Properties

Label 177.10.a.b.1.4
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-28.8751 q^{2} -81.0000 q^{3} +321.769 q^{4} -2145.37 q^{5} +2338.88 q^{6} +2495.81 q^{7} +5492.93 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-28.8751 q^{2} -81.0000 q^{3} +321.769 q^{4} -2145.37 q^{5} +2338.88 q^{6} +2495.81 q^{7} +5492.93 q^{8} +6561.00 q^{9} +61947.6 q^{10} -24876.6 q^{11} -26063.3 q^{12} -127454. q^{13} -72066.7 q^{14} +173775. q^{15} -323354. q^{16} -424429. q^{17} -189449. q^{18} -308992. q^{19} -690313. q^{20} -202161. q^{21} +718312. q^{22} +1.81631e6 q^{23} -444928. q^{24} +2.64948e6 q^{25} +3.68025e6 q^{26} -531441. q^{27} +803074. q^{28} +3.84391e6 q^{29} -5.01776e6 q^{30} -9.38533e6 q^{31} +6.52450e6 q^{32} +2.01500e6 q^{33} +1.22554e7 q^{34} -5.35443e6 q^{35} +2.11113e6 q^{36} +4.96686e6 q^{37} +8.92215e6 q^{38} +1.03238e7 q^{39} -1.17844e7 q^{40} +1.21096e7 q^{41} +5.83740e6 q^{42} +2.79452e7 q^{43} -8.00450e6 q^{44} -1.40758e7 q^{45} -5.24460e7 q^{46} +1.69114e7 q^{47} +2.61917e7 q^{48} -3.41245e7 q^{49} -7.65039e7 q^{50} +3.43788e7 q^{51} -4.10108e7 q^{52} +8.66080e7 q^{53} +1.53454e7 q^{54} +5.33694e7 q^{55} +1.37093e7 q^{56} +2.50283e7 q^{57} -1.10993e8 q^{58} -1.21174e7 q^{59} +5.59153e7 q^{60} +7.59237e7 q^{61} +2.71002e8 q^{62} +1.63750e7 q^{63} -2.28377e7 q^{64} +2.73436e8 q^{65} -5.81833e7 q^{66} -1.33644e8 q^{67} -1.36568e8 q^{68} -1.47121e8 q^{69} +1.54610e8 q^{70} +1.85508e8 q^{71} +3.60391e7 q^{72} +1.90144e8 q^{73} -1.43418e8 q^{74} -2.14608e8 q^{75} -9.94239e7 q^{76} -6.20872e7 q^{77} -2.98100e8 q^{78} +3.35655e8 q^{79} +6.93714e8 q^{80} +4.30467e7 q^{81} -3.49666e8 q^{82} +2.69968e8 q^{83} -6.50490e7 q^{84} +9.10558e8 q^{85} -8.06920e8 q^{86} -3.11357e8 q^{87} -1.36645e8 q^{88} -6.99607e8 q^{89} +4.06438e8 q^{90} -3.18102e8 q^{91} +5.84432e8 q^{92} +7.60212e8 q^{93} -4.88318e8 q^{94} +6.62901e8 q^{95} -5.28484e8 q^{96} -1.03282e9 q^{97} +9.85348e8 q^{98} -1.63215e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −28.8751 −1.27611 −0.638055 0.769991i \(-0.720261\pi\)
−0.638055 + 0.769991i \(0.720261\pi\)
\(3\) −81.0000 −0.577350
\(4\) 321.769 0.628455
\(5\) −2145.37 −1.53510 −0.767550 0.640989i \(-0.778525\pi\)
−0.767550 + 0.640989i \(0.778525\pi\)
\(6\) 2338.88 0.736762
\(7\) 2495.81 0.392890 0.196445 0.980515i \(-0.437060\pi\)
0.196445 + 0.980515i \(0.437060\pi\)
\(8\) 5492.93 0.474132
\(9\) 6561.00 0.333333
\(10\) 61947.6 1.95896
\(11\) −24876.6 −0.512299 −0.256149 0.966637i \(-0.582454\pi\)
−0.256149 + 0.966637i \(0.582454\pi\)
\(12\) −26063.3 −0.362839
\(13\) −127454. −1.23768 −0.618841 0.785516i \(-0.712398\pi\)
−0.618841 + 0.785516i \(0.712398\pi\)
\(14\) −72066.7 −0.501370
\(15\) 173775. 0.886291
\(16\) −323354. −1.23350
\(17\) −424429. −1.23250 −0.616248 0.787552i \(-0.711348\pi\)
−0.616248 + 0.787552i \(0.711348\pi\)
\(18\) −189449. −0.425370
\(19\) −308992. −0.543945 −0.271973 0.962305i \(-0.587676\pi\)
−0.271973 + 0.962305i \(0.587676\pi\)
\(20\) −690313. −0.964742
\(21\) −202161. −0.226835
\(22\) 718312. 0.653749
\(23\) 1.81631e6 1.35336 0.676682 0.736276i \(-0.263417\pi\)
0.676682 + 0.736276i \(0.263417\pi\)
\(24\) −444928. −0.273740
\(25\) 2.64948e6 1.35653
\(26\) 3.68025e6 1.57942
\(27\) −531441. −0.192450
\(28\) 803074. 0.246913
\(29\) 3.84391e6 1.00921 0.504606 0.863350i \(-0.331638\pi\)
0.504606 + 0.863350i \(0.331638\pi\)
\(30\) −5.01776e6 −1.13100
\(31\) −9.38533e6 −1.82525 −0.912624 0.408799i \(-0.865948\pi\)
−0.912624 + 0.408799i \(0.865948\pi\)
\(32\) 6.52450e6 1.09995
\(33\) 2.01500e6 0.295776
\(34\) 1.22554e7 1.57280
\(35\) −5.35443e6 −0.603125
\(36\) 2.11113e6 0.209485
\(37\) 4.96686e6 0.435687 0.217843 0.975984i \(-0.430098\pi\)
0.217843 + 0.975984i \(0.430098\pi\)
\(38\) 8.92215e6 0.694134
\(39\) 1.03238e7 0.714577
\(40\) −1.17844e7 −0.727841
\(41\) 1.21096e7 0.669273 0.334637 0.942347i \(-0.391386\pi\)
0.334637 + 0.942347i \(0.391386\pi\)
\(42\) 5.83740e6 0.289466
\(43\) 2.79452e7 1.24652 0.623261 0.782014i \(-0.285808\pi\)
0.623261 + 0.782014i \(0.285808\pi\)
\(44\) −8.00450e6 −0.321957
\(45\) −1.40758e7 −0.511700
\(46\) −5.24460e7 −1.72704
\(47\) 1.69114e7 0.505521 0.252761 0.967529i \(-0.418662\pi\)
0.252761 + 0.967529i \(0.418662\pi\)
\(48\) 2.61917e7 0.712161
\(49\) −3.41245e7 −0.845638
\(50\) −7.65039e7 −1.73109
\(51\) 3.43788e7 0.711582
\(52\) −4.10108e7 −0.777828
\(53\) 8.66080e7 1.50771 0.753853 0.657043i \(-0.228193\pi\)
0.753853 + 0.657043i \(0.228193\pi\)
\(54\) 1.53454e7 0.245587
\(55\) 5.33694e7 0.786430
\(56\) 1.37093e7 0.186282
\(57\) 2.50283e7 0.314047
\(58\) −1.10993e8 −1.28787
\(59\) −1.21174e7 −0.130189
\(60\) 5.59153e7 0.556994
\(61\) 7.59237e7 0.702091 0.351045 0.936358i \(-0.385826\pi\)
0.351045 + 0.936358i \(0.385826\pi\)
\(62\) 2.71002e8 2.32922
\(63\) 1.63750e7 0.130963
\(64\) −2.28377e7 −0.170154
\(65\) 2.73436e8 1.89997
\(66\) −5.81833e7 −0.377442
\(67\) −1.33644e8 −0.810239 −0.405119 0.914264i \(-0.632770\pi\)
−0.405119 + 0.914264i \(0.632770\pi\)
\(68\) −1.36568e8 −0.774568
\(69\) −1.47121e8 −0.781365
\(70\) 1.54610e8 0.769653
\(71\) 1.85508e8 0.866362 0.433181 0.901307i \(-0.357391\pi\)
0.433181 + 0.901307i \(0.357391\pi\)
\(72\) 3.60391e7 0.158044
\(73\) 1.90144e8 0.783665 0.391832 0.920037i \(-0.371841\pi\)
0.391832 + 0.920037i \(0.371841\pi\)
\(74\) −1.43418e8 −0.555984
\(75\) −2.14608e8 −0.783195
\(76\) −9.94239e7 −0.341845
\(77\) −6.20872e7 −0.201277
\(78\) −2.98100e8 −0.911878
\(79\) 3.35655e8 0.969551 0.484775 0.874639i \(-0.338901\pi\)
0.484775 + 0.874639i \(0.338901\pi\)
\(80\) 6.93714e8 1.89355
\(81\) 4.30467e7 0.111111
\(82\) −3.49666e8 −0.854066
\(83\) 2.69968e8 0.624396 0.312198 0.950017i \(-0.398935\pi\)
0.312198 + 0.950017i \(0.398935\pi\)
\(84\) −6.50490e7 −0.142555
\(85\) 9.10558e8 1.89200
\(86\) −8.06920e8 −1.59070
\(87\) −3.11357e8 −0.582669
\(88\) −1.36645e8 −0.242897
\(89\) −6.99607e8 −1.18195 −0.590975 0.806690i \(-0.701257\pi\)
−0.590975 + 0.806690i \(0.701257\pi\)
\(90\) 4.06438e8 0.652985
\(91\) −3.18102e8 −0.486273
\(92\) 5.84432e8 0.850528
\(93\) 7.60212e8 1.05381
\(94\) −4.88318e8 −0.645100
\(95\) 6.62901e8 0.835011
\(96\) −5.28484e8 −0.635055
\(97\) −1.03282e9 −1.18455 −0.592274 0.805737i \(-0.701770\pi\)
−0.592274 + 0.805737i \(0.701770\pi\)
\(98\) 9.85348e8 1.07913
\(99\) −1.63215e8 −0.170766
\(100\) 8.52521e8 0.852521
\(101\) 1.90296e9 1.81963 0.909816 0.415011i \(-0.136222\pi\)
0.909816 + 0.415011i \(0.136222\pi\)
\(102\) −9.92689e8 −0.908056
\(103\) 6.73363e8 0.589497 0.294749 0.955575i \(-0.404764\pi\)
0.294749 + 0.955575i \(0.404764\pi\)
\(104\) −7.00098e8 −0.586825
\(105\) 4.33709e8 0.348214
\(106\) −2.50081e9 −1.92400
\(107\) −2.71347e8 −0.200123 −0.100062 0.994981i \(-0.531904\pi\)
−0.100062 + 0.994981i \(0.531904\pi\)
\(108\) −1.71001e8 −0.120946
\(109\) −2.15836e9 −1.46455 −0.732275 0.681009i \(-0.761541\pi\)
−0.732275 + 0.681009i \(0.761541\pi\)
\(110\) −1.54104e9 −1.00357
\(111\) −4.02316e8 −0.251544
\(112\) −8.07032e8 −0.484629
\(113\) −1.84597e9 −1.06505 −0.532526 0.846414i \(-0.678757\pi\)
−0.532526 + 0.846414i \(0.678757\pi\)
\(114\) −7.22694e8 −0.400758
\(115\) −3.89665e9 −2.07755
\(116\) 1.23685e9 0.634244
\(117\) −8.36228e8 −0.412561
\(118\) 3.49889e8 0.166135
\(119\) −1.05930e9 −0.484235
\(120\) 9.54534e8 0.420219
\(121\) −1.73910e9 −0.737550
\(122\) −2.19230e9 −0.895944
\(123\) −9.80880e8 −0.386405
\(124\) −3.01991e9 −1.14709
\(125\) −1.49394e9 −0.547316
\(126\) −4.72829e8 −0.167123
\(127\) 8.70427e8 0.296904 0.148452 0.988920i \(-0.452571\pi\)
0.148452 + 0.988920i \(0.452571\pi\)
\(128\) −2.68110e9 −0.882812
\(129\) −2.26356e9 −0.719680
\(130\) −7.89549e9 −2.42457
\(131\) 5.81452e9 1.72502 0.862509 0.506043i \(-0.168892\pi\)
0.862509 + 0.506043i \(0.168892\pi\)
\(132\) 6.48365e8 0.185882
\(133\) −7.71184e8 −0.213710
\(134\) 3.85898e9 1.03395
\(135\) 1.14014e9 0.295430
\(136\) −2.33136e9 −0.584366
\(137\) −2.92848e9 −0.710232 −0.355116 0.934822i \(-0.615559\pi\)
−0.355116 + 0.934822i \(0.615559\pi\)
\(138\) 4.24813e9 0.997107
\(139\) 8.65126e9 1.96568 0.982840 0.184460i \(-0.0590535\pi\)
0.982840 + 0.184460i \(0.0590535\pi\)
\(140\) −1.72289e9 −0.379037
\(141\) −1.36982e9 −0.291863
\(142\) −5.35655e9 −1.10557
\(143\) 3.17062e9 0.634063
\(144\) −2.12153e9 −0.411166
\(145\) −8.24661e9 −1.54924
\(146\) −5.49043e9 −1.00004
\(147\) 2.76409e9 0.488229
\(148\) 1.59818e9 0.273810
\(149\) −7.39405e9 −1.22898 −0.614489 0.788925i \(-0.710638\pi\)
−0.614489 + 0.788925i \(0.710638\pi\)
\(150\) 6.19682e9 0.999443
\(151\) 9.23263e9 1.44520 0.722602 0.691264i \(-0.242946\pi\)
0.722602 + 0.691264i \(0.242946\pi\)
\(152\) −1.69727e9 −0.257902
\(153\) −2.78468e9 −0.410832
\(154\) 1.79277e9 0.256851
\(155\) 2.01350e10 2.80194
\(156\) 3.32188e9 0.449079
\(157\) 1.28742e10 1.69112 0.845558 0.533884i \(-0.179268\pi\)
0.845558 + 0.533884i \(0.179268\pi\)
\(158\) −9.69204e9 −1.23725
\(159\) −7.01525e9 −0.870474
\(160\) −1.39974e10 −1.68853
\(161\) 4.53316e9 0.531722
\(162\) −1.24298e9 −0.141790
\(163\) −1.19819e10 −1.32948 −0.664738 0.747076i \(-0.731457\pi\)
−0.664738 + 0.747076i \(0.731457\pi\)
\(164\) 3.89650e9 0.420608
\(165\) −4.32292e9 −0.454045
\(166\) −7.79533e9 −0.796798
\(167\) −8.91356e9 −0.886802 −0.443401 0.896323i \(-0.646228\pi\)
−0.443401 + 0.896323i \(0.646228\pi\)
\(168\) −1.11046e9 −0.107550
\(169\) 5.64010e9 0.531859
\(170\) −2.62924e10 −2.41441
\(171\) −2.02729e9 −0.181315
\(172\) 8.99191e9 0.783383
\(173\) −1.85349e10 −1.57319 −0.786597 0.617466i \(-0.788159\pi\)
−0.786597 + 0.617466i \(0.788159\pi\)
\(174\) 8.99045e9 0.743549
\(175\) 6.61260e9 0.532968
\(176\) 8.04394e9 0.631920
\(177\) 9.81506e8 0.0751646
\(178\) 2.02012e10 1.50830
\(179\) −7.71197e9 −0.561470 −0.280735 0.959785i \(-0.590578\pi\)
−0.280735 + 0.959785i \(0.590578\pi\)
\(180\) −4.52914e9 −0.321581
\(181\) −1.43389e10 −0.993029 −0.496515 0.868028i \(-0.665387\pi\)
−0.496515 + 0.868028i \(0.665387\pi\)
\(182\) 9.18521e9 0.620537
\(183\) −6.14982e9 −0.405352
\(184\) 9.97686e9 0.641673
\(185\) −1.06558e10 −0.668823
\(186\) −2.19512e10 −1.34477
\(187\) 1.05583e10 0.631406
\(188\) 5.44156e9 0.317697
\(189\) −1.32638e9 −0.0756116
\(190\) −1.91413e10 −1.06557
\(191\) 2.32825e9 0.126584 0.0632920 0.997995i \(-0.479840\pi\)
0.0632920 + 0.997995i \(0.479840\pi\)
\(192\) 1.84986e9 0.0982386
\(193\) 3.88900e9 0.201757 0.100879 0.994899i \(-0.467835\pi\)
0.100879 + 0.994899i \(0.467835\pi\)
\(194\) 2.98228e10 1.51161
\(195\) −2.21484e10 −1.09695
\(196\) −1.09802e10 −0.531445
\(197\) 1.83164e10 0.866448 0.433224 0.901286i \(-0.357376\pi\)
0.433224 + 0.901286i \(0.357376\pi\)
\(198\) 4.71284e9 0.217916
\(199\) −2.09392e10 −0.946502 −0.473251 0.880928i \(-0.656920\pi\)
−0.473251 + 0.880928i \(0.656920\pi\)
\(200\) 1.45534e10 0.643176
\(201\) 1.08252e10 0.467792
\(202\) −5.49481e10 −2.32205
\(203\) 9.59368e9 0.396509
\(204\) 1.10620e10 0.447197
\(205\) −2.59796e10 −1.02740
\(206\) −1.94434e10 −0.752263
\(207\) 1.19168e10 0.451121
\(208\) 4.12129e10 1.52668
\(209\) 7.68664e9 0.278662
\(210\) −1.25234e10 −0.444360
\(211\) −2.12442e10 −0.737854 −0.368927 0.929458i \(-0.620275\pi\)
−0.368927 + 0.929458i \(0.620275\pi\)
\(212\) 2.78678e10 0.947525
\(213\) −1.50261e10 −0.500194
\(214\) 7.83516e9 0.255379
\(215\) −5.99528e10 −1.91354
\(216\) −2.91917e9 −0.0912468
\(217\) −2.34240e10 −0.717121
\(218\) 6.23227e10 1.86893
\(219\) −1.54017e10 −0.452449
\(220\) 1.71726e10 0.494236
\(221\) 5.40954e10 1.52544
\(222\) 1.16169e10 0.320997
\(223\) −1.84899e9 −0.0500682 −0.0250341 0.999687i \(-0.507969\pi\)
−0.0250341 + 0.999687i \(0.507969\pi\)
\(224\) 1.62839e10 0.432158
\(225\) 1.73832e10 0.452178
\(226\) 5.33024e10 1.35912
\(227\) −1.97800e10 −0.494436 −0.247218 0.968960i \(-0.579516\pi\)
−0.247218 + 0.968960i \(0.579516\pi\)
\(228\) 8.05333e9 0.197364
\(229\) −6.46436e9 −0.155334 −0.0776669 0.996979i \(-0.524747\pi\)
−0.0776669 + 0.996979i \(0.524747\pi\)
\(230\) 1.12516e11 2.65118
\(231\) 5.02906e9 0.116207
\(232\) 2.11144e10 0.478500
\(233\) 7.12636e10 1.58404 0.792020 0.610496i \(-0.209030\pi\)
0.792020 + 0.610496i \(0.209030\pi\)
\(234\) 2.41461e10 0.526473
\(235\) −3.62812e10 −0.776026
\(236\) −3.89899e9 −0.0818179
\(237\) −2.71880e10 −0.559770
\(238\) 3.05872e10 0.617936
\(239\) 2.07424e10 0.411214 0.205607 0.978635i \(-0.434083\pi\)
0.205607 + 0.978635i \(0.434083\pi\)
\(240\) −5.61909e10 −1.09324
\(241\) −5.49231e10 −1.04877 −0.524383 0.851483i \(-0.675704\pi\)
−0.524383 + 0.851483i \(0.675704\pi\)
\(242\) 5.02167e10 0.941195
\(243\) −3.48678e9 −0.0641500
\(244\) 2.44299e10 0.441232
\(245\) 7.32097e10 1.29814
\(246\) 2.83230e10 0.493095
\(247\) 3.93823e10 0.673232
\(248\) −5.15530e10 −0.865409
\(249\) −2.18674e10 −0.360495
\(250\) 4.31376e10 0.698435
\(251\) 4.13636e10 0.657790 0.328895 0.944367i \(-0.393324\pi\)
0.328895 + 0.944367i \(0.393324\pi\)
\(252\) 5.26897e9 0.0823045
\(253\) −4.51835e10 −0.693326
\(254\) −2.51336e10 −0.378882
\(255\) −7.37552e10 −1.09235
\(256\) 8.91099e10 1.29672
\(257\) 1.00135e11 1.43182 0.715909 0.698194i \(-0.246013\pi\)
0.715909 + 0.698194i \(0.246013\pi\)
\(258\) 6.53606e10 0.918390
\(259\) 1.23963e10 0.171177
\(260\) 8.79833e10 1.19404
\(261\) 2.52199e10 0.336404
\(262\) −1.67895e11 −2.20131
\(263\) 8.01086e10 1.03247 0.516236 0.856446i \(-0.327333\pi\)
0.516236 + 0.856446i \(0.327333\pi\)
\(264\) 1.10683e10 0.140237
\(265\) −1.85806e11 −2.31448
\(266\) 2.22680e10 0.272718
\(267\) 5.66681e10 0.682399
\(268\) −4.30025e10 −0.509199
\(269\) 1.75676e10 0.204564 0.102282 0.994755i \(-0.467386\pi\)
0.102282 + 0.994755i \(0.467386\pi\)
\(270\) −3.29215e10 −0.377001
\(271\) 1.56167e11 1.75884 0.879421 0.476044i \(-0.157930\pi\)
0.879421 + 0.476044i \(0.157930\pi\)
\(272\) 1.37241e11 1.52028
\(273\) 2.57662e10 0.280750
\(274\) 8.45601e10 0.906334
\(275\) −6.59099e10 −0.694950
\(276\) −4.73390e10 −0.491053
\(277\) −8.99338e10 −0.917834 −0.458917 0.888479i \(-0.651762\pi\)
−0.458917 + 0.888479i \(0.651762\pi\)
\(278\) −2.49806e11 −2.50842
\(279\) −6.15772e10 −0.608416
\(280\) −2.94115e10 −0.285961
\(281\) −2.14664e10 −0.205390 −0.102695 0.994713i \(-0.532747\pi\)
−0.102695 + 0.994713i \(0.532747\pi\)
\(282\) 3.95537e10 0.372449
\(283\) −2.84051e10 −0.263244 −0.131622 0.991300i \(-0.542018\pi\)
−0.131622 + 0.991300i \(0.542018\pi\)
\(284\) 5.96906e10 0.544470
\(285\) −5.36950e10 −0.482094
\(286\) −9.15519e10 −0.809134
\(287\) 3.02233e10 0.262950
\(288\) 4.28072e10 0.366649
\(289\) 6.15525e10 0.519046
\(290\) 2.38121e11 1.97700
\(291\) 8.36586e10 0.683899
\(292\) 6.11825e10 0.492498
\(293\) −4.46352e10 −0.353812 −0.176906 0.984228i \(-0.556609\pi\)
−0.176906 + 0.984228i \(0.556609\pi\)
\(294\) −7.98132e10 −0.623034
\(295\) 2.59962e10 0.199853
\(296\) 2.72826e10 0.206573
\(297\) 1.32204e10 0.0985919
\(298\) 2.13504e11 1.56831
\(299\) −2.31496e11 −1.67503
\(300\) −6.90542e10 −0.492203
\(301\) 6.97460e10 0.489745
\(302\) −2.66593e11 −1.84424
\(303\) −1.54140e11 −1.05057
\(304\) 9.99138e10 0.670956
\(305\) −1.62884e11 −1.07778
\(306\) 8.04078e10 0.524266
\(307\) −1.50592e11 −0.967561 −0.483780 0.875189i \(-0.660737\pi\)
−0.483780 + 0.875189i \(0.660737\pi\)
\(308\) −1.99777e10 −0.126493
\(309\) −5.45424e10 −0.340346
\(310\) −5.81399e11 −3.57558
\(311\) −2.21225e11 −1.34095 −0.670475 0.741932i \(-0.733910\pi\)
−0.670475 + 0.741932i \(0.733910\pi\)
\(312\) 5.67079e10 0.338804
\(313\) −2.23702e11 −1.31741 −0.658703 0.752403i \(-0.728895\pi\)
−0.658703 + 0.752403i \(0.728895\pi\)
\(314\) −3.71745e11 −2.15805
\(315\) −3.51304e10 −0.201042
\(316\) 1.08003e11 0.609319
\(317\) 2.00323e11 1.11420 0.557101 0.830445i \(-0.311914\pi\)
0.557101 + 0.830445i \(0.311914\pi\)
\(318\) 2.02566e11 1.11082
\(319\) −9.56233e10 −0.517018
\(320\) 4.89953e10 0.261204
\(321\) 2.19791e10 0.115541
\(322\) −1.30895e11 −0.678536
\(323\) 1.31145e11 0.670410
\(324\) 1.38511e10 0.0698283
\(325\) −3.37688e11 −1.67896
\(326\) 3.45977e11 1.69656
\(327\) 1.74827e11 0.845558
\(328\) 6.65174e10 0.317324
\(329\) 4.22077e10 0.198614
\(330\) 1.24825e11 0.579412
\(331\) 7.85931e10 0.359881 0.179940 0.983678i \(-0.442410\pi\)
0.179940 + 0.983678i \(0.442410\pi\)
\(332\) 8.68672e10 0.392405
\(333\) 3.25876e10 0.145229
\(334\) 2.57379e11 1.13166
\(335\) 2.86716e11 1.24380
\(336\) 6.53696e10 0.279801
\(337\) −1.96954e11 −0.831820 −0.415910 0.909406i \(-0.636537\pi\)
−0.415910 + 0.909406i \(0.636537\pi\)
\(338\) −1.62858e11 −0.678710
\(339\) 1.49523e11 0.614908
\(340\) 2.92989e11 1.18904
\(341\) 2.33475e11 0.935072
\(342\) 5.85382e10 0.231378
\(343\) −1.85883e11 −0.725132
\(344\) 1.53501e11 0.591016
\(345\) 3.15629e11 1.19947
\(346\) 5.35196e11 2.00757
\(347\) 2.76771e11 1.02480 0.512398 0.858748i \(-0.328757\pi\)
0.512398 + 0.858748i \(0.328757\pi\)
\(348\) −1.00185e11 −0.366181
\(349\) −2.39031e11 −0.862462 −0.431231 0.902241i \(-0.641921\pi\)
−0.431231 + 0.902241i \(0.641921\pi\)
\(350\) −1.90939e11 −0.680125
\(351\) 6.77344e10 0.238192
\(352\) −1.62307e11 −0.563502
\(353\) 1.52600e11 0.523082 0.261541 0.965192i \(-0.415769\pi\)
0.261541 + 0.965192i \(0.415769\pi\)
\(354\) −2.83410e10 −0.0959182
\(355\) −3.97982e11 −1.32995
\(356\) −2.25112e11 −0.742802
\(357\) 8.58030e10 0.279573
\(358\) 2.22683e11 0.716497
\(359\) 3.26001e11 1.03584 0.517922 0.855428i \(-0.326706\pi\)
0.517922 + 0.855428i \(0.326706\pi\)
\(360\) −7.73172e10 −0.242614
\(361\) −2.27212e11 −0.704123
\(362\) 4.14036e11 1.26721
\(363\) 1.40867e11 0.425825
\(364\) −1.02355e11 −0.305600
\(365\) −4.07929e11 −1.20300
\(366\) 1.77576e11 0.517274
\(367\) −1.42428e11 −0.409824 −0.204912 0.978780i \(-0.565691\pi\)
−0.204912 + 0.978780i \(0.565691\pi\)
\(368\) −5.87312e11 −1.66937
\(369\) 7.94513e10 0.223091
\(370\) 3.07685e11 0.853491
\(371\) 2.16157e11 0.592362
\(372\) 2.44613e11 0.662271
\(373\) 5.12349e11 1.37049 0.685245 0.728312i \(-0.259695\pi\)
0.685245 + 0.728312i \(0.259695\pi\)
\(374\) −3.04873e11 −0.805743
\(375\) 1.21009e11 0.315993
\(376\) 9.28932e10 0.239684
\(377\) −4.89923e11 −1.24908
\(378\) 3.82992e10 0.0964887
\(379\) 2.89650e11 0.721103 0.360552 0.932739i \(-0.382588\pi\)
0.360552 + 0.932739i \(0.382588\pi\)
\(380\) 2.13301e11 0.524767
\(381\) −7.05046e10 −0.171418
\(382\) −6.72283e10 −0.161535
\(383\) −5.19188e11 −1.23291 −0.616454 0.787391i \(-0.711431\pi\)
−0.616454 + 0.787391i \(0.711431\pi\)
\(384\) 2.17169e11 0.509692
\(385\) 1.33200e11 0.308980
\(386\) −1.12295e11 −0.257465
\(387\) 1.83349e11 0.415507
\(388\) −3.32330e11 −0.744435
\(389\) 1.76986e11 0.391892 0.195946 0.980615i \(-0.437222\pi\)
0.195946 + 0.980615i \(0.437222\pi\)
\(390\) 6.39535e11 1.39982
\(391\) −7.70895e11 −1.66801
\(392\) −1.87444e11 −0.400944
\(393\) −4.70976e11 −0.995939
\(394\) −5.28887e11 −1.10568
\(395\) −7.20103e11 −1.48836
\(396\) −5.25175e10 −0.107319
\(397\) −2.90776e11 −0.587491 −0.293746 0.955884i \(-0.594902\pi\)
−0.293746 + 0.955884i \(0.594902\pi\)
\(398\) 6.04621e11 1.20784
\(399\) 6.24659e10 0.123386
\(400\) −8.56721e11 −1.67328
\(401\) −3.96976e11 −0.766681 −0.383340 0.923607i \(-0.625226\pi\)
−0.383340 + 0.923607i \(0.625226\pi\)
\(402\) −3.12577e11 −0.596953
\(403\) 1.19620e12 2.25908
\(404\) 6.12314e11 1.14356
\(405\) −9.23511e10 −0.170567
\(406\) −2.77018e11 −0.505989
\(407\) −1.23558e11 −0.223202
\(408\) 1.88840e11 0.337384
\(409\) −5.48005e11 −0.968345 −0.484172 0.874973i \(-0.660879\pi\)
−0.484172 + 0.874973i \(0.660879\pi\)
\(410\) 7.50163e11 1.31108
\(411\) 2.37207e11 0.410053
\(412\) 2.16667e11 0.370472
\(413\) −3.02426e10 −0.0511499
\(414\) −3.44098e11 −0.575680
\(415\) −5.79180e11 −0.958511
\(416\) −8.31575e11 −1.36139
\(417\) −7.00752e11 −1.13489
\(418\) −2.21952e11 −0.355604
\(419\) −3.05974e10 −0.0484977 −0.0242489 0.999706i \(-0.507719\pi\)
−0.0242489 + 0.999706i \(0.507719\pi\)
\(420\) 1.39554e11 0.218837
\(421\) 8.42996e11 1.30784 0.653922 0.756562i \(-0.273122\pi\)
0.653922 + 0.756562i \(0.273122\pi\)
\(422\) 6.13429e11 0.941582
\(423\) 1.10956e11 0.168507
\(424\) 4.75732e11 0.714852
\(425\) −1.12452e12 −1.67192
\(426\) 4.33880e11 0.638303
\(427\) 1.89491e11 0.275844
\(428\) −8.73110e10 −0.125768
\(429\) −2.56821e11 −0.366077
\(430\) 1.73114e12 2.44188
\(431\) −1.24571e12 −1.73887 −0.869436 0.494045i \(-0.835518\pi\)
−0.869436 + 0.494045i \(0.835518\pi\)
\(432\) 1.71844e11 0.237387
\(433\) −2.52602e11 −0.345336 −0.172668 0.984980i \(-0.555239\pi\)
−0.172668 + 0.984980i \(0.555239\pi\)
\(434\) 6.76370e11 0.915125
\(435\) 6.67975e11 0.894455
\(436\) −6.94492e11 −0.920403
\(437\) −5.61224e11 −0.736156
\(438\) 4.44724e11 0.577374
\(439\) 5.17671e11 0.665217 0.332608 0.943065i \(-0.392071\pi\)
0.332608 + 0.943065i \(0.392071\pi\)
\(440\) 2.93154e11 0.372872
\(441\) −2.23891e11 −0.281879
\(442\) −1.56201e12 −1.94663
\(443\) −4.19015e11 −0.516907 −0.258454 0.966024i \(-0.583213\pi\)
−0.258454 + 0.966024i \(0.583213\pi\)
\(444\) −1.29453e11 −0.158084
\(445\) 1.50091e12 1.81441
\(446\) 5.33896e10 0.0638925
\(447\) 5.98918e11 0.709551
\(448\) −5.69986e10 −0.0668518
\(449\) −2.16167e11 −0.251005 −0.125502 0.992093i \(-0.540054\pi\)
−0.125502 + 0.992093i \(0.540054\pi\)
\(450\) −5.01942e11 −0.577029
\(451\) −3.01246e11 −0.342868
\(452\) −5.93975e11 −0.669337
\(453\) −7.47843e11 −0.834389
\(454\) 5.71149e11 0.630955
\(455\) 6.82446e11 0.746478
\(456\) 1.37479e11 0.148900
\(457\) 2.39408e11 0.256753 0.128376 0.991726i \(-0.459023\pi\)
0.128376 + 0.991726i \(0.459023\pi\)
\(458\) 1.86659e11 0.198223
\(459\) 2.25559e11 0.237194
\(460\) −1.25382e12 −1.30565
\(461\) −1.01109e12 −1.04265 −0.521324 0.853359i \(-0.674562\pi\)
−0.521324 + 0.853359i \(0.674562\pi\)
\(462\) −1.45214e11 −0.148293
\(463\) −7.32065e11 −0.740347 −0.370173 0.928963i \(-0.620702\pi\)
−0.370173 + 0.928963i \(0.620702\pi\)
\(464\) −1.24295e12 −1.24486
\(465\) −1.63093e12 −1.61770
\(466\) −2.05774e12 −2.02141
\(467\) 7.33171e11 0.713311 0.356656 0.934236i \(-0.383917\pi\)
0.356656 + 0.934236i \(0.383917\pi\)
\(468\) −2.69072e11 −0.259276
\(469\) −3.33550e11 −0.318334
\(470\) 1.04762e12 0.990294
\(471\) −1.04281e12 −0.976366
\(472\) −6.65599e10 −0.0617267
\(473\) −6.95181e11 −0.638591
\(474\) 7.85056e11 0.714328
\(475\) −8.18667e11 −0.737881
\(476\) −3.40848e11 −0.304320
\(477\) 5.68235e11 0.502569
\(478\) −5.98937e11 −0.524754
\(479\) 1.02765e11 0.0891937 0.0445968 0.999005i \(-0.485800\pi\)
0.0445968 + 0.999005i \(0.485800\pi\)
\(480\) 1.13379e12 0.974874
\(481\) −6.33048e11 −0.539242
\(482\) 1.58591e12 1.33834
\(483\) −3.67186e11 −0.306990
\(484\) −5.59590e11 −0.463517
\(485\) 2.21578e12 1.81840
\(486\) 1.00681e11 0.0818624
\(487\) 1.47685e12 1.18975 0.594875 0.803818i \(-0.297202\pi\)
0.594875 + 0.803818i \(0.297202\pi\)
\(488\) 4.17044e11 0.332884
\(489\) 9.70532e11 0.767574
\(490\) −2.11393e12 −1.65657
\(491\) −7.36405e10 −0.0571808 −0.0285904 0.999591i \(-0.509102\pi\)
−0.0285904 + 0.999591i \(0.509102\pi\)
\(492\) −3.15617e11 −0.242838
\(493\) −1.63147e12 −1.24385
\(494\) −1.13717e12 −0.859118
\(495\) 3.50156e11 0.262143
\(496\) 3.03479e12 2.25144
\(497\) 4.62992e11 0.340385
\(498\) 6.31422e11 0.460031
\(499\) 9.28531e11 0.670415 0.335208 0.942144i \(-0.391194\pi\)
0.335208 + 0.942144i \(0.391194\pi\)
\(500\) −4.80703e11 −0.343963
\(501\) 7.21998e11 0.511996
\(502\) −1.19438e12 −0.839411
\(503\) 9.47552e11 0.660005 0.330003 0.943980i \(-0.392950\pi\)
0.330003 + 0.943980i \(0.392950\pi\)
\(504\) 8.99469e10 0.0620939
\(505\) −4.08255e12 −2.79332
\(506\) 1.30468e12 0.884760
\(507\) −4.56848e11 −0.307069
\(508\) 2.80076e11 0.186591
\(509\) −2.25243e12 −1.48738 −0.743690 0.668525i \(-0.766926\pi\)
−0.743690 + 0.668525i \(0.766926\pi\)
\(510\) 2.12968e12 1.39396
\(511\) 4.74564e11 0.307894
\(512\) −1.20033e12 −0.771943
\(513\) 1.64211e11 0.104682
\(514\) −2.89141e12 −1.82716
\(515\) −1.44461e12 −0.904937
\(516\) −7.28345e11 −0.452286
\(517\) −4.20697e11 −0.258978
\(518\) −3.57945e11 −0.218440
\(519\) 1.50133e12 0.908284
\(520\) 1.50197e12 0.900836
\(521\) −2.15025e12 −1.27856 −0.639278 0.768975i \(-0.720767\pi\)
−0.639278 + 0.768975i \(0.720767\pi\)
\(522\) −7.28226e11 −0.429288
\(523\) −6.92824e11 −0.404916 −0.202458 0.979291i \(-0.564893\pi\)
−0.202458 + 0.979291i \(0.564893\pi\)
\(524\) 1.87093e12 1.08410
\(525\) −5.35621e11 −0.307709
\(526\) −2.31314e12 −1.31755
\(527\) 3.98341e12 2.24961
\(528\) −6.51559e11 −0.364839
\(529\) 1.49783e12 0.831593
\(530\) 5.36516e12 2.95353
\(531\) −7.95020e10 −0.0433963
\(532\) −2.48143e11 −0.134307
\(533\) −1.54342e12 −0.828348
\(534\) −1.63630e12 −0.870815
\(535\) 5.82139e11 0.307209
\(536\) −7.34098e11 −0.384160
\(537\) 6.24669e11 0.324165
\(538\) −5.07267e11 −0.261045
\(539\) 8.48901e11 0.433219
\(540\) 3.66861e11 0.185665
\(541\) 3.05316e12 1.53236 0.766182 0.642624i \(-0.222154\pi\)
0.766182 + 0.642624i \(0.222154\pi\)
\(542\) −4.50933e12 −2.24448
\(543\) 1.16145e12 0.573326
\(544\) −2.76919e12 −1.35568
\(545\) 4.63047e12 2.24823
\(546\) −7.44002e11 −0.358267
\(547\) −3.73886e12 −1.78565 −0.892824 0.450405i \(-0.851280\pi\)
−0.892824 + 0.450405i \(0.851280\pi\)
\(548\) −9.42295e11 −0.446349
\(549\) 4.98136e11 0.234030
\(550\) 1.90315e12 0.886833
\(551\) −1.18774e12 −0.548956
\(552\) −8.08126e11 −0.370470
\(553\) 8.37730e11 0.380926
\(554\) 2.59684e12 1.17126
\(555\) 8.63116e11 0.386145
\(556\) 2.78371e12 1.23534
\(557\) −2.05598e12 −0.905047 −0.452523 0.891753i \(-0.649476\pi\)
−0.452523 + 0.891753i \(0.649476\pi\)
\(558\) 1.77804e12 0.776406
\(559\) −3.56174e12 −1.54280
\(560\) 1.73138e12 0.743954
\(561\) −8.55226e11 −0.364542
\(562\) 6.19842e11 0.262100
\(563\) −4.25676e10 −0.0178563 −0.00892816 0.999960i \(-0.502842\pi\)
−0.00892816 + 0.999960i \(0.502842\pi\)
\(564\) −4.40767e11 −0.183423
\(565\) 3.96028e12 1.63496
\(566\) 8.20200e11 0.335928
\(567\) 1.07436e11 0.0436544
\(568\) 1.01898e12 0.410770
\(569\) −1.17769e12 −0.471003 −0.235502 0.971874i \(-0.575673\pi\)
−0.235502 + 0.971874i \(0.575673\pi\)
\(570\) 1.55044e12 0.615204
\(571\) 1.96003e12 0.771613 0.385807 0.922580i \(-0.373923\pi\)
0.385807 + 0.922580i \(0.373923\pi\)
\(572\) 1.02021e12 0.398480
\(573\) −1.88588e11 −0.0730833
\(574\) −8.72700e11 −0.335553
\(575\) 4.81228e12 1.83588
\(576\) −1.49838e11 −0.0567181
\(577\) −3.04676e12 −1.14432 −0.572159 0.820143i \(-0.693894\pi\)
−0.572159 + 0.820143i \(0.693894\pi\)
\(578\) −1.77733e12 −0.662359
\(579\) −3.15009e11 −0.116485
\(580\) −2.65350e12 −0.973629
\(581\) 6.73788e11 0.245319
\(582\) −2.41565e12 −0.872730
\(583\) −2.15451e12 −0.772395
\(584\) 1.04445e12 0.371561
\(585\) 1.79402e12 0.633323
\(586\) 1.28884e12 0.451503
\(587\) 1.93677e12 0.673297 0.336649 0.941630i \(-0.390707\pi\)
0.336649 + 0.941630i \(0.390707\pi\)
\(588\) 8.89397e11 0.306830
\(589\) 2.89999e12 0.992836
\(590\) −7.50642e11 −0.255034
\(591\) −1.48363e12 −0.500244
\(592\) −1.60606e12 −0.537419
\(593\) −3.95586e11 −0.131370 −0.0656848 0.997840i \(-0.520923\pi\)
−0.0656848 + 0.997840i \(0.520923\pi\)
\(594\) −3.81740e11 −0.125814
\(595\) 2.27258e12 0.743349
\(596\) −2.37918e12 −0.772358
\(597\) 1.69608e12 0.546463
\(598\) 6.68447e12 2.13753
\(599\) 4.29106e12 1.36190 0.680948 0.732331i \(-0.261568\pi\)
0.680948 + 0.732331i \(0.261568\pi\)
\(600\) −1.17883e12 −0.371338
\(601\) 5.88824e12 1.84098 0.920492 0.390760i \(-0.127788\pi\)
0.920492 + 0.390760i \(0.127788\pi\)
\(602\) −2.01392e12 −0.624969
\(603\) −8.76839e11 −0.270080
\(604\) 2.97077e12 0.908246
\(605\) 3.73102e12 1.13221
\(606\) 4.45080e12 1.34064
\(607\) 3.78421e12 1.13142 0.565712 0.824603i \(-0.308601\pi\)
0.565712 + 0.824603i \(0.308601\pi\)
\(608\) −2.01601e12 −0.598312
\(609\) −7.77088e11 −0.228925
\(610\) 4.70329e12 1.37536
\(611\) −2.15543e12 −0.625675
\(612\) −8.96024e11 −0.258189
\(613\) −3.59469e12 −1.02823 −0.514113 0.857722i \(-0.671879\pi\)
−0.514113 + 0.857722i \(0.671879\pi\)
\(614\) 4.34834e12 1.23471
\(615\) 2.10435e12 0.593171
\(616\) −3.41041e11 −0.0954318
\(617\) 1.77279e12 0.492464 0.246232 0.969211i \(-0.420807\pi\)
0.246232 + 0.969211i \(0.420807\pi\)
\(618\) 1.57491e12 0.434319
\(619\) −1.72024e12 −0.470958 −0.235479 0.971879i \(-0.575666\pi\)
−0.235479 + 0.971879i \(0.575666\pi\)
\(620\) 6.47882e12 1.76089
\(621\) −9.65261e11 −0.260455
\(622\) 6.38789e12 1.71120
\(623\) −1.74609e12 −0.464376
\(624\) −3.33825e12 −0.881430
\(625\) −1.96972e12 −0.516349
\(626\) 6.45940e12 1.68115
\(627\) −6.22618e11 −0.160886
\(628\) 4.14253e12 1.06279
\(629\) −2.10808e12 −0.536982
\(630\) 1.01439e12 0.256551
\(631\) −4.51857e12 −1.13467 −0.567334 0.823488i \(-0.692025\pi\)
−0.567334 + 0.823488i \(0.692025\pi\)
\(632\) 1.84373e12 0.459695
\(633\) 1.72078e12 0.426000
\(634\) −5.78434e12 −1.42184
\(635\) −1.86739e12 −0.455777
\(636\) −2.25729e12 −0.547054
\(637\) 4.34932e12 1.04663
\(638\) 2.76113e12 0.659771
\(639\) 1.21712e12 0.288787
\(640\) 5.75195e12 1.35521
\(641\) −5.73413e12 −1.34155 −0.670774 0.741661i \(-0.734038\pi\)
−0.670774 + 0.741661i \(0.734038\pi\)
\(642\) −6.34648e11 −0.147443
\(643\) 1.25881e12 0.290410 0.145205 0.989402i \(-0.453616\pi\)
0.145205 + 0.989402i \(0.453616\pi\)
\(644\) 1.45863e12 0.334164
\(645\) 4.85618e12 1.10478
\(646\) −3.78682e12 −0.855517
\(647\) −7.70837e12 −1.72939 −0.864695 0.502297i \(-0.832488\pi\)
−0.864695 + 0.502297i \(0.832488\pi\)
\(648\) 2.36453e11 0.0526813
\(649\) 3.01438e11 0.0666956
\(650\) 9.75075e12 2.14254
\(651\) 1.89735e12 0.414030
\(652\) −3.85540e12 −0.835516
\(653\) 1.49747e12 0.322290 0.161145 0.986931i \(-0.448481\pi\)
0.161145 + 0.986931i \(0.448481\pi\)
\(654\) −5.04814e12 −1.07902
\(655\) −1.24743e13 −2.64807
\(656\) −3.91570e12 −0.825548
\(657\) 1.24754e12 0.261222
\(658\) −1.21875e12 −0.253453
\(659\) 2.14974e12 0.444020 0.222010 0.975044i \(-0.428738\pi\)
0.222010 + 0.975044i \(0.428738\pi\)
\(660\) −1.39098e12 −0.285347
\(661\) −5.67280e11 −0.115582 −0.0577911 0.998329i \(-0.518406\pi\)
−0.0577911 + 0.998329i \(0.518406\pi\)
\(662\) −2.26938e12 −0.459247
\(663\) −4.38172e12 −0.880713
\(664\) 1.48291e12 0.296046
\(665\) 1.65447e12 0.328067
\(666\) −9.40968e11 −0.185328
\(667\) 6.98173e12 1.36583
\(668\) −2.86811e12 −0.557315
\(669\) 1.49768e11 0.0289069
\(670\) −8.27893e12 −1.58722
\(671\) −1.88872e12 −0.359680
\(672\) −1.31900e12 −0.249507
\(673\) 5.87565e12 1.10405 0.552024 0.833828i \(-0.313856\pi\)
0.552024 + 0.833828i \(0.313856\pi\)
\(674\) 5.68705e12 1.06149
\(675\) −1.40804e12 −0.261065
\(676\) 1.81481e12 0.334250
\(677\) 1.20603e12 0.220653 0.110326 0.993895i \(-0.464810\pi\)
0.110326 + 0.993895i \(0.464810\pi\)
\(678\) −4.31749e12 −0.784690
\(679\) −2.57773e12 −0.465397
\(680\) 5.00163e12 0.897060
\(681\) 1.60218e12 0.285463
\(682\) −6.74160e12 −1.19325
\(683\) −9.77090e11 −0.171807 −0.0859037 0.996303i \(-0.527378\pi\)
−0.0859037 + 0.996303i \(0.527378\pi\)
\(684\) −6.52320e11 −0.113948
\(685\) 6.28268e12 1.09028
\(686\) 5.36739e12 0.925347
\(687\) 5.23613e11 0.0896820
\(688\) −9.03622e12 −1.53758
\(689\) −1.10386e13 −1.86606
\(690\) −9.11380e12 −1.53066
\(691\) 8.68606e12 1.44934 0.724672 0.689094i \(-0.241991\pi\)
0.724672 + 0.689094i \(0.241991\pi\)
\(692\) −5.96395e12 −0.988682
\(693\) −4.07354e11 −0.0670922
\(694\) −7.99177e12 −1.30775
\(695\) −1.85601e13 −3.01752
\(696\) −1.71026e12 −0.276262
\(697\) −5.13968e12 −0.824876
\(698\) 6.90204e12 1.10060
\(699\) −5.77235e12 −0.914546
\(700\) 2.12773e12 0.334946
\(701\) 1.20744e13 1.88858 0.944290 0.329114i \(-0.106750\pi\)
0.944290 + 0.329114i \(0.106750\pi\)
\(702\) −1.95584e12 −0.303959
\(703\) −1.53472e12 −0.236990
\(704\) 5.68124e11 0.0871698
\(705\) 2.93878e12 0.448039
\(706\) −4.40635e12 −0.667510
\(707\) 4.74943e12 0.714915
\(708\) 3.15818e11 0.0472376
\(709\) −4.69445e12 −0.697713 −0.348856 0.937176i \(-0.613430\pi\)
−0.348856 + 0.937176i \(0.613430\pi\)
\(710\) 1.14918e13 1.69717
\(711\) 2.20223e12 0.323184
\(712\) −3.84289e12 −0.560400
\(713\) −1.70467e13 −2.47022
\(714\) −2.47757e12 −0.356766
\(715\) −6.80216e12 −0.973351
\(716\) −2.48147e12 −0.352858
\(717\) −1.68013e12 −0.237415
\(718\) −9.41330e12 −1.32185
\(719\) 1.09474e13 1.52767 0.763837 0.645410i \(-0.223313\pi\)
0.763837 + 0.645410i \(0.223313\pi\)
\(720\) 4.55146e12 0.631182
\(721\) 1.68059e12 0.231607
\(722\) 6.56076e12 0.898538
\(723\) 4.44877e12 0.605505
\(724\) −4.61381e12 −0.624074
\(725\) 1.01844e13 1.36903
\(726\) −4.06756e12 −0.543399
\(727\) −4.97931e12 −0.661095 −0.330548 0.943789i \(-0.607233\pi\)
−0.330548 + 0.943789i \(0.607233\pi\)
\(728\) −1.74731e12 −0.230558
\(729\) 2.82430e11 0.0370370
\(730\) 1.17790e13 1.53516
\(731\) −1.18608e13 −1.53633
\(732\) −1.97882e12 −0.254746
\(733\) −9.67837e11 −0.123832 −0.0619162 0.998081i \(-0.519721\pi\)
−0.0619162 + 0.998081i \(0.519721\pi\)
\(734\) 4.11261e12 0.522980
\(735\) −5.92999e12 −0.749481
\(736\) 1.18505e13 1.48863
\(737\) 3.32460e12 0.415084
\(738\) −2.29416e12 −0.284689
\(739\) 1.52965e13 1.88666 0.943328 0.331861i \(-0.107677\pi\)
0.943328 + 0.331861i \(0.107677\pi\)
\(740\) −3.42869e12 −0.420325
\(741\) −3.18997e12 −0.388691
\(742\) −6.24155e12 −0.755918
\(743\) −1.28476e13 −1.54657 −0.773287 0.634056i \(-0.781389\pi\)
−0.773287 + 0.634056i \(0.781389\pi\)
\(744\) 4.17579e12 0.499644
\(745\) 1.58630e13 1.88661
\(746\) −1.47941e13 −1.74890
\(747\) 1.77126e12 0.208132
\(748\) 3.39735e12 0.396810
\(749\) −6.77230e11 −0.0786264
\(750\) −3.49414e12 −0.403241
\(751\) −1.06353e12 −0.122003 −0.0610015 0.998138i \(-0.519429\pi\)
−0.0610015 + 0.998138i \(0.519429\pi\)
\(752\) −5.46838e12 −0.623560
\(753\) −3.35045e12 −0.379775
\(754\) 1.41466e13 1.59397
\(755\) −1.98074e13 −2.21853
\(756\) −4.26787e11 −0.0475185
\(757\) −1.38378e13 −1.53156 −0.765780 0.643102i \(-0.777647\pi\)
−0.765780 + 0.643102i \(0.777647\pi\)
\(758\) −8.36367e12 −0.920206
\(759\) 3.65986e12 0.400292
\(760\) 3.64127e12 0.395906
\(761\) 9.84509e12 1.06412 0.532058 0.846708i \(-0.321419\pi\)
0.532058 + 0.846708i \(0.321419\pi\)
\(762\) 2.03582e12 0.218747
\(763\) −5.38685e12 −0.575406
\(764\) 7.49157e11 0.0795523
\(765\) 5.97417e12 0.630668
\(766\) 1.49916e13 1.57332
\(767\) 1.54441e12 0.161133
\(768\) −7.21790e12 −0.748661
\(769\) 1.73777e13 1.79194 0.895972 0.444111i \(-0.146480\pi\)
0.895972 + 0.444111i \(0.146480\pi\)
\(770\) −3.84615e12 −0.394292
\(771\) −8.11095e12 −0.826660
\(772\) 1.25136e12 0.126795
\(773\) −8.15528e12 −0.821545 −0.410772 0.911738i \(-0.634741\pi\)
−0.410772 + 0.911738i \(0.634741\pi\)
\(774\) −5.29421e12 −0.530233
\(775\) −2.48663e13 −2.47601
\(776\) −5.67322e12 −0.561632
\(777\) −1.00410e12 −0.0988290
\(778\) −5.11049e12 −0.500097
\(779\) −3.74177e12 −0.364048
\(780\) −7.12665e12 −0.689382
\(781\) −4.61479e12 −0.443836
\(782\) 2.22596e13 2.12857
\(783\) −2.04281e12 −0.194223
\(784\) 1.10343e13 1.04309
\(785\) −2.76200e13 −2.59603
\(786\) 1.35995e13 1.27093
\(787\) −1.52467e13 −1.41673 −0.708367 0.705844i \(-0.750568\pi\)
−0.708367 + 0.705844i \(0.750568\pi\)
\(788\) 5.89365e12 0.544523
\(789\) −6.48880e12 −0.596098
\(790\) 2.07930e13 1.89931
\(791\) −4.60718e12 −0.418448
\(792\) −8.96529e11 −0.0809657
\(793\) −9.67681e12 −0.868966
\(794\) 8.39617e12 0.749703
\(795\) 1.50503e13 1.33627
\(796\) −6.73759e12 −0.594834
\(797\) −1.00864e13 −0.885473 −0.442737 0.896652i \(-0.645992\pi\)
−0.442737 + 0.896652i \(0.645992\pi\)
\(798\) −1.80371e12 −0.157454
\(799\) −7.17770e12 −0.623053
\(800\) 1.72865e13 1.49212
\(801\) −4.59012e12 −0.393983
\(802\) 1.14627e13 0.978368
\(803\) −4.73013e12 −0.401470
\(804\) 3.48320e12 0.293986
\(805\) −9.72531e12 −0.816247
\(806\) −3.45404e13 −2.88283
\(807\) −1.42298e12 −0.118105
\(808\) 1.04528e13 0.862746
\(809\) −1.79784e13 −1.47565 −0.737824 0.674993i \(-0.764146\pi\)
−0.737824 + 0.674993i \(0.764146\pi\)
\(810\) 2.66664e12 0.217662
\(811\) −5.64634e12 −0.458324 −0.229162 0.973388i \(-0.573599\pi\)
−0.229162 + 0.973388i \(0.573599\pi\)
\(812\) 3.08695e12 0.249188
\(813\) −1.26495e13 −1.01547
\(814\) 3.56776e12 0.284830
\(815\) 2.57055e13 2.04088
\(816\) −1.11165e13 −0.877736
\(817\) −8.63484e12 −0.678040
\(818\) 1.58237e13 1.23571
\(819\) −2.08707e12 −0.162091
\(820\) −8.35943e12 −0.645676
\(821\) 2.56455e13 1.97000 0.985001 0.172551i \(-0.0552010\pi\)
0.985001 + 0.172551i \(0.0552010\pi\)
\(822\) −6.84937e12 −0.523272
\(823\) −5.99885e12 −0.455794 −0.227897 0.973685i \(-0.573185\pi\)
−0.227897 + 0.973685i \(0.573185\pi\)
\(824\) 3.69874e12 0.279500
\(825\) 5.33871e12 0.401230
\(826\) 8.73258e11 0.0652728
\(827\) −1.46817e13 −1.09144 −0.545721 0.837967i \(-0.683744\pi\)
−0.545721 + 0.837967i \(0.683744\pi\)
\(828\) 3.83446e12 0.283509
\(829\) −1.57867e12 −0.116091 −0.0580453 0.998314i \(-0.518487\pi\)
−0.0580453 + 0.998314i \(0.518487\pi\)
\(830\) 1.67238e13 1.22316
\(831\) 7.28464e12 0.529911
\(832\) 2.91077e12 0.210597
\(833\) 1.44835e13 1.04224
\(834\) 2.02343e13 1.44824
\(835\) 1.91229e13 1.36133
\(836\) 2.47332e12 0.175127
\(837\) 4.98775e12 0.351269
\(838\) 8.83502e11 0.0618884
\(839\) 3.11330e12 0.216916 0.108458 0.994101i \(-0.465409\pi\)
0.108458 + 0.994101i \(0.465409\pi\)
\(840\) 2.38234e12 0.165100
\(841\) 2.68517e11 0.0185093
\(842\) −2.43416e13 −1.66895
\(843\) 1.73878e12 0.118582
\(844\) −6.83574e12 −0.463708
\(845\) −1.21001e13 −0.816457
\(846\) −3.20385e12 −0.215033
\(847\) −4.34048e12 −0.289776
\(848\) −2.80051e13 −1.85975
\(849\) 2.30082e12 0.151984
\(850\) 3.24705e13 2.13356
\(851\) 9.02136e12 0.589643
\(852\) −4.83494e12 −0.314350
\(853\) 2.45951e13 1.59066 0.795332 0.606175i \(-0.207297\pi\)
0.795332 + 0.606175i \(0.207297\pi\)
\(854\) −5.47157e12 −0.352007
\(855\) 4.34929e12 0.278337
\(856\) −1.49049e12 −0.0948849
\(857\) −2.27715e13 −1.44204 −0.721019 0.692915i \(-0.756326\pi\)
−0.721019 + 0.692915i \(0.756326\pi\)
\(858\) 7.41571e12 0.467154
\(859\) −2.42518e12 −0.151976 −0.0759879 0.997109i \(-0.524211\pi\)
−0.0759879 + 0.997109i \(0.524211\pi\)
\(860\) −1.92910e13 −1.20257
\(861\) −2.44809e12 −0.151814
\(862\) 3.59698e13 2.21899
\(863\) −1.13658e13 −0.697509 −0.348754 0.937214i \(-0.613395\pi\)
−0.348754 + 0.937214i \(0.613395\pi\)
\(864\) −3.46738e12 −0.211685
\(865\) 3.97642e13 2.41501
\(866\) 7.29390e12 0.440686
\(867\) −4.98575e12 −0.299671
\(868\) −7.53712e12 −0.450678
\(869\) −8.34993e12 −0.496699
\(870\) −1.92878e13 −1.14142
\(871\) 1.70335e13 1.00282
\(872\) −1.18557e13 −0.694390
\(873\) −6.77635e12 −0.394849
\(874\) 1.62054e13 0.939415
\(875\) −3.72859e12 −0.215035
\(876\) −4.95578e12 −0.284344
\(877\) 1.76641e13 1.00831 0.504153 0.863614i \(-0.331805\pi\)
0.504153 + 0.863614i \(0.331805\pi\)
\(878\) −1.49478e13 −0.848889
\(879\) 3.61545e12 0.204274
\(880\) −1.72572e13 −0.970061
\(881\) 2.69106e13 1.50498 0.752491 0.658602i \(-0.228852\pi\)
0.752491 + 0.658602i \(0.228852\pi\)
\(882\) 6.46487e12 0.359709
\(883\) 2.45561e13 1.35937 0.679684 0.733505i \(-0.262117\pi\)
0.679684 + 0.733505i \(0.262117\pi\)
\(884\) 1.74062e13 0.958670
\(885\) −2.10569e12 −0.115385
\(886\) 1.20991e13 0.659630
\(887\) −5.29771e12 −0.287364 −0.143682 0.989624i \(-0.545894\pi\)
−0.143682 + 0.989624i \(0.545894\pi\)
\(888\) −2.20989e12 −0.119265
\(889\) 2.17242e12 0.116650
\(890\) −4.33390e13 −2.31539
\(891\) −1.07085e12 −0.0569221
\(892\) −5.94947e11 −0.0314656
\(893\) −5.22548e12 −0.274976
\(894\) −1.72938e13 −0.905465
\(895\) 1.65450e13 0.861913
\(896\) −6.69152e12 −0.346848
\(897\) 1.87512e13 0.967082
\(898\) 6.24185e12 0.320309
\(899\) −3.60764e13 −1.84206
\(900\) 5.59339e12 0.284174
\(901\) −3.67590e13 −1.85824
\(902\) 8.69849e12 0.437537
\(903\) −5.64943e12 −0.282755
\(904\) −1.01398e13 −0.504975
\(905\) 3.07622e13 1.52440
\(906\) 2.15940e13 1.06477
\(907\) 1.40971e13 0.691666 0.345833 0.938296i \(-0.387596\pi\)
0.345833 + 0.938296i \(0.387596\pi\)
\(908\) −6.36460e12 −0.310731
\(909\) 1.24853e13 0.606544
\(910\) −1.97057e13 −0.952587
\(911\) −3.88691e12 −0.186970 −0.0934849 0.995621i \(-0.529801\pi\)
−0.0934849 + 0.995621i \(0.529801\pi\)
\(912\) −8.09302e12 −0.387377
\(913\) −6.71586e12 −0.319877
\(914\) −6.91291e12 −0.327645
\(915\) 1.31936e13 0.622257
\(916\) −2.08003e12 −0.0976203
\(917\) 1.45120e13 0.677741
\(918\) −6.51304e12 −0.302685
\(919\) −9.49994e12 −0.439340 −0.219670 0.975574i \(-0.570498\pi\)
−0.219670 + 0.975574i \(0.570498\pi\)
\(920\) −2.14040e13 −0.985033
\(921\) 1.21979e13 0.558622
\(922\) 2.91954e13 1.33053
\(923\) −2.36438e13 −1.07228
\(924\) 1.61820e12 0.0730310
\(925\) 1.31596e13 0.591024
\(926\) 2.11384e13 0.944764
\(927\) 4.41793e12 0.196499
\(928\) 2.50796e13 1.11008
\(929\) −2.69699e12 −0.118798 −0.0593990 0.998234i \(-0.518918\pi\)
−0.0593990 + 0.998234i \(0.518918\pi\)
\(930\) 4.70933e13 2.06436
\(931\) 1.05442e13 0.459981
\(932\) 2.29304e13 0.995497
\(933\) 1.79192e13 0.774198
\(934\) −2.11703e13 −0.910263
\(935\) −2.26515e13 −0.969271
\(936\) −4.59334e12 −0.195608
\(937\) −3.59174e13 −1.52222 −0.761109 0.648624i \(-0.775345\pi\)
−0.761109 + 0.648624i \(0.775345\pi\)
\(938\) 9.63128e12 0.406229
\(939\) 1.81198e13 0.760605
\(940\) −1.16742e13 −0.487697
\(941\) 8.78230e12 0.365136 0.182568 0.983193i \(-0.441559\pi\)
0.182568 + 0.983193i \(0.441559\pi\)
\(942\) 3.01113e13 1.24595
\(943\) 2.19948e13 0.905770
\(944\) 3.91820e12 0.160588
\(945\) 2.84557e12 0.116071
\(946\) 2.00734e13 0.814912
\(947\) −3.21918e13 −1.30068 −0.650341 0.759643i \(-0.725374\pi\)
−0.650341 + 0.759643i \(0.725374\pi\)
\(948\) −8.74826e12 −0.351790
\(949\) −2.42347e13 −0.969928
\(950\) 2.36391e13 0.941616
\(951\) −1.62262e13 −0.643285
\(952\) −5.81864e12 −0.229591
\(953\) 2.55069e13 1.00171 0.500853 0.865532i \(-0.333020\pi\)
0.500853 + 0.865532i \(0.333020\pi\)
\(954\) −1.64078e13 −0.641332
\(955\) −4.99495e12 −0.194319
\(956\) 6.67425e12 0.258430
\(957\) 7.74549e12 0.298500
\(958\) −2.96734e12 −0.113821
\(959\) −7.30894e12 −0.279043
\(960\) −3.96862e12 −0.150806
\(961\) 6.16448e13 2.33153
\(962\) 1.82793e13 0.688132
\(963\) −1.78031e12 −0.0667078
\(964\) −1.76726e13 −0.659102
\(965\) −8.34333e12 −0.309718
\(966\) 1.06025e13 0.391753
\(967\) 2.28032e13 0.838644 0.419322 0.907838i \(-0.362268\pi\)
0.419322 + 0.907838i \(0.362268\pi\)
\(968\) −9.55279e12 −0.349696
\(969\) −1.06228e13 −0.387062
\(970\) −6.39809e13 −2.32048
\(971\) 1.26730e13 0.457502 0.228751 0.973485i \(-0.426536\pi\)
0.228751 + 0.973485i \(0.426536\pi\)
\(972\) −1.12194e12 −0.0403154
\(973\) 2.15919e13 0.772295
\(974\) −4.26441e13 −1.51825
\(975\) 2.73527e13 0.969348
\(976\) −2.45503e13 −0.866028
\(977\) −3.11077e12 −0.109230 −0.0546150 0.998507i \(-0.517393\pi\)
−0.0546150 + 0.998507i \(0.517393\pi\)
\(978\) −2.80242e13 −0.979508
\(979\) 1.74038e13 0.605511
\(980\) 2.35566e13 0.815822
\(981\) −1.41610e13 −0.488183
\(982\) 2.12637e12 0.0729689
\(983\) −1.07221e12 −0.0366260 −0.0183130 0.999832i \(-0.505830\pi\)
−0.0183130 + 0.999832i \(0.505830\pi\)
\(984\) −5.38791e12 −0.183207
\(985\) −3.92954e13 −1.33008
\(986\) 4.71088e13 1.58729
\(987\) −3.41882e12 −0.114670
\(988\) 1.26720e13 0.423096
\(989\) 5.07572e13 1.68700
\(990\) −1.01108e13 −0.334523
\(991\) −2.00361e12 −0.0659907 −0.0329954 0.999456i \(-0.510505\pi\)
−0.0329954 + 0.999456i \(0.510505\pi\)
\(992\) −6.12346e13 −2.00768
\(993\) −6.36604e12 −0.207777
\(994\) −1.33689e13 −0.434368
\(995\) 4.49223e13 1.45298
\(996\) −7.03624e12 −0.226555
\(997\) −2.90271e13 −0.930411 −0.465206 0.885203i \(-0.654020\pi\)
−0.465206 + 0.885203i \(0.654020\pi\)
\(998\) −2.68114e13 −0.855523
\(999\) −2.63959e12 −0.0838480
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 177.10.a.b.1.4 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.b.1.4 21 1.1 even 1 trivial