CoCalc -- 1845.sagews

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M = ModularForms(169); M

Modular Forms space of dimension 21 for Congruence Subgroup Gamma0(169) of weight 2 over Rational Field

f = M.newforms('a')

[q + a0*q^2 + 2*q^3 + q^4 - a0*q^5 + O(q^6), q + a1*q^2 + (-a1^2 - 2*a1)*q^3 + (a1^2 - 2)*q^4 + (a1^2 + 2*a1 - 2)*q^5 + O(q^6), q + a2*q^2 + (-a2^2 + 2*a2)*q^3 + (a2^2 - 2)*q^4 + (-a2^2 + 2*a2 + 2)*q^5 + O(q^6)]

f[0]

q + a0*q^2 + 2*q^3 + q^4 - a0*q^5 + O(q^6)

f[1]

q + a1*q^2 + (-a1^2 - 2*a1)*q^3 + (a1^2 - 2)*q^4 + (a1^2 + 2*a1 - 2)*q^5 + O(q^6)

f[2]

q + a2*q^2 + (-a2^2 + 2*a2)*q^3 + (a2^2 - 2)*q^4 + (-a2^2 + 2*a2 + 2)*q^5 + O(q^6)

g = f[1]

g.atkin_lehner_eigenvalue(13)

1

f[2].atkin_lehner_eigenvalue(13)

-1

q + a1*q^2 + (-a1^2 - 2*a1)*q^3 + (a1^2 - 2)*q^4 + (a1^2 + 2*a1 - 2)*q^5 + O(q^6)

g.hecke_eigenvalue_field()

Number Field in a1 with defining polynomial x^3 + 2*x^2 - x - 1

time g.q_expansion(500)

q + a1*q^2 + (-a1^2 - 2*a1)*q^3 + (a1^2 - 2)*q^4 + (a1^2 + 2*a1 - 2)*q^5 + (-a1 - 1)*q^6 + (a1^2 - 3)*q^7 + (-2*a1^2 - 3*a1 + 1)*q^8 + (a1^2 + 3*a1 - 1)*q^9 + (-a1 + 1)*q^10 + (-a1^2 - 2*a1 - 2)*q^11 + (a1^2 + 3*a1)*q^12 + (-2*a1^2 - 2*a1 + 1)*q^14 + (a1^2 + a1 - 2)*q^15 + (-a1^2 - a1 + 2)*q^16 + (-a1^2 + a1 + 2)*q^17 + (a1^2 + 1)*q^18 + (-2*a1^2 - a1 + 2)*q^19 + (-3*a1^2 - 3*a1 + 4)*q^20 + (2*a1^2 + 5*a1)*q^21 + (-3*a1 - 1)*q^22 + (2*a1^2 + 4*a1 - 3)*q^23 + (a1^2 + 3*a1 + 3)*q^24 + (-3*a1^2 - 5*a1 + 1)*q^25 + (3*a1^2 + 4*a1 - 3)*q^27 + (-a1 + 4)*q^28 + (5*a1^2 + 8*a1 - 5)*q^29 + (-a1^2 - a1 + 1)*q^30 + (-5*a1^2 - 8*a1 + 3)*q^31 + (5*a1^2 + 7*a1 - 3)*q^32 + (3*a1^2 + 7*a1 + 2)*q^33 + (3*a1^2 + a1 - 1)*q^34 + (-4*a1^2 - 5*a1 + 6)*q^35 + (-4*a1^2 - 4*a1 + 3)*q^36 + (2*a1^2 + 3*a1 + 2)*q^37 + (3*a1^2 - 2)*q^38 + (3*a1^2 + 3*a1 - 5)*q^40 + (-4*a1^2 - 10*a1 - 1)*q^41 + (a1^2 + 2*a1 + 2)*q^42 + (-2*a1^2 - 5*a1 + 5)*q^43 + (-a1^2 + 3*a1 + 4)*q^44 + (-2*a1^2 - 4*a1 + 5)*q^45 + (-a1 + 2)*q^46 + (a1^2 - 8)*q^47 + (-a1^2 - 2*a1 + 1)*q^48 + (-a1^2 - a1)*q^49 + (a1^2 - 2*a1 - 3)*q^50 + (-a1^2 - 4*a1 - 1)*q^51 + (-4*a1^2 - 11*a1 + 1)*q^53 + (-2*a1^2 + 3)*q^54 + (-a1^2 - 3*a1 + 2)*q^55 + (3*a1^2 + 8*a1 - 2)*q^56 + (-a1 + 1)*q^57 + (-2*a1^2 + 5)*q^58 + (-4*a1^2 - 4*a1 - 1)*q^59 + (-a1^2 - 2*a1 + 3)*q^60 + (6*a1^2 + 7*a1 - 6)*q^61 + (2*a1^2 - 2*a1 - 5)*q^62 + (-5*a1^2 - 7*a1 + 4)*q^63 + (-a1^2 + 4*a1 + 1)*q^64 + (a1^2 + 5*a1 + 3)*q^66 + (6*a1^2 + 11*a1 - 5)*q^67 + (-3*a1^2 - 1)*q^68 + (a1^2 - 4)*q^69 + (3*a1^2 + 2*a1 - 4)*q^70 + (3*a1^2 + 3*a1 - 13)*q^71 + (2*a1^2 - a1 - 6)*q^72 + (-6*a1^2 - 3*a1 + 13)*q^73 + (-a1^2 + 4*a1 + 2)*q^74 + (2*a1^2 + 6*a1 + 5)*q^75 + (-2*a1^2 + 3*a1 - 1)*q^76 + (5*a1 + 6)*q^77 + (-a1^2 + 7*a1 + 5)*q^79 + (3*a1^2 + 4*a1 - 5)*q^80 + (-3*a1^2 - 10*a1 - 1)*q^81 + (-2*a1^2 - 5*a1 - 4)*q^82 + (9*a1^2 + 11*a1 - 13)*q^83 + (-4*a1^2 - 7*a1 + 1)*q^84 + (3*a1^2 + 2*a1 - 3)*q^85 + (-a1^2 + 3*a1 - 2)*q^86 + (-3*a1 - 8)*q^87 + (5*a1^2 + 9*a1 + 1)*q^88 + (7*a1^2 + 7*a1 - 13)*q^89 + (3*a1 - 2)*q^90 + (-5*a1^2 - 6*a1 + 6)*q^92 + (2*a1^2 + 7*a1 + 8)*q^93 + (-2*a1^2 - 7*a1 + 1)*q^94 + (4*a1^2 + 3*a1 - 5)*q^95 + (-2*a1^2 - 6*a1 - 7)*q^96 + (-a1^2 - 8*a1 - 1)*q^97 + (a1^2 - a1 - 1)*q^98 + (-2*a1^2 - 8*a1 - 1)*q^99 + (2*a1^2 + 8*a1 - 1)*q^100 + (-3*a1^2 - 13*a1 - 1)*q^101 + (-2*a1^2 - 2*a1 - 1)*q^102 + (8*a1^2 + 9*a1 - 11)*q^103 + (-2*a1^2 - 3*a1 + 5)*q^105 + (-3*a1^2 - 3*a1 - 4)*q^106 + (-3*a1^2 - a1 + 6)*q^107 + (-2*a1^2 - 7*a1 + 4)*q^108 + (2*a1^2 + 8*a1 + 8)*q^109 + (-a1^2 + a1 - 1)*q^110 + (-4*a1^2 - 9*a1 - 3)*q^111 + (2*a1^2 + 3*a1 - 5)*q^112 + (a1^2 + 3*a1 + 9)*q^113 + (-a1^2 + a1)*q^114 + (-5*a1^2 - 8*a1 + 10)*q^115 + (-6*a1^2 - 13*a1 + 8)*q^116 + (4*a1^2 - 5*a1 - 4)*q^118 + (-2*a1^2 - a1 - 3)*q^119 + (2*a1^2 + 4*a1 - 3)*q^120 + (5*a1^2 + 11*a1 - 5)*q^121 + (-5*a1^2 + 6)*q^122 + (5*a1^2 + 16*a1 + 10)*q^123 + (4*a1^2 + 13*a1 - 4)*q^124 + (-a1^2 - 6*a1 + 3)*q^125 + (3*a1^2 - a1 - 5)*q^126 + (-9*a1^2 - 10*a1 + 4)*q^127 + (-4*a1^2 - 14*a1 + 5)*q^128 + (-3*a1^2 - 3*a1 + 5)*q^129 + (5*a1^2 + 4*a1 - 13)*q^131 + (-3*a1^2 - 10*a1 - 3)*q^132 + (4*a1 - 3)*q^133 + (-a1^2 + a1 + 6)*q^134 + (-6*a1^2 - 7*a1 + 10)*q^135 + (-6*a1 - 1)*q^136 + (-4*a1^2 - 4*a1 + 12)*q^137 + (-2*a1^2 - 3*a1 + 1)*q^138 + (-11*a1^2 - 17*a1 + 6)*q^139 + (4*a1^2 + 9*a1 - 9)*q^140 + (7*a1^2 + 15*a1)*q^141 + (-3*a1^2 - 10*a1 + 3)*q^142 + (3*a1^2 + 4*a1 - 4)*q^144 + (-10*a1^2 - 13*a1 + 18)*q^145 + (9*a1^2 + 7*a1 - 6)*q^146 + (a1^2 + 2*a1 + 1)*q^147 + (2*a1^2 - 5*a1 - 5)*q^148 + (3*a1^2 + 3*a1)*q^149 + (2*a1^2 + 7*a1 + 2)*q^150 + (12*a1^2 + 14*a1 - 15)*q^151 + (a1^2 - 3*a1 + 2)*q^152 + (5*a1^2 + 4*a1 - 2)*q^153 + (5*a1^2 + 6*a1)*q^154 + (8*a1^2 + 9*a1 - 14)*q^155 + (a1^2 + 6*a1 - 1)*q^157 + (9*a1^2 + 4*a1 - 1)*q^158 + (3*a1^2 + 13*a1 + 11)*q^159 + (-8*a1^2 - 8*a1 + 13)*q^160 + (-7*a1^2 - 10*a1 + 9)*q^161 + (-4*a1^2 - 4*a1 - 3)*q^162 + (-a1^2 + a1 + 16)*q^163 + (7*a1^2 + 14*a1)*q^164 + (-a1^2 + 3)*q^165 + (-7*a1^2 - 4*a1 + 9)*q^166 + (2*a1^2 + 16*a1 + 2)*q^167 + (-a1^2 - 7*a1 - 8)*q^168 + (-4*a1^2 + 3)*q^170 + (5*a1^2 + 2*a1 - 5)*q^171 + (9*a1^2 + 7*a1 - 11)*q^172 + (-16*a1^2 - 24*a1 + 8)*q^173 + (-3*a1^2 - 8*a1)*q^174 + (5*a1^2 + 13*a1 - 2)*q^175 + (a1^2 - 3)*q^176 + (5*a1^2 + 10*a1 + 4)*q^177 + (-7*a1^2 - 6*a1 + 7)*q^178 + (5*a1^2 + 9*a1 + 1)*q^179 + (7*a1^2 + 6*a1 - 10)*q^180 + (-a1^2 + 7*a1 + 16)*q^181 + (-a1 - 7)*q^183 + (4*a1^2 + 3*a1 - 9)*q^184 + (3*a1 - 1)*q^185 + (3*a1^2 + 10*a1 + 2)*q^186 + (a1^2 - 6*a1 - 5)*q^187 + (-5*a1^2 - a1 + 14)*q^188 + (-5*a1^2 - 11*a1 + 7)*q^189 + (-5*a1^2 - a1 + 4)*q^190 + (4*a1^2 - 5*a1 - 13)*q^191 + (-5*a1 - 4)*q^192 + (-8*a1^2 - 18*a1 + 6)*q^193 + (-6*a1^2 - 2*a1 - 1)*q^194 + (-a1^2 + 2*a1 + 1)*q^196 + (-8*a1^2 - 8*a1 + 11)*q^197 + (-4*a1^2 - 3*a1 - 2)*q^198 + (6*a1^2 + 17*a1 - 6)*q^199 + (2*a1^2 + 5*a1 + 8)*q^200 + (-a1^2 - 7*a1 - 11)*q^201 + (-7*a1^2 - 4*a1 - 3)*q^202 + (-11*a1^2 - 21*a1 + 13)*q^203 + (4*a1^2 + 5*a1)*q^204 + (3*a1^2 + 4*a1 - 8)*q^205 + (-7*a1^2 - 3*a1 + 8)*q^206 + (-3*a1^2 - 5*a1 + 9)*q^207 + (4*a1^2 + a1 - 3)*q^209 + (a1^2 + 3*a1 - 2)*q^210 + (-5*a1^2 + 12)*q^211 + (11*a1^2 + 15*a1 - 5)*q^212 + (10*a1^2 + 20*a1 - 3)*q^213 + (5*a1^2 + 3*a1 - 3)*q^214 + (7*a1^2 + 13*a1 - 15)*q^215 + (a1^2 + 2*a1 - 8)*q^216 + (9*a1^2 + 21*a1 - 7)*q^217 + (4*a1^2 + 10*a1 + 2)*q^218 + (-7*a1^2 - 17*a1 + 3)*q^219 + (5*a1^2 + 4*a1 - 5)*q^220 + (-a1^2 - 7*a1 - 4)*q^222 + (3*a1^2 + 6*a1 - 9)*q^223 + (-7*a1^2 - 19*a1 + 6)*q^224 + (2*a1^2 - 3*a1 - 9)*q^225 + (a1^2 + 10*a1 + 1)*q^226 + (-8*a1^2 - 11*a1 + 7)*q^227 + (3*a1^2 + a1 - 3)*q^228 + (-8*a1^2 - 15*a1 - 7)*q^229 + (2*a1^2 + 5*a1 - 5)*q^230 + (-6*a1^2 - 17*a1 - 5)*q^231 + (3*a1^2 + 2*a1 - 16)*q^232 + (3*a1^2 + 5*a1 - 9)*q^233 + (-9*a1^2 - 15*a1 + 16)*q^235 + (-5*a1^2 + 8*a1 + 6)*q^236 + (-4*a1^2 - 16*a1 - 7)*q^237 + (3*a1^2 - 5*a1 - 2)*q^238 + (-3*a1^2 - 9*a1 - 16)*q^239 + (2*a1^2 + 3*a1 - 4)*q^240 + (-a1^2 - 12*a1 - 10)*q^241 + (a1^2 + 5)*q^242 + (-5*a1^2 + 3*a1 + 19)*q^243 + (-2*a1^2 - 13*a1 + 7)*q^244 + (a1^2 - 1)*q^245 + (6*a1^2 + 15*a1 + 5)*q^246 + (a1^2 + 4*a1 + 14)*q^248 + (4*a1^2 + 6*a1 - 11)*q^249 + (-4*a1^2 + 2*a1 - 1)*q^250 + (-2*a1^2 - 18*a1 - 8)*q^251 + (3*a1^2 + 12*a1 - 5)*q^252 + (-3*a1^2 - 8*a1 + 2)*q^253 + (8*a1^2 - 5*a1 - 9)*q^254 + (a1 - 2)*q^255 + (-4*a1^2 - 7*a1 - 6)*q^256 + (-13*a1^2 - 8*a1 + 29)*q^257 + (3*a1^2 + 2*a1 - 3)*q^258 + (-8*a1 - 7)*q^259 + (-7*a1^2 - 5*a1 + 18)*q^261 + (-6*a1^2 - 8*a1 + 5)*q^262 + (-6*a1^2 - 19*a1 + 2)*q^263 + (-6*a1^2 - 16*a1 - 9)*q^264 + (5*a1^2 + 9*a1 - 13)*q^265 + (4*a1^2 - 3*a1)*q^266 + (6*a1^2 + 12*a1 - 7)*q^267 + (-9*a1^2 - 17*a1 + 9)*q^268 + (3*a1^2 + 2*a1 - 10)*q^269 + (5*a1^2 + 4*a1 - 6)*q^270 + (14*a1^2 + 23*a1 - 21)*q^271 + (-a1 + 2)*q^272 + (4*a1^2 + 8*a1 - 4)*q^274 + (8*a1^2 + 16*a1 + 3)*q^275 + (-a1^2 - a1 + 6)*q^276 + (10*a1^2 + 15*a1 - 5)*q^277 + (5*a1^2 - 5*a1 - 11)*q^278 + (5*a1^2 - a1 - 16)*q^279 + (-5*a1^2 - 9*a1 + 12)*q^280 + (5*a1^2 + 11*a1 - 7)*q^281 + (a1^2 + 7*a1 + 7)*q^282 + (20*a1^2 + 34*a1 - 18)*q^283 + (-10*a1^2 - 6*a1 + 23)*q^284 + (a1^2 + 3*a1 - 3)*q^285 + (11*a1^2 + 24*a1 + 1)*q^287 + (-6*a1^2 + a1 + 15)*q^288 + (6*a1^2 + a1 - 17)*q^289 + (7*a1^2 + 8*a1 - 10)*q^290 + (2*a1^2 + 11*a1 + 8)*q^291 + (a1^2 + 9*a1 - 17)*q^292 + (7*a1^2 + 23*a1 - 8)*q^293 + (2*a1 + 1)*q^294 + (3*a1^2 - 2*a1 - 2)*q^295 + (-7*a1^2 - 11*a1 - 2)*q^296 + (-6*a1^2 - 9*a1 + 2)*q^297 + (-3*a1^2 + 3*a1 + 3)*q^298 + (-a1^2 - 8*a1 - 8)*q^300 + (11*a1^2 + 12*a1 - 16)*q^301 + (-10*a1^2 - 3*a1 + 12)*q^302 + (4*a1^2 + 18*a1 + 13)*q^303 + (-a1^2 - 3*a1 + 3)*q^304 + (-12*a1^2 - 13*a1 + 19)*q^305 + (-6*a1^2 + 3*a1 + 5)*q^306 + (-2*a1^2 + 8*a1 + 14)*q^307 + (-4*a1^2 - 5*a1 - 7)*q^308 + (3*a1^2 + 5*a1 - 9)*q^309 + (-7*a1^2 - 6*a1 + 8)*q^310 + (-15*a1^2 - 12*a1 + 19)*q^311 + (-4*a1^2 - 11*a1 - 12)*q^313 + (4*a1^2 + 1)*q^314 + (9*a1^2 + 10*a1 - 15)*q^315 + (-12*a1^2 - 6*a1 - 1)*q^316 + (-8*a1^2 - 26*a1 + 12)*q^317 + (7*a1^2 + 14*a1 + 3)*q^318 + (-10*a1^2 - 19*a1 + 2)*q^319 + (2*a1^2 - 3*a1 + 2)*q^320 + (-3*a1^2 - 8*a1 + 1)*q^321 + (4*a1^2 + 2*a1 - 7)*q^322 + (5*a1^2 - 3*a1 - 1)*q^323 + (10*a1^2 + 13*a1 - 2)*q^324 + (3*a1^2 + 15*a1 - 1)*q^326 + (-10*a1^2 - 26*a1 - 8)*q^327 + (4*a1^2 + 17*a1 + 15)*q^328 + (-6*a1^2 - a1 + 22)*q^329 + (2*a1^2 + 2*a1 - 1)*q^330 + (11*a1 + 9)*q^331 + (-8*a1^2 - 20*a1 + 19)*q^332 + (a1^2 + 10*a1 + 3)*q^333 + (12*a1^2 + 4*a1 + 2)*q^334 + (-11*a1^2 - 15*a1 + 21)*q^335 + (3*a1^2 + 5*a1 - 3)*q^336 + (-5*a1^2 - 17*a1 - 11)*q^337 + (-10*a1^2 - 22*a1 - 3)*q^339 + (2*a1^2 - 5*a1 + 2)*q^340 + (12*a1^2 + 23*a1 + 2)*q^341 + (-8*a1^2 + 5)*q^342 + (-7*a1^2 + 3*a1 + 22)*q^343 + (-9*a1^2 - 8*a1 + 13)*q^344 + (-5*a1^2 - 7*a1 + 8)*q^345 + (8*a1^2 - 8*a1 - 16)*q^346 + (2*a1^2 + 9*a1 - 7)*q^347 + (-2*a1^2 + 3*a1 + 13)*q^348 + (-4*a1^2 - 7*a1 - 6)*q^349 + (3*a1^2 + 3*a1 + 5)*q^350 + (-12*a1^2 - 20*a1 - 1)*q^352 + (a1^2 - 6*a1 - 3)*q^353 + (9*a1 + 5)*q^354 + (-16*a1^2 - 26*a1 + 29)*q^355 + (-6*a1^2 - 14*a1 + 19)*q^356 + (5*a1^2 + 9*a1 + 1)*q^357 + (-a1^2 + 6*a1 + 5)*q^358 + (10*a1^2 + 28*a1 - 9)*q^359 + (-8*a1^2 - 9*a1 + 11)*q^360 + (5*a1^2 - 4*a1 - 19)*q^361 + (9*a1^2 + 15*a1 - 1)*q^362 + (-6*a1 - 11)*q^363 + (19*a1^2 + 23*a1 - 29)*q^365 + (-a1^2 - 7*a1)*q^366 + (11*a1^2 + 5*a1 - 10)*q^367 + (5*a1^2 + 7*a1 - 8)*q^368 + (-3*a1^2 - 11*a1 - 13)*q^369 + (3*a1^2 - a1)*q^370 + (15*a1^2 + 26*a1 - 6)*q^371 + (-9*a1 - 13)*q^372 + (-16*a1^2 - 21*a1 + 21)*q^373 + (-8*a1^2 - 4*a1 + 1)*q^374 + (-2*a1^2 + a1 + 6)*q^375 + (13*a1^2 + 23*a1 - 7)*q^376 + (-a1^2 + 2*a1 - 5)*q^378 + (-13*a1^2 - 25*a1 + 26)*q^379 + (a1^2 - 7*a1 + 5)*q^380 + (5*a1^2 + 11*a1 + 10)*q^381 + (-13*a1^2 - 9*a1 + 4)*q^382 + (-8*a1^2 - 24*a1 - 6)*q^383 + (-a1^2 + 8*a1 + 14)*q^384 + (6*a1^2 + 7*a1 - 7)*q^385 + (-2*a1^2 - 2*a1 - 8)*q^386 + (4*a1^2 + 11*a1 - 12)*q^387 + (12*a1^2 + 9*a1 - 4)*q^388 + (2*a1^2 - 14*a1 - 6)*q^389 + (5*a1^2 + 5*a1 - 4)*q^391 + (2*a1^2 + 2*a1 + 1)*q^392 + (8*a1^2 + 17*a1 - 4)*q^393 + (8*a1^2 + 3*a1 - 8)*q^394 + (6*a1^2 + 2*a1 - 3)*q^395 + (9*a1^2 + 10*a1 - 2)*q^396 + (11*a1^2 + 21*a1 - 7)*q^397 + (5*a1^2 + 6)*q^398 + (3*a1^2 + 2*a1 - 4)*q^399 + (-3*a1^2 - 6*a1 + 4)*q^400 + (a1^2 + 10*a1 + 18)*q^401 + (-5*a1^2 - 12*a1 - 1)*q^402 + (16*a1^2 + 16*a1 - 5)*q^404 + (2*a1^2 + 5*a1 - 8)*q^405 + (a1^2 + 2*a1 - 11)*q^406 + (-8*a1^2 - 15*a1 - 7)*q^407 + (a1^2 + 8*a1 + 6)*q^408 + (15*a1^2 + 36*a1 - 10)*q^409 + (-2*a1^2 - 5*a1 + 3)*q^410 + (-8*a1^2 - 16*a1 + 4)*q^411 + (-5*a1^2 - 17*a1 + 15)*q^412 + (-a1^2 + 12*a1 + 7)*q^413 + (a1^2 + 6*a1 - 3)*q^414 + (-22*a1^2 - 28*a1 + 37)*q^415 + (5*a1^2 + 16*a1 + 17)*q^417 + (-7*a1^2 + a1 + 4)*q^418 + (-9*a1^2 - 11*a1 - 15)*q^419 + (5*a1^2 + 5*a1 - 9)*q^420 + (-6*a1^2 - a1 - 7)*q^421 + (10*a1^2 + 7*a1 - 5)*q^422 + (-10*a1^2 - 22*a1 + 9)*q^423 + (-a1^2 + 12*a1 + 19)*q^424 + (-a1^2 - 10*a1 - 2)*q^425 + (7*a1 + 10)*q^426 + (-8*a1^2 - 20*a1 + 13)*q^427 + (-a1^2 + 4*a1 - 7)*q^428 + (-a1^2 - 8*a1 + 7)*q^430 + (-6*a1^2 + 4*a1 + 5)*q^431 + (4*a1^2 + 7*a1 - 7)*q^432 + (5*a1^2 - 2*a1 - 16)*q^433 + (3*a1^2 + 2*a1 + 9)*q^434 + (-8*a1^2 - 13*a1 + 13)*q^435 + (-2*a1^2 - 10*a1 - 12)*q^436 + (6*a1^2 + 5*a1 - 8)*q^437 + (-3*a1^2 - 4*a1 - 7)*q^438 + (-9*a1^2 - 23*a1 + 4)*q^439 + (-4*a1^2 - 2*a1 + 7)*q^440 + (a1^2 - 2*a1 - 2)*q^441 + (-6*a1^2 - 10*a1 + 20)*q^443 + (3*a1^2 + 13*a1 + 5)*q^444 + (-20*a1^2 - 26*a1 + 33)*q^445 + (-6*a1 + 3)*q^446 + (-3*a1^2 - 6*a1 - 3)*q^447 + (-9*a1^2 - 7*a1 + 3)*q^448 + (6*a1^2 + 17*a1 - 5)*q^449 + (-7*a1^2 - 7*a1 + 2)*q^450 + (13*a1^2 + 36*a1 + 12)*q^451 + (6*a1^2 - 4*a1 - 17)*q^452 + (3*a1^2 + 4*a1 - 14)*q^453 + (5*a1^2 - a1 - 8)*q^454 + (-3*a1^2 - 2*a1 + 3)*q^456 + (17*a1^2 + 25*a1 - 25)*q^457 + (a1^2 - 15*a1 - 8)*q^458 + (7*a1 - 1)*q^459 + (11*a1^2 + 13*a1 - 18)*q^460 + (-6*a1^2 + a1 + 1)*q^461 + (-5*a1^2 - 11*a1 - 6)*q^462 + (8*a1^2 + 3*a1 - 16)*q^463 + (8*a1^2 + 13*a1 - 13)*q^464 + (6*a1^2 + 11*a1 - 9)*q^465 + (-a1^2 - 6*a1 + 3)*q^466 + (19*a1^2 + 49*a1 - 18)*q^467 + (-15*a1^2 - 28*a1 + 14)*q^469 + (3*a1^2 + 7*a1 - 9)*q^470 + (-5*a1 - 6)*q^471 + (10*a1^2 + 11*a1 + 3)*q^472 + (a1^2 + 7*a1 - 5)*q^473 + (-8*a1^2 - 11*a1 - 4)*q^474 + (a1^2 - 4*a1 + 3)*q^475 + (-7*a1^2 + 3*a1 + 9)*q^476 + (-2*a1^2 - 5*a1 - 16)*q^477 + (-3*a1^2 - 19*a1 - 3)*q^478 + (-3*a1^2 - a1 - 22)*q^479 + (-5*a1^2 - 10*a1 + 8)*q^480 + (-10*a1^2 - 11*a1 - 1)*q^482 + (-2*a1^2 - a1 + 10)*q^483 + (-12*a1^2 - 16*a1 + 11)*q^484 + (5*a1 - 6)*q^485 + (13*a1^2 + 14*a1 - 5)*q^486 + (-11*a1^2 - 42*a1 + 3)*q^487 + (a1^2 + 5*a1 - 14)*q^488 + (-15*a1^2 - 32*a1 - 1)*q^489 + (-2*a1^2 + 1)*q^490 + (11*a1^2 + 19*a1 + 9)*q^491 + (-7*a1^2 - 21*a1 - 14)*q^492 + (4*a1^2 + 13*a1 - 3)*q^493 + (a1^2 + 4*a1 - 6)*q^495 + (-6*a1^2 - 11*a1 + 9)*q^496 + (-13*a1^2 - 9*a1 + 36)*q^497 + (-2*a1^2 - 7*a1 + 4)*q^498 + (15*a1^2 + 21*a1 - 5)*q^499 + O(q^500)
Time: CPU 2.06 s, Wall: 2.25 s