CoCalc -- Collaborative Calculation in the Cloud
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\\ an_s2g0new_601-700.gp
\\ This is a PARI readable nonnormalized basis for S_2(Gamma_0(N)) for N 
\\ in the range:  601 <= N <= 700.
\\ The number of a_n computed is sufficient to satisfy Sturm's bound.
\\ William Stein ([email protected])

E[601,1] = [x^20+5*x^19-13*x^18-96*x^17+29*x^16+740*x^15+323*x^14-2975*x^13-2351*x^12+6757*x^11+6719*x^10-8773*x^9-9894*x^8+6329*x^7+7721*x^6-2423*x^5-3056*x^4+471*x^3+559*x^2-35*x-37, 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E[602,1] = [x, [1,-1,-1,1,2,1,-1,-1,-2,-2,5,-1,2,1,-2,1,0,2,-3,2,1,-5,6,1,-1,-2,5,-1,-9,2,9,-1,-5,0,-2,-2,9,3,-2,-2,0,-1,1,5,-4,-6,12,-1,1,1,0,2,2,-5,10,1,3,9,-4,-2,2,-9,2,1,4,5,15,0,-6,2,3,2,14,-9,1,-3,-5,2,-4,2,1,0,-4,1,0,-1,9,-5,-3,4,-2,6,-9,-12,-6,1,-4,-1,-10,-1,-15,0,1,-2,2,-2,-9,5,-4,-10,-9,-1,-20,-3,12,-9,-4,4,0,2,14,-2,0,9,-12,-2,-20,-1,-1,-4,7,-5,3,-15,10,0,-6,6,8,-2,-12,-3,10,-2,-18,-14,-1,9,10,-1,-3,3,0,5,18,-2,22,4,-2,-2,-6,-1,-18,0,-10,4,21,-1,-9,0,6,1,-3,-9,1,5]];
E[602,2] = [x, [1,-1,3,1,2,-3,-1,-1,6,-2,-3,3,2,1,6,1,0,-6,1,2,-3,3,6,-3,-1,-2,9,-1,-1,-6,5,-1,-9,0,-2,6,-7,-1,6,-2,-8,3,1,-3,12,-6,-12,3,1,1,0,2,-6,-9,-6,1,3,1,12,6,-6,-5,-6,1,4,9,15,0,18,2,-5,-6,-2,7,-3,1,3,-6,4,2,9,8,-12,-3,0,-1,-3,3,-7,-12,-2,6,15,12,2,-3,12,-1,-18,-1,-3,0,-11,-2,-6,6,7,9,4,6,-21,-1,12,-3,12,-1,12,-12,0,-6,-2,6,-24,5,-12,6,12,-1,3,-4,3,-9,-1,-15,18,0,2,-18,-8,-2,-36,5,-6,6,-2,2,3,-7,-22,3,-11,-1,0,-3,10,6,-2,-4,-18,-2,-6,-9,-10,-8,-18,12,-23,3,-9,0,6,1,-15,3,1,-3]];
E[602,3] = [x^3+3*x^2-x-2, [1,-1,x,1,-x^2-2*x+2,-x,-1,-1,x^2-3,x^2+2*x-2,2*x^2+4*x-4,x,-2*x-4,1,x^2+x-2,1,-2*x^2-7*x,-x^2+3,x^2+4*x-2,-x^2-2*x+2,-x,-2*x^2-4*x+4,3*x^2+8*x-4,-x,-2*x^2-5*x+1,2*x+4,-3*x^2-5*x+2,-1,-x+4,-x^2-x+2,-2*x^2-5*x,-1,-2*x^2-2*x+4,2*x^2+7*x,x^2+2*x-2,x^2-3,x-4,-x^2-4*x+2,-2*x^2-4*x,x^2+2*x-2,3*x^2+8*x-2,x,-1,2*x^2+4*x-4,x^2+5*x-4,-3*x^2-8*x+4,-2*x^2-3*x+4,x,1,2*x^2+5*x-1,-x^2-2*x-4,-2*x-4,2*x^2+6*x-6,3*x^2+5*x-2,4*x^2+10*x-12,1,x^2-x+2,x-4,-4,x^2+x-2,4*x+2,2*x^2+5*x,-x^2+3,1,2*x^2+6*x-4,2*x^2+2*x-4,2*x^2+4*x-12,-2*x^2-7*x,-x^2-x+6,-x^2-2*x+2,-4*x^2-14*x+4,-x^2+3,-8,-x+4,x^2-x-4,x^2+4*x-2,-2*x^2-4*x+4,2*x^2+4*x,-x^2-4*x-4,-x^2-2*x+2,x^2-x+3,-3*x^2-8*x+2,-6*x^2-10*x+12,-x,-3*x^2-5*x+10,1,-x^2+4*x,-2*x^2-4*x+4,-4*x+4,-x^2-5*x+4,2*x+4,3*x^2+8*x-4,x^2-2*x-4,2*x^2+3*x-4,4*x^2+7*x-10,-x,x^2-4*x-6,-1,-2*x^2-10*x+8,-2*x^2-5*x+1,2*x^2+4*x-4,x^2+2*x+4,5*x^2+10*x-14,2*x+4,-x^2-x+2,-2*x^2-6*x+6,-2*x^2+2*x+8,-3*x^2-5*x+2,6*x+14,-4*x^2-10*x+12,x^2-4*x,-1,-2*x^2+2*x+14,-x^2+x-2,6*x^2+13*x-18,-x+4,2*x^2+4*x+8,4,2*x^2+7*x,-x^2-x+2,-8*x^2-20*x+13,-4*x-2,-x^2+x+6,-2*x^2-5*x,3*x^2+5*x-2,x^2-3,8*x^2+17*x-6,-1,-x,-2*x^2-6*x+4,4*x^2+15*x,-2*x^2-2*x+4,-x^2-4*x+2,-2*x^2-4*x+12,-x^2-6*x+8,2*x^2+7*x,-4*x-2,x^2+x-6,-8*x^2-16*x+8,x^2+2*x-2,3*x^2+2*x-4,4*x^2+14*x-4,-4*x^2-12*x+8,x^2-3,-5*x^2-9*x+10,8,x,x-4,-x+8,-x^2+x+4,6*x^2+14*x-4,-x^2-4*x+2,7*x^2+16*x-2,2*x^2+4*x-4,-x^2-3*x+6,-2*x^2-4*x,x^2-2*x-18,x^2+4*x+4,-4*x+4,x^2+2*x-2,-3*x^2-8*x+4,-x^2+x-3,-5*x^2-10*x+8,3*x^2+8*x-2,-2*x^2-8*x+8,6*x^2+10*x-12,2*x^2+10*x+14,x,4*x^2+16*x+3,3*x^2+5*x-10,-7*x^2-9*x+8,-1,8*x+4,x^2-4*x,2*x^2+5*x-1,2*x^2+4*x-4]];
E[602,4] = [x^4-5*x^3+2*x^2+17*x-17, [1,-1,x,1,-x^3+2*x^2+5*x-6,-x,1,-1,x^2-3,x^3-2*x^2-5*x+6,-x^3+3*x^2+5*x-10,x,2*x^3-6*x^2-8*x+20,-1,-3*x^3+7*x^2+11*x-17,1,-x^2+2*x+1,-x^2+3,3*x^3-9*x^2-10*x+29,-x^3+2*x^2+5*x-6,x,x^3-3*x^2-5*x+10,x^3-2*x^2-5*x+6,-x,-2*x^3+7*x^2+8*x-20,-2*x^3+6*x^2+8*x-20,x^3-6*x,1,x^3-2*x^2-7*x+9,3*x^3-7*x^2-11*x+17,2*x^3-6*x^2-9*x+18,-1,-2*x^3+7*x^2+7*x-17,x^2-2*x-1,-x^3+2*x^2+5*x-6,x^2-3,-x^3+4*x^2+x-7,-3*x^3+9*x^2+10*x-29,4*x^3-12*x^2-14*x+34,x^3-2*x^2-5*x+6,3*x^3-10*x^2-9*x+26,-x,-1,-x^3+3*x^2+5*x-10,-5*x^3+11*x^2+19*x-33,-x^3+2*x^2+5*x-6,2*x^3-7*x^2-8*x+29,x,1,2*x^3-7*x^2-8*x+20,-x^3+2*x^2+x,2*x^3-6*x^2-8*x+20,2*x^2-2*x-6,-x^3+6*x,-6*x^3+16*x^2+22*x-42,-1,6*x^3-16*x^2-22*x+51,-x^3+2*x^2+7*x-9,-4*x^3+12*x^2+12*x-36,-3*x^3+7*x^2+11*x-17,-2*x^3+4*x^2+8*x-8,-2*x^3+6*x^2+9*x-18,x^2-3,1,6*x^3-18*x^2-22*x+50,2*x^3-7*x^2-7*x+17,-3*x^3+7*x^2+9*x-12,-x^2+2*x+1,3*x^3-7*x^2-11*x+17,x^3-2*x^2-5*x+6,-3*x^3+9*x^2+7*x-20,-x^2+3,-2*x^3+8*x^2+8*x-30,x^3-4*x^2-x+7,-3*x^3+12*x^2+14*x-34,3*x^3-9*x^2-10*x+29,-x^3+3*x^2+5*x-10,-4*x^3+12*x^2+14*x-34,x^3-4*x^2+x+8,-x^3+2*x^2+5*x-6,5*x^3-11*x^2-17*x+26,-3*x^3+10*x^2+9*x-26,-4*x^3+10*x^2+14*x-24,x,x^3-x^2-7*x+11,1,3*x^3-9*x^2-8*x+17,x^3-3*x^2-5*x+10,2*x^3-7*x^2-3*x+19,5*x^3-11*x^2-19*x+33,2*x^3-6*x^2-8*x+20,x^3-2*x^2-5*x+6,4*x^3-13*x^2-16*x+34,-2*x^3+7*x^2+8*x-29,4*x^3-15*x^2-16*x+47,-x,-x^3+2*x^2+9*x-8,-1,2*x^2+2*x-4,-2*x^3+7*x^2+8*x-20,-x^2+x-7,x^3-2*x^2-x,-x^3+3*x^2+4*x-3,-2*x^3+6*x^2+8*x-20,-3*x^3+7*x^2+11*x-17,-2*x^2+2*x+6,-3*x^3+13*x^2+9*x-46,x^3-6*x,-2*x-2,6*x^3-16*x^2-22*x+42,-x^3+3*x^2+10*x-17,1,-4*x^3+12*x^2+8*x-32,-6*x^3+16*x^2+22*x-51,2*x^3-7*x^2-8*x+15,x^3-2*x^2-7*x+9,2*x^3-4*x^2-10*x+8,4*x^3-12*x^2-12*x+36,-x^2+2*x+1,3*x^3-7*x^2-11*x+17,-5*x^3+15*x^2+19*x-47,2*x^3-4*x^2-8*x+8,5*x^3-15*x^2-25*x+51,2*x^3-6*x^2-9*x+18,-9*x^3+25*x^2+31*x-71,-x^2+3,-4*x^3+9*x^2+14*x-17,-1,-x,-6*x^3+18*x^2+22*x-50,2*x^3-4*x^2-9*x+6,-2*x^3+7*x^2+7*x-17,3*x^3-9*x^2-10*x+29,3*x^3-7*x^2-9*x+12,-5*x^3+8*x^2+19*x-34,x^2-2*x-1,2*x^3-4*x^2-8*x+8,-3*x^3+7*x^2+11*x-17,-4*x^2+4*x+12,-x^3+2*x^2+5*x-6,3*x^3-12*x^2-5*x+34,3*x^3-9*x^2-7*x+20,6*x^3-16*x^2-24*x+38,x^2-3,5*x^3-15*x^2-15*x+31,2*x^3-8*x^2-8*x+30,x,-x^3+4*x^2+x-7,3*x^2-2*x-21,3*x^3-12*x^2-14*x+34,-7*x^3+23*x^2+23*x-68,-3*x^3+9*x^2+10*x-29,-3*x^3+6*x^2+11*x-20,x^3-3*x^2-5*x+10,11*x^3-29*x^2-43*x+79,4*x^3-12*x^2-14*x+34,7*x^3-18*x^2-25*x+48,-x^3+4*x^2-x-8,2*x^3-2*x^2-6*x,x^3-2*x^2-5*x+6,x^3-2*x^2-5*x+6,-5*x^3+11*x^2+17*x-26,3*x^3-12*x^2-9*x+38,3*x^3-10*x^2-9*x+26,-14*x^3+34*x^2+60*x-102,4*x^3-10*x^2-14*x+24,-4*x^3+11*x^2+19*x-37,-x,-4*x^3+8*x^2+20*x-21,-x^3+x^2+7*x-11,5*x^3-7*x^2-21*x+15,-1,5*x^2-11*x-15,-3*x^3+9*x^2+8*x-17,-2*x^3+7*x^2+8*x-20,-x^3+3*x^2+5*x-10]];
E[602,5] = [x, [1,-1,0,1,-4,0,-1,-1,-3,4,0,0,2,1,0,1,6,3,4,-4,0,0,0,0,11,-2,0,-1,2,0,2,-1,0,-6,4,-3,2,-4,0,4,-2,0,1,0,12,0,-6,0,1,-11,0,2,-6,0,0,1,0,-2,6,0,12,-2,3,1,-8,0,0,6,0,-4,-8,3,4,-2,0,4,0,0,4,-4,9,2,18,0,-24,-1,0,0,-16,-12,-2,0,0,6,-16,0,18,-1,0,11,18,0,-2,-2,0,6,16,0,-14,0,0,-1,-6,0,0,2,-6,-6,-6,0,-11,-12,0,2,-24,-3,12,-1,0,8,0,0,-4,0,0,-6,-10,0,-2,4,0,8,0,-3,-8,-4,0,2,-10,0,-8,-4,-18,0,-8,0,4,-4,0,4,0,-9,20,-2,0,-18,22,0,-9,24,-12,1,6,0,-11,0]];
E[602,6] = [x^2+3*x+1, [1,1,x,1,-x-3,x,-1,1,-3*x-4,-x-3,-2*x-2,x,2*x,-1,1,1,x-2,-3*x-4,-x-5,-x-3,-x,-2*x-2,3*x+1,x,3*x+3,2*x,2*x+3,-1,3*x+4,1,-9*x-14,1,4*x+2,x-2,x+3,-3*x-4,5*x+4,-x-5,-6*x-2,-x-3,7*x+7,-x,1,-2*x-2,4*x+9,3*x+1,5*x+6,x,1,3*x+3,-5*x-1,2*x,-4*x-4,2*x+3,2*x+4,-1,-2*x+1,3*x+4,4,1,-12*x-18,-9*x-14,3*x+4,1,2,4*x+2,-2*x+2,x-2,-8*x-3,x+3,2*x+8,-3*x-4,-4*x-8,5*x+4,-6*x-3,-x-5,2*x+2,-6*x-2,11*x+13,-x-3,6*x+10,7*x+7,6,-x,2*x+7,1,-5*x-3,-2*x-2,-4*x-8,4*x+9,-2*x,3*x+1,13*x+9,5*x+6,5*x+14,x,x-3,1,-4*x+2,3*x+3,-6*x-6,-5*x-1,3*x-7,2*x,-1,-4*x-4,-4*x+2,2*x+3,10*x+6,2*x+4,-11*x-5,-1,-12*x-20,-2*x+1,-x,3*x+4,10*x+6,4,-x+2,1,-4*x-11,-12*x-18,-14*x-7,-9*x-14,2*x+9,3*x+4,-9*x-18,1,x,2,3*x+12,4*x+2,x+5,-2*x+2,-3*x-7,x-2,10,-8*x-3,12*x+16,x+3,-9*x-5,2*x+8,8*x+4,-3*x-4,-4*x-9,-4*x-8,x,5*x+4,-5*x-16,-6*x-3,-4*x+6,-x-5,11*x+11,2*x+2,14*x+33,-6*x-2,13*x+19,11*x+13,8*x+4,-x-3,-3*x-1,6*x+10,-9*x-25,7*x+7,-2*x-2,6,-8*x-4,-x,-12*x-17,2*x+7,10*x+17,1,-8*x-12,-5*x-3,-3*x-3,-2*x-2]];
E[602,7] = [x^3-x^2-6*x+4, [1,1,x,1,-x^2+x+4,x,1,1,x^2-3,-x^2+x+4,x^2-4,x,-x^2-x+6,1,-2*x+4,1,-2*x-2,x^2-3,-x-4,-x^2+x+4,x,x^2-4,2*x^2-8,x,