Properties

Label 8280.2.a.bv.1.3
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $0$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8280.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(66.1161328736\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \( x^{7} - 3x^{6} - 18x^{5} + 46x^{4} + 60x^{3} - 76x^{2} - 51x - 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(3.22540\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} -2.82985 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} -2.82985 q^{7} +4.94410 q^{11} +4.65799 q^{13} +2.16509 q^{17} -0.347949 q^{19} -1.00000 q^{23} +1.00000 q^{25} -1.32315 q^{29} +10.0343 q^{31} +2.82985 q^{35} -5.95454 q^{37} +4.98690 q^{41} +1.57815 q^{43} -13.0205 q^{47} +1.00804 q^{49} -5.12429 q^{53} -4.94410 q^{55} +12.4243 q^{59} +10.4630 q^{61} -4.65799 q^{65} -12.2600 q^{67} -4.84614 q^{71} +12.3742 q^{73} -13.9910 q^{77} -8.81099 q^{79} +14.0533 q^{83} -2.16509 q^{85} +13.2819 q^{89} -13.1814 q^{91} +0.347949 q^{95} -9.56802 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - 7 q^{5} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - 7 q^{5} - 6 q^{7} + 2 q^{11} - 6 q^{13} + 4 q^{17} - 8 q^{19} - 7 q^{23} + 7 q^{25} - 2 q^{29} - 8 q^{31} + 6 q^{35} - 16 q^{37} - 2 q^{41} - 10 q^{43} + 8 q^{47} + 19 q^{49} + 10 q^{53} - 2 q^{55} + 24 q^{59} + 8 q^{61} + 6 q^{65} - 20 q^{67} + 8 q^{71} + 2 q^{73} + 12 q^{77} - 2 q^{79} + 22 q^{83} - 4 q^{85} + 16 q^{89} - 20 q^{91} + 8 q^{95} + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −2.82985 −1.06958 −0.534791 0.844984i \(-0.679610\pi\)
−0.534791 + 0.844984i \(0.679610\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.94410 1.49070 0.745350 0.666673i \(-0.232282\pi\)
0.745350 + 0.666673i \(0.232282\pi\)
\(12\) 0 0
\(13\) 4.65799 1.29189 0.645947 0.763382i \(-0.276463\pi\)
0.645947 + 0.763382i \(0.276463\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.16509 0.525111 0.262556 0.964917i \(-0.415435\pi\)
0.262556 + 0.964917i \(0.415435\pi\)
\(18\) 0 0
\(19\) −0.347949 −0.0798249 −0.0399125 0.999203i \(-0.512708\pi\)
−0.0399125 + 0.999203i \(0.512708\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.32315 −0.245702 −0.122851 0.992425i \(-0.539204\pi\)
−0.122851 + 0.992425i \(0.539204\pi\)
\(30\) 0 0
\(31\) 10.0343 1.80222 0.901109 0.433593i \(-0.142755\pi\)
0.901109 + 0.433593i \(0.142755\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.82985 0.478332
\(36\) 0 0
\(37\) −5.95454 −0.978920 −0.489460 0.872026i \(-0.662806\pi\)
−0.489460 + 0.872026i \(0.662806\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 4.98690 0.778822 0.389411 0.921064i \(-0.372678\pi\)
0.389411 + 0.921064i \(0.372678\pi\)
\(42\) 0 0
\(43\) 1.57815 0.240665 0.120333 0.992734i \(-0.461604\pi\)
0.120333 + 0.992734i \(0.461604\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −13.0205 −1.89924 −0.949619 0.313406i \(-0.898530\pi\)
−0.949619 + 0.313406i \(0.898530\pi\)
\(48\) 0 0
\(49\) 1.00804 0.144006
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −5.12429 −0.703876 −0.351938 0.936023i \(-0.614477\pi\)
−0.351938 + 0.936023i \(0.614477\pi\)
\(54\) 0 0
\(55\) −4.94410 −0.666662
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.4243 1.61750 0.808752 0.588149i \(-0.200143\pi\)
0.808752 + 0.588149i \(0.200143\pi\)
\(60\) 0 0
\(61\) 10.4630 1.33965 0.669827 0.742517i \(-0.266368\pi\)
0.669827 + 0.742517i \(0.266368\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.65799 −0.577753
\(66\) 0 0
\(67\) −12.2600 −1.49780 −0.748898 0.662686i \(-0.769417\pi\)
−0.748898 + 0.662686i \(0.769417\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.84614 −0.575131 −0.287566 0.957761i \(-0.592846\pi\)
−0.287566 + 0.957761i \(0.592846\pi\)
\(72\) 0 0
\(73\) 12.3742 1.44829 0.724147 0.689646i \(-0.242234\pi\)
0.724147 + 0.689646i \(0.242234\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −13.9910 −1.59443
\(78\) 0 0
\(79\) −8.81099 −0.991313 −0.495657 0.868519i \(-0.665073\pi\)
−0.495657 + 0.868519i \(0.665073\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 14.0533 1.54255 0.771274 0.636503i \(-0.219620\pi\)
0.771274 + 0.636503i \(0.219620\pi\)
\(84\) 0 0
\(85\) −2.16509 −0.234837
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 13.2819 1.40788 0.703940 0.710259i \(-0.251422\pi\)
0.703940 + 0.710259i \(0.251422\pi\)
\(90\) 0 0
\(91\) −13.1814 −1.38179
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.347949 0.0356988
\(96\) 0 0
\(97\) −9.56802 −0.971485 −0.485743 0.874102i \(-0.661451\pi\)
−0.485743 + 0.874102i \(0.661451\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −10.1041 −1.00540 −0.502699 0.864462i \(-0.667660\pi\)
−0.502699 + 0.864462i \(0.667660\pi\)
\(102\) 0 0
\(103\) −11.5213 −1.13523 −0.567613 0.823296i \(-0.692133\pi\)
−0.567613 + 0.823296i \(0.692133\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 17.1192 1.65497 0.827486 0.561486i \(-0.189770\pi\)
0.827486 + 0.561486i \(0.189770\pi\)
\(108\) 0 0
\(109\) 10.6603 1.02107 0.510537 0.859856i \(-0.329447\pi\)
0.510537 + 0.859856i \(0.329447\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2.61589 −0.246082 −0.123041 0.992402i \(-0.539265\pi\)
−0.123041 + 0.992402i \(0.539265\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −6.12687 −0.561650
\(120\) 0 0
\(121\) 13.4441 1.22219
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 4.23348 0.375660 0.187830 0.982202i \(-0.439855\pi\)
0.187830 + 0.982202i \(0.439855\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −9.87807 −0.863051 −0.431525 0.902101i \(-0.642024\pi\)
−0.431525 + 0.902101i \(0.642024\pi\)
\(132\) 0 0
\(133\) 0.984642 0.0853793
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −11.2618 −0.962159 −0.481080 0.876677i \(-0.659755\pi\)
−0.481080 + 0.876677i \(0.659755\pi\)
\(138\) 0 0
\(139\) −22.5163 −1.90981 −0.954905 0.296913i \(-0.904043\pi\)
−0.954905 + 0.296913i \(0.904043\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 23.0296 1.92583
\(144\) 0 0
\(145\) 1.32315 0.109881
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 20.0435 1.64203 0.821015 0.570907i \(-0.193408\pi\)
0.821015 + 0.570907i \(0.193408\pi\)
\(150\) 0 0
\(151\) −17.7448 −1.44405 −0.722025 0.691867i \(-0.756788\pi\)
−0.722025 + 0.691867i \(0.756788\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −10.0343 −0.805976
\(156\) 0 0
\(157\) 3.47753 0.277537 0.138769 0.990325i \(-0.455686\pi\)
0.138769 + 0.990325i \(0.455686\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.82985 0.223023
\(162\) 0 0
\(163\) 7.93108 0.621210 0.310605 0.950539i \(-0.399468\pi\)
0.310605 + 0.950539i \(0.399468\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 7.59285 0.587552 0.293776 0.955874i \(-0.405088\pi\)
0.293776 + 0.955874i \(0.405088\pi\)
\(168\) 0 0
\(169\) 8.69689 0.668992
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 7.24531 0.550850 0.275425 0.961323i \(-0.411181\pi\)
0.275425 + 0.961323i \(0.411181\pi\)
\(174\) 0 0
\(175\) −2.82985 −0.213916
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1.54920 0.115793 0.0578964 0.998323i \(-0.481561\pi\)
0.0578964 + 0.998323i \(0.481561\pi\)
\(180\) 0 0
\(181\) −1.41079 −0.104863 −0.0524316 0.998625i \(-0.516697\pi\)
−0.0524316 + 0.998625i \(0.516697\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5.95454 0.437786
\(186\) 0 0
\(187\) 10.7044 0.782784
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 10.5973 0.766795 0.383398 0.923583i \(-0.374754\pi\)
0.383398 + 0.923583i \(0.374754\pi\)
\(192\) 0 0
\(193\) −20.7209 −1.49152 −0.745760 0.666215i \(-0.767914\pi\)
−0.745760 + 0.666215i \(0.767914\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 20.8915 1.48846 0.744228 0.667926i \(-0.232818\pi\)
0.744228 + 0.667926i \(0.232818\pi\)
\(198\) 0 0
\(199\) −25.0562 −1.77618 −0.888092 0.459665i \(-0.847969\pi\)
−0.888092 + 0.459665i \(0.847969\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 3.74430 0.262799
\(204\) 0 0
\(205\) −4.98690 −0.348300
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.72029 −0.118995
\(210\) 0 0
\(211\) 11.6415 0.801436 0.400718 0.916201i \(-0.368761\pi\)
0.400718 + 0.916201i \(0.368761\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.57815 −0.107629
\(216\) 0 0
\(217\) −28.3956 −1.92762
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 10.0850 0.678388
\(222\) 0 0
\(223\) 19.4037 1.29937 0.649685 0.760204i \(-0.274901\pi\)
0.649685 + 0.760204i \(0.274901\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.44027 0.427456 0.213728 0.976893i \(-0.431439\pi\)
0.213728 + 0.976893i \(0.431439\pi\)
\(228\) 0 0
\(229\) −1.42608 −0.0942380 −0.0471190 0.998889i \(-0.515004\pi\)
−0.0471190 + 0.998889i \(0.515004\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 10.9705 0.718702 0.359351 0.933202i \(-0.382998\pi\)
0.359351 + 0.933202i \(0.382998\pi\)
\(234\) 0 0
\(235\) 13.0205 0.849365
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 14.7873 0.956514 0.478257 0.878220i \(-0.341269\pi\)
0.478257 + 0.878220i \(0.341269\pi\)
\(240\) 0 0
\(241\) 10.0504 0.647401 0.323700 0.946160i \(-0.395073\pi\)
0.323700 + 0.946160i \(0.395073\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.00804 −0.0644013
\(246\) 0 0
\(247\) −1.62074 −0.103125
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −3.54142 −0.223532 −0.111766 0.993735i \(-0.535651\pi\)
−0.111766 + 0.993735i \(0.535651\pi\)
\(252\) 0 0
\(253\) −4.94410 −0.310833
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 19.8020 1.23522 0.617608 0.786486i \(-0.288102\pi\)
0.617608 + 0.786486i \(0.288102\pi\)
\(258\) 0 0
\(259\) 16.8504 1.04703
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −6.13769 −0.378466 −0.189233 0.981932i \(-0.560600\pi\)
−0.189233 + 0.981932i \(0.560600\pi\)
\(264\) 0 0
\(265\) 5.12429 0.314783
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2.27775 0.138877 0.0694385 0.997586i \(-0.477879\pi\)
0.0694385 + 0.997586i \(0.477879\pi\)
\(270\) 0 0
\(271\) 30.8457 1.87374 0.936872 0.349674i \(-0.113707\pi\)
0.936872 + 0.349674i \(0.113707\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 4.94410 0.298140
\(276\) 0 0
\(277\) 8.69943 0.522698 0.261349 0.965244i \(-0.415833\pi\)
0.261349 + 0.965244i \(0.415833\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −5.86657 −0.349970 −0.174985 0.984571i \(-0.555988\pi\)
−0.174985 + 0.984571i \(0.555988\pi\)
\(282\) 0 0
\(283\) −5.30578 −0.315396 −0.157698 0.987487i \(-0.550407\pi\)
−0.157698 + 0.987487i \(0.550407\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −14.1122 −0.833015
\(288\) 0 0
\(289\) −12.3124 −0.724258
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.61142 0.0941401 0.0470701 0.998892i \(-0.485012\pi\)
0.0470701 + 0.998892i \(0.485012\pi\)
\(294\) 0 0
\(295\) −12.4243 −0.723370
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4.65799 −0.269379
\(300\) 0 0
\(301\) −4.46592 −0.257411
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −10.4630 −0.599112
\(306\) 0 0
\(307\) −19.0852 −1.08925 −0.544626 0.838679i \(-0.683328\pi\)
−0.544626 + 0.838679i \(0.683328\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 33.9003 1.92231 0.961155 0.276011i \(-0.0890125\pi\)
0.961155 + 0.276011i \(0.0890125\pi\)
\(312\) 0 0
\(313\) 23.8734 1.34940 0.674702 0.738090i \(-0.264272\pi\)
0.674702 + 0.738090i \(0.264272\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.3541 −0.750041 −0.375021 0.927016i \(-0.622364\pi\)
−0.375021 + 0.927016i \(0.622364\pi\)
\(318\) 0 0
\(319\) −6.54176 −0.366268
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −0.753340 −0.0419170
\(324\) 0 0
\(325\) 4.65799 0.258379
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 36.8461 2.03139
\(330\) 0 0
\(331\) 23.5923 1.29675 0.648376 0.761320i \(-0.275449\pi\)
0.648376 + 0.761320i \(0.275449\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 12.2600 0.669834
\(336\) 0 0
\(337\) 26.1866 1.42647 0.713237 0.700923i \(-0.247228\pi\)
0.713237 + 0.700923i \(0.247228\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 49.6106 2.68657
\(342\) 0 0
\(343\) 16.9563 0.915556
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 33.4133 1.79372 0.896859 0.442316i \(-0.145843\pi\)
0.896859 + 0.442316i \(0.145843\pi\)
\(348\) 0 0
\(349\) 13.7105 0.733904 0.366952 0.930240i \(-0.380401\pi\)
0.366952 + 0.930240i \(0.380401\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 32.6135 1.73584 0.867920 0.496704i \(-0.165456\pi\)
0.867920 + 0.496704i \(0.165456\pi\)
\(354\) 0 0
\(355\) 4.84614 0.257207
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.30182 0.227042 0.113521 0.993536i \(-0.463787\pi\)
0.113521 + 0.993536i \(0.463787\pi\)
\(360\) 0 0
\(361\) −18.8789 −0.993628
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −12.3742 −0.647697
\(366\) 0 0
\(367\) −25.5453 −1.33345 −0.666727 0.745302i \(-0.732305\pi\)
−0.666727 + 0.745302i \(0.732305\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 14.5010 0.752853
\(372\) 0 0
\(373\) −1.08868 −0.0563697 −0.0281848 0.999603i \(-0.508973\pi\)
−0.0281848 + 0.999603i \(0.508973\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6.16321 −0.317421
\(378\) 0 0
\(379\) −21.5620 −1.10756 −0.553782 0.832662i \(-0.686816\pi\)
−0.553782 + 0.832662i \(0.686816\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 6.31231 0.322544 0.161272 0.986910i \(-0.448440\pi\)
0.161272 + 0.986910i \(0.448440\pi\)
\(384\) 0 0
\(385\) 13.9910 0.713049
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7.52936 −0.381754 −0.190877 0.981614i \(-0.561133\pi\)
−0.190877 + 0.981614i \(0.561133\pi\)
\(390\) 0 0
\(391\) −2.16509 −0.109493
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 8.81099 0.443329
\(396\) 0 0
\(397\) 24.5533 1.23229 0.616147 0.787631i \(-0.288693\pi\)
0.616147 + 0.787631i \(0.288693\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 30.4811 1.52215 0.761077 0.648662i \(-0.224671\pi\)
0.761077 + 0.648662i \(0.224671\pi\)
\(402\) 0 0
\(403\) 46.7398 2.32827
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −29.4398 −1.45928
\(408\) 0 0
\(409\) 37.8239 1.87027 0.935136 0.354290i \(-0.115277\pi\)
0.935136 + 0.354290i \(0.115277\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −35.1589 −1.73005
\(414\) 0 0
\(415\) −14.0533 −0.689848
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 21.9254 1.07112 0.535562 0.844496i \(-0.320100\pi\)
0.535562 + 0.844496i \(0.320100\pi\)
\(420\) 0 0
\(421\) 36.1125 1.76002 0.880008 0.474960i \(-0.157537\pi\)
0.880008 + 0.474960i \(0.157537\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.16509 0.105022
\(426\) 0 0
\(427\) −29.6088 −1.43287
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −33.4074 −1.60918 −0.804590 0.593831i \(-0.797615\pi\)
−0.804590 + 0.593831i \(0.797615\pi\)
\(432\) 0 0
\(433\) −24.9892 −1.20090 −0.600451 0.799661i \(-0.705012\pi\)
−0.600451 + 0.799661i \(0.705012\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.347949 0.0166446
\(438\) 0 0
\(439\) 20.5951 0.982950 0.491475 0.870892i \(-0.336458\pi\)
0.491475 + 0.870892i \(0.336458\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 13.4349 0.638312 0.319156 0.947702i \(-0.396601\pi\)
0.319156 + 0.947702i \(0.396601\pi\)
\(444\) 0 0
\(445\) −13.2819 −0.629623
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10.0435 −0.473980 −0.236990 0.971512i \(-0.576161\pi\)
−0.236990 + 0.971512i \(0.576161\pi\)
\(450\) 0 0
\(451\) 24.6557 1.16099
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 13.1814 0.617954
\(456\) 0 0
\(457\) 5.60889 0.262373 0.131186 0.991358i \(-0.458121\pi\)
0.131186 + 0.991358i \(0.458121\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 37.8370 1.76224 0.881121 0.472890i \(-0.156789\pi\)
0.881121 + 0.472890i \(0.156789\pi\)
\(462\) 0 0
\(463\) −39.0326 −1.81400 −0.907000 0.421131i \(-0.861633\pi\)
−0.907000 + 0.421131i \(0.861633\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4.70089 0.217531 0.108766 0.994067i \(-0.465310\pi\)
0.108766 + 0.994067i \(0.465310\pi\)
\(468\) 0 0
\(469\) 34.6939 1.60201
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 7.80251 0.358760
\(474\) 0 0
\(475\) −0.347949 −0.0159650
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −15.8361 −0.723570 −0.361785 0.932262i \(-0.617833\pi\)
−0.361785 + 0.932262i \(0.617833\pi\)
\(480\) 0 0
\(481\) −27.7362 −1.26466
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 9.56802 0.434461
\(486\) 0 0
\(487\) −16.6167 −0.752973 −0.376487 0.926422i \(-0.622868\pi\)
−0.376487 + 0.926422i \(0.622868\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −26.9471 −1.21611 −0.608054 0.793896i \(-0.708049\pi\)
−0.608054 + 0.793896i \(0.708049\pi\)
\(492\) 0 0
\(493\) −2.86473 −0.129021
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 13.7139 0.615150
\(498\) 0 0
\(499\) 15.5034 0.694029 0.347015 0.937860i \(-0.387195\pi\)
0.347015 + 0.937860i \(0.387195\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −31.4518 −1.40236 −0.701182 0.712982i \(-0.747344\pi\)
−0.701182 + 0.712982i \(0.747344\pi\)
\(504\) 0 0
\(505\) 10.1041 0.449628
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.46634 −0.0649943 −0.0324971 0.999472i \(-0.510346\pi\)
−0.0324971 + 0.999472i \(0.510346\pi\)
\(510\) 0 0
\(511\) −35.0172 −1.54907
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 11.5213 0.507688
\(516\) 0 0
\(517\) −64.3747 −2.83120
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 5.58182 0.244544 0.122272 0.992497i \(-0.460982\pi\)
0.122272 + 0.992497i \(0.460982\pi\)
\(522\) 0 0
\(523\) −11.2870 −0.493548 −0.246774 0.969073i \(-0.579371\pi\)
−0.246774 + 0.969073i \(0.579371\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 21.7252 0.946365
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 23.2289 1.00616
\(534\) 0 0
\(535\) −17.1192 −0.740126
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 4.98385 0.214670
\(540\) 0 0
\(541\) 17.9045 0.769773 0.384887 0.922964i \(-0.374241\pi\)
0.384887 + 0.922964i \(0.374241\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −10.6603 −0.456638
\(546\) 0 0
\(547\) −16.1535 −0.690673 −0.345336 0.938479i \(-0.612235\pi\)
−0.345336 + 0.938479i \(0.612235\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0.460387 0.0196132
\(552\) 0 0
\(553\) 24.9338 1.06029
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −7.90248 −0.334839 −0.167419 0.985886i \(-0.553543\pi\)
−0.167419 + 0.985886i \(0.553543\pi\)
\(558\) 0 0
\(559\) 7.35100 0.310914
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7.36386 −0.310350 −0.155175 0.987887i \(-0.549594\pi\)
−0.155175 + 0.987887i \(0.549594\pi\)
\(564\) 0 0
\(565\) 2.61589 0.110051
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.18004 0.0494698 0.0247349 0.999694i \(-0.492126\pi\)
0.0247349 + 0.999694i \(0.492126\pi\)
\(570\) 0 0
\(571\) 9.59220 0.401421 0.200711 0.979651i \(-0.435675\pi\)
0.200711 + 0.979651i \(0.435675\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −21.2966 −0.886589 −0.443294 0.896376i \(-0.646190\pi\)
−0.443294 + 0.896376i \(0.646190\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −39.7686 −1.64988
\(582\) 0 0
\(583\) −25.3350 −1.04927
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −27.2149 −1.12328 −0.561640 0.827382i \(-0.689829\pi\)
−0.561640 + 0.827382i \(0.689829\pi\)
\(588\) 0 0
\(589\) −3.49143 −0.143862
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 24.6044 1.01038 0.505191 0.863008i \(-0.331422\pi\)
0.505191 + 0.863008i \(0.331422\pi\)
\(594\) 0 0
\(595\) 6.12687 0.251177
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −20.9286 −0.855120 −0.427560 0.903987i \(-0.640627\pi\)
−0.427560 + 0.903987i \(0.640627\pi\)
\(600\) 0 0
\(601\) 28.1317 1.14752 0.573758 0.819025i \(-0.305485\pi\)
0.573758 + 0.819025i \(0.305485\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −13.4441 −0.546580
\(606\) 0 0
\(607\) 4.02339 0.163304 0.0816522 0.996661i \(-0.473980\pi\)
0.0816522 + 0.996661i \(0.473980\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −60.6495 −2.45362
\(612\) 0 0
\(613\) −30.9604 −1.25048 −0.625240 0.780432i \(-0.714999\pi\)
−0.625240 + 0.780432i \(0.714999\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −35.4413 −1.42681 −0.713407 0.700750i \(-0.752849\pi\)
−0.713407 + 0.700750i \(0.752849\pi\)
\(618\) 0 0
\(619\) 7.61916 0.306240 0.153120 0.988208i \(-0.451068\pi\)
0.153120 + 0.988208i \(0.451068\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −37.5858 −1.50584
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −12.8921 −0.514042
\(630\) 0 0
\(631\) −21.6842 −0.863235 −0.431618 0.902057i \(-0.642057\pi\)
−0.431618 + 0.902057i \(0.642057\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4.23348 −0.168000
\(636\) 0 0
\(637\) 4.69544 0.186040
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −39.4616 −1.55864 −0.779320 0.626626i \(-0.784435\pi\)
−0.779320 + 0.626626i \(0.784435\pi\)
\(642\) 0 0
\(643\) 3.18996 0.125800 0.0628999 0.998020i \(-0.479965\pi\)
0.0628999 + 0.998020i \(0.479965\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 18.2970 0.719330 0.359665 0.933081i \(-0.382891\pi\)
0.359665 + 0.933081i \(0.382891\pi\)
\(648\) 0 0
\(649\) 61.4269 2.41122
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 33.0406 1.29298 0.646490 0.762923i \(-0.276236\pi\)
0.646490 + 0.762923i \(0.276236\pi\)
\(654\) 0 0
\(655\) 9.87807 0.385968
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 27.7651 1.08157 0.540787 0.841160i \(-0.318127\pi\)
0.540787 + 0.841160i \(0.318127\pi\)
\(660\) 0 0
\(661\) −30.2032 −1.17477 −0.587384 0.809308i \(-0.699842\pi\)
−0.587384 + 0.809308i \(0.699842\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.984642 −0.0381828
\(666\) 0 0
\(667\) 1.32315 0.0512324
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 51.7303 1.99702
\(672\) 0 0
\(673\) −23.3010 −0.898187 −0.449093 0.893485i \(-0.648253\pi\)
−0.449093 + 0.893485i \(0.648253\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 43.2511 1.66228 0.831138 0.556066i \(-0.187690\pi\)
0.831138 + 0.556066i \(0.187690\pi\)
\(678\) 0 0
\(679\) 27.0760 1.03908
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −24.0271 −0.919372 −0.459686 0.888082i \(-0.652038\pi\)
−0.459686 + 0.888082i \(0.652038\pi\)
\(684\) 0 0
\(685\) 11.2618 0.430291
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −23.8689 −0.909333
\(690\) 0 0
\(691\) −18.0742 −0.687574 −0.343787 0.939048i \(-0.611710\pi\)
−0.343787 + 0.939048i \(0.611710\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 22.5163 0.854093
\(696\) 0 0
\(697\) 10.7971 0.408968
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 4.35858 0.164621 0.0823107 0.996607i \(-0.473770\pi\)
0.0823107 + 0.996607i \(0.473770\pi\)
\(702\) 0 0
\(703\) 2.07187 0.0781422
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 28.5931 1.07536
\(708\) 0 0
\(709\) 6.28641 0.236091 0.118045 0.993008i \(-0.462337\pi\)
0.118045 + 0.993008i \(0.462337\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −10.0343 −0.375788
\(714\) 0 0
\(715\) −23.0296 −0.861257
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −44.9514 −1.67640 −0.838202 0.545360i \(-0.816393\pi\)
−0.838202 + 0.545360i \(0.816393\pi\)
\(720\) 0 0
\(721\) 32.6035 1.21422
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.32315 −0.0491404
\(726\) 0 0
\(727\) −22.6212 −0.838972 −0.419486 0.907762i \(-0.637790\pi\)
−0.419486 + 0.907762i \(0.637790\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 3.41683 0.126376
\(732\) 0 0
\(733\) 45.9519 1.69727 0.848636 0.528977i \(-0.177424\pi\)
0.848636 + 0.528977i \(0.177424\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −60.6145 −2.23276
\(738\) 0 0
\(739\) 12.1925 0.448509 0.224255 0.974531i \(-0.428005\pi\)
0.224255 + 0.974531i \(0.428005\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.03362 −0.0746063 −0.0373032 0.999304i \(-0.511877\pi\)
−0.0373032 + 0.999304i \(0.511877\pi\)
\(744\) 0 0
\(745\) −20.0435 −0.734338
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −48.4447 −1.77013
\(750\) 0 0
\(751\) −0.935597 −0.0341404 −0.0170702 0.999854i \(-0.505434\pi\)
−0.0170702 + 0.999854i \(0.505434\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 17.7448 0.645798
\(756\) 0 0
\(757\) −28.4242 −1.03310 −0.516548 0.856258i \(-0.672783\pi\)
−0.516548 + 0.856258i \(0.672783\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 45.5123 1.64982 0.824909 0.565265i \(-0.191226\pi\)
0.824909 + 0.565265i \(0.191226\pi\)
\(762\) 0 0
\(763\) −30.1671 −1.09212
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 57.8723 2.08965
\(768\) 0 0
\(769\) 4.93028 0.177790 0.0888952 0.996041i \(-0.471666\pi\)
0.0888952 + 0.996041i \(0.471666\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −13.2800 −0.477648 −0.238824 0.971063i \(-0.576762\pi\)
−0.238824 + 0.971063i \(0.576762\pi\)
\(774\) 0 0
\(775\) 10.0343 0.360443
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.73518 −0.0621694
\(780\) 0 0
\(781\) −23.9598 −0.857349
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3.47753 −0.124118
\(786\) 0 0
\(787\) −9.94763 −0.354595 −0.177297 0.984157i \(-0.556735\pi\)
−0.177297 + 0.984157i \(0.556735\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 7.40256 0.263205
\(792\) 0 0
\(793\) 48.7368 1.73069
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 30.1642 1.06847 0.534236 0.845335i \(-0.320599\pi\)
0.534236 + 0.845335i \(0.320599\pi\)
\(798\) 0 0
\(799\) −28.1906 −0.997312
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 61.1794 2.15897
\(804\) 0 0
\(805\) −2.82985 −0.0997390
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 21.2734 0.747935 0.373967 0.927442i \(-0.377997\pi\)
0.373967 + 0.927442i \(0.377997\pi\)
\(810\) 0 0
\(811\) −0.697841 −0.0245045 −0.0122523 0.999925i \(-0.503900\pi\)
−0.0122523 + 0.999925i \(0.503900\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −7.93108 −0.277814
\(816\) 0 0
\(817\) −0.549114 −0.0192111
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −30.8586 −1.07697 −0.538486 0.842635i \(-0.681003\pi\)
−0.538486 + 0.842635i \(0.681003\pi\)
\(822\) 0 0
\(823\) 19.6298 0.684253 0.342127 0.939654i \(-0.388853\pi\)
0.342127 + 0.939654i \(0.388853\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 9.73006 0.338347 0.169174 0.985586i \(-0.445890\pi\)
0.169174 + 0.985586i \(0.445890\pi\)
\(828\) 0 0
\(829\) −19.6529 −0.682573 −0.341287 0.939959i \(-0.610863\pi\)
−0.341287 + 0.939959i \(0.610863\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.18250 0.0756191
\(834\) 0 0
\(835\) −7.59285 −0.262761
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 32.1900 1.11132 0.555661 0.831409i \(-0.312465\pi\)
0.555661 + 0.831409i \(0.312465\pi\)
\(840\) 0 0
\(841\) −27.2493 −0.939630
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −8.69689 −0.299182
\(846\) 0 0
\(847\) −38.0447 −1.30723
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 5.95454 0.204119
\(852\) 0 0
\(853\) −55.8766 −1.91318 −0.956590 0.291438i \(-0.905866\pi\)
−0.956590 + 0.291438i \(0.905866\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 6.15146 0.210130 0.105065 0.994465i \(-0.466495\pi\)
0.105065 + 0.994465i \(0.466495\pi\)
\(858\) 0 0
\(859\) −30.7220 −1.04822 −0.524111 0.851650i \(-0.675602\pi\)
−0.524111 + 0.851650i \(0.675602\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −30.2001 −1.02802 −0.514012 0.857783i \(-0.671841\pi\)
−0.514012 + 0.857783i \(0.671841\pi\)
\(864\) 0 0
\(865\) −7.24531 −0.246348
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −43.5624 −1.47775
\(870\) 0 0
\(871\) −57.1069 −1.93499
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2.82985 0.0956663
\(876\) 0 0
\(877\) −19.8280 −0.669546 −0.334773 0.942299i \(-0.608660\pi\)
−0.334773 + 0.942299i \(0.608660\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 55.1069 1.85660 0.928300 0.371833i \(-0.121271\pi\)
0.928300 + 0.371833i \(0.121271\pi\)
\(882\) 0 0
\(883\) −26.8178 −0.902490 −0.451245 0.892400i \(-0.649020\pi\)
−0.451245 + 0.892400i \(0.649020\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 40.8503 1.37162 0.685810 0.727781i \(-0.259448\pi\)
0.685810 + 0.727781i \(0.259448\pi\)
\(888\) 0 0
\(889\) −11.9801 −0.401799
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 4.53047 0.151607
\(894\) 0 0
\(895\) −1.54920 −0.0517841
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −13.2769 −0.442809
\(900\) 0 0
\(901\) −11.0945 −0.369613
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1.41079 0.0468962
\(906\) 0 0
\(907\) −9.16440 −0.304299 −0.152150 0.988357i \(-0.548620\pi\)
−0.152150 + 0.988357i \(0.548620\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −7.72553 −0.255958 −0.127979 0.991777i \(-0.540849\pi\)
−0.127979 + 0.991777i \(0.540849\pi\)
\(912\) 0 0
\(913\) 69.4808 2.29948
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 27.9534 0.923103
\(918\) 0 0
\(919\) 23.8924 0.788139 0.394069 0.919081i \(-0.371067\pi\)
0.394069 + 0.919081i \(0.371067\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −22.5733 −0.743009
\(924\) 0 0
\(925\) −5.95454 −0.195784
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −19.6787 −0.645636 −0.322818 0.946461i \(-0.604630\pi\)
−0.322818 + 0.946461i \(0.604630\pi\)
\(930\) 0 0
\(931\) −0.350746 −0.0114952
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −10.7044 −0.350072
\(936\) 0 0
\(937\) −52.6536 −1.72012 −0.860058 0.510196i \(-0.829573\pi\)
−0.860058 + 0.510196i \(0.829573\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −4.34001 −0.141480 −0.0707401 0.997495i \(-0.522536\pi\)
−0.0707401 + 0.997495i \(0.522536\pi\)
\(942\) 0 0
\(943\) −4.98690 −0.162396
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 18.0278 0.585825 0.292912 0.956139i \(-0.405376\pi\)
0.292912 + 0.956139i \(0.405376\pi\)
\(948\) 0 0
\(949\) 57.6391 1.87104
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 43.3464 1.40413 0.702064 0.712113i \(-0.252262\pi\)
0.702064 + 0.712113i \(0.252262\pi\)
\(954\) 0 0
\(955\) −10.5973 −0.342921
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 31.8691 1.02911
\(960\) 0 0
\(961\) 69.6876 2.24799
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 20.7209 0.667028
\(966\) 0 0
\(967\) 32.5215 1.04582 0.522911 0.852387i \(-0.324846\pi\)
0.522911 + 0.852387i \(0.324846\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 34.0432 1.09250 0.546249 0.837623i \(-0.316055\pi\)
0.546249 + 0.837623i \(0.316055\pi\)
\(972\) 0 0
\(973\) 63.7178 2.04270
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −31.8626 −1.01937 −0.509687 0.860360i \(-0.670239\pi\)
−0.509687 + 0.860360i \(0.670239\pi\)
\(978\) 0 0
\(979\) 65.6671 2.09873
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −17.9450 −0.572357 −0.286178 0.958176i \(-0.592385\pi\)
−0.286178 + 0.958176i \(0.592385\pi\)
\(984\) 0 0
\(985\) −20.8915 −0.665658
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1.57815 −0.0501822
\(990\) 0 0
\(991\) −42.1482 −1.33888 −0.669441 0.742865i \(-0.733466\pi\)
−0.669441 + 0.742865i \(0.733466\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 25.0562 0.794334
\(996\) 0 0
\(997\) −50.0852 −1.58622 −0.793108 0.609082i \(-0.791538\pi\)
−0.793108 + 0.609082i \(0.791538\pi\)
\(998\) 0 0
\(999\) 0 0
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 8280.2.a.bv.1.3 7
3.2 odd 2 8280.2.a.bw.1.3 yes 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8280.2.a.bv.1.3 7 1.1 even 1 trivial
8280.2.a.bw.1.3 yes 7 3.2 odd 2