CoCalc Public Fileswww / Tables / eigen_k4_N1-197_prec97.gp
Author: William A. Stein

\\ This is a table of the first 97 Hecke eigenvalues
\\ of newforms for Gamma_0(N).
\\ Notation:
\\ f[N,k]  = [
\\            [g(x), [wq's], [a2(x),...,ap(x)]],
\\                  ...
\\            [g(x), [wq's], [a2(x),...,ap(x)]]
\\          ];
\\ Where Q_f = Q(...a_n...) = Q[x]/g(x).
\\ The newforms are ordered by dimension,
\\ then W_q's, then traces.

\\ William Stein ([email protected])

\\ uncomment the following two lines to make PARI-readable.
\\ {

f = matrix(197,4);

f[5,4]=[
[x+4, [1], [-4,2,-5,6,32,-38,26,100,-78,-50,-108,266,22,442,-514,2,500,-518,126,412,-878,600,282,-150,386]]];

f[6,4]=[
[x+2, [1,1], [-2,-3,6,-16,12,38,-126,20,168,30,-88,254,42,-52,-96,198,-660,-538,884,792,218,-520,-492,810,1154]]];

f[7,4]=[
[x+1, [1], [-1,-2,16,-7,-8,28,54,-110,48,-110,12,-246,182,128,324,-162,810,-488,244,-768,-702,440,-1302,730,294]]];

f[8,4]=[
[x, [1], [0,-4,-2,24,-44,22,50,44,-56,198,-160,-162,-198,52,528,-242,-668,550,188,728,154,-656,236,714,-478]]];

f[9,4]=[
[x, [1], [0,0,0,20,0,-70,0,56,0,0,308,110,0,-520,0,0,0,182,-880,0,1190,884,0,0,-1330]]];

f[10,4]=[
[x-2, [-1,-1], [2,-8,5,-4,12,-58,66,-100,132,-90,152,-34,-438,32,-204,222,420,902,-1024,432,362,-160,72,810,1106]]];

f[11,4]=[
[x^2-2*x-2, [1], [x,-4*x+3,8*x-7,-4*x+14,-11,-20*x+60,12*x-74,60*x-24,-36*x-13,-56*x+128,28*x-45,-8*x+35,-4*x+272,-16*x-14,-120*x-16,-56*x-190,-132*x+449,184*x+236,-20*x+397,76*x-415,-468*x+268,656*x-498,120*x+114,-328*x-593,144*x+953]]];

f[12,4]=[
[x, [-1,-1], [0,3,-18,8,36,-10,18,-100,72,-234,-16,-226,90,452,432,414,-684,422,332,-360,26,512,-1188,-630,-1054]]];

f[13,4]=[
[x+5, [-1], [-5,-7,-7,-13,-26,13,77,-126,-96,-82,196,-131,336,-201,-105,-432,-294,-56,478,9,98,1304,-308,-1190,70]],
[x^2-x-4, [1], [x,-3*x+4,x-2,11*x-10,12*x+34,-13,-17*x+18,-32*x-26,-12*x+104,96*x-70,-34*x-26,5*x+102,22*x-126,143*x+72,-121*x+278,30*x-74,124*x-246,-190*x-434,-232*x+150,-231*x+50,260*x+98,40*x-524,-182*x+1070,-388*x-166,508*x-718]]];

f[14,4]=[
[x+2, [1,1], [-2,8,-14,-7,-28,18,74,80,-112,190,72,-346,162,-412,24,318,-200,-198,-716,392,538,240,-1072,810,1354]],
[x-2, [-1,-1], [2,-2,-12,7,48,56,-114,2,-120,-54,236,146,126,-376,-12,174,138,380,-484,576,-1150,776,378,-390,-1330]]];

f[15,4]=[
[x-3, [1,1], [3,-3,-5,20,-24,74,54,-124,-120,-78,200,-70,330,92,-24,450,24,-322,-196,-288,-430,-520,156,1026,-286]],
[x-1, [-1,-1], [1,3,5,-24,52,22,-14,-20,-168,230,-288,-34,122,-188,256,-338,100,742,-84,-328,-38,-240,1212,330,866]]];

f[16,4]=[
[x, [1], [0,4,-2,-24,44,22,50,-44,56,198,160,-162,-198,-52,-528,-242,668,550,-188,-728,154,656,-236,714,-478]]];

f[17,4]=[
[x+3, [-1], [-3,-8,6,-28,-24,-58,17,116,-60,30,-172,-58,-342,-148,288,318,252,110,-484,-708,362,-484,756,-774,-382]],
[x^3-x^2-24*x+32, [1], [x,-1/4*x^2-7/4*x+6,-1/2*x^2-3/2*x+6,5/4*x^2+11/4*x-14,-9/4*x^2+17/4*x+26,-7/2*x^2-5/2*x+68,-17,-7/2*x^2+23/2*x+80,43/4*x^2-27/4*x-126,-7/2*x^2-53/2*x-86,-55/4*x^2-9/4*x+302,39/2*x^2+61/2*x-210,28*x^2+32*x-566,-29/2*x^2-83/2*x+436,x^2-45*x+212,-27*x^2+35*x+530,65/2*x^2-65/2*x-308,-7/2*x^2-149/2*x+54,27*x^2+105*x-140,-257/4*x^2-31/4*x+918,16*x+274,87/4*x^2-807/4*x-486,-105/2*x^2-151/2*x+84,83/2*x^2-303/2*x-684,-65*x^2-55*x+990]]];

f[18,4]=[
[x-2, [-1,-1], [2,0,-6,-16,-12,38,126,20,-168,-30,-88,254,-42,-52,96,-198,660,-538,884,-792,218,-520,492,-810,1154]]];

f[19,4]=[
[x+3, [-1], [-3,-5,-12,11,-54,11,-93,19,183,-249,56,-250,240,-196,-168,435,195,-358,-961,-246,353,-34,234,-168,758]],
[x^3-3*x^2-18*x+38, [1], [x,-1/3*x^2-4/3*x+20/3,1/3*x^2-8/3*x+7/3,-4/3*x^2+8/3*x+17/3,-1/3*x^2+8/3*x+23/3,1/3*x^2+16/3*x+34/3,-26/3*x^2+40/3*x+379/3,-19,-25/3*x^2+8/3*x+266/3,55/3*x^2-20/3*x-428/3,44/3*x^2-124/3*x-676/3,-76/3*x^2+20/3*x+830/3,-14/3*x^2+4/3*x+1162/3,27*x^2+56*x-651,17*x^2-16*x-217,-19/3*x^2+68/3*x+1034/3,119/3*x^2-40/3*x-1480/3,-133/3*x^2-64/3*x+3047/3,-25*x^2+4*x+302,-12*x^2-40*x+502,56*x^2-120*x-511,-214/3*x^2+404/3*x+3188/3,70/3*x^2-320/3*x-1496/3,52/3*x^2+556/3*x-1508/3,-106/3*x^2-376/3*x-484/3]]];

f[20,4]=[
[x, [-1,-1], [0,4,5,-16,-60,86,18,44,48,-186,176,254,186,-100,168,-498,-252,-58,-1036,168,506,272,948,-1014,-766]]];

f[21,4]=[
[x-4, [1,1], [4,-3,-4,-7,62,-62,84,100,-42,-10,-48,-246,-248,68,324,258,120,622,904,-678,-642,740,468,200,-1266]],
[x+3, [1,-1], [-3,-3,-18,7,-36,-34,42,-124,0,102,-160,398,-318,-268,240,-498,-132,398,92,-720,-502,-1024,-204,354,-286]],
[x^2+3*x-12, [-1,-1], [x,3,-2*x,7,-10*x-18,12*x+26,2*x,24*x+68,34*x+54,-24*x-162,-72*x-88,36*x-70,30*x-180,48*x+260,-68*x-108,-4*x-558,116*x+576,-72*x-322,-108*x-88,30*x+522,-12*x+518,108*x-124,-96*x+828,142*x+396,-276*x-10]]];

f[22,4]=[
[x-4, [1,1], [-2,4,14,-8,-11,-50,130,-108,-96,142,40,382,-118,220,520,238,-852,190,-12,-112,-6,304,820,202,-1406]],
[x+7, [1,-1], [-2,-7,-19,14,11,-72,-46,-20,-107,120,117,-201,-228,-242,-96,458,435,-668,439,-1113,-72,-70,358,895,409]],
[x-2, [-1,-1], [2,1,-3,-10,11,-16,42,116,189,-120,-163,-409,468,110,144,90,-453,20,-97,-465,848,-742,438,-273,761]]];

f[23,4]=[
[x+2, [-1], [-2,-5,-6,-8,34,-57,-80,-70,23,245,103,-298,95,88,-357,-414,-408,822,926,335,-899,-1322,-36,-460,-964]],
[x^4-2*x^3-24*x^2+61*x+2, [1], [x,-1/11*x^3-5/11*x^2+x+71/11,10/11*x^3+6/11*x^2-20*x+148/11,-20/11*x^3-12/11*x^2+34*x-142/11,-12/11*x^3+28/11*x^2+30*x-600/11,x^3+5*x^2-21*x-19,14/11*x^3+26/11*x^2-12*x+106/11,-8/11*x^3-128/11*x^2+16*x+1778/11,-23,1/11*x^3-127/11*x^2-51*x+1997/11,-65/11*x^3-17/11*x^2+133*x-1545/11,222/11*x^3+186/11*x^2-380*x+1860/11,63/11*x^3+7/11*x^2-137*x+807/11,98/11*x^3-126/11*x^2-182*x+3404/11,-181/11*x^3+19/11*x^2+385*x-5629/11,106/11*x^3+90/11*x^2-306*x+702/11,-108/11*x^3-276/11*x^2+184*x-1396/11,106/11*x^3+90/11*x^2-150*x+2550/11,-68/11*x^3-428/11*x^2+162*x+5488/11,47/11*x^3+587/11*x^2+85*x-8837/11,257/11*x^3-123/11*x^2-579*x+10925/11,-46/11*x^3+298/11*x^2+10*x-6590/11,-310/11*x^3+122/11*x^2+592*x-6854/11,-82/11*x^3-410/11*x^2+242*x+9804/11,-526/11*x^3-562/11*x^2+1184*x-362/11]]];

f[24,4]=[
[x, [-1,-1], [0,3,14,-24,-28,-74,82,92,8,-138,80,30,282,4,240,-130,596,-218,-436,856,-998,-32,-1508,-246,866]]];

f[25,4]=[
[x-1, [1], [1,7,0,6,-43,-28,91,-35,162,160,42,-314,-203,92,196,82,-280,-518,141,412,-763,510,777,-945,1246]],
[x-4, [1], [4,-2,0,-6,32,38,-26,100,78,-50,-108,-266,22,-442,514,-2,500,-518,-126,412,878,600,-282,-150,-386]],
[x+1, [-1], [-1,-7,0,-6,-43,28,-91,-35,-162,160,42,314,-203,-92,-196,-82,-280,-518,-141,412,763,510,-777,-945,-1246]]];

f[26,4]=[
[x+2, [1,1], [-2,3,11,19,-38,-13,-51,90,-52,-190,292,-441,312,373,-41,468,530,592,-206,-863,-322,-460,528,870,-346]],
[x+1, [-1,-1], [2,-1,17,-35,2,13,-19,94,-72,246,-100,-11,-280,241,137,-232,-386,64,-670,55,-838,1016,420,-934,-1154]],
[x-4, [-1,-1], [2,4,-18,20,-48,13,66,-16,168,6,20,254,-390,-124,-468,558,-96,-826,-160,-420,362,776,0,1626,-1294]]];

f[27,4]=[
[x-3, [1], [3,0,15,-25,-15,20,72,2,114,30,101,-430,-30,110,-330,621,-660,-376,-250,-360,785,488,489,-450,-1105]],
[x+3, [-1], [-3,0,-15,-25,15,20,-72,2,-114,-30,101,-430,30,110,330,-621,660,-376,-250,360,785,488,-489,450,-1105]],
[x^2-18, [1], [x,0,-4*x,11,4*x,29,-12*x,29,20*x,64*x,-268,83,-64*x,-232,-92*x,72*x,68*x,767,-511,168*x,137,-475,136*x,-60*x,821]]];

f[28,4]=[
[x+10, [-1,1], [0,-10,-8,-7,-40,-12,-58,26,-64,-62,252,26,6,416,-396,-450,274,-576,-476,-448,-158,-936,530,-390,214]],
[x-4, [-1,-1], [0,4,6,7,-12,-82,-30,68,216,246,-112,110,-246,-172,192,558,540,110,140,-840,-550,-208,516,-1398,1586]]];

f[29,4]=[
[x^2+2*x-1, [-1], [x,-3*x-8,4*x-1,10*x+2,-37*x-50,-26*x-39,18*x+48,32*x-78,48*x+74,29,-63*x-210,-56*x+100,138*x+158,171*x+10,-207*x-272,-122*x+379,248*x-202,-178*x-652,484*x+644,-34*x-364,-640*x-316,-341*x-212,64*x+670,522*x+902,-578*x-566]],
[x^5-33*x^3+28*x^2+192*x-256, [1], [x,1/8*x^4+1/4*x^3-33/8*x^2-15/4*x+25,-11/16*x^4-5/4*x^3+315/16*x^2+16*x-85,3/8*x^4+x^3-83/8*x^2-37/2*x+56,-x^4-13/4*x^3+29*x^2+217/4*x-153,25/16*x^4+17/4*x^3-649/16*x^2-125/2*x+169,9/8*x^4+x^3-265/8*x^2-7/2*x+150,-5/4*x^4-5/2*x^3+141/4*x^2+55/2*x-112,-35/8*x^4-17/2*x^3+1075/8*x^2+140*x-650,-29,-5/4*x^4-3/4*x^3+173/4*x^2+107/4*x-147,49/8*x^4+17/2*x^3-1569/8*x^2-149*x+1080,-29/4*x^4-33/2*x^3+869/4*x^2+527/2*x-1332,29/4*x^4+47/4*x^3-813/4*x^2-423/4*x+795,-35/8*x^4-27/4*x^3+883/8*x^2-107/4*x-287,23/16*x^4+3/4*x^3-551/16*x^2-101/2*x-49,59/8*x^4+31/2*x^3-1579/8*x^2-259*x+874,69/8*x^4+9*x^3-1893/8*x^2-11/2*x+966,-57/4*x^4-11*x^3+1705/4*x^2+104*x-1560,-91/4*x^4-67/2*x^3+2491/4*x^2+733/2*x-2506,-7/8*x^4+13/2*x^3+183/8*x^2-79*x-336,221/8*x^4+291/4*x^3-6381/8*x^2-4481/4*x+4015,-127/8*x^4-53/2*x^3+3823/8*x^2+476*x-2174,-61/2*x^4-147/2*x^3+1729/2*x^2+2243/2*x-3872,83/4*x^4+71/2*x^3-2299/4*x^2-905/2*x+2644]]];

f[30,4]=[
[x+2, [1,-1,-1], [-2,3,5,32,-60,-34,42,-76,0,6,-232,134,234,-412,-360,222,660,-490,812,120,746,152,-804,-678,194]],
[x-2, [-1,-1,1], [2,3,-5,-4,-48,2,-114,140,72,210,272,-334,-198,-268,216,-78,240,302,596,-768,-478,-640,-348,210,-1534]]];

f[31,4]=[
[x^2+5*x+2, [-1], [x,-2*x-6,3*x-5,5*x+3,6*x+2,-20*x-18,-8*x-62,13*x+7,-54*x-130,-62*x-312,31,156*x+406,93*x-59,188*x+580,16*x+296,-106*x-292,-49*x-427,16*x+226,-240*x-388,-229*x-731,124*x-610,132*x-236,130*x+1054,222*x+764,247*x+1299]],
[x^5-3*x^4-30*x^3+79*x^2+167*x-386, [1], [x,5/104*x^4+1/26*x^3-109/52*x^2-59/104*x+867/52,-1/4*x^4+15/2*x^2-5/4*x-65/2,-1/13*x^4+7/13*x^3+15/13*x^2-126/13*x+77/13,93/104*x^4-23/26*x^3-1237/52*x^2+941/104*x+5747/52,-63/104*x^4-23/26*x^3+1103/52*x^2+2033/104*x-7097/52,-51/52*x^4+21/13*x^3+883/26*x^2-1291/52*x-4725/26,8/13*x^4-43/13*x^3-237/13*x^2+813/13*x+1035/13,3/13*x^4+18/13*x^3-240/13*x^2-389/13*x+3058/13,-81/104*x^4-37/26*x^3+1433/52*x^2+5199/104*x-4623/52,-31,-633/104*x^4+71/26*x^3+9369/52*x^2+647/104*x-51335/52,391/52*x^4+8/13*x^3-6033/26*x^2-3085/52*x+33859/26,439/104*x^4-89/26*x^3-6055/52*x^2-3641/104*x+26889/52,-45/13*x^4-62/13*x^3+1572/13*x^2+1545/13*x-11446/13,-131/104*x^4-151/26*x^3+1067/52*x^2+13485/104*x+6363/52,-123/52*x^4-152/13*x^3+1709/26*x^2+16417/52*x-11131/26,-271/104*x^4+289/26*x^3+2767/52*x^2-28127/104*x+4343/52,38/13*x^4+124/13*x^3-1220/13*x^2-1634/13*x+1208/13,35/13*x^4+171/13*x^3-889/13*x^2-5262/13*x+5235/13,-99/13*x^4+212/13*x^3+3006/13*x^2-4271/13*x-14048/13,609/52*x^4-159/13*x^3-7369/26*x^2+12553/52*x+13363/26,375/104*x^4+179/26*x^3-4847/52*x^2-22521/104*x+34969/52,-193/13*x^4+246/13*x^3+5248/13*x^2-1633/13*x-14532/13,-413/52*x^4+518/13*x^3+4391/26*x^2-31849/52*x-4893/26]]];

f[32,4]=[
[x, [1], [0,0,22,0,0,-18,-94,0,0,-130,0,214,-230,0,0,518,0,830,0,0,1098,0,0,-1670,594]],
[x-8, [1], [0,8,-10,16,-40,-50,-30,40,48,-34,320,310,410,152,-416,-410,-200,30,776,400,-630,-1120,552,-326,-110]],
[x+8, [-1], [0,-8,-10,-16,40,-50,-30,-40,-48,-34,-320,310,410,-152,416,-410,200,30,-776,-400,-630,1120,-552,-326,-110]]];

f[33,4]=[
[x+1, [1,-1], [-1,-3,-4,-26,11,-32,74,-60,-182,-90,-8,-66,422,408,-506,348,-200,132,-1036,762,-542,-550,-132,570,14]],
[x+5, [-1,1], [-5,3,-14,-32,-11,-38,-2,72,68,-54,-152,174,94,-528,-340,-438,20,570,-460,-1092,562,-16,372,-966,-526]],
[x^2-x-24, [1,1], [x,-3,-2*x-6,-4*x+14,-11,2*x+14,-14*x+60,-2*x+26,-10*x+72,-6*x-96,8*x+176,52*x-190,-14*x-384,-26*x+206,74*x+96,-54*x-234,-100*x-36,34*x-406,-96*x-340,54*x+288,-28*x+662,144*x+254,156*x-240,72*x-414,192*x-322]],
[x^2-x-8, [-1,-1], [x,3,-4*x+10,-2*x+2,11,8*x-42,30*x-28,-18*x-18,112,46*x+88,104*x-72,44*x-46,2*x-248,-86*x+10,-48*x-8,-128*x+22,196,-52*x-526,152*x+388,184*x+136,-252*x-170,-74*x-78,-324*x+336,8*x+482,420*x-802]]];

f[34,4]=[
[x-16, [1,1], [-2,-2,16,24,62,-62,-17,-20,-12,80,-208,-356,22,-312,24,-462,240,812,-216,732,178,700,-992,-390,-146]],
[x+18, [1,-1], [-2,-2,-18,-10,-6,74,17,-88,-114,-90,-310,86,90,368,-384,-258,240,302,-964,-390,722,-898,912,1446,-1438]],
[x^2-6*x-4, [-1,-1], [2,x,-4*x+10,-x,15*x-48,-14*x+10,17,14*x-60,-9*x+48,20*x+154,-23*x+112,24*x+98,-88*x+466,18*x-364,148*x-472,-152*x+470,-30*x+228,48*x-262,-128*x+652,-39*x+888,156*x-550,-109*x-600,-66*x+12,10*x-1018,-80*x+130]]];

f[35,4]=[
[x-1, [1,-1], [1,-8,-5,7,12,-78,-94,40,32,-50,-248,-434,402,-68,536,22,-560,-278,-164,672,82,-1000,-448,-870,1026]],
[x^2-8*x+14, [1,1], [x,-4*x+17,-5,-7,-32*x+121,4*x+9,44*x-201,44*x-158,-68*x+394,24*x-109,-180*x+660,-60*x+522,124*x-660,68*x-402,-132*x+353,128*x-540,-616,-108*x+600,-64*x+180,-952,-344*x+1714,248*x-485,600*x-2588,44*x-284,220*x+491]],
[x^3+3*x^2-14*x-30, [-1,-1], [x,-x^2+13,5,7,x^2+4*x-33,5*x^2-8*x-55,11*x^2+24*x-129,6*x^2-4*x-22,2*x^2-12*x-78,17*x^2+36*x-63,-4*x^2+20*x+176,-12*x^2+4*x+134,2*x^2+12*x+108,-34*x^2-4*x+410,-13*x^2-64*x-147,-22*x^2-152*x+156,48*x^2-128*x-780,-26*x^2-60*x+668,108*x^2+96*x-1168,-40*x^2+32*x+480,76*x^2+200*x-634,-89*x^2-172*x+581,8*x^2-152*x-804,-82*x^2-180*x+912,-65*x^2-152*x+683]]];

f[36,4]=[
[x, [-1,-1], [0,0,18,8,-36,-10,-18,-100,-72,234,-16,-226,-90,452,-432,-414,684,422,332,360,26,512,1188,630,-1054]]];

f[37,4]=[
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f[38,4]=[
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f[39,4]=[
[x, [1,-1], [0,-3,-12,2,-36,13,-78,74,-96,18,-214,-286,-384,524,300,558,576,74,38,-456,-682,704,-888,-1020,110]],
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f[40,4]=[
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[x+6, [-1,1], [0,-6,-5,-34,16,58,-70,4,-134,-242,100,-438,-138,178,22,162,-268,250,422,-852,306,-456,434,-726,1378]],
[x-4, [-1,-1], [0,4,5,16,36,-42,-110,-116,16,198,240,-258,442,-292,392,142,-348,-570,692,168,-134,784,564,1034,-382]]];

f[41,4]=[
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f[42,4]=[
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f[43,4]=[
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f[44,4]=[
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f[45,4]=[
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[x-4, [-1,-1], [4,0,5,6,-32,-38,-26,100,78,50,-108,266,-22,442,514,-2,-500,-518,126,-412,-878,600,-282,150,386]]];

f[46,4]=[
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f[47,4]=[
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f[58,4]=[
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f[59,4]=[
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f[61,4]=[
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f[63,4]=[
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f[64,4]=[
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f[65,4]=[
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f[66,4]=[
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f[67,4]=[
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f[68,4]=[
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f[69,4]=[
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f[74,4]=[
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f[75,4]=[
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f[76,4]=[
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f[77,4]=[
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f[86,4]=[
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f[87,4]=[
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f[88,4]=[
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f[89,4]=[
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f[92,4]=[
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f[93,4]=[
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f[94,4]=[
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f[95,4]=[
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f[96,4]=[
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f[105,4]=[
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f[106,4]=[
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f[107,4]=[
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f[108,4]=[
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f[116,4]=[
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f[117,4]=[
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f[118,4]=[
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f[119,4]=[
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f[123,4]=[
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f[124,4]=[
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f[125,4]=[
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f[142,4]=[
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f[143,4]=[
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f[154,4]=[
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f[155,4]=[
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f[161,4]=[
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