Properties

Label 1280.2.f.g.129.1
Level $1280$
Weight $2$
Character 1280.129
Analytic conductor $10.221$
Analytic rank $0$
Dimension $4$
CM discriminant -20
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1280 = 2^{8} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1280.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.2208514587\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 160)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 129.1
Root \(0.618034i\) of defining polynomial
Character \(\chi\) \(=\) 1280.129
Dual form 1280.2.f.g.129.2

$q$-expansion

\(f(q)\) \(=\) \(q-3.23607 q^{3} -2.23607i q^{5} +0.763932i q^{7} +7.47214 q^{9} +O(q^{10})\) \(q-3.23607 q^{3} -2.23607i q^{5} +0.763932i q^{7} +7.47214 q^{9} +7.23607i q^{15} -2.47214i q^{21} +5.70820i q^{23} -5.00000 q^{25} -14.4721 q^{27} +6.00000i q^{29} +1.70820 q^{35} +4.47214 q^{41} +11.2361 q^{43} -16.7082i q^{45} -13.7082i q^{47} +6.41641 q^{49} -13.4164i q^{61} +5.70820i q^{63} -8.18034 q^{67} -18.4721i q^{69} +16.1803 q^{75} +24.4164 q^{81} +17.7082 q^{83} -19.4164i q^{87} +6.00000 q^{89} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} + 12 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{3} + 12 q^{9} - 20 q^{25} - 40 q^{27} - 20 q^{35} + 36 q^{43} - 28 q^{49} + 12 q^{67} + 20 q^{75} + 44 q^{81} + 44 q^{83} + 24 q^{89} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(261\) \(511\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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
\(3\) −3.23607 −1.86834 −0.934172 0.356822i \(-0.883860\pi\)
−0.934172 + 0.356822i \(0.883860\pi\)
\(4\) 0 0
\(5\) − 2.23607i − 1.00000i
\(6\) 0 0
\(7\) 0.763932i 0.288739i 0.989524 + 0.144370i \(0.0461154\pi\)
−0.989524 + 0.144370i \(0.953885\pi\)
\(8\) 0 0
\(9\) 7.47214 2.49071
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 7.23607i 1.86834i
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) − 2.47214i − 0.539464i
\(22\) 0 0
\(23\) 5.70820i 1.19024i 0.803636 + 0.595121i \(0.202896\pi\)
−0.803636 + 0.595121i \(0.797104\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) −14.4721 −2.78516
\(28\) 0 0
\(29\) 6.00000i 1.11417i 0.830455 + 0.557086i \(0.188081\pi\)
−0.830455 + 0.557086i \(0.811919\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.70820 0.288739
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 4.47214 0.698430 0.349215 0.937043i \(-0.386448\pi\)
0.349215 + 0.937043i \(0.386448\pi\)
\(42\) 0 0
\(43\) 11.2361 1.71348 0.856742 0.515745i \(-0.172485\pi\)
0.856742 + 0.515745i \(0.172485\pi\)
\(44\) 0 0
\(45\) − 16.7082i − 2.49071i
\(46\) 0 0
\(47\) − 13.7082i − 1.99955i −0.0212814 0.999774i \(-0.506775\pi\)
0.0212814 0.999774i \(-0.493225\pi\)
\(48\) 0 0
\(49\) 6.41641 0.916630
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) − 13.4164i − 1.71780i −0.512148 0.858898i \(-0.671150\pi\)
0.512148 0.858898i \(-0.328850\pi\)
\(62\) 0 0
\(63\) 5.70820i 0.719166i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −8.18034 −0.999388 −0.499694 0.866202i \(-0.666554\pi\)
−0.499694 + 0.866202i \(0.666554\pi\)
\(68\) 0 0
\(69\) − 18.4721i − 2.22378i
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 16.1803 1.86834
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 24.4164 2.71293
\(82\) 0 0
\(83\) 17.7082 1.94373 0.971864 0.235543i \(-0.0756868\pi\)
0.971864 + 0.235543i \(0.0756868\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) − 19.4164i − 2.08166i
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 18.0000i 1.79107i 0.444994 + 0.895533i \(0.353206\pi\)
−0.444994 + 0.895533i \(0.646794\pi\)
\(102\) 0 0
\(103\) − 20.1803i − 1.98843i −0.107418 0.994214i \(-0.534258\pi\)
0.107418 0.994214i \(-0.465742\pi\)
\(104\) 0 0
\(105\) −5.52786 −0.539464
\(106\) 0 0
\(107\) 6.29180 0.608251 0.304125 0.952632i \(-0.401636\pi\)
0.304125 + 0.952632i \(0.401636\pi\)
\(108\) 0 0
\(109\) − 13.4164i − 1.28506i −0.766261 0.642529i \(-0.777885\pi\)
0.766261 0.642529i \(-0.222115\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 12.7639 1.19024
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 11.0000 1.00000
\(122\) 0 0
\(123\) −14.4721 −1.30491
\(124\) 0 0
\(125\) 11.1803i 1.00000i
\(126\) 0 0
\(127\) − 18.6525i − 1.65514i −0.561363 0.827570i \(-0.689723\pi\)
0.561363 0.827570i \(-0.310277\pi\)
\(128\) 0 0
\(129\) −36.3607 −3.20138
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 32.3607i 2.78516i
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 44.3607i 3.73584i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 13.4164 1.11417
\(146\) 0 0
\(147\) −20.7639 −1.71258
\(148\) 0 0
\(149\) − 4.47214i − 0.366372i −0.983078 0.183186i \(-0.941359\pi\)
0.983078 0.183186i \(-0.0586410\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4.36068 −0.343670
\(162\) 0 0
\(163\) 6.65248 0.521062 0.260531 0.965465i \(-0.416102\pi\)
0.260531 + 0.965465i \(0.416102\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) − 10.2918i − 0.796403i −0.917298 0.398202i \(-0.869634\pi\)
0.917298 0.398202i \(-0.130366\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) − 3.81966i − 0.288739i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 2.00000i 0.148659i 0.997234 + 0.0743294i \(0.0236816\pi\)
−0.997234 + 0.0743294i \(0.976318\pi\)
\(182\) 0 0
\(183\) 43.4164i 3.20943i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) − 11.0557i − 0.804186i
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 26.4721 1.86720
\(202\) 0 0
\(203\) −4.58359 −0.321705
\(204\) 0 0
\(205\) − 10.0000i − 0.698430i
\(206\) 0 0
\(207\) 42.6525i 2.96455i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) − 25.1246i − 1.71348i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 23.2361i 1.55600i 0.628263 + 0.778001i \(0.283766\pi\)
−0.628263 + 0.778001i \(0.716234\pi\)
\(224\) 0 0
\(225\) −37.3607 −2.49071
\(226\) 0 0
\(227\) −13.1246 −0.871111 −0.435556 0.900162i \(-0.643448\pi\)
−0.435556 + 0.900162i \(0.643448\pi\)
\(228\) 0 0
\(229\) − 14.0000i − 0.925146i −0.886581 0.462573i \(-0.846926\pi\)
0.886581 0.462573i \(-0.153074\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) −30.6525 −1.99955
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 13.4164 0.864227 0.432113 0.901819i \(-0.357768\pi\)
0.432113 + 0.901819i \(0.357768\pi\)
\(242\) 0 0
\(243\) −35.5967 −2.28353
\(244\) 0 0
\(245\) − 14.3475i − 0.916630i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −57.3050 −3.63155
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 44.8328i 2.77508i
\(262\) 0 0
\(263\) − 9.12461i − 0.562648i −0.959613 0.281324i \(-0.909226\pi\)
0.959613 0.281324i \(-0.0907735\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −19.4164 −1.18826
\(268\) 0 0
\(269\) 22.3607i 1.36335i 0.731653 + 0.681677i \(0.238749\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −31.3050 −1.86750 −0.933748 0.357930i \(-0.883483\pi\)
−0.933748 + 0.357930i \(0.883483\pi\)
\(282\) 0 0
\(283\) 32.1803 1.91292 0.956461 0.291859i \(-0.0942738\pi\)
0.956461 + 0.291859i \(0.0942738\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.41641i 0.201664i
\(288\) 0 0
\(289\) 17.0000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 8.58359i 0.494750i
\(302\) 0 0
\(303\) − 58.2492i − 3.34633i
\(304\) 0 0
\(305\) −30.0000 −1.71780
\(306\) 0 0
\(307\) 27.5967 1.57503 0.787515 0.616296i \(-0.211367\pi\)
0.787515 + 0.616296i \(0.211367\pi\)
\(308\) 0 0
\(309\) 65.3050i 3.71507i
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 12.7639 0.719166
\(316\) 0 0
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −20.3607 −1.13642
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 43.4164i 2.40093i
\(328\) 0 0
\(329\) 10.4721 0.577348
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 18.2918i 0.999388i
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 10.2492i 0.553406i
\(344\) 0 0
\(345\) −41.3050 −2.22378
\(346\) 0 0
\(347\) 37.1246 1.99295 0.996477 0.0838690i \(-0.0267277\pi\)
0.996477 + 0.0838690i \(0.0267277\pi\)
\(348\) 0 0
\(349\) − 26.0000i − 1.39175i −0.718164 0.695874i \(-0.755017\pi\)
0.718164 0.695874i \(-0.244983\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 0 0
\(363\) −35.5967 −1.86834
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) − 24.7639i − 1.29267i −0.763055 0.646333i \(-0.776302\pi\)
0.763055 0.646333i \(-0.223698\pi\)
\(368\) 0 0
\(369\) 33.4164 1.73959
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) − 36.1803i − 1.86834i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 60.3607i 3.09237i
\(382\) 0 0
\(383\) 1.12461i 0.0574650i 0.999587 + 0.0287325i \(0.00914709\pi\)
−0.999587 + 0.0287325i \(0.990853\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 83.9574 4.26780
\(388\) 0 0
\(389\) 31.3050i 1.58722i 0.608424 + 0.793612i \(0.291802\pi\)
−0.608424 + 0.793612i \(0.708198\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) − 54.5967i − 2.71293i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 40.2492 1.99020 0.995098 0.0988936i \(-0.0315304\pi\)
0.995098 + 0.0988936i \(0.0315304\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) − 39.5967i − 1.94373i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) − 40.2492i − 1.96163i −0.194948 0.980814i \(-0.562454\pi\)
0.194948 0.980814i \(-0.437546\pi\)
\(422\) 0 0
\(423\) − 102.430i − 4.98030i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 10.2492 0.495995
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) −43.4164 −2.08166
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 47.9443 2.28306
\(442\) 0 0
\(443\) 22.2918 1.05912 0.529558 0.848274i \(-0.322358\pi\)
0.529558 + 0.848274i \(0.322358\pi\)
\(444\) 0 0
\(445\) − 13.4164i − 0.635999i
\(446\) 0 0
\(447\) 14.4721i 0.684509i
\(448\) 0 0
\(449\) −22.3607 −1.05527 −0.527633 0.849473i \(-0.676920\pi\)
−0.527633 + 0.849473i \(0.676920\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 42.0000i − 1.95614i −0.208288 0.978068i \(-0.566789\pi\)
0.208288 0.978068i \(-0.433211\pi\)
\(462\) 0 0
\(463\) 38.0689i 1.76921i 0.466340 + 0.884606i \(0.345572\pi\)
−0.466340 + 0.884606i \(0.654428\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.87539 0.133057 0.0665285 0.997785i \(-0.478808\pi\)
0.0665285 + 0.997785i \(0.478808\pi\)
\(468\) 0 0
\(469\) − 6.24922i − 0.288562i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 14.1115 0.642093
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 42.6525i 1.93277i 0.257103 + 0.966384i \(0.417232\pi\)
−0.257103 + 0.966384i \(0.582768\pi\)
\(488\) 0 0
\(489\) −21.5279 −0.973524
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 33.3050i 1.48796i
\(502\) 0 0
\(503\) 37.7082i 1.68133i 0.541559 + 0.840663i \(0.317834\pi\)
−0.541559 + 0.840663i \(0.682166\pi\)
\(504\) 0 0
\(505\) 40.2492 1.79107
\(506\) 0 0
\(507\) 42.0689 1.86834
\(508\) 0 0
\(509\) 6.00000i 0.265945i 0.991120 + 0.132973i \(0.0424523\pi\)
−0.991120 + 0.132973i \(0.957548\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −45.1246 −1.98843
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −42.0000 −1.84005 −0.920027 0.391856i \(-0.871833\pi\)
−0.920027 + 0.391856i \(0.871833\pi\)
\(522\) 0 0
\(523\) −3.59675 −0.157275 −0.0786374 0.996903i \(-0.525057\pi\)
−0.0786374 + 0.996903i \(0.525057\pi\)
\(524\) 0 0
\(525\) 12.3607i 0.539464i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −9.58359 −0.416678
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) − 14.0689i − 0.608251i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 38.0000i 1.63375i 0.576816 + 0.816874i \(0.304295\pi\)
−0.576816 + 0.816874i \(0.695705\pi\)
\(542\) 0 0
\(543\) − 6.47214i − 0.277746i
\(544\) 0 0
\(545\) −30.0000 −1.28506
\(546\) 0 0
\(547\) −35.2361 −1.50659 −0.753293 0.657685i \(-0.771536\pi\)
−0.753293 + 0.657685i \(0.771536\pi\)
\(548\) 0 0
\(549\) − 100.249i − 4.27853i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 32.5410 1.37144 0.685720 0.727865i \(-0.259487\pi\)
0.685720 + 0.727865i \(0.259487\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 18.6525i 0.783330i
\(568\) 0 0
\(569\) −31.3050 −1.31237 −0.656186 0.754599i \(-0.727831\pi\)
−0.656186 + 0.754599i \(0.727831\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) − 28.5410i − 1.19024i
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 13.5279i 0.561230i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −40.5410 −1.67331 −0.836653 0.547733i \(-0.815491\pi\)
−0.836653 + 0.547733i \(0.815491\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 40.2492 1.64180 0.820900 0.571072i \(-0.193472\pi\)
0.820900 + 0.571072i \(0.193472\pi\)
\(602\) 0 0
\(603\) −61.1246 −2.48919
\(604\) 0 0
\(605\) − 24.5967i − 1.00000i
\(606\) 0 0
\(607\) 44.1803i 1.79322i 0.442816 + 0.896612i \(0.353979\pi\)
−0.442816 + 0.896612i \(0.646021\pi\)
\(608\) 0 0
\(609\) 14.8328 0.601056
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) 32.3607i 1.30491i
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) − 82.6099i − 3.31502i
\(622\) 0 0
\(623\) 4.58359i 0.183638i
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −41.7082 −1.65514
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 49.1935 1.94303 0.971513 0.236986i \(-0.0761595\pi\)
0.971513 + 0.236986i \(0.0761595\pi\)
\(642\) 0 0
\(643\) −50.0689 −1.97452 −0.987262 0.159103i \(-0.949140\pi\)
−0.987262 + 0.159103i \(0.949140\pi\)
\(644\) 0 0
\(645\) 81.3050i 3.20138i
\(646\) 0 0
\(647\) 20.5410i 0.807551i 0.914858 + 0.403775i \(0.132302\pi\)
−0.914858 + 0.403775i \(0.867698\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) − 40.2492i − 1.56551i −0.622328 0.782757i \(-0.713813\pi\)
0.622328 0.782757i \(-0.286187\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −34.2492 −1.32614
\(668\) 0 0
\(669\) − 75.1935i − 2.90715i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 72.3607 2.78516
\(676\) 0 0
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 42.4721 1.62754
\(682\) 0 0
\(683\) −10.8754 −0.416135 −0.208068 0.978114i \(-0.566717\pi\)
−0.208068 + 0.978114i \(0.566717\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 45.3050i 1.72849i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 22.3607i 0.844551i 0.906467 + 0.422276i \(0.138769\pi\)
−0.906467 + 0.422276i \(0.861231\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 99.1935 3.73584
\(706\) 0 0
\(707\) −13.7508 −0.517151
\(708\) 0 0
\(709\) − 46.0000i − 1.72757i −0.503864 0.863783i \(-0.668089\pi\)
0.503864 0.863783i \(-0.331911\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 15.4164 0.574137
\(722\) 0 0
\(723\) −43.4164 −1.61467
\(724\) 0 0
\(725\) − 30.0000i − 1.11417i
\(726\) 0 0
\(727\) − 35.0132i − 1.29857i −0.760547 0.649283i \(-0.775069\pi\)
0.760547 0.649283i \(-0.224931\pi\)
\(728\) 0 0
\(729\) 41.9443 1.55349
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) 46.4296i 1.71258i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 52.5410i 1.92754i 0.266729 + 0.963772i \(0.414057\pi\)
−0.266729 + 0.963772i \(0.585943\pi\)
\(744\) 0 0
\(745\) −10.0000 −0.366372
\(746\) 0 0
\(747\) 132.318 4.84127
\(748\) 0 0
\(749\) 4.80650i 0.175626i
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −42.0000 −1.52250 −0.761249 0.648459i \(-0.775414\pi\)
−0.761249 + 0.648459i \(0.775414\pi\)
\(762\) 0 0
\(763\) 10.2492 0.371047
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) − 86.8328i − 3.10315i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −2.06888 −0.0737477 −0.0368739 0.999320i \(-0.511740\pi\)
−0.0368739 + 0.999320i \(0.511740\pi\)
\(788\) 0 0
\(789\) 29.5279i 1.05122i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 44.8328 1.58409
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 9.75078i 0.343670i
\(806\) 0 0
\(807\) − 72.3607i − 2.54722i
\(808\) 0 0
\(809\) 54.0000 1.89854 0.949269 0.314464i \(-0.101825\pi\)
0.949269 + 0.314464i \(0.101825\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) − 14.8754i − 0.521062i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 31.3050i 1.09255i 0.837606 + 0.546275i \(0.183955\pi\)
−0.837606 + 0.546275i \(0.816045\pi\)
\(822\) 0 0
\(823\) 27.8197i 0.969732i 0.874588 + 0.484866i \(0.161132\pi\)
−0.874588 + 0.484866i \(0.838868\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −56.5410 −1.96612 −0.983062 0.183274i \(-0.941331\pi\)
−0.983062 + 0.183274i \(0.941331\pi\)
\(828\) 0 0
\(829\) − 13.4164i − 0.465971i −0.972480 0.232986i \(-0.925151\pi\)
0.972480 0.232986i \(-0.0748495\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −23.0132 −0.796403
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −7.00000 −0.241379
\(842\) 0 0
\(843\) 101.305 3.48913
\(844\) 0 0
\(845\) 29.0689i 1.00000i
\(846\) 0 0
\(847\) 8.40325i 0.288739i
\(848\) 0 0
\(849\) −104.138 −3.57400
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) − 11.0557i − 0.376778i
\(862\) 0 0
\(863\) 34.2918i 1.16731i 0.812003 + 0.583653i \(0.198377\pi\)
−0.812003 + 0.583653i \(0.801623\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −55.0132 −1.86834
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −8.54102 −0.288739
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −58.1378 −1.95871 −0.979356 0.202145i \(-0.935209\pi\)
−0.979356 + 0.202145i \(0.935209\pi\)
\(882\) 0 0
\(883\) 54.6525 1.83920 0.919601 0.392853i \(-0.128512\pi\)
0.919601 + 0.392853i \(0.128512\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) − 57.1246i − 1.91806i −0.283310 0.959028i \(-0.591433\pi\)
0.283310 0.959028i \(-0.408567\pi\)
\(888\) 0 0
\(889\) 14.2492 0.477904
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) − 27.7771i − 0.924364i
\(904\) 0 0
\(905\) 4.47214 0.148659
\(906\) 0 0
\(907\) −45.4853 −1.51031 −0.755157 0.655544i \(-0.772439\pi\)
−0.755157 + 0.655544i \(0.772439\pi\)
\(908\) 0 0
\(909\) 134.498i 4.46103i
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 97.0820 3.20943
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) −89.3050 −2.94270
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) − 150.790i − 4.95260i
\(928\) 0 0
\(929\) 49.1935 1.61399 0.806993 0.590561i \(-0.201093\pi\)
0.806993 + 0.590561i \(0.201093\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) − 42.0000i − 1.36916i −0.728937 0.684580i \(-0.759985\pi\)
0.728937 0.684580i \(-0.240015\pi\)
\(942\) 0 0
\(943\) 25.5279i 0.831302i
\(944\) 0 0
\(945\) −24.7214 −0.804186
\(946\) 0 0
\(947\) 49.7082 1.61530 0.807650 0.589662i \(-0.200739\pi\)
0.807650 + 0.589662i \(0.200739\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 47.0132 1.51498
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) − 62.0689i − 1.99600i −0.0632081 0.998000i \(-0.520133\pi\)
0.0632081 0.998000i \(-0.479867\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) − 100.249i − 3.20071i
\(982\) 0 0
\(983\) 4.54102i 0.144836i 0.997374 + 0.0724180i \(0.0230716\pi\)
−0.997374 + 0.0724180i \(0.976928\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −33.8885 −1.07868
\(988\) 0 0
\(989\) 64.1378i 2.03946i
\(990\) 0 0
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) 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 1280.2.f.g.129.1 4
4.3 odd 2 1280.2.f.h.129.3 4
5.4 even 2 1280.2.f.h.129.3 4
8.3 odd 2 inner 1280.2.f.g.129.2 4
8.5 even 2 1280.2.f.h.129.4 4
16.3 odd 4 320.2.c.d.129.4 4
16.5 even 4 160.2.c.b.129.4 yes 4
16.11 odd 4 160.2.c.b.129.1 4
16.13 even 4 320.2.c.d.129.1 4
20.19 odd 2 CM 1280.2.f.g.129.1 4
40.19 odd 2 1280.2.f.h.129.4 4
40.29 even 2 inner 1280.2.f.g.129.2 4
48.5 odd 4 1440.2.f.i.289.1 4
48.11 even 4 1440.2.f.i.289.2 4
48.29 odd 4 2880.2.f.w.1729.3 4
48.35 even 4 2880.2.f.w.1729.4 4
80.3 even 4 1600.2.a.z.1.1 2
80.13 odd 4 1600.2.a.bd.1.2 2
80.19 odd 4 320.2.c.d.129.1 4
80.27 even 4 800.2.a.j.1.1 2
80.29 even 4 320.2.c.d.129.4 4
80.37 odd 4 800.2.a.n.1.2 2
80.43 even 4 800.2.a.n.1.2 2
80.53 odd 4 800.2.a.j.1.1 2
80.59 odd 4 160.2.c.b.129.4 yes 4
80.67 even 4 1600.2.a.bd.1.2 2
80.69 even 4 160.2.c.b.129.1 4
80.77 odd 4 1600.2.a.z.1.1 2
240.29 odd 4 2880.2.f.w.1729.4 4
240.53 even 4 7200.2.a.cb.1.2 2
240.59 even 4 1440.2.f.i.289.1 4
240.107 odd 4 7200.2.a.cb.1.2 2
240.149 odd 4 1440.2.f.i.289.2 4
240.179 even 4 2880.2.f.w.1729.3 4
240.197 even 4 7200.2.a.cr.1.1 2
240.203 odd 4 7200.2.a.cr.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.2.c.b.129.1 4 16.11 odd 4
160.2.c.b.129.1 4 80.69 even 4
160.2.c.b.129.4 yes 4 16.5 even 4
160.2.c.b.129.4 yes 4 80.59 odd 4
320.2.c.d.129.1 4 16.13 even 4
320.2.c.d.129.1 4 80.19 odd 4
320.2.c.d.129.4 4 16.3 odd 4
320.2.c.d.129.4 4 80.29 even 4
800.2.a.j.1.1 2 80.27 even 4
800.2.a.j.1.1 2 80.53 odd 4
800.2.a.n.1.2 2 80.37 odd 4
800.2.a.n.1.2 2 80.43 even 4
1280.2.f.g.129.1 4 1.1 even 1 trivial
1280.2.f.g.129.1 4 20.19 odd 2 CM
1280.2.f.g.129.2 4 8.3 odd 2 inner
1280.2.f.g.129.2 4 40.29 even 2 inner
1280.2.f.h.129.3 4 4.3 odd 2
1280.2.f.h.129.3 4 5.4 even 2
1280.2.f.h.129.4 4 8.5 even 2
1280.2.f.h.129.4 4 40.19 odd 2
1440.2.f.i.289.1 4 48.5 odd 4
1440.2.f.i.289.1 4 240.59 even 4
1440.2.f.i.289.2 4 48.11 even 4
1440.2.f.i.289.2 4 240.149 odd 4
1600.2.a.z.1.1 2 80.3 even 4
1600.2.a.z.1.1 2 80.77 odd 4
1600.2.a.bd.1.2 2 80.13 odd 4
1600.2.a.bd.1.2 2 80.67 even 4
2880.2.f.w.1729.3 4 48.29 odd 4
2880.2.f.w.1729.3 4 240.179 even 4
2880.2.f.w.1729.4 4 48.35 even 4
2880.2.f.w.1729.4 4 240.29 odd 4
7200.2.a.cb.1.2 2 240.53 even 4
7200.2.a.cb.1.2 2 240.107 odd 4
7200.2.a.cr.1.1 2 240.197 even 4
7200.2.a.cr.1.1 2 240.203 odd 4