Properties

Label 177.12.a.c.1.6
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $27$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-64.1897 q^{2} -243.000 q^{3} +2072.32 q^{4} -6307.39 q^{5} +15598.1 q^{6} +84626.9 q^{7} -1560.87 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-64.1897 q^{2} -243.000 q^{3} +2072.32 q^{4} -6307.39 q^{5} +15598.1 q^{6} +84626.9 q^{7} -1560.87 q^{8} +59049.0 q^{9} +404869. q^{10} -902806. q^{11} -503573. q^{12} -1.37458e6 q^{13} -5.43217e6 q^{14} +1.53270e6 q^{15} -4.14391e6 q^{16} +6.10500e6 q^{17} -3.79034e6 q^{18} +1.53727e7 q^{19} -1.30709e7 q^{20} -2.05643e7 q^{21} +5.79509e7 q^{22} +5.45940e7 q^{23} +379292. q^{24} -9.04497e6 q^{25} +8.82338e7 q^{26} -1.43489e7 q^{27} +1.75374e8 q^{28} +3.20407e7 q^{29} -9.83833e7 q^{30} +2.01437e8 q^{31} +2.69193e8 q^{32} +2.19382e8 q^{33} -3.91878e8 q^{34} -5.33774e8 q^{35} +1.22368e8 q^{36} +6.20122e8 q^{37} -9.86768e8 q^{38} +3.34023e8 q^{39} +9.84503e6 q^{40} -1.18981e9 q^{41} +1.32002e9 q^{42} -2.91907e8 q^{43} -1.87090e9 q^{44} -3.72445e8 q^{45} -3.50437e9 q^{46} +6.14694e7 q^{47} +1.00697e9 q^{48} +5.18438e9 q^{49} +5.80594e8 q^{50} -1.48352e9 q^{51} -2.84856e9 q^{52} -3.65243e9 q^{53} +9.21052e8 q^{54} +5.69435e9 q^{55} -1.32092e8 q^{56} -3.73556e9 q^{57} -2.05668e9 q^{58} -7.14924e8 q^{59} +3.17623e9 q^{60} +1.13062e10 q^{61} -1.29302e10 q^{62} +4.99713e9 q^{63} -8.79269e9 q^{64} +8.67000e9 q^{65} -1.40821e10 q^{66} -8.11606e9 q^{67} +1.26515e10 q^{68} -1.32663e10 q^{69} +3.42628e10 q^{70} -1.75527e10 q^{71} -9.21680e7 q^{72} -1.78971e10 q^{73} -3.98055e10 q^{74} +2.19793e9 q^{75} +3.18571e10 q^{76} -7.64017e10 q^{77} -2.14408e10 q^{78} +2.32461e10 q^{79} +2.61373e10 q^{80} +3.48678e9 q^{81} +7.63737e10 q^{82} +8.67597e9 q^{83} -4.26158e10 q^{84} -3.85066e10 q^{85} +1.87374e10 q^{86} -7.78588e9 q^{87} +1.40917e9 q^{88} +7.88055e10 q^{89} +2.39071e10 q^{90} -1.16326e11 q^{91} +1.13136e11 q^{92} -4.89493e10 q^{93} -3.94570e9 q^{94} -9.69615e10 q^{95} -6.54139e10 q^{96} -6.50540e10 q^{97} -3.32784e11 q^{98} -5.33098e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −64.1897 −1.41841 −0.709203 0.705005i \(-0.750945\pi\)
−0.709203 + 0.705005i \(0.750945\pi\)
\(3\) −243.000 −0.577350
\(4\) 2072.32 1.01187
\(5\) −6307.39 −0.902640 −0.451320 0.892362i \(-0.649047\pi\)
−0.451320 + 0.892362i \(0.649047\pi\)
\(6\) 15598.1 0.818917
\(7\) 84626.9 1.90313 0.951566 0.307444i \(-0.0994737\pi\)
0.951566 + 0.307444i \(0.0994737\pi\)
\(8\) −1560.87 −0.0168412
\(9\) 59049.0 0.333333
\(10\) 404869. 1.28031
\(11\) −902806. −1.69019 −0.845094 0.534618i \(-0.820455\pi\)
−0.845094 + 0.534618i \(0.820455\pi\)
\(12\) −503573. −0.584205
\(13\) −1.37458e6 −1.02679 −0.513394 0.858153i \(-0.671612\pi\)
−0.513394 + 0.858153i \(0.671612\pi\)
\(14\) −5.43217e6 −2.69941
\(15\) 1.53270e6 0.521139
\(16\) −4.14391e6 −0.987986
\(17\) 6.10500e6 1.04284 0.521419 0.853301i \(-0.325403\pi\)
0.521419 + 0.853301i \(0.325403\pi\)
\(18\) −3.79034e6 −0.472802
\(19\) 1.53727e7 1.42431 0.712155 0.702022i \(-0.247719\pi\)
0.712155 + 0.702022i \(0.247719\pi\)
\(20\) −1.30709e7 −0.913357
\(21\) −2.05643e7 −1.09877
\(22\) 5.79509e7 2.39737
\(23\) 5.45940e7 1.76865 0.884324 0.466873i \(-0.154619\pi\)
0.884324 + 0.466873i \(0.154619\pi\)
\(24\) 379292. 0.00972326
\(25\) −9.04497e6 −0.185241
\(26\) 8.82338e7 1.45640
\(27\) −1.43489e7 −0.192450
\(28\) 1.75374e8 1.92573
\(29\) 3.20407e7 0.290076 0.145038 0.989426i \(-0.453669\pi\)
0.145038 + 0.989426i \(0.453669\pi\)
\(30\) −9.83833e7 −0.739187
\(31\) 2.01437e8 1.26372 0.631860 0.775083i \(-0.282292\pi\)
0.631860 + 0.775083i \(0.282292\pi\)
\(32\) 2.69193e8 1.41821
\(33\) 2.19382e8 0.975830
\(34\) −3.91878e8 −1.47917
\(35\) −5.33774e8 −1.71784
\(36\) 1.22368e8 0.337291
\(37\) 6.20122e8 1.47017 0.735085 0.677975i \(-0.237142\pi\)
0.735085 + 0.677975i \(0.237142\pi\)
\(38\) −9.86768e8 −2.02025
\(39\) 3.34023e8 0.592817
\(40\) 9.84503e6 0.0152015
\(41\) −1.18981e9 −1.60386 −0.801932 0.597415i \(-0.796194\pi\)
−0.801932 + 0.597415i \(0.796194\pi\)
\(42\) 1.32002e9 1.55851
\(43\) −2.91907e8 −0.302808 −0.151404 0.988472i \(-0.548380\pi\)
−0.151404 + 0.988472i \(0.548380\pi\)
\(44\) −1.87090e9 −1.71026
\(45\) −3.72445e8 −0.300880
\(46\) −3.50437e9 −2.50866
\(47\) 6.14694e7 0.0390950 0.0195475 0.999809i \(-0.493777\pi\)
0.0195475 + 0.999809i \(0.493777\pi\)
\(48\) 1.00697e9 0.570414
\(49\) 5.18438e9 2.62191
\(50\) 5.80594e8 0.262747
\(51\) −1.48352e9 −0.602083
\(52\) −2.84856e9 −1.03898
\(53\) −3.65243e9 −1.19968 −0.599839 0.800120i \(-0.704769\pi\)
−0.599839 + 0.800120i \(0.704769\pi\)
\(54\) 9.21052e8 0.272972
\(55\) 5.69435e9 1.52563
\(56\) −1.32092e8 −0.0320510
\(57\) −3.73556e9 −0.822326
\(58\) −2.05668e9 −0.411446
\(59\) −7.14924e8 −0.130189
\(60\) 3.17623e9 0.527327
\(61\) 1.13062e10 1.71397 0.856987 0.515338i \(-0.172333\pi\)
0.856987 + 0.515338i \(0.172333\pi\)
\(62\) −1.29302e10 −1.79247
\(63\) 4.99713e9 0.634377
\(64\) −8.79269e9 −1.02360
\(65\) 8.67000e9 0.926821
\(66\) −1.40821e10 −1.38412
\(67\) −8.11606e9 −0.734402 −0.367201 0.930142i \(-0.619684\pi\)
−0.367201 + 0.930142i \(0.619684\pi\)
\(68\) 1.26515e10 1.05522
\(69\) −1.32663e10 −1.02113
\(70\) 3.42628e10 2.43660
\(71\) −1.75527e10 −1.15458 −0.577290 0.816539i \(-0.695890\pi\)
−0.577290 + 0.816539i \(0.695890\pi\)
\(72\) −9.21680e7 −0.00561373
\(73\) −1.78971e10 −1.01043 −0.505215 0.862994i \(-0.668587\pi\)
−0.505215 + 0.862994i \(0.668587\pi\)
\(74\) −3.98055e10 −2.08530
\(75\) 2.19793e9 0.106949
\(76\) 3.18571e10 1.44122
\(77\) −7.64017e10 −3.21665
\(78\) −2.14408e10 −0.840855
\(79\) 2.32461e10 0.849963 0.424982 0.905202i \(-0.360281\pi\)
0.424982 + 0.905202i \(0.360281\pi\)
\(80\) 2.61373e10 0.891795
\(81\) 3.48678e9 0.111111
\(82\) 7.63737e10 2.27493
\(83\) 8.67597e9 0.241762 0.120881 0.992667i \(-0.461428\pi\)
0.120881 + 0.992667i \(0.461428\pi\)
\(84\) −4.26158e10 −1.11182
\(85\) −3.85066e10 −0.941307
\(86\) 1.87374e10 0.429505
\(87\) −7.78588e9 −0.167476
\(88\) 1.40917e9 0.0284648
\(89\) 7.88055e10 1.49593 0.747966 0.663737i \(-0.231031\pi\)
0.747966 + 0.663737i \(0.231031\pi\)
\(90\) 2.39071e10 0.426770
\(91\) −1.16326e11 −1.95412
\(92\) 1.13136e11 1.78965
\(93\) −4.89493e10 −0.729609
\(94\) −3.94570e9 −0.0554525
\(95\) −9.69615e10 −1.28564
\(96\) −6.54139e10 −0.818801
\(97\) −6.50540e10 −0.769183 −0.384592 0.923087i \(-0.625658\pi\)
−0.384592 + 0.923087i \(0.625658\pi\)
\(98\) −3.32784e11 −3.71893
\(99\) −5.33098e10 −0.563396
\(100\) −1.87440e10 −0.187440
\(101\) −8.59215e10 −0.813457 −0.406728 0.913549i \(-0.633330\pi\)
−0.406728 + 0.913549i \(0.633330\pi\)
\(102\) 9.52264e10 0.853998
\(103\) −4.71359e10 −0.400633 −0.200317 0.979731i \(-0.564197\pi\)
−0.200317 + 0.979731i \(0.564197\pi\)
\(104\) 2.14554e9 0.0172923
\(105\) 1.29707e11 0.991797
\(106\) 2.34449e11 1.70163
\(107\) 6.98844e10 0.481692 0.240846 0.970563i \(-0.422575\pi\)
0.240846 + 0.970563i \(0.422575\pi\)
\(108\) −2.97355e10 −0.194735
\(109\) −8.79549e9 −0.0547538 −0.0273769 0.999625i \(-0.508715\pi\)
−0.0273769 + 0.999625i \(0.508715\pi\)
\(110\) −3.65519e11 −2.16396
\(111\) −1.50690e11 −0.848803
\(112\) −3.50686e11 −1.88027
\(113\) −1.78906e10 −0.0913468 −0.0456734 0.998956i \(-0.514543\pi\)
−0.0456734 + 0.998956i \(0.514543\pi\)
\(114\) 2.39785e11 1.16639
\(115\) −3.44345e11 −1.59645
\(116\) 6.63984e10 0.293521
\(117\) −8.11675e10 −0.342263
\(118\) 4.58908e10 0.184661
\(119\) 5.16647e11 1.98466
\(120\) −2.39234e9 −0.00877661
\(121\) 5.29748e11 1.85673
\(122\) −7.25745e11 −2.43111
\(123\) 2.89125e11 0.925991
\(124\) 4.17442e11 1.27872
\(125\) 3.65028e11 1.06985
\(126\) −3.20764e11 −0.899804
\(127\) −4.11217e10 −0.110446 −0.0552231 0.998474i \(-0.517587\pi\)
−0.0552231 + 0.998474i \(0.517587\pi\)
\(128\) 1.30926e10 0.0336800
\(129\) 7.09334e10 0.174827
\(130\) −5.56525e11 −1.31461
\(131\) −7.36528e11 −1.66800 −0.834002 0.551762i \(-0.813956\pi\)
−0.834002 + 0.551762i \(0.813956\pi\)
\(132\) 4.54629e11 0.987417
\(133\) 1.30094e12 2.71065
\(134\) 5.20967e11 1.04168
\(135\) 9.05041e10 0.173713
\(136\) −9.52914e9 −0.0175626
\(137\) −5.15534e11 −0.912628 −0.456314 0.889819i \(-0.650831\pi\)
−0.456314 + 0.889819i \(0.650831\pi\)
\(138\) 8.51562e11 1.44838
\(139\) 3.25513e11 0.532092 0.266046 0.963960i \(-0.414283\pi\)
0.266046 + 0.963960i \(0.414283\pi\)
\(140\) −1.10615e12 −1.73824
\(141\) −1.49371e10 −0.0225715
\(142\) 1.12671e12 1.63766
\(143\) 1.24098e12 1.73547
\(144\) −2.44694e11 −0.329329
\(145\) −2.02093e11 −0.261835
\(146\) 1.14881e12 1.43320
\(147\) −1.25980e12 −1.51376
\(148\) 1.28509e12 1.48763
\(149\) 1.16267e12 1.29697 0.648485 0.761227i \(-0.275403\pi\)
0.648485 + 0.761227i \(0.275403\pi\)
\(150\) −1.41084e11 −0.151697
\(151\) 7.93846e11 0.822930 0.411465 0.911425i \(-0.365017\pi\)
0.411465 + 0.911425i \(0.365017\pi\)
\(152\) −2.39948e10 −0.0239871
\(153\) 3.60494e11 0.347613
\(154\) 4.90420e12 4.56251
\(155\) −1.27054e12 −1.14068
\(156\) 6.92201e11 0.599856
\(157\) −1.68630e12 −1.41087 −0.705436 0.708774i \(-0.749249\pi\)
−0.705436 + 0.708774i \(0.749249\pi\)
\(158\) −1.49216e12 −1.20559
\(159\) 8.87541e11 0.692635
\(160\) −1.69791e12 −1.28013
\(161\) 4.62012e12 3.36597
\(162\) −2.23816e11 −0.157601
\(163\) −6.34506e11 −0.431921 −0.215960 0.976402i \(-0.569288\pi\)
−0.215960 + 0.976402i \(0.569288\pi\)
\(164\) −2.46567e12 −1.62291
\(165\) −1.38373e12 −0.880823
\(166\) −5.56908e11 −0.342917
\(167\) −1.56788e12 −0.934056 −0.467028 0.884242i \(-0.654675\pi\)
−0.467028 + 0.884242i \(0.654675\pi\)
\(168\) 3.20983e10 0.0185047
\(169\) 9.73062e10 0.0542955
\(170\) 2.47173e12 1.33516
\(171\) 9.07741e11 0.474770
\(172\) −6.04924e11 −0.306404
\(173\) −1.63986e12 −0.804550 −0.402275 0.915519i \(-0.631780\pi\)
−0.402275 + 0.915519i \(0.631780\pi\)
\(174\) 4.99773e11 0.237548
\(175\) −7.65447e11 −0.352538
\(176\) 3.74115e12 1.66988
\(177\) 1.73727e11 0.0751646
\(178\) −5.05850e12 −2.12184
\(179\) −2.22928e12 −0.906718 −0.453359 0.891328i \(-0.649775\pi\)
−0.453359 + 0.891328i \(0.649775\pi\)
\(180\) −7.71824e11 −0.304452
\(181\) 1.95784e12 0.749111 0.374555 0.927205i \(-0.377795\pi\)
0.374555 + 0.927205i \(0.377795\pi\)
\(182\) 7.46695e12 2.77173
\(183\) −2.74742e12 −0.989564
\(184\) −8.52143e10 −0.0297861
\(185\) −3.91135e12 −1.32703
\(186\) 3.14204e12 1.03488
\(187\) −5.51164e12 −1.76259
\(188\) 1.27384e11 0.0395592
\(189\) −1.21430e12 −0.366258
\(190\) 6.22393e12 1.82356
\(191\) −1.00786e12 −0.286891 −0.143446 0.989658i \(-0.545818\pi\)
−0.143446 + 0.989658i \(0.545818\pi\)
\(192\) 2.13662e12 0.590978
\(193\) 3.80074e12 1.02165 0.510826 0.859684i \(-0.329340\pi\)
0.510826 + 0.859684i \(0.329340\pi\)
\(194\) 4.17580e12 1.09101
\(195\) −2.10681e12 −0.535100
\(196\) 1.07437e13 2.65304
\(197\) −2.35828e12 −0.566280 −0.283140 0.959079i \(-0.591376\pi\)
−0.283140 + 0.959079i \(0.591376\pi\)
\(198\) 3.42194e12 0.799124
\(199\) −1.25177e12 −0.284336 −0.142168 0.989843i \(-0.545407\pi\)
−0.142168 + 0.989843i \(0.545407\pi\)
\(200\) 1.41181e10 0.00311968
\(201\) 1.97220e12 0.424007
\(202\) 5.51528e12 1.15381
\(203\) 2.71150e12 0.552054
\(204\) −3.07431e12 −0.609232
\(205\) 7.50461e12 1.44771
\(206\) 3.02564e12 0.568260
\(207\) 3.22372e12 0.589550
\(208\) 5.69613e12 1.01445
\(209\) −1.38786e13 −2.40735
\(210\) −8.32586e12 −1.40677
\(211\) −4.10909e12 −0.676382 −0.338191 0.941077i \(-0.609815\pi\)
−0.338191 + 0.941077i \(0.609815\pi\)
\(212\) −7.56900e12 −1.21392
\(213\) 4.26532e12 0.666597
\(214\) −4.48586e12 −0.683235
\(215\) 1.84117e12 0.273327
\(216\) 2.23968e10 0.00324109
\(217\) 1.70470e13 2.40503
\(218\) 5.64580e11 0.0776631
\(219\) 4.34899e12 0.583372
\(220\) 1.18005e13 1.54375
\(221\) −8.39181e12 −1.07077
\(222\) 9.67272e12 1.20395
\(223\) 9.53747e12 1.15813 0.579064 0.815282i \(-0.303418\pi\)
0.579064 + 0.815282i \(0.303418\pi\)
\(224\) 2.27810e13 2.69903
\(225\) −5.34096e11 −0.0617470
\(226\) 1.14839e12 0.129567
\(227\) 9.82918e12 1.08237 0.541184 0.840904i \(-0.317976\pi\)
0.541184 + 0.840904i \(0.317976\pi\)
\(228\) −7.74127e12 −0.832090
\(229\) −4.90493e12 −0.514681 −0.257340 0.966321i \(-0.582846\pi\)
−0.257340 + 0.966321i \(0.582846\pi\)
\(230\) 2.21034e13 2.26442
\(231\) 1.85656e13 1.85713
\(232\) −5.00114e10 −0.00488523
\(233\) 1.38224e13 1.31863 0.659317 0.751865i \(-0.270845\pi\)
0.659317 + 0.751865i \(0.270845\pi\)
\(234\) 5.21012e12 0.485468
\(235\) −3.87711e11 −0.0352887
\(236\) −1.48155e12 −0.131735
\(237\) −5.64879e12 −0.490727
\(238\) −3.31634e13 −2.81505
\(239\) −2.29756e12 −0.190581 −0.0952904 0.995450i \(-0.530378\pi\)
−0.0952904 + 0.995450i \(0.530378\pi\)
\(240\) −6.35136e12 −0.514878
\(241\) −4.33916e12 −0.343805 −0.171903 0.985114i \(-0.554991\pi\)
−0.171903 + 0.985114i \(0.554991\pi\)
\(242\) −3.40044e13 −2.63360
\(243\) −8.47289e11 −0.0641500
\(244\) 2.34301e13 1.73433
\(245\) −3.26999e13 −2.36664
\(246\) −1.85588e13 −1.31343
\(247\) −2.11310e13 −1.46247
\(248\) −3.14418e11 −0.0212825
\(249\) −2.10826e12 −0.139581
\(250\) −2.34310e13 −1.51748
\(251\) 8.15418e12 0.516624 0.258312 0.966062i \(-0.416834\pi\)
0.258312 + 0.966062i \(0.416834\pi\)
\(252\) 1.03556e13 0.641910
\(253\) −4.92878e13 −2.98935
\(254\) 2.63959e12 0.156658
\(255\) 9.35711e12 0.543464
\(256\) 1.71670e13 0.975832
\(257\) 1.34438e13 0.747982 0.373991 0.927432i \(-0.377989\pi\)
0.373991 + 0.927432i \(0.377989\pi\)
\(258\) −4.55319e12 −0.247975
\(259\) 5.24790e13 2.79793
\(260\) 1.79670e13 0.937825
\(261\) 1.89197e12 0.0966921
\(262\) 4.72775e13 2.36590
\(263\) 2.31137e13 1.13270 0.566348 0.824166i \(-0.308356\pi\)
0.566348 + 0.824166i \(0.308356\pi\)
\(264\) −3.42427e11 −0.0164341
\(265\) 2.30373e13 1.08288
\(266\) −8.35070e13 −3.84480
\(267\) −1.91497e13 −0.863676
\(268\) −1.68190e13 −0.743122
\(269\) 2.85981e13 1.23794 0.618970 0.785415i \(-0.287550\pi\)
0.618970 + 0.785415i \(0.287550\pi\)
\(270\) −5.80943e12 −0.246396
\(271\) −7.95747e12 −0.330707 −0.165354 0.986234i \(-0.552877\pi\)
−0.165354 + 0.986234i \(0.552877\pi\)
\(272\) −2.52986e13 −1.03031
\(273\) 2.82673e13 1.12821
\(274\) 3.30919e13 1.29448
\(275\) 8.16586e12 0.313092
\(276\) −2.74920e13 −1.03325
\(277\) −1.29393e13 −0.476729 −0.238365 0.971176i \(-0.576611\pi\)
−0.238365 + 0.971176i \(0.576611\pi\)
\(278\) −2.08946e13 −0.754722
\(279\) 1.18947e13 0.421240
\(280\) 8.33154e11 0.0289305
\(281\) 1.93697e13 0.659536 0.329768 0.944062i \(-0.393029\pi\)
0.329768 + 0.944062i \(0.393029\pi\)
\(282\) 9.58806e11 0.0320155
\(283\) 5.69672e13 1.86552 0.932759 0.360499i \(-0.117394\pi\)
0.932759 + 0.360499i \(0.117394\pi\)
\(284\) −3.63748e13 −1.16829
\(285\) 2.35616e13 0.742265
\(286\) −7.96580e13 −2.46159
\(287\) −1.00690e14 −3.05237
\(288\) 1.58956e13 0.472735
\(289\) 2.99918e12 0.0875115
\(290\) 1.29723e13 0.371388
\(291\) 1.58081e13 0.444088
\(292\) −3.70884e13 −1.02243
\(293\) −4.46407e13 −1.20770 −0.603849 0.797098i \(-0.706367\pi\)
−0.603849 + 0.797098i \(0.706367\pi\)
\(294\) 8.08664e13 2.14713
\(295\) 4.50931e12 0.117514
\(296\) −9.67932e11 −0.0247594
\(297\) 1.29543e13 0.325277
\(298\) −7.46311e13 −1.83963
\(299\) −7.50437e13 −1.81603
\(300\) 4.55480e12 0.108219
\(301\) −2.47032e13 −0.576285
\(302\) −5.09567e13 −1.16725
\(303\) 2.08789e13 0.469649
\(304\) −6.37030e13 −1.40720
\(305\) −7.13129e13 −1.54710
\(306\) −2.31400e13 −0.493056
\(307\) 6.66583e13 1.39506 0.697530 0.716556i \(-0.254282\pi\)
0.697530 + 0.716556i \(0.254282\pi\)
\(308\) −1.58328e14 −3.25484
\(309\) 1.14540e13 0.231306
\(310\) 8.15558e13 1.61795
\(311\) −6.84643e13 −1.33439 −0.667194 0.744884i \(-0.732505\pi\)
−0.667194 + 0.744884i \(0.732505\pi\)
\(312\) −5.21367e11 −0.00998374
\(313\) 1.48075e13 0.278603 0.139302 0.990250i \(-0.455514\pi\)
0.139302 + 0.990250i \(0.455514\pi\)
\(314\) 1.08243e14 2.00119
\(315\) −3.15188e13 −0.572614
\(316\) 4.81732e13 0.860055
\(317\) 8.34508e13 1.46421 0.732107 0.681190i \(-0.238537\pi\)
0.732107 + 0.681190i \(0.238537\pi\)
\(318\) −5.69710e13 −0.982437
\(319\) −2.89265e13 −0.490284
\(320\) 5.54589e13 0.923946
\(321\) −1.69819e13 −0.278105
\(322\) −2.96564e14 −4.77431
\(323\) 9.38503e13 1.48533
\(324\) 7.22572e12 0.112430
\(325\) 1.24330e13 0.190203
\(326\) 4.07288e13 0.612639
\(327\) 2.13730e12 0.0316121
\(328\) 1.85715e12 0.0270110
\(329\) 5.20196e12 0.0744029
\(330\) 8.88210e13 1.24936
\(331\) −4.81979e13 −0.666767 −0.333383 0.942791i \(-0.608190\pi\)
−0.333383 + 0.942791i \(0.608190\pi\)
\(332\) 1.79793e13 0.244633
\(333\) 3.66176e13 0.490057
\(334\) 1.00642e14 1.32487
\(335\) 5.11911e13 0.662901
\(336\) 8.52168e13 1.08557
\(337\) 7.78671e13 0.975865 0.487932 0.872881i \(-0.337751\pi\)
0.487932 + 0.872881i \(0.337751\pi\)
\(338\) −6.24605e12 −0.0770130
\(339\) 4.34741e12 0.0527391
\(340\) −7.97979e13 −0.952484
\(341\) −1.81859e14 −2.13592
\(342\) −5.82676e13 −0.673417
\(343\) 2.71403e14 3.08671
\(344\) 4.55630e11 0.00509965
\(345\) 8.36759e13 0.921713
\(346\) 1.05262e14 1.14118
\(347\) −9.04895e13 −0.965575 −0.482788 0.875737i \(-0.660376\pi\)
−0.482788 + 0.875737i \(0.660376\pi\)
\(348\) −1.61348e13 −0.169464
\(349\) 7.98190e13 0.825214 0.412607 0.910909i \(-0.364618\pi\)
0.412607 + 0.910909i \(0.364618\pi\)
\(350\) 4.91338e13 0.500042
\(351\) 1.97237e13 0.197606
\(352\) −2.43029e14 −2.39703
\(353\) 5.16894e13 0.501927 0.250964 0.967996i \(-0.419253\pi\)
0.250964 + 0.967996i \(0.419253\pi\)
\(354\) −1.11515e13 −0.106614
\(355\) 1.10712e14 1.04217
\(356\) 1.63310e14 1.51369
\(357\) −1.25545e14 −1.14584
\(358\) 1.43097e14 1.28609
\(359\) 1.14657e14 1.01480 0.507399 0.861711i \(-0.330607\pi\)
0.507399 + 0.861711i \(0.330607\pi\)
\(360\) 5.81339e11 0.00506718
\(361\) 1.19829e14 1.02866
\(362\) −1.25673e14 −1.06254
\(363\) −1.28729e14 −1.07199
\(364\) −2.41065e14 −1.97732
\(365\) 1.12884e14 0.912054
\(366\) 1.76356e14 1.40360
\(367\) −2.83999e12 −0.0222666 −0.0111333 0.999938i \(-0.503544\pi\)
−0.0111333 + 0.999938i \(0.503544\pi\)
\(368\) −2.26233e14 −1.74740
\(369\) −7.02573e13 −0.534621
\(370\) 2.51068e14 1.88227
\(371\) −3.09094e14 −2.28315
\(372\) −1.01438e14 −0.738272
\(373\) −7.99288e13 −0.573198 −0.286599 0.958051i \(-0.592525\pi\)
−0.286599 + 0.958051i \(0.592525\pi\)
\(374\) 3.53790e14 2.50007
\(375\) −8.87018e13 −0.617676
\(376\) −9.59460e10 −0.000658406 0
\(377\) −4.40424e13 −0.297847
\(378\) 7.79457e13 0.519502
\(379\) −1.32898e14 −0.872974 −0.436487 0.899711i \(-0.643778\pi\)
−0.436487 + 0.899711i \(0.643778\pi\)
\(380\) −2.00935e14 −1.30090
\(381\) 9.99258e12 0.0637662
\(382\) 6.46944e13 0.406928
\(383\) −3.98305e13 −0.246958 −0.123479 0.992347i \(-0.539405\pi\)
−0.123479 + 0.992347i \(0.539405\pi\)
\(384\) −3.18151e12 −0.0194452
\(385\) 4.81895e14 2.90348
\(386\) −2.43968e14 −1.44912
\(387\) −1.72368e13 −0.100936
\(388\) −1.34813e14 −0.778316
\(389\) 1.63688e14 0.931736 0.465868 0.884854i \(-0.345742\pi\)
0.465868 + 0.884854i \(0.345742\pi\)
\(390\) 1.35236e14 0.758989
\(391\) 3.33296e14 1.84441
\(392\) −8.09216e12 −0.0441561
\(393\) 1.78976e14 0.963022
\(394\) 1.51377e14 0.803214
\(395\) −1.46622e14 −0.767211
\(396\) −1.10475e14 −0.570085
\(397\) 2.15879e13 0.109866 0.0549328 0.998490i \(-0.482506\pi\)
0.0549328 + 0.998490i \(0.482506\pi\)
\(398\) 8.03505e13 0.403303
\(399\) −3.16129e14 −1.56500
\(400\) 3.74816e13 0.183015
\(401\) 6.97618e13 0.335988 0.167994 0.985788i \(-0.446271\pi\)
0.167994 + 0.985788i \(0.446271\pi\)
\(402\) −1.26595e14 −0.601414
\(403\) −2.76891e14 −1.29757
\(404\) −1.78057e14 −0.823115
\(405\) −2.19925e13 −0.100293
\(406\) −1.74050e14 −0.783036
\(407\) −5.59850e14 −2.48486
\(408\) 2.31558e12 0.0101398
\(409\) −1.49949e14 −0.647838 −0.323919 0.946085i \(-0.605001\pi\)
−0.323919 + 0.946085i \(0.605001\pi\)
\(410\) −4.81719e14 −2.05344
\(411\) 1.25275e14 0.526906
\(412\) −9.76805e13 −0.405390
\(413\) −6.05018e13 −0.247767
\(414\) −2.06930e14 −0.836220
\(415\) −5.47227e13 −0.218224
\(416\) −3.70027e14 −1.45620
\(417\) −7.90996e13 −0.307203
\(418\) 8.90860e14 3.41460
\(419\) −8.76706e13 −0.331647 −0.165824 0.986155i \(-0.553028\pi\)
−0.165824 + 0.986155i \(0.553028\pi\)
\(420\) 2.68794e14 1.00357
\(421\) 1.73321e14 0.638705 0.319352 0.947636i \(-0.396535\pi\)
0.319352 + 0.947636i \(0.396535\pi\)
\(422\) 2.63761e14 0.959384
\(423\) 3.62971e12 0.0130317
\(424\) 5.70099e12 0.0202040
\(425\) −5.52196e13 −0.193176
\(426\) −2.73789e14 −0.945505
\(427\) 9.56812e14 3.26192
\(428\) 1.44823e14 0.487411
\(429\) −3.01558e14 −1.00197
\(430\) −1.18184e14 −0.387688
\(431\) 1.13774e14 0.368484 0.184242 0.982881i \(-0.441017\pi\)
0.184242 + 0.982881i \(0.441017\pi\)
\(432\) 5.94606e13 0.190138
\(433\) 2.00411e14 0.632758 0.316379 0.948633i \(-0.397533\pi\)
0.316379 + 0.948633i \(0.397533\pi\)
\(434\) −1.09424e15 −3.41130
\(435\) 4.91086e13 0.151170
\(436\) −1.82270e13 −0.0554039
\(437\) 8.39256e14 2.51911
\(438\) −2.79160e14 −0.827458
\(439\) −4.94116e14 −1.44635 −0.723176 0.690664i \(-0.757318\pi\)
−0.723176 + 0.690664i \(0.757318\pi\)
\(440\) −8.88816e12 −0.0256934
\(441\) 3.06132e14 0.873971
\(442\) 5.38668e14 1.51879
\(443\) −1.92652e14 −0.536479 −0.268240 0.963352i \(-0.586442\pi\)
−0.268240 + 0.963352i \(0.586442\pi\)
\(444\) −3.12277e14 −0.858882
\(445\) −4.97057e14 −1.35029
\(446\) −6.12207e14 −1.64269
\(447\) −2.82528e14 −0.748806
\(448\) −7.44098e14 −1.94805
\(449\) 7.18393e14 1.85783 0.928917 0.370287i \(-0.120741\pi\)
0.928917 + 0.370287i \(0.120741\pi\)
\(450\) 3.42835e13 0.0875823
\(451\) 1.07417e15 2.71083
\(452\) −3.70750e13 −0.0924314
\(453\) −1.92905e14 −0.475119
\(454\) −6.30932e14 −1.53524
\(455\) 7.33715e14 1.76386
\(456\) 5.83074e12 0.0138490
\(457\) 2.86012e14 0.671189 0.335595 0.942006i \(-0.391063\pi\)
0.335595 + 0.942006i \(0.391063\pi\)
\(458\) 3.14846e14 0.730026
\(459\) −8.76001e13 −0.200694
\(460\) −7.13593e14 −1.61541
\(461\) −2.80949e14 −0.628451 −0.314226 0.949348i \(-0.601745\pi\)
−0.314226 + 0.949348i \(0.601745\pi\)
\(462\) −1.19172e15 −2.63417
\(463\) −5.41341e14 −1.18243 −0.591215 0.806514i \(-0.701352\pi\)
−0.591215 + 0.806514i \(0.701352\pi\)
\(464\) −1.32774e14 −0.286591
\(465\) 3.08742e14 0.658574
\(466\) −8.87253e14 −1.87036
\(467\) −3.33665e14 −0.695133 −0.347567 0.937655i \(-0.612992\pi\)
−0.347567 + 0.937655i \(0.612992\pi\)
\(468\) −1.68205e14 −0.346327
\(469\) −6.86837e14 −1.39766
\(470\) 2.48871e13 0.0500536
\(471\) 4.09772e14 0.814567
\(472\) 1.11591e12 0.00219254
\(473\) 2.63536e14 0.511803
\(474\) 3.62594e14 0.696049
\(475\) −1.39045e14 −0.263841
\(476\) 1.07066e15 2.00822
\(477\) −2.15673e14 −0.399893
\(478\) 1.47480e14 0.270321
\(479\) 6.72462e14 1.21849 0.609245 0.792982i \(-0.291473\pi\)
0.609245 + 0.792982i \(0.291473\pi\)
\(480\) 4.12591e14 0.739083
\(481\) −8.52407e14 −1.50956
\(482\) 2.78530e14 0.487655
\(483\) −1.12269e15 −1.94335
\(484\) 1.09781e15 1.87878
\(485\) 4.10321e14 0.694295
\(486\) 5.43872e13 0.0909907
\(487\) −2.16358e14 −0.357901 −0.178950 0.983858i \(-0.557270\pi\)
−0.178950 + 0.983858i \(0.557270\pi\)
\(488\) −1.76476e13 −0.0288654
\(489\) 1.54185e14 0.249370
\(490\) 2.09900e15 3.35686
\(491\) 5.66577e14 0.896006 0.448003 0.894032i \(-0.352135\pi\)
0.448003 + 0.894032i \(0.352135\pi\)
\(492\) 5.99158e14 0.936986
\(493\) 1.95608e14 0.302503
\(494\) 1.35639e15 2.07437
\(495\) 3.36246e14 0.508544
\(496\) −8.34739e14 −1.24854
\(497\) −1.48543e15 −2.19732
\(498\) 1.35329e14 0.197983
\(499\) −4.60728e14 −0.666641 −0.333320 0.942814i \(-0.608169\pi\)
−0.333320 + 0.942814i \(0.608169\pi\)
\(500\) 7.56454e14 1.08255
\(501\) 3.80996e14 0.539278
\(502\) −5.23414e14 −0.732782
\(503\) 5.36485e14 0.742906 0.371453 0.928452i \(-0.378860\pi\)
0.371453 + 0.928452i \(0.378860\pi\)
\(504\) −7.79989e12 −0.0106837
\(505\) 5.41940e14 0.734258
\(506\) 3.16377e15 4.24011
\(507\) −2.36454e13 −0.0313475
\(508\) −8.52173e13 −0.111758
\(509\) 1.27284e15 1.65131 0.825653 0.564179i \(-0.190807\pi\)
0.825653 + 0.564179i \(0.190807\pi\)
\(510\) −6.00630e14 −0.770852
\(511\) −1.51457e15 −1.92298
\(512\) −1.12876e15 −1.41781
\(513\) −2.20581e14 −0.274109
\(514\) −8.62956e14 −1.06094
\(515\) 2.97304e14 0.361628
\(516\) 1.46996e14 0.176902
\(517\) −5.54950e13 −0.0660778
\(518\) −3.36861e15 −3.96860
\(519\) 3.98486e14 0.464507
\(520\) −1.35328e13 −0.0156088
\(521\) 4.23962e14 0.483860 0.241930 0.970294i \(-0.422220\pi\)
0.241930 + 0.970294i \(0.422220\pi\)
\(522\) −1.21445e14 −0.137149
\(523\) 1.41638e15 1.58278 0.791390 0.611312i \(-0.209358\pi\)
0.791390 + 0.611312i \(0.209358\pi\)
\(524\) −1.52632e15 −1.68781
\(525\) 1.86004e14 0.203538
\(526\) −1.48366e15 −1.60662
\(527\) 1.22978e15 1.31785
\(528\) −9.09100e14 −0.964106
\(529\) 2.02769e15 2.12812
\(530\) −1.47876e15 −1.53596
\(531\) −4.22156e13 −0.0433963
\(532\) 2.69596e15 2.74284
\(533\) 1.63549e15 1.64683
\(534\) 1.22922e15 1.22504
\(535\) −4.40788e14 −0.434795
\(536\) 1.26681e13 0.0123682
\(537\) 5.41714e14 0.523494
\(538\) −1.83570e15 −1.75590
\(539\) −4.68049e15 −4.43152
\(540\) 1.87553e14 0.175776
\(541\) 3.05136e14 0.283079 0.141540 0.989933i \(-0.454795\pi\)
0.141540 + 0.989933i \(0.454795\pi\)
\(542\) 5.10788e14 0.469077
\(543\) −4.75756e14 −0.432499
\(544\) 1.64343e15 1.47896
\(545\) 5.54766e13 0.0494230
\(546\) −1.81447e15 −1.60026
\(547\) −5.80672e14 −0.506991 −0.253496 0.967337i \(-0.581580\pi\)
−0.253496 + 0.967337i \(0.581580\pi\)
\(548\) −1.06835e15 −0.923464
\(549\) 6.67623e14 0.571325
\(550\) −5.24164e14 −0.444091
\(551\) 4.92551e14 0.413159
\(552\) 2.07071e13 0.0171970
\(553\) 1.96724e15 1.61759
\(554\) 8.30569e14 0.676195
\(555\) 9.50458e14 0.766164
\(556\) 6.74566e14 0.538410
\(557\) 1.27295e15 1.00602 0.503011 0.864280i \(-0.332225\pi\)
0.503011 + 0.864280i \(0.332225\pi\)
\(558\) −7.63515e14 −0.597489
\(559\) 4.01249e14 0.310920
\(560\) 2.21191e15 1.69720
\(561\) 1.33933e15 1.01763
\(562\) −1.24334e15 −0.935490
\(563\) 1.15682e15 0.861923 0.430961 0.902370i \(-0.358175\pi\)
0.430961 + 0.902370i \(0.358175\pi\)
\(564\) −3.09543e13 −0.0228395
\(565\) 1.12843e14 0.0824532
\(566\) −3.65671e15 −2.64606
\(567\) 2.95076e14 0.211459
\(568\) 2.73976e13 0.0194445
\(569\) 2.09256e15 1.47082 0.735412 0.677620i \(-0.236989\pi\)
0.735412 + 0.677620i \(0.236989\pi\)
\(570\) −1.51241e15 −1.05283
\(571\) −2.47949e14 −0.170948 −0.0854740 0.996340i \(-0.527240\pi\)
−0.0854740 + 0.996340i \(0.527240\pi\)
\(572\) 2.57170e15 1.75607
\(573\) 2.44910e14 0.165637
\(574\) 6.46327e15 4.32949
\(575\) −4.93801e14 −0.327626
\(576\) −5.19200e14 −0.341201
\(577\) 3.09646e14 0.201557 0.100778 0.994909i \(-0.467867\pi\)
0.100778 + 0.994909i \(0.467867\pi\)
\(578\) −1.92517e14 −0.124127
\(579\) −9.23579e14 −0.589851
\(580\) −4.18800e14 −0.264943
\(581\) 7.34220e14 0.460105
\(582\) −1.01472e15 −0.629897
\(583\) 3.29744e15 2.02768
\(584\) 2.79350e13 0.0170168
\(585\) 5.11955e14 0.308940
\(586\) 2.86547e15 1.71301
\(587\) −2.08360e15 −1.23397 −0.616986 0.786974i \(-0.711647\pi\)
−0.616986 + 0.786974i \(0.711647\pi\)
\(588\) −2.61071e15 −1.53174
\(589\) 3.09663e15 1.79993
\(590\) −2.89451e14 −0.166682
\(591\) 5.73062e14 0.326942
\(592\) −2.56973e15 −1.45251
\(593\) 2.43608e15 1.36424 0.682119 0.731241i \(-0.261059\pi\)
0.682119 + 0.731241i \(0.261059\pi\)
\(594\) −8.31532e14 −0.461374
\(595\) −3.25870e15 −1.79143
\(596\) 2.40941e15 1.31237
\(597\) 3.04179e14 0.164161
\(598\) 4.81703e15 2.57586
\(599\) −6.60050e14 −0.349727 −0.174863 0.984593i \(-0.555948\pi\)
−0.174863 + 0.984593i \(0.555948\pi\)
\(600\) −3.43069e12 −0.00180115
\(601\) 3.71095e14 0.193052 0.0965261 0.995330i \(-0.469227\pi\)
0.0965261 + 0.995330i \(0.469227\pi\)
\(602\) 1.58569e15 0.817405
\(603\) −4.79245e14 −0.244801
\(604\) 1.64510e15 0.832701
\(605\) −3.34133e15 −1.67596
\(606\) −1.34021e15 −0.666153
\(607\) −2.04336e15 −1.00648 −0.503242 0.864146i \(-0.667859\pi\)
−0.503242 + 0.864146i \(0.667859\pi\)
\(608\) 4.13822e15 2.01997
\(609\) −6.58895e14 −0.318728
\(610\) 4.57755e15 2.19442
\(611\) −8.44945e13 −0.0401423
\(612\) 7.47059e14 0.351740
\(613\) −2.66338e15 −1.24280 −0.621399 0.783494i \(-0.713435\pi\)
−0.621399 + 0.783494i \(0.713435\pi\)
\(614\) −4.27877e15 −1.97876
\(615\) −1.82362e15 −0.835837
\(616\) 1.19253e14 0.0541722
\(617\) −3.42504e15 −1.54205 −0.771024 0.636806i \(-0.780255\pi\)
−0.771024 + 0.636806i \(0.780255\pi\)
\(618\) −7.35230e14 −0.328085
\(619\) 3.05390e15 1.35069 0.675347 0.737500i \(-0.263994\pi\)
0.675347 + 0.737500i \(0.263994\pi\)
\(620\) −2.63297e15 −1.15423
\(621\) −7.83364e14 −0.340377
\(622\) 4.39470e15 1.89270
\(623\) 6.66906e15 2.84696
\(624\) −1.38416e15 −0.585695
\(625\) −1.86073e15 −0.780445
\(626\) −9.50486e14 −0.395173
\(627\) 3.37249e15 1.38989
\(628\) −3.49455e15 −1.42762
\(629\) 3.78585e15 1.53315
\(630\) 2.02319e15 0.812199
\(631\) 2.34415e15 0.932877 0.466438 0.884554i \(-0.345537\pi\)
0.466438 + 0.884554i \(0.345537\pi\)
\(632\) −3.62841e13 −0.0143144
\(633\) 9.98509e14 0.390509
\(634\) −5.35668e15 −2.07685
\(635\) 2.59371e14 0.0996932
\(636\) 1.83927e15 0.700859
\(637\) −7.12633e15 −2.69215
\(638\) 1.85678e15 0.695421
\(639\) −1.03647e15 −0.384860
\(640\) −8.25803e13 −0.0304009
\(641\) 1.76636e14 0.0644703 0.0322351 0.999480i \(-0.489737\pi\)
0.0322351 + 0.999480i \(0.489737\pi\)
\(642\) 1.09006e15 0.394466
\(643\) 5.68123e14 0.203837 0.101918 0.994793i \(-0.467502\pi\)
0.101918 + 0.994793i \(0.467502\pi\)
\(644\) 9.57434e15 3.40594
\(645\) −4.47405e14 −0.157805
\(646\) −6.02422e15 −2.10679
\(647\) −4.50332e15 −1.56156 −0.780782 0.624804i \(-0.785179\pi\)
−0.780782 + 0.624804i \(0.785179\pi\)
\(648\) −5.44243e12 −0.00187124
\(649\) 6.45438e14 0.220044
\(650\) −7.98072e14 −0.269785
\(651\) −4.14242e15 −1.38854
\(652\) −1.31490e15 −0.437049
\(653\) 1.31034e15 0.431879 0.215939 0.976407i \(-0.430719\pi\)
0.215939 + 0.976407i \(0.430719\pi\)
\(654\) −1.37193e14 −0.0448388
\(655\) 4.64557e15 1.50561
\(656\) 4.93048e15 1.58459
\(657\) −1.05680e15 −0.336810
\(658\) −3.33912e14 −0.105533
\(659\) −4.17876e15 −1.30972 −0.654858 0.755752i \(-0.727272\pi\)
−0.654858 + 0.755752i \(0.727272\pi\)
\(660\) −2.86752e15 −0.891282
\(661\) −9.57421e14 −0.295117 −0.147559 0.989053i \(-0.547142\pi\)
−0.147559 + 0.989053i \(0.547142\pi\)
\(662\) 3.09381e15 0.945745
\(663\) 2.03921e15 0.618212
\(664\) −1.35421e13 −0.00407156
\(665\) −8.20554e15 −2.44674
\(666\) −2.35047e15 −0.695099
\(667\) 1.74923e15 0.513043
\(668\) −3.24915e15 −0.945147
\(669\) −2.31761e15 −0.668645
\(670\) −3.28594e15 −0.940262
\(671\) −1.02074e16 −2.89694
\(672\) −5.53577e15 −1.55829
\(673\) 4.38576e15 1.22451 0.612255 0.790660i \(-0.290263\pi\)
0.612255 + 0.790660i \(0.290263\pi\)
\(674\) −4.99827e15 −1.38417
\(675\) 1.29785e14 0.0356496
\(676\) 2.01649e14 0.0549401
\(677\) 1.46162e15 0.395001 0.197500 0.980303i \(-0.436718\pi\)
0.197500 + 0.980303i \(0.436718\pi\)
\(678\) −2.79059e14 −0.0748054
\(679\) −5.50532e15 −1.46386
\(680\) 6.01040e13 0.0158527
\(681\) −2.38849e15 −0.624906
\(682\) 1.16735e16 3.02960
\(683\) 7.08973e14 0.182522 0.0912612 0.995827i \(-0.470910\pi\)
0.0912612 + 0.995827i \(0.470910\pi\)
\(684\) 1.88113e15 0.480407
\(685\) 3.25167e15 0.823775
\(686\) −1.74212e16 −4.37821
\(687\) 1.19190e15 0.297151
\(688\) 1.20964e15 0.299170
\(689\) 5.02056e15 1.23182
\(690\) −5.37113e15 −1.30736
\(691\) −6.30474e15 −1.52243 −0.761216 0.648499i \(-0.775397\pi\)
−0.761216 + 0.648499i \(0.775397\pi\)
\(692\) −3.39831e15 −0.814102
\(693\) −4.51144e15 −1.07222
\(694\) 5.80849e15 1.36958
\(695\) −2.05314e15 −0.480288
\(696\) 1.21528e13 0.00282049
\(697\) −7.26382e15 −1.67257
\(698\) −5.12356e15 −1.17049
\(699\) −3.35883e15 −0.761314
\(700\) −1.58625e15 −0.356724
\(701\) 3.31122e15 0.738820 0.369410 0.929267i \(-0.379560\pi\)
0.369410 + 0.929267i \(0.379560\pi\)
\(702\) −1.26606e15 −0.280285
\(703\) 9.53294e15 2.09398
\(704\) 7.93810e15 1.73008
\(705\) 9.42139e13 0.0203739
\(706\) −3.31793e15 −0.711937
\(707\) −7.27127e15 −1.54812
\(708\) 3.60017e14 0.0760571
\(709\) 2.87126e15 0.601892 0.300946 0.953641i \(-0.402698\pi\)
0.300946 + 0.953641i \(0.402698\pi\)
\(710\) −7.10657e15 −1.47822
\(711\) 1.37266e15 0.283321
\(712\) −1.23005e14 −0.0251933
\(713\) 1.09973e16 2.23508
\(714\) 8.05871e15 1.62527
\(715\) −7.82733e15 −1.56650
\(716\) −4.61977e15 −0.917484
\(717\) 5.58308e14 0.110032
\(718\) −7.35978e15 −1.43940
\(719\) 7.29124e14 0.141512 0.0707558 0.997494i \(-0.477459\pi\)
0.0707558 + 0.997494i \(0.477459\pi\)
\(720\) 1.54338e15 0.297265
\(721\) −3.98896e15 −0.762458
\(722\) −7.69179e15 −1.45906
\(723\) 1.05442e15 0.198496
\(724\) 4.05727e15 0.758005
\(725\) −2.89807e14 −0.0537340
\(726\) 8.26306e15 1.52051
\(727\) 3.25997e15 0.595352 0.297676 0.954667i \(-0.403788\pi\)
0.297676 + 0.954667i \(0.403788\pi\)
\(728\) 1.81571e14 0.0329096
\(729\) 2.05891e14 0.0370370
\(730\) −7.24597e15 −1.29366
\(731\) −1.78209e15 −0.315780
\(732\) −5.69352e15 −1.00131
\(733\) −8.09179e15 −1.41245 −0.706224 0.707988i \(-0.749603\pi\)
−0.706224 + 0.707988i \(0.749603\pi\)
\(734\) 1.82298e14 0.0315831
\(735\) 7.94607e15 1.36638
\(736\) 1.46963e16 2.50831
\(737\) 7.32723e15 1.24128
\(738\) 4.50979e15 0.758310
\(739\) −3.12675e15 −0.521853 −0.260927 0.965359i \(-0.584028\pi\)
−0.260927 + 0.965359i \(0.584028\pi\)
\(740\) −8.10556e15 −1.34279
\(741\) 5.13482e15 0.844356
\(742\) 1.98406e16 3.23843
\(743\) −2.31503e15 −0.375075 −0.187537 0.982257i \(-0.560051\pi\)
−0.187537 + 0.982257i \(0.560051\pi\)
\(744\) 7.64036e13 0.0122875
\(745\) −7.33338e15 −1.17070
\(746\) 5.13060e15 0.813027
\(747\) 5.12307e14 0.0805874
\(748\) −1.14219e16 −1.78352
\(749\) 5.91410e15 0.916724
\(750\) 5.69374e15 0.876115
\(751\) 9.42887e15 1.44026 0.720129 0.693840i \(-0.244083\pi\)
0.720129 + 0.693840i \(0.244083\pi\)
\(752\) −2.54724e14 −0.0386253
\(753\) −1.98147e15 −0.298273
\(754\) 2.82707e15 0.422468
\(755\) −5.00710e15 −0.742810
\(756\) −2.51642e15 −0.370607
\(757\) 1.92231e15 0.281058 0.140529 0.990077i \(-0.455120\pi\)
0.140529 + 0.990077i \(0.455120\pi\)
\(758\) 8.53065e15 1.23823
\(759\) 1.19769e16 1.72590
\(760\) 1.51345e14 0.0216517
\(761\) −5.23339e15 −0.743306 −0.371653 0.928372i \(-0.621209\pi\)
−0.371653 + 0.928372i \(0.621209\pi\)
\(762\) −6.41421e14 −0.0904463
\(763\) −7.44335e14 −0.104204
\(764\) −2.08861e15 −0.290298
\(765\) −2.27378e15 −0.313769
\(766\) 2.55671e15 0.350286
\(767\) 9.82720e14 0.133677
\(768\) −4.17159e15 −0.563397
\(769\) −2.22888e15 −0.298877 −0.149438 0.988771i \(-0.547747\pi\)
−0.149438 + 0.988771i \(0.547747\pi\)
\(770\) −3.09327e16 −4.11831
\(771\) −3.26685e15 −0.431848
\(772\) 7.87633e15 1.03378
\(773\) −6.35866e15 −0.828664 −0.414332 0.910126i \(-0.635985\pi\)
−0.414332 + 0.910126i \(0.635985\pi\)
\(774\) 1.10643e15 0.143168
\(775\) −1.82199e15 −0.234093
\(776\) 1.01541e14 0.0129540
\(777\) −1.27524e16 −1.61539
\(778\) −1.05071e16 −1.32158
\(779\) −1.82906e16 −2.28440
\(780\) −4.36598e15 −0.541454
\(781\) 1.58467e16 1.95146
\(782\) −2.13942e16 −2.61613
\(783\) −4.59748e14 −0.0558252
\(784\) −2.14836e16 −2.59041
\(785\) 1.06362e16 1.27351
\(786\) −1.14884e16 −1.36596
\(787\) −4.68159e15 −0.552755 −0.276378 0.961049i \(-0.589134\pi\)
−0.276378 + 0.961049i \(0.589134\pi\)
\(788\) −4.88710e15 −0.573003
\(789\) −5.61664e15 −0.653962
\(790\) 9.41162e15 1.08822
\(791\) −1.51402e15 −0.173845
\(792\) 8.32099e13 0.00948826
\(793\) −1.55413e16 −1.75989
\(794\) −1.38572e15 −0.155834
\(795\) −5.59807e15 −0.625200
\(796\) −2.59406e15 −0.287712
\(797\) 9.28783e15 1.02304 0.511521 0.859271i \(-0.329082\pi\)
0.511521 + 0.859271i \(0.329082\pi\)
\(798\) 2.02922e16 2.21980
\(799\) 3.75271e14 0.0407697
\(800\) −2.43484e15 −0.262710
\(801\) 4.65339e15 0.498644
\(802\) −4.47799e15 −0.476567
\(803\) 1.61576e16 1.70782
\(804\) 4.08703e15 0.429042
\(805\) −2.91409e16 −3.03826
\(806\) 1.77736e16 1.84048
\(807\) −6.94933e15 −0.714725
\(808\) 1.34113e14 0.0136996
\(809\) 6.57580e15 0.667163 0.333581 0.942721i \(-0.391743\pi\)
0.333581 + 0.942721i \(0.391743\pi\)
\(810\) 1.41169e15 0.142257
\(811\) 8.94290e15 0.895084 0.447542 0.894263i \(-0.352299\pi\)
0.447542 + 0.894263i \(0.352299\pi\)
\(812\) 5.61909e15 0.558609
\(813\) 1.93367e15 0.190934
\(814\) 3.59366e16 3.52454
\(815\) 4.00208e15 0.389869
\(816\) 6.14756e15 0.594849
\(817\) −4.48739e15 −0.431293
\(818\) 9.62521e15 0.918897
\(819\) −6.86895e15 −0.651372
\(820\) 1.55519e16 1.46490
\(821\) −6.28129e15 −0.587708 −0.293854 0.955850i \(-0.594938\pi\)
−0.293854 + 0.955850i \(0.594938\pi\)
\(822\) −8.04134e15 −0.747366
\(823\) 1.30428e16 1.20413 0.602063 0.798449i \(-0.294346\pi\)
0.602063 + 0.798449i \(0.294346\pi\)
\(824\) 7.35731e13 0.00674714
\(825\) −1.98430e15 −0.180764
\(826\) 3.88359e15 0.351434
\(827\) 3.68427e15 0.331185 0.165593 0.986194i \(-0.447046\pi\)
0.165593 + 0.986194i \(0.447046\pi\)
\(828\) 6.68057e15 0.596550
\(829\) 8.52482e15 0.756198 0.378099 0.925765i \(-0.376578\pi\)
0.378099 + 0.925765i \(0.376578\pi\)
\(830\) 3.51263e15 0.309530
\(831\) 3.14425e15 0.275240
\(832\) 1.20862e16 1.05103
\(833\) 3.16506e16 2.73423
\(834\) 5.07738e15 0.435739
\(835\) 9.88925e15 0.843117
\(836\) −2.87608e16 −2.43594
\(837\) −2.89041e15 −0.243203
\(838\) 5.62755e15 0.470410
\(839\) 1.13665e16 0.943920 0.471960 0.881620i \(-0.343547\pi\)
0.471960 + 0.881620i \(0.343547\pi\)
\(840\) −2.02456e14 −0.0167030
\(841\) −1.11739e16 −0.915856
\(842\) −1.11254e16 −0.905942
\(843\) −4.70684e15 −0.380784
\(844\) −8.51534e15 −0.684413
\(845\) −6.13748e14 −0.0490093
\(846\) −2.32990e14 −0.0184842
\(847\) 4.48309e16 3.53361
\(848\) 1.51354e16 1.18527
\(849\) −1.38430e16 −1.07706
\(850\) 3.54453e15 0.274002
\(851\) 3.38549e16 2.60022
\(852\) 8.83909e15 0.674512
\(853\) −2.38523e16 −1.80847 −0.904235 0.427035i \(-0.859558\pi\)
−0.904235 + 0.427035i \(0.859558\pi\)
\(854\) −6.14175e16 −4.62672
\(855\) −5.72548e15 −0.428547
\(856\) −1.09081e14 −0.00811227
\(857\) −1.55491e16 −1.14897 −0.574486 0.818514i \(-0.694798\pi\)
−0.574486 + 0.818514i \(0.694798\pi\)
\(858\) 1.93569e16 1.42120
\(859\) 2.58000e16 1.88216 0.941080 0.338184i \(-0.109813\pi\)
0.941080 + 0.338184i \(0.109813\pi\)
\(860\) 3.81549e15 0.276572
\(861\) 2.44677e16 1.76228
\(862\) −7.30313e15 −0.522660
\(863\) 6.23324e15 0.443256 0.221628 0.975131i \(-0.428863\pi\)
0.221628 + 0.975131i \(0.428863\pi\)
\(864\) −3.86263e15 −0.272934
\(865\) 1.03432e16 0.726219
\(866\) −1.28643e16 −0.897507
\(867\) −7.28802e14 −0.0505248
\(868\) 3.53268e16 2.43358
\(869\) −2.09867e16 −1.43660
\(870\) −3.15226e15 −0.214421
\(871\) 1.11562e16 0.754076
\(872\) 1.37286e13 0.000922119 0
\(873\) −3.84138e15 −0.256394
\(874\) −5.38716e16 −3.57311
\(875\) 3.08912e16 2.03606
\(876\) 9.01248e15 0.590298
\(877\) 2.58853e16 1.68483 0.842413 0.538832i \(-0.181134\pi\)
0.842413 + 0.538832i \(0.181134\pi\)
\(878\) 3.17171e16 2.05151
\(879\) 1.08477e16 0.697265
\(880\) −2.35969e16 −1.50730
\(881\) −1.51066e16 −0.958955 −0.479478 0.877554i \(-0.659174\pi\)
−0.479478 + 0.877554i \(0.659174\pi\)
\(882\) −1.96505e16 −1.23964
\(883\) 1.59585e16 1.00048 0.500240 0.865887i \(-0.333245\pi\)
0.500240 + 0.865887i \(0.333245\pi\)
\(884\) −1.73905e16 −1.08349
\(885\) −1.09576e15 −0.0678466
\(886\) 1.23663e16 0.760945
\(887\) 7.58241e15 0.463690 0.231845 0.972753i \(-0.425524\pi\)
0.231845 + 0.972753i \(0.425524\pi\)
\(888\) 2.35208e14 0.0142949
\(889\) −3.48000e15 −0.210194
\(890\) 3.19059e16 1.91525
\(891\) −3.14789e15 −0.187799
\(892\) 1.97647e16 1.17188
\(893\) 9.44950e14 0.0556834
\(894\) 1.81354e16 1.06211
\(895\) 1.40609e16 0.818440
\(896\) 1.10799e15 0.0640975
\(897\) 1.82356e16 1.04848
\(898\) −4.61134e16 −2.63516
\(899\) 6.45419e15 0.366575
\(900\) −1.10682e15 −0.0624801
\(901\) −2.22981e16 −1.25107
\(902\) −6.89507e16 −3.84506
\(903\) 6.00287e15 0.332718
\(904\) 2.79249e13 0.00153839
\(905\) −1.23489e16 −0.676177
\(906\) 1.23825e16 0.673911
\(907\) 1.27789e16 0.691279 0.345639 0.938367i \(-0.387662\pi\)
0.345639 + 0.938367i \(0.387662\pi\)
\(908\) 2.03692e16 1.09522
\(909\) −5.07358e15 −0.271152
\(910\) −4.70969e16 −2.50187
\(911\) −2.17665e16 −1.14931 −0.574655 0.818396i \(-0.694864\pi\)
−0.574655 + 0.818396i \(0.694864\pi\)
\(912\) 1.54798e16 0.812447
\(913\) −7.83272e15 −0.408623
\(914\) −1.83590e16 −0.952018
\(915\) 1.73290e16 0.893220
\(916\) −1.01646e16 −0.520792
\(917\) −6.23300e16 −3.17443
\(918\) 5.62303e15 0.284666
\(919\) −1.17338e16 −0.590476 −0.295238 0.955424i \(-0.595399\pi\)
−0.295238 + 0.955424i \(0.595399\pi\)
\(920\) 5.37480e14 0.0268862
\(921\) −1.61980e16 −0.805438
\(922\) 1.80340e16 0.891399
\(923\) 2.41276e16 1.18551
\(924\) 3.84738e16 1.87918
\(925\) −5.60899e15 −0.272336
\(926\) 3.47485e16 1.67717
\(927\) −2.78333e15 −0.133544
\(928\) 8.62513e15 0.411388
\(929\) 3.02918e16 1.43628 0.718138 0.695900i \(-0.244995\pi\)
0.718138 + 0.695900i \(0.244995\pi\)
\(930\) −1.98181e16 −0.934125
\(931\) 7.96978e16 3.73442
\(932\) 2.86443e16 1.33429
\(933\) 1.66368e16 0.770409
\(934\) 2.14179e16 0.985980
\(935\) 3.47640e16 1.59099
\(936\) 1.26692e14 0.00576411
\(937\) −4.00930e16 −1.81343 −0.906715 0.421743i \(-0.861418\pi\)
−0.906715 + 0.421743i \(0.861418\pi\)
\(938\) 4.40878e16 1.98245
\(939\) −3.59821e15 −0.160852
\(940\) −8.03461e14 −0.0357077
\(941\) −1.61072e16 −0.711667 −0.355834 0.934549i \(-0.615803\pi\)
−0.355834 + 0.934549i \(0.615803\pi\)
\(942\) −2.63031e16 −1.15539
\(943\) −6.49566e16 −2.83667
\(944\) 2.96258e15 0.128625
\(945\) 7.65908e15 0.330599
\(946\) −1.69163e16 −0.725944
\(947\) −1.00119e16 −0.427162 −0.213581 0.976925i \(-0.568513\pi\)
−0.213581 + 0.976925i \(0.568513\pi\)
\(948\) −1.17061e16 −0.496553
\(949\) 2.46009e16 1.03750
\(950\) 8.92528e15 0.374233
\(951\) −2.02785e16 −0.845364
\(952\) −8.06421e14 −0.0334240
\(953\) 7.97340e15 0.328574 0.164287 0.986413i \(-0.447468\pi\)
0.164287 + 0.986413i \(0.447468\pi\)
\(954\) 1.38440e16 0.567210
\(955\) 6.35698e15 0.258960
\(956\) −4.76128e15 −0.192844
\(957\) 7.02914e15 0.283065
\(958\) −4.31651e16 −1.72831
\(959\) −4.36280e16 −1.73685
\(960\) −1.34765e16 −0.533440
\(961\) 1.51685e16 0.596987
\(962\) 5.47157e16 2.14116
\(963\) 4.12660e15 0.160564
\(964\) −8.99212e15 −0.347887
\(965\) −2.39727e16 −0.922184
\(966\) 7.20650e16 2.75645
\(967\) 1.81277e16 0.689440 0.344720 0.938706i \(-0.387974\pi\)
0.344720 + 0.938706i \(0.387974\pi\)
\(968\) −8.26869e14 −0.0312696
\(969\) −2.28056e16 −0.857553
\(970\) −2.63384e16 −0.984792
\(971\) −3.66253e16 −1.36168 −0.680841 0.732431i \(-0.738386\pi\)
−0.680841 + 0.732431i \(0.738386\pi\)
\(972\) −1.75585e15 −0.0649117
\(973\) 2.75471e16 1.01264
\(974\) 1.38879e16 0.507649
\(975\) −3.02122e15 −0.109814
\(976\) −4.68521e16 −1.69338
\(977\) 4.10970e16 1.47703 0.738516 0.674236i \(-0.235527\pi\)
0.738516 + 0.674236i \(0.235527\pi\)
\(978\) −9.89709e15 −0.353707
\(979\) −7.11461e16 −2.52840
\(980\) −6.77645e16 −2.39474
\(981\) −5.19365e14 −0.0182513
\(982\) −3.63684e16 −1.27090
\(983\) 3.22372e16 1.12024 0.560122 0.828410i \(-0.310754\pi\)
0.560122 + 0.828410i \(0.310754\pi\)
\(984\) −4.51287e14 −0.0155948
\(985\) 1.48746e16 0.511147
\(986\) −1.25560e16 −0.429072
\(987\) −1.26408e15 −0.0429565
\(988\) −4.37900e16 −1.47983
\(989\) −1.59364e16 −0.535562
\(990\) −2.15835e16 −0.721321
\(991\) −5.59817e15 −0.186055 −0.0930274 0.995664i \(-0.529654\pi\)
−0.0930274 + 0.995664i \(0.529654\pi\)
\(992\) 5.42255e16 1.79221
\(993\) 1.17121e16 0.384958
\(994\) 9.53495e16 3.11669
\(995\) 7.89538e15 0.256653
\(996\) −4.36898e15 −0.141239
\(997\) −4.95070e16 −1.59163 −0.795817 0.605538i \(-0.792958\pi\)
−0.795817 + 0.605538i \(0.792958\pi\)
\(998\) 2.95740e16 0.945567
\(999\) −8.89808e15 −0.282934
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.12.a.c.1.6 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.c.1.6 27 1.1 even 1 trivial