Properties

Label 4017.2.a.c.1.1
Level 4017
Weight 2
Character 4017.1
Self dual yes
Analytic conductor 32.076
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -2.00000 q^{4} +1.00000 q^{5} +2.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -2.00000 q^{4} +1.00000 q^{5} +2.00000 q^{7} +1.00000 q^{9} -2.00000 q^{12} -1.00000 q^{13} +1.00000 q^{15} +4.00000 q^{16} -3.00000 q^{17} -4.00000 q^{19} -2.00000 q^{20} +2.00000 q^{21} -8.00000 q^{23} -4.00000 q^{25} +1.00000 q^{27} -4.00000 q^{28} +5.00000 q^{29} -1.00000 q^{31} +2.00000 q^{35} -2.00000 q^{36} +1.00000 q^{37} -1.00000 q^{39} -6.00000 q^{41} -8.00000 q^{43} +1.00000 q^{45} +3.00000 q^{47} +4.00000 q^{48} -3.00000 q^{49} -3.00000 q^{51} +2.00000 q^{52} -4.00000 q^{57} -2.00000 q^{60} +6.00000 q^{61} +2.00000 q^{63} -8.00000 q^{64} -1.00000 q^{65} -12.0000 q^{67} +6.00000 q^{68} -8.00000 q^{69} -1.00000 q^{71} -7.00000 q^{73} -4.00000 q^{75} +8.00000 q^{76} +13.0000 q^{79} +4.00000 q^{80} +1.00000 q^{81} -6.00000 q^{83} -4.00000 q^{84} -3.00000 q^{85} +5.00000 q^{87} +2.00000 q^{89} -2.00000 q^{91} +16.0000 q^{92} -1.00000 q^{93} -4.00000 q^{95} +6.00000 q^{97} +O(q^{100})\)

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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) 1.00000 0.577350
\(4\) −2.00000 −1.00000
\(5\) 1.00000 0.447214 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 0 0
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) −2.00000 −0.577350
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 4.00000 1.00000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) −2.00000 −0.447214
\(21\) 2.00000 0.436436
\(22\) 0 0
\(23\) −8.00000 −1.66812 −0.834058 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −4.00000 −0.755929
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 0 0
\(31\) −1.00000 −0.179605 −0.0898027 0.995960i \(-0.528624\pi\)
−0.0898027 + 0.995960i \(0.528624\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.00000 0.338062
\(36\) −2.00000 −0.333333
\(37\) 1.00000 0.164399 0.0821995 0.996616i \(-0.473806\pi\)
0.0821995 + 0.996616i \(0.473806\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) 4.00000 0.577350
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) −3.00000 −0.420084
\(52\) 2.00000 0.277350
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) −2.00000 −0.258199
\(61\) 6.00000 0.768221 0.384111 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 0 0
\(63\) 2.00000 0.251976
\(64\) −8.00000 −1.00000
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 6.00000 0.727607
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) −1.00000 −0.118678 −0.0593391 0.998238i \(-0.518899\pi\)
−0.0593391 + 0.998238i \(0.518899\pi\)
\(72\) 0 0
\(73\) −7.00000 −0.819288 −0.409644 0.912245i \(-0.634347\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) 0 0
\(75\) −4.00000 −0.461880
\(76\) 8.00000 0.917663
\(77\) 0 0
\(78\) 0 0
\(79\) 13.0000 1.46261 0.731307 0.682048i \(-0.238911\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 4.00000 0.447214
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) −4.00000 −0.436436
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) 5.00000 0.536056
\(88\) 0 0
\(89\) 2.00000 0.212000 0.106000 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) 0 0
\(91\) −2.00000 −0.209657
\(92\) 16.0000 1.66812
\(93\) −1.00000 −0.103695
\(94\) 0 0
\(95\) −4.00000 −0.410391
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 8.00000 0.800000
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 0 0
\(103\) 1.00000 0.0985329
\(104\) 0 0
\(105\) 2.00000 0.195180
\(106\) 0 0
\(107\) −5.00000 −0.483368 −0.241684 0.970355i \(-0.577700\pi\)
−0.241684 + 0.970355i \(0.577700\pi\)
\(108\) −2.00000 −0.192450
\(109\) 11.0000 1.05361 0.526804 0.849987i \(-0.323390\pi\)
0.526804 + 0.849987i \(0.323390\pi\)
\(110\) 0 0
\(111\) 1.00000 0.0949158
\(112\) 8.00000 0.755929
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 0 0
\(115\) −8.00000 −0.746004
\(116\) −10.0000 −0.928477
\(117\) −1.00000 −0.0924500
\(118\) 0 0
\(119\) −6.00000 −0.550019
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) −6.00000 −0.541002
\(124\) 2.00000 0.179605
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 0 0
\(129\) −8.00000 −0.704361
\(130\) 0 0
\(131\) −1.00000 −0.0873704 −0.0436852 0.999045i \(-0.513910\pi\)
−0.0436852 + 0.999045i \(0.513910\pi\)
\(132\) 0 0
\(133\) −8.00000 −0.693688
\(134\) 0 0
\(135\) 1.00000 0.0860663
\(136\) 0 0
\(137\) 8.00000 0.683486 0.341743 0.939793i \(-0.388983\pi\)
0.341743 + 0.939793i \(0.388983\pi\)
\(138\) 0 0
\(139\) −11.0000 −0.933008 −0.466504 0.884519i \(-0.654487\pi\)
−0.466504 + 0.884519i \(0.654487\pi\)
\(140\) −4.00000 −0.338062
\(141\) 3.00000 0.252646
\(142\) 0 0
\(143\) 0 0
\(144\) 4.00000 0.333333
\(145\) 5.00000 0.415227
\(146\) 0 0
\(147\) −3.00000 −0.247436
\(148\) −2.00000 −0.164399
\(149\) 18.0000 1.47462 0.737309 0.675556i \(-0.236096\pi\)
0.737309 + 0.675556i \(0.236096\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) −3.00000 −0.242536
\(154\) 0 0
\(155\) −1.00000 −0.0803219
\(156\) 2.00000 0.160128
\(157\) −14.0000 −1.11732 −0.558661 0.829396i \(-0.688685\pi\)
−0.558661 + 0.829396i \(0.688685\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −16.0000 −1.26098
\(162\) 0 0
\(163\) −20.0000 −1.56652 −0.783260 0.621694i \(-0.786445\pi\)
−0.783260 + 0.621694i \(0.786445\pi\)
\(164\) 12.0000 0.937043
\(165\) 0 0
\(166\) 0 0
\(167\) −20.0000 −1.54765 −0.773823 0.633402i \(-0.781658\pi\)
−0.773823 + 0.633402i \(0.781658\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −4.00000 −0.305888
\(172\) 16.0000 1.21999
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) −8.00000 −0.604743
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 25.0000 1.86859 0.934294 0.356504i \(-0.116031\pi\)
0.934294 + 0.356504i \(0.116031\pi\)
\(180\) −2.00000 −0.149071
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) 6.00000 0.443533
\(184\) 0 0
\(185\) 1.00000 0.0735215
\(186\) 0 0
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) 2.00000 0.145479
\(190\) 0 0
\(191\) −20.0000 −1.44715 −0.723575 0.690246i \(-0.757502\pi\)
−0.723575 + 0.690246i \(0.757502\pi\)
\(192\) −8.00000 −0.577350
\(193\) −2.00000 −0.143963 −0.0719816 0.997406i \(-0.522932\pi\)
−0.0719816 + 0.997406i \(0.522932\pi\)
\(194\) 0 0
\(195\) −1.00000 −0.0716115
\(196\) 6.00000 0.428571
\(197\) −27.0000 −1.92367 −0.961835 0.273629i \(-0.911776\pi\)
−0.961835 + 0.273629i \(0.911776\pi\)
\(198\) 0 0
\(199\) −2.00000 −0.141776 −0.0708881 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) 0 0
\(201\) −12.0000 −0.846415
\(202\) 0 0
\(203\) 10.0000 0.701862
\(204\) 6.00000 0.420084
\(205\) −6.00000 −0.419058
\(206\) 0 0
\(207\) −8.00000 −0.556038
\(208\) −4.00000 −0.277350
\(209\) 0 0
\(210\) 0 0
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 0 0
\(213\) −1.00000 −0.0685189
\(214\) 0 0
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) −2.00000 −0.135769
\(218\) 0 0
\(219\) −7.00000 −0.473016
\(220\) 0 0
\(221\) 3.00000 0.201802
\(222\) 0 0
\(223\) 6.00000 0.401790 0.200895 0.979613i \(-0.435615\pi\)
0.200895 + 0.979613i \(0.435615\pi\)
\(224\) 0 0
\(225\) −4.00000 −0.266667
\(226\) 0 0
\(227\) −25.0000 −1.65931 −0.829654 0.558278i \(-0.811462\pi\)
−0.829654 + 0.558278i \(0.811462\pi\)
\(228\) 8.00000 0.529813
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) 3.00000 0.195698
\(236\) 0 0
\(237\) 13.0000 0.844441
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 4.00000 0.258199
\(241\) −26.0000 −1.67481 −0.837404 0.546585i \(-0.815928\pi\)
−0.837404 + 0.546585i \(0.815928\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) −12.0000 −0.768221
\(245\) −3.00000 −0.191663
\(246\) 0 0
\(247\) 4.00000 0.254514
\(248\) 0 0
\(249\) −6.00000 −0.380235
\(250\) 0 0
\(251\) 28.0000 1.76734 0.883672 0.468106i \(-0.155064\pi\)
0.883672 + 0.468106i \(0.155064\pi\)
\(252\) −4.00000 −0.251976
\(253\) 0 0
\(254\) 0 0
\(255\) −3.00000 −0.187867
\(256\) 16.0000 1.00000
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 2.00000 0.124274
\(260\) 2.00000 0.124035
\(261\) 5.00000 0.309492
\(262\) 0 0
\(263\) 4.00000 0.246651 0.123325 0.992366i \(-0.460644\pi\)
0.123325 + 0.992366i \(0.460644\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 2.00000 0.122398
\(268\) 24.0000 1.46603
\(269\) −5.00000 −0.304855 −0.152428 0.988315i \(-0.548709\pi\)
−0.152428 + 0.988315i \(0.548709\pi\)
\(270\) 0 0
\(271\) 7.00000 0.425220 0.212610 0.977137i \(-0.431804\pi\)
0.212610 + 0.977137i \(0.431804\pi\)
\(272\) −12.0000 −0.727607
\(273\) −2.00000 −0.121046
\(274\) 0 0
\(275\) 0 0
\(276\) 16.0000 0.963087
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 0 0
\(279\) −1.00000 −0.0598684
\(280\) 0 0
\(281\) 11.0000 0.656205 0.328102 0.944642i \(-0.393591\pi\)
0.328102 + 0.944642i \(0.393591\pi\)
\(282\) 0 0
\(283\) −24.0000 −1.42665 −0.713326 0.700832i \(-0.752812\pi\)
−0.713326 + 0.700832i \(0.752812\pi\)
\(284\) 2.00000 0.118678
\(285\) −4.00000 −0.236940
\(286\) 0 0
\(287\) −12.0000 −0.708338
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 6.00000 0.351726
\(292\) 14.0000 0.819288
\(293\) −7.00000 −0.408944 −0.204472 0.978872i \(-0.565548\pi\)
−0.204472 + 0.978872i \(0.565548\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 8.00000 0.462652
\(300\) 8.00000 0.461880
\(301\) −16.0000 −0.922225
\(302\) 0 0
\(303\) 2.00000 0.114897
\(304\) −16.0000 −0.917663
\(305\) 6.00000 0.343559
\(306\) 0 0
\(307\) −23.0000 −1.31268 −0.656340 0.754466i \(-0.727896\pi\)
−0.656340 + 0.754466i \(0.727896\pi\)
\(308\) 0 0
\(309\) 1.00000 0.0568880
\(310\) 0 0
\(311\) 16.0000 0.907277 0.453638 0.891186i \(-0.350126\pi\)
0.453638 + 0.891186i \(0.350126\pi\)
\(312\) 0 0
\(313\) −7.00000 −0.395663 −0.197832 0.980236i \(-0.563390\pi\)
−0.197832 + 0.980236i \(0.563390\pi\)
\(314\) 0 0
\(315\) 2.00000 0.112687
\(316\) −26.0000 −1.46261
\(317\) 12.0000 0.673987 0.336994 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −8.00000 −0.447214
\(321\) −5.00000 −0.279073
\(322\) 0 0
\(323\) 12.0000 0.667698
\(324\) −2.00000 −0.111111
\(325\) 4.00000 0.221880
\(326\) 0 0
\(327\) 11.0000 0.608301
\(328\) 0 0
\(329\) 6.00000 0.330791
\(330\) 0 0
\(331\) −17.0000 −0.934405 −0.467202 0.884150i \(-0.654738\pi\)
−0.467202 + 0.884150i \(0.654738\pi\)
\(332\) 12.0000 0.658586
\(333\) 1.00000 0.0547997
\(334\) 0 0
\(335\) −12.0000 −0.655630
\(336\) 8.00000 0.436436
\(337\) −5.00000 −0.272367 −0.136184 0.990684i \(-0.543484\pi\)
−0.136184 + 0.990684i \(0.543484\pi\)
\(338\) 0 0
\(339\) −12.0000 −0.651751
\(340\) 6.00000 0.325396
\(341\) 0 0
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) 0 0
\(345\) −8.00000 −0.430706
\(346\) 0 0
\(347\) 9.00000 0.483145 0.241573 0.970383i \(-0.422337\pi\)
0.241573 + 0.970383i \(0.422337\pi\)
\(348\) −10.0000 −0.536056
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 17.0000 0.904819 0.452409 0.891810i \(-0.350565\pi\)
0.452409 + 0.891810i \(0.350565\pi\)
\(354\) 0 0
\(355\) −1.00000 −0.0530745
\(356\) −4.00000 −0.212000
\(357\) −6.00000 −0.317554
\(358\) 0 0
\(359\) 32.0000 1.68890 0.844448 0.535638i \(-0.179929\pi\)
0.844448 + 0.535638i \(0.179929\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) −11.0000 −0.577350
\(364\) 4.00000 0.209657
\(365\) −7.00000 −0.366397
\(366\) 0 0
\(367\) 23.0000 1.20059 0.600295 0.799779i \(-0.295050\pi\)
0.600295 + 0.799779i \(0.295050\pi\)
\(368\) −32.0000 −1.66812
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) 0 0
\(372\) 2.00000 0.103695
\(373\) −23.0000 −1.19089 −0.595447 0.803394i \(-0.703025\pi\)
−0.595447 + 0.803394i \(0.703025\pi\)
\(374\) 0 0
\(375\) −9.00000 −0.464758
\(376\) 0 0
\(377\) −5.00000 −0.257513
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 8.00000 0.410391
\(381\) 16.0000 0.819705
\(382\) 0 0
\(383\) −11.0000 −0.562074 −0.281037 0.959697i \(-0.590678\pi\)
−0.281037 + 0.959697i \(0.590678\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −8.00000 −0.406663
\(388\) −12.0000 −0.609208
\(389\) −12.0000 −0.608424 −0.304212 0.952604i \(-0.598393\pi\)
−0.304212 + 0.952604i \(0.598393\pi\)
\(390\) 0 0
\(391\) 24.0000 1.21373
\(392\) 0 0
\(393\) −1.00000 −0.0504433
\(394\) 0 0
\(395\) 13.0000 0.654101
\(396\) 0 0
\(397\) −29.0000 −1.45547 −0.727734 0.685859i \(-0.759427\pi\)
−0.727734 + 0.685859i \(0.759427\pi\)
\(398\) 0 0
\(399\) −8.00000 −0.400501
\(400\) −16.0000 −0.800000
\(401\) −22.0000 −1.09863 −0.549314 0.835616i \(-0.685111\pi\)
−0.549314 + 0.835616i \(0.685111\pi\)
\(402\) 0 0
\(403\) 1.00000 0.0498135
\(404\) −4.00000 −0.199007
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) 8.00000 0.394611
\(412\) −2.00000 −0.0985329
\(413\) 0 0
\(414\) 0 0
\(415\) −6.00000 −0.294528
\(416\) 0 0
\(417\) −11.0000 −0.538672
\(418\) 0 0
\(419\) −15.0000 −0.732798 −0.366399 0.930458i \(-0.619409\pi\)
−0.366399 + 0.930458i \(0.619409\pi\)
\(420\) −4.00000 −0.195180
\(421\) 16.0000 0.779792 0.389896 0.920859i \(-0.372511\pi\)
0.389896 + 0.920859i \(0.372511\pi\)
\(422\) 0 0
\(423\) 3.00000 0.145865
\(424\) 0 0
\(425\) 12.0000 0.582086
\(426\) 0 0
\(427\) 12.0000 0.580721
\(428\) 10.0000 0.483368
\(429\) 0 0
\(430\) 0 0
\(431\) 4.00000 0.192673 0.0963366 0.995349i \(-0.469287\pi\)
0.0963366 + 0.995349i \(0.469287\pi\)
\(432\) 4.00000 0.192450
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 0 0
\(435\) 5.00000 0.239732
\(436\) −22.0000 −1.05361
\(437\) 32.0000 1.53077
\(438\) 0 0
\(439\) 16.0000 0.763638 0.381819 0.924237i \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) 14.0000 0.665160 0.332580 0.943075i \(-0.392081\pi\)
0.332580 + 0.943075i \(0.392081\pi\)
\(444\) −2.00000 −0.0949158
\(445\) 2.00000 0.0948091
\(446\) 0 0
\(447\) 18.0000 0.851371
\(448\) −16.0000 −0.755929
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 24.0000 1.12887
\(453\) 0 0
\(454\) 0 0
\(455\) −2.00000 −0.0937614
\(456\) 0 0
\(457\) 9.00000 0.421002 0.210501 0.977594i \(-0.432490\pi\)
0.210501 + 0.977594i \(0.432490\pi\)
\(458\) 0 0
\(459\) −3.00000 −0.140028
\(460\) 16.0000 0.746004
\(461\) 24.0000 1.11779 0.558896 0.829238i \(-0.311225\pi\)
0.558896 + 0.829238i \(0.311225\pi\)
\(462\) 0 0
\(463\) 13.0000 0.604161 0.302081 0.953282i \(-0.402319\pi\)
0.302081 + 0.953282i \(0.402319\pi\)
\(464\) 20.0000 0.928477
\(465\) −1.00000 −0.0463739
\(466\) 0 0
\(467\) 15.0000 0.694117 0.347059 0.937843i \(-0.387180\pi\)
0.347059 + 0.937843i \(0.387180\pi\)
\(468\) 2.00000 0.0924500
\(469\) −24.0000 −1.10822
\(470\) 0 0
\(471\) −14.0000 −0.645086
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 16.0000 0.734130
\(476\) 12.0000 0.550019
\(477\) 0 0
\(478\) 0 0
\(479\) −1.00000 −0.0456912 −0.0228456 0.999739i \(-0.507273\pi\)
−0.0228456 + 0.999739i \(0.507273\pi\)
\(480\) 0 0
\(481\) −1.00000 −0.0455961
\(482\) 0 0
\(483\) −16.0000 −0.728025
\(484\) 22.0000 1.00000
\(485\) 6.00000 0.272446
\(486\) 0 0
\(487\) 28.0000 1.26880 0.634401 0.773004i \(-0.281247\pi\)
0.634401 + 0.773004i \(0.281247\pi\)
\(488\) 0 0
\(489\) −20.0000 −0.904431
\(490\) 0 0
\(491\) −19.0000 −0.857458 −0.428729 0.903433i \(-0.641038\pi\)
−0.428729 + 0.903433i \(0.641038\pi\)
\(492\) 12.0000 0.541002
\(493\) −15.0000 −0.675566
\(494\) 0 0
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) −2.00000 −0.0897123
\(498\) 0 0
\(499\) 7.00000 0.313363 0.156682 0.987649i \(-0.449920\pi\)
0.156682 + 0.987649i \(0.449920\pi\)
\(500\) 18.0000 0.804984
\(501\) −20.0000 −0.893534
\(502\) 0 0
\(503\) 35.0000 1.56057 0.780286 0.625422i \(-0.215073\pi\)
0.780286 + 0.625422i \(0.215073\pi\)
\(504\) 0 0
\(505\) 2.00000 0.0889988
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) −32.0000 −1.41977
\(509\) −6.00000 −0.265945 −0.132973 0.991120i \(-0.542452\pi\)
−0.132973 + 0.991120i \(0.542452\pi\)
\(510\) 0 0
\(511\) −14.0000 −0.619324
\(512\) 0 0
\(513\) −4.00000 −0.176604
\(514\) 0 0
\(515\) 1.00000 0.0440653
\(516\) 16.0000 0.704361
\(517\) 0 0
\(518\) 0 0
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) 1.00000 0.0437269 0.0218635 0.999761i \(-0.493040\pi\)
0.0218635 + 0.999761i \(0.493040\pi\)
\(524\) 2.00000 0.0873704
\(525\) −8.00000 −0.349149
\(526\) 0 0
\(527\) 3.00000 0.130682
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) 0 0
\(531\) 0 0
\(532\) 16.0000 0.693688
\(533\) 6.00000 0.259889
\(534\) 0 0
\(535\) −5.00000 −0.216169
\(536\) 0 0
\(537\) 25.0000 1.07883
\(538\) 0 0
\(539\) 0 0
\(540\) −2.00000 −0.0860663
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 0 0
\(543\) 10.0000 0.429141
\(544\) 0 0
\(545\) 11.0000 0.471188
\(546\) 0 0
\(547\) −32.0000 −1.36822 −0.684111 0.729378i \(-0.739809\pi\)
−0.684111 + 0.729378i \(0.739809\pi\)
\(548\) −16.0000 −0.683486
\(549\) 6.00000 0.256074
\(550\) 0 0
\(551\) −20.0000 −0.852029
\(552\) 0 0
\(553\) 26.0000 1.10563
\(554\) 0 0
\(555\) 1.00000 0.0424476
\(556\) 22.0000 0.933008
\(557\) −6.00000 −0.254228 −0.127114 0.991888i \(-0.540571\pi\)
−0.127114 + 0.991888i \(0.540571\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 8.00000 0.338062
\(561\) 0 0
\(562\) 0 0
\(563\) 38.0000 1.60151 0.800755 0.598993i \(-0.204432\pi\)
0.800755 + 0.598993i \(0.204432\pi\)
\(564\) −6.00000 −0.252646
\(565\) −12.0000 −0.504844
\(566\) 0 0
\(567\) 2.00000 0.0839921
\(568\) 0 0
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 0 0
\(571\) 16.0000 0.669579 0.334790 0.942293i \(-0.391335\pi\)
0.334790 + 0.942293i \(0.391335\pi\)
\(572\) 0 0
\(573\) −20.0000 −0.835512
\(574\) 0 0
\(575\) 32.0000 1.33449
\(576\) −8.00000 −0.333333
\(577\) 10.0000 0.416305 0.208153 0.978096i \(-0.433255\pi\)
0.208153 + 0.978096i \(0.433255\pi\)
\(578\) 0 0
\(579\) −2.00000 −0.0831172
\(580\) −10.0000 −0.415227
\(581\) −12.0000 −0.497844
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −1.00000 −0.0413449
\(586\) 0 0
\(587\) −10.0000 −0.412744 −0.206372 0.978474i \(-0.566166\pi\)
−0.206372 + 0.978474i \(0.566166\pi\)
\(588\) 6.00000 0.247436
\(589\) 4.00000 0.164817
\(590\) 0 0
\(591\) −27.0000 −1.11063
\(592\) 4.00000 0.164399
\(593\) 18.0000 0.739171 0.369586 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) 0 0
\(595\) −6.00000 −0.245976
\(596\) −36.0000 −1.47462
\(597\) −2.00000 −0.0818546
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 0 0
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 0 0
\(603\) −12.0000 −0.488678
\(604\) 0 0
\(605\) −11.0000 −0.447214
\(606\) 0 0
\(607\) −39.0000 −1.58296 −0.791481 0.611194i \(-0.790689\pi\)
−0.791481 + 0.611194i \(0.790689\pi\)
\(608\) 0 0
\(609\) 10.0000 0.405220
\(610\) 0 0
\(611\) −3.00000 −0.121367
\(612\) 6.00000 0.242536
\(613\) 4.00000 0.161558 0.0807792 0.996732i \(-0.474259\pi\)
0.0807792 + 0.996732i \(0.474259\pi\)
\(614\) 0 0
\(615\) −6.00000 −0.241943
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) 26.0000 1.04503 0.522514 0.852631i \(-0.324994\pi\)
0.522514 + 0.852631i \(0.324994\pi\)
\(620\) 2.00000 0.0803219
\(621\) −8.00000 −0.321029
\(622\) 0 0
\(623\) 4.00000 0.160257
\(624\) −4.00000 −0.160128
\(625\) 11.0000 0.440000
\(626\) 0 0
\(627\) 0 0
\(628\) 28.0000 1.11732
\(629\) −3.00000 −0.119618
\(630\) 0 0
\(631\) −32.0000 −1.27390 −0.636950 0.770905i \(-0.719804\pi\)
−0.636950 + 0.770905i \(0.719804\pi\)
\(632\) 0 0
\(633\) −16.0000 −0.635943
\(634\) 0 0
\(635\) 16.0000 0.634941
\(636\) 0 0
\(637\) 3.00000 0.118864
\(638\) 0 0
\(639\) −1.00000 −0.0395594
\(640\) 0 0
\(641\) −39.0000 −1.54041 −0.770204 0.637798i \(-0.779845\pi\)
−0.770204 + 0.637798i \(0.779845\pi\)
\(642\) 0 0
\(643\) 14.0000 0.552106 0.276053 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) 32.0000 1.26098
\(645\) −8.00000 −0.315000
\(646\) 0 0
\(647\) 39.0000 1.53325 0.766624 0.642096i \(-0.221935\pi\)
0.766624 + 0.642096i \(0.221935\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −2.00000 −0.0783862
\(652\) 40.0000 1.56652
\(653\) 24.0000 0.939193 0.469596 0.882881i \(-0.344399\pi\)
0.469596 + 0.882881i \(0.344399\pi\)
\(654\) 0 0
\(655\) −1.00000 −0.0390732
\(656\) −24.0000 −0.937043
\(657\) −7.00000 −0.273096
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) −17.0000 −0.661223 −0.330612 0.943767i \(-0.607255\pi\)
−0.330612 + 0.943767i \(0.607255\pi\)
\(662\) 0 0
\(663\) 3.00000 0.116510
\(664\) 0 0
\(665\) −8.00000 −0.310227
\(666\) 0 0
\(667\) −40.0000 −1.54881
\(668\) 40.0000 1.54765
\(669\) 6.00000 0.231973
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −19.0000 −0.732396 −0.366198 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) 0 0
\(675\) −4.00000 −0.153960
\(676\) −2.00000 −0.0769231
\(677\) 5.00000 0.192166 0.0960828 0.995373i \(-0.469369\pi\)
0.0960828 + 0.995373i \(0.469369\pi\)
\(678\) 0 0
\(679\) 12.0000 0.460518
\(680\) 0 0
\(681\) −25.0000 −0.958002
\(682\) 0 0
\(683\) −9.00000 −0.344375 −0.172188 0.985064i \(-0.555084\pi\)
−0.172188 + 0.985064i \(0.555084\pi\)
\(684\) 8.00000 0.305888
\(685\) 8.00000 0.305664
\(686\) 0 0
\(687\) 14.0000 0.534133
\(688\) −32.0000 −1.21999
\(689\) 0 0
\(690\) 0 0
\(691\) 25.0000 0.951045 0.475522 0.879704i \(-0.342259\pi\)
0.475522 + 0.879704i \(0.342259\pi\)
\(692\) −12.0000 −0.456172
\(693\) 0 0
\(694\) 0 0
\(695\) −11.0000 −0.417254
\(696\) 0 0
\(697\) 18.0000 0.681799
\(698\) 0 0
\(699\) 0 0
\(700\) 16.0000 0.604743
\(701\) 3.00000 0.113308 0.0566542 0.998394i \(-0.481957\pi\)
0.0566542 + 0.998394i \(0.481957\pi\)
\(702\) 0 0
\(703\) −4.00000 −0.150863
\(704\) 0 0
\(705\) 3.00000 0.112987
\(706\) 0 0
\(707\) 4.00000 0.150435
\(708\) 0 0
\(709\) −20.0000 −0.751116 −0.375558 0.926799i \(-0.622549\pi\)
−0.375558 + 0.926799i \(0.622549\pi\)
\(710\) 0 0
\(711\) 13.0000 0.487538
\(712\) 0 0
\(713\) 8.00000 0.299602
\(714\) 0 0
\(715\) 0 0
\(716\) −50.0000 −1.86859
\(717\) −6.00000 −0.224074
\(718\) 0 0
\(719\) 28.0000 1.04422 0.522112 0.852877i \(-0.325144\pi\)
0.522112 + 0.852877i \(0.325144\pi\)
\(720\) 4.00000 0.149071
\(721\) 2.00000 0.0744839
\(722\) 0 0
\(723\) −26.0000 −0.966950
\(724\) −20.0000 −0.743294
\(725\) −20.0000 −0.742781
\(726\) 0 0
\(727\) −40.0000 −1.48352 −0.741759 0.670667i \(-0.766008\pi\)
−0.741759 + 0.670667i \(0.766008\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 24.0000 0.887672
\(732\) −12.0000 −0.443533
\(733\) −26.0000 −0.960332 −0.480166 0.877178i \(-0.659424\pi\)
−0.480166 + 0.877178i \(0.659424\pi\)
\(734\) 0 0
\(735\) −3.00000 −0.110657
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −4.00000 −0.147142 −0.0735712 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) −2.00000 −0.0735215
\(741\) 4.00000 0.146944
\(742\) 0 0
\(743\) 21.0000 0.770415 0.385208 0.922830i \(-0.374130\pi\)
0.385208 + 0.922830i \(0.374130\pi\)
\(744\) 0 0
\(745\) 18.0000 0.659469
\(746\) 0 0
\(747\) −6.00000 −0.219529
\(748\) 0 0
\(749\) −10.0000 −0.365392
\(750\) 0 0
\(751\) −31.0000 −1.13121 −0.565603 0.824678i \(-0.691357\pi\)
−0.565603 + 0.824678i \(0.691357\pi\)
\(752\) 12.0000 0.437595
\(753\) 28.0000 1.02038
\(754\) 0 0
\(755\) 0 0
\(756\) −4.00000 −0.145479
\(757\) −3.00000 −0.109037 −0.0545184 0.998513i \(-0.517362\pi\)
−0.0545184 + 0.998513i \(0.517362\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 7.00000 0.253750 0.126875 0.991919i \(-0.459505\pi\)
0.126875 + 0.991919i \(0.459505\pi\)
\(762\) 0 0
\(763\) 22.0000 0.796453
\(764\) 40.0000 1.44715
\(765\) −3.00000 −0.108465
\(766\) 0 0
\(767\) 0 0
\(768\) 16.0000 0.577350
\(769\) −37.0000 −1.33425 −0.667127 0.744944i \(-0.732476\pi\)
−0.667127 + 0.744944i \(0.732476\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 4.00000 0.143963
\(773\) 10.0000 0.359675 0.179838 0.983696i \(-0.442443\pi\)
0.179838 + 0.983696i \(0.442443\pi\)
\(774\) 0 0
\(775\) 4.00000 0.143684
\(776\) 0 0
\(777\) 2.00000 0.0717496
\(778\) 0 0
\(779\) 24.0000 0.859889
\(780\) 2.00000 0.0716115
\(781\) 0 0
\(782\) 0 0
\(783\) 5.00000 0.178685
\(784\) −12.0000 −0.428571
\(785\) −14.0000 −0.499681
\(786\) 0 0
\(787\) −52.0000 −1.85360 −0.926800 0.375555i \(-0.877452\pi\)
−0.926800 + 0.375555i \(0.877452\pi\)
\(788\) 54.0000 1.92367
\(789\) 4.00000 0.142404
\(790\) 0 0
\(791\) −24.0000 −0.853342
\(792\) 0 0
\(793\) −6.00000 −0.213066
\(794\) 0 0
\(795\) 0 0
\(796\) 4.00000 0.141776
\(797\) −15.0000 −0.531327 −0.265664 0.964066i \(-0.585591\pi\)
−0.265664 + 0.964066i \(0.585591\pi\)
\(798\) 0 0
\(799\) −9.00000 −0.318397
\(800\) 0 0
\(801\) 2.00000 0.0706665
\(802\) 0 0
\(803\) 0 0
\(804\) 24.0000 0.846415
\(805\) −16.0000 −0.563926
\(806\) 0 0
\(807\) −5.00000 −0.176008
\(808\) 0 0
\(809\) 36.0000 1.26569 0.632846 0.774277i \(-0.281886\pi\)
0.632846 + 0.774277i \(0.281886\pi\)
\(810\) 0 0
\(811\) 47.0000 1.65039 0.825197 0.564846i \(-0.191064\pi\)
0.825197 + 0.564846i \(0.191064\pi\)
\(812\) −20.0000 −0.701862
\(813\) 7.00000 0.245501
\(814\) 0 0
\(815\) −20.0000 −0.700569
\(816\) −12.0000 −0.420084
\(817\) 32.0000 1.11954
\(818\) 0 0
\(819\) −2.00000 −0.0698857
\(820\) 12.0000 0.419058
\(821\) 40.0000 1.39601 0.698005 0.716093i \(-0.254071\pi\)
0.698005 + 0.716093i \(0.254071\pi\)
\(822\) 0 0
\(823\) 8.00000 0.278862 0.139431 0.990232i \(-0.455473\pi\)
0.139431 + 0.990232i \(0.455473\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 9.00000 0.312961 0.156480 0.987681i \(-0.449985\pi\)
0.156480 + 0.987681i \(0.449985\pi\)
\(828\) 16.0000 0.556038
\(829\) −24.0000 −0.833554 −0.416777 0.909009i \(-0.636840\pi\)
−0.416777 + 0.909009i \(0.636840\pi\)
\(830\) 0 0
\(831\) −2.00000 −0.0693792
\(832\) 8.00000 0.277350
\(833\) 9.00000 0.311832
\(834\) 0 0
\(835\) −20.0000 −0.692129
\(836\) 0 0
\(837\) −1.00000 −0.0345651
\(838\) 0 0
\(839\) −10.0000 −0.345238 −0.172619 0.984989i \(-0.555223\pi\)
−0.172619 + 0.984989i \(0.555223\pi\)
\(840\) 0 0
\(841\) −4.00000 −0.137931
\(842\) 0 0
\(843\) 11.0000 0.378860
\(844\) 32.0000 1.10149
\(845\) 1.00000 0.0344010
\(846\) 0 0
\(847\) −22.0000 −0.755929
\(848\) 0 0
\(849\) −24.0000 −0.823678
\(850\) 0 0
\(851\) −8.00000 −0.274236
\(852\) 2.00000 0.0685189
\(853\) −14.0000 −0.479351 −0.239675 0.970853i \(-0.577041\pi\)
−0.239675 + 0.970853i \(0.577041\pi\)
\(854\) 0 0
\(855\) −4.00000 −0.136797
\(856\) 0 0
\(857\) −43.0000 −1.46885 −0.734426 0.678689i \(-0.762549\pi\)
−0.734426 + 0.678689i \(0.762549\pi\)
\(858\) 0 0
\(859\) −18.0000 −0.614152 −0.307076 0.951685i \(-0.599351\pi\)
−0.307076 + 0.951685i \(0.599351\pi\)
\(860\) 16.0000 0.545595
\(861\) −12.0000 −0.408959
\(862\) 0 0
\(863\) −1.00000 −0.0340404 −0.0170202 0.999855i \(-0.505418\pi\)
−0.0170202 + 0.999855i \(0.505418\pi\)
\(864\) 0 0
\(865\) 6.00000 0.204006
\(866\) 0 0
\(867\) −8.00000 −0.271694
\(868\) 4.00000 0.135769
\(869\) 0 0
\(870\) 0 0
\(871\) 12.0000 0.406604
\(872\) 0 0
\(873\) 6.00000 0.203069
\(874\) 0 0
\(875\) −18.0000 −0.608511
\(876\) 14.0000 0.473016
\(877\) −43.0000 −1.45201 −0.726003 0.687691i \(-0.758624\pi\)
−0.726003 + 0.687691i \(0.758624\pi\)
\(878\) 0 0
\(879\) −7.00000 −0.236104
\(880\) 0 0
\(881\) −10.0000 −0.336909 −0.168454 0.985709i \(-0.553878\pi\)
−0.168454 + 0.985709i \(0.553878\pi\)
\(882\) 0 0
\(883\) −47.0000 −1.58168 −0.790838 0.612026i \(-0.790355\pi\)
−0.790838 + 0.612026i \(0.790355\pi\)
\(884\) −6.00000 −0.201802
\(885\) 0 0
\(886\) 0 0
\(887\) 35.0000 1.17518 0.587592 0.809157i \(-0.300076\pi\)
0.587592 + 0.809157i \(0.300076\pi\)
\(888\) 0 0
\(889\) 32.0000 1.07325
\(890\) 0 0
\(891\) 0 0
\(892\) −12.0000 −0.401790
\(893\) −12.0000 −0.401565
\(894\) 0 0
\(895\) 25.0000 0.835658
\(896\) 0 0
\(897\) 8.00000 0.267112
\(898\) 0 0
\(899\) −5.00000 −0.166759
\(900\) 8.00000 0.266667
\(901\) 0 0
\(902\) 0 0
\(903\) −16.0000 −0.532447
\(904\) 0 0
\(905\) 10.0000 0.332411
\(906\) 0 0
\(907\) 17.0000 0.564476 0.282238 0.959344i \(-0.408923\pi\)
0.282238 + 0.959344i \(0.408923\pi\)
\(908\) 50.0000 1.65931
\(909\) 2.00000 0.0663358
\(910\) 0 0
\(911\) −58.0000 −1.92163 −0.960813 0.277198i \(-0.910594\pi\)
−0.960813 + 0.277198i \(0.910594\pi\)
\(912\) −16.0000 −0.529813
\(913\) 0 0
\(914\) 0 0
\(915\) 6.00000 0.198354
\(916\) −28.0000 −0.925146
\(917\) −2.00000 −0.0660458
\(918\) 0 0
\(919\) −18.0000 −0.593765 −0.296883 0.954914i \(-0.595947\pi\)
−0.296883 + 0.954914i \(0.595947\pi\)
\(920\) 0 0
\(921\) −23.0000 −0.757876
\(922\) 0 0
\(923\) 1.00000 0.0329154
\(924\) 0 0
\(925\) −4.00000 −0.131519
\(926\) 0 0
\(927\) 1.00000 0.0328443
\(928\) 0 0
\(929\) −10.0000 −0.328089 −0.164045 0.986453i \(-0.552454\pi\)
−0.164045 + 0.986453i \(0.552454\pi\)
\(930\) 0 0
\(931\) 12.0000 0.393284
\(932\) 0 0
\(933\) 16.0000 0.523816
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 30.0000 0.980057 0.490029 0.871706i \(-0.336986\pi\)
0.490029 + 0.871706i \(0.336986\pi\)
\(938\) 0 0
\(939\) −7.00000 −0.228436
\(940\) −6.00000 −0.195698
\(941\) 36.0000 1.17357 0.586783 0.809744i \(-0.300394\pi\)
0.586783 + 0.809744i \(0.300394\pi\)
\(942\) 0 0
\(943\) 48.0000 1.56310
\(944\) 0 0
\(945\) 2.00000 0.0650600
\(946\) 0 0
\(947\) 40.0000 1.29983 0.649913 0.760009i \(-0.274805\pi\)
0.649913 + 0.760009i \(0.274805\pi\)
\(948\) −26.0000 −0.844441
\(949\) 7.00000 0.227230
\(950\) 0 0
\(951\) 12.0000 0.389127
\(952\) 0 0
\(953\) 17.0000 0.550684 0.275342 0.961346i \(-0.411209\pi\)
0.275342 + 0.961346i \(0.411209\pi\)
\(954\) 0 0
\(955\) −20.0000 −0.647185
\(956\) 12.0000 0.388108
\(957\) 0 0
\(958\) 0 0
\(959\) 16.0000 0.516667
\(960\) −8.00000 −0.258199
\(961\) −30.0000 −0.967742
\(962\) 0 0
\(963\) −5.00000 −0.161123
\(964\) 52.0000 1.67481
\(965\) −2.00000 −0.0643823
\(966\) 0 0
\(967\) −11.0000 −0.353736 −0.176868 0.984235i \(-0.556597\pi\)
−0.176868 + 0.984235i \(0.556597\pi\)
\(968\) 0 0
\(969\) 12.0000 0.385496
\(970\) 0 0
\(971\) −40.0000 −1.28366 −0.641831 0.766846i \(-0.721825\pi\)
−0.641831 + 0.766846i \(0.721825\pi\)
\(972\) −2.00000 −0.0641500
\(973\) −22.0000 −0.705288
\(974\) 0 0
\(975\) 4.00000 0.128103
\(976\) 24.0000 0.768221
\(977\) 32.0000 1.02377 0.511885 0.859054i \(-0.328947\pi\)
0.511885 + 0.859054i \(0.328947\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 6.00000 0.191663
\(981\) 11.0000 0.351203
\(982\) 0 0
\(983\) 24.0000 0.765481 0.382741 0.923856i \(-0.374980\pi\)
0.382741 + 0.923856i \(0.374980\pi\)
\(984\) 0 0
\(985\) −27.0000 −0.860292
\(986\) 0 0
\(987\) 6.00000 0.190982
\(988\) −8.00000 −0.254514
\(989\) 64.0000 2.03508
\(990\) 0 0
\(991\) −40.0000 −1.27064 −0.635321 0.772248i \(-0.719132\pi\)
−0.635321 + 0.772248i \(0.719132\pi\)
\(992\) 0 0
\(993\) −17.0000 −0.539479
\(994\) 0 0
\(995\) −2.00000 −0.0634043
\(996\) 12.0000 0.380235
\(997\) 58.0000 1.83688 0.918439 0.395562i \(-0.129450\pi\)
0.918439 + 0.395562i \(0.129450\pi\)
\(998\) 0 0
\(999\) 1.00000 0.0316386
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 4017.2.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4017.2.a.c.1.1 1 1.1 even 1 trivial