Properties

Label 5520.2.a.ca.1.2
Level $5520$
Weight $2$
Character 5520.1
Self dual yes
Analytic conductor $44.077$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5520.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.0774219157\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.229.1
Defining polynomial: \( x^{3} - 4x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 2760)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.86081\) of defining polynomial
Character \(\chi\) \(=\) 5520.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{5} -1.39821 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.00000 q^{5} -1.39821 q^{7} +1.00000 q^{9} +6.64681 q^{13} -1.00000 q^{15} +3.39821 q^{17} +1.39821 q^{21} -1.00000 q^{23} +1.00000 q^{25} -1.00000 q^{27} +0.601793 q^{29} +6.04502 q^{31} -1.39821 q^{35} -8.69182 q^{37} -6.64681 q^{39} +5.24860 q^{41} +7.44322 q^{43} +1.00000 q^{45} -2.79641 q^{47} -5.04502 q^{49} -3.39821 q^{51} +9.24860 q^{53} +3.24860 q^{59} -9.44322 q^{61} -1.39821 q^{63} +6.64681 q^{65} -10.6918 q^{67} +1.00000 q^{69} +7.89541 q^{71} +4.79641 q^{73} -1.00000 q^{75} -5.85039 q^{79} +1.00000 q^{81} -11.8954 q^{83} +3.39821 q^{85} -0.601793 q^{87} -6.09003 q^{89} -9.29362 q^{91} -6.04502 q^{93} +9.44322 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{3} + 3 q^{5} - q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{3} + 3 q^{5} - q^{7} + 3 q^{9} + 4 q^{13} - 3 q^{15} + 7 q^{17} + q^{21} - 3 q^{23} + 3 q^{25} - 3 q^{27} + 5 q^{29} - q^{31} - q^{35} + 9 q^{37} - 4 q^{39} + 3 q^{41} + 3 q^{45} - 2 q^{47} + 4 q^{49} - 7 q^{51} + 15 q^{53} - 3 q^{59} - 6 q^{61} - q^{63} + 4 q^{65} + 3 q^{67} + 3 q^{69} - 5 q^{71} + 8 q^{73} - 3 q^{75} - 8 q^{79} + 3 q^{81} - 7 q^{83} + 7 q^{85} - 5 q^{87} + 20 q^{89} + 4 q^{91} + q^{93} + 6 q^{97}+O(q^{100}) \) 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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −1.39821 −0.528473 −0.264236 0.964458i \(-0.585120\pi\)
−0.264236 + 0.964458i \(0.585120\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 6.64681 1.84349 0.921747 0.387793i \(-0.126762\pi\)
0.921747 + 0.387793i \(0.126762\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) 3.39821 0.824186 0.412093 0.911142i \(-0.364798\pi\)
0.412093 + 0.911142i \(0.364798\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 1.39821 0.305114
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 0.601793 0.111750 0.0558750 0.998438i \(-0.482205\pi\)
0.0558750 + 0.998438i \(0.482205\pi\)
\(30\) 0 0
\(31\) 6.04502 1.08572 0.542858 0.839824i \(-0.317342\pi\)
0.542858 + 0.839824i \(0.317342\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.39821 −0.236340
\(36\) 0 0
\(37\) −8.69182 −1.42893 −0.714464 0.699673i \(-0.753329\pi\)
−0.714464 + 0.699673i \(0.753329\pi\)
\(38\) 0 0
\(39\) −6.64681 −1.06434
\(40\) 0 0
\(41\) 5.24860 0.819694 0.409847 0.912154i \(-0.365582\pi\)
0.409847 + 0.912154i \(0.365582\pi\)
\(42\) 0 0
\(43\) 7.44322 1.13508 0.567540 0.823346i \(-0.307895\pi\)
0.567540 + 0.823346i \(0.307895\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) −2.79641 −0.407899 −0.203950 0.978981i \(-0.565378\pi\)
−0.203950 + 0.978981i \(0.565378\pi\)
\(48\) 0 0
\(49\) −5.04502 −0.720717
\(50\) 0 0
\(51\) −3.39821 −0.475844
\(52\) 0 0
\(53\) 9.24860 1.27039 0.635197 0.772351i \(-0.280919\pi\)
0.635197 + 0.772351i \(0.280919\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.24860 0.422932 0.211466 0.977385i \(-0.432176\pi\)
0.211466 + 0.977385i \(0.432176\pi\)
\(60\) 0 0
\(61\) −9.44322 −1.20908 −0.604540 0.796574i \(-0.706643\pi\)
−0.604540 + 0.796574i \(0.706643\pi\)
\(62\) 0 0
\(63\) −1.39821 −0.176158
\(64\) 0 0
\(65\) 6.64681 0.824435
\(66\) 0 0
\(67\) −10.6918 −1.30621 −0.653107 0.757266i \(-0.726535\pi\)
−0.653107 + 0.757266i \(0.726535\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 7.89541 0.937013 0.468506 0.883460i \(-0.344792\pi\)
0.468506 + 0.883460i \(0.344792\pi\)
\(72\) 0 0
\(73\) 4.79641 0.561378 0.280689 0.959799i \(-0.409437\pi\)
0.280689 + 0.959799i \(0.409437\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −5.85039 −0.658221 −0.329110 0.944291i \(-0.606749\pi\)
−0.329110 + 0.944291i \(0.606749\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −11.8954 −1.30569 −0.652845 0.757491i \(-0.726425\pi\)
−0.652845 + 0.757491i \(0.726425\pi\)
\(84\) 0 0
\(85\) 3.39821 0.368587
\(86\) 0 0
\(87\) −0.601793 −0.0645189
\(88\) 0 0
\(89\) −6.09003 −0.645542 −0.322771 0.946477i \(-0.604614\pi\)
−0.322771 + 0.946477i \(0.604614\pi\)
\(90\) 0 0
\(91\) −9.29362 −0.974236
\(92\) 0 0
\(93\) −6.04502 −0.626839
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 9.44322 0.958814 0.479407 0.877593i \(-0.340852\pi\)
0.479407 + 0.877593i \(0.340852\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0.601793 0.0598806 0.0299403 0.999552i \(-0.490468\pi\)
0.0299403 + 0.999552i \(0.490468\pi\)
\(102\) 0 0
\(103\) −1.85039 −0.182325 −0.0911624 0.995836i \(-0.529058\pi\)
−0.0911624 + 0.995836i \(0.529058\pi\)
\(104\) 0 0
\(105\) 1.39821 0.136451
\(106\) 0 0
\(107\) 5.39821 0.521864 0.260932 0.965357i \(-0.415970\pi\)
0.260932 + 0.965357i \(0.415970\pi\)
\(108\) 0 0
\(109\) 19.9404 1.90995 0.954973 0.296692i \(-0.0958835\pi\)
0.954973 + 0.296692i \(0.0958835\pi\)
\(110\) 0 0
\(111\) 8.69182 0.824991
\(112\) 0 0
\(113\) −5.89541 −0.554593 −0.277297 0.960784i \(-0.589439\pi\)
−0.277297 + 0.960784i \(0.589439\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 6.64681 0.614498
\(118\) 0 0
\(119\) −4.75140 −0.435560
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) −5.24860 −0.473250
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 8.64681 0.767280 0.383640 0.923483i \(-0.374670\pi\)
0.383640 + 0.923483i \(0.374670\pi\)
\(128\) 0 0
\(129\) −7.44322 −0.655339
\(130\) 0 0
\(131\) −9.29362 −0.811987 −0.405994 0.913876i \(-0.633074\pi\)
−0.405994 + 0.913876i \(0.633074\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 9.44322 0.806789 0.403395 0.915026i \(-0.367830\pi\)
0.403395 + 0.915026i \(0.367830\pi\)
\(138\) 0 0
\(139\) 12.8414 1.08920 0.544598 0.838697i \(-0.316682\pi\)
0.544598 + 0.838697i \(0.316682\pi\)
\(140\) 0 0
\(141\) 2.79641 0.235501
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0.601793 0.0499762
\(146\) 0 0
\(147\) 5.04502 0.416106
\(148\) 0 0
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 3.39821 0.274729
\(154\) 0 0
\(155\) 6.04502 0.485547
\(156\) 0 0
\(157\) −2.19462 −0.175150 −0.0875750 0.996158i \(-0.527912\pi\)
−0.0875750 + 0.996158i \(0.527912\pi\)
\(158\) 0 0
\(159\) −9.24860 −0.733462
\(160\) 0 0
\(161\) 1.39821 0.110194
\(162\) 0 0
\(163\) 18.4972 1.44881 0.724406 0.689373i \(-0.242114\pi\)
0.724406 + 0.689373i \(0.242114\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.20359 0.402666 0.201333 0.979523i \(-0.435473\pi\)
0.201333 + 0.979523i \(0.435473\pi\)
\(168\) 0 0
\(169\) 31.1801 2.39847
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 7.20359 0.547678 0.273839 0.961775i \(-0.411706\pi\)
0.273839 + 0.961775i \(0.411706\pi\)
\(174\) 0 0
\(175\) −1.39821 −0.105695
\(176\) 0 0
\(177\) −3.24860 −0.244180
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) −1.05398 −0.0783416 −0.0391708 0.999233i \(-0.512472\pi\)
−0.0391708 + 0.999233i \(0.512472\pi\)
\(182\) 0 0
\(183\) 9.44322 0.698063
\(184\) 0 0
\(185\) −8.69182 −0.639036
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 1.39821 0.101705
\(190\) 0 0
\(191\) −6.49720 −0.470121 −0.235061 0.971981i \(-0.575529\pi\)
−0.235061 + 0.971981i \(0.575529\pi\)
\(192\) 0 0
\(193\) −12.4972 −0.899568 −0.449784 0.893137i \(-0.648499\pi\)
−0.449784 + 0.893137i \(0.648499\pi\)
\(194\) 0 0
\(195\) −6.64681 −0.475988
\(196\) 0 0
\(197\) −1.70079 −0.121176 −0.0605880 0.998163i \(-0.519298\pi\)
−0.0605880 + 0.998163i \(0.519298\pi\)
\(198\) 0 0
\(199\) −8.64681 −0.612956 −0.306478 0.951878i \(-0.599151\pi\)
−0.306478 + 0.951878i \(0.599151\pi\)
\(200\) 0 0
\(201\) 10.6918 0.754143
\(202\) 0 0
\(203\) −0.841431 −0.0590569
\(204\) 0 0
\(205\) 5.24860 0.366578
\(206\) 0 0
\(207\) −1.00000 −0.0695048
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 4.45219 0.306501 0.153251 0.988187i \(-0.451026\pi\)
0.153251 + 0.988187i \(0.451026\pi\)
\(212\) 0 0
\(213\) −7.89541 −0.540985
\(214\) 0 0
\(215\) 7.44322 0.507624
\(216\) 0 0
\(217\) −8.45219 −0.573772
\(218\) 0 0
\(219\) −4.79641 −0.324112
\(220\) 0 0
\(221\) 22.5872 1.51938
\(222\) 0 0
\(223\) 25.9404 1.73710 0.868550 0.495602i \(-0.165053\pi\)
0.868550 + 0.495602i \(0.165053\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 17.0361 1.13072 0.565361 0.824843i \(-0.308737\pi\)
0.565361 + 0.824843i \(0.308737\pi\)
\(228\) 0 0
\(229\) −22.8269 −1.50844 −0.754221 0.656621i \(-0.771985\pi\)
−0.754221 + 0.656621i \(0.771985\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 18.0900 1.18512 0.592559 0.805527i \(-0.298118\pi\)
0.592559 + 0.805527i \(0.298118\pi\)
\(234\) 0 0
\(235\) −2.79641 −0.182418
\(236\) 0 0
\(237\) 5.85039 0.380024
\(238\) 0 0
\(239\) −27.0811 −1.75173 −0.875864 0.482557i \(-0.839708\pi\)
−0.875864 + 0.482557i \(0.839708\pi\)
\(240\) 0 0
\(241\) 6.09003 0.392293 0.196147 0.980575i \(-0.437157\pi\)
0.196147 + 0.980575i \(0.437157\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −5.04502 −0.322314
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 11.8954 0.753841
\(250\) 0 0
\(251\) 26.9765 1.70274 0.851370 0.524565i \(-0.175772\pi\)
0.851370 + 0.524565i \(0.175772\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −3.39821 −0.212804
\(256\) 0 0
\(257\) 11.5928 0.723141 0.361570 0.932345i \(-0.382241\pi\)
0.361570 + 0.932345i \(0.382241\pi\)
\(258\) 0 0
\(259\) 12.1530 0.755149
\(260\) 0 0
\(261\) 0.601793 0.0372500
\(262\) 0 0
\(263\) 14.0450 0.866053 0.433026 0.901381i \(-0.357446\pi\)
0.433026 + 0.901381i \(0.357446\pi\)
\(264\) 0 0
\(265\) 9.24860 0.568137
\(266\) 0 0
\(267\) 6.09003 0.372704
\(268\) 0 0
\(269\) 13.8054 0.841729 0.420864 0.907124i \(-0.361727\pi\)
0.420864 + 0.907124i \(0.361727\pi\)
\(270\) 0 0
\(271\) −7.33863 −0.445790 −0.222895 0.974842i \(-0.571551\pi\)
−0.222895 + 0.974842i \(0.571551\pi\)
\(272\) 0 0
\(273\) 9.29362 0.562475
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.74244 −0.104693 −0.0523464 0.998629i \(-0.516670\pi\)
−0.0523464 + 0.998629i \(0.516670\pi\)
\(278\) 0 0
\(279\) 6.04502 0.361906
\(280\) 0 0
\(281\) −11.6829 −0.696941 −0.348471 0.937320i \(-0.613299\pi\)
−0.348471 + 0.937320i \(0.613299\pi\)
\(282\) 0 0
\(283\) −14.7819 −0.878690 −0.439345 0.898318i \(-0.644789\pi\)
−0.439345 + 0.898318i \(0.644789\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −7.33863 −0.433186
\(288\) 0 0
\(289\) −5.45219 −0.320717
\(290\) 0 0
\(291\) −9.44322 −0.553572
\(292\) 0 0
\(293\) 8.34423 0.487475 0.243738 0.969841i \(-0.421626\pi\)
0.243738 + 0.969841i \(0.421626\pi\)
\(294\) 0 0
\(295\) 3.24860 0.189141
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −6.64681 −0.384395
\(300\) 0 0
\(301\) −10.4072 −0.599859
\(302\) 0 0
\(303\) −0.601793 −0.0345721
\(304\) 0 0
\(305\) −9.44322 −0.540717
\(306\) 0 0
\(307\) −5.29362 −0.302123 −0.151061 0.988524i \(-0.548269\pi\)
−0.151061 + 0.988524i \(0.548269\pi\)
\(308\) 0 0
\(309\) 1.85039 0.105265
\(310\) 0 0
\(311\) 13.0361 0.739207 0.369603 0.929190i \(-0.379494\pi\)
0.369603 + 0.929190i \(0.379494\pi\)
\(312\) 0 0
\(313\) −2.19462 −0.124047 −0.0620237 0.998075i \(-0.519755\pi\)
−0.0620237 + 0.998075i \(0.519755\pi\)
\(314\) 0 0
\(315\) −1.39821 −0.0787801
\(316\) 0 0
\(317\) 22.9944 1.29149 0.645747 0.763551i \(-0.276546\pi\)
0.645747 + 0.763551i \(0.276546\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −5.39821 −0.301299
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 6.64681 0.368699
\(326\) 0 0
\(327\) −19.9404 −1.10271
\(328\) 0 0
\(329\) 3.90997 0.215564
\(330\) 0 0
\(331\) 15.6378 0.859534 0.429767 0.902940i \(-0.358596\pi\)
0.429767 + 0.902940i \(0.358596\pi\)
\(332\) 0 0
\(333\) −8.69182 −0.476309
\(334\) 0 0
\(335\) −10.6918 −0.584157
\(336\) 0 0
\(337\) −9.74244 −0.530704 −0.265352 0.964152i \(-0.585488\pi\)
−0.265352 + 0.964152i \(0.585488\pi\)
\(338\) 0 0
\(339\) 5.89541 0.320195
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 16.8414 0.909352
\(344\) 0 0
\(345\) 1.00000 0.0538382
\(346\) 0 0
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) 0 0
\(349\) −2.45219 −0.131263 −0.0656313 0.997844i \(-0.520906\pi\)
−0.0656313 + 0.997844i \(0.520906\pi\)
\(350\) 0 0
\(351\) −6.64681 −0.354780
\(352\) 0 0
\(353\) 9.70079 0.516321 0.258160 0.966102i \(-0.416884\pi\)
0.258160 + 0.966102i \(0.416884\pi\)
\(354\) 0 0
\(355\) 7.89541 0.419045
\(356\) 0 0
\(357\) 4.75140 0.251471
\(358\) 0 0
\(359\) −22.4972 −1.18736 −0.593678 0.804702i \(-0.702325\pi\)
−0.593678 + 0.804702i \(0.702325\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 0 0
\(363\) 11.0000 0.577350
\(364\) 0 0
\(365\) 4.79641 0.251056
\(366\) 0 0
\(367\) −4.19462 −0.218958 −0.109479 0.993989i \(-0.534918\pi\)
−0.109479 + 0.993989i \(0.534918\pi\)
\(368\) 0 0
\(369\) 5.24860 0.273231
\(370\) 0 0
\(371\) −12.9315 −0.671368
\(372\) 0 0
\(373\) 28.0305 1.45136 0.725681 0.688031i \(-0.241525\pi\)
0.725681 + 0.688031i \(0.241525\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) 30.8864 1.58653 0.793265 0.608876i \(-0.208379\pi\)
0.793265 + 0.608876i \(0.208379\pi\)
\(380\) 0 0
\(381\) −8.64681 −0.442989
\(382\) 0 0
\(383\) 14.0450 0.717667 0.358833 0.933402i \(-0.383175\pi\)
0.358833 + 0.933402i \(0.383175\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 7.44322 0.378360
\(388\) 0 0
\(389\) 23.2936 1.18103 0.590517 0.807025i \(-0.298924\pi\)
0.590517 + 0.807025i \(0.298924\pi\)
\(390\) 0 0
\(391\) −3.39821 −0.171855
\(392\) 0 0
\(393\) 9.29362 0.468801
\(394\) 0 0
\(395\) −5.85039 −0.294365
\(396\) 0 0
\(397\) −19.9404 −1.00078 −0.500391 0.865800i \(-0.666810\pi\)
−0.500391 + 0.865800i \(0.666810\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −32.2880 −1.61239 −0.806193 0.591652i \(-0.798476\pi\)
−0.806193 + 0.591652i \(0.798476\pi\)
\(402\) 0 0
\(403\) 40.1801 2.00151
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −10.5422 −0.521279 −0.260640 0.965436i \(-0.583933\pi\)
−0.260640 + 0.965436i \(0.583933\pi\)
\(410\) 0 0
\(411\) −9.44322 −0.465800
\(412\) 0 0
\(413\) −4.54222 −0.223508
\(414\) 0 0
\(415\) −11.8954 −0.583923
\(416\) 0 0
\(417\) −12.8414 −0.628848
\(418\) 0 0
\(419\) 3.70079 0.180795 0.0903976 0.995906i \(-0.471186\pi\)
0.0903976 + 0.995906i \(0.471186\pi\)
\(420\) 0 0
\(421\) −18.3476 −0.894207 −0.447104 0.894482i \(-0.647544\pi\)
−0.447104 + 0.894482i \(0.647544\pi\)
\(422\) 0 0
\(423\) −2.79641 −0.135966
\(424\) 0 0
\(425\) 3.39821 0.164837
\(426\) 0 0
\(427\) 13.2036 0.638966
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −14.8864 −0.717055 −0.358527 0.933519i \(-0.616721\pi\)
−0.358527 + 0.933519i \(0.616721\pi\)
\(432\) 0 0
\(433\) −31.5783 −1.51755 −0.758777 0.651350i \(-0.774203\pi\)
−0.758777 + 0.651350i \(0.774203\pi\)
\(434\) 0 0
\(435\) −0.601793 −0.0288537
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −33.4737 −1.59761 −0.798806 0.601589i \(-0.794535\pi\)
−0.798806 + 0.601589i \(0.794535\pi\)
\(440\) 0 0
\(441\) −5.04502 −0.240239
\(442\) 0 0
\(443\) 22.7964 1.08309 0.541545 0.840672i \(-0.317840\pi\)
0.541545 + 0.840672i \(0.317840\pi\)
\(444\) 0 0
\(445\) −6.09003 −0.288695
\(446\) 0 0
\(447\) −6.00000 −0.283790
\(448\) 0 0
\(449\) 33.3386 1.57335 0.786674 0.617369i \(-0.211801\pi\)
0.786674 + 0.617369i \(0.211801\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −9.29362 −0.435691
\(456\) 0 0
\(457\) 21.9854 1.02844 0.514218 0.857660i \(-0.328082\pi\)
0.514218 + 0.857660i \(0.328082\pi\)
\(458\) 0 0
\(459\) −3.39821 −0.158615
\(460\) 0 0
\(461\) −27.0361 −1.25919 −0.629597 0.776922i \(-0.716780\pi\)
−0.629597 + 0.776922i \(0.716780\pi\)
\(462\) 0 0
\(463\) 18.1496 0.843484 0.421742 0.906716i \(-0.361419\pi\)
0.421742 + 0.906716i \(0.361419\pi\)
\(464\) 0 0
\(465\) −6.04502 −0.280331
\(466\) 0 0
\(467\) 39.9854 1.85031 0.925153 0.379595i \(-0.123937\pi\)
0.925153 + 0.379595i \(0.123937\pi\)
\(468\) 0 0
\(469\) 14.9494 0.690299
\(470\) 0 0
\(471\) 2.19462 0.101123
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 9.24860 0.423464
\(478\) 0 0
\(479\) −7.09563 −0.324207 −0.162104 0.986774i \(-0.551828\pi\)
−0.162104 + 0.986774i \(0.551828\pi\)
\(480\) 0 0
\(481\) −57.7729 −2.63422
\(482\) 0 0
\(483\) −1.39821 −0.0636206
\(484\) 0 0
\(485\) 9.44322 0.428795
\(486\) 0 0
\(487\) 24.8269 1.12501 0.562506 0.826793i \(-0.309837\pi\)
0.562506 + 0.826793i \(0.309837\pi\)
\(488\) 0 0
\(489\) −18.4972 −0.836472
\(490\) 0 0
\(491\) 23.3386 1.05326 0.526629 0.850095i \(-0.323456\pi\)
0.526629 + 0.850095i \(0.323456\pi\)
\(492\) 0 0
\(493\) 2.04502 0.0921029
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −11.0394 −0.495186
\(498\) 0 0
\(499\) −32.3330 −1.44743 −0.723713 0.690101i \(-0.757566\pi\)
−0.723713 + 0.690101i \(0.757566\pi\)
\(500\) 0 0
\(501\) −5.20359 −0.232479
\(502\) 0 0
\(503\) 4.75140 0.211854 0.105927 0.994374i \(-0.466219\pi\)
0.105927 + 0.994374i \(0.466219\pi\)
\(504\) 0 0
\(505\) 0.601793 0.0267794
\(506\) 0 0
\(507\) −31.1801 −1.38476
\(508\) 0 0
\(509\) 16.3297 0.723800 0.361900 0.932217i \(-0.382128\pi\)
0.361900 + 0.932217i \(0.382128\pi\)
\(510\) 0 0
\(511\) −6.70638 −0.296673
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.85039 −0.0815381
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −7.20359 −0.316202
\(520\) 0 0
\(521\) 3.20359 0.140352 0.0701758 0.997535i \(-0.477644\pi\)
0.0701758 + 0.997535i \(0.477644\pi\)
\(522\) 0 0
\(523\) 8.55678 0.374162 0.187081 0.982345i \(-0.440097\pi\)
0.187081 + 0.982345i \(0.440097\pi\)
\(524\) 0 0
\(525\) 1.39821 0.0610228
\(526\) 0 0
\(527\) 20.5422 0.894833
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 3.24860 0.140977
\(532\) 0 0
\(533\) 34.8864 1.51110
\(534\) 0 0
\(535\) 5.39821 0.233385
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 35.7729 1.53800 0.768998 0.639251i \(-0.220755\pi\)
0.768998 + 0.639251i \(0.220755\pi\)
\(542\) 0 0
\(543\) 1.05398 0.0452306
\(544\) 0 0
\(545\) 19.9404 0.854154
\(546\) 0 0
\(547\) 22.5872 0.965760 0.482880 0.875686i \(-0.339591\pi\)
0.482880 + 0.875686i \(0.339591\pi\)
\(548\) 0 0
\(549\) −9.44322 −0.403027
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 8.18006 0.347852
\(554\) 0 0
\(555\) 8.69182 0.368947
\(556\) 0 0
\(557\) −2.45219 −0.103902 −0.0519512 0.998650i \(-0.516544\pi\)
−0.0519512 + 0.998650i \(0.516544\pi\)
\(558\) 0 0
\(559\) 49.4737 2.09251
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 26.6018 1.12113 0.560566 0.828110i \(-0.310584\pi\)
0.560566 + 0.828110i \(0.310584\pi\)
\(564\) 0 0
\(565\) −5.89541 −0.248022
\(566\) 0 0
\(567\) −1.39821 −0.0587192
\(568\) 0 0
\(569\) 44.8864 1.88174 0.940869 0.338771i \(-0.110011\pi\)
0.940869 + 0.338771i \(0.110011\pi\)
\(570\) 0 0
\(571\) −41.8629 −1.75191 −0.875954 0.482394i \(-0.839767\pi\)
−0.875954 + 0.482394i \(0.839767\pi\)
\(572\) 0 0
\(573\) 6.49720 0.271425
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −22.3892 −0.932076 −0.466038 0.884765i \(-0.654319\pi\)
−0.466038 + 0.884765i \(0.654319\pi\)
\(578\) 0 0
\(579\) 12.4972 0.519366
\(580\) 0 0
\(581\) 16.6323 0.690022
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 6.64681 0.274812
\(586\) 0 0
\(587\) 11.0956 0.457966 0.228983 0.973430i \(-0.426460\pi\)
0.228983 + 0.973430i \(0.426460\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 1.70079 0.0699610
\(592\) 0 0
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0 0
\(595\) −4.75140 −0.194788
\(596\) 0 0
\(597\) 8.64681 0.353890
\(598\) 0 0
\(599\) 10.0305 0.409833 0.204917 0.978779i \(-0.434308\pi\)
0.204917 + 0.978779i \(0.434308\pi\)
\(600\) 0 0
\(601\) −41.6378 −1.69844 −0.849222 0.528037i \(-0.822928\pi\)
−0.849222 + 0.528037i \(0.822928\pi\)
\(602\) 0 0
\(603\) −10.6918 −0.435405
\(604\) 0 0
\(605\) −11.0000 −0.447214
\(606\) 0 0
\(607\) −0.646809 −0.0262531 −0.0131266 0.999914i \(-0.504178\pi\)
−0.0131266 + 0.999914i \(0.504178\pi\)
\(608\) 0 0
\(609\) 0.841431 0.0340965
\(610\) 0 0
\(611\) −18.5872 −0.751959
\(612\) 0 0
\(613\) 25.6233 1.03491 0.517457 0.855709i \(-0.326879\pi\)
0.517457 + 0.855709i \(0.326879\pi\)
\(614\) 0 0
\(615\) −5.24860 −0.211644
\(616\) 0 0
\(617\) −11.6974 −0.470920 −0.235460 0.971884i \(-0.575660\pi\)
−0.235460 + 0.971884i \(0.575660\pi\)
\(618\) 0 0
\(619\) 13.5928 0.546342 0.273171 0.961965i \(-0.411928\pi\)
0.273171 + 0.961965i \(0.411928\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 8.51513 0.341151
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −29.5366 −1.17770
\(630\) 0 0
\(631\) −35.2340 −1.40265 −0.701323 0.712844i \(-0.747407\pi\)
−0.701323 + 0.712844i \(0.747407\pi\)
\(632\) 0 0
\(633\) −4.45219 −0.176959
\(634\) 0 0
\(635\) 8.64681 0.343138
\(636\) 0 0
\(637\) −33.5333 −1.32864
\(638\) 0 0
\(639\) 7.89541 0.312338
\(640\) 0 0
\(641\) 15.6829 0.619436 0.309718 0.950828i \(-0.399765\pi\)
0.309718 + 0.950828i \(0.399765\pi\)
\(642\) 0 0
\(643\) −17.5783 −0.693219 −0.346610 0.938009i \(-0.612667\pi\)
−0.346610 + 0.938009i \(0.612667\pi\)
\(644\) 0 0
\(645\) −7.44322 −0.293077
\(646\) 0 0
\(647\) 26.5872 1.04525 0.522626 0.852562i \(-0.324952\pi\)
0.522626 + 0.852562i \(0.324952\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 8.45219 0.331267
\(652\) 0 0
\(653\) −50.2701 −1.96722 −0.983610 0.180307i \(-0.942291\pi\)
−0.983610 + 0.180307i \(0.942291\pi\)
\(654\) 0 0
\(655\) −9.29362 −0.363132
\(656\) 0 0
\(657\) 4.79641 0.187126
\(658\) 0 0
\(659\) 19.1857 0.747367 0.373684 0.927556i \(-0.378095\pi\)
0.373684 + 0.927556i \(0.378095\pi\)
\(660\) 0 0
\(661\) −25.6233 −0.996630 −0.498315 0.866996i \(-0.666048\pi\)
−0.498315 + 0.866996i \(0.666048\pi\)
\(662\) 0 0
\(663\) −22.5872 −0.877215
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.601793 −0.0233015
\(668\) 0 0
\(669\) −25.9404 −1.00291
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 11.4737 0.442278 0.221139 0.975242i \(-0.429023\pi\)
0.221139 + 0.975242i \(0.429023\pi\)
\(674\) 0 0
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) 6.63225 0.254898 0.127449 0.991845i \(-0.459321\pi\)
0.127449 + 0.991845i \(0.459321\pi\)
\(678\) 0 0
\(679\) −13.2036 −0.506707
\(680\) 0 0
\(681\) −17.0361 −0.652823
\(682\) 0 0
\(683\) 45.6829 1.74801 0.874003 0.485920i \(-0.161516\pi\)
0.874003 + 0.485920i \(0.161516\pi\)
\(684\) 0 0
\(685\) 9.44322 0.360807
\(686\) 0 0
\(687\) 22.8269 0.870900
\(688\) 0 0
\(689\) 61.4737 2.34196
\(690\) 0 0
\(691\) 27.0665 1.02966 0.514829 0.857293i \(-0.327855\pi\)
0.514829 + 0.857293i \(0.327855\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 12.8414 0.487103
\(696\) 0 0
\(697\) 17.8358 0.675580
\(698\) 0 0
\(699\) −18.0900 −0.684228
\(700\) 0 0
\(701\) −22.9944 −0.868487 −0.434243 0.900796i \(-0.642984\pi\)
−0.434243 + 0.900796i \(0.642984\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 2.79641 0.105319
\(706\) 0 0
\(707\) −0.841431 −0.0316453
\(708\) 0 0
\(709\) −1.44322 −0.0542014 −0.0271007 0.999633i \(-0.508627\pi\)
−0.0271007 + 0.999633i \(0.508627\pi\)
\(710\) 0 0
\(711\) −5.85039 −0.219407
\(712\) 0 0
\(713\) −6.04502 −0.226388
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 27.0811 1.01136
\(718\) 0 0
\(719\) −44.8898 −1.67411 −0.837054 0.547121i \(-0.815724\pi\)
−0.837054 + 0.547121i \(0.815724\pi\)
\(720\) 0 0
\(721\) 2.58723 0.0963536
\(722\) 0 0
\(723\) −6.09003 −0.226491
\(724\) 0 0
\(725\) 0.601793 0.0223500
\(726\) 0 0
\(727\) −41.1890 −1.52762 −0.763808 0.645443i \(-0.776673\pi\)
−0.763808 + 0.645443i \(0.776673\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 25.2936 0.935518
\(732\) 0 0
\(733\) −33.9854 −1.25528 −0.627640 0.778503i \(-0.715979\pi\)
−0.627640 + 0.778503i \(0.715979\pi\)
\(734\) 0 0
\(735\) 5.04502 0.186088
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 22.3442 0.821946 0.410973 0.911648i \(-0.365189\pi\)
0.410973 + 0.911648i \(0.365189\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −10.5872 −0.388408 −0.194204 0.980961i \(-0.562212\pi\)
−0.194204 + 0.980961i \(0.562212\pi\)
\(744\) 0 0
\(745\) 6.00000 0.219823
\(746\) 0 0
\(747\) −11.8954 −0.435230
\(748\) 0 0
\(749\) −7.54781 −0.275791
\(750\) 0 0
\(751\) 8.43763 0.307893 0.153947 0.988079i \(-0.450802\pi\)
0.153947 + 0.988079i \(0.450802\pi\)
\(752\) 0 0
\(753\) −26.9765 −0.983078
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 23.2791 0.846092 0.423046 0.906108i \(-0.360961\pi\)
0.423046 + 0.906108i \(0.360961\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −10.7514 −0.389738 −0.194869 0.980829i \(-0.562428\pi\)
−0.194869 + 0.980829i \(0.562428\pi\)
\(762\) 0 0
\(763\) −27.8809 −1.00935
\(764\) 0 0
\(765\) 3.39821 0.122862
\(766\) 0 0
\(767\) 21.5928 0.779672
\(768\) 0 0
\(769\) −21.4016 −0.771761 −0.385880 0.922549i \(-0.626102\pi\)
−0.385880 + 0.922549i \(0.626102\pi\)
\(770\) 0 0
\(771\) −11.5928 −0.417506
\(772\) 0 0
\(773\) 25.7008 0.924393 0.462197 0.886778i \(-0.347061\pi\)
0.462197 + 0.886778i \(0.347061\pi\)
\(774\) 0 0
\(775\) 6.04502 0.217143
\(776\) 0 0
\(777\) −12.1530 −0.435986
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −0.601793 −0.0215063
\(784\) 0 0
\(785\) −2.19462 −0.0783294
\(786\) 0 0
\(787\) −26.1767 −0.933098 −0.466549 0.884495i \(-0.654503\pi\)
−0.466549 + 0.884495i \(0.654503\pi\)
\(788\) 0 0
\(789\) −14.0450 −0.500016
\(790\) 0 0
\(791\) 8.24301 0.293088
\(792\) 0 0
\(793\) −62.7673 −2.22893
\(794\) 0 0
\(795\) −9.24860 −0.328014
\(796\) 0 0
\(797\) −46.5422 −1.64861 −0.824305 0.566146i \(-0.808434\pi\)
−0.824305 + 0.566146i \(0.808434\pi\)
\(798\) 0 0
\(799\) −9.50280 −0.336185
\(800\) 0 0
\(801\) −6.09003 −0.215181
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 1.39821 0.0492803
\(806\) 0 0
\(807\) −13.8054 −0.485972
\(808\) 0 0
\(809\) 17.1586 0.603263 0.301632 0.953425i \(-0.402469\pi\)
0.301632 + 0.953425i \(0.402469\pi\)
\(810\) 0 0
\(811\) 38.5243 1.35277 0.676385 0.736548i \(-0.263545\pi\)
0.676385 + 0.736548i \(0.263545\pi\)
\(812\) 0 0
\(813\) 7.33863 0.257377
\(814\) 0 0
\(815\) 18.4972 0.647929
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) −9.29362 −0.324745
\(820\) 0 0
\(821\) −35.7312 −1.24703 −0.623515 0.781812i \(-0.714296\pi\)
−0.623515 + 0.781812i \(0.714296\pi\)
\(822\) 0 0
\(823\) 30.0305 1.04680 0.523398 0.852088i \(-0.324664\pi\)
0.523398 + 0.852088i \(0.324664\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −8.58387 −0.298490 −0.149245 0.988800i \(-0.547684\pi\)
−0.149245 + 0.988800i \(0.547684\pi\)
\(828\) 0 0
\(829\) 20.8235 0.723230 0.361615 0.932327i \(-0.382225\pi\)
0.361615 + 0.932327i \(0.382225\pi\)
\(830\) 0 0
\(831\) 1.74244 0.0604444
\(832\) 0 0
\(833\) −17.1440 −0.594005
\(834\) 0 0
\(835\) 5.20359 0.180077
\(836\) 0 0
\(837\) −6.04502 −0.208946
\(838\) 0 0
\(839\) −11.3115 −0.390518 −0.195259 0.980752i \(-0.562555\pi\)
−0.195259 + 0.980752i \(0.562555\pi\)
\(840\) 0 0
\(841\) −28.6378 −0.987512
\(842\) 0 0
\(843\) 11.6829 0.402379
\(844\) 0 0
\(845\) 31.1801 1.07263
\(846\) 0 0
\(847\) 15.3803 0.528473
\(848\) 0 0
\(849\) 14.7819 0.507312
\(850\) 0 0
\(851\) 8.69182 0.297952
\(852\) 0 0
\(853\) −51.2161 −1.75361 −0.876803 0.480849i \(-0.840328\pi\)
−0.876803 + 0.480849i \(0.840328\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −44.5872 −1.52307 −0.761535 0.648123i \(-0.775554\pi\)
−0.761535 + 0.648123i \(0.775554\pi\)
\(858\) 0 0
\(859\) 32.3330 1.10319 0.551595 0.834112i \(-0.314020\pi\)
0.551595 + 0.834112i \(0.314020\pi\)
\(860\) 0 0
\(861\) 7.33863 0.250100
\(862\) 0 0
\(863\) 14.4972 0.493491 0.246745 0.969080i \(-0.420639\pi\)
0.246745 + 0.969080i \(0.420639\pi\)
\(864\) 0 0
\(865\) 7.20359 0.244929
\(866\) 0 0
\(867\) 5.45219 0.185166
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −71.0665 −2.40800
\(872\) 0 0
\(873\) 9.44322 0.319605
\(874\) 0 0
\(875\) −1.39821 −0.0472680
\(876\) 0 0
\(877\) −49.3241 −1.66556 −0.832778 0.553607i \(-0.813251\pi\)
−0.832778 + 0.553607i \(0.813251\pi\)
\(878\) 0 0
\(879\) −8.34423 −0.281444
\(880\) 0 0
\(881\) 39.9888 1.34726 0.673629 0.739070i \(-0.264735\pi\)
0.673629 + 0.739070i \(0.264735\pi\)
\(882\) 0 0
\(883\) 14.7964 0.497939 0.248970 0.968511i \(-0.419908\pi\)
0.248970 + 0.968511i \(0.419908\pi\)
\(884\) 0 0
\(885\) −3.24860 −0.109201
\(886\) 0 0
\(887\) −29.5637 −0.992652 −0.496326 0.868136i \(-0.665318\pi\)
−0.496326 + 0.868136i \(0.665318\pi\)
\(888\) 0 0
\(889\) −12.0900 −0.405487
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 6.64681 0.221930
\(898\) 0 0
\(899\) 3.63785 0.121329
\(900\) 0 0
\(901\) 31.4287 1.04704
\(902\) 0 0
\(903\) 10.4072 0.346329
\(904\) 0 0
\(905\) −1.05398 −0.0350354
\(906\) 0 0
\(907\) −30.3926 −1.00917 −0.504585 0.863362i \(-0.668355\pi\)
−0.504585 + 0.863362i \(0.668355\pi\)
\(908\) 0 0
\(909\) 0.601793 0.0199602
\(910\) 0 0
\(911\) −26.4072 −0.874909 −0.437454 0.899241i \(-0.644120\pi\)
−0.437454 + 0.899241i \(0.644120\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 9.44322 0.312183
\(916\) 0 0
\(917\) 12.9944 0.429113
\(918\) 0 0
\(919\) −14.9639 −0.493615 −0.246808 0.969065i \(-0.579382\pi\)
−0.246808 + 0.969065i \(0.579382\pi\)
\(920\) 0 0
\(921\) 5.29362 0.174431
\(922\) 0 0
\(923\) 52.4793 1.72738
\(924\) 0 0
\(925\) −8.69182 −0.285785
\(926\) 0 0
\(927\) −1.85039 −0.0607749
\(928\) 0 0
\(929\) 11.7458 0.385367 0.192684 0.981261i \(-0.438281\pi\)
0.192684 + 0.981261i \(0.438281\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −13.0361 −0.426781
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −27.7312 −0.905940 −0.452970 0.891526i \(-0.649636\pi\)
−0.452970 + 0.891526i \(0.649636\pi\)
\(938\) 0 0
\(939\) 2.19462 0.0716188
\(940\) 0 0
\(941\) 6.18006 0.201464 0.100732 0.994914i \(-0.467881\pi\)
0.100732 + 0.994914i \(0.467881\pi\)
\(942\) 0 0
\(943\) −5.24860 −0.170918
\(944\) 0 0
\(945\) 1.39821 0.0454837
\(946\) 0 0
\(947\) −50.2880 −1.63414 −0.817071 0.576538i \(-0.804403\pi\)
−0.817071 + 0.576538i \(0.804403\pi\)
\(948\) 0 0
\(949\) 31.8809 1.03490
\(950\) 0 0
\(951\) −22.9944 −0.745645
\(952\) 0 0
\(953\) 21.1440 0.684922 0.342461 0.939532i \(-0.388740\pi\)
0.342461 + 0.939532i \(0.388740\pi\)
\(954\) 0 0
\(955\) −6.49720 −0.210245
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −13.2036 −0.426366
\(960\) 0 0
\(961\) 5.54222 0.178781
\(962\) 0 0
\(963\) 5.39821 0.173955
\(964\) 0 0
\(965\) −12.4972 −0.402299
\(966\) 0 0
\(967\) −36.9460 −1.18810 −0.594052 0.804427i \(-0.702473\pi\)
−0.594052 + 0.804427i \(0.702473\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −23.4016 −0.750992 −0.375496 0.926824i \(-0.622528\pi\)
−0.375496 + 0.926824i \(0.622528\pi\)
\(972\) 0 0
\(973\) −17.9550 −0.575610
\(974\) 0 0
\(975\) −6.64681 −0.212868
\(976\) 0 0
\(977\) −12.2125 −0.390714 −0.195357 0.980732i \(-0.562587\pi\)
−0.195357 + 0.980732i \(0.562587\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 19.9404 0.636649
\(982\) 0 0
\(983\) 43.9438 1.40159 0.700795 0.713363i \(-0.252829\pi\)
0.700795 + 0.713363i \(0.252829\pi\)
\(984\) 0 0
\(985\) −1.70079 −0.0541916
\(986\) 0 0
\(987\) −3.90997 −0.124456
\(988\) 0 0
\(989\) −7.44322 −0.236681
\(990\) 0 0
\(991\) −22.4343 −0.712648 −0.356324 0.934363i \(-0.615970\pi\)
−0.356324 + 0.934363i \(0.615970\pi\)
\(992\) 0 0
\(993\) −15.6378 −0.496252
\(994\) 0 0
\(995\) −8.64681 −0.274122
\(996\) 0 0
\(997\) 16.5389 0.523791 0.261895 0.965096i \(-0.415652\pi\)
0.261895 + 0.965096i \(0.415652\pi\)
\(998\) 0 0
\(999\) 8.69182 0.274997
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 5520.2.a.ca.1.2 3
4.3 odd 2 2760.2.a.t.1.2 3
12.11 even 2 8280.2.a.bh.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2760.2.a.t.1.2 3 4.3 odd 2
5520.2.a.ca.1.2 3 1.1 even 1 trivial
8280.2.a.bh.1.2 3 12.11 even 2