Properties

Label 177.12.a.c.1.20
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $27$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(0\)
Dimension: \(27\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+43.4861 q^{2} -243.000 q^{3} -156.959 q^{4} +1833.80 q^{5} -10567.1 q^{6} +33856.7 q^{7} -95885.1 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q+43.4861 q^{2} -243.000 q^{3} -156.959 q^{4} +1833.80 q^{5} -10567.1 q^{6} +33856.7 q^{7} -95885.1 q^{8} +59049.0 q^{9} +79745.0 q^{10} +908207. q^{11} +38141.1 q^{12} +503420. q^{13} +1.47230e6 q^{14} -445614. q^{15} -3.84821e6 q^{16} +4.40755e6 q^{17} +2.56781e6 q^{18} +1.49769e6 q^{19} -287833. q^{20} -8.22718e6 q^{21} +3.94944e7 q^{22} -1.40606e7 q^{23} +2.33001e7 q^{24} -4.54653e7 q^{25} +2.18918e7 q^{26} -1.43489e7 q^{27} -5.31413e6 q^{28} -7.57535e7 q^{29} -1.93780e7 q^{30} -1.41318e8 q^{31} +2.90288e7 q^{32} -2.20694e8 q^{33} +1.91667e8 q^{34} +6.20866e7 q^{35} -9.26830e6 q^{36} -4.72854e8 q^{37} +6.51288e7 q^{38} -1.22331e8 q^{39} -1.75834e8 q^{40} +1.06497e9 q^{41} -3.57768e8 q^{42} +1.00349e9 q^{43} -1.42552e8 q^{44} +1.08284e8 q^{45} -6.11442e8 q^{46} +1.98049e9 q^{47} +9.35116e8 q^{48} -8.31050e8 q^{49} -1.97711e9 q^{50} -1.07103e9 q^{51} -7.90166e7 q^{52} +4.29679e9 q^{53} -6.23978e8 q^{54} +1.66547e9 q^{55} -3.24635e9 q^{56} -3.63939e8 q^{57} -3.29422e9 q^{58} -7.14924e8 q^{59} +6.99434e7 q^{60} +6.72663e8 q^{61} -6.14535e9 q^{62} +1.99920e9 q^{63} +9.14349e9 q^{64} +9.23174e8 q^{65} -9.59714e9 q^{66} -5.16613e9 q^{67} -6.91806e8 q^{68} +3.41673e9 q^{69} +2.69990e9 q^{70} -1.10100e10 q^{71} -5.66192e9 q^{72} +1.07298e10 q^{73} -2.05626e10 q^{74} +1.10481e10 q^{75} -2.35077e8 q^{76} +3.07489e10 q^{77} -5.31970e9 q^{78} +5.11404e10 q^{79} -7.05687e9 q^{80} +3.48678e9 q^{81} +4.63113e10 q^{82} -6.20725e10 q^{83} +1.29133e9 q^{84} +8.08258e9 q^{85} +4.36380e10 q^{86} +1.84081e10 q^{87} -8.70835e10 q^{88} +4.27674e10 q^{89} +4.70886e9 q^{90} +1.70442e10 q^{91} +2.20695e9 q^{92} +3.43402e10 q^{93} +8.61237e10 q^{94} +2.74647e9 q^{95} -7.05400e9 q^{96} +1.93882e10 q^{97} -3.61391e10 q^{98} +5.36287e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 43.4861 0.960916 0.480458 0.877018i \(-0.340470\pi\)
0.480458 + 0.877018i \(0.340470\pi\)
\(3\) −243.000 −0.577350
\(4\) −156.959 −0.0766403
\(5\) 1833.80 0.262433 0.131216 0.991354i \(-0.458112\pi\)
0.131216 + 0.991354i \(0.458112\pi\)
\(6\) −10567.1 −0.554785
\(7\) 33856.7 0.761387 0.380694 0.924701i \(-0.375685\pi\)
0.380694 + 0.924701i \(0.375685\pi\)
\(8\) −95885.1 −1.03456
\(9\) 59049.0 0.333333
\(10\) 79745.0 0.252176
\(11\) 908207. 1.70030 0.850149 0.526541i \(-0.176511\pi\)
0.850149 + 0.526541i \(0.176511\pi\)
\(12\) 38141.1 0.0442483
\(13\) 503420. 0.376047 0.188024 0.982165i \(-0.439792\pi\)
0.188024 + 0.982165i \(0.439792\pi\)
\(14\) 1.47230e6 0.731629
\(15\) −445614. −0.151516
\(16\) −3.84821e6 −0.917486
\(17\) 4.40755e6 0.752884 0.376442 0.926440i \(-0.377147\pi\)
0.376442 + 0.926440i \(0.377147\pi\)
\(18\) 2.56781e6 0.320305
\(19\) 1.49769e6 0.138764 0.0693821 0.997590i \(-0.477897\pi\)
0.0693821 + 0.997590i \(0.477897\pi\)
\(20\) −287833. −0.0201129
\(21\) −8.22718e6 −0.439587
\(22\) 3.94944e7 1.63384
\(23\) −1.40606e7 −0.455514 −0.227757 0.973718i \(-0.573139\pi\)
−0.227757 + 0.973718i \(0.573139\pi\)
\(24\) 2.33001e7 0.597304
\(25\) −4.54653e7 −0.931129
\(26\) 2.18918e7 0.361350
\(27\) −1.43489e7 −0.192450
\(28\) −5.31413e6 −0.0583530
\(29\) −7.57535e7 −0.685826 −0.342913 0.939367i \(-0.611414\pi\)
−0.342913 + 0.939367i \(0.611414\pi\)
\(30\) −1.93780e7 −0.145594
\(31\) −1.41318e8 −0.886558 −0.443279 0.896384i \(-0.646185\pi\)
−0.443279 + 0.896384i \(0.646185\pi\)
\(32\) 2.90288e7 0.152934
\(33\) −2.20694e8 −0.981668
\(34\) 1.91667e8 0.723458
\(35\) 6.20866e7 0.199813
\(36\) −9.26830e6 −0.0255468
\(37\) −4.72854e8 −1.12103 −0.560515 0.828144i \(-0.689397\pi\)
−0.560515 + 0.828144i \(0.689397\pi\)
\(38\) 6.51288e7 0.133341
\(39\) −1.22331e8 −0.217111
\(40\) −1.75834e8 −0.271503
\(41\) 1.06497e9 1.43557 0.717787 0.696263i \(-0.245155\pi\)
0.717787 + 0.696263i \(0.245155\pi\)
\(42\) −3.57768e8 −0.422406
\(43\) 1.00349e9 1.04097 0.520485 0.853871i \(-0.325751\pi\)
0.520485 + 0.853871i \(0.325751\pi\)
\(44\) −1.42552e8 −0.130311
\(45\) 1.08284e8 0.0874775
\(46\) −6.11442e8 −0.437711
\(47\) 1.98049e9 1.25960 0.629802 0.776756i \(-0.283136\pi\)
0.629802 + 0.776756i \(0.283136\pi\)
\(48\) 9.35116e8 0.529711
\(49\) −8.31050e8 −0.420290
\(50\) −1.97711e9 −0.894737
\(51\) −1.07103e9 −0.434678
\(52\) −7.90166e7 −0.0288204
\(53\) 4.29679e9 1.41132 0.705662 0.708548i \(-0.250650\pi\)
0.705662 + 0.708548i \(0.250650\pi\)
\(54\) −6.23978e8 −0.184928
\(55\) 1.66547e9 0.446214
\(56\) −3.24635e9 −0.787701
\(57\) −3.63939e8 −0.0801156
\(58\) −3.29422e9 −0.659021
\(59\) −7.14924e8 −0.130189
\(60\) 6.99434e7 0.0116122
\(61\) 6.72663e8 0.101973 0.0509863 0.998699i \(-0.483764\pi\)
0.0509863 + 0.998699i \(0.483764\pi\)
\(62\) −6.14535e9 −0.851907
\(63\) 1.99920e9 0.253796
\(64\) 9.14349e9 1.06444
\(65\) 9.23174e8 0.0986871
\(66\) −9.59714e9 −0.943301
\(67\) −5.16613e9 −0.467470 −0.233735 0.972300i \(-0.575095\pi\)
−0.233735 + 0.972300i \(0.575095\pi\)
\(68\) −6.91806e8 −0.0577013
\(69\) 3.41673e9 0.262991
\(70\) 2.69990e9 0.192003
\(71\) −1.10100e10 −0.724215 −0.362107 0.932136i \(-0.617943\pi\)
−0.362107 + 0.932136i \(0.617943\pi\)
\(72\) −5.66192e9 −0.344854
\(73\) 1.07298e10 0.605783 0.302892 0.953025i \(-0.402048\pi\)
0.302892 + 0.953025i \(0.402048\pi\)
\(74\) −2.05626e10 −1.07722
\(75\) 1.10481e10 0.537588
\(76\) −2.35077e8 −0.0106349
\(77\) 3.07489e10 1.29459
\(78\) −5.31970e9 −0.208625
\(79\) 5.11404e10 1.86989 0.934943 0.354798i \(-0.115451\pi\)
0.934943 + 0.354798i \(0.115451\pi\)
\(80\) −7.05687e9 −0.240778
\(81\) 3.48678e9 0.111111
\(82\) 4.63113e10 1.37947
\(83\) −6.20725e10 −1.72970 −0.864848 0.502035i \(-0.832585\pi\)
−0.864848 + 0.502035i \(0.832585\pi\)
\(84\) 1.29133e9 0.0336901
\(85\) 8.08258e9 0.197581
\(86\) 4.36380e10 1.00029
\(87\) 1.84081e10 0.395962
\(88\) −8.70835e10 −1.75906
\(89\) 4.27674e10 0.811835 0.405918 0.913910i \(-0.366952\pi\)
0.405918 + 0.913910i \(0.366952\pi\)
\(90\) 4.70886e9 0.0840586
\(91\) 1.70442e10 0.286317
\(92\) 2.20695e9 0.0349108
\(93\) 3.43402e10 0.511854
\(94\) 8.61237e10 1.21037
\(95\) 2.74647e9 0.0364163
\(96\) −7.05400e9 −0.0882965
\(97\) 1.93882e10 0.229241 0.114621 0.993409i \(-0.463435\pi\)
0.114621 + 0.993409i \(0.463435\pi\)
\(98\) −3.61391e10 −0.403863
\(99\) 5.36287e10 0.566766
\(100\) 7.13621e9 0.0713621
\(101\) 8.04521e10 0.761675 0.380838 0.924642i \(-0.375636\pi\)
0.380838 + 0.924642i \(0.375636\pi\)
\(102\) −4.65751e10 −0.417689
\(103\) −3.11508e9 −0.0264767 −0.0132384 0.999912i \(-0.504214\pi\)
−0.0132384 + 0.999912i \(0.504214\pi\)
\(104\) −4.82705e10 −0.389044
\(105\) −1.50870e10 −0.115362
\(106\) 1.86851e11 1.35616
\(107\) 2.77619e10 0.191354 0.0956771 0.995412i \(-0.469498\pi\)
0.0956771 + 0.995412i \(0.469498\pi\)
\(108\) 2.25220e9 0.0147494
\(109\) −2.05970e11 −1.28221 −0.641104 0.767454i \(-0.721523\pi\)
−0.641104 + 0.767454i \(0.721523\pi\)
\(110\) 7.24250e10 0.428774
\(111\) 1.14904e11 0.647228
\(112\) −1.30288e11 −0.698562
\(113\) 3.60171e11 1.83898 0.919492 0.393109i \(-0.128601\pi\)
0.919492 + 0.393109i \(0.128601\pi\)
\(114\) −1.58263e10 −0.0769844
\(115\) −2.57844e10 −0.119542
\(116\) 1.18902e10 0.0525619
\(117\) 2.97265e10 0.125349
\(118\) −3.10893e10 −0.125101
\(119\) 1.49225e11 0.573236
\(120\) 4.27278e10 0.156752
\(121\) 5.39529e11 1.89102
\(122\) 2.92515e10 0.0979871
\(123\) −2.58787e11 −0.828829
\(124\) 2.21811e10 0.0679461
\(125\) −1.72916e11 −0.506791
\(126\) 8.69376e10 0.243876
\(127\) 6.11224e11 1.64165 0.820823 0.571182i \(-0.193515\pi\)
0.820823 + 0.571182i \(0.193515\pi\)
\(128\) 3.38164e11 0.869906
\(129\) −2.43849e11 −0.601005
\(130\) 4.01452e10 0.0948300
\(131\) 4.87280e10 0.110354 0.0551768 0.998477i \(-0.482428\pi\)
0.0551768 + 0.998477i \(0.482428\pi\)
\(132\) 3.46401e10 0.0752354
\(133\) 5.07069e10 0.105653
\(134\) −2.24655e11 −0.449200
\(135\) −2.63131e10 −0.0505052
\(136\) −4.22618e11 −0.778904
\(137\) 1.10392e12 1.95422 0.977109 0.212738i \(-0.0682381\pi\)
0.977109 + 0.212738i \(0.0682381\pi\)
\(138\) 1.48580e11 0.252712
\(139\) 6.89351e11 1.12683 0.563416 0.826174i \(-0.309487\pi\)
0.563416 + 0.826174i \(0.309487\pi\)
\(140\) −9.74507e9 −0.0153137
\(141\) −4.81259e11 −0.727233
\(142\) −4.78783e11 −0.695909
\(143\) 4.57210e11 0.639393
\(144\) −2.27233e11 −0.305829
\(145\) −1.38917e11 −0.179983
\(146\) 4.66599e11 0.582107
\(147\) 2.01945e11 0.242654
\(148\) 7.42189e10 0.0859162
\(149\) 7.47587e11 0.833945 0.416972 0.908919i \(-0.363091\pi\)
0.416972 + 0.908919i \(0.363091\pi\)
\(150\) 4.80437e11 0.516577
\(151\) −4.44145e11 −0.460417 −0.230209 0.973141i \(-0.573941\pi\)
−0.230209 + 0.973141i \(0.573941\pi\)
\(152\) −1.43606e11 −0.143560
\(153\) 2.60261e11 0.250961
\(154\) 1.33715e12 1.24399
\(155\) −2.59149e11 −0.232662
\(156\) 1.92010e10 0.0166395
\(157\) −2.16780e12 −1.81372 −0.906860 0.421432i \(-0.861528\pi\)
−0.906860 + 0.421432i \(0.861528\pi\)
\(158\) 2.22390e12 1.79680
\(159\) −1.04412e12 −0.814829
\(160\) 5.32331e10 0.0401349
\(161\) −4.76047e11 −0.346823
\(162\) 1.51627e11 0.106768
\(163\) −1.17833e12 −0.802114 −0.401057 0.916053i \(-0.631357\pi\)
−0.401057 + 0.916053i \(0.631357\pi\)
\(164\) −1.67157e11 −0.110023
\(165\) −4.04710e11 −0.257622
\(166\) −2.69929e12 −1.66209
\(167\) −2.26313e12 −1.34825 −0.674124 0.738619i \(-0.735478\pi\)
−0.674124 + 0.738619i \(0.735478\pi\)
\(168\) 7.88864e11 0.454780
\(169\) −1.53873e12 −0.858588
\(170\) 3.51480e11 0.189859
\(171\) 8.84372e10 0.0462548
\(172\) −1.57508e11 −0.0797803
\(173\) 7.73542e11 0.379516 0.189758 0.981831i \(-0.439230\pi\)
0.189758 + 0.981831i \(0.439230\pi\)
\(174\) 8.00497e11 0.380486
\(175\) −1.53931e12 −0.708950
\(176\) −3.49498e12 −1.56000
\(177\) 1.73727e11 0.0751646
\(178\) 1.85979e12 0.780105
\(179\) 4.62740e12 1.88211 0.941055 0.338253i \(-0.109836\pi\)
0.941055 + 0.338253i \(0.109836\pi\)
\(180\) −1.69962e10 −0.00670431
\(181\) 2.35718e12 0.901905 0.450953 0.892548i \(-0.351084\pi\)
0.450953 + 0.892548i \(0.351084\pi\)
\(182\) 7.41184e11 0.275127
\(183\) −1.63457e11 −0.0588739
\(184\) 1.34821e12 0.471257
\(185\) −8.67121e11 −0.294195
\(186\) 1.49332e12 0.491849
\(187\) 4.00297e12 1.28013
\(188\) −3.10856e11 −0.0965365
\(189\) −4.85807e11 −0.146529
\(190\) 1.19433e11 0.0349930
\(191\) −1.88163e12 −0.535614 −0.267807 0.963473i \(-0.586299\pi\)
−0.267807 + 0.963473i \(0.586299\pi\)
\(192\) −2.22187e12 −0.614556
\(193\) 1.29316e12 0.347605 0.173803 0.984780i \(-0.444395\pi\)
0.173803 + 0.984780i \(0.444395\pi\)
\(194\) 8.43117e11 0.220282
\(195\) −2.24331e11 −0.0569770
\(196\) 1.30441e11 0.0322111
\(197\) −1.85691e12 −0.445888 −0.222944 0.974831i \(-0.571567\pi\)
−0.222944 + 0.974831i \(0.571567\pi\)
\(198\) 2.33210e12 0.544615
\(199\) 5.68634e12 1.29164 0.645819 0.763491i \(-0.276516\pi\)
0.645819 + 0.763491i \(0.276516\pi\)
\(200\) 4.35944e12 0.963310
\(201\) 1.25537e12 0.269894
\(202\) 3.49855e12 0.731906
\(203\) −2.56476e12 −0.522179
\(204\) 1.68109e11 0.0333138
\(205\) 1.95294e12 0.376741
\(206\) −1.35463e11 −0.0254419
\(207\) −8.30266e11 −0.151838
\(208\) −1.93727e12 −0.345018
\(209\) 1.36021e12 0.235941
\(210\) −6.56076e11 −0.110853
\(211\) 1.34650e12 0.221642 0.110821 0.993840i \(-0.464652\pi\)
0.110821 + 0.993840i \(0.464652\pi\)
\(212\) −6.74422e11 −0.108164
\(213\) 2.67544e12 0.418125
\(214\) 1.20726e12 0.183875
\(215\) 1.84021e12 0.273185
\(216\) 1.37585e12 0.199101
\(217\) −4.78455e12 −0.675013
\(218\) −8.95684e12 −1.23209
\(219\) −2.60735e12 −0.349749
\(220\) −2.61412e11 −0.0341980
\(221\) 2.21885e12 0.283120
\(222\) 4.99671e12 0.621931
\(223\) −8.91880e12 −1.08300 −0.541501 0.840700i \(-0.682144\pi\)
−0.541501 + 0.840700i \(0.682144\pi\)
\(224\) 9.82820e11 0.116442
\(225\) −2.68468e12 −0.310376
\(226\) 1.56624e13 1.76711
\(227\) 5.85027e12 0.644219 0.322109 0.946702i \(-0.395608\pi\)
0.322109 + 0.946702i \(0.395608\pi\)
\(228\) 5.71237e10 0.00614009
\(229\) 4.86887e12 0.510897 0.255448 0.966823i \(-0.417777\pi\)
0.255448 + 0.966823i \(0.417777\pi\)
\(230\) −1.12126e12 −0.114870
\(231\) −7.47199e12 −0.747429
\(232\) 7.26363e12 0.709529
\(233\) 1.90023e13 1.81280 0.906398 0.422425i \(-0.138821\pi\)
0.906398 + 0.422425i \(0.138821\pi\)
\(234\) 1.29269e12 0.120450
\(235\) 3.63183e12 0.330561
\(236\) 1.12214e11 0.00997772
\(237\) −1.24271e13 −1.07958
\(238\) 6.48922e12 0.550832
\(239\) 6.07560e12 0.503965 0.251983 0.967732i \(-0.418917\pi\)
0.251983 + 0.967732i \(0.418917\pi\)
\(240\) 1.71482e12 0.139013
\(241\) −2.48442e12 −0.196848 −0.0984242 0.995145i \(-0.531380\pi\)
−0.0984242 + 0.995145i \(0.531380\pi\)
\(242\) 2.34620e13 1.81711
\(243\) −8.47289e11 −0.0641500
\(244\) −1.05581e11 −0.00781522
\(245\) −1.52398e12 −0.110298
\(246\) −1.12536e13 −0.796435
\(247\) 7.53969e11 0.0521819
\(248\) 1.35502e13 0.917198
\(249\) 1.50836e13 0.998640
\(250\) −7.51942e12 −0.486984
\(251\) −1.58043e12 −0.100131 −0.0500656 0.998746i \(-0.515943\pi\)
−0.0500656 + 0.998746i \(0.515943\pi\)
\(252\) −3.13794e11 −0.0194510
\(253\) −1.27700e13 −0.774510
\(254\) 2.65797e13 1.57748
\(255\) −1.96407e12 −0.114074
\(256\) −4.02045e12 −0.228536
\(257\) −3.16358e13 −1.76014 −0.880068 0.474847i \(-0.842503\pi\)
−0.880068 + 0.474847i \(0.842503\pi\)
\(258\) −1.06040e13 −0.577515
\(259\) −1.60093e13 −0.853539
\(260\) −1.44901e11 −0.00756341
\(261\) −4.47317e12 −0.228609
\(262\) 2.11899e12 0.106040
\(263\) 2.99328e13 1.46686 0.733432 0.679762i \(-0.237917\pi\)
0.733432 + 0.679762i \(0.237917\pi\)
\(264\) 2.11613e13 1.01560
\(265\) 7.87947e12 0.370378
\(266\) 2.20505e12 0.101524
\(267\) −1.03925e13 −0.468713
\(268\) 8.10873e11 0.0358271
\(269\) 4.52704e13 1.95964 0.979820 0.199880i \(-0.0640553\pi\)
0.979820 + 0.199880i \(0.0640553\pi\)
\(270\) −1.14425e12 −0.0485312
\(271\) 2.56171e12 0.106463 0.0532316 0.998582i \(-0.483048\pi\)
0.0532316 + 0.998582i \(0.483048\pi\)
\(272\) −1.69612e13 −0.690760
\(273\) −4.14173e12 −0.165305
\(274\) 4.80050e13 1.87784
\(275\) −4.12919e13 −1.58320
\(276\) −5.36289e11 −0.0201557
\(277\) −2.63263e13 −0.969953 −0.484977 0.874527i \(-0.661172\pi\)
−0.484977 + 0.874527i \(0.661172\pi\)
\(278\) 2.99772e13 1.08279
\(279\) −8.34466e12 −0.295519
\(280\) −5.95317e12 −0.206719
\(281\) 3.76679e13 1.28259 0.641293 0.767296i \(-0.278398\pi\)
0.641293 + 0.767296i \(0.278398\pi\)
\(282\) −2.09281e13 −0.698810
\(283\) 2.92810e11 0.00958873 0.00479437 0.999989i \(-0.498474\pi\)
0.00479437 + 0.999989i \(0.498474\pi\)
\(284\) 1.72813e12 0.0555041
\(285\) −6.67393e11 −0.0210249
\(286\) 1.98823e13 0.614403
\(287\) 3.60563e13 1.09303
\(288\) 1.71412e12 0.0509780
\(289\) −1.48454e13 −0.433166
\(290\) −6.04096e12 −0.172949
\(291\) −4.71133e12 −0.132352
\(292\) −1.68415e12 −0.0464274
\(293\) 1.90466e13 0.515283 0.257641 0.966241i \(-0.417055\pi\)
0.257641 + 0.966241i \(0.417055\pi\)
\(294\) 8.78181e12 0.233170
\(295\) −1.31103e12 −0.0341658
\(296\) 4.53396e13 1.15977
\(297\) −1.30318e13 −0.327223
\(298\) 3.25096e13 0.801351
\(299\) −7.07841e12 −0.171295
\(300\) −1.73410e12 −0.0412009
\(301\) 3.39750e13 0.792581
\(302\) −1.93141e13 −0.442422
\(303\) −1.95499e13 −0.439753
\(304\) −5.76344e12 −0.127314
\(305\) 1.23353e12 0.0267609
\(306\) 1.13177e13 0.241153
\(307\) −2.57069e12 −0.0538008 −0.0269004 0.999638i \(-0.508564\pi\)
−0.0269004 + 0.999638i \(0.508564\pi\)
\(308\) −4.82633e12 −0.0992175
\(309\) 7.56964e11 0.0152863
\(310\) −1.12694e13 −0.223568
\(311\) −6.65354e13 −1.29679 −0.648397 0.761303i \(-0.724560\pi\)
−0.648397 + 0.761303i \(0.724560\pi\)
\(312\) 1.17297e13 0.224615
\(313\) −2.87328e13 −0.540610 −0.270305 0.962775i \(-0.587125\pi\)
−0.270305 + 0.962775i \(0.587125\pi\)
\(314\) −9.42690e13 −1.74283
\(315\) 3.66615e12 0.0666043
\(316\) −8.02697e12 −0.143309
\(317\) 6.54043e13 1.14757 0.573786 0.819005i \(-0.305474\pi\)
0.573786 + 0.819005i \(0.305474\pi\)
\(318\) −4.54047e13 −0.782982
\(319\) −6.87999e13 −1.16611
\(320\) 1.67674e13 0.279344
\(321\) −6.74613e12 −0.110478
\(322\) −2.07014e13 −0.333267
\(323\) 6.60115e12 0.104473
\(324\) −5.47284e11 −0.00851559
\(325\) −2.28882e13 −0.350149
\(326\) −5.12411e13 −0.770764
\(327\) 5.00508e13 0.740284
\(328\) −1.02115e14 −1.48519
\(329\) 6.70528e13 0.959046
\(330\) −1.75993e13 −0.247553
\(331\) −2.33819e13 −0.323463 −0.161732 0.986835i \(-0.551708\pi\)
−0.161732 + 0.986835i \(0.551708\pi\)
\(332\) 9.74286e12 0.132564
\(333\) −2.79216e13 −0.373677
\(334\) −9.84148e13 −1.29555
\(335\) −9.47367e12 −0.122679
\(336\) 3.16600e13 0.403315
\(337\) −9.97413e13 −1.25000 −0.625001 0.780624i \(-0.714901\pi\)
−0.625001 + 0.780624i \(0.714901\pi\)
\(338\) −6.69133e13 −0.825031
\(339\) −8.75217e13 −1.06174
\(340\) −1.26864e12 −0.0151427
\(341\) −1.28346e14 −1.50741
\(342\) 3.84579e12 0.0444469
\(343\) −9.50824e13 −1.08139
\(344\) −9.62201e13 −1.07695
\(345\) 6.26562e12 0.0690175
\(346\) 3.36383e13 0.364683
\(347\) −8.88536e13 −0.948119 −0.474059 0.880493i \(-0.657212\pi\)
−0.474059 + 0.880493i \(0.657212\pi\)
\(348\) −2.88933e12 −0.0303466
\(349\) 1.09785e14 1.13502 0.567511 0.823366i \(-0.307907\pi\)
0.567511 + 0.823366i \(0.307907\pi\)
\(350\) −6.69384e13 −0.681241
\(351\) −7.22353e12 −0.0723703
\(352\) 2.63642e13 0.260034
\(353\) −1.01555e14 −0.986147 −0.493073 0.869988i \(-0.664127\pi\)
−0.493073 + 0.869988i \(0.664127\pi\)
\(354\) 7.55469e12 0.0722269
\(355\) −2.01902e13 −0.190058
\(356\) −6.71275e12 −0.0622193
\(357\) −3.62617e13 −0.330958
\(358\) 2.01227e14 1.80855
\(359\) −1.37962e14 −1.22107 −0.610535 0.791989i \(-0.709045\pi\)
−0.610535 + 0.791989i \(0.709045\pi\)
\(360\) −1.03828e13 −0.0905008
\(361\) −1.14247e14 −0.980744
\(362\) 1.02505e14 0.866655
\(363\) −1.31106e14 −1.09178
\(364\) −2.67524e12 −0.0219435
\(365\) 1.96764e13 0.158977
\(366\) −7.10811e12 −0.0565729
\(367\) 2.32302e14 1.82134 0.910668 0.413140i \(-0.135568\pi\)
0.910668 + 0.413140i \(0.135568\pi\)
\(368\) 5.41083e13 0.417928
\(369\) 6.28853e13 0.478524
\(370\) −3.77077e13 −0.282697
\(371\) 1.45475e14 1.07456
\(372\) −5.39001e12 −0.0392287
\(373\) 2.28454e14 1.63833 0.819163 0.573561i \(-0.194439\pi\)
0.819163 + 0.573561i \(0.194439\pi\)
\(374\) 1.74073e14 1.23010
\(375\) 4.20185e13 0.292596
\(376\) −1.89899e14 −1.30314
\(377\) −3.81359e13 −0.257903
\(378\) −2.11258e13 −0.140802
\(379\) −2.46243e14 −1.61751 −0.808757 0.588142i \(-0.799859\pi\)
−0.808757 + 0.588142i \(0.799859\pi\)
\(380\) −4.31085e11 −0.00279096
\(381\) −1.48527e14 −0.947805
\(382\) −8.18249e13 −0.514680
\(383\) 3.47857e12 0.0215679 0.0107839 0.999942i \(-0.496567\pi\)
0.0107839 + 0.999942i \(0.496567\pi\)
\(384\) −8.21738e13 −0.502240
\(385\) 5.63875e13 0.339741
\(386\) 5.62344e13 0.334020
\(387\) 5.92553e13 0.346990
\(388\) −3.04316e12 −0.0175691
\(389\) 4.32209e13 0.246021 0.123010 0.992405i \(-0.460745\pi\)
0.123010 + 0.992405i \(0.460745\pi\)
\(390\) −9.75529e12 −0.0547501
\(391\) −6.19729e13 −0.342949
\(392\) 7.96853e13 0.434815
\(393\) −1.18409e13 −0.0637126
\(394\) −8.07496e13 −0.428461
\(395\) 9.37814e13 0.490719
\(396\) −8.41754e12 −0.0434372
\(397\) 2.65109e14 1.34920 0.674600 0.738183i \(-0.264316\pi\)
0.674600 + 0.738183i \(0.264316\pi\)
\(398\) 2.47277e14 1.24116
\(399\) −1.23218e13 −0.0609990
\(400\) 1.74960e14 0.854298
\(401\) −2.39946e14 −1.15563 −0.577816 0.816167i \(-0.696095\pi\)
−0.577816 + 0.816167i \(0.696095\pi\)
\(402\) 5.45911e13 0.259346
\(403\) −7.11422e13 −0.333388
\(404\) −1.26277e13 −0.0583750
\(405\) 6.39408e12 0.0291592
\(406\) −1.11532e14 −0.501770
\(407\) −4.29450e14 −1.90609
\(408\) 1.02696e14 0.449701
\(409\) −3.90926e12 −0.0168895 −0.00844473 0.999964i \(-0.502688\pi\)
−0.00844473 + 0.999964i \(0.502688\pi\)
\(410\) 8.49258e13 0.362017
\(411\) −2.68252e14 −1.12827
\(412\) 4.88941e11 0.00202918
\(413\) −2.42050e13 −0.0991242
\(414\) −3.61050e13 −0.145904
\(415\) −1.13829e14 −0.453928
\(416\) 1.46137e13 0.0575104
\(417\) −1.67512e14 −0.650576
\(418\) 5.91504e13 0.226719
\(419\) 1.38759e11 0.000524909 0 0.000262454 1.00000i \(-0.499916\pi\)
0.000262454 1.00000i \(0.499916\pi\)
\(420\) 2.36805e12 0.00884138
\(421\) −5.33323e13 −0.196534 −0.0982672 0.995160i \(-0.531330\pi\)
−0.0982672 + 0.995160i \(0.531330\pi\)
\(422\) 5.85539e13 0.212979
\(423\) 1.16946e14 0.419868
\(424\) −4.11998e14 −1.46010
\(425\) −2.00390e14 −0.701032
\(426\) 1.16344e14 0.401783
\(427\) 2.27742e13 0.0776406
\(428\) −4.35749e12 −0.0146654
\(429\) −1.11102e14 −0.369154
\(430\) 8.00236e13 0.262507
\(431\) 1.33808e14 0.433369 0.216685 0.976242i \(-0.430476\pi\)
0.216685 + 0.976242i \(0.430476\pi\)
\(432\) 5.52177e13 0.176570
\(433\) 4.98813e13 0.157491 0.0787453 0.996895i \(-0.474909\pi\)
0.0787453 + 0.996895i \(0.474909\pi\)
\(434\) −2.08061e14 −0.648631
\(435\) 3.37568e13 0.103913
\(436\) 3.23290e13 0.0982689
\(437\) −2.10585e13 −0.0632091
\(438\) −1.13383e14 −0.336080
\(439\) 2.35666e14 0.689831 0.344915 0.938634i \(-0.387908\pi\)
0.344915 + 0.938634i \(0.387908\pi\)
\(440\) −1.59694e14 −0.461635
\(441\) −4.90727e13 −0.140097
\(442\) 9.64891e13 0.272054
\(443\) −3.17843e14 −0.885100 −0.442550 0.896744i \(-0.645926\pi\)
−0.442550 + 0.896744i \(0.645926\pi\)
\(444\) −1.80352e13 −0.0496037
\(445\) 7.84270e13 0.213052
\(446\) −3.87844e14 −1.04067
\(447\) −1.81664e14 −0.481478
\(448\) 3.09569e14 0.810453
\(449\) 5.56046e13 0.143799 0.0718995 0.997412i \(-0.477094\pi\)
0.0718995 + 0.997412i \(0.477094\pi\)
\(450\) −1.16746e14 −0.298246
\(451\) 9.67212e14 2.44090
\(452\) −5.65323e13 −0.140940
\(453\) 1.07927e14 0.265822
\(454\) 2.54405e14 0.619040
\(455\) 3.12556e13 0.0751390
\(456\) 3.48963e13 0.0828845
\(457\) 5.44106e14 1.27686 0.638432 0.769679i \(-0.279584\pi\)
0.638432 + 0.769679i \(0.279584\pi\)
\(458\) 2.11728e14 0.490929
\(459\) −6.32435e13 −0.144893
\(460\) 4.04711e12 0.00916172
\(461\) −6.66619e14 −1.49116 −0.745578 0.666419i \(-0.767826\pi\)
−0.745578 + 0.666419i \(0.767826\pi\)
\(462\) −3.24928e14 −0.718217
\(463\) −1.75744e14 −0.383870 −0.191935 0.981408i \(-0.561476\pi\)
−0.191935 + 0.981408i \(0.561476\pi\)
\(464\) 2.91516e14 0.629236
\(465\) 6.29731e13 0.134327
\(466\) 8.26336e14 1.74194
\(467\) −6.97107e14 −1.45230 −0.726151 0.687536i \(-0.758692\pi\)
−0.726151 + 0.687536i \(0.758692\pi\)
\(468\) −4.66585e12 −0.00960680
\(469\) −1.74908e14 −0.355926
\(470\) 1.57934e14 0.317642
\(471\) 5.26774e14 1.04715
\(472\) 6.85506e13 0.134688
\(473\) 9.11381e14 1.76996
\(474\) −5.40407e14 −1.03738
\(475\) −6.80930e13 −0.129207
\(476\) −2.34223e13 −0.0439330
\(477\) 2.53721e14 0.470442
\(478\) 2.64204e14 0.484268
\(479\) 8.55969e14 1.55100 0.775501 0.631346i \(-0.217497\pi\)
0.775501 + 0.631346i \(0.217497\pi\)
\(480\) −1.29356e13 −0.0231719
\(481\) −2.38044e14 −0.421561
\(482\) −1.08038e14 −0.189155
\(483\) 1.15679e14 0.200238
\(484\) −8.46842e13 −0.144928
\(485\) 3.55541e13 0.0601604
\(486\) −3.68453e13 −0.0616428
\(487\) 3.99285e14 0.660502 0.330251 0.943893i \(-0.392867\pi\)
0.330251 + 0.943893i \(0.392867\pi\)
\(488\) −6.44984e13 −0.105497
\(489\) 2.86335e14 0.463100
\(490\) −6.62721e13 −0.105987
\(491\) 3.99664e14 0.632043 0.316022 0.948752i \(-0.397653\pi\)
0.316022 + 0.948752i \(0.397653\pi\)
\(492\) 4.06191e13 0.0635217
\(493\) −3.33887e14 −0.516347
\(494\) 3.27872e13 0.0501424
\(495\) 9.83446e13 0.148738
\(496\) 5.43820e14 0.813404
\(497\) −3.72763e14 −0.551408
\(498\) 6.55927e14 0.959609
\(499\) 8.97290e14 1.29831 0.649157 0.760654i \(-0.275122\pi\)
0.649157 + 0.760654i \(0.275122\pi\)
\(500\) 2.71407e13 0.0388407
\(501\) 5.49941e14 0.778411
\(502\) −6.87267e13 −0.0962177
\(503\) 2.80375e14 0.388253 0.194126 0.980977i \(-0.437813\pi\)
0.194126 + 0.980977i \(0.437813\pi\)
\(504\) −1.91694e14 −0.262567
\(505\) 1.47533e14 0.199888
\(506\) −5.55316e14 −0.744239
\(507\) 3.73911e14 0.495706
\(508\) −9.59373e13 −0.125816
\(509\) 7.16559e14 0.929617 0.464808 0.885411i \(-0.346123\pi\)
0.464808 + 0.885411i \(0.346123\pi\)
\(510\) −8.54096e13 −0.109615
\(511\) 3.63277e14 0.461236
\(512\) −8.67393e14 −1.08951
\(513\) −2.14902e13 −0.0267052
\(514\) −1.37572e15 −1.69134
\(515\) −5.71244e12 −0.00694835
\(516\) 3.82744e13 0.0460612
\(517\) 1.79869e15 2.14170
\(518\) −6.96181e14 −0.820179
\(519\) −1.87971e14 −0.219114
\(520\) −8.85186e13 −0.102098
\(521\) −9.72152e14 −1.10950 −0.554749 0.832017i \(-0.687186\pi\)
−0.554749 + 0.832017i \(0.687186\pi\)
\(522\) −1.94521e14 −0.219674
\(523\) −8.37926e14 −0.936367 −0.468184 0.883631i \(-0.655091\pi\)
−0.468184 + 0.883631i \(0.655091\pi\)
\(524\) −7.64831e12 −0.00845753
\(525\) 3.74051e14 0.409312
\(526\) 1.30166e15 1.40953
\(527\) −6.22864e14 −0.667475
\(528\) 8.49279e14 0.900667
\(529\) −7.55108e14 −0.792507
\(530\) 3.42647e14 0.355902
\(531\) −4.22156e13 −0.0433963
\(532\) −7.95893e12 −0.00809731
\(533\) 5.36127e14 0.539843
\(534\) −4.51928e14 −0.450394
\(535\) 5.09098e13 0.0502176
\(536\) 4.95355e14 0.483626
\(537\) −1.12446e15 −1.08664
\(538\) 1.96863e15 1.88305
\(539\) −7.54766e14 −0.714618
\(540\) 4.13009e12 0.00387073
\(541\) −1.47807e15 −1.37123 −0.685613 0.727966i \(-0.740466\pi\)
−0.685613 + 0.727966i \(0.740466\pi\)
\(542\) 1.11399e14 0.102302
\(543\) −5.72795e14 −0.520715
\(544\) 1.27946e14 0.115142
\(545\) −3.77709e14 −0.336493
\(546\) −1.80108e14 −0.158845
\(547\) 1.93870e15 1.69270 0.846352 0.532624i \(-0.178794\pi\)
0.846352 + 0.532624i \(0.178794\pi\)
\(548\) −1.73270e14 −0.149772
\(549\) 3.97201e13 0.0339909
\(550\) −1.79562e15 −1.52132
\(551\) −1.13455e14 −0.0951681
\(552\) −3.27614e14 −0.272080
\(553\) 1.73145e15 1.42371
\(554\) −1.14483e15 −0.932044
\(555\) 2.10711e14 0.169854
\(556\) −1.08200e14 −0.0863607
\(557\) 6.82212e14 0.539157 0.269579 0.962978i \(-0.413116\pi\)
0.269579 + 0.962978i \(0.413116\pi\)
\(558\) −3.62877e14 −0.283969
\(559\) 5.05179e14 0.391454
\(560\) −2.38922e14 −0.183325
\(561\) −9.72721e14 −0.739082
\(562\) 1.63803e15 1.23246
\(563\) 2.01142e15 1.49867 0.749336 0.662190i \(-0.230373\pi\)
0.749336 + 0.662190i \(0.230373\pi\)
\(564\) 7.55381e13 0.0557354
\(565\) 6.60484e14 0.482609
\(566\) 1.27332e13 0.00921397
\(567\) 1.18051e14 0.0845986
\(568\) 1.05570e15 0.749244
\(569\) −3.82268e14 −0.268689 −0.134345 0.990935i \(-0.542893\pi\)
−0.134345 + 0.990935i \(0.542893\pi\)
\(570\) −2.90223e13 −0.0202032
\(571\) 7.65105e14 0.527500 0.263750 0.964591i \(-0.415041\pi\)
0.263750 + 0.964591i \(0.415041\pi\)
\(572\) −7.17634e13 −0.0490033
\(573\) 4.57237e14 0.309237
\(574\) 1.56795e15 1.05031
\(575\) 6.39271e14 0.424142
\(576\) 5.39914e14 0.354814
\(577\) −1.17709e15 −0.766199 −0.383099 0.923707i \(-0.625143\pi\)
−0.383099 + 0.923707i \(0.625143\pi\)
\(578\) −6.45569e14 −0.416236
\(579\) −3.14237e14 −0.200690
\(580\) 2.18043e13 0.0137940
\(581\) −2.10157e15 −1.31697
\(582\) −2.04877e14 −0.127180
\(583\) 3.90238e15 2.39967
\(584\) −1.02883e15 −0.626720
\(585\) 5.45125e13 0.0328957
\(586\) 8.28263e14 0.495144
\(587\) −9.35500e14 −0.554031 −0.277016 0.960865i \(-0.589345\pi\)
−0.277016 + 0.960865i \(0.589345\pi\)
\(588\) −3.16972e13 −0.0185971
\(589\) −2.11650e14 −0.123023
\(590\) −5.70116e13 −0.0328305
\(591\) 4.51228e14 0.257433
\(592\) 1.81964e15 1.02853
\(593\) 3.41994e14 0.191522 0.0957609 0.995404i \(-0.469472\pi\)
0.0957609 + 0.995404i \(0.469472\pi\)
\(594\) −5.66701e14 −0.314434
\(595\) 2.73649e14 0.150436
\(596\) −1.17341e14 −0.0639138
\(597\) −1.38178e15 −0.745727
\(598\) −3.07812e14 −0.164600
\(599\) −3.20513e15 −1.69824 −0.849118 0.528203i \(-0.822866\pi\)
−0.849118 + 0.528203i \(0.822866\pi\)
\(600\) −1.05934e15 −0.556167
\(601\) −1.84194e15 −0.958221 −0.479110 0.877755i \(-0.659041\pi\)
−0.479110 + 0.877755i \(0.659041\pi\)
\(602\) 1.47744e15 0.761604
\(603\) −3.05055e14 −0.155823
\(604\) 6.97127e13 0.0352865
\(605\) 9.89390e14 0.496264
\(606\) −8.50147e14 −0.422566
\(607\) −1.61378e15 −0.794889 −0.397444 0.917626i \(-0.630103\pi\)
−0.397444 + 0.917626i \(0.630103\pi\)
\(608\) 4.34762e13 0.0212218
\(609\) 6.23238e14 0.301480
\(610\) 5.36415e13 0.0257150
\(611\) 9.97018e14 0.473671
\(612\) −4.08505e13 −0.0192338
\(613\) 1.38006e15 0.643968 0.321984 0.946745i \(-0.395650\pi\)
0.321984 + 0.946745i \(0.395650\pi\)
\(614\) −1.11789e14 −0.0516981
\(615\) −4.74565e14 −0.217512
\(616\) −2.94836e15 −1.33933
\(617\) −5.39967e14 −0.243108 −0.121554 0.992585i \(-0.538788\pi\)
−0.121554 + 0.992585i \(0.538788\pi\)
\(618\) 3.29174e13 0.0146889
\(619\) 1.93355e15 0.855178 0.427589 0.903973i \(-0.359363\pi\)
0.427589 + 0.903973i \(0.359363\pi\)
\(620\) 4.06758e13 0.0178313
\(621\) 2.01755e14 0.0876637
\(622\) −2.89337e15 −1.24611
\(623\) 1.44796e15 0.618121
\(624\) 4.70757e14 0.199196
\(625\) 1.90289e15 0.798131
\(626\) −1.24948e15 −0.519481
\(627\) −3.30532e14 −0.136220
\(628\) 3.40256e14 0.139004
\(629\) −2.08413e15 −0.844006
\(630\) 1.59427e14 0.0640011
\(631\) −2.03258e15 −0.808884 −0.404442 0.914564i \(-0.632534\pi\)
−0.404442 + 0.914564i \(0.632534\pi\)
\(632\) −4.90360e15 −1.93451
\(633\) −3.27199e14 −0.127965
\(634\) 2.84418e15 1.10272
\(635\) 1.12086e15 0.430822
\(636\) 1.63884e14 0.0624487
\(637\) −4.18368e14 −0.158049
\(638\) −2.99184e15 −1.12053
\(639\) −6.50131e14 −0.241405
\(640\) 6.20126e14 0.228292
\(641\) 5.25486e15 1.91797 0.958986 0.283454i \(-0.0914804\pi\)
0.958986 + 0.283454i \(0.0914804\pi\)
\(642\) −2.93363e14 −0.106160
\(643\) −8.43519e14 −0.302646 −0.151323 0.988484i \(-0.548353\pi\)
−0.151323 + 0.988484i \(0.548353\pi\)
\(644\) 7.47200e13 0.0265806
\(645\) −4.47171e14 −0.157723
\(646\) 2.87058e14 0.100390
\(647\) −1.85214e15 −0.642244 −0.321122 0.947038i \(-0.604060\pi\)
−0.321122 + 0.947038i \(0.604060\pi\)
\(648\) −3.34331e14 −0.114951
\(649\) −6.49300e14 −0.221360
\(650\) −9.95316e14 −0.336463
\(651\) 1.16265e15 0.389719
\(652\) 1.84950e14 0.0614743
\(653\) −1.21454e15 −0.400304 −0.200152 0.979765i \(-0.564144\pi\)
−0.200152 + 0.979765i \(0.564144\pi\)
\(654\) 2.17651e15 0.711350
\(655\) 8.93575e13 0.0289604
\(656\) −4.09823e15 −1.31712
\(657\) 6.33586e14 0.201928
\(658\) 2.91587e15 0.921563
\(659\) 1.11485e15 0.349418 0.174709 0.984620i \(-0.444101\pi\)
0.174709 + 0.984620i \(0.444101\pi\)
\(660\) 6.35231e13 0.0197442
\(661\) 2.64586e15 0.815565 0.407782 0.913079i \(-0.366302\pi\)
0.407782 + 0.913079i \(0.366302\pi\)
\(662\) −1.01679e15 −0.310821
\(663\) −5.39180e14 −0.163459
\(664\) 5.95182e15 1.78948
\(665\) 9.29865e13 0.0277269
\(666\) −1.21420e15 −0.359072
\(667\) 1.06514e15 0.312403
\(668\) 3.55220e14 0.103330
\(669\) 2.16727e15 0.625272
\(670\) −4.11973e14 −0.117885
\(671\) 6.10918e14 0.173384
\(672\) −2.38825e14 −0.0672278
\(673\) 1.24861e14 0.0348614 0.0174307 0.999848i \(-0.494451\pi\)
0.0174307 + 0.999848i \(0.494451\pi\)
\(674\) −4.33736e15 −1.20115
\(675\) 6.52377e14 0.179196
\(676\) 2.41518e14 0.0658025
\(677\) −2.13566e15 −0.577159 −0.288579 0.957456i \(-0.593183\pi\)
−0.288579 + 0.957456i \(0.593183\pi\)
\(678\) −3.80598e15 −1.02024
\(679\) 6.56420e14 0.174541
\(680\) −7.74999e14 −0.204410
\(681\) −1.42161e15 −0.371940
\(682\) −5.58125e15 −1.44850
\(683\) −1.84879e15 −0.475962 −0.237981 0.971270i \(-0.576486\pi\)
−0.237981 + 0.971270i \(0.576486\pi\)
\(684\) −1.38811e13 −0.00354498
\(685\) 2.02437e15 0.512851
\(686\) −4.13476e15 −1.03913
\(687\) −1.18314e15 −0.294966
\(688\) −3.86166e15 −0.955076
\(689\) 2.16309e15 0.530725
\(690\) 2.72467e14 0.0663200
\(691\) −2.47818e15 −0.598417 −0.299208 0.954188i \(-0.596723\pi\)
−0.299208 + 0.954188i \(0.596723\pi\)
\(692\) −1.21415e14 −0.0290862
\(693\) 1.81569e15 0.431529
\(694\) −3.86389e15 −0.911063
\(695\) 1.26413e15 0.295717
\(696\) −1.76506e15 −0.409647
\(697\) 4.69390e15 1.08082
\(698\) 4.77413e15 1.09066
\(699\) −4.61756e15 −1.04662
\(700\) 2.41608e14 0.0543341
\(701\) −3.03287e15 −0.676713 −0.338356 0.941018i \(-0.609871\pi\)
−0.338356 + 0.941018i \(0.609871\pi\)
\(702\) −3.14123e14 −0.0695418
\(703\) −7.08190e14 −0.155559
\(704\) 8.30419e15 1.80987
\(705\) −8.82534e14 −0.190850
\(706\) −4.41624e15 −0.947604
\(707\) 2.72384e15 0.579930
\(708\) −2.72680e13 −0.00576064
\(709\) 6.12649e15 1.28427 0.642137 0.766590i \(-0.278048\pi\)
0.642137 + 0.766590i \(0.278048\pi\)
\(710\) −8.77994e14 −0.182629
\(711\) 3.01979e15 0.623295
\(712\) −4.10076e15 −0.839893
\(713\) 1.98702e15 0.403839
\(714\) −1.57688e15 −0.318023
\(715\) 8.38434e14 0.167797
\(716\) −7.26314e14 −0.144246
\(717\) −1.47637e15 −0.290965
\(718\) −5.99943e15 −1.17335
\(719\) 5.78193e15 1.12218 0.561092 0.827754i \(-0.310382\pi\)
0.561092 + 0.827754i \(0.310382\pi\)
\(720\) −4.16701e14 −0.0802594
\(721\) −1.05466e14 −0.0201590
\(722\) −4.96816e15 −0.942413
\(723\) 6.03715e14 0.113650
\(724\) −3.69982e14 −0.0691223
\(725\) 3.44416e15 0.638592
\(726\) −5.70127e15 −1.04911
\(727\) 5.16468e15 0.943201 0.471601 0.881812i \(-0.343676\pi\)
0.471601 + 0.881812i \(0.343676\pi\)
\(728\) −1.63428e15 −0.296213
\(729\) 2.05891e14 0.0370370
\(730\) 8.55650e14 0.152764
\(731\) 4.42295e15 0.783730
\(732\) 2.56561e13 0.00451212
\(733\) 8.31193e14 0.145087 0.0725437 0.997365i \(-0.476888\pi\)
0.0725437 + 0.997365i \(0.476888\pi\)
\(734\) 1.01019e16 1.75015
\(735\) 3.70328e14 0.0636804
\(736\) −4.08163e14 −0.0696636
\(737\) −4.69192e15 −0.794839
\(738\) 2.73464e15 0.459822
\(739\) 2.62994e15 0.438936 0.219468 0.975620i \(-0.429568\pi\)
0.219468 + 0.975620i \(0.429568\pi\)
\(740\) 1.36103e14 0.0225472
\(741\) −1.83214e14 −0.0301272
\(742\) 6.32615e15 1.03257
\(743\) −2.00258e15 −0.324452 −0.162226 0.986754i \(-0.551867\pi\)
−0.162226 + 0.986754i \(0.551867\pi\)
\(744\) −3.29271e15 −0.529544
\(745\) 1.37093e15 0.218854
\(746\) 9.93457e15 1.57429
\(747\) −3.66532e15 −0.576565
\(748\) −6.28304e14 −0.0981094
\(749\) 9.39925e14 0.145695
\(750\) 1.82722e15 0.281160
\(751\) −1.05836e16 −1.61665 −0.808324 0.588738i \(-0.799625\pi\)
−0.808324 + 0.588738i \(0.799625\pi\)
\(752\) −7.62134e15 −1.15567
\(753\) 3.84044e14 0.0578108
\(754\) −1.65838e15 −0.247823
\(755\) −8.14475e14 −0.120828
\(756\) 7.62519e13 0.0112300
\(757\) −1.76057e15 −0.257411 −0.128705 0.991683i \(-0.541082\pi\)
−0.128705 + 0.991683i \(0.541082\pi\)
\(758\) −1.07081e16 −1.55430
\(759\) 3.10310e15 0.447164
\(760\) −2.63346e14 −0.0376749
\(761\) −8.82470e15 −1.25338 −0.626692 0.779267i \(-0.715592\pi\)
−0.626692 + 0.779267i \(0.715592\pi\)
\(762\) −6.45887e15 −0.910761
\(763\) −6.97347e15 −0.976257
\(764\) 2.95340e14 0.0410496
\(765\) 4.77268e14 0.0658604
\(766\) 1.51269e14 0.0207249
\(767\) −3.59907e14 −0.0489572
\(768\) 9.76969e14 0.131945
\(769\) 1.21909e16 1.63471 0.817355 0.576134i \(-0.195440\pi\)
0.817355 + 0.576134i \(0.195440\pi\)
\(770\) 2.45207e15 0.326463
\(771\) 7.68749e15 1.01622
\(772\) −2.02973e14 −0.0266406
\(773\) −6.91060e15 −0.900594 −0.450297 0.892879i \(-0.648682\pi\)
−0.450297 + 0.892879i \(0.648682\pi\)
\(774\) 2.57678e15 0.333428
\(775\) 6.42505e15 0.825500
\(776\) −1.85904e15 −0.237164
\(777\) 3.89026e15 0.492791
\(778\) 1.87951e15 0.236405
\(779\) 1.59499e15 0.199206
\(780\) 3.52109e13 0.00436674
\(781\) −9.99938e15 −1.23138
\(782\) −2.69496e15 −0.329545
\(783\) 1.08698e15 0.131987
\(784\) 3.19806e15 0.385610
\(785\) −3.97531e15 −0.475979
\(786\) −5.14914e14 −0.0612225
\(787\) −4.59089e15 −0.542046 −0.271023 0.962573i \(-0.587362\pi\)
−0.271023 + 0.962573i \(0.587362\pi\)
\(788\) 2.91459e14 0.0341730
\(789\) −7.27366e15 −0.846895
\(790\) 4.07819e15 0.471540
\(791\) 1.21942e16 1.40018
\(792\) −5.14220e15 −0.586354
\(793\) 3.38632e14 0.0383465
\(794\) 1.15286e16 1.29647
\(795\) −1.91471e15 −0.213838
\(796\) −8.92524e14 −0.0989915
\(797\) 1.32732e16 1.46202 0.731012 0.682365i \(-0.239048\pi\)
0.731012 + 0.682365i \(0.239048\pi\)
\(798\) −5.35826e14 −0.0586149
\(799\) 8.72910e15 0.948336
\(800\) −1.31980e15 −0.142401
\(801\) 2.52537e15 0.270612
\(802\) −1.04343e16 −1.11047
\(803\) 9.74491e15 1.03001
\(804\) −1.97042e14 −0.0206848
\(805\) −8.72976e14 −0.0910176
\(806\) −3.09370e15 −0.320357
\(807\) −1.10007e16 −1.13140
\(808\) −7.71415e15 −0.787999
\(809\) −1.20145e16 −1.21896 −0.609480 0.792802i \(-0.708622\pi\)
−0.609480 + 0.792802i \(0.708622\pi\)
\(810\) 2.78053e14 0.0280195
\(811\) −3.59147e15 −0.359465 −0.179733 0.983715i \(-0.557523\pi\)
−0.179733 + 0.983715i \(0.557523\pi\)
\(812\) 4.02564e14 0.0400200
\(813\) −6.22496e14 −0.0614665
\(814\) −1.86751e16 −1.83159
\(815\) −2.16083e15 −0.210501
\(816\) 4.12157e15 0.398811
\(817\) 1.50292e15 0.144449
\(818\) −1.69998e14 −0.0162294
\(819\) 1.00644e15 0.0954392
\(820\) −3.06533e14 −0.0288736
\(821\) −9.48394e15 −0.887363 −0.443682 0.896185i \(-0.646328\pi\)
−0.443682 + 0.896185i \(0.646328\pi\)
\(822\) −1.16652e16 −1.08417
\(823\) 2.01774e16 1.86280 0.931399 0.364000i \(-0.118589\pi\)
0.931399 + 0.364000i \(0.118589\pi\)
\(824\) 2.98689e14 0.0273918
\(825\) 1.00339e16 0.914060
\(826\) −1.05258e15 −0.0952500
\(827\) −7.62814e15 −0.685707 −0.342853 0.939389i \(-0.611393\pi\)
−0.342853 + 0.939389i \(0.611393\pi\)
\(828\) 1.30318e14 0.0116369
\(829\) 2.04342e15 0.181262 0.0906311 0.995885i \(-0.471112\pi\)
0.0906311 + 0.995885i \(0.471112\pi\)
\(830\) −4.94997e15 −0.436187
\(831\) 6.39729e15 0.560003
\(832\) 4.60302e15 0.400281
\(833\) −3.66289e15 −0.316429
\(834\) −7.28445e15 −0.625149
\(835\) −4.15014e15 −0.353824
\(836\) −2.13499e14 −0.0180826
\(837\) 2.02775e15 0.170618
\(838\) 6.03408e12 0.000504393 0
\(839\) 4.12678e15 0.342705 0.171352 0.985210i \(-0.445186\pi\)
0.171352 + 0.985210i \(0.445186\pi\)
\(840\) 1.44662e15 0.119349
\(841\) −6.46191e15 −0.529643
\(842\) −2.31921e15 −0.188853
\(843\) −9.15329e15 −0.740501
\(844\) −2.11345e14 −0.0169867
\(845\) −2.82173e15 −0.225322
\(846\) 5.08552e15 0.403458
\(847\) 1.82667e16 1.43980
\(848\) −1.65350e16 −1.29487
\(849\) −7.11529e13 −0.00553606
\(850\) −8.71420e15 −0.673633
\(851\) 6.64863e15 0.510645
\(852\) −4.19935e14 −0.0320453
\(853\) 2.28613e16 1.73333 0.866665 0.498891i \(-0.166259\pi\)
0.866665 + 0.498891i \(0.166259\pi\)
\(854\) 9.90359e14 0.0746061
\(855\) 1.62176e14 0.0121388
\(856\) −2.66195e15 −0.197968
\(857\) −2.52878e16 −1.86860 −0.934299 0.356491i \(-0.883973\pi\)
−0.934299 + 0.356491i \(0.883973\pi\)
\(858\) −4.83140e15 −0.354726
\(859\) −1.05091e16 −0.766658 −0.383329 0.923612i \(-0.625222\pi\)
−0.383329 + 0.923612i \(0.625222\pi\)
\(860\) −2.88839e14 −0.0209370
\(861\) −8.76168e15 −0.631059
\(862\) 5.81880e15 0.416432
\(863\) −4.46292e15 −0.317366 −0.158683 0.987330i \(-0.550725\pi\)
−0.158683 + 0.987330i \(0.550725\pi\)
\(864\) −4.16532e14 −0.0294322
\(865\) 1.41852e15 0.0995974
\(866\) 2.16914e15 0.151335
\(867\) 3.60744e15 0.250088
\(868\) 7.50980e14 0.0517333
\(869\) 4.64461e16 3.17936
\(870\) 1.46795e15 0.0998519
\(871\) −2.60074e15 −0.175791
\(872\) 1.97495e16 1.32652
\(873\) 1.14485e15 0.0764137
\(874\) −9.15752e14 −0.0607386
\(875\) −5.85435e15 −0.385864
\(876\) 4.09248e14 0.0268049
\(877\) −3.44854e15 −0.224459 −0.112230 0.993682i \(-0.535799\pi\)
−0.112230 + 0.993682i \(0.535799\pi\)
\(878\) 1.02482e16 0.662870
\(879\) −4.62833e15 −0.297499
\(880\) −6.40910e15 −0.409395
\(881\) −9.92748e15 −0.630190 −0.315095 0.949060i \(-0.602036\pi\)
−0.315095 + 0.949060i \(0.602036\pi\)
\(882\) −2.13398e15 −0.134621
\(883\) −1.29961e16 −0.814761 −0.407381 0.913258i \(-0.633558\pi\)
−0.407381 + 0.913258i \(0.633558\pi\)
\(884\) −3.48269e14 −0.0216984
\(885\) 3.18580e14 0.0197256
\(886\) −1.38217e16 −0.850506
\(887\) 6.94619e15 0.424783 0.212391 0.977185i \(-0.431875\pi\)
0.212391 + 0.977185i \(0.431875\pi\)
\(888\) −1.10175e16 −0.669596
\(889\) 2.06940e16 1.24993
\(890\) 3.41048e15 0.204725
\(891\) 3.16672e15 0.188922
\(892\) 1.39989e15 0.0830017
\(893\) 2.96616e15 0.174788
\(894\) −7.89984e15 −0.462660
\(895\) 8.48574e15 0.493927
\(896\) 1.14491e16 0.662335
\(897\) 1.72005e15 0.0988971
\(898\) 2.41803e15 0.138179
\(899\) 1.07053e16 0.608024
\(900\) 4.21386e14 0.0237874
\(901\) 1.89383e16 1.06256
\(902\) 4.20603e16 2.34550
\(903\) −8.25593e15 −0.457597
\(904\) −3.45351e16 −1.90254
\(905\) 4.32261e15 0.236689
\(906\) 4.69333e15 0.255433
\(907\) −1.03723e15 −0.0561093 −0.0280547 0.999606i \(-0.508931\pi\)
−0.0280547 + 0.999606i \(0.508931\pi\)
\(908\) −9.18254e14 −0.0493732
\(909\) 4.75062e15 0.253892
\(910\) 1.35919e15 0.0722023
\(911\) 1.03483e16 0.546407 0.273204 0.961956i \(-0.411917\pi\)
0.273204 + 0.961956i \(0.411917\pi\)
\(912\) 1.40052e15 0.0735049
\(913\) −5.63747e16 −2.94100
\(914\) 2.36610e16 1.22696
\(915\) −2.99748e14 −0.0154504
\(916\) −7.64215e14 −0.0391553
\(917\) 1.64977e15 0.0840217
\(918\) −2.75021e15 −0.139230
\(919\) −2.38504e15 −0.120022 −0.0600108 0.998198i \(-0.519114\pi\)
−0.0600108 + 0.998198i \(0.519114\pi\)
\(920\) 2.47234e15 0.123673
\(921\) 6.24678e14 0.0310619
\(922\) −2.89887e16 −1.43288
\(923\) −5.54267e15 −0.272339
\(924\) 1.17280e15 0.0572832
\(925\) 2.14984e16 1.04382
\(926\) −7.64241e15 −0.368867
\(927\) −1.83942e14 −0.00882557
\(928\) −2.19903e15 −0.104886
\(929\) −1.95390e16 −0.926436 −0.463218 0.886244i \(-0.653305\pi\)
−0.463218 + 0.886244i \(0.653305\pi\)
\(930\) 2.73846e15 0.129077
\(931\) −1.24466e15 −0.0583212
\(932\) −2.98259e15 −0.138933
\(933\) 1.61681e16 0.748704
\(934\) −3.03145e16 −1.39554
\(935\) 7.34066e15 0.335947
\(936\) −2.85033e15 −0.129681
\(937\) 1.28648e16 0.581882 0.290941 0.956741i \(-0.406032\pi\)
0.290941 + 0.956741i \(0.406032\pi\)
\(938\) −7.60607e15 −0.342015
\(939\) 6.98207e15 0.312121
\(940\) −5.70049e14 −0.0253343
\(941\) 1.79692e15 0.0793937 0.0396968 0.999212i \(-0.487361\pi\)
0.0396968 + 0.999212i \(0.487361\pi\)
\(942\) 2.29074e16 1.00623
\(943\) −1.49741e16 −0.653924
\(944\) 2.75118e15 0.119446
\(945\) −8.90874e14 −0.0384540
\(946\) 3.96324e16 1.70078
\(947\) 1.58619e16 0.676755 0.338378 0.941010i \(-0.390122\pi\)
0.338378 + 0.941010i \(0.390122\pi\)
\(948\) 1.95055e15 0.0827393
\(949\) 5.40162e15 0.227803
\(950\) −2.96110e15 −0.124158
\(951\) −1.58932e16 −0.662552
\(952\) −1.43085e16 −0.593048
\(953\) 1.77159e16 0.730048 0.365024 0.930998i \(-0.381061\pi\)
0.365024 + 0.930998i \(0.381061\pi\)
\(954\) 1.10333e16 0.452055
\(955\) −3.45055e15 −0.140562
\(956\) −9.53623e14 −0.0386241
\(957\) 1.67184e16 0.673253
\(958\) 3.72227e16 1.49038
\(959\) 3.73750e16 1.48792
\(960\) −4.07447e15 −0.161280
\(961\) −5.43781e15 −0.214016
\(962\) −1.03516e16 −0.405084
\(963\) 1.63931e15 0.0637847
\(964\) 3.89954e14 0.0150865
\(965\) 2.37140e15 0.0912230
\(966\) 5.03044e15 0.192412
\(967\) 3.19757e16 1.21611 0.608057 0.793894i \(-0.291949\pi\)
0.608057 + 0.793894i \(0.291949\pi\)
\(968\) −5.17328e16 −1.95637
\(969\) −1.60408e15 −0.0603177
\(970\) 1.54611e15 0.0578091
\(971\) 4.28910e16 1.59463 0.797316 0.603563i \(-0.206253\pi\)
0.797316 + 0.603563i \(0.206253\pi\)
\(972\) 1.32990e14 0.00491648
\(973\) 2.33391e16 0.857955
\(974\) 1.73634e16 0.634687
\(975\) 5.56182e15 0.202158
\(976\) −2.58855e15 −0.0935584
\(977\) −5.46717e16 −1.96491 −0.982455 0.186499i \(-0.940286\pi\)
−0.982455 + 0.186499i \(0.940286\pi\)
\(978\) 1.24516e16 0.445001
\(979\) 3.88417e16 1.38036
\(980\) 2.39203e14 0.00845326
\(981\) −1.21623e16 −0.427403
\(982\) 1.73798e16 0.607341
\(983\) 3.39763e16 1.18068 0.590339 0.807155i \(-0.298994\pi\)
0.590339 + 0.807155i \(0.298994\pi\)
\(984\) 2.48138e16 0.857474
\(985\) −3.40520e15 −0.117016
\(986\) −1.45195e16 −0.496166
\(987\) −1.62938e16 −0.553706
\(988\) −1.18342e14 −0.00399924
\(989\) −1.41098e16 −0.474177
\(990\) 4.27662e15 0.142925
\(991\) 1.82981e16 0.608137 0.304069 0.952650i \(-0.401655\pi\)
0.304069 + 0.952650i \(0.401655\pi\)
\(992\) −4.10228e15 −0.135585
\(993\) 5.68179e15 0.186752
\(994\) −1.62100e16 −0.529856
\(995\) 1.04276e16 0.338968
\(996\) −2.36751e15 −0.0765361
\(997\) −6.67267e15 −0.214524 −0.107262 0.994231i \(-0.534208\pi\)
−0.107262 + 0.994231i \(0.534208\pi\)
\(998\) 3.90197e16 1.24757
\(999\) 6.78494e15 0.215743
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.12.a.c.1.20 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.c.1.20 27 1.1 even 1 trivial