Properties

Label 4034.2.a.d.1.10
Level 4034
Weight 2
Character 4034.1
Self dual yes
Analytic conductor 32.212
Analytic rank 0
Dimension 52
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2116521754\)
Analytic rank: \(0\)
Dimension: \(52\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.89942 q^{3} +1.00000 q^{4} +0.311705 q^{5} -1.89942 q^{6} +2.23532 q^{7} +1.00000 q^{8} +0.607790 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.89942 q^{3} +1.00000 q^{4} +0.311705 q^{5} -1.89942 q^{6} +2.23532 q^{7} +1.00000 q^{8} +0.607790 q^{9} +0.311705 q^{10} +4.25242 q^{11} -1.89942 q^{12} +2.41091 q^{13} +2.23532 q^{14} -0.592058 q^{15} +1.00000 q^{16} +6.75619 q^{17} +0.607790 q^{18} -6.91293 q^{19} +0.311705 q^{20} -4.24582 q^{21} +4.25242 q^{22} +5.68562 q^{23} -1.89942 q^{24} -4.90284 q^{25} +2.41091 q^{26} +4.54381 q^{27} +2.23532 q^{28} +6.13276 q^{29} -0.592058 q^{30} -3.55427 q^{31} +1.00000 q^{32} -8.07713 q^{33} +6.75619 q^{34} +0.696762 q^{35} +0.607790 q^{36} -4.53006 q^{37} -6.91293 q^{38} -4.57932 q^{39} +0.311705 q^{40} +2.55236 q^{41} -4.24582 q^{42} +3.90707 q^{43} +4.25242 q^{44} +0.189451 q^{45} +5.68562 q^{46} -1.69908 q^{47} -1.89942 q^{48} -2.00332 q^{49} -4.90284 q^{50} -12.8328 q^{51} +2.41091 q^{52} +2.94978 q^{53} +4.54381 q^{54} +1.32550 q^{55} +2.23532 q^{56} +13.1305 q^{57} +6.13276 q^{58} +2.92742 q^{59} -0.592058 q^{60} -7.23183 q^{61} -3.55427 q^{62} +1.35861 q^{63} +1.00000 q^{64} +0.751491 q^{65} -8.07713 q^{66} -5.67176 q^{67} +6.75619 q^{68} -10.7994 q^{69} +0.696762 q^{70} -11.3055 q^{71} +0.607790 q^{72} +13.3499 q^{73} -4.53006 q^{74} +9.31254 q^{75} -6.91293 q^{76} +9.50554 q^{77} -4.57932 q^{78} -2.07583 q^{79} +0.311705 q^{80} -10.4540 q^{81} +2.55236 q^{82} -1.96803 q^{83} -4.24582 q^{84} +2.10594 q^{85} +3.90707 q^{86} -11.6487 q^{87} +4.25242 q^{88} +10.8323 q^{89} +0.189451 q^{90} +5.38916 q^{91} +5.68562 q^{92} +6.75105 q^{93} -1.69908 q^{94} -2.15479 q^{95} -1.89942 q^{96} -8.30633 q^{97} -2.00332 q^{98} +2.58458 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.89942 −1.09663 −0.548315 0.836272i \(-0.684730\pi\)
−0.548315 + 0.836272i \(0.684730\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.311705 0.139399 0.0696993 0.997568i \(-0.477796\pi\)
0.0696993 + 0.997568i \(0.477796\pi\)
\(6\) −1.89942 −0.775434
\(7\) 2.23532 0.844873 0.422437 0.906392i \(-0.361175\pi\)
0.422437 + 0.906392i \(0.361175\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.607790 0.202597
\(10\) 0.311705 0.0985697
\(11\) 4.25242 1.28215 0.641077 0.767477i \(-0.278488\pi\)
0.641077 + 0.767477i \(0.278488\pi\)
\(12\) −1.89942 −0.548315
\(13\) 2.41091 0.668665 0.334332 0.942455i \(-0.391489\pi\)
0.334332 + 0.942455i \(0.391489\pi\)
\(14\) 2.23532 0.597416
\(15\) −0.592058 −0.152869
\(16\) 1.00000 0.250000
\(17\) 6.75619 1.63862 0.819308 0.573353i \(-0.194358\pi\)
0.819308 + 0.573353i \(0.194358\pi\)
\(18\) 0.607790 0.143257
\(19\) −6.91293 −1.58594 −0.792968 0.609264i \(-0.791465\pi\)
−0.792968 + 0.609264i \(0.791465\pi\)
\(20\) 0.311705 0.0696993
\(21\) −4.24582 −0.926513
\(22\) 4.25242 0.906619
\(23\) 5.68562 1.18553 0.592767 0.805374i \(-0.298036\pi\)
0.592767 + 0.805374i \(0.298036\pi\)
\(24\) −1.89942 −0.387717
\(25\) −4.90284 −0.980568
\(26\) 2.41091 0.472817
\(27\) 4.54381 0.874456
\(28\) 2.23532 0.422437
\(29\) 6.13276 1.13883 0.569413 0.822052i \(-0.307171\pi\)
0.569413 + 0.822052i \(0.307171\pi\)
\(30\) −0.592058 −0.108094
\(31\) −3.55427 −0.638366 −0.319183 0.947693i \(-0.603408\pi\)
−0.319183 + 0.947693i \(0.603408\pi\)
\(32\) 1.00000 0.176777
\(33\) −8.07713 −1.40605
\(34\) 6.75619 1.15868
\(35\) 0.696762 0.117774
\(36\) 0.607790 0.101298
\(37\) −4.53006 −0.744737 −0.372369 0.928085i \(-0.621454\pi\)
−0.372369 + 0.928085i \(0.621454\pi\)
\(38\) −6.91293 −1.12143
\(39\) −4.57932 −0.733278
\(40\) 0.311705 0.0492849
\(41\) 2.55236 0.398611 0.199306 0.979937i \(-0.436131\pi\)
0.199306 + 0.979937i \(0.436131\pi\)
\(42\) −4.24582 −0.655144
\(43\) 3.90707 0.595822 0.297911 0.954594i \(-0.403710\pi\)
0.297911 + 0.954594i \(0.403710\pi\)
\(44\) 4.25242 0.641077
\(45\) 0.189451 0.0282417
\(46\) 5.68562 0.838299
\(47\) −1.69908 −0.247837 −0.123918 0.992292i \(-0.539546\pi\)
−0.123918 + 0.992292i \(0.539546\pi\)
\(48\) −1.89942 −0.274157
\(49\) −2.00332 −0.286189
\(50\) −4.90284 −0.693366
\(51\) −12.8328 −1.79696
\(52\) 2.41091 0.334332
\(53\) 2.94978 0.405184 0.202592 0.979263i \(-0.435063\pi\)
0.202592 + 0.979263i \(0.435063\pi\)
\(54\) 4.54381 0.618334
\(55\) 1.32550 0.178730
\(56\) 2.23532 0.298708
\(57\) 13.1305 1.73918
\(58\) 6.13276 0.805271
\(59\) 2.92742 0.381118 0.190559 0.981676i \(-0.438970\pi\)
0.190559 + 0.981676i \(0.438970\pi\)
\(60\) −0.592058 −0.0764343
\(61\) −7.23183 −0.925941 −0.462970 0.886374i \(-0.653216\pi\)
−0.462970 + 0.886374i \(0.653216\pi\)
\(62\) −3.55427 −0.451393
\(63\) 1.35861 0.171168
\(64\) 1.00000 0.125000
\(65\) 0.751491 0.0932110
\(66\) −8.07713 −0.994225
\(67\) −5.67176 −0.692915 −0.346458 0.938066i \(-0.612616\pi\)
−0.346458 + 0.938066i \(0.612616\pi\)
\(68\) 6.75619 0.819308
\(69\) −10.7994 −1.30009
\(70\) 0.696762 0.0832789
\(71\) −11.3055 −1.34172 −0.670858 0.741586i \(-0.734074\pi\)
−0.670858 + 0.741586i \(0.734074\pi\)
\(72\) 0.607790 0.0716287
\(73\) 13.3499 1.56249 0.781244 0.624226i \(-0.214586\pi\)
0.781244 + 0.624226i \(0.214586\pi\)
\(74\) −4.53006 −0.526609
\(75\) 9.31254 1.07532
\(76\) −6.91293 −0.792968
\(77\) 9.50554 1.08326
\(78\) −4.57932 −0.518506
\(79\) −2.07583 −0.233550 −0.116775 0.993158i \(-0.537256\pi\)
−0.116775 + 0.993158i \(0.537256\pi\)
\(80\) 0.311705 0.0348497
\(81\) −10.4540 −1.16155
\(82\) 2.55236 0.281861
\(83\) −1.96803 −0.216019 −0.108010 0.994150i \(-0.534448\pi\)
−0.108010 + 0.994150i \(0.534448\pi\)
\(84\) −4.24582 −0.463257
\(85\) 2.10594 0.228421
\(86\) 3.90707 0.421310
\(87\) −11.6487 −1.24887
\(88\) 4.25242 0.453310
\(89\) 10.8323 1.14822 0.574109 0.818779i \(-0.305348\pi\)
0.574109 + 0.818779i \(0.305348\pi\)
\(90\) 0.189451 0.0199699
\(91\) 5.38916 0.564937
\(92\) 5.68562 0.592767
\(93\) 6.75105 0.700051
\(94\) −1.69908 −0.175247
\(95\) −2.15479 −0.221077
\(96\) −1.89942 −0.193859
\(97\) −8.30633 −0.843380 −0.421690 0.906740i \(-0.638563\pi\)
−0.421690 + 0.906740i \(0.638563\pi\)
\(98\) −2.00332 −0.202366
\(99\) 2.58458 0.259760
\(100\) −4.90284 −0.490284
\(101\) 2.30019 0.228877 0.114439 0.993430i \(-0.463493\pi\)
0.114439 + 0.993430i \(0.463493\pi\)
\(102\) −12.8328 −1.27064
\(103\) 13.9502 1.37456 0.687279 0.726394i \(-0.258805\pi\)
0.687279 + 0.726394i \(0.258805\pi\)
\(104\) 2.41091 0.236409
\(105\) −1.32344 −0.129155
\(106\) 2.94978 0.286508
\(107\) 12.5091 1.20930 0.604651 0.796490i \(-0.293313\pi\)
0.604651 + 0.796490i \(0.293313\pi\)
\(108\) 4.54381 0.437228
\(109\) −12.7578 −1.22198 −0.610989 0.791639i \(-0.709228\pi\)
−0.610989 + 0.791639i \(0.709228\pi\)
\(110\) 1.32550 0.126381
\(111\) 8.60448 0.816701
\(112\) 2.23532 0.211218
\(113\) 7.72790 0.726980 0.363490 0.931598i \(-0.381585\pi\)
0.363490 + 0.931598i \(0.381585\pi\)
\(114\) 13.1305 1.22979
\(115\) 1.77224 0.165262
\(116\) 6.13276 0.569413
\(117\) 1.46532 0.135469
\(118\) 2.92742 0.269491
\(119\) 15.1023 1.38442
\(120\) −0.592058 −0.0540472
\(121\) 7.08308 0.643917
\(122\) −7.23183 −0.654739
\(123\) −4.84799 −0.437129
\(124\) −3.55427 −0.319183
\(125\) −3.08676 −0.276088
\(126\) 1.35861 0.121034
\(127\) −1.81770 −0.161295 −0.0806474 0.996743i \(-0.525699\pi\)
−0.0806474 + 0.996743i \(0.525699\pi\)
\(128\) 1.00000 0.0883883
\(129\) −7.42115 −0.653396
\(130\) 0.751491 0.0659101
\(131\) 20.7507 1.81300 0.906499 0.422209i \(-0.138745\pi\)
0.906499 + 0.422209i \(0.138745\pi\)
\(132\) −8.07713 −0.703024
\(133\) −15.4526 −1.33991
\(134\) −5.67176 −0.489965
\(135\) 1.41633 0.121898
\(136\) 6.75619 0.579338
\(137\) −9.23510 −0.789008 −0.394504 0.918894i \(-0.629084\pi\)
−0.394504 + 0.918894i \(0.629084\pi\)
\(138\) −10.7994 −0.919303
\(139\) −8.85808 −0.751333 −0.375666 0.926755i \(-0.622586\pi\)
−0.375666 + 0.926755i \(0.622586\pi\)
\(140\) 0.696762 0.0588871
\(141\) 3.22727 0.271785
\(142\) −11.3055 −0.948736
\(143\) 10.2522 0.857331
\(144\) 0.607790 0.0506491
\(145\) 1.91161 0.158751
\(146\) 13.3499 1.10485
\(147\) 3.80515 0.313843
\(148\) −4.53006 −0.372369
\(149\) 7.93318 0.649911 0.324956 0.945729i \(-0.394651\pi\)
0.324956 + 0.945729i \(0.394651\pi\)
\(150\) 9.31254 0.760366
\(151\) −16.7113 −1.35994 −0.679972 0.733238i \(-0.738008\pi\)
−0.679972 + 0.733238i \(0.738008\pi\)
\(152\) −6.91293 −0.560713
\(153\) 4.10634 0.331978
\(154\) 9.50554 0.765978
\(155\) −1.10788 −0.0889874
\(156\) −4.57932 −0.366639
\(157\) 20.4744 1.63404 0.817019 0.576611i \(-0.195625\pi\)
0.817019 + 0.576611i \(0.195625\pi\)
\(158\) −2.07583 −0.165145
\(159\) −5.60287 −0.444337
\(160\) 0.311705 0.0246424
\(161\) 12.7092 1.00163
\(162\) −10.4540 −0.821341
\(163\) 9.00051 0.704974 0.352487 0.935817i \(-0.385336\pi\)
0.352487 + 0.935817i \(0.385336\pi\)
\(164\) 2.55236 0.199306
\(165\) −2.51768 −0.196001
\(166\) −1.96803 −0.152749
\(167\) −8.99976 −0.696423 −0.348211 0.937416i \(-0.613211\pi\)
−0.348211 + 0.937416i \(0.613211\pi\)
\(168\) −4.24582 −0.327572
\(169\) −7.18754 −0.552887
\(170\) 2.10594 0.161518
\(171\) −4.20161 −0.321305
\(172\) 3.90707 0.297911
\(173\) 22.3103 1.69622 0.848111 0.529818i \(-0.177740\pi\)
0.848111 + 0.529818i \(0.177740\pi\)
\(174\) −11.6487 −0.883084
\(175\) −10.9594 −0.828456
\(176\) 4.25242 0.320538
\(177\) −5.56039 −0.417945
\(178\) 10.8323 0.811913
\(179\) 2.24497 0.167797 0.0838983 0.996474i \(-0.473263\pi\)
0.0838983 + 0.996474i \(0.473263\pi\)
\(180\) 0.189451 0.0141208
\(181\) 12.7432 0.947194 0.473597 0.880742i \(-0.342955\pi\)
0.473597 + 0.880742i \(0.342955\pi\)
\(182\) 5.38916 0.399471
\(183\) 13.7363 1.01541
\(184\) 5.68562 0.419149
\(185\) −1.41204 −0.103815
\(186\) 6.75105 0.495011
\(187\) 28.7302 2.10096
\(188\) −1.69908 −0.123918
\(189\) 10.1569 0.738805
\(190\) −2.15479 −0.156325
\(191\) 4.09996 0.296662 0.148331 0.988938i \(-0.452610\pi\)
0.148331 + 0.988938i \(0.452610\pi\)
\(192\) −1.89942 −0.137079
\(193\) 21.8203 1.57066 0.785331 0.619077i \(-0.212493\pi\)
0.785331 + 0.619077i \(0.212493\pi\)
\(194\) −8.30633 −0.596359
\(195\) −1.42740 −0.102218
\(196\) −2.00332 −0.143094
\(197\) −8.72843 −0.621875 −0.310938 0.950430i \(-0.600643\pi\)
−0.310938 + 0.950430i \(0.600643\pi\)
\(198\) 2.58458 0.183678
\(199\) −13.5977 −0.963917 −0.481959 0.876194i \(-0.660074\pi\)
−0.481959 + 0.876194i \(0.660074\pi\)
\(200\) −4.90284 −0.346683
\(201\) 10.7730 0.759872
\(202\) 2.30019 0.161841
\(203\) 13.7087 0.962163
\(204\) −12.8328 −0.898478
\(205\) 0.795582 0.0555659
\(206\) 13.9502 0.971959
\(207\) 3.45566 0.240185
\(208\) 2.41091 0.167166
\(209\) −29.3967 −2.03341
\(210\) −1.32344 −0.0913262
\(211\) −18.8210 −1.29569 −0.647847 0.761771i \(-0.724330\pi\)
−0.647847 + 0.761771i \(0.724330\pi\)
\(212\) 2.94978 0.202592
\(213\) 21.4739 1.47137
\(214\) 12.5091 0.855106
\(215\) 1.21785 0.0830568
\(216\) 4.54381 0.309167
\(217\) −7.94495 −0.539339
\(218\) −12.7578 −0.864068
\(219\) −25.3570 −1.71347
\(220\) 1.32550 0.0893652
\(221\) 16.2885 1.09569
\(222\) 8.60448 0.577495
\(223\) 13.0119 0.871338 0.435669 0.900107i \(-0.356512\pi\)
0.435669 + 0.900107i \(0.356512\pi\)
\(224\) 2.23532 0.149354
\(225\) −2.97990 −0.198660
\(226\) 7.72790 0.514053
\(227\) 25.5480 1.69568 0.847840 0.530252i \(-0.177903\pi\)
0.847840 + 0.530252i \(0.177903\pi\)
\(228\) 13.1305 0.869592
\(229\) 10.1907 0.673420 0.336710 0.941608i \(-0.390686\pi\)
0.336710 + 0.941608i \(0.390686\pi\)
\(230\) 1.77224 0.116858
\(231\) −18.0550 −1.18793
\(232\) 6.13276 0.402636
\(233\) −25.3591 −1.66133 −0.830666 0.556771i \(-0.812040\pi\)
−0.830666 + 0.556771i \(0.812040\pi\)
\(234\) 1.46532 0.0957912
\(235\) −0.529612 −0.0345481
\(236\) 2.92742 0.190559
\(237\) 3.94288 0.256117
\(238\) 15.1023 0.978935
\(239\) 18.9875 1.22820 0.614099 0.789229i \(-0.289519\pi\)
0.614099 + 0.789229i \(0.289519\pi\)
\(240\) −0.592058 −0.0382172
\(241\) 19.6887 1.26826 0.634130 0.773226i \(-0.281358\pi\)
0.634130 + 0.773226i \(0.281358\pi\)
\(242\) 7.08308 0.455318
\(243\) 6.22502 0.399335
\(244\) −7.23183 −0.462970
\(245\) −0.624445 −0.0398944
\(246\) −4.84799 −0.309097
\(247\) −16.6664 −1.06046
\(248\) −3.55427 −0.225697
\(249\) 3.73811 0.236893
\(250\) −3.08676 −0.195224
\(251\) −0.426326 −0.0269095 −0.0134547 0.999909i \(-0.504283\pi\)
−0.0134547 + 0.999909i \(0.504283\pi\)
\(252\) 1.35861 0.0855842
\(253\) 24.1777 1.52004
\(254\) −1.81770 −0.114053
\(255\) −4.00005 −0.250493
\(256\) 1.00000 0.0625000
\(257\) 26.0153 1.62279 0.811394 0.584500i \(-0.198709\pi\)
0.811394 + 0.584500i \(0.198709\pi\)
\(258\) −7.42115 −0.462021
\(259\) −10.1262 −0.629209
\(260\) 0.751491 0.0466055
\(261\) 3.72743 0.230722
\(262\) 20.7507 1.28198
\(263\) −13.9916 −0.862761 −0.431380 0.902170i \(-0.641973\pi\)
−0.431380 + 0.902170i \(0.641973\pi\)
\(264\) −8.07713 −0.497113
\(265\) 0.919462 0.0564821
\(266\) −15.4526 −0.947463
\(267\) −20.5750 −1.25917
\(268\) −5.67176 −0.346458
\(269\) 12.6808 0.773163 0.386581 0.922255i \(-0.373656\pi\)
0.386581 + 0.922255i \(0.373656\pi\)
\(270\) 1.41633 0.0861949
\(271\) 0.812497 0.0493557 0.0246778 0.999695i \(-0.492144\pi\)
0.0246778 + 0.999695i \(0.492144\pi\)
\(272\) 6.75619 0.409654
\(273\) −10.2363 −0.619527
\(274\) −9.23510 −0.557913
\(275\) −20.8489 −1.25724
\(276\) −10.7994 −0.650046
\(277\) −2.28077 −0.137038 −0.0685191 0.997650i \(-0.521827\pi\)
−0.0685191 + 0.997650i \(0.521827\pi\)
\(278\) −8.85808 −0.531272
\(279\) −2.16025 −0.129331
\(280\) 0.696762 0.0416395
\(281\) −21.2897 −1.27004 −0.635018 0.772497i \(-0.719007\pi\)
−0.635018 + 0.772497i \(0.719007\pi\)
\(282\) 3.22727 0.192181
\(283\) −23.5640 −1.40074 −0.700368 0.713782i \(-0.746981\pi\)
−0.700368 + 0.713782i \(0.746981\pi\)
\(284\) −11.3055 −0.670858
\(285\) 4.09286 0.242440
\(286\) 10.2522 0.606224
\(287\) 5.70535 0.336776
\(288\) 0.607790 0.0358144
\(289\) 28.6461 1.68506
\(290\) 1.91161 0.112254
\(291\) 15.7772 0.924875
\(292\) 13.3499 0.781244
\(293\) 6.89229 0.402652 0.201326 0.979524i \(-0.435475\pi\)
0.201326 + 0.979524i \(0.435475\pi\)
\(294\) 3.80515 0.221921
\(295\) 0.912491 0.0531273
\(296\) −4.53006 −0.263304
\(297\) 19.3222 1.12119
\(298\) 7.93318 0.459557
\(299\) 13.7075 0.792725
\(300\) 9.31254 0.537660
\(301\) 8.73356 0.503394
\(302\) −16.7113 −0.961625
\(303\) −4.36902 −0.250994
\(304\) −6.91293 −0.396484
\(305\) −2.25420 −0.129075
\(306\) 4.10634 0.234744
\(307\) −18.3766 −1.04881 −0.524404 0.851470i \(-0.675712\pi\)
−0.524404 + 0.851470i \(0.675712\pi\)
\(308\) 9.50554 0.541629
\(309\) −26.4973 −1.50738
\(310\) −1.10788 −0.0629236
\(311\) −31.6409 −1.79419 −0.897095 0.441837i \(-0.854327\pi\)
−0.897095 + 0.441837i \(0.854327\pi\)
\(312\) −4.57932 −0.259253
\(313\) −3.70011 −0.209142 −0.104571 0.994517i \(-0.533347\pi\)
−0.104571 + 0.994517i \(0.533347\pi\)
\(314\) 20.4744 1.15544
\(315\) 0.423485 0.0238606
\(316\) −2.07583 −0.116775
\(317\) −33.4390 −1.87812 −0.939061 0.343749i \(-0.888303\pi\)
−0.939061 + 0.343749i \(0.888303\pi\)
\(318\) −5.60287 −0.314194
\(319\) 26.0791 1.46015
\(320\) 0.311705 0.0174248
\(321\) −23.7600 −1.32616
\(322\) 12.7092 0.708256
\(323\) −46.7051 −2.59874
\(324\) −10.4540 −0.580776
\(325\) −11.8203 −0.655671
\(326\) 9.00051 0.498492
\(327\) 24.2324 1.34006
\(328\) 2.55236 0.140930
\(329\) −3.79800 −0.209391
\(330\) −2.51768 −0.138594
\(331\) 25.9855 1.42829 0.714146 0.699996i \(-0.246815\pi\)
0.714146 + 0.699996i \(0.246815\pi\)
\(332\) −1.96803 −0.108010
\(333\) −2.75332 −0.150881
\(334\) −8.99976 −0.492445
\(335\) −1.76791 −0.0965915
\(336\) −4.24582 −0.231628
\(337\) 25.7759 1.40410 0.702051 0.712127i \(-0.252268\pi\)
0.702051 + 0.712127i \(0.252268\pi\)
\(338\) −7.18754 −0.390950
\(339\) −14.6785 −0.797228
\(340\) 2.10594 0.114210
\(341\) −15.1143 −0.818483
\(342\) −4.20161 −0.227197
\(343\) −20.1254 −1.08667
\(344\) 3.90707 0.210655
\(345\) −3.36622 −0.181231
\(346\) 22.3103 1.19941
\(347\) −4.89860 −0.262971 −0.131485 0.991318i \(-0.541975\pi\)
−0.131485 + 0.991318i \(0.541975\pi\)
\(348\) −11.6487 −0.624435
\(349\) 9.62083 0.514991 0.257496 0.966279i \(-0.417103\pi\)
0.257496 + 0.966279i \(0.417103\pi\)
\(350\) −10.9594 −0.585807
\(351\) 10.9547 0.584718
\(352\) 4.25242 0.226655
\(353\) 6.69700 0.356446 0.178223 0.983990i \(-0.442965\pi\)
0.178223 + 0.983990i \(0.442965\pi\)
\(354\) −5.56039 −0.295532
\(355\) −3.52398 −0.187033
\(356\) 10.8323 0.574109
\(357\) −28.6855 −1.51820
\(358\) 2.24497 0.118650
\(359\) 22.8379 1.20534 0.602669 0.797991i \(-0.294104\pi\)
0.602669 + 0.797991i \(0.294104\pi\)
\(360\) 0.189451 0.00998494
\(361\) 28.7886 1.51519
\(362\) 12.7432 0.669767
\(363\) −13.4537 −0.706138
\(364\) 5.38916 0.282469
\(365\) 4.16123 0.217809
\(366\) 13.7363 0.718006
\(367\) −3.88121 −0.202597 −0.101299 0.994856i \(-0.532300\pi\)
−0.101299 + 0.994856i \(0.532300\pi\)
\(368\) 5.68562 0.296383
\(369\) 1.55130 0.0807573
\(370\) −1.41204 −0.0734085
\(371\) 6.59373 0.342329
\(372\) 6.75105 0.350026
\(373\) 29.4760 1.52621 0.763104 0.646276i \(-0.223675\pi\)
0.763104 + 0.646276i \(0.223675\pi\)
\(374\) 28.7302 1.48560
\(375\) 5.86305 0.302767
\(376\) −1.69908 −0.0876235
\(377\) 14.7855 0.761492
\(378\) 10.1569 0.522414
\(379\) −34.7667 −1.78585 −0.892924 0.450208i \(-0.851350\pi\)
−0.892924 + 0.450208i \(0.851350\pi\)
\(380\) −2.15479 −0.110539
\(381\) 3.45257 0.176881
\(382\) 4.09996 0.209772
\(383\) −24.4903 −1.25139 −0.625697 0.780066i \(-0.715185\pi\)
−0.625697 + 0.780066i \(0.715185\pi\)
\(384\) −1.89942 −0.0969293
\(385\) 2.96292 0.151005
\(386\) 21.8203 1.11063
\(387\) 2.37468 0.120712
\(388\) −8.30633 −0.421690
\(389\) −13.4112 −0.679974 −0.339987 0.940430i \(-0.610423\pi\)
−0.339987 + 0.940430i \(0.610423\pi\)
\(390\) −1.42740 −0.0722790
\(391\) 38.4131 1.94263
\(392\) −2.00332 −0.101183
\(393\) −39.4143 −1.98819
\(394\) −8.72843 −0.439732
\(395\) −0.647048 −0.0325565
\(396\) 2.58458 0.129880
\(397\) 10.1924 0.511542 0.255771 0.966737i \(-0.417671\pi\)
0.255771 + 0.966737i \(0.417671\pi\)
\(398\) −13.5977 −0.681592
\(399\) 29.3510 1.46939
\(400\) −4.90284 −0.245142
\(401\) −13.8909 −0.693677 −0.346838 0.937925i \(-0.612745\pi\)
−0.346838 + 0.937925i \(0.612745\pi\)
\(402\) 10.7730 0.537310
\(403\) −8.56901 −0.426853
\(404\) 2.30019 0.114439
\(405\) −3.25855 −0.161919
\(406\) 13.7087 0.680352
\(407\) −19.2637 −0.954867
\(408\) −12.8328 −0.635320
\(409\) −10.4113 −0.514807 −0.257403 0.966304i \(-0.582867\pi\)
−0.257403 + 0.966304i \(0.582867\pi\)
\(410\) 0.795582 0.0392910
\(411\) 17.5413 0.865250
\(412\) 13.9502 0.687279
\(413\) 6.54373 0.321996
\(414\) 3.45566 0.169836
\(415\) −0.613444 −0.0301128
\(416\) 2.41091 0.118204
\(417\) 16.8252 0.823934
\(418\) −29.3967 −1.43784
\(419\) −31.1890 −1.52368 −0.761841 0.647765i \(-0.775704\pi\)
−0.761841 + 0.647765i \(0.775704\pi\)
\(420\) −1.32344 −0.0645773
\(421\) −13.4321 −0.654639 −0.327319 0.944914i \(-0.606145\pi\)
−0.327319 + 0.944914i \(0.606145\pi\)
\(422\) −18.8210 −0.916194
\(423\) −1.03269 −0.0502109
\(424\) 2.94978 0.143254
\(425\) −33.1245 −1.60677
\(426\) 21.4739 1.04041
\(427\) −16.1655 −0.782303
\(428\) 12.5091 0.604651
\(429\) −19.4732 −0.940174
\(430\) 1.21785 0.0587300
\(431\) 25.7669 1.24115 0.620573 0.784149i \(-0.286900\pi\)
0.620573 + 0.784149i \(0.286900\pi\)
\(432\) 4.54381 0.218614
\(433\) −31.6498 −1.52099 −0.760495 0.649344i \(-0.775044\pi\)
−0.760495 + 0.649344i \(0.775044\pi\)
\(434\) −7.94495 −0.381370
\(435\) −3.63095 −0.174091
\(436\) −12.7578 −0.610989
\(437\) −39.3043 −1.88018
\(438\) −25.3570 −1.21161
\(439\) −22.3643 −1.06739 −0.533694 0.845678i \(-0.679197\pi\)
−0.533694 + 0.845678i \(0.679197\pi\)
\(440\) 1.32550 0.0631907
\(441\) −1.21760 −0.0579809
\(442\) 16.2885 0.774766
\(443\) 30.5556 1.45174 0.725871 0.687831i \(-0.241437\pi\)
0.725871 + 0.687831i \(0.241437\pi\)
\(444\) 8.60448 0.408350
\(445\) 3.37647 0.160060
\(446\) 13.0119 0.616129
\(447\) −15.0684 −0.712712
\(448\) 2.23532 0.105609
\(449\) 24.7092 1.16610 0.583049 0.812437i \(-0.301859\pi\)
0.583049 + 0.812437i \(0.301859\pi\)
\(450\) −2.97990 −0.140474
\(451\) 10.8537 0.511081
\(452\) 7.72790 0.363490
\(453\) 31.7417 1.49135
\(454\) 25.5480 1.19903
\(455\) 1.67983 0.0787515
\(456\) 13.1305 0.614894
\(457\) −37.6152 −1.75957 −0.879783 0.475376i \(-0.842312\pi\)
−0.879783 + 0.475376i \(0.842312\pi\)
\(458\) 10.1907 0.476180
\(459\) 30.6988 1.43290
\(460\) 1.77224 0.0826309
\(461\) 12.8721 0.599516 0.299758 0.954015i \(-0.403094\pi\)
0.299758 + 0.954015i \(0.403094\pi\)
\(462\) −18.0550 −0.839995
\(463\) 32.6181 1.51589 0.757947 0.652317i \(-0.226203\pi\)
0.757947 + 0.652317i \(0.226203\pi\)
\(464\) 6.13276 0.284706
\(465\) 2.10433 0.0975862
\(466\) −25.3591 −1.17474
\(467\) −4.90131 −0.226805 −0.113403 0.993549i \(-0.536175\pi\)
−0.113403 + 0.993549i \(0.536175\pi\)
\(468\) 1.46532 0.0677346
\(469\) −12.6782 −0.585426
\(470\) −0.529612 −0.0244292
\(471\) −38.8895 −1.79193
\(472\) 2.92742 0.134745
\(473\) 16.6145 0.763935
\(474\) 3.94288 0.181102
\(475\) 33.8930 1.55512
\(476\) 15.1023 0.692212
\(477\) 1.79285 0.0820889
\(478\) 18.9875 0.868467
\(479\) −3.59924 −0.164453 −0.0822267 0.996614i \(-0.526203\pi\)
−0.0822267 + 0.996614i \(0.526203\pi\)
\(480\) −0.592058 −0.0270236
\(481\) −10.9215 −0.497980
\(482\) 19.6887 0.896796
\(483\) −24.1401 −1.09841
\(484\) 7.08308 0.321958
\(485\) −2.58912 −0.117566
\(486\) 6.22502 0.282373
\(487\) 0.985032 0.0446361 0.0223180 0.999751i \(-0.492895\pi\)
0.0223180 + 0.999751i \(0.492895\pi\)
\(488\) −7.23183 −0.327370
\(489\) −17.0957 −0.773095
\(490\) −0.624445 −0.0282096
\(491\) −29.3140 −1.32292 −0.661461 0.749979i \(-0.730063\pi\)
−0.661461 + 0.749979i \(0.730063\pi\)
\(492\) −4.84799 −0.218564
\(493\) 41.4341 1.86610
\(494\) −16.6664 −0.749858
\(495\) 0.805625 0.0362102
\(496\) −3.55427 −0.159592
\(497\) −25.2715 −1.13358
\(498\) 3.73811 0.167509
\(499\) −6.20797 −0.277907 −0.138954 0.990299i \(-0.544374\pi\)
−0.138954 + 0.990299i \(0.544374\pi\)
\(500\) −3.08676 −0.138044
\(501\) 17.0943 0.763718
\(502\) −0.426326 −0.0190279
\(503\) −23.8116 −1.06171 −0.530853 0.847464i \(-0.678128\pi\)
−0.530853 + 0.847464i \(0.678128\pi\)
\(504\) 1.35861 0.0605172
\(505\) 0.716980 0.0319052
\(506\) 24.1777 1.07483
\(507\) 13.6521 0.606313
\(508\) −1.81770 −0.0806474
\(509\) −19.1006 −0.846620 −0.423310 0.905985i \(-0.639132\pi\)
−0.423310 + 0.905985i \(0.639132\pi\)
\(510\) −4.00005 −0.177125
\(511\) 29.8414 1.32010
\(512\) 1.00000 0.0441942
\(513\) −31.4110 −1.38683
\(514\) 26.0153 1.14748
\(515\) 4.34836 0.191612
\(516\) −7.42115 −0.326698
\(517\) −7.22522 −0.317765
\(518\) −10.1262 −0.444918
\(519\) −42.3766 −1.86013
\(520\) 0.751491 0.0329551
\(521\) 11.5950 0.507985 0.253993 0.967206i \(-0.418256\pi\)
0.253993 + 0.967206i \(0.418256\pi\)
\(522\) 3.72743 0.163145
\(523\) 36.8751 1.61244 0.806218 0.591619i \(-0.201511\pi\)
0.806218 + 0.591619i \(0.201511\pi\)
\(524\) 20.7507 0.906499
\(525\) 20.8166 0.908509
\(526\) −13.9916 −0.610064
\(527\) −24.0133 −1.04604
\(528\) −8.07713 −0.351512
\(529\) 9.32628 0.405490
\(530\) 0.919462 0.0399389
\(531\) 1.77926 0.0772131
\(532\) −15.4526 −0.669957
\(533\) 6.15349 0.266537
\(534\) −20.5750 −0.890368
\(535\) 3.89915 0.168575
\(536\) −5.67176 −0.244983
\(537\) −4.26413 −0.184011
\(538\) 12.6808 0.546708
\(539\) −8.51897 −0.366938
\(540\) 1.41633 0.0609490
\(541\) −42.6609 −1.83414 −0.917069 0.398729i \(-0.869451\pi\)
−0.917069 + 0.398729i \(0.869451\pi\)
\(542\) 0.812497 0.0348997
\(543\) −24.2046 −1.03872
\(544\) 6.75619 0.289669
\(545\) −3.97667 −0.170342
\(546\) −10.2363 −0.438072
\(547\) 31.5506 1.34900 0.674502 0.738273i \(-0.264358\pi\)
0.674502 + 0.738273i \(0.264358\pi\)
\(548\) −9.23510 −0.394504
\(549\) −4.39543 −0.187592
\(550\) −20.8489 −0.889002
\(551\) −42.3954 −1.80610
\(552\) −10.7994 −0.459652
\(553\) −4.64017 −0.197320
\(554\) −2.28077 −0.0969006
\(555\) 2.68206 0.113847
\(556\) −8.85808 −0.375666
\(557\) 17.4739 0.740391 0.370195 0.928954i \(-0.379291\pi\)
0.370195 + 0.928954i \(0.379291\pi\)
\(558\) −2.16025 −0.0914507
\(559\) 9.41957 0.398405
\(560\) 0.696762 0.0294436
\(561\) −54.5706 −2.30397
\(562\) −21.2897 −0.898051
\(563\) −18.4483 −0.777503 −0.388752 0.921343i \(-0.627094\pi\)
−0.388752 + 0.921343i \(0.627094\pi\)
\(564\) 3.22727 0.135893
\(565\) 2.40883 0.101340
\(566\) −23.5640 −0.990469
\(567\) −23.3680 −0.981364
\(568\) −11.3055 −0.474368
\(569\) 22.1571 0.928874 0.464437 0.885606i \(-0.346257\pi\)
0.464437 + 0.885606i \(0.346257\pi\)
\(570\) 4.09286 0.171431
\(571\) −12.9261 −0.540940 −0.270470 0.962728i \(-0.587179\pi\)
−0.270470 + 0.962728i \(0.587179\pi\)
\(572\) 10.2522 0.428665
\(573\) −7.78753 −0.325329
\(574\) 5.70535 0.238137
\(575\) −27.8757 −1.16250
\(576\) 0.607790 0.0253246
\(577\) 14.4085 0.599832 0.299916 0.953966i \(-0.403041\pi\)
0.299916 + 0.953966i \(0.403041\pi\)
\(578\) 28.6461 1.19152
\(579\) −41.4459 −1.72243
\(580\) 1.91161 0.0793753
\(581\) −4.39918 −0.182509
\(582\) 15.7772 0.653985
\(583\) 12.5437 0.519508
\(584\) 13.3499 0.552423
\(585\) 0.456748 0.0188842
\(586\) 6.89229 0.284718
\(587\) −43.3978 −1.79122 −0.895609 0.444842i \(-0.853260\pi\)
−0.895609 + 0.444842i \(0.853260\pi\)
\(588\) 3.80515 0.156922
\(589\) 24.5704 1.01241
\(590\) 0.912491 0.0375667
\(591\) 16.5789 0.681967
\(592\) −4.53006 −0.186184
\(593\) 16.3657 0.672061 0.336030 0.941851i \(-0.390916\pi\)
0.336030 + 0.941851i \(0.390916\pi\)
\(594\) 19.3222 0.792799
\(595\) 4.70745 0.192987
\(596\) 7.93318 0.324956
\(597\) 25.8278 1.05706
\(598\) 13.7075 0.560541
\(599\) −27.4661 −1.12224 −0.561118 0.827736i \(-0.689629\pi\)
−0.561118 + 0.827736i \(0.689629\pi\)
\(600\) 9.31254 0.380183
\(601\) −7.28260 −0.297063 −0.148532 0.988908i \(-0.547455\pi\)
−0.148532 + 0.988908i \(0.547455\pi\)
\(602\) 8.73356 0.355953
\(603\) −3.44724 −0.140382
\(604\) −16.7113 −0.679972
\(605\) 2.20783 0.0897611
\(606\) −4.36902 −0.177479
\(607\) −23.0549 −0.935768 −0.467884 0.883790i \(-0.654983\pi\)
−0.467884 + 0.883790i \(0.654983\pi\)
\(608\) −6.91293 −0.280356
\(609\) −26.0386 −1.05514
\(610\) −2.25420 −0.0912697
\(611\) −4.09633 −0.165720
\(612\) 4.10634 0.165989
\(613\) 9.75106 0.393842 0.196921 0.980419i \(-0.436906\pi\)
0.196921 + 0.980419i \(0.436906\pi\)
\(614\) −18.3766 −0.741619
\(615\) −1.51114 −0.0609352
\(616\) 9.50554 0.382989
\(617\) 7.13955 0.287427 0.143714 0.989619i \(-0.454096\pi\)
0.143714 + 0.989619i \(0.454096\pi\)
\(618\) −26.4973 −1.06588
\(619\) −39.9108 −1.60415 −0.802076 0.597222i \(-0.796271\pi\)
−0.802076 + 0.597222i \(0.796271\pi\)
\(620\) −1.10788 −0.0444937
\(621\) 25.8344 1.03670
\(622\) −31.6409 −1.26868
\(623\) 24.2136 0.970099
\(624\) −4.57932 −0.183319
\(625\) 23.5520 0.942082
\(626\) −3.70011 −0.147886
\(627\) 55.8366 2.22990
\(628\) 20.4744 0.817019
\(629\) −30.6059 −1.22034
\(630\) 0.423485 0.0168720
\(631\) −26.4208 −1.05179 −0.525897 0.850548i \(-0.676270\pi\)
−0.525897 + 0.850548i \(0.676270\pi\)
\(632\) −2.07583 −0.0825723
\(633\) 35.7490 1.42090
\(634\) −33.4390 −1.32803
\(635\) −0.566586 −0.0224843
\(636\) −5.60287 −0.222168
\(637\) −4.82982 −0.191365
\(638\) 26.0791 1.03248
\(639\) −6.87137 −0.271827
\(640\) 0.311705 0.0123212
\(641\) −21.0392 −0.830997 −0.415499 0.909594i \(-0.636393\pi\)
−0.415499 + 0.909594i \(0.636393\pi\)
\(642\) −23.7600 −0.937734
\(643\) −26.7612 −1.05536 −0.527679 0.849444i \(-0.676938\pi\)
−0.527679 + 0.849444i \(0.676938\pi\)
\(644\) 12.7092 0.500813
\(645\) −2.31321 −0.0910825
\(646\) −46.7051 −1.83759
\(647\) −39.7126 −1.56126 −0.780632 0.624991i \(-0.785103\pi\)
−0.780632 + 0.624991i \(0.785103\pi\)
\(648\) −10.4540 −0.410670
\(649\) 12.4486 0.488651
\(650\) −11.8203 −0.463630
\(651\) 15.0908 0.591455
\(652\) 9.00051 0.352487
\(653\) 22.9967 0.899929 0.449965 0.893046i \(-0.351437\pi\)
0.449965 + 0.893046i \(0.351437\pi\)
\(654\) 24.2324 0.947563
\(655\) 6.46809 0.252729
\(656\) 2.55236 0.0996528
\(657\) 8.11393 0.316555
\(658\) −3.79800 −0.148062
\(659\) −2.43847 −0.0949893 −0.0474947 0.998871i \(-0.515124\pi\)
−0.0474947 + 0.998871i \(0.515124\pi\)
\(660\) −2.51768 −0.0980005
\(661\) 13.3573 0.519539 0.259770 0.965671i \(-0.416353\pi\)
0.259770 + 0.965671i \(0.416353\pi\)
\(662\) 25.9855 1.00996
\(663\) −30.9387 −1.20156
\(664\) −1.96803 −0.0763743
\(665\) −4.81667 −0.186782
\(666\) −2.75332 −0.106689
\(667\) 34.8686 1.35012
\(668\) −8.99976 −0.348211
\(669\) −24.7150 −0.955535
\(670\) −1.76791 −0.0683005
\(671\) −30.7528 −1.18720
\(672\) −4.24582 −0.163786
\(673\) −12.5602 −0.484159 −0.242079 0.970256i \(-0.577829\pi\)
−0.242079 + 0.970256i \(0.577829\pi\)
\(674\) 25.7759 0.992850
\(675\) −22.2776 −0.857464
\(676\) −7.18754 −0.276444
\(677\) 27.5481 1.05876 0.529380 0.848385i \(-0.322424\pi\)
0.529380 + 0.848385i \(0.322424\pi\)
\(678\) −14.6785 −0.563725
\(679\) −18.5673 −0.712549
\(680\) 2.10594 0.0807590
\(681\) −48.5263 −1.85953
\(682\) −15.1143 −0.578755
\(683\) 14.1796 0.542566 0.271283 0.962500i \(-0.412552\pi\)
0.271283 + 0.962500i \(0.412552\pi\)
\(684\) −4.20161 −0.160653
\(685\) −2.87863 −0.109987
\(686\) −20.1254 −0.768389
\(687\) −19.3564 −0.738493
\(688\) 3.90707 0.148956
\(689\) 7.11165 0.270932
\(690\) −3.36622 −0.128150
\(691\) 32.3025 1.22885 0.614423 0.788977i \(-0.289389\pi\)
0.614423 + 0.788977i \(0.289389\pi\)
\(692\) 22.3103 0.848111
\(693\) 5.77737 0.219464
\(694\) −4.89860 −0.185948
\(695\) −2.76111 −0.104735
\(696\) −11.6487 −0.441542
\(697\) 17.2442 0.653171
\(698\) 9.62083 0.364154
\(699\) 48.1676 1.82187
\(700\) −10.9594 −0.414228
\(701\) 44.5686 1.68333 0.841667 0.539997i \(-0.181575\pi\)
0.841667 + 0.539997i \(0.181575\pi\)
\(702\) 10.9547 0.413458
\(703\) 31.3160 1.18110
\(704\) 4.25242 0.160269
\(705\) 1.00596 0.0378865
\(706\) 6.69700 0.252045
\(707\) 5.14167 0.193372
\(708\) −5.56039 −0.208972
\(709\) −19.6662 −0.738580 −0.369290 0.929314i \(-0.620399\pi\)
−0.369290 + 0.929314i \(0.620399\pi\)
\(710\) −3.52398 −0.132253
\(711\) −1.26167 −0.0473164
\(712\) 10.8323 0.405957
\(713\) −20.2082 −0.756805
\(714\) −28.6855 −1.07353
\(715\) 3.19566 0.119511
\(716\) 2.24497 0.0838983
\(717\) −36.0652 −1.34688
\(718\) 22.8379 0.852303
\(719\) 31.3422 1.16887 0.584433 0.811442i \(-0.301317\pi\)
0.584433 + 0.811442i \(0.301317\pi\)
\(720\) 0.189451 0.00706042
\(721\) 31.1833 1.16133
\(722\) 28.7886 1.07140
\(723\) −37.3971 −1.39081
\(724\) 12.7432 0.473597
\(725\) −30.0679 −1.11670
\(726\) −13.4537 −0.499315
\(727\) 17.0344 0.631772 0.315886 0.948797i \(-0.397698\pi\)
0.315886 + 0.948797i \(0.397698\pi\)
\(728\) 5.38916 0.199735
\(729\) 19.5380 0.723628
\(730\) 4.16123 0.154014
\(731\) 26.3969 0.976324
\(732\) 13.7363 0.507707
\(733\) 29.7272 1.09800 0.548999 0.835823i \(-0.315009\pi\)
0.548999 + 0.835823i \(0.315009\pi\)
\(734\) −3.88121 −0.143258
\(735\) 1.18608 0.0437493
\(736\) 5.68562 0.209575
\(737\) −24.1187 −0.888424
\(738\) 1.55130 0.0571040
\(739\) −25.5193 −0.938743 −0.469371 0.883001i \(-0.655519\pi\)
−0.469371 + 0.883001i \(0.655519\pi\)
\(740\) −1.41204 −0.0519077
\(741\) 31.6565 1.16293
\(742\) 6.59373 0.242063
\(743\) −10.6610 −0.391115 −0.195557 0.980692i \(-0.562652\pi\)
−0.195557 + 0.980692i \(0.562652\pi\)
\(744\) 6.75105 0.247505
\(745\) 2.47281 0.0905968
\(746\) 29.4760 1.07919
\(747\) −1.19615 −0.0437647
\(748\) 28.7302 1.05048
\(749\) 27.9619 1.02171
\(750\) 5.86305 0.214088
\(751\) 34.4688 1.25779 0.628893 0.777492i \(-0.283509\pi\)
0.628893 + 0.777492i \(0.283509\pi\)
\(752\) −1.69908 −0.0619592
\(753\) 0.809772 0.0295097
\(754\) 14.7855 0.538456
\(755\) −5.20898 −0.189574
\(756\) 10.1569 0.369402
\(757\) −51.2999 −1.86453 −0.932263 0.361781i \(-0.882169\pi\)
−0.932263 + 0.361781i \(0.882169\pi\)
\(758\) −34.7667 −1.26278
\(759\) −45.9235 −1.66692
\(760\) −2.15479 −0.0781626
\(761\) 6.00389 0.217641 0.108820 0.994061i \(-0.465293\pi\)
0.108820 + 0.994061i \(0.465293\pi\)
\(762\) 3.45257 0.125073
\(763\) −28.5179 −1.03242
\(764\) 4.09996 0.148331
\(765\) 1.27997 0.0462773
\(766\) −24.4903 −0.884870
\(767\) 7.05773 0.254840
\(768\) −1.89942 −0.0685394
\(769\) −26.9147 −0.970571 −0.485285 0.874356i \(-0.661284\pi\)
−0.485285 + 0.874356i \(0.661284\pi\)
\(770\) 2.96292 0.106776
\(771\) −49.4139 −1.77960
\(772\) 21.8203 0.785331
\(773\) −33.1476 −1.19223 −0.596117 0.802897i \(-0.703291\pi\)
−0.596117 + 0.802897i \(0.703291\pi\)
\(774\) 2.37468 0.0853559
\(775\) 17.4260 0.625961
\(776\) −8.30633 −0.298180
\(777\) 19.2338 0.690009
\(778\) −13.4112 −0.480815
\(779\) −17.6443 −0.632172
\(780\) −1.42740 −0.0511090
\(781\) −48.0757 −1.72029
\(782\) 38.4131 1.37365
\(783\) 27.8661 0.995853
\(784\) −2.00332 −0.0715472
\(785\) 6.38198 0.227783
\(786\) −39.4143 −1.40586
\(787\) −13.2726 −0.473116 −0.236558 0.971617i \(-0.576019\pi\)
−0.236558 + 0.971617i \(0.576019\pi\)
\(788\) −8.72843 −0.310938
\(789\) 26.5760 0.946129
\(790\) −0.647048 −0.0230209
\(791\) 17.2744 0.614206
\(792\) 2.58458 0.0918390
\(793\) −17.4353 −0.619144
\(794\) 10.1924 0.361715
\(795\) −1.74644 −0.0619399
\(796\) −13.5977 −0.481959
\(797\) 9.92091 0.351417 0.175708 0.984442i \(-0.443778\pi\)
0.175708 + 0.984442i \(0.443778\pi\)
\(798\) 29.3510 1.03902
\(799\) −11.4793 −0.406109
\(800\) −4.90284 −0.173342
\(801\) 6.58374 0.232625
\(802\) −13.8909 −0.490504
\(803\) 56.7694 2.00335
\(804\) 10.7730 0.379936
\(805\) 3.96152 0.139625
\(806\) −8.56901 −0.301831
\(807\) −24.0862 −0.847873
\(808\) 2.30019 0.0809203
\(809\) −39.7460 −1.39740 −0.698698 0.715417i \(-0.746237\pi\)
−0.698698 + 0.715417i \(0.746237\pi\)
\(810\) −3.25855 −0.114494
\(811\) −0.443439 −0.0155713 −0.00778563 0.999970i \(-0.502478\pi\)
−0.00778563 + 0.999970i \(0.502478\pi\)
\(812\) 13.7087 0.481082
\(813\) −1.54327 −0.0541249
\(814\) −19.2637 −0.675193
\(815\) 2.80550 0.0982724
\(816\) −12.8328 −0.449239
\(817\) −27.0093 −0.944935
\(818\) −10.4113 −0.364023
\(819\) 3.27547 0.114454
\(820\) 0.795582 0.0277829
\(821\) 27.8231 0.971034 0.485517 0.874227i \(-0.338631\pi\)
0.485517 + 0.874227i \(0.338631\pi\)
\(822\) 17.5413 0.611824
\(823\) −26.9019 −0.937741 −0.468871 0.883267i \(-0.655339\pi\)
−0.468871 + 0.883267i \(0.655339\pi\)
\(824\) 13.9502 0.485980
\(825\) 39.6009 1.37872
\(826\) 6.54373 0.227686
\(827\) 12.6344 0.439339 0.219670 0.975574i \(-0.429502\pi\)
0.219670 + 0.975574i \(0.429502\pi\)
\(828\) 3.45566 0.120093
\(829\) −13.9741 −0.485340 −0.242670 0.970109i \(-0.578023\pi\)
−0.242670 + 0.970109i \(0.578023\pi\)
\(830\) −0.613444 −0.0212929
\(831\) 4.33213 0.150280
\(832\) 2.41091 0.0835831
\(833\) −13.5348 −0.468954
\(834\) 16.8252 0.582609
\(835\) −2.80527 −0.0970804
\(836\) −29.3967 −1.01671
\(837\) −16.1499 −0.558223
\(838\) −31.1890 −1.07741
\(839\) −23.5561 −0.813248 −0.406624 0.913596i \(-0.633294\pi\)
−0.406624 + 0.913596i \(0.633294\pi\)
\(840\) −1.32344 −0.0456631
\(841\) 8.61076 0.296923
\(842\) −13.4321 −0.462899
\(843\) 40.4380 1.39276
\(844\) −18.8210 −0.647847
\(845\) −2.24039 −0.0770717
\(846\) −1.03269 −0.0355044
\(847\) 15.8330 0.544028
\(848\) 2.94978 0.101296
\(849\) 44.7579 1.53609
\(850\) −33.1245 −1.13616
\(851\) −25.7562 −0.882911
\(852\) 21.4739 0.735683
\(853\) 8.49265 0.290783 0.145391 0.989374i \(-0.453556\pi\)
0.145391 + 0.989374i \(0.453556\pi\)
\(854\) −16.1655 −0.553172
\(855\) −1.30966 −0.0447895
\(856\) 12.5091 0.427553
\(857\) −3.80023 −0.129813 −0.0649067 0.997891i \(-0.520675\pi\)
−0.0649067 + 0.997891i \(0.520675\pi\)
\(858\) −19.4732 −0.664804
\(859\) −26.0746 −0.889655 −0.444827 0.895616i \(-0.646735\pi\)
−0.444827 + 0.895616i \(0.646735\pi\)
\(860\) 1.21785 0.0415284
\(861\) −10.8368 −0.369319
\(862\) 25.7669 0.877623
\(863\) −0.305476 −0.0103985 −0.00519925 0.999986i \(-0.501655\pi\)
−0.00519925 + 0.999986i \(0.501655\pi\)
\(864\) 4.54381 0.154583
\(865\) 6.95424 0.236451
\(866\) −31.6498 −1.07550
\(867\) −54.4109 −1.84789
\(868\) −7.94495 −0.269669
\(869\) −8.82732 −0.299446
\(870\) −3.63095 −0.123101
\(871\) −13.6741 −0.463328
\(872\) −12.7578 −0.432034
\(873\) −5.04850 −0.170866
\(874\) −39.3043 −1.32949
\(875\) −6.89992 −0.233260
\(876\) −25.3570 −0.856735
\(877\) −42.4868 −1.43468 −0.717339 0.696725i \(-0.754640\pi\)
−0.717339 + 0.696725i \(0.754640\pi\)
\(878\) −22.3643 −0.754758
\(879\) −13.0913 −0.441560
\(880\) 1.32550 0.0446826
\(881\) −40.5786 −1.36713 −0.683564 0.729891i \(-0.739571\pi\)
−0.683564 + 0.729891i \(0.739571\pi\)
\(882\) −1.21760 −0.0409987
\(883\) 6.01375 0.202379 0.101189 0.994867i \(-0.467735\pi\)
0.101189 + 0.994867i \(0.467735\pi\)
\(884\) 16.2885 0.547843
\(885\) −1.73320 −0.0582609
\(886\) 30.5556 1.02654
\(887\) −12.5847 −0.422554 −0.211277 0.977426i \(-0.567762\pi\)
−0.211277 + 0.977426i \(0.567762\pi\)
\(888\) 8.60448 0.288747
\(889\) −4.06315 −0.136274
\(890\) 3.37647 0.113180
\(891\) −44.4546 −1.48929
\(892\) 13.0119 0.435669
\(893\) 11.7456 0.393053
\(894\) −15.0684 −0.503964
\(895\) 0.699767 0.0233906
\(896\) 2.23532 0.0746770
\(897\) −26.0363 −0.869325
\(898\) 24.7092 0.824556
\(899\) −21.7975 −0.726987
\(900\) −2.97990 −0.0993299
\(901\) 19.9293 0.663941
\(902\) 10.8537 0.361389
\(903\) −16.5887 −0.552037
\(904\) 7.72790 0.257026
\(905\) 3.97211 0.132038
\(906\) 31.7417 1.05455
\(907\) −51.6994 −1.71665 −0.858325 0.513106i \(-0.828495\pi\)
−0.858325 + 0.513106i \(0.828495\pi\)
\(908\) 25.5480 0.847840
\(909\) 1.39803 0.0463697
\(910\) 1.67983 0.0556857
\(911\) −50.3053 −1.66669 −0.833344 0.552754i \(-0.813577\pi\)
−0.833344 + 0.552754i \(0.813577\pi\)
\(912\) 13.1305 0.434796
\(913\) −8.36888 −0.276970
\(914\) −37.6152 −1.24420
\(915\) 4.28166 0.141547
\(916\) 10.1907 0.336710
\(917\) 46.3846 1.53175
\(918\) 30.6988 1.01321
\(919\) −52.6615 −1.73714 −0.868572 0.495563i \(-0.834962\pi\)
−0.868572 + 0.495563i \(0.834962\pi\)
\(920\) 1.77224 0.0584289
\(921\) 34.9048 1.15015
\(922\) 12.8721 0.423922
\(923\) −27.2565 −0.897158
\(924\) −18.0550 −0.593966
\(925\) 22.2102 0.730265
\(926\) 32.6181 1.07190
\(927\) 8.47881 0.278481
\(928\) 6.13276 0.201318
\(929\) 41.1839 1.35120 0.675599 0.737269i \(-0.263885\pi\)
0.675599 + 0.737269i \(0.263885\pi\)
\(930\) 2.10433 0.0690039
\(931\) 13.8488 0.453877
\(932\) −25.3591 −0.830666
\(933\) 60.0993 1.96756
\(934\) −4.90131 −0.160376
\(935\) 8.95533 0.292871
\(936\) 1.46532 0.0478956
\(937\) 19.1598 0.625922 0.312961 0.949766i \(-0.398679\pi\)
0.312961 + 0.949766i \(0.398679\pi\)
\(938\) −12.6782 −0.413959
\(939\) 7.02805 0.229352
\(940\) −0.529612 −0.0172741
\(941\) 9.23612 0.301089 0.150544 0.988603i \(-0.451897\pi\)
0.150544 + 0.988603i \(0.451897\pi\)
\(942\) −38.8895 −1.26709
\(943\) 14.5117 0.472567
\(944\) 2.92742 0.0952794
\(945\) 3.16595 0.102988
\(946\) 16.6145 0.540184
\(947\) −44.5273 −1.44694 −0.723472 0.690354i \(-0.757455\pi\)
−0.723472 + 0.690354i \(0.757455\pi\)
\(948\) 3.94288 0.128059
\(949\) 32.1853 1.04478
\(950\) 33.8930 1.09963
\(951\) 63.5147 2.05961
\(952\) 15.1023 0.489468
\(953\) 33.5663 1.08732 0.543659 0.839306i \(-0.317038\pi\)
0.543659 + 0.839306i \(0.317038\pi\)
\(954\) 1.79285 0.0580456
\(955\) 1.27798 0.0413543
\(956\) 18.9875 0.614099
\(957\) −49.5351 −1.60124
\(958\) −3.59924 −0.116286
\(959\) −20.6435 −0.666612
\(960\) −0.592058 −0.0191086
\(961\) −18.3671 −0.592489
\(962\) −10.9215 −0.352125
\(963\) 7.60291 0.245000
\(964\) 19.6887 0.634130
\(965\) 6.80150 0.218948
\(966\) −24.1401 −0.776695
\(967\) −57.7362 −1.85667 −0.928336 0.371742i \(-0.878760\pi\)
−0.928336 + 0.371742i \(0.878760\pi\)
\(968\) 7.08308 0.227659
\(969\) 88.7125 2.84985
\(970\) −2.58912 −0.0831317
\(971\) 2.55938 0.0821343 0.0410671 0.999156i \(-0.486924\pi\)
0.0410671 + 0.999156i \(0.486924\pi\)
\(972\) 6.22502 0.199668
\(973\) −19.8007 −0.634781
\(974\) 0.985032 0.0315625
\(975\) 22.4517 0.719029
\(976\) −7.23183 −0.231485
\(977\) −21.4124 −0.685045 −0.342522 0.939510i \(-0.611281\pi\)
−0.342522 + 0.939510i \(0.611281\pi\)
\(978\) −17.0957 −0.546661
\(979\) 46.0634 1.47219
\(980\) −0.624445 −0.0199472
\(981\) −7.75407 −0.247568
\(982\) −29.3140 −0.935447
\(983\) −55.2441 −1.76201 −0.881006 0.473104i \(-0.843133\pi\)
−0.881006 + 0.473104i \(0.843133\pi\)
\(984\) −4.84799 −0.154548
\(985\) −2.72069 −0.0866885
\(986\) 41.4341 1.31953
\(987\) 7.21399 0.229624
\(988\) −16.6664 −0.530230
\(989\) 22.2141 0.706367
\(990\) 0.805625 0.0256045
\(991\) −24.2286 −0.769646 −0.384823 0.922990i \(-0.625738\pi\)
−0.384823 + 0.922990i \(0.625738\pi\)
\(992\) −3.55427 −0.112848
\(993\) −49.3574 −1.56631
\(994\) −25.2715 −0.801562
\(995\) −4.23848 −0.134369
\(996\) 3.73811 0.118446
\(997\) −1.27296 −0.0403149 −0.0201575 0.999797i \(-0.506417\pi\)
−0.0201575 + 0.999797i \(0.506417\pi\)
\(998\) −6.20797 −0.196510
\(999\) −20.5837 −0.651240
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 4034.2.a.d.1.10 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.10 52 1.1 even 1 trivial