Properties

Label 9216.2.a.a.1.1
Level $9216$
Weight $2$
Character 9216.1
Self dual yes
Analytic conductor $73.590$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 9216 = 2^{10} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9216.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(73.5901305028\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Defining polynomial: \(x^{2} - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 4608)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.41421\) of defining polynomial
Character \(\chi\) \(=\) 9216.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{5} -4.00000 q^{7} +O(q^{10})\) \(q-1.41421 q^{5} -4.00000 q^{7} +5.65685 q^{11} -4.24264 q^{13} -6.00000 q^{17} -5.65685 q^{19} -8.00000 q^{23} -3.00000 q^{25} +4.24264 q^{29} -4.00000 q^{31} +5.65685 q^{35} -1.41421 q^{37} -2.00000 q^{41} +5.65685 q^{43} +8.00000 q^{47} +9.00000 q^{49} -9.89949 q^{53} -8.00000 q^{55} -4.24264 q^{61} +6.00000 q^{65} -11.3137 q^{67} +10.0000 q^{73} -22.6274 q^{77} -12.0000 q^{79} +5.65685 q^{83} +8.48528 q^{85} +16.0000 q^{89} +16.9706 q^{91} +8.00000 q^{95} +8.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 8 q^{7} + O(q^{10}) \) \( 2 q - 8 q^{7} - 12 q^{17} - 16 q^{23} - 6 q^{25} - 8 q^{31} - 4 q^{41} + 16 q^{47} + 18 q^{49} - 16 q^{55} + 12 q^{65} + 20 q^{73} - 24 q^{79} + 32 q^{89} + 16 q^{95} + 16 q^{97} + O(q^{100}) \)

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
\(5\) −1.41421 −0.632456 −0.316228 0.948683i \(-0.602416\pi\)
−0.316228 + 0.948683i \(0.602416\pi\)
\(6\) 0 0
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 5.65685 1.70561 0.852803 0.522233i \(-0.174901\pi\)
0.852803 + 0.522233i \(0.174901\pi\)
\(12\) 0 0
\(13\) −4.24264 −1.17670 −0.588348 0.808608i \(-0.700222\pi\)
−0.588348 + 0.808608i \(0.700222\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 0 0
\(19\) −5.65685 −1.29777 −0.648886 0.760886i \(-0.724765\pi\)
−0.648886 + 0.760886i \(0.724765\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −8.00000 −1.66812 −0.834058 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) 0 0
\(25\) −3.00000 −0.600000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.24264 0.787839 0.393919 0.919145i \(-0.371119\pi\)
0.393919 + 0.919145i \(0.371119\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 5.65685 0.956183
\(36\) 0 0
\(37\) −1.41421 −0.232495 −0.116248 0.993220i \(-0.537087\pi\)
−0.116248 + 0.993220i \(0.537087\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 5.65685 0.862662 0.431331 0.902194i \(-0.358044\pi\)
0.431331 + 0.902194i \(0.358044\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 0 0
\(49\) 9.00000 1.28571
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −9.89949 −1.35980 −0.679900 0.733305i \(-0.737977\pi\)
−0.679900 + 0.733305i \(0.737977\pi\)
\(54\) 0 0
\(55\) −8.00000 −1.07872
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −4.24264 −0.543214 −0.271607 0.962408i \(-0.587555\pi\)
−0.271607 + 0.962408i \(0.587555\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 6.00000 0.744208
\(66\) 0 0
\(67\) −11.3137 −1.38219 −0.691095 0.722764i \(-0.742871\pi\)
−0.691095 + 0.722764i \(0.742871\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 10.0000 1.17041 0.585206 0.810885i \(-0.301014\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −22.6274 −2.57863
\(78\) 0 0
\(79\) −12.0000 −1.35011 −0.675053 0.737769i \(-0.735879\pi\)
−0.675053 + 0.737769i \(0.735879\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.65685 0.620920 0.310460 0.950586i \(-0.399517\pi\)
0.310460 + 0.950586i \(0.399517\pi\)
\(84\) 0 0
\(85\) 8.48528 0.920358
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 16.0000 1.69600 0.847998 0.529999i \(-0.177808\pi\)
0.847998 + 0.529999i \(0.177808\pi\)
\(90\) 0 0
\(91\) 16.9706 1.77900
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 8.00000 0.820783
\(96\) 0 0
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.89949 0.985037 0.492518 0.870302i \(-0.336076\pi\)
0.492518 + 0.870302i \(0.336076\pi\)
\(102\) 0 0
\(103\) 4.00000 0.394132 0.197066 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −11.3137 −1.09374 −0.546869 0.837218i \(-0.684180\pi\)
−0.546869 + 0.837218i \(0.684180\pi\)
\(108\) 0 0
\(109\) −7.07107 −0.677285 −0.338643 0.940915i \(-0.609968\pi\)
−0.338643 + 0.940915i \(0.609968\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −16.0000 −1.50515 −0.752577 0.658505i \(-0.771189\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 0 0
\(115\) 11.3137 1.05501
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 24.0000 2.20008
\(120\) 0 0
\(121\) 21.0000 1.90909
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.3137 1.01193
\(126\) 0 0
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −11.3137 −0.988483 −0.494242 0.869325i \(-0.664554\pi\)
−0.494242 + 0.869325i \(0.664554\pi\)
\(132\) 0 0
\(133\) 22.6274 1.96205
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.00000 0.170872 0.0854358 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −24.0000 −2.00698
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.41421 0.115857 0.0579284 0.998321i \(-0.481550\pi\)
0.0579284 + 0.998321i \(0.481550\pi\)
\(150\) 0 0
\(151\) 4.00000 0.325515 0.162758 0.986666i \(-0.447961\pi\)
0.162758 + 0.986666i \(0.447961\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 5.65685 0.454369
\(156\) 0 0
\(157\) −4.24264 −0.338600 −0.169300 0.985565i \(-0.554151\pi\)
−0.169300 + 0.985565i \(0.554151\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 32.0000 2.52195
\(162\) 0 0
\(163\) 16.9706 1.32924 0.664619 0.747183i \(-0.268594\pi\)
0.664619 + 0.747183i \(0.268594\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) 5.00000 0.384615
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −15.5563 −1.18273 −0.591364 0.806405i \(-0.701410\pi\)
−0.591364 + 0.806405i \(0.701410\pi\)
\(174\) 0 0
\(175\) 12.0000 0.907115
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −11.3137 −0.845626 −0.422813 0.906217i \(-0.638957\pi\)
−0.422813 + 0.906217i \(0.638957\pi\)
\(180\) 0 0
\(181\) 12.7279 0.946059 0.473029 0.881047i \(-0.343160\pi\)
0.473029 + 0.881047i \(0.343160\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.00000 0.147043
\(186\) 0 0
\(187\) −33.9411 −2.48202
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −24.0000 −1.73658 −0.868290 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) 0 0
\(193\) 8.00000 0.575853 0.287926 0.957653i \(-0.407034\pi\)
0.287926 + 0.957653i \(0.407034\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.41421 0.100759 0.0503793 0.998730i \(-0.483957\pi\)
0.0503793 + 0.998730i \(0.483957\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −16.9706 −1.19110
\(204\) 0 0
\(205\) 2.82843 0.197546
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −32.0000 −2.21349
\(210\) 0 0
\(211\) −22.6274 −1.55774 −0.778868 0.627188i \(-0.784206\pi\)
−0.778868 + 0.627188i \(0.784206\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) 16.0000 1.08615
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 25.4558 1.71235
\(222\) 0 0
\(223\) 12.0000 0.803579 0.401790 0.915732i \(-0.368388\pi\)
0.401790 + 0.915732i \(0.368388\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −16.9706 −1.12638 −0.563188 0.826329i \(-0.690425\pi\)
−0.563188 + 0.826329i \(0.690425\pi\)
\(228\) 0 0
\(229\) 9.89949 0.654177 0.327089 0.944994i \(-0.393932\pi\)
0.327089 + 0.944994i \(0.393932\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −16.0000 −1.04819 −0.524097 0.851658i \(-0.675597\pi\)
−0.524097 + 0.851658i \(0.675597\pi\)
\(234\) 0 0
\(235\) −11.3137 −0.738025
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 8.00000 0.517477 0.258738 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) 0 0
\(241\) 24.0000 1.54598 0.772988 0.634421i \(-0.218761\pi\)
0.772988 + 0.634421i \(0.218761\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −12.7279 −0.813157
\(246\) 0 0
\(247\) 24.0000 1.52708
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5.65685 −0.357057 −0.178529 0.983935i \(-0.557134\pi\)
−0.178529 + 0.983935i \(0.557134\pi\)
\(252\) 0 0
\(253\) −45.2548 −2.84515
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 5.65685 0.351500
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 16.0000 0.986602 0.493301 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) 0 0
\(265\) 14.0000 0.860013
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −4.24264 −0.258678 −0.129339 0.991600i \(-0.541286\pi\)
−0.129339 + 0.991600i \(0.541286\pi\)
\(270\) 0 0
\(271\) 28.0000 1.70088 0.850439 0.526073i \(-0.176336\pi\)
0.850439 + 0.526073i \(0.176336\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −16.9706 −1.02336
\(276\) 0 0
\(277\) 21.2132 1.27458 0.637289 0.770625i \(-0.280056\pi\)
0.637289 + 0.770625i \(0.280056\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 11.3137 0.672530 0.336265 0.941767i \(-0.390836\pi\)
0.336265 + 0.941767i \(0.390836\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8.00000 0.472225
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.41421 0.0826192 0.0413096 0.999146i \(-0.486847\pi\)
0.0413096 + 0.999146i \(0.486847\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 33.9411 1.96287
\(300\) 0 0
\(301\) −22.6274 −1.30422
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6.00000 0.343559
\(306\) 0 0
\(307\) 33.9411 1.93712 0.968561 0.248776i \(-0.0800281\pi\)
0.968561 + 0.248776i \(0.0800281\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −16.0000 −0.907277 −0.453638 0.891186i \(-0.649874\pi\)
−0.453638 + 0.891186i \(0.649874\pi\)
\(312\) 0 0
\(313\) 8.00000 0.452187 0.226093 0.974106i \(-0.427405\pi\)
0.226093 + 0.974106i \(0.427405\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 26.8701 1.50917 0.754586 0.656201i \(-0.227838\pi\)
0.754586 + 0.656201i \(0.227838\pi\)
\(318\) 0 0
\(319\) 24.0000 1.34374
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 33.9411 1.88853
\(324\) 0 0
\(325\) 12.7279 0.706018
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −32.0000 −1.76422
\(330\) 0 0
\(331\) −22.6274 −1.24372 −0.621858 0.783130i \(-0.713622\pi\)
−0.621858 + 0.783130i \(0.713622\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 16.0000 0.874173
\(336\) 0 0
\(337\) 30.0000 1.63420 0.817102 0.576493i \(-0.195579\pi\)
0.817102 + 0.576493i \(0.195579\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −22.6274 −1.22534
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −28.2843 −1.51838 −0.759190 0.650870i \(-0.774404\pi\)
−0.759190 + 0.650870i \(0.774404\pi\)
\(348\) 0 0
\(349\) 15.5563 0.832712 0.416356 0.909202i \(-0.363307\pi\)
0.416356 + 0.909202i \(0.363307\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 16.0000 0.851594 0.425797 0.904819i \(-0.359994\pi\)
0.425797 + 0.904819i \(0.359994\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 16.0000 0.844448 0.422224 0.906492i \(-0.361250\pi\)
0.422224 + 0.906492i \(0.361250\pi\)
\(360\) 0 0
\(361\) 13.0000 0.684211
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −14.1421 −0.740233
\(366\) 0 0
\(367\) −20.0000 −1.04399 −0.521996 0.852948i \(-0.674812\pi\)
−0.521996 + 0.852948i \(0.674812\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 39.5980 2.05582
\(372\) 0 0
\(373\) −21.2132 −1.09838 −0.549189 0.835698i \(-0.685063\pi\)
−0.549189 + 0.835698i \(0.685063\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −18.0000 −0.927047
\(378\) 0 0
\(379\) −16.9706 −0.871719 −0.435860 0.900015i \(-0.643556\pi\)
−0.435860 + 0.900015i \(0.643556\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 24.0000 1.22634 0.613171 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) 0 0
\(385\) 32.0000 1.63087
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 35.3553 1.79259 0.896293 0.443461i \(-0.146250\pi\)
0.896293 + 0.443461i \(0.146250\pi\)
\(390\) 0 0
\(391\) 48.0000 2.42746
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 16.9706 0.853882
\(396\) 0 0
\(397\) −38.1838 −1.91639 −0.958194 0.286119i \(-0.907635\pi\)
−0.958194 + 0.286119i \(0.907635\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6.00000 0.299626 0.149813 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) 0 0
\(403\) 16.9706 0.845364
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −8.00000 −0.396545
\(408\) 0 0
\(409\) 8.00000 0.395575 0.197787 0.980245i \(-0.436624\pi\)
0.197787 + 0.980245i \(0.436624\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −8.00000 −0.392705
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 16.9706 0.829066 0.414533 0.910034i \(-0.363945\pi\)
0.414533 + 0.910034i \(0.363945\pi\)
\(420\) 0 0
\(421\) −12.7279 −0.620321 −0.310160 0.950684i \(-0.600383\pi\)
−0.310160 + 0.950684i \(0.600383\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 18.0000 0.873128
\(426\) 0 0
\(427\) 16.9706 0.821263
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 8.00000 0.385346 0.192673 0.981263i \(-0.438284\pi\)
0.192673 + 0.981263i \(0.438284\pi\)
\(432\) 0 0
\(433\) −8.00000 −0.384455 −0.192228 0.981350i \(-0.561571\pi\)
−0.192228 + 0.981350i \(0.561571\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 45.2548 2.16483
\(438\) 0 0
\(439\) −20.0000 −0.954548 −0.477274 0.878755i \(-0.658375\pi\)
−0.477274 + 0.878755i \(0.658375\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 16.9706 0.806296 0.403148 0.915135i \(-0.367916\pi\)
0.403148 + 0.915135i \(0.367916\pi\)
\(444\) 0 0
\(445\) −22.6274 −1.07264
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 10.0000 0.471929 0.235965 0.971762i \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) 0 0
\(451\) −11.3137 −0.532742
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −24.0000 −1.12514
\(456\) 0 0
\(457\) 8.00000 0.374224 0.187112 0.982339i \(-0.440087\pi\)
0.187112 + 0.982339i \(0.440087\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 26.8701 1.25146 0.625732 0.780038i \(-0.284800\pi\)
0.625732 + 0.780038i \(0.284800\pi\)
\(462\) 0 0
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5.65685 0.261768 0.130884 0.991398i \(-0.458218\pi\)
0.130884 + 0.991398i \(0.458218\pi\)
\(468\) 0 0
\(469\) 45.2548 2.08967
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 32.0000 1.47136
\(474\) 0 0
\(475\) 16.9706 0.778663
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −16.0000 −0.731059 −0.365529 0.930800i \(-0.619112\pi\)
−0.365529 + 0.930800i \(0.619112\pi\)
\(480\) 0 0
\(481\) 6.00000 0.273576
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −11.3137 −0.513729
\(486\) 0 0
\(487\) −12.0000 −0.543772 −0.271886 0.962329i \(-0.587647\pi\)
−0.271886 + 0.962329i \(0.587647\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −11.3137 −0.510581 −0.255290 0.966864i \(-0.582171\pi\)
−0.255290 + 0.966864i \(0.582171\pi\)
\(492\) 0 0
\(493\) −25.4558 −1.14647
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −11.3137 −0.506471 −0.253236 0.967405i \(-0.581495\pi\)
−0.253236 + 0.967405i \(0.581495\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −16.0000 −0.713405 −0.356702 0.934218i \(-0.616099\pi\)
−0.356702 + 0.934218i \(0.616099\pi\)
\(504\) 0 0
\(505\) −14.0000 −0.622992
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −15.5563 −0.689523 −0.344762 0.938690i \(-0.612040\pi\)
−0.344762 + 0.938690i \(0.612040\pi\)
\(510\) 0 0
\(511\) −40.0000 −1.76950
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5.65685 −0.249271
\(516\) 0 0
\(517\) 45.2548 1.99031
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 30.0000 1.31432 0.657162 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 0 0
\(523\) 16.9706 0.742071 0.371035 0.928619i \(-0.379003\pi\)
0.371035 + 0.928619i \(0.379003\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 24.0000 1.04546
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 8.48528 0.367538
\(534\) 0 0
\(535\) 16.0000 0.691740
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 50.9117 2.19292
\(540\) 0 0
\(541\) 4.24264 0.182405 0.0912027 0.995832i \(-0.470929\pi\)
0.0912027 + 0.995832i \(0.470929\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 10.0000 0.428353
\(546\) 0 0
\(547\) 16.9706 0.725609 0.362804 0.931865i \(-0.381819\pi\)
0.362804 + 0.931865i \(0.381819\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −24.0000 −1.02243
\(552\) 0 0
\(553\) 48.0000 2.04117
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −15.5563 −0.659144 −0.329572 0.944131i \(-0.606904\pi\)
−0.329572 + 0.944131i \(0.606904\pi\)
\(558\) 0 0
\(559\) −24.0000 −1.01509
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −28.2843 −1.19204 −0.596020 0.802970i \(-0.703252\pi\)
−0.596020 + 0.802970i \(0.703252\pi\)
\(564\) 0 0
\(565\) 22.6274 0.951943
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −18.0000 −0.754599 −0.377300 0.926091i \(-0.623147\pi\)
−0.377300 + 0.926091i \(0.623147\pi\)
\(570\) 0 0
\(571\) 33.9411 1.42039 0.710196 0.704004i \(-0.248606\pi\)
0.710196 + 0.704004i \(0.248606\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 24.0000 1.00087
\(576\) 0 0
\(577\) −18.0000 −0.749350 −0.374675 0.927156i \(-0.622246\pi\)
−0.374675 + 0.927156i \(0.622246\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −22.6274 −0.938743
\(582\) 0 0
\(583\) −56.0000 −2.31928
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −22.6274 −0.933933 −0.466967 0.884275i \(-0.654653\pi\)
−0.466967 + 0.884275i \(0.654653\pi\)
\(588\) 0 0
\(589\) 22.6274 0.932346
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 16.0000 0.657041 0.328521 0.944497i \(-0.393450\pi\)
0.328521 + 0.944497i \(0.393450\pi\)
\(594\) 0 0
\(595\) −33.9411 −1.39145
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 40.0000 1.63436 0.817178 0.576386i \(-0.195537\pi\)
0.817178 + 0.576386i \(0.195537\pi\)
\(600\) 0 0
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −29.6985 −1.20742
\(606\) 0 0
\(607\) 12.0000 0.487065 0.243532 0.969893i \(-0.421694\pi\)
0.243532 + 0.969893i \(0.421694\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −33.9411 −1.37311
\(612\) 0 0
\(613\) −9.89949 −0.399837 −0.199918 0.979813i \(-0.564068\pi\)
−0.199918 + 0.979813i \(0.564068\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −32.0000 −1.28827 −0.644136 0.764911i \(-0.722783\pi\)
−0.644136 + 0.764911i \(0.722783\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −64.0000 −2.56411
\(624\) 0 0
\(625\) −1.00000 −0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 8.48528 0.338330
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5.65685 0.224485
\(636\) 0 0
\(637\) −38.1838 −1.51290
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −22.0000 −0.868948 −0.434474 0.900684i \(-0.643066\pi\)
−0.434474 + 0.900684i \(0.643066\pi\)
\(642\) 0 0
\(643\) −16.9706 −0.669254 −0.334627 0.942351i \(-0.608610\pi\)
−0.334627 + 0.942351i \(0.608610\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −24.0000 −0.943537 −0.471769 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 26.8701 1.05151 0.525753 0.850637i \(-0.323784\pi\)
0.525753 + 0.850637i \(0.323784\pi\)
\(654\) 0 0
\(655\) 16.0000 0.625172
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 11.3137 0.440720 0.220360 0.975419i \(-0.429277\pi\)
0.220360 + 0.975419i \(0.429277\pi\)
\(660\) 0 0
\(661\) 9.89949 0.385046 0.192523 0.981292i \(-0.438333\pi\)
0.192523 + 0.981292i \(0.438333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −32.0000 −1.24091
\(666\) 0 0
\(667\) −33.9411 −1.31421
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) −8.00000 −0.308377 −0.154189 0.988041i \(-0.549276\pi\)
−0.154189 + 0.988041i \(0.549276\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 12.7279 0.489174 0.244587 0.969627i \(-0.421348\pi\)
0.244587 + 0.969627i \(0.421348\pi\)
\(678\) 0 0
\(679\) −32.0000 −1.22805
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −16.9706 −0.649361 −0.324680 0.945824i \(-0.605257\pi\)
−0.324680 + 0.945824i \(0.605257\pi\)
\(684\) 0 0
\(685\) −2.82843 −0.108069
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 42.0000 1.60007
\(690\) 0 0
\(691\) −50.9117 −1.93677 −0.968386 0.249457i \(-0.919748\pi\)
−0.968386 + 0.249457i \(0.919748\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 12.0000 0.454532
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −15.5563 −0.587555 −0.293778 0.955874i \(-0.594913\pi\)
−0.293778 + 0.955874i \(0.594913\pi\)
\(702\) 0 0
\(703\) 8.00000 0.301726
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −39.5980 −1.48924
\(708\) 0 0
\(709\) 46.6690 1.75269 0.876346 0.481681i \(-0.159974\pi\)
0.876346 + 0.481681i \(0.159974\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 32.0000 1.19841
\(714\) 0 0
\(715\) 33.9411 1.26933
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) −16.0000 −0.595871
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −12.7279 −0.472703
\(726\) 0 0
\(727\) −52.0000 −1.92857 −0.964287 0.264861i \(-0.914674\pi\)
−0.964287 + 0.264861i \(0.914674\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −33.9411 −1.25536
\(732\) 0 0
\(733\) 52.3259 1.93270 0.966351 0.257228i \(-0.0828093\pi\)
0.966351 + 0.257228i \(0.0828093\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −64.0000 −2.35747
\(738\) 0 0
\(739\) −33.9411 −1.24854 −0.624272 0.781207i \(-0.714604\pi\)
−0.624272 + 0.781207i \(0.714604\pi\)
\(740\) 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
\(745\) −2.00000 −0.0732743
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 45.2548 1.65358
\(750\) 0 0
\(751\) 28.0000 1.02173 0.510867 0.859660i \(-0.329324\pi\)
0.510867 + 0.859660i \(0.329324\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −5.65685 −0.205874
\(756\) 0 0
\(757\) −9.89949 −0.359803 −0.179902 0.983685i \(-0.557578\pi\)
−0.179902 + 0.983685i \(0.557578\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 18.0000 0.652499 0.326250 0.945284i \(-0.394215\pi\)
0.326250 + 0.945284i \(0.394215\pi\)
\(762\) 0 0
\(763\) 28.2843 1.02396
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 40.0000 1.44244 0.721218 0.692708i \(-0.243582\pi\)
0.721218 + 0.692708i \(0.243582\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −12.7279 −0.457792 −0.228896 0.973451i \(-0.573511\pi\)
−0.228896 + 0.973451i \(0.573511\pi\)
\(774\) 0 0
\(775\) 12.0000 0.431053
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 11.3137 0.405356
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 6.00000 0.214149
\(786\) 0 0
\(787\) 16.9706 0.604935 0.302468 0.953160i \(-0.402190\pi\)
0.302468 + 0.953160i \(0.402190\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 64.0000 2.27558
\(792\) 0 0
\(793\) 18.0000 0.639199
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −7.07107 −0.250470 −0.125235 0.992127i \(-0.539968\pi\)
−0.125235 + 0.992127i \(0.539968\pi\)
\(798\) 0 0
\(799\) −48.0000 −1.69812
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 56.5685 1.99626
\(804\) 0 0
\(805\) −45.2548 −1.59502
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 2.00000 0.0703163 0.0351581 0.999382i \(-0.488807\pi\)
0.0351581 + 0.999382i \(0.488807\pi\)
\(810\) 0 0
\(811\) −5.65685 −0.198639 −0.0993195 0.995056i \(-0.531667\pi\)
−0.0993195 + 0.995056i \(0.531667\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −24.0000 −0.840683
\(816\) 0 0
\(817\) −32.0000 −1.11954
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −55.1543 −1.92490 −0.962450 0.271460i \(-0.912493\pi\)
−0.962450 + 0.271460i \(0.912493\pi\)
\(822\) 0 0
\(823\) −44.0000 −1.53374 −0.766872 0.641800i \(-0.778188\pi\)
−0.766872 + 0.641800i \(0.778188\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −45.2548 −1.57366 −0.786832 0.617167i \(-0.788280\pi\)
−0.786832 + 0.617167i \(0.788280\pi\)
\(828\) 0 0
\(829\) −41.0122 −1.42441 −0.712206 0.701970i \(-0.752304\pi\)
−0.712206 + 0.701970i \(0.752304\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −54.0000 −1.87099
\(834\) 0 0
\(835\) 11.3137 0.391527
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 48.0000 1.65714 0.828572 0.559883i \(-0.189154\pi\)
0.828572 + 0.559883i \(0.189154\pi\)
\(840\) 0 0
\(841\) −11.0000 −0.379310
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −7.07107 −0.243252
\(846\) 0 0
\(847\) −84.0000 −2.88627
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 11.3137 0.387829
\(852\) 0 0
\(853\) 1.41421 0.0484218 0.0242109 0.999707i \(-0.492293\pi\)
0.0242109 + 0.999707i \(0.492293\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −18.0000 −0.614868 −0.307434 0.951569i \(-0.599470\pi\)
−0.307434 + 0.951569i \(0.599470\pi\)
\(858\) 0 0
\(859\) −16.9706 −0.579028 −0.289514 0.957174i \(-0.593494\pi\)
−0.289514 + 0.957174i \(0.593494\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −24.0000 −0.816970 −0.408485 0.912765i \(-0.633943\pi\)
−0.408485 + 0.912765i \(0.633943\pi\)
\(864\) 0 0
\(865\) 22.0000 0.748022
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −67.8823 −2.30275
\(870\) 0 0
\(871\) 48.0000 1.62642
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −45.2548 −1.52989
\(876\) 0 0
\(877\) 7.07107 0.238773 0.119386 0.992848i \(-0.461907\pi\)
0.119386 + 0.992848i \(0.461907\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) 5.65685 0.190368 0.0951842 0.995460i \(-0.469656\pi\)
0.0951842 + 0.995460i \(0.469656\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −48.0000 −1.61168 −0.805841 0.592132i \(-0.798286\pi\)
−0.805841 + 0.592132i \(0.798286\pi\)
\(888\) 0 0
\(889\) 16.0000 0.536623
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −45.2548 −1.51440
\(894\) 0 0
\(895\) 16.0000 0.534821
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −16.9706 −0.566000
\(900\) 0 0
\(901\) 59.3970 1.97880
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −18.0000 −0.598340
\(906\) 0 0
\(907\) −39.5980 −1.31483 −0.657415 0.753529i \(-0.728350\pi\)
−0.657415 + 0.753529i \(0.728350\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 40.0000 1.32526 0.662630 0.748947i \(-0.269440\pi\)
0.662630 + 0.748947i \(0.269440\pi\)
\(912\) 0 0
\(913\) 32.0000 1.05905
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 45.2548 1.49445
\(918\) 0 0
\(919\) 20.0000 0.659739 0.329870 0.944027i \(-0.392995\pi\)
0.329870 + 0.944027i \(0.392995\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 4.24264 0.139497
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −42.0000 −1.37798 −0.688988 0.724773i \(-0.741945\pi\)
−0.688988 + 0.724773i \(0.741945\pi\)
\(930\) 0 0
\(931\) −50.9117 −1.66856
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 48.0000 1.56977
\(936\) 0 0
\(937\) −26.0000 −0.849383 −0.424691 0.905338i \(-0.639617\pi\)
−0.424691 + 0.905338i \(0.639617\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 49.4975 1.61357 0.806786 0.590844i \(-0.201205\pi\)
0.806786 + 0.590844i \(0.201205\pi\)
\(942\) 0 0
\(943\) 16.0000 0.521032
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −56.5685 −1.83823 −0.919115 0.393989i \(-0.871095\pi\)
−0.919115 + 0.393989i \(0.871095\pi\)
\(948\) 0 0
\(949\) −42.4264 −1.37722
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −18.0000 −0.583077 −0.291539 0.956559i \(-0.594167\pi\)
−0.291539 + 0.956559i \(0.594167\pi\)
\(954\) 0 0
\(955\) 33.9411 1.09831
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −8.00000 −0.258333
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −11.3137 −0.364201
\(966\) 0 0
\(967\) −20.0000 −0.643157 −0.321578 0.946883i \(-0.604213\pi\)
−0.321578 + 0.946883i \(0.604213\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 39.5980 1.27076 0.635380 0.772200i \(-0.280844\pi\)
0.635380 + 0.772200i \(0.280844\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 38.0000 1.21573 0.607864 0.794041i \(-0.292027\pi\)
0.607864 + 0.794041i \(0.292027\pi\)
\(978\) 0 0
\(979\) 90.5097 2.89270
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −32.0000 −1.02064 −0.510321 0.859984i \(-0.670473\pi\)
−0.510321 + 0.859984i \(0.670473\pi\)
\(984\) 0 0
\(985\) −2.00000 −0.0637253
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −45.2548 −1.43902
\(990\) 0 0
\(991\) 44.0000 1.39771 0.698853 0.715265i \(-0.253694\pi\)
0.698853 + 0.715265i \(0.253694\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 5.65685 0.179334
\(996\) 0 0
\(997\) −46.6690 −1.47802 −0.739012 0.673693i \(-0.764707\pi\)
−0.739012 + 0.673693i \(0.764707\pi\)
\(998\) 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 9216.2.a.a.1.1 2
3.2 odd 2 9216.2.a.c.1.2 2
4.3 odd 2 9216.2.a.t.1.1 2
8.3 odd 2 9216.2.a.t.1.2 2
8.5 even 2 inner 9216.2.a.a.1.2 2
12.11 even 2 9216.2.a.v.1.2 2
24.5 odd 2 9216.2.a.c.1.1 2
24.11 even 2 9216.2.a.v.1.1 2
32.3 odd 8 4608.2.k.n.1153.1 yes 2
32.5 even 8 4608.2.k.d.3457.1 yes 2
32.11 odd 8 4608.2.k.n.3457.1 yes 2
32.13 even 8 4608.2.k.d.1153.1 2
32.19 odd 8 4608.2.k.k.1153.1 yes 2
32.21 even 8 4608.2.k.u.3457.1 yes 2
32.27 odd 8 4608.2.k.k.3457.1 yes 2
32.29 even 8 4608.2.k.u.1153.1 yes 2
96.5 odd 8 4608.2.k.t.3457.1 yes 2
96.11 even 8 4608.2.k.l.3457.1 yes 2
96.29 odd 8 4608.2.k.e.1153.1 yes 2
96.35 even 8 4608.2.k.l.1153.1 yes 2
96.53 odd 8 4608.2.k.e.3457.1 yes 2
96.59 even 8 4608.2.k.m.3457.1 yes 2
96.77 odd 8 4608.2.k.t.1153.1 yes 2
96.83 even 8 4608.2.k.m.1153.1 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4608.2.k.d.1153.1 2 32.13 even 8
4608.2.k.d.3457.1 yes 2 32.5 even 8
4608.2.k.e.1153.1 yes 2 96.29 odd 8
4608.2.k.e.3457.1 yes 2 96.53 odd 8
4608.2.k.k.1153.1 yes 2 32.19 odd 8
4608.2.k.k.3457.1 yes 2 32.27 odd 8
4608.2.k.l.1153.1 yes 2 96.35 even 8
4608.2.k.l.3457.1 yes 2 96.11 even 8
4608.2.k.m.1153.1 yes 2 96.83 even 8
4608.2.k.m.3457.1 yes 2 96.59 even 8
4608.2.k.n.1153.1 yes 2 32.3 odd 8
4608.2.k.n.3457.1 yes 2 32.11 odd 8
4608.2.k.t.1153.1 yes 2 96.77 odd 8
4608.2.k.t.3457.1 yes 2 96.5 odd 8
4608.2.k.u.1153.1 yes 2 32.29 even 8
4608.2.k.u.3457.1 yes 2 32.21 even 8
9216.2.a.a.1.1 2 1.1 even 1 trivial
9216.2.a.a.1.2 2 8.5 even 2 inner
9216.2.a.c.1.1 2 24.5 odd 2
9216.2.a.c.1.2 2 3.2 odd 2
9216.2.a.t.1.1 2 4.3 odd 2
9216.2.a.t.1.2 2 8.3 odd 2
9216.2.a.v.1.1 2 24.11 even 2
9216.2.a.v.1.2 2 12.11 even 2