Properties

Label 8280.2.a.bv.1.1
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $0$
Dimension $7$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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 1.1
Root \(-3.70204\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} -5.18676 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} -5.18676 q^{7} -5.53051 q^{11} +1.78900 q^{13} +2.22405 q^{17} -8.22035 q^{19} -1.00000 q^{23} +1.00000 q^{25} -7.06032 q^{29} -2.06612 q^{31} +5.18676 q^{35} -5.02631 q^{37} -11.4917 q^{41} -8.62968 q^{43} -1.37239 q^{47} +19.9025 q^{49} +4.46906 q^{53} +5.53051 q^{55} -11.1486 q^{59} +7.81573 q^{61} -1.78900 q^{65} -1.96903 q^{67} +8.51894 q^{71} -10.7482 q^{73} +28.6854 q^{77} -14.0361 q^{79} -6.83698 q^{83} -2.22405 q^{85} +15.5115 q^{89} -9.27911 q^{91} +8.22035 q^{95} -4.19194 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - 7 q^{5} - 6 q^{7}+O(q^{10}) \) 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
\(7\) −5.18676 −1.96041 −0.980205 0.197983i \(-0.936561\pi\)
−0.980205 + 0.197983i \(0.936561\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −5.53051 −1.66751 −0.833756 0.552132i \(-0.813814\pi\)
−0.833756 + 0.552132i \(0.813814\pi\)
\(12\) 0 0
\(13\) 1.78900 0.496179 0.248090 0.968737i \(-0.420197\pi\)
0.248090 + 0.968737i \(0.420197\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.22405 0.539412 0.269706 0.962943i \(-0.413074\pi\)
0.269706 + 0.962943i \(0.413074\pi\)
\(18\) 0 0
\(19\) −8.22035 −1.88588 −0.942939 0.332967i \(-0.891950\pi\)
−0.942939 + 0.332967i \(0.891950\pi\)
\(20\) 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
\(29\) −7.06032 −1.31107 −0.655534 0.755166i \(-0.727556\pi\)
−0.655534 + 0.755166i \(0.727556\pi\)
\(30\) 0 0
\(31\) −2.06612 −0.371086 −0.185543 0.982636i \(-0.559404\pi\)
−0.185543 + 0.982636i \(0.559404\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 5.18676 0.876722
\(36\) 0 0
\(37\) −5.02631 −0.826320 −0.413160 0.910658i \(-0.635575\pi\)
−0.413160 + 0.910658i \(0.635575\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −11.4917 −1.79470 −0.897348 0.441323i \(-0.854509\pi\)
−0.897348 + 0.441323i \(0.854509\pi\)
\(42\) 0 0
\(43\) −8.62968 −1.31601 −0.658007 0.753012i \(-0.728600\pi\)
−0.658007 + 0.753012i \(0.728600\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.37239 −0.200183 −0.100092 0.994978i \(-0.531914\pi\)
−0.100092 + 0.994978i \(0.531914\pi\)
\(48\) 0 0
\(49\) 19.9025 2.84321
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.46906 0.613873 0.306936 0.951730i \(-0.400696\pi\)
0.306936 + 0.951730i \(0.400696\pi\)
\(54\) 0 0
\(55\) 5.53051 0.745734
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −11.1486 −1.45143 −0.725713 0.687997i \(-0.758490\pi\)
−0.725713 + 0.687997i \(0.758490\pi\)
\(60\) 0 0
\(61\) 7.81573 1.00070 0.500351 0.865823i \(-0.333204\pi\)
0.500351 + 0.865823i \(0.333204\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.78900 −0.221898
\(66\) 0 0
\(67\) −1.96903 −0.240555 −0.120277 0.992740i \(-0.538378\pi\)
−0.120277 + 0.992740i \(0.538378\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.51894 1.01101 0.505506 0.862823i \(-0.331306\pi\)
0.505506 + 0.862823i \(0.331306\pi\)
\(72\) 0 0
\(73\) −10.7482 −1.25799 −0.628994 0.777410i \(-0.716533\pi\)
−0.628994 + 0.777410i \(0.716533\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 28.6854 3.26901
\(78\) 0 0
\(79\) −14.0361 −1.57918 −0.789591 0.613633i \(-0.789707\pi\)
−0.789591 + 0.613633i \(0.789707\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6.83698 −0.750456 −0.375228 0.926933i \(-0.622436\pi\)
−0.375228 + 0.926933i \(0.622436\pi\)
\(84\) 0 0
\(85\) −2.22405 −0.241232
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 15.5115 1.64421 0.822105 0.569335i \(-0.192799\pi\)
0.822105 + 0.569335i \(0.192799\pi\)
\(90\) 0 0
\(91\) −9.27911 −0.972715
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 8.22035 0.843390
\(96\) 0 0
\(97\) −4.19194 −0.425627 −0.212814 0.977093i \(-0.568263\pi\)
−0.212814 + 0.977093i \(0.568263\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −2.10435 −0.209390 −0.104695 0.994504i \(-0.533387\pi\)
−0.104695 + 0.994504i \(0.533387\pi\)
\(102\) 0 0
\(103\) 8.51052 0.838566 0.419283 0.907856i \(-0.362281\pi\)
0.419283 + 0.907856i \(0.362281\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −8.56936 −0.828431 −0.414216 0.910179i \(-0.635944\pi\)
−0.414216 + 0.910179i \(0.635944\pi\)
\(108\) 0 0
\(109\) −20.0678 −1.92214 −0.961071 0.276300i \(-0.910892\pi\)
−0.961071 + 0.276300i \(0.910892\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 11.1800 1.05173 0.525864 0.850569i \(-0.323742\pi\)
0.525864 + 0.850569i \(0.323742\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −11.5356 −1.05747
\(120\) 0 0
\(121\) 19.5866 1.78060
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −15.7755 −1.39985 −0.699926 0.714216i \(-0.746784\pi\)
−0.699926 + 0.714216i \(0.746784\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.23941 0.545140 0.272570 0.962136i \(-0.412126\pi\)
0.272570 + 0.962136i \(0.412126\pi\)
\(132\) 0 0
\(133\) 42.6370 3.69709
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.63201 −0.224867 −0.112434 0.993659i \(-0.535865\pi\)
−0.112434 + 0.993659i \(0.535865\pi\)
\(138\) 0 0
\(139\) 1.02125 0.0866211 0.0433106 0.999062i \(-0.486210\pi\)
0.0433106 + 0.999062i \(0.486210\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −9.89409 −0.827385
\(144\) 0 0
\(145\) 7.06032 0.586327
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −20.6707 −1.69341 −0.846705 0.532062i \(-0.821417\pi\)
−0.846705 + 0.532062i \(0.821417\pi\)
\(150\) 0 0
\(151\) 7.02315 0.571536 0.285768 0.958299i \(-0.407751\pi\)
0.285768 + 0.958299i \(0.407751\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.06612 0.165955
\(156\) 0 0
\(157\) −16.5529 −1.32107 −0.660535 0.750796i \(-0.729670\pi\)
−0.660535 + 0.750796i \(0.729670\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.18676 0.408774
\(162\) 0 0
\(163\) 11.2497 0.881144 0.440572 0.897717i \(-0.354776\pi\)
0.440572 + 0.897717i \(0.354776\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 17.7556 1.37397 0.686984 0.726673i \(-0.258934\pi\)
0.686984 + 0.726673i \(0.258934\pi\)
\(168\) 0 0
\(169\) −9.79948 −0.753806
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −10.0126 −0.761246 −0.380623 0.924730i \(-0.624290\pi\)
−0.380623 + 0.924730i \(0.624290\pi\)
\(174\) 0 0
\(175\) −5.18676 −0.392082
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 15.4041 1.15135 0.575677 0.817677i \(-0.304738\pi\)
0.575677 + 0.817677i \(0.304738\pi\)
\(180\) 0 0
\(181\) 9.47996 0.704640 0.352320 0.935880i \(-0.385393\pi\)
0.352320 + 0.935880i \(0.385393\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5.02631 0.369542
\(186\) 0 0
\(187\) −12.3001 −0.899476
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 11.8994 0.861014 0.430507 0.902587i \(-0.358335\pi\)
0.430507 + 0.902587i \(0.358335\pi\)
\(192\) 0 0
\(193\) 24.6195 1.77215 0.886075 0.463543i \(-0.153422\pi\)
0.886075 + 0.463543i \(0.153422\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.98652 −0.141534 −0.0707670 0.997493i \(-0.522545\pi\)
−0.0707670 + 0.997493i \(0.522545\pi\)
\(198\) 0 0
\(199\) 4.07108 0.288591 0.144296 0.989535i \(-0.453908\pi\)
0.144296 + 0.989535i \(0.453908\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 36.6202 2.57023
\(204\) 0 0
\(205\) 11.4917 0.802613
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 45.4627 3.14472
\(210\) 0 0
\(211\) 2.29266 0.157834 0.0789168 0.996881i \(-0.474854\pi\)
0.0789168 + 0.996881i \(0.474854\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 8.62968 0.588539
\(216\) 0 0
\(217\) 10.7165 0.727481
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3.97883 0.267645
\(222\) 0 0
\(223\) −8.88382 −0.594905 −0.297452 0.954737i \(-0.596137\pi\)
−0.297452 + 0.954737i \(0.596137\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 26.5779 1.76404 0.882018 0.471216i \(-0.156185\pi\)
0.882018 + 0.471216i \(0.156185\pi\)
\(228\) 0 0
\(229\) −15.7078 −1.03800 −0.518999 0.854775i \(-0.673695\pi\)
−0.518999 + 0.854775i \(0.673695\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −20.0578 −1.31403 −0.657016 0.753876i \(-0.728182\pi\)
−0.657016 + 0.753876i \(0.728182\pi\)
\(234\) 0 0
\(235\) 1.37239 0.0895247
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.0908704 −0.00587792 −0.00293896 0.999996i \(-0.500936\pi\)
−0.00293896 + 0.999996i \(0.500936\pi\)
\(240\) 0 0
\(241\) −13.6392 −0.878575 −0.439288 0.898346i \(-0.644769\pi\)
−0.439288 + 0.898346i \(0.644769\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −19.9025 −1.27152
\(246\) 0 0
\(247\) −14.7062 −0.935733
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 5.63107 0.355430 0.177715 0.984082i \(-0.443130\pi\)
0.177715 + 0.984082i \(0.443130\pi\)
\(252\) 0 0
\(253\) 5.53051 0.347700
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 11.8908 0.741727 0.370863 0.928687i \(-0.379062\pi\)
0.370863 + 0.928687i \(0.379062\pi\)
\(258\) 0 0
\(259\) 26.0703 1.61993
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 10.2162 0.629956 0.314978 0.949099i \(-0.398003\pi\)
0.314978 + 0.949099i \(0.398003\pi\)
\(264\) 0 0
\(265\) −4.46906 −0.274532
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.258728 −0.0157749 −0.00788746 0.999969i \(-0.502511\pi\)
−0.00788746 + 0.999969i \(0.502511\pi\)
\(270\) 0 0
\(271\) −5.19036 −0.315292 −0.157646 0.987496i \(-0.550391\pi\)
−0.157646 + 0.987496i \(0.550391\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.53051 −0.333503
\(276\) 0 0
\(277\) −19.9592 −1.19923 −0.599615 0.800288i \(-0.704680\pi\)
−0.599615 + 0.800288i \(0.704680\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 13.2250 0.788938 0.394469 0.918909i \(-0.370929\pi\)
0.394469 + 0.918909i \(0.370929\pi\)
\(282\) 0 0
\(283\) 16.2598 0.966544 0.483272 0.875470i \(-0.339448\pi\)
0.483272 + 0.875470i \(0.339448\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 59.6045 3.51834
\(288\) 0 0
\(289\) −12.0536 −0.709035
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6.28858 0.367383 0.183691 0.982984i \(-0.441195\pi\)
0.183691 + 0.982984i \(0.441195\pi\)
\(294\) 0 0
\(295\) 11.1486 0.649098
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.78900 −0.103461
\(300\) 0 0
\(301\) 44.7601 2.57993
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −7.81573 −0.447527
\(306\) 0 0
\(307\) 23.6636 1.35055 0.675275 0.737566i \(-0.264025\pi\)
0.675275 + 0.737566i \(0.264025\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 13.7175 0.777848 0.388924 0.921270i \(-0.372847\pi\)
0.388924 + 0.921270i \(0.372847\pi\)
\(312\) 0 0
\(313\) −21.1372 −1.19475 −0.597373 0.801964i \(-0.703789\pi\)
−0.597373 + 0.801964i \(0.703789\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −16.9895 −0.954227 −0.477113 0.878842i \(-0.658317\pi\)
−0.477113 + 0.878842i \(0.658317\pi\)
\(318\) 0 0
\(319\) 39.0472 2.18622
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −18.2825 −1.01726
\(324\) 0 0
\(325\) 1.78900 0.0992359
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 7.11825 0.392442
\(330\) 0 0
\(331\) −9.57525 −0.526303 −0.263152 0.964754i \(-0.584762\pi\)
−0.263152 + 0.964754i \(0.584762\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.96903 0.107579
\(336\) 0 0
\(337\) −18.9193 −1.03060 −0.515299 0.857011i \(-0.672319\pi\)
−0.515299 + 0.857011i \(0.672319\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 11.4267 0.618791
\(342\) 0 0
\(343\) −66.9220 −3.61345
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −21.5628 −1.15755 −0.578777 0.815486i \(-0.696470\pi\)
−0.578777 + 0.815486i \(0.696470\pi\)
\(348\) 0 0
\(349\) 1.04297 0.0558291 0.0279145 0.999610i \(-0.491113\pi\)
0.0279145 + 0.999610i \(0.491113\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 7.75247 0.412622 0.206311 0.978486i \(-0.433854\pi\)
0.206311 + 0.978486i \(0.433854\pi\)
\(354\) 0 0
\(355\) −8.51894 −0.452138
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 33.2843 1.75668 0.878340 0.478037i \(-0.158651\pi\)
0.878340 + 0.478037i \(0.158651\pi\)
\(360\) 0 0
\(361\) 48.5741 2.55653
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 10.7482 0.562589
\(366\) 0 0
\(367\) −32.6495 −1.70429 −0.852146 0.523305i \(-0.824699\pi\)
−0.852146 + 0.523305i \(0.824699\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −23.1799 −1.20344
\(372\) 0 0
\(373\) −4.46944 −0.231419 −0.115710 0.993283i \(-0.536914\pi\)
−0.115710 + 0.993283i \(0.536914\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −12.6309 −0.650525
\(378\) 0 0
\(379\) 5.91194 0.303676 0.151838 0.988405i \(-0.451481\pi\)
0.151838 + 0.988405i \(0.451481\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3.80511 −0.194432 −0.0972161 0.995263i \(-0.530994\pi\)
−0.0972161 + 0.995263i \(0.530994\pi\)
\(384\) 0 0
\(385\) −28.6854 −1.46195
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −11.4995 −0.583046 −0.291523 0.956564i \(-0.594162\pi\)
−0.291523 + 0.956564i \(0.594162\pi\)
\(390\) 0 0
\(391\) −2.22405 −0.112475
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 14.0361 0.706232
\(396\) 0 0
\(397\) −4.15253 −0.208409 −0.104205 0.994556i \(-0.533230\pi\)
−0.104205 + 0.994556i \(0.533230\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 36.5628 1.82586 0.912930 0.408116i \(-0.133814\pi\)
0.912930 + 0.408116i \(0.133814\pi\)
\(402\) 0 0
\(403\) −3.69629 −0.184125
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 27.7981 1.37790
\(408\) 0 0
\(409\) 23.9221 1.18287 0.591436 0.806352i \(-0.298561\pi\)
0.591436 + 0.806352i \(0.298561\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 57.8252 2.84539
\(414\) 0 0
\(415\) 6.83698 0.335614
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4.34692 0.212361 0.106180 0.994347i \(-0.466138\pi\)
0.106180 + 0.994347i \(0.466138\pi\)
\(420\) 0 0
\(421\) 5.98865 0.291869 0.145935 0.989294i \(-0.453381\pi\)
0.145935 + 0.989294i \(0.453381\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.22405 0.107882
\(426\) 0 0
\(427\) −40.5383 −1.96179
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −21.2601 −1.02406 −0.512030 0.858967i \(-0.671106\pi\)
−0.512030 + 0.858967i \(0.671106\pi\)
\(432\) 0 0
\(433\) −17.9361 −0.861955 −0.430978 0.902363i \(-0.641831\pi\)
−0.430978 + 0.902363i \(0.641831\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8.22035 0.393233
\(438\) 0 0
\(439\) −40.7767 −1.94616 −0.973082 0.230459i \(-0.925977\pi\)
−0.973082 + 0.230459i \(0.925977\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 23.7585 1.12880 0.564401 0.825501i \(-0.309107\pi\)
0.564401 + 0.825501i \(0.309107\pi\)
\(444\) 0 0
\(445\) −15.5115 −0.735313
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −6.21479 −0.293294 −0.146647 0.989189i \(-0.546848\pi\)
−0.146647 + 0.989189i \(0.546848\pi\)
\(450\) 0 0
\(451\) 63.5548 2.99268
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 9.27911 0.435012
\(456\) 0 0
\(457\) 2.53970 0.118802 0.0594010 0.998234i \(-0.481081\pi\)
0.0594010 + 0.998234i \(0.481081\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 14.8931 0.693641 0.346820 0.937932i \(-0.387261\pi\)
0.346820 + 0.937932i \(0.387261\pi\)
\(462\) 0 0
\(463\) −28.1509 −1.30828 −0.654142 0.756372i \(-0.726970\pi\)
−0.654142 + 0.756372i \(0.726970\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 25.3752 1.17423 0.587113 0.809505i \(-0.300264\pi\)
0.587113 + 0.809505i \(0.300264\pi\)
\(468\) 0 0
\(469\) 10.2129 0.471586
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 47.7266 2.19447
\(474\) 0 0
\(475\) −8.22035 −0.377175
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −8.03440 −0.367101 −0.183551 0.983010i \(-0.558759\pi\)
−0.183551 + 0.983010i \(0.558759\pi\)
\(480\) 0 0
\(481\) −8.99207 −0.410003
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.19194 0.190346
\(486\) 0 0
\(487\) −16.1617 −0.732356 −0.366178 0.930545i \(-0.619334\pi\)
−0.366178 + 0.930545i \(0.619334\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 19.5159 0.880740 0.440370 0.897816i \(-0.354847\pi\)
0.440370 + 0.897816i \(0.354847\pi\)
\(492\) 0 0
\(493\) −15.7025 −0.707205
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −44.1857 −1.98200
\(498\) 0 0
\(499\) 16.2002 0.725222 0.362611 0.931941i \(-0.381885\pi\)
0.362611 + 0.931941i \(0.381885\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −25.7478 −1.14804 −0.574019 0.818842i \(-0.694616\pi\)
−0.574019 + 0.818842i \(0.694616\pi\)
\(504\) 0 0
\(505\) 2.10435 0.0936422
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 29.6907 1.31602 0.658009 0.753010i \(-0.271399\pi\)
0.658009 + 0.753010i \(0.271399\pi\)
\(510\) 0 0
\(511\) 55.7486 2.46617
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −8.51052 −0.375018
\(516\) 0 0
\(517\) 7.59001 0.333808
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −38.5883 −1.69058 −0.845291 0.534305i \(-0.820573\pi\)
−0.845291 + 0.534305i \(0.820573\pi\)
\(522\) 0 0
\(523\) −29.6118 −1.29483 −0.647416 0.762137i \(-0.724150\pi\)
−0.647416 + 0.762137i \(0.724150\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.59515 −0.200168
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −20.5586 −0.890491
\(534\) 0 0
\(535\) 8.56936 0.370486
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −110.071 −4.74109
\(540\) 0 0
\(541\) 7.81422 0.335959 0.167980 0.985790i \(-0.446276\pi\)
0.167980 + 0.985790i \(0.446276\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 20.0678 0.859608
\(546\) 0 0
\(547\) 34.1207 1.45890 0.729448 0.684036i \(-0.239777\pi\)
0.729448 + 0.684036i \(0.239777\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 58.0383 2.47251
\(552\) 0 0
\(553\) 72.8018 3.09585
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −37.2090 −1.57660 −0.788299 0.615293i \(-0.789038\pi\)
−0.788299 + 0.615293i \(0.789038\pi\)
\(558\) 0 0
\(559\) −15.4385 −0.652979
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −30.8233 −1.29905 −0.649523 0.760342i \(-0.725031\pi\)
−0.649523 + 0.760342i \(0.725031\pi\)
\(564\) 0 0
\(565\) −11.1800 −0.470347
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −10.5281 −0.441361 −0.220681 0.975346i \(-0.570828\pi\)
−0.220681 + 0.975346i \(0.570828\pi\)
\(570\) 0 0
\(571\) −34.7410 −1.45387 −0.726933 0.686709i \(-0.759055\pi\)
−0.726933 + 0.686709i \(0.759055\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −12.9327 −0.538397 −0.269199 0.963085i \(-0.586759\pi\)
−0.269199 + 0.963085i \(0.586759\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 35.4618 1.47120
\(582\) 0 0
\(583\) −24.7162 −1.02364
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −24.4522 −1.00925 −0.504626 0.863338i \(-0.668370\pi\)
−0.504626 + 0.863338i \(0.668370\pi\)
\(588\) 0 0
\(589\) 16.9842 0.699823
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −19.5575 −0.803130 −0.401565 0.915831i \(-0.631534\pi\)
−0.401565 + 0.915831i \(0.631534\pi\)
\(594\) 0 0
\(595\) 11.5356 0.472914
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 29.5425 1.20708 0.603538 0.797334i \(-0.293757\pi\)
0.603538 + 0.797334i \(0.293757\pi\)
\(600\) 0 0
\(601\) −22.9919 −0.937861 −0.468930 0.883235i \(-0.655361\pi\)
−0.468930 + 0.883235i \(0.655361\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −19.5866 −0.796308
\(606\) 0 0
\(607\) −47.5502 −1.93000 −0.965001 0.262247i \(-0.915536\pi\)
−0.965001 + 0.262247i \(0.915536\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.45520 −0.0993268
\(612\) 0 0
\(613\) −18.6728 −0.754189 −0.377094 0.926175i \(-0.623077\pi\)
−0.377094 + 0.926175i \(0.623077\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.222177 0.00894452 0.00447226 0.999990i \(-0.498576\pi\)
0.00447226 + 0.999990i \(0.498576\pi\)
\(618\) 0 0
\(619\) 27.3634 1.09983 0.549914 0.835221i \(-0.314660\pi\)
0.549914 + 0.835221i \(0.314660\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −80.4542 −3.22333
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −11.1788 −0.445727
\(630\) 0 0
\(631\) −28.0642 −1.11722 −0.558608 0.829432i \(-0.688664\pi\)
−0.558608 + 0.829432i \(0.688664\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 15.7755 0.626033
\(636\) 0 0
\(637\) 35.6055 1.41074
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7.31916 −0.289089 −0.144545 0.989498i \(-0.546172\pi\)
−0.144545 + 0.989498i \(0.546172\pi\)
\(642\) 0 0
\(643\) −23.0989 −0.910932 −0.455466 0.890253i \(-0.650527\pi\)
−0.455466 + 0.890253i \(0.650527\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −8.19129 −0.322033 −0.161016 0.986952i \(-0.551477\pi\)
−0.161016 + 0.986952i \(0.551477\pi\)
\(648\) 0 0
\(649\) 61.6576 2.42027
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 27.8688 1.09059 0.545296 0.838244i \(-0.316417\pi\)
0.545296 + 0.838244i \(0.316417\pi\)
\(654\) 0 0
\(655\) −6.23941 −0.243794
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −28.9507 −1.12776 −0.563880 0.825856i \(-0.690692\pi\)
−0.563880 + 0.825856i \(0.690692\pi\)
\(660\) 0 0
\(661\) 26.7973 1.04229 0.521147 0.853467i \(-0.325504\pi\)
0.521147 + 0.853467i \(0.325504\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −42.6370 −1.65339
\(666\) 0 0
\(667\) 7.06032 0.273377
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −43.2250 −1.66868
\(672\) 0 0
\(673\) 29.5218 1.13798 0.568991 0.822344i \(-0.307334\pi\)
0.568991 + 0.822344i \(0.307334\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −13.4897 −0.518450 −0.259225 0.965817i \(-0.583467\pi\)
−0.259225 + 0.965817i \(0.583467\pi\)
\(678\) 0 0
\(679\) 21.7426 0.834404
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 24.7128 0.945609 0.472805 0.881167i \(-0.343242\pi\)
0.472805 + 0.881167i \(0.343242\pi\)
\(684\) 0 0
\(685\) 2.63201 0.100564
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 7.99515 0.304591
\(690\) 0 0
\(691\) 19.1923 0.730108 0.365054 0.930986i \(-0.381051\pi\)
0.365054 + 0.930986i \(0.381051\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.02125 −0.0387381
\(696\) 0 0
\(697\) −25.5580 −0.968080
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −0.866603 −0.0327311 −0.0163656 0.999866i \(-0.505210\pi\)
−0.0163656 + 0.999866i \(0.505210\pi\)
\(702\) 0 0
\(703\) 41.3180 1.55834
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 10.9147 0.410491
\(708\) 0 0
\(709\) −36.5381 −1.37222 −0.686108 0.727499i \(-0.740682\pi\)
−0.686108 + 0.727499i \(0.740682\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.06612 0.0773768
\(714\) 0 0
\(715\) 9.89409 0.370018
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 40.2845 1.50236 0.751179 0.660099i \(-0.229486\pi\)
0.751179 + 0.660099i \(0.229486\pi\)
\(720\) 0 0
\(721\) −44.1420 −1.64393
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7.06032 −0.262214
\(726\) 0 0
\(727\) 40.4482 1.50014 0.750071 0.661358i \(-0.230019\pi\)
0.750071 + 0.661358i \(0.230019\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −19.1929 −0.709873
\(732\) 0 0
\(733\) −15.1569 −0.559831 −0.279916 0.960025i \(-0.590306\pi\)
−0.279916 + 0.960025i \(0.590306\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10.8897 0.401128
\(738\) 0 0
\(739\) −1.69715 −0.0624307 −0.0312154 0.999513i \(-0.509938\pi\)
−0.0312154 + 0.999513i \(0.509938\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −18.8438 −0.691314 −0.345657 0.938361i \(-0.612344\pi\)
−0.345657 + 0.938361i \(0.612344\pi\)
\(744\) 0 0
\(745\) 20.6707 0.757316
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 44.4472 1.62407
\(750\) 0 0
\(751\) 6.98309 0.254816 0.127408 0.991850i \(-0.459334\pi\)
0.127408 + 0.991850i \(0.459334\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −7.02315 −0.255598
\(756\) 0 0
\(757\) −42.1359 −1.53146 −0.765728 0.643164i \(-0.777621\pi\)
−0.765728 + 0.643164i \(0.777621\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −41.6359 −1.50930 −0.754649 0.656128i \(-0.772193\pi\)
−0.754649 + 0.656128i \(0.772193\pi\)
\(762\) 0 0
\(763\) 104.087 3.76819
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −19.9449 −0.720168
\(768\) 0 0
\(769\) −7.24030 −0.261092 −0.130546 0.991442i \(-0.541673\pi\)
−0.130546 + 0.991442i \(0.541673\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −23.8204 −0.856759 −0.428379 0.903599i \(-0.640915\pi\)
−0.428379 + 0.903599i \(0.640915\pi\)
\(774\) 0 0
\(775\) −2.06612 −0.0742172
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 94.4655 3.38458
\(780\) 0 0
\(781\) −47.1141 −1.68588
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 16.5529 0.590800
\(786\) 0 0
\(787\) 24.5172 0.873945 0.436972 0.899475i \(-0.356051\pi\)
0.436972 + 0.899475i \(0.356051\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −57.9881 −2.06182
\(792\) 0 0
\(793\) 13.9823 0.496527
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −22.0419 −0.780765 −0.390382 0.920653i \(-0.627657\pi\)
−0.390382 + 0.920653i \(0.627657\pi\)
\(798\) 0 0
\(799\) −3.05226 −0.107981
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 59.4433 2.09771
\(804\) 0 0
\(805\) −5.18676 −0.182809
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −8.44998 −0.297085 −0.148543 0.988906i \(-0.547458\pi\)
−0.148543 + 0.988906i \(0.547458\pi\)
\(810\) 0 0
\(811\) −7.40731 −0.260106 −0.130053 0.991507i \(-0.541515\pi\)
−0.130053 + 0.991507i \(0.541515\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −11.2497 −0.394060
\(816\) 0 0
\(817\) 70.9390 2.48184
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −12.7103 −0.443594 −0.221797 0.975093i \(-0.571192\pi\)
−0.221797 + 0.975093i \(0.571192\pi\)
\(822\) 0 0
\(823\) −1.23216 −0.0429505 −0.0214753 0.999769i \(-0.506836\pi\)
−0.0214753 + 0.999769i \(0.506836\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −34.6839 −1.20608 −0.603039 0.797712i \(-0.706044\pi\)
−0.603039 + 0.797712i \(0.706044\pi\)
\(828\) 0 0
\(829\) −2.83700 −0.0985330 −0.0492665 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 44.2641 1.53366
\(834\) 0 0
\(835\) −17.7556 −0.614457
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −0.353131 −0.0121914 −0.00609571 0.999981i \(-0.501940\pi\)
−0.00609571 + 0.999981i \(0.501940\pi\)
\(840\) 0 0
\(841\) 20.8481 0.718899
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 9.79948 0.337112
\(846\) 0 0
\(847\) −101.591 −3.49071
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 5.02631 0.172300
\(852\) 0 0
\(853\) −30.1917 −1.03374 −0.516872 0.856063i \(-0.672904\pi\)
−0.516872 + 0.856063i \(0.672904\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 37.6661 1.28665 0.643326 0.765593i \(-0.277554\pi\)
0.643326 + 0.765593i \(0.277554\pi\)
\(858\) 0 0
\(859\) 36.2701 1.23752 0.618760 0.785580i \(-0.287635\pi\)
0.618760 + 0.785580i \(0.287635\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 7.17475 0.244231 0.122116 0.992516i \(-0.461032\pi\)
0.122116 + 0.992516i \(0.461032\pi\)
\(864\) 0 0
\(865\) 10.0126 0.340439
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 77.6267 2.63331
\(870\) 0 0
\(871\) −3.52259 −0.119358
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 5.18676 0.175344
\(876\) 0 0
\(877\) −20.5238 −0.693039 −0.346519 0.938043i \(-0.612637\pi\)
−0.346519 + 0.938043i \(0.612637\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 53.5933 1.80561 0.902803 0.430055i \(-0.141506\pi\)
0.902803 + 0.430055i \(0.141506\pi\)
\(882\) 0 0
\(883\) 7.63602 0.256973 0.128486 0.991711i \(-0.458988\pi\)
0.128486 + 0.991711i \(0.458988\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 8.54307 0.286848 0.143424 0.989661i \(-0.454189\pi\)
0.143424 + 0.989661i \(0.454189\pi\)
\(888\) 0 0
\(889\) 81.8238 2.74428
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 11.2815 0.377521
\(894\) 0 0
\(895\) −15.4041 −0.514901
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 14.5875 0.486519
\(900\) 0 0
\(901\) 9.93942 0.331130
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −9.47996 −0.315125
\(906\) 0 0
\(907\) −19.5010 −0.647519 −0.323759 0.946139i \(-0.604947\pi\)
−0.323759 + 0.946139i \(0.604947\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 2.46746 0.0817505 0.0408753 0.999164i \(-0.486985\pi\)
0.0408753 + 0.999164i \(0.486985\pi\)
\(912\) 0 0
\(913\) 37.8120 1.25139
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −32.3623 −1.06870
\(918\) 0 0
\(919\) 44.6343 1.47235 0.736175 0.676792i \(-0.236630\pi\)
0.736175 + 0.676792i \(0.236630\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 15.2404 0.501643
\(924\) 0 0
\(925\) −5.02631 −0.165264
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1.85129 0.0607389 0.0303694 0.999539i \(-0.490332\pi\)
0.0303694 + 0.999539i \(0.490332\pi\)
\(930\) 0 0
\(931\) −163.605 −5.36195
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 12.3001 0.402258
\(936\) 0 0
\(937\) 17.3837 0.567900 0.283950 0.958839i \(-0.408355\pi\)
0.283950 + 0.958839i \(0.408355\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 4.20116 0.136954 0.0684769 0.997653i \(-0.478186\pi\)
0.0684769 + 0.997653i \(0.478186\pi\)
\(942\) 0 0
\(943\) 11.4917 0.374220
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 5.27990 0.171574 0.0857869 0.996314i \(-0.472660\pi\)
0.0857869 + 0.996314i \(0.472660\pi\)
\(948\) 0 0
\(949\) −19.2286 −0.624187
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 41.3188 1.33845 0.669223 0.743061i \(-0.266627\pi\)
0.669223 + 0.743061i \(0.266627\pi\)
\(954\) 0 0
\(955\) −11.8994 −0.385057
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 13.6516 0.440832
\(960\) 0 0
\(961\) −26.7312 −0.862295
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −24.6195 −0.792529
\(966\) 0 0
\(967\) −56.6523 −1.82181 −0.910907 0.412612i \(-0.864617\pi\)
−0.910907 + 0.412612i \(0.864617\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −9.40721 −0.301892 −0.150946 0.988542i \(-0.548232\pi\)
−0.150946 + 0.988542i \(0.548232\pi\)
\(972\) 0 0
\(973\) −5.29697 −0.169813
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −58.7170 −1.87852 −0.939262 0.343200i \(-0.888489\pi\)
−0.939262 + 0.343200i \(0.888489\pi\)
\(978\) 0 0
\(979\) −85.7863 −2.74174
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −37.9057 −1.20900 −0.604502 0.796603i \(-0.706628\pi\)
−0.604502 + 0.796603i \(0.706628\pi\)
\(984\) 0 0
\(985\) 1.98652 0.0632959
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 8.62968 0.274408
\(990\) 0 0
\(991\) −36.0724 −1.14588 −0.572938 0.819599i \(-0.694197\pi\)
−0.572938 + 0.819599i \(0.694197\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −4.07108 −0.129062
\(996\) 0 0
\(997\) −4.37723 −0.138628 −0.0693142 0.997595i \(-0.522081\pi\)
−0.0693142 + 0.997595i \(0.522081\pi\)
\(998\) 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.1.1 7
3.2 odd 2 8280.2.a.bw.1.1 yes 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8280.2.a.bv.1.1 7 1.1 even 1 trivial
8280.2.a.bw.1.1 yes 7 3.2 odd 2