Properties

Label 6008.2.a.b.1.19
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 1.19
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.962699 q^{3} +2.73078 q^{5} -4.42659 q^{7} -2.07321 q^{9} +O(q^{10})\) \(q-0.962699 q^{3} +2.73078 q^{5} -4.42659 q^{7} -2.07321 q^{9} -2.59005 q^{11} +2.44381 q^{13} -2.62892 q^{15} +0.359015 q^{17} +4.11543 q^{19} +4.26147 q^{21} +0.0487888 q^{23} +2.45715 q^{25} +4.88398 q^{27} +1.62661 q^{29} -1.82266 q^{31} +2.49344 q^{33} -12.0880 q^{35} +7.04333 q^{37} -2.35265 q^{39} -2.33305 q^{41} -0.598973 q^{43} -5.66148 q^{45} +12.9710 q^{47} +12.5947 q^{49} -0.345624 q^{51} +3.71721 q^{53} -7.07287 q^{55} -3.96192 q^{57} +0.779197 q^{59} -12.1921 q^{61} +9.17724 q^{63} +6.67350 q^{65} -5.58624 q^{67} -0.0469689 q^{69} -14.3849 q^{71} +10.0286 q^{73} -2.36550 q^{75} +11.4651 q^{77} -5.23078 q^{79} +1.51783 q^{81} -11.6419 q^{83} +0.980391 q^{85} -1.56594 q^{87} +13.4868 q^{89} -10.8177 q^{91} +1.75468 q^{93} +11.2383 q^{95} -6.27432 q^{97} +5.36973 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −0.962699 −0.555815 −0.277907 0.960608i \(-0.589641\pi\)
−0.277907 + 0.960608i \(0.589641\pi\)
\(4\) 0 0
\(5\) 2.73078 1.22124 0.610621 0.791923i \(-0.290920\pi\)
0.610621 + 0.791923i \(0.290920\pi\)
\(6\) 0 0
\(7\) −4.42659 −1.67309 −0.836546 0.547896i \(-0.815429\pi\)
−0.836546 + 0.547896i \(0.815429\pi\)
\(8\) 0 0
\(9\) −2.07321 −0.691070
\(10\) 0 0
\(11\) −2.59005 −0.780931 −0.390465 0.920618i \(-0.627686\pi\)
−0.390465 + 0.920618i \(0.627686\pi\)
\(12\) 0 0
\(13\) 2.44381 0.677791 0.338895 0.940824i \(-0.389947\pi\)
0.338895 + 0.940824i \(0.389947\pi\)
\(14\) 0 0
\(15\) −2.62892 −0.678784
\(16\) 0 0
\(17\) 0.359015 0.0870740 0.0435370 0.999052i \(-0.486137\pi\)
0.0435370 + 0.999052i \(0.486137\pi\)
\(18\) 0 0
\(19\) 4.11543 0.944145 0.472072 0.881560i \(-0.343506\pi\)
0.472072 + 0.881560i \(0.343506\pi\)
\(20\) 0 0
\(21\) 4.26147 0.929930
\(22\) 0 0
\(23\) 0.0487888 0.0101732 0.00508658 0.999987i \(-0.498381\pi\)
0.00508658 + 0.999987i \(0.498381\pi\)
\(24\) 0 0
\(25\) 2.45715 0.491431
\(26\) 0 0
\(27\) 4.88398 0.939922
\(28\) 0 0
\(29\) 1.62661 0.302054 0.151027 0.988530i \(-0.451742\pi\)
0.151027 + 0.988530i \(0.451742\pi\)
\(30\) 0 0
\(31\) −1.82266 −0.327360 −0.163680 0.986513i \(-0.552336\pi\)
−0.163680 + 0.986513i \(0.552336\pi\)
\(32\) 0 0
\(33\) 2.49344 0.434053
\(34\) 0 0
\(35\) −12.0880 −2.04325
\(36\) 0 0
\(37\) 7.04333 1.15792 0.578958 0.815357i \(-0.303459\pi\)
0.578958 + 0.815357i \(0.303459\pi\)
\(38\) 0 0
\(39\) −2.35265 −0.376726
\(40\) 0 0
\(41\) −2.33305 −0.364361 −0.182181 0.983265i \(-0.558316\pi\)
−0.182181 + 0.983265i \(0.558316\pi\)
\(42\) 0 0
\(43\) −0.598973 −0.0913425 −0.0456712 0.998957i \(-0.514543\pi\)
−0.0456712 + 0.998957i \(0.514543\pi\)
\(44\) 0 0
\(45\) −5.66148 −0.843963
\(46\) 0 0
\(47\) 12.9710 1.89202 0.946010 0.324136i \(-0.105074\pi\)
0.946010 + 0.324136i \(0.105074\pi\)
\(48\) 0 0
\(49\) 12.5947 1.79924
\(50\) 0 0
\(51\) −0.345624 −0.0483970
\(52\) 0 0
\(53\) 3.71721 0.510598 0.255299 0.966862i \(-0.417826\pi\)
0.255299 + 0.966862i \(0.417826\pi\)
\(54\) 0 0
\(55\) −7.07287 −0.953705
\(56\) 0 0
\(57\) −3.96192 −0.524770
\(58\) 0 0
\(59\) 0.779197 0.101443 0.0507214 0.998713i \(-0.483848\pi\)
0.0507214 + 0.998713i \(0.483848\pi\)
\(60\) 0 0
\(61\) −12.1921 −1.56104 −0.780522 0.625128i \(-0.785047\pi\)
−0.780522 + 0.625128i \(0.785047\pi\)
\(62\) 0 0
\(63\) 9.17724 1.15622
\(64\) 0 0
\(65\) 6.67350 0.827746
\(66\) 0 0
\(67\) −5.58624 −0.682468 −0.341234 0.939978i \(-0.610845\pi\)
−0.341234 + 0.939978i \(0.610845\pi\)
\(68\) 0 0
\(69\) −0.0469689 −0.00565439
\(70\) 0 0
\(71\) −14.3849 −1.70717 −0.853585 0.520953i \(-0.825577\pi\)
−0.853585 + 0.520953i \(0.825577\pi\)
\(72\) 0 0
\(73\) 10.0286 1.17376 0.586881 0.809673i \(-0.300356\pi\)
0.586881 + 0.809673i \(0.300356\pi\)
\(74\) 0 0
\(75\) −2.36550 −0.273144
\(76\) 0 0
\(77\) 11.4651 1.30657
\(78\) 0 0
\(79\) −5.23078 −0.588509 −0.294254 0.955727i \(-0.595071\pi\)
−0.294254 + 0.955727i \(0.595071\pi\)
\(80\) 0 0
\(81\) 1.51783 0.168647
\(82\) 0 0
\(83\) −11.6419 −1.27786 −0.638930 0.769265i \(-0.720622\pi\)
−0.638930 + 0.769265i \(0.720622\pi\)
\(84\) 0 0
\(85\) 0.980391 0.106338
\(86\) 0 0
\(87\) −1.56594 −0.167886
\(88\) 0 0
\(89\) 13.4868 1.42959 0.714797 0.699332i \(-0.246519\pi\)
0.714797 + 0.699332i \(0.246519\pi\)
\(90\) 0 0
\(91\) −10.8177 −1.13401
\(92\) 0 0
\(93\) 1.75468 0.181951
\(94\) 0 0
\(95\) 11.2383 1.15303
\(96\) 0 0
\(97\) −6.27432 −0.637061 −0.318530 0.947913i \(-0.603189\pi\)
−0.318530 + 0.947913i \(0.603189\pi\)
\(98\) 0 0
\(99\) 5.36973 0.539678
\(100\) 0 0
\(101\) −5.38530 −0.535858 −0.267929 0.963439i \(-0.586339\pi\)
−0.267929 + 0.963439i \(0.586339\pi\)
\(102\) 0 0
\(103\) −13.9396 −1.37351 −0.686754 0.726890i \(-0.740965\pi\)
−0.686754 + 0.726890i \(0.740965\pi\)
\(104\) 0 0
\(105\) 11.6371 1.13567
\(106\) 0 0
\(107\) −6.61587 −0.639581 −0.319790 0.947488i \(-0.603612\pi\)
−0.319790 + 0.947488i \(0.603612\pi\)
\(108\) 0 0
\(109\) −11.7060 −1.12123 −0.560614 0.828077i \(-0.689435\pi\)
−0.560614 + 0.828077i \(0.689435\pi\)
\(110\) 0 0
\(111\) −6.78061 −0.643587
\(112\) 0 0
\(113\) −16.8266 −1.58291 −0.791455 0.611228i \(-0.790676\pi\)
−0.791455 + 0.611228i \(0.790676\pi\)
\(114\) 0 0
\(115\) 0.133231 0.0124239
\(116\) 0 0
\(117\) −5.06653 −0.468401
\(118\) 0 0
\(119\) −1.58921 −0.145683
\(120\) 0 0
\(121\) −4.29162 −0.390147
\(122\) 0 0
\(123\) 2.24603 0.202517
\(124\) 0 0
\(125\) −6.94395 −0.621086
\(126\) 0 0
\(127\) −10.3619 −0.919466 −0.459733 0.888057i \(-0.652055\pi\)
−0.459733 + 0.888057i \(0.652055\pi\)
\(128\) 0 0
\(129\) 0.576631 0.0507695
\(130\) 0 0
\(131\) −10.7168 −0.936327 −0.468163 0.883642i \(-0.655084\pi\)
−0.468163 + 0.883642i \(0.655084\pi\)
\(132\) 0 0
\(133\) −18.2173 −1.57964
\(134\) 0 0
\(135\) 13.3371 1.14787
\(136\) 0 0
\(137\) 8.26324 0.705976 0.352988 0.935628i \(-0.385166\pi\)
0.352988 + 0.935628i \(0.385166\pi\)
\(138\) 0 0
\(139\) −3.86367 −0.327712 −0.163856 0.986484i \(-0.552393\pi\)
−0.163856 + 0.986484i \(0.552393\pi\)
\(140\) 0 0
\(141\) −12.4872 −1.05161
\(142\) 0 0
\(143\) −6.32960 −0.529308
\(144\) 0 0
\(145\) 4.44192 0.368881
\(146\) 0 0
\(147\) −12.1249 −1.00004
\(148\) 0 0
\(149\) 20.5012 1.67952 0.839761 0.542957i \(-0.182695\pi\)
0.839761 + 0.542957i \(0.182695\pi\)
\(150\) 0 0
\(151\) 5.70679 0.464412 0.232206 0.972667i \(-0.425406\pi\)
0.232206 + 0.972667i \(0.425406\pi\)
\(152\) 0 0
\(153\) −0.744314 −0.0601742
\(154\) 0 0
\(155\) −4.97729 −0.399785
\(156\) 0 0
\(157\) 9.28446 0.740980 0.370490 0.928836i \(-0.379190\pi\)
0.370490 + 0.928836i \(0.379190\pi\)
\(158\) 0 0
\(159\) −3.57856 −0.283798
\(160\) 0 0
\(161\) −0.215968 −0.0170206
\(162\) 0 0
\(163\) −0.709508 −0.0555729 −0.0277865 0.999614i \(-0.508846\pi\)
−0.0277865 + 0.999614i \(0.508846\pi\)
\(164\) 0 0
\(165\) 6.80905 0.530083
\(166\) 0 0
\(167\) 1.30141 0.100706 0.0503531 0.998731i \(-0.483965\pi\)
0.0503531 + 0.998731i \(0.483965\pi\)
\(168\) 0 0
\(169\) −7.02780 −0.540600
\(170\) 0 0
\(171\) −8.53215 −0.652470
\(172\) 0 0
\(173\) −14.5407 −1.10551 −0.552753 0.833345i \(-0.686423\pi\)
−0.552753 + 0.833345i \(0.686423\pi\)
\(174\) 0 0
\(175\) −10.8768 −0.822209
\(176\) 0 0
\(177\) −0.750132 −0.0563834
\(178\) 0 0
\(179\) −25.4508 −1.90228 −0.951139 0.308762i \(-0.900085\pi\)
−0.951139 + 0.308762i \(0.900085\pi\)
\(180\) 0 0
\(181\) −18.1748 −1.35092 −0.675461 0.737396i \(-0.736055\pi\)
−0.675461 + 0.737396i \(0.736055\pi\)
\(182\) 0 0
\(183\) 11.7374 0.867652
\(184\) 0 0
\(185\) 19.2338 1.41410
\(186\) 0 0
\(187\) −0.929869 −0.0679988
\(188\) 0 0
\(189\) −21.6193 −1.57258
\(190\) 0 0
\(191\) −18.9402 −1.37047 −0.685233 0.728324i \(-0.740300\pi\)
−0.685233 + 0.728324i \(0.740300\pi\)
\(192\) 0 0
\(193\) −3.96192 −0.285185 −0.142592 0.989781i \(-0.545544\pi\)
−0.142592 + 0.989781i \(0.545544\pi\)
\(194\) 0 0
\(195\) −6.42458 −0.460073
\(196\) 0 0
\(197\) −1.44725 −0.103112 −0.0515562 0.998670i \(-0.516418\pi\)
−0.0515562 + 0.998670i \(0.516418\pi\)
\(198\) 0 0
\(199\) 11.3615 0.805393 0.402696 0.915334i \(-0.368073\pi\)
0.402696 + 0.915334i \(0.368073\pi\)
\(200\) 0 0
\(201\) 5.37787 0.379326
\(202\) 0 0
\(203\) −7.20034 −0.505365
\(204\) 0 0
\(205\) −6.37104 −0.444973
\(206\) 0 0
\(207\) −0.101149 −0.00703036
\(208\) 0 0
\(209\) −10.6592 −0.737312
\(210\) 0 0
\(211\) −1.52224 −0.104796 −0.0523978 0.998626i \(-0.516686\pi\)
−0.0523978 + 0.998626i \(0.516686\pi\)
\(212\) 0 0
\(213\) 13.8483 0.948871
\(214\) 0 0
\(215\) −1.63566 −0.111551
\(216\) 0 0
\(217\) 8.06817 0.547703
\(218\) 0 0
\(219\) −9.65455 −0.652394
\(220\) 0 0
\(221\) 0.877365 0.0590179
\(222\) 0 0
\(223\) −23.3186 −1.56153 −0.780763 0.624827i \(-0.785169\pi\)
−0.780763 + 0.624827i \(0.785169\pi\)
\(224\) 0 0
\(225\) −5.09419 −0.339613
\(226\) 0 0
\(227\) −1.70296 −0.113030 −0.0565148 0.998402i \(-0.517999\pi\)
−0.0565148 + 0.998402i \(0.517999\pi\)
\(228\) 0 0
\(229\) 19.9024 1.31519 0.657593 0.753374i \(-0.271575\pi\)
0.657593 + 0.753374i \(0.271575\pi\)
\(230\) 0 0
\(231\) −11.0374 −0.726211
\(232\) 0 0
\(233\) 17.7608 1.16355 0.581774 0.813351i \(-0.302359\pi\)
0.581774 + 0.813351i \(0.302359\pi\)
\(234\) 0 0
\(235\) 35.4210 2.31061
\(236\) 0 0
\(237\) 5.03567 0.327102
\(238\) 0 0
\(239\) 5.89213 0.381130 0.190565 0.981675i \(-0.438968\pi\)
0.190565 + 0.981675i \(0.438968\pi\)
\(240\) 0 0
\(241\) 28.6483 1.84540 0.922698 0.385523i \(-0.125979\pi\)
0.922698 + 0.385523i \(0.125979\pi\)
\(242\) 0 0
\(243\) −16.1131 −1.03366
\(244\) 0 0
\(245\) 34.3932 2.19730
\(246\) 0 0
\(247\) 10.0573 0.639932
\(248\) 0 0
\(249\) 11.2076 0.710253
\(250\) 0 0
\(251\) 11.9917 0.756908 0.378454 0.925620i \(-0.376456\pi\)
0.378454 + 0.925620i \(0.376456\pi\)
\(252\) 0 0
\(253\) −0.126366 −0.00794454
\(254\) 0 0
\(255\) −0.943822 −0.0591044
\(256\) 0 0
\(257\) −19.4754 −1.21484 −0.607422 0.794379i \(-0.707796\pi\)
−0.607422 + 0.794379i \(0.707796\pi\)
\(258\) 0 0
\(259\) −31.1779 −1.93730
\(260\) 0 0
\(261\) −3.37231 −0.208741
\(262\) 0 0
\(263\) 12.5815 0.775811 0.387906 0.921699i \(-0.373199\pi\)
0.387906 + 0.921699i \(0.373199\pi\)
\(264\) 0 0
\(265\) 10.1509 0.623564
\(266\) 0 0
\(267\) −12.9837 −0.794590
\(268\) 0 0
\(269\) −26.5638 −1.61962 −0.809811 0.586691i \(-0.800430\pi\)
−0.809811 + 0.586691i \(0.800430\pi\)
\(270\) 0 0
\(271\) 25.9338 1.57537 0.787683 0.616081i \(-0.211281\pi\)
0.787683 + 0.616081i \(0.211281\pi\)
\(272\) 0 0
\(273\) 10.4142 0.630297
\(274\) 0 0
\(275\) −6.36416 −0.383773
\(276\) 0 0
\(277\) −3.12691 −0.187878 −0.0939388 0.995578i \(-0.529946\pi\)
−0.0939388 + 0.995578i \(0.529946\pi\)
\(278\) 0 0
\(279\) 3.77876 0.226229
\(280\) 0 0
\(281\) 14.9313 0.890729 0.445364 0.895349i \(-0.353074\pi\)
0.445364 + 0.895349i \(0.353074\pi\)
\(282\) 0 0
\(283\) 19.7259 1.17258 0.586291 0.810100i \(-0.300587\pi\)
0.586291 + 0.810100i \(0.300587\pi\)
\(284\) 0 0
\(285\) −10.8191 −0.640870
\(286\) 0 0
\(287\) 10.3274 0.609610
\(288\) 0 0
\(289\) −16.8711 −0.992418
\(290\) 0 0
\(291\) 6.04028 0.354088
\(292\) 0 0
\(293\) −13.9695 −0.816107 −0.408053 0.912958i \(-0.633792\pi\)
−0.408053 + 0.912958i \(0.633792\pi\)
\(294\) 0 0
\(295\) 2.12781 0.123886
\(296\) 0 0
\(297\) −12.6498 −0.734014
\(298\) 0 0
\(299\) 0.119230 0.00689527
\(300\) 0 0
\(301\) 2.65140 0.152824
\(302\) 0 0
\(303\) 5.18443 0.297838
\(304\) 0 0
\(305\) −33.2941 −1.90641
\(306\) 0 0
\(307\) 17.7964 1.01569 0.507847 0.861447i \(-0.330441\pi\)
0.507847 + 0.861447i \(0.330441\pi\)
\(308\) 0 0
\(309\) 13.4196 0.763416
\(310\) 0 0
\(311\) 25.9023 1.46878 0.734391 0.678727i \(-0.237468\pi\)
0.734391 + 0.678727i \(0.237468\pi\)
\(312\) 0 0
\(313\) 11.6576 0.658925 0.329463 0.944169i \(-0.393132\pi\)
0.329463 + 0.944169i \(0.393132\pi\)
\(314\) 0 0
\(315\) 25.0610 1.41203
\(316\) 0 0
\(317\) −24.5162 −1.37697 −0.688484 0.725251i \(-0.741724\pi\)
−0.688484 + 0.725251i \(0.741724\pi\)
\(318\) 0 0
\(319\) −4.21301 −0.235883
\(320\) 0 0
\(321\) 6.36910 0.355488
\(322\) 0 0
\(323\) 1.47750 0.0822104
\(324\) 0 0
\(325\) 6.00481 0.333087
\(326\) 0 0
\(327\) 11.2693 0.623195
\(328\) 0 0
\(329\) −57.4174 −3.16553
\(330\) 0 0
\(331\) −0.560641 −0.0308156 −0.0154078 0.999881i \(-0.504905\pi\)
−0.0154078 + 0.999881i \(0.504905\pi\)
\(332\) 0 0
\(333\) −14.6023 −0.800201
\(334\) 0 0
\(335\) −15.2548 −0.833458
\(336\) 0 0
\(337\) −1.26878 −0.0691147 −0.0345573 0.999403i \(-0.511002\pi\)
−0.0345573 + 0.999403i \(0.511002\pi\)
\(338\) 0 0
\(339\) 16.1989 0.879805
\(340\) 0 0
\(341\) 4.72080 0.255645
\(342\) 0 0
\(343\) −24.7653 −1.33720
\(344\) 0 0
\(345\) −0.128262 −0.00690538
\(346\) 0 0
\(347\) −10.4243 −0.559607 −0.279803 0.960057i \(-0.590269\pi\)
−0.279803 + 0.960057i \(0.590269\pi\)
\(348\) 0 0
\(349\) 11.2503 0.602216 0.301108 0.953590i \(-0.402643\pi\)
0.301108 + 0.953590i \(0.402643\pi\)
\(350\) 0 0
\(351\) 11.9355 0.637070
\(352\) 0 0
\(353\) 15.5508 0.827686 0.413843 0.910348i \(-0.364186\pi\)
0.413843 + 0.910348i \(0.364186\pi\)
\(354\) 0 0
\(355\) −39.2819 −2.08487
\(356\) 0 0
\(357\) 1.52993 0.0809727
\(358\) 0 0
\(359\) −29.9534 −1.58088 −0.790440 0.612540i \(-0.790148\pi\)
−0.790440 + 0.612540i \(0.790148\pi\)
\(360\) 0 0
\(361\) −2.06323 −0.108591
\(362\) 0 0
\(363\) 4.13154 0.216849
\(364\) 0 0
\(365\) 27.3860 1.43345
\(366\) 0 0
\(367\) −5.19537 −0.271196 −0.135598 0.990764i \(-0.543296\pi\)
−0.135598 + 0.990764i \(0.543296\pi\)
\(368\) 0 0
\(369\) 4.83690 0.251799
\(370\) 0 0
\(371\) −16.4546 −0.854278
\(372\) 0 0
\(373\) −25.3415 −1.31213 −0.656066 0.754704i \(-0.727781\pi\)
−0.656066 + 0.754704i \(0.727781\pi\)
\(374\) 0 0
\(375\) 6.68494 0.345209
\(376\) 0 0
\(377\) 3.97513 0.204729
\(378\) 0 0
\(379\) 5.82446 0.299182 0.149591 0.988748i \(-0.452204\pi\)
0.149591 + 0.988748i \(0.452204\pi\)
\(380\) 0 0
\(381\) 9.97535 0.511053
\(382\) 0 0
\(383\) 25.4681 1.30136 0.650678 0.759353i \(-0.274485\pi\)
0.650678 + 0.759353i \(0.274485\pi\)
\(384\) 0 0
\(385\) 31.3087 1.59564
\(386\) 0 0
\(387\) 1.24180 0.0631240
\(388\) 0 0
\(389\) −30.9788 −1.57069 −0.785343 0.619060i \(-0.787514\pi\)
−0.785343 + 0.619060i \(0.787514\pi\)
\(390\) 0 0
\(391\) 0.0175159 0.000885818 0
\(392\) 0 0
\(393\) 10.3170 0.520424
\(394\) 0 0
\(395\) −14.2841 −0.718711
\(396\) 0 0
\(397\) −17.2785 −0.867186 −0.433593 0.901109i \(-0.642754\pi\)
−0.433593 + 0.901109i \(0.642754\pi\)
\(398\) 0 0
\(399\) 17.5378 0.877988
\(400\) 0 0
\(401\) −34.6417 −1.72992 −0.864962 0.501837i \(-0.832658\pi\)
−0.864962 + 0.501837i \(0.832658\pi\)
\(402\) 0 0
\(403\) −4.45424 −0.221881
\(404\) 0 0
\(405\) 4.14485 0.205959
\(406\) 0 0
\(407\) −18.2426 −0.904253
\(408\) 0 0
\(409\) −9.92750 −0.490883 −0.245442 0.969411i \(-0.578933\pi\)
−0.245442 + 0.969411i \(0.578933\pi\)
\(410\) 0 0
\(411\) −7.95501 −0.392392
\(412\) 0 0
\(413\) −3.44918 −0.169723
\(414\) 0 0
\(415\) −31.7913 −1.56057
\(416\) 0 0
\(417\) 3.71955 0.182147
\(418\) 0 0
\(419\) 23.4441 1.14532 0.572660 0.819793i \(-0.305912\pi\)
0.572660 + 0.819793i \(0.305912\pi\)
\(420\) 0 0
\(421\) 18.9664 0.924364 0.462182 0.886785i \(-0.347067\pi\)
0.462182 + 0.886785i \(0.347067\pi\)
\(422\) 0 0
\(423\) −26.8917 −1.30752
\(424\) 0 0
\(425\) 0.882156 0.0427908
\(426\) 0 0
\(427\) 53.9696 2.61177
\(428\) 0 0
\(429\) 6.09350 0.294197
\(430\) 0 0
\(431\) 9.35894 0.450804 0.225402 0.974266i \(-0.427630\pi\)
0.225402 + 0.974266i \(0.427630\pi\)
\(432\) 0 0
\(433\) 8.91181 0.428274 0.214137 0.976804i \(-0.431306\pi\)
0.214137 + 0.976804i \(0.431306\pi\)
\(434\) 0 0
\(435\) −4.27623 −0.205030
\(436\) 0 0
\(437\) 0.200787 0.00960493
\(438\) 0 0
\(439\) −2.80387 −0.133821 −0.0669107 0.997759i \(-0.521314\pi\)
−0.0669107 + 0.997759i \(0.521314\pi\)
\(440\) 0 0
\(441\) −26.1114 −1.24340
\(442\) 0 0
\(443\) −31.4842 −1.49586 −0.747931 0.663777i \(-0.768952\pi\)
−0.747931 + 0.663777i \(0.768952\pi\)
\(444\) 0 0
\(445\) 36.8294 1.74588
\(446\) 0 0
\(447\) −19.7365 −0.933503
\(448\) 0 0
\(449\) 2.79800 0.132046 0.0660230 0.997818i \(-0.478969\pi\)
0.0660230 + 0.997818i \(0.478969\pi\)
\(450\) 0 0
\(451\) 6.04273 0.284541
\(452\) 0 0
\(453\) −5.49392 −0.258127
\(454\) 0 0
\(455\) −29.5408 −1.38490
\(456\) 0 0
\(457\) −29.6301 −1.38604 −0.693020 0.720919i \(-0.743720\pi\)
−0.693020 + 0.720919i \(0.743720\pi\)
\(458\) 0 0
\(459\) 1.75342 0.0818427
\(460\) 0 0
\(461\) 28.4306 1.32415 0.662074 0.749439i \(-0.269677\pi\)
0.662074 + 0.749439i \(0.269677\pi\)
\(462\) 0 0
\(463\) −9.60304 −0.446291 −0.223146 0.974785i \(-0.571633\pi\)
−0.223146 + 0.974785i \(0.571633\pi\)
\(464\) 0 0
\(465\) 4.79163 0.222207
\(466\) 0 0
\(467\) −24.5788 −1.13737 −0.568685 0.822555i \(-0.692548\pi\)
−0.568685 + 0.822555i \(0.692548\pi\)
\(468\) 0 0
\(469\) 24.7280 1.14183
\(470\) 0 0
\(471\) −8.93814 −0.411848
\(472\) 0 0
\(473\) 1.55137 0.0713322
\(474\) 0 0
\(475\) 10.1122 0.463982
\(476\) 0 0
\(477\) −7.70656 −0.352859
\(478\) 0 0
\(479\) 22.4632 1.02637 0.513186 0.858278i \(-0.328465\pi\)
0.513186 + 0.858278i \(0.328465\pi\)
\(480\) 0 0
\(481\) 17.2126 0.784825
\(482\) 0 0
\(483\) 0.207912 0.00946032
\(484\) 0 0
\(485\) −17.1338 −0.778005
\(486\) 0 0
\(487\) 23.4568 1.06293 0.531465 0.847081i \(-0.321642\pi\)
0.531465 + 0.847081i \(0.321642\pi\)
\(488\) 0 0
\(489\) 0.683043 0.0308883
\(490\) 0 0
\(491\) 18.3499 0.828119 0.414059 0.910250i \(-0.364111\pi\)
0.414059 + 0.910250i \(0.364111\pi\)
\(492\) 0 0
\(493\) 0.583978 0.0263011
\(494\) 0 0
\(495\) 14.6635 0.659077
\(496\) 0 0
\(497\) 63.6759 2.85625
\(498\) 0 0
\(499\) 28.9004 1.29376 0.646880 0.762592i \(-0.276074\pi\)
0.646880 + 0.762592i \(0.276074\pi\)
\(500\) 0 0
\(501\) −1.25287 −0.0559740
\(502\) 0 0
\(503\) −24.5369 −1.09404 −0.547022 0.837118i \(-0.684239\pi\)
−0.547022 + 0.837118i \(0.684239\pi\)
\(504\) 0 0
\(505\) −14.7061 −0.654412
\(506\) 0 0
\(507\) 6.76566 0.300473
\(508\) 0 0
\(509\) 28.2975 1.25426 0.627132 0.778913i \(-0.284228\pi\)
0.627132 + 0.778913i \(0.284228\pi\)
\(510\) 0 0
\(511\) −44.3926 −1.96381
\(512\) 0 0
\(513\) 20.0997 0.887422
\(514\) 0 0
\(515\) −38.0659 −1.67739
\(516\) 0 0
\(517\) −33.5957 −1.47754
\(518\) 0 0
\(519\) 13.9983 0.614457
\(520\) 0 0
\(521\) −34.1186 −1.49476 −0.747381 0.664395i \(-0.768689\pi\)
−0.747381 + 0.664395i \(0.768689\pi\)
\(522\) 0 0
\(523\) 36.0230 1.57518 0.787588 0.616202i \(-0.211330\pi\)
0.787588 + 0.616202i \(0.211330\pi\)
\(524\) 0 0
\(525\) 10.4711 0.456996
\(526\) 0 0
\(527\) −0.654364 −0.0285045
\(528\) 0 0
\(529\) −22.9976 −0.999897
\(530\) 0 0
\(531\) −1.61544 −0.0701040
\(532\) 0 0
\(533\) −5.70153 −0.246961
\(534\) 0 0
\(535\) −18.0665 −0.781082
\(536\) 0 0
\(537\) 24.5014 1.05731
\(538\) 0 0
\(539\) −32.6209 −1.40508
\(540\) 0 0
\(541\) −5.10069 −0.219296 −0.109648 0.993970i \(-0.534972\pi\)
−0.109648 + 0.993970i \(0.534972\pi\)
\(542\) 0 0
\(543\) 17.4969 0.750863
\(544\) 0 0
\(545\) −31.9664 −1.36929
\(546\) 0 0
\(547\) −13.3585 −0.571169 −0.285584 0.958354i \(-0.592188\pi\)
−0.285584 + 0.958354i \(0.592188\pi\)
\(548\) 0 0
\(549\) 25.2769 1.07879
\(550\) 0 0
\(551\) 6.69421 0.285183
\(552\) 0 0
\(553\) 23.1545 0.984630
\(554\) 0 0
\(555\) −18.5164 −0.785975
\(556\) 0 0
\(557\) −35.8853 −1.52051 −0.760255 0.649625i \(-0.774926\pi\)
−0.760255 + 0.649625i \(0.774926\pi\)
\(558\) 0 0
\(559\) −1.46377 −0.0619111
\(560\) 0 0
\(561\) 0.895185 0.0377947
\(562\) 0 0
\(563\) −12.3579 −0.520822 −0.260411 0.965498i \(-0.583858\pi\)
−0.260411 + 0.965498i \(0.583858\pi\)
\(564\) 0 0
\(565\) −45.9496 −1.93311
\(566\) 0 0
\(567\) −6.71879 −0.282163
\(568\) 0 0
\(569\) −15.4665 −0.648389 −0.324194 0.945990i \(-0.605093\pi\)
−0.324194 + 0.945990i \(0.605093\pi\)
\(570\) 0 0
\(571\) 13.4153 0.561412 0.280706 0.959794i \(-0.409431\pi\)
0.280706 + 0.959794i \(0.409431\pi\)
\(572\) 0 0
\(573\) 18.2337 0.761725
\(574\) 0 0
\(575\) 0.119881 0.00499940
\(576\) 0 0
\(577\) −9.17308 −0.381880 −0.190940 0.981602i \(-0.561154\pi\)
−0.190940 + 0.981602i \(0.561154\pi\)
\(578\) 0 0
\(579\) 3.81413 0.158510
\(580\) 0 0
\(581\) 51.5337 2.13798
\(582\) 0 0
\(583\) −9.62778 −0.398742
\(584\) 0 0
\(585\) −13.8356 −0.572030
\(586\) 0 0
\(587\) 35.6720 1.47234 0.736170 0.676796i \(-0.236632\pi\)
0.736170 + 0.676796i \(0.236632\pi\)
\(588\) 0 0
\(589\) −7.50104 −0.309075
\(590\) 0 0
\(591\) 1.39327 0.0573114
\(592\) 0 0
\(593\) 14.7902 0.607361 0.303681 0.952774i \(-0.401784\pi\)
0.303681 + 0.952774i \(0.401784\pi\)
\(594\) 0 0
\(595\) −4.33979 −0.177914
\(596\) 0 0
\(597\) −10.9377 −0.447649
\(598\) 0 0
\(599\) −11.7824 −0.481416 −0.240708 0.970598i \(-0.577380\pi\)
−0.240708 + 0.970598i \(0.577380\pi\)
\(600\) 0 0
\(601\) 21.8868 0.892783 0.446391 0.894838i \(-0.352709\pi\)
0.446391 + 0.894838i \(0.352709\pi\)
\(602\) 0 0
\(603\) 11.5814 0.471633
\(604\) 0 0
\(605\) −11.7195 −0.476464
\(606\) 0 0
\(607\) −38.8295 −1.57604 −0.788020 0.615650i \(-0.788894\pi\)
−0.788020 + 0.615650i \(0.788894\pi\)
\(608\) 0 0
\(609\) 6.93176 0.280889
\(610\) 0 0
\(611\) 31.6987 1.28239
\(612\) 0 0
\(613\) −8.98728 −0.362993 −0.181496 0.983392i \(-0.558094\pi\)
−0.181496 + 0.983392i \(0.558094\pi\)
\(614\) 0 0
\(615\) 6.13340 0.247323
\(616\) 0 0
\(617\) −27.9125 −1.12371 −0.561857 0.827234i \(-0.689913\pi\)
−0.561857 + 0.827234i \(0.689913\pi\)
\(618\) 0 0
\(619\) −30.7965 −1.23782 −0.618909 0.785463i \(-0.712425\pi\)
−0.618909 + 0.785463i \(0.712425\pi\)
\(620\) 0 0
\(621\) 0.238283 0.00956197
\(622\) 0 0
\(623\) −59.7003 −2.39184
\(624\) 0 0
\(625\) −31.2482 −1.24993
\(626\) 0 0
\(627\) 10.2616 0.409809
\(628\) 0 0
\(629\) 2.52866 0.100824
\(630\) 0 0
\(631\) 20.0024 0.796282 0.398141 0.917324i \(-0.369655\pi\)
0.398141 + 0.917324i \(0.369655\pi\)
\(632\) 0 0
\(633\) 1.46546 0.0582469
\(634\) 0 0
\(635\) −28.2959 −1.12289
\(636\) 0 0
\(637\) 30.7790 1.21951
\(638\) 0 0
\(639\) 29.8229 1.17977
\(640\) 0 0
\(641\) −2.52474 −0.0997212 −0.0498606 0.998756i \(-0.515878\pi\)
−0.0498606 + 0.998756i \(0.515878\pi\)
\(642\) 0 0
\(643\) −26.6427 −1.05069 −0.525343 0.850890i \(-0.676063\pi\)
−0.525343 + 0.850890i \(0.676063\pi\)
\(644\) 0 0
\(645\) 1.57465 0.0620018
\(646\) 0 0
\(647\) 21.1454 0.831312 0.415656 0.909522i \(-0.363552\pi\)
0.415656 + 0.909522i \(0.363552\pi\)
\(648\) 0 0
\(649\) −2.01816 −0.0792198
\(650\) 0 0
\(651\) −7.76723 −0.304422
\(652\) 0 0
\(653\) −28.1936 −1.10330 −0.551650 0.834076i \(-0.686002\pi\)
−0.551650 + 0.834076i \(0.686002\pi\)
\(654\) 0 0
\(655\) −29.2651 −1.14348
\(656\) 0 0
\(657\) −20.7914 −0.811151
\(658\) 0 0
\(659\) −11.2653 −0.438835 −0.219418 0.975631i \(-0.570416\pi\)
−0.219418 + 0.975631i \(0.570416\pi\)
\(660\) 0 0
\(661\) −6.65340 −0.258787 −0.129394 0.991593i \(-0.541303\pi\)
−0.129394 + 0.991593i \(0.541303\pi\)
\(662\) 0 0
\(663\) −0.844639 −0.0328030
\(664\) 0 0
\(665\) −49.7474 −1.92912
\(666\) 0 0
\(667\) 0.0793604 0.00307285
\(668\) 0 0
\(669\) 22.4488 0.867919
\(670\) 0 0
\(671\) 31.5783 1.21907
\(672\) 0 0
\(673\) −41.0956 −1.58412 −0.792059 0.610444i \(-0.790991\pi\)
−0.792059 + 0.610444i \(0.790991\pi\)
\(674\) 0 0
\(675\) 12.0007 0.461906
\(676\) 0 0
\(677\) −42.8256 −1.64592 −0.822960 0.568099i \(-0.807679\pi\)
−0.822960 + 0.568099i \(0.807679\pi\)
\(678\) 0 0
\(679\) 27.7738 1.06586
\(680\) 0 0
\(681\) 1.63944 0.0628235
\(682\) 0 0
\(683\) −4.31978 −0.165292 −0.0826459 0.996579i \(-0.526337\pi\)
−0.0826459 + 0.996579i \(0.526337\pi\)
\(684\) 0 0
\(685\) 22.5651 0.862167
\(686\) 0 0
\(687\) −19.1600 −0.731000
\(688\) 0 0
\(689\) 9.08415 0.346079
\(690\) 0 0
\(691\) 20.9671 0.797626 0.398813 0.917032i \(-0.369422\pi\)
0.398813 + 0.917032i \(0.369422\pi\)
\(692\) 0 0
\(693\) −23.7696 −0.902931
\(694\) 0 0
\(695\) −10.5508 −0.400215
\(696\) 0 0
\(697\) −0.837600 −0.0317264
\(698\) 0 0
\(699\) −17.0983 −0.646717
\(700\) 0 0
\(701\) 7.59617 0.286903 0.143452 0.989657i \(-0.454180\pi\)
0.143452 + 0.989657i \(0.454180\pi\)
\(702\) 0 0
\(703\) 28.9863 1.09324
\(704\) 0 0
\(705\) −34.0998 −1.28427
\(706\) 0 0
\(707\) 23.8385 0.896539
\(708\) 0 0
\(709\) −13.0690 −0.490816 −0.245408 0.969420i \(-0.578922\pi\)
−0.245408 + 0.969420i \(0.578922\pi\)
\(710\) 0 0
\(711\) 10.8445 0.406701
\(712\) 0 0
\(713\) −0.0889255 −0.00333028
\(714\) 0 0
\(715\) −17.2847 −0.646412
\(716\) 0 0
\(717\) −5.67235 −0.211838
\(718\) 0 0
\(719\) −26.7304 −0.996876 −0.498438 0.866925i \(-0.666093\pi\)
−0.498438 + 0.866925i \(0.666093\pi\)
\(720\) 0 0
\(721\) 61.7048 2.29801
\(722\) 0 0
\(723\) −27.5797 −1.02570
\(724\) 0 0
\(725\) 3.99683 0.148439
\(726\) 0 0
\(727\) −43.7784 −1.62365 −0.811826 0.583899i \(-0.801526\pi\)
−0.811826 + 0.583899i \(0.801526\pi\)
\(728\) 0 0
\(729\) 10.9586 0.405875
\(730\) 0 0
\(731\) −0.215040 −0.00795356
\(732\) 0 0
\(733\) 5.89844 0.217864 0.108932 0.994049i \(-0.465257\pi\)
0.108932 + 0.994049i \(0.465257\pi\)
\(734\) 0 0
\(735\) −33.1104 −1.22129
\(736\) 0 0
\(737\) 14.4687 0.532960
\(738\) 0 0
\(739\) 11.2819 0.415010 0.207505 0.978234i \(-0.433466\pi\)
0.207505 + 0.978234i \(0.433466\pi\)
\(740\) 0 0
\(741\) −9.68218 −0.355684
\(742\) 0 0
\(743\) 2.51753 0.0923591 0.0461796 0.998933i \(-0.485295\pi\)
0.0461796 + 0.998933i \(0.485295\pi\)
\(744\) 0 0
\(745\) 55.9842 2.05110
\(746\) 0 0
\(747\) 24.1360 0.883090
\(748\) 0 0
\(749\) 29.2857 1.07008
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −11.5444 −0.420701
\(754\) 0 0
\(755\) 15.5840 0.567159
\(756\) 0 0
\(757\) −17.9539 −0.652545 −0.326272 0.945276i \(-0.605793\pi\)
−0.326272 + 0.945276i \(0.605793\pi\)
\(758\) 0 0
\(759\) 0.121652 0.00441569
\(760\) 0 0
\(761\) 20.3575 0.737957 0.368979 0.929438i \(-0.379708\pi\)
0.368979 + 0.929438i \(0.379708\pi\)
\(762\) 0 0
\(763\) 51.8174 1.87592
\(764\) 0 0
\(765\) −2.03256 −0.0734873
\(766\) 0 0
\(767\) 1.90421 0.0687570
\(768\) 0 0
\(769\) −23.5643 −0.849750 −0.424875 0.905252i \(-0.639682\pi\)
−0.424875 + 0.905252i \(0.639682\pi\)
\(770\) 0 0
\(771\) 18.7490 0.675228
\(772\) 0 0
\(773\) 24.7255 0.889315 0.444658 0.895701i \(-0.353325\pi\)
0.444658 + 0.895701i \(0.353325\pi\)
\(774\) 0 0
\(775\) −4.47856 −0.160875
\(776\) 0 0
\(777\) 30.0150 1.07678
\(778\) 0 0
\(779\) −9.60150 −0.344010
\(780\) 0 0
\(781\) 37.2576 1.33318
\(782\) 0 0
\(783\) 7.94433 0.283907
\(784\) 0 0
\(785\) 25.3538 0.904916
\(786\) 0 0
\(787\) −15.8678 −0.565627 −0.282814 0.959175i \(-0.591268\pi\)
−0.282814 + 0.959175i \(0.591268\pi\)
\(788\) 0 0
\(789\) −12.1122 −0.431207
\(790\) 0 0
\(791\) 74.4842 2.64835
\(792\) 0 0
\(793\) −29.7953 −1.05806
\(794\) 0 0
\(795\) −9.77225 −0.346586
\(796\) 0 0
\(797\) 26.6301 0.943287 0.471643 0.881789i \(-0.343661\pi\)
0.471643 + 0.881789i \(0.343661\pi\)
\(798\) 0 0
\(799\) 4.65680 0.164746
\(800\) 0 0
\(801\) −27.9609 −0.987950
\(802\) 0 0
\(803\) −25.9747 −0.916627
\(804\) 0 0
\(805\) −0.589760 −0.0207863
\(806\) 0 0
\(807\) 25.5729 0.900210
\(808\) 0 0
\(809\) −18.5436 −0.651957 −0.325978 0.945377i \(-0.605694\pi\)
−0.325978 + 0.945377i \(0.605694\pi\)
\(810\) 0 0
\(811\) −29.6575 −1.04142 −0.520708 0.853735i \(-0.674332\pi\)
−0.520708 + 0.853735i \(0.674332\pi\)
\(812\) 0 0
\(813\) −24.9664 −0.875611
\(814\) 0 0
\(815\) −1.93751 −0.0678680
\(816\) 0 0
\(817\) −2.46503 −0.0862405
\(818\) 0 0
\(819\) 22.4274 0.783678
\(820\) 0 0
\(821\) 2.21087 0.0771599 0.0385799 0.999256i \(-0.487717\pi\)
0.0385799 + 0.999256i \(0.487717\pi\)
\(822\) 0 0
\(823\) −33.1404 −1.15520 −0.577601 0.816319i \(-0.696011\pi\)
−0.577601 + 0.816319i \(0.696011\pi\)
\(824\) 0 0
\(825\) 6.12677 0.213307
\(826\) 0 0
\(827\) −15.0829 −0.524485 −0.262243 0.965002i \(-0.584462\pi\)
−0.262243 + 0.965002i \(0.584462\pi\)
\(828\) 0 0
\(829\) −21.8670 −0.759473 −0.379736 0.925095i \(-0.623985\pi\)
−0.379736 + 0.925095i \(0.623985\pi\)
\(830\) 0 0
\(831\) 3.01027 0.104425
\(832\) 0 0
\(833\) 4.52168 0.156667
\(834\) 0 0
\(835\) 3.55387 0.122987
\(836\) 0 0
\(837\) −8.90184 −0.307693
\(838\) 0 0
\(839\) −47.4485 −1.63810 −0.819052 0.573719i \(-0.805500\pi\)
−0.819052 + 0.573719i \(0.805500\pi\)
\(840\) 0 0
\(841\) −26.3541 −0.908763
\(842\) 0 0
\(843\) −14.3744 −0.495080
\(844\) 0 0
\(845\) −19.1914 −0.660203
\(846\) 0 0
\(847\) 18.9972 0.652752
\(848\) 0 0
\(849\) −18.9901 −0.651739
\(850\) 0 0
\(851\) 0.343635 0.0117797
\(852\) 0 0
\(853\) 22.3940 0.766758 0.383379 0.923591i \(-0.374760\pi\)
0.383379 + 0.923591i \(0.374760\pi\)
\(854\) 0 0
\(855\) −23.2994 −0.796823
\(856\) 0 0
\(857\) 37.4144 1.27805 0.639025 0.769186i \(-0.279338\pi\)
0.639025 + 0.769186i \(0.279338\pi\)
\(858\) 0 0
\(859\) 49.2153 1.67920 0.839601 0.543203i \(-0.182789\pi\)
0.839601 + 0.543203i \(0.182789\pi\)
\(860\) 0 0
\(861\) −9.94223 −0.338830
\(862\) 0 0
\(863\) −15.8303 −0.538871 −0.269435 0.963018i \(-0.586837\pi\)
−0.269435 + 0.963018i \(0.586837\pi\)
\(864\) 0 0
\(865\) −39.7073 −1.35009
\(866\) 0 0
\(867\) 16.2418 0.551601
\(868\) 0 0
\(869\) 13.5480 0.459585
\(870\) 0 0
\(871\) −13.6517 −0.462570
\(872\) 0 0
\(873\) 13.0080 0.440253
\(874\) 0 0
\(875\) 30.7380 1.03913
\(876\) 0 0
\(877\) −12.3618 −0.417430 −0.208715 0.977977i \(-0.566928\pi\)
−0.208715 + 0.977977i \(0.566928\pi\)
\(878\) 0 0
\(879\) 13.4484 0.453604
\(880\) 0 0
\(881\) 23.4019 0.788431 0.394215 0.919018i \(-0.371016\pi\)
0.394215 + 0.919018i \(0.371016\pi\)
\(882\) 0 0
\(883\) 8.79278 0.295901 0.147950 0.988995i \(-0.452732\pi\)
0.147950 + 0.988995i \(0.452732\pi\)
\(884\) 0 0
\(885\) −2.04845 −0.0688577
\(886\) 0 0
\(887\) −5.37404 −0.180443 −0.0902213 0.995922i \(-0.528757\pi\)
−0.0902213 + 0.995922i \(0.528757\pi\)
\(888\) 0 0
\(889\) 45.8676 1.53835
\(890\) 0 0
\(891\) −3.93126 −0.131702
\(892\) 0 0
\(893\) 53.3814 1.78634
\(894\) 0 0
\(895\) −69.5004 −2.32314
\(896\) 0 0
\(897\) −0.114783 −0.00383249
\(898\) 0 0
\(899\) −2.96476 −0.0988804
\(900\) 0 0
\(901\) 1.33454 0.0444598
\(902\) 0 0
\(903\) −2.55251 −0.0849421
\(904\) 0 0
\(905\) −49.6314 −1.64980
\(906\) 0 0
\(907\) −36.7558 −1.22046 −0.610228 0.792226i \(-0.708922\pi\)
−0.610228 + 0.792226i \(0.708922\pi\)
\(908\) 0 0
\(909\) 11.1649 0.370315
\(910\) 0 0
\(911\) 47.6696 1.57936 0.789682 0.613516i \(-0.210246\pi\)
0.789682 + 0.613516i \(0.210246\pi\)
\(912\) 0 0
\(913\) 30.1530 0.997920
\(914\) 0 0
\(915\) 32.0522 1.05961
\(916\) 0 0
\(917\) 47.4386 1.56656
\(918\) 0 0
\(919\) 2.25440 0.0743657 0.0371828 0.999308i \(-0.488162\pi\)
0.0371828 + 0.999308i \(0.488162\pi\)
\(920\) 0 0
\(921\) −17.1326 −0.564538
\(922\) 0 0
\(923\) −35.1539 −1.15710
\(924\) 0 0
\(925\) 17.3065 0.569036
\(926\) 0 0
\(927\) 28.8997 0.949190
\(928\) 0 0
\(929\) −10.6970 −0.350958 −0.175479 0.984483i \(-0.556147\pi\)
−0.175479 + 0.984483i \(0.556147\pi\)
\(930\) 0 0
\(931\) 51.8325 1.69874
\(932\) 0 0
\(933\) −24.9361 −0.816371
\(934\) 0 0
\(935\) −2.53927 −0.0830429
\(936\) 0 0
\(937\) 11.0765 0.361853 0.180927 0.983497i \(-0.442090\pi\)
0.180927 + 0.983497i \(0.442090\pi\)
\(938\) 0 0
\(939\) −11.2227 −0.366240
\(940\) 0 0
\(941\) −0.169037 −0.00551045 −0.00275523 0.999996i \(-0.500877\pi\)
−0.00275523 + 0.999996i \(0.500877\pi\)
\(942\) 0 0
\(943\) −0.113827 −0.00370670
\(944\) 0 0
\(945\) −59.0376 −1.92049
\(946\) 0 0
\(947\) 49.8062 1.61848 0.809241 0.587476i \(-0.199879\pi\)
0.809241 + 0.587476i \(0.199879\pi\)
\(948\) 0 0
\(949\) 24.5080 0.795565
\(950\) 0 0
\(951\) 23.6018 0.765339
\(952\) 0 0
\(953\) 0.922640 0.0298873 0.0149436 0.999888i \(-0.495243\pi\)
0.0149436 + 0.999888i \(0.495243\pi\)
\(954\) 0 0
\(955\) −51.7216 −1.67367
\(956\) 0 0
\(957\) 4.05587 0.131108
\(958\) 0 0
\(959\) −36.5779 −1.18116
\(960\) 0 0
\(961\) −27.6779 −0.892836
\(962\) 0 0
\(963\) 13.7161 0.441995
\(964\) 0 0
\(965\) −10.8191 −0.348280
\(966\) 0 0
\(967\) −7.89127 −0.253766 −0.126883 0.991918i \(-0.540497\pi\)
−0.126883 + 0.991918i \(0.540497\pi\)
\(968\) 0 0
\(969\) −1.42239 −0.0456938
\(970\) 0 0
\(971\) −33.6352 −1.07940 −0.539702 0.841856i \(-0.681463\pi\)
−0.539702 + 0.841856i \(0.681463\pi\)
\(972\) 0 0
\(973\) 17.1028 0.548292
\(974\) 0 0
\(975\) −5.78083 −0.185135
\(976\) 0 0
\(977\) 18.7841 0.600957 0.300479 0.953789i \(-0.402854\pi\)
0.300479 + 0.953789i \(0.402854\pi\)
\(978\) 0 0
\(979\) −34.9315 −1.11641
\(980\) 0 0
\(981\) 24.2689 0.774847
\(982\) 0 0
\(983\) −11.1163 −0.354554 −0.177277 0.984161i \(-0.556729\pi\)
−0.177277 + 0.984161i \(0.556729\pi\)
\(984\) 0 0
\(985\) −3.95212 −0.125925
\(986\) 0 0
\(987\) 55.2757 1.75945
\(988\) 0 0
\(989\) −0.0292231 −0.000929242 0
\(990\) 0 0
\(991\) 11.3653 0.361030 0.180515 0.983572i \(-0.442224\pi\)
0.180515 + 0.983572i \(0.442224\pi\)
\(992\) 0 0
\(993\) 0.539729 0.0171278
\(994\) 0 0
\(995\) 31.0256 0.983579
\(996\) 0 0
\(997\) −4.96012 −0.157088 −0.0785442 0.996911i \(-0.525027\pi\)
−0.0785442 + 0.996911i \(0.525027\pi\)
\(998\) 0 0
\(999\) 34.3995 1.08835
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.1.19 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.19 44 1.1 even 1 trivial