Properties

Label 6008.2.a.b.1.11
Level 6008
Weight 2
Character 6008.1
Self dual yes
Analytic conductor 47.974
Analytic rank 1
Dimension 44
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(1\)
Dimension: \(44\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.09991 q^{3} -2.89043 q^{5} -1.97185 q^{7} +1.40961 q^{9} +O(q^{10})\) \(q-2.09991 q^{3} -2.89043 q^{5} -1.97185 q^{7} +1.40961 q^{9} -4.41294 q^{11} +5.29065 q^{13} +6.06963 q^{15} +4.12104 q^{17} -5.91013 q^{19} +4.14069 q^{21} -4.03817 q^{23} +3.35457 q^{25} +3.33966 q^{27} +2.04388 q^{29} -9.54912 q^{31} +9.26677 q^{33} +5.69947 q^{35} +3.08799 q^{37} -11.1099 q^{39} +4.34162 q^{41} +1.34956 q^{43} -4.07438 q^{45} +7.33832 q^{47} -3.11183 q^{49} -8.65381 q^{51} +7.15085 q^{53} +12.7553 q^{55} +12.4107 q^{57} +7.09371 q^{59} -2.47997 q^{61} -2.77954 q^{63} -15.2922 q^{65} +15.5327 q^{67} +8.47978 q^{69} -10.9144 q^{71} +8.28494 q^{73} -7.04428 q^{75} +8.70164 q^{77} +7.28942 q^{79} -11.2418 q^{81} +11.7101 q^{83} -11.9116 q^{85} -4.29197 q^{87} -5.72998 q^{89} -10.4323 q^{91} +20.0523 q^{93} +17.0828 q^{95} -3.73835 q^{97} -6.22054 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.09991 −1.21238 −0.606191 0.795319i \(-0.707303\pi\)
−0.606191 + 0.795319i \(0.707303\pi\)
\(4\) 0 0
\(5\) −2.89043 −1.29264 −0.646319 0.763067i \(-0.723692\pi\)
−0.646319 + 0.763067i \(0.723692\pi\)
\(6\) 0 0
\(7\) −1.97185 −0.745287 −0.372644 0.927974i \(-0.621549\pi\)
−0.372644 + 0.927974i \(0.621549\pi\)
\(8\) 0 0
\(9\) 1.40961 0.469871
\(10\) 0 0
\(11\) −4.41294 −1.33055 −0.665276 0.746597i \(-0.731686\pi\)
−0.665276 + 0.746597i \(0.731686\pi\)
\(12\) 0 0
\(13\) 5.29065 1.46736 0.733681 0.679494i \(-0.237801\pi\)
0.733681 + 0.679494i \(0.237801\pi\)
\(14\) 0 0
\(15\) 6.06963 1.56717
\(16\) 0 0
\(17\) 4.12104 0.999500 0.499750 0.866170i \(-0.333425\pi\)
0.499750 + 0.866170i \(0.333425\pi\)
\(18\) 0 0
\(19\) −5.91013 −1.35588 −0.677938 0.735119i \(-0.737126\pi\)
−0.677938 + 0.735119i \(0.737126\pi\)
\(20\) 0 0
\(21\) 4.14069 0.903573
\(22\) 0 0
\(23\) −4.03817 −0.842016 −0.421008 0.907057i \(-0.638324\pi\)
−0.421008 + 0.907057i \(0.638324\pi\)
\(24\) 0 0
\(25\) 3.35457 0.670913
\(26\) 0 0
\(27\) 3.33966 0.642719
\(28\) 0 0
\(29\) 2.04388 0.379540 0.189770 0.981829i \(-0.439226\pi\)
0.189770 + 0.981829i \(0.439226\pi\)
\(30\) 0 0
\(31\) −9.54912 −1.71507 −0.857536 0.514424i \(-0.828006\pi\)
−0.857536 + 0.514424i \(0.828006\pi\)
\(32\) 0 0
\(33\) 9.26677 1.61314
\(34\) 0 0
\(35\) 5.69947 0.963387
\(36\) 0 0
\(37\) 3.08799 0.507662 0.253831 0.967249i \(-0.418309\pi\)
0.253831 + 0.967249i \(0.418309\pi\)
\(38\) 0 0
\(39\) −11.1099 −1.77900
\(40\) 0 0
\(41\) 4.34162 0.678047 0.339023 0.940778i \(-0.389903\pi\)
0.339023 + 0.940778i \(0.389903\pi\)
\(42\) 0 0
\(43\) 1.34956 0.205806 0.102903 0.994691i \(-0.467187\pi\)
0.102903 + 0.994691i \(0.467187\pi\)
\(44\) 0 0
\(45\) −4.07438 −0.607373
\(46\) 0 0
\(47\) 7.33832 1.07040 0.535202 0.844724i \(-0.320235\pi\)
0.535202 + 0.844724i \(0.320235\pi\)
\(48\) 0 0
\(49\) −3.11183 −0.444547
\(50\) 0 0
\(51\) −8.65381 −1.21178
\(52\) 0 0
\(53\) 7.15085 0.982245 0.491122 0.871091i \(-0.336587\pi\)
0.491122 + 0.871091i \(0.336587\pi\)
\(54\) 0 0
\(55\) 12.7553 1.71992
\(56\) 0 0
\(57\) 12.4107 1.64384
\(58\) 0 0
\(59\) 7.09371 0.923523 0.461761 0.887004i \(-0.347218\pi\)
0.461761 + 0.887004i \(0.347218\pi\)
\(60\) 0 0
\(61\) −2.47997 −0.317528 −0.158764 0.987317i \(-0.550751\pi\)
−0.158764 + 0.987317i \(0.550751\pi\)
\(62\) 0 0
\(63\) −2.77954 −0.350189
\(64\) 0 0
\(65\) −15.2922 −1.89677
\(66\) 0 0
\(67\) 15.5327 1.89762 0.948808 0.315854i \(-0.102291\pi\)
0.948808 + 0.315854i \(0.102291\pi\)
\(68\) 0 0
\(69\) 8.47978 1.02085
\(70\) 0 0
\(71\) −10.9144 −1.29530 −0.647651 0.761937i \(-0.724248\pi\)
−0.647651 + 0.761937i \(0.724248\pi\)
\(72\) 0 0
\(73\) 8.28494 0.969679 0.484840 0.874603i \(-0.338878\pi\)
0.484840 + 0.874603i \(0.338878\pi\)
\(74\) 0 0
\(75\) −7.04428 −0.813403
\(76\) 0 0
\(77\) 8.70164 0.991644
\(78\) 0 0
\(79\) 7.28942 0.820124 0.410062 0.912058i \(-0.365507\pi\)
0.410062 + 0.912058i \(0.365507\pi\)
\(80\) 0 0
\(81\) −11.2418 −1.24909
\(82\) 0 0
\(83\) 11.7101 1.28535 0.642673 0.766140i \(-0.277825\pi\)
0.642673 + 0.766140i \(0.277825\pi\)
\(84\) 0 0
\(85\) −11.9116 −1.29199
\(86\) 0 0
\(87\) −4.29197 −0.460147
\(88\) 0 0
\(89\) −5.72998 −0.607376 −0.303688 0.952771i \(-0.598218\pi\)
−0.303688 + 0.952771i \(0.598218\pi\)
\(90\) 0 0
\(91\) −10.4323 −1.09361
\(92\) 0 0
\(93\) 20.0523 2.07932
\(94\) 0 0
\(95\) 17.0828 1.75266
\(96\) 0 0
\(97\) −3.73835 −0.379572 −0.189786 0.981825i \(-0.560779\pi\)
−0.189786 + 0.981825i \(0.560779\pi\)
\(98\) 0 0
\(99\) −6.22054 −0.625188
\(100\) 0 0
\(101\) 18.9438 1.88498 0.942490 0.334234i \(-0.108478\pi\)
0.942490 + 0.334234i \(0.108478\pi\)
\(102\) 0 0
\(103\) 16.3823 1.61420 0.807098 0.590418i \(-0.201037\pi\)
0.807098 + 0.590418i \(0.201037\pi\)
\(104\) 0 0
\(105\) −11.9684 −1.16799
\(106\) 0 0
\(107\) 6.88047 0.665160 0.332580 0.943075i \(-0.392081\pi\)
0.332580 + 0.943075i \(0.392081\pi\)
\(108\) 0 0
\(109\) −13.6772 −1.31004 −0.655020 0.755611i \(-0.727340\pi\)
−0.655020 + 0.755611i \(0.727340\pi\)
\(110\) 0 0
\(111\) −6.48450 −0.615481
\(112\) 0 0
\(113\) −12.9608 −1.21925 −0.609627 0.792689i \(-0.708681\pi\)
−0.609627 + 0.792689i \(0.708681\pi\)
\(114\) 0 0
\(115\) 11.6720 1.08842
\(116\) 0 0
\(117\) 7.45777 0.689471
\(118\) 0 0
\(119\) −8.12606 −0.744915
\(120\) 0 0
\(121\) 8.47406 0.770369
\(122\) 0 0
\(123\) −9.11700 −0.822052
\(124\) 0 0
\(125\) 4.75601 0.425390
\(126\) 0 0
\(127\) 16.3378 1.44975 0.724873 0.688882i \(-0.241898\pi\)
0.724873 + 0.688882i \(0.241898\pi\)
\(128\) 0 0
\(129\) −2.83395 −0.249515
\(130\) 0 0
\(131\) −19.3472 −1.69038 −0.845188 0.534469i \(-0.820512\pi\)
−0.845188 + 0.534469i \(0.820512\pi\)
\(132\) 0 0
\(133\) 11.6539 1.01052
\(134\) 0 0
\(135\) −9.65306 −0.830803
\(136\) 0 0
\(137\) −12.1142 −1.03498 −0.517492 0.855688i \(-0.673134\pi\)
−0.517492 + 0.855688i \(0.673134\pi\)
\(138\) 0 0
\(139\) −0.515599 −0.0437326 −0.0218663 0.999761i \(-0.506961\pi\)
−0.0218663 + 0.999761i \(0.506961\pi\)
\(140\) 0 0
\(141\) −15.4098 −1.29774
\(142\) 0 0
\(143\) −23.3473 −1.95240
\(144\) 0 0
\(145\) −5.90769 −0.490607
\(146\) 0 0
\(147\) 6.53455 0.538961
\(148\) 0 0
\(149\) 21.7701 1.78347 0.891737 0.452555i \(-0.149487\pi\)
0.891737 + 0.452555i \(0.149487\pi\)
\(150\) 0 0
\(151\) −9.84607 −0.801262 −0.400631 0.916240i \(-0.631209\pi\)
−0.400631 + 0.916240i \(0.631209\pi\)
\(152\) 0 0
\(153\) 5.80908 0.469636
\(154\) 0 0
\(155\) 27.6010 2.21697
\(156\) 0 0
\(157\) −10.8582 −0.866582 −0.433291 0.901254i \(-0.642648\pi\)
−0.433291 + 0.901254i \(0.642648\pi\)
\(158\) 0 0
\(159\) −15.0161 −1.19086
\(160\) 0 0
\(161\) 7.96264 0.627544
\(162\) 0 0
\(163\) −9.59871 −0.751829 −0.375914 0.926654i \(-0.622671\pi\)
−0.375914 + 0.926654i \(0.622671\pi\)
\(164\) 0 0
\(165\) −26.7849 −2.08520
\(166\) 0 0
\(167\) −12.0922 −0.935725 −0.467863 0.883801i \(-0.654976\pi\)
−0.467863 + 0.883801i \(0.654976\pi\)
\(168\) 0 0
\(169\) 14.9910 1.15315
\(170\) 0 0
\(171\) −8.33100 −0.637087
\(172\) 0 0
\(173\) −5.12459 −0.389615 −0.194808 0.980841i \(-0.562408\pi\)
−0.194808 + 0.980841i \(0.562408\pi\)
\(174\) 0 0
\(175\) −6.61468 −0.500023
\(176\) 0 0
\(177\) −14.8961 −1.11966
\(178\) 0 0
\(179\) 0.475026 0.0355051 0.0177525 0.999842i \(-0.494349\pi\)
0.0177525 + 0.999842i \(0.494349\pi\)
\(180\) 0 0
\(181\) −4.30749 −0.320174 −0.160087 0.987103i \(-0.551177\pi\)
−0.160087 + 0.987103i \(0.551177\pi\)
\(182\) 0 0
\(183\) 5.20771 0.384965
\(184\) 0 0
\(185\) −8.92561 −0.656224
\(186\) 0 0
\(187\) −18.1859 −1.32989
\(188\) 0 0
\(189\) −6.58530 −0.479010
\(190\) 0 0
\(191\) −7.85517 −0.568380 −0.284190 0.958768i \(-0.591725\pi\)
−0.284190 + 0.958768i \(0.591725\pi\)
\(192\) 0 0
\(193\) −6.27241 −0.451498 −0.225749 0.974186i \(-0.572483\pi\)
−0.225749 + 0.974186i \(0.572483\pi\)
\(194\) 0 0
\(195\) 32.1123 2.29961
\(196\) 0 0
\(197\) 0.105331 0.00750452 0.00375226 0.999993i \(-0.498806\pi\)
0.00375226 + 0.999993i \(0.498806\pi\)
\(198\) 0 0
\(199\) −15.0373 −1.06596 −0.532982 0.846126i \(-0.678929\pi\)
−0.532982 + 0.846126i \(0.678929\pi\)
\(200\) 0 0
\(201\) −32.6171 −2.30064
\(202\) 0 0
\(203\) −4.03022 −0.282866
\(204\) 0 0
\(205\) −12.5491 −0.876469
\(206\) 0 0
\(207\) −5.69226 −0.395639
\(208\) 0 0
\(209\) 26.0810 1.80406
\(210\) 0 0
\(211\) 3.04136 0.209376 0.104688 0.994505i \(-0.466616\pi\)
0.104688 + 0.994505i \(0.466616\pi\)
\(212\) 0 0
\(213\) 22.9192 1.57040
\(214\) 0 0
\(215\) −3.90080 −0.266032
\(216\) 0 0
\(217\) 18.8294 1.27822
\(218\) 0 0
\(219\) −17.3976 −1.17562
\(220\) 0 0
\(221\) 21.8030 1.46663
\(222\) 0 0
\(223\) 1.15246 0.0771746 0.0385873 0.999255i \(-0.487714\pi\)
0.0385873 + 0.999255i \(0.487714\pi\)
\(224\) 0 0
\(225\) 4.72864 0.315243
\(226\) 0 0
\(227\) −9.93986 −0.659732 −0.329866 0.944028i \(-0.607004\pi\)
−0.329866 + 0.944028i \(0.607004\pi\)
\(228\) 0 0
\(229\) −27.1287 −1.79272 −0.896358 0.443331i \(-0.853797\pi\)
−0.896358 + 0.443331i \(0.853797\pi\)
\(230\) 0 0
\(231\) −18.2726 −1.20225
\(232\) 0 0
\(233\) 2.77608 0.181867 0.0909334 0.995857i \(-0.471015\pi\)
0.0909334 + 0.995857i \(0.471015\pi\)
\(234\) 0 0
\(235\) −21.2109 −1.38365
\(236\) 0 0
\(237\) −15.3071 −0.994304
\(238\) 0 0
\(239\) −14.4247 −0.933059 −0.466530 0.884506i \(-0.654496\pi\)
−0.466530 + 0.884506i \(0.654496\pi\)
\(240\) 0 0
\(241\) −16.7229 −1.07722 −0.538608 0.842557i \(-0.681050\pi\)
−0.538608 + 0.842557i \(0.681050\pi\)
\(242\) 0 0
\(243\) 13.5878 0.871659
\(244\) 0 0
\(245\) 8.99451 0.574638
\(246\) 0 0
\(247\) −31.2684 −1.98956
\(248\) 0 0
\(249\) −24.5901 −1.55833
\(250\) 0 0
\(251\) 17.6720 1.11545 0.557724 0.830026i \(-0.311675\pi\)
0.557724 + 0.830026i \(0.311675\pi\)
\(252\) 0 0
\(253\) 17.8202 1.12035
\(254\) 0 0
\(255\) 25.0132 1.56639
\(256\) 0 0
\(257\) 12.7688 0.796494 0.398247 0.917278i \(-0.369619\pi\)
0.398247 + 0.917278i \(0.369619\pi\)
\(258\) 0 0
\(259\) −6.08904 −0.378354
\(260\) 0 0
\(261\) 2.88109 0.178335
\(262\) 0 0
\(263\) −15.7003 −0.968120 −0.484060 0.875035i \(-0.660838\pi\)
−0.484060 + 0.875035i \(0.660838\pi\)
\(264\) 0 0
\(265\) −20.6690 −1.26969
\(266\) 0 0
\(267\) 12.0324 0.736373
\(268\) 0 0
\(269\) 13.3357 0.813090 0.406545 0.913631i \(-0.366733\pi\)
0.406545 + 0.913631i \(0.366733\pi\)
\(270\) 0 0
\(271\) −25.1916 −1.53028 −0.765141 0.643862i \(-0.777331\pi\)
−0.765141 + 0.643862i \(0.777331\pi\)
\(272\) 0 0
\(273\) 21.9070 1.32587
\(274\) 0 0
\(275\) −14.8035 −0.892685
\(276\) 0 0
\(277\) −23.7112 −1.42467 −0.712334 0.701841i \(-0.752362\pi\)
−0.712334 + 0.701841i \(0.752362\pi\)
\(278\) 0 0
\(279\) −13.4606 −0.805863
\(280\) 0 0
\(281\) 29.9519 1.78678 0.893390 0.449281i \(-0.148320\pi\)
0.893390 + 0.449281i \(0.148320\pi\)
\(282\) 0 0
\(283\) 21.8458 1.29860 0.649298 0.760534i \(-0.275063\pi\)
0.649298 + 0.760534i \(0.275063\pi\)
\(284\) 0 0
\(285\) −35.8723 −2.12489
\(286\) 0 0
\(287\) −8.56100 −0.505340
\(288\) 0 0
\(289\) −0.0170072 −0.00100042
\(290\) 0 0
\(291\) 7.85020 0.460187
\(292\) 0 0
\(293\) −24.3170 −1.42061 −0.710306 0.703893i \(-0.751443\pi\)
−0.710306 + 0.703893i \(0.751443\pi\)
\(294\) 0 0
\(295\) −20.5039 −1.19378
\(296\) 0 0
\(297\) −14.7377 −0.855171
\(298\) 0 0
\(299\) −21.3645 −1.23554
\(300\) 0 0
\(301\) −2.66112 −0.153384
\(302\) 0 0
\(303\) −39.7803 −2.28532
\(304\) 0 0
\(305\) 7.16818 0.410449
\(306\) 0 0
\(307\) 3.60794 0.205916 0.102958 0.994686i \(-0.467169\pi\)
0.102958 + 0.994686i \(0.467169\pi\)
\(308\) 0 0
\(309\) −34.4013 −1.95702
\(310\) 0 0
\(311\) 13.9685 0.792082 0.396041 0.918233i \(-0.370384\pi\)
0.396041 + 0.918233i \(0.370384\pi\)
\(312\) 0 0
\(313\) 5.77462 0.326401 0.163200 0.986593i \(-0.447818\pi\)
0.163200 + 0.986593i \(0.447818\pi\)
\(314\) 0 0
\(315\) 8.03406 0.452668
\(316\) 0 0
\(317\) 8.43702 0.473870 0.236935 0.971525i \(-0.423857\pi\)
0.236935 + 0.971525i \(0.423857\pi\)
\(318\) 0 0
\(319\) −9.01954 −0.504997
\(320\) 0 0
\(321\) −14.4484 −0.806429
\(322\) 0 0
\(323\) −24.3559 −1.35520
\(324\) 0 0
\(325\) 17.7478 0.984472
\(326\) 0 0
\(327\) 28.7209 1.58827
\(328\) 0 0
\(329\) −14.4700 −0.797759
\(330\) 0 0
\(331\) −10.2240 −0.561965 −0.280982 0.959713i \(-0.590660\pi\)
−0.280982 + 0.959713i \(0.590660\pi\)
\(332\) 0 0
\(333\) 4.35287 0.238536
\(334\) 0 0
\(335\) −44.8960 −2.45293
\(336\) 0 0
\(337\) −9.08017 −0.494628 −0.247314 0.968935i \(-0.579548\pi\)
−0.247314 + 0.968935i \(0.579548\pi\)
\(338\) 0 0
\(339\) 27.2166 1.47820
\(340\) 0 0
\(341\) 42.1397 2.28199
\(342\) 0 0
\(343\) 19.9390 1.07660
\(344\) 0 0
\(345\) −24.5102 −1.31958
\(346\) 0 0
\(347\) 31.4036 1.68583 0.842917 0.538044i \(-0.180837\pi\)
0.842917 + 0.538044i \(0.180837\pi\)
\(348\) 0 0
\(349\) 0.772048 0.0413268 0.0206634 0.999786i \(-0.493422\pi\)
0.0206634 + 0.999786i \(0.493422\pi\)
\(350\) 0 0
\(351\) 17.6690 0.943101
\(352\) 0 0
\(353\) −12.7804 −0.680232 −0.340116 0.940384i \(-0.610466\pi\)
−0.340116 + 0.940384i \(0.610466\pi\)
\(354\) 0 0
\(355\) 31.5473 1.67436
\(356\) 0 0
\(357\) 17.0640 0.903121
\(358\) 0 0
\(359\) 20.8730 1.10164 0.550819 0.834625i \(-0.314316\pi\)
0.550819 + 0.834625i \(0.314316\pi\)
\(360\) 0 0
\(361\) 15.9296 0.838399
\(362\) 0 0
\(363\) −17.7948 −0.933982
\(364\) 0 0
\(365\) −23.9470 −1.25344
\(366\) 0 0
\(367\) 27.0813 1.41363 0.706816 0.707398i \(-0.250131\pi\)
0.706816 + 0.707398i \(0.250131\pi\)
\(368\) 0 0
\(369\) 6.12001 0.318595
\(370\) 0 0
\(371\) −14.1004 −0.732055
\(372\) 0 0
\(373\) 5.50935 0.285263 0.142632 0.989776i \(-0.454444\pi\)
0.142632 + 0.989776i \(0.454444\pi\)
\(374\) 0 0
\(375\) −9.98718 −0.515736
\(376\) 0 0
\(377\) 10.8135 0.556922
\(378\) 0 0
\(379\) −13.3596 −0.686236 −0.343118 0.939292i \(-0.611483\pi\)
−0.343118 + 0.939292i \(0.611483\pi\)
\(380\) 0 0
\(381\) −34.3079 −1.75765
\(382\) 0 0
\(383\) −11.8274 −0.604351 −0.302176 0.953252i \(-0.597713\pi\)
−0.302176 + 0.953252i \(0.597713\pi\)
\(384\) 0 0
\(385\) −25.1514 −1.28184
\(386\) 0 0
\(387\) 1.90236 0.0967022
\(388\) 0 0
\(389\) 35.3923 1.79446 0.897231 0.441562i \(-0.145576\pi\)
0.897231 + 0.441562i \(0.145576\pi\)
\(390\) 0 0
\(391\) −16.6415 −0.841595
\(392\) 0 0
\(393\) 40.6274 2.04938
\(394\) 0 0
\(395\) −21.0695 −1.06012
\(396\) 0 0
\(397\) −11.4346 −0.573885 −0.286943 0.957948i \(-0.592639\pi\)
−0.286943 + 0.957948i \(0.592639\pi\)
\(398\) 0 0
\(399\) −24.4720 −1.22513
\(400\) 0 0
\(401\) 1.01272 0.0505729 0.0252865 0.999680i \(-0.491950\pi\)
0.0252865 + 0.999680i \(0.491950\pi\)
\(402\) 0 0
\(403\) −50.5210 −2.51663
\(404\) 0 0
\(405\) 32.4937 1.61462
\(406\) 0 0
\(407\) −13.6271 −0.675471
\(408\) 0 0
\(409\) 12.5396 0.620041 0.310021 0.950730i \(-0.399664\pi\)
0.310021 + 0.950730i \(0.399664\pi\)
\(410\) 0 0
\(411\) 25.4387 1.25480
\(412\) 0 0
\(413\) −13.9877 −0.688290
\(414\) 0 0
\(415\) −33.8471 −1.66149
\(416\) 0 0
\(417\) 1.08271 0.0530206
\(418\) 0 0
\(419\) 25.3823 1.24001 0.620004 0.784598i \(-0.287131\pi\)
0.620004 + 0.784598i \(0.287131\pi\)
\(420\) 0 0
\(421\) 17.9439 0.874531 0.437266 0.899332i \(-0.355947\pi\)
0.437266 + 0.899332i \(0.355947\pi\)
\(422\) 0 0
\(423\) 10.3442 0.502952
\(424\) 0 0
\(425\) 13.8243 0.670577
\(426\) 0 0
\(427\) 4.89012 0.236650
\(428\) 0 0
\(429\) 49.0273 2.36706
\(430\) 0 0
\(431\) 12.0439 0.580132 0.290066 0.957007i \(-0.406323\pi\)
0.290066 + 0.957007i \(0.406323\pi\)
\(432\) 0 0
\(433\) −32.1076 −1.54299 −0.771496 0.636234i \(-0.780491\pi\)
−0.771496 + 0.636234i \(0.780491\pi\)
\(434\) 0 0
\(435\) 12.4056 0.594804
\(436\) 0 0
\(437\) 23.8661 1.14167
\(438\) 0 0
\(439\) 34.6980 1.65605 0.828023 0.560694i \(-0.189466\pi\)
0.828023 + 0.560694i \(0.189466\pi\)
\(440\) 0 0
\(441\) −4.38647 −0.208880
\(442\) 0 0
\(443\) −0.700396 −0.0332768 −0.0166384 0.999862i \(-0.505296\pi\)
−0.0166384 + 0.999862i \(0.505296\pi\)
\(444\) 0 0
\(445\) 16.5621 0.785118
\(446\) 0 0
\(447\) −45.7151 −2.16225
\(448\) 0 0
\(449\) −8.73390 −0.412178 −0.206089 0.978533i \(-0.566074\pi\)
−0.206089 + 0.978533i \(0.566074\pi\)
\(450\) 0 0
\(451\) −19.1593 −0.902177
\(452\) 0 0
\(453\) 20.6758 0.971436
\(454\) 0 0
\(455\) 30.1539 1.41364
\(456\) 0 0
\(457\) −14.6599 −0.685760 −0.342880 0.939379i \(-0.611402\pi\)
−0.342880 + 0.939379i \(0.611402\pi\)
\(458\) 0 0
\(459\) 13.7629 0.642397
\(460\) 0 0
\(461\) 16.1571 0.752513 0.376256 0.926516i \(-0.377211\pi\)
0.376256 + 0.926516i \(0.377211\pi\)
\(462\) 0 0
\(463\) −19.0293 −0.884367 −0.442184 0.896925i \(-0.645796\pi\)
−0.442184 + 0.896925i \(0.645796\pi\)
\(464\) 0 0
\(465\) −57.9596 −2.68781
\(466\) 0 0
\(467\) −11.5429 −0.534142 −0.267071 0.963677i \(-0.586056\pi\)
−0.267071 + 0.963677i \(0.586056\pi\)
\(468\) 0 0
\(469\) −30.6280 −1.41427
\(470\) 0 0
\(471\) 22.8013 1.05063
\(472\) 0 0
\(473\) −5.95553 −0.273835
\(474\) 0 0
\(475\) −19.8259 −0.909675
\(476\) 0 0
\(477\) 10.0799 0.461529
\(478\) 0 0
\(479\) −18.0719 −0.825726 −0.412863 0.910793i \(-0.635471\pi\)
−0.412863 + 0.910793i \(0.635471\pi\)
\(480\) 0 0
\(481\) 16.3375 0.744925
\(482\) 0 0
\(483\) −16.7208 −0.760824
\(484\) 0 0
\(485\) 10.8054 0.490650
\(486\) 0 0
\(487\) 3.74602 0.169748 0.0848741 0.996392i \(-0.472951\pi\)
0.0848741 + 0.996392i \(0.472951\pi\)
\(488\) 0 0
\(489\) 20.1564 0.911504
\(490\) 0 0
\(491\) 16.0230 0.723109 0.361555 0.932351i \(-0.382246\pi\)
0.361555 + 0.932351i \(0.382246\pi\)
\(492\) 0 0
\(493\) 8.42293 0.379350
\(494\) 0 0
\(495\) 17.9800 0.808142
\(496\) 0 0
\(497\) 21.5215 0.965372
\(498\) 0 0
\(499\) −23.4994 −1.05198 −0.525988 0.850492i \(-0.676304\pi\)
−0.525988 + 0.850492i \(0.676304\pi\)
\(500\) 0 0
\(501\) 25.3926 1.13446
\(502\) 0 0
\(503\) 35.1526 1.56738 0.783688 0.621155i \(-0.213336\pi\)
0.783688 + 0.621155i \(0.213336\pi\)
\(504\) 0 0
\(505\) −54.7557 −2.43660
\(506\) 0 0
\(507\) −31.4797 −1.39806
\(508\) 0 0
\(509\) −16.3998 −0.726911 −0.363455 0.931612i \(-0.618403\pi\)
−0.363455 + 0.931612i \(0.618403\pi\)
\(510\) 0 0
\(511\) −16.3366 −0.722690
\(512\) 0 0
\(513\) −19.7378 −0.871447
\(514\) 0 0
\(515\) −47.3518 −2.08657
\(516\) 0 0
\(517\) −32.3836 −1.42423
\(518\) 0 0
\(519\) 10.7612 0.472363
\(520\) 0 0
\(521\) 3.05660 0.133912 0.0669560 0.997756i \(-0.478671\pi\)
0.0669560 + 0.997756i \(0.478671\pi\)
\(522\) 0 0
\(523\) −9.71108 −0.424636 −0.212318 0.977201i \(-0.568101\pi\)
−0.212318 + 0.977201i \(0.568101\pi\)
\(524\) 0 0
\(525\) 13.8902 0.606219
\(526\) 0 0
\(527\) −39.3523 −1.71421
\(528\) 0 0
\(529\) −6.69319 −0.291008
\(530\) 0 0
\(531\) 9.99940 0.433937
\(532\) 0 0
\(533\) 22.9700 0.994941
\(534\) 0 0
\(535\) −19.8875 −0.859811
\(536\) 0 0
\(537\) −0.997510 −0.0430458
\(538\) 0 0
\(539\) 13.7323 0.591493
\(540\) 0 0
\(541\) 14.8780 0.639657 0.319829 0.947475i \(-0.396375\pi\)
0.319829 + 0.947475i \(0.396375\pi\)
\(542\) 0 0
\(543\) 9.04534 0.388173
\(544\) 0 0
\(545\) 39.5330 1.69341
\(546\) 0 0
\(547\) −9.71572 −0.415414 −0.207707 0.978191i \(-0.566600\pi\)
−0.207707 + 0.978191i \(0.566600\pi\)
\(548\) 0 0
\(549\) −3.49580 −0.149197
\(550\) 0 0
\(551\) −12.0796 −0.514609
\(552\) 0 0
\(553\) −14.3736 −0.611228
\(554\) 0 0
\(555\) 18.7430 0.795594
\(556\) 0 0
\(557\) −38.0351 −1.61160 −0.805799 0.592189i \(-0.798264\pi\)
−0.805799 + 0.592189i \(0.798264\pi\)
\(558\) 0 0
\(559\) 7.14004 0.301992
\(560\) 0 0
\(561\) 38.1888 1.61233
\(562\) 0 0
\(563\) −40.4869 −1.70632 −0.853159 0.521651i \(-0.825316\pi\)
−0.853159 + 0.521651i \(0.825316\pi\)
\(564\) 0 0
\(565\) 37.4624 1.57605
\(566\) 0 0
\(567\) 22.1671 0.930933
\(568\) 0 0
\(569\) −24.8529 −1.04189 −0.520945 0.853590i \(-0.674420\pi\)
−0.520945 + 0.853590i \(0.674420\pi\)
\(570\) 0 0
\(571\) −35.3272 −1.47840 −0.739199 0.673487i \(-0.764796\pi\)
−0.739199 + 0.673487i \(0.764796\pi\)
\(572\) 0 0
\(573\) 16.4951 0.689094
\(574\) 0 0
\(575\) −13.5463 −0.564920
\(576\) 0 0
\(577\) −12.5172 −0.521097 −0.260548 0.965461i \(-0.583903\pi\)
−0.260548 + 0.965461i \(0.583903\pi\)
\(578\) 0 0
\(579\) 13.1715 0.547388
\(580\) 0 0
\(581\) −23.0904 −0.957953
\(582\) 0 0
\(583\) −31.5563 −1.30693
\(584\) 0 0
\(585\) −21.5561 −0.891237
\(586\) 0 0
\(587\) 10.1042 0.417046 0.208523 0.978017i \(-0.433134\pi\)
0.208523 + 0.978017i \(0.433134\pi\)
\(588\) 0 0
\(589\) 56.4365 2.32542
\(590\) 0 0
\(591\) −0.221185 −0.00909834
\(592\) 0 0
\(593\) −21.4288 −0.879974 −0.439987 0.898004i \(-0.645017\pi\)
−0.439987 + 0.898004i \(0.645017\pi\)
\(594\) 0 0
\(595\) 23.4878 0.962905
\(596\) 0 0
\(597\) 31.5769 1.29236
\(598\) 0 0
\(599\) 14.5511 0.594540 0.297270 0.954793i \(-0.403924\pi\)
0.297270 + 0.954793i \(0.403924\pi\)
\(600\) 0 0
\(601\) 5.49282 0.224057 0.112028 0.993705i \(-0.464265\pi\)
0.112028 + 0.993705i \(0.464265\pi\)
\(602\) 0 0
\(603\) 21.8950 0.891635
\(604\) 0 0
\(605\) −24.4937 −0.995809
\(606\) 0 0
\(607\) −32.9903 −1.33903 −0.669517 0.742797i \(-0.733499\pi\)
−0.669517 + 0.742797i \(0.733499\pi\)
\(608\) 0 0
\(609\) 8.46310 0.342942
\(610\) 0 0
\(611\) 38.8245 1.57067
\(612\) 0 0
\(613\) −24.6648 −0.996203 −0.498102 0.867119i \(-0.665969\pi\)
−0.498102 + 0.867119i \(0.665969\pi\)
\(614\) 0 0
\(615\) 26.3520 1.06262
\(616\) 0 0
\(617\) 22.6424 0.911548 0.455774 0.890096i \(-0.349363\pi\)
0.455774 + 0.890096i \(0.349363\pi\)
\(618\) 0 0
\(619\) 9.27370 0.372742 0.186371 0.982479i \(-0.440327\pi\)
0.186371 + 0.982479i \(0.440327\pi\)
\(620\) 0 0
\(621\) −13.4861 −0.541180
\(622\) 0 0
\(623\) 11.2986 0.452670
\(624\) 0 0
\(625\) −30.5197 −1.22079
\(626\) 0 0
\(627\) −54.7678 −2.18722
\(628\) 0 0
\(629\) 12.7257 0.507408
\(630\) 0 0
\(631\) −44.9639 −1.78998 −0.894992 0.446082i \(-0.852819\pi\)
−0.894992 + 0.446082i \(0.852819\pi\)
\(632\) 0 0
\(633\) −6.38659 −0.253844
\(634\) 0 0
\(635\) −47.2233 −1.87400
\(636\) 0 0
\(637\) −16.4636 −0.652311
\(638\) 0 0
\(639\) −15.3851 −0.608625
\(640\) 0 0
\(641\) −1.81672 −0.0717563 −0.0358782 0.999356i \(-0.511423\pi\)
−0.0358782 + 0.999356i \(0.511423\pi\)
\(642\) 0 0
\(643\) 45.4931 1.79407 0.897037 0.441955i \(-0.145715\pi\)
0.897037 + 0.441955i \(0.145715\pi\)
\(644\) 0 0
\(645\) 8.19132 0.322533
\(646\) 0 0
\(647\) 6.18806 0.243278 0.121639 0.992574i \(-0.461185\pi\)
0.121639 + 0.992574i \(0.461185\pi\)
\(648\) 0 0
\(649\) −31.3041 −1.22880
\(650\) 0 0
\(651\) −39.5400 −1.54969
\(652\) 0 0
\(653\) 17.5778 0.687871 0.343935 0.938993i \(-0.388240\pi\)
0.343935 + 0.938993i \(0.388240\pi\)
\(654\) 0 0
\(655\) 55.9218 2.18504
\(656\) 0 0
\(657\) 11.6786 0.455624
\(658\) 0 0
\(659\) 23.8460 0.928909 0.464454 0.885597i \(-0.346250\pi\)
0.464454 + 0.885597i \(0.346250\pi\)
\(660\) 0 0
\(661\) −13.8308 −0.537957 −0.268979 0.963146i \(-0.586686\pi\)
−0.268979 + 0.963146i \(0.586686\pi\)
\(662\) 0 0
\(663\) −45.7843 −1.77811
\(664\) 0 0
\(665\) −33.6846 −1.30623
\(666\) 0 0
\(667\) −8.25355 −0.319579
\(668\) 0 0
\(669\) −2.42007 −0.0935651
\(670\) 0 0
\(671\) 10.9440 0.422488
\(672\) 0 0
\(673\) 44.8723 1.72970 0.864851 0.502029i \(-0.167413\pi\)
0.864851 + 0.502029i \(0.167413\pi\)
\(674\) 0 0
\(675\) 11.2031 0.431208
\(676\) 0 0
\(677\) −7.94340 −0.305290 −0.152645 0.988281i \(-0.548779\pi\)
−0.152645 + 0.988281i \(0.548779\pi\)
\(678\) 0 0
\(679\) 7.37145 0.282890
\(680\) 0 0
\(681\) 20.8728 0.799847
\(682\) 0 0
\(683\) −7.31154 −0.279768 −0.139884 0.990168i \(-0.544673\pi\)
−0.139884 + 0.990168i \(0.544673\pi\)
\(684\) 0 0
\(685\) 35.0152 1.33786
\(686\) 0 0
\(687\) 56.9678 2.17346
\(688\) 0 0
\(689\) 37.8326 1.44131
\(690\) 0 0
\(691\) −24.1709 −0.919506 −0.459753 0.888047i \(-0.652062\pi\)
−0.459753 + 0.888047i \(0.652062\pi\)
\(692\) 0 0
\(693\) 12.2660 0.465945
\(694\) 0 0
\(695\) 1.49030 0.0565304
\(696\) 0 0
\(697\) 17.8920 0.677708
\(698\) 0 0
\(699\) −5.82950 −0.220492
\(700\) 0 0
\(701\) −29.4680 −1.11299 −0.556496 0.830850i \(-0.687854\pi\)
−0.556496 + 0.830850i \(0.687854\pi\)
\(702\) 0 0
\(703\) −18.2504 −0.688327
\(704\) 0 0
\(705\) 44.5409 1.67751
\(706\) 0 0
\(707\) −37.3543 −1.40485
\(708\) 0 0
\(709\) −10.5574 −0.396493 −0.198246 0.980152i \(-0.563525\pi\)
−0.198246 + 0.980152i \(0.563525\pi\)
\(710\) 0 0
\(711\) 10.2753 0.385353
\(712\) 0 0
\(713\) 38.5609 1.44412
\(714\) 0 0
\(715\) 67.4838 2.52375
\(716\) 0 0
\(717\) 30.2906 1.13122
\(718\) 0 0
\(719\) −50.0779 −1.86759 −0.933795 0.357810i \(-0.883524\pi\)
−0.933795 + 0.357810i \(0.883524\pi\)
\(720\) 0 0
\(721\) −32.3033 −1.20304
\(722\) 0 0
\(723\) 35.1165 1.30600
\(724\) 0 0
\(725\) 6.85634 0.254638
\(726\) 0 0
\(727\) 18.2111 0.675412 0.337706 0.941252i \(-0.390349\pi\)
0.337706 + 0.941252i \(0.390349\pi\)
\(728\) 0 0
\(729\) 5.19233 0.192308
\(730\) 0 0
\(731\) 5.56159 0.205703
\(732\) 0 0
\(733\) −33.7659 −1.24717 −0.623587 0.781754i \(-0.714325\pi\)
−0.623587 + 0.781754i \(0.714325\pi\)
\(734\) 0 0
\(735\) −18.8876 −0.696681
\(736\) 0 0
\(737\) −68.5447 −2.52488
\(738\) 0 0
\(739\) −6.13414 −0.225648 −0.112824 0.993615i \(-0.535990\pi\)
−0.112824 + 0.993615i \(0.535990\pi\)
\(740\) 0 0
\(741\) 65.6608 2.41211
\(742\) 0 0
\(743\) 29.9677 1.09941 0.549705 0.835359i \(-0.314740\pi\)
0.549705 + 0.835359i \(0.314740\pi\)
\(744\) 0 0
\(745\) −62.9248 −2.30539
\(746\) 0 0
\(747\) 16.5067 0.603947
\(748\) 0 0
\(749\) −13.5672 −0.495736
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −37.1096 −1.35235
\(754\) 0 0
\(755\) 28.4593 1.03574
\(756\) 0 0
\(757\) 51.9666 1.88876 0.944379 0.328859i \(-0.106664\pi\)
0.944379 + 0.328859i \(0.106664\pi\)
\(758\) 0 0
\(759\) −37.4208 −1.35829
\(760\) 0 0
\(761\) 14.4458 0.523658 0.261829 0.965114i \(-0.415674\pi\)
0.261829 + 0.965114i \(0.415674\pi\)
\(762\) 0 0
\(763\) 26.9694 0.976357
\(764\) 0 0
\(765\) −16.7907 −0.607070
\(766\) 0 0
\(767\) 37.5303 1.35514
\(768\) 0 0
\(769\) 33.6452 1.21328 0.606638 0.794978i \(-0.292518\pi\)
0.606638 + 0.794978i \(0.292518\pi\)
\(770\) 0 0
\(771\) −26.8133 −0.965656
\(772\) 0 0
\(773\) −12.9501 −0.465782 −0.232891 0.972503i \(-0.574819\pi\)
−0.232891 + 0.972503i \(0.574819\pi\)
\(774\) 0 0
\(775\) −32.0331 −1.15066
\(776\) 0 0
\(777\) 12.7864 0.458710
\(778\) 0 0
\(779\) −25.6595 −0.919348
\(780\) 0 0
\(781\) 48.1646 1.72347
\(782\) 0 0
\(783\) 6.82589 0.243937
\(784\) 0 0
\(785\) 31.3849 1.12018
\(786\) 0 0
\(787\) −30.1698 −1.07544 −0.537719 0.843124i \(-0.680714\pi\)
−0.537719 + 0.843124i \(0.680714\pi\)
\(788\) 0 0
\(789\) 32.9691 1.17373
\(790\) 0 0
\(791\) 25.5568 0.908694
\(792\) 0 0
\(793\) −13.1207 −0.465928
\(794\) 0 0
\(795\) 43.4030 1.53935
\(796\) 0 0
\(797\) 10.8381 0.383906 0.191953 0.981404i \(-0.438518\pi\)
0.191953 + 0.981404i \(0.438518\pi\)
\(798\) 0 0
\(799\) 30.2415 1.06987
\(800\) 0 0
\(801\) −8.07706 −0.285389
\(802\) 0 0
\(803\) −36.5610 −1.29021
\(804\) 0 0
\(805\) −23.0154 −0.811187
\(806\) 0 0
\(807\) −28.0037 −0.985777
\(808\) 0 0
\(809\) 22.2234 0.781333 0.390666 0.920532i \(-0.372245\pi\)
0.390666 + 0.920532i \(0.372245\pi\)
\(810\) 0 0
\(811\) 14.9385 0.524562 0.262281 0.964992i \(-0.415525\pi\)
0.262281 + 0.964992i \(0.415525\pi\)
\(812\) 0 0
\(813\) 52.9001 1.85529
\(814\) 0 0
\(815\) 27.7444 0.971843
\(816\) 0 0
\(817\) −7.97606 −0.279047
\(818\) 0 0
\(819\) −14.7056 −0.513854
\(820\) 0 0
\(821\) 14.7104 0.513395 0.256698 0.966492i \(-0.417366\pi\)
0.256698 + 0.966492i \(0.417366\pi\)
\(822\) 0 0
\(823\) 37.8706 1.32009 0.660043 0.751227i \(-0.270538\pi\)
0.660043 + 0.751227i \(0.270538\pi\)
\(824\) 0 0
\(825\) 31.0860 1.08228
\(826\) 0 0
\(827\) −44.9679 −1.56369 −0.781844 0.623475i \(-0.785720\pi\)
−0.781844 + 0.623475i \(0.785720\pi\)
\(828\) 0 0
\(829\) −38.2724 −1.32926 −0.664628 0.747174i \(-0.731410\pi\)
−0.664628 + 0.747174i \(0.731410\pi\)
\(830\) 0 0
\(831\) 49.7913 1.72724
\(832\) 0 0
\(833\) −12.8240 −0.444324
\(834\) 0 0
\(835\) 34.9517 1.20955
\(836\) 0 0
\(837\) −31.8908 −1.10231
\(838\) 0 0
\(839\) 8.02596 0.277087 0.138543 0.990356i \(-0.455758\pi\)
0.138543 + 0.990356i \(0.455758\pi\)
\(840\) 0 0
\(841\) −24.8225 −0.855950
\(842\) 0 0
\(843\) −62.8963 −2.16626
\(844\) 0 0
\(845\) −43.3303 −1.49061
\(846\) 0 0
\(847\) −16.7095 −0.574147
\(848\) 0 0
\(849\) −45.8741 −1.57440
\(850\) 0 0
\(851\) −12.4698 −0.427460
\(852\) 0 0
\(853\) 26.1733 0.896157 0.448079 0.893994i \(-0.352108\pi\)
0.448079 + 0.893994i \(0.352108\pi\)
\(854\) 0 0
\(855\) 24.0801 0.823523
\(856\) 0 0
\(857\) −5.02809 −0.171756 −0.0858781 0.996306i \(-0.527370\pi\)
−0.0858781 + 0.996306i \(0.527370\pi\)
\(858\) 0 0
\(859\) −54.7992 −1.86972 −0.934862 0.355011i \(-0.884477\pi\)
−0.934862 + 0.355011i \(0.884477\pi\)
\(860\) 0 0
\(861\) 17.9773 0.612665
\(862\) 0 0
\(863\) 13.0412 0.443927 0.221964 0.975055i \(-0.428753\pi\)
0.221964 + 0.975055i \(0.428753\pi\)
\(864\) 0 0
\(865\) 14.8123 0.503632
\(866\) 0 0
\(867\) 0.0357135 0.00121289
\(868\) 0 0
\(869\) −32.1678 −1.09122
\(870\) 0 0
\(871\) 82.1778 2.78449
\(872\) 0 0
\(873\) −5.26963 −0.178350
\(874\) 0 0
\(875\) −9.37811 −0.317038
\(876\) 0 0
\(877\) 31.8047 1.07397 0.536984 0.843593i \(-0.319564\pi\)
0.536984 + 0.843593i \(0.319564\pi\)
\(878\) 0 0
\(879\) 51.0634 1.72233
\(880\) 0 0
\(881\) −25.2272 −0.849928 −0.424964 0.905210i \(-0.639713\pi\)
−0.424964 + 0.905210i \(0.639713\pi\)
\(882\) 0 0
\(883\) 0.311631 0.0104872 0.00524361 0.999986i \(-0.498331\pi\)
0.00524361 + 0.999986i \(0.498331\pi\)
\(884\) 0 0
\(885\) 43.0562 1.44732
\(886\) 0 0
\(887\) −15.9413 −0.535257 −0.267628 0.963522i \(-0.586240\pi\)
−0.267628 + 0.963522i \(0.586240\pi\)
\(888\) 0 0
\(889\) −32.2156 −1.08048
\(890\) 0 0
\(891\) 49.6096 1.66198
\(892\) 0 0
\(893\) −43.3704 −1.45134
\(894\) 0 0
\(895\) −1.37303 −0.0458952
\(896\) 0 0
\(897\) 44.8636 1.49795
\(898\) 0 0
\(899\) −19.5173 −0.650938
\(900\) 0 0
\(901\) 29.4690 0.981753
\(902\) 0 0
\(903\) 5.58811 0.185961
\(904\) 0 0
\(905\) 12.4505 0.413868
\(906\) 0 0
\(907\) 17.6497 0.586050 0.293025 0.956105i \(-0.405338\pi\)
0.293025 + 0.956105i \(0.405338\pi\)
\(908\) 0 0
\(909\) 26.7035 0.885698
\(910\) 0 0
\(911\) −25.1042 −0.831741 −0.415870 0.909424i \(-0.636523\pi\)
−0.415870 + 0.909424i \(0.636523\pi\)
\(912\) 0 0
\(913\) −51.6758 −1.71022
\(914\) 0 0
\(915\) −15.0525 −0.497621
\(916\) 0 0
\(917\) 38.1498 1.25982
\(918\) 0 0
\(919\) 39.8300 1.31387 0.656935 0.753947i \(-0.271852\pi\)
0.656935 + 0.753947i \(0.271852\pi\)
\(920\) 0 0
\(921\) −7.57635 −0.249649
\(922\) 0 0
\(923\) −57.7443 −1.90068
\(924\) 0 0
\(925\) 10.3589 0.340597
\(926\) 0 0
\(927\) 23.0927 0.758464
\(928\) 0 0
\(929\) −47.4815 −1.55782 −0.778909 0.627138i \(-0.784226\pi\)
−0.778909 + 0.627138i \(0.784226\pi\)
\(930\) 0 0
\(931\) 18.3913 0.602750
\(932\) 0 0
\(933\) −29.3326 −0.960307
\(934\) 0 0
\(935\) 52.5651 1.71906
\(936\) 0 0
\(937\) −23.5092 −0.768011 −0.384005 0.923331i \(-0.625456\pi\)
−0.384005 + 0.923331i \(0.625456\pi\)
\(938\) 0 0
\(939\) −12.1262 −0.395722
\(940\) 0 0
\(941\) 39.5348 1.28880 0.644399 0.764690i \(-0.277108\pi\)
0.644399 + 0.764690i \(0.277108\pi\)
\(942\) 0 0
\(943\) −17.5322 −0.570927
\(944\) 0 0
\(945\) 19.0343 0.619187
\(946\) 0 0
\(947\) 22.6545 0.736174 0.368087 0.929791i \(-0.380013\pi\)
0.368087 + 0.929791i \(0.380013\pi\)
\(948\) 0 0
\(949\) 43.8327 1.42287
\(950\) 0 0
\(951\) −17.7170 −0.574512
\(952\) 0 0
\(953\) 59.1832 1.91713 0.958565 0.284873i \(-0.0919515\pi\)
0.958565 + 0.284873i \(0.0919515\pi\)
\(954\) 0 0
\(955\) 22.7048 0.734709
\(956\) 0 0
\(957\) 18.9402 0.612250
\(958\) 0 0
\(959\) 23.8873 0.771361
\(960\) 0 0
\(961\) 60.1856 1.94147
\(962\) 0 0
\(963\) 9.69881 0.312540
\(964\) 0 0
\(965\) 18.1299 0.583623
\(966\) 0 0
\(967\) 59.1032 1.90063 0.950315 0.311291i \(-0.100761\pi\)
0.950315 + 0.311291i \(0.100761\pi\)
\(968\) 0 0
\(969\) 51.1451 1.64302
\(970\) 0 0
\(971\) −0.0391488 −0.00125634 −0.000628172 1.00000i \(-0.500200\pi\)
−0.000628172 1.00000i \(0.500200\pi\)
\(972\) 0 0
\(973\) 1.01668 0.0325933
\(974\) 0 0
\(975\) −37.2688 −1.19356
\(976\) 0 0
\(977\) −9.86262 −0.315533 −0.157767 0.987476i \(-0.550429\pi\)
−0.157767 + 0.987476i \(0.550429\pi\)
\(978\) 0 0
\(979\) 25.2861 0.808146
\(980\) 0 0
\(981\) −19.2796 −0.615550
\(982\) 0 0
\(983\) 56.4875 1.80167 0.900835 0.434161i \(-0.142955\pi\)
0.900835 + 0.434161i \(0.142955\pi\)
\(984\) 0 0
\(985\) −0.304451 −0.00970062
\(986\) 0 0
\(987\) 30.3857 0.967189
\(988\) 0 0
\(989\) −5.44975 −0.173292
\(990\) 0 0
\(991\) −38.1156 −1.21078 −0.605391 0.795928i \(-0.706983\pi\)
−0.605391 + 0.795928i \(0.706983\pi\)
\(992\) 0 0
\(993\) 21.4696 0.681316
\(994\) 0 0
\(995\) 43.4642 1.37791
\(996\) 0 0
\(997\) 49.7368 1.57518 0.787589 0.616200i \(-0.211329\pi\)
0.787589 + 0.616200i \(0.211329\pi\)
\(998\) 0 0
\(999\) 10.3129 0.326284
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 6008.2.a.b.1.11 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.11 44 1.1 even 1 trivial