Properties

Label 177.10.a.b.1.5
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 1.5
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-24.7118 q^{2} -81.0000 q^{3} +98.6742 q^{4} +583.392 q^{5} +2001.66 q^{6} +10055.1 q^{7} +10214.0 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-24.7118 q^{2} -81.0000 q^{3} +98.6742 q^{4} +583.392 q^{5} +2001.66 q^{6} +10055.1 q^{7} +10214.0 q^{8} +6561.00 q^{9} -14416.7 q^{10} +33314.0 q^{11} -7992.61 q^{12} -72674.0 q^{13} -248479. q^{14} -47254.7 q^{15} -302929. q^{16} -336269. q^{17} -162134. q^{18} +317254. q^{19} +57565.7 q^{20} -814461. q^{21} -823249. q^{22} -1.35598e6 q^{23} -827337. q^{24} -1.61278e6 q^{25} +1.79591e6 q^{26} -531441. q^{27} +992176. q^{28} +2.66208e6 q^{29} +1.16775e6 q^{30} +5.69989e6 q^{31} +2.25633e6 q^{32} -2.69843e6 q^{33} +8.30983e6 q^{34} +5.86605e6 q^{35} +647401. q^{36} -6.10000e6 q^{37} -7.83993e6 q^{38} +5.88659e6 q^{39} +5.95878e6 q^{40} +2.11049e6 q^{41} +2.01268e7 q^{42} -2.57854e7 q^{43} +3.28723e6 q^{44} +3.82763e6 q^{45} +3.35086e7 q^{46} -3.88147e7 q^{47} +2.45372e7 q^{48} +6.07508e7 q^{49} +3.98547e7 q^{50} +2.72378e7 q^{51} -7.17105e6 q^{52} -9.44146e6 q^{53} +1.31329e7 q^{54} +1.94351e7 q^{55} +1.02703e8 q^{56} -2.56976e7 q^{57} -6.57849e7 q^{58} -1.21174e7 q^{59} -4.66282e6 q^{60} -5.09326e7 q^{61} -1.40855e8 q^{62} +6.59713e7 q^{63} +9.93414e7 q^{64} -4.23974e7 q^{65} +6.66831e7 q^{66} -1.19930e8 q^{67} -3.31811e7 q^{68} +1.09834e8 q^{69} -1.44961e8 q^{70} +2.67018e8 q^{71} +6.70143e7 q^{72} -3.11741e8 q^{73} +1.50742e8 q^{74} +1.30635e8 q^{75} +3.13048e7 q^{76} +3.34974e8 q^{77} -1.45468e8 q^{78} +4.14333e8 q^{79} -1.76726e8 q^{80} +4.30467e7 q^{81} -5.21542e7 q^{82} +2.74165e8 q^{83} -8.03662e7 q^{84} -1.96177e8 q^{85} +6.37203e8 q^{86} -2.15629e8 q^{87} +3.40270e8 q^{88} -7.08062e8 q^{89} -9.45878e7 q^{90} -7.30742e8 q^{91} -1.33800e8 q^{92} -4.61691e8 q^{93} +9.59181e8 q^{94} +1.85083e8 q^{95} -1.82763e8 q^{96} -3.69989e8 q^{97} -1.50126e9 q^{98} +2.18573e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −24.7118 −1.09212 −0.546059 0.837747i \(-0.683873\pi\)
−0.546059 + 0.837747i \(0.683873\pi\)
\(3\) −81.0000 −0.577350
\(4\) 98.6742 0.192723
\(5\) 583.392 0.417441 0.208721 0.977975i \(-0.433070\pi\)
0.208721 + 0.977975i \(0.433070\pi\)
\(6\) 2001.66 0.630535
\(7\) 10055.1 1.58287 0.791433 0.611256i \(-0.209336\pi\)
0.791433 + 0.611256i \(0.209336\pi\)
\(8\) 10214.0 0.881642
\(9\) 6561.00 0.333333
\(10\) −14416.7 −0.455895
\(11\) 33314.0 0.686055 0.343028 0.939325i \(-0.388548\pi\)
0.343028 + 0.939325i \(0.388548\pi\)
\(12\) −7992.61 −0.111269
\(13\) −72674.0 −0.705722 −0.352861 0.935676i \(-0.614791\pi\)
−0.352861 + 0.935676i \(0.614791\pi\)
\(14\) −248479. −1.72868
\(15\) −47254.7 −0.241010
\(16\) −302929. −1.15558
\(17\) −336269. −0.976489 −0.488244 0.872707i \(-0.662362\pi\)
−0.488244 + 0.872707i \(0.662362\pi\)
\(18\) −162134. −0.364040
\(19\) 317254. 0.558491 0.279245 0.960220i \(-0.409916\pi\)
0.279245 + 0.960220i \(0.409916\pi\)
\(20\) 57565.7 0.0804505
\(21\) −814461. −0.913868
\(22\) −823249. −0.749254
\(23\) −1.35598e6 −1.01036 −0.505181 0.863014i \(-0.668574\pi\)
−0.505181 + 0.863014i \(0.668574\pi\)
\(24\) −827337. −0.509016
\(25\) −1.61278e6 −0.825743
\(26\) 1.79591e6 0.770733
\(27\) −531441. −0.192450
\(28\) 992176. 0.305055
\(29\) 2.66208e6 0.698925 0.349462 0.936950i \(-0.386364\pi\)
0.349462 + 0.936950i \(0.386364\pi\)
\(30\) 1.16775e6 0.263211
\(31\) 5.69989e6 1.10851 0.554254 0.832348i \(-0.313004\pi\)
0.554254 + 0.832348i \(0.313004\pi\)
\(32\) 2.25633e6 0.380389
\(33\) −2.69843e6 −0.396094
\(34\) 8.30983e6 1.06644
\(35\) 5.86605e6 0.660753
\(36\) 647401. 0.0642410
\(37\) −6.10000e6 −0.535084 −0.267542 0.963546i \(-0.586211\pi\)
−0.267542 + 0.963546i \(0.586211\pi\)
\(38\) −7.83993e6 −0.609938
\(39\) 5.88659e6 0.407449
\(40\) 5.95878e6 0.368034
\(41\) 2.11049e6 0.116642 0.0583212 0.998298i \(-0.481425\pi\)
0.0583212 + 0.998298i \(0.481425\pi\)
\(42\) 2.01268e7 0.998052
\(43\) −2.57854e7 −1.15018 −0.575089 0.818091i \(-0.695033\pi\)
−0.575089 + 0.818091i \(0.695033\pi\)
\(44\) 3.28723e6 0.132219
\(45\) 3.82763e6 0.139147
\(46\) 3.35086e7 1.10343
\(47\) −3.88147e7 −1.16026 −0.580130 0.814524i \(-0.696998\pi\)
−0.580130 + 0.814524i \(0.696998\pi\)
\(48\) 2.45372e7 0.667175
\(49\) 6.07508e7 1.50546
\(50\) 3.98547e7 0.901809
\(51\) 2.72378e7 0.563776
\(52\) −7.17105e6 −0.136009
\(53\) −9.44146e6 −0.164361 −0.0821803 0.996617i \(-0.526188\pi\)
−0.0821803 + 0.996617i \(0.526188\pi\)
\(54\) 1.31329e7 0.210178
\(55\) 1.94351e7 0.286388
\(56\) 1.02703e8 1.39552
\(57\) −2.56976e7 −0.322445
\(58\) −6.57849e7 −0.763308
\(59\) −1.21174e7 −0.130189
\(60\) −4.66282e6 −0.0464481
\(61\) −5.09326e7 −0.470990 −0.235495 0.971876i \(-0.575671\pi\)
−0.235495 + 0.971876i \(0.575671\pi\)
\(62\) −1.40855e8 −1.21062
\(63\) 6.59713e7 0.527622
\(64\) 9.93414e7 0.740151
\(65\) −4.23974e7 −0.294598
\(66\) 6.66831e7 0.432582
\(67\) −1.19930e8 −0.727092 −0.363546 0.931576i \(-0.618434\pi\)
−0.363546 + 0.931576i \(0.618434\pi\)
\(68\) −3.31811e7 −0.188192
\(69\) 1.09834e8 0.583333
\(70\) −1.44961e8 −0.721621
\(71\) 2.67018e8 1.24703 0.623517 0.781810i \(-0.285703\pi\)
0.623517 + 0.781810i \(0.285703\pi\)
\(72\) 6.70143e7 0.293881
\(73\) −3.11741e8 −1.28481 −0.642407 0.766363i \(-0.722064\pi\)
−0.642407 + 0.766363i \(0.722064\pi\)
\(74\) 1.50742e8 0.584375
\(75\) 1.30635e8 0.476743
\(76\) 3.13048e7 0.107634
\(77\) 3.34974e8 1.08593
\(78\) −1.45468e8 −0.444983
\(79\) 4.14333e8 1.19682 0.598408 0.801191i \(-0.295800\pi\)
0.598408 + 0.801191i \(0.295800\pi\)
\(80\) −1.76726e8 −0.482387
\(81\) 4.30467e7 0.111111
\(82\) −5.21542e7 −0.127387
\(83\) 2.74165e8 0.634104 0.317052 0.948408i \(-0.397307\pi\)
0.317052 + 0.948408i \(0.397307\pi\)
\(84\) −8.03662e7 −0.176123
\(85\) −1.96177e8 −0.407627
\(86\) 6.37203e8 1.25613
\(87\) −2.15629e8 −0.403524
\(88\) 3.40270e8 0.604855
\(89\) −7.08062e8 −1.19623 −0.598117 0.801409i \(-0.704084\pi\)
−0.598117 + 0.801409i \(0.704084\pi\)
\(90\) −9.45878e7 −0.151965
\(91\) −7.30742e8 −1.11706
\(92\) −1.33800e8 −0.194720
\(93\) −4.61691e8 −0.639997
\(94\) 9.59181e8 1.26714
\(95\) 1.85083e8 0.233137
\(96\) −1.82763e8 −0.219618
\(97\) −3.69989e8 −0.424342 −0.212171 0.977233i \(-0.568053\pi\)
−0.212171 + 0.977233i \(0.568053\pi\)
\(98\) −1.50126e9 −1.64414
\(99\) 2.18573e8 0.228685
\(100\) −1.59140e8 −0.159140
\(101\) 2.73696e8 0.261711 0.130856 0.991401i \(-0.458228\pi\)
0.130856 + 0.991401i \(0.458228\pi\)
\(102\) −6.73096e8 −0.615710
\(103\) 1.11582e8 0.0976844 0.0488422 0.998807i \(-0.484447\pi\)
0.0488422 + 0.998807i \(0.484447\pi\)
\(104\) −7.42295e8 −0.622195
\(105\) −4.75150e8 −0.381486
\(106\) 2.33316e8 0.179501
\(107\) 1.30638e9 0.963482 0.481741 0.876314i \(-0.340005\pi\)
0.481741 + 0.876314i \(0.340005\pi\)
\(108\) −5.24395e7 −0.0370896
\(109\) −1.76066e9 −1.19469 −0.597346 0.801984i \(-0.703778\pi\)
−0.597346 + 0.801984i \(0.703778\pi\)
\(110\) −4.80276e8 −0.312769
\(111\) 4.94100e8 0.308931
\(112\) −3.04597e9 −1.82913
\(113\) −1.20055e9 −0.692674 −0.346337 0.938110i \(-0.612575\pi\)
−0.346337 + 0.938110i \(0.612575\pi\)
\(114\) 6.35034e8 0.352148
\(115\) −7.91065e8 −0.421767
\(116\) 2.62679e8 0.134699
\(117\) −4.76814e8 −0.235241
\(118\) 2.99442e8 0.142182
\(119\) −3.38121e9 −1.54565
\(120\) −4.82661e8 −0.212484
\(121\) −1.24813e9 −0.529328
\(122\) 1.25864e9 0.514377
\(123\) −1.70950e8 −0.0673436
\(124\) 5.62432e8 0.213635
\(125\) −2.08032e9 −0.762140
\(126\) −1.63027e9 −0.576226
\(127\) 4.28292e9 1.46091 0.730454 0.682961i \(-0.239308\pi\)
0.730454 + 0.682961i \(0.239308\pi\)
\(128\) −3.61015e9 −1.18872
\(129\) 2.08861e9 0.664056
\(130\) 1.04772e9 0.321735
\(131\) −5.40976e8 −0.160494 −0.0802468 0.996775i \(-0.525571\pi\)
−0.0802468 + 0.996775i \(0.525571\pi\)
\(132\) −2.66265e8 −0.0763365
\(133\) 3.19001e9 0.884016
\(134\) 2.96368e9 0.794071
\(135\) −3.10038e8 −0.0803366
\(136\) −3.43467e9 −0.860914
\(137\) −3.01617e9 −0.731498 −0.365749 0.930714i \(-0.619187\pi\)
−0.365749 + 0.930714i \(0.619187\pi\)
\(138\) −2.71420e9 −0.637068
\(139\) −4.53487e9 −1.03038 −0.515190 0.857076i \(-0.672279\pi\)
−0.515190 + 0.857076i \(0.672279\pi\)
\(140\) 5.78827e8 0.127342
\(141\) 3.14399e9 0.669877
\(142\) −6.59851e9 −1.36191
\(143\) −2.42106e9 −0.484165
\(144\) −1.98751e9 −0.385194
\(145\) 1.55304e9 0.291760
\(146\) 7.70368e9 1.40317
\(147\) −4.92082e9 −0.869179
\(148\) −6.01912e8 −0.103123
\(149\) −6.01406e7 −0.00999608 −0.00499804 0.999988i \(-0.501591\pi\)
−0.00499804 + 0.999988i \(0.501591\pi\)
\(150\) −3.22823e9 −0.520660
\(151\) −1.44002e9 −0.225409 −0.112705 0.993629i \(-0.535951\pi\)
−0.112705 + 0.993629i \(0.535951\pi\)
\(152\) 3.24044e9 0.492389
\(153\) −2.20626e9 −0.325496
\(154\) −8.27782e9 −1.18597
\(155\) 3.32527e9 0.462737
\(156\) 5.80855e8 0.0785248
\(157\) −1.10621e10 −1.45308 −0.726542 0.687122i \(-0.758874\pi\)
−0.726542 + 0.687122i \(0.758874\pi\)
\(158\) −1.02389e10 −1.30707
\(159\) 7.64758e8 0.0948937
\(160\) 1.31633e9 0.158790
\(161\) −1.36344e10 −1.59927
\(162\) −1.06376e9 −0.121347
\(163\) 3.14291e9 0.348729 0.174365 0.984681i \(-0.444213\pi\)
0.174365 + 0.984681i \(0.444213\pi\)
\(164\) 2.08251e8 0.0224797
\(165\) −1.57424e9 −0.165346
\(166\) −6.77512e9 −0.692517
\(167\) 9.21149e9 0.916444 0.458222 0.888838i \(-0.348487\pi\)
0.458222 + 0.888838i \(0.348487\pi\)
\(168\) −8.31893e9 −0.805704
\(169\) −5.32299e9 −0.501956
\(170\) 4.84789e9 0.445176
\(171\) 2.08150e9 0.186164
\(172\) −2.54435e9 −0.221666
\(173\) 2.07454e10 1.76082 0.880409 0.474215i \(-0.157268\pi\)
0.880409 + 0.474215i \(0.157268\pi\)
\(174\) 5.32857e9 0.440696
\(175\) −1.62166e10 −1.30704
\(176\) −1.00917e10 −0.792792
\(177\) 9.81506e8 0.0751646
\(178\) 1.74975e10 1.30643
\(179\) 1.59637e10 1.16224 0.581121 0.813817i \(-0.302614\pi\)
0.581121 + 0.813817i \(0.302614\pi\)
\(180\) 3.77689e8 0.0268168
\(181\) −1.49143e10 −1.03288 −0.516438 0.856325i \(-0.672742\pi\)
−0.516438 + 0.856325i \(0.672742\pi\)
\(182\) 1.80580e10 1.21997
\(183\) 4.12554e9 0.271926
\(184\) −1.38500e10 −0.890778
\(185\) −3.55869e9 −0.223366
\(186\) 1.14092e10 0.698953
\(187\) −1.12025e10 −0.669925
\(188\) −3.83001e9 −0.223609
\(189\) −5.34368e9 −0.304623
\(190\) −4.57375e9 −0.254613
\(191\) 1.06714e10 0.580190 0.290095 0.956998i \(-0.406313\pi\)
0.290095 + 0.956998i \(0.406313\pi\)
\(192\) −8.04665e9 −0.427326
\(193\) −2.65737e10 −1.37862 −0.689309 0.724468i \(-0.742086\pi\)
−0.689309 + 0.724468i \(0.742086\pi\)
\(194\) 9.14311e9 0.463432
\(195\) 3.43419e9 0.170086
\(196\) 5.99454e9 0.290137
\(197\) −2.11193e10 −0.999038 −0.499519 0.866303i \(-0.666490\pi\)
−0.499519 + 0.866303i \(0.666490\pi\)
\(198\) −5.40133e9 −0.249751
\(199\) 2.77406e10 1.25394 0.626970 0.779043i \(-0.284295\pi\)
0.626970 + 0.779043i \(0.284295\pi\)
\(200\) −1.64730e10 −0.728010
\(201\) 9.71429e9 0.419787
\(202\) −6.76353e9 −0.285820
\(203\) 2.67674e10 1.10630
\(204\) 2.68767e9 0.108653
\(205\) 1.23124e9 0.0486914
\(206\) −2.75739e9 −0.106683
\(207\) −8.89656e9 −0.336787
\(208\) 2.20150e10 0.815519
\(209\) 1.05690e10 0.383156
\(210\) 1.17418e10 0.416628
\(211\) −2.28234e10 −0.792700 −0.396350 0.918100i \(-0.629723\pi\)
−0.396350 + 0.918100i \(0.629723\pi\)
\(212\) −9.31629e8 −0.0316761
\(213\) −2.16285e10 −0.719975
\(214\) −3.22831e10 −1.05224
\(215\) −1.50430e10 −0.480132
\(216\) −5.42816e9 −0.169672
\(217\) 5.73128e10 1.75462
\(218\) 4.35091e10 1.30474
\(219\) 2.52510e10 0.741788
\(220\) 1.91774e9 0.0551935
\(221\) 2.44380e10 0.689130
\(222\) −1.22101e10 −0.337389
\(223\) −1.01621e10 −0.275177 −0.137589 0.990489i \(-0.543935\pi\)
−0.137589 + 0.990489i \(0.543935\pi\)
\(224\) 2.26876e10 0.602105
\(225\) −1.05814e10 −0.275248
\(226\) 2.96679e10 0.756482
\(227\) 6.52813e10 1.63182 0.815911 0.578178i \(-0.196236\pi\)
0.815911 + 0.578178i \(0.196236\pi\)
\(228\) −2.53569e9 −0.0621425
\(229\) −1.14856e10 −0.275990 −0.137995 0.990433i \(-0.544066\pi\)
−0.137995 + 0.990433i \(0.544066\pi\)
\(230\) 1.95487e10 0.460619
\(231\) −2.71329e10 −0.626964
\(232\) 2.71906e10 0.616201
\(233\) −3.31036e10 −0.735823 −0.367911 0.929861i \(-0.619927\pi\)
−0.367911 + 0.929861i \(0.619927\pi\)
\(234\) 1.17829e10 0.256911
\(235\) −2.26442e10 −0.484341
\(236\) −1.19567e9 −0.0250904
\(237\) −3.35610e10 −0.690982
\(238\) 8.35559e10 1.68803
\(239\) 7.69117e9 0.152476 0.0762381 0.997090i \(-0.475709\pi\)
0.0762381 + 0.997090i \(0.475709\pi\)
\(240\) 1.43148e10 0.278506
\(241\) −9.28482e9 −0.177295 −0.0886475 0.996063i \(-0.528254\pi\)
−0.0886475 + 0.996063i \(0.528254\pi\)
\(242\) 3.08435e10 0.578089
\(243\) −3.48678e9 −0.0641500
\(244\) −5.02574e9 −0.0907707
\(245\) 3.54415e10 0.628442
\(246\) 4.22449e9 0.0735472
\(247\) −2.30561e10 −0.394140
\(248\) 5.82188e10 0.977307
\(249\) −2.22074e10 −0.366100
\(250\) 5.14085e10 0.832347
\(251\) 5.11894e10 0.814044 0.407022 0.913418i \(-0.366567\pi\)
0.407022 + 0.913418i \(0.366567\pi\)
\(252\) 6.50967e9 0.101685
\(253\) −4.51729e10 −0.693164
\(254\) −1.05839e11 −1.59549
\(255\) 1.58903e10 0.235343
\(256\) 3.83506e10 0.558074
\(257\) 4.21976e10 0.603377 0.301688 0.953407i \(-0.402450\pi\)
0.301688 + 0.953407i \(0.402450\pi\)
\(258\) −5.16135e10 −0.725227
\(259\) −6.13359e10 −0.846966
\(260\) −4.18353e9 −0.0567757
\(261\) 1.74659e10 0.232975
\(262\) 1.33685e10 0.175278
\(263\) −2.08366e10 −0.268550 −0.134275 0.990944i \(-0.542871\pi\)
−0.134275 + 0.990944i \(0.542871\pi\)
\(264\) −2.75619e10 −0.349213
\(265\) −5.50807e9 −0.0686109
\(266\) −7.88310e10 −0.965450
\(267\) 5.73530e10 0.690646
\(268\) −1.18339e10 −0.140127
\(269\) 3.97522e10 0.462888 0.231444 0.972848i \(-0.425655\pi\)
0.231444 + 0.972848i \(0.425655\pi\)
\(270\) 7.66161e9 0.0877371
\(271\) −9.42541e10 −1.06155 −0.530773 0.847514i \(-0.678098\pi\)
−0.530773 + 0.847514i \(0.678098\pi\)
\(272\) 1.01866e11 1.12841
\(273\) 5.91901e10 0.644937
\(274\) 7.45350e10 0.798883
\(275\) −5.37281e10 −0.566505
\(276\) 1.08378e10 0.112422
\(277\) 1.23332e11 1.25868 0.629342 0.777129i \(-0.283325\pi\)
0.629342 + 0.777129i \(0.283325\pi\)
\(278\) 1.12065e11 1.12530
\(279\) 3.73970e10 0.369502
\(280\) 5.99160e10 0.582548
\(281\) 9.76161e10 0.933992 0.466996 0.884260i \(-0.345336\pi\)
0.466996 + 0.884260i \(0.345336\pi\)
\(282\) −7.76937e10 −0.731585
\(283\) −1.91585e11 −1.77551 −0.887756 0.460314i \(-0.847737\pi\)
−0.887756 + 0.460314i \(0.847737\pi\)
\(284\) 2.63478e10 0.240332
\(285\) −1.49918e10 −0.134602
\(286\) 5.98288e10 0.528765
\(287\) 2.12212e10 0.184629
\(288\) 1.48038e10 0.126796
\(289\) −5.51079e9 −0.0464701
\(290\) −3.83784e10 −0.318636
\(291\) 2.99691e10 0.244994
\(292\) −3.07607e10 −0.247613
\(293\) −1.07936e11 −0.855584 −0.427792 0.903877i \(-0.640708\pi\)
−0.427792 + 0.903877i \(0.640708\pi\)
\(294\) 1.21602e11 0.949247
\(295\) −7.06917e9 −0.0543462
\(296\) −6.23056e10 −0.471753
\(297\) −1.77044e10 −0.132031
\(298\) 1.48618e9 0.0109169
\(299\) 9.85442e10 0.713035
\(300\) 1.28903e10 0.0918793
\(301\) −2.59274e11 −1.82058
\(302\) 3.55855e10 0.246174
\(303\) −2.21694e10 −0.151099
\(304\) −9.61054e10 −0.645381
\(305\) −2.97137e10 −0.196611
\(306\) 5.45208e10 0.355480
\(307\) −2.31525e11 −1.48756 −0.743781 0.668424i \(-0.766969\pi\)
−0.743781 + 0.668424i \(0.766969\pi\)
\(308\) 3.30533e10 0.209284
\(309\) −9.03811e9 −0.0563981
\(310\) −8.21734e10 −0.505363
\(311\) 1.61621e11 0.979661 0.489831 0.871818i \(-0.337059\pi\)
0.489831 + 0.871818i \(0.337059\pi\)
\(312\) 6.01259e10 0.359224
\(313\) 2.96549e10 0.174641 0.0873206 0.996180i \(-0.472170\pi\)
0.0873206 + 0.996180i \(0.472170\pi\)
\(314\) 2.73366e11 1.58694
\(315\) 3.84871e10 0.220251
\(316\) 4.08840e10 0.230654
\(317\) −2.78281e11 −1.54781 −0.773904 0.633303i \(-0.781699\pi\)
−0.773904 + 0.633303i \(0.781699\pi\)
\(318\) −1.88986e10 −0.103635
\(319\) 8.86845e10 0.479501
\(320\) 5.79549e10 0.308969
\(321\) −1.05817e11 −0.556266
\(322\) 3.36932e11 1.74659
\(323\) −1.06683e11 −0.545360
\(324\) 4.24760e9 0.0214137
\(325\) 1.17207e11 0.582745
\(326\) −7.76671e10 −0.380854
\(327\) 1.42613e11 0.689756
\(328\) 2.15567e10 0.102837
\(329\) −3.90284e11 −1.83654
\(330\) 3.89024e10 0.180577
\(331\) −3.77481e11 −1.72850 −0.864249 0.503064i \(-0.832206\pi\)
−0.864249 + 0.503064i \(0.832206\pi\)
\(332\) 2.70530e10 0.122206
\(333\) −4.00221e10 −0.178361
\(334\) −2.27633e11 −1.00087
\(335\) −6.99659e10 −0.303518
\(336\) 2.46723e11 1.05605
\(337\) −1.60848e11 −0.679331 −0.339665 0.940546i \(-0.610314\pi\)
−0.339665 + 0.940546i \(0.610314\pi\)
\(338\) 1.31541e11 0.548195
\(339\) 9.72449e10 0.399915
\(340\) −1.93576e10 −0.0785590
\(341\) 1.89886e11 0.760497
\(342\) −5.14378e10 −0.203313
\(343\) 2.05096e11 0.800079
\(344\) −2.63373e11 −1.01405
\(345\) 6.40763e10 0.243507
\(346\) −5.12657e11 −1.92302
\(347\) −5.57316e10 −0.206357 −0.103178 0.994663i \(-0.532901\pi\)
−0.103178 + 0.994663i \(0.532901\pi\)
\(348\) −2.12770e10 −0.0777684
\(349\) −5.47751e10 −0.197637 −0.0988185 0.995105i \(-0.531506\pi\)
−0.0988185 + 0.995105i \(0.531506\pi\)
\(350\) 4.00742e11 1.42744
\(351\) 3.86219e10 0.135816
\(352\) 7.51673e10 0.260968
\(353\) −5.18865e10 −0.177856 −0.0889279 0.996038i \(-0.528344\pi\)
−0.0889279 + 0.996038i \(0.528344\pi\)
\(354\) −2.42548e10 −0.0820887
\(355\) 1.55776e11 0.520563
\(356\) −6.98674e10 −0.230542
\(357\) 2.73878e11 0.892381
\(358\) −3.94493e11 −1.26931
\(359\) 4.27875e9 0.0135954 0.00679770 0.999977i \(-0.497836\pi\)
0.00679770 + 0.999977i \(0.497836\pi\)
\(360\) 3.90956e10 0.122678
\(361\) −2.22037e11 −0.688088
\(362\) 3.68559e11 1.12802
\(363\) 1.01098e11 0.305608
\(364\) −7.21054e10 −0.215284
\(365\) −1.81867e11 −0.536334
\(366\) −1.01950e11 −0.296976
\(367\) 1.77664e11 0.511214 0.255607 0.966781i \(-0.417725\pi\)
0.255607 + 0.966781i \(0.417725\pi\)
\(368\) 4.10764e11 1.16755
\(369\) 1.38470e10 0.0388808
\(370\) 8.79417e10 0.243942
\(371\) −9.49346e10 −0.260161
\(372\) −4.55570e10 −0.123342
\(373\) −4.80359e11 −1.28492 −0.642460 0.766319i \(-0.722086\pi\)
−0.642460 + 0.766319i \(0.722086\pi\)
\(374\) 2.76833e11 0.731638
\(375\) 1.68506e11 0.440022
\(376\) −3.96454e11 −1.02293
\(377\) −1.93464e11 −0.493247
\(378\) 1.32052e11 0.332684
\(379\) 3.08183e11 0.767243 0.383621 0.923490i \(-0.374677\pi\)
0.383621 + 0.923490i \(0.374677\pi\)
\(380\) 1.82630e10 0.0449309
\(381\) −3.46916e11 −0.843456
\(382\) −2.63709e11 −0.633636
\(383\) −2.66534e11 −0.632934 −0.316467 0.948604i \(-0.602497\pi\)
−0.316467 + 0.948604i \(0.602497\pi\)
\(384\) 2.92422e11 0.686309
\(385\) 1.95421e11 0.453313
\(386\) 6.56684e11 1.50561
\(387\) −1.69178e11 −0.383393
\(388\) −3.65084e10 −0.0817805
\(389\) 5.77946e11 1.27972 0.639858 0.768493i \(-0.278993\pi\)
0.639858 + 0.768493i \(0.278993\pi\)
\(390\) −8.48651e10 −0.185754
\(391\) 4.55973e11 0.986607
\(392\) 6.20511e11 1.32728
\(393\) 4.38191e10 0.0926610
\(394\) 5.21897e11 1.09107
\(395\) 2.41718e11 0.499600
\(396\) 2.15675e10 0.0440729
\(397\) −1.36491e11 −0.275769 −0.137885 0.990448i \(-0.544030\pi\)
−0.137885 + 0.990448i \(0.544030\pi\)
\(398\) −6.85521e11 −1.36945
\(399\) −2.58391e11 −0.510387
\(400\) 4.88557e11 0.954213
\(401\) −7.29742e11 −1.40935 −0.704676 0.709529i \(-0.748908\pi\)
−0.704676 + 0.709529i \(0.748908\pi\)
\(402\) −2.40058e11 −0.458457
\(403\) −4.14233e11 −0.782298
\(404\) 2.70067e10 0.0504378
\(405\) 2.51131e10 0.0463824
\(406\) −6.61472e11 −1.20821
\(407\) −2.03215e11 −0.367097
\(408\) 2.78208e11 0.497049
\(409\) 5.94538e11 1.05057 0.525285 0.850926i \(-0.323959\pi\)
0.525285 + 0.850926i \(0.323959\pi\)
\(410\) −3.04263e10 −0.0531768
\(411\) 2.44310e11 0.422331
\(412\) 1.10102e10 0.0188260
\(413\) −1.21841e11 −0.206072
\(414\) 2.19850e11 0.367812
\(415\) 1.59946e11 0.264701
\(416\) −1.63977e11 −0.268449
\(417\) 3.67324e11 0.594891
\(418\) −2.61179e11 −0.418451
\(419\) −1.07046e12 −1.69671 −0.848357 0.529425i \(-0.822408\pi\)
−0.848357 + 0.529425i \(0.822408\pi\)
\(420\) −4.68850e10 −0.0735211
\(421\) 4.16461e11 0.646108 0.323054 0.946381i \(-0.395290\pi\)
0.323054 + 0.946381i \(0.395290\pi\)
\(422\) 5.64007e11 0.865722
\(423\) −2.54663e11 −0.386754
\(424\) −9.64354e10 −0.144907
\(425\) 5.42328e11 0.806328
\(426\) 5.34479e11 0.786299
\(427\) −5.12131e11 −0.745514
\(428\) 1.28906e11 0.185685
\(429\) 1.96106e11 0.279533
\(430\) 3.71739e11 0.524361
\(431\) −9.10399e11 −1.27082 −0.635410 0.772175i \(-0.719169\pi\)
−0.635410 + 0.772175i \(0.719169\pi\)
\(432\) 1.60989e11 0.222392
\(433\) −4.34129e11 −0.593504 −0.296752 0.954955i \(-0.595903\pi\)
−0.296752 + 0.954955i \(0.595903\pi\)
\(434\) −1.41630e12 −1.91625
\(435\) −1.25796e11 −0.168448
\(436\) −1.73732e11 −0.230245
\(437\) −4.30189e11 −0.564278
\(438\) −6.23998e11 −0.810120
\(439\) −3.72886e11 −0.479166 −0.239583 0.970876i \(-0.577011\pi\)
−0.239583 + 0.970876i \(0.577011\pi\)
\(440\) 1.98511e11 0.252492
\(441\) 3.98586e11 0.501821
\(442\) −6.03908e11 −0.752611
\(443\) −1.16812e12 −1.44102 −0.720511 0.693444i \(-0.756093\pi\)
−0.720511 + 0.693444i \(0.756093\pi\)
\(444\) 4.87549e10 0.0595381
\(445\) −4.13078e11 −0.499357
\(446\) 2.51124e11 0.300526
\(447\) 4.87139e9 0.00577124
\(448\) 9.98884e11 1.17156
\(449\) −3.08179e11 −0.357844 −0.178922 0.983863i \(-0.557261\pi\)
−0.178922 + 0.983863i \(0.557261\pi\)
\(450\) 2.61487e11 0.300603
\(451\) 7.03089e10 0.0800232
\(452\) −1.18464e11 −0.133494
\(453\) 1.16642e11 0.130140
\(454\) −1.61322e12 −1.78214
\(455\) −4.26309e11 −0.466308
\(456\) −2.62476e11 −0.284281
\(457\) 8.35294e11 0.895811 0.447906 0.894081i \(-0.352170\pi\)
0.447906 + 0.894081i \(0.352170\pi\)
\(458\) 2.83830e11 0.301414
\(459\) 1.78707e11 0.187925
\(460\) −7.80577e10 −0.0812841
\(461\) −1.21807e12 −1.25608 −0.628041 0.778180i \(-0.716143\pi\)
−0.628041 + 0.778180i \(0.716143\pi\)
\(462\) 6.70504e11 0.684719
\(463\) 6.81687e11 0.689399 0.344699 0.938713i \(-0.387981\pi\)
0.344699 + 0.938713i \(0.387981\pi\)
\(464\) −8.06420e11 −0.807664
\(465\) −2.69347e11 −0.267161
\(466\) 8.18049e11 0.803605
\(467\) −9.80497e11 −0.953938 −0.476969 0.878920i \(-0.658265\pi\)
−0.476969 + 0.878920i \(0.658265\pi\)
\(468\) −4.70492e10 −0.0453363
\(469\) −1.20590e12 −1.15089
\(470\) 5.59578e11 0.528957
\(471\) 8.96033e11 0.838938
\(472\) −1.23767e11 −0.114780
\(473\) −8.59012e11 −0.789086
\(474\) 8.29353e11 0.754635
\(475\) −5.11661e11 −0.461170
\(476\) −3.33638e11 −0.297882
\(477\) −6.19454e10 −0.0547869
\(478\) −1.90063e11 −0.166522
\(479\) −4.03930e11 −0.350587 −0.175294 0.984516i \(-0.556088\pi\)
−0.175294 + 0.984516i \(0.556088\pi\)
\(480\) −1.06622e11 −0.0916775
\(481\) 4.43311e11 0.377621
\(482\) 2.29445e11 0.193627
\(483\) 1.10439e12 0.923337
\(484\) −1.23158e11 −0.102014
\(485\) −2.15849e11 −0.177138
\(486\) 8.61648e10 0.0700594
\(487\) −1.82775e12 −1.47243 −0.736217 0.676745i \(-0.763390\pi\)
−0.736217 + 0.676745i \(0.763390\pi\)
\(488\) −5.20228e11 −0.415245
\(489\) −2.54576e11 −0.201339
\(490\) −8.75825e11 −0.686333
\(491\) 1.13125e12 0.878401 0.439201 0.898389i \(-0.355262\pi\)
0.439201 + 0.898389i \(0.355262\pi\)
\(492\) −1.68684e10 −0.0129787
\(493\) −8.95176e11 −0.682492
\(494\) 5.69759e11 0.430447
\(495\) 1.27514e11 0.0954626
\(496\) −1.72666e12 −1.28097
\(497\) 2.68489e12 1.97389
\(498\) 5.48784e11 0.399825
\(499\) 1.24403e12 0.898209 0.449105 0.893479i \(-0.351743\pi\)
0.449105 + 0.893479i \(0.351743\pi\)
\(500\) −2.05274e11 −0.146882
\(501\) −7.46131e11 −0.529109
\(502\) −1.26498e12 −0.889033
\(503\) 2.15528e11 0.150123 0.0750616 0.997179i \(-0.476085\pi\)
0.0750616 + 0.997179i \(0.476085\pi\)
\(504\) 6.73833e11 0.465174
\(505\) 1.59672e11 0.109249
\(506\) 1.11631e12 0.757017
\(507\) 4.31162e11 0.289804
\(508\) 4.22613e11 0.281551
\(509\) −3.70298e9 −0.00244524 −0.00122262 0.999999i \(-0.500389\pi\)
−0.00122262 + 0.999999i \(0.500389\pi\)
\(510\) −3.92679e11 −0.257023
\(511\) −3.13457e12 −2.03369
\(512\) 9.00684e11 0.579238
\(513\) −1.68602e11 −0.107482
\(514\) −1.04278e12 −0.658959
\(515\) 6.50958e10 0.0407775
\(516\) 2.06092e11 0.127979
\(517\) −1.29307e12 −0.796003
\(518\) 1.51572e12 0.924987
\(519\) −1.68038e12 −1.01661
\(520\) −4.33049e11 −0.259730
\(521\) 1.81848e12 1.08128 0.540640 0.841254i \(-0.318182\pi\)
0.540640 + 0.841254i \(0.318182\pi\)
\(522\) −4.31615e11 −0.254436
\(523\) −2.89336e12 −1.69101 −0.845503 0.533970i \(-0.820700\pi\)
−0.845503 + 0.533970i \(0.820700\pi\)
\(524\) −5.33804e10 −0.0309308
\(525\) 1.31355e12 0.754620
\(526\) 5.14910e11 0.293289
\(527\) −1.91670e12 −1.08244
\(528\) 8.17432e11 0.457719
\(529\) 3.75193e10 0.0208307
\(530\) 1.36114e11 0.0749312
\(531\) −7.95020e10 −0.0433963
\(532\) 3.14772e11 0.170370
\(533\) −1.53378e11 −0.0823172
\(534\) −1.41730e12 −0.754268
\(535\) 7.62133e11 0.402197
\(536\) −1.22496e12 −0.641035
\(537\) −1.29306e12 −0.671020
\(538\) −9.82350e11 −0.505529
\(539\) 2.02385e12 1.03283
\(540\) −3.05928e10 −0.0154827
\(541\) 1.25468e12 0.629717 0.314858 0.949139i \(-0.398043\pi\)
0.314858 + 0.949139i \(0.398043\pi\)
\(542\) 2.32919e12 1.15933
\(543\) 1.20806e12 0.596331
\(544\) −7.58735e11 −0.371446
\(545\) −1.02715e12 −0.498713
\(546\) −1.46270e12 −0.704348
\(547\) 3.38178e12 1.61511 0.807555 0.589792i \(-0.200790\pi\)
0.807555 + 0.589792i \(0.200790\pi\)
\(548\) −2.97618e11 −0.140977
\(549\) −3.34169e11 −0.156997
\(550\) 1.32772e12 0.618691
\(551\) 8.44556e11 0.390343
\(552\) 1.12185e12 0.514291
\(553\) 4.16615e12 1.89440
\(554\) −3.04776e12 −1.37463
\(555\) 2.88254e11 0.128960
\(556\) −4.47474e11 −0.198578
\(557\) 4.26701e12 1.87835 0.939173 0.343445i \(-0.111594\pi\)
0.939173 + 0.343445i \(0.111594\pi\)
\(558\) −9.24147e11 −0.403540
\(559\) 1.87392e12 0.811706
\(560\) −1.77699e12 −0.763554
\(561\) 9.07400e11 0.386781
\(562\) −2.41227e12 −1.02003
\(563\) 1.91024e12 0.801310 0.400655 0.916229i \(-0.368783\pi\)
0.400655 + 0.916229i \(0.368783\pi\)
\(564\) 3.10230e11 0.129101
\(565\) −7.00393e11 −0.289150
\(566\) 4.73443e12 1.93907
\(567\) 4.32838e11 0.175874
\(568\) 2.72733e12 1.09944
\(569\) 2.79896e12 1.11942 0.559708 0.828690i \(-0.310913\pi\)
0.559708 + 0.828690i \(0.310913\pi\)
\(570\) 3.70474e11 0.147001
\(571\) −2.87023e10 −0.0112994 −0.00564969 0.999984i \(-0.501798\pi\)
−0.00564969 + 0.999984i \(0.501798\pi\)
\(572\) −2.38896e11 −0.0933097
\(573\) −8.64381e11 −0.334973
\(574\) −5.24414e11 −0.201637
\(575\) 2.18689e12 0.834299
\(576\) 6.51779e11 0.246717
\(577\) −3.08998e12 −1.16055 −0.580276 0.814420i \(-0.697055\pi\)
−0.580276 + 0.814420i \(0.697055\pi\)
\(578\) 1.36182e11 0.0507508
\(579\) 2.15247e12 0.795945
\(580\) 1.53245e11 0.0562288
\(581\) 2.75675e12 1.00370
\(582\) −7.40592e11 −0.267563
\(583\) −3.14532e11 −0.112760
\(584\) −3.18413e12 −1.13275
\(585\) −2.78169e11 −0.0981992
\(586\) 2.66730e12 0.934399
\(587\) −9.98356e11 −0.347067 −0.173534 0.984828i \(-0.555519\pi\)
−0.173534 + 0.984828i \(0.555519\pi\)
\(588\) −4.85558e11 −0.167511
\(589\) 1.80831e12 0.619091
\(590\) 1.74692e11 0.0593525
\(591\) 1.71067e12 0.576795
\(592\) 1.84786e12 0.618333
\(593\) 2.87076e12 0.953348 0.476674 0.879080i \(-0.341842\pi\)
0.476674 + 0.879080i \(0.341842\pi\)
\(594\) 4.37508e11 0.144194
\(595\) −1.97257e12 −0.645218
\(596\) −5.93433e9 −0.00192648
\(597\) −2.24699e12 −0.723963
\(598\) −2.43521e12 −0.778719
\(599\) −3.72134e12 −1.18108 −0.590539 0.807009i \(-0.701085\pi\)
−0.590539 + 0.807009i \(0.701085\pi\)
\(600\) 1.33431e12 0.420317
\(601\) 4.44903e12 1.39101 0.695505 0.718521i \(-0.255181\pi\)
0.695505 + 0.718521i \(0.255181\pi\)
\(602\) 6.40712e12 1.98829
\(603\) −7.86858e11 −0.242364
\(604\) −1.42093e11 −0.0434416
\(605\) −7.28148e11 −0.220963
\(606\) 5.47846e11 0.165018
\(607\) 1.63535e12 0.488947 0.244474 0.969656i \(-0.421385\pi\)
0.244474 + 0.969656i \(0.421385\pi\)
\(608\) 7.15831e11 0.212444
\(609\) −2.16816e12 −0.638725
\(610\) 7.34279e11 0.214722
\(611\) 2.82082e12 0.818822
\(612\) −2.17701e11 −0.0627306
\(613\) 3.00016e12 0.858168 0.429084 0.903265i \(-0.358836\pi\)
0.429084 + 0.903265i \(0.358836\pi\)
\(614\) 5.72140e12 1.62459
\(615\) −9.97308e10 −0.0281120
\(616\) 3.42144e12 0.957405
\(617\) 2.70641e12 0.751815 0.375907 0.926657i \(-0.377331\pi\)
0.375907 + 0.926657i \(0.377331\pi\)
\(618\) 2.23348e11 0.0615934
\(619\) −7.12632e12 −1.95100 −0.975500 0.219997i \(-0.929395\pi\)
−0.975500 + 0.219997i \(0.929395\pi\)
\(620\) 3.28118e11 0.0891800
\(621\) 7.20621e11 0.194444
\(622\) −3.99395e12 −1.06991
\(623\) −7.11961e12 −1.89348
\(624\) −1.78322e12 −0.470840
\(625\) 1.93632e12 0.507594
\(626\) −7.32826e11 −0.190729
\(627\) −8.56088e11 −0.221215
\(628\) −1.09155e12 −0.280043
\(629\) 2.05124e12 0.522503
\(630\) −9.51087e11 −0.240540
\(631\) −1.93984e12 −0.487117 −0.243558 0.969886i \(-0.578315\pi\)
−0.243558 + 0.969886i \(0.578315\pi\)
\(632\) 4.23201e12 1.05516
\(633\) 1.84869e12 0.457665
\(634\) 6.87683e12 1.69039
\(635\) 2.49862e12 0.609843
\(636\) 7.54619e10 0.0182882
\(637\) −4.41501e12 −1.06244
\(638\) −2.19155e12 −0.523672
\(639\) 1.75191e12 0.415678
\(640\) −2.10613e12 −0.496221
\(641\) −5.51853e12 −1.29111 −0.645553 0.763715i \(-0.723373\pi\)
−0.645553 + 0.763715i \(0.723373\pi\)
\(642\) 2.61493e12 0.607509
\(643\) 3.98103e12 0.918431 0.459216 0.888325i \(-0.348131\pi\)
0.459216 + 0.888325i \(0.348131\pi\)
\(644\) −1.34537e12 −0.308215
\(645\) 1.21848e12 0.277204
\(646\) 2.63633e12 0.595598
\(647\) −1.27610e11 −0.0286297 −0.0143148 0.999898i \(-0.504557\pi\)
−0.0143148 + 0.999898i \(0.504557\pi\)
\(648\) 4.39681e11 0.0979602
\(649\) −4.03677e11 −0.0893168
\(650\) −2.89640e12 −0.636427
\(651\) −4.64233e12 −1.01303
\(652\) 3.10124e11 0.0672081
\(653\) 1.16332e12 0.250375 0.125188 0.992133i \(-0.460047\pi\)
0.125188 + 0.992133i \(0.460047\pi\)
\(654\) −3.52424e12 −0.753295
\(655\) −3.15601e11 −0.0669966
\(656\) −6.39329e11 −0.134790
\(657\) −2.04533e12 −0.428272
\(658\) 9.64464e12 2.00572
\(659\) 5.75734e12 1.18915 0.594576 0.804040i \(-0.297320\pi\)
0.594576 + 0.804040i \(0.297320\pi\)
\(660\) −1.55337e11 −0.0318660
\(661\) −2.31031e12 −0.470721 −0.235360 0.971908i \(-0.575627\pi\)
−0.235360 + 0.971908i \(0.575627\pi\)
\(662\) 9.32824e12 1.88773
\(663\) −1.97948e12 −0.397869
\(664\) 2.80033e12 0.559053
\(665\) 1.86103e12 0.369025
\(666\) 9.89018e11 0.194792
\(667\) −3.60972e12 −0.706167
\(668\) 9.08936e11 0.176620
\(669\) 8.23131e11 0.158874
\(670\) 1.72899e12 0.331478
\(671\) −1.69677e12 −0.323125
\(672\) −1.83769e12 −0.347625
\(673\) 2.38685e12 0.448495 0.224248 0.974532i \(-0.428008\pi\)
0.224248 + 0.974532i \(0.428008\pi\)
\(674\) 3.97485e12 0.741910
\(675\) 8.57097e11 0.158914
\(676\) −5.25242e11 −0.0967385
\(677\) −6.20512e12 −1.13528 −0.567638 0.823278i \(-0.692143\pi\)
−0.567638 + 0.823278i \(0.692143\pi\)
\(678\) −2.40310e12 −0.436755
\(679\) −3.72027e12 −0.671677
\(680\) −2.00376e12 −0.359381
\(681\) −5.28779e12 −0.942133
\(682\) −4.69242e12 −0.830553
\(683\) −9.18735e12 −1.61546 −0.807731 0.589551i \(-0.799305\pi\)
−0.807731 + 0.589551i \(0.799305\pi\)
\(684\) 2.05391e11 0.0358780
\(685\) −1.75961e12 −0.305357
\(686\) −5.06829e12 −0.873781
\(687\) 9.30333e11 0.159343
\(688\) 7.81112e12 1.32912
\(689\) 6.86149e11 0.115993
\(690\) −1.58344e12 −0.265939
\(691\) −9.24435e12 −1.54250 −0.771250 0.636532i \(-0.780368\pi\)
−0.771250 + 0.636532i \(0.780368\pi\)
\(692\) 2.04704e12 0.339350
\(693\) 2.19777e12 0.361978
\(694\) 1.37723e12 0.225366
\(695\) −2.64560e12 −0.430123
\(696\) −2.20244e12 −0.355764
\(697\) −7.09695e11 −0.113900
\(698\) 1.35359e12 0.215843
\(699\) 2.68139e12 0.424827
\(700\) −1.60016e12 −0.251897
\(701\) −1.11505e13 −1.74407 −0.872033 0.489447i \(-0.837199\pi\)
−0.872033 + 0.489447i \(0.837199\pi\)
\(702\) −9.54418e11 −0.148328
\(703\) −1.93525e12 −0.298839
\(704\) 3.30945e12 0.507784
\(705\) 1.83418e12 0.279634
\(706\) 1.28221e12 0.194240
\(707\) 2.75203e12 0.414254
\(708\) 9.68493e10 0.0144859
\(709\) 5.08517e12 0.755783 0.377892 0.925850i \(-0.376649\pi\)
0.377892 + 0.925850i \(0.376649\pi\)
\(710\) −3.84951e12 −0.568517
\(711\) 2.71844e12 0.398939
\(712\) −7.23217e12 −1.05465
\(713\) −7.72891e12 −1.11999
\(714\) −6.76803e12 −0.974586
\(715\) −1.41243e12 −0.202110
\(716\) 1.57521e12 0.223991
\(717\) −6.22985e11 −0.0880322
\(718\) −1.05736e11 −0.0148478
\(719\) −1.03787e13 −1.44832 −0.724158 0.689634i \(-0.757771\pi\)
−0.724158 + 0.689634i \(0.757771\pi\)
\(720\) −1.15950e12 −0.160796
\(721\) 1.12196e12 0.154621
\(722\) 5.48695e12 0.751474
\(723\) 7.52070e11 0.102361
\(724\) −1.47165e12 −0.199059
\(725\) −4.29335e12 −0.577132
\(726\) −2.49832e12 −0.333760
\(727\) 5.48173e12 0.727802 0.363901 0.931438i \(-0.381445\pi\)
0.363901 + 0.931438i \(0.381445\pi\)
\(728\) −7.46382e12 −0.984850
\(729\) 2.82430e11 0.0370370
\(730\) 4.49426e12 0.585741
\(731\) 8.67083e12 1.12314
\(732\) 4.07085e11 0.0524065
\(733\) 4.00237e12 0.512093 0.256047 0.966664i \(-0.417580\pi\)
0.256047 + 0.966664i \(0.417580\pi\)
\(734\) −4.39041e12 −0.558306
\(735\) −2.87076e12 −0.362831
\(736\) −3.05953e12 −0.384331
\(737\) −3.99533e12 −0.498826
\(738\) −3.42183e11 −0.0424625
\(739\) −1.25819e13 −1.55184 −0.775920 0.630832i \(-0.782714\pi\)
−0.775920 + 0.630832i \(0.782714\pi\)
\(740\) −3.51151e11 −0.0430478
\(741\) 1.86755e12 0.227557
\(742\) 2.34601e12 0.284126
\(743\) −5.63633e12 −0.678495 −0.339247 0.940697i \(-0.610172\pi\)
−0.339247 + 0.940697i \(0.610172\pi\)
\(744\) −4.71573e12 −0.564248
\(745\) −3.50856e10 −0.00417278
\(746\) 1.18705e13 1.40329
\(747\) 1.79880e12 0.211368
\(748\) −1.10539e12 −0.129110
\(749\) 1.31358e13 1.52506
\(750\) −4.16409e12 −0.480556
\(751\) −3.92028e12 −0.449715 −0.224857 0.974392i \(-0.572192\pi\)
−0.224857 + 0.974392i \(0.572192\pi\)
\(752\) 1.17581e13 1.34077
\(753\) −4.14634e12 −0.469989
\(754\) 4.78085e12 0.538684
\(755\) −8.40095e11 −0.0940951
\(756\) −5.27283e11 −0.0587078
\(757\) 1.70392e13 1.88590 0.942948 0.332940i \(-0.108041\pi\)
0.942948 + 0.332940i \(0.108041\pi\)
\(758\) −7.61577e12 −0.837920
\(759\) 3.65901e12 0.400198
\(760\) 1.89045e12 0.205544
\(761\) −1.25446e13 −1.35590 −0.677949 0.735109i \(-0.737131\pi\)
−0.677949 + 0.735109i \(0.737131\pi\)
\(762\) 8.57294e12 0.921154
\(763\) −1.77035e13 −1.89104
\(764\) 1.05299e12 0.111816
\(765\) −1.28712e12 −0.135876
\(766\) 6.58654e12 0.691239
\(767\) 8.80617e11 0.0918772
\(768\) −3.10640e12 −0.322204
\(769\) −1.86068e12 −0.191868 −0.0959342 0.995388i \(-0.530584\pi\)
−0.0959342 + 0.995388i \(0.530584\pi\)
\(770\) −4.82921e12 −0.495072
\(771\) −3.41800e12 −0.348360
\(772\) −2.62214e12 −0.265691
\(773\) −3.51001e12 −0.353590 −0.176795 0.984248i \(-0.556573\pi\)
−0.176795 + 0.984248i \(0.556573\pi\)
\(774\) 4.18069e12 0.418710
\(775\) −9.19266e12 −0.915342
\(776\) −3.77908e12 −0.374118
\(777\) 4.96821e12 0.488996
\(778\) −1.42821e13 −1.39760
\(779\) 6.69563e11 0.0651438
\(780\) 3.38866e11 0.0327795
\(781\) 8.89543e12 0.855534
\(782\) −1.12679e13 −1.07749
\(783\) −1.41474e12 −0.134508
\(784\) −1.84032e13 −1.73968
\(785\) −6.45356e12 −0.606577
\(786\) −1.08285e12 −0.101197
\(787\) 1.24989e12 0.116141 0.0580706 0.998312i \(-0.481505\pi\)
0.0580706 + 0.998312i \(0.481505\pi\)
\(788\) −2.08393e12 −0.192538
\(789\) 1.68776e12 0.155048
\(790\) −5.97330e12 −0.545623
\(791\) −1.20717e13 −1.09641
\(792\) 2.23251e12 0.201618
\(793\) 3.70148e12 0.332388
\(794\) 3.37293e12 0.301173
\(795\) 4.46154e11 0.0396125
\(796\) 2.73728e12 0.241663
\(797\) −5.24321e12 −0.460294 −0.230147 0.973156i \(-0.573921\pi\)
−0.230147 + 0.973156i \(0.573921\pi\)
\(798\) 6.38531e12 0.557403
\(799\) 1.30522e13 1.13298
\(800\) −3.63896e12 −0.314104
\(801\) −4.64559e12 −0.398745
\(802\) 1.80333e13 1.53918
\(803\) −1.03853e13 −0.881454
\(804\) 9.58550e11 0.0809026
\(805\) −7.95422e12 −0.667600
\(806\) 1.02365e13 0.854363
\(807\) −3.21993e12 −0.267249
\(808\) 2.79554e12 0.230736
\(809\) 7.17872e12 0.589221 0.294611 0.955617i \(-0.404810\pi\)
0.294611 + 0.955617i \(0.404810\pi\)
\(810\) −6.20591e11 −0.0506550
\(811\) 5.28665e12 0.429128 0.214564 0.976710i \(-0.431167\pi\)
0.214564 + 0.976710i \(0.431167\pi\)
\(812\) 2.64125e12 0.213210
\(813\) 7.63458e12 0.612883
\(814\) 5.02181e12 0.400914
\(815\) 1.83355e12 0.145574
\(816\) −8.25111e12 −0.651489
\(817\) −8.18051e12 −0.642364
\(818\) −1.46921e13 −1.14735
\(819\) −4.79440e12 −0.372354
\(820\) 1.21492e11 0.00938395
\(821\) 7.85159e12 0.603134 0.301567 0.953445i \(-0.402490\pi\)
0.301567 + 0.953445i \(0.402490\pi\)
\(822\) −6.03734e12 −0.461235
\(823\) 4.98524e12 0.378780 0.189390 0.981902i \(-0.439349\pi\)
0.189390 + 0.981902i \(0.439349\pi\)
\(824\) 1.13970e12 0.0861227
\(825\) 4.35197e12 0.327072
\(826\) 3.01091e12 0.225055
\(827\) 9.30138e12 0.691469 0.345735 0.938332i \(-0.387630\pi\)
0.345735 + 0.938332i \(0.387630\pi\)
\(828\) −8.77861e11 −0.0649066
\(829\) −3.32785e12 −0.244719 −0.122360 0.992486i \(-0.539046\pi\)
−0.122360 + 0.992486i \(0.539046\pi\)
\(830\) −3.95255e12 −0.289085
\(831\) −9.98988e12 −0.726701
\(832\) −7.21953e12 −0.522341
\(833\) −2.04286e13 −1.47007
\(834\) −9.07725e12 −0.649691
\(835\) 5.37391e12 0.382561
\(836\) 1.04289e12 0.0738429
\(837\) −3.02915e12 −0.213332
\(838\) 2.64531e13 1.85301
\(839\) 7.16300e12 0.499075 0.249538 0.968365i \(-0.419721\pi\)
0.249538 + 0.968365i \(0.419721\pi\)
\(840\) −4.85320e12 −0.336334
\(841\) −7.42047e12 −0.511504
\(842\) −1.02915e13 −0.705627
\(843\) −7.90690e12 −0.539240
\(844\) −2.25208e12 −0.152771
\(845\) −3.10539e12 −0.209537
\(846\) 6.29319e12 0.422381
\(847\) −1.25500e13 −0.837855
\(848\) 2.86009e12 0.189932
\(849\) 1.55184e13 1.02509
\(850\) −1.34019e13 −0.880606
\(851\) 8.27145e12 0.540628
\(852\) −2.13417e12 −0.138756
\(853\) 1.95050e13 1.26146 0.630732 0.776001i \(-0.282755\pi\)
0.630732 + 0.776001i \(0.282755\pi\)
\(854\) 1.26557e13 0.814190
\(855\) 1.21433e12 0.0777124
\(856\) 1.33434e13 0.849446
\(857\) −1.86203e13 −1.17916 −0.589581 0.807709i \(-0.700707\pi\)
−0.589581 + 0.807709i \(0.700707\pi\)
\(858\) −4.84613e12 −0.305283
\(859\) 2.15213e13 1.34865 0.674324 0.738436i \(-0.264435\pi\)
0.674324 + 0.738436i \(0.264435\pi\)
\(860\) −1.48435e12 −0.0925324
\(861\) −1.71891e12 −0.106596
\(862\) 2.24976e13 1.38789
\(863\) −2.03644e13 −1.24975 −0.624874 0.780725i \(-0.714850\pi\)
−0.624874 + 0.780725i \(0.714850\pi\)
\(864\) −1.19911e12 −0.0732059
\(865\) 1.21027e13 0.735038
\(866\) 1.07281e13 0.648176
\(867\) 4.46374e11 0.0268295
\(868\) 5.65529e12 0.338155
\(869\) 1.38031e13 0.821082
\(870\) 3.10865e12 0.183965
\(871\) 8.71576e12 0.513125
\(872\) −1.79834e13 −1.05329
\(873\) −2.42750e12 −0.141447
\(874\) 1.06308e13 0.616258
\(875\) −2.09178e13 −1.20637
\(876\) 2.49162e12 0.142960
\(877\) −6.72050e12 −0.383622 −0.191811 0.981432i \(-0.561436\pi\)
−0.191811 + 0.981432i \(0.561436\pi\)
\(878\) 9.21470e12 0.523306
\(879\) 8.74283e12 0.493972
\(880\) −5.88744e12 −0.330944
\(881\) 1.12208e13 0.627526 0.313763 0.949501i \(-0.398410\pi\)
0.313763 + 0.949501i \(0.398410\pi\)
\(882\) −9.84979e12 −0.548048
\(883\) −5.14531e12 −0.284832 −0.142416 0.989807i \(-0.545487\pi\)
−0.142416 + 0.989807i \(0.545487\pi\)
\(884\) 2.41140e12 0.132811
\(885\) 5.72603e11 0.0313768
\(886\) 2.88664e13 1.57377
\(887\) 2.87791e13 1.56106 0.780531 0.625117i \(-0.214949\pi\)
0.780531 + 0.625117i \(0.214949\pi\)
\(888\) 5.04675e12 0.272366
\(889\) 4.30651e13 2.31242
\(890\) 1.02079e13 0.545358
\(891\) 1.43406e12 0.0762284
\(892\) −1.00274e12 −0.0530329
\(893\) −1.23141e13 −0.647995
\(894\) −1.20381e11 −0.00630288
\(895\) 9.31312e12 0.485167
\(896\) −3.63003e13 −1.88159
\(897\) −7.98208e12 −0.411671
\(898\) 7.61566e12 0.390808
\(899\) 1.51736e13 0.774763
\(900\) −1.04412e12 −0.0530465
\(901\) 3.17487e12 0.160496
\(902\) −1.73746e12 −0.0873948
\(903\) 2.10012e13 1.05111
\(904\) −1.22625e13 −0.610690
\(905\) −8.70086e12 −0.431165
\(906\) −2.88242e12 −0.142128
\(907\) −5.53089e11 −0.0271370 −0.0135685 0.999908i \(-0.504319\pi\)
−0.0135685 + 0.999908i \(0.504319\pi\)
\(908\) 6.44158e12 0.314490
\(909\) 1.79572e12 0.0872371
\(910\) 1.05349e13 0.509264
\(911\) −1.02219e13 −0.491700 −0.245850 0.969308i \(-0.579067\pi\)
−0.245850 + 0.969308i \(0.579067\pi\)
\(912\) 7.78453e12 0.372611
\(913\) 9.13352e12 0.435030
\(914\) −2.06416e13 −0.978332
\(915\) 2.40681e12 0.113513
\(916\) −1.13333e12 −0.0531897
\(917\) −5.43956e12 −0.254040
\(918\) −4.41618e12 −0.205237
\(919\) −8.14184e12 −0.376533 −0.188266 0.982118i \(-0.560287\pi\)
−0.188266 + 0.982118i \(0.560287\pi\)
\(920\) −8.07997e12 −0.371847
\(921\) 1.87535e13 0.858844
\(922\) 3.01007e13 1.37179
\(923\) −1.94053e13 −0.880060
\(924\) −2.67732e12 −0.120830
\(925\) 9.83795e12 0.441842
\(926\) −1.68457e13 −0.752905
\(927\) 7.32087e11 0.0325615
\(928\) 6.00654e12 0.265863
\(929\) −3.34987e13 −1.47556 −0.737781 0.675040i \(-0.764126\pi\)
−0.737781 + 0.675040i \(0.764126\pi\)
\(930\) 6.65604e12 0.291772
\(931\) 1.92735e13 0.840787
\(932\) −3.26647e12 −0.141810
\(933\) −1.30913e13 −0.565608
\(934\) 2.42299e13 1.04181
\(935\) −6.53542e12 −0.279654
\(936\) −4.87019e12 −0.207398
\(937\) −2.93698e13 −1.24472 −0.622362 0.782730i \(-0.713827\pi\)
−0.622362 + 0.782730i \(0.713827\pi\)
\(938\) 2.98000e13 1.25691
\(939\) −2.40205e12 −0.100829
\(940\) −2.23439e12 −0.0933436
\(941\) 2.86861e13 1.19267 0.596333 0.802737i \(-0.296624\pi\)
0.596333 + 0.802737i \(0.296624\pi\)
\(942\) −2.21426e13 −0.916220
\(943\) −2.86178e12 −0.117851
\(944\) 3.67070e12 0.150444
\(945\) −3.11746e12 −0.127162
\(946\) 2.12278e13 0.861775
\(947\) 9.95289e12 0.402137 0.201069 0.979577i \(-0.435559\pi\)
0.201069 + 0.979577i \(0.435559\pi\)
\(948\) −3.31160e12 −0.133168
\(949\) 2.26554e13 0.906722
\(950\) 1.26441e13 0.503652
\(951\) 2.25408e13 0.893627
\(952\) −3.45358e13 −1.36271
\(953\) −2.34797e12 −0.0922092 −0.0461046 0.998937i \(-0.514681\pi\)
−0.0461046 + 0.998937i \(0.514681\pi\)
\(954\) 1.53078e12 0.0598338
\(955\) 6.22559e12 0.242195
\(956\) 7.58920e11 0.0293857
\(957\) −7.18344e12 −0.276840
\(958\) 9.98185e12 0.382883
\(959\) −3.03278e13 −1.15786
\(960\) −4.69435e12 −0.178384
\(961\) 6.04908e12 0.228788
\(962\) −1.09550e13 −0.412407
\(963\) 8.57118e12 0.321161
\(964\) −9.16172e11 −0.0341688
\(965\) −1.55029e13 −0.575492
\(966\) −2.72915e13 −1.00839
\(967\) −4.11035e13 −1.51168 −0.755840 0.654756i \(-0.772771\pi\)
−0.755840 + 0.654756i \(0.772771\pi\)
\(968\) −1.27484e13 −0.466678
\(969\) 8.64131e12 0.314864
\(970\) 5.33402e12 0.193456
\(971\) 1.57004e13 0.566793 0.283396 0.959003i \(-0.408539\pi\)
0.283396 + 0.959003i \(0.408539\pi\)
\(972\) −3.44056e11 −0.0123632
\(973\) −4.55984e13 −1.63095
\(974\) 4.51670e13 1.60807
\(975\) −9.49377e12 −0.336448
\(976\) 1.54290e13 0.544267
\(977\) −3.32213e13 −1.16652 −0.583258 0.812287i \(-0.698223\pi\)
−0.583258 + 0.812287i \(0.698223\pi\)
\(978\) 6.29104e12 0.219886
\(979\) −2.35883e13 −0.820683
\(980\) 3.49716e12 0.121115
\(981\) −1.15517e13 −0.398231
\(982\) −2.79553e13 −0.959318
\(983\) 1.42131e13 0.485510 0.242755 0.970088i \(-0.421949\pi\)
0.242755 + 0.970088i \(0.421949\pi\)
\(984\) −1.74609e12 −0.0593729
\(985\) −1.23208e13 −0.417040
\(986\) 2.21214e13 0.745362
\(987\) 3.16130e13 1.06032
\(988\) −2.27504e12 −0.0759598
\(989\) 3.49643e13 1.16210
\(990\) −3.15109e12 −0.104256
\(991\) 5.46920e12 0.180133 0.0900664 0.995936i \(-0.471292\pi\)
0.0900664 + 0.995936i \(0.471292\pi\)
\(992\) 1.28608e13 0.421664
\(993\) 3.05759e13 0.997949
\(994\) −6.63485e13 −2.15572
\(995\) 1.61836e13 0.523446
\(996\) −2.19129e12 −0.0705559
\(997\) −2.15200e13 −0.689784 −0.344892 0.938642i \(-0.612084\pi\)
−0.344892 + 0.938642i \(0.612084\pi\)
\(998\) −3.07422e13 −0.980951
\(999\) 3.24179e12 0.102977
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.1.5 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.b.1.5 21 1.1 even 1 trivial