Properties

Label 6008.2.a.b.1.40
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 1.40
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.35947 q^{3} -3.32176 q^{5} +1.00106 q^{7} +2.56708 q^{9} +O(q^{10})\) \(q+2.35947 q^{3} -3.32176 q^{5} +1.00106 q^{7} +2.56708 q^{9} -0.281563 q^{11} +0.731357 q^{13} -7.83758 q^{15} +4.74830 q^{17} -5.22975 q^{19} +2.36197 q^{21} -6.35333 q^{23} +6.03409 q^{25} -1.02147 q^{27} +2.12534 q^{29} +1.17035 q^{31} -0.664339 q^{33} -3.32529 q^{35} +1.39991 q^{37} +1.72561 q^{39} -2.17976 q^{41} -11.2304 q^{43} -8.52721 q^{45} +2.59008 q^{47} -5.99787 q^{49} +11.2035 q^{51} +9.36544 q^{53} +0.935286 q^{55} -12.3394 q^{57} -12.9879 q^{59} +13.7202 q^{61} +2.56980 q^{63} -2.42939 q^{65} -2.15886 q^{67} -14.9905 q^{69} +4.52588 q^{71} +3.16162 q^{73} +14.2372 q^{75} -0.281862 q^{77} -12.5522 q^{79} -10.1113 q^{81} -2.06328 q^{83} -15.7727 q^{85} +5.01465 q^{87} -18.0090 q^{89} +0.732134 q^{91} +2.76139 q^{93} +17.3720 q^{95} -15.6753 q^{97} -0.722795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) 2.35947 1.36224 0.681119 0.732173i \(-0.261494\pi\)
0.681119 + 0.732173i \(0.261494\pi\)
\(4\) 0 0
\(5\) −3.32176 −1.48554 −0.742768 0.669549i \(-0.766487\pi\)
−0.742768 + 0.669549i \(0.766487\pi\)
\(6\) 0 0
\(7\) 1.00106 0.378366 0.189183 0.981942i \(-0.439416\pi\)
0.189183 + 0.981942i \(0.439416\pi\)
\(8\) 0 0
\(9\) 2.56708 0.855692
\(10\) 0 0
\(11\) −0.281563 −0.0848945 −0.0424473 0.999099i \(-0.513515\pi\)
−0.0424473 + 0.999099i \(0.513515\pi\)
\(12\) 0 0
\(13\) 0.731357 0.202842 0.101421 0.994844i \(-0.467661\pi\)
0.101421 + 0.994844i \(0.467661\pi\)
\(14\) 0 0
\(15\) −7.83758 −2.02365
\(16\) 0 0
\(17\) 4.74830 1.15163 0.575816 0.817579i \(-0.304684\pi\)
0.575816 + 0.817579i \(0.304684\pi\)
\(18\) 0 0
\(19\) −5.22975 −1.19979 −0.599894 0.800080i \(-0.704790\pi\)
−0.599894 + 0.800080i \(0.704790\pi\)
\(20\) 0 0
\(21\) 2.36197 0.515425
\(22\) 0 0
\(23\) −6.35333 −1.32476 −0.662380 0.749168i \(-0.730454\pi\)
−0.662380 + 0.749168i \(0.730454\pi\)
\(24\) 0 0
\(25\) 6.03409 1.20682
\(26\) 0 0
\(27\) −1.02147 −0.196581
\(28\) 0 0
\(29\) 2.12534 0.394665 0.197332 0.980337i \(-0.436772\pi\)
0.197332 + 0.980337i \(0.436772\pi\)
\(30\) 0 0
\(31\) 1.17035 0.210200 0.105100 0.994462i \(-0.466484\pi\)
0.105100 + 0.994462i \(0.466484\pi\)
\(32\) 0 0
\(33\) −0.664339 −0.115647
\(34\) 0 0
\(35\) −3.32529 −0.562076
\(36\) 0 0
\(37\) 1.39991 0.230143 0.115072 0.993357i \(-0.463290\pi\)
0.115072 + 0.993357i \(0.463290\pi\)
\(38\) 0 0
\(39\) 1.72561 0.276319
\(40\) 0 0
\(41\) −2.17976 −0.340421 −0.170210 0.985408i \(-0.554445\pi\)
−0.170210 + 0.985408i \(0.554445\pi\)
\(42\) 0 0
\(43\) −11.2304 −1.71261 −0.856307 0.516466i \(-0.827247\pi\)
−0.856307 + 0.516466i \(0.827247\pi\)
\(44\) 0 0
\(45\) −8.52721 −1.27116
\(46\) 0 0
\(47\) 2.59008 0.377801 0.188901 0.981996i \(-0.439508\pi\)
0.188901 + 0.981996i \(0.439508\pi\)
\(48\) 0 0
\(49\) −5.99787 −0.856839
\(50\) 0 0
\(51\) 11.2035 1.56880
\(52\) 0 0
\(53\) 9.36544 1.28644 0.643221 0.765680i \(-0.277598\pi\)
0.643221 + 0.765680i \(0.277598\pi\)
\(54\) 0 0
\(55\) 0.935286 0.126114
\(56\) 0 0
\(57\) −12.3394 −1.63440
\(58\) 0 0
\(59\) −12.9879 −1.69089 −0.845443 0.534066i \(-0.820664\pi\)
−0.845443 + 0.534066i \(0.820664\pi\)
\(60\) 0 0
\(61\) 13.7202 1.75669 0.878347 0.478023i \(-0.158646\pi\)
0.878347 + 0.478023i \(0.158646\pi\)
\(62\) 0 0
\(63\) 2.56980 0.323765
\(64\) 0 0
\(65\) −2.42939 −0.301329
\(66\) 0 0
\(67\) −2.15886 −0.263747 −0.131873 0.991267i \(-0.542099\pi\)
−0.131873 + 0.991267i \(0.542099\pi\)
\(68\) 0 0
\(69\) −14.9905 −1.80464
\(70\) 0 0
\(71\) 4.52588 0.537123 0.268562 0.963262i \(-0.413452\pi\)
0.268562 + 0.963262i \(0.413452\pi\)
\(72\) 0 0
\(73\) 3.16162 0.370040 0.185020 0.982735i \(-0.440765\pi\)
0.185020 + 0.982735i \(0.440765\pi\)
\(74\) 0 0
\(75\) 14.2372 1.64397
\(76\) 0 0
\(77\) −0.281862 −0.0321212
\(78\) 0 0
\(79\) −12.5522 −1.41223 −0.706115 0.708097i \(-0.749554\pi\)
−0.706115 + 0.708097i \(0.749554\pi\)
\(80\) 0 0
\(81\) −10.1113 −1.12348
\(82\) 0 0
\(83\) −2.06328 −0.226474 −0.113237 0.993568i \(-0.536122\pi\)
−0.113237 + 0.993568i \(0.536122\pi\)
\(84\) 0 0
\(85\) −15.7727 −1.71079
\(86\) 0 0
\(87\) 5.01465 0.537627
\(88\) 0 0
\(89\) −18.0090 −1.90895 −0.954475 0.298291i \(-0.903583\pi\)
−0.954475 + 0.298291i \(0.903583\pi\)
\(90\) 0 0
\(91\) 0.732134 0.0767485
\(92\) 0 0
\(93\) 2.76139 0.286343
\(94\) 0 0
\(95\) 17.3720 1.78233
\(96\) 0 0
\(97\) −15.6753 −1.59158 −0.795791 0.605571i \(-0.792945\pi\)
−0.795791 + 0.605571i \(0.792945\pi\)
\(98\) 0 0
\(99\) −0.722795 −0.0726436
\(100\) 0 0
\(101\) 7.86739 0.782835 0.391417 0.920213i \(-0.371985\pi\)
0.391417 + 0.920213i \(0.371985\pi\)
\(102\) 0 0
\(103\) −11.2716 −1.11063 −0.555314 0.831641i \(-0.687402\pi\)
−0.555314 + 0.831641i \(0.687402\pi\)
\(104\) 0 0
\(105\) −7.84590 −0.765682
\(106\) 0 0
\(107\) 6.77306 0.654777 0.327388 0.944890i \(-0.393832\pi\)
0.327388 + 0.944890i \(0.393832\pi\)
\(108\) 0 0
\(109\) −3.15680 −0.302367 −0.151183 0.988506i \(-0.548308\pi\)
−0.151183 + 0.988506i \(0.548308\pi\)
\(110\) 0 0
\(111\) 3.30303 0.313510
\(112\) 0 0
\(113\) 12.1854 1.14631 0.573154 0.819448i \(-0.305720\pi\)
0.573154 + 0.819448i \(0.305720\pi\)
\(114\) 0 0
\(115\) 21.1042 1.96798
\(116\) 0 0
\(117\) 1.87745 0.173570
\(118\) 0 0
\(119\) 4.75335 0.435739
\(120\) 0 0
\(121\) −10.9207 −0.992793
\(122\) 0 0
\(123\) −5.14306 −0.463734
\(124\) 0 0
\(125\) −3.43499 −0.307235
\(126\) 0 0
\(127\) −0.769542 −0.0682858 −0.0341429 0.999417i \(-0.510870\pi\)
−0.0341429 + 0.999417i \(0.510870\pi\)
\(128\) 0 0
\(129\) −26.4977 −2.33299
\(130\) 0 0
\(131\) −20.2493 −1.76919 −0.884595 0.466360i \(-0.845565\pi\)
−0.884595 + 0.466360i \(0.845565\pi\)
\(132\) 0 0
\(133\) −5.23531 −0.453959
\(134\) 0 0
\(135\) 3.39306 0.292028
\(136\) 0 0
\(137\) 0.378221 0.0323136 0.0161568 0.999869i \(-0.494857\pi\)
0.0161568 + 0.999869i \(0.494857\pi\)
\(138\) 0 0
\(139\) 4.74189 0.402202 0.201101 0.979570i \(-0.435548\pi\)
0.201101 + 0.979570i \(0.435548\pi\)
\(140\) 0 0
\(141\) 6.11120 0.514656
\(142\) 0 0
\(143\) −0.205923 −0.0172202
\(144\) 0 0
\(145\) −7.05985 −0.586289
\(146\) 0 0
\(147\) −14.1518 −1.16722
\(148\) 0 0
\(149\) −6.70197 −0.549047 −0.274523 0.961580i \(-0.588520\pi\)
−0.274523 + 0.961580i \(0.588520\pi\)
\(150\) 0 0
\(151\) −3.28695 −0.267488 −0.133744 0.991016i \(-0.542700\pi\)
−0.133744 + 0.991016i \(0.542700\pi\)
\(152\) 0 0
\(153\) 12.1893 0.985443
\(154\) 0 0
\(155\) −3.88761 −0.312260
\(156\) 0 0
\(157\) −12.1914 −0.972981 −0.486491 0.873686i \(-0.661723\pi\)
−0.486491 + 0.873686i \(0.661723\pi\)
\(158\) 0 0
\(159\) 22.0974 1.75244
\(160\) 0 0
\(161\) −6.36008 −0.501244
\(162\) 0 0
\(163\) 23.1424 1.81265 0.906325 0.422582i \(-0.138876\pi\)
0.906325 + 0.422582i \(0.138876\pi\)
\(164\) 0 0
\(165\) 2.20677 0.171797
\(166\) 0 0
\(167\) −15.8096 −1.22339 −0.611693 0.791096i \(-0.709511\pi\)
−0.611693 + 0.791096i \(0.709511\pi\)
\(168\) 0 0
\(169\) −12.4651 −0.958855
\(170\) 0 0
\(171\) −13.4252 −1.02665
\(172\) 0 0
\(173\) 11.5671 0.879432 0.439716 0.898137i \(-0.355079\pi\)
0.439716 + 0.898137i \(0.355079\pi\)
\(174\) 0 0
\(175\) 6.04050 0.456619
\(176\) 0 0
\(177\) −30.6446 −2.30339
\(178\) 0 0
\(179\) −4.49731 −0.336145 −0.168072 0.985775i \(-0.553754\pi\)
−0.168072 + 0.985775i \(0.553754\pi\)
\(180\) 0 0
\(181\) 5.94503 0.441891 0.220945 0.975286i \(-0.429086\pi\)
0.220945 + 0.975286i \(0.429086\pi\)
\(182\) 0 0
\(183\) 32.3724 2.39304
\(184\) 0 0
\(185\) −4.65015 −0.341886
\(186\) 0 0
\(187\) −1.33695 −0.0977673
\(188\) 0 0
\(189\) −1.02255 −0.0743796
\(190\) 0 0
\(191\) 12.9688 0.938393 0.469196 0.883094i \(-0.344544\pi\)
0.469196 + 0.883094i \(0.344544\pi\)
\(192\) 0 0
\(193\) −25.0382 −1.80229 −0.901146 0.433516i \(-0.857273\pi\)
−0.901146 + 0.433516i \(0.857273\pi\)
\(194\) 0 0
\(195\) −5.73207 −0.410482
\(196\) 0 0
\(197\) −2.83492 −0.201980 −0.100990 0.994887i \(-0.532201\pi\)
−0.100990 + 0.994887i \(0.532201\pi\)
\(198\) 0 0
\(199\) 1.83273 0.129918 0.0649592 0.997888i \(-0.479308\pi\)
0.0649592 + 0.997888i \(0.479308\pi\)
\(200\) 0 0
\(201\) −5.09376 −0.359286
\(202\) 0 0
\(203\) 2.12759 0.149328
\(204\) 0 0
\(205\) 7.24063 0.505707
\(206\) 0 0
\(207\) −16.3095 −1.13359
\(208\) 0 0
\(209\) 1.47251 0.101855
\(210\) 0 0
\(211\) −2.22122 −0.152915 −0.0764576 0.997073i \(-0.524361\pi\)
−0.0764576 + 0.997073i \(0.524361\pi\)
\(212\) 0 0
\(213\) 10.6787 0.731690
\(214\) 0 0
\(215\) 37.3046 2.54415
\(216\) 0 0
\(217\) 1.17159 0.0795327
\(218\) 0 0
\(219\) 7.45974 0.504082
\(220\) 0 0
\(221\) 3.47271 0.233599
\(222\) 0 0
\(223\) −23.9230 −1.60200 −0.801000 0.598665i \(-0.795698\pi\)
−0.801000 + 0.598665i \(0.795698\pi\)
\(224\) 0 0
\(225\) 15.4900 1.03266
\(226\) 0 0
\(227\) 16.5119 1.09594 0.547968 0.836499i \(-0.315401\pi\)
0.547968 + 0.836499i \(0.315401\pi\)
\(228\) 0 0
\(229\) 8.88608 0.587209 0.293604 0.955927i \(-0.405145\pi\)
0.293604 + 0.955927i \(0.405145\pi\)
\(230\) 0 0
\(231\) −0.665045 −0.0437567
\(232\) 0 0
\(233\) 10.6385 0.696950 0.348475 0.937318i \(-0.386700\pi\)
0.348475 + 0.937318i \(0.386700\pi\)
\(234\) 0 0
\(235\) −8.60361 −0.561238
\(236\) 0 0
\(237\) −29.6164 −1.92379
\(238\) 0 0
\(239\) 8.24149 0.533098 0.266549 0.963821i \(-0.414117\pi\)
0.266549 + 0.963821i \(0.414117\pi\)
\(240\) 0 0
\(241\) 18.2794 1.17748 0.588738 0.808324i \(-0.299625\pi\)
0.588738 + 0.808324i \(0.299625\pi\)
\(242\) 0 0
\(243\) −20.7930 −1.33387
\(244\) 0 0
\(245\) 19.9235 1.27287
\(246\) 0 0
\(247\) −3.82481 −0.243367
\(248\) 0 0
\(249\) −4.86823 −0.308512
\(250\) 0 0
\(251\) −10.3594 −0.653880 −0.326940 0.945045i \(-0.606018\pi\)
−0.326940 + 0.945045i \(0.606018\pi\)
\(252\) 0 0
\(253\) 1.78886 0.112465
\(254\) 0 0
\(255\) −37.2152 −2.33051
\(256\) 0 0
\(257\) −0.578155 −0.0360643 −0.0180322 0.999837i \(-0.505740\pi\)
−0.0180322 + 0.999837i \(0.505740\pi\)
\(258\) 0 0
\(259\) 1.40139 0.0870783
\(260\) 0 0
\(261\) 5.45590 0.337712
\(262\) 0 0
\(263\) −10.1021 −0.622922 −0.311461 0.950259i \(-0.600818\pi\)
−0.311461 + 0.950259i \(0.600818\pi\)
\(264\) 0 0
\(265\) −31.1097 −1.91106
\(266\) 0 0
\(267\) −42.4916 −2.60044
\(268\) 0 0
\(269\) 8.98048 0.547550 0.273775 0.961794i \(-0.411728\pi\)
0.273775 + 0.961794i \(0.411728\pi\)
\(270\) 0 0
\(271\) −23.3306 −1.41723 −0.708615 0.705595i \(-0.750680\pi\)
−0.708615 + 0.705595i \(0.750680\pi\)
\(272\) 0 0
\(273\) 1.72744 0.104550
\(274\) 0 0
\(275\) −1.69898 −0.102452
\(276\) 0 0
\(277\) −9.90856 −0.595348 −0.297674 0.954668i \(-0.596211\pi\)
−0.297674 + 0.954668i \(0.596211\pi\)
\(278\) 0 0
\(279\) 3.00437 0.179867
\(280\) 0 0
\(281\) −11.4329 −0.682029 −0.341015 0.940058i \(-0.610771\pi\)
−0.341015 + 0.940058i \(0.610771\pi\)
\(282\) 0 0
\(283\) 0.871740 0.0518196 0.0259098 0.999664i \(-0.491752\pi\)
0.0259098 + 0.999664i \(0.491752\pi\)
\(284\) 0 0
\(285\) 40.9886 2.42795
\(286\) 0 0
\(287\) −2.18207 −0.128804
\(288\) 0 0
\(289\) 5.54639 0.326258
\(290\) 0 0
\(291\) −36.9853 −2.16811
\(292\) 0 0
\(293\) −6.39060 −0.373343 −0.186671 0.982422i \(-0.559770\pi\)
−0.186671 + 0.982422i \(0.559770\pi\)
\(294\) 0 0
\(295\) 43.1428 2.51187
\(296\) 0 0
\(297\) 0.287607 0.0166887
\(298\) 0 0
\(299\) −4.64655 −0.268717
\(300\) 0 0
\(301\) −11.2423 −0.647995
\(302\) 0 0
\(303\) 18.5628 1.06641
\(304\) 0 0
\(305\) −45.5753 −2.60963
\(306\) 0 0
\(307\) −31.7537 −1.81228 −0.906141 0.422976i \(-0.860986\pi\)
−0.906141 + 0.422976i \(0.860986\pi\)
\(308\) 0 0
\(309\) −26.5951 −1.51294
\(310\) 0 0
\(311\) −18.9859 −1.07659 −0.538296 0.842756i \(-0.680932\pi\)
−0.538296 + 0.842756i \(0.680932\pi\)
\(312\) 0 0
\(313\) −15.9397 −0.900967 −0.450483 0.892785i \(-0.648748\pi\)
−0.450483 + 0.892785i \(0.648748\pi\)
\(314\) 0 0
\(315\) −8.53627 −0.480964
\(316\) 0 0
\(317\) 26.8663 1.50896 0.754481 0.656322i \(-0.227889\pi\)
0.754481 + 0.656322i \(0.227889\pi\)
\(318\) 0 0
\(319\) −0.598416 −0.0335049
\(320\) 0 0
\(321\) 15.9808 0.891961
\(322\) 0 0
\(323\) −24.8324 −1.38171
\(324\) 0 0
\(325\) 4.41307 0.244793
\(326\) 0 0
\(327\) −7.44837 −0.411896
\(328\) 0 0
\(329\) 2.59283 0.142947
\(330\) 0 0
\(331\) 23.8734 1.31220 0.656100 0.754674i \(-0.272205\pi\)
0.656100 + 0.754674i \(0.272205\pi\)
\(332\) 0 0
\(333\) 3.59367 0.196932
\(334\) 0 0
\(335\) 7.17121 0.391805
\(336\) 0 0
\(337\) 28.5800 1.55685 0.778426 0.627736i \(-0.216018\pi\)
0.778426 + 0.627736i \(0.216018\pi\)
\(338\) 0 0
\(339\) 28.7511 1.56155
\(340\) 0 0
\(341\) −0.329527 −0.0178449
\(342\) 0 0
\(343\) −13.0117 −0.702565
\(344\) 0 0
\(345\) 49.7947 2.68086
\(346\) 0 0
\(347\) −14.9783 −0.804075 −0.402037 0.915623i \(-0.631698\pi\)
−0.402037 + 0.915623i \(0.631698\pi\)
\(348\) 0 0
\(349\) 31.8116 1.70284 0.851419 0.524487i \(-0.175743\pi\)
0.851419 + 0.524487i \(0.175743\pi\)
\(350\) 0 0
\(351\) −0.747056 −0.0398749
\(352\) 0 0
\(353\) −29.5078 −1.57054 −0.785271 0.619153i \(-0.787476\pi\)
−0.785271 + 0.619153i \(0.787476\pi\)
\(354\) 0 0
\(355\) −15.0339 −0.797916
\(356\) 0 0
\(357\) 11.2154 0.593580
\(358\) 0 0
\(359\) −37.5327 −1.98090 −0.990449 0.137878i \(-0.955972\pi\)
−0.990449 + 0.137878i \(0.955972\pi\)
\(360\) 0 0
\(361\) 8.35029 0.439489
\(362\) 0 0
\(363\) −25.7671 −1.35242
\(364\) 0 0
\(365\) −10.5021 −0.549707
\(366\) 0 0
\(367\) 27.8906 1.45588 0.727938 0.685643i \(-0.240479\pi\)
0.727938 + 0.685643i \(0.240479\pi\)
\(368\) 0 0
\(369\) −5.59560 −0.291295
\(370\) 0 0
\(371\) 9.37539 0.486746
\(372\) 0 0
\(373\) −17.4996 −0.906096 −0.453048 0.891486i \(-0.649663\pi\)
−0.453048 + 0.891486i \(0.649663\pi\)
\(374\) 0 0
\(375\) −8.10473 −0.418527
\(376\) 0 0
\(377\) 1.55438 0.0800546
\(378\) 0 0
\(379\) −27.5811 −1.41675 −0.708373 0.705839i \(-0.750570\pi\)
−0.708373 + 0.705839i \(0.750570\pi\)
\(380\) 0 0
\(381\) −1.81571 −0.0930215
\(382\) 0 0
\(383\) 2.11485 0.108064 0.0540320 0.998539i \(-0.482793\pi\)
0.0540320 + 0.998539i \(0.482793\pi\)
\(384\) 0 0
\(385\) 0.936279 0.0477172
\(386\) 0 0
\(387\) −28.8292 −1.46547
\(388\) 0 0
\(389\) −15.6467 −0.793317 −0.396659 0.917966i \(-0.629830\pi\)
−0.396659 + 0.917966i \(0.629830\pi\)
\(390\) 0 0
\(391\) −30.1675 −1.52564
\(392\) 0 0
\(393\) −47.7775 −2.41006
\(394\) 0 0
\(395\) 41.6953 2.09792
\(396\) 0 0
\(397\) 13.4630 0.675688 0.337844 0.941202i \(-0.390302\pi\)
0.337844 + 0.941202i \(0.390302\pi\)
\(398\) 0 0
\(399\) −12.3525 −0.618400
\(400\) 0 0
\(401\) 34.8957 1.74261 0.871304 0.490743i \(-0.163275\pi\)
0.871304 + 0.490743i \(0.163275\pi\)
\(402\) 0 0
\(403\) 0.855941 0.0426375
\(404\) 0 0
\(405\) 33.5875 1.66897
\(406\) 0 0
\(407\) −0.394162 −0.0195379
\(408\) 0 0
\(409\) −21.7972 −1.07780 −0.538901 0.842369i \(-0.681160\pi\)
−0.538901 + 0.842369i \(0.681160\pi\)
\(410\) 0 0
\(411\) 0.892399 0.0440188
\(412\) 0 0
\(413\) −13.0017 −0.639774
\(414\) 0 0
\(415\) 6.85372 0.336436
\(416\) 0 0
\(417\) 11.1883 0.547895
\(418\) 0 0
\(419\) 24.5024 1.19702 0.598511 0.801115i \(-0.295759\pi\)
0.598511 + 0.801115i \(0.295759\pi\)
\(420\) 0 0
\(421\) −35.7316 −1.74145 −0.870725 0.491770i \(-0.836350\pi\)
−0.870725 + 0.491770i \(0.836350\pi\)
\(422\) 0 0
\(423\) 6.64893 0.323282
\(424\) 0 0
\(425\) 28.6517 1.38981
\(426\) 0 0
\(427\) 13.7348 0.664674
\(428\) 0 0
\(429\) −0.485869 −0.0234580
\(430\) 0 0
\(431\) 0.467028 0.0224960 0.0112480 0.999937i \(-0.496420\pi\)
0.0112480 + 0.999937i \(0.496420\pi\)
\(432\) 0 0
\(433\) 4.96811 0.238752 0.119376 0.992849i \(-0.461911\pi\)
0.119376 + 0.992849i \(0.461911\pi\)
\(434\) 0 0
\(435\) −16.6575 −0.798665
\(436\) 0 0
\(437\) 33.2263 1.58943
\(438\) 0 0
\(439\) 12.2159 0.583033 0.291516 0.956566i \(-0.405840\pi\)
0.291516 + 0.956566i \(0.405840\pi\)
\(440\) 0 0
\(441\) −15.3970 −0.733191
\(442\) 0 0
\(443\) 33.0371 1.56964 0.784820 0.619724i \(-0.212755\pi\)
0.784820 + 0.619724i \(0.212755\pi\)
\(444\) 0 0
\(445\) 59.8216 2.83581
\(446\) 0 0
\(447\) −15.8131 −0.747933
\(448\) 0 0
\(449\) 27.8097 1.31242 0.656210 0.754578i \(-0.272158\pi\)
0.656210 + 0.754578i \(0.272158\pi\)
\(450\) 0 0
\(451\) 0.613739 0.0288999
\(452\) 0 0
\(453\) −7.75545 −0.364383
\(454\) 0 0
\(455\) −2.43197 −0.114013
\(456\) 0 0
\(457\) −13.0900 −0.612325 −0.306163 0.951979i \(-0.599045\pi\)
−0.306163 + 0.951979i \(0.599045\pi\)
\(458\) 0 0
\(459\) −4.85023 −0.226389
\(460\) 0 0
\(461\) −35.6113 −1.65858 −0.829291 0.558817i \(-0.811256\pi\)
−0.829291 + 0.558817i \(0.811256\pi\)
\(462\) 0 0
\(463\) −15.7844 −0.733562 −0.366781 0.930307i \(-0.619540\pi\)
−0.366781 + 0.930307i \(0.619540\pi\)
\(464\) 0 0
\(465\) −9.17268 −0.425373
\(466\) 0 0
\(467\) 32.0685 1.48395 0.741976 0.670426i \(-0.233889\pi\)
0.741976 + 0.670426i \(0.233889\pi\)
\(468\) 0 0
\(469\) −2.16115 −0.0997928
\(470\) 0 0
\(471\) −28.7652 −1.32543
\(472\) 0 0
\(473\) 3.16206 0.145392
\(474\) 0 0
\(475\) −31.5568 −1.44792
\(476\) 0 0
\(477\) 24.0418 1.10080
\(478\) 0 0
\(479\) −7.20104 −0.329024 −0.164512 0.986375i \(-0.552605\pi\)
−0.164512 + 0.986375i \(0.552605\pi\)
\(480\) 0 0
\(481\) 1.02383 0.0466827
\(482\) 0 0
\(483\) −15.0064 −0.682814
\(484\) 0 0
\(485\) 52.0695 2.36435
\(486\) 0 0
\(487\) −11.7204 −0.531100 −0.265550 0.964097i \(-0.585554\pi\)
−0.265550 + 0.964097i \(0.585554\pi\)
\(488\) 0 0
\(489\) 54.6036 2.46926
\(490\) 0 0
\(491\) 16.3757 0.739024 0.369512 0.929226i \(-0.379525\pi\)
0.369512 + 0.929226i \(0.379525\pi\)
\(492\) 0 0
\(493\) 10.0917 0.454509
\(494\) 0 0
\(495\) 2.40095 0.107915
\(496\) 0 0
\(497\) 4.53069 0.203229
\(498\) 0 0
\(499\) 31.2214 1.39766 0.698830 0.715287i \(-0.253704\pi\)
0.698830 + 0.715287i \(0.253704\pi\)
\(500\) 0 0
\(501\) −37.3023 −1.66654
\(502\) 0 0
\(503\) 28.5996 1.27519 0.637596 0.770371i \(-0.279929\pi\)
0.637596 + 0.770371i \(0.279929\pi\)
\(504\) 0 0
\(505\) −26.1336 −1.16293
\(506\) 0 0
\(507\) −29.4110 −1.30619
\(508\) 0 0
\(509\) 19.4787 0.863378 0.431689 0.902022i \(-0.357918\pi\)
0.431689 + 0.902022i \(0.357918\pi\)
\(510\) 0 0
\(511\) 3.16498 0.140010
\(512\) 0 0
\(513\) 5.34201 0.235856
\(514\) 0 0
\(515\) 37.4417 1.64988
\(516\) 0 0
\(517\) −0.729270 −0.0320733
\(518\) 0 0
\(519\) 27.2922 1.19800
\(520\) 0 0
\(521\) 32.3164 1.41581 0.707904 0.706309i \(-0.249641\pi\)
0.707904 + 0.706309i \(0.249641\pi\)
\(522\) 0 0
\(523\) −9.37424 −0.409907 −0.204954 0.978772i \(-0.565704\pi\)
−0.204954 + 0.978772i \(0.565704\pi\)
\(524\) 0 0
\(525\) 14.2523 0.622023
\(526\) 0 0
\(527\) 5.55716 0.242074
\(528\) 0 0
\(529\) 17.3648 0.754991
\(530\) 0 0
\(531\) −33.3411 −1.44688
\(532\) 0 0
\(533\) −1.59418 −0.0690516
\(534\) 0 0
\(535\) −22.4985 −0.972694
\(536\) 0 0
\(537\) −10.6113 −0.457909
\(538\) 0 0
\(539\) 1.68878 0.0727410
\(540\) 0 0
\(541\) −9.81510 −0.421984 −0.210992 0.977488i \(-0.567669\pi\)
−0.210992 + 0.977488i \(0.567669\pi\)
\(542\) 0 0
\(543\) 14.0271 0.601960
\(544\) 0 0
\(545\) 10.4861 0.449177
\(546\) 0 0
\(547\) 5.69646 0.243563 0.121781 0.992557i \(-0.461139\pi\)
0.121781 + 0.992557i \(0.461139\pi\)
\(548\) 0 0
\(549\) 35.2209 1.50319
\(550\) 0 0
\(551\) −11.1150 −0.473514
\(552\) 0 0
\(553\) −12.5655 −0.534340
\(554\) 0 0
\(555\) −10.9719 −0.465730
\(556\) 0 0
\(557\) 6.97777 0.295658 0.147829 0.989013i \(-0.452772\pi\)
0.147829 + 0.989013i \(0.452772\pi\)
\(558\) 0 0
\(559\) −8.21341 −0.347390
\(560\) 0 0
\(561\) −3.15448 −0.133182
\(562\) 0 0
\(563\) 11.4472 0.482441 0.241220 0.970470i \(-0.422452\pi\)
0.241220 + 0.970470i \(0.422452\pi\)
\(564\) 0 0
\(565\) −40.4771 −1.70288
\(566\) 0 0
\(567\) −10.1221 −0.425088
\(568\) 0 0
\(569\) −16.5466 −0.693669 −0.346835 0.937926i \(-0.612744\pi\)
−0.346835 + 0.937926i \(0.612744\pi\)
\(570\) 0 0
\(571\) 2.28957 0.0958155 0.0479078 0.998852i \(-0.484745\pi\)
0.0479078 + 0.998852i \(0.484745\pi\)
\(572\) 0 0
\(573\) 30.5995 1.27831
\(574\) 0 0
\(575\) −38.3365 −1.59874
\(576\) 0 0
\(577\) 17.7527 0.739054 0.369527 0.929220i \(-0.379520\pi\)
0.369527 + 0.929220i \(0.379520\pi\)
\(578\) 0 0
\(579\) −59.0769 −2.45515
\(580\) 0 0
\(581\) −2.06547 −0.0856902
\(582\) 0 0
\(583\) −2.63696 −0.109212
\(584\) 0 0
\(585\) −6.23644 −0.257845
\(586\) 0 0
\(587\) 29.0713 1.19990 0.599950 0.800037i \(-0.295187\pi\)
0.599950 + 0.800037i \(0.295187\pi\)
\(588\) 0 0
\(589\) −6.12062 −0.252196
\(590\) 0 0
\(591\) −6.68889 −0.275144
\(592\) 0 0
\(593\) 8.72077 0.358119 0.179060 0.983838i \(-0.442695\pi\)
0.179060 + 0.983838i \(0.442695\pi\)
\(594\) 0 0
\(595\) −15.7895 −0.647306
\(596\) 0 0
\(597\) 4.32425 0.176980
\(598\) 0 0
\(599\) −13.9845 −0.571392 −0.285696 0.958320i \(-0.592225\pi\)
−0.285696 + 0.958320i \(0.592225\pi\)
\(600\) 0 0
\(601\) 26.5770 1.08410 0.542048 0.840347i \(-0.317649\pi\)
0.542048 + 0.840347i \(0.317649\pi\)
\(602\) 0 0
\(603\) −5.54196 −0.225686
\(604\) 0 0
\(605\) 36.2760 1.47483
\(606\) 0 0
\(607\) 35.8461 1.45495 0.727474 0.686136i \(-0.240694\pi\)
0.727474 + 0.686136i \(0.240694\pi\)
\(608\) 0 0
\(609\) 5.01998 0.203420
\(610\) 0 0
\(611\) 1.89427 0.0766340
\(612\) 0 0
\(613\) 36.8956 1.49020 0.745099 0.666954i \(-0.232402\pi\)
0.745099 + 0.666954i \(0.232402\pi\)
\(614\) 0 0
\(615\) 17.0840 0.688894
\(616\) 0 0
\(617\) −16.8681 −0.679083 −0.339542 0.940591i \(-0.610272\pi\)
−0.339542 + 0.940591i \(0.610272\pi\)
\(618\) 0 0
\(619\) −8.20858 −0.329931 −0.164965 0.986299i \(-0.552751\pi\)
−0.164965 + 0.986299i \(0.552751\pi\)
\(620\) 0 0
\(621\) 6.48971 0.260423
\(622\) 0 0
\(623\) −18.0281 −0.722282
\(624\) 0 0
\(625\) −18.7602 −0.750409
\(626\) 0 0
\(627\) 3.47433 0.138751
\(628\) 0 0
\(629\) 6.64718 0.265040
\(630\) 0 0
\(631\) 22.4666 0.894383 0.447192 0.894438i \(-0.352424\pi\)
0.447192 + 0.894438i \(0.352424\pi\)
\(632\) 0 0
\(633\) −5.24090 −0.208307
\(634\) 0 0
\(635\) 2.55623 0.101441
\(636\) 0 0
\(637\) −4.38659 −0.173803
\(638\) 0 0
\(639\) 11.6183 0.459612
\(640\) 0 0
\(641\) 17.0927 0.675123 0.337561 0.941303i \(-0.390398\pi\)
0.337561 + 0.941303i \(0.390398\pi\)
\(642\) 0 0
\(643\) 12.4259 0.490028 0.245014 0.969519i \(-0.421207\pi\)
0.245014 + 0.969519i \(0.421207\pi\)
\(644\) 0 0
\(645\) 88.0189 3.46574
\(646\) 0 0
\(647\) −12.1415 −0.477330 −0.238665 0.971102i \(-0.576710\pi\)
−0.238665 + 0.971102i \(0.576710\pi\)
\(648\) 0 0
\(649\) 3.65693 0.143547
\(650\) 0 0
\(651\) 2.76432 0.108342
\(652\) 0 0
\(653\) 42.3458 1.65712 0.828561 0.559900i \(-0.189160\pi\)
0.828561 + 0.559900i \(0.189160\pi\)
\(654\) 0 0
\(655\) 67.2633 2.62820
\(656\) 0 0
\(657\) 8.11613 0.316640
\(658\) 0 0
\(659\) −30.1150 −1.17311 −0.586556 0.809908i \(-0.699517\pi\)
−0.586556 + 0.809908i \(0.699517\pi\)
\(660\) 0 0
\(661\) −32.2119 −1.25290 −0.626449 0.779462i \(-0.715493\pi\)
−0.626449 + 0.779462i \(0.715493\pi\)
\(662\) 0 0
\(663\) 8.19373 0.318218
\(664\) 0 0
\(665\) 17.3904 0.674372
\(666\) 0 0
\(667\) −13.5030 −0.522836
\(668\) 0 0
\(669\) −56.4454 −2.18230
\(670\) 0 0
\(671\) −3.86311 −0.149134
\(672\) 0 0
\(673\) −26.9776 −1.03991 −0.519954 0.854194i \(-0.674051\pi\)
−0.519954 + 0.854194i \(0.674051\pi\)
\(674\) 0 0
\(675\) −6.16361 −0.237238
\(676\) 0 0
\(677\) −5.26957 −0.202526 −0.101263 0.994860i \(-0.532288\pi\)
−0.101263 + 0.994860i \(0.532288\pi\)
\(678\) 0 0
\(679\) −15.6919 −0.602201
\(680\) 0 0
\(681\) 38.9594 1.49293
\(682\) 0 0
\(683\) 29.3817 1.12426 0.562130 0.827049i \(-0.309982\pi\)
0.562130 + 0.827049i \(0.309982\pi\)
\(684\) 0 0
\(685\) −1.25636 −0.0480030
\(686\) 0 0
\(687\) 20.9664 0.799918
\(688\) 0 0
\(689\) 6.84948 0.260944
\(690\) 0 0
\(691\) 19.5268 0.742835 0.371417 0.928466i \(-0.378872\pi\)
0.371417 + 0.928466i \(0.378872\pi\)
\(692\) 0 0
\(693\) −0.723563 −0.0274859
\(694\) 0 0
\(695\) −15.7514 −0.597486
\(696\) 0 0
\(697\) −10.3501 −0.392040
\(698\) 0 0
\(699\) 25.1011 0.949412
\(700\) 0 0
\(701\) −1.64757 −0.0622279 −0.0311139 0.999516i \(-0.509905\pi\)
−0.0311139 + 0.999516i \(0.509905\pi\)
\(702\) 0 0
\(703\) −7.32116 −0.276123
\(704\) 0 0
\(705\) −20.2999 −0.764539
\(706\) 0 0
\(707\) 7.87575 0.296198
\(708\) 0 0
\(709\) 1.40550 0.0527847 0.0263923 0.999652i \(-0.491598\pi\)
0.0263923 + 0.999652i \(0.491598\pi\)
\(710\) 0 0
\(711\) −32.2224 −1.20843
\(712\) 0 0
\(713\) −7.43559 −0.278465
\(714\) 0 0
\(715\) 0.684028 0.0255812
\(716\) 0 0
\(717\) 19.4455 0.726206
\(718\) 0 0
\(719\) −48.1292 −1.79492 −0.897458 0.441100i \(-0.854588\pi\)
−0.897458 + 0.441100i \(0.854588\pi\)
\(720\) 0 0
\(721\) −11.2836 −0.420224
\(722\) 0 0
\(723\) 43.1295 1.60400
\(724\) 0 0
\(725\) 12.8245 0.476288
\(726\) 0 0
\(727\) 16.6350 0.616959 0.308480 0.951231i \(-0.400180\pi\)
0.308480 + 0.951231i \(0.400180\pi\)
\(728\) 0 0
\(729\) −18.7263 −0.693565
\(730\) 0 0
\(731\) −53.3252 −1.97230
\(732\) 0 0
\(733\) 37.3466 1.37943 0.689714 0.724082i \(-0.257736\pi\)
0.689714 + 0.724082i \(0.257736\pi\)
\(734\) 0 0
\(735\) 47.0088 1.73395
\(736\) 0 0
\(737\) 0.607856 0.0223907
\(738\) 0 0
\(739\) 49.4985 1.82083 0.910416 0.413693i \(-0.135761\pi\)
0.910416 + 0.413693i \(0.135761\pi\)
\(740\) 0 0
\(741\) −9.02452 −0.331524
\(742\) 0 0
\(743\) 26.6742 0.978581 0.489290 0.872121i \(-0.337256\pi\)
0.489290 + 0.872121i \(0.337256\pi\)
\(744\) 0 0
\(745\) 22.2623 0.815629
\(746\) 0 0
\(747\) −5.29660 −0.193792
\(748\) 0 0
\(749\) 6.78026 0.247745
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −24.4427 −0.890741
\(754\) 0 0
\(755\) 10.9185 0.397364
\(756\) 0 0
\(757\) −0.115052 −0.00418163 −0.00209082 0.999998i \(-0.500666\pi\)
−0.00209082 + 0.999998i \(0.500666\pi\)
\(758\) 0 0
\(759\) 4.22076 0.153204
\(760\) 0 0
\(761\) 34.5931 1.25400 0.626999 0.779020i \(-0.284283\pi\)
0.626999 + 0.779020i \(0.284283\pi\)
\(762\) 0 0
\(763\) −3.16016 −0.114405
\(764\) 0 0
\(765\) −40.4898 −1.46391
\(766\) 0 0
\(767\) −9.49882 −0.342983
\(768\) 0 0
\(769\) 12.0756 0.435458 0.217729 0.976009i \(-0.430135\pi\)
0.217729 + 0.976009i \(0.430135\pi\)
\(770\) 0 0
\(771\) −1.36414 −0.0491282
\(772\) 0 0
\(773\) 40.5322 1.45784 0.728922 0.684597i \(-0.240022\pi\)
0.728922 + 0.684597i \(0.240022\pi\)
\(774\) 0 0
\(775\) 7.06197 0.253673
\(776\) 0 0
\(777\) 3.30654 0.118621
\(778\) 0 0
\(779\) 11.3996 0.408432
\(780\) 0 0
\(781\) −1.27432 −0.0455988
\(782\) 0 0
\(783\) −2.17096 −0.0775837
\(784\) 0 0
\(785\) 40.4970 1.44540
\(786\) 0 0
\(787\) −54.8747 −1.95607 −0.978036 0.208434i \(-0.933163\pi\)
−0.978036 + 0.208434i \(0.933163\pi\)
\(788\) 0 0
\(789\) −23.8356 −0.848568
\(790\) 0 0
\(791\) 12.1984 0.433724
\(792\) 0 0
\(793\) 10.0344 0.356331
\(794\) 0 0
\(795\) −73.4024 −2.60331
\(796\) 0 0
\(797\) −26.6234 −0.943051 −0.471525 0.881852i \(-0.656296\pi\)
−0.471525 + 0.881852i \(0.656296\pi\)
\(798\) 0 0
\(799\) 12.2985 0.435089
\(800\) 0 0
\(801\) −46.2305 −1.63347
\(802\) 0 0
\(803\) −0.890196 −0.0314144
\(804\) 0 0
\(805\) 21.1267 0.744617
\(806\) 0 0
\(807\) 21.1891 0.745893
\(808\) 0 0
\(809\) 47.1837 1.65889 0.829445 0.558588i \(-0.188657\pi\)
0.829445 + 0.558588i \(0.188657\pi\)
\(810\) 0 0
\(811\) −11.9553 −0.419807 −0.209904 0.977722i \(-0.567315\pi\)
−0.209904 + 0.977722i \(0.567315\pi\)
\(812\) 0 0
\(813\) −55.0477 −1.93061
\(814\) 0 0
\(815\) −76.8733 −2.69276
\(816\) 0 0
\(817\) 58.7320 2.05477
\(818\) 0 0
\(819\) 1.87944 0.0656731
\(820\) 0 0
\(821\) 42.5235 1.48408 0.742041 0.670355i \(-0.233858\pi\)
0.742041 + 0.670355i \(0.233858\pi\)
\(822\) 0 0
\(823\) −32.4576 −1.13140 −0.565701 0.824611i \(-0.691394\pi\)
−0.565701 + 0.824611i \(0.691394\pi\)
\(824\) 0 0
\(825\) −4.00868 −0.139564
\(826\) 0 0
\(827\) 43.0834 1.49816 0.749078 0.662482i \(-0.230497\pi\)
0.749078 + 0.662482i \(0.230497\pi\)
\(828\) 0 0
\(829\) 0.335496 0.0116523 0.00582613 0.999983i \(-0.498145\pi\)
0.00582613 + 0.999983i \(0.498145\pi\)
\(830\) 0 0
\(831\) −23.3789 −0.811006
\(832\) 0 0
\(833\) −28.4797 −0.986764
\(834\) 0 0
\(835\) 52.5158 1.81738
\(836\) 0 0
\(837\) −1.19547 −0.0413214
\(838\) 0 0
\(839\) −52.7061 −1.81962 −0.909808 0.415029i \(-0.863771\pi\)
−0.909808 + 0.415029i \(0.863771\pi\)
\(840\) 0 0
\(841\) −24.4830 −0.844240
\(842\) 0 0
\(843\) −26.9755 −0.929086
\(844\) 0 0
\(845\) 41.4061 1.42441
\(846\) 0 0
\(847\) −10.9323 −0.375639
\(848\) 0 0
\(849\) 2.05684 0.0705906
\(850\) 0 0
\(851\) −8.89407 −0.304885
\(852\) 0 0
\(853\) −20.1373 −0.689490 −0.344745 0.938696i \(-0.612035\pi\)
−0.344745 + 0.938696i \(0.612035\pi\)
\(854\) 0 0
\(855\) 44.5952 1.52512
\(856\) 0 0
\(857\) −2.09060 −0.0714137 −0.0357068 0.999362i \(-0.511368\pi\)
−0.0357068 + 0.999362i \(0.511368\pi\)
\(858\) 0 0
\(859\) −32.8173 −1.11971 −0.559856 0.828590i \(-0.689144\pi\)
−0.559856 + 0.828590i \(0.689144\pi\)
\(860\) 0 0
\(861\) −5.14852 −0.175461
\(862\) 0 0
\(863\) 9.60960 0.327114 0.163557 0.986534i \(-0.447703\pi\)
0.163557 + 0.986534i \(0.447703\pi\)
\(864\) 0 0
\(865\) −38.4232 −1.30643
\(866\) 0 0
\(867\) 13.0865 0.444441
\(868\) 0 0
\(869\) 3.53423 0.119891
\(870\) 0 0
\(871\) −1.57890 −0.0534989
\(872\) 0 0
\(873\) −40.2396 −1.36191
\(874\) 0 0
\(875\) −3.43864 −0.116247
\(876\) 0 0
\(877\) −55.1799 −1.86329 −0.931647 0.363364i \(-0.881628\pi\)
−0.931647 + 0.363364i \(0.881628\pi\)
\(878\) 0 0
\(879\) −15.0784 −0.508582
\(880\) 0 0
\(881\) 35.9126 1.20993 0.604963 0.796254i \(-0.293188\pi\)
0.604963 + 0.796254i \(0.293188\pi\)
\(882\) 0 0
\(883\) 1.62196 0.0545834 0.0272917 0.999628i \(-0.491312\pi\)
0.0272917 + 0.999628i \(0.491312\pi\)
\(884\) 0 0
\(885\) 101.794 3.42177
\(886\) 0 0
\(887\) 41.9062 1.40707 0.703537 0.710659i \(-0.251603\pi\)
0.703537 + 0.710659i \(0.251603\pi\)
\(888\) 0 0
\(889\) −0.770359 −0.0258370
\(890\) 0 0
\(891\) 2.84698 0.0953775
\(892\) 0 0
\(893\) −13.5455 −0.453281
\(894\) 0 0
\(895\) 14.9390 0.499355
\(896\) 0 0
\(897\) −10.9634 −0.366057
\(898\) 0 0
\(899\) 2.48738 0.0829587
\(900\) 0 0
\(901\) 44.4700 1.48151
\(902\) 0 0
\(903\) −26.5258 −0.882724
\(904\) 0 0
\(905\) −19.7480 −0.656444
\(906\) 0 0
\(907\) −55.8895 −1.85578 −0.927889 0.372856i \(-0.878379\pi\)
−0.927889 + 0.372856i \(0.878379\pi\)
\(908\) 0 0
\(909\) 20.1962 0.669866
\(910\) 0 0
\(911\) −46.6680 −1.54618 −0.773089 0.634297i \(-0.781290\pi\)
−0.773089 + 0.634297i \(0.781290\pi\)
\(912\) 0 0
\(913\) 0.580944 0.0192264
\(914\) 0 0
\(915\) −107.533 −3.55494
\(916\) 0 0
\(917\) −20.2708 −0.669401
\(918\) 0 0
\(919\) −8.89643 −0.293466 −0.146733 0.989176i \(-0.546876\pi\)
−0.146733 + 0.989176i \(0.546876\pi\)
\(920\) 0 0
\(921\) −74.9219 −2.46876
\(922\) 0 0
\(923\) 3.31004 0.108951
\(924\) 0 0
\(925\) 8.44715 0.277741
\(926\) 0 0
\(927\) −28.9352 −0.950356
\(928\) 0 0
\(929\) −17.2744 −0.566754 −0.283377 0.959009i \(-0.591455\pi\)
−0.283377 + 0.959009i \(0.591455\pi\)
\(930\) 0 0
\(931\) 31.3674 1.02802
\(932\) 0 0
\(933\) −44.7966 −1.46658
\(934\) 0 0
\(935\) 4.44102 0.145237
\(936\) 0 0
\(937\) 25.8783 0.845408 0.422704 0.906268i \(-0.361081\pi\)
0.422704 + 0.906268i \(0.361081\pi\)
\(938\) 0 0
\(939\) −37.6092 −1.22733
\(940\) 0 0
\(941\) −50.4155 −1.64350 −0.821749 0.569850i \(-0.807001\pi\)
−0.821749 + 0.569850i \(0.807001\pi\)
\(942\) 0 0
\(943\) 13.8487 0.450976
\(944\) 0 0
\(945\) 3.39667 0.110494
\(946\) 0 0
\(947\) −2.34953 −0.0763495 −0.0381747 0.999271i \(-0.512154\pi\)
−0.0381747 + 0.999271i \(0.512154\pi\)
\(948\) 0 0
\(949\) 2.31227 0.0750596
\(950\) 0 0
\(951\) 63.3901 2.05556
\(952\) 0 0
\(953\) −11.6309 −0.376761 −0.188380 0.982096i \(-0.560324\pi\)
−0.188380 + 0.982096i \(0.560324\pi\)
\(954\) 0 0
\(955\) −43.0794 −1.39402
\(956\) 0 0
\(957\) −1.41194 −0.0456416
\(958\) 0 0
\(959\) 0.378623 0.0122264
\(960\) 0 0
\(961\) −29.6303 −0.955816
\(962\) 0 0
\(963\) 17.3870 0.560287
\(964\) 0 0
\(965\) 83.1710 2.67737
\(966\) 0 0
\(967\) 7.09441 0.228141 0.114070 0.993473i \(-0.463611\pi\)
0.114070 + 0.993473i \(0.463611\pi\)
\(968\) 0 0
\(969\) −58.5913 −1.88222
\(970\) 0 0
\(971\) 16.0048 0.513617 0.256809 0.966462i \(-0.417329\pi\)
0.256809 + 0.966462i \(0.417329\pi\)
\(972\) 0 0
\(973\) 4.74693 0.152180
\(974\) 0 0
\(975\) 10.4125 0.333467
\(976\) 0 0
\(977\) 54.2809 1.73660 0.868300 0.496040i \(-0.165213\pi\)
0.868300 + 0.496040i \(0.165213\pi\)
\(978\) 0 0
\(979\) 5.07067 0.162059
\(980\) 0 0
\(981\) −8.10376 −0.258733
\(982\) 0 0
\(983\) 43.6941 1.39363 0.696813 0.717253i \(-0.254601\pi\)
0.696813 + 0.717253i \(0.254601\pi\)
\(984\) 0 0
\(985\) 9.41692 0.300048
\(986\) 0 0
\(987\) 6.11769 0.194728
\(988\) 0 0
\(989\) 71.3502 2.26881
\(990\) 0 0
\(991\) −31.2775 −0.993562 −0.496781 0.867876i \(-0.665485\pi\)
−0.496781 + 0.867876i \(0.665485\pi\)
\(992\) 0 0
\(993\) 56.3285 1.78753
\(994\) 0 0
\(995\) −6.08787 −0.192999
\(996\) 0 0
\(997\) 23.9404 0.758200 0.379100 0.925356i \(-0.376234\pi\)
0.379100 + 0.925356i \(0.376234\pi\)
\(998\) 0 0
\(999\) −1.42996 −0.0452418
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.1.40 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.40 44 1.1 even 1 trivial