Properties

Label 8004.2.a.i.1.10
Level $8004$
Weight $2$
Character 8004.1
Self dual yes
Analytic conductor $63.912$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8004.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 5 x^{15} - 43 x^{14} + 234 x^{13} + 634 x^{12} - 4048 x^{11} - 3483 x^{10} + 32512 x^{9} - 137 x^{8} - 121665 x^{7} + 60168 x^{6} + 172218 x^{5} - 138024 x^{4} - 17844 x^{3} + 14352 x^{2} + 72 x - 208\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(1.27509\) of defining polynomial
Character \(\chi\) \(=\) 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.27509 q^{5} +1.05879 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.27509 q^{5} +1.05879 q^{7} +1.00000 q^{9} +2.86975 q^{11} -0.442370 q^{13} -1.27509 q^{15} +7.11949 q^{17} +5.55811 q^{19} -1.05879 q^{21} +1.00000 q^{23} -3.37415 q^{25} -1.00000 q^{27} +1.00000 q^{29} +9.86978 q^{31} -2.86975 q^{33} +1.35005 q^{35} +3.13742 q^{37} +0.442370 q^{39} +0.570057 q^{41} +3.31512 q^{43} +1.27509 q^{45} +7.62112 q^{47} -5.87896 q^{49} -7.11949 q^{51} -0.0892956 q^{53} +3.65919 q^{55} -5.55811 q^{57} -7.70376 q^{59} +0.605364 q^{61} +1.05879 q^{63} -0.564061 q^{65} -2.08669 q^{67} -1.00000 q^{69} -9.62182 q^{71} +9.39503 q^{73} +3.37415 q^{75} +3.03847 q^{77} -4.40635 q^{79} +1.00000 q^{81} -11.8541 q^{83} +9.07799 q^{85} -1.00000 q^{87} -15.9142 q^{89} -0.468378 q^{91} -9.86978 q^{93} +7.08708 q^{95} +1.77186 q^{97} +2.86975 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{3} + 5q^{5} - 4q^{7} + 16q^{9} + O(q^{10}) \) \( 16q - 16q^{3} + 5q^{5} - 4q^{7} + 16q^{9} + 5q^{11} + 8q^{13} - 5q^{15} + 7q^{17} + q^{19} + 4q^{21} + 16q^{23} + 31q^{25} - 16q^{27} + 16q^{29} - 2q^{31} - 5q^{33} + 5q^{35} + 14q^{37} - 8q^{39} - q^{41} - 13q^{43} + 5q^{45} - 4q^{47} + 30q^{49} - 7q^{51} + 19q^{53} - 37q^{55} - q^{57} + 12q^{59} + 21q^{61} - 4q^{63} + 26q^{65} - 11q^{67} - 16q^{69} + 7q^{71} - 13q^{73} - 31q^{75} + 4q^{77} - 18q^{79} + 16q^{81} + 25q^{83} + 48q^{85} - 16q^{87} + 12q^{89} - 11q^{91} + 2q^{93} - q^{95} + 5q^{97} + 5q^{99} + O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 1.27509 0.570237 0.285119 0.958492i \(-0.407967\pi\)
0.285119 + 0.958492i \(0.407967\pi\)
\(6\) 0 0
\(7\) 1.05879 0.400186 0.200093 0.979777i \(-0.435876\pi\)
0.200093 + 0.979777i \(0.435876\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.86975 0.865263 0.432631 0.901571i \(-0.357585\pi\)
0.432631 + 0.901571i \(0.357585\pi\)
\(12\) 0 0
\(13\) −0.442370 −0.122691 −0.0613457 0.998117i \(-0.519539\pi\)
−0.0613457 + 0.998117i \(0.519539\pi\)
\(14\) 0 0
\(15\) −1.27509 −0.329227
\(16\) 0 0
\(17\) 7.11949 1.72673 0.863366 0.504579i \(-0.168352\pi\)
0.863366 + 0.504579i \(0.168352\pi\)
\(18\) 0 0
\(19\) 5.55811 1.27512 0.637559 0.770402i \(-0.279944\pi\)
0.637559 + 0.770402i \(0.279944\pi\)
\(20\) 0 0
\(21\) −1.05879 −0.231047
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −3.37415 −0.674830
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 9.86978 1.77266 0.886332 0.463050i \(-0.153245\pi\)
0.886332 + 0.463050i \(0.153245\pi\)
\(32\) 0 0
\(33\) −2.86975 −0.499560
\(34\) 0 0
\(35\) 1.35005 0.228201
\(36\) 0 0
\(37\) 3.13742 0.515789 0.257894 0.966173i \(-0.416971\pi\)
0.257894 + 0.966173i \(0.416971\pi\)
\(38\) 0 0
\(39\) 0.442370 0.0708359
\(40\) 0 0
\(41\) 0.570057 0.0890280 0.0445140 0.999009i \(-0.485826\pi\)
0.0445140 + 0.999009i \(0.485826\pi\)
\(42\) 0 0
\(43\) 3.31512 0.505551 0.252775 0.967525i \(-0.418657\pi\)
0.252775 + 0.967525i \(0.418657\pi\)
\(44\) 0 0
\(45\) 1.27509 0.190079
\(46\) 0 0
\(47\) 7.62112 1.11166 0.555828 0.831298i \(-0.312401\pi\)
0.555828 + 0.831298i \(0.312401\pi\)
\(48\) 0 0
\(49\) −5.87896 −0.839851
\(50\) 0 0
\(51\) −7.11949 −0.996929
\(52\) 0 0
\(53\) −0.0892956 −0.0122657 −0.00613285 0.999981i \(-0.501952\pi\)
−0.00613285 + 0.999981i \(0.501952\pi\)
\(54\) 0 0
\(55\) 3.65919 0.493405
\(56\) 0 0
\(57\) −5.55811 −0.736189
\(58\) 0 0
\(59\) −7.70376 −1.00294 −0.501472 0.865174i \(-0.667208\pi\)
−0.501472 + 0.865174i \(0.667208\pi\)
\(60\) 0 0
\(61\) 0.605364 0.0775089 0.0387544 0.999249i \(-0.487661\pi\)
0.0387544 + 0.999249i \(0.487661\pi\)
\(62\) 0 0
\(63\) 1.05879 0.133395
\(64\) 0 0
\(65\) −0.564061 −0.0699632
\(66\) 0 0
\(67\) −2.08669 −0.254930 −0.127465 0.991843i \(-0.540684\pi\)
−0.127465 + 0.991843i \(0.540684\pi\)
\(68\) 0 0
\(69\) −1.00000 −0.120386
\(70\) 0 0
\(71\) −9.62182 −1.14190 −0.570950 0.820985i \(-0.693425\pi\)
−0.570950 + 0.820985i \(0.693425\pi\)
\(72\) 0 0
\(73\) 9.39503 1.09960 0.549802 0.835295i \(-0.314703\pi\)
0.549802 + 0.835295i \(0.314703\pi\)
\(74\) 0 0
\(75\) 3.37415 0.389613
\(76\) 0 0
\(77\) 3.03847 0.346266
\(78\) 0 0
\(79\) −4.40635 −0.495754 −0.247877 0.968792i \(-0.579733\pi\)
−0.247877 + 0.968792i \(0.579733\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −11.8541 −1.30116 −0.650580 0.759438i \(-0.725474\pi\)
−0.650580 + 0.759438i \(0.725474\pi\)
\(84\) 0 0
\(85\) 9.07799 0.984646
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) −15.9142 −1.68690 −0.843449 0.537209i \(-0.819479\pi\)
−0.843449 + 0.537209i \(0.819479\pi\)
\(90\) 0 0
\(91\) −0.468378 −0.0490993
\(92\) 0 0
\(93\) −9.86978 −1.02345
\(94\) 0 0
\(95\) 7.08708 0.727119
\(96\) 0 0
\(97\) 1.77186 0.179905 0.0899527 0.995946i \(-0.471328\pi\)
0.0899527 + 0.995946i \(0.471328\pi\)
\(98\) 0 0
\(99\) 2.86975 0.288421
\(100\) 0 0
\(101\) 17.1221 1.70371 0.851856 0.523776i \(-0.175477\pi\)
0.851856 + 0.523776i \(0.175477\pi\)
\(102\) 0 0
\(103\) 17.4005 1.71452 0.857262 0.514880i \(-0.172164\pi\)
0.857262 + 0.514880i \(0.172164\pi\)
\(104\) 0 0
\(105\) −1.35005 −0.131752
\(106\) 0 0
\(107\) −0.113485 −0.0109710 −0.00548548 0.999985i \(-0.501746\pi\)
−0.00548548 + 0.999985i \(0.501746\pi\)
\(108\) 0 0
\(109\) 3.63082 0.347769 0.173885 0.984766i \(-0.444368\pi\)
0.173885 + 0.984766i \(0.444368\pi\)
\(110\) 0 0
\(111\) −3.13742 −0.297791
\(112\) 0 0
\(113\) 4.66039 0.438413 0.219206 0.975679i \(-0.429653\pi\)
0.219206 + 0.975679i \(0.429653\pi\)
\(114\) 0 0
\(115\) 1.27509 0.118903
\(116\) 0 0
\(117\) −0.442370 −0.0408971
\(118\) 0 0
\(119\) 7.53806 0.691013
\(120\) 0 0
\(121\) −2.76453 −0.251321
\(122\) 0 0
\(123\) −0.570057 −0.0514003
\(124\) 0 0
\(125\) −10.6778 −0.955050
\(126\) 0 0
\(127\) 3.38250 0.300149 0.150074 0.988675i \(-0.452049\pi\)
0.150074 + 0.988675i \(0.452049\pi\)
\(128\) 0 0
\(129\) −3.31512 −0.291880
\(130\) 0 0
\(131\) 5.55867 0.485663 0.242832 0.970068i \(-0.421924\pi\)
0.242832 + 0.970068i \(0.421924\pi\)
\(132\) 0 0
\(133\) 5.88488 0.510284
\(134\) 0 0
\(135\) −1.27509 −0.109742
\(136\) 0 0
\(137\) −2.15471 −0.184090 −0.0920448 0.995755i \(-0.529340\pi\)
−0.0920448 + 0.995755i \(0.529340\pi\)
\(138\) 0 0
\(139\) −15.7527 −1.33613 −0.668065 0.744103i \(-0.732877\pi\)
−0.668065 + 0.744103i \(0.732877\pi\)
\(140\) 0 0
\(141\) −7.62112 −0.641814
\(142\) 0 0
\(143\) −1.26949 −0.106160
\(144\) 0 0
\(145\) 1.27509 0.105890
\(146\) 0 0
\(147\) 5.87896 0.484888
\(148\) 0 0
\(149\) 24.0193 1.96774 0.983869 0.178890i \(-0.0572506\pi\)
0.983869 + 0.178890i \(0.0572506\pi\)
\(150\) 0 0
\(151\) −22.3745 −1.82081 −0.910405 0.413719i \(-0.864230\pi\)
−0.910405 + 0.413719i \(0.864230\pi\)
\(152\) 0 0
\(153\) 7.11949 0.575577
\(154\) 0 0
\(155\) 12.5848 1.01084
\(156\) 0 0
\(157\) −6.34045 −0.506023 −0.253011 0.967463i \(-0.581421\pi\)
−0.253011 + 0.967463i \(0.581421\pi\)
\(158\) 0 0
\(159\) 0.0892956 0.00708160
\(160\) 0 0
\(161\) 1.05879 0.0834445
\(162\) 0 0
\(163\) −8.59993 −0.673599 −0.336799 0.941576i \(-0.609344\pi\)
−0.336799 + 0.941576i \(0.609344\pi\)
\(164\) 0 0
\(165\) −3.65919 −0.284867
\(166\) 0 0
\(167\) −16.5821 −1.28316 −0.641582 0.767055i \(-0.721721\pi\)
−0.641582 + 0.767055i \(0.721721\pi\)
\(168\) 0 0
\(169\) −12.8043 −0.984947
\(170\) 0 0
\(171\) 5.55811 0.425039
\(172\) 0 0
\(173\) 16.7748 1.27537 0.637683 0.770299i \(-0.279893\pi\)
0.637683 + 0.770299i \(0.279893\pi\)
\(174\) 0 0
\(175\) −3.57252 −0.270057
\(176\) 0 0
\(177\) 7.70376 0.579050
\(178\) 0 0
\(179\) −20.3735 −1.52279 −0.761395 0.648288i \(-0.775485\pi\)
−0.761395 + 0.648288i \(0.775485\pi\)
\(180\) 0 0
\(181\) 10.7827 0.801471 0.400736 0.916194i \(-0.368755\pi\)
0.400736 + 0.916194i \(0.368755\pi\)
\(182\) 0 0
\(183\) −0.605364 −0.0447498
\(184\) 0 0
\(185\) 4.00049 0.294122
\(186\) 0 0
\(187\) 20.4312 1.49408
\(188\) 0 0
\(189\) −1.05879 −0.0770158
\(190\) 0 0
\(191\) −14.5647 −1.05386 −0.526931 0.849908i \(-0.676657\pi\)
−0.526931 + 0.849908i \(0.676657\pi\)
\(192\) 0 0
\(193\) −26.9558 −1.94032 −0.970160 0.242464i \(-0.922044\pi\)
−0.970160 + 0.242464i \(0.922044\pi\)
\(194\) 0 0
\(195\) 0.564061 0.0403933
\(196\) 0 0
\(197\) 7.37900 0.525732 0.262866 0.964832i \(-0.415332\pi\)
0.262866 + 0.964832i \(0.415332\pi\)
\(198\) 0 0
\(199\) −4.10097 −0.290710 −0.145355 0.989380i \(-0.546432\pi\)
−0.145355 + 0.989380i \(0.546432\pi\)
\(200\) 0 0
\(201\) 2.08669 0.147184
\(202\) 0 0
\(203\) 1.05879 0.0743126
\(204\) 0 0
\(205\) 0.726873 0.0507670
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 15.9504 1.10331
\(210\) 0 0
\(211\) 17.3554 1.19479 0.597397 0.801946i \(-0.296202\pi\)
0.597397 + 0.801946i \(0.296202\pi\)
\(212\) 0 0
\(213\) 9.62182 0.659276
\(214\) 0 0
\(215\) 4.22707 0.288284
\(216\) 0 0
\(217\) 10.4500 0.709395
\(218\) 0 0
\(219\) −9.39503 −0.634857
\(220\) 0 0
\(221\) −3.14945 −0.211855
\(222\) 0 0
\(223\) 13.1742 0.882212 0.441106 0.897455i \(-0.354586\pi\)
0.441106 + 0.897455i \(0.354586\pi\)
\(224\) 0 0
\(225\) −3.37415 −0.224943
\(226\) 0 0
\(227\) −22.4629 −1.49091 −0.745457 0.666554i \(-0.767769\pi\)
−0.745457 + 0.666554i \(0.767769\pi\)
\(228\) 0 0
\(229\) −1.02268 −0.0675808 −0.0337904 0.999429i \(-0.510758\pi\)
−0.0337904 + 0.999429i \(0.510758\pi\)
\(230\) 0 0
\(231\) −3.03847 −0.199917
\(232\) 0 0
\(233\) 8.36599 0.548074 0.274037 0.961719i \(-0.411641\pi\)
0.274037 + 0.961719i \(0.411641\pi\)
\(234\) 0 0
\(235\) 9.71761 0.633907
\(236\) 0 0
\(237\) 4.40635 0.286223
\(238\) 0 0
\(239\) −25.0231 −1.61861 −0.809304 0.587390i \(-0.800156\pi\)
−0.809304 + 0.587390i \(0.800156\pi\)
\(240\) 0 0
\(241\) 7.76619 0.500264 0.250132 0.968212i \(-0.419526\pi\)
0.250132 + 0.968212i \(0.419526\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −7.49620 −0.478914
\(246\) 0 0
\(247\) −2.45874 −0.156446
\(248\) 0 0
\(249\) 11.8541 0.751225
\(250\) 0 0
\(251\) 19.1812 1.21071 0.605354 0.795957i \(-0.293032\pi\)
0.605354 + 0.795957i \(0.293032\pi\)
\(252\) 0 0
\(253\) 2.86975 0.180420
\(254\) 0 0
\(255\) −9.07799 −0.568486
\(256\) 0 0
\(257\) 16.6896 1.04107 0.520533 0.853842i \(-0.325733\pi\)
0.520533 + 0.853842i \(0.325733\pi\)
\(258\) 0 0
\(259\) 3.32187 0.206411
\(260\) 0 0
\(261\) 1.00000 0.0618984
\(262\) 0 0
\(263\) −21.2779 −1.31205 −0.656025 0.754739i \(-0.727763\pi\)
−0.656025 + 0.754739i \(0.727763\pi\)
\(264\) 0 0
\(265\) −0.113860 −0.00699435
\(266\) 0 0
\(267\) 15.9142 0.973931
\(268\) 0 0
\(269\) 15.8508 0.966441 0.483221 0.875499i \(-0.339467\pi\)
0.483221 + 0.875499i \(0.339467\pi\)
\(270\) 0 0
\(271\) 2.60058 0.157974 0.0789869 0.996876i \(-0.474831\pi\)
0.0789869 + 0.996876i \(0.474831\pi\)
\(272\) 0 0
\(273\) 0.468378 0.0283475
\(274\) 0 0
\(275\) −9.68297 −0.583905
\(276\) 0 0
\(277\) −15.4758 −0.929852 −0.464926 0.885350i \(-0.653919\pi\)
−0.464926 + 0.885350i \(0.653919\pi\)
\(278\) 0 0
\(279\) 9.86978 0.590888
\(280\) 0 0
\(281\) 27.1129 1.61742 0.808710 0.588208i \(-0.200166\pi\)
0.808710 + 0.588208i \(0.200166\pi\)
\(282\) 0 0
\(283\) −6.74351 −0.400860 −0.200430 0.979708i \(-0.564234\pi\)
−0.200430 + 0.979708i \(0.564234\pi\)
\(284\) 0 0
\(285\) −7.08708 −0.419803
\(286\) 0 0
\(287\) 0.603572 0.0356277
\(288\) 0 0
\(289\) 33.6872 1.98160
\(290\) 0 0
\(291\) −1.77186 −0.103868
\(292\) 0 0
\(293\) 0.678749 0.0396530 0.0198265 0.999803i \(-0.493689\pi\)
0.0198265 + 0.999803i \(0.493689\pi\)
\(294\) 0 0
\(295\) −9.82298 −0.571916
\(296\) 0 0
\(297\) −2.86975 −0.166520
\(298\) 0 0
\(299\) −0.442370 −0.0255829
\(300\) 0 0
\(301\) 3.51002 0.202314
\(302\) 0 0
\(303\) −17.1221 −0.983639
\(304\) 0 0
\(305\) 0.771893 0.0441984
\(306\) 0 0
\(307\) −19.8221 −1.13131 −0.565654 0.824643i \(-0.691376\pi\)
−0.565654 + 0.824643i \(0.691376\pi\)
\(308\) 0 0
\(309\) −17.4005 −0.989881
\(310\) 0 0
\(311\) 27.9653 1.58577 0.792883 0.609374i \(-0.208579\pi\)
0.792883 + 0.609374i \(0.208579\pi\)
\(312\) 0 0
\(313\) −4.12103 −0.232934 −0.116467 0.993195i \(-0.537157\pi\)
−0.116467 + 0.993195i \(0.537157\pi\)
\(314\) 0 0
\(315\) 1.35005 0.0760669
\(316\) 0 0
\(317\) 1.06358 0.0597366 0.0298683 0.999554i \(-0.490491\pi\)
0.0298683 + 0.999554i \(0.490491\pi\)
\(318\) 0 0
\(319\) 2.86975 0.160675
\(320\) 0 0
\(321\) 0.113485 0.00633409
\(322\) 0 0
\(323\) 39.5709 2.20179
\(324\) 0 0
\(325\) 1.49262 0.0827958
\(326\) 0 0
\(327\) −3.63082 −0.200785
\(328\) 0 0
\(329\) 8.06918 0.444869
\(330\) 0 0
\(331\) 12.6301 0.694211 0.347105 0.937826i \(-0.387165\pi\)
0.347105 + 0.937826i \(0.387165\pi\)
\(332\) 0 0
\(333\) 3.13742 0.171930
\(334\) 0 0
\(335\) −2.66072 −0.145370
\(336\) 0 0
\(337\) 19.6462 1.07020 0.535098 0.844790i \(-0.320275\pi\)
0.535098 + 0.844790i \(0.320275\pi\)
\(338\) 0 0
\(339\) −4.66039 −0.253118
\(340\) 0 0
\(341\) 28.3238 1.53382
\(342\) 0 0
\(343\) −13.6361 −0.736282
\(344\) 0 0
\(345\) −1.27509 −0.0686485
\(346\) 0 0
\(347\) −16.5051 −0.886042 −0.443021 0.896511i \(-0.646093\pi\)
−0.443021 + 0.896511i \(0.646093\pi\)
\(348\) 0 0
\(349\) −6.96572 −0.372867 −0.186433 0.982468i \(-0.559693\pi\)
−0.186433 + 0.982468i \(0.559693\pi\)
\(350\) 0 0
\(351\) 0.442370 0.0236120
\(352\) 0 0
\(353\) −18.6023 −0.990100 −0.495050 0.868864i \(-0.664850\pi\)
−0.495050 + 0.868864i \(0.664850\pi\)
\(354\) 0 0
\(355\) −12.2687 −0.651153
\(356\) 0 0
\(357\) −7.53806 −0.398957
\(358\) 0 0
\(359\) 32.8220 1.73228 0.866138 0.499804i \(-0.166595\pi\)
0.866138 + 0.499804i \(0.166595\pi\)
\(360\) 0 0
\(361\) 11.8926 0.625925
\(362\) 0 0
\(363\) 2.76453 0.145100
\(364\) 0 0
\(365\) 11.9795 0.627035
\(366\) 0 0
\(367\) −6.30126 −0.328923 −0.164462 0.986383i \(-0.552589\pi\)
−0.164462 + 0.986383i \(0.552589\pi\)
\(368\) 0 0
\(369\) 0.570057 0.0296760
\(370\) 0 0
\(371\) −0.0945455 −0.00490856
\(372\) 0 0
\(373\) 8.07809 0.418268 0.209134 0.977887i \(-0.432936\pi\)
0.209134 + 0.977887i \(0.432936\pi\)
\(374\) 0 0
\(375\) 10.6778 0.551398
\(376\) 0 0
\(377\) −0.442370 −0.0227832
\(378\) 0 0
\(379\) 3.83382 0.196930 0.0984651 0.995141i \(-0.468607\pi\)
0.0984651 + 0.995141i \(0.468607\pi\)
\(380\) 0 0
\(381\) −3.38250 −0.173291
\(382\) 0 0
\(383\) 12.7371 0.650833 0.325416 0.945571i \(-0.394496\pi\)
0.325416 + 0.945571i \(0.394496\pi\)
\(384\) 0 0
\(385\) 3.87432 0.197454
\(386\) 0 0
\(387\) 3.31512 0.168517
\(388\) 0 0
\(389\) −5.42536 −0.275077 −0.137538 0.990496i \(-0.543919\pi\)
−0.137538 + 0.990496i \(0.543919\pi\)
\(390\) 0 0
\(391\) 7.11949 0.360048
\(392\) 0 0
\(393\) −5.55867 −0.280398
\(394\) 0 0
\(395\) −5.61849 −0.282697
\(396\) 0 0
\(397\) −36.9473 −1.85433 −0.927166 0.374651i \(-0.877763\pi\)
−0.927166 + 0.374651i \(0.877763\pi\)
\(398\) 0 0
\(399\) −5.88488 −0.294613
\(400\) 0 0
\(401\) 31.3298 1.56454 0.782269 0.622941i \(-0.214062\pi\)
0.782269 + 0.622941i \(0.214062\pi\)
\(402\) 0 0
\(403\) −4.36609 −0.217491
\(404\) 0 0
\(405\) 1.27509 0.0633597
\(406\) 0 0
\(407\) 9.00361 0.446293
\(408\) 0 0
\(409\) 3.22224 0.159329 0.0796646 0.996822i \(-0.474615\pi\)
0.0796646 + 0.996822i \(0.474615\pi\)
\(410\) 0 0
\(411\) 2.15471 0.106284
\(412\) 0 0
\(413\) −8.15668 −0.401364
\(414\) 0 0
\(415\) −15.1151 −0.741969
\(416\) 0 0
\(417\) 15.7527 0.771415
\(418\) 0 0
\(419\) 24.3527 1.18971 0.594854 0.803834i \(-0.297210\pi\)
0.594854 + 0.803834i \(0.297210\pi\)
\(420\) 0 0
\(421\) −25.3720 −1.23655 −0.618277 0.785960i \(-0.712169\pi\)
−0.618277 + 0.785960i \(0.712169\pi\)
\(422\) 0 0
\(423\) 7.62112 0.370552
\(424\) 0 0
\(425\) −24.0222 −1.16525
\(426\) 0 0
\(427\) 0.640954 0.0310179
\(428\) 0 0
\(429\) 1.26949 0.0612917
\(430\) 0 0
\(431\) 3.18144 0.153245 0.0766224 0.997060i \(-0.475586\pi\)
0.0766224 + 0.997060i \(0.475586\pi\)
\(432\) 0 0
\(433\) 37.0333 1.77971 0.889854 0.456246i \(-0.150806\pi\)
0.889854 + 0.456246i \(0.150806\pi\)
\(434\) 0 0
\(435\) −1.27509 −0.0611358
\(436\) 0 0
\(437\) 5.55811 0.265880
\(438\) 0 0
\(439\) 27.5051 1.31275 0.656373 0.754436i \(-0.272090\pi\)
0.656373 + 0.754436i \(0.272090\pi\)
\(440\) 0 0
\(441\) −5.87896 −0.279950
\(442\) 0 0
\(443\) −8.27771 −0.393286 −0.196643 0.980475i \(-0.563004\pi\)
−0.196643 + 0.980475i \(0.563004\pi\)
\(444\) 0 0
\(445\) −20.2920 −0.961932
\(446\) 0 0
\(447\) −24.0193 −1.13607
\(448\) 0 0
\(449\) −32.2605 −1.52247 −0.761234 0.648477i \(-0.775406\pi\)
−0.761234 + 0.648477i \(0.775406\pi\)
\(450\) 0 0
\(451\) 1.63592 0.0770326
\(452\) 0 0
\(453\) 22.3745 1.05124
\(454\) 0 0
\(455\) −0.597223 −0.0279983
\(456\) 0 0
\(457\) −34.4054 −1.60942 −0.804708 0.593671i \(-0.797678\pi\)
−0.804708 + 0.593671i \(0.797678\pi\)
\(458\) 0 0
\(459\) −7.11949 −0.332310
\(460\) 0 0
\(461\) −13.9731 −0.650793 −0.325396 0.945578i \(-0.605498\pi\)
−0.325396 + 0.945578i \(0.605498\pi\)
\(462\) 0 0
\(463\) −21.7584 −1.01120 −0.505600 0.862768i \(-0.668729\pi\)
−0.505600 + 0.862768i \(0.668729\pi\)
\(464\) 0 0
\(465\) −12.5848 −0.583608
\(466\) 0 0
\(467\) 33.0522 1.52948 0.764738 0.644342i \(-0.222869\pi\)
0.764738 + 0.644342i \(0.222869\pi\)
\(468\) 0 0
\(469\) −2.20937 −0.102019
\(470\) 0 0
\(471\) 6.34045 0.292152
\(472\) 0 0
\(473\) 9.51356 0.437434
\(474\) 0 0
\(475\) −18.7539 −0.860487
\(476\) 0 0
\(477\) −0.0892956 −0.00408856
\(478\) 0 0
\(479\) −26.2669 −1.20016 −0.600082 0.799939i \(-0.704865\pi\)
−0.600082 + 0.799939i \(0.704865\pi\)
\(480\) 0 0
\(481\) −1.38790 −0.0632828
\(482\) 0 0
\(483\) −1.05879 −0.0481767
\(484\) 0 0
\(485\) 2.25928 0.102589
\(486\) 0 0
\(487\) −24.6659 −1.11772 −0.558858 0.829263i \(-0.688760\pi\)
−0.558858 + 0.829263i \(0.688760\pi\)
\(488\) 0 0
\(489\) 8.59993 0.388902
\(490\) 0 0
\(491\) 25.5713 1.15402 0.577008 0.816738i \(-0.304220\pi\)
0.577008 + 0.816738i \(0.304220\pi\)
\(492\) 0 0
\(493\) 7.11949 0.320646
\(494\) 0 0
\(495\) 3.65919 0.164468
\(496\) 0 0
\(497\) −10.1875 −0.456972
\(498\) 0 0
\(499\) −21.5606 −0.965185 −0.482593 0.875845i \(-0.660305\pi\)
−0.482593 + 0.875845i \(0.660305\pi\)
\(500\) 0 0
\(501\) 16.5821 0.740835
\(502\) 0 0
\(503\) −5.45317 −0.243145 −0.121572 0.992583i \(-0.538794\pi\)
−0.121572 + 0.992583i \(0.538794\pi\)
\(504\) 0 0
\(505\) 21.8322 0.971520
\(506\) 0 0
\(507\) 12.8043 0.568659
\(508\) 0 0
\(509\) −23.6991 −1.05045 −0.525223 0.850965i \(-0.676018\pi\)
−0.525223 + 0.850965i \(0.676018\pi\)
\(510\) 0 0
\(511\) 9.94738 0.440046
\(512\) 0 0
\(513\) −5.55811 −0.245396
\(514\) 0 0
\(515\) 22.1872 0.977685
\(516\) 0 0
\(517\) 21.8707 0.961874
\(518\) 0 0
\(519\) −16.7748 −0.736332
\(520\) 0 0
\(521\) 38.0359 1.66638 0.833191 0.552986i \(-0.186512\pi\)
0.833191 + 0.552986i \(0.186512\pi\)
\(522\) 0 0
\(523\) 34.1791 1.49455 0.747273 0.664517i \(-0.231363\pi\)
0.747273 + 0.664517i \(0.231363\pi\)
\(524\) 0 0
\(525\) 3.57252 0.155918
\(526\) 0 0
\(527\) 70.2678 3.06091
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −7.70376 −0.334315
\(532\) 0 0
\(533\) −0.252176 −0.0109230
\(534\) 0 0
\(535\) −0.144703 −0.00625605
\(536\) 0 0
\(537\) 20.3735 0.879183
\(538\) 0 0
\(539\) −16.8712 −0.726692
\(540\) 0 0
\(541\) 7.81012 0.335783 0.167892 0.985805i \(-0.446304\pi\)
0.167892 + 0.985805i \(0.446304\pi\)
\(542\) 0 0
\(543\) −10.7827 −0.462730
\(544\) 0 0
\(545\) 4.62961 0.198311
\(546\) 0 0
\(547\) −14.6738 −0.627408 −0.313704 0.949521i \(-0.601570\pi\)
−0.313704 + 0.949521i \(0.601570\pi\)
\(548\) 0 0
\(549\) 0.605364 0.0258363
\(550\) 0 0
\(551\) 5.55811 0.236783
\(552\) 0 0
\(553\) −4.66541 −0.198394
\(554\) 0 0
\(555\) −4.00049 −0.169811
\(556\) 0 0
\(557\) 26.9549 1.14211 0.571057 0.820910i \(-0.306533\pi\)
0.571057 + 0.820910i \(0.306533\pi\)
\(558\) 0 0
\(559\) −1.46651 −0.0620267
\(560\) 0 0
\(561\) −20.4312 −0.862605
\(562\) 0 0
\(563\) −5.18284 −0.218431 −0.109215 0.994018i \(-0.534834\pi\)
−0.109215 + 0.994018i \(0.534834\pi\)
\(564\) 0 0
\(565\) 5.94241 0.249999
\(566\) 0 0
\(567\) 1.05879 0.0444651
\(568\) 0 0
\(569\) 43.1031 1.80697 0.903487 0.428615i \(-0.140998\pi\)
0.903487 + 0.428615i \(0.140998\pi\)
\(570\) 0 0
\(571\) 22.6916 0.949615 0.474808 0.880090i \(-0.342518\pi\)
0.474808 + 0.880090i \(0.342518\pi\)
\(572\) 0 0
\(573\) 14.5647 0.608447
\(574\) 0 0
\(575\) −3.37415 −0.140712
\(576\) 0 0
\(577\) −40.6126 −1.69072 −0.845362 0.534194i \(-0.820615\pi\)
−0.845362 + 0.534194i \(0.820615\pi\)
\(578\) 0 0
\(579\) 26.9558 1.12024
\(580\) 0 0
\(581\) −12.5511 −0.520705
\(582\) 0 0
\(583\) −0.256256 −0.0106130
\(584\) 0 0
\(585\) −0.564061 −0.0233211
\(586\) 0 0
\(587\) −2.01872 −0.0833215 −0.0416608 0.999132i \(-0.513265\pi\)
−0.0416608 + 0.999132i \(0.513265\pi\)
\(588\) 0 0
\(589\) 54.8573 2.26036
\(590\) 0 0
\(591\) −7.37900 −0.303532
\(592\) 0 0
\(593\) 39.5678 1.62486 0.812428 0.583061i \(-0.198145\pi\)
0.812428 + 0.583061i \(0.198145\pi\)
\(594\) 0 0
\(595\) 9.61170 0.394041
\(596\) 0 0
\(597\) 4.10097 0.167841
\(598\) 0 0
\(599\) −28.4345 −1.16180 −0.580902 0.813973i \(-0.697300\pi\)
−0.580902 + 0.813973i \(0.697300\pi\)
\(600\) 0 0
\(601\) 22.3696 0.912474 0.456237 0.889858i \(-0.349197\pi\)
0.456237 + 0.889858i \(0.349197\pi\)
\(602\) 0 0
\(603\) −2.08669 −0.0849766
\(604\) 0 0
\(605\) −3.52502 −0.143312
\(606\) 0 0
\(607\) −13.9477 −0.566119 −0.283059 0.959102i \(-0.591349\pi\)
−0.283059 + 0.959102i \(0.591349\pi\)
\(608\) 0 0
\(609\) −1.05879 −0.0429044
\(610\) 0 0
\(611\) −3.37136 −0.136391
\(612\) 0 0
\(613\) 20.6578 0.834362 0.417181 0.908824i \(-0.363018\pi\)
0.417181 + 0.908824i \(0.363018\pi\)
\(614\) 0 0
\(615\) −0.726873 −0.0293104
\(616\) 0 0
\(617\) 11.9068 0.479348 0.239674 0.970853i \(-0.422959\pi\)
0.239674 + 0.970853i \(0.422959\pi\)
\(618\) 0 0
\(619\) −23.4110 −0.940969 −0.470485 0.882408i \(-0.655921\pi\)
−0.470485 + 0.882408i \(0.655921\pi\)
\(620\) 0 0
\(621\) −1.00000 −0.0401286
\(622\) 0 0
\(623\) −16.8498 −0.675073
\(624\) 0 0
\(625\) 3.25562 0.130225
\(626\) 0 0
\(627\) −15.9504 −0.636997
\(628\) 0 0
\(629\) 22.3368 0.890628
\(630\) 0 0
\(631\) 7.21302 0.287146 0.143573 0.989640i \(-0.454141\pi\)
0.143573 + 0.989640i \(0.454141\pi\)
\(632\) 0 0
\(633\) −17.3554 −0.689815
\(634\) 0 0
\(635\) 4.31299 0.171156
\(636\) 0 0
\(637\) 2.60068 0.103043
\(638\) 0 0
\(639\) −9.62182 −0.380633
\(640\) 0 0
\(641\) 14.3952 0.568577 0.284289 0.958739i \(-0.408243\pi\)
0.284289 + 0.958739i \(0.408243\pi\)
\(642\) 0 0
\(643\) 19.1830 0.756503 0.378251 0.925703i \(-0.376526\pi\)
0.378251 + 0.925703i \(0.376526\pi\)
\(644\) 0 0
\(645\) −4.22707 −0.166441
\(646\) 0 0
\(647\) −10.3169 −0.405599 −0.202799 0.979220i \(-0.565004\pi\)
−0.202799 + 0.979220i \(0.565004\pi\)
\(648\) 0 0
\(649\) −22.1079 −0.867810
\(650\) 0 0
\(651\) −10.4500 −0.409569
\(652\) 0 0
\(653\) −16.5857 −0.649049 −0.324525 0.945877i \(-0.605204\pi\)
−0.324525 + 0.945877i \(0.605204\pi\)
\(654\) 0 0
\(655\) 7.08780 0.276943
\(656\) 0 0
\(657\) 9.39503 0.366535
\(658\) 0 0
\(659\) 27.5776 1.07427 0.537135 0.843496i \(-0.319506\pi\)
0.537135 + 0.843496i \(0.319506\pi\)
\(660\) 0 0
\(661\) 14.0135 0.545060 0.272530 0.962147i \(-0.412140\pi\)
0.272530 + 0.962147i \(0.412140\pi\)
\(662\) 0 0
\(663\) 3.14945 0.122315
\(664\) 0 0
\(665\) 7.50375 0.290983
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 0 0
\(669\) −13.1742 −0.509345
\(670\) 0 0
\(671\) 1.73724 0.0670655
\(672\) 0 0
\(673\) 20.9827 0.808823 0.404411 0.914577i \(-0.367476\pi\)
0.404411 + 0.914577i \(0.367476\pi\)
\(674\) 0 0
\(675\) 3.37415 0.129871
\(676\) 0 0
\(677\) 7.83936 0.301291 0.150646 0.988588i \(-0.451865\pi\)
0.150646 + 0.988588i \(0.451865\pi\)
\(678\) 0 0
\(679\) 1.87603 0.0719955
\(680\) 0 0
\(681\) 22.4629 0.860779
\(682\) 0 0
\(683\) −20.3927 −0.780304 −0.390152 0.920751i \(-0.627578\pi\)
−0.390152 + 0.920751i \(0.627578\pi\)
\(684\) 0 0
\(685\) −2.74745 −0.104975
\(686\) 0 0
\(687\) 1.02268 0.0390178
\(688\) 0 0
\(689\) 0.0395017 0.00150490
\(690\) 0 0
\(691\) −9.09234 −0.345889 −0.172944 0.984932i \(-0.555328\pi\)
−0.172944 + 0.984932i \(0.555328\pi\)
\(692\) 0 0
\(693\) 3.03847 0.115422
\(694\) 0 0
\(695\) −20.0861 −0.761911
\(696\) 0 0
\(697\) 4.05852 0.153727
\(698\) 0 0
\(699\) −8.36599 −0.316431
\(700\) 0 0
\(701\) 6.45943 0.243969 0.121985 0.992532i \(-0.461074\pi\)
0.121985 + 0.992532i \(0.461074\pi\)
\(702\) 0 0
\(703\) 17.4381 0.657691
\(704\) 0 0
\(705\) −9.71761 −0.365986
\(706\) 0 0
\(707\) 18.1287 0.681801
\(708\) 0 0
\(709\) −32.0419 −1.20336 −0.601680 0.798737i \(-0.705502\pi\)
−0.601680 + 0.798737i \(0.705502\pi\)
\(710\) 0 0
\(711\) −4.40635 −0.165251
\(712\) 0 0
\(713\) 9.86978 0.369626
\(714\) 0 0
\(715\) −1.61872 −0.0605365
\(716\) 0 0
\(717\) 25.0231 0.934504
\(718\) 0 0
\(719\) −30.7996 −1.14863 −0.574315 0.818634i \(-0.694732\pi\)
−0.574315 + 0.818634i \(0.694732\pi\)
\(720\) 0 0
\(721\) 18.4235 0.686128
\(722\) 0 0
\(723\) −7.76619 −0.288828
\(724\) 0 0
\(725\) −3.37415 −0.125313
\(726\) 0 0
\(727\) −33.6829 −1.24923 −0.624615 0.780933i \(-0.714744\pi\)
−0.624615 + 0.780933i \(0.714744\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 23.6020 0.872950
\(732\) 0 0
\(733\) 34.2762 1.26602 0.633010 0.774144i \(-0.281819\pi\)
0.633010 + 0.774144i \(0.281819\pi\)
\(734\) 0 0
\(735\) 7.49620 0.276501
\(736\) 0 0
\(737\) −5.98828 −0.220581
\(738\) 0 0
\(739\) 45.5235 1.67461 0.837305 0.546737i \(-0.184130\pi\)
0.837305 + 0.546737i \(0.184130\pi\)
\(740\) 0 0
\(741\) 2.45874 0.0903241
\(742\) 0 0
\(743\) 37.6596 1.38160 0.690799 0.723047i \(-0.257259\pi\)
0.690799 + 0.723047i \(0.257259\pi\)
\(744\) 0 0
\(745\) 30.6267 1.12208
\(746\) 0 0
\(747\) −11.8541 −0.433720
\(748\) 0 0
\(749\) −0.120157 −0.00439042
\(750\) 0 0
\(751\) −15.9505 −0.582043 −0.291022 0.956716i \(-0.593995\pi\)
−0.291022 + 0.956716i \(0.593995\pi\)
\(752\) 0 0
\(753\) −19.1812 −0.699002
\(754\) 0 0
\(755\) −28.5295 −1.03829
\(756\) 0 0
\(757\) −50.1992 −1.82452 −0.912261 0.409610i \(-0.865665\pi\)
−0.912261 + 0.409610i \(0.865665\pi\)
\(758\) 0 0
\(759\) −2.86975 −0.104165
\(760\) 0 0
\(761\) −35.9729 −1.30402 −0.652009 0.758211i \(-0.726074\pi\)
−0.652009 + 0.758211i \(0.726074\pi\)
\(762\) 0 0
\(763\) 3.84428 0.139172
\(764\) 0 0
\(765\) 9.07799 0.328215
\(766\) 0 0
\(767\) 3.40791 0.123053
\(768\) 0 0
\(769\) 36.1256 1.30272 0.651360 0.758768i \(-0.274199\pi\)
0.651360 + 0.758768i \(0.274199\pi\)
\(770\) 0 0
\(771\) −16.6896 −0.601060
\(772\) 0 0
\(773\) 32.1947 1.15796 0.578982 0.815340i \(-0.303450\pi\)
0.578982 + 0.815340i \(0.303450\pi\)
\(774\) 0 0
\(775\) −33.3021 −1.19625
\(776\) 0 0
\(777\) −3.32187 −0.119172
\(778\) 0 0
\(779\) 3.16844 0.113521
\(780\) 0 0
\(781\) −27.6122 −0.988043
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) −8.08463 −0.288553
\(786\) 0 0
\(787\) 23.4543 0.836055 0.418027 0.908434i \(-0.362722\pi\)
0.418027 + 0.908434i \(0.362722\pi\)
\(788\) 0 0
\(789\) 21.2779 0.757512
\(790\) 0 0
\(791\) 4.93438 0.175447
\(792\) 0 0
\(793\) −0.267795 −0.00950967
\(794\) 0 0
\(795\) 0.113860 0.00403819
\(796\) 0 0
\(797\) −8.05138 −0.285194 −0.142597 0.989781i \(-0.545545\pi\)
−0.142597 + 0.989781i \(0.545545\pi\)
\(798\) 0 0
\(799\) 54.2586 1.91953
\(800\) 0 0
\(801\) −15.9142 −0.562299
\(802\) 0 0
\(803\) 26.9614 0.951447
\(804\) 0 0
\(805\) 1.35005 0.0475831
\(806\) 0 0
\(807\) −15.8508 −0.557975
\(808\) 0 0
\(809\) 31.7619 1.11669 0.558345 0.829609i \(-0.311437\pi\)
0.558345 + 0.829609i \(0.311437\pi\)
\(810\) 0 0
\(811\) 56.1925 1.97319 0.986593 0.163202i \(-0.0521823\pi\)
0.986593 + 0.163202i \(0.0521823\pi\)
\(812\) 0 0
\(813\) −2.60058 −0.0912062
\(814\) 0 0
\(815\) −10.9657 −0.384111
\(816\) 0 0
\(817\) 18.4258 0.644636
\(818\) 0 0
\(819\) −0.468378 −0.0163664
\(820\) 0 0
\(821\) 30.5428 1.06595 0.532976 0.846131i \(-0.321074\pi\)
0.532976 + 0.846131i \(0.321074\pi\)
\(822\) 0 0
\(823\) −22.9871 −0.801281 −0.400640 0.916235i \(-0.631212\pi\)
−0.400640 + 0.916235i \(0.631212\pi\)
\(824\) 0 0
\(825\) 9.68297 0.337118
\(826\) 0 0
\(827\) 9.10724 0.316690 0.158345 0.987384i \(-0.449384\pi\)
0.158345 + 0.987384i \(0.449384\pi\)
\(828\) 0 0
\(829\) 29.3903 1.02077 0.510384 0.859947i \(-0.329503\pi\)
0.510384 + 0.859947i \(0.329503\pi\)
\(830\) 0 0
\(831\) 15.4758 0.536850
\(832\) 0 0
\(833\) −41.8552 −1.45020
\(834\) 0 0
\(835\) −21.1437 −0.731707
\(836\) 0 0
\(837\) −9.86978 −0.341149
\(838\) 0 0
\(839\) 57.1937 1.97455 0.987273 0.159036i \(-0.0508386\pi\)
0.987273 + 0.159036i \(0.0508386\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −27.1129 −0.933818
\(844\) 0 0
\(845\) −16.3266 −0.561653
\(846\) 0 0
\(847\) −2.92706 −0.100575
\(848\) 0 0
\(849\) 6.74351 0.231437
\(850\) 0 0
\(851\) 3.13742 0.107549
\(852\) 0 0
\(853\) −21.3277 −0.730248 −0.365124 0.930959i \(-0.618973\pi\)
−0.365124 + 0.930959i \(0.618973\pi\)
\(854\) 0 0
\(855\) 7.08708 0.242373
\(856\) 0 0
\(857\) 4.60456 0.157289 0.0786444 0.996903i \(-0.474941\pi\)
0.0786444 + 0.996903i \(0.474941\pi\)
\(858\) 0 0
\(859\) −3.20234 −0.109262 −0.0546312 0.998507i \(-0.517398\pi\)
−0.0546312 + 0.998507i \(0.517398\pi\)
\(860\) 0 0
\(861\) −0.603572 −0.0205697
\(862\) 0 0
\(863\) −50.0387 −1.70334 −0.851669 0.524080i \(-0.824409\pi\)
−0.851669 + 0.524080i \(0.824409\pi\)
\(864\) 0 0
\(865\) 21.3894 0.727260
\(866\) 0 0
\(867\) −33.6872 −1.14408
\(868\) 0 0
\(869\) −12.6451 −0.428957
\(870\) 0 0
\(871\) 0.923090 0.0312777
\(872\) 0 0
\(873\) 1.77186 0.0599684
\(874\) 0 0
\(875\) −11.3056 −0.382197
\(876\) 0 0
\(877\) −53.0266 −1.79058 −0.895290 0.445483i \(-0.853032\pi\)
−0.895290 + 0.445483i \(0.853032\pi\)
\(878\) 0 0
\(879\) −0.678749 −0.0228936
\(880\) 0 0
\(881\) −43.3377 −1.46008 −0.730042 0.683403i \(-0.760499\pi\)
−0.730042 + 0.683403i \(0.760499\pi\)
\(882\) 0 0
\(883\) −19.9719 −0.672107 −0.336054 0.941843i \(-0.609092\pi\)
−0.336054 + 0.941843i \(0.609092\pi\)
\(884\) 0 0
\(885\) 9.82298 0.330196
\(886\) 0 0
\(887\) −8.94174 −0.300234 −0.150117 0.988668i \(-0.547965\pi\)
−0.150117 + 0.988668i \(0.547965\pi\)
\(888\) 0 0
\(889\) 3.58137 0.120115
\(890\) 0 0
\(891\) 2.86975 0.0961403
\(892\) 0 0
\(893\) 42.3590 1.41749
\(894\) 0 0
\(895\) −25.9781 −0.868351
\(896\) 0 0
\(897\) 0.442370 0.0147703
\(898\) 0 0
\(899\) 9.86978 0.329176
\(900\) 0 0
\(901\) −0.635740 −0.0211796
\(902\) 0 0
\(903\) −3.51002 −0.116806
\(904\) 0 0
\(905\) 13.7489 0.457028
\(906\) 0 0
\(907\) −14.9439 −0.496205 −0.248102 0.968734i \(-0.579807\pi\)
−0.248102 + 0.968734i \(0.579807\pi\)
\(908\) 0 0
\(909\) 17.1221 0.567904
\(910\) 0 0
\(911\) −14.7265 −0.487910 −0.243955 0.969787i \(-0.578445\pi\)
−0.243955 + 0.969787i \(0.578445\pi\)
\(912\) 0 0
\(913\) −34.0184 −1.12584
\(914\) 0 0
\(915\) −0.771893 −0.0255180
\(916\) 0 0
\(917\) 5.88548 0.194356
\(918\) 0 0
\(919\) −50.4312 −1.66357 −0.831786 0.555097i \(-0.812681\pi\)
−0.831786 + 0.555097i \(0.812681\pi\)
\(920\) 0 0
\(921\) 19.8221 0.653161
\(922\) 0 0
\(923\) 4.25640 0.140101
\(924\) 0 0
\(925\) −10.5861 −0.348069
\(926\) 0 0
\(927\) 17.4005 0.571508
\(928\) 0 0
\(929\) −47.0385 −1.54328 −0.771641 0.636058i \(-0.780564\pi\)
−0.771641 + 0.636058i \(0.780564\pi\)
\(930\) 0 0
\(931\) −32.6759 −1.07091
\(932\) 0 0
\(933\) −27.9653 −0.915542
\(934\) 0 0
\(935\) 26.0516 0.851977
\(936\) 0 0
\(937\) 28.9908 0.947089 0.473545 0.880770i \(-0.342974\pi\)
0.473545 + 0.880770i \(0.342974\pi\)
\(938\) 0 0
\(939\) 4.12103 0.134485
\(940\) 0 0
\(941\) 8.51175 0.277475 0.138738 0.990329i \(-0.455696\pi\)
0.138738 + 0.990329i \(0.455696\pi\)
\(942\) 0 0
\(943\) 0.570057 0.0185636
\(944\) 0 0
\(945\) −1.35005 −0.0439173
\(946\) 0 0
\(947\) 2.39763 0.0779126 0.0389563 0.999241i \(-0.487597\pi\)
0.0389563 + 0.999241i \(0.487597\pi\)
\(948\) 0 0
\(949\) −4.15608 −0.134912
\(950\) 0 0
\(951\) −1.06358 −0.0344890
\(952\) 0 0
\(953\) −16.9655 −0.549566 −0.274783 0.961506i \(-0.588606\pi\)
−0.274783 + 0.961506i \(0.588606\pi\)
\(954\) 0 0
\(955\) −18.5712 −0.600951
\(956\) 0 0
\(957\) −2.86975 −0.0927659
\(958\) 0 0
\(959\) −2.28139 −0.0736700
\(960\) 0 0
\(961\) 66.4125 2.14234
\(962\) 0 0
\(963\) −0.113485 −0.00365699
\(964\) 0 0
\(965\) −34.3710 −1.10644
\(966\) 0 0
\(967\) −51.4075 −1.65315 −0.826577 0.562824i \(-0.809715\pi\)
−0.826577 + 0.562824i \(0.809715\pi\)
\(968\) 0 0
\(969\) −39.5709 −1.27120
\(970\) 0 0
\(971\) 47.1585 1.51339 0.756694 0.653770i \(-0.226813\pi\)
0.756694 + 0.653770i \(0.226813\pi\)
\(972\) 0 0
\(973\) −16.6789 −0.534700
\(974\) 0 0
\(975\) −1.49262 −0.0478022
\(976\) 0 0
\(977\) 2.02506 0.0647874 0.0323937 0.999475i \(-0.489687\pi\)
0.0323937 + 0.999475i \(0.489687\pi\)
\(978\) 0 0
\(979\) −45.6697 −1.45961
\(980\) 0 0
\(981\) 3.63082 0.115923
\(982\) 0 0
\(983\) 23.1217 0.737467 0.368734 0.929535i \(-0.379791\pi\)
0.368734 + 0.929535i \(0.379791\pi\)
\(984\) 0 0
\(985\) 9.40888 0.299792
\(986\) 0 0
\(987\) −8.06918 −0.256845
\(988\) 0 0
\(989\) 3.31512 0.105415
\(990\) 0 0
\(991\) −21.7655 −0.691404 −0.345702 0.938344i \(-0.612359\pi\)
−0.345702 + 0.938344i \(0.612359\pi\)
\(992\) 0 0
\(993\) −12.6301 −0.400803
\(994\) 0 0
\(995\) −5.22910 −0.165774
\(996\) 0 0
\(997\) 16.6418 0.527050 0.263525 0.964653i \(-0.415115\pi\)
0.263525 + 0.964653i \(0.415115\pi\)
\(998\) 0 0
\(999\) −3.13742 −0.0992636
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 8004.2.a.i.1.10 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8004.2.a.i.1.10 16 1.1 even 1 trivial