Properties

Label 4006.2.a.g.1.12
Level 4006
Weight 2
Character 4006.1
Self dual yes
Analytic conductor 31.988
Analytic rank 1
Dimension 40
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4006 = 2 \cdot 2003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4006.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9880710497\)
Analytic rank: \(1\)
Dimension: \(40\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 4006.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.69686 q^{3} +1.00000 q^{4} +3.10338 q^{5} +1.69686 q^{6} +1.10094 q^{7} -1.00000 q^{8} -0.120661 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.69686 q^{3} +1.00000 q^{4} +3.10338 q^{5} +1.69686 q^{6} +1.10094 q^{7} -1.00000 q^{8} -0.120661 q^{9} -3.10338 q^{10} -4.72621 q^{11} -1.69686 q^{12} -3.35011 q^{13} -1.10094 q^{14} -5.26601 q^{15} +1.00000 q^{16} -0.0655032 q^{17} +0.120661 q^{18} -0.989928 q^{19} +3.10338 q^{20} -1.86814 q^{21} +4.72621 q^{22} +5.99797 q^{23} +1.69686 q^{24} +4.63099 q^{25} +3.35011 q^{26} +5.29533 q^{27} +1.10094 q^{28} +8.91879 q^{29} +5.26601 q^{30} +2.81936 q^{31} -1.00000 q^{32} +8.01972 q^{33} +0.0655032 q^{34} +3.41664 q^{35} -0.120661 q^{36} -10.8162 q^{37} +0.989928 q^{38} +5.68468 q^{39} -3.10338 q^{40} -8.08940 q^{41} +1.86814 q^{42} +2.83603 q^{43} -4.72621 q^{44} -0.374456 q^{45} -5.99797 q^{46} +4.73833 q^{47} -1.69686 q^{48} -5.78793 q^{49} -4.63099 q^{50} +0.111150 q^{51} -3.35011 q^{52} -9.29937 q^{53} -5.29533 q^{54} -14.6672 q^{55} -1.10094 q^{56} +1.67977 q^{57} -8.91879 q^{58} +14.3626 q^{59} -5.26601 q^{60} +12.4972 q^{61} -2.81936 q^{62} -0.132840 q^{63} +1.00000 q^{64} -10.3967 q^{65} -8.01972 q^{66} +0.610984 q^{67} -0.0655032 q^{68} -10.1777 q^{69} -3.41664 q^{70} -15.0768 q^{71} +0.120661 q^{72} +1.56280 q^{73} +10.8162 q^{74} -7.85816 q^{75} -0.989928 q^{76} -5.20327 q^{77} -5.68468 q^{78} -15.1504 q^{79} +3.10338 q^{80} -8.62346 q^{81} +8.08940 q^{82} -5.26349 q^{83} -1.86814 q^{84} -0.203281 q^{85} -2.83603 q^{86} -15.1340 q^{87} +4.72621 q^{88} -4.59042 q^{89} +0.374456 q^{90} -3.68827 q^{91} +5.99797 q^{92} -4.78406 q^{93} -4.73833 q^{94} -3.07213 q^{95} +1.69686 q^{96} -2.77239 q^{97} +5.78793 q^{98} +0.570267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + O(q^{10}) \) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + 23q^{10} - 28q^{11} - q^{12} - 12q^{13} - 12q^{14} - 14q^{15} + 40q^{16} - 10q^{17} - 29q^{18} + 3q^{19} - 23q^{20} - 40q^{21} + 28q^{22} - 10q^{23} + q^{24} + 43q^{25} + 12q^{26} - 7q^{27} + 12q^{28} - 37q^{29} + 14q^{30} - 16q^{31} - 40q^{32} - 11q^{33} + 10q^{34} - 24q^{35} + 29q^{36} - 17q^{37} - 3q^{38} - 10q^{39} + 23q^{40} - 58q^{41} + 40q^{42} + 37q^{43} - 28q^{44} - 66q^{45} + 10q^{46} - 34q^{47} - q^{48} + 28q^{49} - 43q^{50} - 7q^{51} - 12q^{52} - 43q^{53} + 7q^{54} + 28q^{55} - 12q^{56} - 25q^{57} + 37q^{58} - 92q^{59} - 14q^{60} - 37q^{61} + 16q^{62} + 14q^{63} + 40q^{64} - 54q^{65} + 11q^{66} - 10q^{67} - 10q^{68} - 49q^{69} + 24q^{70} - 87q^{71} - 29q^{72} + 12q^{73} + 17q^{74} - 31q^{75} + 3q^{76} - 53q^{77} + 10q^{78} + 14q^{79} - 23q^{80} - 4q^{81} + 58q^{82} - 42q^{83} - 40q^{84} - 24q^{85} - 37q^{86} + 24q^{87} + 28q^{88} - 118q^{89} + 66q^{90} - 35q^{91} - 10q^{92} - 22q^{93} + 34q^{94} - 18q^{95} + q^{96} + 2q^{97} - 28q^{98} - 48q^{99} + O(q^{100}) \)

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
\(3\) −1.69686 −0.979684 −0.489842 0.871811i \(-0.662945\pi\)
−0.489842 + 0.871811i \(0.662945\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.10338 1.38788 0.693938 0.720035i \(-0.255874\pi\)
0.693938 + 0.720035i \(0.255874\pi\)
\(6\) 1.69686 0.692741
\(7\) 1.10094 0.416116 0.208058 0.978116i \(-0.433286\pi\)
0.208058 + 0.978116i \(0.433286\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.120661 −0.0402202
\(10\) −3.10338 −0.981376
\(11\) −4.72621 −1.42500 −0.712502 0.701670i \(-0.752438\pi\)
−0.712502 + 0.701670i \(0.752438\pi\)
\(12\) −1.69686 −0.489842
\(13\) −3.35011 −0.929154 −0.464577 0.885533i \(-0.653794\pi\)
−0.464577 + 0.885533i \(0.653794\pi\)
\(14\) −1.10094 −0.294239
\(15\) −5.26601 −1.35968
\(16\) 1.00000 0.250000
\(17\) −0.0655032 −0.0158868 −0.00794342 0.999968i \(-0.502528\pi\)
−0.00794342 + 0.999968i \(0.502528\pi\)
\(18\) 0.120661 0.0284400
\(19\) −0.989928 −0.227105 −0.113553 0.993532i \(-0.536223\pi\)
−0.113553 + 0.993532i \(0.536223\pi\)
\(20\) 3.10338 0.693938
\(21\) −1.86814 −0.407662
\(22\) 4.72621 1.00763
\(23\) 5.99797 1.25066 0.625332 0.780359i \(-0.284964\pi\)
0.625332 + 0.780359i \(0.284964\pi\)
\(24\) 1.69686 0.346370
\(25\) 4.63099 0.926199
\(26\) 3.35011 0.657011
\(27\) 5.29533 1.01909
\(28\) 1.10094 0.208058
\(29\) 8.91879 1.65618 0.828089 0.560597i \(-0.189428\pi\)
0.828089 + 0.560597i \(0.189428\pi\)
\(30\) 5.26601 0.961438
\(31\) 2.81936 0.506371 0.253186 0.967418i \(-0.418522\pi\)
0.253186 + 0.967418i \(0.418522\pi\)
\(32\) −1.00000 −0.176777
\(33\) 8.01972 1.39605
\(34\) 0.0655032 0.0112337
\(35\) 3.41664 0.577517
\(36\) −0.120661 −0.0201101
\(37\) −10.8162 −1.77818 −0.889089 0.457734i \(-0.848661\pi\)
−0.889089 + 0.457734i \(0.848661\pi\)
\(38\) 0.989928 0.160587
\(39\) 5.68468 0.910277
\(40\) −3.10338 −0.490688
\(41\) −8.08940 −1.26335 −0.631676 0.775233i \(-0.717633\pi\)
−0.631676 + 0.775233i \(0.717633\pi\)
\(42\) 1.86814 0.288261
\(43\) 2.83603 0.432491 0.216246 0.976339i \(-0.430619\pi\)
0.216246 + 0.976339i \(0.430619\pi\)
\(44\) −4.72621 −0.712502
\(45\) −0.374456 −0.0558206
\(46\) −5.99797 −0.884353
\(47\) 4.73833 0.691157 0.345578 0.938390i \(-0.387683\pi\)
0.345578 + 0.938390i \(0.387683\pi\)
\(48\) −1.69686 −0.244921
\(49\) −5.78793 −0.826847
\(50\) −4.63099 −0.654921
\(51\) 0.111150 0.0155641
\(52\) −3.35011 −0.464577
\(53\) −9.29937 −1.27737 −0.638683 0.769470i \(-0.720521\pi\)
−0.638683 + 0.769470i \(0.720521\pi\)
\(54\) −5.29533 −0.720603
\(55\) −14.6672 −1.97773
\(56\) −1.10094 −0.147119
\(57\) 1.67977 0.222491
\(58\) −8.91879 −1.17109
\(59\) 14.3626 1.86985 0.934926 0.354843i \(-0.115466\pi\)
0.934926 + 0.354843i \(0.115466\pi\)
\(60\) −5.26601 −0.679839
\(61\) 12.4972 1.60010 0.800049 0.599934i \(-0.204807\pi\)
0.800049 + 0.599934i \(0.204807\pi\)
\(62\) −2.81936 −0.358059
\(63\) −0.132840 −0.0167363
\(64\) 1.00000 0.125000
\(65\) −10.3967 −1.28955
\(66\) −8.01972 −0.987159
\(67\) 0.610984 0.0746436 0.0373218 0.999303i \(-0.488117\pi\)
0.0373218 + 0.999303i \(0.488117\pi\)
\(68\) −0.0655032 −0.00794342
\(69\) −10.1777 −1.22525
\(70\) −3.41664 −0.408367
\(71\) −15.0768 −1.78929 −0.894646 0.446776i \(-0.852572\pi\)
−0.894646 + 0.446776i \(0.852572\pi\)
\(72\) 0.120661 0.0142200
\(73\) 1.56280 0.182912 0.0914558 0.995809i \(-0.470848\pi\)
0.0914558 + 0.995809i \(0.470848\pi\)
\(74\) 10.8162 1.25736
\(75\) −7.85816 −0.907382
\(76\) −0.989928 −0.113553
\(77\) −5.20327 −0.592968
\(78\) −5.68468 −0.643663
\(79\) −15.1504 −1.70455 −0.852274 0.523095i \(-0.824777\pi\)
−0.852274 + 0.523095i \(0.824777\pi\)
\(80\) 3.10338 0.346969
\(81\) −8.62346 −0.958162
\(82\) 8.08940 0.893325
\(83\) −5.26349 −0.577743 −0.288872 0.957368i \(-0.593280\pi\)
−0.288872 + 0.957368i \(0.593280\pi\)
\(84\) −1.86814 −0.203831
\(85\) −0.203281 −0.0220490
\(86\) −2.83603 −0.305817
\(87\) −15.1340 −1.62253
\(88\) 4.72621 0.503815
\(89\) −4.59042 −0.486584 −0.243292 0.969953i \(-0.578227\pi\)
−0.243292 + 0.969953i \(0.578227\pi\)
\(90\) 0.374456 0.0394711
\(91\) −3.68827 −0.386636
\(92\) 5.99797 0.625332
\(93\) −4.78406 −0.496084
\(94\) −4.73833 −0.488722
\(95\) −3.07213 −0.315193
\(96\) 1.69686 0.173185
\(97\) −2.77239 −0.281493 −0.140747 0.990046i \(-0.544950\pi\)
−0.140747 + 0.990046i \(0.544950\pi\)
\(98\) 5.78793 0.584669
\(99\) 0.570267 0.0573139
\(100\) 4.63099 0.463099
\(101\) 12.4047 1.23431 0.617157 0.786840i \(-0.288284\pi\)
0.617157 + 0.786840i \(0.288284\pi\)
\(102\) −0.111150 −0.0110055
\(103\) 4.25770 0.419524 0.209762 0.977753i \(-0.432731\pi\)
0.209762 + 0.977753i \(0.432731\pi\)
\(104\) 3.35011 0.328506
\(105\) −5.79756 −0.565784
\(106\) 9.29937 0.903235
\(107\) −10.4483 −1.01007 −0.505037 0.863098i \(-0.668521\pi\)
−0.505037 + 0.863098i \(0.668521\pi\)
\(108\) 5.29533 0.509543
\(109\) −13.4323 −1.28658 −0.643290 0.765623i \(-0.722431\pi\)
−0.643290 + 0.765623i \(0.722431\pi\)
\(110\) 14.6672 1.39847
\(111\) 18.3537 1.74205
\(112\) 1.10094 0.104029
\(113\) −0.270586 −0.0254546 −0.0127273 0.999919i \(-0.504051\pi\)
−0.0127273 + 0.999919i \(0.504051\pi\)
\(114\) −1.67977 −0.157325
\(115\) 18.6140 1.73577
\(116\) 8.91879 0.828089
\(117\) 0.404226 0.0373707
\(118\) −14.3626 −1.32218
\(119\) −0.0721150 −0.00661077
\(120\) 5.26601 0.480719
\(121\) 11.3370 1.03064
\(122\) −12.4972 −1.13144
\(123\) 13.7266 1.23769
\(124\) 2.81936 0.253186
\(125\) −1.14517 −0.102427
\(126\) 0.132840 0.0118343
\(127\) −2.70772 −0.240272 −0.120136 0.992757i \(-0.538333\pi\)
−0.120136 + 0.992757i \(0.538333\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −4.81236 −0.423704
\(130\) 10.3967 0.911850
\(131\) −14.5970 −1.27535 −0.637674 0.770306i \(-0.720103\pi\)
−0.637674 + 0.770306i \(0.720103\pi\)
\(132\) 8.01972 0.698027
\(133\) −1.08985 −0.0945021
\(134\) −0.610984 −0.0527810
\(135\) 16.4334 1.41437
\(136\) 0.0655032 0.00561685
\(137\) −1.80758 −0.154432 −0.0772161 0.997014i \(-0.524603\pi\)
−0.0772161 + 0.997014i \(0.524603\pi\)
\(138\) 10.1777 0.866386
\(139\) 14.5191 1.23149 0.615745 0.787945i \(-0.288855\pi\)
0.615745 + 0.787945i \(0.288855\pi\)
\(140\) 3.41664 0.288759
\(141\) −8.04029 −0.677115
\(142\) 15.0768 1.26522
\(143\) 15.8333 1.32405
\(144\) −0.120661 −0.0100550
\(145\) 27.6784 2.29857
\(146\) −1.56280 −0.129338
\(147\) 9.82132 0.810049
\(148\) −10.8162 −0.889089
\(149\) −6.16805 −0.505306 −0.252653 0.967557i \(-0.581303\pi\)
−0.252653 + 0.967557i \(0.581303\pi\)
\(150\) 7.85816 0.641616
\(151\) 8.22272 0.669156 0.334578 0.942368i \(-0.391406\pi\)
0.334578 + 0.942368i \(0.391406\pi\)
\(152\) 0.989928 0.0802937
\(153\) 0.00790365 0.000638972 0
\(154\) 5.20327 0.419291
\(155\) 8.74955 0.702780
\(156\) 5.68468 0.455138
\(157\) −19.5862 −1.56315 −0.781575 0.623812i \(-0.785583\pi\)
−0.781575 + 0.623812i \(0.785583\pi\)
\(158\) 15.1504 1.20530
\(159\) 15.7797 1.25141
\(160\) −3.10338 −0.245344
\(161\) 6.60341 0.520421
\(162\) 8.62346 0.677523
\(163\) 20.0890 1.57349 0.786747 0.617275i \(-0.211764\pi\)
0.786747 + 0.617275i \(0.211764\pi\)
\(164\) −8.08940 −0.631676
\(165\) 24.8883 1.93755
\(166\) 5.26349 0.408526
\(167\) 2.21258 0.171215 0.0856075 0.996329i \(-0.472717\pi\)
0.0856075 + 0.996329i \(0.472717\pi\)
\(168\) 1.86814 0.144130
\(169\) −1.77675 −0.136673
\(170\) 0.203281 0.0155910
\(171\) 0.119445 0.00913420
\(172\) 2.83603 0.216246
\(173\) −17.6460 −1.34160 −0.670800 0.741638i \(-0.734049\pi\)
−0.670800 + 0.741638i \(0.734049\pi\)
\(174\) 15.1340 1.14730
\(175\) 5.09845 0.385406
\(176\) −4.72621 −0.356251
\(177\) −24.3714 −1.83186
\(178\) 4.59042 0.344067
\(179\) −19.2376 −1.43789 −0.718943 0.695069i \(-0.755374\pi\)
−0.718943 + 0.695069i \(0.755374\pi\)
\(180\) −0.374456 −0.0279103
\(181\) −14.9357 −1.11016 −0.555081 0.831796i \(-0.687313\pi\)
−0.555081 + 0.831796i \(0.687313\pi\)
\(182\) 3.68827 0.273393
\(183\) −21.2060 −1.56759
\(184\) −5.99797 −0.442176
\(185\) −33.5669 −2.46789
\(186\) 4.78406 0.350784
\(187\) 0.309581 0.0226388
\(188\) 4.73833 0.345578
\(189\) 5.82984 0.424058
\(190\) 3.07213 0.222875
\(191\) −1.63198 −0.118086 −0.0590428 0.998255i \(-0.518805\pi\)
−0.0590428 + 0.998255i \(0.518805\pi\)
\(192\) −1.69686 −0.122460
\(193\) −4.81891 −0.346872 −0.173436 0.984845i \(-0.555487\pi\)
−0.173436 + 0.984845i \(0.555487\pi\)
\(194\) 2.77239 0.199046
\(195\) 17.6417 1.26335
\(196\) −5.78793 −0.413424
\(197\) −8.63017 −0.614874 −0.307437 0.951568i \(-0.599471\pi\)
−0.307437 + 0.951568i \(0.599471\pi\)
\(198\) −0.570267 −0.0405271
\(199\) 1.38982 0.0985218 0.0492609 0.998786i \(-0.484313\pi\)
0.0492609 + 0.998786i \(0.484313\pi\)
\(200\) −4.63099 −0.327461
\(201\) −1.03675 −0.0731271
\(202\) −12.4047 −0.872791
\(203\) 9.81905 0.689162
\(204\) 0.111150 0.00778204
\(205\) −25.1045 −1.75338
\(206\) −4.25770 −0.296648
\(207\) −0.723719 −0.0503019
\(208\) −3.35011 −0.232288
\(209\) 4.67860 0.323626
\(210\) 5.79756 0.400070
\(211\) −13.4931 −0.928900 −0.464450 0.885599i \(-0.653748\pi\)
−0.464450 + 0.885599i \(0.653748\pi\)
\(212\) −9.29937 −0.638683
\(213\) 25.5833 1.75294
\(214\) 10.4483 0.714230
\(215\) 8.80130 0.600244
\(216\) −5.29533 −0.360302
\(217\) 3.10394 0.210709
\(218\) 13.4323 0.909749
\(219\) −2.65185 −0.179195
\(220\) −14.6672 −0.988865
\(221\) 0.219443 0.0147613
\(222\) −18.3537 −1.23182
\(223\) 11.3543 0.760341 0.380171 0.924916i \(-0.375865\pi\)
0.380171 + 0.924916i \(0.375865\pi\)
\(224\) −1.10094 −0.0735596
\(225\) −0.558778 −0.0372519
\(226\) 0.270586 0.0179991
\(227\) −5.06546 −0.336206 −0.168103 0.985769i \(-0.553764\pi\)
−0.168103 + 0.985769i \(0.553764\pi\)
\(228\) 1.67977 0.111246
\(229\) −10.9776 −0.725419 −0.362709 0.931902i \(-0.618148\pi\)
−0.362709 + 0.931902i \(0.618148\pi\)
\(230\) −18.6140 −1.22737
\(231\) 8.82923 0.580921
\(232\) −8.91879 −0.585547
\(233\) −17.4661 −1.14424 −0.572121 0.820169i \(-0.693879\pi\)
−0.572121 + 0.820169i \(0.693879\pi\)
\(234\) −0.404226 −0.0264251
\(235\) 14.7049 0.959240
\(236\) 14.3626 0.934926
\(237\) 25.7081 1.66992
\(238\) 0.0721150 0.00467452
\(239\) 25.3558 1.64013 0.820067 0.572268i \(-0.193936\pi\)
0.820067 + 0.572268i \(0.193936\pi\)
\(240\) −5.26601 −0.339920
\(241\) −2.09101 −0.134694 −0.0673469 0.997730i \(-0.521453\pi\)
−0.0673469 + 0.997730i \(0.521453\pi\)
\(242\) −11.3370 −0.728772
\(243\) −1.25317 −0.0803909
\(244\) 12.4972 0.800049
\(245\) −17.9622 −1.14756
\(246\) −13.7266 −0.875175
\(247\) 3.31637 0.211016
\(248\) −2.81936 −0.179029
\(249\) 8.93142 0.566006
\(250\) 1.14517 0.0724269
\(251\) −28.2124 −1.78075 −0.890376 0.455225i \(-0.849559\pi\)
−0.890376 + 0.455225i \(0.849559\pi\)
\(252\) −0.132840 −0.00836813
\(253\) −28.3477 −1.78220
\(254\) 2.70772 0.169898
\(255\) 0.344941 0.0216010
\(256\) 1.00000 0.0625000
\(257\) −6.61315 −0.412517 −0.206259 0.978498i \(-0.566129\pi\)
−0.206259 + 0.978498i \(0.566129\pi\)
\(258\) 4.81236 0.299604
\(259\) −11.9080 −0.739929
\(260\) −10.3967 −0.644775
\(261\) −1.07615 −0.0666117
\(262\) 14.5970 0.901808
\(263\) 17.7963 1.09737 0.548685 0.836029i \(-0.315129\pi\)
0.548685 + 0.836029i \(0.315129\pi\)
\(264\) −8.01972 −0.493580
\(265\) −28.8595 −1.77283
\(266\) 1.08985 0.0668230
\(267\) 7.78931 0.476698
\(268\) 0.610984 0.0373218
\(269\) 11.9618 0.729322 0.364661 0.931140i \(-0.381185\pi\)
0.364661 + 0.931140i \(0.381185\pi\)
\(270\) −16.4334 −1.00011
\(271\) −9.81810 −0.596407 −0.298204 0.954502i \(-0.596387\pi\)
−0.298204 + 0.954502i \(0.596387\pi\)
\(272\) −0.0655032 −0.00397171
\(273\) 6.25849 0.378781
\(274\) 1.80758 0.109200
\(275\) −21.8870 −1.31984
\(276\) −10.1777 −0.612627
\(277\) 0.176183 0.0105858 0.00529290 0.999986i \(-0.498315\pi\)
0.00529290 + 0.999986i \(0.498315\pi\)
\(278\) −14.5191 −0.870796
\(279\) −0.340185 −0.0203663
\(280\) −3.41664 −0.204183
\(281\) −5.12252 −0.305584 −0.152792 0.988258i \(-0.548826\pi\)
−0.152792 + 0.988258i \(0.548826\pi\)
\(282\) 8.04029 0.478793
\(283\) −1.16754 −0.0694029 −0.0347015 0.999398i \(-0.511048\pi\)
−0.0347015 + 0.999398i \(0.511048\pi\)
\(284\) −15.0768 −0.894646
\(285\) 5.21297 0.308790
\(286\) −15.8333 −0.936244
\(287\) −8.90594 −0.525701
\(288\) 0.120661 0.00710999
\(289\) −16.9957 −0.999748
\(290\) −27.6784 −1.62533
\(291\) 4.70436 0.275774
\(292\) 1.56280 0.0914558
\(293\) −4.67725 −0.273248 −0.136624 0.990623i \(-0.543625\pi\)
−0.136624 + 0.990623i \(0.543625\pi\)
\(294\) −9.82132 −0.572791
\(295\) 44.5727 2.59512
\(296\) 10.8162 0.628681
\(297\) −25.0268 −1.45220
\(298\) 6.16805 0.357306
\(299\) −20.0939 −1.16206
\(300\) −7.85816 −0.453691
\(301\) 3.12230 0.179967
\(302\) −8.22272 −0.473165
\(303\) −21.0491 −1.20924
\(304\) −0.989928 −0.0567763
\(305\) 38.7835 2.22074
\(306\) −0.00790365 −0.000451821 0
\(307\) 19.6394 1.12088 0.560440 0.828195i \(-0.310632\pi\)
0.560440 + 0.828195i \(0.310632\pi\)
\(308\) −5.20327 −0.296484
\(309\) −7.22473 −0.411000
\(310\) −8.74955 −0.496941
\(311\) 5.40469 0.306472 0.153236 0.988190i \(-0.451031\pi\)
0.153236 + 0.988190i \(0.451031\pi\)
\(312\) −5.68468 −0.321831
\(313\) 19.2759 1.08954 0.544771 0.838585i \(-0.316617\pi\)
0.544771 + 0.838585i \(0.316617\pi\)
\(314\) 19.5862 1.10531
\(315\) −0.412253 −0.0232279
\(316\) −15.1504 −0.852274
\(317\) 2.18365 0.122646 0.0613229 0.998118i \(-0.480468\pi\)
0.0613229 + 0.998118i \(0.480468\pi\)
\(318\) −15.7797 −0.884884
\(319\) −42.1520 −2.36006
\(320\) 3.10338 0.173484
\(321\) 17.7293 0.989552
\(322\) −6.60341 −0.367994
\(323\) 0.0648434 0.00360798
\(324\) −8.62346 −0.479081
\(325\) −15.5143 −0.860581
\(326\) −20.0890 −1.11263
\(327\) 22.7927 1.26044
\(328\) 8.08940 0.446662
\(329\) 5.21662 0.287602
\(330\) −24.8883 −1.37005
\(331\) 25.2610 1.38847 0.694234 0.719750i \(-0.255743\pi\)
0.694234 + 0.719750i \(0.255743\pi\)
\(332\) −5.26349 −0.288872
\(333\) 1.30509 0.0715187
\(334\) −2.21258 −0.121067
\(335\) 1.89612 0.103596
\(336\) −1.86814 −0.101916
\(337\) 24.5823 1.33908 0.669541 0.742775i \(-0.266491\pi\)
0.669541 + 0.742775i \(0.266491\pi\)
\(338\) 1.77675 0.0966424
\(339\) 0.459147 0.0249374
\(340\) −0.203281 −0.0110245
\(341\) −13.3249 −0.721582
\(342\) −0.119445 −0.00645886
\(343\) −14.0787 −0.760181
\(344\) −2.83603 −0.152909
\(345\) −31.5854 −1.70050
\(346\) 17.6460 0.948654
\(347\) −31.8185 −1.70810 −0.854052 0.520187i \(-0.825862\pi\)
−0.854052 + 0.520187i \(0.825862\pi\)
\(348\) −15.1340 −0.811265
\(349\) −12.7475 −0.682360 −0.341180 0.939998i \(-0.610827\pi\)
−0.341180 + 0.939998i \(0.610827\pi\)
\(350\) −5.09845 −0.272523
\(351\) −17.7399 −0.946888
\(352\) 4.72621 0.251908
\(353\) −1.51393 −0.0805784 −0.0402892 0.999188i \(-0.512828\pi\)
−0.0402892 + 0.999188i \(0.512828\pi\)
\(354\) 24.3714 1.29532
\(355\) −46.7892 −2.48331
\(356\) −4.59042 −0.243292
\(357\) 0.122369 0.00647647
\(358\) 19.2376 1.01674
\(359\) −28.3026 −1.49376 −0.746878 0.664962i \(-0.768448\pi\)
−0.746878 + 0.664962i \(0.768448\pi\)
\(360\) 0.374456 0.0197356
\(361\) −18.0200 −0.948423
\(362\) 14.9357 0.785003
\(363\) −19.2374 −1.00970
\(364\) −3.68827 −0.193318
\(365\) 4.84996 0.253859
\(366\) 21.2060 1.10845
\(367\) 32.9712 1.72108 0.860541 0.509381i \(-0.170126\pi\)
0.860541 + 0.509381i \(0.170126\pi\)
\(368\) 5.99797 0.312666
\(369\) 0.976071 0.0508122
\(370\) 33.5669 1.74506
\(371\) −10.2380 −0.531533
\(372\) −4.78406 −0.248042
\(373\) 23.5082 1.21721 0.608605 0.793474i \(-0.291730\pi\)
0.608605 + 0.793474i \(0.291730\pi\)
\(374\) −0.309581 −0.0160081
\(375\) 1.94319 0.100346
\(376\) −4.73833 −0.244361
\(377\) −29.8789 −1.53884
\(378\) −5.82984 −0.299855
\(379\) −13.4273 −0.689716 −0.344858 0.938655i \(-0.612073\pi\)
−0.344858 + 0.938655i \(0.612073\pi\)
\(380\) −3.07213 −0.157597
\(381\) 4.59463 0.235390
\(382\) 1.63198 0.0834991
\(383\) −8.49327 −0.433986 −0.216993 0.976173i \(-0.569625\pi\)
−0.216993 + 0.976173i \(0.569625\pi\)
\(384\) 1.69686 0.0865926
\(385\) −16.1477 −0.822965
\(386\) 4.81891 0.245276
\(387\) −0.342197 −0.0173949
\(388\) −2.77239 −0.140747
\(389\) −12.3274 −0.625023 −0.312512 0.949914i \(-0.601170\pi\)
−0.312512 + 0.949914i \(0.601170\pi\)
\(390\) −17.6417 −0.893324
\(391\) −0.392886 −0.0198691
\(392\) 5.78793 0.292335
\(393\) 24.7691 1.24944
\(394\) 8.63017 0.434782
\(395\) −47.0174 −2.36570
\(396\) 0.570267 0.0286570
\(397\) −28.8419 −1.44753 −0.723767 0.690045i \(-0.757591\pi\)
−0.723767 + 0.690045i \(0.757591\pi\)
\(398\) −1.38982 −0.0696655
\(399\) 1.84933 0.0925821
\(400\) 4.63099 0.231550
\(401\) −0.547787 −0.0273552 −0.0136776 0.999906i \(-0.504354\pi\)
−0.0136776 + 0.999906i \(0.504354\pi\)
\(402\) 1.03675 0.0517086
\(403\) −9.44516 −0.470497
\(404\) 12.4047 0.617157
\(405\) −26.7619 −1.32981
\(406\) −9.81905 −0.487311
\(407\) 51.1198 2.53391
\(408\) −0.111150 −0.00550274
\(409\) 17.5247 0.866540 0.433270 0.901264i \(-0.357360\pi\)
0.433270 + 0.901264i \(0.357360\pi\)
\(410\) 25.1045 1.23982
\(411\) 3.06722 0.151295
\(412\) 4.25770 0.209762
\(413\) 15.8124 0.778075
\(414\) 0.723719 0.0355688
\(415\) −16.3346 −0.801836
\(416\) 3.35011 0.164253
\(417\) −24.6368 −1.20647
\(418\) −4.67860 −0.228838
\(419\) 11.7030 0.571728 0.285864 0.958270i \(-0.407719\pi\)
0.285864 + 0.958270i \(0.407719\pi\)
\(420\) −5.79756 −0.282892
\(421\) 6.40915 0.312363 0.156181 0.987728i \(-0.450082\pi\)
0.156181 + 0.987728i \(0.450082\pi\)
\(422\) 13.4931 0.656832
\(423\) −0.571730 −0.0277984
\(424\) 9.29937 0.451617
\(425\) −0.303345 −0.0147144
\(426\) −25.5833 −1.23952
\(427\) 13.7586 0.665827
\(428\) −10.4483 −0.505037
\(429\) −26.8670 −1.29715
\(430\) −8.80130 −0.424436
\(431\) −11.8112 −0.568925 −0.284463 0.958687i \(-0.591815\pi\)
−0.284463 + 0.958687i \(0.591815\pi\)
\(432\) 5.29533 0.254772
\(433\) −2.78930 −0.134045 −0.0670227 0.997751i \(-0.521350\pi\)
−0.0670227 + 0.997751i \(0.521350\pi\)
\(434\) −3.10394 −0.148994
\(435\) −46.9665 −2.25187
\(436\) −13.4323 −0.643290
\(437\) −5.93756 −0.284032
\(438\) 2.65185 0.126710
\(439\) −14.4678 −0.690510 −0.345255 0.938509i \(-0.612208\pi\)
−0.345255 + 0.938509i \(0.612208\pi\)
\(440\) 14.6672 0.699233
\(441\) 0.698375 0.0332559
\(442\) −0.219443 −0.0104378
\(443\) −14.4703 −0.687507 −0.343753 0.939060i \(-0.611698\pi\)
−0.343753 + 0.939060i \(0.611698\pi\)
\(444\) 18.3537 0.871026
\(445\) −14.2458 −0.675317
\(446\) −11.3543 −0.537642
\(447\) 10.4663 0.495040
\(448\) 1.10094 0.0520145
\(449\) −6.56567 −0.309853 −0.154926 0.987926i \(-0.549514\pi\)
−0.154926 + 0.987926i \(0.549514\pi\)
\(450\) 0.558778 0.0263411
\(451\) 38.2322 1.80028
\(452\) −0.270586 −0.0127273
\(453\) −13.9528 −0.655561
\(454\) 5.06546 0.237734
\(455\) −11.4461 −0.536603
\(456\) −1.67977 −0.0786625
\(457\) 26.1503 1.22326 0.611630 0.791144i \(-0.290514\pi\)
0.611630 + 0.791144i \(0.290514\pi\)
\(458\) 10.9776 0.512949
\(459\) −0.346861 −0.0161901
\(460\) 18.6140 0.867883
\(461\) 14.0435 0.654072 0.327036 0.945012i \(-0.393950\pi\)
0.327036 + 0.945012i \(0.393950\pi\)
\(462\) −8.82923 −0.410773
\(463\) −22.8998 −1.06424 −0.532122 0.846668i \(-0.678605\pi\)
−0.532122 + 0.846668i \(0.678605\pi\)
\(464\) 8.91879 0.414044
\(465\) −14.8468 −0.688502
\(466\) 17.4661 0.809101
\(467\) 24.2008 1.11988 0.559940 0.828533i \(-0.310824\pi\)
0.559940 + 0.828533i \(0.310824\pi\)
\(468\) 0.404226 0.0186854
\(469\) 0.672656 0.0310604
\(470\) −14.7049 −0.678285
\(471\) 33.2351 1.53139
\(472\) −14.3626 −0.661092
\(473\) −13.4037 −0.616302
\(474\) −25.7081 −1.18081
\(475\) −4.58435 −0.210344
\(476\) −0.0721150 −0.00330539
\(477\) 1.12207 0.0513759
\(478\) −25.3558 −1.15975
\(479\) 2.46499 0.112628 0.0563141 0.998413i \(-0.482065\pi\)
0.0563141 + 0.998413i \(0.482065\pi\)
\(480\) 5.26601 0.240360
\(481\) 36.2356 1.65220
\(482\) 2.09101 0.0952430
\(483\) −11.2051 −0.509848
\(484\) 11.3370 0.515319
\(485\) −8.60379 −0.390678
\(486\) 1.25317 0.0568449
\(487\) −11.8352 −0.536303 −0.268152 0.963377i \(-0.586413\pi\)
−0.268152 + 0.963377i \(0.586413\pi\)
\(488\) −12.4972 −0.565720
\(489\) −34.0883 −1.54153
\(490\) 17.9622 0.811448
\(491\) 15.4683 0.698075 0.349038 0.937109i \(-0.386509\pi\)
0.349038 + 0.937109i \(0.386509\pi\)
\(492\) 13.7266 0.618843
\(493\) −0.584209 −0.0263114
\(494\) −3.31637 −0.149210
\(495\) 1.76976 0.0795446
\(496\) 2.81936 0.126593
\(497\) −16.5987 −0.744553
\(498\) −8.93142 −0.400226
\(499\) −32.7714 −1.46705 −0.733526 0.679662i \(-0.762127\pi\)
−0.733526 + 0.679662i \(0.762127\pi\)
\(500\) −1.14517 −0.0512135
\(501\) −3.75445 −0.167736
\(502\) 28.2124 1.25918
\(503\) 34.5762 1.54168 0.770838 0.637032i \(-0.219838\pi\)
0.770838 + 0.637032i \(0.219838\pi\)
\(504\) 0.132840 0.00591716
\(505\) 38.4965 1.71307
\(506\) 28.3477 1.26021
\(507\) 3.01490 0.133896
\(508\) −2.70772 −0.120136
\(509\) −44.7255 −1.98242 −0.991212 0.132286i \(-0.957768\pi\)
−0.991212 + 0.132286i \(0.957768\pi\)
\(510\) −0.344941 −0.0152742
\(511\) 1.72055 0.0761125
\(512\) −1.00000 −0.0441942
\(513\) −5.24199 −0.231440
\(514\) 6.61315 0.291694
\(515\) 13.2133 0.582247
\(516\) −4.81236 −0.211852
\(517\) −22.3943 −0.984902
\(518\) 11.9080 0.523209
\(519\) 29.9428 1.31434
\(520\) 10.3967 0.455925
\(521\) 26.5235 1.16201 0.581007 0.813898i \(-0.302659\pi\)
0.581007 + 0.813898i \(0.302659\pi\)
\(522\) 1.07615 0.0471016
\(523\) −32.1592 −1.40622 −0.703111 0.711080i \(-0.748206\pi\)
−0.703111 + 0.711080i \(0.748206\pi\)
\(524\) −14.5970 −0.637674
\(525\) −8.65136 −0.377576
\(526\) −17.7963 −0.775958
\(527\) −0.184677 −0.00804465
\(528\) 8.01972 0.349013
\(529\) 12.9757 0.564160
\(530\) 28.8595 1.25358
\(531\) −1.73300 −0.0752058
\(532\) −1.08985 −0.0472510
\(533\) 27.1004 1.17385
\(534\) −7.78931 −0.337076
\(535\) −32.4250 −1.40186
\(536\) −0.610984 −0.0263905
\(537\) 32.6436 1.40867
\(538\) −11.9618 −0.515709
\(539\) 27.3550 1.17826
\(540\) 16.4334 0.707183
\(541\) −24.9187 −1.07134 −0.535670 0.844427i \(-0.679941\pi\)
−0.535670 + 0.844427i \(0.679941\pi\)
\(542\) 9.81810 0.421724
\(543\) 25.3438 1.08761
\(544\) 0.0655032 0.00280842
\(545\) −41.6855 −1.78561
\(546\) −6.25849 −0.267839
\(547\) −5.55760 −0.237626 −0.118813 0.992917i \(-0.537909\pi\)
−0.118813 + 0.992917i \(0.537909\pi\)
\(548\) −1.80758 −0.0772161
\(549\) −1.50792 −0.0643563
\(550\) 21.8870 0.933266
\(551\) −8.82896 −0.376126
\(552\) 10.1777 0.433193
\(553\) −16.6796 −0.709290
\(554\) −0.176183 −0.00748529
\(555\) 56.9585 2.41775
\(556\) 14.5191 0.615745
\(557\) 17.9958 0.762505 0.381252 0.924471i \(-0.375493\pi\)
0.381252 + 0.924471i \(0.375493\pi\)
\(558\) 0.340185 0.0144012
\(559\) −9.50103 −0.401851
\(560\) 3.41664 0.144379
\(561\) −0.525317 −0.0221789
\(562\) 5.12252 0.216080
\(563\) 29.6820 1.25095 0.625474 0.780245i \(-0.284906\pi\)
0.625474 + 0.780245i \(0.284906\pi\)
\(564\) −8.04029 −0.338557
\(565\) −0.839732 −0.0353278
\(566\) 1.16754 0.0490753
\(567\) −9.49391 −0.398707
\(568\) 15.0768 0.632610
\(569\) −19.5871 −0.821133 −0.410566 0.911831i \(-0.634669\pi\)
−0.410566 + 0.911831i \(0.634669\pi\)
\(570\) −5.21297 −0.218347
\(571\) −31.4220 −1.31497 −0.657484 0.753468i \(-0.728379\pi\)
−0.657484 + 0.753468i \(0.728379\pi\)
\(572\) 15.8333 0.662024
\(573\) 2.76924 0.115687
\(574\) 8.90594 0.371727
\(575\) 27.7766 1.15836
\(576\) −0.120661 −0.00502752
\(577\) 26.3178 1.09562 0.547812 0.836602i \(-0.315461\pi\)
0.547812 + 0.836602i \(0.315461\pi\)
\(578\) 16.9957 0.706928
\(579\) 8.17702 0.339825
\(580\) 27.6784 1.14928
\(581\) −5.79479 −0.240408
\(582\) −4.70436 −0.195002
\(583\) 43.9507 1.82025
\(584\) −1.56280 −0.0646690
\(585\) 1.25447 0.0518659
\(586\) 4.67725 0.193215
\(587\) −34.5807 −1.42730 −0.713649 0.700504i \(-0.752959\pi\)
−0.713649 + 0.700504i \(0.752959\pi\)
\(588\) 9.82132 0.405024
\(589\) −2.79096 −0.114999
\(590\) −44.5727 −1.83503
\(591\) 14.6442 0.602382
\(592\) −10.8162 −0.444545
\(593\) −31.4655 −1.29213 −0.646066 0.763281i \(-0.723587\pi\)
−0.646066 + 0.763281i \(0.723587\pi\)
\(594\) 25.0268 1.02686
\(595\) −0.223801 −0.00917493
\(596\) −6.16805 −0.252653
\(597\) −2.35833 −0.0965202
\(598\) 20.0939 0.821700
\(599\) 12.7811 0.522223 0.261111 0.965309i \(-0.415911\pi\)
0.261111 + 0.965309i \(0.415911\pi\)
\(600\) 7.85816 0.320808
\(601\) 31.5946 1.28877 0.644386 0.764701i \(-0.277113\pi\)
0.644386 + 0.764701i \(0.277113\pi\)
\(602\) −3.12230 −0.127256
\(603\) −0.0737216 −0.00300218
\(604\) 8.22272 0.334578
\(605\) 35.1832 1.43040
\(606\) 21.0491 0.855059
\(607\) 34.2402 1.38977 0.694884 0.719122i \(-0.255456\pi\)
0.694884 + 0.719122i \(0.255456\pi\)
\(608\) 0.989928 0.0401469
\(609\) −16.6616 −0.675161
\(610\) −38.7835 −1.57030
\(611\) −15.8739 −0.642191
\(612\) 0.00790365 0.000319486 0
\(613\) 24.4987 0.989491 0.494746 0.869038i \(-0.335261\pi\)
0.494746 + 0.869038i \(0.335261\pi\)
\(614\) −19.6394 −0.792582
\(615\) 42.5989 1.71775
\(616\) 5.20327 0.209646
\(617\) 11.3368 0.456404 0.228202 0.973614i \(-0.426715\pi\)
0.228202 + 0.973614i \(0.426715\pi\)
\(618\) 7.22473 0.290621
\(619\) 10.2001 0.409977 0.204988 0.978764i \(-0.434284\pi\)
0.204988 + 0.978764i \(0.434284\pi\)
\(620\) 8.74955 0.351390
\(621\) 31.7612 1.27453
\(622\) −5.40469 −0.216708
\(623\) −5.05378 −0.202475
\(624\) 5.68468 0.227569
\(625\) −26.7089 −1.06835
\(626\) −19.2759 −0.770422
\(627\) −7.93894 −0.317051
\(628\) −19.5862 −0.781575
\(629\) 0.708498 0.0282497
\(630\) 0.412253 0.0164246
\(631\) 33.4482 1.33155 0.665776 0.746151i \(-0.268100\pi\)
0.665776 + 0.746151i \(0.268100\pi\)
\(632\) 15.1504 0.602649
\(633\) 22.8958 0.910028
\(634\) −2.18365 −0.0867237
\(635\) −8.40311 −0.333467
\(636\) 15.7797 0.625707
\(637\) 19.3902 0.768268
\(638\) 42.1520 1.66882
\(639\) 1.81918 0.0719656
\(640\) −3.10338 −0.122672
\(641\) −37.7966 −1.49288 −0.746438 0.665455i \(-0.768237\pi\)
−0.746438 + 0.665455i \(0.768237\pi\)
\(642\) −17.7293 −0.699719
\(643\) −40.1016 −1.58145 −0.790725 0.612171i \(-0.790296\pi\)
−0.790725 + 0.612171i \(0.790296\pi\)
\(644\) 6.60341 0.260211
\(645\) −14.9346 −0.588049
\(646\) −0.0648434 −0.00255123
\(647\) 15.5390 0.610901 0.305450 0.952208i \(-0.401193\pi\)
0.305450 + 0.952208i \(0.401193\pi\)
\(648\) 8.62346 0.338761
\(649\) −67.8806 −2.66455
\(650\) 15.5143 0.608523
\(651\) −5.26696 −0.206428
\(652\) 20.0890 0.786747
\(653\) 8.28750 0.324315 0.162157 0.986765i \(-0.448155\pi\)
0.162157 + 0.986765i \(0.448155\pi\)
\(654\) −22.7927 −0.891266
\(655\) −45.3002 −1.77003
\(656\) −8.08940 −0.315838
\(657\) −0.188568 −0.00735674
\(658\) −5.21662 −0.203365
\(659\) −23.9302 −0.932187 −0.466094 0.884735i \(-0.654339\pi\)
−0.466094 + 0.884735i \(0.654339\pi\)
\(660\) 24.8883 0.968775
\(661\) 15.6173 0.607444 0.303722 0.952761i \(-0.401771\pi\)
0.303722 + 0.952761i \(0.401771\pi\)
\(662\) −25.2610 −0.981795
\(663\) −0.372364 −0.0144614
\(664\) 5.26349 0.204263
\(665\) −3.38223 −0.131157
\(666\) −1.30509 −0.0505713
\(667\) 53.4947 2.07132
\(668\) 2.21258 0.0856075
\(669\) −19.2667 −0.744894
\(670\) −1.89612 −0.0732534
\(671\) −59.0642 −2.28015
\(672\) 1.86814 0.0720652
\(673\) −33.9584 −1.30900 −0.654501 0.756061i \(-0.727121\pi\)
−0.654501 + 0.756061i \(0.727121\pi\)
\(674\) −24.5823 −0.946874
\(675\) 24.5226 0.943877
\(676\) −1.77675 −0.0683365
\(677\) −47.5964 −1.82928 −0.914639 0.404273i \(-0.867525\pi\)
−0.914639 + 0.404273i \(0.867525\pi\)
\(678\) −0.459147 −0.0176334
\(679\) −3.05223 −0.117134
\(680\) 0.203281 0.00779549
\(681\) 8.59538 0.329376
\(682\) 13.3249 0.510235
\(683\) 18.4911 0.707544 0.353772 0.935332i \(-0.384899\pi\)
0.353772 + 0.935332i \(0.384899\pi\)
\(684\) 0.119445 0.00456710
\(685\) −5.60962 −0.214333
\(686\) 14.0787 0.537529
\(687\) 18.6274 0.710681
\(688\) 2.83603 0.108123
\(689\) 31.1539 1.18687
\(690\) 31.5854 1.20244
\(691\) −11.0169 −0.419101 −0.209551 0.977798i \(-0.567200\pi\)
−0.209551 + 0.977798i \(0.567200\pi\)
\(692\) −17.6460 −0.670800
\(693\) 0.627829 0.0238493
\(694\) 31.8185 1.20781
\(695\) 45.0582 1.70916
\(696\) 15.1340 0.573651
\(697\) 0.529881 0.0200707
\(698\) 12.7475 0.482502
\(699\) 29.6375 1.12099
\(700\) 5.09845 0.192703
\(701\) −17.5274 −0.662001 −0.331000 0.943631i \(-0.607386\pi\)
−0.331000 + 0.943631i \(0.607386\pi\)
\(702\) 17.7399 0.669551
\(703\) 10.7073 0.403833
\(704\) −4.72621 −0.178126
\(705\) −24.9521 −0.939751
\(706\) 1.51393 0.0569775
\(707\) 13.6568 0.513618
\(708\) −24.3714 −0.915931
\(709\) −20.8363 −0.782525 −0.391262 0.920279i \(-0.627962\pi\)
−0.391262 + 0.920279i \(0.627962\pi\)
\(710\) 46.7892 1.75597
\(711\) 1.82805 0.0685572
\(712\) 4.59042 0.172033
\(713\) 16.9104 0.633300
\(714\) −0.122369 −0.00457955
\(715\) 49.1369 1.83762
\(716\) −19.2376 −0.718943
\(717\) −43.0254 −1.60681
\(718\) 28.3026 1.05624
\(719\) −28.6963 −1.07019 −0.535097 0.844791i \(-0.679725\pi\)
−0.535097 + 0.844791i \(0.679725\pi\)
\(720\) −0.374456 −0.0139551
\(721\) 4.68747 0.174571
\(722\) 18.0200 0.670637
\(723\) 3.54816 0.131957
\(724\) −14.9357 −0.555081
\(725\) 41.3029 1.53395
\(726\) 19.2374 0.713966
\(727\) −21.7490 −0.806626 −0.403313 0.915062i \(-0.632141\pi\)
−0.403313 + 0.915062i \(0.632141\pi\)
\(728\) 3.68827 0.136696
\(729\) 27.9968 1.03692
\(730\) −4.84996 −0.179505
\(731\) −0.185769 −0.00687092
\(732\) −21.2060 −0.783795
\(733\) 44.2991 1.63622 0.818112 0.575059i \(-0.195021\pi\)
0.818112 + 0.575059i \(0.195021\pi\)
\(734\) −32.9712 −1.21699
\(735\) 30.4793 1.12425
\(736\) −5.99797 −0.221088
\(737\) −2.88764 −0.106367
\(738\) −0.976071 −0.0359297
\(739\) −29.7433 −1.09412 −0.547062 0.837092i \(-0.684254\pi\)
−0.547062 + 0.837092i \(0.684254\pi\)
\(740\) −33.5669 −1.23395
\(741\) −5.62742 −0.206728
\(742\) 10.2380 0.375850
\(743\) −4.80753 −0.176371 −0.0881855 0.996104i \(-0.528107\pi\)
−0.0881855 + 0.996104i \(0.528107\pi\)
\(744\) 4.78406 0.175392
\(745\) −19.1418 −0.701302
\(746\) −23.5082 −0.860697
\(747\) 0.635096 0.0232369
\(748\) 0.309581 0.0113194
\(749\) −11.5029 −0.420308
\(750\) −1.94319 −0.0709554
\(751\) 9.14523 0.333714 0.166857 0.985981i \(-0.446638\pi\)
0.166857 + 0.985981i \(0.446638\pi\)
\(752\) 4.73833 0.172789
\(753\) 47.8726 1.74457
\(754\) 29.8789 1.08813
\(755\) 25.5183 0.928705
\(756\) 5.82984 0.212029
\(757\) 6.83634 0.248471 0.124235 0.992253i \(-0.460352\pi\)
0.124235 + 0.992253i \(0.460352\pi\)
\(758\) 13.4273 0.487703
\(759\) 48.1021 1.74599
\(760\) 3.07213 0.111438
\(761\) −17.8132 −0.645727 −0.322863 0.946446i \(-0.604645\pi\)
−0.322863 + 0.946446i \(0.604645\pi\)
\(762\) −4.59463 −0.166446
\(763\) −14.7881 −0.535366
\(764\) −1.63198 −0.0590428
\(765\) 0.0245280 0.000886813 0
\(766\) 8.49327 0.306874
\(767\) −48.1163 −1.73738
\(768\) −1.69686 −0.0612302
\(769\) 42.8978 1.54694 0.773468 0.633835i \(-0.218520\pi\)
0.773468 + 0.633835i \(0.218520\pi\)
\(770\) 16.1477 0.581924
\(771\) 11.2216 0.404136
\(772\) −4.81891 −0.173436
\(773\) −28.2458 −1.01593 −0.507965 0.861378i \(-0.669602\pi\)
−0.507965 + 0.861378i \(0.669602\pi\)
\(774\) 0.342197 0.0123000
\(775\) 13.0564 0.469000
\(776\) 2.77239 0.0995229
\(777\) 20.2063 0.724896
\(778\) 12.3274 0.441958
\(779\) 8.00792 0.286914
\(780\) 17.6417 0.631675
\(781\) 71.2562 2.54975
\(782\) 0.392886 0.0140496
\(783\) 47.2279 1.68779
\(784\) −5.78793 −0.206712
\(785\) −60.7835 −2.16946
\(786\) −24.7691 −0.883486
\(787\) −34.2621 −1.22131 −0.610655 0.791897i \(-0.709094\pi\)
−0.610655 + 0.791897i \(0.709094\pi\)
\(788\) −8.63017 −0.307437
\(789\) −30.1979 −1.07508
\(790\) 47.0174 1.67280
\(791\) −0.297899 −0.0105921
\(792\) −0.570267 −0.0202635
\(793\) −41.8669 −1.48674
\(794\) 28.8419 1.02356
\(795\) 48.9706 1.73681
\(796\) 1.38982 0.0492609
\(797\) 26.9633 0.955088 0.477544 0.878608i \(-0.341527\pi\)
0.477544 + 0.878608i \(0.341527\pi\)
\(798\) −1.84933 −0.0654654
\(799\) −0.310376 −0.0109803
\(800\) −4.63099 −0.163730
\(801\) 0.553882 0.0195705
\(802\) 0.547787 0.0193430
\(803\) −7.38610 −0.260650
\(804\) −1.03675 −0.0365635
\(805\) 20.4929 0.722280
\(806\) 9.44516 0.332692
\(807\) −20.2975 −0.714505
\(808\) −12.4047 −0.436396
\(809\) −10.2619 −0.360790 −0.180395 0.983594i \(-0.557738\pi\)
−0.180395 + 0.983594i \(0.557738\pi\)
\(810\) 26.7619 0.940318
\(811\) −20.1632 −0.708027 −0.354014 0.935240i \(-0.615183\pi\)
−0.354014 + 0.935240i \(0.615183\pi\)
\(812\) 9.81905 0.344581
\(813\) 16.6600 0.584290
\(814\) −51.1198 −1.79175
\(815\) 62.3440 2.18381
\(816\) 0.111150 0.00389102
\(817\) −2.80747 −0.0982209
\(818\) −17.5247 −0.612736
\(819\) 0.445029 0.0155506
\(820\) −25.1045 −0.876688
\(821\) −3.40593 −0.118868 −0.0594340 0.998232i \(-0.518930\pi\)
−0.0594340 + 0.998232i \(0.518930\pi\)
\(822\) −3.06722 −0.106982
\(823\) 35.4925 1.23719 0.618595 0.785710i \(-0.287702\pi\)
0.618595 + 0.785710i \(0.287702\pi\)
\(824\) −4.25770 −0.148324
\(825\) 37.1393 1.29302
\(826\) −15.8124 −0.550182
\(827\) −12.6139 −0.438629 −0.219315 0.975654i \(-0.570382\pi\)
−0.219315 + 0.975654i \(0.570382\pi\)
\(828\) −0.723719 −0.0251510
\(829\) 23.6983 0.823076 0.411538 0.911392i \(-0.364992\pi\)
0.411538 + 0.911392i \(0.364992\pi\)
\(830\) 16.3346 0.566984
\(831\) −0.298958 −0.0103707
\(832\) −3.35011 −0.116144
\(833\) 0.379128 0.0131360
\(834\) 24.6368 0.853104
\(835\) 6.86650 0.237625
\(836\) 4.67860 0.161813
\(837\) 14.9294 0.516036
\(838\) −11.7030 −0.404273
\(839\) −46.3536 −1.60030 −0.800152 0.599797i \(-0.795248\pi\)
−0.800152 + 0.599797i \(0.795248\pi\)
\(840\) 5.79756 0.200035
\(841\) 50.5448 1.74292
\(842\) −6.40915 −0.220874
\(843\) 8.69220 0.299375
\(844\) −13.4931 −0.464450
\(845\) −5.51393 −0.189685
\(846\) 0.571730 0.0196565
\(847\) 12.4814 0.428865
\(848\) −9.29937 −0.319342
\(849\) 1.98115 0.0679929
\(850\) 0.303345 0.0104046
\(851\) −64.8755 −2.22390
\(852\) 25.5833 0.876470
\(853\) 18.2913 0.626281 0.313140 0.949707i \(-0.398619\pi\)
0.313140 + 0.949707i \(0.398619\pi\)
\(854\) −13.7586 −0.470811
\(855\) 0.370684 0.0126771
\(856\) 10.4483 0.357115
\(857\) 20.0439 0.684686 0.342343 0.939575i \(-0.388779\pi\)
0.342343 + 0.939575i \(0.388779\pi\)
\(858\) 26.8670 0.917223
\(859\) 50.0262 1.70687 0.853436 0.521197i \(-0.174514\pi\)
0.853436 + 0.521197i \(0.174514\pi\)
\(860\) 8.80130 0.300122
\(861\) 15.1122 0.515021
\(862\) 11.8112 0.402291
\(863\) 43.5480 1.48239 0.741195 0.671290i \(-0.234259\pi\)
0.741195 + 0.671290i \(0.234259\pi\)
\(864\) −5.29533 −0.180151
\(865\) −54.7623 −1.86197
\(866\) 2.78930 0.0947844
\(867\) 28.8394 0.979436
\(868\) 3.10394 0.105355
\(869\) 71.6037 2.42899
\(870\) 46.9665 1.59231
\(871\) −2.04686 −0.0693554
\(872\) 13.4323 0.454875
\(873\) 0.334518 0.0113217
\(874\) 5.93756 0.200841
\(875\) −1.26076 −0.0426216
\(876\) −2.65185 −0.0895977
\(877\) 18.3635 0.620092 0.310046 0.950721i \(-0.399655\pi\)
0.310046 + 0.950721i \(0.399655\pi\)
\(878\) 14.4678 0.488265
\(879\) 7.93665 0.267696
\(880\) −14.6672 −0.494432
\(881\) −29.4314 −0.991569 −0.495785 0.868446i \(-0.665119\pi\)
−0.495785 + 0.868446i \(0.665119\pi\)
\(882\) −0.698375 −0.0235155
\(883\) −41.5248 −1.39742 −0.698711 0.715404i \(-0.746243\pi\)
−0.698711 + 0.715404i \(0.746243\pi\)
\(884\) 0.219443 0.00738066
\(885\) −75.6337 −2.54240
\(886\) 14.4703 0.486141
\(887\) −52.2679 −1.75498 −0.877492 0.479592i \(-0.840785\pi\)
−0.877492 + 0.479592i \(0.840785\pi\)
\(888\) −18.3537 −0.615909
\(889\) −2.98104 −0.0999809
\(890\) 14.2458 0.477522
\(891\) 40.7562 1.36539
\(892\) 11.3543 0.380171
\(893\) −4.69061 −0.156965
\(894\) −10.4663 −0.350046
\(895\) −59.7017 −1.99561
\(896\) −1.10094 −0.0367798
\(897\) 34.0965 1.13845
\(898\) 6.56567 0.219099
\(899\) 25.1452 0.838641
\(900\) −0.558778 −0.0186259
\(901\) 0.609138 0.0202933
\(902\) −38.2322 −1.27299
\(903\) −5.29811 −0.176310
\(904\) 0.270586 0.00899955
\(905\) −46.3512 −1.54077
\(906\) 13.9528 0.463552
\(907\) 28.6674 0.951884 0.475942 0.879477i \(-0.342107\pi\)
0.475942 + 0.879477i \(0.342107\pi\)
\(908\) −5.06546 −0.168103
\(909\) −1.49676 −0.0496443
\(910\) 11.4461 0.379435
\(911\) −3.09718 −0.102614 −0.0513071 0.998683i \(-0.516339\pi\)
−0.0513071 + 0.998683i \(0.516339\pi\)
\(912\) 1.67977 0.0556228
\(913\) 24.8763 0.823287
\(914\) −26.1503 −0.864975
\(915\) −65.8103 −2.17562
\(916\) −10.9776 −0.362709
\(917\) −16.0705 −0.530693
\(918\) 0.346861 0.0114481
\(919\) −35.6913 −1.17735 −0.588674 0.808371i \(-0.700350\pi\)
−0.588674 + 0.808371i \(0.700350\pi\)
\(920\) −18.6140 −0.613686
\(921\) −33.3254 −1.09811
\(922\) −14.0435 −0.462499
\(923\) 50.5091 1.66253
\(924\) 8.82923 0.290460
\(925\) −50.0899 −1.64695
\(926\) 22.8998 0.752534
\(927\) −0.513736 −0.0168733
\(928\) −8.91879 −0.292774
\(929\) −54.8722 −1.80030 −0.900149 0.435583i \(-0.856542\pi\)
−0.900149 + 0.435583i \(0.856542\pi\)
\(930\) 14.8468 0.486845
\(931\) 5.72963 0.187781
\(932\) −17.4661 −0.572121
\(933\) −9.17101 −0.300245
\(934\) −24.2008 −0.791874
\(935\) 0.960750 0.0314199
\(936\) −0.404226 −0.0132125
\(937\) 4.16071 0.135924 0.0679622 0.997688i \(-0.478350\pi\)
0.0679622 + 0.997688i \(0.478350\pi\)
\(938\) −0.672656 −0.0219630
\(939\) −32.7086 −1.06741
\(940\) 14.7049 0.479620
\(941\) 11.8000 0.384670 0.192335 0.981329i \(-0.438394\pi\)
0.192335 + 0.981329i \(0.438394\pi\)
\(942\) −33.2351 −1.08286
\(943\) −48.5200 −1.58003
\(944\) 14.3626 0.467463
\(945\) 18.0922 0.588540
\(946\) 13.4037 0.435791
\(947\) 34.6398 1.12564 0.562821 0.826579i \(-0.309716\pi\)
0.562821 + 0.826579i \(0.309716\pi\)
\(948\) 25.7081 0.834959
\(949\) −5.23555 −0.169953
\(950\) 4.58435 0.148736
\(951\) −3.70535 −0.120154
\(952\) 0.0721150 0.00233726
\(953\) 6.07255 0.196709 0.0983545 0.995151i \(-0.468642\pi\)
0.0983545 + 0.995151i \(0.468642\pi\)
\(954\) −1.12207 −0.0363282
\(955\) −5.06465 −0.163888
\(956\) 25.3558 0.820067
\(957\) 71.5262 2.31211
\(958\) −2.46499 −0.0796402
\(959\) −1.99004 −0.0642618
\(960\) −5.26601 −0.169960
\(961\) −23.0512 −0.743588
\(962\) −36.2356 −1.16828
\(963\) 1.26069 0.0406253
\(964\) −2.09101 −0.0673469
\(965\) −14.9549 −0.481416
\(966\) 11.2051 0.360517
\(967\) 22.3102 0.717449 0.358724 0.933444i \(-0.383212\pi\)
0.358724 + 0.933444i \(0.383212\pi\)
\(968\) −11.3370 −0.364386
\(969\) −0.110030 −0.00353468
\(970\) 8.60379 0.276251
\(971\) −3.01548 −0.0967715 −0.0483857 0.998829i \(-0.515408\pi\)
−0.0483857 + 0.998829i \(0.515408\pi\)
\(972\) −1.25317 −0.0401954
\(973\) 15.9846 0.512443
\(974\) 11.8352 0.379224
\(975\) 26.3257 0.843097
\(976\) 12.4972 0.400025
\(977\) 57.7911 1.84890 0.924451 0.381301i \(-0.124524\pi\)
0.924451 + 0.381301i \(0.124524\pi\)
\(978\) 34.0883 1.09002
\(979\) 21.6953 0.693384
\(980\) −17.9622 −0.573781
\(981\) 1.62075 0.0517464
\(982\) −15.4683 −0.493614
\(983\) 17.6435 0.562739 0.281370 0.959599i \(-0.409211\pi\)
0.281370 + 0.959599i \(0.409211\pi\)
\(984\) −13.7266 −0.437588
\(985\) −26.7827 −0.853369
\(986\) 0.584209 0.0186050
\(987\) −8.85188 −0.281758
\(988\) 3.31637 0.105508
\(989\) 17.0105 0.540901
\(990\) −1.76976 −0.0562465
\(991\) 26.3910 0.838336 0.419168 0.907909i \(-0.362322\pi\)
0.419168 + 0.907909i \(0.362322\pi\)
\(992\) −2.81936 −0.0895147
\(993\) −42.8643 −1.36026
\(994\) 16.5987 0.526479
\(995\) 4.31315 0.136736
\(996\) 8.93142 0.283003
\(997\) 26.2794 0.832277 0.416139 0.909301i \(-0.363383\pi\)
0.416139 + 0.909301i \(0.363383\pi\)
\(998\) 32.7714 1.03736
\(999\) −57.2755 −1.81212
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 4006.2.a.g.1.12 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.g.1.12 40 1.1 even 1 trivial