Properties

Label 177.14.a.c.1.13
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $0$
Dimension $31$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(0\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-50.5493 q^{2} +729.000 q^{3} -5636.77 q^{4} +37474.1 q^{5} -36850.4 q^{6} +131476. q^{7} +699034. q^{8} +531441. q^{9} +O(q^{10})\) \(q-50.5493 q^{2} +729.000 q^{3} -5636.77 q^{4} +37474.1 q^{5} -36850.4 q^{6} +131476. q^{7} +699034. q^{8} +531441. q^{9} -1.89429e6 q^{10} +4.83579e6 q^{11} -4.10921e6 q^{12} +7.84739e6 q^{13} -6.64603e6 q^{14} +2.73186e7 q^{15} +1.08408e7 q^{16} +1.27632e8 q^{17} -2.68639e7 q^{18} +1.07870e8 q^{19} -2.11233e8 q^{20} +9.58462e7 q^{21} -2.44446e8 q^{22} +4.53568e8 q^{23} +5.09596e8 q^{24} +1.83602e8 q^{25} -3.96680e8 q^{26} +3.87420e8 q^{27} -7.41102e8 q^{28} +2.96893e9 q^{29} -1.38093e9 q^{30} +5.30309e9 q^{31} -6.27448e9 q^{32} +3.52529e9 q^{33} -6.45171e9 q^{34} +4.92695e9 q^{35} -2.99561e9 q^{36} +1.26704e10 q^{37} -5.45275e9 q^{38} +5.72075e9 q^{39} +2.61956e10 q^{40} +4.56042e10 q^{41} -4.84495e9 q^{42} +2.06237e10 q^{43} -2.72582e10 q^{44} +1.99153e10 q^{45} -2.29275e10 q^{46} -3.67643e10 q^{47} +7.90293e9 q^{48} -7.96030e10 q^{49} -9.28094e9 q^{50} +9.30439e10 q^{51} -4.42340e10 q^{52} -1.16034e11 q^{53} -1.95838e10 q^{54} +1.81217e11 q^{55} +9.19064e10 q^{56} +7.86372e10 q^{57} -1.50077e11 q^{58} -4.21805e10 q^{59} -1.53989e11 q^{60} -2.48903e11 q^{61} -2.68067e11 q^{62} +6.98719e10 q^{63} +2.28363e11 q^{64} +2.94074e11 q^{65} -1.78201e11 q^{66} +7.76631e11 q^{67} -7.19434e11 q^{68} +3.30651e11 q^{69} -2.49054e11 q^{70} +6.93339e9 q^{71} +3.71495e11 q^{72} +1.40771e12 q^{73} -6.40479e11 q^{74} +1.33846e11 q^{75} -6.08038e11 q^{76} +6.35791e11 q^{77} -2.89180e11 q^{78} -1.00584e12 q^{79} +4.06248e11 q^{80} +2.82430e11 q^{81} -2.30526e12 q^{82} -3.96993e12 q^{83} -5.40263e11 q^{84} +4.78290e12 q^{85} -1.04251e12 q^{86} +2.16435e12 q^{87} +3.38038e12 q^{88} -3.15383e12 q^{89} -1.00670e12 q^{90} +1.03175e12 q^{91} -2.55666e12 q^{92} +3.86595e12 q^{93} +1.85841e12 q^{94} +4.04232e12 q^{95} -4.57410e12 q^{96} -3.57023e12 q^{97} +4.02387e12 q^{98} +2.56994e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −50.5493 −0.558496 −0.279248 0.960219i \(-0.590085\pi\)
−0.279248 + 0.960219i \(0.590085\pi\)
\(3\) 729.000 0.577350
\(4\) −5636.77 −0.688083
\(5\) 37474.1 1.07257 0.536285 0.844037i \(-0.319827\pi\)
0.536285 + 0.844037i \(0.319827\pi\)
\(6\) −36850.4 −0.322448
\(7\) 131476. 0.422386 0.211193 0.977444i \(-0.432265\pi\)
0.211193 + 0.977444i \(0.432265\pi\)
\(8\) 699034. 0.942787
\(9\) 531441. 0.333333
\(10\) −1.89429e6 −0.599026
\(11\) 4.83579e6 0.823028 0.411514 0.911403i \(-0.365000\pi\)
0.411514 + 0.911403i \(0.365000\pi\)
\(12\) −4.10921e6 −0.397265
\(13\) 7.84739e6 0.450914 0.225457 0.974253i \(-0.427613\pi\)
0.225457 + 0.974253i \(0.427613\pi\)
\(14\) −6.64603e6 −0.235901
\(15\) 2.73186e7 0.619249
\(16\) 1.08408e7 0.161540
\(17\) 1.27632e8 1.28246 0.641228 0.767351i \(-0.278425\pi\)
0.641228 + 0.767351i \(0.278425\pi\)
\(18\) −2.68639e7 −0.186165
\(19\) 1.07870e8 0.526020 0.263010 0.964793i \(-0.415285\pi\)
0.263010 + 0.964793i \(0.415285\pi\)
\(20\) −2.11233e8 −0.738017
\(21\) 9.58462e7 0.243865
\(22\) −2.44446e8 −0.459658
\(23\) 4.53568e8 0.638869 0.319435 0.947608i \(-0.396507\pi\)
0.319435 + 0.947608i \(0.396507\pi\)
\(24\) 5.09596e8 0.544318
\(25\) 1.83602e8 0.150407
\(26\) −3.96680e8 −0.251833
\(27\) 3.87420e8 0.192450
\(28\) −7.41102e8 −0.290637
\(29\) 2.96893e9 0.926858 0.463429 0.886134i \(-0.346619\pi\)
0.463429 + 0.886134i \(0.346619\pi\)
\(30\) −1.38093e9 −0.345848
\(31\) 5.30309e9 1.07319 0.536596 0.843839i \(-0.319710\pi\)
0.536596 + 0.843839i \(0.319710\pi\)
\(32\) −6.27448e9 −1.03301
\(33\) 3.52529e9 0.475176
\(34\) −6.45171e9 −0.716246
\(35\) 4.92695e9 0.453039
\(36\) −2.99561e9 −0.229361
\(37\) 1.26704e10 0.811856 0.405928 0.913905i \(-0.366948\pi\)
0.405928 + 0.913905i \(0.366948\pi\)
\(38\) −5.45275e9 −0.293780
\(39\) 5.72075e9 0.260335
\(40\) 2.61956e10 1.01120
\(41\) 4.56042e10 1.49937 0.749687 0.661792i \(-0.230204\pi\)
0.749687 + 0.661792i \(0.230204\pi\)
\(42\) −4.84495e9 −0.136198
\(43\) 2.06237e10 0.497533 0.248766 0.968564i \(-0.419975\pi\)
0.248766 + 0.968564i \(0.419975\pi\)
\(44\) −2.72582e10 −0.566312
\(45\) 1.99153e10 0.357523
\(46\) −2.29275e10 −0.356806
\(47\) −3.67643e10 −0.497496 −0.248748 0.968568i \(-0.580019\pi\)
−0.248748 + 0.968568i \(0.580019\pi\)
\(48\) 7.90293e9 0.0932653
\(49\) −7.96030e10 −0.821590
\(50\) −9.28094e9 −0.0840015
\(51\) 9.30439e10 0.740426
\(52\) −4.42340e10 −0.310266
\(53\) −1.16034e11 −0.719105 −0.359552 0.933125i \(-0.617071\pi\)
−0.359552 + 0.933125i \(0.617071\pi\)
\(54\) −1.95838e10 −0.107483
\(55\) 1.81217e11 0.882756
\(56\) 9.19064e10 0.398220
\(57\) 7.86372e10 0.303698
\(58\) −1.50077e11 −0.517646
\(59\) −4.21805e10 −0.130189
\(60\) −1.53989e11 −0.426094
\(61\) −2.48903e11 −0.618565 −0.309283 0.950970i \(-0.600089\pi\)
−0.309283 + 0.950970i \(0.600089\pi\)
\(62\) −2.68067e11 −0.599373
\(63\) 6.98719e10 0.140795
\(64\) 2.28363e11 0.415389
\(65\) 2.94074e11 0.483637
\(66\) −1.78201e11 −0.265384
\(67\) 7.76631e11 1.04889 0.524443 0.851445i \(-0.324274\pi\)
0.524443 + 0.851445i \(0.324274\pi\)
\(68\) −7.19434e11 −0.882435
\(69\) 3.30651e11 0.368851
\(70\) −2.49054e11 −0.253020
\(71\) 6.93339e9 0.00642342 0.00321171 0.999995i \(-0.498978\pi\)
0.00321171 + 0.999995i \(0.498978\pi\)
\(72\) 3.71495e11 0.314262
\(73\) 1.40771e12 1.08871 0.544357 0.838853i \(-0.316774\pi\)
0.544357 + 0.838853i \(0.316774\pi\)
\(74\) −6.40479e11 −0.453418
\(75\) 1.33846e11 0.0868373
\(76\) −6.08038e11 −0.361945
\(77\) 6.35791e11 0.347636
\(78\) −2.89180e11 −0.145396
\(79\) −1.00584e12 −0.465535 −0.232767 0.972532i \(-0.574778\pi\)
−0.232767 + 0.972532i \(0.574778\pi\)
\(80\) 4.06248e11 0.173263
\(81\) 2.82430e11 0.111111
\(82\) −2.30526e12 −0.837394
\(83\) −3.96993e12 −1.33283 −0.666416 0.745580i \(-0.732172\pi\)
−0.666416 + 0.745580i \(0.732172\pi\)
\(84\) −5.40263e11 −0.167799
\(85\) 4.78290e12 1.37552
\(86\) −1.04251e12 −0.277870
\(87\) 2.16435e12 0.535122
\(88\) 3.38038e12 0.775940
\(89\) −3.15383e12 −0.672671 −0.336335 0.941742i \(-0.609188\pi\)
−0.336335 + 0.941742i \(0.609188\pi\)
\(90\) −1.00670e12 −0.199675
\(91\) 1.03175e12 0.190460
\(92\) −2.55666e12 −0.439595
\(93\) 3.86595e12 0.619608
\(94\) 1.85841e12 0.277850
\(95\) 4.04232e12 0.564193
\(96\) −4.57410e12 −0.596406
\(97\) −3.57023e12 −0.435191 −0.217595 0.976039i \(-0.569821\pi\)
−0.217595 + 0.976039i \(0.569821\pi\)
\(98\) 4.02387e12 0.458854
\(99\) 2.56994e12 0.274343
\(100\) −1.03492e12 −0.103492
\(101\) 5.34316e12 0.500852 0.250426 0.968136i \(-0.419429\pi\)
0.250426 + 0.968136i \(0.419429\pi\)
\(102\) −4.70330e12 −0.413525
\(103\) −9.32875e11 −0.0769807 −0.0384903 0.999259i \(-0.512255\pi\)
−0.0384903 + 0.999259i \(0.512255\pi\)
\(104\) 5.48559e12 0.425116
\(105\) 3.59175e12 0.261562
\(106\) 5.86543e12 0.401617
\(107\) −2.96981e13 −1.91309 −0.956543 0.291591i \(-0.905815\pi\)
−0.956543 + 0.291591i \(0.905815\pi\)
\(108\) −2.18380e12 −0.132422
\(109\) −1.10515e13 −0.631175 −0.315587 0.948897i \(-0.602202\pi\)
−0.315587 + 0.948897i \(0.602202\pi\)
\(110\) −9.16037e12 −0.493015
\(111\) 9.23672e12 0.468725
\(112\) 1.42531e12 0.0682324
\(113\) −2.10986e13 −0.953332 −0.476666 0.879085i \(-0.658155\pi\)
−0.476666 + 0.879085i \(0.658155\pi\)
\(114\) −3.97505e12 −0.169614
\(115\) 1.69970e13 0.685232
\(116\) −1.67352e13 −0.637755
\(117\) 4.17042e12 0.150305
\(118\) 2.13219e12 0.0727099
\(119\) 1.67806e13 0.541692
\(120\) 1.90966e13 0.583819
\(121\) −1.11379e13 −0.322624
\(122\) 1.25818e13 0.345466
\(123\) 3.32455e13 0.865664
\(124\) −2.98923e13 −0.738445
\(125\) −3.88644e13 −0.911248
\(126\) −3.53197e12 −0.0786337
\(127\) 2.42799e13 0.513480 0.256740 0.966481i \(-0.417352\pi\)
0.256740 + 0.966481i \(0.417352\pi\)
\(128\) 3.98570e13 0.801013
\(129\) 1.50347e13 0.287251
\(130\) −1.48652e13 −0.270109
\(131\) 3.33833e13 0.577119 0.288560 0.957462i \(-0.406824\pi\)
0.288560 + 0.957462i \(0.406824\pi\)
\(132\) −1.98713e13 −0.326960
\(133\) 1.41823e13 0.222184
\(134\) −3.92581e13 −0.585798
\(135\) 1.45182e13 0.206416
\(136\) 8.92193e13 1.20908
\(137\) 3.87450e13 0.500647 0.250324 0.968162i \(-0.419463\pi\)
0.250324 + 0.968162i \(0.419463\pi\)
\(138\) −1.67142e13 −0.206002
\(139\) 1.49591e12 0.0175918 0.00879588 0.999961i \(-0.497200\pi\)
0.00879588 + 0.999961i \(0.497200\pi\)
\(140\) −2.77721e13 −0.311728
\(141\) −2.68012e13 −0.287230
\(142\) −3.50477e11 −0.00358745
\(143\) 3.79483e13 0.371115
\(144\) 5.76124e12 0.0538467
\(145\) 1.11258e14 0.994120
\(146\) −7.11586e13 −0.608042
\(147\) −5.80306e13 −0.474345
\(148\) −7.14202e13 −0.558624
\(149\) −2.11317e14 −1.58206 −0.791031 0.611776i \(-0.790456\pi\)
−0.791031 + 0.611776i \(0.790456\pi\)
\(150\) −6.76581e12 −0.0484983
\(151\) −1.29104e14 −0.886318 −0.443159 0.896443i \(-0.646142\pi\)
−0.443159 + 0.896443i \(0.646142\pi\)
\(152\) 7.54048e13 0.495924
\(153\) 6.78290e13 0.427485
\(154\) −3.21388e13 −0.194153
\(155\) 1.98728e14 1.15107
\(156\) −3.22466e13 −0.179132
\(157\) 1.12893e14 0.601618 0.300809 0.953684i \(-0.402743\pi\)
0.300809 + 0.953684i \(0.402743\pi\)
\(158\) 5.08444e13 0.259999
\(159\) −8.45888e13 −0.415175
\(160\) −2.35130e14 −1.10797
\(161\) 5.96335e13 0.269850
\(162\) −1.42766e13 −0.0620551
\(163\) −1.72378e14 −0.719883 −0.359942 0.932975i \(-0.617203\pi\)
−0.359942 + 0.932975i \(0.617203\pi\)
\(164\) −2.57061e14 −1.03169
\(165\) 1.32107e14 0.509659
\(166\) 2.00677e14 0.744380
\(167\) −1.24963e14 −0.445784 −0.222892 0.974843i \(-0.571550\pi\)
−0.222892 + 0.974843i \(0.571550\pi\)
\(168\) 6.69998e13 0.229913
\(169\) −2.41294e14 −0.796677
\(170\) −2.41772e14 −0.768224
\(171\) 5.73265e13 0.175340
\(172\) −1.16251e14 −0.342344
\(173\) −5.39672e14 −1.53049 −0.765245 0.643739i \(-0.777382\pi\)
−0.765245 + 0.643739i \(0.777382\pi\)
\(174\) −1.09406e14 −0.298863
\(175\) 2.41393e13 0.0635298
\(176\) 5.24237e13 0.132952
\(177\) −3.07496e13 −0.0751646
\(178\) 1.59424e14 0.375684
\(179\) −3.85664e14 −0.876324 −0.438162 0.898896i \(-0.644370\pi\)
−0.438162 + 0.898896i \(0.644370\pi\)
\(180\) −1.12258e14 −0.246006
\(181\) 3.33508e14 0.705011 0.352505 0.935810i \(-0.385330\pi\)
0.352505 + 0.935810i \(0.385330\pi\)
\(182\) −5.21540e13 −0.106371
\(183\) −1.81450e14 −0.357129
\(184\) 3.17060e14 0.602317
\(185\) 4.74811e14 0.870773
\(186\) −1.95421e14 −0.346048
\(187\) 6.17202e14 1.05550
\(188\) 2.07232e14 0.342319
\(189\) 5.09366e13 0.0812883
\(190\) −2.04337e14 −0.315099
\(191\) −7.47095e14 −1.11342 −0.556710 0.830707i \(-0.687936\pi\)
−0.556710 + 0.830707i \(0.687936\pi\)
\(192\) 1.66476e14 0.239825
\(193\) 8.67669e14 1.20846 0.604229 0.796811i \(-0.293481\pi\)
0.604229 + 0.796811i \(0.293481\pi\)
\(194\) 1.80472e14 0.243052
\(195\) 2.14380e14 0.279228
\(196\) 4.48704e14 0.565322
\(197\) 1.35605e14 0.165289 0.0826447 0.996579i \(-0.473663\pi\)
0.0826447 + 0.996579i \(0.473663\pi\)
\(198\) −1.29908e14 −0.153219
\(199\) 6.88092e14 0.785419 0.392709 0.919663i \(-0.371538\pi\)
0.392709 + 0.919663i \(0.371538\pi\)
\(200\) 1.28344e14 0.141801
\(201\) 5.66164e14 0.605575
\(202\) −2.70093e14 −0.279724
\(203\) 3.90344e14 0.391492
\(204\) −5.24467e14 −0.509474
\(205\) 1.70898e15 1.60818
\(206\) 4.71562e13 0.0429934
\(207\) 2.41045e14 0.212956
\(208\) 8.50718e13 0.0728407
\(209\) 5.21636e14 0.432929
\(210\) −1.81560e14 −0.146081
\(211\) 1.75853e15 1.37187 0.685936 0.727662i \(-0.259393\pi\)
0.685936 + 0.727662i \(0.259393\pi\)
\(212\) 6.54058e14 0.494804
\(213\) 5.05444e12 0.00370856
\(214\) 1.50122e15 1.06845
\(215\) 7.72854e14 0.533639
\(216\) 2.70820e14 0.181439
\(217\) 6.97230e14 0.453302
\(218\) 5.58646e14 0.352508
\(219\) 1.02622e15 0.628570
\(220\) −1.02148e15 −0.607409
\(221\) 1.00158e15 0.578277
\(222\) −4.66909e14 −0.261781
\(223\) 4.86298e14 0.264802 0.132401 0.991196i \(-0.457731\pi\)
0.132401 + 0.991196i \(0.457731\pi\)
\(224\) −8.24945e14 −0.436328
\(225\) 9.75736e13 0.0501356
\(226\) 1.06652e15 0.532432
\(227\) 3.06890e15 1.48873 0.744363 0.667775i \(-0.232753\pi\)
0.744363 + 0.667775i \(0.232753\pi\)
\(228\) −4.43260e14 −0.208969
\(229\) 3.73527e15 1.71156 0.855779 0.517341i \(-0.173078\pi\)
0.855779 + 0.517341i \(0.173078\pi\)
\(230\) −8.59188e14 −0.382699
\(231\) 4.63492e14 0.200708
\(232\) 2.07538e15 0.873830
\(233\) 2.87430e15 1.17684 0.588421 0.808555i \(-0.299750\pi\)
0.588421 + 0.808555i \(0.299750\pi\)
\(234\) −2.10812e14 −0.0839445
\(235\) −1.37771e15 −0.533600
\(236\) 2.37762e14 0.0895807
\(237\) −7.33256e14 −0.268777
\(238\) −8.48247e14 −0.302533
\(239\) 4.07439e15 1.41409 0.707043 0.707170i \(-0.250029\pi\)
0.707043 + 0.707170i \(0.250029\pi\)
\(240\) 2.96155e14 0.100034
\(241\) −3.84825e15 −1.26518 −0.632591 0.774486i \(-0.718008\pi\)
−0.632591 + 0.774486i \(0.718008\pi\)
\(242\) 5.63011e14 0.180184
\(243\) 2.05891e14 0.0641500
\(244\) 1.40301e15 0.425624
\(245\) −2.98305e15 −0.881213
\(246\) −1.68053e15 −0.483470
\(247\) 8.46498e14 0.237190
\(248\) 3.70704e15 1.01179
\(249\) −2.89408e15 −0.769510
\(250\) 1.96457e15 0.508928
\(251\) 1.83859e15 0.464094 0.232047 0.972705i \(-0.425458\pi\)
0.232047 + 0.972705i \(0.425458\pi\)
\(252\) −3.93852e14 −0.0968789
\(253\) 2.19336e15 0.525807
\(254\) −1.22733e15 −0.286776
\(255\) 3.48673e15 0.794159
\(256\) −3.88549e15 −0.862752
\(257\) 5.98665e15 1.29604 0.648020 0.761623i \(-0.275597\pi\)
0.648020 + 0.761623i \(0.275597\pi\)
\(258\) −7.59992e14 −0.160428
\(259\) 1.66586e15 0.342917
\(260\) −1.65763e15 −0.332782
\(261\) 1.57781e15 0.308953
\(262\) −1.68750e15 −0.322319
\(263\) 8.06577e15 1.50291 0.751456 0.659783i \(-0.229352\pi\)
0.751456 + 0.659783i \(0.229352\pi\)
\(264\) 2.46430e15 0.447989
\(265\) −4.34827e15 −0.771290
\(266\) −7.16906e14 −0.124089
\(267\) −2.29914e15 −0.388367
\(268\) −4.37769e15 −0.721720
\(269\) −4.03220e15 −0.648862 −0.324431 0.945909i \(-0.605173\pi\)
−0.324431 + 0.945909i \(0.605173\pi\)
\(270\) −7.33885e14 −0.115283
\(271\) −3.67388e15 −0.563410 −0.281705 0.959501i \(-0.590900\pi\)
−0.281705 + 0.959501i \(0.590900\pi\)
\(272\) 1.38363e15 0.207168
\(273\) 7.52142e14 0.109962
\(274\) −1.95853e15 −0.279609
\(275\) 8.87860e14 0.123789
\(276\) −1.86381e15 −0.253800
\(277\) 1.16773e16 1.55319 0.776596 0.629999i \(-0.216945\pi\)
0.776596 + 0.629999i \(0.216945\pi\)
\(278\) −7.56172e13 −0.00982493
\(279\) 2.81828e15 0.357731
\(280\) 3.44411e15 0.427119
\(281\) 2.58808e15 0.313608 0.156804 0.987630i \(-0.449881\pi\)
0.156804 + 0.987630i \(0.449881\pi\)
\(282\) 1.35478e15 0.160416
\(283\) −1.06904e16 −1.23704 −0.618520 0.785769i \(-0.712267\pi\)
−0.618520 + 0.785769i \(0.712267\pi\)
\(284\) −3.90819e13 −0.00441984
\(285\) 2.94685e15 0.325737
\(286\) −1.91826e15 −0.207266
\(287\) 5.99587e15 0.633316
\(288\) −3.33452e15 −0.344335
\(289\) 6.38541e15 0.644693
\(290\) −5.62401e15 −0.555212
\(291\) −2.60269e15 −0.251257
\(292\) −7.93493e15 −0.749126
\(293\) −1.26671e16 −1.16960 −0.584802 0.811176i \(-0.698828\pi\)
−0.584802 + 0.811176i \(0.698828\pi\)
\(294\) 2.93340e15 0.264920
\(295\) −1.58068e15 −0.139637
\(296\) 8.85704e15 0.765407
\(297\) 1.87348e15 0.158392
\(298\) 1.06819e16 0.883575
\(299\) 3.55933e15 0.288075
\(300\) −7.54458e14 −0.0597513
\(301\) 2.71153e15 0.210151
\(302\) 6.52611e15 0.495005
\(303\) 3.89516e15 0.289167
\(304\) 1.16939e15 0.0849734
\(305\) −9.32739e15 −0.663455
\(306\) −3.42871e15 −0.238749
\(307\) −2.07449e16 −1.41420 −0.707102 0.707112i \(-0.749998\pi\)
−0.707102 + 0.707112i \(0.749998\pi\)
\(308\) −3.58381e15 −0.239202
\(309\) −6.80066e14 −0.0444448
\(310\) −1.00456e16 −0.642870
\(311\) −2.62817e15 −0.164707 −0.0823533 0.996603i \(-0.526244\pi\)
−0.0823533 + 0.996603i \(0.526244\pi\)
\(312\) 3.99900e15 0.245441
\(313\) 1.92988e15 0.116009 0.0580046 0.998316i \(-0.481526\pi\)
0.0580046 + 0.998316i \(0.481526\pi\)
\(314\) −5.70668e15 −0.336001
\(315\) 2.61838e15 0.151013
\(316\) 5.66968e15 0.320326
\(317\) 2.88022e16 1.59419 0.797095 0.603854i \(-0.206369\pi\)
0.797095 + 0.603854i \(0.206369\pi\)
\(318\) 4.27590e15 0.231874
\(319\) 1.43571e16 0.762830
\(320\) 8.55768e15 0.445534
\(321\) −2.16499e16 −1.10452
\(322\) −3.01443e15 −0.150710
\(323\) 1.37677e16 0.674597
\(324\) −1.59199e15 −0.0764536
\(325\) 1.44080e15 0.0678204
\(326\) 8.71357e15 0.402052
\(327\) −8.05656e15 −0.364409
\(328\) 3.18789e16 1.41359
\(329\) −4.83363e15 −0.210136
\(330\) −6.67791e15 −0.284642
\(331\) 2.39044e16 0.999069 0.499534 0.866294i \(-0.333504\pi\)
0.499534 + 0.866294i \(0.333504\pi\)
\(332\) 2.23776e16 0.917098
\(333\) 6.73357e15 0.270619
\(334\) 6.31678e15 0.248968
\(335\) 2.91035e16 1.12500
\(336\) 1.03905e15 0.0393940
\(337\) −3.42727e15 −0.127454 −0.0637271 0.997967i \(-0.520299\pi\)
−0.0637271 + 0.997967i \(0.520299\pi\)
\(338\) 1.21972e16 0.444941
\(339\) −1.53809e16 −0.550406
\(340\) −2.69601e16 −0.946474
\(341\) 2.56446e16 0.883268
\(342\) −2.89781e15 −0.0979266
\(343\) −2.32045e16 −0.769415
\(344\) 1.44167e16 0.469067
\(345\) 1.23908e16 0.395619
\(346\) 2.72800e16 0.854772
\(347\) −2.56153e16 −0.787696 −0.393848 0.919176i \(-0.628856\pi\)
−0.393848 + 0.919176i \(0.628856\pi\)
\(348\) −1.22000e16 −0.368208
\(349\) −2.32184e16 −0.687808 −0.343904 0.939005i \(-0.611749\pi\)
−0.343904 + 0.939005i \(0.611749\pi\)
\(350\) −1.22022e15 −0.0354811
\(351\) 3.04024e15 0.0867784
\(352\) −3.03421e16 −0.850194
\(353\) 2.19899e16 0.604906 0.302453 0.953164i \(-0.402195\pi\)
0.302453 + 0.953164i \(0.402195\pi\)
\(354\) 1.55437e15 0.0419791
\(355\) 2.59822e14 0.00688956
\(356\) 1.77774e16 0.462853
\(357\) 1.22331e16 0.312746
\(358\) 1.94950e16 0.489423
\(359\) 5.31112e16 1.30940 0.654700 0.755889i \(-0.272795\pi\)
0.654700 + 0.755889i \(0.272795\pi\)
\(360\) 1.39214e16 0.337068
\(361\) −3.04171e16 −0.723303
\(362\) −1.68586e16 −0.393745
\(363\) −8.11950e15 −0.186267
\(364\) −5.81571e15 −0.131052
\(365\) 5.27525e16 1.16772
\(366\) 9.17217e15 0.199455
\(367\) −2.82440e16 −0.603389 −0.301694 0.953405i \(-0.597552\pi\)
−0.301694 + 0.953405i \(0.597552\pi\)
\(368\) 4.91704e15 0.103203
\(369\) 2.42360e16 0.499792
\(370\) −2.40014e16 −0.486323
\(371\) −1.52557e16 −0.303740
\(372\) −2.17915e16 −0.426341
\(373\) −7.71493e16 −1.48329 −0.741643 0.670795i \(-0.765953\pi\)
−0.741643 + 0.670795i \(0.765953\pi\)
\(374\) −3.11991e16 −0.589491
\(375\) −2.83321e16 −0.526110
\(376\) −2.56995e16 −0.469033
\(377\) 2.32984e16 0.417933
\(378\) −2.57481e15 −0.0453992
\(379\) −2.09459e16 −0.363031 −0.181515 0.983388i \(-0.558100\pi\)
−0.181515 + 0.983388i \(0.558100\pi\)
\(380\) −2.27857e16 −0.388211
\(381\) 1.77001e16 0.296458
\(382\) 3.77651e16 0.621840
\(383\) −8.59456e16 −1.39133 −0.695667 0.718364i \(-0.744891\pi\)
−0.695667 + 0.718364i \(0.744891\pi\)
\(384\) 2.90557e16 0.462465
\(385\) 2.38257e16 0.372864
\(386\) −4.38600e16 −0.674918
\(387\) 1.09603e16 0.165844
\(388\) 2.01246e16 0.299447
\(389\) −6.66476e16 −0.975241 −0.487621 0.873056i \(-0.662135\pi\)
−0.487621 + 0.873056i \(0.662135\pi\)
\(390\) −1.08367e16 −0.155947
\(391\) 5.78899e16 0.819321
\(392\) −5.56452e16 −0.774584
\(393\) 2.43364e16 0.333200
\(394\) −6.85473e15 −0.0923134
\(395\) −3.76928e16 −0.499319
\(396\) −1.44861e16 −0.188771
\(397\) −3.52260e16 −0.451570 −0.225785 0.974177i \(-0.572495\pi\)
−0.225785 + 0.974177i \(0.572495\pi\)
\(398\) −3.47825e16 −0.438653
\(399\) 1.03389e16 0.128278
\(400\) 1.99039e15 0.0242967
\(401\) −7.75262e16 −0.931129 −0.465564 0.885014i \(-0.654149\pi\)
−0.465564 + 0.885014i \(0.654149\pi\)
\(402\) −2.86192e16 −0.338211
\(403\) 4.16154e16 0.483917
\(404\) −3.01182e16 −0.344628
\(405\) 1.05838e16 0.119174
\(406\) −1.97316e16 −0.218647
\(407\) 6.12714e16 0.668181
\(408\) 6.50409e16 0.698064
\(409\) 1.31106e17 1.38491 0.692455 0.721461i \(-0.256529\pi\)
0.692455 + 0.721461i \(0.256529\pi\)
\(410\) −8.63875e16 −0.898164
\(411\) 2.82451e16 0.289049
\(412\) 5.25841e15 0.0529691
\(413\) −5.54574e15 −0.0549900
\(414\) −1.21846e16 −0.118935
\(415\) −1.48769e17 −1.42956
\(416\) −4.92383e16 −0.465797
\(417\) 1.09052e15 0.0101566
\(418\) −2.63683e16 −0.241789
\(419\) 1.72833e16 0.156040 0.0780198 0.996952i \(-0.475140\pi\)
0.0780198 + 0.996952i \(0.475140\pi\)
\(420\) −2.02459e16 −0.179976
\(421\) 1.22446e17 1.07179 0.535896 0.844284i \(-0.319974\pi\)
0.535896 + 0.844284i \(0.319974\pi\)
\(422\) −8.88924e16 −0.766185
\(423\) −1.95380e16 −0.165832
\(424\) −8.11118e16 −0.677963
\(425\) 2.34335e16 0.192890
\(426\) −2.55498e14 −0.00207122
\(427\) −3.27248e16 −0.261274
\(428\) 1.67402e17 1.31636
\(429\) 2.76643e16 0.214263
\(430\) −3.90672e16 −0.298035
\(431\) 7.09734e16 0.533327 0.266663 0.963790i \(-0.414079\pi\)
0.266663 + 0.963790i \(0.414079\pi\)
\(432\) 4.19994e15 0.0310884
\(433\) −1.40125e17 −1.02175 −0.510875 0.859655i \(-0.670679\pi\)
−0.510875 + 0.859655i \(0.670679\pi\)
\(434\) −3.52444e16 −0.253167
\(435\) 8.11070e16 0.573956
\(436\) 6.22949e16 0.434300
\(437\) 4.89264e16 0.336058
\(438\) −5.18746e16 −0.351053
\(439\) −2.30870e16 −0.153939 −0.0769694 0.997033i \(-0.524524\pi\)
−0.0769694 + 0.997033i \(0.524524\pi\)
\(440\) 1.26677e17 0.832250
\(441\) −4.23043e16 −0.273863
\(442\) −5.06291e16 −0.322965
\(443\) 2.20068e17 1.38335 0.691676 0.722208i \(-0.256873\pi\)
0.691676 + 0.722208i \(0.256873\pi\)
\(444\) −5.20653e16 −0.322522
\(445\) −1.18187e17 −0.721487
\(446\) −2.45820e16 −0.147891
\(447\) −1.54050e17 −0.913404
\(448\) 3.00243e16 0.175455
\(449\) 6.32643e16 0.364382 0.182191 0.983263i \(-0.441681\pi\)
0.182191 + 0.983263i \(0.441681\pi\)
\(450\) −4.93227e15 −0.0280005
\(451\) 2.20532e17 1.23403
\(452\) 1.18928e17 0.655971
\(453\) −9.41169e16 −0.511716
\(454\) −1.55131e17 −0.831447
\(455\) 3.86637e16 0.204282
\(456\) 5.49701e16 0.286322
\(457\) −1.15038e17 −0.590728 −0.295364 0.955385i \(-0.595441\pi\)
−0.295364 + 0.955385i \(0.595441\pi\)
\(458\) −1.88815e17 −0.955898
\(459\) 4.94473e16 0.246809
\(460\) −9.58085e16 −0.471496
\(461\) −2.24004e17 −1.08693 −0.543464 0.839433i \(-0.682887\pi\)
−0.543464 + 0.839433i \(0.682887\pi\)
\(462\) −2.34292e16 −0.112094
\(463\) −1.51465e17 −0.714556 −0.357278 0.933998i \(-0.616295\pi\)
−0.357278 + 0.933998i \(0.616295\pi\)
\(464\) 3.21855e16 0.149725
\(465\) 1.44873e17 0.664573
\(466\) −1.45294e17 −0.657261
\(467\) −1.19765e17 −0.534281 −0.267141 0.963658i \(-0.586079\pi\)
−0.267141 + 0.963658i \(0.586079\pi\)
\(468\) −2.35077e16 −0.103422
\(469\) 1.02109e17 0.443035
\(470\) 6.96420e16 0.298013
\(471\) 8.22993e16 0.347344
\(472\) −2.94856e16 −0.122740
\(473\) 9.97319e16 0.409484
\(474\) 3.70656e16 0.150111
\(475\) 1.98051e16 0.0791169
\(476\) −9.45885e16 −0.372729
\(477\) −6.16652e16 −0.239702
\(478\) −2.05957e17 −0.789761
\(479\) −1.49450e17 −0.565348 −0.282674 0.959216i \(-0.591222\pi\)
−0.282674 + 0.959216i \(0.591222\pi\)
\(480\) −1.71410e17 −0.639688
\(481\) 9.94296e16 0.366077
\(482\) 1.94526e17 0.706598
\(483\) 4.34728e16 0.155798
\(484\) 6.27816e16 0.221992
\(485\) −1.33791e17 −0.466772
\(486\) −1.04076e16 −0.0358275
\(487\) −2.25150e17 −0.764774 −0.382387 0.924002i \(-0.624898\pi\)
−0.382387 + 0.924002i \(0.624898\pi\)
\(488\) −1.73991e17 −0.583175
\(489\) −1.25663e17 −0.415625
\(490\) 1.50791e17 0.492153
\(491\) −3.25842e17 −1.04949 −0.524744 0.851260i \(-0.675839\pi\)
−0.524744 + 0.851260i \(0.675839\pi\)
\(492\) −1.87397e17 −0.595649
\(493\) 3.78931e17 1.18865
\(494\) −4.27898e16 −0.132469
\(495\) 9.63059e16 0.294252
\(496\) 5.74896e16 0.173364
\(497\) 9.11575e14 0.00271316
\(498\) 1.46294e17 0.429768
\(499\) −3.24801e17 −0.941811 −0.470906 0.882184i \(-0.656073\pi\)
−0.470906 + 0.882184i \(0.656073\pi\)
\(500\) 2.19070e17 0.627014
\(501\) −9.10980e16 −0.257373
\(502\) −9.29395e16 −0.259195
\(503\) 1.20825e17 0.332633 0.166316 0.986072i \(-0.446813\pi\)
0.166316 + 0.986072i \(0.446813\pi\)
\(504\) 4.88428e16 0.132740
\(505\) 2.00230e17 0.537199
\(506\) −1.10873e17 −0.293661
\(507\) −1.75903e17 −0.459962
\(508\) −1.36860e17 −0.353316
\(509\) 4.57191e17 1.16528 0.582642 0.812729i \(-0.302019\pi\)
0.582642 + 0.812729i \(0.302019\pi\)
\(510\) −1.76252e17 −0.443534
\(511\) 1.85080e17 0.459858
\(512\) −1.30100e17 −0.319170
\(513\) 4.17910e16 0.101233
\(514\) −3.02621e17 −0.723833
\(515\) −3.49586e16 −0.0825672
\(516\) −8.47471e16 −0.197652
\(517\) −1.77784e17 −0.409454
\(518\) −8.42078e16 −0.191518
\(519\) −3.93421e17 −0.883629
\(520\) 2.05567e17 0.455966
\(521\) 5.22701e17 1.14501 0.572503 0.819902i \(-0.305972\pi\)
0.572503 + 0.819902i \(0.305972\pi\)
\(522\) −7.97572e16 −0.172549
\(523\) −2.81260e17 −0.600961 −0.300481 0.953788i \(-0.597147\pi\)
−0.300481 + 0.953788i \(0.597147\pi\)
\(524\) −1.88174e17 −0.397106
\(525\) 1.75975e16 0.0366789
\(526\) −4.07719e17 −0.839370
\(527\) 6.76845e17 1.37632
\(528\) 3.82169e16 0.0767600
\(529\) −2.98312e17 −0.591846
\(530\) 2.19802e17 0.430762
\(531\) −2.24165e16 −0.0433963
\(532\) −7.99426e16 −0.152881
\(533\) 3.57874e17 0.676089
\(534\) 1.16220e17 0.216901
\(535\) −1.11291e18 −2.05192
\(536\) 5.42892e17 0.988876
\(537\) −2.81149e17 −0.505946
\(538\) 2.03825e17 0.362386
\(539\) −3.84943e17 −0.676192
\(540\) −8.18359e16 −0.142031
\(541\) −2.86138e17 −0.490674 −0.245337 0.969438i \(-0.578899\pi\)
−0.245337 + 0.969438i \(0.578899\pi\)
\(542\) 1.85712e17 0.314662
\(543\) 2.43127e17 0.407038
\(544\) −8.00826e17 −1.32478
\(545\) −4.14145e17 −0.676979
\(546\) −3.80202e16 −0.0614133
\(547\) 1.02844e18 1.64157 0.820786 0.571236i \(-0.193536\pi\)
0.820786 + 0.571236i \(0.193536\pi\)
\(548\) −2.18397e17 −0.344487
\(549\) −1.32277e17 −0.206188
\(550\) −4.48807e16 −0.0691356
\(551\) 3.20258e17 0.487546
\(552\) 2.31137e17 0.347748
\(553\) −1.32244e17 −0.196636
\(554\) −5.90280e17 −0.867451
\(555\) 3.46137e17 0.502741
\(556\) −8.43211e15 −0.0121046
\(557\) 1.07069e17 0.151916 0.0759580 0.997111i \(-0.475799\pi\)
0.0759580 + 0.997111i \(0.475799\pi\)
\(558\) −1.42462e17 −0.199791
\(559\) 1.61842e17 0.224344
\(560\) 5.34120e16 0.0731840
\(561\) 4.49941e17 0.609392
\(562\) −1.30826e17 −0.175149
\(563\) 2.92192e17 0.386691 0.193346 0.981131i \(-0.438066\pi\)
0.193346 + 0.981131i \(0.438066\pi\)
\(564\) 1.51072e17 0.197638
\(565\) −7.90651e17 −1.02252
\(566\) 5.40393e17 0.690881
\(567\) 3.71328e16 0.0469318
\(568\) 4.84667e15 0.00605591
\(569\) −1.23283e18 −1.52290 −0.761452 0.648222i \(-0.775513\pi\)
−0.761452 + 0.648222i \(0.775513\pi\)
\(570\) −1.48961e17 −0.181923
\(571\) −3.24861e17 −0.392250 −0.196125 0.980579i \(-0.562836\pi\)
−0.196125 + 0.980579i \(0.562836\pi\)
\(572\) −2.13906e17 −0.255358
\(573\) −5.44632e17 −0.642833
\(574\) −3.03087e17 −0.353704
\(575\) 8.32760e16 0.0960902
\(576\) 1.21361e17 0.138463
\(577\) 9.43612e17 1.06451 0.532256 0.846583i \(-0.321344\pi\)
0.532256 + 0.846583i \(0.321344\pi\)
\(578\) −3.22778e17 −0.360058
\(579\) 6.32530e17 0.697703
\(580\) −6.27136e17 −0.684037
\(581\) −5.21951e17 −0.562970
\(582\) 1.31564e17 0.140326
\(583\) −5.61116e17 −0.591844
\(584\) 9.84036e17 1.02643
\(585\) 1.56283e17 0.161212
\(586\) 6.40314e17 0.653219
\(587\) −2.58102e17 −0.260401 −0.130201 0.991488i \(-0.541562\pi\)
−0.130201 + 0.991488i \(0.541562\pi\)
\(588\) 3.27105e17 0.326389
\(589\) 5.72043e17 0.564520
\(590\) 7.99020e16 0.0779865
\(591\) 9.88560e16 0.0954298
\(592\) 1.37357e17 0.131147
\(593\) 3.35694e16 0.0317021 0.0158511 0.999874i \(-0.494954\pi\)
0.0158511 + 0.999874i \(0.494954\pi\)
\(594\) −9.47032e16 −0.0884612
\(595\) 6.28837e17 0.581003
\(596\) 1.19115e18 1.08859
\(597\) 5.01619e17 0.453462
\(598\) −1.79921e17 −0.160889
\(599\) 1.41440e18 1.25112 0.625559 0.780177i \(-0.284871\pi\)
0.625559 + 0.780177i \(0.284871\pi\)
\(600\) 9.35628e16 0.0818691
\(601\) 1.01261e18 0.876512 0.438256 0.898850i \(-0.355596\pi\)
0.438256 + 0.898850i \(0.355596\pi\)
\(602\) −1.37066e17 −0.117368
\(603\) 4.12733e17 0.349629
\(604\) 7.27730e17 0.609860
\(605\) −4.17381e17 −0.346037
\(606\) −1.96898e17 −0.161499
\(607\) 8.06416e17 0.654384 0.327192 0.944958i \(-0.393898\pi\)
0.327192 + 0.944958i \(0.393898\pi\)
\(608\) −6.76828e17 −0.543382
\(609\) 2.84561e17 0.226028
\(610\) 4.71493e17 0.370537
\(611\) −2.88504e17 −0.224328
\(612\) −3.82337e17 −0.294145
\(613\) −8.03049e17 −0.611293 −0.305646 0.952145i \(-0.598873\pi\)
−0.305646 + 0.952145i \(0.598873\pi\)
\(614\) 1.04864e18 0.789827
\(615\) 1.24584e18 0.928486
\(616\) 4.44440e17 0.327747
\(617\) 1.06814e18 0.779424 0.389712 0.920937i \(-0.372575\pi\)
0.389712 + 0.920937i \(0.372575\pi\)
\(618\) 3.43768e16 0.0248222
\(619\) 1.16855e18 0.834945 0.417473 0.908689i \(-0.362916\pi\)
0.417473 + 0.908689i \(0.362916\pi\)
\(620\) −1.12019e18 −0.792034
\(621\) 1.75722e17 0.122950
\(622\) 1.32852e17 0.0919879
\(623\) −4.14653e17 −0.284127
\(624\) 6.20174e16 0.0420546
\(625\) −1.68053e18 −1.12778
\(626\) −9.75540e16 −0.0647906
\(627\) 3.80273e17 0.249952
\(628\) −6.36355e17 −0.413963
\(629\) 1.61715e18 1.04117
\(630\) −1.32357e17 −0.0843401
\(631\) 1.21646e17 0.0767198 0.0383599 0.999264i \(-0.487787\pi\)
0.0383599 + 0.999264i \(0.487787\pi\)
\(632\) −7.03115e17 −0.438900
\(633\) 1.28197e18 0.792051
\(634\) −1.45593e18 −0.890348
\(635\) 9.09867e17 0.550743
\(636\) 4.76808e17 0.285675
\(637\) −6.24676e17 −0.370466
\(638\) −7.25742e17 −0.426038
\(639\) 3.68469e15 0.00214114
\(640\) 1.49360e18 0.859143
\(641\) −2.14933e18 −1.22384 −0.611921 0.790919i \(-0.709603\pi\)
−0.611921 + 0.790919i \(0.709603\pi\)
\(642\) 1.09439e18 0.616870
\(643\) −1.31472e18 −0.733602 −0.366801 0.930299i \(-0.619547\pi\)
−0.366801 + 0.930299i \(0.619547\pi\)
\(644\) −3.36140e17 −0.185679
\(645\) 5.63410e17 0.308097
\(646\) −6.95946e17 −0.376760
\(647\) 1.16316e18 0.623393 0.311696 0.950182i \(-0.399103\pi\)
0.311696 + 0.950182i \(0.399103\pi\)
\(648\) 1.97428e17 0.104754
\(649\) −2.03976e17 −0.107149
\(650\) −7.28312e16 −0.0378774
\(651\) 5.08280e17 0.261714
\(652\) 9.71655e17 0.495339
\(653\) −7.99999e16 −0.0403788 −0.0201894 0.999796i \(-0.506427\pi\)
−0.0201894 + 0.999796i \(0.506427\pi\)
\(654\) 4.07253e17 0.203521
\(655\) 1.25101e18 0.619001
\(656\) 4.94386e17 0.242209
\(657\) 7.48114e17 0.362905
\(658\) 2.44336e17 0.117360
\(659\) −4.14903e18 −1.97329 −0.986646 0.162880i \(-0.947922\pi\)
−0.986646 + 0.162880i \(0.947922\pi\)
\(660\) −7.44657e17 −0.350688
\(661\) −1.23438e18 −0.575624 −0.287812 0.957687i \(-0.592928\pi\)
−0.287812 + 0.957687i \(0.592928\pi\)
\(662\) −1.20835e18 −0.557976
\(663\) 7.30152e17 0.333868
\(664\) −2.77512e18 −1.25658
\(665\) 5.31470e17 0.238308
\(666\) −3.40377e17 −0.151139
\(667\) 1.34661e18 0.592141
\(668\) 7.04388e17 0.306736
\(669\) 3.54511e17 0.152883
\(670\) −1.47116e18 −0.628310
\(671\) −1.20364e18 −0.509097
\(672\) −6.01385e17 −0.251914
\(673\) −1.37752e18 −0.571478 −0.285739 0.958307i \(-0.592239\pi\)
−0.285739 + 0.958307i \(0.592239\pi\)
\(674\) 1.73246e17 0.0711826
\(675\) 7.11311e16 0.0289458
\(676\) 1.36012e18 0.548179
\(677\) −2.42610e18 −0.968462 −0.484231 0.874940i \(-0.660901\pi\)
−0.484231 + 0.874940i \(0.660901\pi\)
\(678\) 7.77493e17 0.307400
\(679\) −4.69400e17 −0.183819
\(680\) 3.34341e18 1.29683
\(681\) 2.23723e18 0.859517
\(682\) −1.29632e18 −0.493301
\(683\) 4.97289e18 1.87445 0.937226 0.348723i \(-0.113384\pi\)
0.937226 + 0.348723i \(0.113384\pi\)
\(684\) −3.23137e17 −0.120648
\(685\) 1.45193e18 0.536979
\(686\) 1.17297e18 0.429715
\(687\) 2.72301e18 0.988169
\(688\) 2.23577e17 0.0803716
\(689\) −9.10564e17 −0.324254
\(690\) −6.26348e17 −0.220951
\(691\) 1.17508e18 0.410638 0.205319 0.978695i \(-0.434177\pi\)
0.205319 + 0.978695i \(0.434177\pi\)
\(692\) 3.04201e18 1.05310
\(693\) 3.37886e17 0.115879
\(694\) 1.29484e18 0.439925
\(695\) 5.60578e16 0.0188684
\(696\) 1.51296e18 0.504506
\(697\) 5.82057e18 1.92288
\(698\) 1.17367e18 0.384138
\(699\) 2.09536e18 0.679450
\(700\) −1.36068e17 −0.0437137
\(701\) −1.07940e18 −0.343571 −0.171785 0.985134i \(-0.554954\pi\)
−0.171785 + 0.985134i \(0.554954\pi\)
\(702\) −1.53682e17 −0.0484654
\(703\) 1.36676e18 0.427052
\(704\) 1.10431e18 0.341877
\(705\) −1.00435e18 −0.308074
\(706\) −1.11157e18 −0.337837
\(707\) 7.02499e17 0.211553
\(708\) 1.73329e17 0.0517195
\(709\) 1.40723e18 0.416069 0.208035 0.978121i \(-0.433293\pi\)
0.208035 + 0.978121i \(0.433293\pi\)
\(710\) −1.31338e16 −0.00384779
\(711\) −5.34544e17 −0.155178
\(712\) −2.20463e18 −0.634185
\(713\) 2.40531e18 0.685629
\(714\) −6.18372e17 −0.174667
\(715\) 1.42208e18 0.398047
\(716\) 2.17390e18 0.602983
\(717\) 2.97023e18 0.816423
\(718\) −2.68473e18 −0.731294
\(719\) 5.79677e18 1.56476 0.782381 0.622801i \(-0.214005\pi\)
0.782381 + 0.622801i \(0.214005\pi\)
\(720\) 2.15897e17 0.0577544
\(721\) −1.22651e17 −0.0325156
\(722\) 1.53756e18 0.403962
\(723\) −2.80538e18 −0.730453
\(724\) −1.87991e18 −0.485106
\(725\) 5.45102e17 0.139406
\(726\) 4.10435e17 0.104029
\(727\) −2.50807e18 −0.630037 −0.315019 0.949085i \(-0.602011\pi\)
−0.315019 + 0.949085i \(0.602011\pi\)
\(728\) 7.21225e17 0.179563
\(729\) 1.50095e17 0.0370370
\(730\) −2.66660e18 −0.652168
\(731\) 2.63225e18 0.638064
\(732\) 1.02279e18 0.245734
\(733\) −2.09009e18 −0.497726 −0.248863 0.968539i \(-0.580057\pi\)
−0.248863 + 0.968539i \(0.580057\pi\)
\(734\) 1.42772e18 0.336990
\(735\) −2.17464e18 −0.508768
\(736\) −2.84591e18 −0.659956
\(737\) 3.75562e18 0.863263
\(738\) −1.22511e18 −0.279131
\(739\) −6.12341e18 −1.38294 −0.691471 0.722404i \(-0.743037\pi\)
−0.691471 + 0.722404i \(0.743037\pi\)
\(740\) −2.67640e18 −0.599164
\(741\) 6.17097e17 0.136941
\(742\) 7.71165e17 0.169638
\(743\) −2.69022e18 −0.586626 −0.293313 0.956016i \(-0.594758\pi\)
−0.293313 + 0.956016i \(0.594758\pi\)
\(744\) 2.70243e18 0.584158
\(745\) −7.91891e18 −1.69687
\(746\) 3.89984e18 0.828408
\(747\) −2.10978e18 −0.444277
\(748\) −3.47903e18 −0.726269
\(749\) −3.90460e18 −0.808062
\(750\) 1.43217e18 0.293830
\(751\) 3.80510e18 0.773938 0.386969 0.922093i \(-0.373522\pi\)
0.386969 + 0.922093i \(0.373522\pi\)
\(752\) −3.98553e17 −0.0803657
\(753\) 1.34033e18 0.267945
\(754\) −1.17772e18 −0.233414
\(755\) −4.83805e18 −0.950639
\(756\) −2.87118e17 −0.0559331
\(757\) −2.06600e18 −0.399032 −0.199516 0.979895i \(-0.563937\pi\)
−0.199516 + 0.979895i \(0.563937\pi\)
\(758\) 1.05880e18 0.202751
\(759\) 1.59896e18 0.303575
\(760\) 2.82572e18 0.531914
\(761\) −3.14582e18 −0.587130 −0.293565 0.955939i \(-0.594842\pi\)
−0.293565 + 0.955939i \(0.594842\pi\)
\(762\) −8.94725e17 −0.165570
\(763\) −1.45301e18 −0.266600
\(764\) 4.21120e18 0.766125
\(765\) 2.54183e18 0.458508
\(766\) 4.34448e18 0.777054
\(767\) −3.31007e17 −0.0587040
\(768\) −2.83252e18 −0.498110
\(769\) 1.51535e18 0.264236 0.132118 0.991234i \(-0.457822\pi\)
0.132118 + 0.991234i \(0.457822\pi\)
\(770\) −1.20437e18 −0.208243
\(771\) 4.36427e18 0.748269
\(772\) −4.89085e18 −0.831519
\(773\) −6.82449e18 −1.15055 −0.575273 0.817962i \(-0.695104\pi\)
−0.575273 + 0.817962i \(0.695104\pi\)
\(774\) −5.54034e17 −0.0926233
\(775\) 9.73657e17 0.161415
\(776\) −2.49571e18 −0.410292
\(777\) 1.21441e18 0.197983
\(778\) 3.36899e18 0.544668
\(779\) 4.91933e18 0.788701
\(780\) −1.20841e18 −0.192132
\(781\) 3.35284e16 0.00528665
\(782\) −2.92629e18 −0.457587
\(783\) 1.15022e18 0.178374
\(784\) −8.62959e17 −0.132720
\(785\) 4.23057e18 0.645278
\(786\) −1.23019e18 −0.186091
\(787\) −1.16429e18 −0.174673 −0.0873367 0.996179i \(-0.527836\pi\)
−0.0873367 + 0.996179i \(0.527836\pi\)
\(788\) −7.64374e17 −0.113733
\(789\) 5.87995e18 0.867706
\(790\) 1.90535e18 0.278867
\(791\) −2.77397e18 −0.402674
\(792\) 1.79647e18 0.258647
\(793\) −1.95324e18 −0.278920
\(794\) 1.78065e18 0.252200
\(795\) −3.16989e18 −0.445305
\(796\) −3.87862e18 −0.540433
\(797\) 2.02210e17 0.0279462 0.0139731 0.999902i \(-0.495552\pi\)
0.0139731 + 0.999902i \(0.495552\pi\)
\(798\) −5.22625e17 −0.0716426
\(799\) −4.69231e18 −0.638017
\(800\) −1.15201e18 −0.155371
\(801\) −1.67607e18 −0.224224
\(802\) 3.91889e18 0.520031
\(803\) 6.80738e18 0.896043
\(804\) −3.19134e18 −0.416685
\(805\) 2.23471e18 0.289433
\(806\) −2.10363e18 −0.270266
\(807\) −2.93947e18 −0.374620
\(808\) 3.73505e18 0.472197
\(809\) 5.98015e18 0.749975 0.374987 0.927030i \(-0.377647\pi\)
0.374987 + 0.927030i \(0.377647\pi\)
\(810\) −5.35002e17 −0.0665584
\(811\) 1.53057e18 0.188894 0.0944471 0.995530i \(-0.469892\pi\)
0.0944471 + 0.995530i \(0.469892\pi\)
\(812\) −2.20028e18 −0.269379
\(813\) −2.67826e18 −0.325285
\(814\) −3.09722e18 −0.373176
\(815\) −6.45970e18 −0.772125
\(816\) 1.00867e18 0.119609
\(817\) 2.22468e18 0.261712
\(818\) −6.62732e18 −0.773467
\(819\) 5.48312e17 0.0634866
\(820\) −9.63311e18 −1.10656
\(821\) −2.74455e18 −0.312782 −0.156391 0.987695i \(-0.549986\pi\)
−0.156391 + 0.987695i \(0.549986\pi\)
\(822\) −1.42777e18 −0.161433
\(823\) −8.61227e18 −0.966092 −0.483046 0.875595i \(-0.660470\pi\)
−0.483046 + 0.875595i \(0.660470\pi\)
\(824\) −6.52112e17 −0.0725764
\(825\) 6.47250e17 0.0714696
\(826\) 2.80333e17 0.0307117
\(827\) −6.85627e18 −0.745250 −0.372625 0.927982i \(-0.621542\pi\)
−0.372625 + 0.927982i \(0.621542\pi\)
\(828\) −1.35872e18 −0.146532
\(829\) −1.12805e19 −1.20705 −0.603525 0.797344i \(-0.706238\pi\)
−0.603525 + 0.797344i \(0.706238\pi\)
\(830\) 7.52018e18 0.798400
\(831\) 8.51277e18 0.896735
\(832\) 1.79205e18 0.187305
\(833\) −1.01599e19 −1.05365
\(834\) −5.51249e16 −0.00567242
\(835\) −4.68287e18 −0.478134
\(836\) −2.94034e18 −0.297891
\(837\) 2.05452e18 0.206536
\(838\) −8.73656e17 −0.0871474
\(839\) 1.13544e19 1.12386 0.561930 0.827185i \(-0.310059\pi\)
0.561930 + 0.827185i \(0.310059\pi\)
\(840\) 2.51075e18 0.246597
\(841\) −1.44607e18 −0.140934
\(842\) −6.18954e18 −0.598591
\(843\) 1.88671e18 0.181061
\(844\) −9.91243e18 −0.943961
\(845\) −9.04225e18 −0.854492
\(846\) 9.87633e17 0.0926165
\(847\) −1.46436e18 −0.136272
\(848\) −1.25790e18 −0.116164
\(849\) −7.79333e18 −0.714205
\(850\) −1.18455e18 −0.107728
\(851\) 5.74689e18 0.518670
\(852\) −2.84907e16 −0.00255180
\(853\) 1.96407e19 1.74577 0.872887 0.487922i \(-0.162245\pi\)
0.872887 + 0.487922i \(0.162245\pi\)
\(854\) 1.65421e18 0.145920
\(855\) 2.14826e18 0.188064
\(856\) −2.07600e19 −1.80363
\(857\) 1.13444e19 0.978149 0.489074 0.872242i \(-0.337335\pi\)
0.489074 + 0.872242i \(0.337335\pi\)
\(858\) −1.39841e18 −0.119665
\(859\) 2.24083e18 0.190306 0.0951532 0.995463i \(-0.469666\pi\)
0.0951532 + 0.995463i \(0.469666\pi\)
\(860\) −4.35640e18 −0.367188
\(861\) 4.37099e18 0.365645
\(862\) −3.58765e18 −0.297861
\(863\) −9.16519e17 −0.0755216 −0.0377608 0.999287i \(-0.512023\pi\)
−0.0377608 + 0.999287i \(0.512023\pi\)
\(864\) −2.43086e18 −0.198802
\(865\) −2.02237e19 −1.64156
\(866\) 7.08322e18 0.570643
\(867\) 4.65496e18 0.372213
\(868\) −3.93013e18 −0.311909
\(869\) −4.86402e18 −0.383148
\(870\) −4.09990e18 −0.320552
\(871\) 6.09453e18 0.472957
\(872\) −7.72539e18 −0.595063
\(873\) −1.89736e18 −0.145064
\(874\) −2.47319e18 −0.187687
\(875\) −5.10974e18 −0.384899
\(876\) −5.78457e18 −0.432508
\(877\) 6.09511e17 0.0452360 0.0226180 0.999744i \(-0.492800\pi\)
0.0226180 + 0.999744i \(0.492800\pi\)
\(878\) 1.16703e18 0.0859742
\(879\) −9.23434e18 −0.675271
\(880\) 1.96453e18 0.142601
\(881\) 1.39303e19 1.00373 0.501864 0.864946i \(-0.332648\pi\)
0.501864 + 0.864946i \(0.332648\pi\)
\(882\) 2.13845e18 0.152951
\(883\) 1.02586e18 0.0728353 0.0364176 0.999337i \(-0.488405\pi\)
0.0364176 + 0.999337i \(0.488405\pi\)
\(884\) −5.64568e18 −0.397902
\(885\) −1.15231e18 −0.0806193
\(886\) −1.11243e19 −0.772596
\(887\) −1.27239e19 −0.877240 −0.438620 0.898673i \(-0.644533\pi\)
−0.438620 + 0.898673i \(0.644533\pi\)
\(888\) 6.45678e18 0.441908
\(889\) 3.19223e18 0.216887
\(890\) 5.97425e18 0.402947
\(891\) 1.36577e18 0.0914476
\(892\) −2.74115e18 −0.182206
\(893\) −3.96576e18 −0.261693
\(894\) 7.78712e18 0.510132
\(895\) −1.44524e19 −0.939919
\(896\) 5.24025e18 0.338337
\(897\) 2.59475e18 0.166320
\(898\) −3.19796e18 −0.203506
\(899\) 1.57445e19 0.994697
\(900\) −5.50000e17 −0.0344974
\(901\) −1.48097e19 −0.922220
\(902\) −1.11478e19 −0.689199
\(903\) 1.97670e18 0.121331
\(904\) −1.47487e19 −0.898789
\(905\) 1.24979e19 0.756173
\(906\) 4.75754e18 0.285791
\(907\) 5.55451e18 0.331282 0.165641 0.986186i \(-0.447031\pi\)
0.165641 + 0.986186i \(0.447031\pi\)
\(908\) −1.72987e19 −1.02437
\(909\) 2.83958e18 0.166951
\(910\) −1.95442e18 −0.114090
\(911\) −1.15177e19 −0.667567 −0.333784 0.942650i \(-0.608326\pi\)
−0.333784 + 0.942650i \(0.608326\pi\)
\(912\) 8.52489e17 0.0490594
\(913\) −1.91977e19 −1.09696
\(914\) 5.81510e18 0.329919
\(915\) −6.79967e18 −0.383046
\(916\) −2.10549e19 −1.17769
\(917\) 4.38911e18 0.243767
\(918\) −2.49953e18 −0.137842
\(919\) 2.72242e19 1.49075 0.745374 0.666647i \(-0.232271\pi\)
0.745374 + 0.666647i \(0.232271\pi\)
\(920\) 1.18815e19 0.646028
\(921\) −1.51230e19 −0.816491
\(922\) 1.13233e19 0.607044
\(923\) 5.44090e16 0.00289641
\(924\) −2.61260e18 −0.138104
\(925\) 2.32631e18 0.122109
\(926\) 7.65645e18 0.399076
\(927\) −4.95768e17 −0.0256602
\(928\) −1.86285e19 −0.957450
\(929\) −1.58452e19 −0.808714 −0.404357 0.914601i \(-0.632505\pi\)
−0.404357 + 0.914601i \(0.632505\pi\)
\(930\) −7.32321e18 −0.371161
\(931\) −8.58677e18 −0.432172
\(932\) −1.62018e19 −0.809764
\(933\) −1.91594e18 −0.0950934
\(934\) 6.05403e18 0.298394
\(935\) 2.31291e19 1.13210
\(936\) 2.91527e18 0.141705
\(937\) −2.19948e19 −1.06172 −0.530862 0.847458i \(-0.678132\pi\)
−0.530862 + 0.847458i \(0.678132\pi\)
\(938\) −5.16151e18 −0.247433
\(939\) 1.40688e18 0.0669779
\(940\) 7.76582e18 0.367161
\(941\) 3.77332e19 1.77170 0.885852 0.463968i \(-0.153575\pi\)
0.885852 + 0.463968i \(0.153575\pi\)
\(942\) −4.16017e18 −0.193990
\(943\) 2.06846e19 0.957904
\(944\) −4.57270e17 −0.0210307
\(945\) 1.90880e18 0.0871874
\(946\) −5.04137e18 −0.228695
\(947\) 6.17356e17 0.0278138 0.0139069 0.999903i \(-0.495573\pi\)
0.0139069 + 0.999903i \(0.495573\pi\)
\(948\) 4.13320e18 0.184941
\(949\) 1.10468e19 0.490916
\(950\) −1.00113e18 −0.0441864
\(951\) 2.09968e19 0.920406
\(952\) 1.17302e19 0.510700
\(953\) 7.22414e18 0.312379 0.156190 0.987727i \(-0.450079\pi\)
0.156190 + 0.987727i \(0.450079\pi\)
\(954\) 3.11713e18 0.133872
\(955\) −2.79967e19 −1.19422
\(956\) −2.29664e19 −0.973008
\(957\) 1.04663e19 0.440420
\(958\) 7.55460e18 0.315745
\(959\) 5.09405e18 0.211467
\(960\) 6.23855e18 0.257229
\(961\) 3.70516e18 0.151742
\(962\) −5.02609e18 −0.204452
\(963\) −1.57828e19 −0.637695
\(964\) 2.16917e19 0.870549
\(965\) 3.25151e19 1.29616
\(966\) −2.19752e18 −0.0870124
\(967\) 4.16904e17 0.0163970 0.00819849 0.999966i \(-0.497390\pi\)
0.00819849 + 0.999966i \(0.497390\pi\)
\(968\) −7.78575e18 −0.304166
\(969\) 1.00366e19 0.389479
\(970\) 6.76303e18 0.260690
\(971\) 1.84255e19 0.705496 0.352748 0.935718i \(-0.385247\pi\)
0.352748 + 0.935718i \(0.385247\pi\)
\(972\) −1.16056e18 −0.0441405
\(973\) 1.96677e17 0.00743052
\(974\) 1.13811e19 0.427123
\(975\) 1.05034e18 0.0391562
\(976\) −2.69830e18 −0.0999232
\(977\) 1.95997e19 0.720997 0.360499 0.932760i \(-0.382607\pi\)
0.360499 + 0.932760i \(0.382607\pi\)
\(978\) 6.35220e18 0.232125
\(979\) −1.52512e19 −0.553627
\(980\) 1.68148e19 0.606347
\(981\) −5.87323e18 −0.210392
\(982\) 1.64711e19 0.586135
\(983\) 4.19418e19 1.48269 0.741343 0.671126i \(-0.234189\pi\)
0.741343 + 0.671126i \(0.234189\pi\)
\(984\) 2.32397e19 0.816137
\(985\) 5.08167e18 0.177284
\(986\) −1.91547e19 −0.663858
\(987\) −3.52371e18 −0.121322
\(988\) −4.77151e18 −0.163206
\(989\) 9.35426e18 0.317858
\(990\) −4.86819e18 −0.164338
\(991\) −1.17649e19 −0.394558 −0.197279 0.980347i \(-0.563211\pi\)
−0.197279 + 0.980347i \(0.563211\pi\)
\(992\) −3.32741e19 −1.10861
\(993\) 1.74263e19 0.576813
\(994\) −4.60795e16 −0.00151529
\(995\) 2.57856e19 0.842417
\(996\) 1.63133e19 0.529487
\(997\) −3.12611e19 −1.00806 −0.504028 0.863687i \(-0.668149\pi\)
−0.504028 + 0.863687i \(0.668149\pi\)
\(998\) 1.64184e19 0.525997
\(999\) 4.90877e18 0.156242
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 177.14.a.c.1.13 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.13 31 1.1 even 1 trivial