Properties

Label 4016.2.a.g.1.1
Level 4016
Weight 2
Character 4016.1
Self dual yes
Analytic conductor 32.068
Analytic rank 0
Dimension 7
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4016 = 2^{4} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0679214517\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1004)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.18229\)
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.18229 q^{3} -1.66714 q^{5} +1.81734 q^{7} +1.76240 q^{9} +O(q^{10})\) \(q-2.18229 q^{3} -1.66714 q^{5} +1.81734 q^{7} +1.76240 q^{9} +3.97535 q^{11} -4.88440 q^{13} +3.63819 q^{15} -3.09643 q^{17} +3.71976 q^{19} -3.96596 q^{21} -2.52167 q^{23} -2.22063 q^{25} +2.70081 q^{27} +4.16232 q^{29} -4.17959 q^{31} -8.67538 q^{33} -3.02977 q^{35} +11.0695 q^{37} +10.6592 q^{39} -0.0987896 q^{41} +2.04789 q^{43} -2.93817 q^{45} -0.469170 q^{47} -3.69728 q^{49} +6.75731 q^{51} -3.85883 q^{53} -6.62749 q^{55} -8.11759 q^{57} -7.09924 q^{59} -0.640361 q^{61} +3.20287 q^{63} +8.14300 q^{65} -1.93468 q^{67} +5.50301 q^{69} -0.867080 q^{71} -6.51437 q^{73} +4.84606 q^{75} +7.22456 q^{77} +9.82946 q^{79} -11.1811 q^{81} -12.6647 q^{83} +5.16219 q^{85} -9.08339 q^{87} -9.81448 q^{89} -8.87662 q^{91} +9.12109 q^{93} -6.20137 q^{95} -1.98395 q^{97} +7.00615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 3q^{3} - 2q^{5} + 6q^{7} + O(q^{10}) \) \( 7q + 3q^{3} - 2q^{5} + 6q^{7} + 5q^{11} - q^{13} + 6q^{15} - 8q^{17} + 15q^{19} - 3q^{21} + 5q^{23} - 9q^{25} + 9q^{27} + 21q^{31} + 7q^{35} - q^{37} + 23q^{39} - 10q^{41} + 23q^{43} - 4q^{45} + 10q^{47} - 13q^{49} + 20q^{51} - q^{53} + 23q^{55} - 6q^{57} + 4q^{59} + 3q^{61} + 4q^{63} + 4q^{65} + 28q^{67} + 18q^{69} + 18q^{71} - 7q^{73} - 11q^{75} + 6q^{77} + 30q^{79} - 5q^{81} - 13q^{83} + q^{85} + 7q^{87} + 18q^{91} + 36q^{93} - 2q^{97} + 10q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.18229 −1.25995 −0.629973 0.776617i \(-0.716934\pi\)
−0.629973 + 0.776617i \(0.716934\pi\)
\(4\) 0 0
\(5\) −1.66714 −0.745569 −0.372785 0.927918i \(-0.621597\pi\)
−0.372785 + 0.927918i \(0.621597\pi\)
\(6\) 0 0
\(7\) 1.81734 0.686890 0.343445 0.939173i \(-0.388406\pi\)
0.343445 + 0.939173i \(0.388406\pi\)
\(8\) 0 0
\(9\) 1.76240 0.587466
\(10\) 0 0
\(11\) 3.97535 1.19861 0.599307 0.800519i \(-0.295443\pi\)
0.599307 + 0.800519i \(0.295443\pi\)
\(12\) 0 0
\(13\) −4.88440 −1.35469 −0.677345 0.735666i \(-0.736869\pi\)
−0.677345 + 0.735666i \(0.736869\pi\)
\(14\) 0 0
\(15\) 3.63819 0.939378
\(16\) 0 0
\(17\) −3.09643 −0.750994 −0.375497 0.926824i \(-0.622528\pi\)
−0.375497 + 0.926824i \(0.622528\pi\)
\(18\) 0 0
\(19\) 3.71976 0.853370 0.426685 0.904400i \(-0.359681\pi\)
0.426685 + 0.904400i \(0.359681\pi\)
\(20\) 0 0
\(21\) −3.96596 −0.865444
\(22\) 0 0
\(23\) −2.52167 −0.525804 −0.262902 0.964823i \(-0.584680\pi\)
−0.262902 + 0.964823i \(0.584680\pi\)
\(24\) 0 0
\(25\) −2.22063 −0.444126
\(26\) 0 0
\(27\) 2.70081 0.519771
\(28\) 0 0
\(29\) 4.16232 0.772923 0.386461 0.922306i \(-0.373697\pi\)
0.386461 + 0.922306i \(0.373697\pi\)
\(30\) 0 0
\(31\) −4.17959 −0.750677 −0.375338 0.926888i \(-0.622473\pi\)
−0.375338 + 0.926888i \(0.622473\pi\)
\(32\) 0 0
\(33\) −8.67538 −1.51019
\(34\) 0 0
\(35\) −3.02977 −0.512124
\(36\) 0 0
\(37\) 11.0695 1.81981 0.909903 0.414820i \(-0.136156\pi\)
0.909903 + 0.414820i \(0.136156\pi\)
\(38\) 0 0
\(39\) 10.6592 1.70684
\(40\) 0 0
\(41\) −0.0987896 −0.0154283 −0.00771417 0.999970i \(-0.502456\pi\)
−0.00771417 + 0.999970i \(0.502456\pi\)
\(42\) 0 0
\(43\) 2.04789 0.312301 0.156150 0.987733i \(-0.450092\pi\)
0.156150 + 0.987733i \(0.450092\pi\)
\(44\) 0 0
\(45\) −2.93817 −0.437996
\(46\) 0 0
\(47\) −0.469170 −0.0684355 −0.0342177 0.999414i \(-0.510894\pi\)
−0.0342177 + 0.999414i \(0.510894\pi\)
\(48\) 0 0
\(49\) −3.69728 −0.528183
\(50\) 0 0
\(51\) 6.75731 0.946213
\(52\) 0 0
\(53\) −3.85883 −0.530050 −0.265025 0.964241i \(-0.585380\pi\)
−0.265025 + 0.964241i \(0.585380\pi\)
\(54\) 0 0
\(55\) −6.62749 −0.893650
\(56\) 0 0
\(57\) −8.11759 −1.07520
\(58\) 0 0
\(59\) −7.09924 −0.924242 −0.462121 0.886817i \(-0.652911\pi\)
−0.462121 + 0.886817i \(0.652911\pi\)
\(60\) 0 0
\(61\) −0.640361 −0.0819898 −0.0409949 0.999159i \(-0.513053\pi\)
−0.0409949 + 0.999159i \(0.513053\pi\)
\(62\) 0 0
\(63\) 3.20287 0.403524
\(64\) 0 0
\(65\) 8.14300 1.01002
\(66\) 0 0
\(67\) −1.93468 −0.236359 −0.118180 0.992992i \(-0.537706\pi\)
−0.118180 + 0.992992i \(0.537706\pi\)
\(68\) 0 0
\(69\) 5.50301 0.662485
\(70\) 0 0
\(71\) −0.867080 −0.102903 −0.0514517 0.998675i \(-0.516385\pi\)
−0.0514517 + 0.998675i \(0.516385\pi\)
\(72\) 0 0
\(73\) −6.51437 −0.762450 −0.381225 0.924482i \(-0.624498\pi\)
−0.381225 + 0.924482i \(0.624498\pi\)
\(74\) 0 0
\(75\) 4.84606 0.559575
\(76\) 0 0
\(77\) 7.22456 0.823315
\(78\) 0 0
\(79\) 9.82946 1.10590 0.552950 0.833214i \(-0.313502\pi\)
0.552950 + 0.833214i \(0.313502\pi\)
\(80\) 0 0
\(81\) −11.1811 −1.24235
\(82\) 0 0
\(83\) −12.6647 −1.39013 −0.695064 0.718948i \(-0.744624\pi\)
−0.695064 + 0.718948i \(0.744624\pi\)
\(84\) 0 0
\(85\) 5.16219 0.559918
\(86\) 0 0
\(87\) −9.08339 −0.973842
\(88\) 0 0
\(89\) −9.81448 −1.04033 −0.520166 0.854065i \(-0.674130\pi\)
−0.520166 + 0.854065i \(0.674130\pi\)
\(90\) 0 0
\(91\) −8.87662 −0.930522
\(92\) 0 0
\(93\) 9.12109 0.945813
\(94\) 0 0
\(95\) −6.20137 −0.636247
\(96\) 0 0
\(97\) −1.98395 −0.201439 −0.100720 0.994915i \(-0.532115\pi\)
−0.100720 + 0.994915i \(0.532115\pi\)
\(98\) 0 0
\(99\) 7.00615 0.704145
\(100\) 0 0
\(101\) 11.6322 1.15745 0.578724 0.815523i \(-0.303551\pi\)
0.578724 + 0.815523i \(0.303551\pi\)
\(102\) 0 0
\(103\) −8.01880 −0.790116 −0.395058 0.918656i \(-0.629275\pi\)
−0.395058 + 0.918656i \(0.629275\pi\)
\(104\) 0 0
\(105\) 6.61183 0.645249
\(106\) 0 0
\(107\) 13.9472 1.34833 0.674165 0.738580i \(-0.264504\pi\)
0.674165 + 0.738580i \(0.264504\pi\)
\(108\) 0 0
\(109\) −7.73637 −0.741010 −0.370505 0.928831i \(-0.620815\pi\)
−0.370505 + 0.928831i \(0.620815\pi\)
\(110\) 0 0
\(111\) −24.1568 −2.29286
\(112\) 0 0
\(113\) −5.22437 −0.491468 −0.245734 0.969337i \(-0.579029\pi\)
−0.245734 + 0.969337i \(0.579029\pi\)
\(114\) 0 0
\(115\) 4.20398 0.392023
\(116\) 0 0
\(117\) −8.60826 −0.795834
\(118\) 0 0
\(119\) −5.62726 −0.515850
\(120\) 0 0
\(121\) 4.80343 0.436676
\(122\) 0 0
\(123\) 0.215588 0.0194389
\(124\) 0 0
\(125\) 12.0378 1.07670
\(126\) 0 0
\(127\) 17.3142 1.53639 0.768195 0.640215i \(-0.221155\pi\)
0.768195 + 0.640215i \(0.221155\pi\)
\(128\) 0 0
\(129\) −4.46910 −0.393482
\(130\) 0 0
\(131\) −0.297840 −0.0260224 −0.0130112 0.999915i \(-0.504142\pi\)
−0.0130112 + 0.999915i \(0.504142\pi\)
\(132\) 0 0
\(133\) 6.76006 0.586171
\(134\) 0 0
\(135\) −4.50264 −0.387526
\(136\) 0 0
\(137\) 10.9689 0.937133 0.468567 0.883428i \(-0.344771\pi\)
0.468567 + 0.883428i \(0.344771\pi\)
\(138\) 0 0
\(139\) 22.5994 1.91685 0.958427 0.285338i \(-0.0921058\pi\)
0.958427 + 0.285338i \(0.0921058\pi\)
\(140\) 0 0
\(141\) 1.02387 0.0862251
\(142\) 0 0
\(143\) −19.4172 −1.62375
\(144\) 0 0
\(145\) −6.93918 −0.576268
\(146\) 0 0
\(147\) 8.06854 0.665482
\(148\) 0 0
\(149\) 8.53848 0.699499 0.349750 0.936843i \(-0.386267\pi\)
0.349750 + 0.936843i \(0.386267\pi\)
\(150\) 0 0
\(151\) 11.5305 0.938341 0.469170 0.883108i \(-0.344553\pi\)
0.469170 + 0.883108i \(0.344553\pi\)
\(152\) 0 0
\(153\) −5.45714 −0.441183
\(154\) 0 0
\(155\) 6.96798 0.559682
\(156\) 0 0
\(157\) 0.177058 0.0141308 0.00706539 0.999975i \(-0.497751\pi\)
0.00706539 + 0.999975i \(0.497751\pi\)
\(158\) 0 0
\(159\) 8.42108 0.667835
\(160\) 0 0
\(161\) −4.58272 −0.361169
\(162\) 0 0
\(163\) 13.7654 1.07819 0.539095 0.842245i \(-0.318766\pi\)
0.539095 + 0.842245i \(0.318766\pi\)
\(164\) 0 0
\(165\) 14.4631 1.12595
\(166\) 0 0
\(167\) 9.58570 0.741764 0.370882 0.928680i \(-0.379055\pi\)
0.370882 + 0.928680i \(0.379055\pi\)
\(168\) 0 0
\(169\) 10.8574 0.835184
\(170\) 0 0
\(171\) 6.55568 0.501326
\(172\) 0 0
\(173\) −7.27316 −0.552968 −0.276484 0.961019i \(-0.589169\pi\)
−0.276484 + 0.961019i \(0.589169\pi\)
\(174\) 0 0
\(175\) −4.03564 −0.305066
\(176\) 0 0
\(177\) 15.4926 1.16450
\(178\) 0 0
\(179\) 17.2832 1.29180 0.645902 0.763420i \(-0.276481\pi\)
0.645902 + 0.763420i \(0.276481\pi\)
\(180\) 0 0
\(181\) 19.8478 1.47528 0.737639 0.675195i \(-0.235941\pi\)
0.737639 + 0.675195i \(0.235941\pi\)
\(182\) 0 0
\(183\) 1.39745 0.103303
\(184\) 0 0
\(185\) −18.4544 −1.35679
\(186\) 0 0
\(187\) −12.3094 −0.900152
\(188\) 0 0
\(189\) 4.90829 0.357025
\(190\) 0 0
\(191\) 23.3899 1.69244 0.846218 0.532837i \(-0.178874\pi\)
0.846218 + 0.532837i \(0.178874\pi\)
\(192\) 0 0
\(193\) −12.5992 −0.906909 −0.453454 0.891280i \(-0.649808\pi\)
−0.453454 + 0.891280i \(0.649808\pi\)
\(194\) 0 0
\(195\) −17.7704 −1.27257
\(196\) 0 0
\(197\) 2.28151 0.162551 0.0812753 0.996692i \(-0.474101\pi\)
0.0812753 + 0.996692i \(0.474101\pi\)
\(198\) 0 0
\(199\) 2.10342 0.149108 0.0745538 0.997217i \(-0.476247\pi\)
0.0745538 + 0.997217i \(0.476247\pi\)
\(200\) 0 0
\(201\) 4.22204 0.297800
\(202\) 0 0
\(203\) 7.56434 0.530913
\(204\) 0 0
\(205\) 0.164696 0.0115029
\(206\) 0 0
\(207\) −4.44418 −0.308892
\(208\) 0 0
\(209\) 14.7873 1.02286
\(210\) 0 0
\(211\) −0.501747 −0.0345417 −0.0172709 0.999851i \(-0.505498\pi\)
−0.0172709 + 0.999851i \(0.505498\pi\)
\(212\) 0 0
\(213\) 1.89222 0.129653
\(214\) 0 0
\(215\) −3.41413 −0.232842
\(216\) 0 0
\(217\) −7.59573 −0.515632
\(218\) 0 0
\(219\) 14.2163 0.960646
\(220\) 0 0
\(221\) 15.1242 1.01736
\(222\) 0 0
\(223\) −0.964032 −0.0645563 −0.0322782 0.999479i \(-0.510276\pi\)
−0.0322782 + 0.999479i \(0.510276\pi\)
\(224\) 0 0
\(225\) −3.91363 −0.260909
\(226\) 0 0
\(227\) −20.6598 −1.37124 −0.685619 0.727961i \(-0.740468\pi\)
−0.685619 + 0.727961i \(0.740468\pi\)
\(228\) 0 0
\(229\) 7.37963 0.487660 0.243830 0.969818i \(-0.421596\pi\)
0.243830 + 0.969818i \(0.421596\pi\)
\(230\) 0 0
\(231\) −15.7661 −1.03733
\(232\) 0 0
\(233\) 21.1272 1.38409 0.692045 0.721854i \(-0.256710\pi\)
0.692045 + 0.721854i \(0.256710\pi\)
\(234\) 0 0
\(235\) 0.782174 0.0510234
\(236\) 0 0
\(237\) −21.4508 −1.39338
\(238\) 0 0
\(239\) 1.35509 0.0876538 0.0438269 0.999039i \(-0.486045\pi\)
0.0438269 + 0.999039i \(0.486045\pi\)
\(240\) 0 0
\(241\) 26.2538 1.69115 0.845577 0.533854i \(-0.179257\pi\)
0.845577 + 0.533854i \(0.179257\pi\)
\(242\) 0 0
\(243\) 16.2981 1.04552
\(244\) 0 0
\(245\) 6.16390 0.393797
\(246\) 0 0
\(247\) −18.1688 −1.15605
\(248\) 0 0
\(249\) 27.6380 1.75149
\(250\) 0 0
\(251\) −1.00000 −0.0631194
\(252\) 0 0
\(253\) −10.0245 −0.630236
\(254\) 0 0
\(255\) −11.2654 −0.705467
\(256\) 0 0
\(257\) 8.74279 0.545360 0.272680 0.962105i \(-0.412090\pi\)
0.272680 + 0.962105i \(0.412090\pi\)
\(258\) 0 0
\(259\) 20.1169 1.25001
\(260\) 0 0
\(261\) 7.33565 0.454066
\(262\) 0 0
\(263\) −19.4251 −1.19780 −0.598901 0.800823i \(-0.704396\pi\)
−0.598901 + 0.800823i \(0.704396\pi\)
\(264\) 0 0
\(265\) 6.43322 0.395189
\(266\) 0 0
\(267\) 21.4180 1.31076
\(268\) 0 0
\(269\) 7.73284 0.471480 0.235740 0.971816i \(-0.424249\pi\)
0.235740 + 0.971816i \(0.424249\pi\)
\(270\) 0 0
\(271\) 23.7030 1.43985 0.719927 0.694050i \(-0.244175\pi\)
0.719927 + 0.694050i \(0.244175\pi\)
\(272\) 0 0
\(273\) 19.3714 1.17241
\(274\) 0 0
\(275\) −8.82779 −0.532336
\(276\) 0 0
\(277\) 1.75856 0.105662 0.0528308 0.998603i \(-0.483176\pi\)
0.0528308 + 0.998603i \(0.483176\pi\)
\(278\) 0 0
\(279\) −7.36610 −0.440997
\(280\) 0 0
\(281\) 20.0290 1.19483 0.597414 0.801933i \(-0.296195\pi\)
0.597414 + 0.801933i \(0.296195\pi\)
\(282\) 0 0
\(283\) −5.84251 −0.347301 −0.173651 0.984807i \(-0.555556\pi\)
−0.173651 + 0.984807i \(0.555556\pi\)
\(284\) 0 0
\(285\) 13.5332 0.801637
\(286\) 0 0
\(287\) −0.179534 −0.0105976
\(288\) 0 0
\(289\) −7.41213 −0.436008
\(290\) 0 0
\(291\) 4.32955 0.253803
\(292\) 0 0
\(293\) −3.05347 −0.178385 −0.0891927 0.996014i \(-0.528429\pi\)
−0.0891927 + 0.996014i \(0.528429\pi\)
\(294\) 0 0
\(295\) 11.8354 0.689087
\(296\) 0 0
\(297\) 10.7367 0.623005
\(298\) 0 0
\(299\) 12.3168 0.712301
\(300\) 0 0
\(301\) 3.72172 0.214516
\(302\) 0 0
\(303\) −25.3849 −1.45832
\(304\) 0 0
\(305\) 1.06757 0.0611291
\(306\) 0 0
\(307\) 14.0535 0.802073 0.401037 0.916062i \(-0.368650\pi\)
0.401037 + 0.916062i \(0.368650\pi\)
\(308\) 0 0
\(309\) 17.4994 0.995504
\(310\) 0 0
\(311\) 23.9822 1.35990 0.679952 0.733256i \(-0.262000\pi\)
0.679952 + 0.733256i \(0.262000\pi\)
\(312\) 0 0
\(313\) 27.3953 1.54847 0.774237 0.632896i \(-0.218134\pi\)
0.774237 + 0.632896i \(0.218134\pi\)
\(314\) 0 0
\(315\) −5.33965 −0.300855
\(316\) 0 0
\(317\) −12.5013 −0.702143 −0.351072 0.936349i \(-0.614183\pi\)
−0.351072 + 0.936349i \(0.614183\pi\)
\(318\) 0 0
\(319\) 16.5467 0.926436
\(320\) 0 0
\(321\) −30.4369 −1.69882
\(322\) 0 0
\(323\) −11.5180 −0.640876
\(324\) 0 0
\(325\) 10.8465 0.601653
\(326\) 0 0
\(327\) 16.8830 0.933633
\(328\) 0 0
\(329\) −0.852641 −0.0470076
\(330\) 0 0
\(331\) −25.6129 −1.40782 −0.703908 0.710292i \(-0.748563\pi\)
−0.703908 + 0.710292i \(0.748563\pi\)
\(332\) 0 0
\(333\) 19.5088 1.06907
\(334\) 0 0
\(335\) 3.22540 0.176222
\(336\) 0 0
\(337\) −9.84964 −0.536544 −0.268272 0.963343i \(-0.586453\pi\)
−0.268272 + 0.963343i \(0.586453\pi\)
\(338\) 0 0
\(339\) 11.4011 0.619223
\(340\) 0 0
\(341\) −16.6154 −0.899772
\(342\) 0 0
\(343\) −19.4406 −1.04969
\(344\) 0 0
\(345\) −9.17431 −0.493928
\(346\) 0 0
\(347\) 6.11780 0.328421 0.164210 0.986425i \(-0.447492\pi\)
0.164210 + 0.986425i \(0.447492\pi\)
\(348\) 0 0
\(349\) −9.79907 −0.524532 −0.262266 0.964996i \(-0.584470\pi\)
−0.262266 + 0.964996i \(0.584470\pi\)
\(350\) 0 0
\(351\) −13.1918 −0.704129
\(352\) 0 0
\(353\) −6.86642 −0.365463 −0.182731 0.983163i \(-0.558494\pi\)
−0.182731 + 0.983163i \(0.558494\pi\)
\(354\) 0 0
\(355\) 1.44555 0.0767216
\(356\) 0 0
\(357\) 12.2803 0.649944
\(358\) 0 0
\(359\) −34.4483 −1.81811 −0.909055 0.416676i \(-0.863195\pi\)
−0.909055 + 0.416676i \(0.863195\pi\)
\(360\) 0 0
\(361\) −5.16342 −0.271759
\(362\) 0 0
\(363\) −10.4825 −0.550188
\(364\) 0 0
\(365\) 10.8604 0.568459
\(366\) 0 0
\(367\) 33.8538 1.76716 0.883578 0.468285i \(-0.155128\pi\)
0.883578 + 0.468285i \(0.155128\pi\)
\(368\) 0 0
\(369\) −0.174106 −0.00906362
\(370\) 0 0
\(371\) −7.01279 −0.364086
\(372\) 0 0
\(373\) −36.7580 −1.90325 −0.951627 0.307254i \(-0.900590\pi\)
−0.951627 + 0.307254i \(0.900590\pi\)
\(374\) 0 0
\(375\) −26.2701 −1.35658
\(376\) 0 0
\(377\) −20.3304 −1.04707
\(378\) 0 0
\(379\) 21.6407 1.11161 0.555803 0.831314i \(-0.312411\pi\)
0.555803 + 0.831314i \(0.312411\pi\)
\(380\) 0 0
\(381\) −37.7847 −1.93577
\(382\) 0 0
\(383\) −24.3327 −1.24334 −0.621671 0.783279i \(-0.713546\pi\)
−0.621671 + 0.783279i \(0.713546\pi\)
\(384\) 0 0
\(385\) −12.0444 −0.613839
\(386\) 0 0
\(387\) 3.60920 0.183466
\(388\) 0 0
\(389\) 25.6714 1.30159 0.650797 0.759252i \(-0.274435\pi\)
0.650797 + 0.759252i \(0.274435\pi\)
\(390\) 0 0
\(391\) 7.80816 0.394876
\(392\) 0 0
\(393\) 0.649973 0.0327868
\(394\) 0 0
\(395\) −16.3871 −0.824526
\(396\) 0 0
\(397\) 18.8682 0.946970 0.473485 0.880802i \(-0.342996\pi\)
0.473485 + 0.880802i \(0.342996\pi\)
\(398\) 0 0
\(399\) −14.7524 −0.738544
\(400\) 0 0
\(401\) −0.851616 −0.0425277 −0.0212638 0.999774i \(-0.506769\pi\)
−0.0212638 + 0.999774i \(0.506769\pi\)
\(402\) 0 0
\(403\) 20.4148 1.01693
\(404\) 0 0
\(405\) 18.6406 0.926258
\(406\) 0 0
\(407\) 44.0050 2.18125
\(408\) 0 0
\(409\) 4.86899 0.240756 0.120378 0.992728i \(-0.461589\pi\)
0.120378 + 0.992728i \(0.461589\pi\)
\(410\) 0 0
\(411\) −23.9373 −1.18074
\(412\) 0 0
\(413\) −12.9017 −0.634852
\(414\) 0 0
\(415\) 21.1138 1.03644
\(416\) 0 0
\(417\) −49.3184 −2.41513
\(418\) 0 0
\(419\) −10.3339 −0.504843 −0.252422 0.967617i \(-0.581227\pi\)
−0.252422 + 0.967617i \(0.581227\pi\)
\(420\) 0 0
\(421\) 24.5337 1.19570 0.597849 0.801608i \(-0.296022\pi\)
0.597849 + 0.801608i \(0.296022\pi\)
\(422\) 0 0
\(423\) −0.826864 −0.0402035
\(424\) 0 0
\(425\) 6.87602 0.333536
\(426\) 0 0
\(427\) −1.16375 −0.0563179
\(428\) 0 0
\(429\) 42.3741 2.04584
\(430\) 0 0
\(431\) −1.65100 −0.0795257 −0.0397628 0.999209i \(-0.512660\pi\)
−0.0397628 + 0.999209i \(0.512660\pi\)
\(432\) 0 0
\(433\) 19.0172 0.913907 0.456953 0.889491i \(-0.348941\pi\)
0.456953 + 0.889491i \(0.348941\pi\)
\(434\) 0 0
\(435\) 15.1433 0.726067
\(436\) 0 0
\(437\) −9.37998 −0.448705
\(438\) 0 0
\(439\) 31.7908 1.51729 0.758645 0.651504i \(-0.225862\pi\)
0.758645 + 0.651504i \(0.225862\pi\)
\(440\) 0 0
\(441\) −6.51607 −0.310289
\(442\) 0 0
\(443\) −7.00408 −0.332774 −0.166387 0.986061i \(-0.553210\pi\)
−0.166387 + 0.986061i \(0.553210\pi\)
\(444\) 0 0
\(445\) 16.3621 0.775640
\(446\) 0 0
\(447\) −18.6334 −0.881332
\(448\) 0 0
\(449\) −39.4671 −1.86257 −0.931283 0.364295i \(-0.881310\pi\)
−0.931283 + 0.364295i \(0.881310\pi\)
\(450\) 0 0
\(451\) −0.392723 −0.0184926
\(452\) 0 0
\(453\) −25.1630 −1.18226
\(454\) 0 0
\(455\) 14.7986 0.693769
\(456\) 0 0
\(457\) −14.8500 −0.694654 −0.347327 0.937744i \(-0.612911\pi\)
−0.347327 + 0.937744i \(0.612911\pi\)
\(458\) 0 0
\(459\) −8.36287 −0.390345
\(460\) 0 0
\(461\) −23.5063 −1.09480 −0.547399 0.836872i \(-0.684382\pi\)
−0.547399 + 0.836872i \(0.684382\pi\)
\(462\) 0 0
\(463\) 7.59484 0.352962 0.176481 0.984304i \(-0.443529\pi\)
0.176481 + 0.984304i \(0.443529\pi\)
\(464\) 0 0
\(465\) −15.2062 −0.705169
\(466\) 0 0
\(467\) −1.26788 −0.0586707 −0.0293354 0.999570i \(-0.509339\pi\)
−0.0293354 + 0.999570i \(0.509339\pi\)
\(468\) 0 0
\(469\) −3.51597 −0.162353
\(470\) 0 0
\(471\) −0.386393 −0.0178040
\(472\) 0 0
\(473\) 8.14110 0.374328
\(474\) 0 0
\(475\) −8.26020 −0.379004
\(476\) 0 0
\(477\) −6.80078 −0.311386
\(478\) 0 0
\(479\) 11.4831 0.524674 0.262337 0.964976i \(-0.415507\pi\)
0.262337 + 0.964976i \(0.415507\pi\)
\(480\) 0 0
\(481\) −54.0677 −2.46527
\(482\) 0 0
\(483\) 10.0008 0.455054
\(484\) 0 0
\(485\) 3.30752 0.150187
\(486\) 0 0
\(487\) 18.5144 0.838968 0.419484 0.907763i \(-0.362211\pi\)
0.419484 + 0.907763i \(0.362211\pi\)
\(488\) 0 0
\(489\) −30.0401 −1.35846
\(490\) 0 0
\(491\) −11.3486 −0.512155 −0.256077 0.966656i \(-0.582430\pi\)
−0.256077 + 0.966656i \(0.582430\pi\)
\(492\) 0 0
\(493\) −12.8883 −0.580461
\(494\) 0 0
\(495\) −11.6803 −0.524989
\(496\) 0 0
\(497\) −1.57578 −0.0706833
\(498\) 0 0
\(499\) 11.8934 0.532423 0.266212 0.963915i \(-0.414228\pi\)
0.266212 + 0.963915i \(0.414228\pi\)
\(500\) 0 0
\(501\) −20.9188 −0.934583
\(502\) 0 0
\(503\) 26.9893 1.20339 0.601697 0.798725i \(-0.294492\pi\)
0.601697 + 0.798725i \(0.294492\pi\)
\(504\) 0 0
\(505\) −19.3926 −0.862958
\(506\) 0 0
\(507\) −23.6940 −1.05229
\(508\) 0 0
\(509\) 0.334531 0.0148278 0.00741391 0.999973i \(-0.497640\pi\)
0.00741391 + 0.999973i \(0.497640\pi\)
\(510\) 0 0
\(511\) −11.8388 −0.523719
\(512\) 0 0
\(513\) 10.0464 0.443557
\(514\) 0 0
\(515\) 13.3685 0.589086
\(516\) 0 0
\(517\) −1.86512 −0.0820277
\(518\) 0 0
\(519\) 15.8721 0.696710
\(520\) 0 0
\(521\) 22.3238 0.978023 0.489012 0.872277i \(-0.337358\pi\)
0.489012 + 0.872277i \(0.337358\pi\)
\(522\) 0 0
\(523\) 14.1603 0.619188 0.309594 0.950869i \(-0.399807\pi\)
0.309594 + 0.950869i \(0.399807\pi\)
\(524\) 0 0
\(525\) 8.80694 0.384366
\(526\) 0 0
\(527\) 12.9418 0.563754
\(528\) 0 0
\(529\) −16.6412 −0.723530
\(530\) 0 0
\(531\) −12.5117 −0.542960
\(532\) 0 0
\(533\) 0.482528 0.0209006
\(534\) 0 0
\(535\) −23.2521 −1.00527
\(536\) 0 0
\(537\) −37.7169 −1.62760
\(538\) 0 0
\(539\) −14.6980 −0.633087
\(540\) 0 0
\(541\) 18.9931 0.816577 0.408289 0.912853i \(-0.366126\pi\)
0.408289 + 0.912853i \(0.366126\pi\)
\(542\) 0 0
\(543\) −43.3138 −1.85877
\(544\) 0 0
\(545\) 12.8976 0.552474
\(546\) 0 0
\(547\) 29.9596 1.28098 0.640490 0.767967i \(-0.278731\pi\)
0.640490 + 0.767967i \(0.278731\pi\)
\(548\) 0 0
\(549\) −1.12857 −0.0481662
\(550\) 0 0
\(551\) 15.4828 0.659589
\(552\) 0 0
\(553\) 17.8635 0.759632
\(554\) 0 0
\(555\) 40.2728 1.70949
\(556\) 0 0
\(557\) −38.9749 −1.65142 −0.825709 0.564096i \(-0.809225\pi\)
−0.825709 + 0.564096i \(0.809225\pi\)
\(558\) 0 0
\(559\) −10.0027 −0.423071
\(560\) 0 0
\(561\) 26.8627 1.13414
\(562\) 0 0
\(563\) −10.0149 −0.422080 −0.211040 0.977477i \(-0.567685\pi\)
−0.211040 + 0.977477i \(0.567685\pi\)
\(564\) 0 0
\(565\) 8.70978 0.366423
\(566\) 0 0
\(567\) −20.3199 −0.853357
\(568\) 0 0
\(569\) 5.81832 0.243917 0.121958 0.992535i \(-0.461083\pi\)
0.121958 + 0.992535i \(0.461083\pi\)
\(570\) 0 0
\(571\) 16.0941 0.673516 0.336758 0.941591i \(-0.390670\pi\)
0.336758 + 0.941591i \(0.390670\pi\)
\(572\) 0 0
\(573\) −51.0436 −2.13238
\(574\) 0 0
\(575\) 5.59969 0.233523
\(576\) 0 0
\(577\) 0.178763 0.00744199 0.00372100 0.999993i \(-0.498816\pi\)
0.00372100 + 0.999993i \(0.498816\pi\)
\(578\) 0 0
\(579\) 27.4951 1.14266
\(580\) 0 0
\(581\) −23.0160 −0.954864
\(582\) 0 0
\(583\) −15.3402 −0.635326
\(584\) 0 0
\(585\) 14.3512 0.593349
\(586\) 0 0
\(587\) −25.2001 −1.04012 −0.520060 0.854130i \(-0.674090\pi\)
−0.520060 + 0.854130i \(0.674090\pi\)
\(588\) 0 0
\(589\) −15.5471 −0.640605
\(590\) 0 0
\(591\) −4.97891 −0.204805
\(592\) 0 0
\(593\) −18.9359 −0.777605 −0.388802 0.921321i \(-0.627111\pi\)
−0.388802 + 0.921321i \(0.627111\pi\)
\(594\) 0 0
\(595\) 9.38145 0.384602
\(596\) 0 0
\(597\) −4.59028 −0.187868
\(598\) 0 0
\(599\) 20.8791 0.853097 0.426549 0.904465i \(-0.359729\pi\)
0.426549 + 0.904465i \(0.359729\pi\)
\(600\) 0 0
\(601\) −18.7344 −0.764193 −0.382097 0.924122i \(-0.624798\pi\)
−0.382097 + 0.924122i \(0.624798\pi\)
\(602\) 0 0
\(603\) −3.40968 −0.138853
\(604\) 0 0
\(605\) −8.00801 −0.325572
\(606\) 0 0
\(607\) −12.1694 −0.493943 −0.246971 0.969023i \(-0.579435\pi\)
−0.246971 + 0.969023i \(0.579435\pi\)
\(608\) 0 0
\(609\) −16.5076 −0.668922
\(610\) 0 0
\(611\) 2.29162 0.0927089
\(612\) 0 0
\(613\) 43.7814 1.76832 0.884158 0.467188i \(-0.154733\pi\)
0.884158 + 0.467188i \(0.154733\pi\)
\(614\) 0 0
\(615\) −0.359416 −0.0144930
\(616\) 0 0
\(617\) −47.6870 −1.91980 −0.959902 0.280335i \(-0.909555\pi\)
−0.959902 + 0.280335i \(0.909555\pi\)
\(618\) 0 0
\(619\) 25.3980 1.02083 0.510416 0.859927i \(-0.329491\pi\)
0.510416 + 0.859927i \(0.329491\pi\)
\(620\) 0 0
\(621\) −6.81055 −0.273298
\(622\) 0 0
\(623\) −17.8362 −0.714593
\(624\) 0 0
\(625\) −8.96565 −0.358626
\(626\) 0 0
\(627\) −32.2703 −1.28875
\(628\) 0 0
\(629\) −34.2758 −1.36666
\(630\) 0 0
\(631\) −11.7365 −0.467221 −0.233611 0.972330i \(-0.575054\pi\)
−0.233611 + 0.972330i \(0.575054\pi\)
\(632\) 0 0
\(633\) 1.09496 0.0435207
\(634\) 0 0
\(635\) −28.8653 −1.14549
\(636\) 0 0
\(637\) 18.0590 0.715524
\(638\) 0 0
\(639\) −1.52814 −0.0604522
\(640\) 0 0
\(641\) 33.1285 1.30850 0.654250 0.756279i \(-0.272985\pi\)
0.654250 + 0.756279i \(0.272985\pi\)
\(642\) 0 0
\(643\) −4.01084 −0.158172 −0.0790861 0.996868i \(-0.525200\pi\)
−0.0790861 + 0.996868i \(0.525200\pi\)
\(644\) 0 0
\(645\) 7.45064 0.293368
\(646\) 0 0
\(647\) −14.5470 −0.571903 −0.285952 0.958244i \(-0.592310\pi\)
−0.285952 + 0.958244i \(0.592310\pi\)
\(648\) 0 0
\(649\) −28.2220 −1.10781
\(650\) 0 0
\(651\) 16.5761 0.649669
\(652\) 0 0
\(653\) 23.2618 0.910306 0.455153 0.890413i \(-0.349585\pi\)
0.455153 + 0.890413i \(0.349585\pi\)
\(654\) 0 0
\(655\) 0.496542 0.0194015
\(656\) 0 0
\(657\) −11.4809 −0.447913
\(658\) 0 0
\(659\) −24.0497 −0.936843 −0.468422 0.883505i \(-0.655177\pi\)
−0.468422 + 0.883505i \(0.655177\pi\)
\(660\) 0 0
\(661\) 23.5895 0.917526 0.458763 0.888559i \(-0.348293\pi\)
0.458763 + 0.888559i \(0.348293\pi\)
\(662\) 0 0
\(663\) −33.0054 −1.28182
\(664\) 0 0
\(665\) −11.2700 −0.437031
\(666\) 0 0
\(667\) −10.4960 −0.406406
\(668\) 0 0
\(669\) 2.10380 0.0813375
\(670\) 0 0
\(671\) −2.54566 −0.0982741
\(672\) 0 0
\(673\) 45.6895 1.76120 0.880600 0.473861i \(-0.157140\pi\)
0.880600 + 0.473861i \(0.157140\pi\)
\(674\) 0 0
\(675\) −5.99750 −0.230844
\(676\) 0 0
\(677\) 30.6141 1.17660 0.588298 0.808644i \(-0.299798\pi\)
0.588298 + 0.808644i \(0.299798\pi\)
\(678\) 0 0
\(679\) −3.60550 −0.138367
\(680\) 0 0
\(681\) 45.0856 1.72769
\(682\) 0 0
\(683\) −5.23237 −0.200211 −0.100106 0.994977i \(-0.531918\pi\)
−0.100106 + 0.994977i \(0.531918\pi\)
\(684\) 0 0
\(685\) −18.2867 −0.698698
\(686\) 0 0
\(687\) −16.1045 −0.614425
\(688\) 0 0
\(689\) 18.8481 0.718054
\(690\) 0 0
\(691\) 25.1535 0.956884 0.478442 0.878119i \(-0.341202\pi\)
0.478442 + 0.878119i \(0.341202\pi\)
\(692\) 0 0
\(693\) 12.7325 0.483670
\(694\) 0 0
\(695\) −37.6764 −1.42915
\(696\) 0 0
\(697\) 0.305895 0.0115866
\(698\) 0 0
\(699\) −46.1058 −1.74388
\(700\) 0 0
\(701\) −32.9520 −1.24458 −0.622291 0.782786i \(-0.713798\pi\)
−0.622291 + 0.782786i \(0.713798\pi\)
\(702\) 0 0
\(703\) 41.1757 1.55297
\(704\) 0 0
\(705\) −1.70693 −0.0642868
\(706\) 0 0
\(707\) 21.1397 0.795039
\(708\) 0 0
\(709\) 39.6164 1.48782 0.743912 0.668278i \(-0.232968\pi\)
0.743912 + 0.668278i \(0.232968\pi\)
\(710\) 0 0
\(711\) 17.3234 0.649679
\(712\) 0 0
\(713\) 10.5395 0.394709
\(714\) 0 0
\(715\) 32.3713 1.21062
\(716\) 0 0
\(717\) −2.95721 −0.110439
\(718\) 0 0
\(719\) −8.58402 −0.320130 −0.160065 0.987106i \(-0.551170\pi\)
−0.160065 + 0.987106i \(0.551170\pi\)
\(720\) 0 0
\(721\) −14.5729 −0.542722
\(722\) 0 0
\(723\) −57.2934 −2.13076
\(724\) 0 0
\(725\) −9.24297 −0.343275
\(726\) 0 0
\(727\) −12.3751 −0.458968 −0.229484 0.973312i \(-0.573704\pi\)
−0.229484 + 0.973312i \(0.573704\pi\)
\(728\) 0 0
\(729\) −2.02375 −0.0749536
\(730\) 0 0
\(731\) −6.34116 −0.234536
\(732\) 0 0
\(733\) 27.5222 1.01656 0.508278 0.861193i \(-0.330282\pi\)
0.508278 + 0.861193i \(0.330282\pi\)
\(734\) 0 0
\(735\) −13.4514 −0.496163
\(736\) 0 0
\(737\) −7.69105 −0.283303
\(738\) 0 0
\(739\) 34.1948 1.25788 0.628938 0.777455i \(-0.283490\pi\)
0.628938 + 0.777455i \(0.283490\pi\)
\(740\) 0 0
\(741\) 39.6496 1.45656
\(742\) 0 0
\(743\) 47.7219 1.75075 0.875373 0.483448i \(-0.160616\pi\)
0.875373 + 0.483448i \(0.160616\pi\)
\(744\) 0 0
\(745\) −14.2349 −0.521525
\(746\) 0 0
\(747\) −22.3202 −0.816652
\(748\) 0 0
\(749\) 25.3469 0.926154
\(750\) 0 0
\(751\) 23.0917 0.842627 0.421313 0.906915i \(-0.361569\pi\)
0.421313 + 0.906915i \(0.361569\pi\)
\(752\) 0 0
\(753\) 2.18229 0.0795271
\(754\) 0 0
\(755\) −19.2230 −0.699598
\(756\) 0 0
\(757\) −40.4049 −1.46854 −0.734271 0.678856i \(-0.762476\pi\)
−0.734271 + 0.678856i \(0.762476\pi\)
\(758\) 0 0
\(759\) 21.8764 0.794064
\(760\) 0 0
\(761\) −6.33788 −0.229748 −0.114874 0.993380i \(-0.536646\pi\)
−0.114874 + 0.993380i \(0.536646\pi\)
\(762\) 0 0
\(763\) −14.0596 −0.508992
\(764\) 0 0
\(765\) 9.09783 0.328933
\(766\) 0 0
\(767\) 34.6755 1.25206
\(768\) 0 0
\(769\) −23.8100 −0.858612 −0.429306 0.903159i \(-0.641242\pi\)
−0.429306 + 0.903159i \(0.641242\pi\)
\(770\) 0 0
\(771\) −19.0793 −0.687125
\(772\) 0 0
\(773\) 2.96887 0.106783 0.0533914 0.998574i \(-0.482997\pi\)
0.0533914 + 0.998574i \(0.482997\pi\)
\(774\) 0 0
\(775\) 9.28133 0.333395
\(776\) 0 0
\(777\) −43.9010 −1.57494
\(778\) 0 0
\(779\) −0.367473 −0.0131661
\(780\) 0 0
\(781\) −3.44695 −0.123341
\(782\) 0 0
\(783\) 11.2416 0.401743
\(784\) 0 0
\(785\) −0.295182 −0.0105355
\(786\) 0 0
\(787\) −12.7084 −0.453004 −0.226502 0.974011i \(-0.572729\pi\)
−0.226502 + 0.974011i \(0.572729\pi\)
\(788\) 0 0
\(789\) 42.3912 1.50917
\(790\) 0 0
\(791\) −9.49446 −0.337584
\(792\) 0 0
\(793\) 3.12778 0.111071
\(794\) 0 0
\(795\) −14.0392 −0.497918
\(796\) 0 0
\(797\) −39.5534 −1.40105 −0.700526 0.713627i \(-0.747051\pi\)
−0.700526 + 0.713627i \(0.747051\pi\)
\(798\) 0 0
\(799\) 1.45275 0.0513947
\(800\) 0 0
\(801\) −17.2970 −0.611159
\(802\) 0 0
\(803\) −25.8969 −0.913883
\(804\) 0 0
\(805\) 7.64006 0.269277
\(806\) 0 0
\(807\) −16.8753 −0.594039
\(808\) 0 0
\(809\) 31.6668 1.11335 0.556673 0.830732i \(-0.312078\pi\)
0.556673 + 0.830732i \(0.312078\pi\)
\(810\) 0 0
\(811\) −30.5085 −1.07130 −0.535650 0.844440i \(-0.679933\pi\)
−0.535650 + 0.844440i \(0.679933\pi\)
\(812\) 0 0
\(813\) −51.7268 −1.81414
\(814\) 0 0
\(815\) −22.9489 −0.803865
\(816\) 0 0
\(817\) 7.61766 0.266508
\(818\) 0 0
\(819\) −15.6441 −0.546650
\(820\) 0 0
\(821\) −1.76561 −0.0616202 −0.0308101 0.999525i \(-0.509809\pi\)
−0.0308101 + 0.999525i \(0.509809\pi\)
\(822\) 0 0
\(823\) 20.9524 0.730356 0.365178 0.930938i \(-0.381008\pi\)
0.365178 + 0.930938i \(0.381008\pi\)
\(824\) 0 0
\(825\) 19.2648 0.670715
\(826\) 0 0
\(827\) 19.7468 0.686663 0.343331 0.939214i \(-0.388445\pi\)
0.343331 + 0.939214i \(0.388445\pi\)
\(828\) 0 0
\(829\) −10.1170 −0.351379 −0.175689 0.984446i \(-0.556215\pi\)
−0.175689 + 0.984446i \(0.556215\pi\)
\(830\) 0 0
\(831\) −3.83769 −0.133128
\(832\) 0 0
\(833\) 11.4484 0.396662
\(834\) 0 0
\(835\) −15.9807 −0.553036
\(836\) 0 0
\(837\) −11.2883 −0.390180
\(838\) 0 0
\(839\) 6.51976 0.225087 0.112544 0.993647i \(-0.464100\pi\)
0.112544 + 0.993647i \(0.464100\pi\)
\(840\) 0 0
\(841\) −11.6751 −0.402590
\(842\) 0 0
\(843\) −43.7091 −1.50542
\(844\) 0 0
\(845\) −18.1008 −0.622688
\(846\) 0 0
\(847\) 8.72946 0.299948
\(848\) 0 0
\(849\) 12.7501 0.437581
\(850\) 0 0
\(851\) −27.9135 −0.956861
\(852\) 0 0
\(853\) 20.2508 0.693375 0.346688 0.937981i \(-0.387306\pi\)
0.346688 + 0.937981i \(0.387306\pi\)
\(854\) 0 0
\(855\) −10.9293 −0.373773
\(856\) 0 0
\(857\) 11.2976 0.385919 0.192960 0.981207i \(-0.438191\pi\)
0.192960 + 0.981207i \(0.438191\pi\)
\(858\) 0 0
\(859\) 14.6057 0.498341 0.249171 0.968460i \(-0.419842\pi\)
0.249171 + 0.968460i \(0.419842\pi\)
\(860\) 0 0
\(861\) 0.391796 0.0133524
\(862\) 0 0
\(863\) −36.5862 −1.24541 −0.622704 0.782457i \(-0.713966\pi\)
−0.622704 + 0.782457i \(0.713966\pi\)
\(864\) 0 0
\(865\) 12.1254 0.412276
\(866\) 0 0
\(867\) 16.1754 0.549346
\(868\) 0 0
\(869\) 39.0756 1.32555
\(870\) 0 0
\(871\) 9.44977 0.320193
\(872\) 0 0
\(873\) −3.49650 −0.118339
\(874\) 0 0
\(875\) 21.8768 0.739571
\(876\) 0 0
\(877\) −12.6561 −0.427366 −0.213683 0.976903i \(-0.568546\pi\)
−0.213683 + 0.976903i \(0.568546\pi\)
\(878\) 0 0
\(879\) 6.66356 0.224756
\(880\) 0 0
\(881\) −49.7832 −1.67724 −0.838619 0.544719i \(-0.816636\pi\)
−0.838619 + 0.544719i \(0.816636\pi\)
\(882\) 0 0
\(883\) 47.1957 1.58826 0.794132 0.607746i \(-0.207926\pi\)
0.794132 + 0.607746i \(0.207926\pi\)
\(884\) 0 0
\(885\) −25.8284 −0.868212
\(886\) 0 0
\(887\) 12.6299 0.424070 0.212035 0.977262i \(-0.431991\pi\)
0.212035 + 0.977262i \(0.431991\pi\)
\(888\) 0 0
\(889\) 31.4659 1.05533
\(890\) 0 0
\(891\) −44.4490 −1.48910
\(892\) 0 0
\(893\) −1.74520 −0.0584008
\(894\) 0 0
\(895\) −28.8135 −0.963130
\(896\) 0 0
\(897\) −26.8789 −0.897461
\(898\) 0 0
\(899\) −17.3968 −0.580215
\(900\) 0 0
\(901\) 11.9486 0.398065
\(902\) 0 0
\(903\) −8.12187 −0.270279
\(904\) 0 0
\(905\) −33.0892 −1.09992
\(906\) 0 0
\(907\) −13.5677 −0.450510 −0.225255 0.974300i \(-0.572321\pi\)
−0.225255 + 0.974300i \(0.572321\pi\)
\(908\) 0 0
\(909\) 20.5006 0.679961
\(910\) 0 0
\(911\) 43.1151 1.42847 0.714233 0.699908i \(-0.246776\pi\)
0.714233 + 0.699908i \(0.246776\pi\)
\(912\) 0 0
\(913\) −50.3465 −1.66623
\(914\) 0 0
\(915\) −2.32976 −0.0770194
\(916\) 0 0
\(917\) −0.541276 −0.0178745
\(918\) 0 0
\(919\) −47.3464 −1.56181 −0.780906 0.624649i \(-0.785242\pi\)
−0.780906 + 0.624649i \(0.785242\pi\)
\(920\) 0 0
\(921\) −30.6687 −1.01057
\(922\) 0 0
\(923\) 4.23517 0.139402
\(924\) 0 0
\(925\) −24.5812 −0.808224
\(926\) 0 0
\(927\) −14.1323 −0.464166
\(928\) 0 0
\(929\) 14.3288 0.470111 0.235056 0.971982i \(-0.424473\pi\)
0.235056 + 0.971982i \(0.424473\pi\)
\(930\) 0 0
\(931\) −13.7530 −0.450736
\(932\) 0 0
\(933\) −52.3361 −1.71341
\(934\) 0 0
\(935\) 20.5215 0.671126
\(936\) 0 0
\(937\) −4.34255 −0.141865 −0.0709324 0.997481i \(-0.522597\pi\)
−0.0709324 + 0.997481i \(0.522597\pi\)
\(938\) 0 0
\(939\) −59.7846 −1.95100
\(940\) 0 0
\(941\) 24.8718 0.810798 0.405399 0.914140i \(-0.367133\pi\)
0.405399 + 0.914140i \(0.367133\pi\)
\(942\) 0 0
\(943\) 0.249114 0.00811228
\(944\) 0 0
\(945\) −8.18282 −0.266187
\(946\) 0 0
\(947\) −19.0827 −0.620105 −0.310053 0.950719i \(-0.600347\pi\)
−0.310053 + 0.950719i \(0.600347\pi\)
\(948\) 0 0
\(949\) 31.8188 1.03288
\(950\) 0 0
\(951\) 27.2815 0.884663
\(952\) 0 0
\(953\) −60.9942 −1.97580 −0.987899 0.155102i \(-0.950430\pi\)
−0.987899 + 0.155102i \(0.950430\pi\)
\(954\) 0 0
\(955\) −38.9944 −1.26183
\(956\) 0 0
\(957\) −36.1097 −1.16726
\(958\) 0 0
\(959\) 19.9341 0.643707
\(960\) 0 0
\(961\) −13.5310 −0.436484
\(962\) 0 0
\(963\) 24.5806 0.792098
\(964\) 0 0
\(965\) 21.0046 0.676163
\(966\) 0 0
\(967\) −26.1329 −0.840377 −0.420188 0.907437i \(-0.638036\pi\)
−0.420188 + 0.907437i \(0.638036\pi\)
\(968\) 0 0
\(969\) 25.1355 0.807470
\(970\) 0 0
\(971\) −29.1801 −0.936435 −0.468217 0.883613i \(-0.655104\pi\)
−0.468217 + 0.883613i \(0.655104\pi\)
\(972\) 0 0
\(973\) 41.0707 1.31667
\(974\) 0 0
\(975\) −23.6701 −0.758051
\(976\) 0 0
\(977\) 48.9495 1.56603 0.783017 0.622000i \(-0.213680\pi\)
0.783017 + 0.622000i \(0.213680\pi\)
\(978\) 0 0
\(979\) −39.0160 −1.24696
\(980\) 0 0
\(981\) −13.6346 −0.435318
\(982\) 0 0
\(983\) −56.2456 −1.79396 −0.896979 0.442074i \(-0.854243\pi\)
−0.896979 + 0.442074i \(0.854243\pi\)
\(984\) 0 0
\(985\) −3.80360 −0.121193
\(986\) 0 0
\(987\) 1.86071 0.0592271
\(988\) 0 0
\(989\) −5.16411 −0.164209
\(990\) 0 0
\(991\) 9.10217 0.289140 0.144570 0.989495i \(-0.453820\pi\)
0.144570 + 0.989495i \(0.453820\pi\)
\(992\) 0 0
\(993\) 55.8949 1.77377
\(994\) 0 0
\(995\) −3.50671 −0.111170
\(996\) 0 0
\(997\) 39.1557 1.24007 0.620037 0.784573i \(-0.287118\pi\)
0.620037 + 0.784573i \(0.287118\pi\)
\(998\) 0 0
\(999\) 29.8965 0.945883
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 4016.2.a.g.1.1 7
4.3 odd 2 1004.2.a.a.1.7 7
12.11 even 2 9036.2.a.i.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1004.2.a.a.1.7 7 4.3 odd 2
4016.2.a.g.1.1 7 1.1 even 1 trivial
9036.2.a.i.1.5 7 12.11 even 2