Properties

Label 177.12.a.d.1.8
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $28$
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: \(28\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-40.3996 q^{2} +243.000 q^{3} -415.876 q^{4} +13699.0 q^{5} -9817.09 q^{6} +81088.1 q^{7} +99539.5 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-40.3996 q^{2} +243.000 q^{3} -415.876 q^{4} +13699.0 q^{5} -9817.09 q^{6} +81088.1 q^{7} +99539.5 q^{8} +59049.0 q^{9} -553432. q^{10} +243519. q^{11} -101058. q^{12} -2.52179e6 q^{13} -3.27592e6 q^{14} +3.32885e6 q^{15} -3.16964e6 q^{16} -6.01606e6 q^{17} -2.38555e6 q^{18} +1.38791e7 q^{19} -5.69706e6 q^{20} +1.97044e7 q^{21} -9.83808e6 q^{22} +3.48489e7 q^{23} +2.41881e7 q^{24} +1.38833e8 q^{25} +1.01879e8 q^{26} +1.43489e7 q^{27} -3.37226e7 q^{28} +6.14157e7 q^{29} -1.34484e8 q^{30} -3.78178e7 q^{31} -7.58049e7 q^{32} +5.91752e7 q^{33} +2.43046e8 q^{34} +1.11082e9 q^{35} -2.45570e7 q^{36} -1.90765e7 q^{37} -5.60708e8 q^{38} -6.12796e8 q^{39} +1.36359e9 q^{40} +6.76940e8 q^{41} -7.96049e8 q^{42} -2.86835e8 q^{43} -1.01274e8 q^{44} +8.08910e8 q^{45} -1.40788e9 q^{46} -2.03944e9 q^{47} -7.70222e8 q^{48} +4.59795e9 q^{49} -5.60881e9 q^{50} -1.46190e9 q^{51} +1.04875e9 q^{52} -1.43758e9 q^{53} -5.79690e8 q^{54} +3.33596e9 q^{55} +8.07146e9 q^{56} +3.37261e9 q^{57} -2.48117e9 q^{58} +7.14924e8 q^{59} -1.38439e9 q^{60} -5.11606e9 q^{61} +1.52782e9 q^{62} +4.78817e9 q^{63} +9.55390e9 q^{64} -3.45460e10 q^{65} -2.39065e9 q^{66} +1.62352e10 q^{67} +2.50193e9 q^{68} +8.46828e9 q^{69} -4.48767e10 q^{70} -1.34058e10 q^{71} +5.87771e9 q^{72} +1.98131e10 q^{73} +7.70681e8 q^{74} +3.37365e10 q^{75} -5.77196e9 q^{76} +1.97465e10 q^{77} +2.47567e10 q^{78} +3.88114e10 q^{79} -4.34207e10 q^{80} +3.48678e9 q^{81} -2.73481e10 q^{82} +8.01748e9 q^{83} -8.19458e9 q^{84} -8.24138e10 q^{85} +1.15880e10 q^{86} +1.49240e10 q^{87} +2.42398e10 q^{88} -5.58096e10 q^{89} -3.26796e10 q^{90} -2.04487e11 q^{91} -1.44928e10 q^{92} -9.18972e9 q^{93} +8.23925e10 q^{94} +1.90129e11 q^{95} -1.84206e10 q^{96} +6.19919e10 q^{97} -1.85755e11 q^{98} +1.43796e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + O(q^{10}) \) \( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + 616281q^{10} + 1082362q^{11} + 7099002q^{12} + 503712q^{13} + 1321669q^{14} + 6454566q^{15} + 34870338q^{16} + 13513579q^{17} + 5668704q^{18} + 35971687q^{19} + 96105997q^{20} + 34586919q^{21} - 47598882q^{22} + 61380539q^{23} + 80756433q^{24} + 294744746q^{25} + 62820734q^{26} + 401769396q^{27} + 148068294q^{28} + 322339307q^{29} + 149756283q^{30} + 151247077q^{31} + 466383494q^{32} + 263013966q^{33} + 684479860q^{34} + 960297361q^{35} + 1725057486q^{36} + 863508437q^{37} + 992640509q^{38} + 122402016q^{39} + 3067680252q^{40} + 3081170377q^{41} + 321165567q^{42} + 2554238300q^{43} + 4350123570q^{44} + 1568459538q^{45} - 1987059155q^{46} + 6203398333q^{47} + 8473492134q^{48} + 10327857997q^{49} + 17577682253q^{50} + 3283799697q^{51} + 32137181618q^{52} + 14571770754q^{53} + 1377495072q^{54} + 18251419334q^{55} + 33498842836q^{56} + 8741119941q^{57} + 11860778276q^{58} + 20017880372q^{59} + 23353757271q^{60} + 2761613771q^{61} + 13785829526q^{62} + 8404621317q^{63} + 86547545293q^{64} + 32034985256q^{65} - 11566528326q^{66} + 39381333296q^{67} + 38995496621q^{68} + 14915470977q^{69} + 8551800364q^{70} + 26130020296q^{71} + 19623813219q^{72} + 41382402799q^{73} + 23815315058q^{74} + 71622973278q^{75} + 10611720128q^{76} - 8426124313q^{77} + 15265438362q^{78} + 59825111206q^{79} + 4009687655q^{80} + 97629963228q^{81} - 39592715115q^{82} + 35433122727q^{83} + 35980595442q^{84} - 8950496085q^{85} - 182032360688q^{86} + 78328451601q^{87} - 220003602335q^{88} + 102303043039q^{89} + 36390776769q^{90} - 111146323655q^{91} - 163000203526q^{92} + 36753039711q^{93} - 81314346008q^{94} + 208102168887q^{95} + 113331189042q^{96} - 171891031490q^{97} + 72304707792q^{98} + 63912393738q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −40.3996 −0.892713 −0.446356 0.894855i \(-0.647279\pi\)
−0.446356 + 0.894855i \(0.647279\pi\)
\(3\) 243.000 0.577350
\(4\) −415.876 −0.203064
\(5\) 13699.0 1.96044 0.980218 0.197922i \(-0.0634193\pi\)
0.980218 + 0.197922i \(0.0634193\pi\)
\(6\) −9817.09 −0.515408
\(7\) 81088.1 1.82355 0.911775 0.410690i \(-0.134712\pi\)
0.911775 + 0.410690i \(0.134712\pi\)
\(8\) 99539.5 1.07399
\(9\) 59049.0 0.333333
\(10\) −553432. −1.75011
\(11\) 243519. 0.455904 0.227952 0.973672i \(-0.426797\pi\)
0.227952 + 0.973672i \(0.426797\pi\)
\(12\) −101058. −0.117239
\(13\) −2.52179e6 −1.88374 −0.941870 0.335976i \(-0.890934\pi\)
−0.941870 + 0.335976i \(0.890934\pi\)
\(14\) −3.27592e6 −1.62791
\(15\) 3.32885e6 1.13186
\(16\) −3.16964e6 −0.755701
\(17\) −6.01606e6 −1.02765 −0.513823 0.857896i \(-0.671771\pi\)
−0.513823 + 0.857896i \(0.671771\pi\)
\(18\) −2.38555e6 −0.297571
\(19\) 1.38791e7 1.28592 0.642962 0.765898i \(-0.277705\pi\)
0.642962 + 0.765898i \(0.277705\pi\)
\(20\) −5.69706e6 −0.398094
\(21\) 1.97044e7 1.05283
\(22\) −9.83808e6 −0.406992
\(23\) 3.48489e7 1.12898 0.564490 0.825440i \(-0.309073\pi\)
0.564490 + 0.825440i \(0.309073\pi\)
\(24\) 2.41881e7 0.620069
\(25\) 1.38833e8 2.84331
\(26\) 1.01879e8 1.68164
\(27\) 1.43489e7 0.192450
\(28\) −3.37226e7 −0.370298
\(29\) 6.14157e7 0.556020 0.278010 0.960578i \(-0.410325\pi\)
0.278010 + 0.960578i \(0.410325\pi\)
\(30\) −1.34484e8 −1.01042
\(31\) −3.78178e7 −0.237250 −0.118625 0.992939i \(-0.537849\pi\)
−0.118625 + 0.992939i \(0.537849\pi\)
\(32\) −7.58049e7 −0.399367
\(33\) 5.91752e7 0.263217
\(34\) 2.43046e8 0.917392
\(35\) 1.11082e9 3.57495
\(36\) −2.45570e7 −0.0676881
\(37\) −1.90765e7 −0.0452260 −0.0226130 0.999744i \(-0.507199\pi\)
−0.0226130 + 0.999744i \(0.507199\pi\)
\(38\) −5.60708e8 −1.14796
\(39\) −6.12796e8 −1.08758
\(40\) 1.36359e9 2.10549
\(41\) 6.76940e8 0.912513 0.456257 0.889848i \(-0.349190\pi\)
0.456257 + 0.889848i \(0.349190\pi\)
\(42\) −7.96049e8 −0.939872
\(43\) −2.86835e8 −0.297547 −0.148774 0.988871i \(-0.547533\pi\)
−0.148774 + 0.988871i \(0.547533\pi\)
\(44\) −1.01274e8 −0.0925779
\(45\) 8.08910e8 0.653478
\(46\) −1.40788e9 −1.00785
\(47\) −2.03944e9 −1.29710 −0.648549 0.761173i \(-0.724624\pi\)
−0.648549 + 0.761173i \(0.724624\pi\)
\(48\) −7.70222e8 −0.436304
\(49\) 4.59795e9 2.32533
\(50\) −5.60881e9 −2.53826
\(51\) −1.46190e9 −0.593311
\(52\) 1.04875e9 0.382520
\(53\) −1.43758e9 −0.472186 −0.236093 0.971730i \(-0.575867\pi\)
−0.236093 + 0.971730i \(0.575867\pi\)
\(54\) −5.79690e8 −0.171803
\(55\) 3.33596e9 0.893771
\(56\) 8.07146e9 1.95848
\(57\) 3.37261e9 0.742429
\(58\) −2.48117e9 −0.496366
\(59\) 7.14924e8 0.130189
\(60\) −1.38439e9 −0.229840
\(61\) −5.11606e9 −0.775571 −0.387785 0.921750i \(-0.626760\pi\)
−0.387785 + 0.921750i \(0.626760\pi\)
\(62\) 1.52782e9 0.211796
\(63\) 4.78817e9 0.607850
\(64\) 9.55390e9 1.11222
\(65\) −3.45460e10 −3.69295
\(66\) −2.39065e9 −0.234977
\(67\) 1.62352e10 1.46909 0.734543 0.678562i \(-0.237397\pi\)
0.734543 + 0.678562i \(0.237397\pi\)
\(68\) 2.50193e9 0.208678
\(69\) 8.46828e9 0.651817
\(70\) −4.48767e10 −3.19140
\(71\) −1.34058e10 −0.881801 −0.440901 0.897556i \(-0.645341\pi\)
−0.440901 + 0.897556i \(0.645341\pi\)
\(72\) 5.87771e9 0.357997
\(73\) 1.98131e10 1.11860 0.559302 0.828964i \(-0.311069\pi\)
0.559302 + 0.828964i \(0.311069\pi\)
\(74\) 7.70681e8 0.0403738
\(75\) 3.37365e10 1.64158
\(76\) −5.77196e9 −0.261125
\(77\) 1.97465e10 0.831365
\(78\) 2.47567e10 0.970895
\(79\) 3.88114e10 1.41909 0.709546 0.704659i \(-0.248900\pi\)
0.709546 + 0.704659i \(0.248900\pi\)
\(80\) −4.34207e10 −1.48150
\(81\) 3.48678e9 0.111111
\(82\) −2.73481e10 −0.814612
\(83\) 8.01748e9 0.223413 0.111706 0.993741i \(-0.464368\pi\)
0.111706 + 0.993741i \(0.464368\pi\)
\(84\) −8.19458e9 −0.213792
\(85\) −8.24138e10 −2.01463
\(86\) 1.15880e10 0.265624
\(87\) 1.49240e10 0.321018
\(88\) 2.42398e10 0.489637
\(89\) −5.58096e10 −1.05941 −0.529705 0.848182i \(-0.677697\pi\)
−0.529705 + 0.848182i \(0.677697\pi\)
\(90\) −3.26796e10 −0.583368
\(91\) −2.04487e11 −3.43510
\(92\) −1.44928e10 −0.229255
\(93\) −9.18972e9 −0.136976
\(94\) 8.23925e10 1.15794
\(95\) 1.90129e11 2.52097
\(96\) −1.84206e10 −0.230575
\(97\) 6.19919e10 0.732978 0.366489 0.930422i \(-0.380560\pi\)
0.366489 + 0.930422i \(0.380560\pi\)
\(98\) −1.85755e11 −2.07586
\(99\) 1.43796e10 0.151968
\(100\) −5.77374e10 −0.577374
\(101\) 9.69644e10 0.918004 0.459002 0.888435i \(-0.348207\pi\)
0.459002 + 0.888435i \(0.348207\pi\)
\(102\) 5.90602e10 0.529656
\(103\) −5.00427e10 −0.425340 −0.212670 0.977124i \(-0.568216\pi\)
−0.212670 + 0.977124i \(0.568216\pi\)
\(104\) −2.51018e11 −2.02312
\(105\) 2.69930e11 2.06400
\(106\) 5.80774e10 0.421527
\(107\) 2.73516e10 0.188526 0.0942630 0.995547i \(-0.469951\pi\)
0.0942630 + 0.995547i \(0.469951\pi\)
\(108\) −5.96736e9 −0.0390797
\(109\) −1.07991e11 −0.672270 −0.336135 0.941814i \(-0.609120\pi\)
−0.336135 + 0.941814i \(0.609120\pi\)
\(110\) −1.34771e11 −0.797881
\(111\) −4.63558e9 −0.0261113
\(112\) −2.57020e11 −1.37806
\(113\) 2.16520e11 1.10552 0.552759 0.833341i \(-0.313575\pi\)
0.552759 + 0.833341i \(0.313575\pi\)
\(114\) −1.36252e11 −0.662775
\(115\) 4.77394e11 2.21329
\(116\) −2.55413e10 −0.112908
\(117\) −1.48909e11 −0.627914
\(118\) −2.88826e10 −0.116221
\(119\) −4.87831e11 −1.87396
\(120\) 3.31352e11 1.21560
\(121\) −2.26010e11 −0.792151
\(122\) 2.06687e11 0.692362
\(123\) 1.64496e11 0.526840
\(124\) 1.57275e10 0.0481770
\(125\) 1.23298e12 3.61369
\(126\) −1.93440e11 −0.542635
\(127\) −4.06073e10 −0.109065 −0.0545323 0.998512i \(-0.517367\pi\)
−0.0545323 + 0.998512i \(0.517367\pi\)
\(128\) −2.30725e11 −0.593526
\(129\) −6.97009e10 −0.171789
\(130\) 1.39564e12 3.29674
\(131\) −5.09433e11 −1.15371 −0.576853 0.816848i \(-0.695719\pi\)
−0.576853 + 0.816848i \(0.695719\pi\)
\(132\) −2.46095e10 −0.0534499
\(133\) 1.12543e12 2.34495
\(134\) −6.55896e11 −1.31147
\(135\) 1.96565e11 0.377286
\(136\) −5.98836e11 −1.10368
\(137\) −5.93432e11 −1.05053 −0.525264 0.850939i \(-0.676034\pi\)
−0.525264 + 0.850939i \(0.676034\pi\)
\(138\) −3.42115e11 −0.581885
\(139\) −6.07937e11 −0.993751 −0.496875 0.867822i \(-0.665519\pi\)
−0.496875 + 0.867822i \(0.665519\pi\)
\(140\) −4.61964e11 −0.725945
\(141\) −4.95584e11 −0.748880
\(142\) 5.41587e11 0.787195
\(143\) −6.14106e11 −0.858806
\(144\) −1.87164e11 −0.251900
\(145\) 8.41331e11 1.09004
\(146\) −8.00440e11 −0.998592
\(147\) 1.11730e12 1.34253
\(148\) 7.93344e9 0.00918379
\(149\) −3.40159e9 −0.00379452 −0.00189726 0.999998i \(-0.500604\pi\)
−0.00189726 + 0.999998i \(0.500604\pi\)
\(150\) −1.36294e12 −1.46546
\(151\) −1.30730e10 −0.0135520 −0.00677598 0.999977i \(-0.502157\pi\)
−0.00677598 + 0.999977i \(0.502157\pi\)
\(152\) 1.38151e12 1.38107
\(153\) −3.55242e11 −0.342548
\(154\) −7.97751e11 −0.742170
\(155\) −5.18064e11 −0.465114
\(156\) 2.54847e11 0.220848
\(157\) −2.11552e12 −1.76999 −0.884993 0.465605i \(-0.845837\pi\)
−0.884993 + 0.465605i \(0.845837\pi\)
\(158\) −1.56797e12 −1.26684
\(159\) −3.49331e11 −0.272617
\(160\) −1.03845e12 −0.782934
\(161\) 2.82583e12 2.05875
\(162\) −1.40865e11 −0.0991903
\(163\) 1.09655e12 0.746443 0.373222 0.927742i \(-0.378253\pi\)
0.373222 + 0.927742i \(0.378253\pi\)
\(164\) −2.81523e11 −0.185299
\(165\) 8.10639e11 0.516019
\(166\) −3.23903e11 −0.199444
\(167\) 5.82427e11 0.346977 0.173488 0.984836i \(-0.444496\pi\)
0.173488 + 0.984836i \(0.444496\pi\)
\(168\) 1.96137e12 1.13073
\(169\) 4.56728e12 2.54848
\(170\) 3.32948e12 1.79849
\(171\) 8.19545e11 0.428641
\(172\) 1.19288e11 0.0604212
\(173\) −1.73135e12 −0.849438 −0.424719 0.905325i \(-0.639627\pi\)
−0.424719 + 0.905325i \(0.639627\pi\)
\(174\) −6.02923e11 −0.286577
\(175\) 1.12577e13 5.18491
\(176\) −7.71868e11 −0.344527
\(177\) 1.73727e11 0.0751646
\(178\) 2.25468e12 0.945749
\(179\) 1.76913e12 0.719563 0.359781 0.933037i \(-0.382851\pi\)
0.359781 + 0.933037i \(0.382851\pi\)
\(180\) −3.36406e11 −0.132698
\(181\) 4.22975e12 1.61839 0.809194 0.587541i \(-0.199904\pi\)
0.809194 + 0.587541i \(0.199904\pi\)
\(182\) 8.26120e12 3.06655
\(183\) −1.24320e12 −0.447776
\(184\) 3.46884e12 1.21251
\(185\) −2.61328e11 −0.0886627
\(186\) 3.71260e11 0.122281
\(187\) −1.46503e12 −0.468508
\(188\) 8.48154e11 0.263394
\(189\) 1.16352e12 0.350942
\(190\) −7.68112e12 −2.25050
\(191\) 1.64378e12 0.467906 0.233953 0.972248i \(-0.424834\pi\)
0.233953 + 0.972248i \(0.424834\pi\)
\(192\) 2.32160e12 0.642141
\(193\) −9.12185e11 −0.245198 −0.122599 0.992456i \(-0.539123\pi\)
−0.122599 + 0.992456i \(0.539123\pi\)
\(194\) −2.50445e12 −0.654338
\(195\) −8.39467e12 −2.13213
\(196\) −1.91217e12 −0.472192
\(197\) 5.60318e12 1.34546 0.672729 0.739889i \(-0.265122\pi\)
0.672729 + 0.739889i \(0.265122\pi\)
\(198\) −5.80929e11 −0.135664
\(199\) −6.58348e12 −1.49542 −0.747710 0.664025i \(-0.768847\pi\)
−0.747710 + 0.664025i \(0.768847\pi\)
\(200\) 1.38194e13 3.05369
\(201\) 3.94516e12 0.848177
\(202\) −3.91732e12 −0.819514
\(203\) 4.98008e12 1.01393
\(204\) 6.07970e11 0.120480
\(205\) 9.27338e12 1.78892
\(206\) 2.02170e12 0.379706
\(207\) 2.05779e12 0.376326
\(208\) 7.99317e12 1.42354
\(209\) 3.37982e12 0.586259
\(210\) −1.09050e13 −1.84256
\(211\) −5.28623e12 −0.870146 −0.435073 0.900395i \(-0.643277\pi\)
−0.435073 + 0.900395i \(0.643277\pi\)
\(212\) 5.97853e11 0.0958842
\(213\) −3.25760e12 −0.509108
\(214\) −1.10499e12 −0.168300
\(215\) −3.92934e12 −0.583322
\(216\) 1.42828e12 0.206690
\(217\) −3.06657e12 −0.432637
\(218\) 4.36281e12 0.600144
\(219\) 4.81458e12 0.645826
\(220\) −1.38735e12 −0.181493
\(221\) 1.51713e13 1.93582
\(222\) 1.87275e11 0.0233098
\(223\) −1.45141e11 −0.0176244 −0.00881219 0.999961i \(-0.502805\pi\)
−0.00881219 + 0.999961i \(0.502805\pi\)
\(224\) −6.14687e12 −0.728266
\(225\) 8.19797e12 0.947769
\(226\) −8.74729e12 −0.986909
\(227\) −6.12191e11 −0.0674131 −0.0337066 0.999432i \(-0.510731\pi\)
−0.0337066 + 0.999432i \(0.510731\pi\)
\(228\) −1.40259e12 −0.150761
\(229\) −1.04956e13 −1.10131 −0.550656 0.834732i \(-0.685622\pi\)
−0.550656 + 0.834732i \(0.685622\pi\)
\(230\) −1.92865e13 −1.97583
\(231\) 4.79840e12 0.479989
\(232\) 6.11329e12 0.597160
\(233\) 1.51599e13 1.44624 0.723120 0.690723i \(-0.242707\pi\)
0.723120 + 0.690723i \(0.242707\pi\)
\(234\) 6.01587e12 0.560546
\(235\) −2.79382e13 −2.54288
\(236\) −2.97320e11 −0.0264367
\(237\) 9.43118e12 0.819314
\(238\) 1.97081e13 1.67291
\(239\) −1.63433e13 −1.35567 −0.677833 0.735216i \(-0.737081\pi\)
−0.677833 + 0.735216i \(0.737081\pi\)
\(240\) −1.05512e13 −0.855346
\(241\) −1.46376e13 −1.15978 −0.579892 0.814694i \(-0.696905\pi\)
−0.579892 + 0.814694i \(0.696905\pi\)
\(242\) 9.13070e12 0.707163
\(243\) 8.47289e11 0.0641500
\(244\) 2.12764e12 0.157491
\(245\) 6.29871e13 4.55867
\(246\) −6.64558e12 −0.470316
\(247\) −3.50001e13 −2.42235
\(248\) −3.76436e12 −0.254804
\(249\) 1.94825e12 0.128988
\(250\) −4.98118e13 −3.22598
\(251\) −1.96061e13 −1.24218 −0.621091 0.783739i \(-0.713310\pi\)
−0.621091 + 0.783739i \(0.713310\pi\)
\(252\) −1.99128e12 −0.123433
\(253\) 8.48639e12 0.514707
\(254\) 1.64052e12 0.0973633
\(255\) −2.00265e13 −1.16315
\(256\) −1.02452e13 −0.582372
\(257\) −5.08443e12 −0.282885 −0.141443 0.989946i \(-0.545174\pi\)
−0.141443 + 0.989946i \(0.545174\pi\)
\(258\) 2.81589e12 0.153358
\(259\) −1.54687e12 −0.0824719
\(260\) 1.43668e13 0.749907
\(261\) 3.62653e12 0.185340
\(262\) 2.05809e13 1.02993
\(263\) −3.25812e13 −1.59665 −0.798326 0.602226i \(-0.794281\pi\)
−0.798326 + 0.602226i \(0.794281\pi\)
\(264\) 5.89027e12 0.282692
\(265\) −1.96933e13 −0.925691
\(266\) −4.54667e13 −2.09336
\(267\) −1.35617e13 −0.611651
\(268\) −6.75184e12 −0.298319
\(269\) 1.22091e13 0.528503 0.264251 0.964454i \(-0.414875\pi\)
0.264251 + 0.964454i \(0.414875\pi\)
\(270\) −7.94114e12 −0.336808
\(271\) 4.35296e13 1.80906 0.904531 0.426407i \(-0.140221\pi\)
0.904531 + 0.426407i \(0.140221\pi\)
\(272\) 1.90687e13 0.776592
\(273\) −4.96904e13 −1.98325
\(274\) 2.39744e13 0.937820
\(275\) 3.38086e13 1.29628
\(276\) −3.52175e12 −0.132361
\(277\) 8.69092e12 0.320204 0.160102 0.987100i \(-0.448818\pi\)
0.160102 + 0.987100i \(0.448818\pi\)
\(278\) 2.45604e13 0.887134
\(279\) −2.23310e12 −0.0790834
\(280\) 1.10571e14 3.83946
\(281\) 1.49019e13 0.507407 0.253704 0.967282i \(-0.418351\pi\)
0.253704 + 0.967282i \(0.418351\pi\)
\(282\) 2.00214e13 0.668535
\(283\) −1.55611e13 −0.509584 −0.254792 0.966996i \(-0.582007\pi\)
−0.254792 + 0.966996i \(0.582007\pi\)
\(284\) 5.57513e12 0.179062
\(285\) 4.62013e13 1.45548
\(286\) 2.48096e13 0.766667
\(287\) 5.48918e13 1.66401
\(288\) −4.47620e12 −0.133122
\(289\) 1.92110e12 0.0560548
\(290\) −3.39894e13 −0.973093
\(291\) 1.50640e13 0.423185
\(292\) −8.23978e12 −0.227149
\(293\) 3.73651e13 1.01087 0.505434 0.862865i \(-0.331333\pi\)
0.505434 + 0.862865i \(0.331333\pi\)
\(294\) −4.51385e13 −1.19850
\(295\) 9.79372e12 0.255227
\(296\) −1.89886e12 −0.0485723
\(297\) 3.49424e12 0.0877389
\(298\) 1.37423e11 0.00338742
\(299\) −8.78817e13 −2.12670
\(300\) −1.40302e13 −0.333347
\(301\) −2.32589e13 −0.542592
\(302\) 5.28144e11 0.0120980
\(303\) 2.35623e13 0.530010
\(304\) −4.39916e13 −0.971774
\(305\) −7.00847e13 −1.52046
\(306\) 1.43516e13 0.305797
\(307\) 5.48864e13 1.14869 0.574346 0.818613i \(-0.305256\pi\)
0.574346 + 0.818613i \(0.305256\pi\)
\(308\) −8.21210e12 −0.168820
\(309\) −1.21604e13 −0.245570
\(310\) 2.09296e13 0.415213
\(311\) −2.07281e13 −0.403997 −0.201998 0.979386i \(-0.564744\pi\)
−0.201998 + 0.979386i \(0.564744\pi\)
\(312\) −6.09974e13 −1.16805
\(313\) −1.47776e13 −0.278042 −0.139021 0.990289i \(-0.544396\pi\)
−0.139021 + 0.990289i \(0.544396\pi\)
\(314\) 8.54662e13 1.58009
\(315\) 6.55929e13 1.19165
\(316\) −1.61407e13 −0.288167
\(317\) 6.52417e13 1.14472 0.572360 0.820002i \(-0.306028\pi\)
0.572360 + 0.820002i \(0.306028\pi\)
\(318\) 1.41128e13 0.243369
\(319\) 1.49559e13 0.253492
\(320\) 1.30879e14 2.18044
\(321\) 6.64643e12 0.108846
\(322\) −1.14162e14 −1.83787
\(323\) −8.34973e13 −1.32147
\(324\) −1.45007e12 −0.0225627
\(325\) −3.50109e14 −5.35605
\(326\) −4.43002e13 −0.666359
\(327\) −2.62419e13 −0.388135
\(328\) 6.73823e13 0.980030
\(329\) −1.65374e14 −2.36532
\(330\) −3.27495e13 −0.460657
\(331\) 3.77281e13 0.521928 0.260964 0.965348i \(-0.415960\pi\)
0.260964 + 0.965348i \(0.415960\pi\)
\(332\) −3.33428e12 −0.0453672
\(333\) −1.12645e12 −0.0150753
\(334\) −2.35298e13 −0.309751
\(335\) 2.22406e14 2.88005
\(336\) −6.24558e13 −0.795622
\(337\) −1.04357e14 −1.30784 −0.653922 0.756562i \(-0.726877\pi\)
−0.653922 + 0.756562i \(0.726877\pi\)
\(338\) −1.84516e14 −2.27506
\(339\) 5.26142e13 0.638271
\(340\) 3.42739e13 0.409100
\(341\) −9.20936e12 −0.108163
\(342\) −3.31092e13 −0.382654
\(343\) 2.12501e14 2.41681
\(344\) −2.85514e13 −0.319563
\(345\) 1.16007e14 1.27784
\(346\) 6.99458e13 0.758304
\(347\) −4.74108e13 −0.505901 −0.252950 0.967479i \(-0.581401\pi\)
−0.252950 + 0.967479i \(0.581401\pi\)
\(348\) −6.20653e12 −0.0651873
\(349\) 1.29110e14 1.33481 0.667406 0.744694i \(-0.267405\pi\)
0.667406 + 0.744694i \(0.267405\pi\)
\(350\) −4.54807e14 −4.62864
\(351\) −3.61850e13 −0.362526
\(352\) −1.84600e13 −0.182073
\(353\) 1.30632e14 1.26849 0.634246 0.773132i \(-0.281311\pi\)
0.634246 + 0.773132i \(0.281311\pi\)
\(354\) −7.01848e12 −0.0671004
\(355\) −1.83645e14 −1.72871
\(356\) 2.32099e13 0.215128
\(357\) −1.18543e14 −1.08193
\(358\) −7.14722e13 −0.642363
\(359\) 8.73656e13 0.773252 0.386626 0.922237i \(-0.373640\pi\)
0.386626 + 0.922237i \(0.373640\pi\)
\(360\) 8.05185e13 0.701830
\(361\) 7.61381e13 0.653601
\(362\) −1.70880e14 −1.44476
\(363\) −5.49204e13 −0.457349
\(364\) 8.50413e13 0.697545
\(365\) 2.71419e14 2.19295
\(366\) 5.02248e13 0.399735
\(367\) −7.59876e13 −0.595771 −0.297886 0.954602i \(-0.596281\pi\)
−0.297886 + 0.954602i \(0.596281\pi\)
\(368\) −1.10458e14 −0.853170
\(369\) 3.99726e13 0.304171
\(370\) 1.05575e13 0.0791503
\(371\) −1.16570e14 −0.861056
\(372\) 3.82178e12 0.0278150
\(373\) 1.89148e14 1.35645 0.678225 0.734854i \(-0.262749\pi\)
0.678225 + 0.734854i \(0.262749\pi\)
\(374\) 5.91865e13 0.418243
\(375\) 2.99614e14 2.08636
\(376\) −2.03005e14 −1.39307
\(377\) −1.54878e14 −1.04740
\(378\) −4.70059e13 −0.313291
\(379\) −2.08609e14 −1.37031 −0.685153 0.728399i \(-0.740265\pi\)
−0.685153 + 0.728399i \(0.740265\pi\)
\(380\) −7.90699e13 −0.511919
\(381\) −9.86757e12 −0.0629684
\(382\) −6.64078e13 −0.417706
\(383\) 9.82899e13 0.609418 0.304709 0.952445i \(-0.401441\pi\)
0.304709 + 0.952445i \(0.401441\pi\)
\(384\) −5.60662e13 −0.342672
\(385\) 2.70507e14 1.62984
\(386\) 3.68519e13 0.218892
\(387\) −1.69373e13 −0.0991823
\(388\) −2.57809e13 −0.148842
\(389\) 2.48814e14 1.41629 0.708145 0.706067i \(-0.249532\pi\)
0.708145 + 0.706067i \(0.249532\pi\)
\(390\) 3.39141e14 1.90338
\(391\) −2.09653e14 −1.16019
\(392\) 4.57677e14 2.49739
\(393\) −1.23792e14 −0.666092
\(394\) −2.26366e14 −1.20111
\(395\) 5.31676e14 2.78204
\(396\) −5.98012e12 −0.0308593
\(397\) −2.14738e14 −1.09285 −0.546424 0.837508i \(-0.684011\pi\)
−0.546424 + 0.837508i \(0.684011\pi\)
\(398\) 2.65969e14 1.33498
\(399\) 2.73479e14 1.35386
\(400\) −4.40052e14 −2.14869
\(401\) 3.08242e14 1.48456 0.742280 0.670090i \(-0.233745\pi\)
0.742280 + 0.670090i \(0.233745\pi\)
\(402\) −1.59383e14 −0.757178
\(403\) 9.53686e13 0.446918
\(404\) −4.03251e13 −0.186414
\(405\) 4.77653e13 0.217826
\(406\) −2.01193e14 −0.905148
\(407\) −4.64549e12 −0.0206187
\(408\) −1.45517e14 −0.637211
\(409\) 1.12336e14 0.485335 0.242668 0.970110i \(-0.421978\pi\)
0.242668 + 0.970110i \(0.421978\pi\)
\(410\) −3.74640e14 −1.59699
\(411\) −1.44204e14 −0.606523
\(412\) 2.08116e13 0.0863714
\(413\) 5.79718e13 0.237406
\(414\) −8.31339e13 −0.335951
\(415\) 1.09831e14 0.437987
\(416\) 1.91164e14 0.752304
\(417\) −1.47729e14 −0.573742
\(418\) −1.36543e14 −0.523360
\(419\) −2.45661e14 −0.929307 −0.464653 0.885493i \(-0.653821\pi\)
−0.464653 + 0.885493i \(0.653821\pi\)
\(420\) −1.12257e14 −0.419125
\(421\) −1.51149e14 −0.556998 −0.278499 0.960437i \(-0.589837\pi\)
−0.278499 + 0.960437i \(0.589837\pi\)
\(422\) 2.13561e14 0.776790
\(423\) −1.20427e14 −0.432366
\(424\) −1.43096e14 −0.507124
\(425\) −8.35230e14 −2.92191
\(426\) 1.31606e14 0.454487
\(427\) −4.14851e14 −1.41429
\(428\) −1.13749e13 −0.0382829
\(429\) −1.49228e14 −0.495832
\(430\) 1.58744e14 0.520739
\(431\) 2.50477e14 0.811227 0.405614 0.914045i \(-0.367058\pi\)
0.405614 + 0.914045i \(0.367058\pi\)
\(432\) −4.54808e13 −0.145435
\(433\) −2.39225e14 −0.755306 −0.377653 0.925947i \(-0.623269\pi\)
−0.377653 + 0.925947i \(0.623269\pi\)
\(434\) 1.23888e14 0.386221
\(435\) 2.04443e14 0.629336
\(436\) 4.49110e13 0.136514
\(437\) 4.83670e14 1.45178
\(438\) −1.94507e14 −0.576537
\(439\) 1.61931e14 0.473997 0.236999 0.971510i \(-0.423836\pi\)
0.236999 + 0.971510i \(0.423836\pi\)
\(440\) 3.32060e14 0.959902
\(441\) 2.71504e14 0.775112
\(442\) −6.12912e14 −1.72813
\(443\) 4.08945e14 1.13879 0.569396 0.822063i \(-0.307177\pi\)
0.569396 + 0.822063i \(0.307177\pi\)
\(444\) 1.92783e12 0.00530226
\(445\) −7.64534e14 −2.07691
\(446\) 5.86364e12 0.0157335
\(447\) −8.26585e11 −0.00219077
\(448\) 7.74707e14 2.02819
\(449\) −3.70093e13 −0.0957098 −0.0478549 0.998854i \(-0.515239\pi\)
−0.0478549 + 0.998854i \(0.515239\pi\)
\(450\) −3.31194e14 −0.846085
\(451\) 1.64848e14 0.416019
\(452\) −9.00452e13 −0.224491
\(453\) −3.17674e12 −0.00782423
\(454\) 2.47322e13 0.0601805
\(455\) −2.80126e15 −6.73428
\(456\) 3.35708e14 0.797361
\(457\) −4.04975e14 −0.950362 −0.475181 0.879888i \(-0.657617\pi\)
−0.475181 + 0.879888i \(0.657617\pi\)
\(458\) 4.24016e14 0.983155
\(459\) −8.63239e13 −0.197770
\(460\) −1.98536e14 −0.449440
\(461\) 4.27921e14 0.957212 0.478606 0.878030i \(-0.341142\pi\)
0.478606 + 0.878030i \(0.341142\pi\)
\(462\) −1.93853e14 −0.428492
\(463\) −3.91795e14 −0.855783 −0.427892 0.903830i \(-0.640743\pi\)
−0.427892 + 0.903830i \(0.640743\pi\)
\(464\) −1.94665e14 −0.420185
\(465\) −1.25890e14 −0.268533
\(466\) −6.12455e14 −1.29108
\(467\) 1.59037e14 0.331326 0.165663 0.986182i \(-0.447024\pi\)
0.165663 + 0.986182i \(0.447024\pi\)
\(468\) 6.19278e13 0.127507
\(469\) 1.31648e15 2.67895
\(470\) 1.12869e15 2.27006
\(471\) −5.14072e14 −1.02190
\(472\) 7.11632e13 0.139822
\(473\) −6.98499e13 −0.135653
\(474\) −3.81016e14 −0.731411
\(475\) 1.92688e15 3.65628
\(476\) 2.02877e14 0.380535
\(477\) −8.48874e13 −0.157395
\(478\) 6.60264e14 1.21022
\(479\) −2.13649e14 −0.387128 −0.193564 0.981088i \(-0.562005\pi\)
−0.193564 + 0.981088i \(0.562005\pi\)
\(480\) −2.52343e14 −0.452027
\(481\) 4.81069e13 0.0851941
\(482\) 5.91354e14 1.03535
\(483\) 6.86677e14 1.18862
\(484\) 9.39920e13 0.160858
\(485\) 8.49225e14 1.43696
\(486\) −3.42301e13 −0.0572675
\(487\) 2.97727e14 0.492504 0.246252 0.969206i \(-0.420801\pi\)
0.246252 + 0.969206i \(0.420801\pi\)
\(488\) −5.09250e14 −0.832956
\(489\) 2.66462e14 0.430959
\(490\) −2.54465e15 −4.06958
\(491\) −7.38058e14 −1.16719 −0.583596 0.812044i \(-0.698355\pi\)
−0.583596 + 0.812044i \(0.698355\pi\)
\(492\) −6.84101e13 −0.106982
\(493\) −3.69481e14 −0.571391
\(494\) 1.41399e15 2.16246
\(495\) 1.96985e14 0.297924
\(496\) 1.19869e14 0.179290
\(497\) −1.08705e15 −1.60801
\(498\) −7.87084e13 −0.115149
\(499\) −6.14412e14 −0.889010 −0.444505 0.895776i \(-0.646620\pi\)
−0.444505 + 0.895776i \(0.646620\pi\)
\(500\) −5.12766e14 −0.733810
\(501\) 1.41530e14 0.200327
\(502\) 7.92076e14 1.10891
\(503\) 6.02635e14 0.834508 0.417254 0.908790i \(-0.362993\pi\)
0.417254 + 0.908790i \(0.362993\pi\)
\(504\) 4.76612e14 0.652825
\(505\) 1.32831e15 1.79969
\(506\) −3.42846e14 −0.459485
\(507\) 1.10985e15 1.47137
\(508\) 1.68876e13 0.0221471
\(509\) 2.20861e14 0.286531 0.143266 0.989684i \(-0.454240\pi\)
0.143266 + 0.989684i \(0.454240\pi\)
\(510\) 8.09064e14 1.03836
\(511\) 1.60660e15 2.03983
\(512\) 8.86427e14 1.11342
\(513\) 1.99149e14 0.247476
\(514\) 2.05409e14 0.252535
\(515\) −6.85533e14 −0.833852
\(516\) 2.89869e13 0.0348842
\(517\) −4.96644e14 −0.591353
\(518\) 6.24930e13 0.0736237
\(519\) −4.20718e14 −0.490423
\(520\) −3.43869e15 −3.96620
\(521\) −1.64552e15 −1.87800 −0.939000 0.343916i \(-0.888247\pi\)
−0.939000 + 0.343916i \(0.888247\pi\)
\(522\) −1.46510e14 −0.165455
\(523\) −8.38560e14 −0.937077 −0.468538 0.883443i \(-0.655219\pi\)
−0.468538 + 0.883443i \(0.655219\pi\)
\(524\) 2.11861e14 0.234276
\(525\) 2.73563e15 2.99351
\(526\) 1.31626e15 1.42535
\(527\) 2.27514e14 0.243809
\(528\) −1.87564e14 −0.198913
\(529\) 2.61636e14 0.274594
\(530\) 7.95600e14 0.826376
\(531\) 4.22156e13 0.0433963
\(532\) −4.68037e14 −0.476175
\(533\) −1.70710e15 −1.71894
\(534\) 5.47888e14 0.546028
\(535\) 3.74688e14 0.369593
\(536\) 1.61605e15 1.57778
\(537\) 4.29899e14 0.415440
\(538\) −4.93243e14 −0.471801
\(539\) 1.11969e15 1.06013
\(540\) −8.17466e13 −0.0766133
\(541\) −3.43251e14 −0.318439 −0.159220 0.987243i \(-0.550898\pi\)
−0.159220 + 0.987243i \(0.550898\pi\)
\(542\) −1.75858e15 −1.61497
\(543\) 1.02783e15 0.934377
\(544\) 4.56047e14 0.410408
\(545\) −1.47937e15 −1.31794
\(546\) 2.00747e15 1.77048
\(547\) 7.83013e14 0.683657 0.341829 0.939762i \(-0.388954\pi\)
0.341829 + 0.939762i \(0.388954\pi\)
\(548\) 2.46794e14 0.213325
\(549\) −3.02098e14 −0.258524
\(550\) −1.36585e15 −1.15720
\(551\) 8.52392e14 0.714999
\(552\) 8.42929e14 0.700045
\(553\) 3.14714e15 2.58779
\(554\) −3.51109e14 −0.285850
\(555\) −6.35026e13 −0.0511894
\(556\) 2.52826e14 0.201795
\(557\) −1.49786e15 −1.18377 −0.591886 0.806022i \(-0.701616\pi\)
−0.591886 + 0.806022i \(0.701616\pi\)
\(558\) 9.02163e13 0.0705987
\(559\) 7.23339e14 0.560501
\(560\) −3.52090e15 −2.70159
\(561\) −3.56002e14 −0.270493
\(562\) −6.02030e14 −0.452969
\(563\) 1.62851e15 1.21337 0.606686 0.794941i \(-0.292498\pi\)
0.606686 + 0.794941i \(0.292498\pi\)
\(564\) 2.06101e14 0.152071
\(565\) 2.96609e15 2.16730
\(566\) 6.28663e14 0.454912
\(567\) 2.82737e14 0.202617
\(568\) −1.33440e15 −0.947046
\(569\) 1.83836e15 1.29215 0.646075 0.763274i \(-0.276410\pi\)
0.646075 + 0.763274i \(0.276410\pi\)
\(570\) −1.86651e15 −1.29933
\(571\) −3.60398e14 −0.248476 −0.124238 0.992252i \(-0.539649\pi\)
−0.124238 + 0.992252i \(0.539649\pi\)
\(572\) 2.55392e14 0.174393
\(573\) 3.99437e14 0.270146
\(574\) −2.21760e15 −1.48549
\(575\) 4.83819e15 3.21004
\(576\) 5.64148e14 0.370740
\(577\) 2.10156e15 1.36797 0.683983 0.729498i \(-0.260246\pi\)
0.683983 + 0.729498i \(0.260246\pi\)
\(578\) −7.76117e13 −0.0500408
\(579\) −2.21661e14 −0.141565
\(580\) −3.49889e14 −0.221348
\(581\) 6.50122e14 0.407405
\(582\) −6.08581e14 −0.377782
\(583\) −3.50078e14 −0.215272
\(584\) 1.97218e15 1.20137
\(585\) −2.03990e15 −1.23098
\(586\) −1.50953e15 −0.902414
\(587\) −1.67311e15 −0.990868 −0.495434 0.868646i \(-0.664991\pi\)
−0.495434 + 0.868646i \(0.664991\pi\)
\(588\) −4.64658e14 −0.272620
\(589\) −5.24875e14 −0.305086
\(590\) −3.95662e14 −0.227844
\(591\) 1.36157e15 0.776801
\(592\) 6.04655e13 0.0341773
\(593\) −1.24514e15 −0.697297 −0.348648 0.937254i \(-0.613359\pi\)
−0.348648 + 0.937254i \(0.613359\pi\)
\(594\) −1.41166e14 −0.0783256
\(595\) −6.68277e15 −3.67378
\(596\) 1.41464e12 0.000770532 0
\(597\) −1.59978e15 −0.863381
\(598\) 3.55038e15 1.89854
\(599\) −1.49657e15 −0.792958 −0.396479 0.918044i \(-0.629768\pi\)
−0.396479 + 0.918044i \(0.629768\pi\)
\(600\) 3.35811e15 1.76305
\(601\) −1.44646e14 −0.0752484 −0.0376242 0.999292i \(-0.511979\pi\)
−0.0376242 + 0.999292i \(0.511979\pi\)
\(602\) 9.39649e14 0.484379
\(603\) 9.58674e14 0.489695
\(604\) 5.43674e12 0.00275192
\(605\) −3.09610e15 −1.55296
\(606\) −9.51908e14 −0.473147
\(607\) 2.85266e15 1.40512 0.702558 0.711626i \(-0.252041\pi\)
0.702558 + 0.711626i \(0.252041\pi\)
\(608\) −1.05210e15 −0.513556
\(609\) 1.21016e15 0.585393
\(610\) 2.83139e15 1.35733
\(611\) 5.14305e15 2.44340
\(612\) 1.47737e14 0.0695594
\(613\) −4.25071e15 −1.98348 −0.991742 0.128247i \(-0.959065\pi\)
−0.991742 + 0.128247i \(0.959065\pi\)
\(614\) −2.21739e15 −1.02545
\(615\) 2.25343e15 1.03284
\(616\) 1.96556e15 0.892878
\(617\) −2.26950e15 −1.02179 −0.510895 0.859643i \(-0.670686\pi\)
−0.510895 + 0.859643i \(0.670686\pi\)
\(618\) 4.91274e14 0.219224
\(619\) −3.23002e15 −1.42859 −0.714293 0.699847i \(-0.753251\pi\)
−0.714293 + 0.699847i \(0.753251\pi\)
\(620\) 2.15450e14 0.0944480
\(621\) 5.00044e14 0.217272
\(622\) 8.37407e14 0.360653
\(623\) −4.52549e15 −1.93189
\(624\) 1.94234e15 0.821884
\(625\) 1.01115e16 4.24109
\(626\) 5.97010e14 0.248212
\(627\) 8.21297e14 0.338477
\(628\) 8.79794e14 0.359421
\(629\) 1.14765e14 0.0464763
\(630\) −2.64993e15 −1.06380
\(631\) −3.18248e15 −1.26650 −0.633248 0.773949i \(-0.718279\pi\)
−0.633248 + 0.773949i \(0.718279\pi\)
\(632\) 3.86327e15 1.52409
\(633\) −1.28455e15 −0.502379
\(634\) −2.63574e15 −1.02191
\(635\) −5.56278e14 −0.213814
\(636\) 1.45278e14 0.0553588
\(637\) −1.15951e16 −4.38033
\(638\) −6.04212e14 −0.226295
\(639\) −7.91597e14 −0.293934
\(640\) −3.16069e15 −1.16357
\(641\) −1.47472e15 −0.538257 −0.269129 0.963104i \(-0.586736\pi\)
−0.269129 + 0.963104i \(0.586736\pi\)
\(642\) −2.68513e14 −0.0971678
\(643\) −3.97386e15 −1.42578 −0.712889 0.701277i \(-0.752614\pi\)
−0.712889 + 0.701277i \(0.752614\pi\)
\(644\) −1.17519e15 −0.418059
\(645\) −9.54830e14 −0.336781
\(646\) 3.37325e15 1.17970
\(647\) 2.37355e15 0.823048 0.411524 0.911399i \(-0.364997\pi\)
0.411524 + 0.911399i \(0.364997\pi\)
\(648\) 3.47073e14 0.119332
\(649\) 1.74098e14 0.0593537
\(650\) 1.41443e16 4.78142
\(651\) −7.45176e14 −0.249783
\(652\) −4.56029e14 −0.151576
\(653\) −1.53417e15 −0.505652 −0.252826 0.967512i \(-0.581360\pi\)
−0.252826 + 0.967512i \(0.581360\pi\)
\(654\) 1.06016e15 0.346493
\(655\) −6.97870e15 −2.26176
\(656\) −2.14566e15 −0.689587
\(657\) 1.16994e15 0.372868
\(658\) 6.68105e15 2.11155
\(659\) 1.56688e15 0.491097 0.245548 0.969384i \(-0.421032\pi\)
0.245548 + 0.969384i \(0.421032\pi\)
\(660\) −3.37125e14 −0.104785
\(661\) 1.01475e15 0.312789 0.156394 0.987695i \(-0.450013\pi\)
0.156394 + 0.987695i \(0.450013\pi\)
\(662\) −1.52420e15 −0.465932
\(663\) 3.68662e15 1.11764
\(664\) 7.98056e14 0.239943
\(665\) 1.54172e16 4.59712
\(666\) 4.55079e13 0.0134579
\(667\) 2.14027e15 0.627735
\(668\) −2.42217e14 −0.0704586
\(669\) −3.52693e13 −0.0101754
\(670\) −8.98510e15 −2.57105
\(671\) −1.24586e15 −0.353586
\(672\) −1.49369e15 −0.420465
\(673\) 1.80573e15 0.504161 0.252081 0.967706i \(-0.418885\pi\)
0.252081 + 0.967706i \(0.418885\pi\)
\(674\) 4.21596e15 1.16753
\(675\) 1.99211e15 0.547195
\(676\) −1.89942e15 −0.517505
\(677\) 4.58025e15 1.23780 0.618901 0.785469i \(-0.287578\pi\)
0.618901 + 0.785469i \(0.287578\pi\)
\(678\) −2.12559e15 −0.569792
\(679\) 5.02681e15 1.33662
\(680\) −8.20343e15 −2.16370
\(681\) −1.48762e14 −0.0389210
\(682\) 3.72054e14 0.0965588
\(683\) −2.47746e15 −0.637811 −0.318906 0.947786i \(-0.603315\pi\)
−0.318906 + 0.947786i \(0.603315\pi\)
\(684\) −3.40829e14 −0.0870418
\(685\) −8.12940e15 −2.05949
\(686\) −8.58494e15 −2.15752
\(687\) −2.55042e15 −0.635843
\(688\) 9.09163e14 0.224856
\(689\) 3.62527e15 0.889477
\(690\) −4.68662e15 −1.14075
\(691\) 2.68415e15 0.648153 0.324077 0.946031i \(-0.394946\pi\)
0.324077 + 0.946031i \(0.394946\pi\)
\(692\) 7.20027e14 0.172491
\(693\) 1.16601e15 0.277122
\(694\) 1.91538e15 0.451624
\(695\) −8.32811e15 −1.94818
\(696\) 1.48553e15 0.344771
\(697\) −4.07251e15 −0.937740
\(698\) −5.21599e15 −1.19160
\(699\) 3.68387e15 0.834987
\(700\) −4.68182e15 −1.05287
\(701\) −7.26486e15 −1.62098 −0.810491 0.585751i \(-0.800800\pi\)
−0.810491 + 0.585751i \(0.800800\pi\)
\(702\) 1.46186e15 0.323632
\(703\) −2.64763e14 −0.0581572
\(704\) 2.32656e15 0.507066
\(705\) −6.78899e15 −1.46813
\(706\) −5.27746e15 −1.13240
\(707\) 7.86265e15 1.67403
\(708\) −7.22487e13 −0.0152632
\(709\) 3.38334e15 0.709237 0.354618 0.935011i \(-0.384611\pi\)
0.354618 + 0.935011i \(0.384611\pi\)
\(710\) 7.41918e15 1.54324
\(711\) 2.29178e15 0.473031
\(712\) −5.55526e15 −1.13780
\(713\) −1.31791e15 −0.267851
\(714\) 4.78908e15 0.965855
\(715\) −8.41261e15 −1.68363
\(716\) −7.35739e14 −0.146118
\(717\) −3.97143e15 −0.782694
\(718\) −3.52953e15 −0.690291
\(719\) 6.46634e15 1.25502 0.627509 0.778610i \(-0.284075\pi\)
0.627509 + 0.778610i \(0.284075\pi\)
\(720\) −2.56395e15 −0.493834
\(721\) −4.05787e15 −0.775629
\(722\) −3.07595e15 −0.583478
\(723\) −3.55694e15 −0.669601
\(724\) −1.75905e15 −0.328637
\(725\) 8.52655e15 1.58094
\(726\) 2.21876e15 0.408281
\(727\) −2.69385e15 −0.491965 −0.245983 0.969274i \(-0.579111\pi\)
−0.245983 + 0.969274i \(0.579111\pi\)
\(728\) −2.03546e16 −3.68926
\(729\) 2.05891e14 0.0370370
\(730\) −1.09652e16 −1.95767
\(731\) 1.72562e15 0.305773
\(732\) 5.17018e14 0.0909273
\(733\) −4.65478e15 −0.812508 −0.406254 0.913760i \(-0.633165\pi\)
−0.406254 + 0.913760i \(0.633165\pi\)
\(734\) 3.06987e15 0.531852
\(735\) 1.53059e16 2.63195
\(736\) −2.64172e15 −0.450877
\(737\) 3.95360e15 0.669763
\(738\) −1.61488e15 −0.271537
\(739\) 6.77408e15 1.13059 0.565296 0.824888i \(-0.308762\pi\)
0.565296 + 0.824888i \(0.308762\pi\)
\(740\) 1.08680e14 0.0180042
\(741\) −8.50503e15 −1.39854
\(742\) 4.70939e15 0.768675
\(743\) −2.48045e15 −0.401876 −0.200938 0.979604i \(-0.564399\pi\)
−0.200938 + 0.979604i \(0.564399\pi\)
\(744\) −9.14740e14 −0.147111
\(745\) −4.65982e13 −0.00743891
\(746\) −7.64151e15 −1.21092
\(747\) 4.73424e14 0.0744710
\(748\) 6.09270e14 0.0951373
\(749\) 2.21789e15 0.343787
\(750\) −1.21043e16 −1.86252
\(751\) 3.82204e15 0.583815 0.291908 0.956447i \(-0.405710\pi\)
0.291908 + 0.956447i \(0.405710\pi\)
\(752\) 6.46429e15 0.980218
\(753\) −4.76427e15 −0.717174
\(754\) 6.25699e15 0.935025
\(755\) −1.79087e14 −0.0265677
\(756\) −4.83882e14 −0.0712639
\(757\) −3.65438e14 −0.0534301 −0.0267150 0.999643i \(-0.508505\pi\)
−0.0267150 + 0.999643i \(0.508505\pi\)
\(758\) 8.42772e15 1.22329
\(759\) 2.06219e15 0.297166
\(760\) 1.89253e16 2.70750
\(761\) 3.79818e15 0.539461 0.269730 0.962936i \(-0.413065\pi\)
0.269730 + 0.962936i \(0.413065\pi\)
\(762\) 3.98646e14 0.0562127
\(763\) −8.75682e15 −1.22592
\(764\) −6.83606e14 −0.0950151
\(765\) −4.86645e15 −0.671544
\(766\) −3.97087e15 −0.544035
\(767\) −1.80289e15 −0.245242
\(768\) −2.48958e15 −0.336233
\(769\) 4.53653e15 0.608316 0.304158 0.952622i \(-0.401625\pi\)
0.304158 + 0.952622i \(0.401625\pi\)
\(770\) −1.09284e16 −1.45498
\(771\) −1.23552e15 −0.163324
\(772\) 3.79355e14 0.0497910
\(773\) −1.07123e16 −1.39604 −0.698018 0.716080i \(-0.745934\pi\)
−0.698018 + 0.716080i \(0.745934\pi\)
\(774\) 6.84260e14 0.0885413
\(775\) −5.25037e15 −0.674575
\(776\) 6.17065e15 0.787211
\(777\) −3.75890e14 −0.0476152
\(778\) −1.00520e16 −1.26434
\(779\) 9.39530e15 1.17342
\(780\) 3.49114e15 0.432959
\(781\) −3.26456e15 −0.402017
\(782\) 8.46989e15 1.03572
\(783\) 8.81248e14 0.107006
\(784\) −1.45738e16 −1.75726
\(785\) −2.89805e16 −3.46994
\(786\) 5.00115e15 0.594629
\(787\) 2.44806e15 0.289042 0.144521 0.989502i \(-0.453836\pi\)
0.144521 + 0.989502i \(0.453836\pi\)
\(788\) −2.33023e15 −0.273215
\(789\) −7.91722e15 −0.921827
\(790\) −2.14795e16 −2.48356
\(791\) 1.75571e16 2.01597
\(792\) 1.43134e15 0.163212
\(793\) 1.29016e16 1.46097
\(794\) 8.67530e15 0.975600
\(795\) −4.78547e15 −0.534448
\(796\) 2.73791e15 0.303666
\(797\) 6.35980e15 0.700523 0.350262 0.936652i \(-0.386093\pi\)
0.350262 + 0.936652i \(0.386093\pi\)
\(798\) −1.10484e16 −1.20860
\(799\) 1.22694e16 1.33296
\(800\) −1.05242e16 −1.13552
\(801\) −3.29550e15 −0.353137
\(802\) −1.24528e16 −1.32528
\(803\) 4.82487e15 0.509977
\(804\) −1.64070e15 −0.172234
\(805\) 3.87109e16 4.03605
\(806\) −3.85285e15 −0.398969
\(807\) 2.96682e15 0.305131
\(808\) 9.65178e15 0.985928
\(809\) −1.83448e16 −1.86122 −0.930609 0.366016i \(-0.880722\pi\)
−0.930609 + 0.366016i \(0.880722\pi\)
\(810\) −1.92970e15 −0.194456
\(811\) 1.63616e16 1.63761 0.818806 0.574070i \(-0.194636\pi\)
0.818806 + 0.574070i \(0.194636\pi\)
\(812\) −2.07109e15 −0.205893
\(813\) 1.05777e16 1.04446
\(814\) 1.87676e14 0.0184066
\(815\) 1.50216e16 1.46335
\(816\) 4.63370e15 0.448366
\(817\) −3.98100e15 −0.382623
\(818\) −4.53833e15 −0.433265
\(819\) −1.20748e16 −1.14503
\(820\) −3.85657e15 −0.363266
\(821\) −1.29000e16 −1.20699 −0.603493 0.797368i \(-0.706225\pi\)
−0.603493 + 0.797368i \(0.706225\pi\)
\(822\) 5.82578e15 0.541451
\(823\) 1.23403e16 1.13927 0.569635 0.821898i \(-0.307085\pi\)
0.569635 + 0.821898i \(0.307085\pi\)
\(824\) −4.98123e15 −0.456811
\(825\) 8.21550e15 0.748406
\(826\) −2.34204e15 −0.211935
\(827\) −1.93782e16 −1.74194 −0.870969 0.491339i \(-0.836508\pi\)
−0.870969 + 0.491339i \(0.836508\pi\)
\(828\) −8.55786e14 −0.0764185
\(829\) 7.37677e15 0.654359 0.327180 0.944962i \(-0.393902\pi\)
0.327180 + 0.944962i \(0.393902\pi\)
\(830\) −4.43713e15 −0.390996
\(831\) 2.11189e15 0.184870
\(832\) −2.40930e16 −2.09514
\(833\) −2.76615e16 −2.38962
\(834\) 5.96818e15 0.512187
\(835\) 7.97864e15 0.680226
\(836\) −1.40559e15 −0.119048
\(837\) −5.42644e14 −0.0456588
\(838\) 9.92460e15 0.829604
\(839\) −6.24517e15 −0.518625 −0.259312 0.965793i \(-0.583496\pi\)
−0.259312 + 0.965793i \(0.583496\pi\)
\(840\) 2.68687e16 2.21672
\(841\) −8.42862e15 −0.690842
\(842\) 6.10635e15 0.497239
\(843\) 3.62116e15 0.292952
\(844\) 2.19841e15 0.176696
\(845\) 6.25670e16 4.99613
\(846\) 4.86520e15 0.385979
\(847\) −1.83267e16 −1.44453
\(848\) 4.55660e15 0.356832
\(849\) −3.78135e15 −0.294208
\(850\) 3.37429e16 2.60843
\(851\) −6.64794e14 −0.0510592
\(852\) 1.35476e15 0.103382
\(853\) 1.86753e16 1.41595 0.707974 0.706239i \(-0.249609\pi\)
0.707974 + 0.706239i \(0.249609\pi\)
\(854\) 1.67598e16 1.26256
\(855\) 1.12269e16 0.840324
\(856\) 2.72256e15 0.202475
\(857\) −1.10225e16 −0.814487 −0.407243 0.913320i \(-0.633510\pi\)
−0.407243 + 0.913320i \(0.633510\pi\)
\(858\) 6.02873e15 0.442635
\(859\) −2.69302e16 −1.96462 −0.982308 0.187274i \(-0.940035\pi\)
−0.982308 + 0.187274i \(0.940035\pi\)
\(860\) 1.63412e15 0.118452
\(861\) 1.33387e16 0.960718
\(862\) −1.01192e16 −0.724193
\(863\) −6.34538e15 −0.451230 −0.225615 0.974217i \(-0.572439\pi\)
−0.225615 + 0.974217i \(0.572439\pi\)
\(864\) −1.08772e15 −0.0768583
\(865\) −2.37177e16 −1.66527
\(866\) 9.66458e15 0.674271
\(867\) 4.66828e14 0.0323632
\(868\) 1.27531e15 0.0878532
\(869\) 9.45134e15 0.646971
\(870\) −8.25942e15 −0.561816
\(871\) −4.09419e16 −2.76738
\(872\) −1.07494e16 −0.722012
\(873\) 3.66056e15 0.244326
\(874\) −1.95401e16 −1.29602
\(875\) 9.99798e16 6.58974
\(876\) −2.00227e15 −0.131144
\(877\) −9.50822e15 −0.618873 −0.309437 0.950920i \(-0.600140\pi\)
−0.309437 + 0.950920i \(0.600140\pi\)
\(878\) −6.54195e15 −0.423143
\(879\) 9.07972e15 0.583624
\(880\) −1.05738e16 −0.675424
\(881\) 1.54562e16 0.981151 0.490575 0.871399i \(-0.336787\pi\)
0.490575 + 0.871399i \(0.336787\pi\)
\(882\) −1.09686e16 −0.691952
\(883\) 5.14415e15 0.322500 0.161250 0.986914i \(-0.448447\pi\)
0.161250 + 0.986914i \(0.448447\pi\)
\(884\) −6.30936e15 −0.393095
\(885\) 2.37987e15 0.147355
\(886\) −1.65212e16 −1.01661
\(887\) 3.16092e14 0.0193301 0.00966504 0.999953i \(-0.496923\pi\)
0.00966504 + 0.999953i \(0.496923\pi\)
\(888\) −4.61423e14 −0.0280432
\(889\) −3.29277e15 −0.198885
\(890\) 3.08868e16 1.85408
\(891\) 8.49100e14 0.0506561
\(892\) 6.03607e13 0.00357888
\(893\) −2.83055e16 −1.66797
\(894\) 3.33937e13 0.00195573
\(895\) 2.42353e16 1.41066
\(896\) −1.87090e16 −1.08232
\(897\) −2.13553e16 −1.22785
\(898\) 1.49516e15 0.0854413
\(899\) −2.32260e15 −0.131916
\(900\) −3.40934e15 −0.192458
\(901\) 8.64855e15 0.485240
\(902\) −6.65979e15 −0.371385
\(903\) −5.65191e15 −0.313266
\(904\) 2.15522e16 1.18732
\(905\) 5.79432e16 3.17275
\(906\) 1.28339e14 0.00698479
\(907\) −8.28539e15 −0.448201 −0.224101 0.974566i \(-0.571944\pi\)
−0.224101 + 0.974566i \(0.571944\pi\)
\(908\) 2.54595e14 0.0136892
\(909\) 5.72565e15 0.306001
\(910\) 1.13170e17 6.01178
\(911\) 1.57578e16 0.832041 0.416021 0.909355i \(-0.363424\pi\)
0.416021 + 0.909355i \(0.363424\pi\)
\(912\) −1.06900e16 −0.561054
\(913\) 1.95241e15 0.101855
\(914\) 1.63608e16 0.848400
\(915\) −1.70306e16 −0.877836
\(916\) 4.36485e15 0.223637
\(917\) −4.13089e16 −2.10384
\(918\) 3.48745e15 0.176552
\(919\) −2.20165e16 −1.10793 −0.553966 0.832539i \(-0.686886\pi\)
−0.553966 + 0.832539i \(0.686886\pi\)
\(920\) 4.75195e16 2.37705
\(921\) 1.33374e16 0.663198
\(922\) −1.72878e16 −0.854516
\(923\) 3.38066e16 1.66108
\(924\) −1.99554e15 −0.0974685
\(925\) −2.64845e15 −0.128591
\(926\) 1.58284e16 0.763968
\(927\) −2.95497e15 −0.141780
\(928\) −4.65561e15 −0.222056
\(929\) 2.69393e16 1.27732 0.638660 0.769489i \(-0.279489\pi\)
0.638660 + 0.769489i \(0.279489\pi\)
\(930\) 5.08588e15 0.239723
\(931\) 6.38152e16 2.99020
\(932\) −6.30465e15 −0.293680
\(933\) −5.03693e15 −0.233248
\(934\) −6.42503e15 −0.295779
\(935\) −2.00694e16 −0.918480
\(936\) −1.48224e16 −0.674373
\(937\) 9.92259e15 0.448804 0.224402 0.974497i \(-0.427957\pi\)
0.224402 + 0.974497i \(0.427957\pi\)
\(938\) −5.31854e16 −2.39153
\(939\) −3.59097e15 −0.160528
\(940\) 1.16188e16 0.516368
\(941\) −3.58941e16 −1.58591 −0.792957 0.609277i \(-0.791460\pi\)
−0.792957 + 0.609277i \(0.791460\pi\)
\(942\) 2.07683e16 0.912264
\(943\) 2.35906e16 1.03021
\(944\) −2.26605e15 −0.0983838
\(945\) 1.59391e16 0.688000
\(946\) 2.82190e15 0.121099
\(947\) −2.97714e16 −1.27021 −0.635103 0.772427i \(-0.719042\pi\)
−0.635103 + 0.772427i \(0.719042\pi\)
\(948\) −3.92220e15 −0.166373
\(949\) −4.99645e16 −2.10716
\(950\) −7.78450e16 −3.26400
\(951\) 1.58537e16 0.660905
\(952\) −4.85584e16 −2.01262
\(953\) −2.67158e16 −1.10093 −0.550463 0.834860i \(-0.685549\pi\)
−0.550463 + 0.834860i \(0.685549\pi\)
\(954\) 3.42941e15 0.140509
\(955\) 2.25180e16 0.917300
\(956\) 6.79680e15 0.275287
\(957\) 3.63429e15 0.146354
\(958\) 8.63131e15 0.345594
\(959\) −4.81203e16 −1.91569
\(960\) 3.18035e16 1.25888
\(961\) −2.39783e16 −0.943712
\(962\) −1.94350e15 −0.0760538
\(963\) 1.61508e15 0.0628420
\(964\) 6.08743e15 0.235511
\(965\) −1.24960e16 −0.480696
\(966\) −2.77414e16 −1.06110
\(967\) 1.42091e16 0.540407 0.270204 0.962803i \(-0.412909\pi\)
0.270204 + 0.962803i \(0.412909\pi\)
\(968\) −2.24969e16 −0.850763
\(969\) −2.02898e16 −0.762953
\(970\) −3.43083e16 −1.28279
\(971\) 3.06573e16 1.13980 0.569899 0.821715i \(-0.306982\pi\)
0.569899 + 0.821715i \(0.306982\pi\)
\(972\) −3.52367e14 −0.0130266
\(973\) −4.92965e16 −1.81215
\(974\) −1.20281e16 −0.439664
\(975\) −8.50765e16 −3.09232
\(976\) 1.62161e16 0.586099
\(977\) 1.34379e16 0.482959 0.241480 0.970406i \(-0.422367\pi\)
0.241480 + 0.970406i \(0.422367\pi\)
\(978\) −1.07649e16 −0.384723
\(979\) −1.35907e16 −0.482990
\(980\) −2.61948e16 −0.925703
\(981\) −6.37679e15 −0.224090
\(982\) 2.98172e16 1.04197
\(983\) 2.54085e16 0.882946 0.441473 0.897275i \(-0.354456\pi\)
0.441473 + 0.897275i \(0.354456\pi\)
\(984\) 1.63739e16 0.565821
\(985\) 7.67577e16 2.63768
\(986\) 1.49269e16 0.510088
\(987\) −4.01860e16 −1.36562
\(988\) 1.45557e16 0.491892
\(989\) −9.99588e15 −0.335924
\(990\) −7.95812e15 −0.265960
\(991\) −4.18641e16 −1.39135 −0.695675 0.718356i \(-0.744895\pi\)
−0.695675 + 0.718356i \(0.744895\pi\)
\(992\) 2.86677e15 0.0947499
\(993\) 9.16793e15 0.301336
\(994\) 4.39162e16 1.43549
\(995\) −9.01868e16 −2.93168
\(996\) −8.10229e14 −0.0261928
\(997\) 4.12186e16 1.32516 0.662582 0.748989i \(-0.269460\pi\)
0.662582 + 0.748989i \(0.269460\pi\)
\(998\) 2.48220e16 0.793631
\(999\) −2.73726e14 −0.00870375
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.d.1.8 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.d.1.8 28 1.1 even 1 trivial