Properties

Label 9360.2.a.bu.1.1
Level $9360$
Weight $2$
Character 9360.1
Self dual yes
Analytic conductor $74.740$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9360 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9360.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(74.7399762919\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 585)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 9360.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} +1.00000 q^{7} +3.00000 q^{11} +1.00000 q^{13} -3.00000 q^{17} +4.00000 q^{19} +9.00000 q^{23} +1.00000 q^{25} -6.00000 q^{29} -2.00000 q^{31} +1.00000 q^{35} -1.00000 q^{37} -3.00000 q^{41} -2.00000 q^{43} +6.00000 q^{47} -6.00000 q^{49} +9.00000 q^{53} +3.00000 q^{55} +12.0000 q^{59} +5.00000 q^{61} +1.00000 q^{65} +4.00000 q^{67} -9.00000 q^{71} +14.0000 q^{73} +3.00000 q^{77} +7.00000 q^{79} -3.00000 q^{85} +15.0000 q^{89} +1.00000 q^{91} +4.00000 q^{95} +5.00000 q^{97} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 0 0
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 9.00000 1.87663 0.938315 0.345782i \(-0.112386\pi\)
0.938315 + 0.345782i \(0.112386\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.00000 −0.468521 −0.234261 0.972174i \(-0.575267\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(42\) 0 0
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9.00000 1.23625 0.618123 0.786082i \(-0.287894\pi\)
0.618123 + 0.786082i \(0.287894\pi\)
\(54\) 0 0
\(55\) 3.00000 0.404520
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 0 0
\(61\) 5.00000 0.640184 0.320092 0.947386i \(-0.396286\pi\)
0.320092 + 0.947386i \(0.396286\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) 0 0
\(73\) 14.0000 1.63858 0.819288 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.00000 0.341882
\(78\) 0 0
\(79\) 7.00000 0.787562 0.393781 0.919204i \(-0.371167\pi\)
0.393781 + 0.919204i \(0.371167\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 15.0000 1.59000 0.794998 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.00000 0.410391
\(96\) 0 0
\(97\) 5.00000 0.507673 0.253837 0.967247i \(-0.418307\pi\)
0.253837 + 0.967247i \(0.418307\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −12.0000 −1.19404 −0.597022 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(102\) 0 0
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 9.00000 0.839254
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −3.00000 −0.275010
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −20.0000 −1.77471 −0.887357 0.461084i \(-0.847461\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) 4.00000 0.346844
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −12.0000 −1.02523 −0.512615 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(138\) 0 0
\(139\) 1.00000 0.0848189 0.0424094 0.999100i \(-0.486497\pi\)
0.0424094 + 0.999100i \(0.486497\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.00000 0.250873
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 15.0000 1.22885 0.614424 0.788976i \(-0.289388\pi\)
0.614424 + 0.788976i \(0.289388\pi\)
\(150\) 0 0
\(151\) 16.0000 1.30206 0.651031 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.00000 −0.160644
\(156\) 0 0
\(157\) 8.00000 0.638470 0.319235 0.947676i \(-0.396574\pi\)
0.319235 + 0.947676i \(0.396574\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 9.00000 0.709299
\(162\) 0 0
\(163\) −11.0000 −0.861586 −0.430793 0.902451i \(-0.641766\pi\)
−0.430793 + 0.902451i \(0.641766\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.00000 0.464294 0.232147 0.972681i \(-0.425425\pi\)
0.232147 + 0.972681i \(0.425425\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 18.0000 1.34538 0.672692 0.739923i \(-0.265138\pi\)
0.672692 + 0.739923i \(0.265138\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.00000 −0.0735215
\(186\) 0 0
\(187\) −9.00000 −0.658145
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 18.0000 1.30243 0.651217 0.758891i \(-0.274259\pi\)
0.651217 + 0.758891i \(0.274259\pi\)
\(192\) 0 0
\(193\) −13.0000 −0.935760 −0.467880 0.883792i \(-0.654982\pi\)
−0.467880 + 0.883792i \(0.654982\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 24.0000 1.70993 0.854965 0.518686i \(-0.173579\pi\)
0.854965 + 0.518686i \(0.173579\pi\)
\(198\) 0 0
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −6.00000 −0.421117
\(204\) 0 0
\(205\) −3.00000 −0.209529
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.00000 −0.136399
\(216\) 0 0
\(217\) −2.00000 −0.135769
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) 0 0
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −12.0000 −0.796468 −0.398234 0.917284i \(-0.630377\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(228\) 0 0
\(229\) −4.00000 −0.264327 −0.132164 0.991228i \(-0.542192\pi\)
−0.132164 + 0.991228i \(0.542192\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3.00000 0.196537 0.0982683 0.995160i \(-0.468670\pi\)
0.0982683 + 0.995160i \(0.468670\pi\)
\(234\) 0 0
\(235\) 6.00000 0.391397
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 15.0000 0.970269 0.485135 0.874439i \(-0.338771\pi\)
0.485135 + 0.874439i \(0.338771\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −6.00000 −0.383326
\(246\) 0 0
\(247\) 4.00000 0.254514
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 27.0000 1.69748
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.00000 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 0 0
\(259\) −1.00000 −0.0621370
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 24.0000 1.47990 0.739952 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 0 0
\(265\) 9.00000 0.552866
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −18.0000 −1.09748 −0.548740 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) 0 0
\(271\) −20.0000 −1.21491 −0.607457 0.794353i \(-0.707810\pi\)
−0.607457 + 0.794353i \(0.707810\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.00000 0.180907
\(276\) 0 0
\(277\) 26.0000 1.56219 0.781094 0.624413i \(-0.214662\pi\)
0.781094 + 0.624413i \(0.214662\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 0 0
\(283\) 16.0000 0.951101 0.475551 0.879688i \(-0.342249\pi\)
0.475551 + 0.879688i \(0.342249\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.00000 −0.177084
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −30.0000 −1.75262 −0.876309 0.481749i \(-0.840002\pi\)
−0.876309 + 0.481749i \(0.840002\pi\)
\(294\) 0 0
\(295\) 12.0000 0.698667
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 9.00000 0.520483
\(300\) 0 0
\(301\) −2.00000 −0.115278
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 5.00000 0.286299
\(306\) 0 0
\(307\) 1.00000 0.0570730 0.0285365 0.999593i \(-0.490915\pi\)
0.0285365 + 0.999593i \(0.490915\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 30.0000 1.70114 0.850572 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) 0 0
\(313\) −28.0000 −1.58265 −0.791327 0.611393i \(-0.790609\pi\)
−0.791327 + 0.611393i \(0.790609\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 0 0
\(319\) −18.0000 −1.00781
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −12.0000 −0.667698
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6.00000 0.330791
\(330\) 0 0
\(331\) 16.0000 0.879440 0.439720 0.898135i \(-0.355078\pi\)
0.439720 + 0.898135i \(0.355078\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 4.00000 0.218543
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −6.00000 −0.324918
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 33.0000 1.77153 0.885766 0.464131i \(-0.153633\pi\)
0.885766 + 0.464131i \(0.153633\pi\)
\(348\) 0 0
\(349\) 20.0000 1.07058 0.535288 0.844670i \(-0.320203\pi\)
0.535288 + 0.844670i \(0.320203\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 18.0000 0.958043 0.479022 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) 0 0
\(355\) −9.00000 −0.477670
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 14.0000 0.732793
\(366\) 0 0
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 9.00000 0.467257
\(372\) 0 0
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6.00000 −0.309016
\(378\) 0 0
\(379\) −2.00000 −0.102733 −0.0513665 0.998680i \(-0.516358\pi\)
−0.0513665 + 0.998680i \(0.516358\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −24.0000 −1.22634 −0.613171 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) 0 0
\(385\) 3.00000 0.152894
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) −27.0000 −1.36545
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7.00000 0.352208
\(396\) 0 0
\(397\) −13.0000 −0.652451 −0.326226 0.945292i \(-0.605777\pi\)
−0.326226 + 0.945292i \(0.605777\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 30.0000 1.49813 0.749064 0.662497i \(-0.230503\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) 0 0
\(403\) −2.00000 −0.0996271
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.00000 −0.148704
\(408\) 0 0
\(409\) 32.0000 1.58230 0.791149 0.611623i \(-0.209483\pi\)
0.791149 + 0.611623i \(0.209483\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 12.0000 0.590481
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −18.0000 −0.879358 −0.439679 0.898155i \(-0.644908\pi\)
−0.439679 + 0.898155i \(0.644908\pi\)
\(420\) 0 0
\(421\) −28.0000 −1.36464 −0.682318 0.731055i \(-0.739028\pi\)
−0.682318 + 0.731055i \(0.739028\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.00000 −0.145521
\(426\) 0 0
\(427\) 5.00000 0.241967
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) −28.0000 −1.34559 −0.672797 0.739827i \(-0.734907\pi\)
−0.672797 + 0.739827i \(0.734907\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 36.0000 1.72211
\(438\) 0 0
\(439\) −11.0000 −0.525001 −0.262501 0.964932i \(-0.584547\pi\)
−0.262501 + 0.964932i \(0.584547\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −15.0000 −0.712672 −0.356336 0.934358i \(-0.615974\pi\)
−0.356336 + 0.934358i \(0.615974\pi\)
\(444\) 0 0
\(445\) 15.0000 0.711068
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 21.0000 0.991051 0.495526 0.868593i \(-0.334975\pi\)
0.495526 + 0.868593i \(0.334975\pi\)
\(450\) 0 0
\(451\) −9.00000 −0.423793
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.00000 0.0468807
\(456\) 0 0
\(457\) 17.0000 0.795226 0.397613 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 21.0000 0.978068 0.489034 0.872265i \(-0.337349\pi\)
0.489034 + 0.872265i \(0.337349\pi\)
\(462\) 0 0
\(463\) 1.00000 0.0464739 0.0232370 0.999730i \(-0.492603\pi\)
0.0232370 + 0.999730i \(0.492603\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −15.0000 −0.694117 −0.347059 0.937843i \(-0.612820\pi\)
−0.347059 + 0.937843i \(0.612820\pi\)
\(468\) 0 0
\(469\) 4.00000 0.184703
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −6.00000 −0.275880
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 9.00000 0.411220 0.205610 0.978634i \(-0.434082\pi\)
0.205610 + 0.978634i \(0.434082\pi\)
\(480\) 0 0
\(481\) −1.00000 −0.0455961
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5.00000 0.227038
\(486\) 0 0
\(487\) 43.0000 1.94852 0.974258 0.225436i \(-0.0723806\pi\)
0.974258 + 0.225436i \(0.0723806\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −18.0000 −0.812329 −0.406164 0.913800i \(-0.633134\pi\)
−0.406164 + 0.913800i \(0.633134\pi\)
\(492\) 0 0
\(493\) 18.0000 0.810679
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −9.00000 −0.403705
\(498\) 0 0
\(499\) 22.0000 0.984855 0.492428 0.870353i \(-0.336110\pi\)
0.492428 + 0.870353i \(0.336110\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) −12.0000 −0.533993
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 15.0000 0.664863 0.332432 0.943127i \(-0.392131\pi\)
0.332432 + 0.943127i \(0.392131\pi\)
\(510\) 0 0
\(511\) 14.0000 0.619324
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −14.0000 −0.616914
\(516\) 0 0
\(517\) 18.0000 0.791639
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6.00000 0.261364
\(528\) 0 0
\(529\) 58.0000 2.52174
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3.00000 −0.129944
\(534\) 0 0
\(535\) −3.00000 −0.129701
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −18.0000 −0.775315
\(540\) 0 0
\(541\) −28.0000 −1.20381 −0.601907 0.798566i \(-0.705592\pi\)
−0.601907 + 0.798566i \(0.705592\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −10.0000 −0.428353
\(546\) 0 0
\(547\) −38.0000 −1.62476 −0.812381 0.583127i \(-0.801829\pi\)
−0.812381 + 0.583127i \(0.801829\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −24.0000 −1.02243
\(552\) 0 0
\(553\) 7.00000 0.297670
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 18.0000 0.762684 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) 0 0
\(559\) −2.00000 −0.0845910
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −15.0000 −0.632175 −0.316087 0.948730i \(-0.602369\pi\)
−0.316087 + 0.948730i \(0.602369\pi\)
\(564\) 0 0
\(565\) −6.00000 −0.252422
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 0 0
\(571\) 19.0000 0.795125 0.397563 0.917575i \(-0.369856\pi\)
0.397563 + 0.917575i \(0.369856\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 9.00000 0.375326
\(576\) 0 0
\(577\) 41.0000 1.70685 0.853426 0.521214i \(-0.174521\pi\)
0.853426 + 0.521214i \(0.174521\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 27.0000 1.11823
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 42.0000 1.72473 0.862367 0.506284i \(-0.168981\pi\)
0.862367 + 0.506284i \(0.168981\pi\)
\(594\) 0 0
\(595\) −3.00000 −0.122988
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 6.00000 0.245153 0.122577 0.992459i \(-0.460884\pi\)
0.122577 + 0.992459i \(0.460884\pi\)
\(600\) 0 0
\(601\) −37.0000 −1.50926 −0.754631 0.656150i \(-0.772184\pi\)
−0.754631 + 0.656150i \(0.772184\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2.00000 −0.0813116
\(606\) 0 0
\(607\) 16.0000 0.649420 0.324710 0.945814i \(-0.394733\pi\)
0.324710 + 0.945814i \(0.394733\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.00000 0.242734
\(612\) 0 0
\(613\) −31.0000 −1.25208 −0.626039 0.779792i \(-0.715325\pi\)
−0.626039 + 0.779792i \(0.715325\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 42.0000 1.69086 0.845428 0.534089i \(-0.179345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(618\) 0 0
\(619\) −8.00000 −0.321547 −0.160774 0.986991i \(-0.551399\pi\)
−0.160774 + 0.986991i \(0.551399\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 15.0000 0.600962
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3.00000 0.119618
\(630\) 0 0
\(631\) 34.0000 1.35352 0.676759 0.736204i \(-0.263384\pi\)
0.676759 + 0.736204i \(0.263384\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −20.0000 −0.793676
\(636\) 0 0
\(637\) −6.00000 −0.237729
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) −23.0000 −0.907031 −0.453516 0.891248i \(-0.649830\pi\)
−0.453516 + 0.891248i \(0.649830\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 39.0000 1.53325 0.766624 0.642096i \(-0.221935\pi\)
0.766624 + 0.642096i \(0.221935\pi\)
\(648\) 0 0
\(649\) 36.0000 1.41312
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 18.0000 0.704394 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) 0 0
\(655\) −12.0000 −0.468879
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −30.0000 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4.00000 0.155113
\(666\) 0 0
\(667\) −54.0000 −2.09089
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 15.0000 0.579069
\(672\) 0 0
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3.00000 −0.115299 −0.0576497 0.998337i \(-0.518361\pi\)
−0.0576497 + 0.998337i \(0.518361\pi\)
\(678\) 0 0
\(679\) 5.00000 0.191882
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −24.0000 −0.918334 −0.459167 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 9.00000 0.342873
\(690\) 0 0
\(691\) 28.0000 1.06517 0.532585 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.00000 0.0379322
\(696\) 0 0
\(697\) 9.00000 0.340899
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 24.0000 0.906467 0.453234 0.891392i \(-0.350270\pi\)
0.453234 + 0.891392i \(0.350270\pi\)
\(702\) 0 0
\(703\) −4.00000 −0.150863
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −12.0000 −0.451306
\(708\) 0 0
\(709\) 44.0000 1.65245 0.826227 0.563337i \(-0.190483\pi\)
0.826227 + 0.563337i \(0.190483\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −18.0000 −0.674105
\(714\) 0 0
\(715\) 3.00000 0.112194
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) −14.0000 −0.521387
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6.00000 −0.222834
\(726\) 0 0
\(727\) −2.00000 −0.0741759 −0.0370879 0.999312i \(-0.511808\pi\)
−0.0370879 + 0.999312i \(0.511808\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 6.00000 0.221918
\(732\) 0 0
\(733\) −49.0000 −1.80986 −0.904928 0.425564i \(-0.860076\pi\)
−0.904928 + 0.425564i \(0.860076\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 12.0000 0.442026
\(738\) 0 0
\(739\) −38.0000 −1.39785 −0.698926 0.715194i \(-0.746338\pi\)
−0.698926 + 0.715194i \(0.746338\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 0 0
\(745\) 15.0000 0.549557
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.00000 −0.109618
\(750\) 0 0
\(751\) −11.0000 −0.401396 −0.200698 0.979653i \(-0.564321\pi\)
−0.200698 + 0.979653i \(0.564321\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 16.0000 0.582300
\(756\) 0 0
\(757\) 14.0000 0.508839 0.254419 0.967094i \(-0.418116\pi\)
0.254419 + 0.967094i \(0.418116\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −6.00000 −0.217500 −0.108750 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) 0 0
\(763\) −10.0000 −0.362024
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 12.0000 0.433295
\(768\) 0 0
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −48.0000 −1.72644 −0.863220 0.504828i \(-0.831556\pi\)
−0.863220 + 0.504828i \(0.831556\pi\)
\(774\) 0 0
\(775\) −2.00000 −0.0718421
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −12.0000 −0.429945
\(780\) 0 0
\(781\) −27.0000 −0.966136
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 8.00000 0.285532
\(786\) 0 0
\(787\) 52.0000 1.85360 0.926800 0.375555i \(-0.122548\pi\)
0.926800 + 0.375555i \(0.122548\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −6.00000 −0.213335
\(792\) 0 0
\(793\) 5.00000 0.177555
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 39.0000 1.38145 0.690725 0.723117i \(-0.257291\pi\)
0.690725 + 0.723117i \(0.257291\pi\)
\(798\) 0 0
\(799\) −18.0000 −0.636794
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 42.0000 1.48215
\(804\) 0 0
\(805\) 9.00000 0.317208
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −48.0000 −1.68759 −0.843795 0.536666i \(-0.819684\pi\)
−0.843795 + 0.536666i \(0.819684\pi\)
\(810\) 0 0
\(811\) 22.0000 0.772524 0.386262 0.922389i \(-0.373766\pi\)
0.386262 + 0.922389i \(0.373766\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −11.0000 −0.385313
\(816\) 0 0
\(817\) −8.00000 −0.279885
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −15.0000 −0.523504 −0.261752 0.965135i \(-0.584300\pi\)
−0.261752 + 0.965135i \(0.584300\pi\)
\(822\) 0 0
\(823\) 4.00000 0.139431 0.0697156 0.997567i \(-0.477791\pi\)
0.0697156 + 0.997567i \(0.477791\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 18.0000 0.625921 0.312961 0.949766i \(-0.398679\pi\)
0.312961 + 0.949766i \(0.398679\pi\)
\(828\) 0 0
\(829\) −22.0000 −0.764092 −0.382046 0.924143i \(-0.624780\pi\)
−0.382046 + 0.924143i \(0.624780\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 18.0000 0.623663
\(834\) 0 0
\(835\) 6.00000 0.207639
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 51.0000 1.76072 0.880358 0.474310i \(-0.157302\pi\)
0.880358 + 0.474310i \(0.157302\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.00000 0.0344010
\(846\) 0 0
\(847\) −2.00000 −0.0687208
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −9.00000 −0.308516
\(852\) 0 0
\(853\) 17.0000 0.582069 0.291034 0.956713i \(-0.406001\pi\)
0.291034 + 0.956713i \(0.406001\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −33.0000 −1.12726 −0.563629 0.826028i \(-0.690595\pi\)
−0.563629 + 0.826028i \(0.690595\pi\)
\(858\) 0 0
\(859\) 13.0000 0.443554 0.221777 0.975097i \(-0.428814\pi\)
0.221777 + 0.975097i \(0.428814\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 18.0000 0.612727 0.306364 0.951915i \(-0.400888\pi\)
0.306364 + 0.951915i \(0.400888\pi\)
\(864\) 0 0
\(865\) 6.00000 0.204006
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 21.0000 0.712376
\(870\) 0 0
\(871\) 4.00000 0.135535
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1.00000 0.0338062
\(876\) 0 0
\(877\) −46.0000 −1.55331 −0.776655 0.629926i \(-0.783085\pi\)
−0.776655 + 0.629926i \(0.783085\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −54.0000 −1.81931 −0.909653 0.415369i \(-0.863653\pi\)
−0.909653 + 0.415369i \(0.863653\pi\)
\(882\) 0 0
\(883\) 10.0000 0.336527 0.168263 0.985742i \(-0.446184\pi\)
0.168263 + 0.985742i \(0.446184\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −9.00000 −0.302190 −0.151095 0.988519i \(-0.548280\pi\)
−0.151095 + 0.988519i \(0.548280\pi\)
\(888\) 0 0
\(889\) −20.0000 −0.670778
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 24.0000 0.803129
\(894\) 0 0
\(895\) 18.0000 0.601674
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 12.0000 0.400222
\(900\) 0 0
\(901\) −27.0000 −0.899500
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −7.00000 −0.232688
\(906\) 0 0
\(907\) −50.0000 −1.66022 −0.830111 0.557598i \(-0.811723\pi\)
−0.830111 + 0.557598i \(0.811723\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 48.0000 1.59031 0.795155 0.606406i \(-0.207389\pi\)
0.795155 + 0.606406i \(0.207389\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −12.0000 −0.396275
\(918\) 0 0
\(919\) −29.0000 −0.956622 −0.478311 0.878191i \(-0.658751\pi\)
−0.478311 + 0.878191i \(0.658751\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −9.00000 −0.296239
\(924\) 0 0
\(925\) −1.00000 −0.0328798
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −21.0000 −0.688988 −0.344494 0.938789i \(-0.611949\pi\)
−0.344494 + 0.938789i \(0.611949\pi\)
\(930\) 0 0
\(931\) −24.0000 −0.786568
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −9.00000 −0.294331
\(936\) 0 0
\(937\) −4.00000 −0.130674 −0.0653372 0.997863i \(-0.520812\pi\)
−0.0653372 + 0.997863i \(0.520812\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −33.0000 −1.07577 −0.537885 0.843018i \(-0.680776\pi\)
−0.537885 + 0.843018i \(0.680776\pi\)
\(942\) 0 0
\(943\) −27.0000 −0.879241
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −42.0000 −1.36482 −0.682408 0.730971i \(-0.739067\pi\)
−0.682408 + 0.730971i \(0.739067\pi\)
\(948\) 0 0
\(949\) 14.0000 0.454459
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 9.00000 0.291539 0.145769 0.989319i \(-0.453434\pi\)
0.145769 + 0.989319i \(0.453434\pi\)
\(954\) 0 0
\(955\) 18.0000 0.582466
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −12.0000 −0.387500
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −13.0000 −0.418485
\(966\) 0 0
\(967\) −56.0000 −1.80084 −0.900419 0.435023i \(-0.856740\pi\)
−0.900419 + 0.435023i \(0.856740\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 1.00000 0.0320585
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −54.0000 −1.72761 −0.863807 0.503824i \(-0.831926\pi\)
−0.863807 + 0.503824i \(0.831926\pi\)
\(978\) 0 0
\(979\) 45.0000 1.43821
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 36.0000 1.14822 0.574111 0.818778i \(-0.305348\pi\)
0.574111 + 0.818778i \(0.305348\pi\)
\(984\) 0 0
\(985\) 24.0000 0.764704
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −18.0000 −0.572367
\(990\) 0 0
\(991\) −23.0000 −0.730619 −0.365310 0.930886i \(-0.619037\pi\)
−0.365310 + 0.930886i \(0.619037\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 16.0000 0.507234
\(996\) 0 0
\(997\) −46.0000 −1.45683 −0.728417 0.685134i \(-0.759744\pi\)
−0.728417 + 0.685134i \(0.759744\pi\)
\(998\) 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 9360.2.a.bu.1.1 1
3.2 odd 2 9360.2.a.r.1.1 1
4.3 odd 2 585.2.a.f.1.1 yes 1
12.11 even 2 585.2.a.e.1.1 1
20.3 even 4 2925.2.c.l.2224.2 2
20.7 even 4 2925.2.c.l.2224.1 2
20.19 odd 2 2925.2.a.i.1.1 1
52.51 odd 2 7605.2.a.j.1.1 1
60.23 odd 4 2925.2.c.m.2224.2 2
60.47 odd 4 2925.2.c.m.2224.1 2
60.59 even 2 2925.2.a.k.1.1 1
156.155 even 2 7605.2.a.m.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.a.e.1.1 1 12.11 even 2
585.2.a.f.1.1 yes 1 4.3 odd 2
2925.2.a.i.1.1 1 20.19 odd 2
2925.2.a.k.1.1 1 60.59 even 2
2925.2.c.l.2224.1 2 20.7 even 4
2925.2.c.l.2224.2 2 20.3 even 4
2925.2.c.m.2224.1 2 60.47 odd 4
2925.2.c.m.2224.2 2 60.23 odd 4
7605.2.a.j.1.1 1 52.51 odd 2
7605.2.a.m.1.1 1 156.155 even 2
9360.2.a.r.1.1 1 3.2 odd 2
9360.2.a.bu.1.1 1 1.1 even 1 trivial