 3430214*x^7 - 156745*x^6 - 1399829*x^5 + 108715*x^4 + 249906*x^3 - 21297*x^2 - 6102*x + 223
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 115 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 115 ]
], torsion_upper_bounds := [ 1, 1, 1, 115 ], torsion_lower_bounds := [ 1, 1, 1, 115 ], l_ratios := [ 0, 0, 0, 1/115 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1 ], eigenvalues := [*
[
a,
a - 1,
2*a + 1,
-2*a - 2,
-2*a - 1,
-1,
-3*a + 3,
a - 3,
-2*a - 4,
2*a - 1,
0,
3*a - 1
],
[
a,
2*a^2 + 3*a - 2,
-2*a^2 - 4*a + 1,
-1,
-a^2 - 3*a - 3,
-2*a^2 - a + 2,
2*a^2 + 5*a + 1,
-a^2 - a - 1,
3*a^2 + 4*a,
6*a^2 + 9*a - 6,
3*a^2 + 4*a - 9,
-5*a^2 - 8*a + 4
],
[
a,
a^5 - 6*a^3 + a^2 + 6*a - 1,
-a^5 + 6*a^3 - a^2 - 7*a,
-2*a^5 + 12*a^3 - 4*a^2 - 13*a + 5,
a^6 + 2*a^5 - 6*a^4 - 11*a^3 + 8*a^2 + 13*a - 1,
-a^6 + 2*a^5 + 6*a^4 - 14*a^3 - 2*a^2 + 16*a - 7,
2*a^6 - 2*a^5 - 13*a^4 + 15*a^3 + 16*a^2 - 18*a - 4,
2*a^6 - 2*a^5 - 12*a^4 + 17*a^3 + 11*a^2 - 23*a - 1,
-2*a^6 + a^5 + 15*a^4 - 8*a^3 - 26*a^2 + 10*a + 6,
-a^6 - a^5 + 4*a^4 + 4*a^3 + 4*a^2 - 5*a - 10,
2*a^6 - 14*a^4 + 21*a^2 + 6*a - 5,
3*a^6 + 3*a^5 - 19*a^4 - 13*a^3 + 29*a^2 + 14*a - 10
],
[
a,
-18411620439/79452970167808*a^25 + 126031151319/19863242541952*a^24 - 470141107935/79452970167808*a^23 - 20612532444589/79452970167808*a^22 + 36754184162415/79452970167808*a^21 + 22764870934587/4965810635488*a^20 - 376755454739613/39726485083904*a^19 - 227622383281801/4965810635488*a^18 + 2018423496755725/19863242541952*a^17 + 11326187917526589/39726485083904*a^16 - 26228962700185675/39726485083904*a^15 - 45346845828395343/39726485083904*a^14 + 217656635876641153/79452970167808*a^13 + 233496124711315187/79452970167808*a^12 - 291123266455105609/39726485083904*a^11 - 186910251706688363/39726485083904*a^10 + 491677426961778207/39726485083904*a^9 + 343467078638191121/79452970167808*a^8 - 992645198412472247/79452970167808*a^7 - 150194664903861945/79452970167808*a^6 + 33623281419871289/4965810635488*a^5 + 13620998787985797/79452970167808*a^4 - 15604395470821721/9931621270976*a^3 + 2882108350923733/39726485083904*a^2 + 4325996849510437/79452970167808*a - 48453363884879/79452970167808,
-66708447915/9931621270976*a^25 + 1070948233227/79452970167808*a^24 + 22722271687947/79452970167808*a^23 - 5520329320915/9931621270976*a^22 - 422227565561867/79452970167808*a^21 + 394820114143867/39726485083904*a^20 + 1124752237877955/19863242541952*a^19 - 2006819824054707/19863242541952*a^18 - 15190685955581691/39726485083904*a^17 + 3195486240749447/4965810635488*a^16 + 33922841696430085/19863242541952*a^15 - 53002421103439993/19863242541952*a^14 - 101545454520251913/19863242541952*a^13 + 576100090591804269/79452970167808*a^12 + 101105735051602811/9931621270976*a^11 - 503425332035968073/39726485083904*a^10 - 130315349099232313/9931621270976*a^9 + 539895927632019101/39726485083904*a^8 + 823928140449728253/79452970167808*a^7 - 81202495763665461/9931621270976*a^6 - 358732742406467765/79452970167808*a^5 + 183920627873384021/79452970167808*a^4 + 127308678222668/155181582359*a^3 - 7698956149363327/39726485083904*a^2 - 88440564889987/39726485083904*a + 94898764459539/79452970167808,
134986310209/39726485083904*a^25 - 225519826069/39726485083904*a^24 - 369877425839/2482905317744*a^23 + 9407163275881/39726485083904*a^22 + 57043913829535/19863242541952*a^21 - 21390306431563/4965810635488*a^20 - 636385462338977/19863242541952*a^19 + 891413207208671/19863242541952*a^18 + 4549950049989865/19863242541952*a^17 - 367128514188453/1241452658872*a^16 - 21811234967951493/19863242541952*a^15 + 3188720575098113/2482905317744*a^14 + 142502138509697805/39726485083904*a^13 - 73744083555671587/19863242541952*a^12 - 157944985051604145/19863242541952*a^11 + 69929455528581719/9931621270976*a^10 + 231857784944446415/19863242541952*a^9 - 333506203840142317/39726485083904*a^8 - 213927999988339131/19863242541952*a^7 + 229261867508367987/39726485083904*a^6 + 223507617872364169/39726485083904*a^5 - 38233185025212671/19863242541952*a^4 - 12957876382463147/9931621270976*a^3 + 4327660884127357/19863242541952*a^2 + 1957652666438971/39726485083904*a - 67557870131361/19863242541952,
-654486464095/79452970167808*a^25 + 2148325256257/79452970167808*a^24 + 6496572109073/19863242541952*a^23 - 88816208595081/79452970167808*a^22 - 220320799354331/39726485083904*a^21 + 99425645318785/4965810635488*a^20 + 518644303261825/9931621270976*a^19 - 8090481763598131/39726485083904*a^18 - 5883528544434441/19863242541952*a^17 + 12867741258759761/9931621270976*a^16 + 10094087718921487/9931621270976*a^15 - 26578370375021325/4965810635488*a^14 - 153557123852975485/79452970167808*a^13 + 286616405147251015/19863242541952*a^12 + 48565206237547849/39726485083904*a^11 - 246876899706545611/9931621270976*a^10 + 90448954185759211/39726485083904*a^9 + 2066518903949019575/79452970167808*a^8 - 3069536255204099/620726329436*a^7 - 1194265712543343851/79452970167808*a^6 + 264312392250545123/79452970167808*a^5 + 39697453469731843/9931621270976*a^4 - 31432328321029291/39726485083904*a^3 - 11618431809321535/39726485083904*a^2 + 1892099576957565/79452970167808*a + 104525183946031/19863242541952,
255589912167/19863242541952*a^25 - 1475482310713/39726485083904*a^24 - 20761175829129/39726485083904*a^23 + 30491050325005/19863242541952*a^22 + 363366019136511/39726485083904*a^21 - 272988162097069/9931621270976*a^20 - 1792107785174111/19863242541952*a^19 + 5551313599531537/19863242541952*a^18 + 1366728673015023/2482905317744*a^17 - 35293777849825571/19863242541952*a^16 - 42589410541860253/19863242541952*a^15 + 145601539668576133/19863242541952*a^14 + 52711935399555833/9931621270976*a^13 - 782702040196782319/39726485083904*a^12 - 39933939419955829/4965810635488*a^11 + 669385327624253147/19863242541952*a^10 + 68705267787917029/9931621270976*a^9 - 85971741876398599/2482905317744*a^8 - 122684280458123357/39726485083904*a^7 + 188567793908914639/9931621270976*a^6 + 35108008136135037/39726485083904*a^5 - 165241435990433233/39726485083904*a^4 - 5182356150084189/19863242541952*a^3 - 46910812983423/4965810635488*a^2 + 733271797518791/19863242541952*a + 170585471510307/39726485083904,
-146465896685/39726485083904*a^25 + 1363761679523/79452970167808*a^24 + 10730239086177/79452970167808*a^23 - 28320846337741/39726485083904*a^22 - 159790030772685/79452970167808*a^21 + 509584325843241/39726485083904*a^20 + 74018458376191/4965810635488*a^19 - 325447285501243/2482905317744*a^18 - 1839687255381395/39726485083904*a^17 + 4160763639676075/4965810635488*a^16 - 930715509545949/9931621270976*a^15 - 69110730830587623/19863242541952*a^14 + 55456558940103853/39726485083904*a^13 + 749823533249269627/79452970167808*a^12 - 109655714476121229/19863242541952*a^11 - 651022474323610171/39726485083904*a^10 + 226290277188598423/19863242541952*a^9 + 86190413031941927/4965810635488*a^8 - 1026505322535081365/79452970167808*a^7 - 407353146738415087/39726485083904*a^6 + 594964629034538111/79452970167808*a^5 + 226592473836418915/79452970167808*a^4 - 4471554250587305/2482905317744*a^3 - 9125570378924811/39726485083904*a^2 + 636452553281923/9931621270976*a + 148846416186893/79452970167808,
30709045003/19863242541952*a^25 - 62107158425/19863242541952*a^24 - 652558119177/9931621270976*a^23 + 2597734694667/19863242541952*a^22 + 187838265329/155181582359*a^21 - 5860299000845/2482905317744*a^20 - 125975231551235/9931621270976*a^19 + 239178773494679/9931621270976*a^18 + 828489843531799/9931621270976*a^17 - 759321283641333/4965810635488*a^16 - 3560388067990971/9931621270976*a^15 + 3110250247078521/4965810635488*a^14 + 20201114255306147/19863242541952*a^13 - 8229255789354419/4965810635488*a^12 - 18705752117561631/9931621270976*a^11 + 13618047564771939/4965810635488*a^10 + 21935779193970513/9931621270976*a^9 - 51571935765997079/19863242541952*a^8 - 965804839592009/620726329436*a^7 + 21177469098014429/19863242541952*a^6 + 11868173647588553/19863242541952*a^5 + 130787100800585/1241452658872*a^4 - 468124106910965/4965810635488*a^3 - 1488434787750435/9931621270976*a^2 + 67359472572025/19863242541952*a + 14422797991597/2482905317744,
-135601064743/9931621270976*a^25 + 714228650355/39726485083904*a^24 + 24100965413519/39726485083904*a^23 - 930191571773/1241452658872*a^22 - 470330041978875/39726485083904*a^21 + 269535627229685/19863242541952*a^20 + 1325955590935025/9931621270976*a^19 - 348072514916843/2482905317744*a^18 - 19130031232332563/19863242541952*a^17 + 9058213355858821/9931621270976*a^16 + 46148237973736069/9931621270976*a^15 - 9666801745443219/2482905317744*a^14 - 2362574715916353/155181582359*a^13 + 437789148310366389/39726485083904*a^12 + 167261583508772937/4965810635488*a^11 - 405638424106463425/19863242541952*a^10 - 243274569648163053/4965810635488*a^9 + 473732240305580211/19863242541952*a^8 + 1760038540109037577/39726485083904*a^7 - 161590610371948035/9931621270976*a^6 - 886483669493431737/39726485083904*a^5 + 222239734452630721/39726485083904*a^4 + 23993139639087753/4965810635488*a^3 - 13992727453374137/19863242541952*a^2 - 2066732531714833/19863242541952*a + 239604003251763/39726485083904,
-60026660177/9931621270976*a^25 + 195185724023/19863242541952*a^24 + 2645015587525/9931621270976*a^23 - 4100299989867/9931621270976*a^22 - 102218739882291/19863242541952*a^21 + 149494886919161/19863242541952*a^20 + 1139785003632797/19863242541952*a^19 - 1550720457923985/19863242541952*a^18 - 8122815303868847/19863242541952*a^17 + 10087885593124871/19863242541952*a^16 + 38726604550186743/19863242541952*a^15 - 42762289611061755/19863242541952*a^14 - 125690745958903673/19863242541952*a^13 + 59410327638308253/9931621270976*a^12 + 138592864541552737/9931621270976*a^11 - 52986541146594091/4965810635488*a^10 - 50861950366590195/2482905317744*a^9 + 57472819695779053/4965810635488*a^8 + 379194665128353561/19863242541952*a^7 - 135207294693684525/19863242541952*a^6 - 101223698195912811/9931621270976*a^5 + 32492317370425887/19863242541952*a^4 + 47690299403153447/19863242541952*a^3 - 472725788093605/19863242541952*a^2 - 1395370868154421/19863242541952*a + 8194587867063/4965810635488,
-688413474255/79452970167808*a^25 + 1246190459547/79452970167808*a^24 + 15042415075061/39726485083904*a^23 - 52198936956765/79452970167808*a^22 - 144102623923179/19863242541952*a^21 + 237326972786893/19863242541952*a^20 + 1592960066321727/19863242541952*a^19 - 4915898065069579/39726485083904*a^18 - 11253653663565721/19863242541952*a^17 + 3995117108017761/4965810635488*a^16 + 53183500078955927/19863242541952*a^15 - 33890688961130807/9931621270976*a^14 - 684226775042464625/79452970167808*a^13 + 377402781788403877/39726485083904*a^12 + 746907424682649489/39726485083904*a^11 - 337701670513548349/19863242541952*a^10 - 1082347965820212017/39726485083904*a^9 + 1471634963057707587/79452970167808*a^8 + 989353429377570243/39726485083904*a^7 - 869086089696285367/79452970167808*a^6 - 1023515656467856259/79452970167808*a^5 + 103603087030085811/39726485083904*a^4 + 113808354060710219/39726485083904*a^3 + 106985458250667/39726485083904*a^2 - 4414409494712907/79452970167808*a - 294631617940265/39726485083904,
157719948323/39726485083904*a^25 - 47317100369/2482905317744*a^24 - 5763048527635/39726485083904*a^23 + 31492003110789/39726485083904*a^22 + 85282564175321/39726485083904*a^21 - 283551167781677/19863242541952*a^20 - 77720042640047/4965810635488*a^19 + 2896255290649451/19863242541952*a^18 + 900673749513715/19863242541952*a^17 - 9233579669196231/9931621270976*a^16 + 650539995734539/4965810635488*a^15 + 19050582854149131/4965810635488*a^14 - 64479973549777735/39726485083904*a^13 - 407880779948765293/39726485083904*a^12 + 123467744433484091/19863242541952*a^11 + 344523452206298341/19863242541952*a^10 - 249097437093544875/19863242541952*a^9 - 688233831476651349/39726485083904*a^8 + 549260326664870779/39726485083904*a^7 + 353676940443156771/39726485083904*a^6 - 151826798932209995/19863242541952*a^5 - 63331315038364461/39726485083904*a^4 + 32790523469740769/19863242541952*a^3 - 128377822607601/1241452658872*a^2 - 145177269453103/39726485083904*a - 193423338487051/39726485083904
]
*], q_expansions := [*
q + a*q^2 + (a - 1)*q^3 + (-a - 1)*q^4 + (2*a + 1)*q^5 + (-2*a + 1)*q^6 + (-2*a - 2)*q^7 + (-2*a - 1)*q^8 + (-3*a - 1)*q^9 + (-a + 2)*q^10 + (-2*a - 1)*q^11 + a*q^12 - q^13 - 2*q^14 + (-3*a + 1)*q^15 + 3*a*q^16 + (-3*a + 3)*q^17 + (2*a - 3)*q^18 + (a - 3)*q^19 + (-a - 3)*q^20 + 2*a*q^21 + (a - 2)*q^22 + (-2*a - 4)*q^23 + (3*a - 1)*q^24 - a*q^26 + (2*a + 1)*q^27 + (2*a + 4)*q^28 + (2*a - 1)*q^29 + (4*a - 3)*q^30 + (a + 5)*q^32 + (3*a - 1)*q^33 + (6*a - 3)*q^34 + (-2*a - 6)*q^35 + (a + 4)*q^36 + (3*a - 1)*q^37 + O(q^38),
q + a*q^2 + (2*a^2 + 3*a - 2)*q^3 + (a^2 - 2)*q^4 + (-2*a^2 - 4*a + 1)*q^5 + (-a^2 + 2)*q^6 - q^7 + (-2*a^2 - 3*a + 1)*q^8 + (-3*a^2 - 4*a + 5)*q^9 + (-a - 2)*q^10 + (-a^2 - 3*a - 3)*q^11 + (-2*a^2 - 5*a + 3)*q^12 + (-2*a^2 - a + 2)*q^13 - a*q^14 + (2*a^2 + a - 8)*q^15 + (-a^2 - a + 2)*q^16 + (2*a^2 + 5*a + 1)*q^17 + (2*a^2 + 2*a - 3)*q^18 + (-a^2 - a - 1)*q^19 + (3*a^2 + 6*a - 2)*q^20 + (-2*a^2 - 3*a + 2)*q^21 + (-a^2 - 4*a - 1)*q^22 + (3*a^2 + 4*a)*q^23 + (a^2 + a - 6)*q^24 + (4*a + 4)*q^25 + (3*a^2 - 2)*q^26 + (2*a^2 + 3*a - 9)*q^27 + (-a^2 + 2)*q^28 + (6*a^2 + 9*a - 6)*q^29 + (-3*a^2 - 6*a + 2)*q^30 + (3*a^2 + 4*a - 9)*q^31 + (5*a^2 + 7*a - 3)*q^32 + (-5*a^2 - 10*a + 1)*q^33 + (a^2 + 3*a + 2)*q^34 + (2*a^2 + 4*a - 1)*q^35 + (4*a^2 + 7*a - 8)*q^36 + (-5*a^2 - 8*a + 4)*q^37 + O(q^38),
q + a*q^2 + (a^5 - 6*a^3 + a^2 + 6*a - 1)*q^3 + (a^2 - 2)*q^4 + (-a^5 + 6*a^3 - a^2 - 7*a)*q^5 + (a^6 - 6*a^4 + a^3 + 6*a^2 - a)*q^6 + (-2*a^5 + 12*a^3 - 4*a^2 - 13*a + 5)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^6 + 12*a^4 - 3*a^3 - 12*a^2 + 4*a - 3)*q^9 + (-a^6 + 6*a^4 - a^3 - 7*a^2)*q^10 + (a^6 + 2*a^5 - 6*a^4 - 11*a^3 + 8*a^2 + 13*a - 1)*q^11 + (-a^2 + 1)*q^12 + (-a^6 + 2*a^5 + 6*a^4 - 14*a^3 - 2*a^2 + 16*a - 7)*q^13 + (-2*a^6 + 12*a^4 - 4*a^3 - 13*a^2 + 5*a)*q^14 + (a^6 - a^5 - 6*a^4 + 8*a^3 + 5*a^2 - 9*a + 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^6 - 2*a^5 - 13*a^4 + 15*a^3 + 16*a^2 - 18*a - 4)*q^17 + (-4*a^5 - a^4 + 24*a^3 - 27*a + 2)*q^18 + (2*a^6 - 2*a^5 - 12*a^4 + 17*a^3 + 11*a^2 - 23*a - 1)*q^19 + (-a^3 + 2*a + 1)*q^20 + (3*a^6 - a^5 - 18*a^4 + 11*a^3 + 19*a^2 - 13*a - 1)*q^21 + (2*a^6 + 2*a^5 - 12*a^4 - 10*a^3 + 15*a^2 + 11*a - 1)*q^22 + (-2*a^6 + a^5 + 15*a^4 - 8*a^3 - 26*a^2 + 10*a + 6)*q^23 + (-2*a^6 + 12*a^4 - 3*a^3 - 12*a^2 + 3*a)*q^24 + (2*a^5 - 13*a^3 + 3*a^2 + 16*a - 6)*q^25 + (2*a^6 - 2*a^5 - 13*a^4 + 16*a^3 + 14*a^2 - 19*a + 1)*q^26 + (2*a^5 + 2*a^4 - 11*a^3 - 6*a^2 + 11*a + 2)*q^27 + (-2*a^4 - a^3 + 9*a^2 + 2*a - 8)*q^28 + (-a^6 - a^5 + 4*a^4 + 4*a^3 + 4*a^2 - 5*a - 10)*q^29 + (-a^6 + 2*a^5 + 7*a^4 - 13*a^3 - 7*a^2 + 13*a - 1)*q^30 + (2*a^6 - 14*a^4 + 21*a^2 + 6*a - 5)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-2*a^6 - 3*a^5 + 11*a^4 + 14*a^3 - 11*a^2 - 12*a + 1)*q^33 + (-2*a^6 + 3*a^5 + 13*a^4 - 20*a^3 - 14*a^2 + 20*a - 2)*q^34 + (-a^6 + 3*a^5 + 6*a^4 - 19*a^3 - 2*a^2 + 21*a - 4)*q^35 + (-a^5 + 6*a^3 - 3*a^2 - 6*a + 6)*q^36 + (3*a^6 + 3*a^5 - 19*a^4 - 13*a^3 + 29*a^2 + 14*a - 10)*q^37 + O(q^38),
q + a*q^2 + (-18411620439/79452970167808*a^25 + 126031151319/19863242541952*a^24 - 470141107935/79452970167808*a^23 - 20612532444589/79452970167808*a^22 + 36754184162415/79452970167808*a^21 + 22764870934587/4965810635488*a^20 - 376755454739613/39726485083904*a^19 - 227622383281801/4965810635488*a^18 + 2018423496755725/19863242541952*a^17 + 11326187917526589/39726485083904*a^16 - 26228962700185675/39726485083904*a^15 - 45346845828395343/39726485083904*a^14 + 217656635876641153/79452970167808*a^13 + 233496124711315187/79452970167808*a^12 - 291123266455105609/39726485083904*a^11 - 186910251706688363/39726485083904*a^10 + 491677426961778207/39726485083904*a^9 + 343467078638191121/79452970167808*a^8 - 992645198412472247/79452970167808*a^7 - 150194664903861945/79452970167808*a^6 + 33623281419871289/4965810635488*a^5 + 13620998787985797/79452970167808*a^4 - 15604395470821721/9931621270976*a^3 + 2882108350923733/39726485083904*a^2 + 4325996849510437/79452970167808*a - 48453363884879/79452970167808)*q^3 + (a^2 - 2)*q^4 + (-66708447915/9931621270976*a^25 + 1070948233227/79452970167808*a^24 + 22722271687947/79452970167808*a^23 - 5520329320915/9931621270976*a^22 - 422227565561867/79452970167808*a^21 + 394820114143867/39726485083904*a^20 + 1124752237877955/19863242541952*a^19 - 2006819824054707/19863242541952*a^18 - 15190685955581691/39726485083904*a^17 + 3195486240749447/4965810635488*a^16 + 33922841696430085/19863242541952*a^15 - 53002421103439993/19863242541952*a^14 - 101545454520251913/19863242541952*a^13 + 576100090591804269/79452970167808*a^12 + 101105735051602811/9931621270976*a^11 - 503425332035968073/39726485083904*a^10 - 130315349099232313/9931621270976*a^9 + 539895927632019101/39726485083904*a^8 + 823928140449728253/79452970167808*a^7 - 81202495763665461/9931621270976*a^6 - 358732742406467765/79452970167808*a^5 + 183920627873384021/79452970167808*a^4 + 127308678222668/155181582359*a^3 - 7698956149363327/39726485083904*a^2 - 88440564889987/39726485083904*a + 94898764459539/79452970167808)*q^5 + (448889743959/79452970167808*a^25 - 612508772967/39726485083904*a^24 - 18292668269275/79452970167808*a^23 + 50121020601129/79452970167808*a^22 + 321835973082375/79452970167808*a^21 - 110911217948625/9931621270976*a^20 - 1599542507234555/39726485083904*a^19 + 2226217045030279/19863242541952*a^18 + 308331459600777/1241452658872*a^17 - 27884388317097043/39726485083904*a^16 - 39016746605262753/39726485083904*a^15 + 113030871567434741/39726485083904*a^14 + 196931898509651039/79452970167808*a^13 - 595202661331792445/79452970167808*a^12 - 152065302621618035/39726485083904*a^11 + 496938842088149481/39726485083904*a^10 + 129163065092010613/39726485083904*a^9 - 994706158381173029/79452970167808*a^8 - 87038866711317999/79452970167808*a^7 + 535086573272229569/79452970167808*a^6 - 6076060719759567/39726485083904*a^5 - 122833544450547883/79452970167808*a^4 + 1295673889909525/9931621270976*a^3 + 1966942284510527/39726485083904*a^2 - 160801071803657/79452970167808*a + 4105791357897/79452970167808)*q^6 + (134986310209/39726485083904*a^25 - 225519826069/39726485083904*a^24 - 369877425839/2482905317744*a^23 + 9407163275881/39726485083904*a^22 + 57043913829535/19863242541952*a^21 - 21390306431563/4965810635488*a^20 - 636385462338977/19863242541952*a^19 + 891413207208671/19863242541952*a^18 + 4549950049989865/19863242541952*a^17 - 367128514188453/1241452658872*a^16 - 21811234967951493/19863242541952*a^15 + 3188720575098113/2482905317744*a^14 + 142502138509697805/39726485083904*a^13 - 73744083555671587/19863242541952*a^12 - 157944985051604145/19863242541952*a^11 + 69929455528581719/9931621270976*a^10 + 231857784944446415/19863242541952*a^9 - 333506203840142317/39726485083904*a^8 - 213927999988339131/19863242541952*a^7 + 229261867508367987/39726485083904*a^6 + 223507617872364169/39726485083904*a^5 - 38233185025212671/19863242541952*a^4 - 12957876382463147/9931621270976*a^3 + 4327660884127357/19863242541952*a^2 + 1957652666438971/39726485083904*a - 67557870131361/19863242541952)*q^7 + (a^3 - 4*a)*q^8 + (-221164430577/79452970167808*a^25 + 696566226429/39726485083904*a^24 + 7284297020557/79452970167808*a^23 - 57517955298179/79452970167808*a^22 - 88281865594749/79452970167808*a^21 + 257280009230141/19863242541952*a^20 + 170542620954021/39726485083904*a^19 - 1307152131185953/9931621270976*a^18 + 159882016611509/4965810635488*a^17 + 33216679933976919/39726485083904*a^16 - 18765264858311277/39726485083904*a^15 - 136819520945164933/39726485083904*a^14 + 205867848746380815/79452970167808*a^13 + 732721351234874679/79452970167808*a^12 - 314528371871341331/39726485083904*a^11 - 620852103303315395/39726485083904*a^10 + 564420018681695613/39726485083904*a^9 + 1246293507094846147/79452970167808*a^8 - 1148816961260830863/79452970167808*a^7 - 638954685874027687/79452970167808*a^6 + 297535531144334283/39726485083904*a^5 + 102944372558794205/79452970167808*a^4 - 15481756177578481/9931621270976*a^3 + 7646591525893441/39726485083904*a^2 + 2127384435621311/79452970167808*a - 195726918313523/79452970167808)*q^9 + (-530054516733/79452970167808*a^25 + 841900771827/79452970167808*a^24 + 2884935116375/9931621270976*a^23 - 34784900071547/79452970167808*a^22 - 219698108049113/39726485083904*a^21 + 155345072777175/19863242541952*a^20 + 1202390188240113/19863242541952*a^19 - 3144741264882651/39726485083904*a^18 - 1046412983856089/2482905317744*a^17 + 9931281820696165/19863242541952*a^16 + 38737704807184607/19863242541952*a^15 - 40639173988002783/19863242541952*a^14 - 483727440486049971/79452970167808*a^13 + 13540866803238179/2482905317744*a^12 + 506568320111464567/39726485083904*a^11 - 92189336445476533/9931621270976*a^10 - 694024909310277199/39726485083904*a^9 + 764190458508054093/79452970167808*a^8 + 147621756192638349/9931621270976*a^7 - 442382467753961165/79452970167808*a^6 - 563122731617868259/79452970167808*a^5 + 15399964321329977/9931621270976*a^4 + 58984409389220633/39726485083904*a^3 - 5771199825873007/39726485083904*a^2 - 3161540828959101/79452970167808*a + 14875983885045/9931621270976)*q^10 + (-654486464095/79452970167808*a^25 + 2148325256257/79452970167808*a^24 + 6496572109073/19863242541952*a^23 - 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6400279101052553/19863242541952*a^2 - 2850469864041633/39726485083904*a + 115108280104505/19863242541952)*q^28 + (-60026660177/9931621270976*a^25 + 195185724023/19863242541952*a^24 + 2645015587525/9931621270976*a^23 - 4100299989867/9931621270976*a^22 - 102218739882291/19863242541952*a^21 + 149494886919161/19863242541952*a^20 + 1139785003632797/19863242541952*a^19 - 1550720457923985/19863242541952*a^18 - 8122815303868847/19863242541952*a^17 + 10087885593124871/19863242541952*a^16 + 38726604550186743/19863242541952*a^15 - 42762289611061755/19863242541952*a^14 - 125690745958903673/19863242541952*a^13 + 59410327638308253/9931621270976*a^12 + 138592864541552737/9931621270976*a^11 - 52986541146594091/4965810635488*a^10 - 50861950366590195/2482905317744*a^9 + 57472819695779053/4965810635488*a^8 + 379194665128353561/19863242541952*a^7 - 135207294693684525/19863242541952*a^6 - 101223698195912811/9931621270976*a^5 + 32492317370425887/19863242541952*a^4 + 47690299403153447/19863242541952*a^3 - 472725788093605/19863242541952*a^2 - 1395370868154421/19863242541952*a + 8194587867063/4965810635488)*q^29 + (-48509805481/9931621270976*a^25 + 71635849595/9931621270976*a^24 + 4179751538411/19863242541952*a^23 - 2937916651783/9931621270976*a^22 - 39035175347171/9931621270976*a^21 + 103279525715567/19863242541952*a^20 + 829051315003057/19863242541952*a^19 - 1016548389225431/19863242541952*a^18 - 5515054169271401/19863242541952*a^17 + 6139835889500935/19863242541952*a^16 + 23865486731901155/19863242541952*a^15 - 23425047859307729/19863242541952*a^14 - 67516218081122965/19863242541952*a^13 + 55868394773285175/19863242541952*a^12 + 30542662126932665/4965810635488*a^11 - 39511513728305957/9931621270976*a^10 - 67017980542053387/9931621270976*a^9 + 29213180619438783/9931621270976*a^8 + 20075989201332083/4965810635488*a^7 - 16163473318673087/19863242541952*a^6 - 21009859293568831/19863242541952*a^5 + 37179998267311/4965810635488*a^4 + 971697471834417/19863242541952*a^3 - 158499537241473/19863242541952*a^2 + 132100965150155/19863242541952*a - 3561406036957/19863242541952)*q^30 + (-688413474255/79452970167808*a^25 + 1246190459547/79452970167808*a^24 + 15042415075061/39726485083904*a^23 - 52198936956765/79452970167808*a^22 - 144102623923179/19863242541952*a^21 + 237326972786893/19863242541952*a^20 + 1592960066321727/19863242541952*a^19 - 4915898065069579/39726485083904*a^18 - 11253653663565721/19863242541952*a^17 + 3995117108017761/4965810635488*a^16 + 53183500078955927/19863242541952*a^15 - 33890688961130807/9931621270976*a^14 - 684226775042464625/79452970167808*a^13 + 377402781788403877/39726485083904*a^12 + 746907424682649489/39726485083904*a^11 - 337701670513548349/19863242541952*a^10 - 1082347965820212017/39726485083904*a^9 + 1471634963057707587/79452970167808*a^8 + 989353429377570243/39726485083904*a^7 - 869086089696285367/79452970167808*a^6 - 1023515656467856259/79452970167808*a^5 + 103603087030085811/39726485083904*a^4 + 113808354060710219/39726485083904*a^3 + 106985458250667/39726485083904*a^2 - 4414409494712907/79452970167808*a - 294631617940265/39726485083904)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (160834774179/19863242541952*a^25 - 899361697011/79452970167808*a^24 - 28716394928695/79452970167808*a^23 + 9365576957203/19863242541952*a^22 + 563520211064047/79452970167808*a^21 - 338783066253887/39726485083904*a^20 - 1599645928478159/19863242541952*a^19 + 1745754426347129/19863242541952*a^18 + 23277426028335915/39726485083904*a^17 - 1413795747031997/2482905317744*a^16 - 56753376251053697/19863242541952*a^15 + 47931621078601533/19863242541952*a^14 + 94190457018920185/9931621270976*a^13 - 535643702978447201/79452970167808*a^12 - 52907707614933275/2482905317744*a^11 + 484204821712806737/39726485083904*a^10 + 156682711754967081/4965810635488*a^9 - 537982147517070327/39726485083904*a^8 - 2313734941339610113/79452970167808*a^7 + 164186178104931397/19863242541952*a^6 + 1193528544223130445/79452970167808*a^5 - 166709307834638041/79452970167808*a^4 - 33418734457176325/9931621270976*a^3 + 1522154329024531/39726485083904*a^2 + 3438381984469445/39726485083904*a + 348887621188665/79452970167808)*q^33 + (484966299413/79452970167808*a^25 - 1279964441993/79452970167808*a^24 - 9866143355431/39726485083904*a^23 + 52878451213935/79452970167808*a^22 + 86136682888843/19863242541952*a^21 - 236036769151841/19863242541952*a^20 - 842032944579449/19863242541952*a^19 + 4772369184566245/39726485083904*a^18 + 5031970599000925/19863242541952*a^17 - 7515236360916809/9931621270976*a^16 - 18754290891317773/19863242541952*a^15 + 477811921490898/155181582359*a^14 + 168080910978398787/79452970167808*a^13 - 322378455188200163/39726485083904*a^12 - 96633822917629931/39726485083904*a^11 + 268145250620684133/19863242541952*a^10 + 12220325885606491/39726485083904*a^9 - 1059295521621332425/79452970167808*a^8 + 95056222593025503/39726485083904*a^7 + 549049035082757461/79452970167808*a^6 - 183461945544914815/79452970167808*a^5 - 55621828051287105/39726485083904*a^4 + 27477135998036799/39726485083904*a^3 - 573473988572753/39726485083904*a^2 - 1638623386956847/79452970167808*a + 32661894960755/39726485083904)*q^34 + (-136207800655/39726485083904*a^25 - 373855140151/79452970167808*a^24 + 14523146519097/79452970167808*a^23 + 7185608896501/39726485083904*a^22 - 336163602638779/79452970167808*a^21 - 456188618492/155181582359*a^20 + 2226797393940275/39726485083904*a^19 + 1036246522686861/39726485083904*a^18 - 4677919930250999/9931621270976*a^17 - 5360350263420963/39726485083904*a^16 + 104299222521688325/39726485083904*a^15 + 15492897942991169/39726485083904*a^14 - 195698123458020345/19863242541952*a^13 - 35596659482956365/79452970167808*a^12 + 245470135477151297/9931621270976*a^11 - 25579108656884959/39726485083904*a^10 - 799717981261542125/19863242541952*a^9 + 13373785082653909/4965810635488*a^8 + 3189706313236765405/79452970167808*a^7 - 60647070559277293/19863242541952*a^6 - 1740880291558610385/79452970167808*a^5 + 93973985817708281/79452970167808*a^4 + 203630793254307353/39726485083904*a^3 - 1906188433383701/19863242541952*a^2 - 6555499116353571/39726485083904*a + 327907117005249/79452970167808)*q^35 + (847801711435/79452970167808*a^25 - 1261148172493/39726485083904*a^24 - 34219617338963/79452970167808*a^23 + 105096232919889/79452970167808*a^22 + 591027208600539/79452970167808*a^21 - 473502441370203/19863242541952*a^20 - 2845275772906355/39726485083904*a^19 + 604479475282139/2482905317744*a^18 + 2079178886526035/4965810635488*a^17 - 61611021681189577/39726485083904*a^16 - 59910788213692485/39726485083904*a^15 + 253846805992821875/39726485083904*a^14 + 252589455653800211/79452970167808*a^13 - 1356574568030713129/79452970167808*a^12 - 124202016576580847/39726485083904*a^11 + 1144979004565748589/39726485083904*a^10 - 28589859511074903/39726485083904*a^9 - 2291226025578232377/79452970167808*a^8 + 355220100693447249/79452970167808*a^7 + 1185628650927529861/79452970167808*a^6 - 134291112823269571/39726485083904*a^5 - 214647965279947571/79452970167808*a^4 + 3924008762392161/4965810635488*a^3 - 8296256581373211/39726485083904*a^2 + 246808957973003/79452970167808*a + 228744303695725/79452970167808)*q^36 + (157719948323/39726485083904*a^25 - 47317100369/2482905317744*a^24 - 5763048527635/39726485083904*a^23 + 31492003110789/39726485083904*a^22 + 85282564175321/39726485083904*a^21 - 283551167781677/19863242541952*a^20 - 77720042640047/4965810635488*a^19 + 2896255290649451/19863242541952*a^18 + 900673749513715/19863242541952*a^17 - 9233579669196231/9931621270976*a^16 + 650539995734539/4965810635488*a^15 + 19050582854149131/4965810635488*a^14 - 64479973549777735/39726485083904*a^13 - 407880779948765293/39726485083904*a^12 + 123467744433484091/19863242541952*a^11 + 344523452206298341/19863242541952*a^10 - 249097437093544875/19863242541952*a^9 - 688233831476651349/39726485083904*a^8 + 549260326664870779/39726485083904*a^7 + 353676940443156771/39726485083904*a^6 - 151826798932209995/19863242541952*a^5 - 63331315038364461/39726485083904*a^4 + 32790523469740769/19863242541952*a^3 - 128377822607601/1241452658872*a^2 - 145177269453103/39726485083904*a - 193423338487051/39726485083904)*q^37 + O(q^38)
*]> ;  // time = 16.42 seconds




J[462] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 462, 462, 462, 462, 462, 462, 462, 462, 231, 231, 231, 231, 231, 154, 154, 154, 154, 77, 77, 77, 77, 66, 66, 66, 42, 33, 21, 14, 11 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 4, 6, 6, 2, 2, 2, 4, 4, 4, 4, 8, 2, 2, 2, 2, 4, 4, 4, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 25, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 0, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 25, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 9, 1, 1, 9, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 49, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 49, 9, 1, 9, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 9, 1, 1, 81, 1, 1, 1, 1, 1, 1, 3, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 625, 3, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 625, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 0, 1, 1, 81, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 9, 1, 1, 1, 1, 25, 1, 81, 1, 1, 1, 1, 25, 1, 81, 1, 1, 0 ], ap_traces := [
[ -1, -1, 0, -1, -1, -2, -4, 6, -4, -10, 6, -6 ],
[ -1, -1, 2, -1, 1, 2, 6, -8, 4, 2, 8, 6 ],
[ -1, -1, -2, 1, 1, 2, -6, -4, -4, 2, -4, -2 ],
[ -1, 1, 0, -1, -1, 6, 4, 6, -4, 6, -2, 10 ],
[ 1, -1, -4, 1, -1, -6, -4, -2, -8, -6, 6, -6 ],
[ 1, 1, 2, -1, 1, -2, -2, 0, 0, -2, 4, -2 ],
[ 1, 1, 0, 1, -1, 2, 0, 2, 0, -6, 2, 2 ],
[ -2, 2, 0, 2, 2, 4, 0, 4, 0, -12, 4, 4 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 12
], atkin_lehners := [
[ 1, 1, 1, 1 ],
[ 1, 1, 1, -1 ],
[ 1, 1, -1, -1 ],
[ 1, -1, 1, 1 ],
[ -1, 1, -1, 1 ],
[ -1, -1, 1, -1 ],
[ -1, -1, -1, 1 ],
[ 1, -1, -1, -1 ]
], component_group_orders := [
[ 1, 1, 1, 1 ],
[ 5, 3, 1, 1 ],
[ 1, 1, 1, 1 ],
[ 13, 1, 5, 1 ],
[ 7, 1, 3, 1 ],
[ 1, 1, 3, 1 ],
[ 3, 3, 1, 1 ],
[ 11, 3, 1, 3 ]
], tamagawa_numbers := [
[ 1, 1, 1, 1 ],
[ 1, 1, 1, 1 ],
[ 1, 1, 1, 1 ],
[ 1, 1, 1, 1 ],
[ 7, 1, 3, 1 ],
[ 1, 1, 1, 1 ],
[ 3, 3, 1, 1 ],
[ 1, 3, 1, 3 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 3, 3 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 0, 1, 0, 1, 1, 1 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1, 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1, 0, 1, 1/9, 1/9 ], eigenvalues := [*
[ -1, -1, 0, -1, -1, -2, -4, 6, -4, -10, 6, -6 ],
[ -1, -1, 2, -1, 1, 2, 6, -8, 4, 2, 8, 6 ],
[ -1, -1, -2, 1, 1, 2, -6, -4, -4, 2, -4, -2 ],
[ -1, 1, 0, -1, -1, 6, 4, 6, -4, 6, -2, 10 ],
[ 1, -1, -4, 1, -1, -6, -4, -2, -8, -6, 6, -6 ],
[ 1, 1, 2, -1, 1, -2, -2, 0, 0, -2, 4, -2 ],
[ 1, 1, 0, 1, -1, 2, 0, 2, 0, -6, 2, 2 ],
[
-1,
1,
a,
1,
1,
2,
-a,
-a + 2,
-2*a,
-6,
-a + 2,
2*a + 2
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + q^6 - q^7 - q^8 + q^9 - q^11 - q^12 - 2*q^13 + q^14 + q^16 - 4*q^17 - q^18 + 6*q^19 + q^21 + q^22 - 4*q^23 + q^24 - 5*q^25 + 2*q^26 - q^27 - q^28 - 10*q^29 + 6*q^31 - q^32 + q^33 + 4*q^34 + q^36 - 6*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + 2*q^5 + q^6 - q^7 - q^8 + q^9 - 2*q^10 + q^11 - q^12 + 2*q^13 + q^14 - 2*q^15 + q^16 + 6*q^17 - q^18 - 8*q^19 + 2*q^20 + q^21 - q^22 + 4*q^23 + q^24 - q^25 - 2*q^26 - q^27 - q^28 + 2*q^29 + 2*q^30 + 8*q^31 - q^32 - q^33 - 6*q^34 - 2*q^35 + q^36 + 6*q^37 + O(q^38),
q - q^2 - q^3 + q^4 - 2*q^5 + q^6 + q^7 - q^8 + q^9 + 2*q^10 + q^11 - q^12 + 2*q^13 - q^14 + 2*q^15 + q^16 - 6*q^17 - q^18 - 4*q^19 - 2*q^20 - q^21 - q^22 - 4*q^23 + q^24 - q^25 - 2*q^26 - q^27 + q^28 + 2*q^29 - 2*q^30 - 4*q^31 - q^32 - q^33 + 6*q^34 - 2*q^35 + q^36 - 2*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - q^6 - q^7 - q^8 + q^9 - q^11 + q^12 + 6*q^13 + q^14 + q^16 + 4*q^17 - q^18 + 6*q^19 - q^21 + q^22 - 4*q^23 - q^24 - 5*q^25 - 6*q^26 + q^27 - q^28 + 6*q^29 - 2*q^31 - q^32 - q^33 - 4*q^34 + q^36 + 10*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 4*q^5 - q^6 + q^7 + q^8 + q^9 - 4*q^10 - q^11 - q^12 - 6*q^13 + q^14 + 4*q^15 + q^16 - 4*q^17 + q^18 - 2*q^19 - 4*q^20 - q^21 - q^22 - 8*q^23 - q^24 + 11*q^25 - 6*q^26 - q^27 + q^28 - 6*q^29 + 4*q^30 + 6*q^31 + q^32 + q^33 - 4*q^34 - 4*q^35 + q^36 - 6*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + 2*q^5 + q^6 - q^7 + q^8 + q^9 + 2*q^10 + q^11 + q^12 - 2*q^13 - q^14 + 2*q^15 + q^16 - 2*q^17 + q^18 + 2*q^20 - q^21 + q^22 + q^24 - q^25 - 2*q^26 + q^27 - q^28 - 2*q^29 + 2*q^30 + 4*q^31 + q^32 + q^33 - 2*q^34 - 2*q^35 + q^36 - 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^6 + q^7 + q^8 + q^9 - q^11 + q^12 + 2*q^13 + q^14 + q^16 + q^18 + 2*q^19 + q^21 - q^22 + q^24 - 5*q^25 + 2*q^26 + q^27 + q^28 - 6*q^29 + 2*q^31 + q^32 - q^33 + q^36 + 2*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + a*q^5 - q^6 + q^7 - q^8 + q^9 - a*q^10 + q^11 + q^12 + 2*q^13 - q^14 + a*q^15 + q^16 - a*q^17 - q^18 + (-a + 2)*q^19 + a*q^20 + q^21 - q^22 - 2*a*q^23 - q^24 + 7*q^25 - 2*q^26 + q^27 + q^28 - 6*q^29 - a*q^30 + (-a + 2)*q^31 - q^32 + q^33 + a*q^34 + a*q^35 + q^36 + (2*a + 2)*q^37 + O(q^38)
*]> ;  // time = 817.11 seconds




J[463] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 463, 463 ], new_dimensions := [ 16, 22 ], dimensions := [ 16, 22 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -9, -6, -16, -10, -7, -17, -46, -7, -16, -10, 4, 1 ],
[ 8, 4, 14, 2, 3, 13, 56, 3, 0, 8, -4, -1 ]
], hecke_fields := [
x^16 + 9*x^15 + 17*x^14 - 70*x^13 - 282*x^12 + 7*x^11 + 1223*x^10 + 1073*x^9 - 2045*x^8 - 2946*x^7 + 1137*x^6 + 2847*x^5 + 88*x^4 - 954*x^3 - 47*x^2 + 118*x - 9,
x^22 - 8*x^21 - x^20 + 161*x^19 - 281*x^18 - 1216*x^17 + 3523*x^16 + 3859*x^15 - 19383*x^14 - 1030*x^13 + 56835*x^12 - 26406*x^11 - 90387*x^10 + 71356*x^9 + 71796*x^8 - 76057*x^7 - 22452*x^6 + 32959*x^5 + 1404*x^4 - 4772*x^3 - 174*x^2 + 237*x + 25
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 77 ]
], tamagawa_numbers := [
[ 1 ],
[ 77 ]
], torsion_upper_bounds := [ 1, 77 ], torsion_lower_bounds := [ 1, 77 ], l_ratios := [ 0, 1/77 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
16567/27157*a^15 + 123555/27157*a^14 + 7867/2089*a^13 - 1241603/27157*a^12 - 2734229/27157*a^11 + 3506452/27157*a^10 + 13535438/27157*a^9 - 203986/27157*a^8 - 2042287/2089*a^7 - 10979775/27157*a^6 + 21686537/27157*a^5 + 12171527/27157*a^4 - 6229152/27157*a^3 - 202430/2089*a^2 + 913821/27157*a - 7771/27157,
6394/2089*a^15 + 42479/2089*a^14 + 6706/2089*a^13 - 475877/2089*a^12 - 683687/2089*a^11 + 1793911/2089*a^10 + 3791707/2089*a^9 - 2575474/2089*a^8 - 8085535/2089*a^7 + 839943/2089*a^6 + 7462280/2089*a^5 + 668947/2089*a^4 - 2727902/2089*a^3 - 128487/2089*a^2 + 371447/2089*a - 33144/2089,
-100601/27157*a^15 - 682759/27157*a^14 - 15891/2089*a^13 + 7436061/27157*a^12 + 11817341/27157*a^11 - 26290788/27157*a^10 - 63030099/27157*a^9 + 30652400/27157*a^8 + 9949387/2089*a^7 + 5968668/27157*a^6 - 111675910/27157*a^5 - 24976422/27157*a^4 + 35430488/27157*a^3 + 363111/2089*a^2 - 4565284/27157*a + 330669/27157,
51912/27157*a^15 + 357832/27157*a^14 + 12242/2089*a^13 - 3738178/27157*a^12 - 6545388/27157*a^11 + 11919997/27157*a^10 + 33076029/27157*a^9 - 8494259/27157*a^8 - 4846435/2089*a^7 - 15977128/27157*a^6 + 46393421/27157*a^5 + 21152721/27157*a^4 - 8688081/27157*a^3 - 231023/2089*a^2 + 593608/27157*a - 175870/27157,
-178593/27157*a^15 - 1226292/27157*a^14 - 35551/2089*a^13 + 13173181/27157*a^12 + 21987011/27157*a^11 - 45123967/27157*a^10 - 115304471/27157*a^9 + 46716958/27157*a^8 + 17954689/2089*a^7 + 24575881/27157*a^6 - 197951075/27157*a^5 - 53985991/27157*a^4 + 60659504/27157*a^3 + 783143/2089*a^2 - 7530115/27157*a + 452346/27157,
-101253/27157*a^15 - 664997/27157*a^14 - 3438/2089*a^13 + 7617746/27157*a^12 + 10288033/27157*a^11 - 30017111/27157*a^10 - 59206352/27157*a^9 + 48027286/27157*a^8 + 10113851/2089*a^7 - 25919185/27157*a^6 - 129162684/27157*a^5 - 2426140/27157*a^4 + 52168763/27157*a^3 + 83680/2089*a^2 - 7273051/27157*a + 539102/27157,
42335/27157*a^15 + 263275/27157*a^14 - 5836/2089*a^13 - 3182760/27157*a^12 - 3240864/27157*a^11 + 13851296/27157*a^10 + 20711147/27157*a^9 - 27147067/27157*a^8 - 3755094/2089*a^7 + 24467270/27157*a^6 + 50768076/27157*a^5 - 8605659/27157*a^4 - 21474637/27157*a^3 + 45181/2089*a^2 + 2488625/27157*a - 56265/27157,
-27166/27157*a^15 - 205265/27157*a^14 - 15172/2089*a^13 + 1969766/27157*a^12 + 4737696/27157*a^11 - 4735478/27157*a^10 - 22601446/27157*a^9 - 4193168/27157*a^8 + 3246641/2089*a^7 + 26574256/27157*a^6 - 31409704/27157*a^5 - 27189684/27157*a^4 + 6724780/27157*a^3 + 513071/2089*a^2 - 621211/27157*a - 234580/27157,
-13163/27157*a^15 - 51180/27157*a^14 + 20123/2089*a^13 + 1242380/27157*a^12 - 1250376/27157*a^11 - 9968287/27157*a^10 - 1178686/27157*a^9 + 34924343/27157*a^8 + 1573915/2089*a^7 - 55789717/27157*a^6 - 45635702/27157*a^5 + 36586703/27157*a^4 + 34940154/27157*a^3 - 482514/2089*a^2 - 6086245/27157*a + 654954/27157,
86868/27157*a^15 + 603456/27157*a^14 + 22134/2089*a^13 - 6300668/27157*a^12 - 11251811/27157*a^11 + 20042259/27157*a^10 + 56992762/27157*a^9 - 13822675/27157*a^8 - 8466365/2089*a^7 - 29252213/27157*a^6 + 84620802/27157*a^5 + 40772913/27157*a^4 - 19482627/27157*a^3 - 704864/2089*a^2 + 1971317/27157*a + 141384/27157,
270507/27157*a^15 + 1868887/27157*a^14 + 56319/2089*a^13 - 20213611/27157*a^12 - 34095586/27157*a^11 + 70256093/27157*a^10 + 181118989/27157*a^9 - 76528966/27157*a^8 - 28979196/2089*a^7 - 30147921/27157*a^6 + 338072718/27157*a^5 + 79128431/27157*a^4 - 118297503/27157*a^3 - 1178379/2089*a^2 + 16602237/27157*a - 1442668/27157
],
[
a,
88081079557/2192028849037*a^21 - 14422074891/115369939423*a^20 - 2628417572230/2192028849037*a^19 + 8497220344229/2192028849037*a^18 + 32189971934528/2192028849037*a^17 - 109880752912386/2192028849037*a^16 - 208266773801349/2192028849037*a^15 + 771496154587641/2192028849037*a^14 + 755393757720071/2192028849037*a^13 - 3202984347030693/2192028849037*a^12 - 1452100823408494/2192028849037*a^11 + 8005041723954874/2192028849037*a^10 + 999239360848340/2192028849037*a^9 - 11686683734002023/2192028849037*a^8 + 993848469210485/2192028849037*a^7 + 9112869445104238/2192028849037*a^6 - 1892870464522139/2192028849037*a^5 - 162616003952727/115369939423*a^4 + 771221864284476/2192028849037*a^3 + 13552403923130/115369939423*a^2 - 57299624398580/2192028849037*a - 4959079589235/2192028849037,
-97598814399/2192028849037*a^21 - 12060154791/115369939423*a^20 + 6158276837549/2192028849037*a^19 - 2974529732687/2192028849037*a^18 - 107461690992292/2192028849037*a^17 + 138090235403933/2192028849037*a^16 + 872349945365154/2192028849037*a^15 - 1503806189886096/2192028849037*a^14 - 3795322820045360/2192028849037*a^13 + 7940622433385189/2192028849037*a^12 + 8965478486377590/2192028849037*a^11 - 23099866942251974/2192028849037*a^10 - 10123163282652780/2192028849037*a^9 + 37400061934068795/2192028849037*a^8 + 1939259022320828/2192028849037*a^7 - 31536458444330130/2192028849037*a^6 + 5092393651938517/2192028849037*a^5 + 616389647891872/115369939423*a^4 - 2812510092495637/2192028849037*a^3 - 71953936327624/115369939423*a^2 + 225193380521624/2192028849037*a + 56904893671196/2192028849037,
-222625289944/2192028849037*a^21 + 104367160850/115369939423*a^20 - 901430985342/2192028849037*a^19 - 38899721488001/2192028849037*a^18 + 88315032444433/2192028849037*a^17 + 278295627293925/2192028849037*a^16 - 1026555612083387/2192028849037*a^15 - 739309575040831/2192028849037*a^14 + 5523724445972888/2192028849037*a^13 - 823645537379160/2192028849037*a^12 - 16093317475926696/2192028849037*a^11 + 9581679579189143/2192028849037*a^10 + 25700475951367957/2192028849037*a^9 - 22473039772819819/2192028849037*a^8 - 20833485990737514/2192028849037*a^7 + 22689966688318300/2192028849037*a^6 + 6991023755631008/2192028849037*a^5 - 490147675928233/115369939423*a^4 - 617237644097082/2192028849037*a^3 + 58642933476640/115369939423*a^2 + 21782425702458/2192028849037*a - 26555072225671/2192028849037,
-377503382094/2192028849037*a^21 + 161920021237/115369939423*a^20 + 264598916261/2192028849037*a^19 - 62513375389721/2192028849037*a^18 + 109084437083606/2192028849037*a^17 + 482375572081841/2192028849037*a^16 - 1363387321551088/2192028849037*a^15 - 1635812937585184/2192028849037*a^14 + 7518281570385921/2192028849037*a^13 + 1244080279270289/2192028849037*a^12 - 22160897233422553/2192028849037*a^11 + 7367200619029801/2192028849037*a^10 + 35571494323123671/2192028849037*a^9 - 21980826006363710/2192028849037*a^8 - 28767100539855269/2192028849037*a^7 + 23077657560880722/2192028849037*a^6 + 9419865419517220/2192028849037*a^5 - 470749222297896/115369939423*a^4 - 713138500460331/2192028849037*a^3 + 42194862635974/115369939423*a^2 + 44460554853556/2192028849037*a - 5346927633707/2192028849037,
-185526721264/2192028849037*a^21 + 46321696138/115369939423*a^20 + 3478976124052/2192028849037*a^19 - 20528968497307/2192028849037*a^18 - 23280988978840/2192028849037*a^17 + 198754862672365/2192028849037*a^16 + 53710403893317/2192028849037*a^15 - 1039476970694517/2192028849037*a^14 + 90359649147676/2192028849037*a^13 + 3199445832292557/2192028849037*a^12 - 704435592600010/2192028849037*a^11 - 5940627969286164/2192028849037*a^10 + 1288720310058817/2192028849037*a^9 + 6649399195956646/2192028849037*a^8 - 761357837048641/2192028849037*a^7 - 4500790243338669/2192028849037*a^6 - 143120577976740/2192028849037*a^5 + 96904157671244/115369939423*a^4 + 161930939692913/2192028849037*a^3 - 19386056764491/115369939423*a^2 + 4468507737272/2192028849037*a + 18152844079943/2192028849037,
942220397459/2192028849037*a^21 - 342562738532/115369939423*a^20 - 7043861092395/2192028849037*a^19 + 138022374248054/2192028849037*a^18 - 126980759363803/2192028849037*a^17 - 1151457961648849/2192028849037*a^16 + 2050054929501081/2192028849037*a^15 + 4675777484018986/2192028849037*a^14 - 12119511022402491/2192028849037*a^13 - 8579410915247792/2192028849037*a^12 + 36881899270311071/2192028849037*a^11 + 890728920926339/2192028849037*a^10 - 60324016294552892/2192028849037*a^9 + 20852330365885051/2192028849037*a^8 + 49513176455522328/2192028849037*a^7 - 28051921511621284/2192028849037*a^6 - 16518783274273842/2192028849037*a^5 + 617454070112045/115369939423*a^4 + 1277918674900624/2192028849037*a^3 - 57403794095820/115369939423*a^2 - 50655474734857/2192028849037*a + 22010586320984/2192028849037,
-245215183679/2192028849037*a^21 + 83799520203/115369939423*a^20 + 2804841300515/2192028849037*a^19 - 36519583048610/2192028849037*a^18 + 13499008227907/2192028849037*a^17 + 344612867411533/2192028849037*a^16 - 384765592590090/2192028849037*a^15 - 1733869741312447/2192028849037*a^14 + 2662063981670221/2192028849037*a^13 + 5032955247769979/2192028849037*a^12 - 9280455509774705/2192028849037*a^11 - 8530735446274825/2192028849037*a^10 + 18098528400942363/2192028849037*a^9 + 8236168572389438/2192028849037*a^8 - 19715049711377152/2192028849037*a^7 - 4407609512093720/2192028849037*a^6 + 11294502689358286/2192028849037*a^5 + 73240136951301/115369939423*a^4 - 2961244366479204/2192028849037*a^3 - 15390941484210/115369939423*a^2 + 224637856808414/2192028849037*a + 35653309161728/2192028849037,
-53290737426/115369939423*a^21 + 411261981150/115369939423*a^20 + 138399388704/115369939423*a^19 - 8350147644968/115369939423*a^18 + 12986051755585/115369939423*a^17 + 64275521772287/115369939423*a^16 - 168556964363505/115369939423*a^15 - 215954234181577/115369939423*a^14 + 933829177454324/115369939423*a^13 + 147450488909587/115369939423*a^12 - 2732056584700595/115369939423*a^11 + 1059041688073627/115369939423*a^10 + 4295608397237125/115369939423*a^9 - 3104195641223828/115369939423*a^8 - 3303874120518632/115369939423*a^7 + 3286395600446275/115369939423*a^6 + 911754781231712/115369939423*a^5 - 1318214535174254/115369939423*a^4 + 8053077740243/115369939423*a^3 + 139955155524479/115369939423*a^2 - 4013827021570/115369939423*a - 3550742613354/115369939423,
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52800808808/115369939423*a^19 - 8166932054711/115369939423*a^18 + 16068814650029/115369939423*a^17 + 60298719110910/115369939423*a^16 - 193790598022556/115369939423*a^15 - 179092648594047/115369939423*a^14 + 1051630929569580/115369939423*a^13 - 35079903720469/115369939423*a^12 - 3057216031847922/115369939423*a^11 + 1574013412010999/115369939423*a^10 + 4819621781981300/115369939423*a^9 - 3925395004678685/115369939423*a^8 - 3771634980292799/115369939423*a^7 + 3973778053445855/115369939423*a^6 + 1126798027439655/115369939423*a^5 - 1569822501187991/115369939423*a^4 - 41411946093582/115369939423*a^3 + 163702288557914/115369939423*a^2 - 758555721841/115369939423*a - 3026706639310/115369939423)*q^27 + (936984197386/2192028849037*a^21 - 359001483301/115369939423*a^20 - 4957583651425/2192028849037*a^19 + 142137337682061/2192028849037*a^18 - 173276716796373/2192028849037*a^17 - 1148343309769539/2192028849037*a^16 + 2482273025623428/2192028849037*a^15 + 4340526500539216/2192028849037*a^14 - 14279825065209292/2192028849037*a^13 - 6128850071861131/2192028849037*a^12 + 43097997309659809/2192028849037*a^11 - 7494948612070615/2192028849037*a^10 - 70662870525340892/2192028849037*a^9 + 36202928163897122/2192028849037*a^8 + 59021129211717434/2192028849037*a^7 - 42820517953910435/2192028849037*a^6 - 20943571632811204/2192028849037*a^5 + 968099390080666/115369939423*a^4 + 2181339584492022/2192028849037*a^3 - 114056890550169/115369939423*a^2 - 85866994730042/2192028849037*a + 48060801036392/2192028849037)*q^28 + (-1282403682668/2192028849037*a^21 + 476563615009/115369939423*a^20 + 8541900644959/2192028849037*a^19 - 191313765924786/2192028849037*a^18 + 198253458733597/2192028849037*a^17 + 1584519121394344/2192028849037*a^16 - 3048642493860153/2192028849037*a^15 - 6326627879602590/2192028849037*a^14 + 17924946488940473/2192028849037*a^13 + 10956411234513852/2192028849037*a^12 - 54897141004158222/2192028849037*a^11 + 1871485407205770/2192028849037*a^10 + 91499473277160316/2192028849037*a^9 - 34762876427624861/2192028849037*a^8 - 78626438451677320/2192028849037*a^7 + 44934050115961093/2192028849037*a^6 + 30017450973688511/2192028849037*a^5 - 1015824662544047/115369939423*a^4 - 4118350372717030/2192028849037*a^3 + 107715471126882/115369939423*a^2 + 254550401122197/2192028849037*a - 21869935989285/2192028849037)*q^29 + (-1235913868976/2192028849037*a^21 + 381847890594/115369939423*a^20 + 16272475564197/2192028849037*a^19 - 161454588193027/2192028849037*a^18 + 6242469664698/2192028849037*a^17 + 1457566599265051/2192028849037*a^16 - 1194934649092208/2192028849037*a^15 - 6841728611952503/2192028849037*a^14 + 8561060760781249/2192028849037*a^13 + 17614845146870301/2192028849037*a^12 - 28091792343069442/2192028849037*a^11 - 23499835602119927/2192028849037*a^10 + 48044555233489385/2192028849037*a^9 + 12053734518336283/2192028849037*a^8 - 41081756560193023/2192028849037*a^7 + 2602715787457032/2192028849037*a^6 + 14621177146645083/2192028849037*a^5 - 169869865229238/115369939423*a^4 - 1309648130131276/2192028849037*a^3 + 20643922710961/115369939423*a^2 + 18166032852056/2192028849037*a - 10256353807425/2192028849037)*q^30 + (701994617345/2192028849037*a^21 - 232285219714/115369939423*a^20 - 7378966336936/2192028849037*a^19 + 94944539142470/2192028849037*a^18 - 44899093838930/2192028849037*a^17 - 810972514432872/2192028849037*a^16 + 1047621194046386/2192028849037*a^15 + 3445462613574825/2192028849037*a^14 - 6543591632110941/2192028849037*a^13 - 7138710561651195/2192028849037*a^12 + 19991537071464541/2192028849037*a^11 + 4208454028581150/2192028849037*a^10 - 31704123909679719/2192028849037*a^9 + 8568983962813193/2192028849037*a^8 + 23632472639059946/2192028849037*a^7 - 14457973110325390/2192028849037*a^6 - 5351019357953792/2192028849037*a^5 + 331139690972657/115369939423*a^4 - 748272646595414/2192028849037*a^3 - 30483465398408/115369939423*a^2 + 105080101476212/2192028849037*a + 16646473762773/2192028849037)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (281406248935/2192028849037*a^21 - 57576490476/115369939423*a^20 - 7279146415771/2192028849037*a^19 + 31297605657439/2192028849037*a^18 + 75070191091822/2192028849037*a^17 - 377243802668334/2192028849037*a^16 - 376059360083552/2192028849037*a^15 + 2491124120542925/2192028849037*a^14 + 762791070155886/2192028849037*a^13 - 9804486432522873/2192028849037*a^12 + 1003807391774363/2192028849037*a^11 + 23407021308841045/2192028849037*a^10 - 8683428659573638/2192028849037*a^9 - 32945949747617015/2192028849037*a^8 + 18338416769746510/2192028849037*a^7 + 25221725016171386/2192028849037*a^6 - 17069677889561028/2192028849037*a^5 - 471372036320228/115369939423*a^4 + 6329295442863829/2192028849037*a^3 + 62445314560176/115369939423*a^2 - 571378961275433/2192028849037*a - 78677994647140/2192028849037)*q^33 + (1029071147564/2192028849037*a^21 - 321138983944/115369939423*a^20 - 13675109742845/2192028849037*a^19 + 137783172322176/2192028849037*a^18 - 5717958338705/2192028849037*a^17 - 1269387530746976/2192028849037*a^16 + 1039748970224705/2192028849037*a^15 + 6143546941545306/2192028849037*a^14 - 7608923905865022/2192028849037*a^13 - 16669197019271194/2192028849037*a^12 + 25771000736228693/2192028849037*a^11 + 24840458770573741/2192028849037*a^10 - 46380748315199353/2192028849037*a^9 - 18134479200444036/2192028849037*a^8 + 43610535257917879/2192028849037*a^7 + 4635949089475626/2192028849037*a^6 - 19323014747722326/2192028849037*a^5 - 2366250691148/115369939423*a^4 + 3405603648853768/2192028849037*a^3 + 5962677601211/115369939423*a^2 - 201295647876799/2192028849037*a - 23555509936475/2192028849037)*q^34 + (60502481965/2192028849037*a^21 - 12215698193/115369939423*a^20 - 1961005763313/2192028849037*a^19 + 8591185111285/2192028849037*a^18 + 23197556024997/2192028849037*a^17 - 125587172135968/2192028849037*a^16 - 120380822012085/2192028849037*a^15 + 968065082859278/2192028849037*a^14 + 163723413391846/2192028849037*a^13 - 4354042316155491/2192028849037*a^12 + 1099768529729219/2192028849037*a^11 + 11794376083680718/2192028849037*a^10 - 5771817363355270/2192028849037*a^9 - 19022351719084919/2192028849037*a^8 + 11584529197320249/2192028849037*a^7 + 17375166377363201/2192028849037*a^6 - 10928588229211270/2192028849037*a^5 - 433348378270790/115369939423*a^4 + 4357977387457521/2192028849037*a^3 + 95329482240198/115369939423*a^2 - 506599196566386/2192028849037*a - 131930371474918/2192028849037)*q^35 + (1319632761204/2192028849037*a^21 - 438719797610/115369939423*a^20 - 13633903981152/2192028849037*a^19 + 178519438190589/2192028849037*a^18 - 88041023591913/2192028849037*a^17 - 1514165901806444/2192028849037*a^16 + 1979850784684783/2192028849037*a^15 + 6351508384988856/2192028849037*a^14 - 12178383112764967/2192028849037*a^13 - 12751056723552062/2192028849037*a^12 + 36437560338912619/2192028849037*a^11 + 6001875875384456/2192028849037*a^10 - 55459265182662095/2192028849037*a^9 + 19114015935587602/2192028849037*a^8 + 36764514439294550/2192028849037*a^7 - 29685880610598512/2192028849037*a^6 - 2858766059253433/2192028849037*a^5 + 679344596826249/115369939423*a^4 - 4324141266137504/2192028849037*a^3 - 73465493933699/115369939423*a^2 + 479171484541078/2192028849037*a + 68271352004347/2192028849037)*q^36 + (-568399264883/2192028849037*a^21 + 209784044822/115369939423*a^20 + 3844135559901/2192028849037*a^19 - 83740138281462/2192028849037*a^18 + 85333441398052/2192028849037*a^17 + 687032857031352/2192028849037*a^16 - 1311557836226886/2192028849037*a^15 - 2690969730482398/2192028849037*a^14 + 7631183954716764/2192028849037*a^13 + 4378163194684718/2192028849037*a^12 - 22919532359219667/2192028849037*a^11 + 2013639858079556/2192028849037*a^10 + 36793840319635030/2192028849037*a^9 - 17092372070706707/2192028849037*a^8 - 29015168924051042/2192028849037*a^7 + 21230800204608899/2192028849037*a^6 + 8390386837745160/2192028849037*a^5 - 482493199247130/115369939423*a^4 + 87029526971215/2192028849037*a^3 + 61140785421201/115369939423*a^2 - 111960744819716/2192028849037*a - 51860617410258/2192028849037)*q^37 + O(q^38)
*]> ;  // time = 12.229 seconds




J[465] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 465, 465, 465, 465, 465, 465, 465, 465, 155, 155, 155, 155, 155, 93, 93, 31, 15 ], new_dimensions := [ 1, 1, 2, 2, 3, 3, 3, 4, 1, 1, 1, 4, 4, 2, 3, 2, 1 ], dimensions := [ 1, 1, 2, 2, 3, 3, 3, 4, 2, 2, 2, 8, 8, 4, 6, 8, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 41, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 1, 1, 29, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 29, 59, 1, 1, 1, 1, 1, 3, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 25, 1, 1, 1, 1, 23, 41, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 2401, 1, 1, 1, 1, 1, 1, 1, 1, 29, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 59, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 29, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 25, 2401, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 1, -1, 1, -2, -4, 0, 2, -8, -8, 0, 1, 8 ],
[ -1, 1, 1, -4, -4, 2, -6, -4, 0, -6, -1, 10 ],
[ 0, -2, -2, -6, 4, -6, 4, 4, -8, -2, -2, -10 ],
[ -2, 2, -2, -4, 0, -8, -8, 0, -12, -4, 2, 0 ],
[ 1, -3, -3, 8, 2, 4, 4, -4, 6, -2, 3, 10 ],
[ 3, 3, -3, 2, 2, -6, 4, -8, 14, 16, -3, -8 ],
[ 1, 3, 3, 2, 6, -2, 0, 0, 2, 8, 3, 0 ],
[ 2, -4, 4, 4, 6, 2, -10, 16, 6, 0, -4, 8 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 3,
x^2 + 2*x - 1,
x^3 - x^2 - 5*x + 3,
x^3 - 3*x^2 - x + 5,
x^3 - x^2 - 3*x + 1,
x^4 - 2*x^3 - 6*x^2 + 12*x - 1
], atkin_lehners := [
[ 1, -1, -1 ],
[ -1, -1, 1 ],
[ 1, 1, 1 ],
[ -1, 1, -1 ],
[ 1, 1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ],
[ 1, -1, 1 ]
], component_group_orders := [
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 3, 11, 1 ],
[ 23, 1, 1 ],
[ 123, 1, 1 ],
[ 5, 29, 1 ],
[ 25, 5, 1 ],
[ 29, 59, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 23, 1, 1 ],
[ 1, 1, 1 ],
[ 5, 1, 1 ],
[ 25, 5, 1 ],
[ 1, 59, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 5, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 0, 0, 0, 1, 5, 5, 59 ], analytic_sha_upper_bounds := [ 0, 0, 0, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 0, 1, 1, 1/25, 1 ], eigenvalues := [*
[ 1, -1, 1, -2, -4, 0, 2, -8, -8, 0, 1, 8 ],
[ -1, 1, 1, -4, -4, 2, -6, -4, 0, -6, -1, 10 ],
[
a,
-1,
-1,
-a - 3,
-2*a + 2,
a - 3,
-2*a + 2,
2*a + 2,
2*a - 4,
a - 1,
-1,
-a - 5
],
[
a,
1,
-1,
-a - 3,
2*a + 2,
-a - 5,
-4,
-2*a - 2,
-6,
-3*a - 5,
1,
a + 1
],
[
a,
-1,
-1,
-a + 3,
2*a,
a + 1,
-a^2 + 5,
-2*a^2 + 6,
a^2 - 2*a - 1,
-a^2 - 3*a + 4,
1,
a + 3
],
[
a,
1,
-1,
-2*a^2 + 3*a + 5,
-2*a^2 + 2*a + 6,
-a - 1,
-a^2 + 5,
2*a^2 - 4*a - 6,
a^2 - 2*a + 3,
-a^2 - a + 10,
-1,
2*a^2 - a - 9
],
[
a,
1,
1,
-a + 1,
2,
-2*a^2 + 3*a + 3,
-a^2 - 2*a + 3,
0,
-a^2 + 3,
3*a^2 - a - 4,
1,
4*a^2 - 7*a - 7
],
[
a,
-1,
1,
-a^3 + a^2 + 6*a - 4,
a^3 - a^2 - 7*a + 7,
-2*a^3 + 11*a - 1,
a^3 - 5*a - 2,
4,
-a^3 - 2*a^2 + 7*a + 8,
a^3 - 6*a + 1,
-1,
a^3 - a^2 - 8*a + 8
]
*], q_expansions := [*
q + q^2 - q^3 - q^4 + q^5 - q^6 - 2*q^7 - 3*q^8 + q^9 + q^10 - 4*q^11 + q^12 - 2*q^14 - q^15 - q^16 + 2*q^17 + q^18 - 8*q^19 - q^20 + 2*q^21 - 4*q^22 - 8*q^23 + 3*q^24 + q^25 - q^27 + 2*q^28 - q^30 + q^31 + 5*q^32 + 4*q^33 + 2*q^34 - 2*q^35 - q^36 + 8*q^37 + O(q^38),
q - q^2 + q^3 - q^4 + q^5 - q^6 - 4*q^7 + 3*q^8 + q^9 - q^10 - 4*q^11 - q^12 + 2*q^13 + 4*q^14 + q^15 - q^16 - 6*q^17 - q^18 - 4*q^19 - q^20 - 4*q^21 + 4*q^22 + 3*q^24 + q^25 - 2*q^26 + q^27 + 4*q^28 - 6*q^29 - q^30 - q^31 - 5*q^32 - 4*q^33 + 6*q^34 - 4*q^35 - q^36 + 10*q^37 + O(q^38),
q + a*q^2 - q^3 + q^4 - q^5 - a*q^6 + (-a - 3)*q^7 - a*q^8 + q^9 - a*q^10 + (-2*a + 2)*q^11 - q^12 + (a - 3)*q^13 + (-3*a - 3)*q^14 + q^15 - 5*q^16 + (-2*a + 2)*q^17 + a*q^18 + (2*a + 2)*q^19 - q^20 + (a + 3)*q^21 + (2*a - 6)*q^22 + (2*a - 4)*q^23 + a*q^24 + q^25 + (-3*a + 3)*q^26 - q^27 + (-a - 3)*q^28 + (a - 1)*q^29 + a*q^30 - q^31 - 3*a*q^32 + (2*a - 2)*q^33 + (2*a - 6)*q^34 + (a + 3)*q^35 + q^36 + (-a - 5)*q^37 + O(q^38),
q + a*q^2 + q^3 + (-2*a - 1)*q^4 - q^5 + a*q^6 + (-a - 3)*q^7 + (a - 2)*q^8 + q^9 - a*q^10 + (2*a + 2)*q^11 + (-2*a - 1)*q^12 + (-a - 5)*q^13 + (-a - 1)*q^14 - q^15 + 3*q^16 - 4*q^17 + a*q^18 + (-2*a - 2)*q^19 + (2*a + 1)*q^20 + (-a - 3)*q^21 + (-2*a + 2)*q^22 - 6*q^23 + (a - 2)*q^24 + q^25 + (-3*a - 1)*q^26 + q^27 + (3*a + 5)*q^28 + (-3*a - 5)*q^29 - a*q^30 + q^31 + (a + 4)*q^32 + (2*a + 2)*q^33 - 4*a*q^34 + (a + 3)*q^35 + (-2*a - 1)*q^36 + (a + 1)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 - q^5 - a*q^6 + (-a + 3)*q^7 + (a^2 + a - 3)*q^8 + q^9 - a*q^10 + 2*a*q^11 + (-a^2 + 2)*q^12 + (a + 1)*q^13 + (-a^2 + 3*a)*q^14 + q^15 + (2*a + 1)*q^16 + (-a^2 + 5)*q^17 + a*q^18 + (-2*a^2 + 6)*q^19 + (-a^2 + 2)*q^20 + (a - 3)*q^21 + 2*a^2*q^22 + (a^2 - 2*a - 1)*q^23 + (-a^2 - a + 3)*q^24 + q^25 + (a^2 + a)*q^26 - q^27 + (2*a^2 - 3*a - 3)*q^28 + (-a^2 - 3*a + 4)*q^29 + a*q^30 + q^31 + (-a + 6)*q^32 - 2*a*q^33 + (-a^2 + 3)*q^34 + (a - 3)*q^35 + (a^2 - 2)*q^36 + (a + 3)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 - q^5 + a*q^6 + (-2*a^2 + 3*a + 5)*q^7 + (3*a^2 - 3*a - 5)*q^8 + q^9 - a*q^10 + (-2*a^2 + 2*a + 6)*q^11 + (a^2 - 2)*q^12 + (-a - 1)*q^13 + (-3*a^2 + 3*a + 10)*q^14 - q^15 + (4*a^2 - 2*a - 11)*q^16 + (-a^2 + 5)*q^17 + a*q^18 + (2*a^2 - 4*a - 6)*q^19 + (-a^2 + 2)*q^20 + (-2*a^2 + 3*a + 5)*q^21 + (-4*a^2 + 4*a + 10)*q^22 + (a^2 - 2*a + 3)*q^23 + (3*a^2 - 3*a - 5)*q^24 + q^25 + (-a^2 - a)*q^26 + q^27 + (-2*a^2 + a + 5)*q^28 + (-a^2 - a + 10)*q^29 - a*q^30 - q^31 + (4*a^2 - a - 10)*q^32 + (-2*a^2 + 2*a + 6)*q^33 + (-3*a^2 + 4*a + 5)*q^34 + (2*a^2 - 3*a - 5)*q^35 + (a^2 - 2)*q^36 + (2*a^2 - a - 9)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + q^5 + a*q^6 + (-a + 1)*q^7 + (a^2 - a - 1)*q^8 + q^9 + a*q^10 + 2*q^11 + (a^2 - 2)*q^12 + (-2*a^2 + 3*a + 3)*q^13 + (-a^2 + a)*q^14 + q^15 + (-2*a^2 + 2*a + 3)*q^16 + (-a^2 - 2*a + 3)*q^17 + a*q^18 + (a^2 - 2)*q^20 + (-a + 1)*q^21 + 2*a*q^22 + (-a^2 + 3)*q^23 + (a^2 - a - 1)*q^24 + q^25 + (a^2 - 3*a + 2)*q^26 + q^27 + (-a - 1)*q^28 + (3*a^2 - a - 4)*q^29 + a*q^30 + q^31 + (-2*a^2 - a + 4)*q^32 + 2*q^33 + (-3*a^2 + 1)*q^34 + (-a + 1)*q^35 + (a^2 - 2)*q^36 + (4*a^2 - 7*a - 7)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + q^5 - a*q^6 + (-a^3 + a^2 + 6*a - 4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + a*q^10 + (a^3 - a^2 - 7*a + 7)*q^11 + (-a^2 + 2)*q^12 + (-2*a^3 + 11*a - 1)*q^13 + (-a^3 + 8*a - 1)*q^14 - q^15 + (2*a^3 - 12*a + 5)*q^16 + (a^3 - 5*a - 2)*q^17 + a*q^18 + 4*q^19 + (a^2 - 2)*q^20 + (a^3 - a^2 - 6*a + 4)*q^21 + (a^3 - a^2 - 5*a + 1)*q^22 + (-a^3 - 2*a^2 + 7*a + 8)*q^23 + (-a^3 + 4*a)*q^24 + q^25 + (-4*a^3 - a^2 + 23*a - 2)*q^26 - q^27 + (-a + 7)*q^28 + (a^3 - 6*a + 1)*q^29 - a*q^30 - q^31 + (2*a^3 - 11*a + 2)*q^32 + (-a^3 + a^2 + 7*a - 7)*q^33 + (2*a^3 + a^2 - 14*a + 1)*q^34 + (-a^3 + a^2 + 6*a - 4)*q^35 + (a^2 - 2)*q^36 + (a^3 - a^2 - 8*a + 8)*q^37 + O(q^38)
*]> ;  // time = 184.249 seconds




J[466] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 466, 466, 466, 466, 466, 466, 233, 233, 233 ], new_dimensions := [ 1, 1, 3, 3, 5, 6, 1, 7, 11 ], dimensions := [ 1, 1, 3, 3, 5, 6, 2, 14, 22 ], intersection_graph := [ 0, 1, 5, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 0, 1, 1, 1, 1, 1, 733, 1, 1, 1, 0, 1, 1, 1, 1, 211, 1, 1, 1, 1, 0, 1, 1, 257, 1, 1, 1, 1, 1, 1, 0, 1, 1699, 1, 1, 1, 1, 1, 1, 1, 0, 1, 729, 1, 1, 1, 1, 257, 1699, 1, 0, 1, 1, 1, 733, 211, 1, 1, 729, 1, 0 ], ap_traces := [
[ -1, 2, 0, 0, 2, 2, 6, 0, 8, -2, 0, 2 ],
[ 1, 1, 0, 2, 0, 5, 0, -4, 6, 3, -4, -7 ],
[ -3, -2, 5, 3, 8, -5, -4, 3, 1, 17, 4, -14 ],
[ 3, -4, -7, -1, -10, -7, -8, -3, 1, -5, 4, -4 ],
[ -5, 0, -5, -5, -12, 5, -12, -9, -7, -9, -16, 4 ],
[ 6, 1, 7, -3, 6, 2, 12, 9, -13, 2, -4, 5 ]
], hecke_fields := [
x - 1,
x - 1,
x^3 + 2*x^2 - 3*x - 5,
x^3 + 4*x^2 + 3*x - 1,
x^5 - 8*x^3 + x^2 + 5*x - 1,
x^6 - x^5 - 13*x^4 + 10*x^3 + 43*x^2 - 12*x - 36
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ],
[ 1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 1 ],
[ 733, 1 ],
[ 211, 1 ],
[ 257, 1 ],
[ 22087, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 211, 1 ],
[ 1, 1 ],
[ 22087, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 1, 1, 13 ], torsion_lower_bounds := [ 1, 3, 1, 1, 1, 13 ], l_ratios := [ 1, 1/3, 1, 0, 0, 1699/13 ], analytic_sha_upper_bounds := [ 1, 1, 1, 0, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 0, 0, 1 ], eigenvalues := [*
[ -1, 2, 0, 0, 2, 2, 6, 0, 8, -2, 0, 2 ],
[ 1, 1, 0, 2, 0, 5, 0, -4, 6, 3, -4, -7 ],
[
-1,
a,
a^2 + a - 1,
2*a^2 + a - 5,
-a^2 + 6,
-2*a^2 + 5,
-a - 2,
-a^2 - 2*a + 3,
a^2 - 3*a - 5,
-a + 5,
-a^2 - 4*a + 2,
-a^2 - a - 2
],
[
1,
a,
-a^2 - 3*a - 3,
2*a^2 + 3*a - 3,
-3*a^2 - 8*a - 4,
2*a^2 + 6*a - 1,
-2*a^2 - 3*a,
3*a^2 + 12*a + 5,
-3*a^2 - 7*a + 1,
4*a^2 + 9*a - 3,
-a^2 - 2*a + 2,
a^2 + 5*a + 2
],
[
-1,
a,
a^4 - 8*a^2 + 3,
-7/5*a^4 - 1/5*a^3 + 53/5*a^2 - 3/5*a - 24/5,
-4/5*a^4 + 3/5*a^3 + 31/5*a^2 - 21/5*a - 23/5,
4/5*a^4 + 2/5*a^3 - 26/5*a^2 - 14/5*a + 3/5,
-7/5*a^4 - 6/5*a^3 + 53/5*a^2 + 32/5*a - 34/5,
-4/5*a^4 - 2/5*a^3 + 31/5*a^2 + 4/5*a - 23/5,
13/5*a^4 + 4/5*a^3 - 102/5*a^2 - 18/5*a + 41/5,
11/5*a^4 - 2/5*a^3 - 89/5*a^2 + 24/5*a + 37/5,
-8/5*a^4 - 9/5*a^3 + 57/5*a^2 + 63/5*a - 31/5,
11/5*a^4 + 8/5*a^3 - 94/5*a^2 - 46/5*a + 72/5
],
[
1,
a,
1/4*a^5 - 3/4*a^4 - 11/4*a^3 + 7*a^2 + 19/4*a - 13/2,
-1/6*a^5 + 1/6*a^4 + 13/6*a^3 - 5/3*a^2 - 37/6*a + 1,
a^4 - 10*a^2 + a + 16,
1/6*a^5 - 1/6*a^4 - 13/6*a^3 + 5/3*a^2 + 31/6*a - 1,
-1/2*a^5 + 1/2*a^4 + 11/2*a^3 - 5*a^2 - 23/2*a + 7,
-1/3*a^5 + 4/3*a^4 + 10/3*a^3 - 40/3*a^2 - 13/3*a + 20,
1/3*a^5 - 1/3*a^4 - 10/3*a^3 + 13/3*a^2 + 13/3*a - 10,
-1/3*a^5 + 1/3*a^4 + 10/3*a^3 - 10/3*a^2 - 19/3*a + 4,
-1/6*a^5 + 1/6*a^4 + 7/6*a^3 - 2/3*a^2 - 1/6*a - 3,
-a^4 + 10*a^2 - 2*a - 14
]
*], q_expansions := [*
q - q^2 + 2*q^3 + q^4 - 2*q^6 - q^8 + q^9 + 2*q^11 + 2*q^12 + 2*q^13 + q^16 + 6*q^17 - q^18 - 2*q^22 + 8*q^23 - 2*q^24 - 5*q^25 - 2*q^26 - 4*q^27 - 2*q^29 - q^32 + 4*q^33 - 6*q^34 + q^36 + 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^6 + 2*q^7 + q^8 - 2*q^9 + q^12 + 5*q^13 + 2*q^14 + q^16 - 2*q^18 - 4*q^19 + 2*q^21 + 6*q^23 + q^24 - 5*q^25 + 5*q^26 - 5*q^27 + 2*q^28 + 3*q^29 - 4*q^31 + q^32 - 2*q^36 - 7*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (a^2 + a - 1)*q^5 - a*q^6 + (2*a^2 + a - 5)*q^7 - q^8 + (a^2 - 3)*q^9 + (-a^2 - a + 1)*q^10 + (-a^2 + 6)*q^11 + a*q^12 + (-2*a^2 + 5)*q^13 + (-2*a^2 - a + 5)*q^14 + (-a^2 + 2*a + 5)*q^15 + q^16 + (-a - 2)*q^17 + (-a^2 + 3)*q^18 + (-a^2 - 2*a + 3)*q^19 + (a^2 + a - 1)*q^20 + (-3*a^2 + a + 10)*q^21 + (a^2 - 6)*q^22 + (a^2 - 3*a - 5)*q^23 - a*q^24 + (2*a^2 + 3*a - 4)*q^25 + (2*a^2 - 5)*q^26 + (-2*a^2 - 3*a + 5)*q^27 + (2*a^2 + a - 5)*q^28 + (-a + 5)*q^29 + (a^2 - 2*a - 5)*q^30 + (-a^2 - 4*a + 2)*q^31 - q^32 + (2*a^2 + 3*a - 5)*q^33 + (a + 2)*q^34 + (2*a^2 + a)*q^35 + (a^2 - 3)*q^36 + (-a^2 - a - 2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a^2 - 3*a - 3)*q^5 + a*q^6 + (2*a^2 + 3*a - 3)*q^7 + q^8 + (a^2 - 3)*q^9 + (-a^2 - 3*a - 3)*q^10 + (-3*a^2 - 8*a - 4)*q^11 + a*q^12 + (2*a^2 + 6*a - 1)*q^13 + (2*a^2 + 3*a - 3)*q^14 + (a^2 - 1)*q^15 + q^16 + (-2*a^2 - 3*a)*q^17 + (a^2 - 3)*q^18 + (3*a^2 + 12*a + 5)*q^19 + (-a^2 - 3*a - 3)*q^20 + (-5*a^2 - 9*a + 2)*q^21 + (-3*a^2 - 8*a - 4)*q^22 + (-3*a^2 - 7*a + 1)*q^23 + a*q^24 + (4*a^2 + 13*a + 6)*q^25 + (2*a^2 + 6*a - 1)*q^26 + (-4*a^2 - 9*a + 1)*q^27 + (2*a^2 + 3*a - 3)*q^28 + (4*a^2 + 9*a - 3)*q^29 + (a^2 - 1)*q^30 + (-a^2 - 2*a + 2)*q^31 + q^32 + (4*a^2 + 5*a - 3)*q^33 + (-2*a^2 - 3*a)*q^34 + (-2*a^2 + a + 8)*q^35 + (a^2 - 3)*q^36 + (a^2 + 5*a + 2)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (a^4 - 8*a^2 + 3)*q^5 - a*q^6 + (-7/5*a^4 - 1/5*a^3 + 53/5*a^2 - 3/5*a - 24/5)*q^7 - q^8 + (a^2 - 3)*q^9 + (-a^4 + 8*a^2 - 3)*q^10 + (-4/5*a^4 + 3/5*a^3 + 31/5*a^2 - 21/5*a - 23/5)*q^11 + a*q^12 + (4/5*a^4 + 2/5*a^3 - 26/5*a^2 - 14/5*a + 3/5)*q^13 + (7/5*a^4 + 1/5*a^3 - 53/5*a^2 + 3/5*a + 24/5)*q^14 + (-a^2 - 2*a + 1)*q^15 + q^16 + (-7/5*a^4 - 6/5*a^3 + 53/5*a^2 + 32/5*a - 34/5)*q^17 + (-a^2 + 3)*q^18 + (-4/5*a^4 - 2/5*a^3 + 31/5*a^2 + 4/5*a - 23/5)*q^19 + (a^4 - 8*a^2 + 3)*q^20 + (-1/5*a^4 - 3/5*a^3 + 4/5*a^2 + 11/5*a - 7/5)*q^21 + (4/5*a^4 - 3/5*a^3 - 31/5*a^2 + 21/5*a + 23/5)*q^22 + (13/5*a^4 + 4/5*a^3 - 102/5*a^2 - 18/5*a + 41/5)*q^23 - a*q^24 + (a^4 + a^3 - 7*a^2 - 3*a + 3)*q^25 + (-4/5*a^4 - 2/5*a^3 + 26/5*a^2 + 14/5*a - 3/5)*q^26 + (a^3 - 6*a)*q^27 + (-7/5*a^4 - 1/5*a^3 + 53/5*a^2 - 3/5*a - 24/5)*q^28 + (11/5*a^4 - 2/5*a^3 - 89/5*a^2 + 24/5*a + 37/5)*q^29 + (a^2 + 2*a - 1)*q^30 + (-8/5*a^4 - 9/5*a^3 + 57/5*a^2 + 63/5*a - 31/5)*q^31 - q^32 + (3/5*a^4 - 1/5*a^3 - 17/5*a^2 - 3/5*a - 4/5)*q^33 + (7/5*a^4 + 6/5*a^3 - 53/5*a^2 - 32/5*a + 34/5)*q^34 + (-9/5*a^4 - 2/5*a^3 + 81/5*a^2 + 24/5*a - 68/5)*q^35 + (a^2 - 3)*q^36 + (11/5*a^4 + 8/5*a^3 - 94/5*a^2 - 46/5*a + 72/5)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (1/4*a^5 - 3/4*a^4 - 11/4*a^3 + 7*a^2 + 19/4*a - 13/2)*q^5 + a*q^6 + (-1/6*a^5 + 1/6*a^4 + 13/6*a^3 - 5/3*a^2 - 37/6*a + 1)*q^7 + q^8 + (a^2 - 3)*q^9 + (1/4*a^5 - 3/4*a^4 - 11/4*a^3 + 7*a^2 + 19/4*a - 13/2)*q^10 + (a^4 - 10*a^2 + a + 16)*q^11 + a*q^12 + (1/6*a^5 - 1/6*a^4 - 13/6*a^3 + 5/3*a^2 + 31/6*a - 1)*q^13 + (-1/6*a^5 + 1/6*a^4 + 13/6*a^3 - 5/3*a^2 - 37/6*a + 1)*q^14 + (-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 6*a^2 - 7/2*a + 9)*q^15 + q^16 + (-1/2*a^5 + 1/2*a^4 + 11/2*a^3 - 5*a^2 - 23/2*a + 7)*q^17 + (a^2 - 3)*q^18 + (-1/3*a^5 + 4/3*a^4 + 10/3*a^3 - 40/3*a^2 - 13/3*a + 20)*q^19 + (1/4*a^5 - 3/4*a^4 - 11/4*a^3 + 7*a^2 + 19/4*a - 13/2)*q^20 + (a^2 - a - 6)*q^21 + (a^4 - 10*a^2 + a + 16)*q^22 + (1/3*a^5 - 1/3*a^4 - 10/3*a^3 + 13/3*a^2 + 13/3*a - 10)*q^23 + a*q^24 + (a^5 - 2*a^4 - 10*a^3 + 19*a^2 + 14*a - 19)*q^25 + (1/6*a^5 - 1/6*a^4 - 13/6*a^3 + 5/3*a^2 + 31/6*a - 1)*q^26 + (a^3 - 6*a)*q^27 + (-1/6*a^5 + 1/6*a^4 + 13/6*a^3 - 5/3*a^2 - 37/6*a + 1)*q^28 + (-1/3*a^5 + 1/3*a^4 + 10/3*a^3 - 10/3*a^2 - 19/3*a + 4)*q^29 + (-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 6*a^2 - 7/2*a + 9)*q^30 + (-1/6*a^5 + 1/6*a^4 + 7/6*a^3 - 2/3*a^2 - 1/6*a - 3)*q^31 + q^32 + (a^5 - 10*a^3 + a^2 + 16*a)*q^33 + (-1/2*a^5 + 1/2*a^4 + 11/2*a^3 - 5*a^2 - 23/2*a + 7)*q^34 + (1/3*a^5 - 4/3*a^4 - 7/3*a^3 + 43/3*a^2 - 11/3*a - 26)*q^35 + (a^2 - 3)*q^36 + (-a^4 + 10*a^2 - 2*a - 14)*q^37 + O(q^38)
*]> ;  // time = 151.191 seconds




J[467] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 467, 467, 467 ], new_dimensions := [ 1, 12, 26 ], dimensions := [ 1, 12, 26 ], intersection_graph := [ 0, 17, 1, 17, 0, 1, 1, 1, 0 ], ap_traces := [
[ 0, -3, 2, 1, 4, -6, -7, 2, -7, -8, 6, -2 ],
[ -5, -3, -7, -12, -6, -29, -1, -8, 5, -15, -11, -51 ],
[ 5, 4, 3, 11, 0, 47, 14, 4, 4, 17, 7, 71 ]
], hecke_fields := [
x - 1,
x^12 + 5*x^11 - 3*x^10 - 46*x^9 - 28*x^8 + 144*x^7 + 140*x^6 - 182*x^5 - 197*x^4 + 102*x^3 + 104*x^2 - 22*x - 17,
x^26 - 5*x^25 - 30*x^24 + 181*x^23 + 338*x^22 - 2813*x^21 - 1420*x^20 + 24571*x^19 - 4052*x^18 - 132574*x^17 + 73889*x^16 + 457016*x^15 - 370842*x^14 - 1004824*x^13 + 992642*x^12 + 1361654*x^11 - 1526411*x^10 - 1049992*x^9 + 1309411*x^8 + 383566*x^7 - 569750*x^6 - 29300*x^5 + 105328*x^4 - 5888*x^3 - 6944*x^2 + 448*x + 128
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 233 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 233 ]
], torsion_upper_bounds := [ 1, 1, 233 ], torsion_lower_bounds := [ 1, 1, 233 ], l_ratios := [ 0, 0, 1/233 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[ 0, -3, 2, 1, 4, -6, -7, 2, -7, -8, 6, -2 ],
[
a,
-3/7*a^11 - 10/7*a^10 + 4*a^9 + 103/7*a^8 - 97/7*a^7 - 387/7*a^6 + 155/7*a^5 + 633/7*a^4 - 114/7*a^3 - 417/7*a^2 + 40/7*a + 81/7,
a^6 + 3*a^5 - 3*a^4 - 13*a^3 - 3*a^2 + 8*a + 2,
1/7*a^11 + 1/7*a^10 - 3*a^9 - 25/7*a^8 + 149/7*a^7 + 192/7*a^6 - 425/7*a^5 - 554/7*a^4 + 458/7*a^3 + 545/7*a^2 - 172/7*a - 146/7,
4/7*a^11 + 11/7*a^10 - 7*a^9 - 135/7*a^8 + 204/7*a^7 + 544/7*a^6 - 377/7*a^5 - 858/7*a^4 + 355/7*a^3 + 528/7*a^2 - 128/7*a - 108/7,
-2/7*a^11 - 16/7*a^10 - 3*a^9 + 113/7*a^8 + 276/7*a^7 - 188/7*a^6 - 830/7*a^5 - 103/7*a^4 + 792/7*a^3 + 247/7*a^2 - 237/7*a - 93/7,
3/7*a^11 + 17/7*a^10 - 152/7*a^8 - 176/7*a^7 + 429/7*a^6 + 678/7*a^5 - 423/7*a^4 - 719/7*a^3 + 200/7*a^2 + 205/7*a - 32/7,
12/7*a^11 + 61/7*a^10 - 2*a^9 - 489/7*a^8 - 480/7*a^7 + 1121/7*a^6 + 1816/7*a^5 - 432/7*a^4 - 1840/7*a^3 - 453/7*a^2 + 561/7*a + 201/7,
4/7*a^11 + 32/7*a^10 + 7*a^9 - 198/7*a^8 - 573/7*a^7 + 215/7*a^6 + 1646/7*a^5 + 465/7*a^4 - 1577/7*a^3 - 648/7*a^2 + 460/7*a + 172/7,
-2*a^10 - 9*a^9 + 8*a^8 + 75*a^7 + 20*a^6 - 207*a^5 - 110*a^4 + 211*a^3 + 106*a^2 - 68*a - 25,
-15/7*a^11 - 64/7*a^10 + 11*a^9 + 571/7*a^8 + 75/7*a^7 - 1662/7*a^6 - 737/7*a^5 + 1772/7*a^4 + 641/7*a^3 - 762/7*a^2 - 73/7*a + 76/7,
-11/7*a^11 - 53/7*a^10 + 4*a^9 + 429/7*a^8 + 251/7*a^7 - 1104/7*a^6 - 967/7*a^5 + 970/7*a^4 + 807/7*a^3 - 318/7*a^2 - 131/7*a + 3/7
],
[
a,
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5539631980151634831/47737948510484985416*a^25 - 24943768875661465677/47737948510484985416*a^24 - 178279866466378877963/47737948510484985416*a^23 + 228311239337119265811/11934487127621246354*a^22 + 289322471040218933412/5967243563810623177*a^21 - 7201833424821692437247/23868974255242492708*a^20 - 7414314072166685840055/23868974255242492708*a^19 + 32074284427417296266701/11934487127621246354*a^18 + 9852461150934733127487/11934487127621246354*a^17 - 710913431898261385033623/47737948510484985416*a^16 + 67899423761855046172989/47737948510484985416*a^15 + 636053532700214641836159/11934487127621246354*a^14 - 839738506785233058105021/47737948510484985416*a^13 - 2954850900032745687392281/23868974255242492708*a^12 + 675845470349281103458917/11934487127621246354*a^11 + 4360704123038690772277361/23868974255242492708*a^10 - 4388094444460064779928967/47737948510484985416*a^9 - 971194395853022086907797/5967243563810623177*a^8 + 1853701281537468968421953/23868974255242492708*a^7 + 1894403822222040463303045/23868974255242492708*a^6 - 1481868911759459805558399/47737948510484985416*a^5 - 207653872116574842664415/11934487127621246354*a^4 + 117249175946869486425735/23868974255242492708*a^3 + 9038615292801684305042/5967243563810623177*a^2 - 1338136797015159583850/5967243563810623177*a - 248976659248758607976/5967243563810623177,
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50423454409563560927/190951794041939941664*a^25 - 58121932663996767785/47737948510484985416*a^24 - 1602717763062865443289/190951794041939941664*a^23 + 8500614863796788613097/190951794041939941664*a^22 + 20335145116972222857597/190951794041939941664*a^21 - 133842772223097289695153/190951794041939941664*a^20 - 123459703099394604451251/190951794041939941664*a^19 + 1189512222199603634336325/190951794041939941664*a^18 + 256985540528105996271725/190951794041939941664*a^17 - 3285853668326176175426309/95475897020969970832*a^16 + 1173197302860000888310377/190951794041939941664*a^15 + 23424244688079093996944319/190951794041939941664*a^14 - 4788487807307942646596921/95475897020969970832*a^13 - 27053452380219276552037521/95475897020969970832*a^12 + 14445205234997813957531475/95475897020969970832*a^11 + 2475543159741233195018290/5967243563810623177*a^10 - 45764955574419155575706211/190951794041939941664*a^9 - 69744703496696066472519797/190951794041939941664*a^8 + 38237516414595947781021225/190951794041939941664*a^7 + 33367001398898525050678787/190951794041939941664*a^6 - 3795430292742448231658917/47737948510484985416*a^5 - 3512337920526945404230245/95475897020969970832*a^4 + 589844430299441684658747/47737948510484985416*a^3 + 71068738507351819901549/23868974255242492708*a^2 - 3161524018081672279897/5967243563810623177*a - 451370094226384450815/5967243563810623177,
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]
*], q_expansions := [*
q - 3*q^3 - 2*q^4 + 2*q^5 + q^7 + 6*q^9 + 4*q^11 + 6*q^12 - 6*q^13 - 6*q^15 + 4*q^16 - 7*q^17 + 2*q^19 - 4*q^20 - 3*q^21 - 7*q^23 - q^25 - 9*q^27 - 2*q^28 - 8*q^29 + 6*q^31 - 12*q^33 + 2*q^35 - 12*q^36 - 2*q^37 + O(q^38),
q + a*q^2 + (-3/7*a^11 - 10/7*a^10 + 4*a^9 + 103/7*a^8 - 97/7*a^7 - 387/7*a^6 + 155/7*a^5 + 633/7*a^4 - 114/7*a^3 - 417/7*a^2 + 40/7*a + 81/7)*q^3 + (a^2 - 2)*q^4 + (a^6 + 3*a^5 - 3*a^4 - 13*a^3 - 3*a^2 + 8*a + 2)*q^5 + (5/7*a^11 + 19/7*a^10 - 5*a^9 - 181/7*a^8 + 45/7*a^7 + 575/7*a^6 + 87/7*a^5 - 705/7*a^4 - 111/7*a^3 + 352/7*a^2 + 15/7*a - 51/7)*q^6 + (1/7*a^11 + 1/7*a^10 - 3*a^9 - 25/7*a^8 + 149/7*a^7 + 192/7*a^6 - 425/7*a^5 - 554/7*a^4 + 458/7*a^3 + 545/7*a^2 - 172/7*a - 146/7)*q^7 + (a^3 - 4*a)*q^8 + (2/7*a^11 + 9/7*a^10 - a^9 - 71/7*a^8 - 17/7*a^7 + 195/7*a^6 + 67/7*a^5 - 233/7*a^4 - 22/7*a^3 + 124/7*a^2 - 29/7*a - 26/7)*q^9 + (a^7 + 3*a^6 - 3*a^5 - 13*a^4 - 3*a^3 + 8*a^2 + 2*a)*q^10 + (4/7*a^11 + 11/7*a^10 - 7*a^9 - 135/7*a^8 + 204/7*a^7 + 544/7*a^6 - 377/7*a^5 - 858/7*a^4 + 355/7*a^3 + 528/7*a^2 - 128/7*a - 108/7)*q^11 + (-a^9 - 3*a^8 + 7*a^7 + 23*a^6 - 15*a^5 - 56*a^4 + 10*a^3 + 47*a^2 - 3*a - 11)*q^12 + (-2/7*a^11 - 16/7*a^10 - 3*a^9 + 113/7*a^8 + 276/7*a^7 - 188/7*a^6 - 830/7*a^5 - 103/7*a^4 + 792/7*a^3 + 247/7*a^2 - 237/7*a - 93/7)*q^13 + (-4/7*a^11 - 18/7*a^10 + 3*a^9 + 177/7*a^8 + 48/7*a^7 - 565/7*a^6 - 372/7*a^5 + 655/7*a^4 + 443/7*a^3 - 276/7*a^2 - 124/7*a + 17/7)*q^14 + (1/7*a^11 + 1/7*a^10 - 3*a^9 - 32/7*a^8 + 121/7*a^7 + 213/7*a^6 - 250/7*a^5 - 498/7*a^4 + 157/7*a^3 + 377/7*a^2 - 39/7*a - 76/7)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (3/7*a^11 + 17/7*a^10 - 152/7*a^8 - 176/7*a^7 + 429/7*a^6 + 678/7*a^5 - 423/7*a^4 - 719/7*a^3 + 200/7*a^2 + 205/7*a - 32/7)*q^17 + (-1/7*a^11 - 1/7*a^10 + 3*a^9 + 39/7*a^8 - 93/7*a^7 - 213/7*a^6 + 131/7*a^5 + 372/7*a^4 - 80/7*a^3 - 237/7*a^2 + 18/7*a + 34/7)*q^18 + (12/7*a^11 + 61/7*a^10 - 2*a^9 - 489/7*a^8 - 480/7*a^7 + 1121/7*a^6 + 1816/7*a^5 - 432/7*a^4 - 1840/7*a^3 - 453/7*a^2 + 561/7*a + 201/7)*q^19 + (a^8 + 3*a^7 - 5*a^6 - 19*a^5 + 3*a^4 + 34*a^3 + 8*a^2 - 16*a - 4)*q^20 + (-2/7*a^11 - 9/7*a^10 + 2*a^9 + 92/7*a^8 - 32/7*a^7 - 356/7*a^6 + 38/7*a^5 + 618/7*a^4 - 55/7*a^3 - 411/7*a^2 + 71/7*a + 47/7)*q^21 + (-9/7*a^11 - 37/7*a^10 + 7*a^9 + 316/7*a^8 - 32/7*a^7 - 937/7*a^6 - 130/7*a^5 + 1143/7*a^4 + 120/7*a^3 - 544/7*a^2 - 20/7*a + 68/7)*q^22 + (4/7*a^11 + 32/7*a^10 + 7*a^9 - 198/7*a^8 - 573/7*a^7 + 215/7*a^6 + 1646/7*a^5 + 465/7*a^4 - 1577/7*a^3 - 648/7*a^2 + 460/7*a + 172/7)*q^23 + (-10/7*a^11 - 45/7*a^10 + 7*a^9 + 411/7*a^8 + 71/7*a^7 - 1255/7*a^6 - 566/7*a^5 + 1480/7*a^4 + 551/7*a^3 - 725/7*a^2 - 107/7*a + 102/7)*q^24 + (a^11 + 6*a^10 + 2*a^9 - 47*a^8 - 68*a^7 + 99*a^6 + 224*a^5 - 14*a^4 - 202*a^3 - 52*a^2 + 54*a + 16)*q^25 + (-6/7*a^11 - 27/7*a^10 + 3*a^9 + 220/7*a^8 + 100/7*a^7 - 550/7*a^6 - 467/7*a^5 + 398/7*a^4 + 451/7*a^3 - 29/7*a^2 - 137/7*a - 34/7)*q^26 + (6/7*a^11 + 13/7*a^10 - 13*a^9 - 192/7*a^8 + 467/7*a^7 + 935/7*a^6 - 996/7*a^5 - 1819/7*a^4 + 830/7*a^3 + 1296/7*a^2 - 241/7*a - 267/7)*q^27 + (a^10 + 5*a^9 - 2*a^8 - 41*a^7 - 28*a^6 + 111*a^5 + 109*a^4 - 112*a^3 - 114*a^2 + 39*a + 32)*q^28 + (-2*a^10 - 9*a^9 + 8*a^8 + 75*a^7 + 20*a^6 - 207*a^5 - 110*a^4 + 211*a^3 + 106*a^2 - 68*a - 25)*q^29 + (-4/7*a^11 - 18/7*a^10 + 2*a^9 + 149/7*a^8 + 69/7*a^7 - 390/7*a^6 - 316/7*a^5 + 354/7*a^4 + 275/7*a^3 - 143/7*a^2 - 54/7*a + 17/7)*q^30 + (-15/7*a^11 - 64/7*a^10 + 11*a^9 + 571/7*a^8 + 75/7*a^7 - 1662/7*a^6 - 737/7*a^5 + 1772/7*a^4 + 641/7*a^3 - 762/7*a^2 - 73/7*a + 76/7)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (4/7*a^11 + 18/7*a^10 - 3*a^9 - 156/7*a^8 + 36/7*a^7 + 523/7*a^6 - 69/7*a^5 - 837/7*a^4 + 103/7*a^3 + 542/7*a^2 - 58/7*a - 101/7)*q^33 + (2/7*a^11 + 9/7*a^10 - 2*a^9 - 92/7*a^8 - 3/7*a^7 + 258/7*a^6 + 123/7*a^5 - 128/7*a^4 - 106/7*a^3 - 107/7*a^2 + 34/7*a + 51/7)*q^34 + (-12/7*a^11 - 61/7*a^10 + 3*a^9 + 503/7*a^8 + 389/7*a^7 - 1317/7*a^6 - 1508/7*a^5 + 1146/7*a^4 + 1553/7*a^3 - 268/7*a^2 - 456/7*a - 54/7)*q^35 + (a^9 + 3*a^8 - 5*a^7 - 17*a^6 + 8*a^5 + 27*a^4 - 13*a^3 - 18*a^2 + 10*a + 5)*q^36 + (-11/7*a^11 - 53/7*a^10 + 4*a^9 + 429/7*a^8 + 251/7*a^7 - 1104/7*a^6 - 967/7*a^5 + 970/7*a^4 + 807/7*a^3 - 318/7*a^2 - 131/7*a + 3/7)*q^37 + O(q^38),
q + a*q^2 + (-10363332061373394879/190951794041939941664*a^25 + 51389231163521491841/190951794041939941664*a^24 + 80019126352002634403/47737948510484985416*a^23 - 1882904756544570716139/190951794041939941664*a^22 - 959680986289643624655/47737948510484985416*a^21 + 29730865760402852498863/190951794041939941664*a^20 + 10015383816473721072581/95475897020969970832*a^19 - 265271003727621598421621/190951794041939941664*a^18 - 2881811573462802471715/95475897020969970832*a^17 + 736837612793348039826313/95475897020969970832*a^16 - 496365418214858053022663/190951794041939941664*a^15 - 2647270102974250620737669/95475897020969970832*a^14 + 1423878514093438197846391/95475897020969970832*a^13 + 1546441062721262435079611/23868974255242492708*a^12 - 3923850587050531791151451/95475897020969970832*a^11 - 9211780225271573005475419/95475897020969970832*a^10 + 11902990260931105127268297/190951794041939941664*a^9 + 8314765549120022629884007/95475897020969970832*a^8 - 9631358723228384283624077/190951794041939941664*a^7 - 2058648482385531448474417/47737948510484985416*a^6 + 1836658457006210980201059/95475897020969970832*a^5 + 451129485124831156674183/47737948510484985416*a^4 - 67520378971189597291845/23868974255242492708*a^3 - 18805552891279119484097/23868974255242492708*a^2 + 648925921645097637440/5967243563810623177*a + 109989621903187974549/5967243563810623177)*q^3 + (a^2 - 2)*q^4 + (-4029184431302972343/190951794041939941664*a^25 + 15763452463375189915/190951794041939941664*a^24 + 68601516212658445503/95475897020969970832*a^23 - 578651503020959378503/190951794041939941664*a^22 - 979105098377673291591/95475897020969970832*a^21 + 9152059304801185273007/190951794041939941664*a^20 + 3773930036834474796649/47737948510484985416*a^19 - 81757147036446757376673/190951794041939941664*a^18 - 16695201479502400540563/47737948510484985416*a^17 + 227176371461999730195255/95475897020969970832*a^16 + 159660039055582213638969/190951794041939941664*a^15 - 203827603637749118458689/23868974255242492708*a^14 - 62983940073826103474403/95475897020969970832*a^13 + 474711165586489754761095/23868974255242492708*a^12 - 147857694587039073009851/95475897020969970832*a^11 - 2810056512575026906278885/95475897020969970832*a^10 + 823023238886017952063445/190951794041939941664*a^9 + 628620678135233452422751/23868974255242492708*a^8 - 728731115144094434535201/190951794041939941664*a^7 - 1241362696239549483505069/95475897020969970832*a^6 + 114544613380854490108475/95475897020969970832*a^5 + 141932788991934379222389/47737948510484985416*a^4 - 2177601531082898401825/23868974255242492708*a^3 - 3244467657779586060113/11934487127621246354*a^2 + 6840037831302791688/5967243563810623177*a + 38004299798490972900/5967243563810623177)*q^5 + (-213714571672741277/95475897020969970832*a^25 + 4588271783404345621/95475897020969970832*a^24 - 223176669874570095/5967243563810623177*a^23 - 167958854207183514759/95475897020969970832*a^22 + 144703167939873176059/47737948510484985416*a^21 + 2657418052898610708491/95475897020969970832*a^20 - 664598227975994553107/11934487127621246354*a^19 - 23877922329805300496569/95475897020969970832*a^18 + 6235427555136226685255/11934487127621246354*a^17 + 33671353058495090148971/23868974255242492708*a^16 - 279165820293938903727137/95475897020969970832*a^15 - 124425220014619513503167/23868974255242492708*a^14 + 122387732908289959046287/11934487127621246354*a^13 + 304922186245593232147177/23868974255242492708*a^12 - 1078071973961454345095243/47737948510484985416*a^11 - 978928448550479980845243/47737948510484985416*a^10 + 2874057670227235811988523/95475897020969970832*a^9 + 246156392161663379892637/11934487127621246354*a^8 - 2129786052044689106869577/95475897020969970832*a^7 - 557797881988767442977033/47737948510484985416*a^6 + 93804519443817759796377/11934487127621246354*a^5 + 68923250948852519685069/23868974255242492708*a^4 - 26432965288449938115041/23868974255242492708*a^3 - 1599917135672929051303/5967243563810623177*a^2 + 255076270762415502855/5967243563810623177*a + 41453328245493579516/5967243563810623177)*q^6 + (-24058256997224544661/381903588083879883328*a^25 + 104771983448012659849/381903588083879883328*a^24 + 392166681247250988043/190951794041939941664*a^23 - 3836511191260278131057/381903588083879883328*a^22 - 5207672470421337122625/190951794041939941664*a^21 + 60511751116108371014929/381903588083879883328*a^20 + 17504036413243302622977/95475897020969970832*a^19 - 538910129304975291308647/381903588083879883328*a^18 - 54968371946281115618649/95475897020969970832*a^17 + 1492379569288074670110699/190951794041939941664*a^16 - 34470232451786793377853/381903588083879883328*a^15 - 1333923458153226212647391/47737948510484985416*a^14 + 1380417207011523733264985/190951794041939941664*a^13 + 386641590828689103611019/5967243563810623177*a^12 - 4914093636737770210468421/190951794041939941664*a^11 - 18211319986093291653856943/190951794041939941664*a^10 + 16532879257118188567265383/381903588083879883328*a^9 + 4043439679190274925829591/47737948510484985416*a^8 - 14211645013372546337052079/381903588083879883328*a^7 - 7886327995460899147685679/190951794041939941664*a^6 + 2858349078854733632467191/190951794041939941664*a^5 + 880337007242497500805807/95475897020969970832*a^4 - 27372181925020789340219/11934487127621246354*a^3 - 19915642953182849296567/23868974255242492708*a^2 + 547854074294746894132/5967243563810623177*a + 135151403670025766004/5967243563810623177)*q^7 + (a^3 - 4*a)*q^8 + (-7852743697913892871/190951794041939941664*a^25 + 17890524558831894289/95475897020969970832*a^24 + 251903720451782299997/190951794041939941664*a^23 - 1311516999484429165975/190951794041939941664*a^22 - 3248746528189214587955/190951794041939941664*a^21 + 20711259698534487247919/190951794041939941664*a^20 + 20470142697420422479025/190951794041939941664*a^19 - 184728644861194873056239/190951794041939941664*a^18 - 50570272843912912162939/190951794041939941664*a^17 + 128124157205386069603357/23868974255242492708*a^16 - 127902347518922086449893/190951794041939941664*a^15 - 3672622054988148371302309/190951794041939941664*a^14 + 328017828519435062882117/47737948510484985416*a^13 + 4268334977584759770435423/95475897020969970832*a^12 - 2066809592779119318460933/95475897020969970832*a^11 - 3147838679456357356473193/47737948510484985416*a^10 + 6688530080863459675859235/190951794041939941664*a^9 + 11178342454511466403958911/190951794041939941664*a^8 - 5684277464555556755434135/190951794041939941664*a^7 - 5393345877885911411768873/190951794041939941664*a^6 + 1153592490864470486944527/95475897020969970832*a^5 + 572741622697642489882365/95475897020969970832*a^4 - 23454699639156907474767/11934487127621246354*a^3 - 2855215553515523746018/5967243563810623177*a^2 + 590166630166411766235/5967243563810623177*a + 71737074229018725688/5967243563810623177)*q^9 + (-547808711642458975/23868974255242492708*a^25 + 4081874871556930179/47737948510484985416*a^24 + 37657719761219653895/47737948510484985416*a^23 - 37271616185933870703/11934487127621246354*a^22 - 545509125113518981963/47737948510484985416*a^21 + 585892390930479903721/11934487127621246354*a^20 + 4310985906274644015795/47737948510484985416*a^19 - 10388382654206155762011/23868974255242492708*a^18 - 19953088467890198752593/47737948510484985416*a^17 + 28585777968757971068181/11934487127621246354*a^16 + 6586903842323945644968/5967243563810623177*a^15 - 405039673255227269142903/47737948510484985416*a^14 - 15683243269228740218367/11934487127621246354*a^13 + 462977787885420865810063/23868974255242492708*a^12 - 8359870470539769363903/11934487127621246354*a^11 - 665896024760447920623441/23868974255242492708*a^10 + 24948562677787408844086/5967243563810623177*a^9 + 1136781825058190471021193/47737948510484985416*a^8 - 117158404612742884661875/23868974255242492708*a^7 - 516634650743289878051825/47737948510484985416*a^6 + 56209506516320053404957/23868974255242492708*a^5 + 50870640691452035466113/23868974255242492708*a^4 - 4727207528499079882337/11934487127621246354*a^3 - 867492983761442206743/5967243563810623177*a^2 + 94412881836732585702/5967243563810623177*a + 16116737725211889372/5967243563810623177)*q^10 + (5539631980151634831/47737948510484985416*a^25 - 24943768875661465677/47737948510484985416*a^24 - 178279866466378877963/47737948510484985416*a^23 + 228311239337119265811/11934487127621246354*a^22 + 289322471040218933412/5967243563810623177*a^21 - 7201833424821692437247/23868974255242492708*a^20 - 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129543470970414748268/5967243563810623177)*q^36 + (-14902137356564986245/190951794041939941664*a^25 + 68656013161373511961/190951794041939941664*a^24 + 237123073096773823985/95475897020969970832*a^23 - 2510387444720408906765/190951794041939941664*a^22 - 3016234250771970244181/95475897020969970832*a^21 + 39528059334983992822413/190951794041939941664*a^20 + 9215815624922139657407/47737948510484985416*a^19 - 351326072709899080792435/190951794041939941664*a^18 - 19849635958909341614093/47737948510484985416*a^17 + 970585686653737312505061/95475897020969970832*a^16 - 327866701648655589507005/190951794041939941664*a^15 - 216252890029407838555207/5967243563810623177*a^14 + 1384575539114640314638567/95475897020969970832*a^13 + 999229481875768047929113/11934487127621246354*a^12 - 4216222880472616079515873/95475897020969970832*a^11 - 11707907274818658546245791/95475897020969970832*a^10 + 13476038895976466536899759/190951794041939941664*a^9 + 644907939094442221062533/5967243563810623177*a^8 - 11421770642928817782444451/190951794041939941664*a^7 - 4957163170464776777750439/95475897020969970832*a^6 + 2330894840173182588230833/95475897020969970832*a^5 + 531641301290226644016245/47737948510484985416*a^4 - 94601500880844918269361/23868974255242492708*a^3 - 5503233125956697148110/5967243563810623177*a^2 + 1013905331770887883393/5967243563810623177*a + 151775525334551101400/5967243563810623177)*q^37 + O(q^38)
*]> ;  // time = 15.789 seconds




J[469] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 469, 469, 469, 469, 469, 469, 469, 469, 469, 67, 67, 67 ], new_dimensions := [ 1, 1, 2, 2, 3, 3, 5, 7, 9, 1, 2, 2 ], dimensions := [ 1, 1, 2, 2, 3, 3, 5, 7, 9, 2, 4, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 17, 1, 1, 1, 5, 1, 5, 1, 1, 1, 1, 17, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 9, 1, 1, 1, 9, 1, 1, 1, 1, 0, 1, 1, 61, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 71, 1, 1, 1, 1, 5, 1, 1, 1, 3, 0, 1, 25, 5, 1, 1, 1, 1, 1, 9, 61, 1, 1, 0, 1, 1, 1, 1, 1, 5, 1, 1, 1, 71, 25, 1, 0 ], ap_traces := [
[ 1, 1, -3, -1, 0, -1, -8, 8, 3, -3, -1, -3 ],
[ -1, -3, 1, -1, 0, 3, 0, -4, 3, -3, -5, 5 ],
[ 1, -1, -3, 2, 8, -7, 9, 9, 0, 12, -1, -4 ],
[ 2, -1, -1, 2, 8, 9, 2, 2, 3, -1, -15, -13 ],
[ -1, -1, -9, 3, -12, 5, 10, -4, -7, -9, -3, -9 ],
[ -3, -3, 3, 3, -6, -3, -9, -3, -12, -12, -3, -3 ],
[ 2, -2, -4, -5, -16, -4, -4, -8, -20, 0, 4, 9 ],
[ 1, 6, 6, 7, 8, -8, -7, -11, 19, 3, 18, 20 ],
[ -1, 8, 8, -9, 18, 4, 7, 13, 1, -7, 6, -18 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - x - 4,
x^2 - 5*x - 32,
x^3 + x^2 - 3*x - 1,
x^3 + 3*x^2 - 3,
x^5 - 2*x^4 - 5*x^3 + 9*x^2 + 3*x - 4,
x^7 - x^6 - 12*x^5 + 9*x^4 + 43*x^3 - 17*x^2 - 44*x - 11,
x^9 + x^8 - 13*x^7 - 10*x^6 + 53*x^5 + 28*x^4 - 69*x^3 - 12*x^2 + 12*x + 1
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 5, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 25, 1 ],
[ 1, 1 ],
[ 9, 1 ],
[ 1037, 1 ],
[ 213, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 25, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1037, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 3, 1, 17, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 17, 1 ], l_ratios := [ 0, 0, 1, 1, 0, 0, 0, 61/17, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1, 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1, 0, 0, 0, 1, 1 ], eigenvalues := [*
[ 1, 1, -3, -1, 0, -1, -8, 8, 3, -3, -1, -3 ],
[ -1, -3, 1, -1, 0, 3, 0, -4, 3, -3, -5, 5 ],
[
a,
-a,
a - 2,
1,
4,
a - 4,
-a + 5,
-a + 5,
-2*a + 1,
-2*a + 7,
3*a - 2,
-2*a - 1
],
[
1,
-1/3*a + 1/3,
-1/3*a + 1/3,
1,
4,
1/3*a + 11/3,
-2/3*a + 8/3,
-2/3*a + 8/3,
a - 1,
a - 3,
1/3*a - 25/3,
-1/3*a - 17/3
],
[
a,
-a^2 + 2,
-3,
1,
-4,
-2*a + 1,
3*a^2 + 2*a - 3,
2*a^2 - 6,
a^2 + 2*a - 4,
2*a^2 + 2*a - 7,
a^2 + 4*a - 2,
-2*a^2 - 2*a + 1
],
[
a,
-a - 2,
a^2 + 2*a,
1,
-3*a^2 - 4*a + 3,
-2*a^2 - 3*a + 2,
a^2 + 3*a - 3,
-3*a - 4,
-2*a - 6,
a^2 - 2*a - 9,
-2*a^2 + 5,
3*a^2 + 3*a - 7
],
[
a,
-a,
-a^2 + 2,
-1,
-a^4 + 6*a^2 + a - 8,
2*a^4 - 2*a^3 - 10*a^2 + 7*a + 4,
-a^4 + a^3 + 5*a^2 - 4*a - 3,
a^3 - a^2 - 5*a + 1,
-2*a^4 + 3*a^3 + 9*a^2 - 10*a - 7,
a^4 - 3*a^3 - 5*a^2 + 13*a + 3,
a^4 - 3*a^2 - 3*a - 2,
-2*a^3 + 3*a^2 + 7*a - 5
],
[
a,
1/4*a^6 - 3*a^4 + 1/4*a^3 + 9*a^2 - 5/4*a - 9/4,
-1/4*a^6 - 1/2*a^5 + 5/2*a^4 + 21/4*a^3 - 5*a^2 - 51/4*a - 9/4,
1,
1/2*a^6 - 5*a^4 - 3/2*a^3 + 12*a^2 + 13/2*a - 1/2,
-1/4*a^6 + 1/2*a^5 + 5/2*a^4 - 15/4*a^3 - 7*a^2 + 21/4*a + 15/4,
-1/2*a^6 + a^5 + 5*a^4 - 17/2*a^3 - 14*a^2 + 31/2*a + 19/2,
-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 3*a^2 - 9*a - 1/2,
-3/4*a^6 + a^5 + 8*a^4 - 35/4*a^3 - 22*a^2 + 67/4*a + 51/4,
-1/4*a^6 - a^5 + 3*a^4 + 39/4*a^3 - 8*a^2 - 83/4*a - 7/4,
-1/4*a^6 + 2*a^4 - 1/4*a^3 - 4*a^2 + 5/4*a + 25/4,
1/4*a^6 - a^4 - 7/4*a^3 - 4*a^2 + 35/4*a + 43/4
],
[
a,
1/2*a^6 - 5*a^4 + 3/2*a^3 + 12*a^2 - 11/2*a - 3/2,
-1/4*a^8 - 1/2*a^7 + 13/4*a^6 + 21/4*a^5 - 14*a^4 - 31/2*a^3 + 81/4*a^2 + 39/4*a - 9/4,
-1,
-1/2*a^7 - 1/2*a^6 + 5*a^5 + 7/2*a^4 - 27/2*a^3 - 13/2*a^2 + 8*a + 9/2,
1/4*a^8 - 1/2*a^7 - 13/4*a^6 + 19/4*a^5 + 10*a^4 - 17/2*a^3 - 13/4*a^2 - 19/4*a + 5/4,
1/2*a^8 + a^7 - 13/2*a^6 - 21/2*a^5 + 28*a^4 + 30*a^3 - 81/2*a^2 - 29/2*a + 13/2,
-1/4*a^8 - 1/2*a^7 + 15/4*a^6 + 25/4*a^5 - 17*a^4 - 20*a^3 + 85/4*a^2 + 29/4*a + 5/4,
-1/2*a^8 - a^7 + 7*a^6 + 21/2*a^5 - 33*a^4 - 57/2*a^3 + 103/2*a^2 + 9*a - 5,
-a^8 - 1/2*a^7 + 13*a^6 + 5*a^5 - 101/2*a^4 - 14*a^3 + 115/2*a^2 - 3/2*a - 8,
-1/2*a^8 + 5*a^6 - 1/2*a^5 - 10*a^4 - 5/2*a^3 - 15/2*a^2 + 15*a + 3,
2*a^8 + a^7 - 49/2*a^6 - 8*a^5 + 88*a^4 + 37/2*a^3 - 88*a^2 + 1/2*a + 13/2
]
*], q_expansions := [*
q + q^2 + q^3 - q^4 - 3*q^5 + q^6 - q^7 - 3*q^8 - 2*q^9 - 3*q^10 - q^12 - q^13 - q^14 - 3*q^15 - q^16 - 8*q^17 - 2*q^18 + 8*q^19 + 3*q^20 - q^21 + 3*q^23 - 3*q^24 + 4*q^25 - q^26 - 5*q^27 + q^28 - 3*q^29 - 3*q^30 - q^31 + 5*q^32 - 8*q^34 + 3*q^35 + 2*q^36 - 3*q^37 + O(q^38),
q - q^2 - 3*q^3 - q^4 + q^5 + 3*q^6 - q^7 + 3*q^8 + 6*q^9 - q^10 + 3*q^12 + 3*q^13 + q^14 - 3*q^15 - q^16 - 6*q^18 - 4*q^19 - q^20 + 3*q^21 + 3*q^23 - 9*q^24 - 4*q^25 - 3*q^26 - 9*q^27 + q^28 - 3*q^29 + 3*q^30 - 5*q^31 - 5*q^32 - q^35 - 6*q^36 + 5*q^37 + O(q^38),
q + a*q^2 - a*q^3 + (a + 2)*q^4 + (a - 2)*q^5 + (-a - 4)*q^6 + q^7 + (a + 4)*q^8 + (a + 1)*q^9 + (-a + 4)*q^10 + 4*q^11 + (-3*a - 4)*q^12 + (a - 4)*q^13 + a*q^14 + (a - 4)*q^15 + 3*a*q^16 + (-a + 5)*q^17 + (2*a + 4)*q^18 + (-a + 5)*q^19 + a*q^20 - a*q^21 + 4*a*q^22 + (-2*a + 1)*q^23 + (-5*a - 4)*q^24 + (-3*a + 3)*q^25 + (-3*a + 4)*q^26 + (a - 4)*q^27 + (a + 2)*q^28 + (-2*a + 7)*q^29 + (-3*a + 4)*q^30 + (3*a - 2)*q^31 + (a + 4)*q^32 - 4*a*q^33 + (4*a - 4)*q^34 + (a - 2)*q^35 + (4*a + 6)*q^36 + (-2*a - 1)*q^37 + O(q^38),
q + q^2 + (-1/3*a + 1/3)*q^3 - q^4 + (-1/3*a + 1/3)*q^5 + (-1/3*a + 1/3)*q^6 + q^7 - 3*q^8 + (1/3*a + 2/3)*q^9 + (-1/3*a + 1/3)*q^10 + 4*q^11 + (1/3*a - 1/3)*q^12 + (1/3*a + 11/3)*q^13 + q^14 + (1/3*a + 11/3)*q^15 - q^16 + (-2/3*a + 8/3)*q^17 + (1/3*a + 2/3)*q^18 + (-2/3*a + 8/3)*q^19 + (1/3*a - 1/3)*q^20 + (-1/3*a + 1/3)*q^21 + 4*q^22 + (a - 1)*q^23 + (a - 1)*q^24 + (1/3*a - 4/3)*q^25 + (1/3*a + 11/3)*q^26 + (1/3*a - 13/3)*q^27 - q^28 + (a - 3)*q^29 + (1/3*a + 11/3)*q^30 + (1/3*a - 25/3)*q^31 + 5*q^32 + (-4/3*a + 4/3)*q^33 + (-2/3*a + 8/3)*q^34 + (-1/3*a + 1/3)*q^35 + (-1/3*a - 2/3)*q^36 + (-1/3*a - 17/3)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + 2)*q^3 + (a^2 - 2)*q^4 - 3*q^5 + (a^2 - a - 1)*q^6 + q^7 + (-a^2 - a + 1)*q^8 - 2*a*q^9 - 3*a*q^10 - 4*q^11 + (2*a - 3)*q^12 + (-2*a + 1)*q^13 + a*q^14 + (3*a^2 - 6)*q^15 + (-2*a^2 - 2*a + 3)*q^16 + (3*a^2 + 2*a - 3)*q^17 - 2*a^2*q^18 + (2*a^2 - 6)*q^19 + (-3*a^2 + 6)*q^20 + (-a^2 + 2)*q^21 - 4*a*q^22 + (a^2 + 2*a - 4)*q^23 + (-a + 2)*q^24 + 4*q^25 + (-2*a^2 + a)*q^26 + (a^2 + 2*a - 4)*q^27 + (a^2 - 2)*q^28 + (2*a^2 + 2*a - 7)*q^29 + (-3*a^2 + 3*a + 3)*q^30 + (a^2 + 4*a - 2)*q^31 + (2*a^2 - a - 4)*q^32 + (4*a^2 - 8)*q^33 + (-a^2 + 6*a + 3)*q^34 - 3*q^35 + (2*a^2 - 2*a - 2)*q^36 + (-2*a^2 - 2*a + 1)*q^37 + O(q^38),
q + a*q^2 + (-a - 2)*q^3 + (a^2 - 2)*q^4 + (a^2 + 2*a)*q^5 + (-a^2 - 2*a)*q^6 + q^7 + (-3*a^2 - 4*a + 3)*q^8 + (a^2 + 4*a + 1)*q^9 + (-a^2 + 3)*q^10 + (-3*a^2 - 4*a + 3)*q^11 + (a^2 + 2*a + 1)*q^12 + (-2*a^2 - 3*a + 2)*q^13 + a*q^14 + (-a^2 - 4*a - 3)*q^15 + (3*a^2 + 3*a - 5)*q^16 + (a^2 + 3*a - 3)*q^17 + (a^2 + a + 3)*q^18 + (-3*a - 4)*q^19 + (a^2 - a - 3)*q^20 + (-a - 2)*q^21 + (5*a^2 + 3*a - 9)*q^22 + (-2*a - 6)*q^23 + (a^2 + 5*a + 3)*q^24 + (a^2 + 3*a - 2)*q^25 + (3*a^2 + 2*a - 6)*q^26 + (-3*a^2 - 6*a + 1)*q^27 + (a^2 - 2)*q^28 + (a^2 - 2*a - 9)*q^29 + (-a^2 - 3*a - 3)*q^30 + (-2*a^2 + 5)*q^31 + (3*a + 3)*q^32 + (a^2 + 5*a + 3)*q^33 + (-3*a + 3)*q^34 + (a^2 + 2*a)*q^35 + (-4*a^2 - 5*a + 1)*q^36 + (3*a^2 + 3*a - 7)*q^37 + O(q^38),
q + a*q^2 - a*q^3 + (a^2 - 2)*q^4 + (-a^2 + 2)*q^5 - a^2*q^6 - q^7 + (a^3 - 4*a)*q^8 + (a^2 - 3)*q^9 + (-a^3 + 2*a)*q^10 + (-a^4 + 6*a^2 + a - 8)*q^11 + (-a^3 + 2*a)*q^12 + (2*a^4 - 2*a^3 - 10*a^2 + 7*a + 4)*q^13 - a*q^14 + (a^3 - 2*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 + a^3 + 5*a^2 - 4*a - 3)*q^17 + (a^3 - 3*a)*q^18 + (a^3 - a^2 - 5*a + 1)*q^19 + (-a^4 + 4*a^2 - 4)*q^20 + a*q^21 + (-2*a^4 + a^3 + 10*a^2 - 5*a - 4)*q^22 + (-2*a^4 + 3*a^3 + 9*a^2 - 10*a - 7)*q^23 + (-a^4 + 4*a^2)*q^24 + (a^4 - 4*a^2 - 1)*q^25 + (2*a^4 - 11*a^2 - 2*a + 8)*q^26 + (-a^3 + 6*a)*q^27 + (-a^2 + 2)*q^28 + (a^4 - 3*a^3 - 5*a^2 + 13*a + 3)*q^29 + (a^4 - 2*a^2)*q^30 + (a^4 - 3*a^2 - 3*a - 2)*q^31 + (2*a^4 - 3*a^3 - 9*a^2 + 9*a + 4)*q^32 + (2*a^4 - a^3 - 10*a^2 + 5*a + 4)*q^33 + (-a^4 + 5*a^2 - 4)*q^34 + (a^2 - 2)*q^35 + (a^4 - 5*a^2 + 6)*q^36 + (-2*a^3 + 3*a^2 + 7*a - 5)*q^37 + O(q^38),
q + a*q^2 + (1/4*a^6 - 3*a^4 + 1/4*a^3 + 9*a^2 - 5/4*a - 9/4)*q^3 + (a^2 - 2)*q^4 + (-1/4*a^6 - 1/2*a^5 + 5/2*a^4 + 21/4*a^3 - 5*a^2 - 51/4*a - 9/4)*q^5 + (1/4*a^6 - 2*a^4 - 7/4*a^3 + 3*a^2 + 35/4*a + 11/4)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (3/4*a^6 - 8*a^4 - 5/4*a^3 + 21*a^2 + 17/4*a - 11/4)*q^9 + (-3/4*a^6 - 1/2*a^5 + 15/2*a^4 + 23/4*a^3 - 17*a^2 - 53/4*a - 11/4)*q^10 + (1/2*a^6 - 5*a^4 - 3/2*a^3 + 12*a^2 + 13/2*a - 1/2)*q^11 + (-1/4*a^6 + a^5 + 2*a^4 - 33/4*a^3 - 5*a^2 + 65/4*a + 29/4)*q^12 + (-1/4*a^6 + 1/2*a^5 + 5/2*a^4 - 15/4*a^3 - 7*a^2 + 21/4*a + 15/4)*q^13 + a*q^14 + (-1/4*a^6 - a^5 + 2*a^4 + 47/4*a^3 - a^2 - 127/4*a - 43/4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^6 + a^5 + 5*a^4 - 17/2*a^3 - 14*a^2 + 31/2*a + 19/2)*q^17 + (3/4*a^6 + a^5 - 8*a^4 - 45/4*a^3 + 17*a^2 + 121/4*a + 33/4)*q^18 + (-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 3*a^2 - 9*a - 1/2)*q^19 + (-3/4*a^6 - 1/2*a^5 + 15/2*a^4 + 19/4*a^3 - 16*a^2 - 41/4*a - 15/4)*q^20 + (1/4*a^6 - 3*a^4 + 1/4*a^3 + 9*a^2 - 5/4*a - 9/4)*q^21 + (1/2*a^6 + a^5 - 6*a^4 - 19/2*a^3 + 15*a^2 + 43/2*a + 11/2)*q^22 + (-3/4*a^6 + a^5 + 8*a^4 - 35/4*a^3 - 22*a^2 + 67/4*a + 51/4)*q^23 + (1/4*a^6 - a^5 - 2*a^4 + 37/4*a^3 + 6*a^2 - 85/4*a - 33/4)*q^24 + (1/4*a^6 - a^5 - 3*a^4 + 37/4*a^3 + 11*a^2 - 73/4*a - 41/4)*q^25 + (1/4*a^6 - 1/2*a^5 - 3/2*a^4 + 15/4*a^3 + a^2 - 29/4*a - 11/4)*q^26 + (3/4*a^6 + a^5 - 8*a^4 - 45/4*a^3 + 17*a^2 + 117/4*a + 49/4)*q^27 + (a^2 - 2)*q^28 + (-1/4*a^6 - a^5 + 3*a^4 + 39/4*a^3 - 8*a^2 - 83/4*a - 7/4)*q^29 + (-5/4*a^6 - a^5 + 14*a^4 + 39/4*a^3 - 36*a^2 - 87/4*a - 11/4)*q^30 + (-1/4*a^6 + 2*a^4 - 1/4*a^3 - 4*a^2 + 5/4*a + 25/4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^6 + a^5 - 11*a^4 - 11*a^3 + 26*a^2 + 30*a + 8)*q^33 + (1/2*a^6 - a^5 - 4*a^4 + 15/2*a^3 + 7*a^2 - 25/2*a - 11/2)*q^34 + (-1/4*a^6 - 1/2*a^5 + 5/2*a^4 + 21/4*a^3 - 5*a^2 - 51/4*a - 9/4)*q^35 + (1/4*a^6 + a^5 - 2*a^4 - 51/4*a^3 + a^2 + 131/4*a + 55/4)*q^36 + (1/4*a^6 - a^4 - 7/4*a^3 - 4*a^2 + 35/4*a + 43/4)*q^37 + O(q^38),
q + a*q^2 + (1/2*a^6 - 5*a^4 + 3/2*a^3 + 12*a^2 - 11/2*a - 3/2)*q^3 + (a^2 - 2)*q^4 + (-1/4*a^8 - 1/2*a^7 + 13/4*a^6 + 21/4*a^5 - 14*a^4 - 31/2*a^3 + 81/4*a^2 + 39/4*a - 9/4)*q^5 + (1/2*a^7 - 5*a^5 + 3/2*a^4 + 12*a^3 - 11/2*a^2 - 3/2*a)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-1/2*a^8 + 7*a^6 - 1/2*a^5 - 30*a^4 + 7/2*a^3 + 79/2*a^2 - 9*a - 3)*q^9 + (-1/4*a^8 + 11/4*a^6 - 3/4*a^5 - 17/2*a^4 + 3*a^3 + 27/4*a^2 + 3/4*a + 1/4)*q^10 + (-1/2*a^7 - 1/2*a^6 + 5*a^5 + 7/2*a^4 - 27/2*a^3 - 13/2*a^2 + 8*a + 9/2)*q^11 + (1/2*a^8 - 6*a^6 + 3/2*a^5 + 22*a^4 - 17/2*a^3 - 51/2*a^2 + 11*a + 3)*q^12 + (1/4*a^8 - 1/2*a^7 - 13/4*a^6 + 19/4*a^5 + 10*a^4 - 17/2*a^3 - 13/4*a^2 - 19/4*a + 5/4)*q^13 - a*q^14 + (a^8 + a^7 - 25/2*a^6 - 10*a^5 + 47*a^4 + 55/2*a^3 - 50*a^2 - 17/2*a + 5/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/2*a^8 + a^7 - 13/2*a^6 - 21/2*a^5 + 28*a^4 + 30*a^3 - 81/2*a^2 - 29/2*a + 13/2)*q^17 + (1/2*a^8 + 1/2*a^7 - 11/2*a^6 - 7/2*a^5 + 35/2*a^4 + 5*a^3 - 15*a^2 + 3*a + 1/2)*q^18 + (-1/4*a^8 - 1/2*a^7 + 15/4*a^6 + 25/4*a^5 - 17*a^4 - 20*a^3 + 85/4*a^2 + 29/4*a + 5/4)*q^19 + (3/4*a^8 + 1/2*a^7 - 39/4*a^6 - 23/4*a^5 + 38*a^4 + 41/2*a^3 - 171/4*a^2 - 65/4*a + 19/4)*q^20 + (-1/2*a^6 + 5*a^4 - 3/2*a^3 - 12*a^2 + 11/2*a + 3/2)*q^21 + (-1/2*a^8 - 1/2*a^7 + 5*a^6 + 7/2*a^5 - 27/2*a^4 - 13/2*a^3 + 8*a^2 + 9/2*a)*q^22 + (-1/2*a^8 - a^7 + 7*a^6 + 21/2*a^5 - 33*a^4 - 57/2*a^3 + 103/2*a^2 + 9*a - 5)*q^23 + (-1/2*a^8 - 1/2*a^7 + 13/2*a^6 + 11/2*a^5 - 51/2*a^4 - 15*a^3 + 28*a^2 - 1/2)*q^24 + (-1/2*a^7 + 6*a^5 - 1/2*a^4 - 21*a^3 - 1/2*a^2 + 41/2*a + 5)*q^25 + (-3/4*a^8 + 29/4*a^6 - 13/4*a^5 - 31/2*a^4 + 14*a^3 - 7/4*a^2 - 7/4*a - 1/4)*q^26 + (-a^8 + 25/2*a^6 - 2*a^5 - 46*a^4 + 21/2*a^3 + 47*a^2 - 29/2*a + 7/2)*q^27 + (-a^2 + 2)*q^28 + (-a^8 - 1/2*a^7 + 13*a^6 + 5*a^5 - 101/2*a^4 - 14*a^3 + 115/2*a^2 - 3/2*a - 8)*q^29 + (1/2*a^7 - 6*a^5 - 1/2*a^4 + 19*a^3 + 7/2*a^2 - 19/2*a - 1)*q^30 + (-1/2*a^8 + 5*a^6 - 1/2*a^5 - 10*a^4 - 5/2*a^3 - 15/2*a^2 + 15*a + 3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^5 - a^4 + 8*a^3 + 6*a^2 - 15*a - 5)*q^33 + (1/2*a^8 - 11/2*a^6 + 3/2*a^5 + 16*a^4 - 6*a^3 - 17/2*a^2 + 1/2*a - 1/2)*q^34 + (1/4*a^8 + 1/2*a^7 - 13/4*a^6 - 21/4*a^5 + 14*a^4 + 31/2*a^3 - 81/4*a^2 - 39/4*a + 9/4)*q^35 + (a^8 + a^7 - 25/2*a^6 - 8*a^5 + 51*a^4 + 25/2*a^3 - 70*a^2 + 25/2*a + 11/2)*q^36 + (2*a^8 + a^7 - 49/2*a^6 - 8*a^5 + 88*a^4 + 37/2*a^3 - 88*a^2 + 1/2*a + 13/2)*q^37 + O(q^38)
*]> ;  // time = 90.891 seconds




J[470] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 470, 470, 470, 470, 470, 470, 470, 470, 470, 470, 235, 235, 235, 235, 235, 94, 94, 47 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 1, 1, 1, 5, 7, 1, 2, 4 ], dimensions := [ 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 2, 2, 2, 10, 14, 2, 4, 16 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 7, 3, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 43, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 31, 1, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 1, 1, 227, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 81, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 9, 0, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 227, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 43, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 7, 1, 1, 1, 1, 31, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2209, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23, 81, 9, 9, 1, 1, 1, 2209, 0 ], ap_traces := [
[ -1, 1, -1, -1, -3, -5, 2, -7, 8, -2, -5, -4 ],
[ -1, 1, 1, -1, 3, 5, 6, -1, 0, -6, 5, 8 ],
[ -1, -1, 1, -1, 1, -5, 0, 5, -6, -6, -11, -8 ],
[ 1, 1, -1, 5, -3, 5, 0, -7, 6, -6, 5, 8 ],
[ 1, -1, -1, -3, -5, -1, 2, -1, 0, 2, -7, 0 ],
[ 1, -3, 1, -3, -1, -1, -8, -5, -2, -2, -5, -4 ],
[ -2, 1, 2, 8, -5, 2, -8, -1, 1, 1, -2, -1 ],
[ -3, 0, -3, 3, 0, 3, 0, 12, -3, 9, 9, 15 ],
[ 3, 3, -3, 0, 5, 0, -2, 9, -11, -3, 2, -5 ],
[ 3, 2, 3, 1, 0, -1, 2, 4, 7, -9, 1, -11 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - x - 5,
x^3 - 6*x - 1,
x^3 - 3*x^2 - 5*x + 12,
x^3 - 2*x^2 - 4*x + 7
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ 1, -1, -1 ],
[ -1, 1, 1 ],
[ -1, 1, -1 ],
[ -1, -1, 1 ],
[ 1, -1, 1 ],
[ 1, 1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 7, 1 ],
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 7, 3, 1 ],
[ 43, 1, 1 ],
[ 5, 31, 3 ],
[ 227, 3, 1 ],
[ 23, 23, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 7, 1 ],
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 7, 3, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 3 ],
[ 227, 1, 1 ],
[ 23, 23, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 3, 1, 1, 1, 3, 1, 23 ], torsion_lower_bounds := [ 1, 3, 1, 3, 1, 1, 1, 3, 1, 1 ], l_ratios := [ 0, 1/3, 0, 1/3, 0, 0, 1, 1/3, 227, 1 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1, 0, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1, 0, 0, 1, 1, 1, 1/529 ], eigenvalues := [*
[ -1, 1, -1, -1, -3, -5, 2, -7, 8, -2, -5, -4 ],
[ -1, 1, 1, -1, 3, 5, 6, -1, 0, -6, 5, 8 ],
[ -1, -1, 1, -1, 1, -5, 0, 5, -6, -6, -11, -8 ],
[ 1, 1, -1, 5, -3, 5, 0, -7, 6, -6, 5, 8 ],
[ 1, -1, -1, -3, -5, -1, 2, -1, 0, 2, -7, 0 ],
[ 1, -3, 1, -3, -1, -1, -8, -5, -2, -2, -5, -4 ],
[
-1,
a,
1,
4,
a - 3,
-2*a + 2,
-4,
-a,
-a + 1,
-3*a + 2,
2*a - 2,
-3*a + 1
],
[
-1,
a,
-1,
-a^2 + a + 5,
-a^2 + 4,
a^2 + a - 3,
0,
a + 4,
a - 1,
-a^2 + 7,
-a^2 - a + 7,
-3*a + 5
],
[
1,
a,
-1,
0,
-a^2 + 8,
-2*a + 2,
-2*a^2 + 2*a + 10,
-a + 4,
a^2 - 2*a - 8,
a - 2,
2*a^2 - 4*a - 8,
a^2 + 2*a - 10
],
[
1,
a,
1,
-a^2 - a + 5,
a^2 - 4,
-a^2 + a + 3,
2*a^2 - 2*a - 6,
-2*a^2 - a + 10,
4*a^2 - a - 13,
-3*a^2 + 9,
a^2 - a - 3,
-2*a^2 - a + 5
]
*], q_expansions := [*
q - q^2 + q^3 + q^4 - q^5 - q^6 - q^7 - q^8 - 2*q^9 + q^10 - 3*q^11 + q^12 - 5*q^13 + q^14 - q^15 + q^16 + 2*q^17 + 2*q^18 - 7*q^19 - q^20 - q^21 + 3*q^22 + 8*q^23 - q^24 + q^25 + 5*q^26 - 5*q^27 - q^28 - 2*q^29 + q^30 - 5*q^31 - q^32 - 3*q^33 - 2*q^34 + q^35 - 2*q^36 - 4*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + q^5 - q^6 - q^7 - q^8 - 2*q^9 - q^10 + 3*q^11 + q^12 + 5*q^13 + q^14 + q^15 + q^16 + 6*q^17 + 2*q^18 - q^19 + q^20 - q^21 - 3*q^22 - q^24 + q^25 - 5*q^26 - 5*q^27 - q^28 - 6*q^29 - q^30 + 5*q^31 - q^32 + 3*q^33 - 6*q^34 - q^35 - 2*q^36 + 8*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + q^5 + q^6 - q^7 - q^8 - 2*q^9 - q^10 + q^11 - q^12 - 5*q^13 + q^14 - q^15 + q^16 + 2*q^18 + 5*q^19 + q^20 + q^21 - q^22 - 6*q^23 + q^24 + q^25 + 5*q^26 + 5*q^27 - q^28 - 6*q^29 + q^30 - 11*q^31 - q^32 - q^33 - q^35 - 2*q^36 - 8*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - q^5 + q^6 + 5*q^7 + q^8 - 2*q^9 - q^10 - 3*q^11 + q^12 + 5*q^13 + 5*q^14 - q^15 + q^16 - 2*q^18 - 7*q^19 - q^20 + 5*q^21 - 3*q^22 + 6*q^23 + q^24 + q^25 + 5*q^26 - 5*q^27 + 5*q^28 - 6*q^29 - q^30 + 5*q^31 + q^32 - 3*q^33 - 5*q^35 - 2*q^36 + 8*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - q^5 - q^6 - 3*q^7 + q^8 - 2*q^9 - q^10 - 5*q^11 - q^12 - q^13 - 3*q^14 + q^15 + q^16 + 2*q^17 - 2*q^18 - q^19 - q^20 + 3*q^21 - 5*q^22 - q^24 + q^25 - q^26 + 5*q^27 - 3*q^28 + 2*q^29 + q^30 - 7*q^31 + q^32 + 5*q^33 + 2*q^34 + 3*q^35 - 2*q^36 + O(q^38),
q + q^2 - 3*q^3 + q^4 + q^5 - 3*q^6 - 3*q^7 + q^8 + 6*q^9 + q^10 - q^11 - 3*q^12 - q^13 - 3*q^14 - 3*q^15 + q^16 - 8*q^17 + 6*q^18 - 5*q^19 + q^20 + 9*q^21 - q^22 - 2*q^23 - 3*q^24 + q^25 - q^26 - 9*q^27 - 3*q^28 - 2*q^29 - 3*q^30 - 5*q^31 + q^32 + 3*q^33 - 8*q^34 - 3*q^35 + 6*q^36 - 4*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + q^5 - a*q^6 + 4*q^7 - q^8 + (a + 2)*q^9 - q^10 + (a - 3)*q^11 + a*q^12 + (-2*a + 2)*q^13 - 4*q^14 + a*q^15 + q^16 - 4*q^17 + (-a - 2)*q^18 - a*q^19 + q^20 + 4*a*q^21 + (-a + 3)*q^22 + (-a + 1)*q^23 - a*q^24 + q^25 + (2*a - 2)*q^26 + 5*q^27 + 4*q^28 + (-3*a + 2)*q^29 - a*q^30 + (2*a - 2)*q^31 - q^32 + (-2*a + 5)*q^33 + 4*q^34 + 4*q^35 + (a + 2)*q^36 + (-3*a + 1)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - q^5 - a*q^6 + (-a^2 + a + 5)*q^7 - q^8 + (a^2 - 3)*q^9 + q^10 + (-a^2 + 4)*q^11 + a*q^12 + (a^2 + a - 3)*q^13 + (a^2 - a - 5)*q^14 - a*q^15 + q^16 + (-a^2 + 3)*q^18 + (a + 4)*q^19 - q^20 + (a^2 - a - 1)*q^21 + (a^2 - 4)*q^22 + (a - 1)*q^23 - a*q^24 + q^25 + (-a^2 - a + 3)*q^26 + q^27 + (-a^2 + a + 5)*q^28 + (-a^2 + 7)*q^29 + a*q^30 + (-a^2 - a + 7)*q^31 - q^32 + (-2*a - 1)*q^33 + (a^2 - a - 5)*q^35 + (a^2 - 3)*q^36 + (-3*a + 5)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - q^5 + a*q^6 + q^8 + (a^2 - 3)*q^9 - q^10 + (-a^2 + 8)*q^11 + a*q^12 + (-2*a + 2)*q^13 - a*q^15 + q^16 + (-2*a^2 + 2*a + 10)*q^17 + (a^2 - 3)*q^18 + (-a + 4)*q^19 - q^20 + (-a^2 + 8)*q^22 + (a^2 - 2*a - 8)*q^23 + a*q^24 + q^25 + (-2*a + 2)*q^26 + (3*a^2 - a - 12)*q^27 + (a - 2)*q^29 - a*q^30 + (2*a^2 - 4*a - 8)*q^31 + q^32 + (-3*a^2 + 3*a + 12)*q^33 + (-2*a^2 + 2*a + 10)*q^34 + (a^2 - 3)*q^36 + (a^2 + 2*a - 10)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + q^5 + a*q^6 + (-a^2 - a + 5)*q^7 + q^8 + (a^2 - 3)*q^9 + q^10 + (a^2 - 4)*q^11 + a*q^12 + (-a^2 + a + 3)*q^13 + (-a^2 - a + 5)*q^14 + a*q^15 + q^16 + (2*a^2 - 2*a - 6)*q^17 + (a^2 - 3)*q^18 + (-2*a^2 - a + 10)*q^19 + q^20 + (-3*a^2 + a + 7)*q^21 + (a^2 - 4)*q^22 + (4*a^2 - a - 13)*q^23 + a*q^24 + q^25 + (-a^2 + a + 3)*q^26 + (2*a^2 - 2*a - 7)*q^27 + (-a^2 - a + 5)*q^28 + (-3*a^2 + 9)*q^29 + a*q^30 + (a^2 - a - 3)*q^31 + q^32 + (2*a^2 - 7)*q^33 + (2*a^2 - 2*a - 6)*q^34 + (-a^2 - a + 5)*q^35 + (a^2 - 3)*q^36 + (-2*a^2 - a + 5)*q^37 + O(q^38)
*]> ;  // time = 259.99 seconds




J[471] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 471, 471, 471, 471, 471, 157, 157 ], new_dimensions := [ 1, 2, 3, 9, 12, 5, 7 ], dimensions := [ 1, 2, 3, 9, 12, 10, 14 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 19, 1, 1, 0, 1, 1, 53, 1, 1, 1, 1, 0, 1, 1, 6881, 1, 1, 1, 1, 0, 3851, 1, 1, 1, 53, 1, 3851, 0, 1, 1, 19, 1, 6881, 1, 1, 0 ], ap_traces := [
[ -1, -1, -2, 3, 0, 1, -3, -2, -9, 0, -2, 1 ],
[ -1, 2, -2, -6, -1, -3, -4, -6, 2, -1, -3, 6 ],
[ 0, -3, -2, -3, -5, -2, -9, 4, 3, -17, -1, -5 ],
[ 2, -9, 8, -2, 7, -1, 20, 2, 8, 19, 5, -8 ],
[ -1, 12, 4, 8, -1, 15, 10, 14, -8, 5, 5, 4 ]
], hecke_fields := [
x - 1,
x^2 + x - 1,
x^3 - 4*x + 1,
x^9 - 2*x^8 - 11*x^7 + 19*x^6 + 39*x^5 - 53*x^4 - 49*x^3 + 45*x^2 + 14*x - 1,
x^12 + x^11 - 20*x^10 - 17*x^9 + 149*x^8 + 106*x^7 - 500*x^6 - 294*x^5 + 711*x^4 + 349*x^3 - 290*x^2 - 173*x - 15
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 19, 1 ],
[ 53, 1 ],
[ 6881, 1 ],
[ 304229, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 19, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 304229, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 79 ], torsion_lower_bounds := [ 1, 1, 1, 1, 79 ], l_ratios := [ 0, 0, 0, 1, 3851/79 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ -1, -1, -2, 3, 0, 1, -3, -2, -9, 0, -2, 1 ],
[
a,
1,
-1,
-3,
-3*a - 2,
-a - 2,
2*a - 1,
2*a - 2,
1,
-a - 1,
7*a + 2,
-2*a + 2
],
[
a,
-1,
-a^2 - a + 2,
-1,
-a^2 + 1,
2*a^2 - a - 6,
-3,
2*a^2 - 4,
-2*a + 1,
2*a^2 + 3*a - 11,
a^2 - 3,
-a^2 + 3*a + 1
],
[
a,
-1,
-8/59*a^8 + 41/59*a^7 + 41/59*a^6 - 376/59*a^5 + 37/59*a^4 + 950/59*a^3 - 143/59*a^2 - 599/59*a - 47/59,
-31/59*a^8 + 63/59*a^7 + 299/59*a^6 - 513/59*a^5 - 867/59*a^4 + 1041/59*a^3 + 825/59*a^2 - 411/59*a - 160/59,
15/59*a^8 - 40/59*a^7 - 158/59*a^6 + 410/59*a^5 + 528/59*a^4 - 1324/59*a^3 - 580/59*a^2 + 1396/59*a + 125/59,
17/59*a^8 - 6/59*a^7 - 242/59*a^6 + 32/59*a^5 + 1094/59*a^4 + 2/59*a^3 - 1562/59*a^2 + 56/59*a + 299/59,
-45/59*a^8 + 61/59*a^7 + 533/59*a^6 - 581/59*a^5 - 1997/59*a^4 + 1671/59*a^3 + 2389/59*a^2 - 1533/59*a - 198/59,
9/59*a^8 - 24/59*a^7 - 83/59*a^6 + 246/59*a^5 + 246/59*a^4 - 818/59*a^3 - 407/59*a^2 + 932/59*a + 311/59,
3/59*a^8 - 8/59*a^7 - 67/59*a^6 + 141/59*a^5 + 377/59*a^4 - 607/59*a^3 - 647/59*a^2 + 586/59*a + 320/59,
-24/59*a^8 + 64/59*a^7 + 241/59*a^6 - 597/59*a^5 - 715/59*a^4 + 1493/59*a^3 + 515/59*a^2 - 912/59*a + 331/59,
-38/59*a^8 + 62/59*a^7 + 475/59*a^6 - 606/59*a^5 - 1904/59*a^4 + 1710/59*a^3 + 2433/59*a^2 - 1444/59*a - 356/59,
17/59*a^8 - 6/59*a^7 - 183/59*a^6 - 86/59*a^5 + 622/59*a^4 + 828/59*a^3 - 677/59*a^2 - 1124/59*a + 63/59
],
[
a,
1,
a^11 - 21*a^9 + a^8 + 162*a^7 - 14*a^6 - 553*a^5 + 64*a^4 + 776*a^3 - 100*a^2 - 285*a - 25,
1/2*a^11 + 1/2*a^10 - 19/2*a^9 - 7*a^8 + 68*a^7 + 32*a^6 - 222*a^5 - 49*a^4 + 615/2*a^3 + 19/2*a^2 - 219/2*a - 16,
a^10 + 3*a^9 - 14*a^8 - 42*a^7 + 66*a^6 + 194*a^5 - 120*a^4 - 322*a^3 + 75*a^2 + 137*a + 18,
-a^11 - 3/2*a^10 + 35/2*a^9 + 41/2*a^8 - 115*a^7 - 90*a^6 + 348*a^5 + 128*a^4 - 462*a^3 - 33/2*a^2 + 317/2*a + 37/2,
-a^11 + 1/2*a^10 + 45/2*a^9 - 15/2*a^8 - 183*a^7 + 40*a^6 + 650*a^5 - 94*a^4 - 938*a^3 + 195/2*a^2 + 723/2*a + 89/2,
a^10 + 3*a^9 - 14*a^8 - 42*a^7 + 67*a^6 + 194*a^5 - 130*a^4 - 320*a^3 + 100*a^2 + 129*a + 10,
3/2*a^11 - 1/2*a^10 - 69/2*a^9 + 7*a^8 + 287*a^7 - 38*a^6 - 1044*a^5 + 113*a^4 + 3077/2*a^3 - 355/2*a^2 - 1163/2*a - 58,
-a^10 - 4*a^9 + 13*a^8 + 57*a^7 - 56*a^6 - 270*a^5 + 96*a^4 + 462*a^3 - 75*a^2 - 195*a - 23,
a^6 - 10*a^4 + 4*a^3 + 25*a^2 - 18*a - 8,
4*a^11 + 5/2*a^10 - 157/2*a^9 - 65/2*a^8 + 573*a^7 + 127*a^6 - 1876*a^5 - 110*a^4 + 2567*a^3 - 271/2*a^2 - 1843/2*a - 205/2
]
*], q_expansions := [*
q - q^2 - q^3 - q^4 - 2*q^5 + q^6 + 3*q^7 + 3*q^8 + q^9 + 2*q^10 + q^12 + q^13 - 3*q^14 + 2*q^15 - q^16 - 3*q^17 - q^18 - 2*q^19 + 2*q^20 - 3*q^21 - 9*q^23 - 3*q^24 - q^25 - q^26 - q^27 - 3*q^28 - 2*q^30 - 2*q^31 - 5*q^32 + 3*q^34 - 6*q^35 - q^36 + q^37 + O(q^38),
q + a*q^2 + q^3 + (-a - 1)*q^4 - q^5 + a*q^6 - 3*q^7 + (-2*a - 1)*q^8 + q^9 - a*q^10 + (-3*a - 2)*q^11 + (-a - 1)*q^12 + (-a - 2)*q^13 - 3*a*q^14 - q^15 + 3*a*q^16 + (2*a - 1)*q^17 + a*q^18 + (2*a - 2)*q^19 + (a + 1)*q^20 - 3*q^21 + (a - 3)*q^22 + q^23 + (-2*a - 1)*q^24 - 4*q^25 + (-a - 1)*q^26 + q^27 + (3*a + 3)*q^28 + (-a - 1)*q^29 - a*q^30 + (7*a + 2)*q^31 + (a + 5)*q^32 + (-3*a - 2)*q^33 + (-3*a + 2)*q^34 + 3*q^35 + (-a - 1)*q^36 + (-2*a + 2)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 - a + 2)*q^5 - a*q^6 - q^7 - q^8 + q^9 + (-a^2 - 2*a + 1)*q^10 + (-a^2 + 1)*q^11 + (-a^2 + 2)*q^12 + (2*a^2 - a - 6)*q^13 - a*q^14 + (a^2 + a - 2)*q^15 + (-2*a^2 - a + 4)*q^16 - 3*q^17 + a*q^18 + (2*a^2 - 4)*q^19 + (-a - 3)*q^20 + q^21 + (-3*a + 1)*q^22 + (-2*a + 1)*q^23 + q^24 + (a^2 + 3*a - 3)*q^25 + (-a^2 + 2*a - 2)*q^26 - q^27 + (-a^2 + 2)*q^28 + (2*a^2 + 3*a - 11)*q^29 + (a^2 + 2*a - 1)*q^30 + (a^2 - 3)*q^31 + (-a^2 - 4*a + 4)*q^32 + (a^2 - 1)*q^33 - 3*a*q^34 + (a^2 + a - 2)*q^35 + (a^2 - 2)*q^36 + (-a^2 + 3*a + 1)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-8/59*a^8 + 41/59*a^7 + 41/59*a^6 - 376/59*a^5 + 37/59*a^4 + 950/59*a^3 - 143/59*a^2 - 599/59*a - 47/59)*q^5 - a*q^6 + (-31/59*a^8 + 63/59*a^7 + 299/59*a^6 - 513/59*a^5 - 867/59*a^4 + 1041/59*a^3 + 825/59*a^2 - 411/59*a - 160/59)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (25/59*a^8 - 47/59*a^7 - 224/59*a^6 + 349/59*a^5 + 526/59*a^4 - 535/59*a^3 - 239/59*a^2 + 65/59*a - 8/59)*q^10 + (15/59*a^8 - 40/59*a^7 - 158/59*a^6 + 410/59*a^5 + 528/59*a^4 - 1324/59*a^3 - 580/59*a^2 + 1396/59*a + 125/59)*q^11 + (-a^2 + 2)*q^12 + (17/59*a^8 - 6/59*a^7 - 242/59*a^6 + 32/59*a^5 + 1094/59*a^4 + 2/59*a^3 - 1562/59*a^2 + 56/59*a + 299/59)*q^13 + (1/59*a^8 - 42/59*a^7 + 76/59*a^6 + 342/59*a^5 - 602/59*a^4 - 694/59*a^3 + 984/59*a^2 + 274/59*a - 31/59)*q^14 + (8/59*a^8 - 41/59*a^7 - 41/59*a^6 + 376/59*a^5 - 37/59*a^4 - 950/59*a^3 + 143/59*a^2 + 599/59*a + 47/59)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-45/59*a^8 + 61/59*a^7 + 533/59*a^6 - 581/59*a^5 - 1997/59*a^4 + 1671/59*a^3 + 2389/59*a^2 - 1533/59*a - 198/59)*q^17 + a*q^18 + (9/59*a^8 - 24/59*a^7 - 83/59*a^6 + 246/59*a^5 + 246/59*a^4 - 818/59*a^3 - 407/59*a^2 + 932/59*a + 311/59)*q^19 + (19/59*a^8 - 31/59*a^7 - 208/59*a^6 + 303/59*a^5 + 716/59*a^4 - 914/59*a^3 - 774/59*a^2 + 840/59*a + 119/59)*q^20 + (31/59*a^8 - 63/59*a^7 - 299/59*a^6 + 513/59*a^5 + 867/59*a^4 - 1041/59*a^3 - 825/59*a^2 + 411/59*a + 160/59)*q^21 + (-10/59*a^8 + 7/59*a^7 + 125/59*a^6 - 57/59*a^5 - 529/59*a^4 + 155/59*a^3 + 721/59*a^2 - 85/59*a + 15/59)*q^22 + (3/59*a^8 - 8/59*a^7 - 67/59*a^6 + 141/59*a^5 + 377/59*a^4 - 607/59*a^3 - 647/59*a^2 + 586/59*a + 320/59)*q^23 + (-a^3 + 4*a)*q^24 + (24/59*a^8 - 5/59*a^7 - 300/59*a^6 + 7/59*a^5 + 1069/59*a^4 + 159/59*a^3 - 810/59*a^2 - 327/59*a - 154/59)*q^25 + (28/59*a^8 - 55/59*a^7 - 291/59*a^6 + 431/59*a^5 + 903/59*a^4 - 729/59*a^3 - 709/59*a^2 + 61/59*a + 17/59)*q^26 - q^27 + (22/59*a^8 - 39/59*a^7 - 275/59*a^6 + 385/59*a^5 + 1093/59*a^4 - 1049/59*a^3 - 1421/59*a^2 + 777/59*a + 321/59)*q^28 + (-24/59*a^8 + 64/59*a^7 + 241/59*a^6 - 597/59*a^5 - 715/59*a^4 + 1493/59*a^3 + 515/59*a^2 - 912/59*a + 331/59)*q^29 + (-25/59*a^8 + 47/59*a^7 + 224/59*a^6 - 349/59*a^5 - 526/59*a^4 + 535/59*a^3 + 239/59*a^2 - 65/59*a + 8/59)*q^30 + (-38/59*a^8 + 62/59*a^7 + 475/59*a^6 - 606/59*a^5 - 1904/59*a^4 + 1710/59*a^3 + 2433/59*a^2 - 1444/59*a - 356/59)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-15/59*a^8 + 40/59*a^7 + 158/59*a^6 - 410/59*a^5 - 528/59*a^4 + 1324/59*a^3 + 580/59*a^2 - 1396/59*a - 125/59)*q^33 + (-29/59*a^8 + 38/59*a^7 + 274/59*a^6 - 242/59*a^5 - 714/59*a^4 + 184/59*a^3 + 492/59*a^2 + 432/59*a - 45/59)*q^34 + (25/59*a^8 - 47/59*a^7 - 283/59*a^6 + 467/59*a^5 + 939/59*a^4 - 1243/59*a^3 - 829/59*a^2 + 537/59*a + 228/59)*q^35 + (a^2 - 2)*q^36 + (17/59*a^8 - 6/59*a^7 - 183/59*a^6 - 86/59*a^5 + 622/59*a^4 + 828/59*a^3 - 677/59*a^2 - 1124/59*a + 63/59)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (a^11 - 21*a^9 + a^8 + 162*a^7 - 14*a^6 - 553*a^5 + 64*a^4 + 776*a^3 - 100*a^2 - 285*a - 25)*q^5 + a*q^6 + (1/2*a^11 + 1/2*a^10 - 19/2*a^9 - 7*a^8 + 68*a^7 + 32*a^6 - 222*a^5 - 49*a^4 + 615/2*a^3 + 19/2*a^2 - 219/2*a - 16)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^11 - a^10 + 18*a^9 + 13*a^8 - 120*a^7 - 53*a^6 + 358*a^5 + 65*a^4 - 449*a^3 + 5*a^2 + 148*a + 15)*q^10 + (a^10 + 3*a^9 - 14*a^8 - 42*a^7 + 66*a^6 + 194*a^5 - 120*a^4 - 322*a^3 + 75*a^2 + 137*a + 18)*q^11 + (a^2 - 2)*q^12 + (-a^11 - 3/2*a^10 + 35/2*a^9 + 41/2*a^8 - 115*a^7 - 90*a^6 + 348*a^5 + 128*a^4 - 462*a^3 - 33/2*a^2 + 317/2*a + 37/2)*q^13 + (1/2*a^10 + 3/2*a^9 - 13/2*a^8 - 21*a^7 + 28*a^6 + 98*a^5 - 48*a^4 - 165*a^3 + 71/2*a^2 + 141/2*a + 15/2)*q^14 + (a^11 - 21*a^9 + a^8 + 162*a^7 - 14*a^6 - 553*a^5 + 64*a^4 + 776*a^3 - 100*a^2 - 285*a - 25)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^11 + 1/2*a^10 + 45/2*a^9 - 15/2*a^8 - 183*a^7 + 40*a^6 + 650*a^5 - 94*a^4 - 938*a^3 + 195/2*a^2 + 723/2*a + 89/2)*q^17 + a*q^18 + (a^10 + 3*a^9 - 14*a^8 - 42*a^7 + 67*a^6 + 194*a^5 - 130*a^4 - 320*a^3 + 100*a^2 + 129*a + 10)*q^19 + (-2*a^11 - 2*a^10 + 38*a^9 + 27*a^8 - 271*a^7 - 114*a^6 + 877*a^5 + 134*a^4 - 1198*a^3 + 58*a^2 + 412*a + 35)*q^20 + (1/2*a^11 + 1/2*a^10 - 19/2*a^9 - 7*a^8 + 68*a^7 + 32*a^6 - 222*a^5 - 49*a^4 + 615/2*a^3 + 19/2*a^2 - 219/2*a - 16)*q^21 + (a^11 + 3*a^10 - 14*a^9 - 42*a^8 + 66*a^7 + 194*a^6 - 120*a^5 - 322*a^4 + 75*a^3 + 137*a^2 + 18*a)*q^22 + (3/2*a^11 - 1/2*a^10 - 69/2*a^9 + 7*a^8 + 287*a^7 - 38*a^6 - 1044*a^5 + 113*a^4 + 3077/2*a^3 - 355/2*a^2 - 1163/2*a - 58)*q^23 + (a^3 - 4*a)*q^24 + (-3*a^11 - 2*a^10 + 59*a^9 + 27*a^8 - 432*a^7 - 113*a^6 + 1420*a^5 + 124*a^4 - 1947*a^3 + 83*a^2 + 687*a + 80)*q^25 + (-1/2*a^11 - 5/2*a^10 + 7/2*a^9 + 34*a^8 + 16*a^7 - 152*a^6 - 166*a^5 + 249*a^4 + 665/2*a^3 - 263/2*a^2 - 309/2*a - 15)*q^26 + q^27 + (-1/2*a^11 + 1/2*a^10 + 25/2*a^9 - 7*a^8 - 108*a^7 + 34*a^6 + 396*a^5 - 67*a^4 - 1159/2*a^3 + 103/2*a^2 + 453/2*a + 32)*q^28 + (-a^10 - 4*a^9 + 13*a^8 + 57*a^7 - 56*a^6 - 270*a^5 + 96*a^4 + 462*a^3 - 75*a^2 - 195*a - 23)*q^29 + (-a^11 - a^10 + 18*a^9 + 13*a^8 - 120*a^7 - 53*a^6 + 358*a^5 + 65*a^4 - 449*a^3 + 5*a^2 + 148*a + 15)*q^30 + (a^6 - 10*a^4 + 4*a^3 + 25*a^2 - 18*a - 8)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^10 + 3*a^9 - 14*a^8 - 42*a^7 + 66*a^6 + 194*a^5 - 120*a^4 - 322*a^3 + 75*a^2 + 137*a + 18)*q^33 + (3/2*a^11 + 5/2*a^10 - 49/2*a^9 - 34*a^8 + 146*a^7 + 150*a^6 - 388*a^5 - 227*a^4 + 893/2*a^3 + 143/2*a^2 - 257/2*a - 15)*q^34 + (a^11 + a^10 - 18*a^9 - 13*a^8 + 120*a^7 + 54*a^6 - 360*a^5 - 78*a^4 + 465*a^3 + 37*a^2 - 172*a - 35)*q^35 + (a^2 - 2)*q^36 + (4*a^11 + 5/2*a^10 - 157/2*a^9 - 65/2*a^8 + 573*a^7 + 127*a^6 - 1876*a^5 - 110*a^4 + 2567*a^3 - 271/2*a^2 - 1843/2*a - 205/2)*q^37 + O(q^38)
*]> ;  // time = 94.76 seconds




J[473] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 473, 473, 473, 473, 473, 473, 473, 43, 43, 11 ], new_dimensions := [ 1, 2, 2, 5, 5, 9, 11, 1, 2, 1 ], dimensions := [ 1, 2, 2, 5, 5, 9, 11, 2, 4, 2 ], intersection_graph := [ 0, 1, 1, 17, 1, 1, 1, 3, 1, 1, 1, 0, 1, 11, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 19, 1, 1, 1, 1, 5, 17, 11, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 0, 1, 1, 1, 23, 1, 1, 1, 1, 1, 1, 0, 1, 9, 1, 19, 1, 1, 1, 1, 1, 1, 0, 1, 113, 1, 3, 5, 1, 1, 1, 9, 1, 0, 1, 1, 1, 1, 1, 1, 23, 1, 113, 1, 0, 1, 1, 1, 5, 1, 1, 19, 1, 1, 1, 0 ], ap_traces := [
[ -2, 1, -1, 0, -1, -2, 6, -8, -1, 6, -1, -3 ],
[ 1, -4, 2, 0, -2, 0, -6, -4, -12, -2, -12, 0 ],
[ 1, -2, 2, -4, 2, -12, -4, 0, -12, -10, 4, 6 ],
[ 1, -3, -6, -15, -5, -1, 5, -3, -4, 4, -18, -17 ],
[ -3, -1, -4, -9, 5, -9, -13, -7, 8, 10, -22, -13 ],
[ 4, 5, 0, 19, 9, 11, 3, 17, 0, 18, 14, 15 ],
[ -1, 6, 3, 17, -11, 11, -5, 5, 11, -16, 33, 8 ]
], hecke_fields := [
x - 1,
x^2 - x - 1,
x^2 - x - 1,
x^5 - x^4 - 6*x^3 + 5*x^2 + x - 1,
x^5 + 3*x^4 - 4*x^3 - 13*x^2 + 3*x + 9,
x^9 - 4*x^8 - 5*x^7 + 36*x^6 - 20*x^5 - 65*x^4 + 66*x^3 + 4*x^2 - 8*x + 1,
x^11 + x^10 - 17*x^9 - 15*x^8 + 102*x^7 + 77*x^6 - 255*x^5 - 150*x^4 + 248*x^3 + 59*x^2 - 93*x + 18
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 3, 1 ],
[ 5, 1 ],
[ 1, 5 ],
[ 1, 1 ],
[ 23, 1 ],
[ 99, 19 ],
[ 339, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 5 ],
[ 1, 1 ],
[ 23, 1 ],
[ 99, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 1, 1, 5, 1, 1, 11, 3 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 11, 3 ], l_ratios := [ 0, 0, 0, 0, 0, 9/11, 1/3 ], analytic_sha_upper_bounds := [ 0, 0, 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 0, 0, 1, 1 ], eigenvalues := [*
[ -2, 1, -1, 0, -1, -2, 6, -8, -1, 6, -1, -3 ],
[
a,
-2,
-2*a + 2,
2*a - 1,
-1,
-4*a + 2,
-2*a - 2,
2*a - 3,
2*a - 7,
8*a - 5,
-2*a - 5,
4*a - 2
],
[
a,
-2*a,
2*a,
-2*a - 1,
1,
-6,
-2,
-2*a + 1,
2*a - 7,
-5,
-2*a + 3,
6*a
],
[
a,
2*a^4 - a^3 - 13*a^2 + 4*a + 4,
-5*a^4 + 2*a^3 + 31*a^2 - 7*a - 9,
a^3 - a^2 - 6*a,
-1,
3*a^4 - a^3 - 18*a^2 + 3*a + 3,
7*a^4 - 4*a^3 - 43*a^2 + 14*a + 11,
-9*a^4 + 2*a^3 + 57*a^2 - 5*a - 18,
-4*a^4 + 3*a^3 + 25*a^2 - 14*a - 7,
-9*a^4 + 3*a^3 + 57*a^2 - 7*a - 17,
-12*a^4 + 4*a^3 + 75*a^2 - 8*a - 25,
10*a^4 - 4*a^3 - 63*a^2 + 13*a + 15
],
[
a,
-2/3*a^4 - a^3 + 11/3*a^2 + 8/3*a - 4,
1/3*a^4 - 7/3*a^2 - 1/3*a + 1,
2/3*a^4 + a^3 - 11/3*a^2 - 8/3*a + 2,
1,
-1/3*a^4 - a^3 - 2/3*a^2 + 7/3*a + 3,
a^4 + 2*a^3 - 3*a^2 - 4*a - 3,
1/3*a^4 + 2*a^3 + 5/3*a^2 - 13/3*a - 6,
-2/3*a^4 - a^3 + 11/3*a^2 + 14/3*a - 1,
1/3*a^4 + a^3 - 7/3*a^2 - 19/3*a + 5,
-a^2 - 1,
-2*a^3 - 5*a^2 + 7*a + 9
],
[
a,
a^8 - 3*a^7 - 7*a^6 + 27*a^5 - 2*a^4 - 49*a^3 + 33*a^2 + 4*a - 3,
-5*a^8 + 18*a^7 + 31*a^6 - 165*a^5 + 45*a^4 + 320*a^3 - 224*a^2 - 69*a + 21,
2*a^8 - 8*a^7 - 11*a^6 + 74*a^5 - 31*a^4 - 148*a^3 + 115*a^2 + 40*a - 9,
1,
4*a^8 - 14*a^7 - 26*a^6 + 128*a^5 - 25*a^4 - 245*a^3 + 158*a^2 + 43*a - 13,
-a^8 + 14*a^6 - 61*a^4 - a^3 + 81*a^2 + 7*a - 3,
-4*a^8 + 16*a^7 + 21*a^6 - 147*a^5 + 71*a^4 + 287*a^3 - 246*a^2 - 66*a + 24,
-8*a^8 + 28*a^7 + 51*a^6 - 257*a^5 + 60*a^4 + 500*a^3 - 340*a^2 - 109*a + 35,
5*a^8 - 16*a^7 - 35*a^6 + 147*a^5 - 9*a^4 - 287*a^3 + 158*a^2 + 63*a - 11,
5*a^8 - 19*a^7 - 29*a^6 + 174*a^5 - 63*a^4 - 336*a^3 + 256*a^2 + 71*a - 21,
-a^7 + 2*a^6 + 10*a^5 - 18*a^4 - 26*a^3 + 34*a^2 + 21*a - 4
],
[
a,
-19/18*a^10 - 11/9*a^9 + 311/18*a^8 + 56/3*a^7 - 293/3*a^6 - 1769/18*a^5 + 655/3*a^4 + 601/3*a^3 - 1465/9*a^2 - 1829/18*a + 136/3,
-7/9*a^10 - 10/9*a^9 + 116/9*a^8 + 52/3*a^7 - 223/3*a^6 - 836/9*a^5 + 515/3*a^4 + 572/3*a^3 - 1214/9*a^2 - 878/9*a + 125/3,
-1/3*a^10 - 1/3*a^9 + 17/3*a^8 + 5*a^7 - 33*a^6 - 77/3*a^5 + 74*a^4 + 50*a^3 - 149/3*a^2 - 59/3*a + 10,
-1,
1/3*a^10 + 1/3*a^9 - 17/3*a^8 - 5*a^7 + 34*a^6 + 77/3*a^5 - 84*a^4 - 51*a^3 + 224/3*a^2 + 80/3*a - 18,
10/9*a^10 + 13/9*a^9 - 167/9*a^8 - 67/3*a^7 + 322/3*a^6 + 1076/9*a^5 - 740/3*a^4 - 749/3*a^3 + 1733/9*a^2 + 1199/9*a - 176/3,
2/3*a^10 + 2/3*a^9 - 34/3*a^8 - 10*a^7 + 67*a^6 + 157/3*a^5 - 159*a^4 - 109*a^3 + 394/3*a^2 + 172/3*a - 32,
8/9*a^10 + 14/9*a^9 - 130/9*a^8 - 74/3*a^7 + 245/3*a^6 + 1201/9*a^5 - 556/3*a^4 - 820/3*a^3 + 1300/9*a^2 + 1285/9*a - 157/3,
-31/18*a^10 - 26/9*a^9 + 515/18*a^8 + 134/3*a^7 - 497/3*a^6 - 4277/18*a^5 + 1159/3*a^4 + 1471/3*a^3 - 2854/9*a^2 - 4859/18*a + 325/3,
5/3*a^10 + 8/3*a^9 - 82/3*a^8 - 41*a^7 + 155*a^6 + 649/3*a^5 - 349*a^4 - 440*a^3 + 808/3*a^2 + 688/3*a - 89,
1/3*a^10 + 1/3*a^9 - 17/3*a^8 - 6*a^7 + 34*a^6 + 113/3*a^5 - 85*a^4 - 92*a^3 + 242/3*a^2 + 182/3*a - 27
]
*], q_expansions := [*
q - 2*q^2 + q^3 + 2*q^4 - q^5 - 2*q^6 - 2*q^9 + 2*q^10 - q^11 + 2*q^12 - 2*q^13 - q^15 - 4*q^16 + 6*q^17 + 4*q^18 - 8*q^19 - 2*q^20 + 2*q^22 - q^23 - 4*q^25 + 4*q^26 - 5*q^27 + 6*q^29 + 2*q^30 - q^31 + 8*q^32 - q^33 - 12*q^34 - 4*q^36 - 3*q^37 + O(q^38),
q + a*q^2 - 2*q^3 + (a - 1)*q^4 + (-2*a + 2)*q^5 - 2*a*q^6 + (2*a - 1)*q^7 + (-2*a + 1)*q^8 + q^9 - 2*q^10 - q^11 + (-2*a + 2)*q^12 + (-4*a + 2)*q^13 + (a + 2)*q^14 + (4*a - 4)*q^15 - 3*a*q^16 + (-2*a - 2)*q^17 + a*q^18 + (2*a - 3)*q^19 + (2*a - 4)*q^20 + (-4*a + 2)*q^21 - a*q^22 + (2*a - 7)*q^23 + (4*a - 2)*q^24 + (-4*a + 3)*q^25 + (-2*a - 4)*q^26 + 4*q^27 + (-a + 3)*q^28 + (8*a - 5)*q^29 + 4*q^30 + (-2*a - 5)*q^31 + (a - 5)*q^32 + 2*q^33 + (-4*a - 2)*q^34 + (2*a - 6)*q^35 + (a - 1)*q^36 + (4*a - 2)*q^37 + O(q^38),
q + a*q^2 - 2*a*q^3 + (a - 1)*q^4 + 2*a*q^5 + (-2*a - 2)*q^6 + (-2*a - 1)*q^7 + (-2*a + 1)*q^8 + (4*a + 1)*q^9 + (2*a + 2)*q^10 + q^11 - 2*q^12 - 6*q^13 + (-3*a - 2)*q^14 + (-4*a - 4)*q^15 - 3*a*q^16 - 2*q^17 + (5*a + 4)*q^18 + (-2*a + 1)*q^19 + 2*q^20 + (6*a + 4)*q^21 + a*q^22 + (2*a - 7)*q^23 + (2*a + 4)*q^24 + (4*a - 1)*q^25 - 6*a*q^26 + (-4*a - 8)*q^27 + (-a - 1)*q^28 - 5*q^29 + (-8*a - 4)*q^30 + (-2*a + 3)*q^31 + (a - 5)*q^32 - 2*a*q^33 - 2*a*q^34 + (-6*a - 4)*q^35 + (a + 3)*q^36 + 6*a*q^37 + O(q^38),
q + a*q^2 + (2*a^4 - a^3 - 13*a^2 + 4*a + 4)*q^3 + (a^2 - 2)*q^4 + (-5*a^4 + 2*a^3 + 31*a^2 - 7*a - 9)*q^5 + (a^4 - a^3 - 6*a^2 + 2*a + 2)*q^6 + (a^3 - a^2 - 6*a)*q^7 + (a^3 - 4*a)*q^8 + (6*a^4 - 3*a^3 - 36*a^2 + 10*a + 8)*q^9 + (-3*a^4 + a^3 + 18*a^2 - 4*a - 5)*q^10 - q^11 + (-4*a^4 + 2*a^3 + 23*a^2 - 7*a - 7)*q^12 + (3*a^4 - a^3 - 18*a^2 + 3*a + 3)*q^13 + (a^4 - a^3 - 6*a^2)*q^14 + (-10*a^4 + 5*a^3 + 63*a^2 - 17*a - 19)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (7*a^4 - 4*a^3 - 43*a^2 + 14*a + 11)*q^17 + (3*a^4 - 20*a^2 + 2*a + 6)*q^18 + (-9*a^4 + 2*a^3 + 57*a^2 - 5*a - 18)*q^19 + (8*a^4 - 4*a^3 - 51*a^2 + 12*a + 15)*q^20 + (-6*a^4 + 3*a^3 + 40*a^2 - 12*a - 13)*q^21 - a*q^22 + (-4*a^4 + 3*a^3 + 25*a^2 - 14*a - 7)*q^23 + (-4*a^4 + a^3 + 25*a^2 - 7*a - 8)*q^24 + (15*a^4 - 7*a^3 - 93*a^2 + 27*a + 24)*q^25 + (2*a^4 - 12*a^2 + 3)*q^26 + (2*a^4 - 14*a^2 + a + 4)*q^27 + (-2*a^3 - 3*a^2 + 11*a + 1)*q^28 + (-9*a^4 + 3*a^3 + 57*a^2 - 7*a - 17)*q^29 + (-5*a^4 + 3*a^3 + 33*a^2 - 9*a - 10)*q^30 + (-12*a^4 + 4*a^3 + 75*a^2 - 8*a - 25)*q^31 + (a^4 - 2*a^3 - 5*a^2 + 11*a + 1)*q^32 + (-2*a^4 + a^3 + 13*a^2 - 4*a - 4)*q^33 + (3*a^4 - a^3 - 21*a^2 + 4*a + 7)*q^34 + (18*a^4 - 7*a^3 - 111*a^2 + 25*a + 31)*q^35 + (-9*a^4 + 4*a^3 + 59*a^2 - 17*a - 13)*q^36 + (10*a^4 - 4*a^3 - 63*a^2 + 13*a + 15)*q^37 + O(q^38),
q + a*q^2 + (-2/3*a^4 - a^3 + 11/3*a^2 + 8/3*a - 4)*q^3 + (a^2 - 2)*q^4 + (1/3*a^4 - 7/3*a^2 - 1/3*a + 1)*q^5 + (a^4 + a^3 - 6*a^2 - 2*a + 6)*q^6 + (2/3*a^4 + a^3 - 11/3*a^2 - 8/3*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (a^3 - 6*a + 2)*q^9 + (-a^4 - a^3 + 4*a^2 - 3)*q^10 + q^11 + (-2/3*a^4 + 11/3*a^2 - 7/3*a - 1)*q^12 + (-1/3*a^4 - a^3 - 2/3*a^2 + 7/3*a + 3)*q^13 + (-a^4 - a^3 + 6*a^2 - 6)*q^14 + (2/3*a^4 + a^3 - 11/3*a^2 - 5/3*a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 + 2*a^3 - 3*a^2 - 4*a - 3)*q^17 + (a^4 - 6*a^2 + 2*a)*q^18 + (1/3*a^4 + 2*a^3 + 5/3*a^2 - 13/3*a - 6)*q^19 + (4/3*a^4 - 25/3*a^2 + 2/3*a + 7)*q^20 + (4/3*a^4 + a^3 - 22/3*a^2 + 2/3*a + 3)*q^21 + a*q^22 + (-2/3*a^4 - a^3 + 11/3*a^2 + 14/3*a - 1)*q^23 + (-a^3 + a^2 + 5*a - 6)*q^24 + (1/3*a^4 + a^3 + 5/3*a^2 - 1/3*a - 6)*q^25 + (-2*a^3 - 2*a^2 + 4*a + 3)*q^26 + (-4/3*a^4 - 2*a^3 + 28/3*a^2 + 19/3*a - 14)*q^27 + (2/3*a^4 - 17/3*a^2 + 7/3*a + 5)*q^28 + (1/3*a^4 + a^3 - 7/3*a^2 - 19/3*a + 5)*q^29 + (-a^4 - a^3 + 7*a^2 + a - 6)*q^30 + (-a^2 - 1)*q^31 + (-3*a^4 - 4*a^3 + 13*a^2 + 9*a - 9)*q^32 + (-2/3*a^4 - a^3 + 11/3*a^2 + 8/3*a - 4)*q^33 + (-a^4 + a^3 + 9*a^2 - 6*a - 9)*q^34 + (-4/3*a^4 - a^3 + 25/3*a^2 + 7/3*a - 5)*q^35 + (-3*a^4 - 4*a^3 + 15*a^2 + 9*a - 13)*q^36 + (-2*a^3 - 5*a^2 + 7*a + 9)*q^37 + O(q^38),
q + a*q^2 + (a^8 - 3*a^7 - 7*a^6 + 27*a^5 - 2*a^4 - 49*a^3 + 33*a^2 + 4*a - 3)*q^3 + (a^2 - 2)*q^4 + (-5*a^8 + 18*a^7 + 31*a^6 - 165*a^5 + 45*a^4 + 320*a^3 - 224*a^2 - 69*a + 21)*q^5 + (a^8 - 2*a^7 - 9*a^6 + 18*a^5 + 16*a^4 - 33*a^3 + 5*a - 1)*q^6 + (2*a^8 - 8*a^7 - 11*a^6 + 74*a^5 - 31*a^4 - 148*a^3 + 115*a^2 + 40*a - 9)*q^7 + (a^3 - 4*a)*q^8 + (a^7 - 2*a^6 - 10*a^5 + 18*a^4 + 25*a^3 - 33*a^2 - 16*a + 3)*q^9 + (-2*a^8 + 6*a^7 + 15*a^6 - 55*a^5 - 5*a^4 + 106*a^3 - 49*a^2 - 19*a + 5)*q^10 + q^11 + (2*a^7 - 4*a^6 - 18*a^5 + 36*a^4 + 32*a^3 - 65*a^2 - a + 5)*q^12 + (4*a^8 - 14*a^7 - 26*a^6 + 128*a^5 - 25*a^4 - 245*a^3 + 158*a^2 + 43*a - 13)*q^13 + (-a^7 + 2*a^6 + 9*a^5 - 18*a^4 - 17*a^3 + 32*a^2 + 7*a - 2)*q^14 + (3*a^8 - 14*a^7 - 12*a^6 + 129*a^5 - 87*a^4 - 254*a^3 + 246*a^2 + 61*a - 22)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^8 + 14*a^6 - 61*a^4 - a^3 + 81*a^2 + 7*a - 3)*q^17 + (a^8 - 2*a^7 - 10*a^6 + 18*a^5 + 25*a^4 - 33*a^3 - 16*a^2 + 3*a)*q^18 + (-4*a^8 + 16*a^7 + 21*a^6 - 147*a^5 + 71*a^4 + 287*a^3 - 246*a^2 - 66*a + 24)*q^19 + (8*a^8 - 31*a^7 - 45*a^6 + 285*a^5 - 114*a^4 - 557*a^3 + 437*a^2 + 127*a - 40)*q^20 + (-a^8 + 5*a^7 + 4*a^6 - 46*a^5 + 28*a^4 + 90*a^3 - 75*a^2 - 21*a + 4)*q^21 + a*q^22 + (-8*a^8 + 28*a^7 + 51*a^6 - 257*a^5 + 60*a^4 + 500*a^3 - 340*a^2 - 109*a + 35)*q^23 + (a^3 - a^2 - 5*a + 2)*q^24 + (6*a^8 - 21*a^7 - 39*a^6 + 194*a^5 - 38*a^4 - 386*a^3 + 240*a^2 + 99*a - 20)*q^25 + (2*a^8 - 6*a^7 - 16*a^6 + 55*a^5 + 15*a^4 - 106*a^3 + 27*a^2 + 19*a - 4)*q^26 + (2*a^8 - 3*a^7 - 21*a^6 + 27*a^5 + 60*a^4 - 49*a^3 - 56*a^2 + 4*a + 7)*q^27 + (-5*a^8 + 18*a^7 + 31*a^6 - 166*a^5 + 45*a^4 + 328*a^3 - 223*a^2 - 82*a + 18)*q^28 + (5*a^8 - 16*a^7 - 35*a^6 + 147*a^5 - 9*a^4 - 287*a^3 + 158*a^2 + 63*a - 11)*q^29 + (-2*a^8 + 3*a^7 + 21*a^6 - 27*a^5 - 59*a^4 + 48*a^3 + 49*a^2 + 2*a - 3)*q^30 + (5*a^8 - 19*a^7 - 29*a^6 + 174*a^5 - 63*a^4 - 336*a^3 + 256*a^2 + 71*a - 21)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^8 - 3*a^7 - 7*a^6 + 27*a^5 - 2*a^4 - 49*a^3 + 33*a^2 + 4*a - 3)*q^33 + (-4*a^8 + 9*a^7 + 36*a^6 - 81*a^5 - 66*a^4 + 147*a^3 + 11*a^2 - 11*a + 1)*q^34 + (-17*a^8 + 62*a^7 + 104*a^6 - 569*a^5 + 165*a^4 + 1108*a^3 - 780*a^2 - 249*a + 68)*q^35 + (2*a^8 - 7*a^7 - 14*a^6 + 65*a^5 - 4*a^4 - 132*a^3 + 65*a^2 + 40*a - 7)*q^36 + (-a^7 + 2*a^6 + 10*a^5 - 18*a^4 - 26*a^3 + 34*a^2 + 21*a - 4)*q^37 + O(q^38),
q + a*q^2 + (-19/18*a^10 - 11/9*a^9 + 311/18*a^8 + 56/3*a^7 - 293/3*a^6 - 1769/18*a^5 + 655/3*a^4 + 601/3*a^3 - 1465/9*a^2 - 1829/18*a + 136/3)*q^3 + (a^2 - 2)*q^4 + (-7/9*a^10 - 10/9*a^9 + 116/9*a^8 + 52/3*a^7 - 223/3*a^6 - 836/9*a^5 + 515/3*a^4 + 572/3*a^3 - 1214/9*a^2 - 878/9*a + 125/3)*q^5 + (-1/6*a^10 - 2/3*a^9 + 17/6*a^8 + 10*a^7 - 17*a^6 - 305/6*a^5 + 42*a^4 + 99*a^3 - 118/3*a^2 - 317/6*a + 19)*q^6 + (-1/3*a^10 - 1/3*a^9 + 17/3*a^8 + 5*a^7 - 33*a^6 - 77/3*a^5 + 74*a^4 + 50*a^3 - 149/3*a^2 - 59/3*a + 10)*q^7 + (a^3 - 4*a)*q^8 + (-11/18*a^10 - 4/9*a^9 + 181/18*a^8 + 19/3*a^7 - 172/3*a^6 - 559/18*a^5 + 392/3*a^4 + 179/3*a^3 - 923/9*a^2 - 481/18*a + 71/3)*q^9 + (-1/3*a^10 - 1/3*a^9 + 17/3*a^8 + 5*a^7 - 33*a^6 - 80/3*a^5 + 74*a^4 + 58*a^3 - 155/3*a^2 - 92/3*a + 14)*q^10 - q^11 + (29/18*a^10 + 22/9*a^9 - 487/18*a^8 - 112/3*a^7 + 472/3*a^6 + 3529/18*a^5 - 1088/3*a^4 - 1196/3*a^3 + 2543/9*a^2 + 3721/18*a - 263/3)*q^12 + (1/3*a^10 + 1/3*a^9 - 17/3*a^8 - 5*a^7 + 34*a^6 + 77/3*a^5 - 84*a^4 - 51*a^3 + 224/3*a^2 + 80/3*a - 18)*q^13 + (a^7 - 11*a^5 + 33*a^3 - 21*a + 6)*q^14 + (-4/9*a^10 - 7/9*a^9 + 65/9*a^8 + 37/3*a^7 - 124/3*a^6 - 605/9*a^5 + 296/3*a^4 + 422/3*a^3 - 830/9*a^2 - 701/9*a + 119/3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (10/9*a^10 + 13/9*a^9 - 167/9*a^8 - 67/3*a^7 + 322/3*a^6 + 1076/9*a^5 - 740/3*a^4 - 749/3*a^3 + 1733/9*a^2 + 1199/9*a - 176/3)*q^17 + (1/6*a^10 - 1/3*a^9 - 17/6*a^8 + 5*a^7 + 16*a^6 - 151/6*a^5 - 32*a^4 + 49*a^3 + 28/3*a^2 - 199/6*a + 11)*q^18 + (2/3*a^10 + 2/3*a^9 - 34/3*a^8 - 10*a^7 + 67*a^6 + 157/3*a^5 - 159*a^4 - 109*a^3 + 394/3*a^2 + 172/3*a - 32)*q^19 + (14/9*a^10 + 20/9*a^9 - 232/9*a^8 - 101/3*a^7 + 443/3*a^6 + 1573/9*a^5 - 1006/3*a^4 - 1051/3*a^3 + 2329/9*a^2 + 1603/9*a - 232/3)*q^20 + (-4/9*a^10 + 2/9*a^9 + 65/9*a^8 - 11/3*a^7 - 118/3*a^6 + 178/9*a^5 + 236/3*a^4 - 118/3*a^3 - 353/9*a^2 + 271/9*a - 10/3)*q^21 - a*q^22 + (8/9*a^10 + 14/9*a^9 - 130/9*a^8 - 74/3*a^7 + 245/3*a^6 + 1201/9*a^5 - 556/3*a^4 - 820/3*a^3 + 1300/9*a^2 + 1285/9*a - 157/3)*q^23 + (7/6*a^10 + 5/3*a^9 - 113/6*a^8 - 27*a^7 + 106*a^6 + 899/6*a^5 - 241*a^4 - 315*a^3 + 571/3*a^2 + 1007/6*a - 67)*q^24 + (-2/3*a^10 - 2/3*a^9 + 34/3*a^8 + 11*a^7 - 67*a^6 - 190/3*a^5 + 158*a^4 + 142*a^3 - 376/3*a^2 - 241/3*a + 38)*q^25 + (a^5 - a^4 - 8*a^3 + 7*a^2 + 13*a - 6)*q^26 + (-5/2*a^10 - 3*a^9 + 83/2*a^8 + 46*a^7 - 239*a^6 - 487/2*a^5 + 549*a^4 + 501*a^3 - 430*a^2 - 527/2*a + 124)*q^27 + (2/3*a^10 + 2/3*a^9 - 31/3*a^8 - 10*a^7 + 55*a^6 + 154/3*a^5 - 115*a^4 - 100*a^3 + 235/3*a^2 + 136/3*a - 20)*q^28 + (-31/18*a^10 - 26/9*a^9 + 515/18*a^8 + 134/3*a^7 - 497/3*a^6 - 4277/18*a^5 + 1159/3*a^4 + 1471/3*a^3 - 2854/9*a^2 - 4859/18*a + 325/3)*q^29 + (-1/3*a^10 - 1/3*a^9 + 17/3*a^8 + 4*a^7 - 33*a^6 - 44/3*a^5 + 74*a^4 + 18*a^3 - 155/3*a^2 - 5/3*a + 8)*q^30 + (5/3*a^10 + 8/3*a^9 - 82/3*a^8 - 41*a^7 + 155*a^6 + 649/3*a^5 - 349*a^4 - 440*a^3 + 808/3*a^2 + 688/3*a - 89)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (19/18*a^10 + 11/9*a^9 - 311/18*a^8 - 56/3*a^7 + 293/3*a^6 + 1769/18*a^5 - 655/3*a^4 - 601/3*a^3 + 1465/9*a^2 + 1829/18*a - 136/3)*q^33 + (1/3*a^10 + 1/3*a^9 - 17/3*a^8 - 6*a^7 + 34*a^6 + 110/3*a^5 - 83*a^4 - 83*a^3 + 203/3*a^2 + 134/3*a - 20)*q^34 + (4/9*a^10 - 2/9*a^9 - 65/9*a^8 + 14/3*a^7 + 118/3*a^6 - 277/9*a^5 - 239/3*a^4 + 214/3*a^3 + 398/9*a^2 - 433/9*a + 34/3)*q^35 + (13/18*a^10 + 8/9*a^9 - 227/18*a^8 - 41/3*a^7 + 230/3*a^6 + 1307/18*a^5 - 562/3*a^4 - 454/3*a^3 + 1459/9*a^2 + 1439/18*a - 151/3)*q^36 + (1/3*a^10 + 1/3*a^9 - 17/3*a^8 - 6*a^7 + 34*a^6 + 113/3*a^5 - 85*a^4 - 92*a^3 + 242/3*a^2 + 182/3*a - 27)*q^37 + O(q^38)
*]> ;  // time = 93.459 seconds




J[474] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 474, 474, 474, 474, 474, 474, 237, 237, 237, 158, 158, 158, 158, 158, 158, 79, 79 ], new_dimensions := [ 1, 1, 2, 2, 3, 4, 2, 4, 7, 1, 1, 1, 1, 1, 2, 1, 5 ], dimensions := [ 1, 1, 2, 2, 3, 4, 4, 8, 14, 2, 2, 2, 2, 2, 4, 4, 20 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 7, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 139, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 13, 1, 1, 1, 1, 1, 0, 1, 139, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 961, 7, 1, 1, 1, 1, 139, 1, 0, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 139, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 25, 1, 3, 1, 1, 5, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 5, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 9, 0, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 25, 1, 1, 1, 0, 1, 2809, 1, 1, 1, 1, 1, 1, 1, 9, 25, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 13, 1, 961, 1, 1, 1, 1, 1, 1, 1, 2809, 1, 0 ], ap_traces := [
[ -1, -1, 2, -3, -5, -1, 5, -6, 3, -5, -4, -8 ],
[ -1, 1, -2, -1, -5, -1, -1, -2, -5, 1, 0, 4 ],
[ -2, -2, -1, 1, 0, 0, -3, 11, 1, 0, 12, 7 ],
[ -2, 2, 3, -1, 8, -4, 7, 3, -3, 8, -4, -15 ],
[ 3, 3, 3, 0, 1, -1, 0, -3, 0, 3, -8, -1 ],
[ 4, -4, 1, 4, 5, 9, 2, 5, 4, 7, 4, 3 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + x - 7,
x^2 - 3*x + 1,
x^3 - 3*x^2 - x + 2,
x^4 - x^3 - 19*x^2 + 20*x - 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, -1, -1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 7, 3, 1 ],
[ 1, 5, 1 ],
[ 7, 25, 1 ],
[ 139, 5, 1 ],
[ 13, 91, 1 ],
[ 139, 9, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 5, 1 ],
[ 1, 1, 1 ],
[ 1, 5, 1 ],
[ 13, 91, 1 ],
[ 139, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 13, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 0, 1, 5, 7, 139 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1, 1/169, 1 ], eigenvalues := [*
[ -1, -1, 2, -3, -5, -1, 5, -6, 3, -5, -4, -8 ],
[ -1, 1, -2, -1, -5, -1, -1, -2, -5, 1, 0, 4 ],
[
-1,
-1,
a,
a + 1,
0,
0,
-a - 2,
-a + 5,
a + 1,
0,
6,
a + 4
],
[
-1,
1,
a,
3*a - 5,
4,
-4*a + 4,
a + 2,
-5*a + 9,
-7*a + 9,
4,
-2,
3*a - 12
],
[
1,
1,
a,
-a + 1,
-a^2 + a + 3,
a^2 - a - 3,
3*a^2 - 8*a - 3,
-3*a^2 + 8*a + 2,
-3*a + 3,
-3*a^2 + 7*a + 5,
2*a^2 - 6*a - 4,
-2*a^2 + 5*a + 2
],
[
1,
-1,
a,
3/4*a^3 - 1/4*a^2 - 59/4*a + 15/2,
-5/4*a^3 + 3/4*a^2 + 93/4*a - 25/2,
-1/4*a^3 - 1/4*a^2 + 17/4*a + 7/2,
-1/4*a^3 - 1/4*a^2 + 21/4*a + 3/2,
1/2*a^3 - 1/2*a^2 - 21/2*a + 9,
3/4*a^3 - 1/4*a^2 - 59/4*a + 15/2,
1/4*a^3 + 1/4*a^2 - 17/4*a + 1/2,
-a^3 + a^2 + 19*a - 14,
-1/2*a^3 - 1/2*a^2 + 19/2*a + 3
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + 2*q^5 + q^6 - 3*q^7 - q^8 + q^9 - 2*q^10 - 5*q^11 - q^12 - q^13 + 3*q^14 - 2*q^15 + q^16 + 5*q^17 - q^18 - 6*q^19 + 2*q^20 + 3*q^21 + 5*q^22 + 3*q^23 + q^24 - q^25 + q^26 - q^27 - 3*q^28 - 5*q^29 + 2*q^30 - 4*q^31 - q^32 + 5*q^33 - 5*q^34 - 6*q^35 + q^36 - 8*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - 2*q^5 - q^6 - q^7 - q^8 + q^9 + 2*q^10 - 5*q^11 + q^12 - q^13 + q^14 - 2*q^15 + q^16 - q^17 - q^18 - 2*q^19 - 2*q^20 - q^21 + 5*q^22 - 5*q^23 - q^24 - q^25 + q^26 + q^27 - q^28 + q^29 + 2*q^30 - q^32 - 5*q^33 + q^34 + 2*q^35 + q^36 + 4*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + a*q^5 + q^6 + (a + 1)*q^7 - q^8 + q^9 - a*q^10 - q^12 + (-a - 1)*q^14 - a*q^15 + q^16 + (-a - 2)*q^17 - q^18 + (-a + 5)*q^19 + a*q^20 + (-a - 1)*q^21 + (a + 1)*q^23 + q^24 + (-a + 2)*q^25 - q^27 + (a + 1)*q^28 + a*q^30 + 6*q^31 - q^32 + (a + 2)*q^34 + 7*q^35 + q^36 + (a + 4)*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + a*q^5 - q^6 + (3*a - 5)*q^7 - q^8 + q^9 - a*q^10 + 4*q^11 + q^12 + (-4*a + 4)*q^13 + (-3*a + 5)*q^14 + a*q^15 + q^16 + (a + 2)*q^17 - q^18 + (-5*a + 9)*q^19 + a*q^20 + (3*a - 5)*q^21 - 4*q^22 + (-7*a + 9)*q^23 - q^24 + (3*a - 6)*q^25 + (4*a - 4)*q^26 + q^27 + (3*a - 5)*q^28 + 4*q^29 - a*q^30 - 2*q^31 - q^32 + 4*q^33 + (-a - 2)*q^34 + (4*a - 3)*q^35 + q^36 + (3*a - 12)*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + a*q^5 + q^6 + (-a + 1)*q^7 + q^8 + q^9 + a*q^10 + (-a^2 + a + 3)*q^11 + q^12 + (a^2 - a - 3)*q^13 + (-a + 1)*q^14 + a*q^15 + q^16 + (3*a^2 - 8*a - 3)*q^17 + q^18 + (-3*a^2 + 8*a + 2)*q^19 + a*q^20 + (-a + 1)*q^21 + (-a^2 + a + 3)*q^22 + (-3*a + 3)*q^23 + q^24 + (a^2 - 5)*q^25 + (a^2 - a - 3)*q^26 + q^27 + (-a + 1)*q^28 + (-3*a^2 + 7*a + 5)*q^29 + a*q^30 + (2*a^2 - 6*a - 4)*q^31 + q^32 + (-a^2 + a + 3)*q^33 + (3*a^2 - 8*a - 3)*q^34 + (-a^2 + a)*q^35 + q^36 + (-2*a^2 + 5*a + 2)*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + a*q^5 - q^6 + (3/4*a^3 - 1/4*a^2 - 59/4*a + 15/2)*q^7 + q^8 + q^9 + a*q^10 + (-5/4*a^3 + 3/4*a^2 + 93/4*a - 25/2)*q^11 - q^12 + (-1/4*a^3 - 1/4*a^2 + 17/4*a + 7/2)*q^13 + (3/4*a^3 - 1/4*a^2 - 59/4*a + 15/2)*q^14 - a*q^15 + q^16 + (-1/4*a^3 - 1/4*a^2 + 21/4*a + 3/2)*q^17 + q^18 + (1/2*a^3 - 1/2*a^2 - 21/2*a + 9)*q^19 + a*q^20 + (-3/4*a^3 + 1/4*a^2 + 59/4*a - 15/2)*q^21 + (-5/4*a^3 + 3/4*a^2 + 93/4*a - 25/2)*q^22 + (3/4*a^3 - 1/4*a^2 - 59/4*a + 15/2)*q^23 - q^24 + (a^2 - 5)*q^25 + (-1/4*a^3 - 1/4*a^2 + 17/4*a + 7/2)*q^26 - q^27 + (3/4*a^3 - 1/4*a^2 - 59/4*a + 15/2)*q^28 + (1/4*a^3 + 1/4*a^2 - 17/4*a + 1/2)*q^29 - a*q^30 + (-a^3 + a^2 + 19*a - 14)*q^31 + q^32 + (5/4*a^3 - 3/4*a^2 - 93/4*a + 25/2)*q^33 + (-1/4*a^3 - 1/4*a^2 + 21/4*a + 3/2)*q^34 + (1/2*a^3 - 1/2*a^2 - 15/2*a + 3)*q^35 + q^36 + (-1/2*a^3 - 1/2*a^2 + 19/2*a + 3)*q^37 + O(q^38)
*]> ;  // time = 359.23 seconds




J[478] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 478, 478, 478, 478, 239, 239 ], new_dimensions := [ 4, 4, 5, 6, 3, 17 ], dimensions := [ 4, 4, 5, 6, 6, 34 ], intersection_graph := [ 0, 1, 1, 1, 13, 1, 1, 0, 1, 1, 1, 9119, 1, 1, 0, 1, 29, 1, 1, 1, 1, 0, 1, 741371, 13, 1, 29, 1, 0, 1, 1, 9119, 1, 741371, 1, 0 ], ap_traces := [
[ -4, -2, -3, -2, -3, -3, -14, 4, -11, -4, 7, -6 ],
[ 4, -6, -7, -6, -3, -9, -14, -16, -5, -2, -7, 8 ],
[ 5, 2, 3, 4, 5, 1, 8, 4, 1, -4, 5, -4 ],
[ -6, 2, 5, 0, 5, 3, 26, -10, 7, 12, -17, -6 ]
], hecke_fields := [
x^4 + 2*x^3 - 4*x^2 - 5*x - 1,
x^4 + 6*x^3 + 10*x^2 + 3*x - 1,
x^5 - 2*x^4 - 6*x^3 + 11*x^2 + 7*x - 12,
x^6 - 2*x^5 - 12*x^4 + 19*x^3 + 35*x^2 - 32*x - 32
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 13, 1 ],
[ 9119, 1 ],
[ 145, 1 ],
[ 741371, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 9119, 1 ],
[ 145, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 5, 1 ], torsion_lower_bounds := [ 1, 1, 5, 1 ], l_ratios := [ 0, 0, 29/5, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
-1,
a,
-a^3 - 2*a^2 + 4*a + 3,
2*a^3 + 3*a^2 - 10*a - 6,
-3*a^3 - 4*a^2 + 13*a + 5,
3*a^3 + 5*a^2 - 14*a - 10,
-a^2 - a - 1,
2*a^3 + 3*a^2 - 9*a - 4,
-a^3 - 2*a^2 + 4*a + 1,
a^2 + 2*a - 3,
-5*a^3 - 7*a^2 + 25*a + 14,
-4*a^3 - 5*a^2 + 21*a + 7
],
[
1,
a,
-a^3 - 4*a^2 - 4*a - 3,
2*a^3 + 7*a^2 + 2*a - 4,
a^3 + 8*a^2 + 15*a + 1,
-3*a^3 - 15*a^2 - 16*a,
-3*a^2 - 9*a - 5,
2*a^3 + 11*a^2 + 17*a,
-3*a^3 - 12*a^2 - 8*a + 1,
2*a^3 + 9*a^2 + 6*a - 5,
-3*a^3 - 17*a^2 - 23*a - 2,
-6*a^3 - 27*a^2 - 25*a + 5
],
[
1,
a,
-a^4 + a^3 + 6*a^2 - 3*a - 6,
-a^2 + 4,
a^4 - a^3 - 6*a^2 + 2*a + 8,
2*a^4 - a^3 - 13*a^2 + 2*a + 16,
a^4 - 2*a^3 - 5*a^2 + 6*a + 6,
a^2 - a - 2,
a^4 + a^3 - 8*a^2 - 5*a + 12,
a^4 - 9*a^2 + a + 14,
-2*a^4 + a^3 + 15*a^2 - 5*a - 20,
-3*a^4 + 21*a^2 + 2*a - 28
],
[
-1,
a,
4/31*a^5 - 17/31*a^4 - 33/31*a^3 + 158/31*a^2 + 17/31*a - 174/31,
19/62*a^5 - 21/31*a^4 - 90/31*a^3 + 363/62*a^2 + 197/62*a - 204/31,
11/62*a^5 - 4/31*a^4 - 57/31*a^3 - 15/62*a^2 + 225/62*a + 156/31,
-41/124*a^5 + 29/62*a^4 + 102/31*a^3 - 519/124*a^2 - 523/124*a + 194/31,
-14/31*a^5 + 13/31*a^4 + 162/31*a^3 - 57/31*a^2 - 354/31*a + 20/31,
27/124*a^5 - 7/62*a^4 - 77/31*a^3 - 3/124*a^2 + 789/124*a + 28/31,
5/31*a^5 + 33/31*a^4 - 111/31*a^3 - 345/31*a^2 + 432/31*a + 604/31,
-1/62*a^5 + 6/31*a^4 + 8/31*a^3 - 117/62*a^2 - 105/62*a + 138/31,
-37/62*a^5 + 5/31*a^4 + 203/31*a^3 + 135/62*a^2 - 785/62*a - 474/31,
87/124*a^5 - 57/62*a^4 - 255/31*a^3 + 817/124*a^2 + 2005/124*a - 82/31
]
*], q_expansions := [*
q - q^2 + a*q^3 + q^4 + (-a^3 - 2*a^2 + 4*a + 3)*q^5 - a*q^6 + (2*a^3 + 3*a^2 - 10*a - 6)*q^7 - q^8 + (a^2 - 3)*q^9 + (a^3 + 2*a^2 - 4*a - 3)*q^10 + (-3*a^3 - 4*a^2 + 13*a + 5)*q^11 + a*q^12 + (3*a^3 + 5*a^2 - 14*a - 10)*q^13 + (-2*a^3 - 3*a^2 + 10*a + 6)*q^14 + (-2*a - 1)*q^15 + q^16 + (-a^2 - a - 1)*q^17 + (-a^2 + 3)*q^18 + (2*a^3 + 3*a^2 - 9*a - 4)*q^19 + (-a^3 - 2*a^2 + 4*a + 3)*q^20 + (-a^3 - 2*a^2 + 4*a + 2)*q^21 + (3*a^3 + 4*a^2 - 13*a - 5)*q^22 + (-a^3 - 2*a^2 + 4*a + 1)*q^23 - a*q^24 + (-a^3 - a^2 + 6*a)*q^25 + (-3*a^3 - 5*a^2 + 14*a + 10)*q^26 + (a^3 - 6*a)*q^27 + (2*a^3 + 3*a^2 - 10*a - 6)*q^28 + (a^2 + 2*a - 3)*q^29 + (2*a + 1)*q^30 + (-5*a^3 - 7*a^2 + 25*a + 14)*q^31 - q^32 + (2*a^3 + a^2 - 10*a - 3)*q^33 + (a^2 + a + 1)*q^34 + (2*a^3 + 4*a^2 - 7*a - 8)*q^35 + (a^2 - 3)*q^36 + (-4*a^3 - 5*a^2 + 21*a + 7)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a^3 - 4*a^2 - 4*a - 3)*q^5 + a*q^6 + (2*a^3 + 7*a^2 + 2*a - 4)*q^7 + q^8 + (a^2 - 3)*q^9 + (-a^3 - 4*a^2 - 4*a - 3)*q^10 + (a^3 + 8*a^2 + 15*a + 1)*q^11 + a*q^12 + (-3*a^3 - 15*a^2 - 16*a)*q^13 + (2*a^3 + 7*a^2 + 2*a - 4)*q^14 + (2*a^3 + 6*a^2 - 1)*q^15 + q^16 + (-3*a^2 - 9*a - 5)*q^17 + (a^2 - 3)*q^18 + (2*a^3 + 11*a^2 + 17*a)*q^19 + (-a^3 - 4*a^2 - 4*a - 3)*q^20 + (-5*a^3 - 18*a^2 - 10*a + 2)*q^21 + (a^3 + 8*a^2 + 15*a + 1)*q^22 + (-3*a^3 - 12*a^2 - 8*a + 1)*q^23 + a*q^24 + (3*a^3 + 15*a^2 + 20*a + 6)*q^25 + (-3*a^3 - 15*a^2 - 16*a)*q^26 + (a^3 - 6*a)*q^27 + (2*a^3 + 7*a^2 + 2*a - 4)*q^28 + (2*a^3 + 9*a^2 + 6*a - 5)*q^29 + (2*a^3 + 6*a^2 - 1)*q^30 + (-3*a^3 - 17*a^2 - 23*a - 2)*q^31 + q^32 + (2*a^3 + 5*a^2 - 2*a + 1)*q^33 + (-3*a^2 - 9*a - 5)*q^34 + (-2*a^3 - 6*a^2 + 7*a + 12)*q^35 + (a^2 - 3)*q^36 + (-6*a^3 - 27*a^2 - 25*a + 5)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a^4 + a^3 + 6*a^2 - 3*a - 6)*q^5 + a*q^6 + (-a^2 + 4)*q^7 + q^8 + (a^2 - 3)*q^9 + (-a^4 + a^3 + 6*a^2 - 3*a - 6)*q^10 + (a^4 - a^3 - 6*a^2 + 2*a + 8)*q^11 + a*q^12 + (2*a^4 - a^3 - 13*a^2 + 2*a + 16)*q^13 + (-a^2 + 4)*q^14 + (-a^4 + 8*a^2 + a - 12)*q^15 + q^16 + (a^4 - 2*a^3 - 5*a^2 + 6*a + 6)*q^17 + (a^2 - 3)*q^18 + (a^2 - a - 2)*q^19 + (-a^4 + a^3 + 6*a^2 - 3*a - 6)*q^20 + (-a^3 + 4*a)*q^21 + (a^4 - a^3 - 6*a^2 + 2*a + 8)*q^22 + (a^4 + a^3 - 8*a^2 - 5*a + 12)*q^23 + a*q^24 + (-a^4 + a^3 + 5*a^2 - 3*a - 5)*q^25 + (2*a^4 - a^3 - 13*a^2 + 2*a + 16)*q^26 + (a^3 - 6*a)*q^27 + (-a^2 + 4)*q^28 + (a^4 - 9*a^2 + a + 14)*q^29 + (-a^4 + 8*a^2 + a - 12)*q^30 + (-2*a^4 + a^3 + 15*a^2 - 5*a - 20)*q^31 + q^32 + (a^4 - 9*a^2 + a + 12)*q^33 + (a^4 - 2*a^3 - 5*a^2 + 6*a + 6)*q^34 + (-2*a^4 + 2*a^3 + 12*a^2 - 7*a - 12)*q^35 + (a^2 - 3)*q^36 + (-3*a^4 + 21*a^2 + 2*a - 28)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (4/31*a^5 - 17/31*a^4 - 33/31*a^3 + 158/31*a^2 + 17/31*a - 174/31)*q^5 - a*q^6 + (19/62*a^5 - 21/31*a^4 - 90/31*a^3 + 363/62*a^2 + 197/62*a - 204/31)*q^7 - q^8 + (a^2 - 3)*q^9 + (-4/31*a^5 + 17/31*a^4 + 33/31*a^3 - 158/31*a^2 - 17/31*a + 174/31)*q^10 + (11/62*a^5 - 4/31*a^4 - 57/31*a^3 - 15/62*a^2 + 225/62*a + 156/31)*q^11 + a*q^12 + (-41/124*a^5 + 29/62*a^4 + 102/31*a^3 - 519/124*a^2 - 523/124*a + 194/31)*q^13 + (-19/62*a^5 + 21/31*a^4 + 90/31*a^3 - 363/62*a^2 - 197/62*a + 204/31)*q^14 + (-9/31*a^5 + 15/31*a^4 + 82/31*a^3 - 123/31*a^2 - 46/31*a + 128/31)*q^15 + q^16 + (-14/31*a^5 + 13/31*a^4 + 162/31*a^3 - 57/31*a^2 - 354/31*a + 20/31)*q^17 + (-a^2 + 3)*q^18 + (27/124*a^5 - 7/62*a^4 - 77/31*a^3 - 3/124*a^2 + 789/124*a + 28/31)*q^19 + (4/31*a^5 - 17/31*a^4 - 33/31*a^3 + 158/31*a^2 + 17/31*a - 174/31)*q^20 + (-2/31*a^5 + 24/31*a^4 + 1/31*a^3 - 234/31*a^2 + 100/31*a + 304/31)*q^21 + (-11/62*a^5 + 4/31*a^4 + 57/31*a^3 + 15/62*a^2 - 225/62*a - 156/31)*q^22 + (5/31*a^5 + 33/31*a^4 - 111/31*a^3 - 345/31*a^2 + 432/31*a + 604/31)*q^23 - a*q^24 + (-1/31*a^5 - 19/31*a^4 + 47/31*a^3 + 162/31*a^2 - 260/31*a - 127/31)*q^25 + (41/124*a^5 - 29/62*a^4 - 102/31*a^3 + 519/124*a^2 + 523/124*a - 194/31)*q^26 + (a^3 - 6*a)*q^27 + (19/62*a^5 - 21/31*a^4 - 90/31*a^3 + 363/62*a^2 + 197/62*a - 204/31)*q^28 + (-1/62*a^5 + 6/31*a^4 + 8/31*a^3 - 117/62*a^2 - 105/62*a + 138/31)*q^29 + (9/31*a^5 - 15/31*a^4 - 82/31*a^3 + 123/31*a^2 + 46/31*a - 128/31)*q^30 + (-37/62*a^5 + 5/31*a^4 + 203/31*a^3 + 135/62*a^2 - 785/62*a - 474/31)*q^31 - q^32 + (7/31*a^5 + 9/31*a^4 - 112/31*a^3 - 80/31*a^2 + 332/31*a + 176/31)*q^33 + (14/31*a^5 - 13/31*a^4 - 162/31*a^3 + 57/31*a^2 + 354/31*a - 20/31)*q^34 + (6/31*a^5 - 10/31*a^4 - 34/31*a^3 + 20/31*a^2 - 145/31*a + 328/31)*q^35 + (a^2 - 3)*q^36 + (87/124*a^5 - 57/62*a^4 - 255/31*a^3 + 817/124*a^2 + 2005/124*a - 82/31)*q^37 + O(q^38)
*]> ;  // time = 133.849 seconds




J[479] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 479, 479 ], new_dimensions := [ 8, 32 ], dimensions := [ 8, 32 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -2, -3, -4, -4, -5, -9, -4, -11, 0, -9, -19, -21 ],
[ 3, 5, 6, 8, 11, 13, 0, 19, 0, 21, 37, 49 ]
], hecke_fields := [
x^8 + 2*x^7 - 6*x^6 - 11*x^5 + 10*x^4 + 17*x^3 - 4*x^2 - 7*x - 1,
x^32 - 3*x^31 - 49*x^30 + 150*x^29 + 1068*x^28 - 3349*x^27 - 13663*x^26 + 44102*x^25 + 114017*x^24 - 381227*x^23 - 652363*x^22 + 2278423*x^21 + 2617329*x^20 - 9659993*x^19 - 7391907*x^18 + 29333039*x^17 + 14485613*x^16 - 63589225*x^15 - 18892591*x^14 + 96842403*x^13 + 14744217*x^12 - 100301909*x^11 - 4507611*x^10 + 66698107*x^9 - 2210691*x^8 - 25684834*x^7 + 2153748*x^6 + 4689118*x^5 - 470371*x^4 - 268239*x^3 + 38414*x^2 - 242*x - 7
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 239 ]
], tamagawa_numbers := [
[ 1 ],
[ 239 ]
], torsion_upper_bounds := [ 1, 239 ], torsion_lower_bounds := [ 1, 239 ], l_ratios := [ 0, 1/239 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^6 - a^5 + 6*a^4 + 3*a^3 - 9*a^2 - a + 2,
a^7 + 2*a^6 - 6*a^5 - 10*a^4 + 11*a^3 + 12*a^2 - 7*a - 3,
a^6 + 2*a^5 - 5*a^4 - 9*a^3 + 5*a^2 + 8*a,
a^7 + a^6 - 7*a^5 - 5*a^4 + 14*a^3 + 9*a^2 - 9*a - 6,
a^7 + a^6 - 8*a^5 - 6*a^4 + 19*a^3 + 11*a^2 - 13*a - 6,
-3*a^7 - 4*a^6 + 20*a^5 + 19*a^4 - 39*a^3 - 23*a^2 + 22*a + 5,
-2*a^7 - 2*a^6 + 12*a^5 + 6*a^4 - 17*a^3 - a^2 + 3*a - 2,
-2*a^7 - 3*a^6 + 11*a^5 + 13*a^4 - 14*a^3 - 14*a^2 + 3*a + 3,
-a^4 - 3*a^3 + 3*a^2 + 9*a - 2,
a^7 - a^6 - 8*a^5 + 10*a^4 + 17*a^3 - 19*a^2 - 8*a + 1,
-2*a^7 - 4*a^6 + 13*a^5 + 22*a^4 - 26*a^3 - 31*a^2 + 17*a + 6
],
[
a,
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*], q_expansions := [*
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13110433243391035216911611848913835615308811516916/43299557505812608642127324159129260658424597*a^16 - 31274152197109245183254498224507736850496856618444/129898672517437825926381972477387781975273791*a^15 + 85403010787456758034382567675854182616036910527604/129898672517437825926381972477387781975273791*a^14 + 14683005484662163616290129739403601063909849981348/43299557505812608642127324159129260658424597*a^13 - 43544284986206477437471898001012206795344803987968/43299557505812608642127324159129260658424597*a^12 - 4353242470368140415408768083888367349078396613140/14433185835270869547375774719709753552808199*a^11 + 136321004253307400922069391438603257793549405366268/129898672517437825926381972477387781975273791*a^10 + 17889906337491595599906128310048125773205971453256/129898672517437825926381972477387781975273791*a^9 - 91583813678297991692612602995104162419832318935436/129898672517437825926381972477387781975273791*a^8 - 122154093926759995646787667634554142289064130264/129898672517437825926381972477387781975273791*a^7 + 35623592160529033768366220459786328700560281033618/129898672517437825926381972477387781975273791*a^6 - 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209042534363267162176129324351789899174096859234/43299557505812608642127324159129260658424597*a^3 - 39379446779006039079751175146568489802853901008/43299557505812608642127324159129260658424597*a^2 + 3661886866099848174065881962175754712897620575/14433185835270869547375774719709753552808199*a - 171825674550071500711968386862085197597437893/43299557505812608642127324159129260658424597)*q^36 + (484973495852492644306610251657909927395850/129898672517437825926381972477387781975273791*a^31 - 1156669637031345665973719855800381391290496/129898672517437825926381972477387781975273791*a^30 - 2675908665880290556965800967445563260302035/14433185835270869547375774719709753552808199*a^29 + 19219565281221611409905924494642429803434969/43299557505812608642127324159129260658424597*a^28 + 177583485550467562965358490329514648091506149/43299557505812608642127324159129260658424597*a^27 - 1282220208184964990332343738585736898300207693/129898672517437825926381972477387781975273791*a^26 - 6927755086764288973173656123748377866829241356/129898672517437825926381972477387781975273791*a^25 + 5599074758163193363046022062023433051048344273/43299557505812608642127324159129260658424597*a^24 + 58853279332981431383608576449687292467559371443/129898672517437825926381972477387781975273791*a^23 - 16022851296313187471017366849435553725453826405/14433185835270869547375774719709753552808199*a^22 - 343312006282132896330667146401263799790305883667/129898672517437825926381972477387781975273791*a^21 + 94903138598602368673038597405321341014961278193/14433185835270869547375774719709753552808199*a^20 + 468794055083605251568245455482969786193741334451/43299557505812608642127324159129260658424597*a^19 - 3578964870018383019802532039142765998004503508743/129898672517437825926381972477387781975273791*a^18 - 4063063092075256063955330792414551182580661054375/129898672517437825926381972477387781975273791*a^17 + 1189233720911735427048562783668630183738966877085/14433185835270869547375774719709753552808199*a^16 + 8174214687987753362469800586755209112310690599987/129898672517437825926381972477387781975273791*a^15 - 22751883034987991194646249240825444536565256386105/129898672517437825926381972477387781975273791*a^14 - 3685468369845549693934741802982140264056206457643/43299557505812608642127324159129260658424597*a^13 + 11265636901922245141400485102716837278062836709897/43299557505812608642127324159129260658424597*a^12 + 3095958190309698507400535974131103240121639192495/43299557505812608642127324159129260658424597*a^11 - 33927884362859940217844529922851658917816080223605/129898672517437825926381972477387781975273791*a^10 - 3869987591853551219138569952095932152653220285369/129898672517437825926381972477387781975273791*a^9 + 21709169733214556079633988558097568540551566103387/129898672517437825926381972477387781975273791*a^8 - 103541631853557950203870811019591876169927433695/129898672517437825926381972477387781975273791*a^7 - 7982820038357832934932238559795365477561804671167/129898672517437825926381972477387781975273791*a^6 + 653273436014435760419578577440939450006038152263/129898672517437825926381972477387781975273791*a^5 + 1384931275846660779606616922111393068584439892852/129898672517437825926381972477387781975273791*a^4 - 143910731427367374383526463533723552036803141516/129898672517437825926381972477387781975273791*a^3 - 76727084262337592982968623264855389851913669098/129898672517437825926381972477387781975273791*a^2 + 2542854081855927962379672770764024364002875406/43299557505812608642127324159129260658424597*a - 249393558243792901018187384178224965915590215/129898672517437825926381972477387781975273791)*q^37 + O(q^38)
*]> ;  // time = 18.789 seconds




J[481] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 481, 481, 481, 481, 481, 37, 37 ], new_dimensions := [ 1, 7, 7, 11, 11, 1, 1 ], dimensions := [ 1, 7, 7, 11, 11, 2, 2 ], intersection_graph := [ 0, 19, 1, 1, 1, 3, 1, 19, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 3, 5, 1, 1, 0 ], ap_traces := [
[ 1, 0, -2, 2, -2, -1, -6, 0, 2, -6, 8, -1 ],
[ -5, 1, -4, -8, -13, -7, 2, -8, -18, -9, -25, -7 ],
[ -1, -7, -2, -2, -13, 7, -10, -2, -24, -17, -11, 7 ],
[ 3, 1, 4, 4, 21, -11, -6, 0, 10, 13, 5, 11 ],
[ 3, 5, 2, 0, 11, 11, 6, -6, 34, 17, 19, -11 ]
], hecke_fields := [
x - 1,
x^7 + 5*x^6 + 2*x^5 - 21*x^4 - 25*x^3 + 8*x^2 + 13*x - 2,
x^7 + x^6 - 8*x^5 - 7*x^4 + 17*x^3 + 12*x^2 - 9*x - 6,
x^11 - 3*x^10 - 14*x^9 + 45*x^8 + 64*x^7 - 237*x^6 - 99*x^5 + 529*x^4 - 7*x^3 - 460*x^2 + 67*x + 110,
x^11 - 3*x^10 - 12*x^9 + 39*x^8 + 38*x^7 - 149*x^6 - 23*x^5 + 175*x^4 - 5*x^3 - 48*x^2 + 5*x + 2
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 5, 7 ],
[ 19, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 1, 7 ],
[ 19, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 7, 19 ], torsion_lower_bounds := [ 1, 1, 1, 7, 19 ], l_ratios := [ 0, 0, 0, 1/7, 1/19 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ 1, 0, -2, 2, -2, -1, -6, 0, 2, -6, 8, -1 ],
[
a,
-4*a^6 - 15*a^5 + 10*a^4 + 69*a^3 + 15*a^2 - 42*a + 5,
-3*a^6 - 11*a^5 + 10*a^4 + 54*a^3 - 41*a + 8,
8*a^6 + 30*a^5 - 21*a^4 - 140*a^3 - 26*a^2 + 88*a - 13,
9*a^6 + 34*a^5 - 24*a^4 - 160*a^3 - 27*a^2 + 105*a - 15,
-1,
-a^6 - 4*a^5 + 2*a^4 + 18*a^3 + 6*a^2 - 8*a,
9*a^6 + 32*a^5 - 30*a^4 - 154*a^3 - 3*a^2 + 111*a - 22,
-8*a^6 - 30*a^5 + 22*a^4 + 143*a^3 + 23*a^2 - 99*a + 8,
-15*a^6 - 56*a^5 + 41*a^4 + 263*a^3 + 41*a^2 - 171*a + 24,
-13*a^6 - 48*a^5 + 36*a^4 + 225*a^3 + 36*a^2 - 147*a + 14,
-1
],
[
a,
-2*a^6 - a^5 + 16*a^4 + 5*a^3 - 33*a^2 - 2*a + 13,
a^6 + a^5 - 8*a^4 - 6*a^3 + 16*a^2 + 5*a - 6,
a^4 - 6*a^2 + 5,
3*a^6 - 26*a^4 + 2*a^3 + 61*a^2 - 9*a - 33,
1,
a^6 - 10*a^4 + 2*a^3 + 28*a^2 - 8*a - 18,
-3*a^6 + 26*a^4 - 2*a^3 - 59*a^2 + 9*a + 26,
-a^3 + a^2 + 3*a - 6,
-a^6 - 2*a^5 + 7*a^4 + 13*a^3 - 11*a^2 - 15*a,
7*a^6 - 58*a^4 + 5*a^3 + 128*a^2 - 21*a - 64,
1
],
[
a,
-13/86*a^10 + 17/43*a^9 + 81/43*a^8 - 397/86*a^7 - 687/86*a^6 + 684/43*a^5 + 1403/86*a^4 - 721/43*a^3 - 1575/86*a^2 + 287/86*a + 268/43,
-2/43*a^10 + 27/86*a^9 - 13/86*a^8 - 271/86*a^7 + 278/43*a^6 + 583/86*a^5 - 2489/86*a^4 + 228/43*a^3 + 1739/43*a^2 - 1119/86*a - 675/43,
23/172*a^10 + 3/86*a^9 - 269/86*a^8 + 107/172*a^7 + 4113/172*a^6 - 843/86*a^5 - 12273/172*a^4 + 1387/43*a^3 + 13047/172*a^2 - 4477/172*a - 1741/86,
-7/172*a^10 - 7/43*a^9 + 40/43*a^8 + 375/172*a^7 - 1177/172*a^6 - 398/43*a^5 + 3395/172*a^4 + 565/43*a^3 - 3739/172*a^2 - 421/172*a + 743/86,
-1,
55/86*a^10 - 62/43*a^9 - 389/43*a^8 + 1587/86*a^7 + 3879/86*a^6 - 3261/43*a^5 - 8701/86*a^4 + 4992/43*a^3 + 8873/86*a^2 - 4727/86*a - 1587/43,
57/86*a^10 - 58/43*a^9 - 418/43*a^8 + 1529/86*a^7 + 4375/86*a^6 - 3310/43*a^5 - 10359/86*a^4 + 5523/43*a^3 + 11047/86*a^2 - 5909/86*a - 1959/43,
-97/172*a^10 + 107/86*a^9 + 697/86*a^8 - 2777/172*a^7 - 7071/172*a^6 + 5795/86*a^5 + 15999/172*a^4 - 4438/43*a^3 - 16257/172*a^2 + 7791/172*a + 3121/86,
16/43*a^10 - 65/43*a^9 - 120/43*a^8 + 740/43*a^7 - 117/43*a^6 - 2418/43*a^5 + 1829/43*a^4 + 2261/43*a^3 - 2474/43*a^2 - 340/43*a + 842/43,
40/43*a^10 - 98/43*a^9 - 515/43*a^8 + 1205/43*a^7 + 2223/43*a^6 - 4669/43*a^5 - 4221/43*a^4 + 6663/43*a^3 + 3963/43*a^2 - 3129/43*a - 1292/43,
1
],
[
a,
-5/4*a^10 + 5/2*a^9 + 16*a^8 - 129/4*a^7 - 241/4*a^6 + 120*a^5 + 293/4*a^4 - 130*a^3 - 139/4*a^2 + 101/4*a + 5/2,
-1/4*a^10 + 5/4*a^9 + 11/4*a^8 - 16*a^7 - 27/4*a^6 + 237/4*a^5 - 125/2*a^3 - 13/4*a^2 + 9*a + 1,
3/8*a^10 - 1/4*a^9 - 11/2*a^8 + 27/8*a^7 + 215/8*a^6 - 13*a^5 - 423/8*a^4 + 27/2*a^3 + 321/8*a^2 + 17/8*a - 21/4,
3/8*a^10 - 1/2*a^9 - 19/4*a^8 + 53/8*a^7 + 139/8*a^6 - 103/4*a^5 - 145/8*a^4 + 32*a^3 + 29/8*a^2 - 97/8*a + 1/4,
1,
1/4*a^10 + 1/2*a^9 - 4*a^8 - 27/4*a^7 + 89/4*a^6 + 29*a^5 - 201/4*a^4 - 45*a^3 + 159/4*a^2 + 83/4*a - 11/2,
7/4*a^10 - 4*a^9 - 45/2*a^8 + 209/4*a^7 + 343/4*a^6 - 401/2*a^5 - 437/4*a^4 + 235*a^3 + 229/4*a^2 - 217/4*a - 3/2,
9/8*a^10 - 13/4*a^9 - 14*a^8 + 333/8*a^7 + 397/8*a^6 - 307/2*a^5 - 441/8*a^4 + 321/2*a^3 + 283/8*a^2 - 185/8*a - 7/4,
1/2*a^10 - 4*a^9 - 6*a^8 + 105/2*a^7 + 39/2*a^6 - 206*a^5 - 47/2*a^4 + 249*a^3 + 71/2*a^2 - 97/2*a - 1,
-a^10 + 7/2*a^9 + 25/2*a^8 - 91/2*a^7 - 45*a^6 + 347/2*a^5 + 111/2*a^4 - 196*a^3 - 47*a^2 + 63/2*a + 7,
-1
]
*], q_expansions := [*
q + q^2 - q^4 - 2*q^5 + 2*q^7 - 3*q^8 - 3*q^9 - 2*q^10 - 2*q^11 - q^13 + 2*q^14 - q^16 - 6*q^17 - 3*q^18 + 2*q^20 - 2*q^22 + 2*q^23 - q^25 - q^26 - 2*q^28 - 6*q^29 + 8*q^31 + 5*q^32 - 6*q^34 - 4*q^35 + 3*q^36 - q^37 + O(q^38),
q + a*q^2 + (-4*a^6 - 15*a^5 + 10*a^4 + 69*a^3 + 15*a^2 - 42*a + 5)*q^3 + (a^2 - 2)*q^4 + (-3*a^6 - 11*a^5 + 10*a^4 + 54*a^3 - 41*a + 8)*q^5 + (5*a^6 + 18*a^5 - 15*a^4 - 85*a^3 - 10*a^2 + 57*a - 8)*q^6 + (8*a^6 + 30*a^5 - 21*a^4 - 140*a^3 - 26*a^2 + 88*a - 13)*q^7 + (a^3 - 4*a)*q^8 + (-a^6 - 4*a^5 + a^4 + 17*a^3 + 11*a^2 - 6*a - 2)*q^9 + (4*a^6 + 16*a^5 - 9*a^4 - 75*a^3 - 17*a^2 + 47*a - 6)*q^10 + (9*a^6 + 34*a^5 - 24*a^4 - 160*a^3 - 27*a^2 + 105*a - 15)*q^11 + (a^6 + 5*a^5 - 23*a^3 - 13*a^2 + 11*a)*q^12 - q^13 + (-10*a^6 - 37*a^5 + 28*a^4 + 174*a^3 + 24*a^2 - 117*a + 16)*q^14 + (3*a^6 + 11*a^5 - 7*a^4 - 48*a^3 - 14*a^2 + 21*a - 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^6 - 4*a^5 + 2*a^4 + 18*a^3 + 6*a^2 - 8*a)*q^17 + (a^6 + 3*a^5 - 4*a^4 - 14*a^3 + 2*a^2 + 11*a - 2)*q^18 + (9*a^6 + 32*a^5 - 30*a^4 - 154*a^3 - 3*a^2 + 111*a - 22)*q^19 + (2*a^6 + 5*a^5 - 11*a^4 - 25*a^3 + 15*a^2 + 24*a - 8)*q^20 + (2*a^6 + 9*a^5 - 38*a^3 - 26*a^2 + 16*a - 1)*q^21 + (-11*a^6 - 42*a^5 + 29*a^4 + 198*a^3 + 33*a^2 - 132*a + 18)*q^22 + (-8*a^6 - 30*a^5 + 22*a^4 + 143*a^3 + 23*a^2 - 99*a + 8)*q^23 + (-10*a^6 - 38*a^5 + 28*a^4 + 182*a^3 + 23*a^2 - 127*a + 18)*q^24 + (4*a^6 + 15*a^5 - 13*a^4 - 75*a^3 - 2*a^2 + 60*a - 9)*q^25 - a*q^26 + (11*a^6 + 41*a^5 - 29*a^4 - 191*a^3 - 36*a^2 + 122*a - 13)*q^27 + (-3*a^6 - 12*a^5 + 6*a^4 + 54*a^3 + 15*a^2 - 30*a + 6)*q^28 + (-15*a^6 - 56*a^5 + 41*a^4 + 263*a^3 + 41*a^2 - 171*a + 24)*q^29 + (-4*a^6 - 13*a^5 + 15*a^4 + 61*a^3 - 3*a^2 - 43*a + 6)*q^30 + (-13*a^6 - 48*a^5 + 36*a^4 + 225*a^3 + 36*a^2 - 147*a + 14)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (6*a^6 + 23*a^5 - 14*a^4 - 107*a^3 - 26*a^2 + 70*a - 9)*q^33 + (a^6 + 4*a^5 - 3*a^4 - 19*a^3 + 13*a - 2)*q^34 + (-5*a^6 - 20*a^5 + 8*a^4 + 87*a^3 + 36*a^2 - 36*a + 2)*q^35 + (2*a^5 + 5*a^4 - 7*a^3 - 19*a^2 - 3*a + 6)*q^36 - q^37 + O(q^38),
q + a*q^2 + (-2*a^6 - a^5 + 16*a^4 + 5*a^3 - 33*a^2 - 2*a + 13)*q^3 + (a^2 - 2)*q^4 + (a^6 + a^5 - 8*a^4 - 6*a^3 + 16*a^2 + 5*a - 6)*q^5 + (a^6 - 9*a^4 + a^3 + 22*a^2 - 5*a - 12)*q^6 + (a^4 - 6*a^2 + 5)*q^7 + (a^3 - 4*a)*q^8 + (3*a^6 + 2*a^5 - 23*a^4 - 11*a^3 + 43*a^2 + 8*a - 14)*q^9 + (a^4 - a^3 - 7*a^2 + 3*a + 6)*q^10 + (3*a^6 - 26*a^4 + 2*a^3 + 61*a^2 - 9*a - 33)*q^11 + (3*a^6 + a^5 - 24*a^4 - 5*a^3 + 49*a^2 + a - 20)*q^12 + q^13 + (a^5 - 6*a^3 + 5*a)*q^14 + (a^6 - a^5 - 9*a^4 + 8*a^3 + 24*a^2 - 13*a - 18)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 - 10*a^4 + 2*a^3 + 28*a^2 - 8*a - 18)*q^17 + (-a^6 + a^5 + 10*a^4 - 8*a^3 - 28*a^2 + 13*a + 18)*q^18 + (-3*a^6 + 26*a^4 - 2*a^3 - 59*a^2 + 9*a + 26)*q^19 + (-2*a^6 - a^5 + 15*a^4 + 5*a^3 - 29*a^2 - 4*a + 12)*q^20 + (-4*a^6 - a^5 + 32*a^4 + 4*a^3 - 66*a^2 + 2*a + 29)*q^21 + (-3*a^6 - 2*a^5 + 23*a^4 + 10*a^3 - 45*a^2 - 6*a + 18)*q^22 + (-a^3 + a^2 + 3*a - 6)*q^23 + (-4*a^6 + 34*a^4 - 4*a^3 - 79*a^2 + 17*a + 42)*q^24 + (-2*a^6 + a^5 + 17*a^4 - 7*a^3 - 38*a^2 + 12*a + 19)*q^25 + a*q^26 + (a^6 - a^5 - 11*a^4 + 9*a^3 + 36*a^2 - 18*a - 29)*q^27 + (a^6 - 8*a^4 + 17*a^2 - 10)*q^28 + (-a^6 - 2*a^5 + 7*a^4 + 13*a^3 - 11*a^2 - 15*a)*q^29 + (-2*a^6 - a^5 + 15*a^4 + 7*a^3 - 25*a^2 - 9*a + 6)*q^30 + (7*a^6 - 58*a^4 + 5*a^3 + 128*a^2 - 21*a - 64)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2*a^6 + 3*a^5 - 14*a^4 - 19*a^3 + 22*a^2 + 24*a - 3)*q^33 + (-a^6 - 2*a^5 + 9*a^4 + 11*a^3 - 20*a^2 - 9*a + 6)*q^34 + (3*a^6 - 24*a^4 + a^3 + 50*a^2 - 2*a - 24)*q^35 + (-4*a^6 - 2*a^5 + 31*a^4 + 11*a^3 - 61*a^2 - 7*a + 22)*q^36 + q^37 + O(q^38),
q + a*q^2 + (-13/86*a^10 + 17/43*a^9 + 81/43*a^8 - 397/86*a^7 - 687/86*a^6 + 684/43*a^5 + 1403/86*a^4 - 721/43*a^3 - 1575/86*a^2 + 287/86*a + 268/43)*q^3 + (a^2 - 2)*q^4 + (-2/43*a^10 + 27/86*a^9 - 13/86*a^8 - 271/86*a^7 + 278/43*a^6 + 583/86*a^5 - 2489/86*a^4 + 228/43*a^3 + 1739/43*a^2 - 1119/86*a - 675/43)*q^5 + (-5/86*a^10 - 10/43*a^9 + 94/43*a^8 + 145/86*a^7 - 1713/86*a^6 + 58/43*a^5 + 5435/86*a^4 - 833/43*a^3 - 5693/86*a^2 + 1407/86*a + 715/43)*q^6 + (23/172*a^10 + 3/86*a^9 - 269/86*a^8 + 107/172*a^7 + 4113/172*a^6 - 843/86*a^5 - 12273/172*a^4 + 1387/43*a^3 + 13047/172*a^2 - 4477/172*a - 1741/86)*q^7 + (a^3 - 4*a)*q^8 + (-11/43*a^10 + 42/43*a^9 + 104/43*a^8 - 498/43*a^7 - 191/43*a^6 + 1786/43*a^5 - 169/43*a^4 - 2186/43*a^3 + 40/43*a^2 + 868/43*a + 394/43)*q^9 + (15/86*a^10 - 69/86*a^9 - 91/86*a^8 + 406/43*a^7 - 365/86*a^6 - 2885/86*a^5 + 1286/43*a^4 + 1725/43*a^3 - 2959/86*a^2 - 541/43*a + 220/43)*q^10 + (-7/172*a^10 - 7/43*a^9 + 40/43*a^8 + 375/172*a^7 - 1177/172*a^6 - 398/43*a^5 + 3395/172*a^4 + 565/43*a^3 - 3739/172*a^2 - 421/172*a + 743/86)*q^11 + (-9/86*a^10 + 25/43*a^9 + 23/43*a^8 - 599/86*a^7 + 305/86*a^6 + 1102/43*a^5 - 1827/86*a^4 - 1422/43*a^3 + 2257/86*a^2 + 1191/86*a - 261/43)*q^12 - q^13 + (75/172*a^10 - 54/43*a^9 - 232/43*a^8 + 2641/172*a^7 + 3765/172*a^6 - 2499/43*a^5 - 6619/172*a^4 + 3302/43*a^3 + 6103/172*a^2 - 5023/172*a - 1265/86)*q^14 + (-42/43*a^10 + 90/43*a^9 + 616/43*a^8 - 1190/43*a^7 - 3235/43*a^6 + 5197/43*a^5 + 7685/43*a^4 - 8886/43*a^3 - 8072/43*a^2 + 5085/43*a + 2810/43)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (55/86*a^10 - 62/43*a^9 - 389/43*a^8 + 1587/86*a^7 + 3879/86*a^6 - 3261/43*a^5 - 8701/86*a^4 + 4992/43*a^3 + 8873/86*a^2 - 4727/86*a - 1587/43)*q^17 + (9/43*a^10 - 50/43*a^9 - 3/43*a^8 + 513/43*a^7 - 821/43*a^6 - 1258/43*a^5 + 3633/43*a^4 - 37/43*a^3 - 4192/43*a^2 + 1131/43*a + 1210/43)*q^18 + (57/86*a^10 - 58/43*a^9 - 418/43*a^8 + 1529/86*a^7 + 4375/86*a^6 - 3310/43*a^5 - 10359/86*a^4 + 5523/43*a^3 + 11047/86*a^2 - 5909/86*a - 1959/43)*q^19 + (-8/43*a^10 + 65/86*a^9 + 163/86*a^8 - 783/86*a^7 - 221/43*a^6 + 2891/86*a^5 + 493/86*a^4 - 1883/43*a^3 - 569/43*a^2 + 1673/86*a + 525/43)*q^20 + (10/43*a^10 - 3/43*a^9 - 204/43*a^8 + 97/43*a^7 + 1405/43*a^6 - 791/43*a^5 - 3775/43*a^4 + 2085/43*a^3 + 3431/43*a^2 - 1438/43*a - 753/43)*q^21 + (-49/172*a^10 + 31/86*a^9 + 345/86*a^8 - 729/172*a^7 - 3251/172*a^6 + 1351/86*a^5 + 5963/172*a^4 - 947/43*a^3 - 3641/172*a^2 + 1955/172*a + 385/86)*q^22 + (-97/172*a^10 + 107/86*a^9 + 697/86*a^8 - 2777/172*a^7 - 7071/172*a^6 + 5795/86*a^5 + 15999/172*a^4 - 4438/43*a^3 - 16257/172*a^2 + 7791/172*a + 3121/86)*q^23 + (33/86*a^10 - 20/43*a^9 - 285/43*a^8 + 591/86*a^7 + 3497/86*a^6 - 1475/43*a^5 - 8953/86*a^4 + 2763/43*a^3 + 8437/86*a^2 - 2733/86*a - 935/43)*q^24 + (-36/43*a^10 + 71/43*a^9 + 528/43*a^8 - 934/43*a^7 - 2736/43*a^6 + 4043/43*a^5 + 6237/43*a^4 - 6775/43*a^3 - 6151/43*a^2 + 3689/43*a + 2255/43)*q^25 - a*q^26 + (17/43*a^10 - 18/43*a^9 - 321/43*a^8 + 324/43*a^7 + 2152/43*a^6 - 1994/43*a^5 - 6095/43*a^4 + 4727/43*a^3 + 6826/43*a^2 - 3425/43*a - 2325/43)*q^27 + (-37/172*a^10 + 55/86*a^9 + 171/86*a^8 - 1249/172*a^7 - 447/172*a^6 + 2089/86*a^5 - 1921/172*a^4 - 1117/43*a^3 + 3383/172*a^2 + 1399/172*a - 643/86)*q^28 + (16/43*a^10 - 65/43*a^9 - 120/43*a^8 + 740/43*a^7 - 117/43*a^6 - 2418/43*a^5 + 1829/43*a^4 + 2261/43*a^3 - 2474/43*a^2 - 340/43*a + 842/43)*q^29 + (-36/43*a^10 + 28/43*a^9 + 700/43*a^8 - 547/43*a^7 - 4757/43*a^6 + 3527/43*a^5 + 13332/43*a^4 - 8366/43*a^3 - 14235/43*a^2 + 5624/43*a + 4620/43)*q^30 + (40/43*a^10 - 98/43*a^9 - 515/43*a^8 + 1205/43*a^7 + 2223/43*a^6 - 4669/43*a^5 - 4221/43*a^4 + 6663/43*a^3 + 3963/43*a^2 - 3129/43*a - 1292/43)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-40/43*a^10 + 55/43*a^9 + 644/43*a^8 - 732/43*a^7 - 3728/43*a^6 + 3207/43*a^5 + 9424/43*a^4 - 5287/43*a^3 - 9725/43*a^2 + 2441/43*a + 2969/43)*q^33 + (41/86*a^10 - 4/43*a^9 - 444/43*a^8 + 359/86*a^7 + 6513/86*a^6 - 1628/43*a^5 - 19111/86*a^4 + 4629/43*a^3 + 20573/86*a^2 - 6859/86*a - 3025/43)*q^34 + (38/43*a^10 - 83/86*a^9 - 1301/86*a^8 + 1193/86*a^7 + 4006/43*a^6 - 5831/86*a^5 - 21337/86*a^4 + 5601/43*a^3 + 11378/43*a^2 - 6947/86*a - 3515/43)*q^35 + (-1/43*a^10 + 39/43*a^9 - 100/43*a^8 - 401/43*a^7 + 1257/43*a^6 + 952/43*a^5 - 4460/43*a^4 + 243/43*a^3 + 5191/43*a^2 - 1129/43*a - 1778/43)*q^36 + q^37 + O(q^38),
q + a*q^2 + (-5/4*a^10 + 5/2*a^9 + 16*a^8 - 129/4*a^7 - 241/4*a^6 + 120*a^5 + 293/4*a^4 - 130*a^3 - 139/4*a^2 + 101/4*a + 5/2)*q^3 + (a^2 - 2)*q^4 + (-1/4*a^10 + 5/4*a^9 + 11/4*a^8 - 16*a^7 - 27/4*a^6 + 237/4*a^5 - 125/2*a^3 - 13/4*a^2 + 9*a + 1)*q^5 + (-5/4*a^10 + a^9 + 33/2*a^8 - 51/4*a^7 - 265/4*a^6 + 89/2*a^5 + 355/4*a^4 - 41*a^3 - 139/4*a^2 + 35/4*a + 5/2)*q^6 + (3/8*a^10 - 1/4*a^9 - 11/2*a^8 + 27/8*a^7 + 215/8*a^6 - 13*a^5 - 423/8*a^4 + 27/2*a^3 + 321/8*a^2 + 17/8*a - 21/4)*q^7 + (a^3 - 4*a)*q^8 + (-a^10 + 3*a^9 + 13*a^8 - 39*a^7 - 51*a^6 + 149*a^5 + 74*a^4 - 172*a^3 - 58*a^2 + 37*a + 8)*q^9 + (1/2*a^10 - 1/4*a^9 - 25/4*a^8 + 11/4*a^7 + 22*a^6 - 23/4*a^5 - 75/4*a^4 - 9/2*a^3 - 3*a^2 + 9/4*a + 1/2)*q^10 + (3/8*a^10 - 1/2*a^9 - 19/4*a^8 + 53/8*a^7 + 139/8*a^6 - 103/4*a^5 - 145/8*a^4 + 32*a^3 + 29/8*a^2 - 97/8*a + 1/4)*q^11 + (-1/4*a^10 - 7/2*a^9 + 4*a^8 + 183/4*a^7 - 85/4*a^6 - 180*a^5 + 125/4*a^4 + 219*a^3 + 73/4*a^2 - 167/4*a - 5/2)*q^12 + q^13 + (7/8*a^10 - a^9 - 45/4*a^8 + 101/8*a^7 + 343/8*a^6 - 177/4*a^5 - 417/8*a^4 + 42*a^3 + 161/8*a^2 - 57/8*a - 3/4)*q^14 + (3/2*a^9 - 1/2*a^8 - 39/2*a^7 + 6*a^6 + 151/2*a^5 - 31/2*a^4 - 89*a^3 - a^2 + 33/2*a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/4*a^10 + 1/2*a^9 - 4*a^8 - 27/4*a^7 + 89/4*a^6 + 29*a^5 - 201/4*a^4 - 45*a^3 + 159/4*a^2 + 83/4*a - 11/2)*q^17 + (a^9 - 13*a^7 + 51*a^5 + 3*a^4 - 63*a^3 - 11*a^2 + 13*a + 2)*q^18 + (7/4*a^10 - 4*a^9 - 45/2*a^8 + 209/4*a^7 + 343/4*a^6 - 401/2*a^5 - 437/4*a^4 + 235*a^3 + 229/4*a^2 - 217/4*a - 3/2)*q^19 + (7/4*a^10 - 11/4*a^9 - 89/4*a^8 + 35*a^7 + 329/4*a^6 - 503/4*a^5 - 92*a^4 + 249/2*a^3 + 131/4*a^2 - 20*a - 3)*q^20 + (a^8 - 13*a^6 + 50*a^4 + 3*a^3 - 57*a^2 - 11*a + 9)*q^21 + (5/8*a^10 - 1/4*a^9 - 8*a^8 + 25/8*a^7 + 241/8*a^6 - 19/2*a^5 - 269/8*a^4 + 11/2*a^3 + 47/8*a^2 - 13/8*a - 3/4)*q^22 + (9/8*a^10 - 13/4*a^9 - 14*a^8 + 333/8*a^7 + 397/8*a^6 - 307/2*a^5 - 441/8*a^4 + 321/2*a^3 + 283/8*a^2 - 185/8*a - 7/4)*q^23 + (-7/4*a^10 - a^9 + 45/2*a^8 + 55/4*a^7 - 339/4*a^6 - 127/2*a^5 + 341/4*a^4 + 99*a^3 + 63/4*a^2 - 75/4*a - 9/2)*q^24 + (-a^10 + 3/2*a^9 + 25/2*a^8 - 39/2*a^7 - 44*a^6 + 145/2*a^5 + 77/2*a^4 - 76*a^3 + 5*a^2 + 17/2*a - 4)*q^25 + a*q^26 + (-5/2*a^10 + 5*a^9 + 33*a^8 - 131/2*a^7 - 267/2*a^6 + 252*a^5 + 393/2*a^4 - 297*a^3 - 257/2*a^2 + 145/2*a + 18)*q^27 + (7/8*a^10 - 1/4*a^9 - 21/2*a^8 + 23/8*a^7 + 259/8*a^6 - 6*a^5 - 43/8*a^4 - 5/2*a^3 - 363/8*a^2 - 75/8*a + 35/4)*q^28 + (1/2*a^10 - 4*a^9 - 6*a^8 + 105/2*a^7 + 39/2*a^6 - 206*a^5 - 47/2*a^4 + 249*a^3 + 71/2*a^2 - 97/2*a - 1)*q^29 + (3/2*a^10 - 1/2*a^9 - 39/2*a^8 + 6*a^7 + 151/2*a^6 - 31/2*a^5 - 89*a^4 - a^3 + 33/2*a^2 + 3*a)*q^30 + (-a^10 + 7/2*a^9 + 25/2*a^8 - 91/2*a^7 - 45*a^6 + 347/2*a^5 + 111/2*a^4 - 196*a^3 - 47*a^2 + 63/2*a + 7)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^10 - 3*a^9 - 7*a^8 + 79/2*a^7 + 65/2*a^6 - 156*a^5 - 143/2*a^4 + 191*a^3 + 173/2*a^2 - 73/2*a - 12)*q^33 + (5/4*a^10 - a^9 - 33/2*a^8 + 51/4*a^7 + 265/4*a^6 - 89/2*a^5 - 355/4*a^4 + 41*a^3 + 131/4*a^2 - 27/4*a - 1/2)*q^34 + (-3/4*a^10 + 3/4*a^9 + 41/4*a^8 - 10*a^7 - 177/4*a^6 + 155/4*a^5 + 70*a^4 - 89/2*a^3 - 147/4*a^2 + 5*a + 3)*q^35 + (3*a^10 - 6*a^9 - 39*a^8 + 78*a^7 + 153*a^6 - 295*a^5 - 211*a^4 + 333*a^3 + 129*a^2 - 72*a - 16)*q^36 - q^37 + O(q^38)
*]> ;  // time = 88.77 seconds




J[482] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 482, 482, 482, 482, 482, 241, 241 ], new_dimensions := [ 1, 2, 3, 6, 9, 7, 12 ], dimensions := [ 1, 2, 3, 6, 9, 14, 24 ], intersection_graph := [ 0, 1, 1, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 55, 1, 1, 0, 1, 1, 13, 1, 1, 1, 1, 0, 1, 1, 11863, 1, 1, 1, 1, 0, 3761, 1, 7, 1, 13, 1, 3761, 0, 1, 1, 55, 1, 11863, 1, 1, 0 ], ap_traces := [
[ -1, -2, -1, 1, 4, -2, 4, -5, -9, 9, -8, -8 ],
[ 2, -2, -3, -4, -6, -7, 1, 0, 3, -5, 4, -14 ],
[ -3, -2, 2, -9, -2, -5, -7, 3, 0, -4, -2, -6 ],
[ -6, 2, -5, 10, -4, 9, 1, 10, 9, -1, 14, 20 ],
[ 9, 4, 5, 6, 2, 5, 3, 2, -3, 11, -4, 4 ]
], hecke_fields := [
x - 1,
x^2 - 4*x - 1,
x^3 + 2*x^2 - 5*x - 2,
x^6 - 2*x^5 - 10*x^4 + 16*x^3 + 26*x^2 - 30*x - 13,
x^9 - 4*x^8 - 12*x^7 + 58*x^6 + 24*x^5 - 252*x^4 + 97*x^3 + 336*x^2 - 244*x - 16
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 7, 1 ],
[ 55, 1 ],
[ 13, 1 ],
[ 35589, 3 ],
[ 455081, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 55, 1 ],
[ 1, 1 ],
[ 1, 3 ],
[ 455081, 1 ]
], torsion_upper_bounds := [ 1, 5, 1, 3, 121 ], torsion_lower_bounds := [ 1, 1, 1, 3, 121 ], l_ratios := [ 0, 0, 0, 1/3, 3761/121 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ -1, -2, -1, 1, 4, -2, 4, -5, -9, 9, -8, -8 ],
[
1,
-1,
-1/2*a - 1/2,
a - 4,
-3,
-1/2*a - 5/2,
5/2*a - 9/2,
-3*a + 6,
-5/2*a + 13/2,
-1/2*a - 3/2,
3*a - 4,
-a - 5
],
[
-1,
a,
-1/2*a^2 - 3/2*a + 2,
-3,
a^2 + 2*a - 4,
-1/2*a^2 - 5/2*a - 1,
-1/2*a^2 - 3/2*a - 1,
a^2 + a - 3,
1/2*a^2 + 1/2*a - 2,
-1/2*a^2 + 3/2*a + 2,
-a^2 + 4,
-a^2 - a + 2
],
[
-1,
a,
1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 3/2*a^2 + 17/2*a + 1/2,
-1/2*a^4 + 1/2*a^3 + 4*a^2 - 3/2*a - 7/2,
-a^2 + a + 3,
1/2*a^3 - a^2 - 2*a + 9/2,
-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 5/2*a^2 - 15/2*a + 5/2,
a^3 - a^2 - 5*a + 4,
-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 1/2*a^2 - 19/2*a - 7/2,
-1/2*a^5 - 1/2*a^4 + 13/2*a^3 + 11/2*a^2 - 33/2*a - 19/2,
-1/2*a^5 - 1/2*a^4 + 6*a^3 + 9/2*a^2 - 29/2*a - 2,
3/2*a^4 - 5/2*a^3 - 11*a^2 + 19/2*a + 33/2
],
[
1,
a,
15/16*a^8 - 39/16*a^7 - 237/16*a^6 + 547/16*a^5 + 1149/16*a^4 - 2273/16*a^3 - 109*a^2 + 717/4*a + 15,
1/4*a^8 - 3/4*a^7 - 15/4*a^6 + 43/4*a^5 + 67/4*a^4 - 183/4*a^3 - 45/2*a^2 + 115/2*a + 2,
13/8*a^8 - 33/8*a^7 - 203/8*a^6 + 453/8*a^5 + 963/8*a^4 - 1823/8*a^3 - 351/2*a^2 + 555/2*a + 20,
-91/16*a^8 + 239/16*a^7 + 1421/16*a^6 - 3331/16*a^5 - 6757/16*a^4 + 13697/16*a^3 + 2475/4*a^2 - 4261/4*a - 61,
-31/16*a^8 + 83/16*a^7 + 481/16*a^6 - 1159/16*a^5 - 2273/16*a^4 + 4773/16*a^3 + 839/4*a^2 - 1481/4*a - 27,
-17/4*a^8 + 45/4*a^7 + 265/4*a^6 - 627/4*a^5 - 1261/4*a^4 + 2577/4*a^3 + 935/2*a^2 - 1603/2*a - 56,
71/16*a^8 - 187/16*a^7 - 1105/16*a^6 + 2599/16*a^5 + 5233/16*a^4 - 10645/16*a^3 - 1913/4*a^2 + 3295/4*a + 51,
67/16*a^8 - 179/16*a^7 - 1041/16*a^6 + 2495/16*a^5 + 4929/16*a^4 - 10245/16*a^3 - 905/2*a^2 + 3165/4*a + 51,
1/4*a^8 - 3/4*a^7 - 15/4*a^6 + 43/4*a^5 + 69/4*a^4 - 187/4*a^3 - 53/2*a^2 + 63*a + 4,
9/8*a^8 - 25/8*a^7 - 139/8*a^6 + 353/8*a^5 + 651/8*a^4 - 1479/8*a^3 - 231/2*a^2 + 467/2*a + 6
]
*], q_expansions := [*
q - q^2 - 2*q^3 + q^4 - q^5 + 2*q^6 + q^7 - q^8 + q^9 + q^10 + 4*q^11 - 2*q^12 - 2*q^13 - q^14 + 2*q^15 + q^16 + 4*q^17 - q^18 - 5*q^19 - q^20 - 2*q^21 - 4*q^22 - 9*q^23 + 2*q^24 - 4*q^25 + 2*q^26 + 4*q^27 + q^28 + 9*q^29 - 2*q^30 - 8*q^31 - q^32 - 8*q^33 - 4*q^34 - q^35 + q^36 - 8*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + (-1/2*a - 1/2)*q^5 - q^6 + (a - 4)*q^7 + q^8 - 2*q^9 + (-1/2*a - 1/2)*q^10 - 3*q^11 - q^12 + (-1/2*a - 5/2)*q^13 + (a - 4)*q^14 + (1/2*a + 1/2)*q^15 + q^16 + (5/2*a - 9/2)*q^17 - 2*q^18 + (-3*a + 6)*q^19 + (-1/2*a - 1/2)*q^20 + (-a + 4)*q^21 - 3*q^22 + (-5/2*a + 13/2)*q^23 - q^24 + (3/2*a - 9/2)*q^25 + (-1/2*a - 5/2)*q^26 + 5*q^27 + (a - 4)*q^28 + (-1/2*a - 3/2)*q^29 + (1/2*a + 1/2)*q^30 + (3*a - 4)*q^31 + q^32 + 3*q^33 + (5/2*a - 9/2)*q^34 + (-1/2*a + 3/2)*q^35 - 2*q^36 + (-a - 5)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-1/2*a^2 - 3/2*a + 2)*q^5 - a*q^6 - 3*q^7 - q^8 + (a^2 - 3)*q^9 + (1/2*a^2 + 3/2*a - 2)*q^10 + (a^2 + 2*a - 4)*q^11 + a*q^12 + (-1/2*a^2 - 5/2*a - 1)*q^13 + 3*q^14 + (-1/2*a^2 - 1/2*a - 1)*q^15 + q^16 + (-1/2*a^2 - 3/2*a - 1)*q^17 + (-a^2 + 3)*q^18 + (a^2 + a - 3)*q^19 + (-1/2*a^2 - 3/2*a + 2)*q^20 - 3*a*q^21 + (-a^2 - 2*a + 4)*q^22 + (1/2*a^2 + 1/2*a - 2)*q^23 - a*q^24 + (-1/2*a^2 - 1/2*a + 1)*q^25 + (1/2*a^2 + 5/2*a + 1)*q^26 + (-2*a^2 - a + 2)*q^27 - 3*q^28 + (-1/2*a^2 + 3/2*a + 2)*q^29 + (1/2*a^2 + 1/2*a + 1)*q^30 + (-a^2 + 4)*q^31 - q^32 + (a + 2)*q^33 + (1/2*a^2 + 3/2*a + 1)*q^34 + (3/2*a^2 + 9/2*a - 6)*q^35 + (a^2 - 3)*q^36 + (-a^2 - a + 2)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 3/2*a^2 + 17/2*a + 1/2)*q^5 - a*q^6 + (-1/2*a^4 + 1/2*a^3 + 4*a^2 - 3/2*a - 7/2)*q^7 - q^8 + (a^2 - 3)*q^9 + (-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 3/2*a^2 - 17/2*a - 1/2)*q^10 + (-a^2 + a + 3)*q^11 + a*q^12 + (1/2*a^3 - a^2 - 2*a + 9/2)*q^13 + (1/2*a^4 - 1/2*a^3 - 4*a^2 + 3/2*a + 7/2)*q^14 + (1/2*a^5 + 1/2*a^4 - 13/2*a^3 - 9/2*a^2 + 31/2*a + 13/2)*q^15 + q^16 + (-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 5/2*a^2 - 15/2*a + 5/2)*q^17 + (-a^2 + 3)*q^18 + (a^3 - a^2 - 5*a + 4)*q^19 + (1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 3/2*a^2 + 17/2*a + 1/2)*q^20 + (-1/2*a^5 + 1/2*a^4 + 4*a^3 - 3/2*a^2 - 7/2*a)*q^21 + (a^2 - a - 3)*q^22 + (-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 1/2*a^2 - 19/2*a - 7/2)*q^23 - a*q^24 + (-1/2*a^5 + 1/2*a^4 + 7/2*a^3 - 1/2*a^2 - 7/2*a - 3/2)*q^25 + (-1/2*a^3 + a^2 + 2*a - 9/2)*q^26 + (a^3 - 6*a)*q^27 + (-1/2*a^4 + 1/2*a^3 + 4*a^2 - 3/2*a - 7/2)*q^28 + (-1/2*a^5 - 1/2*a^4 + 13/2*a^3 + 11/2*a^2 - 33/2*a - 19/2)*q^29 + (-1/2*a^5 - 1/2*a^4 + 13/2*a^3 + 9/2*a^2 - 31/2*a - 13/2)*q^30 + (-1/2*a^5 - 1/2*a^4 + 6*a^3 + 9/2*a^2 - 29/2*a - 2)*q^31 - q^32 + (-a^3 + a^2 + 3*a)*q^33 + (1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 5/2*a^2 + 15/2*a - 5/2)*q^34 + (3/2*a^5 - 1/2*a^4 - 29/2*a^3 - 7/2*a^2 + 53/2*a + 29/2)*q^35 + (a^2 - 3)*q^36 + (3/2*a^4 - 5/2*a^3 - 11*a^2 + 19/2*a + 33/2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (15/16*a^8 - 39/16*a^7 - 237/16*a^6 + 547/16*a^5 + 1149/16*a^4 - 2273/16*a^3 - 109*a^2 + 717/4*a + 15)*q^5 + a*q^6 + (1/4*a^8 - 3/4*a^7 - 15/4*a^6 + 43/4*a^5 + 67/4*a^4 - 183/4*a^3 - 45/2*a^2 + 115/2*a + 2)*q^7 + q^8 + (a^2 - 3)*q^9 + (15/16*a^8 - 39/16*a^7 - 237/16*a^6 + 547/16*a^5 + 1149/16*a^4 - 2273/16*a^3 - 109*a^2 + 717/4*a + 15)*q^10 + (13/8*a^8 - 33/8*a^7 - 203/8*a^6 + 453/8*a^5 + 963/8*a^4 - 1823/8*a^3 - 351/2*a^2 + 555/2*a + 20)*q^11 + a*q^12 + (-91/16*a^8 + 239/16*a^7 + 1421/16*a^6 - 3331/16*a^5 - 6757/16*a^4 + 13697/16*a^3 + 2475/4*a^2 - 4261/4*a - 61)*q^13 + (1/4*a^8 - 3/4*a^7 - 15/4*a^6 + 43/4*a^5 + 67/4*a^4 - 183/4*a^3 - 45/2*a^2 + 115/2*a + 2)*q^14 + (21/16*a^8 - 57/16*a^7 - 323/16*a^6 + 789/16*a^5 + 1507/16*a^4 - 3199/16*a^3 - 543/4*a^2 + 975/4*a + 15)*q^15 + q^16 + (-31/16*a^8 + 83/16*a^7 + 481/16*a^6 - 1159/16*a^5 - 2273/16*a^4 + 4773/16*a^3 + 839/4*a^2 - 1481/4*a - 27)*q^17 + (a^2 - 3)*q^18 + (-17/4*a^8 + 45/4*a^7 + 265/4*a^6 - 627/4*a^5 - 1261/4*a^4 + 2577/4*a^3 + 935/2*a^2 - 1603/2*a - 56)*q^19 + (15/16*a^8 - 39/16*a^7 - 237/16*a^6 + 547/16*a^5 + 1149/16*a^4 - 2273/16*a^3 - 109*a^2 + 717/4*a + 15)*q^20 + (1/4*a^8 - 3/4*a^7 - 15/4*a^6 + 43/4*a^5 + 69/4*a^4 - 187/4*a^3 - 53/2*a^2 + 63*a + 4)*q^21 + (13/8*a^8 - 33/8*a^7 - 203/8*a^6 + 453/8*a^5 + 963/8*a^4 - 1823/8*a^3 - 351/2*a^2 + 555/2*a + 20)*q^22 + (71/16*a^8 - 187/16*a^7 - 1105/16*a^6 + 2599/16*a^5 + 5233/16*a^4 - 10645/16*a^3 - 1913/4*a^2 + 3295/4*a + 51)*q^23 + a*q^24 + (15/16*a^8 - 39/16*a^7 - 237/16*a^6 + 547/16*a^5 + 1149/16*a^4 - 2257/16*a^3 - 110*a^2 + 689/4*a + 20)*q^25 + (-91/16*a^8 + 239/16*a^7 + 1421/16*a^6 - 3331/16*a^5 - 6757/16*a^4 + 13697/16*a^3 + 2475/4*a^2 - 4261/4*a - 61)*q^26 + (a^3 - 6*a)*q^27 + (1/4*a^8 - 3/4*a^7 - 15/4*a^6 + 43/4*a^5 + 67/4*a^4 - 183/4*a^3 - 45/2*a^2 + 115/2*a + 2)*q^28 + (67/16*a^8 - 179/16*a^7 - 1041/16*a^6 + 2495/16*a^5 + 4929/16*a^4 - 10245/16*a^3 - 905/2*a^2 + 3165/4*a + 51)*q^29 + (21/16*a^8 - 57/16*a^7 - 323/16*a^6 + 789/16*a^5 + 1507/16*a^4 - 3199/16*a^3 - 543/4*a^2 + 975/4*a + 15)*q^30 + (1/4*a^8 - 3/4*a^7 - 15/4*a^6 + 43/4*a^5 + 69/4*a^4 - 187/4*a^3 - 53/2*a^2 + 63*a + 4)*q^31 + q^32 + (19/8*a^8 - 47/8*a^7 - 301/8*a^6 + 651/8*a^5 + 1453/8*a^4 - 2665/8*a^3 - 537/2*a^2 + 833/2*a + 26)*q^33 + (-31/16*a^8 + 83/16*a^7 + 481/16*a^6 - 1159/16*a^5 - 2273/16*a^4 + 4773/16*a^3 + 839/4*a^2 - 1481/4*a - 27)*q^34 + (57/16*a^8 - 149/16*a^7 - 895/16*a^6 + 2089/16*a^5 + 4287/16*a^4 - 8683/16*a^3 - 1583/4*a^2 + 2741/4*a + 37)*q^35 + (a^2 - 3)*q^36 + (9/8*a^8 - 25/8*a^7 - 139/8*a^6 + 353/8*a^5 + 651/8*a^4 - 1479/8*a^3 - 231/2*a^2 + 467/2*a + 6)*q^37 + O(q^38)
*]> ;  // time = 157.35 seconds




J[483] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 483, 483, 483, 483, 483, 483, 483, 483, 483, 483, 161, 161, 161, 161, 69, 69, 23, 21 ], new_dimensions := [ 1, 1, 2, 2, 2, 2, 2, 3, 4, 4, 1, 2, 3, 5, 1, 2, 2, 1 ], dimensions := [ 1, 1, 2, 2, 2, 2, 2, 3, 4, 4, 2, 4, 6, 10, 2, 4, 8, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 59, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 5, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 43, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 167, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 25, 1, 1, 1, 1, 5, 1, 9, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 43, 1, 1, 1, 0, 1, 1, 1, 361, 1, 1, 1, 1, 1, 1, 59, 1, 1, 1, 167, 25, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 0, 121, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 361, 1, 1, 121, 0, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 2, 1, 4, -1, -5, -2, 0, -5, -1, -2, 6, 6 ],
[ 2, 1, 0, 1, 1, 2, 4, -3, 1, -6, -2, -2 ],
[ -1, -2, 1, -2, 0, -7, 0, 2, -2, -12, 0, -22 ],
[ 1, -2, -3, 2, 0, -7, -2, -12, 2, 8, -10, -10 ],
[ -1, 2, -5, -2, -10, 1, -4, 4, 2, -2, 6, -18 ],
[ -3, 2, -5, 2, -2, -7, -2, -6, -2, -6, -12, -6 ],
[ -1, 2, 5, 2, 2, -1, -2, 4, 2, 8, -4, -4 ],
[ 0, 3, 3, -3, 6, 9, 6, -6, -3, 6, -18, 6 ],
[ 2, -4, 5, -4, 1, 7, 2, -1, 4, 2, 6, 16 ],
[ 0, -4, 5, 4, -5, 7, 12, 3, -4, 6, 4, 20 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + x - 1,
x^2 - x - 1,
x^2 + x - 3,
x^2 + 3*x + 1,
x^2 + x - 1,
x^3 - 6*x - 1,
x^4 - 2*x^3 - 4*x^2 + 5*x + 2,
x^4 - 6*x^2 + x + 2
], atkin_lehners := [
[ -1, 1, 1 ],
[ -1, -1, -1 ],
[ 1, 1, 1 ],
[ 1, -1, -1 ],
[ -1, 1, -1 ],
[ -1, -1, 1 ],
[ -1, -1, -1 ],
[ -1, 1, 1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ]
], component_group_orders := [
[ 5, 1, 3 ],
[ 1, 1, 1 ],
[ 9, 1, 1 ],
[ 1, 11, 1 ],
[ 13, 1, 3 ],
[ 59, 5, 1 ],
[ 11, 11, 1 ],
[ 5, 3, 1 ],
[ 43, 19, 1 ],
[ 167, 1, 1 ]
], tamagawa_numbers := [
[ 5, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 11, 1 ],
[ 13, 1, 3 ],
[ 59, 5, 1 ],
[ 11, 11, 1 ],
[ 5, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 11, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 5, 1, 0, 0, 0, 0, 1, 5, 1, 1 ], analytic_sha_upper_bounds := [ 1, 1, 0, 0, 0, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 0, 0, 0, 1/121, 1, 1, 1 ], eigenvalues := [*
[ 2, 1, 4, -1, -5, -2, 0, -5, -1, -2, 6, 6 ],
[ 2, 1, 0, 1, 1, 2, 4, -3, 1, -6, -2, -2 ],
[
a,
-1,
a + 1,
-1,
-2*a - 1,
-a - 4,
-6*a - 3,
4*a + 3,
-1,
2*a - 5,
-6*a - 3,
-11
],
[
a,
-1,
-a - 1,
1,
-2*a + 1,
-3*a - 2,
4*a - 3,
2*a - 7,
1,
6*a + 1,
-5,
-4*a - 3
],
[
a,
1,
-a - 3,
-1,
-5,
-a,
2*a - 1,
2*a + 3,
1,
-4*a - 3,
3,
-9
],
[
a,
1,
a - 1,
1,
-4*a - 7,
a - 2,
-1,
-3,
-1,
-4*a - 9,
2*a - 3,
4*a + 3
],
[
a,
1,
a + 3,
1,
1,
a,
-4*a - 3,
2*a + 3,
1,
-2*a + 3,
-6*a - 5,
2*a - 1
],
[
a,
1,
-a + 1,
-1,
a^2 - a - 2,
-a^2 + 7,
-a^2 - a + 6,
-a^2 + a + 2,
-1,
-a^2 + 3*a + 6,
-a^2 + a - 2,
a^2 - 3*a - 2
],
[
a,
-1,
-a^3 + 2*a^2 + 3*a - 2,
-1,
-a^3 + a^2 + 5*a - 1,
-a^3 + a^2 + 2*a + 2,
-a^2 + 3*a + 2,
a^3 - a^2 - 5*a + 1,
1,
-3*a^2 + 3*a + 8,
a^2 - 3*a,
2*a^3 - 3*a^2 - 7*a + 8
],
[
a,
-1,
a^3 - 5*a + 2,
1,
-a^3 - a^2 + 5*a + 1,
-a^3 + a^2 + 6*a - 2,
-a^2 - a + 6,
-a^3 - a^2 + 7*a + 3,
-1,
2*a^3 + a^2 - 11*a,
-a^2 - a + 4,
-a^2 - 3*a + 8
]
*], q_expansions := [*
q + 2*q^2 + q^3 + 2*q^4 + 4*q^5 + 2*q^6 - q^7 + q^9 + 8*q^10 - 5*q^11 + 2*q^12 - 2*q^13 - 2*q^14 + 4*q^15 - 4*q^16 + 2*q^18 - 5*q^19 + 8*q^20 - q^21 - 10*q^22 - q^23 + 11*q^25 - 4*q^26 + q^27 - 2*q^28 - 2*q^29 + 8*q^30 + 6*q^31 - 8*q^32 - 5*q^33 - 4*q^35 + 2*q^36 + 6*q^37 + O(q^38),
q + 2*q^2 + q^3 + 2*q^4 + 2*q^6 + q^7 + q^9 + q^11 + 2*q^12 + 2*q^13 + 2*q^14 - 4*q^16 + 4*q^17 + 2*q^18 - 3*q^19 + q^21 + 2*q^22 + q^23 - 5*q^25 + 4*q^26 + q^27 + 2*q^28 - 6*q^29 - 2*q^31 - 8*q^32 + q^33 + 8*q^34 + 2*q^36 - 2*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a - 1)*q^4 + (a + 1)*q^5 - a*q^6 - q^7 + (-2*a - 1)*q^8 + q^9 + q^10 + (-2*a - 1)*q^11 + (a + 1)*q^12 + (-a - 4)*q^13 - a*q^14 + (-a - 1)*q^15 + 3*a*q^16 + (-6*a - 3)*q^17 + a*q^18 + (4*a + 3)*q^19 + (-a - 2)*q^20 + q^21 + (a - 2)*q^22 - q^23 + (2*a + 1)*q^24 + (a - 3)*q^25 + (-3*a - 1)*q^26 - q^27 + (a + 1)*q^28 + (2*a - 5)*q^29 - q^30 + (-6*a - 3)*q^31 + (a + 5)*q^32 + (2*a + 1)*q^33 + (3*a - 6)*q^34 + (-a - 1)*q^35 + (-a - 1)*q^36 - 11*q^37 + O(q^38),
q + a*q^2 - q^3 + (a - 1)*q^4 + (-a - 1)*q^5 - a*q^6 + q^7 + (-2*a + 1)*q^8 + q^9 + (-2*a - 1)*q^10 + (-2*a + 1)*q^11 + (-a + 1)*q^12 + (-3*a - 2)*q^13 + a*q^14 + (a + 1)*q^15 - 3*a*q^16 + (4*a - 3)*q^17 + a*q^18 + (2*a - 7)*q^19 - a*q^20 - q^21 + (-a - 2)*q^22 + q^23 + (2*a - 1)*q^24 + (3*a - 3)*q^25 + (-5*a - 3)*q^26 - q^27 + (a - 1)*q^28 + (6*a + 1)*q^29 + (2*a + 1)*q^30 - 5*q^31 + (a - 5)*q^32 + (2*a - 1)*q^33 + (a + 4)*q^34 + (-a - 1)*q^35 + (a - 1)*q^36 + (-4*a - 3)*q^37 + O(q^38),
q + a*q^2 + q^3 + (-a + 1)*q^4 + (-a - 3)*q^5 + a*q^6 - q^7 - 3*q^8 + q^9 + (-2*a - 3)*q^10 - 5*q^11 + (-a + 1)*q^12 - a*q^13 - a*q^14 + (-a - 3)*q^15 + (-a - 2)*q^16 + (2*a - 1)*q^17 + a*q^18 + (2*a + 3)*q^19 + a*q^20 - q^21 - 5*a*q^22 + q^23 - 3*q^24 + (5*a + 7)*q^25 + (a - 3)*q^26 + q^27 + (a - 1)*q^28 + (-4*a - 3)*q^29 + (-2*a - 3)*q^30 + 3*q^31 + (-a + 3)*q^32 - 5*q^33 + (-3*a + 6)*q^34 + (a + 3)*q^35 + (-a + 1)*q^36 - 9*q^37 + O(q^38),
q + a*q^2 + q^3 + (-3*a - 3)*q^4 + (a - 1)*q^5 + a*q^6 + q^7 + (4*a + 3)*q^8 + q^9 + (-4*a - 1)*q^10 + (-4*a - 7)*q^11 + (-3*a - 3)*q^12 + (a - 2)*q^13 + a*q^14 + (a - 1)*q^15 + (-3*a + 2)*q^16 - q^17 + a*q^18 - 3*q^19 + (9*a + 6)*q^20 + q^21 + (5*a + 4)*q^22 - q^23 + (4*a + 3)*q^24 + (-5*a - 5)*q^25 + (-5*a - 1)*q^26 + q^27 + (-3*a - 3)*q^28 + (-4*a - 9)*q^29 + (-4*a - 1)*q^30 + (2*a - 3)*q^31 + (3*a - 3)*q^32 + (-4*a - 7)*q^33 - a*q^34 + (a - 1)*q^35 + (-3*a - 3)*q^36 + (4*a + 3)*q^37 + O(q^38),
q + a*q^2 + q^3 + (-a - 1)*q^4 + (a + 3)*q^5 + a*q^6 + q^7 + (-2*a - 1)*q^8 + q^9 + (2*a + 1)*q^10 + q^11 + (-a - 1)*q^12 + a*q^13 + a*q^14 + (a + 3)*q^15 + 3*a*q^16 + (-4*a - 3)*q^17 + a*q^18 + (2*a + 3)*q^19 + (-3*a - 4)*q^20 + q^21 + a*q^22 + q^23 + (-2*a - 1)*q^24 + (5*a + 5)*q^25 + (-a + 1)*q^26 + q^27 + (-a - 1)*q^28 + (-2*a + 3)*q^29 + (2*a + 1)*q^30 + (-6*a - 5)*q^31 + (a + 5)*q^32 + q^33 + (a - 4)*q^34 + (a + 3)*q^35 + (-a - 1)*q^36 + (2*a - 1)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a + 1)*q^5 + a*q^6 - q^7 + (2*a + 1)*q^8 + q^9 + (-a^2 + a)*q^10 + (a^2 - a - 2)*q^11 + (a^2 - 2)*q^12 + (-a^2 + 7)*q^13 - a*q^14 + (-a + 1)*q^15 + (a + 4)*q^16 + (-a^2 - a + 6)*q^17 + a*q^18 + (-a^2 + a + 2)*q^19 + (a^2 - 4*a - 3)*q^20 - q^21 + (-a^2 + 4*a + 1)*q^22 - q^23 + (2*a + 1)*q^24 + (a^2 - 2*a - 4)*q^25 + (a - 1)*q^26 + q^27 + (-a^2 + 2)*q^28 + (-a^2 + 3*a + 6)*q^29 + (-a^2 + a)*q^30 + (-a^2 + a - 2)*q^31 + (a^2 - 2)*q^32 + (a^2 - a - 2)*q^33 + (-a^2 - 1)*q^34 + (a - 1)*q^35 + (a^2 - 2)*q^36 + (a^2 - 3*a - 2)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^3 + 2*a^2 + 3*a - 2)*q^5 - a*q^6 - q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^2 + 3*a + 2)*q^10 + (-a^3 + a^2 + 5*a - 1)*q^11 + (-a^2 + 2)*q^12 + (-a^3 + a^2 + 2*a + 2)*q^13 - a*q^14 + (a^3 - 2*a^2 - 3*a + 2)*q^15 + (2*a^3 - 2*a^2 - 5*a + 2)*q^16 + (-a^2 + 3*a + 2)*q^17 + a*q^18 + (a^3 - a^2 - 5*a + 1)*q^19 + (a^3 - a^2 - 4*a + 4)*q^20 + q^21 + (-a^3 + a^2 + 4*a + 2)*q^22 + q^23 + (-a^3 + 4*a)*q^24 + (-a^3 + a^2 + 2*a + 3)*q^25 + (-a^3 - 2*a^2 + 7*a + 2)*q^26 - q^27 + (-a^2 + 2)*q^28 + (-3*a^2 + 3*a + 8)*q^29 + (a^2 - 3*a - 2)*q^30 + (a^2 - 3*a)*q^31 + (3*a^2 - 4)*q^32 + (a^3 - a^2 - 5*a + 1)*q^33 + (-a^3 + 3*a^2 + 2*a)*q^34 + (a^3 - 2*a^2 - 3*a + 2)*q^35 + (a^2 - 2)*q^36 + (2*a^3 - 3*a^2 - 7*a + 8)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (a^3 - 5*a + 2)*q^5 - a*q^6 + q^7 + (a^3 - 4*a)*q^8 + q^9 + (a^2 + a - 2)*q^10 + (-a^3 - a^2 + 5*a + 1)*q^11 + (-a^2 + 2)*q^12 + (-a^3 + a^2 + 6*a - 2)*q^13 + a*q^14 + (-a^3 + 5*a - 2)*q^15 + (-a + 2)*q^16 + (-a^2 - a + 6)*q^17 + a*q^18 + (-a^3 - a^2 + 7*a + 3)*q^19 + (-a^3 + a^2 + 8*a - 4)*q^20 - q^21 + (-a^3 - a^2 + 2*a + 2)*q^22 - q^23 + (-a^3 + 4*a)*q^24 + (3*a^3 - a^2 - 16*a + 7)*q^25 + (a^3 - a + 2)*q^26 - q^27 + (a^2 - 2)*q^28 + (2*a^3 + a^2 - 11*a)*q^29 + (-a^2 - a + 2)*q^30 + (-a^2 - a + 4)*q^31 + (-2*a^3 - a^2 + 10*a)*q^32 + (a^3 + a^2 - 5*a - 1)*q^33 + (-a^3 - a^2 + 6*a)*q^34 + (a^3 - 5*a + 2)*q^35 + (a^2 - 2)*q^36 + (-a^2 - 3*a + 8)*q^37 + O(q^38)
*]> ;  // time = 189.22 seconds




J[485] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 485, 485, 485, 485, 485, 485, 485, 485, 485, 97, 97 ], new_dimensions := [ 1, 1, 2, 2, 3, 4, 6, 7, 7, 3, 4 ], dimensions := [ 1, 1, 2, 2, 3, 4, 6, 7, 7, 6, 8 ], intersection_graph := [ 0, 1, 5, 1, 1, 1, 1, 1, 7, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 1, 1, 5, 1, 0, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 0, 5, 1, 1, 1, 1, 7, 1, 1, 1, 1, 5, 0, 1, 71, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 59, 1, 1, 1, 1, 71, 1, 0, 1, 1, 43, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 83, 1, 7, 1, 1, 1, 1, 1, 1, 1, 0, 1, 31, 1, 1, 1, 7, 1, 1, 43, 83, 1, 0, 1, 1, 1, 11, 1, 1, 59, 1, 1, 31, 1, 0 ], ap_traces := [
[ 0, -2, -1, -1, -3, 5, -6, 2, 9, 0, 5, -7 ],
[ 0, 0, 1, -1, 1, 1, -6, -8, -7, 6, -7, 1 ],
[ 0, 1, -2, 8, -6, 5, -7, -1, -2, 10, 10, 11 ],
[ 2, 1, 2, 0, 2, 7, -1, 7, -6, -2, 6, -7 ],
[ -2, 6, 3, 5, 5, -1, -6, 6, -5, 8, -3, 3 ],
[ -1, -4, 4, -3, -16, -4, 6, -13, 8, -22, -7, 3 ],
[ -1, -1, 6, 3, 6, 1, 7, 16, 0, -4, 3, 2 ],
[ -1, -6, -7, -10, 5, -9, -10, -25, -7, 8, 2, -2 ],
[ 2, 9, -7, 3, 6, 5, 21, 20, -2, -26, -1, 2 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 5,
x^2 - 4*x - 25,
x^3 + 2*x^2 - 5*x - 8,
x^4 + x^3 - 4*x^2 - 2*x + 3,
x^6 + x^5 - 9*x^4 - 9*x^3 + 17*x^2 + 14*x + 1,
x^7 + x^6 - 9*x^5 - 7*x^4 + 23*x^3 + 12*x^2 - 15*x - 8,
x^7 - 2*x^6 - 10*x^5 + 18*x^4 + 26*x^3 - 35*x^2 - 21*x + 7
], atkin_lehners := [
[ 1, -1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 3, 3 ],
[ 1, 1 ],
[ 11, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 59, 1 ],
[ 2107, 1 ],
[ 83, 1 ],
[ 31, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 59, 1 ],
[ 2107, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 3, 1, 1, 1, 1, 1, 49, 1, 1 ], torsion_lower_bounds := [ 3, 1, 1, 1, 1, 1, 49, 1, 1 ], l_ratios := [ 1/3, 0, 1, 7, 1, 0, 43/49, 0, 1 ], analytic_sha_upper_bounds := [ 1, 0, 1, 1, 1, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1, 1, 1, 0, 1, 0, 1 ], eigenvalues := [*
[ 0, -2, -1, -1, -3, 5, -6, 2, 9, 0, 5, -7 ],
[ 0, 0, 1, -1, 1, 1, -6, -8, -7, 6, -7, 1 ],
[
a,
1/2*a + 1/2,
-1,
4,
-a - 3,
-1/2*a + 5/2,
-3/2*a - 7/2,
1/2*a - 1/2,
a - 1,
a + 5,
a + 5,
-1/2*a + 11/2
],
[
1,
1/2*a - 1/2,
1,
0,
-a + 3,
1/2*a + 5/2,
-1/2*a + 1/2,
1/2*a + 5/2,
-a - 1,
-a + 1,
-a + 5,
1/2*a - 9/2
],
[
a,
2,
1,
-a + 1,
a^2 - 3,
-a^2 - 2*a + 3,
-2,
a^2 + a - 2,
-2*a^2 - a + 7,
2*a + 4,
-3*a^2 + 13,
-a^2 + 2*a + 7
],
[
a,
-a^3 - a^2 + 2*a,
1,
a^3 + 2*a^2 - 2*a - 4,
-a^2 - a - 2,
2*a^3 - 6*a + 1,
-a^2 - 3*a + 3,
-2*a^3 - 3*a^2 + 4*a + 1,
-2*a^3 - 2*a^2 + 8*a + 5,
3*a^2 + a - 12,
-a^3 - 5*a^2 + a + 8,
-2*a^3 + 2*a^2 + 9*a - 5
],
[
a,
-1/4*a^5 - 1/2*a^4 + 11/4*a^3 + 3*a^2 - 25/4*a - 7/4,
1,
a^4 - 2*a^3 - 6*a^2 + 10*a + 5,
-1/2*a^5 - a^4 + 11/2*a^3 + 7*a^2 - 27/2*a - 11/2,
3/4*a^5 - 1/2*a^4 - 21/4*a^3 + 2*a^2 + 27/4*a + 1/4,
-3/4*a^5 - 1/2*a^4 + 25/4*a^3 + 3*a^2 - 39/4*a + 3/4,
3/4*a^5 + 1/2*a^4 - 25/4*a^3 - 5*a^2 + 35/4*a + 37/4,
-1/2*a^5 + 9/2*a^3 - 17/2*a + 1/2,
-1/2*a^5 + a^4 + 7/2*a^3 - 7*a^2 - 11/2*a + 13/2,
3/2*a^5 - 25/2*a^3 - a^2 + 41/2*a + 3/2,
7/4*a^5 + 3/2*a^4 - 65/4*a^3 - 12*a^2 + 131/4*a + 53/4
],
[
a,
a^6 - 9*a^4 + a^3 + 22*a^2 - 5*a - 12,
-1,
-a^6 + 10*a^4 - 2*a^3 - 29*a^2 + 9*a + 17,
a^5 + 2*a^4 - 7*a^3 - 11*a^2 + 10*a + 9,
-a^5 - 3*a^4 + 8*a^3 + 18*a^2 - 15*a - 17,
-2*a^6 - 2*a^5 + 15*a^4 + 11*a^3 - 27*a^2 - 7*a + 6,
a^5 - 7*a^3 - a^2 + 9*a,
a^6 + a^5 - 8*a^4 - 6*a^3 + 17*a^2 + 4*a - 9,
-3*a^6 - 2*a^5 + 25*a^4 + 10*a^3 - 54*a^2 - 2*a + 22,
-a^6 - 2*a^5 + 10*a^4 + 12*a^3 - 26*a^2 - 8*a + 9,
3*a^6 + 2*a^5 - 27*a^4 - 8*a^3 + 67*a^2 - 6*a - 33
],
[
a,
1/4*a^6 + 1/4*a^5 - 11/4*a^4 - 11/4*a^3 + 29/4*a^2 + 6*a - 1/4,
-1,
-1/2*a^6 + 1/2*a^5 + 9/2*a^4 - 7/2*a^3 - 17/2*a^2 + 3*a + 5/2,
-a^2 + a + 4,
-1/2*a^6 + 11/2*a^4 - 29/2*a^2 + 1/2*a + 5,
1/4*a^6 - 3/4*a^5 - 7/4*a^4 + 25/4*a^3 + 5/4*a^2 - 10*a + 11/4,
-a^6 + 1/2*a^5 + 10*a^4 - 5/2*a^3 - 22*a^2 - 5/2*a + 11/2,
1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 5/2*a^3 + 17/2*a^2 + a - 3/2,
-a^2 - a,
1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 7/2*a^3 + 15/2*a^2 - 4*a + 3/2,
-1/4*a^6 - 1/4*a^5 + 11/4*a^4 + 15/4*a^3 - 33/4*a^2 - 13*a + 21/4
]
*], q_expansions := [*
q - 2*q^3 - 2*q^4 - q^5 - q^7 + q^9 - 3*q^11 + 4*q^12 + 5*q^13 + 2*q^15 + 4*q^16 - 6*q^17 + 2*q^19 + 2*q^20 + 2*q^21 + 9*q^23 + q^25 + 4*q^27 + 2*q^28 + 5*q^31 + 6*q^33 + q^35 - 2*q^36 - 7*q^37 + O(q^38),
q - 2*q^4 + q^5 - q^7 - 3*q^9 + q^11 + q^13 + 4*q^16 - 6*q^17 - 8*q^19 - 2*q^20 - 7*q^23 + q^25 + 2*q^28 + 6*q^29 - 7*q^31 - q^35 + 6*q^36 + q^37 + O(q^38),
q + a*q^2 + (1/2*a + 1/2)*q^3 + 3*q^4 - q^5 + (1/2*a + 5/2)*q^6 + 4*q^7 + a*q^8 + (1/2*a - 3/2)*q^9 - a*q^10 + (-a - 3)*q^11 + (3/2*a + 3/2)*q^12 + (-1/2*a + 5/2)*q^13 + 4*a*q^14 + (-1/2*a - 1/2)*q^15 - q^16 + (-3/2*a - 7/2)*q^17 + (-3/2*a + 5/2)*q^18 + (1/2*a - 1/2)*q^19 - 3*q^20 + (2*a + 2)*q^21 + (-3*a - 5)*q^22 + (a - 1)*q^23 + (1/2*a + 5/2)*q^24 + q^25 + (5/2*a - 5/2)*q^26 + (-2*a - 1)*q^27 + 12*q^28 + (a + 5)*q^29 + (-1/2*a - 5/2)*q^30 + (a + 5)*q^31 - 3*a*q^32 + (-2*a - 4)*q^33 + (-7/2*a - 15/2)*q^34 - 4*q^35 + (3/2*a - 9/2)*q^36 + (-1/2*a + 11/2)*q^37 + O(q^38),
q + q^2 + (1/2*a - 1/2)*q^3 - q^4 + q^5 + (1/2*a - 1/2)*q^6 - 3*q^8 + (1/2*a + 7/2)*q^9 + q^10 + (-a + 3)*q^11 + (-1/2*a + 1/2)*q^12 + (1/2*a + 5/2)*q^13 + (1/2*a - 1/2)*q^15 - q^16 + (-1/2*a + 1/2)*q^17 + (1/2*a + 7/2)*q^18 + (1/2*a + 5/2)*q^19 - q^20 + (-a + 3)*q^22 + (-a - 1)*q^23 + (-3/2*a + 3/2)*q^24 + q^25 + (1/2*a + 5/2)*q^26 + (a + 6)*q^27 + (-a + 1)*q^29 + (1/2*a - 1/2)*q^30 + (-a + 5)*q^31 + 5*q^32 - 14*q^33 + (-1/2*a + 1/2)*q^34 + (-1/2*a - 7/2)*q^36 + (1/2*a - 9/2)*q^37 + O(q^38),
q + a*q^2 + 2*q^3 + (a^2 - 2)*q^4 + q^5 + 2*a*q^6 + (-a + 1)*q^7 + (-2*a^2 + a + 8)*q^8 + q^9 + a*q^10 + (a^2 - 3)*q^11 + (2*a^2 - 4)*q^12 + (-a^2 - 2*a + 3)*q^13 + (-a^2 + a)*q^14 + 2*q^15 + (3*a^2 - 2*a - 12)*q^16 - 2*q^17 + a*q^18 + (a^2 + a - 2)*q^19 + (a^2 - 2)*q^20 + (-2*a + 2)*q^21 + (-2*a^2 + 2*a + 8)*q^22 + (-2*a^2 - a + 7)*q^23 + (-4*a^2 + 2*a + 16)*q^24 + q^25 + (-2*a - 8)*q^26 - 4*q^27 + (3*a^2 - 3*a - 10)*q^28 + (2*a + 4)*q^29 + 2*a*q^30 + (-3*a^2 + 13)*q^31 + (-4*a^2 + a + 8)*q^32 + (2*a^2 - 6)*q^33 - 2*a*q^34 + (-a + 1)*q^35 + (a^2 - 2)*q^36 + (-a^2 + 2*a + 7)*q^37 + O(q^38),
q + a*q^2 + (-a^3 - a^2 + 2*a)*q^3 + (a^2 - 2)*q^4 + q^5 + (-2*a^2 - 2*a + 3)*q^6 + (a^3 + 2*a^2 - 2*a - 4)*q^7 + (a^3 - 4*a)*q^8 + (2*a^3 + 3*a^2 - 3*a - 3)*q^9 + a*q^10 + (-a^2 - a - 2)*q^11 - a*q^12 + (2*a^3 - 6*a + 1)*q^13 + (a^3 + 2*a^2 - 2*a - 3)*q^14 + (-a^3 - a^2 + 2*a)*q^15 + (-a^3 - 2*a^2 + 2*a + 1)*q^16 + (-a^2 - 3*a + 3)*q^17 + (a^3 + 5*a^2 + a - 6)*q^18 + (-2*a^3 - 3*a^2 + 4*a + 1)*q^19 + (a^2 - 2)*q^20 + (-a^2 - 2*a)*q^21 + (-a^3 - a^2 - 2*a)*q^22 + (-2*a^3 - 2*a^2 + 8*a + 5)*q^23 + (3*a^2 + 4*a - 6)*q^24 + q^25 + (-2*a^3 + 2*a^2 + 5*a - 6)*q^26 + (-4*a^2 - 5*a + 3)*q^27 + (-a^3 - 2*a^2 + 3*a + 5)*q^28 + (3*a^2 + a - 12)*q^29 + (-2*a^2 - 2*a + 3)*q^30 + (-a^3 - 5*a^2 + a + 8)*q^31 + (-3*a^3 - 2*a^2 + 7*a + 3)*q^32 + (4*a^3 + 6*a^2 - 5*a - 3)*q^33 + (-a^3 - 3*a^2 + 3*a)*q^34 + (a^3 + 2*a^2 - 2*a - 4)*q^35 + (-a^2 + 2*a + 3)*q^36 + (-2*a^3 + 2*a^2 + 9*a - 5)*q^37 + O(q^38),
q + a*q^2 + (-1/4*a^5 - 1/2*a^4 + 11/4*a^3 + 3*a^2 - 25/4*a - 7/4)*q^3 + (a^2 - 2)*q^4 + q^5 + (-1/4*a^5 + 1/2*a^4 + 3/4*a^3 - 2*a^2 + 7/4*a + 1/4)*q^6 + (a^4 - 2*a^3 - 6*a^2 + 10*a + 5)*q^7 + (a^3 - 4*a)*q^8 + (-5/4*a^5 + 1/2*a^4 + 39/4*a^3 - a^2 - 65/4*a - 11/4)*q^9 + a*q^10 + (-1/2*a^5 - a^4 + 11/2*a^3 + 7*a^2 - 27/2*a - 11/2)*q^11 + (5/4*a^5 - 1/2*a^4 - 39/4*a^3 + 65/4*a + 15/4)*q^12 + (3/4*a^5 - 1/2*a^4 - 21/4*a^3 + 2*a^2 + 27/4*a + 1/4)*q^13 + (a^5 - 2*a^4 - 6*a^3 + 10*a^2 + 5*a)*q^14 + (-1/4*a^5 - 1/2*a^4 + 11/4*a^3 + 3*a^2 - 25/4*a - 7/4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3/4*a^5 - 1/2*a^4 + 25/4*a^3 + 3*a^2 - 39/4*a + 3/4)*q^17 + (7/4*a^5 - 3/2*a^4 - 49/4*a^3 + 5*a^2 + 59/4*a + 5/4)*q^18 + (3/4*a^5 + 1/2*a^4 - 25/4*a^3 - 5*a^2 + 35/4*a + 37/4)*q^19 + (a^2 - 2)*q^20 + (a^5 - a^4 - 8*a^3 + 5*a^2 + 15*a - 4)*q^21 + (-1/2*a^5 + a^4 + 5/2*a^3 - 5*a^2 + 3/2*a + 1/2)*q^22 + (-1/2*a^5 + 9/2*a^3 - 17/2*a + 1/2)*q^23 + (-5/4*a^5 + 1/2*a^4 + 39/4*a^3 - a^2 - 69/4*a - 7/4)*q^24 + q^25 + (-5/4*a^5 + 3/2*a^4 + 35/4*a^3 - 6*a^2 - 41/4*a - 3/4)*q^26 + (1/2*a^5 - 5/2*a^3 - 2*a^2 - 1/2*a + 11/2)*q^27 + (-3*a^5 + a^4 + 23*a^3 - 34*a - 11)*q^28 + (-1/2*a^5 + a^4 + 7/2*a^3 - 7*a^2 - 11/2*a + 13/2)*q^29 + (-1/4*a^5 + 1/2*a^4 + 3/4*a^3 - 2*a^2 + 7/4*a + 1/4)*q^30 + (3/2*a^5 - 25/2*a^3 - a^2 + 41/2*a + 3/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^5 + 9*a^3 - 18*a + 4)*q^33 + (1/4*a^5 - 1/2*a^4 - 15/4*a^3 + 3*a^2 + 45/4*a + 3/4)*q^34 + (a^4 - 2*a^3 - 6*a^2 + 10*a + 5)*q^35 + (-3/4*a^5 + 5/2*a^4 + 5/4*a^3 - 13*a^2 + 37/4*a + 15/4)*q^36 + (7/4*a^5 + 3/2*a^4 - 65/4*a^3 - 12*a^2 + 131/4*a + 53/4)*q^37 + O(q^38),
q + a*q^2 + (a^6 - 9*a^4 + a^3 + 22*a^2 - 5*a - 12)*q^3 + (a^2 - 2)*q^4 - q^5 + (-a^6 + 8*a^4 - a^3 - 17*a^2 + 3*a + 8)*q^6 + (-a^6 + 10*a^4 - 2*a^3 - 29*a^2 + 9*a + 17)*q^7 + (a^3 - 4*a)*q^8 + (-a^6 + 9*a^4 - 22*a^2 + 13)*q^9 - a*q^10 + (a^5 + 2*a^4 - 7*a^3 - 11*a^2 + 10*a + 9)*q^11 + (-a^6 - a^5 + 10*a^4 + 4*a^3 - 29*a^2 + 3*a + 16)*q^12 + (-a^5 - 3*a^4 + 8*a^3 + 18*a^2 - 15*a - 17)*q^13 + (a^6 + a^5 - 9*a^4 - 6*a^3 + 21*a^2 + 2*a - 8)*q^14 + (-a^6 + 9*a^4 - a^3 - 22*a^2 + 5*a + 12)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-2*a^6 - 2*a^5 + 15*a^4 + 11*a^3 - 27*a^2 - 7*a + 6)*q^17 + (a^6 - 7*a^4 + a^3 + 12*a^2 - 2*a - 8)*q^18 + (a^5 - 7*a^3 - a^2 + 9*a)*q^19 + (-a^2 + 2)*q^20 + (a^5 - a^4 - 6*a^3 + 9*a^2 + 7*a - 12)*q^21 + (a^6 + 2*a^5 - 7*a^4 - 11*a^3 + 10*a^2 + 9*a)*q^22 + (a^6 + a^5 - 8*a^4 - 6*a^3 + 17*a^2 + 4*a - 9)*q^23 + (2*a^6 + a^5 - 19*a^4 - 4*a^3 + 49*a^2 - 5*a - 24)*q^24 + q^25 + (-a^6 - 3*a^5 + 8*a^4 + 18*a^3 - 15*a^2 - 17*a)*q^26 + (2*a^6 + a^5 - 18*a^4 - 5*a^3 + 44*a^2 + 2*a - 24)*q^27 + (2*a^6 - 19*a^4 + 2*a^3 + 48*a^2 - 11*a - 26)*q^28 + (-3*a^6 - 2*a^5 + 25*a^4 + 10*a^3 - 54*a^2 - 2*a + 22)*q^29 + (a^6 - 8*a^4 + a^3 + 17*a^2 - 3*a - 8)*q^30 + (-a^6 - 2*a^5 + 10*a^4 + 12*a^3 - 26*a^2 - 8*a + 9)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^5 + 5*a^3 - 2*a - 4)*q^33 + (-3*a^5 - 3*a^4 + 19*a^3 + 17*a^2 - 24*a - 16)*q^34 + (a^6 - 10*a^4 + 2*a^3 + 29*a^2 - 9*a - 17)*q^35 + (a^6 + 2*a^5 - 10*a^4 - 11*a^3 + 30*a^2 + 7*a - 18)*q^36 + (3*a^6 + 2*a^5 - 27*a^4 - 8*a^3 + 67*a^2 - 6*a - 33)*q^37 + O(q^38),
q + a*q^2 + (1/4*a^6 + 1/4*a^5 - 11/4*a^4 - 11/4*a^3 + 29/4*a^2 + 6*a - 1/4)*q^3 + (a^2 - 2)*q^4 - q^5 + (3/4*a^6 - 1/4*a^5 - 29/4*a^4 + 3/4*a^3 + 59/4*a^2 + 5*a - 7/4)*q^6 + (-1/2*a^6 + 1/2*a^5 + 9/2*a^4 - 7/2*a^3 - 17/2*a^2 + 3*a + 5/2)*q^7 + (a^3 - 4*a)*q^8 + (1/2*a^5 - a^4 - 9/2*a^3 + 7*a^2 + 15/2*a - 5/2)*q^9 - a*q^10 + (-a^2 + a + 4)*q^11 + (3/4*a^6 - 1/4*a^5 - 29/4*a^4 + 3/4*a^3 + 67/4*a^2 + 2*a - 19/4)*q^12 + (-1/2*a^6 + 11/2*a^4 - 29/2*a^2 + 1/2*a + 5)*q^13 + (-1/2*a^6 - 1/2*a^5 + 11/2*a^4 + 9/2*a^3 - 29/2*a^2 - 8*a + 7/2)*q^14 + (-1/4*a^6 - 1/4*a^5 + 11/4*a^4 + 11/4*a^3 - 29/4*a^2 - 6*a + 1/4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/4*a^6 - 3/4*a^5 - 7/4*a^4 + 25/4*a^3 + 5/4*a^2 - 10*a + 11/4)*q^17 + (1/2*a^6 - a^5 - 9/2*a^4 + 7*a^3 + 15/2*a^2 - 5/2*a)*q^18 + (-a^6 + 1/2*a^5 + 10*a^4 - 5/2*a^3 - 22*a^2 - 5/2*a + 11/2)*q^19 + (-a^2 + 2)*q^20 + (a^5 - a^4 - 8*a^3 + 5*a^2 + 9*a + 2)*q^21 + (-a^3 + a^2 + 4*a)*q^22 + (1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 5/2*a^3 + 17/2*a^2 + a - 3/2)*q^23 + (-1/4*a^6 + 3/4*a^5 + 7/4*a^4 - 17/4*a^3 - 5/4*a^2 + a - 7/4)*q^24 + q^25 + (-a^6 + 1/2*a^5 + 9*a^4 - 3/2*a^3 - 17*a^2 - 11/2*a + 7/2)*q^26 + (3/4*a^6 + 1/4*a^5 - 37/4*a^4 - 11/4*a^3 + 115/4*a^2 + 9/2*a - 33/4)*q^27 + (-1/2*a^6 - 1/2*a^5 + 9/2*a^4 + 11/2*a^3 - 17/2*a^2 - 13*a - 3/2)*q^28 + (-a^2 - a)*q^29 + (-3/4*a^6 + 1/4*a^5 + 29/4*a^4 - 3/4*a^3 - 59/4*a^2 - 5*a + 7/4)*q^30 + (1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 7/2*a^3 + 15/2*a^2 - 4*a + 3/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^6 + 1/2*a^5 - 11/2*a^4 - 11/2*a^3 + 25/2*a^2 + 15*a + 5/2)*q^33 + (-1/4*a^6 + 3/4*a^5 + 7/4*a^4 - 21/4*a^3 - 5/4*a^2 + 8*a - 7/4)*q^34 + (1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 7/2*a^3 + 17/2*a^2 - 3*a - 5/2)*q^35 + (-1/2*a^5 + 7/2*a^3 + a^2 - 9/2*a + 3/2)*q^36 + (-1/4*a^6 - 1/4*a^5 + 11/4*a^4 + 15/4*a^3 - 33/4*a^2 - 13*a + 21/4)*q^37 + O(q^38)
*]> ;  // time = 99.67 seconds




J[487] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 487, 487, 487, 487, 487 ], new_dimensions := [ 2, 2, 3, 16, 17 ], dimensions := [ 2, 2, 3, 16, 17 ], intersection_graph := [ 0, 1, 3, 25, 1, 1, 0, 1, 51, 1, 3, 1, 0, 1957, 1, 25, 51, 1957, 0, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 0, -1, 3, 0, -2, 9, 8, -8, 10, 10, 16, 3 ],
[ 0, 3, 1, -2, 4, 3, 6, 8, -8, 2, -8, 11 ],
[ 0, 6, 6, 6, 4, -6, 2, -1, 4, -3, -5, 2 ],
[ 7, -4, 9, 1, 1, 4, 38, 7, 8, 6, -10, -8 ],
[ -8, -6, -19, -11, -11, -12, -54, -2, -18, -11, 1, -6 ]
], hecke_fields := [
x^2 + x - 3,
x^2 - 6*x - 4,
x^3 - 5*x + 3,
x^16 - 7*x^15 - 5*x^14 + 131*x^13 - 132*x^12 - 977*x^11 + 1666*x^10 + 3671*x^9 - 8191*x^8 - 7212*x^7 + 20571*x^6 + 6937*x^5 - 27100*x^4 - 2748*x^3 + 17207*x^2 + 360*x - 3825,
x^17 + 8*x^16 + 7*x^15 - 97*x^14 - 239*x^13 + 327*x^12 + 1500*x^11 + 70*x^10 - 3964*x^9 - 2280*x^8 + 4849*x^7 + 4192*x^6 - 2492*x^5 - 2765*x^4 + 364*x^3 + 588*x^2 - 16
], atkin_lehners := [
[ -1 ],
[ -1 ],
[ -1 ],
[ -1 ],
[ 1 ]
], component_group_orders := [
[ 1 ],
[ 3 ],
[ 1 ],
[ 27 ],
[ 1 ]
], tamagawa_numbers := [
[ 1 ],
[ 3 ],
[ 1 ],
[ 27 ],
[ 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 27, 1 ], torsion_lower_bounds := [ 1, 3, 1, 27, 1 ], l_ratios := [ 1, 1/3, 1, 1/27, 0 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 0 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1, 0 ], eigenvalues := [*
[
0,
a,
-a + 1,
2*a + 1,
-1,
a + 5,
2*a + 5,
-2*a - 5,
5,
2*a + 6,
8,
-3*a
],
[
0,
1/2*a,
1/2*a - 1,
-1,
-a + 5,
-1/2*a + 3,
3,
-a + 7,
-a - 1,
a - 2,
-4,
1/2*a + 4
],
[
a,
2,
2,
2,
-2*a^2 - 4*a + 8,
-2,
2*a^2 - 6,
-a^2 + 3,
-2*a^2 + 8,
3*a^2 + 2*a - 11,
-2*a^2 + a + 5,
2*a^2 + 4*a - 6
],
[
a,
-7/15*a^15 + 49/15*a^14 + 1/3*a^13 - 707/15*a^12 + 313/5*a^11 + 3839/15*a^10 - 7567/15*a^9 - 9707/15*a^8 + 24712/15*a^7 + 3888/5*a^6 - 12804/5*a^5 - 6799/15*a^4 + 5450/3*a^3 + 867/5*a^2 - 6464/15*a - 37,
43/35*a^15 - 276/35*a^14 - 44/7*a^13 + 629/5*a^12 - 3121/35*a^11 - 4023/5*a^10 + 4709/5*a^9 + 94118/35*a^8 - 121943/35*a^7 - 26023/5*a^6 + 211363/35*a^5 + 212736/35*a^4 - 4744*a^3 - 137484/35*a^2 + 41761/35*a + 6381/7,
-6/35*a^15 - 73/35*a^14 + 166/7*a^13 - 93/5*a^12 - 10898/35*a^11 + 2936/5*a^10 + 7872/5*a^9 - 142811/35*a^8 - 124834/35*a^7 + 63331/5*a^6 + 115764/35*a^5 - 674122/35*a^4 - 764*a^3 + 474463/35*a^2 - 1877/35*a - 22396/7,
-a^4 + a^3 + 6*a^2 - 3*a - 6,
146/105*a^15 - 557/105*a^14 - 635/21*a^13 + 1948/15*a^12 + 8276/35*a^11 - 18526/15*a^10 - 11962/15*a^9 + 622486/105*a^8 + 92914/105*a^7 - 77067/5*a^6 + 31587/35*a^5 + 2251292/105*a^4 - 6565/3*a^3 - 506381/35*a^2 + 78247/105*a + 23451/7,
17/105*a^15 - 359/105*a^14 + 274/21*a^13 + 466/15*a^12 - 7643/35*a^11 + 113/15*a^10 + 19541/15*a^9 - 96458/105*a^8 - 386717/105*a^7 + 18191/5*a^6 + 180304/35*a^5 - 595696/105*a^4 - 10060/3*a^3 + 130168/35*a^2 + 79489/105*a - 5708/7,
-122/105*a^15 + 569/105*a^14 + 398/21*a^13 - 1681/15*a^12 - 3662/35*a^11 + 14167/15*a^10 + 2224/15*a^9 - 437677/105*a^8 + 64787/105*a^7 + 51444/5*a^6 - 85559/35*a^5 - 1468814/105*a^4 + 8257/3*a^3 + 330152/35*a^2 - 83374/105*a - 15362/7,
6/7*a^15 - 53/7*a^14 + 73/7*a^13 + 87*a^12 - 1898/7*a^11 - 254*a^10 + 1749*a^9 - 3531/7*a^8 - 34934/7*a^7 + 3975*a^6 + 47343/7*a^5 - 51540/7*a^4 - 4120*a^3 + 37531/7*a^2 + 6147/7*a - 8805/7,
-14/15*a^15 + 143/15*a^14 - 49/3*a^13 - 1729/15*a^12 + 1906/5*a^11 + 6193/15*a^10 - 37454/15*a^9 + 476/15*a^8 + 112409/15*a^7 - 15114/5*a^6 - 55423/5*a^5 + 87607/15*a^4 + 22876/3*a^3 - 19501/5*a^2 - 26623/15*a + 842,
19/21*a^15 - 169/21*a^14 + 244/21*a^13 + 272/3*a^12 - 2061/7*a^11 - 719/3*a^10 + 5653/3*a^9 - 15490/21*a^8 - 111931/21*a^7 + 4893*a^6 + 49853/7*a^5 - 188165/21*a^4 - 12694/3*a^3 + 46128/7*a^2 + 18230/21*a - 10959/7,
-14/15*a^15 + 188/15*a^14 - 124/3*a^13 - 1459/15*a^12 + 3616/5*a^11 - 4487/15*a^10 - 62819/15*a^9 + 77021/15*a^8 + 165044/15*a^7 - 95694/5*a^6 - 67138/5*a^5 + 461227/15*a^4 + 20920/3*a^3 - 108721/5*a^2 - 18853/15*a + 5101
],
[
a,
2051597/5519352*a^16 + 2320017/919892*a^15 - 2246177/5519352*a^14 - 194312419/5519352*a^13 - 255697165/5519352*a^12 + 952370821/5519352*a^11 + 316838171/919892*a^10 - 333837097/919892*a^9 - 692060953/689919*a^8 + 199298603/689919*a^7 + 7559117149/5519352*a^6 + 53771099/2759676*a^5 - 585217951/689919*a^4 - 536428025/5519352*a^3 + 534808235/2759676*a^2 + 11558689/689919*a - 1419265/229973,
245351/1839784*a^16 + 195516/229973*a^15 - 739599/1839784*a^14 - 22219639/1839784*a^13 - 23525985/1839784*a^12 + 112542009/1839784*a^11 + 47012571/459946*a^10 - 127161247/919892*a^9 - 139176933/459946*a^8 + 31899834/229973*a^7 + 760642671/1839784*a^6 - 12185753/229973*a^5 - 117634509/459946*a^4 + 28044613/1839784*a^3 + 27884025/459946*a^2 - 4834517/459946*a - 713685/229973,
-176497/689919*a^16 - 5153635/2759676*a^15 - 516091/1379838*a^14 + 23628433/919892*a^13 + 116755489/2759676*a^12 - 112847543/919892*a^11 - 830184023/2759676*a^10 + 113437745/459946*a^9 + 1221803159/1379838*a^8 - 125739106/689919*a^7 - 868582156/689919*a^6 - 15859435/2759676*a^5 + 1159018501/1379838*a^4 + 22483547/689919*a^3 - 610602493/2759676*a^2 + 1077397/459946*a + 6823418/689919,
-169505/2759676*a^16 - 798485/2759676*a^15 + 1957139/2759676*a^14 + 2099503/459946*a^13 - 2701367/1379838*a^12 - 12155875/459946*a^11 - 9076057/2759676*a^10 + 15574064/229973*a^9 + 30335509/1379838*a^8 - 42502274/689919*a^7 - 96951377/2759676*a^6 - 85529477/2759676*a^5 + 47286869/1379838*a^4 + 185364793/2759676*a^3 - 54038027/2759676*a^2 - 9781153/459946*a + 900244/689919,
-1140325/1839784*a^16 - 1006590/229973*a^15 - 699563/1839784*a^14 + 109433557/1839784*a^13 + 170067299/1839784*a^12 - 508099803/1839784*a^11 - 300309645/459946*a^10 + 469239185/919892*a^9 + 854723399/459946*a^8 - 52594293/229973*a^7 - 4570546013/1839784*a^6 - 68869738/229973*a^5 + 683429423/459946*a^4 + 445962905/1839784*a^3 - 142595543/459946*a^2 - 7117781/459946*a + 926055/229973,
425449/919892*a^16 + 8085559/2759676*a^15 - 1393563/919892*a^14 - 57418769/1379838*a^13 - 57769519/1379838*a^12 + 291377357/1379838*a^11 + 926538911/2759676*a^10 - 110422418/229973*a^9 - 452992393/459946*a^8 + 333012053/689919*a^7 + 3670555151/2759676*a^6 - 426161293/2759676*a^5 - 1121561951/1379838*a^4 - 29980879/2759676*a^3 + 513169709/2759676*a^2 - 5342801/1379838*a - 6621122/689919,
-112957/229973*a^16 - 4477219/1379838*a^15 + 278689/229973*a^14 + 64564567/1379838*a^13 + 71946365/1379838*a^12 - 336927853/1379838*a^11 - 570212879/1379838*a^10 + 135078734/229973*a^9 + 286413959/229973*a^8 - 467591491/689919*a^7 - 1209004657/689919*a^6 + 487480651/1379838*a^5 + 767019347/689919*a^4 - 59206303/689919*a^3 - 347957189/1379838*a^2 + 15340919/689919*a + 3834265/689919,
-185236/689919*a^16 - 4224653/2759676*a^15 + 2440025/1379838*a^14 + 61890169/2759676*a^13 + 9157657/919892*a^12 - 332237323/2759676*a^11 - 289303741/2759676*a^10 + 140052995/459946*a^9 + 390047459/1379838*a^8 - 88127800/229973*a^7 - 60543171/229973*a^6 + 211667917/919892*a^5 + 3176433/459946*a^4 - 14234685/229973*a^3 + 62682999/919892*a^2 + 6687761/1379838*a - 6072464/689919,
253022/689919*a^16 + 3894001/1379838*a^15 + 1037179/689919*a^14 - 16855585/459946*a^13 - 99889975/1379838*a^12 + 71224507/459946*a^11 + 652172705/1379838*a^10 - 50468986/229973*a^9 - 886056809/689919*a^8 - 48869305/689919*a^7 + 1129165208/689919*a^6 + 502643419/1379838*a^5 - 630155971/689919*a^4 - 127231912/689919*a^3 + 231112825/1379838*a^2 + 520043/229973*a - 368596/689919,
711691/2759676*a^16 + 1118726/689919*a^15 - 2973667/2759676*a^14 - 66186811/2759676*a^13 - 19353791/919892*a^12 + 359943325/2759676*a^11 + 126345583/689919*a^10 - 154749135/459946*a^9 - 388738180/689919*a^8 + 102223657/229973*a^7 + 720069541/919892*a^6 - 72274884/229973*a^5 - 108012847/229973*a^4 + 115498135/919892*a^3 + 23264470/229973*a^2 - 13799596/689919*a - 4624942/689919,
521533/1839784*a^16 + 5354231/2759676*a^15 - 499641/1839784*a^14 - 150692101/5519352*a^13 - 201219707/5519352*a^12 + 749623771/5519352*a^11 + 755063689/2759676*a^10 - 270628339/919892*a^9 - 186515066/229973*a^8 + 173880025/689919*a^7 + 6230067047/5519352*a^6 + 3032203/2759676*a^5 - 480561569/689919*a^4 - 543719947/5519352*a^3 + 391289311/2759676*a^2 + 19978366/689919*a - 1247245/689919
]
*], q_expansions := [*
q + a*q^3 - 2*q^4 + (-a + 1)*q^5 + (2*a + 1)*q^7 - a*q^9 - q^11 - 2*a*q^12 + (a + 5)*q^13 + (2*a - 3)*q^15 + 4*q^16 + (2*a + 5)*q^17 + (-2*a - 5)*q^19 + (2*a - 2)*q^20 + (-a + 6)*q^21 + 5*q^23 + (-3*a - 1)*q^25 + (-2*a - 3)*q^27 + (-4*a - 2)*q^28 + (2*a + 6)*q^29 + 8*q^31 - a*q^33 + (3*a - 5)*q^35 + 2*a*q^36 - 3*a*q^37 + O(q^38),
q + 1/2*a*q^3 - 2*q^4 + (1/2*a - 1)*q^5 - q^7 + (3/2*a - 2)*q^9 + (-a + 5)*q^11 - a*q^12 + (-1/2*a + 3)*q^13 + (a + 1)*q^15 + 4*q^16 + 3*q^17 + (-a + 7)*q^19 + (-a + 2)*q^20 - 1/2*a*q^21 + (-a - 1)*q^23 + (1/2*a - 3)*q^25 + (2*a + 3)*q^27 + 2*q^28 + (a - 2)*q^29 - 4*q^31 + (-1/2*a - 2)*q^33 + (-1/2*a + 1)*q^35 + (-3*a + 4)*q^36 + (1/2*a + 4)*q^37 + O(q^38),
q + a*q^2 + 2*q^3 + (a^2 - 2)*q^4 + 2*q^5 + 2*a*q^6 + 2*q^7 + (a - 3)*q^8 + q^9 + 2*a*q^10 + (-2*a^2 - 4*a + 8)*q^11 + (2*a^2 - 4)*q^12 - 2*q^13 + 2*a*q^14 + 4*q^15 + (-a^2 - 3*a + 4)*q^16 + (2*a^2 - 6)*q^17 + a*q^18 + (-a^2 + 3)*q^19 + (2*a^2 - 4)*q^20 + 4*q^21 + (-4*a^2 - 2*a + 6)*q^22 + (-2*a^2 + 8)*q^23 + (2*a - 6)*q^24 - q^25 - 2*a*q^26 - 4*q^27 + (2*a^2 - 4)*q^28 + (3*a^2 + 2*a - 11)*q^29 + 4*a*q^30 + (-2*a^2 + a + 5)*q^31 + (-3*a^2 - 3*a + 9)*q^32 + (-4*a^2 - 8*a + 16)*q^33 + (4*a - 6)*q^34 + 4*q^35 + (a^2 - 2)*q^36 + (2*a^2 + 4*a - 6)*q^37 + O(q^38),
q + a*q^2 + (-7/15*a^15 + 49/15*a^14 + 1/3*a^13 - 707/15*a^12 + 313/5*a^11 + 3839/15*a^10 - 7567/15*a^9 - 9707/15*a^8 + 24712/15*a^7 + 3888/5*a^6 - 12804/5*a^5 - 6799/15*a^4 + 5450/3*a^3 + 867/5*a^2 - 6464/15*a - 37)*q^3 + (a^2 - 2)*q^4 + (43/35*a^15 - 276/35*a^14 - 44/7*a^13 + 629/5*a^12 - 3121/35*a^11 - 4023/5*a^10 + 4709/5*a^9 + 94118/35*a^8 - 121943/35*a^7 - 26023/5*a^6 + 211363/35*a^5 + 212736/35*a^4 - 4744*a^3 - 137484/35*a^2 + 41761/35*a + 6381/7)*q^5 + (-2*a^14 + 14*a^13 + a^12 - 200*a^11 + 273*a^10 + 1066*a^9 - 2175*a^8 - 2588*a^7 + 7039*a^6 + 2784*a^5 - 10830*a^4 - 1109*a^3 + 7599*a^2 + 131*a - 1785)*q^6 + (-6/35*a^15 - 73/35*a^14 + 166/7*a^13 - 93/5*a^12 - 10898/35*a^11 + 2936/5*a^10 + 7872/5*a^9 - 142811/35*a^8 - 124834/35*a^7 + 63331/5*a^6 + 115764/35*a^5 - 674122/35*a^4 - 764*a^3 + 474463/35*a^2 - 1877/35*a - 22396/7)*q^7 + (a^3 - 4*a)*q^8 + (2/15*a^15 - 59/15*a^14 + 64/3*a^13 + 187/15*a^12 - 1603/5*a^11 + 5591/15*a^10 + 25952/15*a^9 - 49283/15*a^8 - 63077/15*a^7 + 54667/5*a^6 + 22439/5*a^5 - 255346/15*a^4 - 5242/3*a^3 + 60153/5*a^2 + 3079/15*a - 2833)*q^9 + (5/7*a^15 - 1/7*a^14 - 246/7*a^13 + 73*a^12 + 2770/7*a^11 - 1105*a^10 - 1821*a^9 + 46054/7*a^8 + 25591/7*a^7 - 19234*a^6 - 17111/7*a^5 + 199852/7*a^4 - 552*a^3 - 139628/7*a^2 + 3285/7*a + 32895/7)*q^10 + (-a^4 + a^3 + 6*a^2 - 3*a - 6)*q^11 + (-16/15*a^15 + 112/15*a^14 + 1/3*a^13 - 1586/15*a^12 + 739/5*a^11 + 8312/15*a^10 - 17491/15*a^9 - 19406/15*a^8 + 56161/15*a^7 + 6144/5*a^6 - 28542/5*a^5 - 3037/15*a^4 + 11897/3*a^3 - 1079/5*a^2 - 13847/15*a + 74)*q^12 + (146/105*a^15 - 557/105*a^14 - 635/21*a^13 + 1948/15*a^12 + 8276/35*a^11 - 18526/15*a^10 - 11962/15*a^9 + 622486/105*a^8 + 92914/105*a^7 - 77067/5*a^6 + 31587/35*a^5 + 2251292/105*a^4 - 6565/3*a^3 - 506381/35*a^2 + 78247/105*a + 23451/7)*q^13 + (-23/7*a^15 + 160/7*a^14 + 27/7*a^13 - 334*a^12 + 2938/7*a^11 + 1860*a^10 - 3451*a^9 - 34796/7*a^8 + 80009/7*a^7 + 6834*a^6 - 126500/7*a^5 - 37868/7*a^4 + 13085*a^3 + 20273/7*a^2 - 21964/7*a - 4590/7)*q^14 + (-1/35*a^15 + 192/35*a^14 - 271/7*a^13 + 17/5*a^12 + 19207/35*a^11 - 4214/5*a^10 - 14313/5*a^9 + 228694/35*a^8 + 232711/35*a^7 - 105184/5*a^6 - 224901/35*a^5 + 1136913/35*a^4 + 1768*a^3 - 805822/35*a^2 + 8/35*a + 38181/7)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (17/105*a^15 - 359/105*a^14 + 274/21*a^13 + 466/15*a^12 - 7643/35*a^11 + 113/15*a^10 + 19541/15*a^9 - 96458/105*a^8 - 386717/105*a^7 + 18191/5*a^6 + 180304/35*a^5 - 595696/105*a^4 - 10060/3*a^3 + 130168/35*a^2 + 79489/105*a - 5708/7)*q^17 + (-3*a^15 + 22*a^14 - 5*a^13 - 303*a^12 + 503*a^11 + 1508*a^10 - 3775*a^9 - 3113*a^8 + 11895*a^7 + 1745*a^6 - 17948*a^5 + 1866*a^4 + 12397*a^3 - 2089*a^2 - 2881*a + 510)*q^18 + (-122/105*a^15 + 569/105*a^14 + 398/21*a^13 - 1681/15*a^12 - 3662/35*a^11 + 14167/15*a^10 + 2224/15*a^9 - 437677/105*a^8 + 64787/105*a^7 + 51444/5*a^6 - 85559/35*a^5 - 1468814/105*a^4 + 8257/3*a^3 + 330152/35*a^2 - 83374/105*a - 15362/7)*q^19 + (12/5*a^15 - 79/5*a^14 - 8*a^13 + 1192/5*a^12 - 1144/5*a^11 - 7009/5*a^10 + 10367/5*a^9 + 20642/5*a^8 - 35572/5*a^7 - 33644/5*a^6 + 57587/5*a^5 + 33244/5*a^4 - 8496*a^3 - 19826/5*a^2 + 10279/5*a + 909)*q^20 + (-206/105*a^15 + 1787/105*a^14 - 400/21*a^13 - 3178/15*a^12 + 19669/35*a^11 + 12346/15*a^10 - 56723/15*a^9 - 40336/105*a^8 + 1186166/105*a^7 - 22203/5*a^6 - 571317/35*a^5 + 1023298/105*a^4 + 32458/3*a^3 - 250309/35*a^2 - 257737/105*a + 11581/7)*q^21 + (-a^5 + a^4 + 6*a^3 - 3*a^2 - 6*a)*q^22 + (6/7*a^15 - 53/7*a^14 + 73/7*a^13 + 87*a^12 - 1898/7*a^11 - 254*a^10 + 1749*a^9 - 3531/7*a^8 - 34934/7*a^7 + 3975*a^6 + 47343/7*a^5 - 51540/7*a^4 - 4120*a^3 + 37531/7*a^2 + 6147/7*a - 8805/7)*q^23 + (-a^14 + 6*a^13 + 5*a^12 - 88*a^11 + 65*a^10 + 490*a^9 - 643*a^8 - 1288*a^7 + 2156*a^6 + 1629*a^5 - 3281*a^4 - 929*a^3 + 2233*a^2 + 196*a - 510)*q^24 + (89/35*a^15 - 673/35*a^14 + 46/7*a^13 + 1327/5*a^12 - 16298/35*a^11 - 6639/5*a^10 + 17312/5*a^9 + 97644/35*a^8 - 383664/35*a^7 - 8899/5*a^6 + 585694/35*a^5 - 39422/35*a^4 - 11734*a^3 + 47188/35*a^2 + 96273/35*a - 2150/7)*q^25 + (31/7*a^15 - 163/7*a^14 - 366/7*a^13 + 420*a^12 + 864/7*a^11 - 3114*a^10 + 824*a^9 + 85920/7*a^8 - 37697/7*a^7 - 27701*a^6 + 82566/7*a^5 + 248455/7*a^4 - 10647*a^3 - 162265/7*a^2 + 19947/7*a + 37230/7)*q^26 + (-61/15*a^15 + 427/15*a^14 + 10/3*a^13 - 6191/15*a^12 + 2699/5*a^11 + 34007/15*a^10 - 65686/15*a^9 - 88451/15*a^8 + 216166/15*a^7 + 38229/5*a^6 - 113327/5*a^5 - 81517/15*a^4 + 49016/3*a^3 + 13436/5*a^2 - 58817/15*a - 604)*q^27 + (1/5*a^15 - 42/5*a^14 + 49*a^13 + 116/5*a^12 - 3637/5*a^11 + 4243/5*a^10 + 19711/5*a^9 - 36614/5*a^8 - 48646/5*a^7 + 120933/5*a^6 + 53841/5*a^5 - 187183/5*a^4 - 4605*a^3 + 131437/5*a^2 + 3172/5*a - 6169)*q^28 + (-14/15*a^15 + 143/15*a^14 - 49/3*a^13 - 1729/15*a^12 + 1906/5*a^11 + 6193/15*a^10 - 37454/15*a^9 + 476/15*a^8 + 112409/15*a^7 - 15114/5*a^6 - 55423/5*a^5 + 87607/15*a^4 + 22876/3*a^3 - 19501/5*a^2 - 26623/15*a + 842)*q^29 + (37/7*a^15 - 272/7*a^14 + 50/7*a^13 + 545*a^12 - 6095/7*a^11 - 2815*a^10 + 6639*a^9 + 44904/7*a^8 - 148700/7*a^7 - 5838*a^6 + 228770/7*a^5 + 6956/7*a^4 - 23102*a^3 + 3443/7*a^2 + 38253/7*a - 765/7)*q^30 + (19/21*a^15 - 169/21*a^14 + 244/21*a^13 + 272/3*a^12 - 2061/7*a^11 - 719/3*a^10 + 5653/3*a^9 - 15490/21*a^8 - 111931/21*a^7 + 4893*a^6 + 49853/7*a^5 - 188165/21*a^4 - 12694/3*a^3 + 46128/7*a^2 + 18230/21*a - 10959/7)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-1/5*a^15 - 3/5*a^14 + 15*a^13 - 116/5*a^12 - 913/5*a^11 + 2222/5*a^10 + 4379/5*a^9 - 14116/5*a^8 - 9194/5*a^7 + 42342/5*a^6 + 6994/5*a^5 - 63402/5*a^4 + 27*a^3 + 44288/5*a^2 - 737/5*a - 2073)*q^33 + (-16/7*a^15 + 97/7*a^14 + 69/7*a^13 - 197*a^12 + 1160/7*a^11 + 1033*a^10 - 1513*a^9 - 16498/7*a^8 + 33641/7*a^7 + 1821*a^6 - 47575/7*a^5 + 7240/7*a^4 + 4164*a^3 - 14202/7*a^2 - 6116/7*a + 4335/7)*q^34 + (1/35*a^15 - 192/35*a^14 + 278/7*a^13 - 42/5*a^12 - 19592/35*a^11 + 4619/5*a^10 + 14448/5*a^9 - 246824/35*a^8 - 229561/35*a^7 + 113459/5*a^6 + 207471/35*a^5 - 1232708/35*a^4 - 1096*a^3 + 880512/35*a^2 - 7603/35*a - 41877/7)*q^35 + (11/15*a^15 - 182/15*a^14 + 142/3*a^13 + 1231/15*a^12 - 3909/5*a^11 + 7163/15*a^10 + 66596/15*a^9 - 91604/15*a^8 - 172211/15*a^7 + 109491/5*a^6 + 68507/5*a^5 - 522853/15*a^4 - 20515/3*a^3 + 123394/5*a^2 + 17692/15*a - 5809)*q^36 + (-14/15*a^15 + 188/15*a^14 - 124/3*a^13 - 1459/15*a^12 + 3616/5*a^11 - 4487/15*a^10 - 62819/15*a^9 + 77021/15*a^8 + 165044/15*a^7 - 95694/5*a^6 - 67138/5*a^5 + 461227/15*a^4 + 20920/3*a^3 - 108721/5*a^2 - 18853/15*a + 5101)*q^37 + O(q^38),
q + a*q^2 + (2051597/5519352*a^16 + 2320017/919892*a^15 - 2246177/5519352*a^14 - 194312419/5519352*a^13 - 255697165/5519352*a^12 + 952370821/5519352*a^11 + 316838171/919892*a^10 - 333837097/919892*a^9 - 692060953/689919*a^8 + 199298603/689919*a^7 + 7559117149/5519352*a^6 + 53771099/2759676*a^5 - 585217951/689919*a^4 - 536428025/5519352*a^3 + 534808235/2759676*a^2 + 11558689/689919*a - 1419265/229973)*q^3 + (a^2 - 2)*q^4 + (245351/1839784*a^16 + 195516/229973*a^15 - 739599/1839784*a^14 - 22219639/1839784*a^13 - 23525985/1839784*a^12 + 112542009/1839784*a^11 + 47012571/459946*a^10 - 127161247/919892*a^9 - 139176933/459946*a^8 + 31899834/229973*a^7 + 760642671/1839784*a^6 - 12185753/229973*a^5 - 117634509/459946*a^4 + 28044613/1839784*a^3 + 27884025/459946*a^2 - 4834517/459946*a - 713685/229973)*q^5 + (-1246337/2759676*a^16 - 4151839/1379838*a^15 + 2346245/2759676*a^14 + 39105753/919892*a^13 + 140749301/2759676*a^12 - 196061079/919892*a^11 - 536658593/1379838*a^10 + 216336907/459946*a^9 + 784003748/689919*a^8 - 298634588/689919*a^7 - 4246376213/2759676*a^6 + 107709029/1379838*a^5 + 642029710/689919*a^4 + 161417581/2759676*a^3 - 278467381/1379838*a^2 - 1419265/229973*a + 4103194/689919)*q^6 + (-176497/689919*a^16 - 5153635/2759676*a^15 - 516091/1379838*a^14 + 23628433/919892*a^13 + 116755489/2759676*a^12 - 112847543/919892*a^11 - 830184023/2759676*a^10 + 113437745/459946*a^9 + 1221803159/1379838*a^8 - 125739106/689919*a^7 - 868582156/689919*a^6 - 15859435/2759676*a^5 + 1159018501/1379838*a^4 + 22483547/689919*a^3 - 610602493/2759676*a^2 + 1077397/459946*a + 6823418/689919)*q^7 + (a^3 - 4*a)*q^8 + (-549397/919892*a^16 - 10741435/2759676*a^15 + 1211653/919892*a^14 + 74994653/1379838*a^13 + 43767863/689919*a^12 - 183801415/689919*a^11 - 1333199441/2759676*a^10 + 257127397/459946*a^9 + 638635549/459946*a^8 - 300465404/689919*a^7 - 5056078163/2759676*a^6 - 153358727/2759676*a^5 + 738358450/689919*a^4 + 456430039/2759676*a^3 - 617455337/2759676*a^2 - 18067574/689919*a + 5010782/689919)*q^9 + (-49835/229973*a^16 - 307132/229973*a^15 + 197426/229973*a^14 + 4389113/229973*a^13 + 4039029/229973*a^12 - 22497027/229973*a^11 - 33937133/229973*a^10 + 51982954/229973*a^9 + 101824869/229973*a^8 - 53633041/229973*a^7 - 140749677/229973*a^6 + 17609582/229973*a^5 + 88305016/229973*a^4 + 2778542/229973*a^3 - 20450557/229973*a^2 - 713685/229973*a + 490702/229973)*q^10 + (-169505/2759676*a^16 - 798485/2759676*a^15 + 1957139/2759676*a^14 + 2099503/459946*a^13 - 2701367/1379838*a^12 - 12155875/459946*a^11 - 9076057/2759676*a^10 + 15574064/229973*a^9 + 30335509/1379838*a^8 - 42502274/689919*a^7 - 96951377/2759676*a^6 - 85529477/2759676*a^5 + 47286869/1379838*a^4 + 185364793/2759676*a^3 - 54038027/2759676*a^2 - 9781153/459946*a + 900244/689919)*q^11 + (-128193/919892*a^16 - 1424749/1379838*a^15 - 443751/919892*a^14 + 37187177/2759676*a^13 + 75066127/2759676*a^12 - 156182507/2759676*a^11 - 257881997/1379838*a^10 + 33092951/459946*a^9 + 125025076/229973*a^8 + 50680769/689919*a^7 - 2119054387/2759676*a^6 - 322647581/1379838*a^5 + 349259846/689919*a^4 + 433159931/2759676*a^3 - 176900747/1379838*a^2 - 19014184/689919*a + 3530242/689919)*q^12 + (-1140325/1839784*a^16 - 1006590/229973*a^15 - 699563/1839784*a^14 + 109433557/1839784*a^13 + 170067299/1839784*a^12 - 508099803/1839784*a^11 - 300309645/459946*a^10 + 469239185/919892*a^9 + 854723399/459946*a^8 - 52594293/229973*a^7 - 4570546013/1839784*a^6 - 68869738/229973*a^5 + 683429423/459946*a^4 + 445962905/1839784*a^3 - 142595543/459946*a^2 - 7117781/459946*a + 926055/229973)*q^13 + (494269/2759676*a^16 + 1954867/1379838*a^15 + 2404463/2759676*a^14 - 51975643/2759676*a^13 - 35894851/919892*a^12 + 228797977/2759676*a^11 + 365022815/1379838*a^10 - 59155019/459946*a^9 - 528152266/689919*a^8 - 4249401/229973*a^7 + 981214087/919892*a^6 + 93119151/459946*a^5 - 155176886/229973*a^4 - 117874287/919892*a^3 + 70264221/459946*a^2 + 6823418/689919*a - 2823952/689919)*q^14 + (-137099/459946*a^16 - 824675/459946*a^15 + 756869/459946*a^14 + 6139271/229973*a^13 + 4035085/229973*a^12 - 33785957/229973*a^11 - 77470217/459946*a^10 + 88523663/229973*a^9 + 119955141/229973*a^8 - 116215907/229973*a^7 - 333317835/459946*a^6 + 141137141/459946*a^5 + 103080318/229973*a^4 - 28244413/459946*a^3 - 44912855/459946*a^2 - 964701/229973*a - 9651/229973)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (425449/919892*a^16 + 8085559/2759676*a^15 - 1393563/919892*a^14 - 57418769/1379838*a^13 - 57769519/1379838*a^12 + 291377357/1379838*a^11 + 926538911/2759676*a^10 - 110422418/229973*a^9 - 452992393/459946*a^8 + 333012053/689919*a^7 + 3670555151/2759676*a^6 - 426161293/2759676*a^5 - 1121561951/1379838*a^4 - 29980879/2759676*a^3 + 513169709/2759676*a^2 - 5342801/1379838*a - 6621122/689919)*q^17 + (2444093/2759676*a^16 + 1264358/229973*a^15 - 9885221/2759676*a^14 - 218846197/2759676*a^13 - 196247203/2759676*a^12 + 1139087059/2759676*a^11 + 138178146/229973*a^10 - 450269305/459946*a^9 - 1239934274/689919*a^8 + 733999999/689919*a^7 + 6755857945/2759676*a^6 - 288464543/689919*a^5 - 1025204519/689919*a^4 - 17513813/2759676*a^3 + 224216503/689919*a^2 + 5010782/689919*a - 2197588/229973)*q^18 + (-112957/229973*a^16 - 4477219/1379838*a^15 + 278689/229973*a^14 + 64564567/1379838*a^13 + 71946365/1379838*a^12 - 336927853/1379838*a^11 - 570212879/1379838*a^10 + 135078734/229973*a^9 + 286413959/229973*a^8 - 467591491/689919*a^7 - 1209004657/689919*a^6 + 487480651/1379838*a^5 + 767019347/689919*a^4 - 59206303/689919*a^3 - 347957189/1379838*a^2 + 15340919/689919*a + 3834265/689919)*q^19 + (120841/919892*a^16 + 155239/229973*a^15 - 1039929/919892*a^14 - 9266505/919892*a^13 - 1277943/919892*a^12 + 50719459/919892*a^11 + 8458833/229973*a^10 - 64280895/459946*a^9 - 28079908/229973*a^8 + 37100570/229973*a^7 + 145428937/919892*a^6 - 11512298/229973*a^5 - 17380724/229973*a^4 - 37287081/919892*a^3 + 705270/229973*a^2 + 5325219/229973*a + 630010/229973)*q^20 + (-285259/1379838*a^16 - 3027685/2759676*a^15 + 2897815/1379838*a^14 + 50288555/2759676*a^13 - 1065391/919892*a^12 - 324938783/2759676*a^11 - 143026415/2759676*a^10 + 88675150/229973*a^9 + 310699189/1379838*a^8 - 157483155/229973*a^7 - 179342059/459946*a^6 + 587620677/919892*a^5 + 70720541/229973*a^4 - 125434957/459946*a^3 - 89234065/919892*a^2 + 25639229/689919*a + 1721606/689919)*q^21 + (557555/2759676*a^16 + 1571837/1379838*a^15 - 3844967/2759676*a^14 - 45914429/2759676*a^13 - 5835705/919892*a^12 + 245181443/2759676*a^11 + 99377059/1379838*a^10 - 101874467/459946*a^9 - 139120124/689919*a^8 + 60414864/229973*a^7 + 208345161/919892*a^6 - 54638787/459946*a^5 - 23609711/229973*a^4 + 2553931/919892*a^3 + 6830337/459946*a^2 + 900244/689919*a - 678020/689919)*q^22 + (-185236/689919*a^16 - 4224653/2759676*a^15 + 2440025/1379838*a^14 + 61890169/2759676*a^13 + 9157657/919892*a^12 - 332237323/2759676*a^11 - 289303741/2759676*a^10 + 140052995/459946*a^9 + 390047459/1379838*a^8 - 88127800/229973*a^7 - 60543171/229973*a^6 + 211667917/919892*a^5 + 3176433/459946*a^4 - 14234685/229973*a^3 + 62682999/919892*a^2 + 6687761/1379838*a - 6072464/689919)*q^23 + (679952/689919*a^16 + 4492039/689919*a^15 - 1202369/689919*a^14 - 62870693/689919*a^13 - 25993648/229973*a^12 + 309367745/689919*a^11 + 593028152/689919*a^10 - 218351094/229973*a^9 - 1736536757/689919*a^8 + 177903824/229973*a^7 + 788301036/229973*a^6 + 652700/229973*a^5 - 480536557/229973*a^4 - 44720825/229973*a^3 + 105328770/229973*a^2 + 12045832/689919*a - 9744704/689919)*q^24 + (-47303/919892*a^16 - 114291/919892*a^15 + 1196623/919892*a^14 + 1445507/459946*a^13 - 2847094/229973*a^12 - 6672519/229973*a^11 + 53992043/919892*a^10 + 58170771/459946*a^9 - 71390607/459946*a^8 - 64583667/229973*a^7 + 215384357/919892*a^6 + 291826977/919892*a^5 - 41426720/229973*a^4 - 157511041/919892*a^3 + 44861463/919892*a^2 + 7989292/229973*a - 125577/229973)*q^25 + (133735/229973*a^16 + 910339/229973*a^15 - 147246/229973*a^14 - 12808797/229973*a^13 - 16901691/229973*a^12 + 63656115/229973*a^11 + 127287640/229973*a^10 - 137669338/229973*a^9 - 377586918/229973*a^8 + 119861239/229973*a^7 + 528660562/229973*a^6 - 13496526/229973*a^5 - 338379465/229973*a^4 - 19412984/229973*a^3 + 80254997/229973*a^2 + 926055/229973*a - 2280650/229973)*q^26 + (-219689/2759676*a^16 - 991599/919892*a^15 - 7861009/2759676*a^14 + 16411079/1379838*a^13 + 74892941/1379838*a^12 - 39247181/1379838*a^11 - 298187707/919892*a^10 - 17730278/229973*a^9 + 1240083331/1379838*a^8 + 279408854/689919*a^7 - 3441850933/2759676*a^6 - 1482338581/2759676*a^5 + 1115092465/1379838*a^4 + 650092205/2759676*a^3 - 523233439/2759676*a^2 - 20201803/1379838*a + 240284/229973)*q^27 + (683779/1379838*a^16 + 1541975/459946*a^15 - 983593/1379838*a^14 - 32831215/689919*a^13 - 41584741/689919*a^12 + 166431847/689919*a^11 + 211806517/459946*a^10 - 126214974/229973*a^9 - 952818032/689919*a^8 + 388211182/689919*a^7 + 2717698253/1379838*a^6 - 299342707/1379838*a^5 - 905760770/689919*a^4 + 30901517/1379838*a^3 + 478934243/1379838*a^2 - 6056143/689919*a - 3889920/229973)*q^28 + (253022/689919*a^16 + 3894001/1379838*a^15 + 1037179/689919*a^14 - 16855585/459946*a^13 - 99889975/1379838*a^12 + 71224507/459946*a^11 + 652172705/1379838*a^10 - 50468986/229973*a^9 - 886056809/689919*a^8 - 48869305/689919*a^7 + 1129165208/689919*a^6 + 502643419/1379838*a^5 - 630155971/689919*a^4 - 127231912/689919*a^3 + 231112825/1379838*a^2 + 520043/229973*a - 368596/689919)*q^29 + (272117/459946*a^16 + 858281/229973*a^15 - 1020061/459946*a^14 - 24696491/459946*a^13 - 22740541/459946*a^12 + 128178283/459946*a^11 + 93322128/229973*a^10 - 151775077/229973*a^9 - 272508767/229973*a^8 + 165737608/229973*a^7 + 715856149/459946*a^6 - 67745036/229973*a^5 - 203661574/229973*a^4 + 4991181/459946*a^3 + 39342405/229973*a^2 - 9651/229973*a - 1096792/229973)*q^30 + (711691/2759676*a^16 + 1118726/689919*a^15 - 2973667/2759676*a^14 - 66186811/2759676*a^13 - 19353791/919892*a^12 + 359943325/2759676*a^11 + 126345583/689919*a^10 - 154749135/459946*a^9 - 388738180/689919*a^8 + 102223657/229973*a^7 + 720069541/919892*a^6 - 72274884/229973*a^5 - 108012847/229973*a^4 + 115498135/919892*a^3 + 23264470/229973*a^2 - 13799596/689919*a - 4624942/689919)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (743495/2759676*a^16 + 1431957/919892*a^15 - 4223855/2759676*a^14 - 30708791/1379838*a^13 - 9534166/689919*a^12 + 78310351/689919*a^11 + 117709679/919892*a^10 - 117196711/459946*a^9 - 483028033/1379838*a^8 + 156119305/689919*a^7 + 1012578007/2759676*a^6 + 30416827/2759676*a^5 - 66073844/689919*a^4 - 284979755/2759676*a^3 - 53479139/2759676*a^2 + 18921128/689919*a - 1407162/229973)*q^33 + (-2125217/2759676*a^16 - 2185853/459946*a^15 + 8968121/2759676*a^14 + 189507895/2759676*a^13 + 165389245/2759676*a^12 - 987981589/2759676*a^11 - 235735551/459946*a^10 + 390247525/459946*a^9 + 1060529843/689919*a^8 - 629612863/689919*a^7 - 5776607917/2759676*a^6 + 468766411/1379838*a^5 + 874779644/689919*a^4 + 48579401/2759676*a^3 - 380588819/1379838*a^2 - 6621122/689919*a + 1701796/229973)*q^34 + (-232185/459946*a^16 - 3235761/919892*a^15 - 167375/459946*a^14 + 42785059/919892*a^13 + 68426379/919892*a^12 - 185788951/919892*a^11 - 469988259/919892*a^10 + 67651917/229973*a^9 + 639318819/459946*a^8 + 31705156/229973*a^7 - 788589995/459946*a^6 - 628414777/919892*a^5 + 201095340/229973*a^4 + 212849333/459946*a^3 - 108896575/919892*a^2 - 14721236/229973*a - 1010751/229973)*q^35 + (-542033/1379838*a^16 - 2755501/1379838*a^15 + 5480453/1379838*a^14 + 21978103/689919*a^13 - 856188/229973*a^12 - 134397607/689919*a^11 - 103151729/1379838*a^10 + 136926566/229973*a^9 + 211226362/689919*a^8 - 224318815/229973*a^7 - 214556617/459946*a^6 + 382763189/459946*a^5 + 69461311/229973*a^4 - 150940653/459946*a^3 - 30362147/459946*a^2 + 29542384/689919*a - 245192/689919)*q^36 + (521533/1839784*a^16 + 5354231/2759676*a^15 - 499641/1839784*a^14 - 150692101/5519352*a^13 - 201219707/5519352*a^12 + 749623771/5519352*a^11 + 755063689/2759676*a^10 - 270628339/919892*a^9 - 186515066/229973*a^8 + 173880025/689919*a^7 + 6230067047/5519352*a^6 + 3032203/2759676*a^5 - 480561569/689919*a^4 - 543719947/5519352*a^3 + 391289311/2759676*a^2 + 19978366/689919*a - 1247245/689919)*q^37 + O(q^38)
*]> ;  // time = 15.039 seconds




J[489] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 489, 489, 489, 489, 163, 163, 163 ], new_dimensions := [ 4, 5, 8, 10, 1, 5, 7 ], dimensions := [ 4, 5, 8, 10, 2, 10, 14 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 101, 1, 0, 1, 1, 1, 73, 1, 1, 1, 0, 1, 1, 1, 4121, 1, 1, 1, 0, 1, 1879, 1, 1, 1, 1, 1, 0, 9, 1, 1, 73, 1, 1879, 9, 0, 1, 101, 1, 4121, 1, 1, 1, 0 ], ap_traces := [
[ -2, 4, -3, -10, -8, -14, 3, -13, -5, 1, -13, -8 ],
[ -2, -5, -3, -4, -10, 10, -7, -9, -9, -11, -7, 16 ],
[ 4, -8, 5, 4, 14, -14, 5, 9, 19, 13, 9, -16 ],
[ 1, 10, -1, 14, 4, 16, -3, 13, -1, -5, 11, 22 ]
], hecke_fields := [
x^4 + 2*x^3 - 2*x^2 - 3*x + 1,
x^5 + 2*x^4 - 4*x^3 - 7*x^2 + 3*x + 4,
x^8 - 4*x^7 - 6*x^6 + 35*x^5 - 86*x^3 + 36*x^2 + 39*x - 19,
x^10 - x^9 - 16*x^8 + 15*x^7 + 87*x^6 - 72*x^5 - 188*x^4 + 125*x^3 + 132*x^2 - 55*x + 4
], atkin_lehners := [
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 101, 1 ],
[ 73, 1 ],
[ 4121, 1 ],
[ 77039, 1 ]
], tamagawa_numbers := [
[ 101, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 77039, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 41 ], torsion_lower_bounds := [ 1, 1, 1, 41 ], l_ratios := [ 0, 0, 1, 1879/41 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
a,
1,
-a^3 - a^2 + a - 1,
-a^2 - a - 1,
2*a^3 + a^2 - 5*a - 1,
2*a^3 + 4*a^2 - 2*a - 7,
3*a^3 + 7*a^2 - 2*a - 6,
-3*a^3 - 7*a^2 + 5*a + 5,
-5*a^3 - 8*a^2 + 8*a + 5,
a^3 + 6*a^2 + 2*a - 8,
-a^3 + 3*a^2 + 6*a - 9,
-2*a^3 - a^2 + 5*a - 3
],
[
a,
-1,
a^4 + a^3 - 5*a^2 - 2*a + 4,
-a^4 - 2*a^3 + 3*a^2 + 4*a - 2,
-a^4 + 5*a^2 - 2*a - 6,
-a^4 + 6*a^2 - a - 4,
2*a^4 + a^3 - 9*a^2 - 2*a + 4,
a^4 + a^3 - 3*a^2 - 2*a - 2,
a^4 + 3*a^3 - 5*a - 6,
-3*a^3 - 2*a^2 + 10*a,
-3*a^4 - 3*a^3 + 11*a^2 + 5*a - 6,
-a^4 + 7*a^2 + 2*a - 4
],
[
a,
-1,
-1/2*a^7 + a^6 + 11/2*a^5 - 19/2*a^4 - 35/2*a^3 + 49/2*a^2 + 25/2*a - 11,
-1/2*a^6 + 2*a^5 + 1/2*a^4 - 19/2*a^3 + 15/2*a^2 + 13/2*a - 9/2,
a^7 - 2*a^6 - 9*a^5 + 14*a^4 + 23*a^3 - 24*a^2 - 9*a + 10,
a^7 - 2*a^6 - 10*a^5 + 17*a^4 + 27*a^3 - 38*a^2 - 8*a + 13,
1/2*a^7 - 3*a^6 - 1/2*a^5 + 43/2*a^4 - 13/2*a^3 - 87/2*a^2 - 1/2*a + 18,
-a^7 + 5/2*a^6 + 8*a^5 - 33/2*a^4 - 41/2*a^3 + 53/2*a^2 + 29/2*a - 17/2,
-a^7 + 3*a^6 + 6*a^5 - 19*a^4 - 9*a^3 + 29*a^2 + 4*a - 5,
1/2*a^7 + a^6 - 19/2*a^5 - 13/2*a^4 + 75/2*a^3 + 29/2*a^2 - 47/2*a - 2,
-1/2*a^6 + 3*a^5 - 3/2*a^4 - 29/2*a^3 + 29/2*a^2 + 17/2*a - 5/2,
-a^7 + 2*a^6 + 9*a^5 - 14*a^4 - 21*a^3 + 22*a^2 - a - 6
],
[
a,
1,
-21/68*a^9 + 4/17*a^8 + 161/34*a^7 - 227/68*a^6 - 414/17*a^5 + 243/17*a^4 + 836/17*a^3 - 1369/68*a^2 - 2201/68*a + 95/17,
3/34*a^9 + 5/34*a^8 - 23/17*a^7 - 36/17*a^6 + 239/34*a^5 + 325/34*a^4 - 485/34*a^3 - 224/17*a^2 + 295/34*a + 36/17,
1/17*a^9 - 4/17*a^8 - 21/17*a^7 + 61/17*a^6 + 159/17*a^5 - 294/17*a^4 - 513/17*a^3 + 457/17*a^2 + 580/17*a - 78/17,
9/34*a^9 - 1/17*a^8 - 69/17*a^7 + 39/34*a^6 + 350/17*a^5 - 116/17*a^4 - 668/17*a^3 + 475/34*a^2 + 749/34*a - 62/17,
-9/34*a^9 + 1/17*a^8 + 155/34*a^7 - 39/34*a^6 - 921/34*a^5 + 249/34*a^4 + 2169/34*a^3 - 297/17*a^2 - 808/17*a + 164/17,
29/68*a^9 - 7/34*a^8 - 114/17*a^7 + 205/68*a^6 + 596/17*a^5 - 236/17*a^4 - 1182/17*a^3 + 1557/68*a^2 + 2795/68*a - 115/17,
-4/17*a^9 - 1/17*a^8 + 67/17*a^7 + 11/17*a^6 - 381/17*a^5 - 31/17*a^4 + 845/17*a^3 - 9/17*a^2 - 603/17*a + 74/17,
6/17*a^9 - 7/17*a^8 - 201/34*a^7 + 94/17*a^6 + 1143/34*a^5 - 757/34*a^4 - 2569/34*a^3 + 945/34*a^2 + 1877/34*a - 94/17,
-9/68*a^9 + 1/34*a^8 + 43/17*a^7 - 73/68*a^6 - 294/17*a^5 + 160/17*a^4 + 827/17*a^3 - 1733/68*a^2 - 3095/68*a + 235/17,
1/17*a^9 - 4/17*a^8 - 21/17*a^7 + 61/17*a^6 + 159/17*a^5 - 294/17*a^4 - 479/17*a^3 + 457/17*a^2 + 410/17*a - 44/17
]
*], q_expansions := [*
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^3 - a^2 + a - 1)*q^5 + a*q^6 + (-a^2 - a - 1)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (a^3 - a^2 - 4*a + 1)*q^10 + (2*a^3 + a^2 - 5*a - 1)*q^11 + (a^2 - 2)*q^12 + (2*a^3 + 4*a^2 - 2*a - 7)*q^13 + (-a^3 - a^2 - a)*q^14 + (-a^3 - a^2 + a - 1)*q^15 + (-2*a^3 - 4*a^2 + 3*a + 3)*q^16 + (3*a^3 + 7*a^2 - 2*a - 6)*q^17 + a*q^18 + (-3*a^3 - 7*a^2 + 5*a + 5)*q^19 + (-a^3 + 2*a + 1)*q^20 + (-a^2 - a - 1)*q^21 + (-3*a^3 - a^2 + 5*a - 2)*q^22 + (-5*a^3 - 8*a^2 + 8*a + 5)*q^23 + (a^3 - 4*a)*q^24 + (a^3 + 4*a^2 + a - 5)*q^25 + (2*a^2 - a - 2)*q^26 + q^27 + (a^3 - a^2 - a + 3)*q^28 + (a^3 + 6*a^2 + 2*a - 8)*q^29 + (a^3 - a^2 - 4*a + 1)*q^30 + (-a^3 + 3*a^2 + 6*a - 9)*q^31 + (-2*a^3 - a^2 + 5*a + 2)*q^32 + (2*a^3 + a^2 - 5*a - 1)*q^33 + (a^3 + 4*a^2 + 3*a - 3)*q^34 + (3*a^3 + 4*a^2 - a + 1)*q^35 + (a^2 - 2)*q^36 + (-2*a^3 - a^2 + 5*a - 3)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (a^4 + a^3 - 5*a^2 - 2*a + 4)*q^5 - a*q^6 + (-a^4 - 2*a^3 + 3*a^2 + 4*a - 2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^4 - a^3 + 5*a^2 + a - 4)*q^10 + (-a^4 + 5*a^2 - 2*a - 6)*q^11 + (-a^2 + 2)*q^12 + (-a^4 + 6*a^2 - a - 4)*q^13 + (-a^3 - 3*a^2 + a + 4)*q^14 + (-a^4 - a^3 + 5*a^2 + 2*a - 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^4 + a^3 - 9*a^2 - 2*a + 4)*q^17 + a*q^18 + (a^4 + a^3 - 3*a^2 - 2*a - 2)*q^19 + (-a^4 - a^3 + 4*a^2 + 3*a - 4)*q^20 + (a^4 + 2*a^3 - 3*a^2 - 4*a + 2)*q^21 + (2*a^4 + a^3 - 9*a^2 - 3*a + 4)*q^22 + (a^4 + 3*a^3 - 5*a - 6)*q^23 + (-a^3 + 4*a)*q^24 + (a^3 - 5*a - 1)*q^25 + (2*a^4 + 2*a^3 - 8*a^2 - a + 4)*q^26 - q^27 + (a^4 + a^3 - 5*a^2 - 4*a + 4)*q^28 + (-3*a^3 - 2*a^2 + 10*a)*q^29 + (a^4 + a^3 - 5*a^2 - a + 4)*q^30 + (-3*a^4 - 3*a^3 + 11*a^2 + 5*a - 6)*q^31 + (-2*a^4 - 4*a^3 + 7*a^2 + 9*a - 4)*q^32 + (a^4 - 5*a^2 + 2*a + 6)*q^33 + (-3*a^4 - a^3 + 12*a^2 - 2*a - 8)*q^34 + (-a^4 - a^3 + 6*a^2 + 4*a - 8)*q^35 + (a^2 - 2)*q^36 + (-a^4 + 7*a^2 + 2*a - 4)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-1/2*a^7 + a^6 + 11/2*a^5 - 19/2*a^4 - 35/2*a^3 + 49/2*a^2 + 25/2*a - 11)*q^5 - a*q^6 + (-1/2*a^6 + 2*a^5 + 1/2*a^4 - 19/2*a^3 + 15/2*a^2 + 13/2*a - 9/2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^7 + 5/2*a^6 + 8*a^5 - 35/2*a^4 - 37/2*a^3 + 61/2*a^2 + 17/2*a - 19/2)*q^10 + (a^7 - 2*a^6 - 9*a^5 + 14*a^4 + 23*a^3 - 24*a^2 - 9*a + 10)*q^11 + (-a^2 + 2)*q^12 + (a^7 - 2*a^6 - 10*a^5 + 17*a^4 + 27*a^3 - 38*a^2 - 8*a + 13)*q^13 + (-1/2*a^7 + 2*a^6 + 1/2*a^5 - 19/2*a^4 + 15/2*a^3 + 13/2*a^2 - 9/2*a)*q^14 + (1/2*a^7 - a^6 - 11/2*a^5 + 19/2*a^4 + 35/2*a^3 - 49/2*a^2 - 25/2*a + 11)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/2*a^7 - 3*a^6 - 1/2*a^5 + 43/2*a^4 - 13/2*a^3 - 87/2*a^2 - 1/2*a + 18)*q^17 + a*q^18 + (-a^7 + 5/2*a^6 + 8*a^5 - 33/2*a^4 - 41/2*a^3 + 53/2*a^2 + 29/2*a - 17/2)*q^19 + (-1/2*a^7 + 13/2*a^5 + 1/2*a^4 - 41/2*a^3 - 9/2*a^2 + 9/2*a + 3)*q^20 + (1/2*a^6 - 2*a^5 - 1/2*a^4 + 19/2*a^3 - 15/2*a^2 - 13/2*a + 9/2)*q^21 + (2*a^7 - 3*a^6 - 21*a^5 + 23*a^4 + 62*a^3 - 45*a^2 - 29*a + 19)*q^22 + (-a^7 + 3*a^6 + 6*a^5 - 19*a^4 - 9*a^3 + 29*a^2 + 4*a - 5)*q^23 + (-a^3 + 4*a)*q^24 + (-a^7 + 5/2*a^6 + 11*a^5 - 53/2*a^4 - 65/2*a^3 + 145/2*a^2 + 35/2*a - 53/2)*q^25 + (2*a^7 - 4*a^6 - 18*a^5 + 27*a^4 + 48*a^3 - 44*a^2 - 26*a + 19)*q^26 - q^27 + (-3/2*a^6 + 4*a^5 + 13/2*a^4 - 35/2*a^3 - 3/2*a^2 + 13/2*a - 1/2)*q^28 + (1/2*a^7 + a^6 - 19/2*a^5 - 13/2*a^4 + 75/2*a^3 + 29/2*a^2 - 47/2*a - 2)*q^29 + (a^7 - 5/2*a^6 - 8*a^5 + 35/2*a^4 + 37/2*a^3 - 61/2*a^2 - 17/2*a + 19/2)*q^30 + (-1/2*a^6 + 3*a^5 - 3/2*a^4 - 29/2*a^3 + 29/2*a^2 + 17/2*a - 5/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^7 + 2*a^6 + 9*a^5 - 14*a^4 - 23*a^3 + 24*a^2 + 9*a - 10)*q^33 + (-a^7 + 5/2*a^6 + 4*a^5 - 13/2*a^4 - 1/2*a^3 - 37/2*a^2 - 3/2*a + 19/2)*q^34 + (-a^7 + a^6 + 14*a^5 - 15*a^4 - 47*a^3 + 47*a^2 + 23*a - 17)*q^35 + (a^2 - 2)*q^36 + (-a^7 + 2*a^6 + 9*a^5 - 14*a^4 - 21*a^3 + 22*a^2 - a - 6)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-21/68*a^9 + 4/17*a^8 + 161/34*a^7 - 227/68*a^6 - 414/17*a^5 + 243/17*a^4 + 836/17*a^3 - 1369/68*a^2 - 2201/68*a + 95/17)*q^5 + a*q^6 + (3/34*a^9 + 5/34*a^8 - 23/17*a^7 - 36/17*a^6 + 239/34*a^5 + 325/34*a^4 - 485/34*a^3 - 224/17*a^2 + 295/34*a + 36/17)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-5/68*a^9 - 7/34*a^8 + 22/17*a^7 + 171/68*a^6 - 135/17*a^5 - 151/17*a^4 + 314/17*a^3 + 571/68*a^2 - 775/68*a + 21/17)*q^10 + (1/17*a^9 - 4/17*a^8 - 21/17*a^7 + 61/17*a^6 + 159/17*a^5 - 294/17*a^4 - 513/17*a^3 + 457/17*a^2 + 580/17*a - 78/17)*q^11 + (a^2 - 2)*q^12 + (9/34*a^9 - 1/17*a^8 - 69/17*a^7 + 39/34*a^6 + 350/17*a^5 - 116/17*a^4 - 668/17*a^3 + 475/34*a^2 + 749/34*a - 62/17)*q^13 + (4/17*a^9 + 1/17*a^8 - 117/34*a^7 - 11/17*a^6 + 541/34*a^5 + 79/34*a^4 - 823/34*a^3 - 101/34*a^2 + 237/34*a - 6/17)*q^14 + (-21/68*a^9 + 4/17*a^8 + 161/34*a^7 - 227/68*a^6 - 414/17*a^5 + 243/17*a^4 + 836/17*a^3 - 1369/68*a^2 - 2201/68*a + 95/17)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-9/34*a^9 + 1/17*a^8 + 155/34*a^7 - 39/34*a^6 - 921/34*a^5 + 249/34*a^4 + 2169/34*a^3 - 297/17*a^2 - 808/17*a + 164/17)*q^17 + a*q^18 + (29/68*a^9 - 7/34*a^8 - 114/17*a^7 + 205/68*a^6 + 596/17*a^5 - 236/17*a^4 - 1182/17*a^3 + 1557/68*a^2 + 2795/68*a - 115/17)*q^19 + (23/68*a^9 - 6/17*a^8 - 199/34*a^7 + 349/68*a^6 + 587/17*a^5 - 407/17*a^4 - 1373/17*a^3 + 2623/68*a^2 + 4211/68*a - 185/17)*q^20 + (3/34*a^9 + 5/34*a^8 - 23/17*a^7 - 36/17*a^6 + 239/34*a^5 + 325/34*a^4 - 485/34*a^3 - 224/17*a^2 + 295/34*a + 36/17)*q^21 + (-3/17*a^9 - 5/17*a^8 + 46/17*a^7 + 72/17*a^6 - 222/17*a^5 - 325/17*a^4 + 332/17*a^3 + 448/17*a^2 - 23/17*a - 4/17)*q^22 + (-4/17*a^9 - 1/17*a^8 + 67/17*a^7 + 11/17*a^6 - 381/17*a^5 - 31/17*a^4 + 845/17*a^3 - 9/17*a^2 - 603/17*a + 74/17)*q^23 + (a^3 - 4*a)*q^24 + (5/34*a^9 - 3/34*a^8 - 44/17*a^7 + 25/17*a^6 + 557/34*a^5 - 263/34*a^4 - 1477/34*a^3 + 233/17*a^2 + 1285/34*a - 59/17)*q^25 + (7/34*a^9 + 3/17*a^8 - 48/17*a^7 - 83/34*a^6 + 208/17*a^5 + 178/17*a^4 - 325/17*a^3 - 439/34*a^2 + 371/34*a - 18/17)*q^26 + q^27 + (2/17*a^9 + 1/34*a^8 - 25/17*a^7 - 11/34*a^6 + 177/34*a^5 + 31/34*a^4 - 131/34*a^3 + 77/34*a^2 - 81/17*a - 88/17)*q^28 + (6/17*a^9 - 7/17*a^8 - 201/34*a^7 + 94/17*a^6 + 1143/34*a^5 - 757/34*a^4 - 2569/34*a^3 + 945/34*a^2 + 1877/34*a - 94/17)*q^29 + (-5/68*a^9 - 7/34*a^8 + 22/17*a^7 + 171/68*a^6 - 135/17*a^5 - 151/17*a^4 + 314/17*a^3 + 571/68*a^2 - 775/68*a + 21/17)*q^30 + (-9/68*a^9 + 1/34*a^8 + 43/17*a^7 - 73/68*a^6 - 294/17*a^5 + 160/17*a^4 + 827/17*a^3 - 1733/68*a^2 - 3095/68*a + 235/17)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/17*a^9 - 4/17*a^8 - 21/17*a^7 + 61/17*a^6 + 159/17*a^5 - 294/17*a^4 - 513/17*a^3 + 457/17*a^2 + 580/17*a - 78/17)*q^33 + (-7/34*a^9 + 11/34*a^8 + 48/17*a^7 - 69/17*a^6 - 399/34*a^5 + 477/34*a^4 + 531/34*a^3 - 214/17*a^2 - 167/34*a + 18/17)*q^34 + (-47/68*a^9 + 13/17*a^8 + 183/17*a^7 - 725/68*a^6 - 1943/34*a^5 + 1537/34*a^4 + 4227/34*a^3 - 4309/68*a^2 - 6605/68*a + 279/17)*q^35 + (a^2 - 2)*q^36 + (1/17*a^9 - 4/17*a^8 - 21/17*a^7 + 61/17*a^6 + 159/17*a^5 - 294/17*a^4 - 479/17*a^3 + 457/17*a^2 + 410/17*a - 44/17)*q^37 + O(q^38)
*]> ;  // time = 100.161 seconds




J[491] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 491, 491, 491 ], new_dimensions := [ 2, 10, 29 ], dimensions := [ 2, 10, 29 ], intersection_graph := [ 0, 19, 1, 19, 0, 1, 1, 1, 0 ], ap_traces := [
[ 1, -1, -1, 1, -3, -8, 0, 1, 2, -7, -14, -4 ],
[ -3, -4, -9, -6, -3, -15, -3, -23, -3, -5, -12, -18 ],
[ 0, 5, 12, 3, 0, 35, 3, 24, -5, 12, 36, 40 ]
], hecke_fields := [
x^2 - x - 1,
x^10 + 3*x^9 - 7*x^8 - 25*x^7 + 10*x^6 + 60*x^5 + 3*x^4 - 45*x^3 - 2*x^2 + 7*x - 1,
x^29 - 49*x^27 + x^26 + 1068*x^25 - 39*x^24 - 13655*x^23 + 658*x^22 + 113723*x^21 - 6306*x^20 - 647801*x^19 + 37953*x^18 + 2578721*x^17 - 150115*x^16 - 7201417*x^15 + 398246*x^14 + 13959112*x^13 - 711934*x^12 - 18310154*x^11 + 839798*x^10 + 15574775*x^9 - 585854*x^8 - 8065060*x^7 + 132680*x^6 + 2339280*x^5 + 83968*x^4 - 350400*x^3 - 36608*x^2 + 20992*x + 3584
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 245 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 245 ]
], torsion_upper_bounds := [ 1, 1, 245 ], torsion_lower_bounds := [ 1, 1, 245 ], l_ratios := [ 0, 0, 1/245 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[
a,
-a,
a - 1,
-3*a + 2,
a - 2,
2*a - 5,
-4*a + 2,
3*a - 1,
2*a,
-a - 3,
-7,
2*a - 3
],
[
a,
-4*a^9 - 14*a^8 + 23*a^7 + 115*a^6 - 267*a^4 - 100*a^3 + 184*a^2 + 61*a - 21,
6*a^9 + 19*a^8 - 38*a^7 - 155*a^6 + 27*a^5 + 355*a^4 + 95*a^3 - 238*a^2 - 66*a + 25,
4*a^9 + 14*a^8 - 23*a^7 - 115*a^6 + 267*a^4 + 100*a^3 - 184*a^2 - 61*a + 20,
3*a^9 + 11*a^8 - 17*a^7 - 92*a^6 - 2*a^5 + 221*a^4 + 79*a^3 - 162*a^2 - 47*a + 19,
6*a^9 + 19*a^8 - 38*a^7 - 155*a^6 + 27*a^5 + 354*a^4 + 95*a^3 - 233*a^2 - 66*a + 22,
-4*a^9 - 11*a^8 + 28*a^7 + 89*a^6 - 38*a^5 - 201*a^4 - 26*a^3 + 132*a^2 + 32*a - 16,
-19*a^9 - 62*a^8 + 118*a^7 + 508*a^6 - 68*a^5 - 1172*a^4 - 335*a^3 + 792*a^2 + 222*a - 86,
-5*a^9 - 16*a^8 + 33*a^7 + 133*a^6 - 34*a^5 - 316*a^4 - 51*a^3 + 227*a^2 + 35*a - 26,
-15*a^9 - 48*a^8 + 95*a^7 + 393*a^6 - 66*a^5 - 905*a^4 - 248*a^3 + 610*a^2 + 178*a - 68,
21*a^9 + 66*a^8 - 134*a^7 - 538*a^6 + 102*a^5 + 1228*a^4 + 319*a^3 - 811*a^2 - 224*a + 84,
-5*a^9 - 16*a^8 + 31*a^7 + 129*a^6 - 17*a^5 - 286*a^4 - 92*a^3 + 172*a^2 + 63*a - 14
],
[
a,
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-171824350194538719749765/218089520041081175482624*a^28 + 33925498314875089993417/109044760020540587741312*a^27 + 8392003393509165935542057/218089520041081175482624*a^26 - 3486923839404147171670743/218089520041081175482624*a^25 - 91052675044686652662150423/109044760020540587741312*a^24 + 78665712910948454606532303/218089520041081175482624*a^23 + 2314699784449233277681909973/218089520041081175482624*a^22 - 257035529896073402175288765/54522380010270293870656*a^21 - 19128978011943208506595585039/218089520041081175482624*a^20 + 1081106202058947217152854649/27261190005135146935328*a^19 + 107855969261458849927327758309/218089520041081175482624*a^18 - 49193708535720373013497698319/218089520041081175482624*a^17 - 423500276190332398750127602903/218089520041081175482624*a^16 + 193409196631308710783380055765/218089520041081175482624*a^15 + 1160554890658830898303968785723/218089520041081175482624*a^14 - 131976459508302568346970611323/54522380010270293870656*a^13 - 68415932788106092990572029509/6815297501283786733832*a^12 + 494652026958414216011477306583/109044760020540587741312*a^11 + 1377462794281388485615914136355/109044760020540587741312*a^10 - 617685793370819668014781920205/109044760020540587741312*a^9 - 2188547107869363318764532511983/218089520041081175482624*a^8 + 241836104912691213799662704827/54522380010270293870656*a^7 + 251138408517132197227828478001/54522380010270293870656*a^6 - 52557397676009138800787546297/27261190005135146935328*a^5 - 3694270605623988728894769539/3407648750641893366916*a^4 + 1235723756752576719726367603/3407648750641893366916*a^3 + 454926047432291179644593957/3407648750641893366916*a^2 - 40655395294668517923224803/1703824375320946683458*a - 6108805648537077360817812/851912187660473341729
]
*], q_expansions := [*
q + a*q^2 - a*q^3 + (a - 1)*q^4 + (a - 1)*q^5 + (-a - 1)*q^6 + (-3*a + 2)*q^7 + (-2*a + 1)*q^8 + (a - 2)*q^9 + q^10 + (a - 2)*q^11 - q^12 + (2*a - 5)*q^13 + (-a - 3)*q^14 - q^15 - 3*a*q^16 + (-4*a + 2)*q^17 + (-a + 1)*q^18 + (3*a - 1)*q^19 + (-a + 2)*q^20 + (a + 3)*q^21 + (-a + 1)*q^22 + 2*a*q^23 + (a + 2)*q^24 + (-a - 3)*q^25 + (-3*a + 2)*q^26 + (4*a - 1)*q^27 + (2*a - 5)*q^28 + (-a - 3)*q^29 - a*q^30 - 7*q^31 + (a - 5)*q^32 + (a - 1)*q^33 + (-2*a - 4)*q^34 + (2*a - 5)*q^35 + (-2*a + 3)*q^36 + (2*a - 3)*q^37 + O(q^38),
q + a*q^2 + (-4*a^9 - 14*a^8 + 23*a^7 + 115*a^6 - 267*a^4 - 100*a^3 + 184*a^2 + 61*a - 21)*q^3 + (a^2 - 2)*q^4 + (6*a^9 + 19*a^8 - 38*a^7 - 155*a^6 + 27*a^5 + 355*a^4 + 95*a^3 - 238*a^2 - 66*a + 25)*q^5 + (-2*a^9 - 5*a^8 + 15*a^7 + 40*a^6 - 27*a^5 - 88*a^4 + 4*a^3 + 53*a^2 + 7*a - 4)*q^6 + (4*a^9 + 14*a^8 - 23*a^7 - 115*a^6 + 267*a^4 + 100*a^3 - 184*a^2 - 61*a + 20)*q^7 + (a^3 - 4*a)*q^8 + (-7*a^9 - 22*a^8 + 45*a^7 + 180*a^6 - 37*a^5 - 414*a^4 - 97*a^3 + 277*a^2 + 64*a - 27)*q^9 + (a^9 + 4*a^8 - 5*a^7 - 33*a^6 - 5*a^5 + 77*a^4 + 32*a^3 - 54*a^2 - 17*a + 6)*q^10 + (3*a^9 + 11*a^8 - 17*a^7 - 92*a^6 - 2*a^5 + 221*a^4 + 79*a^3 - 162*a^2 - 47*a + 19)*q^11 + (9*a^9 + 29*a^8 - 56*a^7 - 237*a^6 + 32*a^5 + 544*a^4 + 163*a^3 - 365*a^2 - 112*a + 40)*q^12 + (6*a^9 + 19*a^8 - 38*a^7 - 155*a^6 + 27*a^5 + 354*a^4 + 95*a^3 - 233*a^2 - 66*a + 22)*q^13 + (2*a^9 + 5*a^8 - 15*a^7 - 40*a^6 + 27*a^5 + 88*a^4 - 4*a^3 - 53*a^2 - 8*a + 4)*q^14 + (5*a^9 + 18*a^8 - 28*a^7 - 148*a^6 - 5*a^5 + 344*a^4 + 132*a^3 - 236*a^2 - 76*a + 24)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-4*a^9 - 11*a^8 + 28*a^7 + 89*a^6 - 38*a^5 - 201*a^4 - 26*a^3 + 132*a^2 + 32*a - 16)*q^17 + (-a^9 - 4*a^8 + 5*a^7 + 33*a^6 + 6*a^5 - 76*a^4 - 38*a^3 + 50*a^2 + 22*a - 7)*q^18 + (-19*a^9 - 62*a^8 + 118*a^7 + 508*a^6 - 68*a^5 - 1172*a^4 - 335*a^3 + 792*a^2 + 222*a - 86)*q^19 + (-11*a^9 - 36*a^8 + 68*a^7 + 295*a^6 - 37*a^5 - 681*a^4 - 199*a^3 + 461*a^2 + 131*a - 49)*q^20 + (11*a^9 + 36*a^8 - 68*a^7 - 295*a^6 + 37*a^5 + 681*a^4 + 197*a^3 - 461*a^2 - 125*a + 45)*q^21 + (2*a^9 + 4*a^8 - 17*a^7 - 32*a^6 + 41*a^5 + 70*a^4 - 27*a^3 - 41*a^2 - 2*a + 3)*q^22 + (-5*a^9 - 16*a^8 + 33*a^7 + 133*a^6 - 34*a^5 - 316*a^4 - 51*a^3 + 227*a^2 + 35*a - 26)*q^23 + (6*a^9 + 17*a^8 - 42*a^7 - 138*a^6 + 58*a^5 + 312*a^4 + 32*a^3 - 200*a^2 - 37*a + 17)*q^24 + (-6*a^9 - 18*a^8 + 39*a^7 + 145*a^6 - 35*a^5 - 324*a^4 - 78*a^3 + 208*a^2 + 60*a - 24)*q^25 + (a^9 + 4*a^8 - 5*a^7 - 33*a^6 - 6*a^5 + 77*a^4 + 37*a^3 - 54*a^2 - 20*a + 6)*q^26 + (11*a^9 + 36*a^8 - 69*a^7 - 296*a^6 + 46*a^5 + 688*a^4 + 174*a^3 - 472*a^2 - 110*a + 47)*q^27 + (-9*a^9 - 29*a^8 + 56*a^7 + 237*a^6 - 32*a^5 - 544*a^4 - 163*a^3 + 364*a^2 + 112*a - 38)*q^28 + (-15*a^9 - 48*a^8 + 95*a^7 + 393*a^6 - 66*a^5 - 905*a^4 - 248*a^3 + 610*a^2 + 178*a - 68)*q^29 + (3*a^9 + 7*a^8 - 23*a^7 - 55*a^6 + 44*a^5 + 117*a^4 - 11*a^3 - 66*a^2 - 11*a + 5)*q^30 + (21*a^9 + 66*a^8 - 134*a^7 - 538*a^6 + 102*a^5 + 1228*a^4 + 319*a^3 - 811*a^2 - 224*a + 84)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-3*a^9 - 11*a^8 + 17*a^7 + 91*a^6 + a^5 - 213*a^4 - 73*a^3 + 147*a^2 + 42*a - 17)*q^33 + (a^9 - 11*a^7 + 2*a^6 + 39*a^5 - 14*a^4 - 48*a^3 + 24*a^2 + 12*a - 4)*q^34 + (-11*a^9 - 37*a^8 + 66*a^7 + 303*a^6 - 22*a^5 - 699*a^4 - 227*a^3 + 474*a^2 + 142*a - 49)*q^35 + (13*a^9 + 42*a^8 - 82*a^7 - 344*a^6 + 58*a^5 + 793*a^4 + 199*a^3 - 534*a^2 - 128*a + 53)*q^36 + (-5*a^9 - 16*a^8 + 31*a^7 + 129*a^6 - 17*a^5 - 286*a^4 - 92*a^3 + 172*a^2 + 63*a - 14)*q^37 + O(q^38),
q + a*q^2 + (23108313731491005958945/218089520041081175482624*a^28 - 4990921243167303783455/109044760020540587741312*a^27 - 1128237043944943824602305/218089520041081175482624*a^26 + 510789038220329400741103/218089520041081175482624*a^25 + 12235940192251196566205495/109044760020540587741312*a^24 - 11486392256760376002059439/218089520041081175482624*a^23 - 310884227120062146619354149/218089520041081175482624*a^22 + 37441678869415215565124865/54522380010270293870656*a^21 + 2567387872825066096992801631/218089520041081175482624*a^20 - 314422047663874124131196579/54522380010270293870656*a^19 - 14462925102759462326803330109/218089520041081175482624*a^18 + 7144730506518246130810302047/218089520041081175482624*a^17 + 56723385490790397675247041219/218089520041081175482624*a^16 - 28062356711339419523041158657/218089520041081175482624*a^15 - 155202108078989193851145985279/218089520041081175482624*a^14 + 19128539572470952946010911329/54522380010270293870656*a^13 + 73033019213460611902799783449/54522380010270293870656*a^12 - 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21330737248031017375519769/218089520041081175482624*a^23 - 624974105843270153900174245/218089520041081175482624*a^22 + 139349391489420176348280481/109044760020540587741312*a^21 + 5164987186501287486885159437/218089520041081175482624*a^20 - 1171885420233881582783868231/109044760020540587741312*a^19 - 29122846557622810688666145047/218089520041081175482624*a^18 + 13327490858026602210543250555/218089520041081175482624*a^17 + 114356044958796382283112755879/218089520041081175482624*a^16 - 52383951831533553402571383693/218089520041081175482624*a^15 - 313395683406478584247391816415/218089520041081175482624*a^14 + 71469683156800433541820547015/109044760020540587741312*a^13 + 147810722720736126192852171027/54522380010270293870656*a^12 - 133890950984541638690786833049/109044760020540587741312*a^11 - 372034250554197688812806961967/109044760020540587741312*a^10 + 167126736004092685116375453133/109044760020540587741312*a^9 + 591174263418013248190082402749/218089520041081175482624*a^8 - 130803458946685504966057124841/109044760020540587741312*a^7 - 33922494148411792015317901443/27261190005135146935328*a^6 + 7102753082548731859023170365/13630595002567573467664*a^5 + 997800743541289215828456651/3407648750641893366916*a^4 - 667587883910328388526351711/6815297501283786733832*a^3 - 30679456747676303654145250/851912187660473341729*a^2 + 10976915534645600786004999/1703824375320946683458*a + 1644794886766733723348133/851912187660473341729)*q^5 + (-4990921243167303783455/109044760020540587741312*a^28 + 254395556132216711625/13630595002567573467664*a^27 + 243840362244419197391079/109044760020540587741312*a^26 - 103899340365000615871135/109044760020540587741312*a^25 - 1323146002654028346207573/27261190005135146935328*a^24 + 2329898441723769875019913/109044760020540587741312*a^23 + 67280722521169890169756825/109044760020540587741312*a^22 - 15139722415321393419075151/54522380010270293870656*a^21 - 555983582132357106473839573/109044760020540587741312*a^20 + 126665910203535706101799959/54522380010270293870656*a^19 + 3133850337733483990825231231/109044760020540587741312*a^18 - 1433254201596910351104784063/109044760020540587741312*a^17 - 12296726097768323581757064991/109044760020540587741312*a^16 + 5605247634151785904350919893/109044760020540587741312*a^15 + 33655682389786222312458817423/109044760020540587741312*a^14 - 7609865663794607890595380761/54522380010270293870656*a^13 - 7919233774794389045716130039/13630595002567573467664*a^12 + 14189037744920373834191991509/54522380010270293870656*a^11 + 39717858551987275634604296675/54522380010270293870656*a^10 - 17633466236270922301178146181/54522380010270293870656*a^9 - 62716063084078039687899435753/109044760020540587741312*a^8 + 13742006799889509477414125757/54522380010270293870656*a^7 + 7116468393162222021040061677/27261190005135146935328*a^6 - 741782629967977214219328569/6815297501283786733832*a^5 - 204943403322384721571296237/3407648750641893366916*a^4 + 68703837933733626150073699/3407648750641893366916*a^3 + 12300723717156969126535205/1703824375320946683458*a^2 - 1106873192244187761962981/851912187660473341729*a - 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131976459508302568346970611323/54522380010270293870656*a^13 - 68415932788106092990572029509/6815297501283786733832*a^12 + 494652026958414216011477306583/109044760020540587741312*a^11 + 1377462794281388485615914136355/109044760020540587741312*a^10 - 617685793370819668014781920205/109044760020540587741312*a^9 - 2188547107869363318764532511983/218089520041081175482624*a^8 + 241836104912691213799662704827/54522380010270293870656*a^7 + 251138408517132197227828478001/54522380010270293870656*a^6 - 52557397676009138800787546297/27261190005135146935328*a^5 - 3694270605623988728894769539/3407648750641893366916*a^4 + 1235723756752576719726367603/3407648750641893366916*a^3 + 454926047432291179644593957/3407648750641893366916*a^2 - 40655395294668517923224803/1703824375320946683458*a - 6108805648537077360817812/851912187660473341729)*q^37 + O(q^38)
*]> ;  // time = 18.371 seconds




J[493] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 493, 493, 493, 493, 493, 493, 493, 493, 29, 17 ], new_dimensions := [ 1, 1, 2, 4, 5, 6, 8, 10, 2, 1 ], dimensions := [ 1, 1, 2, 4, 5, 6, 8, 10, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 13, 1, 1, 1, 9, 1, 0, 1, 1, 5, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 53, 1, 1, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 7, 1, 13, 1, 1, 53, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 31, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 7, 1, 31, 1, 0, 1, 9, 3, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, -2, -5, 0, 7, 1, 5, 4, -1, 4, -11 ],
[ -1, -3, 1, -2, 3, 1, 1, -4, -2, 1, 1, -2 ],
[ 2, -1, 3, 5, 1, 0, -2, -1, 10, 2, 3, 5 ],
[ 2, 3, 3, 1, 15, -2, 4, 11, -2, -4, -15, 5 ],
[ -2, -2, -1, -4, -14, -8, 5, -8, -14, 5, 5, 7 ],
[ 5, 2, 1, 2, 0, -6, 6, -2, 10, -6, -1, 5 ],
[ 3, 6, 1, 3, 10, 3, -8, -13, 20, 8, -7, -6 ],
[ -5, -9, -4, -4, -19, -1, -10, 4, -22, -10, -14, -9 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - x - 4,
x^4 - 2*x^3 - 6*x^2 + 12*x - 1,
x^5 + 2*x^4 - 5*x^3 - 7*x^2 + 7*x + 3,
x^6 - 5*x^5 + 3*x^4 + 16*x^3 - 20*x^2 + 1,
x^8 - 3*x^7 - 10*x^6 + 29*x^5 + 37*x^4 - 88*x^3 - 65*x^2 + 80*x + 51,
x^10 + 5*x^9 - 3*x^8 - 44*x^7 - 25*x^6 + 119*x^5 + 98*x^4 - 116*x^3 - 94*x^2 + 28*x + 11
], atkin_lehners := [
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ],
[ 1, 1 ]
], component_group_orders := [
[ 1, 9 ],
[ 1, 3 ],
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 5, 1 ],
[ 31, 3 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 3 ],
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 5, 1 ],
[ 1, 3 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 7, 5, 3, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 5, 3, 1 ], l_ratios := [ 1, 0, 1, 1, 0, 1/5, 1/3, 0 ], analytic_sha_upper_bounds := [ 1, 0, 1, 1, 0, 1, 1, 0 ], analytic_sha_lower_bounds := [ 1, 0, 1, 1, 0, 1, 1, 0 ], eigenvalues := [*
[ -1, 0, -2, -5, 0, 7, 1, 5, 4, -1, 4, -11 ],
[ -1, -3, 1, -2, 3, 1, 1, -4, -2, 1, 1, -2 ],
[
1,
a - 1,
a + 1,
a + 2,
-a + 1,
-2*a + 1,
-1,
-a,
-2*a + 6,
1,
-3*a + 3,
a + 2
],
[
a,
-1/2*a^3 - 1/2*a^2 + 5/2*a + 5/2,
1/2*a^3 - 1/2*a^2 - 7/2*a + 7/2,
-1/2*a^3 + 1/2*a^2 + 7/2*a - 5/2,
-1/2*a^3 + 1/2*a^2 + 5/2*a + 3/2,
a^3 - 7*a + 1,
1,
1/2*a^3 - 1/2*a^2 - 3/2*a + 9/2,
a^3 + a^2 - 7*a - 3,
-1,
-3/2*a^3 - 1/2*a^2 + 19/2*a - 7/2,
-5/2*a^3 + 5/2*a^2 + 27/2*a - 21/2
],
[
a,
-a^2 - a + 2,
-a^4 - a^3 + 4*a^2 + a - 2,
a^4 + 2*a^3 - 2*a^2 - 3*a - 2,
-a^3 + 3*a - 5,
-a^3 - a^2 + 3*a - 1,
1,
-2*a^3 - 3*a^2 + 5*a + 2,
-a^4 - 3*a^3 + 2*a^2 + 8*a - 3,
1,
a^4 + 3*a^3 - 7*a - 4,
a^4 + 2*a^3 - 6*a^2 - 4*a + 11
],
[
a,
a^2 - a - 2,
a^5 - 5*a^4 + 2*a^3 + 17*a^2 - 16*a - 1,
-a^4 + 2*a^3 + 4*a^2 - 7*a,
a^5 - 2*a^4 - 6*a^3 + 7*a^2 + 10*a,
-a^3 + a^2 + 5*a - 3,
1,
-2*a^4 + 6*a^3 + 5*a^2 - 19*a + 2,
a^5 - 5*a^4 + 4*a^3 + 15*a^2 - 23*a + 2,
-1,
3*a^5 - 13*a^4 + 2*a^3 + 43*a^2 - 34*a - 3,
a^4 - 8*a^2 + 9
],
[
a,
-a^2 + a + 4,
a^6 - 2*a^5 - 8*a^4 + 12*a^3 + 21*a^2 - 16*a - 18,
-1/2*a^7 + a^6 + 4*a^5 - 11/2*a^4 - 11*a^3 + 5*a^2 + 21/2*a + 7/2,
-a^5 + 2*a^4 + 6*a^3 - 9*a^2 - 8*a + 6,
-1/2*a^7 + a^6 + 4*a^5 - 13/2*a^4 - 10*a^3 + 10*a^2 + 17/2*a + 1/2,
-1,
1/2*a^7 - 7*a^5 - 1/2*a^4 + 29*a^3 + 6*a^2 - 69/2*a - 29/2,
-a^6 + 2*a^5 + 8*a^4 - 12*a^3 - 21*a^2 + 15*a + 21,
1,
2*a^6 - 3*a^5 - 17*a^4 + 18*a^3 + 43*a^2 - 24*a - 31,
1/2*a^7 - a^6 - 4*a^5 + 7/2*a^4 + 15*a^3 + 7*a^2 - 51/2*a - 41/2
],
[
a,
5/22*a^9 + 23/22*a^8 - a^7 - 17/2*a^6 - 15/22*a^5 + 218/11*a^4 + 1/22*a^3 - 167/11*a^2 + 119/22*a + 1,
7/22*a^9 + 19/22*a^8 - 4*a^7 - 21/2*a^6 + 353/22*a^5 + 435/11*a^4 - 465/22*a^3 - 500/11*a^2 + 127/22*a + 6,
-9/22*a^9 - 13/11*a^8 + 9/2*a^7 + 25/2*a^6 - 190/11*a^5 - 919/22*a^4 + 601/22*a^3 + 973/22*a^2 - 333/22*a - 11/2,
15/22*a^9 + 47/22*a^8 - 7*a^7 - 43/2*a^6 + 571/22*a^5 + 742/11*a^4 - 965/22*a^3 - 732/11*a^2 + 577/22*a + 5,
-7/22*a^9 - 19/22*a^8 + 4*a^7 + 19/2*a^6 - 397/22*a^5 - 347/11*a^4 + 751/22*a^3 + 324/11*a^2 - 501/22*a - 1,
-1,
a^7 + 3*a^6 - 7*a^5 - 22*a^4 + 12*a^3 + 39*a^2 - 6*a - 12,
-9/22*a^9 - 13/11*a^8 + 11/2*a^7 + 31/2*a^6 - 256/11*a^5 - 1359/22*a^4 + 689/22*a^3 + 1567/22*a^2 - 135/22*a - 19/2,
-1,
1/22*a^9 + 9/22*a^8 + a^7 - 1/2*a^6 - 135/22*a^5 - 117/11*a^4 - 35/22*a^3 + 202/11*a^2 + 367/22*a - 4,
6/11*a^9 + 21/11*a^8 - 4*a^7 - 16*a^6 + 103/11*a^5 + 433/11*a^4 - 166/11*a^3 - 337/11*a^2 + 123/11*a - 1
]
*], q_expansions := [*
q - q^2 - q^4 - 2*q^5 - 5*q^7 + 3*q^8 - 3*q^9 + 2*q^10 + 7*q^13 + 5*q^14 - q^16 + q^17 + 3*q^18 + 5*q^19 + 2*q^20 + 4*q^23 - q^25 - 7*q^26 + 5*q^28 - q^29 + 4*q^31 - 5*q^32 - q^34 + 10*q^35 + 3*q^36 - 11*q^37 + O(q^38),
q - q^2 - 3*q^3 - q^4 + q^5 + 3*q^6 - 2*q^7 + 3*q^8 + 6*q^9 - q^10 + 3*q^11 + 3*q^12 + q^13 + 2*q^14 - 3*q^15 - q^16 + q^17 - 6*q^18 - 4*q^19 - q^20 + 6*q^21 - 3*q^22 - 2*q^23 - 9*q^24 - 4*q^25 - q^26 - 9*q^27 + 2*q^28 + q^29 + 3*q^30 + q^31 - 5*q^32 - 9*q^33 - q^34 - 2*q^35 - 6*q^36 - 2*q^37 + O(q^38),
q + q^2 + (a - 1)*q^3 - q^4 + (a + 1)*q^5 + (a - 1)*q^6 + (a + 2)*q^7 - 3*q^8 + (-a + 2)*q^9 + (a + 1)*q^10 + (-a + 1)*q^11 + (-a + 1)*q^12 + (-2*a + 1)*q^13 + (a + 2)*q^14 + (a + 3)*q^15 - q^16 - q^17 + (-a + 2)*q^18 - a*q^19 + (-a - 1)*q^20 + (2*a + 2)*q^21 + (-a + 1)*q^22 + (-2*a + 6)*q^23 + (-3*a + 3)*q^24 + 3*a*q^25 + (-2*a + 1)*q^26 + (-a - 3)*q^27 + (-a - 2)*q^28 + q^29 + (a + 3)*q^30 + (-3*a + 3)*q^31 + 5*q^32 + (a - 5)*q^33 - q^34 + (4*a + 6)*q^35 + (a - 2)*q^36 + (a + 2)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^3 - 1/2*a^2 + 5/2*a + 5/2)*q^3 + (a^2 - 2)*q^4 + (1/2*a^3 - 1/2*a^2 - 7/2*a + 7/2)*q^5 + (-3/2*a^3 - 1/2*a^2 + 17/2*a - 1/2)*q^6 + (-1/2*a^3 + 1/2*a^2 + 7/2*a - 5/2)*q^7 + (a^3 - 4*a)*q^8 + (1/2*a^3 - 1/2*a^2 - 3/2*a + 9/2)*q^9 + (1/2*a^3 - 1/2*a^2 - 5/2*a + 1/2)*q^10 + (-1/2*a^3 + 1/2*a^2 + 5/2*a + 3/2)*q^11 + (-5/2*a^3 + 1/2*a^2 + 25/2*a - 13/2)*q^12 + (a^3 - 7*a + 1)*q^13 + (-1/2*a^3 + 1/2*a^2 + 7/2*a - 1/2)*q^14 + (3/2*a^3 - 3/2*a^2 - 19/2*a + 19/2)*q^15 + (2*a^3 - 12*a + 5)*q^16 + q^17 + (1/2*a^3 + 3/2*a^2 - 3/2*a + 1/2)*q^18 + (1/2*a^3 - 1/2*a^2 - 3/2*a + 9/2)*q^19 + (-1/2*a^3 + 3/2*a^2 + 3/2*a - 13/2)*q^20 + (-2*a^3 + a^2 + 12*a - 7)*q^21 + (-1/2*a^3 - 1/2*a^2 + 15/2*a - 1/2)*q^22 + (a^3 + a^2 - 7*a - 3)*q^23 + (-3/2*a^3 - 3/2*a^2 + 13/2*a - 3/2)*q^24 + (1/2*a^3 - 3/2*a^2 - 7/2*a + 11/2)*q^25 + (2*a^3 - a^2 - 11*a + 1)*q^26 + (-1/2*a^3 - 3/2*a^2 + 5/2*a + 7/2)*q^27 + (1/2*a^3 - 1/2*a^2 - 3/2*a + 9/2)*q^28 - q^29 + (3/2*a^3 - 1/2*a^2 - 17/2*a + 3/2)*q^30 + (-3/2*a^3 - 1/2*a^2 + 19/2*a - 7/2)*q^31 + (2*a^3 - 11*a + 2)*q^32 + (-5/2*a^3 - 1/2*a^2 + 27/2*a + 7/2)*q^33 + a*q^34 + (a^2 - 7)*q^35 + (3/2*a^3 + 5/2*a^2 - 5/2*a - 17/2)*q^36 + (-5/2*a^3 + 5/2*a^2 + 27/2*a - 21/2)*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 2)*q^3 + (a^2 - 2)*q^4 + (-a^4 - a^3 + 4*a^2 + a - 2)*q^5 + (-a^3 - a^2 + 2*a)*q^6 + (a^4 + 2*a^3 - 2*a^2 - 3*a - 2)*q^7 + (a^3 - 4*a)*q^8 + (a^4 + 2*a^3 - 3*a^2 - 4*a + 1)*q^9 + (a^4 - a^3 - 6*a^2 + 5*a + 3)*q^10 + (-a^3 + 3*a - 5)*q^11 + (-a^4 - a^3 + 4*a^2 + 2*a - 4)*q^12 + (-a^3 - a^2 + 3*a - 1)*q^13 + (3*a^3 + 4*a^2 - 9*a - 3)*q^14 + (2*a^2 + a - 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + q^17 + (2*a^3 + 3*a^2 - 6*a - 3)*q^18 + (-2*a^3 - 3*a^2 + 5*a + 2)*q^19 + (-a^4 + a^3 + 4*a^2 - 6*a + 1)*q^20 + (-a^4 - 3*a^3 + a^2 + 6*a - 1)*q^21 + (-a^4 + 3*a^2 - 5*a)*q^22 + (-a^4 - 3*a^3 + 2*a^2 + 8*a - 3)*q^23 + (a^4 + a^3 - 3*a^2 - a + 3)*q^24 + (-a^4 + 6*a^2 - 5*a - 4)*q^25 + (-a^4 - a^3 + 3*a^2 - a)*q^26 + (-a^3 + 4*a - 1)*q^27 + (a^4 - 5*a^2 + 3*a + 4)*q^28 + q^29 + (2*a^3 + a^2 - 4*a)*q^30 + (a^4 + 3*a^3 - 7*a - 4)*q^31 + (-2*a^4 - 3*a^3 + 7*a^2 + 5*a - 3)*q^32 + (-a^4 + 9*a^2 + 4*a - 13)*q^33 + a*q^34 + (2*a^4 + a^3 - 11*a^2 + a + 4)*q^35 + (-a^3 + 5*a - 2)*q^36 + (a^4 + 2*a^3 - 6*a^2 - 4*a + 11)*q^37 + O(q^38),
q + a*q^2 + (a^2 - a - 2)*q^3 + (a^2 - 2)*q^4 + (a^5 - 5*a^4 + 2*a^3 + 17*a^2 - 16*a - 1)*q^5 + (a^3 - a^2 - 2*a)*q^6 + (-a^4 + 2*a^3 + 4*a^2 - 7*a)*q^7 + (a^3 - 4*a)*q^8 + (a^4 - 2*a^3 - 3*a^2 + 4*a + 1)*q^9 + (-a^4 + a^3 + 4*a^2 - a - 1)*q^10 + (a^5 - 2*a^4 - 6*a^3 + 7*a^2 + 10*a)*q^11 + (a^4 - a^3 - 4*a^2 + 2*a + 4)*q^12 + (-a^3 + a^2 + 5*a - 3)*q^13 + (-a^5 + 2*a^4 + 4*a^3 - 7*a^2)*q^14 + (-3*a^5 + 12*a^4 - a^3 - 39*a^2 + 32*a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + q^17 + (a^5 - 2*a^4 - 3*a^3 + 4*a^2 + a)*q^18 + (-2*a^4 + 6*a^3 + 5*a^2 - 19*a + 2)*q^19 + (-3*a^5 + 11*a^4 - 35*a^2 + 31*a + 2)*q^20 + (-2*a^5 + 7*a^4 + a^3 - 21*a^2 + 14*a + 1)*q^21 + (3*a^5 - 9*a^4 - 9*a^3 + 30*a^2 - 1)*q^22 + (a^5 - 5*a^4 + 4*a^3 + 15*a^2 - 23*a + 2)*q^23 + (a^5 - a^4 - 6*a^3 + 4*a^2 + 8*a)*q^24 + (a^5 - a^4 - 7*a^3 + a^2 + 14*a + 7)*q^25 + (-a^4 + a^3 + 5*a^2 - 3*a)*q^26 + (2*a^5 - 6*a^4 - 5*a^3 + 20*a^2 - 6*a + 3)*q^27 + (-3*a^5 + 9*a^4 + 5*a^3 - 28*a^2 + 14*a + 1)*q^28 - q^29 + (-3*a^5 + 8*a^4 + 9*a^3 - 28*a^2 + 3*a + 3)*q^30 + (3*a^5 - 13*a^4 + 2*a^3 + 43*a^2 - 34*a - 3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^5 - 5*a^4 + 3*a^3 + 16*a^2 - 21*a - 2)*q^33 + a*q^34 + (a^5 - 2*a^4 - 4*a^3 + 6*a^2 + 2*a + 5)*q^35 + (3*a^5 - 8*a^4 - 8*a^3 + 27*a^2 - 8*a - 3)*q^36 + (a^4 - 8*a^2 + 9)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + a + 4)*q^3 + (a^2 - 2)*q^4 + (a^6 - 2*a^5 - 8*a^4 + 12*a^3 + 21*a^2 - 16*a - 18)*q^5 + (-a^3 + a^2 + 4*a)*q^6 + (-1/2*a^7 + a^6 + 4*a^5 - 11/2*a^4 - 11*a^3 + 5*a^2 + 21/2*a + 7/2)*q^7 + (a^3 - 4*a)*q^8 + (a^4 - 2*a^3 - 7*a^2 + 8*a + 13)*q^9 + (a^7 - 2*a^6 - 8*a^5 + 12*a^4 + 21*a^3 - 16*a^2 - 18*a)*q^10 + (-a^5 + 2*a^4 + 6*a^3 - 9*a^2 - 8*a + 6)*q^11 + (-a^4 + a^3 + 6*a^2 - 2*a - 8)*q^12 + (-1/2*a^7 + a^6 + 4*a^5 - 13/2*a^4 - 10*a^3 + 10*a^2 + 17/2*a + 1/2)*q^13 + (-1/2*a^7 - a^6 + 9*a^5 + 15/2*a^4 - 39*a^3 - 22*a^2 + 87/2*a + 51/2)*q^14 + (a^5 - 4*a^4 - 3*a^3 + 21*a^2 - 2*a - 21)*q^15 + (a^4 - 6*a^2 + 4)*q^16 - q^17 + (a^5 - 2*a^4 - 7*a^3 + 8*a^2 + 13*a)*q^18 + (1/2*a^7 - 7*a^5 - 1/2*a^4 + 29*a^3 + 6*a^2 - 69/2*a - 29/2)*q^19 + (a^7 - 13*a^5 + 48*a^3 + 5*a^2 - 48*a - 15)*q^20 + (-a^6 + 3*a^5 + 6*a^4 - 17*a^3 - 13*a^2 + 20*a + 14)*q^21 + (-a^6 + 2*a^5 + 6*a^4 - 9*a^3 - 8*a^2 + 6*a)*q^22 + (-a^6 + 2*a^5 + 8*a^4 - 12*a^3 - 21*a^2 + 15*a + 21)*q^23 + (-a^5 + a^4 + 8*a^3 - 4*a^2 - 16*a)*q^24 + (-a^5 + 3*a^4 + 5*a^3 - 15*a^2 - 6*a + 13)*q^25 + (-1/2*a^7 - a^6 + 8*a^5 + 17/2*a^4 - 34*a^3 - 24*a^2 + 81/2*a + 51/2)*q^26 + (-a^6 + 3*a^5 + 9*a^4 - 23*a^3 - 30*a^2 + 42*a + 40)*q^27 + (-3/2*a^7 + 2*a^6 + 14*a^5 - 19/2*a^4 - 44*a^3 + a^2 + 89/2*a + 37/2)*q^28 + q^29 + (a^6 - 4*a^5 - 3*a^4 + 21*a^3 - 2*a^2 - 21*a)*q^30 + (2*a^6 - 3*a^5 - 17*a^4 + 18*a^3 + 43*a^2 - 24*a - 31)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^7 - 3*a^6 - 8*a^5 + 23*a^4 + 23*a^3 - 50*a^2 - 26*a + 24)*q^33 - a*q^34 + (a^6 - 2*a^5 - 7*a^4 + 10*a^3 + 16*a^2 - 12*a - 12)*q^35 + (a^6 - 2*a^5 - 9*a^4 + 12*a^3 + 27*a^2 - 16*a - 26)*q^36 + (1/2*a^7 - a^6 - 4*a^5 + 7/2*a^4 + 15*a^3 + 7*a^2 - 51/2*a - 41/2)*q^37 + O(q^38),
q + a*q^2 + (5/22*a^9 + 23/22*a^8 - a^7 - 17/2*a^6 - 15/22*a^5 + 218/11*a^4 + 1/22*a^3 - 167/11*a^2 + 119/22*a + 1)*q^3 + (a^2 - 2)*q^4 + (7/22*a^9 + 19/22*a^8 - 4*a^7 - 21/2*a^6 + 353/22*a^5 + 435/11*a^4 - 465/22*a^3 - 500/11*a^2 + 127/22*a + 6)*q^5 + (-1/11*a^9 - 7/22*a^8 + 3/2*a^7 + 5*a^6 - 159/22*a^5 - 489/22*a^4 + 123/11*a^3 + 589/22*a^2 - 59/11*a - 5/2)*q^6 + (-9/22*a^9 - 13/11*a^8 + 9/2*a^7 + 25/2*a^6 - 190/11*a^5 - 919/22*a^4 + 601/22*a^3 + 973/22*a^2 - 333/22*a - 11/2)*q^7 + (a^3 - 4*a)*q^8 + (-23/22*a^9 - 97/22*a^8 + 6*a^7 + 75/2*a^6 - 107/22*a^5 - 1038/11*a^4 + 57/22*a^3 + 865/11*a^2 - 257/22*a - 9)*q^9 + (-8/11*a^9 - 67/22*a^8 + 7/2*a^7 + 24*a^6 + 37/22*a^5 - 1151/22*a^4 - 94/11*a^3 + 785/22*a^2 - 32/11*a - 7/2)*q^10 + (15/22*a^9 + 47/22*a^8 - 7*a^7 - 43/2*a^6 + 571/22*a^5 + 742/11*a^4 - 965/22*a^3 - 732/11*a^2 + 577/22*a + 5)*q^11 + (-7/22*a^9 - 19/22*a^8 + 3*a^7 + 15/2*a^6 - 221/22*a^5 - 215/11*a^4 + 355/22*a^3 + 181/11*a^2 - 237/22*a - 1)*q^12 + (-7/22*a^9 - 19/22*a^8 + 4*a^7 + 19/2*a^6 - 397/22*a^5 - 347/11*a^4 + 751/22*a^3 + 324/11*a^2 - 501/22*a - 1)*q^13 + (19/22*a^9 + 36/11*a^8 - 11/2*a^7 - 55/2*a^6 + 76/11*a^5 + 1483/22*a^4 - 71/22*a^3 - 1179/22*a^2 + 131/22*a + 9/2)*q^14 + (-9/11*a^9 - 63/22*a^8 + 15/2*a^7 + 29*a^6 - 485/22*a^5 - 2025/22*a^4 + 293/11*a^3 + 2045/22*a^2 - 157/11*a - 23/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 - q^17 + (9/11*a^9 + 63/22*a^8 - 17/2*a^7 - 31*a^6 + 661/22*a^5 + 2311/22*a^4 - 469/11*a^3 - 2419/22*a^2 + 223/11*a + 23/2)*q^18 + (a^7 + 3*a^6 - 7*a^5 - 22*a^4 + 12*a^3 + 39*a^2 - 6*a - 12)*q^19 + (-1/22*a^9 - 9/22*a^8 + 9/2*a^6 + 47/22*a^5 - 180/11*a^4 - 141/22*a^3 + 216/11*a^2 + 117/22*a - 4)*q^20 + (14/11*a^9 + 49/11*a^8 - 11*a^7 - 43*a^6 + 332/11*a^5 + 1421/11*a^4 - 391/11*a^3 - 1362/11*a^2 + 210/11*a + 11)*q^21 + (-14/11*a^9 - 109/22*a^8 + 17/2*a^7 + 43*a^6 - 301/22*a^5 - 2435/22*a^4 + 138/11*a^3 + 1987/22*a^2 - 155/11*a - 15/2)*q^22 + (-9/22*a^9 - 13/11*a^8 + 11/2*a^7 + 31/2*a^6 - 256/11*a^5 - 1359/22*a^4 + 689/22*a^3 + 1567/22*a^2 - 135/22*a - 19/2)*q^23 + (10/11*a^9 + 59/22*a^8 - 19/2*a^7 - 28*a^6 + 721/22*a^5 + 2019/22*a^4 - 471/11*a^3 - 2073/22*a^2 + 205/11*a + 17/2)*q^24 + (-15/22*a^9 - 47/22*a^8 + 7*a^7 + 43/2*a^6 - 571/22*a^5 - 753/11*a^4 + 943/22*a^3 + 798/11*a^2 - 489/22*a - 10)*q^25 + (8/11*a^9 + 67/22*a^8 - 9/2*a^7 - 26*a^6 + 139/22*a^5 + 1437/22*a^4 - 82/11*a^3 - 1159/22*a^2 + 87/11*a + 7/2)*q^26 + (21/11*a^9 + 169/22*a^8 - 25/2*a^7 - 68*a^6 + 391/22*a^5 + 4021/22*a^4 - 97/11*a^3 - 3613/22*a^2 + 95/11*a + 35/2)*q^27 + (-5/22*a^9 - 6/11*a^8 + 3/2*a^7 + 7/2*a^6 - 9/11*a^5 - 95/22*a^4 - 177/22*a^3 - 29/22*a^2 + 233/22*a + 3/2)*q^28 - q^29 + (27/22*a^9 + 111/22*a^8 - 7*a^7 - 85/2*a^6 + 117/22*a^5 + 1175/11*a^4 - 43/22*a^3 - 1003/11*a^2 + 251/22*a + 9)*q^30 + (1/22*a^9 + 9/22*a^8 + a^7 - 1/2*a^6 - 135/22*a^5 - 117/11*a^4 - 35/22*a^3 + 202/11*a^2 + 367/22*a - 4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-35/22*a^9 - 139/22*a^8 + 11*a^7 + 113/2*a^6 - 445/22*a^5 - 1680/11*a^4 + 543/22*a^3 + 1455/11*a^2 - 591/22*a - 8)*q^33 - a*q^34 + (a^9 + 4*a^8 - 7*a^7 - 36*a^6 + 14*a^5 + 100*a^4 - 19*a^3 - 95*a^2 + 17*a + 11)*q^35 + (19/22*a^9 + 61/22*a^8 - 7*a^7 - 49/2*a^6 + 383/22*a^5 + 725/11*a^4 - 445/22*a^3 - 661/11*a^2 + 263/22*a + 9)*q^36 + (6/11*a^9 + 21/11*a^8 - 4*a^7 - 16*a^6 + 103/11*a^5 + 433/11*a^4 - 166/11*a^3 - 337/11*a^2 + 123/11*a - 1)*q^37 + O(q^38)
*]> ;  // time = 97.359 seconds




J[494] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 494, 494, 494, 494, 494, 494, 494, 494, 247, 247, 247, 247, 247, 38, 38, 26, 26, 19 ], new_dimensions := [ 1, 1, 1, 1, 3, 3, 3, 4, 2, 3, 4, 5, 5, 1, 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 1, 3, 3, 3, 4, 4, 6, 8, 10, 10, 2, 2, 2, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 17, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 19, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 3, 1, 1, 1, 1, 17, 19, 1, 0, 1, 1, 1, 1, 1, 1, 449, 1, 19, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 11, 1, 1, 1, 31, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 113, 1, 1, 1, 13, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 51, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 11, 1, 1, 0, 1, 1, 1, 961, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 51, 1, 0, 1, 1, 1, 3, 1, 3, 1, 9, 5, 1, 1, 1, 1, 1, 113, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 449, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 7, 25, 1, 1, 1, 13, 1, 31, 1, 1, 961, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 3, 1, 9, 1, 1, 1, 3, 1, 1, 13, 1, 5, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 3, 1, 1, 1, 3, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 7, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 9, 1, 25, 1, 9, 1, 3, 1, 0 ], ap_traces := [
[ -1, -1, 1, -1, 0, -1, -3, -1, 6, -8, -8, -5 ],
[ -1, 0, 2, 4, 4, -1, 2, 1, -8, 2, 0, 10 ],
[ -1, 3, -3, 3, 0, -1, 5, 1, 6, -8, 8, -5 ],
[ 1, -1, -1, -3, -4, 1, -3, -1, 2, 4, -8, 1 ],
[ -3, -3, 3, -6, -3, -3, 3, 3, 3, -3, 3, -12 ],
[ -3, -1, 1, 2, -1, 3, -5, -3, -1, 7, 19, 20 ],
[ 3, 5, 5, -2, -1, -3, -5, -3, -1, 5, 9, -12 ],
[ 4, 2, 2, 7, 1, 4, -8, 4, 5, -5, 9, 5 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^3 + 3*x^2 - 6*x - 17,
x^3 + x^2 - 6*x - 7,
x^3 - 5*x^2 + 6*x - 1,
x^4 - 2*x^3 - 5*x^2 + 7*x + 5
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ 1, 1, -1 ],
[ -1, -1, 1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 5, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 13, 3, 1 ],
[ 449, 19, 1 ],
[ 341, 1, 11 ],
[ 113, 13, 13 ],
[ 459, 3, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 13, 3, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 113, 1, 1 ],
[ 459, 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 1, 9 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 1, 0, 1, 1, 113, 17 ], analytic_sha_upper_bounds := [ 0, 1, 1, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 0, 1, 1, 1, 1/81 ], eigenvalues := [*
[ -1, -1, 1, -1, 0, -1, -3, -1, 6, -8, -8, -5 ],
[ -1, 0, 2, 4, 4, -1, 2, 1, -8, 2, 0, 10 ],
[ -1, 3, -3, 3, 0, -1, 5, 1, 6, -8, 8, -5 ],
[ 1, -1, -1, -3, -4, 1, -3, -1, 2, 4, -8, 1 ],
[
-1,
a,
5/3*a^2 + 4/3*a - 28/3,
2/3*a^2 - 2/3*a - 22/3,
1/3*a^2 + 5/3*a - 5/3,
-1,
a + 2,
1,
7/3*a^2 + 5/3*a - 41/3,
1/3*a^2 - 1/3*a - 11/3,
5/3*a^2 - 2/3*a - 34/3,
4/3*a^2 + 2/3*a - 38/3
],
[
-1,
a,
a^2 - 4,
-2*a^2 + 2*a + 10,
a^2 - a - 5,
1,
-a - 2,
-1,
-3*a^2 + a + 13,
a^2 - 3*a - 3,
-a^2 - 2*a + 10,
-2*a + 6
],
[
1,
a,
a^2 - 4*a + 4,
-2*a^2 + 6*a - 2,
a^2 - 7*a + 7,
-1,
-4*a^2 + 13*a - 6,
-1,
a^2 - a - 3,
3*a^2 - 11*a + 7,
a^2 - 2*a + 2,
-4*a^2 + 14*a - 10
],
[
1,
a,
-a^2 + 4,
a^3 - a^2 - 4*a + 3,
-a^3 + 2*a^2 + 3*a - 4,
1,
-2*a^3 + 2*a^2 + 7*a - 4,
1,
-a^3 + 3*a + 4,
a^3 + 2*a^2 - 5*a - 10,
a^3 + 2*a^2 - 8*a - 5,
-a^3 - a^2 + 8*a + 5
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + q^5 + q^6 - q^7 - q^8 - 2*q^9 - q^10 - q^12 - q^13 + q^14 - q^15 + q^16 - 3*q^17 + 2*q^18 - q^19 + q^20 + q^21 + 6*q^23 + q^24 - 4*q^25 + q^26 + 5*q^27 - q^28 - 8*q^29 + q^30 - 8*q^31 - q^32 + 3*q^34 - q^35 - 2*q^36 - 5*q^37 + O(q^38),
q - q^2 + q^4 + 2*q^5 + 4*q^7 - q^8 - 3*q^9 - 2*q^10 + 4*q^11 - q^13 - 4*q^14 + q^16 + 2*q^17 + 3*q^18 + q^19 + 2*q^20 - 4*q^22 - 8*q^23 - q^25 + q^26 + 4*q^28 + 2*q^29 - q^32 - 2*q^34 + 8*q^35 - 3*q^36 + 10*q^37 + O(q^38),
q - q^2 + 3*q^3 + q^4 - 3*q^5 - 3*q^6 + 3*q^7 - q^8 + 6*q^9 + 3*q^10 + 3*q^12 - q^13 - 3*q^14 - 9*q^15 + q^16 + 5*q^17 - 6*q^18 + q^19 - 3*q^20 + 9*q^21 + 6*q^23 - 3*q^24 + 4*q^25 + q^26 + 9*q^27 + 3*q^28 - 8*q^29 + 9*q^30 + 8*q^31 - q^32 - 5*q^34 - 9*q^35 + 6*q^36 - 5*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - q^5 - q^6 - 3*q^7 + q^8 - 2*q^9 - q^10 - 4*q^11 - q^12 + q^13 - 3*q^14 + q^15 + q^16 - 3*q^17 - 2*q^18 - q^19 - q^20 + 3*q^21 - 4*q^22 + 2*q^23 - q^24 - 4*q^25 + q^26 + 5*q^27 - 3*q^28 + 4*q^29 + q^30 - 8*q^31 + q^32 + 4*q^33 - 3*q^34 + 3*q^35 - 2*q^36 + q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (5/3*a^2 + 4/3*a - 28/3)*q^5 - a*q^6 + (2/3*a^2 - 2/3*a - 22/3)*q^7 - q^8 + (a^2 - 3)*q^9 + (-5/3*a^2 - 4/3*a + 28/3)*q^10 + (1/3*a^2 + 5/3*a - 5/3)*q^11 + a*q^12 - q^13 + (-2/3*a^2 + 2/3*a + 22/3)*q^14 + (-11/3*a^2 + 2/3*a + 85/3)*q^15 + q^16 + (a + 2)*q^17 + (-a^2 + 3)*q^18 + q^19 + (5/3*a^2 + 4/3*a - 28/3)*q^20 + (-8/3*a^2 - 10/3*a + 34/3)*q^21 + (-1/3*a^2 - 5/3*a + 5/3)*q^22 + (7/3*a^2 + 5/3*a - 41/3)*q^23 - a*q^24 + (-a^2 - a + 16)*q^25 + q^26 + (-3*a^2 + 17)*q^27 + (2/3*a^2 - 2/3*a - 22/3)*q^28 + (1/3*a^2 - 1/3*a - 11/3)*q^29 + (11/3*a^2 - 2/3*a - 85/3)*q^30 + (5/3*a^2 - 2/3*a - 34/3)*q^31 - q^32 + (2/3*a^2 + 1/3*a + 17/3)*q^33 + (-a - 2)*q^34 + (-2*a^2 - 6*a + 8)*q^35 + (a^2 - 3)*q^36 + (4/3*a^2 + 2/3*a - 38/3)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (a^2 - 4)*q^5 - a*q^6 + (-2*a^2 + 2*a + 10)*q^7 - q^8 + (a^2 - 3)*q^9 + (-a^2 + 4)*q^10 + (a^2 - a - 5)*q^11 + a*q^12 + q^13 + (2*a^2 - 2*a - 10)*q^14 + (-a^2 + 2*a + 7)*q^15 + q^16 + (-a - 2)*q^17 + (-a^2 + 3)*q^18 - q^19 + (a^2 - 4)*q^20 + (4*a^2 - 2*a - 14)*q^21 + (-a^2 + a + 5)*q^22 + (-3*a^2 + a + 13)*q^23 - a*q^24 + (-a^2 + a + 4)*q^25 - q^26 + (-a^2 + 7)*q^27 + (-2*a^2 + 2*a + 10)*q^28 + (a^2 - 3*a - 3)*q^29 + (a^2 - 2*a - 7)*q^30 + (-a^2 - 2*a + 10)*q^31 - q^32 + (-2*a^2 + a + 7)*q^33 + (a + 2)*q^34 + (2*a^2 + 2*a - 12)*q^35 + (a^2 - 3)*q^36 + (-2*a + 6)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (a^2 - 4*a + 4)*q^5 + a*q^6 + (-2*a^2 + 6*a - 2)*q^7 + q^8 + (a^2 - 3)*q^9 + (a^2 - 4*a + 4)*q^10 + (a^2 - 7*a + 7)*q^11 + a*q^12 - q^13 + (-2*a^2 + 6*a - 2)*q^14 + (a^2 - 2*a + 1)*q^15 + q^16 + (-4*a^2 + 13*a - 6)*q^17 + (a^2 - 3)*q^18 - q^19 + (a^2 - 4*a + 4)*q^20 + (-4*a^2 + 10*a - 2)*q^21 + (a^2 - 7*a + 7)*q^22 + (a^2 - a - 3)*q^23 + a*q^24 + (3*a^2 - 13*a + 8)*q^25 - q^26 + (5*a^2 - 12*a + 1)*q^27 + (-2*a^2 + 6*a - 2)*q^28 + (3*a^2 - 11*a + 7)*q^29 + (a^2 - 2*a + 1)*q^30 + (a^2 - 2*a + 2)*q^31 + q^32 + (-2*a^2 + a + 1)*q^33 + (-4*a^2 + 13*a - 6)*q^34 + (-2*a^2 + 6*a - 4)*q^35 + (a^2 - 3)*q^36 + (-4*a^2 + 14*a - 10)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a^2 + 4)*q^5 + a*q^6 + (a^3 - a^2 - 4*a + 3)*q^7 + q^8 + (a^2 - 3)*q^9 + (-a^2 + 4)*q^10 + (-a^3 + 2*a^2 + 3*a - 4)*q^11 + a*q^12 + q^13 + (a^3 - a^2 - 4*a + 3)*q^14 + (-a^3 + 4*a)*q^15 + q^16 + (-2*a^3 + 2*a^2 + 7*a - 4)*q^17 + (a^2 - 3)*q^18 + q^19 + (-a^2 + 4)*q^20 + (a^3 + a^2 - 4*a - 5)*q^21 + (-a^3 + 2*a^2 + 3*a - 4)*q^22 + (-a^3 + 3*a + 4)*q^23 + a*q^24 + (2*a^3 - 3*a^2 - 7*a + 6)*q^25 + q^26 + (a^3 - 6*a)*q^27 + (a^3 - a^2 - 4*a + 3)*q^28 + (a^3 + 2*a^2 - 5*a - 10)*q^29 + (-a^3 + 4*a)*q^30 + (a^3 + 2*a^2 - 8*a - 5)*q^31 + q^32 + (-2*a^2 + 3*a + 5)*q^33 + (-2*a^3 + 2*a^2 + 7*a - 4)*q^34 + (a^3 - 5*a^2 - 4*a + 17)*q^35 + (a^2 - 3)*q^36 + (-a^3 - a^2 + 8*a + 5)*q^37 + O(q^38)
*]> ;  // time = 271.281 seconds




J[497] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 497, 497, 497, 497, 497, 71, 71 ], new_dimensions := [ 1, 2, 8, 9, 15, 3, 3 ], dimensions := [ 1, 2, 8, 9, 15, 6, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 5, 1, 0, 1, 1, 1, 7, 1, 1, 1, 0, 1, 1, 61, 61, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 61, 1, 1, 0, 81, 5, 1, 61, 1, 1, 81, 0 ], ap_traces := [
[ 1, -1, 0, 1, 1, -3, -2, -4, -9, -1, 4, -3 ],
[ -2, -2, 0, 2, -2, -2, 0, 4, -2, -2, -16, -6 ],
[ 0, 5, 2, -8, -1, 9, 4, 6, 17, -5, 20, 1 ],
[ -2, -7, -4, -9, 1, -15, -8, -14, -9, -1, -22, -7 ],
[ 2, 5, 0, 15, 5, 5, -8, 0, 19, -5, 10, 17 ]
], hecke_fields := [
x - 1,
x^2 - 4*x - 14,
x^8 - 12*x^6 + 42*x^4 + 4*x^3 - 44*x^2 - 8*x + 1,
x^9 + 2*x^8 - 9*x^7 - 16*x^6 + 26*x^5 + 36*x^4 - 28*x^3 - 19*x^2 + 10*x + 1,
x^15 - 2*x^14 - 24*x^13 + 46*x^12 + 224*x^11 - 406*x^10 - 1026*x^9 + 1731*x^8 + 2373*x^7 - 3662*x^6 - 2504*x^5 + 3488*x^4 + 818*x^3 - 1062*x^2 - 54*x + 27
], atkin_lehners := [
[ -1, -1 ],
[ -1, -1 ],
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 7, 1 ],
[ 3721, 1 ],
[ 1, 1 ],
[ 9, 3 ]
], tamagawa_numbers := [
[ 5, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 9, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 27 ], torsion_lower_bounds := [ 1, 1, 1, 1, 9 ], l_ratios := [ 0, 0, 1, 0, 1/9 ], analytic_sha_upper_bounds := [ 0, 0, 1, 0, 9 ], analytic_sha_lower_bounds := [ 0, 0, 1, 0, 1 ], eigenvalues := [*
[ 1, -1, 0, 1, 1, -3, -2, -4, -9, -1, 4, -3 ],
[
-1,
-1/3*a - 1/3,
0,
1,
-1,
a - 3,
2/3*a - 4/3,
-4/3*a + 14/3,
-2/3*a + 1/3,
4/3*a - 11/3,
2/3*a - 28/3,
-3
],
[
a,
1/4*a^7 - 1/4*a^6 - 11/4*a^5 + 9/4*a^4 + 31/4*a^3 - 11/4*a^2 - 21/4*a - 5/4,
1/2*a^7 - 11/2*a^5 + 33/2*a^3 + 2*a^2 - 27/2*a - 2,
-1,
3/4*a^7 - 1/4*a^6 - 33/4*a^5 + 11/4*a^4 + 97/4*a^3 - 19/4*a^2 - 75/4*a + 1/4,
-1/4*a^7 - 1/4*a^6 + 13/4*a^5 + 11/4*a^4 - 51/4*a^3 - 31/4*a^2 + 59/4*a + 17/4,
1/2*a^7 - 1/2*a^6 - 6*a^5 + 5*a^4 + 41/2*a^3 - 19/2*a^2 - 22*a,
1/2*a^5 + 1/2*a^4 - 4*a^3 - 3*a^2 + 9/2*a + 7/2,
1/4*a^7 + 1/4*a^6 - 15/4*a^5 - 11/4*a^4 + 67/4*a^3 + 31/4*a^2 - 81/4*a - 9/4,
3/4*a^7 - 1/4*a^6 - 37/4*a^5 + 11/4*a^4 + 133/4*a^3 - 23/4*a^2 - 143/4*a + 1/4,
-a^7 + 1/2*a^6 + 11*a^5 - 11/2*a^4 - 32*a^3 + 23/2*a^2 + 24*a - 1/2,
1/4*a^7 + 1/4*a^6 - 15/4*a^5 - 11/4*a^4 + 71/4*a^3 + 35/4*a^2 - 109/4*a - 29/4
],
[
a,
-1/2*a^8 - 3/2*a^7 + 4*a^6 + 12*a^5 - 10*a^4 - 26*a^3 + 9*a^2 + 21/2*a - 5/2,
a^8 + 2*a^7 - 8*a^6 - 15*a^5 + 18*a^4 + 30*a^3 - 11*a^2 - 11*a + 2,
-1,
-a^6 - a^5 + 7*a^4 + 5*a^3 - 11*a^2 - 5*a + 1,
3/2*a^8 + 5/2*a^7 - 12*a^6 - 18*a^5 + 25*a^4 + 35*a^3 - 7*a^2 - 31/2*a - 5/2,
-a^8 + 10*a^6 - 2*a^5 - 30*a^4 + 8*a^3 + 26*a^2 - 3*a - 4,
-2*a^8 - 4*a^7 + 15*a^6 + 30*a^5 - 26*a^4 - 62*a^3 - 4*a^2 + 29*a + 2,
a^8 - 9*a^6 + 3*a^5 + 21*a^4 - 15*a^3 - 5*a^2 + 14*a - 5,
-3*a^8 - 7*a^7 + 23*a^6 + 55*a^5 - 44*a^4 - 118*a^3 + 7*a^2 + 50*a,
-2*a^8 - 6*a^7 + 14*a^6 + 48*a^5 - 22*a^4 - 106*a^3 - 4*a^2 + 50*a,
2*a^8 + 8*a^7 - 12*a^6 - 65*a^5 + 9*a^4 + 145*a^3 + 25*a^2 - 64*a - 7
],
[
a,
-433/36186*a^14 - 383/72372*a^13 + 2199/6031*a^12 + 7771/72372*a^11 - 2116/489*a^10 - 56773/72372*a^9 + 304817/12062*a^8 + 61935/24124*a^7 - 1808897/24124*a^6 - 161119/36186*a^5 + 7457797/72372*a^4 + 130151/18093*a^3 - 3456883/72372*a^2 - 85085/12062*a + 87343/24124,
-4051/36186*a^14 + 4121/36186*a^13 + 16311/6031*a^12 - 44429/18093*a^11 - 24983/978*a^10 + 705535/36186*a^9 + 721195/6031*a^8 - 836063/12062*a^7 - 3479137/12062*a^6 + 1872493/18093*a^5 + 5996392/18093*a^4 - 1517627/36186*a^3 - 4765871/36186*a^2 - 22552/6031*a + 30228/6031,
1,
-2049/24124*a^14 + 1765/12062*a^13 + 49663/24124*a^12 - 18575/6031*a^11 - 12625/652*a^10 + 286447/12062*a^9 + 2148733/24124*a^8 - 1963813/24124*a^7 - 1245778/6031*a^6 + 2815609/24124*a^5 + 1341876/6031*a^4 - 1094923/24124*a^3 - 983403/12062*a^2 - 148693/24124*a + 20022/6031,
-11269/72372*a^14 + 7735/36186*a^13 + 97481/24124*a^12 - 85675/18093*a^11 - 80699/1956*a^10 + 714844/18093*a^9 + 5042117/24124*a^8 - 3721257/24124*a^7 - 3255180/6031*a^6 + 20381369/72372*a^5 + 11573540/18093*a^4 - 14590109/72372*a^3 - 4218059/18093*a^2 + 733715/24124*a + 63571/12062,
2230/18093*a^14 - 2273/18093*a^13 - 38183/12062*a^12 + 47347/18093*a^11 + 15689/489*a^10 - 357151/18093*a^9 - 1957317/12062*a^8 + 384432/6031*a^7 + 2547206/6031*a^6 - 2599897/36186*a^5 - 9265727/18093*a^4 - 333478/18093*a^3 + 3560603/18093*a^2 + 424683/12062*a - 12324/6031,
-18/6031*a^14 + 583/12062*a^13 + 3813/12062*a^12 - 14065/12062*a^11 - 945/163*a^10 + 129723/12062*a^9 + 514007/12062*a^8 - 565611/12062*a^7 - 1721069/12062*a^6 + 1162343/12062*a^5 + 2405873/12062*a^4 - 470712/6031*a^3 - 849359/12062*a^2 + 203457/12062*a - 11741/12062,
-4171/36186*a^14 + 2077/72372*a^13 + 16419/6031*a^12 - 44315/72372*a^11 - 24437/978*a^10 + 352001/72372*a^9 + 678400/6031*a^8 - 442257/24124*a^7 - 6170497/24124*a^6 + 1228613/36186*a^5 + 19155451/72372*a^4 - 1025045/36186*a^3 - 6049129/72372*a^2 + 32180/6031*a + 71367/24124,
-182/6031*a^14 - 3623/24124*a^13 + 10409/12062*a^12 + 80785/24124*a^11 - 1568/163*a^10 - 683711/24124*a^9 + 632385/12062*a^8 + 2749011/24124*a^7 - 3450011/24124*a^6 - 1346503/6031*a^5 + 4206979/24124*a^4 + 1195186/6031*a^3 - 1571049/24124*a^2 - 773373/12062*a + 28605/24124,
43/18093*a^14 + 2963/36186*a^13 - 1361/12062*a^12 - 33626/18093*a^11 + 872/489*a^10 + 581689/36186*a^9 - 152761/12062*a^8 - 398844/6031*a^7 + 516871/12062*a^6 + 4763717/36186*a^5 - 1154009/18093*a^4 - 2069941/18093*a^3 + 1110637/36186*a^2 + 344927/12062*a + 19808/6031,
-475/18093*a^14 + 3965/72372*a^13 + 7741/12062*a^12 - 88291/72372*a^11 - 3014/489*a^10 + 702913/72372*a^9 + 356729/12062*a^8 - 753959/24124*a^7 - 1775113/24124*a^6 + 430016/18093*a^5 + 6093947/72372*a^4 + 832561/18093*a^3 - 1648001/72372*a^2 - 454199/12062*a + 4307/24124
]
*], q_expansions := [*
q + q^2 - q^3 - q^4 - q^6 + q^7 - 3*q^8 - 2*q^9 + q^11 + q^12 - 3*q^13 + q^14 - q^16 - 2*q^17 - 2*q^18 - 4*q^19 - q^21 + q^22 - 9*q^23 + 3*q^24 - 5*q^25 - 3*q^26 + 5*q^27 - q^28 - q^29 + 4*q^31 + 5*q^32 - q^33 - 2*q^34 + 2*q^36 - 3*q^37 + O(q^38),
q - q^2 + (-1/3*a - 1/3)*q^3 - q^4 + (1/3*a + 1/3)*q^6 + q^7 + 3*q^8 + (2/3*a - 4/3)*q^9 - q^11 + (1/3*a + 1/3)*q^12 + (a - 3)*q^13 - q^14 - q^16 + (2/3*a - 4/3)*q^17 + (-2/3*a + 4/3)*q^18 + (-4/3*a + 14/3)*q^19 + (-1/3*a - 1/3)*q^21 + q^22 + (-2/3*a + 1/3)*q^23 + (-a - 1)*q^24 - 5*q^25 + (-a + 3)*q^26 + (1/3*a - 5/3)*q^27 - q^28 + (4/3*a - 11/3)*q^29 + (2/3*a - 28/3)*q^31 - 5*q^32 + (1/3*a + 1/3)*q^33 + (-2/3*a + 4/3)*q^34 + (-2/3*a + 4/3)*q^36 - 3*q^37 + O(q^38),
q + a*q^2 + (1/4*a^7 - 1/4*a^6 - 11/4*a^5 + 9/4*a^4 + 31/4*a^3 - 11/4*a^2 - 21/4*a - 5/4)*q^3 + (a^2 - 2)*q^4 + (1/2*a^7 - 11/2*a^5 + 33/2*a^3 + 2*a^2 - 27/2*a - 2)*q^5 + (-1/4*a^7 + 1/4*a^6 + 9/4*a^5 - 11/4*a^4 - 15/4*a^3 + 23/4*a^2 + 3/4*a - 1/4)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-1/4*a^7 - 1/4*a^6 + 11/4*a^5 + 7/4*a^4 - 35/4*a^3 - 7/4*a^2 + 33/4*a - 3/4)*q^9 + (1/2*a^6 - 9/2*a^4 + 17/2*a^2 + 2*a - 1/2)*q^10 + (3/4*a^7 - 1/4*a^6 - 33/4*a^5 + 11/4*a^4 + 97/4*a^3 - 19/4*a^2 - 75/4*a + 1/4)*q^11 + (-1/4*a^7 - 1/4*a^6 + 11/4*a^5 + 9/4*a^4 - 35/4*a^3 - 19/4*a^2 + 33/4*a + 11/4)*q^12 + (-1/4*a^7 - 1/4*a^6 + 13/4*a^5 + 11/4*a^4 - 51/4*a^3 - 31/4*a^2 + 59/4*a + 17/4)*q^13 - a*q^14 + (a^5 - 9*a^3 + 16*a + 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/2*a^7 - 1/2*a^6 - 6*a^5 + 5*a^4 + 41/2*a^3 - 19/2*a^2 - 22*a)*q^17 + (-1/4*a^7 - 1/4*a^6 + 7/4*a^5 + 7/4*a^4 - 3/4*a^3 - 11/4*a^2 - 11/4*a + 1/4)*q^18 + (1/2*a^5 + 1/2*a^4 - 4*a^3 - 3*a^2 + 9/2*a + 7/2)*q^19 + (-1/2*a^7 + 13/2*a^5 - 49/2*a^3 - 2*a^2 + 53/2*a + 4)*q^20 + (-1/4*a^7 + 1/4*a^6 + 11/4*a^5 - 9/4*a^4 - 31/4*a^3 + 11/4*a^2 + 21/4*a + 5/4)*q^21 + (-1/4*a^7 + 3/4*a^6 + 11/4*a^5 - 29/4*a^4 - 31/4*a^3 + 57/4*a^2 + 25/4*a - 3/4)*q^22 + (1/4*a^7 + 1/4*a^6 - 15/4*a^5 - 11/4*a^4 + 67/4*a^3 + 31/4*a^2 - 81/4*a - 9/4)*q^23 + (1/4*a^7 - 3/4*a^6 - 9/4*a^5 + 29/4*a^4 + 15/4*a^3 - 57/4*a^2 - 3/4*a + 3/4)*q^24 + (a^5 - 10*a^3 + 21*a + 3)*q^25 + (-1/4*a^7 + 1/4*a^6 + 11/4*a^5 - 9/4*a^4 - 27/4*a^3 + 15/4*a^2 + 9/4*a + 1/4)*q^26 + (-3/4*a^7 - 1/4*a^6 + 31/4*a^5 + 7/4*a^4 - 81/4*a^3 - 19/4*a^2 + 49/4*a + 17/4)*q^27 + (-a^2 + 2)*q^28 + (3/4*a^7 - 1/4*a^6 - 37/4*a^5 + 11/4*a^4 + 133/4*a^3 - 23/4*a^2 - 143/4*a + 1/4)*q^29 + (a^6 - 9*a^4 + 16*a^2 + 4*a)*q^30 + (-a^7 + 1/2*a^6 + 11*a^5 - 11/2*a^4 - 32*a^3 + 23/2*a^2 + 24*a - 1/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-1/4*a^7 + 3/4*a^6 + 13/4*a^5 - 29/4*a^4 - 47/4*a^3 + 57/4*a^2 + 47/4*a + 5/4)*q^33 + (-1/2*a^7 + 5*a^5 - 1/2*a^4 - 23/2*a^3 + 4*a - 1/2)*q^34 + (-1/2*a^7 + 11/2*a^5 - 33/2*a^3 - 2*a^2 + 27/2*a + 2)*q^35 + (1/4*a^7 - 3/4*a^6 - 15/4*a^5 + 25/4*a^4 + 63/4*a^3 - 41/4*a^2 - 73/4*a + 7/4)*q^36 + (1/4*a^7 + 1/4*a^6 - 15/4*a^5 - 11/4*a^4 + 71/4*a^3 + 35/4*a^2 - 109/4*a - 29/4)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^8 - 3/2*a^7 + 4*a^6 + 12*a^5 - 10*a^4 - 26*a^3 + 9*a^2 + 21/2*a - 5/2)*q^3 + (a^2 - 2)*q^4 + (a^8 + 2*a^7 - 8*a^6 - 15*a^5 + 18*a^4 + 30*a^3 - 11*a^2 - 11*a + 2)*q^5 + (-1/2*a^8 - 1/2*a^7 + 4*a^6 + 3*a^5 - 8*a^4 - 5*a^3 + a^2 + 5/2*a + 1/2)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (a^7 - 9*a^5 + 3*a^4 + 23*a^3 - 13*a^2 - 14*a + 7)*q^9 + (a^7 + a^6 - 8*a^5 - 6*a^4 + 17*a^3 + 8*a^2 - 8*a - 1)*q^10 + (-a^6 - a^5 + 7*a^4 + 5*a^3 - 11*a^2 - 5*a + 1)*q^11 + (3/2*a^8 + 5/2*a^7 - 13*a^6 - 19*a^5 + 33*a^4 + 39*a^3 - 25*a^2 - 31/2*a + 11/2)*q^12 + (3/2*a^8 + 5/2*a^7 - 12*a^6 - 18*a^5 + 25*a^4 + 35*a^3 - 7*a^2 - 31/2*a - 5/2)*q^13 - a*q^14 + (-a^8 - a^7 + 9*a^6 + 7*a^5 - 24*a^4 - 14*a^3 + 21*a^2 + 8*a - 9)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^8 + 10*a^6 - 2*a^5 - 30*a^4 + 8*a^3 + 26*a^2 - 3*a - 4)*q^17 + (a^8 - 9*a^6 + 3*a^5 + 23*a^4 - 13*a^3 - 14*a^2 + 7*a)*q^18 + (-2*a^8 - 4*a^7 + 15*a^6 + 30*a^5 - 26*a^4 - 62*a^3 - 4*a^2 + 29*a + 2)*q^19 + (-a^8 - 3*a^7 + 8*a^6 + 24*a^5 - 19*a^4 - 52*a^3 + 14*a^2 + 21*a - 4)*q^20 + (1/2*a^8 + 3/2*a^7 - 4*a^6 - 12*a^5 + 10*a^4 + 26*a^3 - 9*a^2 - 21/2*a + 5/2)*q^21 + (-a^7 - a^6 + 7*a^5 + 5*a^4 - 11*a^3 - 5*a^2 + a)*q^22 + (a^8 - 9*a^6 + 3*a^5 + 21*a^4 - 15*a^3 - 5*a^2 + 14*a - 5)*q^23 + (1/2*a^8 + 3/2*a^7 - 3*a^6 - 12*a^5 + a^4 + 27*a^3 + 11*a^2 - 29/2*a - 5/2)*q^24 + (a^7 - 10*a^5 + a^4 + 27*a^3 - 4*a^2 - 14*a + 2)*q^25 + (-1/2*a^8 + 3/2*a^7 + 6*a^6 - 14*a^5 - 19*a^4 + 35*a^3 + 13*a^2 - 35/2*a - 3/2)*q^26 + (1/2*a^8 + 3/2*a^7 - 2*a^6 - 11*a^5 - 8*a^4 + 20*a^3 + 34*a^2 - 5/2*a - 35/2)*q^27 + (-a^2 + 2)*q^28 + (-3*a^8 - 7*a^7 + 23*a^6 + 55*a^5 - 44*a^4 - 118*a^3 + 7*a^2 + 50*a)*q^29 + (a^8 - 9*a^6 + 2*a^5 + 22*a^4 - 7*a^3 - 11*a^2 + a + 1)*q^30 + (-2*a^8 - 6*a^7 + 14*a^6 + 48*a^5 - 22*a^4 - 106*a^3 - 4*a^2 + 50*a)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (5/2*a^8 + 7/2*a^7 - 20*a^6 - 24*a^5 + 41*a^4 + 43*a^3 - 9*a^2 - 25/2*a - 11/2)*q^33 + (2*a^8 + a^7 - 18*a^6 - 4*a^5 + 44*a^4 - 2*a^3 - 22*a^2 + 6*a + 1)*q^34 + (-a^8 - 2*a^7 + 8*a^6 + 15*a^5 - 18*a^4 - 30*a^3 + 11*a^2 + 11*a - 2)*q^35 + (-2*a^8 - 2*a^7 + 19*a^6 + 15*a^5 - 55*a^4 - 32*a^3 + 52*a^2 + 18*a - 15)*q^36 + (2*a^8 + 8*a^7 - 12*a^6 - 65*a^5 + 9*a^4 + 145*a^3 + 25*a^2 - 64*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-433/36186*a^14 - 383/72372*a^13 + 2199/6031*a^12 + 7771/72372*a^11 - 2116/489*a^10 - 56773/72372*a^9 + 304817/12062*a^8 + 61935/24124*a^7 - 1808897/24124*a^6 - 161119/36186*a^5 + 7457797/72372*a^4 + 130151/18093*a^3 - 3456883/72372*a^2 - 85085/12062*a + 87343/24124)*q^3 + (a^2 - 2)*q^4 + (-4051/36186*a^14 + 4121/36186*a^13 + 16311/6031*a^12 - 44429/18093*a^11 - 24983/978*a^10 + 705535/36186*a^9 + 721195/6031*a^8 - 836063/12062*a^7 - 3479137/12062*a^6 + 1872493/18093*a^5 + 5996392/18093*a^4 - 1517627/36186*a^3 - 4765871/36186*a^2 - 22552/6031*a + 30228/6031)*q^5 + (-705/24124*a^14 + 467/6031*a^13 + 15869/24124*a^12 - 9932/6031*a^11 - 3679/652*a^10 + 156731/12062*a^9 + 561617/24124*a^8 - 1123891/24124*a^7 - 582255/12062*a^6 + 1763111/24124*a^5 + 295101/6031*a^4 - 916165/24124*a^3 - 238367/12062*a^2 + 71755/24124*a + 3897/12062)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (13937/72372*a^14 - 4450/18093*a^13 - 111933/24124*a^12 + 195649/36186*a^11 + 85153/1956*a^10 - 805937/18093*a^9 - 4845939/24124*a^8 + 4108781/24124*a^7 + 5671277/12062*a^6 - 21672421/72372*a^5 - 18355499/36186*a^4 + 14541211/72372*a^3 + 3102337/18093*a^2 - 636857/24124*a - 7561/12062)*q^9 + (-1327/12062*a^14 + 107/6031*a^13 + 16248/6031*a^12 - 5649/12062*a^11 - 8461/326*a^10 + 28474/6031*a^9 + 750682/6031*a^8 - 137398/6031*a^7 - 1848296/6031*a^6 + 308180/6031*a^5 + 4204087/12062*a^4 - 484051/12062*a^3 - 739579/6031*a^2 - 6231/6031*a + 36459/12062)*q^10 + (-2049/24124*a^14 + 1765/12062*a^13 + 49663/24124*a^12 - 18575/6031*a^11 - 12625/652*a^10 + 286447/12062*a^9 + 2148733/24124*a^8 - 1963813/24124*a^7 - 1245778/6031*a^6 + 2815609/24124*a^5 + 1341876/6031*a^4 - 1094923/24124*a^3 - 983403/12062*a^2 - 148693/24124*a + 20022/6031)*q^11 + (1553/36186*a^14 - 2387/72372*a^13 - 12445/12062*a^12 + 49849/72372*a^11 + 4784/489*a^10 - 371593/72372*a^9 - 280701/6031*a^8 + 384585/24124*a^7 + 2799195/24124*a^6 - 277568/18093*a^5 - 10286969/72372*a^4 - 185335/18093*a^3 + 4882901/72372*a^2 + 77516/6031*a - 155651/24124)*q^12 + (-11269/72372*a^14 + 7735/36186*a^13 + 97481/24124*a^12 - 85675/18093*a^11 - 80699/1956*a^10 + 714844/18093*a^9 + 5042117/24124*a^8 - 3721257/24124*a^7 - 3255180/6031*a^6 + 20381369/72372*a^5 + 11573540/18093*a^4 - 14590109/72372*a^3 - 4218059/18093*a^2 + 733715/24124*a + 63571/12062)*q^13 + a*q^14 + (239/978*a^14 - 289/978*a^13 - 1995/326*a^12 + 6257/978*a^11 + 58795/978*a^10 - 50441/978*a^9 - 95427/326*a^8 + 31076/163*a^7 + 237421/326*a^6 - 308719/978*a^5 - 820165/978*a^4 + 177553/978*a^3 + 295411/978*a^2 - 1943/326*a - 1059/326)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2230/18093*a^14 - 2273/18093*a^13 - 38183/12062*a^12 + 47347/18093*a^11 + 15689/489*a^10 - 357151/18093*a^9 - 1957317/12062*a^8 + 384432/6031*a^7 + 2547206/6031*a^6 - 2599897/36186*a^5 - 9265727/18093*a^4 - 333478/18093*a^3 + 3560603/18093*a^2 + 424683/12062*a - 12324/6031)*q^17 + (1679/12062*a^14 - 437/24124*a^13 - 20817/6031*a^12 + 9591/24124*a^11 + 10967/326*a^10 - 79485/24124*a^9 - 983217/6031*a^8 + 318387/24124*a^7 + 9788291/24124*a^6 - 302125/12062*a^5 - 11357015/24124*a^4 + 168147/12062*a^3 + 4296841/24124*a^2 + 58936/6031*a - 125433/24124)*q^18 + (-18/6031*a^14 + 583/12062*a^13 + 3813/12062*a^12 - 14065/12062*a^11 - 945/163*a^10 + 129723/12062*a^9 + 514007/12062*a^8 - 565611/12062*a^7 - 1721069/12062*a^6 + 1162343/12062*a^5 + 2405873/12062*a^4 - 470712/6031*a^3 - 849359/12062*a^2 + 203457/12062*a - 11741/12062)*q^19 + (391/18093*a^14 - 3149/18093*a^13 - 9851/12062*a^12 + 130289/36186*a^11 + 5450/489*a^10 - 495742/18093*a^9 - 862539/12062*a^8 + 1124505/12062*a^7 + 1357580/6031*a^6 - 4846135/36186*a^5 - 11551993/36186*a^4 + 927119/18093*a^3 + 2633267/18093*a^2 + 55009/12062*a - 85083/12062)*q^20 + (-433/36186*a^14 - 383/72372*a^13 + 2199/6031*a^12 + 7771/72372*a^11 - 2116/489*a^10 - 56773/72372*a^9 + 304817/12062*a^8 + 61935/24124*a^7 - 1808897/24124*a^6 - 161119/36186*a^5 + 7457797/72372*a^4 + 130151/18093*a^3 - 3456883/72372*a^2 - 85085/12062*a + 87343/24124)*q^21 + (-142/6031*a^14 + 487/24124*a^13 + 9977/12062*a^12 - 8149/24124*a^11 - 1750/163*a^10 + 46459/24124*a^9 + 791503/12062*a^8 - 120835/24124*a^7 - 4687829/24124*a^6 + 59202/6031*a^5 + 6051989/24124*a^4 - 72681/6031*a^3 - 2324731/24124*a^2 - 15279/12062*a + 55323/24124)*q^22 + (-4171/36186*a^14 + 2077/72372*a^13 + 16419/6031*a^12 - 44315/72372*a^11 - 24437/978*a^10 + 352001/72372*a^9 + 678400/6031*a^8 - 442257/24124*a^7 - 6170497/24124*a^6 + 1228613/36186*a^5 + 19155451/72372*a^4 - 1025045/36186*a^3 - 6049129/72372*a^2 + 32180/6031*a + 71367/24124)*q^23 + (2685/24124*a^14 - 1889/12062*a^13 - 62747/24124*a^12 + 20888/6031*a^11 + 15371/652*a^10 - 171869/6031*a^9 - 2530811/24124*a^8 + 2590131/24124*a^7 + 1437580/6031*a^6 - 4362737/24124*a^5 - 1554791/6031*a^4 + 2613061/24124*a^3 + 590764/6031*a^2 - 243253/24124*a - 21771/12062)*q^24 + (136/6031*a^14 + 478/6031*a^13 - 4353/6031*a^12 - 9856/6031*a^11 + 1435/163*a^10 + 74839/6031*a^9 - 312094/6031*a^8 - 255544/6031*a^7 + 915770/6031*a^6 + 376767/6031*a^5 - 1233141/6031*a^4 - 186750/6031*a^3 + 575823/6031*a^2 + 11394/6031*a - 27347/6031)*q^25 + (-589/6031*a^14 + 7329/24124*a^13 + 29279/12062*a^12 - 153869/24124*a^11 - 7729/326*a^10 + 1188119/24124*a^9 + 695239/6031*a^8 - 4106941/24124*a^7 - 6961903/24124*a^6 + 1506382/6031*a^5 + 8238721/24124*a^4 - 1275699/12062*a^3 - 3255511/24124*a^2 - 18925/6031*a + 101421/24124)*q^26 + (-1505/6031*a^14 + 3675/24124*a^13 + 38282/6031*a^12 - 74943/24124*a^11 - 20779/326*a^10 + 539841/24124*a^9 + 3857285/12062*a^8 - 1552543/24124*a^7 - 19989737/24124*a^6 + 473349/12062*a^5 + 24374103/24124*a^4 + 1207295/12062*a^3 - 9865685/24124*a^2 - 1044543/12062*a + 371311/24124)*q^27 + (a^2 - 2)*q^28 + (-182/6031*a^14 - 3623/24124*a^13 + 10409/12062*a^12 + 80785/24124*a^11 - 1568/163*a^10 - 683711/24124*a^9 + 632385/12062*a^8 + 2749011/24124*a^7 - 3450011/24124*a^6 - 1346503/6031*a^5 + 4206979/24124*a^4 + 1195186/6031*a^3 - 1571049/24124*a^2 - 773373/12062*a + 28605/24124)*q^29 + (63/326*a^14 - 83/326*a^13 - 1579/326*a^12 + 1753/326*a^11 + 15531/326*a^10 - 13689/326*a^9 - 75751/326*a^8 + 24186/163*a^7 + 188833/326*a^6 - 73903/326*a^5 - 218693/326*a^4 + 33303/326*a^3 + 82663/326*a^2 + 3243/326*a - 2151/326)*q^30 + (43/18093*a^14 + 2963/36186*a^13 - 1361/12062*a^12 - 33626/18093*a^11 + 872/489*a^10 + 581689/36186*a^9 - 152761/12062*a^8 - 398844/6031*a^7 + 516871/12062*a^6 + 4763717/36186*a^5 - 1154009/18093*a^4 - 2069941/18093*a^3 + 1110637/36186*a^2 + 344927/12062*a + 19808/6031)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1187/12062*a^14 - 4605/24124*a^13 - 15870/6031*a^12 + 103607/24124*a^11 + 4549/163*a^10 - 876043/24124*a^9 - 1788867/12062*a^8 + 3433833/24124*a^7 + 9791559/24124*a^6 - 3066633/12062*a^5 - 12351615/24124*a^4 + 999783/6031*a^3 + 4593887/24124*a^2 - 213545/12062*a - 20163/24124)*q^33 + (729/6031*a^14 - 2503/12062*a^13 - 18411/6031*a^12 + 26991/6031*a^11 + 4939/163*a^10 - 431997/12062*a^9 - 902278/6031*a^8 + 783276/6031*a^7 + 4577541/12062*a^6 - 1227269/6031*a^5 - 2703906/6031*a^4 + 578821/6031*a^3 + 2003523/12062*a^2 + 27816/6031*a - 20070/6031)*q^34 + (-4051/36186*a^14 + 4121/36186*a^13 + 16311/6031*a^12 - 44429/18093*a^11 - 24983/978*a^10 + 705535/36186*a^9 + 721195/6031*a^8 - 836063/12062*a^7 - 3479137/12062*a^6 + 1872493/18093*a^5 + 5996392/18093*a^4 - 1517627/36186*a^3 - 4765871/36186*a^2 - 22552/6031*a + 30228/6031)*q^35 + (-9037/72372*a^14 + 6893/18093*a^13 + 78989/24124*a^12 - 302249/36186*a^11 - 66209/1956*a^10 + 1246204/18093*a^9 + 4197567/24124*a^8 - 6397805/24124*a^7 - 5496181/12062*a^6 + 34499093/72372*a^5 + 19646383/36186*a^4 - 24432431/72372*a^3 - 3353219/18093*a^2 + 1329613/24124*a - 30211/12062)*q^36 + (-475/18093*a^14 + 3965/72372*a^13 + 7741/12062*a^12 - 88291/72372*a^11 - 3014/489*a^10 + 702913/72372*a^9 + 356729/12062*a^8 - 753959/24124*a^7 - 1775113/24124*a^6 + 430016/18093*a^5 + 6093947/72372*a^4 + 832561/18093*a^3 - 1648001/72372*a^2 - 454199/12062*a + 4307/24124)*q^37 + O(q^38)
*]> ;  // time = 97.071 seconds




J[498] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 498, 498, 498, 498, 498, 498, 498, 249, 249, 249, 249, 249, 166, 166, 166, 83, 83 ], new_dimensions := [ 1, 1, 2, 2, 2, 3, 4, 1, 1, 2, 4, 5, 1, 2, 3, 1, 6 ], dimensions := [ 1, 1, 2, 2, 2, 3, 4, 2, 2, 4, 8, 10, 2, 4, 6, 4, 24 ], intersection_graph := [ 0, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 7, 1, 0, 1, 1, 1, 1, 1, 1, 1, 37, 1, 5, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 61, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 1, 1, 1, 1, 41, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 1, 961, 1, 1, 37, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 25, 1, 1, 1, 1, 1, 61, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 7349521, 1, 1, 5, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 17161, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 25, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 41, 1, 1, 961, 1, 7349521, 1, 17161, 1, 1, 0 ], ap_traces := [
[ -1, 1, 2, 4, 0, 0, -2, 0, -6, 0, -4, 10 ],
[ -1, 1, -1, -4, 3, -6, -4, -3, -1, 4, -2, 3 ],
[ -2, 2, -3, 1, 0, 7, 3, 7, 9, 0, 13, -8 ],
[ 2, -2, 3, 0, 1, 4, 6, 1, 1, 2, -2, 5 ],
[ 2, -2, -5, -3, -4, -7, -9, -3, -3, -8, 5, 8 ],
[ -3, -3, 0, -3, -3, -3, -9, 6, -18, -12, -9, -9 ],
[ 4, 4, 2, 1, -1, 7, 1, 0, -6, -4, -5, -3 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + 3*x - 3,
x^2 - 3*x - 2,
x^2 + 5*x + 5,
x^3 - 12*x - 7,
x^4 - 2*x^3 - 8*x^2 + 11*x + 14
], atkin_lehners := [
[ 1, -1, 1 ],
[ 1, -1, -1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, 1, -1 ],
[ 1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 1, 5, 1 ],
[ 37, 15, 1 ],
[ 1, 13, 1 ],
[ 61, 1, 1 ],
[ 1, 3, 1 ],
[ 287, 41, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 5, 1 ],
[ 1, 15, 1 ],
[ 1, 1, 1 ],
[ 61, 1, 1 ],
[ 1, 1, 1 ],
[ 287, 41, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 1, 1, 41 ], torsion_lower_bounds := [ 1, 1, 3, 1, 1, 1, 1 ], l_ratios := [ 1, 0, 5/3, 1, 0, 0, 7 ], analytic_sha_upper_bounds := [ 1, 0, 1, 1, 0, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1, 1, 0, 0, 1/1681 ], eigenvalues := [*
[ -1, 1, 2, 4, 0, 0, -2, 0, -6, 0, -4, 10 ],
[ -1, 1, -1, -4, 3, -6, -4, -3, -1, 4, -2, 3 ],
[
-1,
1,
a,
-a - 1,
0,
a + 5,
-a,
a + 5,
a + 6,
-4*a - 6,
a + 8,
-4
],
[
1,
-1,
a,
0,
-a + 2,
2,
-2*a + 6,
-a + 2,
-a + 2,
2*a - 2,
2*a - 4,
-a + 4
],
[
1,
-1,
a,
-3*a - 9,
4*a + 8,
a - 1,
-3*a - 12,
-3*a - 9,
3*a + 6,
-4*a - 14,
7*a + 20,
4
],
[
-1,
-1,
a,
-a - 1,
1/3*a^2 - 5/3*a - 11/3,
-2/3*a^2 + 1/3*a + 13/3,
-1/3*a^2 + 2/3*a - 1/3,
a^2 - 6,
a - 6,
-2/3*a^2 - 2/3*a + 4/3,
-5/3*a^2 + 4/3*a + 31/3,
-1/3*a^2 + 5/3*a - 1/3
],
[
1,
1,
a,
a^3 - 7*a - 2,
-a^3 + a^2 + 5*a - 2,
-a^3 - 2*a^2 + 7*a + 14,
-a^3 + a^2 + 6*a - 2,
a^2 - 2*a - 4,
-2*a^2 + a + 8,
-2*a^2 + 2*a + 8,
a^3 + a^2 - 8*a - 8,
a^3 + a^2 - 7*a - 8
]
*], q_expansions := [*
q - q^2 + q^3 + q^4 + 2*q^5 - q^6 + 4*q^7 - q^8 + q^9 - 2*q^10 + q^12 - 4*q^14 + 2*q^15 + q^16 - 2*q^17 - q^18 + 2*q^20 + 4*q^21 - 6*q^23 - q^24 - q^25 + q^27 + 4*q^28 - 2*q^30 - 4*q^31 - q^32 + 2*q^34 + 8*q^35 + q^36 + 10*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - q^5 - q^6 - 4*q^7 - q^8 + q^9 + q^10 + 3*q^11 + q^12 - 6*q^13 + 4*q^14 - q^15 + q^16 - 4*q^17 - q^18 - 3*q^19 - q^20 - 4*q^21 - 3*q^22 - q^23 - q^24 - 4*q^25 + 6*q^26 + q^27 - 4*q^28 + 4*q^29 + q^30 - 2*q^31 - q^32 + 3*q^33 + 4*q^34 + 4*q^35 + q^36 + 3*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + a*q^5 - q^6 + (-a - 1)*q^7 - q^8 + q^9 - a*q^10 + q^12 + (a + 5)*q^13 + (a + 1)*q^14 + a*q^15 + q^16 - a*q^17 - q^18 + (a + 5)*q^19 + a*q^20 + (-a - 1)*q^21 + (a + 6)*q^23 - q^24 + (-3*a - 2)*q^25 + (-a - 5)*q^26 + q^27 + (-a - 1)*q^28 + (-4*a - 6)*q^29 - a*q^30 + (a + 8)*q^31 - q^32 + a*q^34 + (2*a - 3)*q^35 + q^36 - 4*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + a*q^5 - q^6 + q^8 + q^9 + a*q^10 + (-a + 2)*q^11 - q^12 + 2*q^13 - a*q^15 + q^16 + (-2*a + 6)*q^17 + q^18 + (-a + 2)*q^19 + a*q^20 + (-a + 2)*q^22 + (-a + 2)*q^23 - q^24 + (3*a - 3)*q^25 + 2*q^26 - q^27 + (2*a - 2)*q^29 - a*q^30 + (2*a - 4)*q^31 + q^32 + (a - 2)*q^33 + (-2*a + 6)*q^34 + q^36 + (-a + 4)*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + a*q^5 - q^6 + (-3*a - 9)*q^7 + q^8 + q^9 + a*q^10 + (4*a + 8)*q^11 - q^12 + (a - 1)*q^13 + (-3*a - 9)*q^14 - a*q^15 + q^16 + (-3*a - 12)*q^17 + q^18 + (-3*a - 9)*q^19 + a*q^20 + (3*a + 9)*q^21 + (4*a + 8)*q^22 + (3*a + 6)*q^23 - q^24 + (-5*a - 10)*q^25 + (a - 1)*q^26 - q^27 + (-3*a - 9)*q^28 + (-4*a - 14)*q^29 - a*q^30 + (7*a + 20)*q^31 + q^32 + (-4*a - 8)*q^33 + (-3*a - 12)*q^34 + (6*a + 15)*q^35 + q^36 + 4*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + a*q^5 + q^6 + (-a - 1)*q^7 - q^8 + q^9 - a*q^10 + (1/3*a^2 - 5/3*a - 11/3)*q^11 - q^12 + (-2/3*a^2 + 1/3*a + 13/3)*q^13 + (a + 1)*q^14 - a*q^15 + q^16 + (-1/3*a^2 + 2/3*a - 1/3)*q^17 - q^18 + (a^2 - 6)*q^19 + a*q^20 + (a + 1)*q^21 + (-1/3*a^2 + 5/3*a + 11/3)*q^22 + (a - 6)*q^23 + q^24 + (a^2 - 5)*q^25 + (2/3*a^2 - 1/3*a - 13/3)*q^26 - q^27 + (-a - 1)*q^28 + (-2/3*a^2 - 2/3*a + 4/3)*q^29 + a*q^30 + (-5/3*a^2 + 4/3*a + 31/3)*q^31 - q^32 + (-1/3*a^2 + 5/3*a + 11/3)*q^33 + (1/3*a^2 - 2/3*a + 1/3)*q^34 + (-a^2 - a)*q^35 + q^36 + (-1/3*a^2 + 5/3*a - 1/3)*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + a*q^5 + q^6 + (a^3 - 7*a - 2)*q^7 + q^8 + q^9 + a*q^10 + (-a^3 + a^2 + 5*a - 2)*q^11 + q^12 + (-a^3 - 2*a^2 + 7*a + 14)*q^13 + (a^3 - 7*a - 2)*q^14 + a*q^15 + q^16 + (-a^3 + a^2 + 6*a - 2)*q^17 + q^18 + (a^2 - 2*a - 4)*q^19 + a*q^20 + (a^3 - 7*a - 2)*q^21 + (-a^3 + a^2 + 5*a - 2)*q^22 + (-2*a^2 + a + 8)*q^23 + q^24 + (a^2 - 5)*q^25 + (-a^3 - 2*a^2 + 7*a + 14)*q^26 + q^27 + (a^3 - 7*a - 2)*q^28 + (-2*a^2 + 2*a + 8)*q^29 + a*q^30 + (a^3 + a^2 - 8*a - 8)*q^31 + q^32 + (-a^3 + a^2 + 5*a - 2)*q^33 + (-a^3 + a^2 + 6*a - 2)*q^34 + (2*a^3 + a^2 - 13*a - 14)*q^35 + q^36 + (a^3 + a^2 - 7*a - 8)*q^37 + O(q^38)
*]> ;  // time = 393.32 seconds




J[499] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 499, 499, 499 ], new_dimensions := [ 2, 16, 23 ], dimensions := [ 2, 16, 23 ], intersection_graph := [ 0, 71, 1, 71, 0, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, -5, -2, -2, 0, 1, 2, 7, -9, 7, 6 ],
[ -5, -5, -20, -4, -18, -14, -25, -20, -15, -40, -16, -11 ],
[ 4, 1, 25, 2, 10, 14, 18, 4, 4, 57, 5, 11 ]
], hecke_fields := [
x^2 + x - 1,
x^16 + 5*x^15 - 11*x^14 - 85*x^13 + 9*x^12 + 548*x^11 + 293*x^10 - 1718*x^9 - 1408*x^8 + 2735*x^7 + 2662*x^6 - 2058*x^5 - 2241*x^4 + 585*x^3 + 738*x^2 - 54*x - 81,
x^23 - 4*x^22 - 26*x^21 + 117*x^20 + 268*x^19 - 1447*x^18 - 1325*x^17 + 9859*x^16 + 2497*x^15 - 40388*x^14 + 4836*x^13 + 101760*x^12 - 34790*x^11 - 154579*x^10 + 72287*x^9 + 132753*x^8 - 68227*x^7 - 57242*x^6 + 26996*x^5 + 11011*x^4 - 4109*x^3 - 660*x^2 + 172*x - 8
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 83 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 83 ]
], torsion_upper_bounds := [ 1, 1, 83 ], torsion_lower_bounds := [ 1, 1, 83 ], l_ratios := [ 0, 0, 1/83 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[
a,
2*a + 1,
-a - 3,
-1,
-4*a - 3,
-6*a - 3,
5*a + 3,
4*a + 3,
-a + 3,
3*a - 3,
-a + 3,
-6*a
],
[
a,
-175/108*a^15 - 469/54*a^14 + 1511/108*a^13 + 7595/54*a^12 + 189/4*a^11 - 90257/108*a^10 - 22667/27*a^9 + 122191/54*a^8 + 175661/54*a^7 - 282515/108*a^6 - 580537/108*a^5 + 16955/36*a^4 + 3677*a^3 + 11477/12*a^2 - 7789/12*a - 973/4,
833/1404*a^15 + 203/54*a^14 - 4093/1404*a^13 - 41875/702*a^12 - 25427/468*a^11 + 36919/108*a^10 + 189727/351*a^9 - 603329/702*a^8 - 1328191/702*a^7 + 1105621/1404*a^6 + 4215899/1404*a^5 + 133363/468*a^4 - 78469/39*a^3 - 37481/52*a^2 + 55115/156*a + 8179/52,
3479/1404*a^15 + 713/54*a^14 - 31483/1404*a^13 - 151453/702*a^12 - 2849/52*a^11 + 140581/108*a^10 + 411178/351*a^9 - 2545769/702*a^8 - 3246949/702*a^7 + 6316195/1404*a^6 + 10786625/1404*a^5 - 666139/468*a^4 - 205213/39*a^3 - 161573/156*a^2 + 144689/156*a + 15577/52,
575/468*a^15 + 43/6*a^14 - 411/52*a^13 - 8855/78*a^12 - 38003/468*a^11 + 23341/36*a^10 + 107993/117*a^9 - 126151/78*a^8 - 260033/78*a^7 + 673547/468*a^6 + 837563/156*a^5 + 296039/468*a^4 - 47115/13*a^3 - 223667/156*a^2 + 32693/52*a + 16307/52,
-2531/702*a^15 - 560/27*a^14 + 18559/702*a^13 + 117343/351*a^12 + 42917/234*a^11 - 106357/54*a^10 - 827111/351*a^9 + 1838360/351*a^8 + 3049642/351*a^7 - 4022641/702*a^6 - 9875987/702*a^5 + 74201/234*a^4 + 370856/39*a^3 + 221795/78*a^2 - 129461/78*a - 17789/26,
44/117*a^15 + 4/3*a^14 - 196/39*a^13 - 830/39*a^12 + 2095/117*a^11 + 1102/9*a^10 + 2492/117*a^9 - 11987/39*a^8 - 10276/39*a^7 + 32732/117*a^6 + 7395/13*a^5 + 11432/117*a^4 - 5740/13*a^3 - 9463/39*a^2 + 1015/13*a + 641/13,
2363/1404*a^15 + 455/54*a^14 - 23263/1404*a^13 - 96181/702*a^12 - 6581/468*a^11 + 88705/108*a^10 + 226276/351*a^9 - 1594895/702*a^8 - 1874527/702*a^7 + 3940387/1404*a^6 + 6307265/1404*a^5 - 430223/468*a^4 - 40078/13*a^3 - 91229/156*a^2 + 84437/156*a + 8769/52,
-265/468*a^15 - 65/18*a^14 + 1381/468*a^13 + 13465/234*a^12 + 22553/468*a^11 - 11975/36*a^10 - 18958/39*a^9 + 199649/234*a^8 + 396145/234*a^7 - 130931/156*a^6 - 1245863/468*a^5 - 70049/468*a^4 + 22872/13*a^3 + 94145/156*a^2 - 15419/52*a - 7037/52,
-1403/351*a^15 - 538/27*a^14 + 13990/351*a^13 + 114110/351*a^12 + 3134/117*a^11 - 52855/27*a^10 - 528001/351*a^9 + 1910833/351*a^8 + 2214926/351*a^7 - 2374024/351*a^6 - 3753140/351*a^5 + 258722/117*a^4 + 287569/39*a^3 + 57376/39*a^2 - 50588/39*a - 5731/13,
-4331/702*a^15 - 911/27*a^14 + 35317/702*a^13 + 190909/351*a^12 + 53675/234*a^11 - 173155/54*a^10 - 1231094/351*a^9 + 3001997/351*a^8 + 4676140/351*a^7 - 6662377/702*a^6 - 15341129/702*a^5 + 207371/234*a^4 + 193450/13*a^3 + 336881/78*a^2 - 203063/78*a - 27421/26,
1076/351*a^15 + 499/27*a^14 - 7273/351*a^13 - 105041/351*a^12 - 7177/39*a^11 + 47989/27*a^10 + 761038/351*a^9 - 1684273/351*a^8 - 2750771/351*a^7 + 1912972/351*a^6 + 4406795/351*a^5 - 80029/117*a^4 - 109521/13*a^3 - 91775/39*a^2 + 57020/39*a + 7625/13
],
[
a,
-1457220813884701/1119607386952032*a^22 + 5678233870539797/1119607386952032*a^21 + 12812639971943875/373202462317344*a^20 - 2521524232667719/16963748287152*a^19 - 203340747288778115/559803693476016*a^18 + 2063684757695578313/1119607386952032*a^17 + 59203350560299631/31100205193112*a^16 - 14111945429885894323/1119607386952032*a^15 - 278427646172501711/62200410386224*a^14 + 29055114289972584661/559803693476016*a^13 - 63009797614745081/50891244861456*a^12 - 73775262078446439089/559803693476016*a^11 + 1512968414477349809/46650307789668*a^10 + 226941728109628150159/1119607386952032*a^9 - 4623180623304583463/62200410386224*a^8 - 66403952066170100845/373202462317344*a^7 + 3638809823414437039/50891244861456*a^6 + 5600810411424635725/69975461684502*a^5 - 2558476348252351199/93300615579336*a^4 - 18557784237638262739/1119607386952032*a^3 + 176744858830480247/46650307789668*a^2 + 36775045061594979/31100205193112*a - 16516913580078455/139950923369004,
-242663548546313/101782489722912*a^22 + 950681453049337/101782489722912*a^21 + 2129923853100575/33927496574304*a^20 - 4645170296009629/16963748287152*a^19 - 33696924056548279/50891244861456*a^18 + 345737378888832517/101782489722912*a^17 + 9744365181128857/2827291381192*a^16 - 2365332990617505479/101782489722912*a^15 - 44783444211472943/5654582762384*a^14 + 4872980377742124737/50891244861456*a^13 - 174539643146152295/50891244861456*a^12 - 12383579565344688445/50891244861456*a^11 + 264514357627864705/4240937071788*a^10 + 38139133934727385955/101782489722912*a^9 - 795562187639542087/5654582762384*a^8 - 11180282968025346281/33927496574304*a^7 + 6864272795414184421/50891244861456*a^6 + 945848406467241149/6361405607682*a^5 - 439966499551976071/8481874143576*a^4 - 3146397897209671703/101782489722912*a^3 + 7642060837744102/1060234267947*a^2 + 6266389905103503/2827291381192*a - 2834280764085187/12722811215364,
-111443814688433/101782489722912*a^22 + 434210662829977/101782489722912*a^21 + 980985889054799/33927496574304*a^20 - 2122478308056217/16963748287152*a^19 - 15599468386756567/50891244861456*a^18 + 158063078961249661/101782489722912*a^17 + 4560797549719091/2827291381192*a^16 - 1082225321957754335/101782489722912*a^15 - 21738976939382403/5654582762384*a^14 + 2232097782373224449/50891244861456*a^13 - 36886095630525431/50891244861456*a^12 - 5681988754181963437/50891244861456*a^11 + 112432832110798963/4240937071788*a^10 + 17545451686899744443/101782489722912*a^9 - 347346916319970371/5654582762384*a^8 - 5165034573815599361/33927496574304*a^7 + 3019366993620490513/50891244861456*a^6 + 219896477460578890/3180702803841*a^5 - 193557982098698047/8481874143576*a^4 - 1469598669399711599/101782489722912*a^3 + 13414056096062587/4240937071788*a^2 + 2919842363982943/2827291381192*a - 1268037448737115/12722811215364,
93341323749263/38607151274208*a^22 - 366648281217655/38607151274208*a^21 - 818811642480641/12869050424736*a^20 + 162895789019741/584956837488*a^19 + 12941582714998633/19303575637104*a^18 - 133398987385157731/38607151274208*a^17 - 3734950085205777/1072420868728*a^16 + 912908261018231777/38607151274208*a^15 + 17054650739349781/2144841737456*a^14 - 1881423741234911615/19303575637104*a^13 + 6638828427402283/1754870512464*a^12 + 4783318646282299939/19303575637104*a^11 - 102865769602728049/1608631303092*a^10 - 14739480640682958533/38607151274208*a^9 + 307964449937683109/2144841737456*a^8 + 4323244310361099359/12869050424736*a^7 - 241076922418852757/1754870512464*a^6 - 182910800990062324/1206473477319*a^5 + 169644344911163209/3217262606184*a^4 + 1213874623881109745/38607151274208*a^3 - 11750096933005987/1608631303092*a^2 - 2389497645455593/1072420868728*a + 1094244516597829/4825893909276,
252815014564693/186601231158672*a^22 - 979044305170397/186601231158672*a^21 - 2227323823976667/62200410386224*a^20 + 434717231032079/2827291381192*a^19 + 35467961506621739/93300615579336*a^18 - 355743375269664737/186601231158672*a^17 - 31192846357587989/15550102596556*a^16 + 2432357038857843835/186601231158672*a^15 + 149853893619326293/31100205193112*a^14 - 5007396106755423829/93300615579336*a^13 + 5738659770548369/8481874143576*a^12 + 12713343248059249841/93300615579336*a^11 - 251471908325129203/7775051298278*a^10 - 39106297724503029751/186601231158672*a^9 + 2347209386753979213/31100205193112*a^8 + 11442958481571458421/62200410386224*a^7 - 620009996245187551/8481874143576*a^6 - 965013072009068008/11662576947417*a^5 + 437610739739366275/15550102596556*a^4 + 3190841856710180923/186601231158672*a^3 - 30147583527448555/7775051298278*a^2 - 18814267364636461/15550102596556*a + 2744311873308683/23325153894834,
-55795569467893/139950923369004*a^22 + 219522429373265/139950923369004*a^21 + 490309546245895/46650307789668*a^20 - 97671067870273/2120468535894*a^19 - 7773336667299119/69975461684502*a^18 + 80141644052833613/139950923369004*a^17 + 2257878327316063/3887525649139*a^16 - 549935309747458315/139950923369004*a^15 - 10528016473295955/7775051298278*a^14 + 1137764481753229069/69975461684502*a^13 - 2917093226634977/6361405607682*a^12 - 2909218803554899703/69975461684502*a^11 + 118652405113679245/11662576947417*a^10 + 9043737822613721167/139950923369004*a^9 - 180642960658034573/7775051298278*a^8 - 2690420416142375557/46650307789668*a^7 + 142880093517719947/6361405607682*a^6 + 931583162542757845/34987730842251*a^5 - 102279000891337925/11662576947417*a^4 - 792123358025447275/139950923369004*a^3 + 14773622858396275/11662576947417*a^2 + 1600246210888610/3887525649139*a - 1473350335133278/34987730842251,
4116756582785501/1119607386952032*a^22 - 16128632147809477/1119607386952032*a^21 - 36142224302024099/373202462317344*a^20 + 7165292418763343/16963748287152*a^19 + 572037109490180203/559803693476016*a^18 - 5867528940748697785/1119607386952032*a^17 - 165573233443637231/31100205193112*a^16 + 40152815753593794611/1119607386952032*a^15 + 763360850545886119/62200410386224*a^14 - 82752063544824319325/559803693476016*a^13 + 257012498662355185/50891244861456*a^12 + 210407348180317845961/559803693476016*a^11 - 4459848486914378347/46650307789668*a^10 - 648527417743945685183/1119607386952032*a^9 + 13444222277830495543/62200410386224*a^8 + 190342686208087623725/373202462317344*a^7 - 10555151849813183735/50891244861456*a^6 - 8065710145743126955/34987730842251*a^5 + 7446204762069156739/93300615579336*a^4 + 53717880277204232483/1119607386952032*a^3 - 516911759591700871/46650307789668*a^2 - 106869767653013483/31100205193112*a + 48126088853374951/139950923369004,
646860966473739/124400820772448*a^22 - 2532208205579843/124400820772448*a^21 - 17031672621189167/124400820772448*a^20 + 3373665096091371/5654582762384*a^19 + 89805075526448437/62200410386224*a^18 - 920445170753683775/124400820772448*a^17 - 233654987877508389/31100205193112*a^16 + 6294832572305498757/124400820772448*a^15 + 1072758899967380793/62200410386224*a^14 - 12961865854360830691/62200410386224*a^13 + 42874815137152271/5654582762384*a^12 + 32915872199840876727/62200410386224*a^11 - 2118699501906573921/15550102596556*a^10 - 101263626494227522057/124400820772448*a^9 + 19097572611345303281/62200410386224*a^8 + 88895088241564494257/124400820772448*a^7 - 1662648795732412369/5654582762384*a^6 - 2499147367874756293/7775051298278*a^5 + 3508096610157348571/31100205193112*a^4 + 8281261222948173381/124400820772448*a^3 - 242461512392486085/15550102596556*a^2 - 147867770668537805/31100205193112*a + 7434646263576489/15550102596556,
-131876087328559/93300615579336*a^22 + 523951868104727/93300615579336*a^21 + 1151669270768161/31100205193112*a^20 - 232764919643747/1413645690596*a^19 - 18060114649676873/46650307789668*a^18 + 190594319989481207/93300615579336*a^17 + 7688256760297769/3887525649139*a^16 - 1304086860488044885/93300615579336*a^15 - 66246787443566399/15550102596556*a^14 + 2686824312505194403/46650307789668*a^13 - 15898118127460793/4240937071788*a^12 - 6827614164828955541/46650307789668*a^11 + 319262996322119889/7775051298278*a^10 + 21021172163763945289/93300615579336*a^9 - 1385257994981418873/15550102596556*a^8 - 6157020267313362043/31100205193112*a^7 + 356670281801679997/4240937071788*a^6 + 1039976453150805131/11662576947417*a^5 - 124336749330569625/3887525649139*a^4 - 1727370953443520773/93300615579336*a^3 + 33963545056493717/7775051298278*a^2 + 5150291811146981/3887525649139*a - 1500970495855637/11662576947417,
10023060635317/50891244861456*a^22 - 42087207896069/50891244861456*a^21 - 85957231501843/16963748287152*a^20 + 205788815091053/8481874143576*a^19 + 1305668307086867/25445622430728*a^18 - 15326121828013769/50891244861456*a^17 - 345274589466791/1413645690596*a^16 + 104886876698755267/50891244861456*a^15 + 1103146818542467/2827291381192*a^14 - 216011395745285821/25445622430728*a^13 + 33260929019740759/25445622430728*a^12 + 547967590970704037/25445622430728*a^11 - 8009554793870221/1060234267947*a^10 - 1679439315552414895/50891244861456*a^9 + 42232787604101735/2827291381192*a^8 + 486546046050816925/16963748287152*a^7 - 346468609565527001/25445622430728*a^6 - 40012772807349751/3180702803841*a^5 + 21753103072045301/4240937071788*a^4 + 125350015072020163/50891244861456*a^3 - 1528148279555447/2120468535894*a^2 - 228074516478177/1413645690596*a + 168446065693751/6361405607682,
3003673932743/2827291381192*a^22 - 11861218081699/2827291381192*a^21 - 78825037931751/2827291381192*a^20 + 173826988045959/1413645690596*a^19 + 413281359521333/1413645690596*a^18 - 4311232052994659/2827291381192*a^17 - 531369812974012/353411422649*a^16 + 29481350932388241/2827291381192*a^15 + 4694325186171867/1413645690596*a^14 - 60694930976613683/1413645690596*a^13 + 3270580444501969/1413645690596*a^12 + 154079032674431095/1413645690596*a^11 - 10430135071256530/353411422649*a^10 - 473718080038594941/2827291381192*a^9 + 91456785541213759/1413645690596*a^8 + 415375918593513381/2827291381192*a^7 - 86196073677061529/1413645690596*a^6 - 23307637363995087/353411422649*a^5 + 16180608534853555/706822845298*a^4 + 38539593764052769/2827291381192*a^3 - 2162367535942613/706822845298*a^2 - 688959239532035/706822845298*a + 32937570732297/353411422649
]
*], q_expansions := [*
q + a*q^2 + (2*a + 1)*q^3 + (-a - 1)*q^4 + (-a - 3)*q^5 + (-a + 2)*q^6 - q^7 + (-2*a - 1)*q^8 + 2*q^9 + (-2*a - 1)*q^10 + (-4*a - 3)*q^11 + (-a - 3)*q^12 + (-6*a - 3)*q^13 - a*q^14 + (-5*a - 5)*q^15 + 3*a*q^16 + (5*a + 3)*q^17 + 2*a*q^18 + (4*a + 3)*q^19 + (3*a + 4)*q^20 + (-2*a - 1)*q^21 + (a - 4)*q^22 + (-a + 3)*q^23 - 5*q^24 + (5*a + 5)*q^25 + (3*a - 6)*q^26 + (-2*a - 1)*q^27 + (a + 1)*q^28 + (3*a - 3)*q^29 - 5*q^30 + (-a + 3)*q^31 + (a + 5)*q^32 + (-2*a - 11)*q^33 + (-2*a + 5)*q^34 + (a + 3)*q^35 + (-2*a - 2)*q^36 - 6*a*q^37 + O(q^38),
q + a*q^2 + (-175/108*a^15 - 469/54*a^14 + 1511/108*a^13 + 7595/54*a^12 + 189/4*a^11 - 90257/108*a^10 - 22667/27*a^9 + 122191/54*a^8 + 175661/54*a^7 - 282515/108*a^6 - 580537/108*a^5 + 16955/36*a^4 + 3677*a^3 + 11477/12*a^2 - 7789/12*a - 973/4)*q^3 + (a^2 - 2)*q^4 + (833/1404*a^15 + 203/54*a^14 - 4093/1404*a^13 - 41875/702*a^12 - 25427/468*a^11 + 36919/108*a^10 + 189727/351*a^9 - 603329/702*a^8 - 1328191/702*a^7 + 1105621/1404*a^6 + 4215899/1404*a^5 + 133363/468*a^4 - 78469/39*a^3 - 37481/52*a^2 + 55115/156*a + 8179/52)*q^5 + (-7/12*a^15 - 23/6*a^14 + 35/12*a^13 + 371/6*a^12 + 209/4*a^11 - 1459/4*a^10 - 521*a^9 + 1943/2*a^8 + 10895/6*a^7 - 12743/12*a^6 - 11455/4*a^5 + 183/4*a^4 + 5713/3*a^3 + 2187/4*a^2 - 1323/4*a - 525/4)*q^6 + (3479/1404*a^15 + 713/54*a^14 - 31483/1404*a^13 - 151453/702*a^12 - 2849/52*a^11 + 140581/108*a^10 + 411178/351*a^9 - 2545769/702*a^8 - 3246949/702*a^7 + 6316195/1404*a^6 + 10786625/1404*a^5 - 666139/468*a^4 - 205213/39*a^3 - 161573/156*a^2 + 144689/156*a + 15577/52)*q^7 + (a^3 - 4*a)*q^8 + (301/108*a^15 + 805/54*a^14 - 2633/108*a^13 - 13055/54*a^12 - 2723/36*a^11 + 155507/108*a^10 + 37952/27*a^9 - 211393/54*a^8 - 295331/54*a^7 + 493433/108*a^6 + 976531/108*a^5 - 10819/12*a^4 - 18545/3*a^3 - 19183/12*a^2 + 13051/12*a + 1655/4)*q^9 + (371/468*a^15 + 65/18*a^14 - 4315/468*a^13 - 13963/234*a^12 + 869/52*a^11 + 13201/36*a^10 + 18703/117*a^9 - 247253/234*a^8 - 195439/234*a^7 + 666151/468*a^6 + 704801/468*a^5 - 106459/156*a^4 - 41647/39*a^3 - 4397/52*a^2 + 9845/52*a + 2499/52)*q^10 + (575/468*a^15 + 43/6*a^14 - 411/52*a^13 - 8855/78*a^12 - 38003/468*a^11 + 23341/36*a^10 + 107993/117*a^9 - 126151/78*a^8 - 260033/78*a^7 + 673547/468*a^6 + 837563/156*a^5 + 296039/468*a^4 - 47115/13*a^3 - 223667/156*a^2 + 32693/52*a + 16307/52)*q^11 + (251/108*a^15 + 749/54*a^14 - 1699/108*a^13 - 12085/54*a^12 - 1675/12*a^11 + 142705/108*a^10 + 44506/27*a^9 - 190679/54*a^8 - 322513/54*a^7 + 423451/108*a^6 + 1036361/108*a^5 - 12415/36*a^4 - 6466*a^3 - 21757/12*a^2 + 13625/12*a + 1757/4)*q^12 + (-2531/702*a^15 - 560/27*a^14 + 18559/702*a^13 + 117343/351*a^12 + 42917/234*a^11 - 106357/54*a^10 - 827111/351*a^9 + 1838360/351*a^8 + 3049642/351*a^7 - 4022641/702*a^6 - 9875987/702*a^5 + 74201/234*a^4 + 370856/39*a^3 + 221795/78*a^2 - 129461/78*a - 17789/26)*q^13 + (127/156*a^15 + 29/6*a^14 - 799/156*a^13 - 6013/78*a^12 - 8771/156*a^11 + 5345/12*a^10 + 8198/13*a^9 - 88637/78*a^8 - 177715/78*a^7 + 56501/52*a^6 + 573485/156*a^5 + 45419/156*a^4 - 32309/13*a^3 - 46863/52*a^2 + 22535/52*a + 10437/52)*q^14 + (-2233/1404*a^15 - 481/54*a^14 + 17309/1404*a^13 + 100757/702*a^12 + 3623/52*a^11 - 91379/108*a^10 - 339974/351*a^9 + 1586263/702*a^8 + 2540855/702*a^7 - 3544433/1404*a^6 - 8266651/1404*a^5 + 130157/468*a^4 + 155360/39*a^3 + 173155/156*a^2 - 108799/156*a - 14307/52)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (44/117*a^15 + 4/3*a^14 - 196/39*a^13 - 830/39*a^12 + 2095/117*a^11 + 1102/9*a^10 + 2492/117*a^9 - 11987/39*a^8 - 10276/39*a^7 + 32732/117*a^6 + 7395/13*a^5 + 11432/117*a^4 - 5740/13*a^3 - 9463/39*a^2 + 1015/13*a + 641/13)*q^17 + (35/36*a^15 + 113/18*a^14 - 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*]> ;  // time = 16.77 seconds


