Properties

Label 9576.2.a.co.1.1
Level $9576$
Weight $2$
Character 9576.1
Self dual yes
Analytic conductor $76.465$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9576.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(76.4647449756\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.135076.1
Defining polynomial: \( x^{5} - x^{4} - 5x^{3} + 4x^{2} + 4x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 3192)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.15154\) of defining polynomial
Character \(\chi\) \(=\) 9576.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.30308 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q-4.30308 q^{5} +1.00000 q^{7} +2.56627 q^{11} +2.81429 q^{13} +7.96536 q^{17} +1.00000 q^{19} +0.814291 q^{23} +13.5165 q^{25} -3.48879 q^{29} +3.38056 q^{31} -4.30308 q^{35} +3.75198 q^{37} -6.60615 q^{41} -10.2533 q^{47} +1.00000 q^{49} -0.511215 q^{53} -11.0428 q^{55} +13.9901 q^{59} +6.00000 q^{61} -12.1101 q^{65} +11.9805 q^{67} -5.02768 q^{71} +16.0204 q^{73} +2.56627 q^{77} -14.8347 q^{79} +2.01517 q^{83} -34.2756 q^{85} -17.6490 q^{89} +2.81429 q^{91} -4.30308 q^{95} -5.66847 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 2 q^{5} + 5 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 2 q^{5} + 5 q^{7} - 2 q^{11} + 8 q^{13} + 2 q^{17} + 5 q^{19} - 2 q^{23} + 19 q^{25} - 4 q^{29} - 4 q^{31} - 2 q^{35} + 10 q^{37} + 6 q^{41} + 2 q^{47} + 5 q^{49} - 16 q^{53} - 16 q^{55} + 12 q^{59} + 30 q^{61} - 4 q^{65} + 18 q^{67} + 10 q^{71} + 14 q^{73} - 2 q^{77} - 2 q^{79} + 6 q^{83} + 12 q^{85} - 10 q^{89} + 8 q^{91} - 2 q^{95} + 8 q^{97}+O(q^{100}) \) 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
\(5\) −4.30308 −1.92439 −0.962197 0.272354i \(-0.912198\pi\)
−0.962197 + 0.272354i \(0.912198\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.56627 0.773759 0.386880 0.922130i \(-0.373553\pi\)
0.386880 + 0.922130i \(0.373553\pi\)
\(12\) 0 0
\(13\) 2.81429 0.780544 0.390272 0.920700i \(-0.372381\pi\)
0.390272 + 0.920700i \(0.372381\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.96536 1.93188 0.965942 0.258757i \(-0.0833130\pi\)
0.965942 + 0.258757i \(0.0833130\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.814291 0.169791 0.0848957 0.996390i \(-0.472944\pi\)
0.0848957 + 0.996390i \(0.472944\pi\)
\(24\) 0 0
\(25\) 13.5165 2.70329
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3.48879 −0.647851 −0.323926 0.946083i \(-0.605003\pi\)
−0.323926 + 0.946083i \(0.605003\pi\)
\(30\) 0 0
\(31\) 3.38056 0.607166 0.303583 0.952805i \(-0.401817\pi\)
0.303583 + 0.952805i \(0.401817\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.30308 −0.727353
\(36\) 0 0
\(37\) 3.75198 0.616821 0.308411 0.951253i \(-0.400203\pi\)
0.308411 + 0.951253i \(0.400203\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −6.60615 −1.03171 −0.515854 0.856677i \(-0.672525\pi\)
−0.515854 + 0.856677i \(0.672525\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10.2533 −1.49559 −0.747797 0.663928i \(-0.768888\pi\)
−0.747797 + 0.663928i \(0.768888\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.511215 −0.0702207 −0.0351104 0.999383i \(-0.511178\pi\)
−0.0351104 + 0.999383i \(0.511178\pi\)
\(54\) 0 0
\(55\) −11.0428 −1.48902
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 13.9901 1.82135 0.910677 0.413120i \(-0.135561\pi\)
0.910677 + 0.413120i \(0.135561\pi\)
\(60\) 0 0
\(61\) 6.00000 0.768221 0.384111 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −12.1101 −1.50207
\(66\) 0 0
\(67\) 11.9805 1.46366 0.731828 0.681490i \(-0.238668\pi\)
0.731828 + 0.681490i \(0.238668\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −5.02768 −0.596676 −0.298338 0.954460i \(-0.596432\pi\)
−0.298338 + 0.954460i \(0.596432\pi\)
\(72\) 0 0
\(73\) 16.0204 1.87505 0.937524 0.347920i \(-0.113112\pi\)
0.937524 + 0.347920i \(0.113112\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.56627 0.292453
\(78\) 0 0
\(79\) −14.8347 −1.66904 −0.834518 0.550981i \(-0.814254\pi\)
−0.834518 + 0.550981i \(0.814254\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 2.01517 0.221194 0.110597 0.993865i \(-0.464724\pi\)
0.110597 + 0.993865i \(0.464724\pi\)
\(84\) 0 0
\(85\) −34.2756 −3.71771
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −17.6490 −1.87079 −0.935395 0.353604i \(-0.884956\pi\)
−0.935395 + 0.353604i \(0.884956\pi\)
\(90\) 0 0
\(91\) 2.81429 0.295018
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.30308 −0.441486
\(96\) 0 0
\(97\) −5.66847 −0.575545 −0.287773 0.957699i \(-0.592915\pi\)
−0.287773 + 0.957699i \(0.592915\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.90923 0.488486 0.244243 0.969714i \(-0.421460\pi\)
0.244243 + 0.969714i \(0.421460\pi\)
\(102\) 0 0
\(103\) 1.47025 0.144868 0.0724339 0.997373i \(-0.476923\pi\)
0.0724339 + 0.997373i \(0.476923\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 10.3767 1.00315 0.501575 0.865114i \(-0.332754\pi\)
0.501575 + 0.865114i \(0.332754\pi\)
\(108\) 0 0
\(109\) −5.98671 −0.573423 −0.286711 0.958017i \(-0.592562\pi\)
−0.286711 + 0.958017i \(0.592562\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 9.14771 0.860544 0.430272 0.902699i \(-0.358418\pi\)
0.430272 + 0.902699i \(0.358418\pi\)
\(114\) 0 0
\(115\) −3.50396 −0.326746
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 7.96536 0.730184
\(120\) 0 0
\(121\) −4.41427 −0.401297
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −36.6470 −3.27781
\(126\) 0 0
\(127\) 0.599976 0.0532392 0.0266196 0.999646i \(-0.491526\pi\)
0.0266196 + 0.999646i \(0.491526\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −7.14771 −0.624498 −0.312249 0.950000i \(-0.601082\pi\)
−0.312249 + 0.950000i \(0.601082\pi\)
\(132\) 0 0
\(133\) 1.00000 0.0867110
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −11.6286 −0.993497 −0.496748 0.867895i \(-0.665473\pi\)
−0.496748 + 0.867895i \(0.665473\pi\)
\(138\) 0 0
\(139\) −3.01251 −0.255518 −0.127759 0.991805i \(-0.540778\pi\)
−0.127759 + 0.991805i \(0.540778\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 7.22223 0.603953
\(144\) 0 0
\(145\) 15.0125 1.24672
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −12.8542 −1.05306 −0.526528 0.850158i \(-0.676506\pi\)
−0.526528 + 0.850158i \(0.676506\pi\)
\(150\) 0 0
\(151\) −17.8123 −1.44954 −0.724771 0.688989i \(-0.758055\pi\)
−0.724771 + 0.688989i \(0.758055\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −14.5468 −1.16843
\(156\) 0 0
\(157\) 1.92023 0.153251 0.0766256 0.997060i \(-0.475585\pi\)
0.0766256 + 0.997060i \(0.475585\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.814291 0.0641751
\(162\) 0 0
\(163\) 22.5468 1.76600 0.883001 0.469371i \(-0.155519\pi\)
0.883001 + 0.469371i \(0.155519\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 10.5165 0.813788 0.406894 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(168\) 0 0
\(169\) −5.07977 −0.390751
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 24.4101 1.85587 0.927933 0.372746i \(-0.121584\pi\)
0.927933 + 0.372746i \(0.121584\pi\)
\(174\) 0 0
\(175\) 13.5165 1.02175
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −7.08703 −0.529709 −0.264855 0.964288i \(-0.585324\pi\)
−0.264855 + 0.964288i \(0.585324\pi\)
\(180\) 0 0
\(181\) 2.56964 0.191000 0.0954998 0.995429i \(-0.469555\pi\)
0.0954998 + 0.995429i \(0.469555\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −16.1450 −1.18701
\(186\) 0 0
\(187\) 20.4413 1.49481
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −27.2265 −1.97004 −0.985022 0.172429i \(-0.944838\pi\)
−0.985022 + 0.172429i \(0.944838\pi\)
\(192\) 0 0
\(193\) −14.5369 −1.04639 −0.523194 0.852214i \(-0.675260\pi\)
−0.523194 + 0.852214i \(0.675260\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 8.32779 0.593330 0.296665 0.954982i \(-0.404125\pi\)
0.296665 + 0.954982i \(0.404125\pi\)
\(198\) 0 0
\(199\) 14.0204 0.993881 0.496941 0.867785i \(-0.334457\pi\)
0.496941 + 0.867785i \(0.334457\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.48879 −0.244865
\(204\) 0 0
\(205\) 28.4268 1.98541
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.56627 0.177512
\(210\) 0 0
\(211\) 4.44624 0.306092 0.153046 0.988219i \(-0.451092\pi\)
0.153046 + 0.988219i \(0.451092\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 3.38056 0.229487
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 22.4169 1.50792
\(222\) 0 0
\(223\) 16.0238 1.07303 0.536516 0.843890i \(-0.319740\pi\)
0.536516 + 0.843890i \(0.319740\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3.25930 −0.216327 −0.108164 0.994133i \(-0.534497\pi\)
−0.108164 + 0.994133i \(0.534497\pi\)
\(228\) 0 0
\(229\) 23.7387 1.56870 0.784348 0.620321i \(-0.212998\pi\)
0.784348 + 0.620321i \(0.212998\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −21.3673 −1.39982 −0.699908 0.714233i \(-0.746776\pi\)
−0.699908 + 0.714233i \(0.746776\pi\)
\(234\) 0 0
\(235\) 44.1206 2.87811
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 29.3208 1.89661 0.948303 0.317365i \(-0.102798\pi\)
0.948303 + 0.317365i \(0.102798\pi\)
\(240\) 0 0
\(241\) −14.6216 −0.941862 −0.470931 0.882170i \(-0.656082\pi\)
−0.470931 + 0.882170i \(0.656082\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4.30308 −0.274913
\(246\) 0 0
\(247\) 2.81429 0.179069
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 20.8931 1.31876 0.659381 0.751809i \(-0.270818\pi\)
0.659381 + 0.751809i \(0.270818\pi\)
\(252\) 0 0
\(253\) 2.08969 0.131378
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −8.54680 −0.533135 −0.266567 0.963816i \(-0.585890\pi\)
−0.266567 + 0.963816i \(0.585890\pi\)
\(258\) 0 0
\(259\) 3.75198 0.233137
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.24107 0.0765274 0.0382637 0.999268i \(-0.487817\pi\)
0.0382637 + 0.999268i \(0.487817\pi\)
\(264\) 0 0
\(265\) 2.19980 0.135132
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 20.6266 1.25762 0.628812 0.777557i \(-0.283541\pi\)
0.628812 + 0.777557i \(0.283541\pi\)
\(270\) 0 0
\(271\) −17.7758 −1.07980 −0.539900 0.841729i \(-0.681538\pi\)
−0.539900 + 0.841729i \(0.681538\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 34.6869 2.09170
\(276\) 0 0
\(277\) −22.8613 −1.37360 −0.686801 0.726845i \(-0.740986\pi\)
−0.686801 + 0.726845i \(0.740986\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 16.0949 0.960143 0.480072 0.877229i \(-0.340611\pi\)
0.480072 + 0.877229i \(0.340611\pi\)
\(282\) 0 0
\(283\) 16.4042 0.975128 0.487564 0.873087i \(-0.337886\pi\)
0.487564 + 0.873087i \(0.337886\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −6.60615 −0.389949
\(288\) 0 0
\(289\) 46.4470 2.73218
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 14.3918 0.840780 0.420390 0.907343i \(-0.361893\pi\)
0.420390 + 0.907343i \(0.361893\pi\)
\(294\) 0 0
\(295\) −60.2004 −3.50500
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.29165 0.132530
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −25.8185 −1.47836
\(306\) 0 0
\(307\) 17.9901 1.02675 0.513374 0.858165i \(-0.328395\pi\)
0.513374 + 0.858165i \(0.328395\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 12.0916 0.685650 0.342825 0.939399i \(-0.388616\pi\)
0.342825 + 0.939399i \(0.388616\pi\)
\(312\) 0 0
\(313\) −25.2024 −1.42452 −0.712261 0.701914i \(-0.752329\pi\)
−0.712261 + 0.701914i \(0.752329\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 11.8806 0.667282 0.333641 0.942700i \(-0.391723\pi\)
0.333641 + 0.942700i \(0.391723\pi\)
\(318\) 0 0
\(319\) −8.95316 −0.501281
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 7.96536 0.443205
\(324\) 0 0
\(325\) 38.0393 2.11004
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −10.2533 −0.565281
\(330\) 0 0
\(331\) 6.28454 0.345429 0.172715 0.984972i \(-0.444746\pi\)
0.172715 + 0.984972i \(0.444746\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −51.5532 −2.81665
\(336\) 0 0
\(337\) 31.1430 1.69647 0.848235 0.529621i \(-0.177666\pi\)
0.848235 + 0.529621i \(0.177666\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 8.67542 0.469800
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −31.3196 −1.68132 −0.840662 0.541560i \(-0.817834\pi\)
−0.840662 + 0.541560i \(0.817834\pi\)
\(348\) 0 0
\(349\) −14.6432 −0.783834 −0.391917 0.920001i \(-0.628188\pi\)
−0.391917 + 0.920001i \(0.628188\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 9.85309 0.524427 0.262214 0.965010i \(-0.415548\pi\)
0.262214 + 0.965010i \(0.415548\pi\)
\(354\) 0 0
\(355\) 21.6345 1.14824
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.26548 −0.172345 −0.0861726 0.996280i \(-0.527464\pi\)
−0.0861726 + 0.996280i \(0.527464\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −68.9371 −3.60833
\(366\) 0 0
\(367\) −4.03034 −0.210382 −0.105191 0.994452i \(-0.533545\pi\)
−0.105191 + 0.994452i \(0.533545\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −0.511215 −0.0265409
\(372\) 0 0
\(373\) 14.6194 0.756966 0.378483 0.925608i \(-0.376446\pi\)
0.378483 + 0.925608i \(0.376446\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −9.81846 −0.505676
\(378\) 0 0
\(379\) 19.3175 0.992272 0.496136 0.868245i \(-0.334752\pi\)
0.496136 + 0.868245i \(0.334752\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 14.2954 0.730462 0.365231 0.930917i \(-0.380990\pi\)
0.365231 + 0.930917i \(0.380990\pi\)
\(384\) 0 0
\(385\) −11.0428 −0.562796
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 20.9946 1.06447 0.532235 0.846597i \(-0.321352\pi\)
0.532235 + 0.846597i \(0.321352\pi\)
\(390\) 0 0
\(391\) 6.48612 0.328017
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 63.8349 3.21188
\(396\) 0 0
\(397\) −10.6365 −0.533830 −0.266915 0.963720i \(-0.586004\pi\)
−0.266915 + 0.963720i \(0.586004\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 35.0011 1.74787 0.873936 0.486041i \(-0.161560\pi\)
0.873936 + 0.486041i \(0.161560\pi\)
\(402\) 0 0
\(403\) 9.51388 0.473920
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 9.62858 0.477271
\(408\) 0 0
\(409\) 4.98845 0.246663 0.123331 0.992366i \(-0.460642\pi\)
0.123331 + 0.992366i \(0.460642\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 13.9901 0.688407
\(414\) 0 0
\(415\) −8.67143 −0.425664
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −13.6991 −0.669245 −0.334623 0.942352i \(-0.608609\pi\)
−0.334623 + 0.942352i \(0.608609\pi\)
\(420\) 0 0
\(421\) 18.9399 0.923073 0.461536 0.887121i \(-0.347298\pi\)
0.461536 + 0.887121i \(0.347298\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 107.664 5.22245
\(426\) 0 0
\(427\) 6.00000 0.290360
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −9.20706 −0.443488 −0.221744 0.975105i \(-0.571175\pi\)
−0.221744 + 0.975105i \(0.571175\pi\)
\(432\) 0 0
\(433\) −11.6236 −0.558595 −0.279297 0.960205i \(-0.590102\pi\)
−0.279297 + 0.960205i \(0.590102\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.814291 0.0389528
\(438\) 0 0
\(439\) 4.43333 0.211591 0.105796 0.994388i \(-0.466261\pi\)
0.105796 + 0.994388i \(0.466261\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −13.2847 −0.631175 −0.315587 0.948897i \(-0.602202\pi\)
−0.315587 + 0.948897i \(0.602202\pi\)
\(444\) 0 0
\(445\) 75.9450 3.60014
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 38.9213 1.83681 0.918406 0.395640i \(-0.129477\pi\)
0.918406 + 0.395640i \(0.129477\pi\)
\(450\) 0 0
\(451\) −16.9532 −0.798293
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −12.1101 −0.567731
\(456\) 0 0
\(457\) 19.1820 0.897294 0.448647 0.893709i \(-0.351906\pi\)
0.448647 + 0.893709i \(0.351906\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −10.6356 −0.495348 −0.247674 0.968843i \(-0.579666\pi\)
−0.247674 + 0.968843i \(0.579666\pi\)
\(462\) 0 0
\(463\) −12.1794 −0.566024 −0.283012 0.959116i \(-0.591334\pi\)
−0.283012 + 0.959116i \(0.591334\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 19.3765 0.896638 0.448319 0.893874i \(-0.352023\pi\)
0.448319 + 0.893874i \(0.352023\pi\)
\(468\) 0 0
\(469\) 11.9805 0.553210
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 13.5165 0.620178
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −4.65503 −0.212694 −0.106347 0.994329i \(-0.533915\pi\)
−0.106347 + 0.994329i \(0.533915\pi\)
\(480\) 0 0
\(481\) 10.5592 0.481456
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 24.3918 1.10758
\(486\) 0 0
\(487\) 28.5431 1.29341 0.646705 0.762740i \(-0.276147\pi\)
0.646705 + 0.762740i \(0.276147\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −20.2443 −0.913611 −0.456806 0.889566i \(-0.651007\pi\)
−0.456806 + 0.889566i \(0.651007\pi\)
\(492\) 0 0
\(493\) −27.7894 −1.25157
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.02768 −0.225522
\(498\) 0 0
\(499\) −29.6345 −1.32662 −0.663311 0.748344i \(-0.730849\pi\)
−0.663311 + 0.748344i \(0.730849\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.03089 0.179729 0.0898643 0.995954i \(-0.471357\pi\)
0.0898643 + 0.995954i \(0.471357\pi\)
\(504\) 0 0
\(505\) −21.1248 −0.940040
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 14.5409 0.644513 0.322256 0.946652i \(-0.395559\pi\)
0.322256 + 0.946652i \(0.395559\pi\)
\(510\) 0 0
\(511\) 16.0204 0.708702
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −6.32659 −0.278783
\(516\) 0 0
\(517\) −26.3126 −1.15723
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 32.0631 1.40471 0.702355 0.711827i \(-0.252132\pi\)
0.702355 + 0.711827i \(0.252132\pi\)
\(522\) 0 0
\(523\) −39.0837 −1.70901 −0.854505 0.519443i \(-0.826139\pi\)
−0.854505 + 0.519443i \(0.826139\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 26.9274 1.17298
\(528\) 0 0
\(529\) −22.3369 −0.971171
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −18.5916 −0.805293
\(534\) 0 0
\(535\) −44.6516 −1.93046
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2.56627 0.110537
\(540\) 0 0
\(541\) 28.3166 1.21743 0.608714 0.793390i \(-0.291686\pi\)
0.608714 + 0.793390i \(0.291686\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 25.7613 1.10349
\(546\) 0 0
\(547\) −25.2621 −1.08013 −0.540065 0.841623i \(-0.681600\pi\)
−0.540065 + 0.841623i \(0.681600\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3.48879 −0.148627
\(552\) 0 0
\(553\) −14.8347 −0.630836
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.67480 −0.367563 −0.183781 0.982967i \(-0.558834\pi\)
−0.183781 + 0.982967i \(0.558834\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5.97958 0.252009 0.126005 0.992030i \(-0.459785\pi\)
0.126005 + 0.992030i \(0.459785\pi\)
\(564\) 0 0
\(565\) −39.3633 −1.65603
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 30.7830 1.29049 0.645246 0.763975i \(-0.276755\pi\)
0.645246 + 0.763975i \(0.276755\pi\)
\(570\) 0 0
\(571\) 11.5389 0.482888 0.241444 0.970415i \(-0.422379\pi\)
0.241444 + 0.970415i \(0.422379\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 11.0063 0.458996
\(576\) 0 0
\(577\) 24.7345 1.02971 0.514856 0.857277i \(-0.327845\pi\)
0.514856 + 0.857277i \(0.327845\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2.01517 0.0836033
\(582\) 0 0
\(583\) −1.31191 −0.0543339
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 23.5745 0.973023 0.486511 0.873674i \(-0.338269\pi\)
0.486511 + 0.873674i \(0.338269\pi\)
\(588\) 0 0
\(589\) 3.38056 0.139294
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 13.0608 0.536344 0.268172 0.963371i \(-0.413580\pi\)
0.268172 + 0.963371i \(0.413580\pi\)
\(594\) 0 0
\(595\) −34.2756 −1.40516
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 5.38643 0.220084 0.110042 0.993927i \(-0.464902\pi\)
0.110042 + 0.993927i \(0.464902\pi\)
\(600\) 0 0
\(601\) −25.8213 −1.05327 −0.526636 0.850091i \(-0.676547\pi\)
−0.526636 + 0.850091i \(0.676547\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 18.9949 0.772253
\(606\) 0 0
\(607\) −26.6095 −1.08005 −0.540024 0.841650i \(-0.681585\pi\)
−0.540024 + 0.841650i \(0.681585\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −28.8557 −1.16738
\(612\) 0 0
\(613\) −12.4101 −0.501240 −0.250620 0.968086i \(-0.580634\pi\)
−0.250620 + 0.968086i \(0.580634\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 36.3448 1.46319 0.731594 0.681740i \(-0.238777\pi\)
0.731594 + 0.681740i \(0.238777\pi\)
\(618\) 0 0
\(619\) −26.3371 −1.05858 −0.529288 0.848442i \(-0.677541\pi\)
−0.529288 + 0.848442i \(0.677541\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −17.6490 −0.707092
\(624\) 0 0
\(625\) 90.1125 3.60450
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 29.8859 1.19163
\(630\) 0 0
\(631\) −23.2024 −0.923672 −0.461836 0.886965i \(-0.652809\pi\)
−0.461836 + 0.886965i \(0.652809\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2.58174 −0.102453
\(636\) 0 0
\(637\) 2.81429 0.111506
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −27.8540 −1.10017 −0.550084 0.835109i \(-0.685404\pi\)
−0.550084 + 0.835109i \(0.685404\pi\)
\(642\) 0 0
\(643\) 33.5593 1.32345 0.661725 0.749747i \(-0.269825\pi\)
0.661725 + 0.749747i \(0.269825\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 22.0534 0.867010 0.433505 0.901151i \(-0.357277\pi\)
0.433505 + 0.901151i \(0.357277\pi\)
\(648\) 0 0
\(649\) 35.9023 1.40929
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.41949 0.0555489 0.0277745 0.999614i \(-0.491158\pi\)
0.0277745 + 0.999614i \(0.491158\pi\)
\(654\) 0 0
\(655\) 30.7571 1.20178
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 2.46852 0.0961600 0.0480800 0.998843i \(-0.484690\pi\)
0.0480800 + 0.998843i \(0.484690\pi\)
\(660\) 0 0
\(661\) −6.78771 −0.264011 −0.132006 0.991249i \(-0.542142\pi\)
−0.132006 + 0.991249i \(0.542142\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −4.30308 −0.166866
\(666\) 0 0
\(667\) −2.84089 −0.110000
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 15.3976 0.594418
\(672\) 0 0
\(673\) 23.6087 0.910050 0.455025 0.890479i \(-0.349630\pi\)
0.455025 + 0.890479i \(0.349630\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 14.2817 0.548891 0.274446 0.961603i \(-0.411506\pi\)
0.274446 + 0.961603i \(0.411506\pi\)
\(678\) 0 0
\(679\) −5.66847 −0.217536
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −38.0560 −1.45617 −0.728086 0.685485i \(-0.759590\pi\)
−0.728086 + 0.685485i \(0.759590\pi\)
\(684\) 0 0
\(685\) 50.0387 1.91188
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.43871 −0.0548104
\(690\) 0 0
\(691\) −18.3838 −0.699352 −0.349676 0.936871i \(-0.613708\pi\)
−0.349676 + 0.936871i \(0.613708\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 12.9631 0.491717
\(696\) 0 0
\(697\) −52.6204 −1.99314
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −32.7583 −1.23726 −0.618632 0.785681i \(-0.712313\pi\)
−0.618632 + 0.785681i \(0.712313\pi\)
\(702\) 0 0
\(703\) 3.75198 0.141509
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4.90923 0.184631
\(708\) 0 0
\(709\) 2.39583 0.0899773 0.0449886 0.998987i \(-0.485675\pi\)
0.0449886 + 0.998987i \(0.485675\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.75276 0.103092
\(714\) 0 0
\(715\) −31.0778 −1.16224
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −17.7999 −0.663825 −0.331912 0.943310i \(-0.607694\pi\)
−0.331912 + 0.943310i \(0.607694\pi\)
\(720\) 0 0
\(721\) 1.47025 0.0547549
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −47.1560 −1.75133
\(726\) 0 0
\(727\) −20.0921 −0.745175 −0.372588 0.927997i \(-0.621529\pi\)
−0.372588 + 0.927997i \(0.621529\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 45.3474 1.67495 0.837473 0.546479i \(-0.184032\pi\)
0.837473 + 0.546479i \(0.184032\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 30.7453 1.13252
\(738\) 0 0
\(739\) −6.15710 −0.226493 −0.113246 0.993567i \(-0.536125\pi\)
−0.113246 + 0.993567i \(0.536125\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −31.5785 −1.15850 −0.579251 0.815149i \(-0.696655\pi\)
−0.579251 + 0.815149i \(0.696655\pi\)
\(744\) 0 0
\(745\) 55.3125 2.02649
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 10.3767 0.379155
\(750\) 0 0
\(751\) −38.3207 −1.39834 −0.699171 0.714955i \(-0.746447\pi\)
−0.699171 + 0.714955i \(0.746447\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 76.6476 2.78949
\(756\) 0 0
\(757\) −28.0924 −1.02104 −0.510518 0.859867i \(-0.670546\pi\)
−0.510518 + 0.859867i \(0.670546\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −16.4348 −0.595762 −0.297881 0.954603i \(-0.596280\pi\)
−0.297881 + 0.954603i \(0.596280\pi\)
\(762\) 0 0
\(763\) −5.98671 −0.216733
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 39.3721 1.42165
\(768\) 0 0
\(769\) 11.0679 0.399117 0.199559 0.979886i \(-0.436049\pi\)
0.199559 + 0.979886i \(0.436049\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.596231 0.0214449 0.0107225 0.999943i \(-0.496587\pi\)
0.0107225 + 0.999943i \(0.496587\pi\)
\(774\) 0 0
\(775\) 45.6932 1.64135
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.60615 −0.236690
\(780\) 0 0
\(781\) −12.9024 −0.461683
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −8.26291 −0.294916
\(786\) 0 0
\(787\) −26.8567 −0.957339 −0.478670 0.877995i \(-0.658881\pi\)
−0.478670 + 0.877995i \(0.658881\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 9.14771 0.325255
\(792\) 0 0
\(793\) 16.8857 0.599630
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −7.04742 −0.249632 −0.124816 0.992180i \(-0.539834\pi\)
−0.124816 + 0.992180i \(0.539834\pi\)
\(798\) 0 0
\(799\) −81.6710 −2.88931
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 41.1127 1.45084
\(804\) 0 0
\(805\) −3.50396 −0.123498
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −28.1531 −0.989811 −0.494905 0.868947i \(-0.664797\pi\)
−0.494905 + 0.868947i \(0.664797\pi\)
\(810\) 0 0
\(811\) −6.75550 −0.237218 −0.118609 0.992941i \(-0.537843\pi\)
−0.118609 + 0.992941i \(0.537843\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −97.0206 −3.39848
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −35.1260 −1.22591 −0.612953 0.790120i \(-0.710018\pi\)
−0.612953 + 0.790120i \(0.710018\pi\)
\(822\) 0 0
\(823\) −11.4393 −0.398748 −0.199374 0.979923i \(-0.563891\pi\)
−0.199374 + 0.979923i \(0.563891\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −18.7134 −0.650730 −0.325365 0.945588i \(-0.605487\pi\)
−0.325365 + 0.945588i \(0.605487\pi\)
\(828\) 0 0
\(829\) 37.2244 1.29286 0.646429 0.762974i \(-0.276262\pi\)
0.646429 + 0.762974i \(0.276262\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 7.96536 0.275984
\(834\) 0 0
\(835\) −45.2531 −1.56605
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 32.6127 1.12591 0.562957 0.826486i \(-0.309664\pi\)
0.562957 + 0.826486i \(0.309664\pi\)
\(840\) 0 0
\(841\) −16.8284 −0.580289
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 21.8586 0.751960
\(846\) 0 0
\(847\) −4.41427 −0.151676
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 3.05520 0.104731
\(852\) 0 0
\(853\) 6.56346 0.224729 0.112364 0.993667i \(-0.464158\pi\)
0.112364 + 0.993667i \(0.464158\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −19.6939 −0.672729 −0.336365 0.941732i \(-0.609197\pi\)
−0.336365 + 0.941732i \(0.609197\pi\)
\(858\) 0 0
\(859\) −1.41988 −0.0484458 −0.0242229 0.999707i \(-0.507711\pi\)
−0.0242229 + 0.999707i \(0.507711\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 31.9991 1.08926 0.544631 0.838676i \(-0.316670\pi\)
0.544631 + 0.838676i \(0.316670\pi\)
\(864\) 0 0
\(865\) −105.039 −3.57142
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −38.0698 −1.29143
\(870\) 0 0
\(871\) 33.7167 1.14245
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −36.6470 −1.23889
\(876\) 0 0
\(877\) −26.4933 −0.894614 −0.447307 0.894381i \(-0.647617\pi\)
−0.447307 + 0.894381i \(0.647617\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 17.5630 0.591713 0.295856 0.955232i \(-0.404395\pi\)
0.295856 + 0.955232i \(0.404395\pi\)
\(882\) 0 0
\(883\) −5.05551 −0.170132 −0.0850658 0.996375i \(-0.527110\pi\)
−0.0850658 + 0.996375i \(0.527110\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 15.7390 0.528464 0.264232 0.964459i \(-0.414882\pi\)
0.264232 + 0.964459i \(0.414882\pi\)
\(888\) 0 0
\(889\) 0.599976 0.0201225
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −10.2533 −0.343113
\(894\) 0 0
\(895\) 30.4960 1.01937
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −11.7940 −0.393353
\(900\) 0 0
\(901\) −4.07201 −0.135658
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −11.0573 −0.367558
\(906\) 0 0
\(907\) 19.0379 0.632142 0.316071 0.948736i \(-0.397636\pi\)
0.316071 + 0.948736i \(0.397636\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −52.9775 −1.75522 −0.877611 0.479373i \(-0.840864\pi\)
−0.877611 + 0.479373i \(0.840864\pi\)
\(912\) 0 0
\(913\) 5.17147 0.171151
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −7.14771 −0.236038
\(918\) 0 0
\(919\) −37.5222 −1.23774 −0.618872 0.785492i \(-0.712410\pi\)
−0.618872 + 0.785492i \(0.712410\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −14.1493 −0.465731
\(924\) 0 0
\(925\) 50.7135 1.66745
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 57.3372 1.88117 0.940586 0.339555i \(-0.110276\pi\)
0.940586 + 0.339555i \(0.110276\pi\)
\(930\) 0 0
\(931\) 1.00000 0.0327737
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −87.9603 −2.87661
\(936\) 0 0
\(937\) −11.3469 −0.370685 −0.185343 0.982674i \(-0.559340\pi\)
−0.185343 + 0.982674i \(0.559340\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 34.7123 1.13159 0.565794 0.824547i \(-0.308570\pi\)
0.565794 + 0.824547i \(0.308570\pi\)
\(942\) 0 0
\(943\) −5.37933 −0.175175
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 16.2357 0.527589 0.263794 0.964579i \(-0.415026\pi\)
0.263794 + 0.964579i \(0.415026\pi\)
\(948\) 0 0
\(949\) 45.0861 1.46356
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 19.4158 0.628938 0.314469 0.949268i \(-0.398174\pi\)
0.314469 + 0.949268i \(0.398174\pi\)
\(954\) 0 0
\(955\) 117.158 3.79114
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −11.6286 −0.375506
\(960\) 0 0
\(961\) −19.5718 −0.631349
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 62.5533 2.01366
\(966\) 0 0
\(967\) −1.38578 −0.0445638 −0.0222819 0.999752i \(-0.507093\pi\)
−0.0222819 + 0.999752i \(0.507093\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.33450 0.0428261 0.0214131 0.999771i \(-0.493183\pi\)
0.0214131 + 0.999771i \(0.493183\pi\)
\(972\) 0 0
\(973\) −3.01251 −0.0965766
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 13.0460 0.417377 0.208689 0.977982i \(-0.433080\pi\)
0.208689 + 0.977982i \(0.433080\pi\)
\(978\) 0 0
\(979\) −45.2921 −1.44754
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −13.0877 −0.417433 −0.208717 0.977976i \(-0.566929\pi\)
−0.208717 + 0.977976i \(0.566929\pi\)
\(984\) 0 0
\(985\) −35.8351 −1.14180
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −4.81643 −0.152999 −0.0764994 0.997070i \(-0.524374\pi\)
−0.0764994 + 0.997070i \(0.524374\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −60.3309 −1.91262
\(996\) 0 0
\(997\) −11.1127 −0.351943 −0.175971 0.984395i \(-0.556307\pi\)
−0.175971 + 0.984395i \(0.556307\pi\)
\(998\) 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 9576.2.a.co.1.1 5
3.2 odd 2 3192.2.a.ba.1.5 5
12.11 even 2 6384.2.a.ce.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3192.2.a.ba.1.5 5 3.2 odd 2
6384.2.a.ce.1.5 5 12.11 even 2
9576.2.a.co.1.1 5 1.1 even 1 trivial