Properties

Label 1280.2.f.g.129.3
Level $1280$
Weight $2$
Character 1280.129
Analytic conductor $10.221$
Analytic rank $0$
Dimension $4$
CM discriminant -20
Inner twists $4$

Related objects

Downloads

Learn more

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 129.3
Root \(1.61803i\) of defining polynomial
Character \(\chi\) \(=\) 1280.129
Dual form 1280.2.f.g.129.4

$q$-expansion

\(f(q)\) \(=\) \(q+1.23607 q^{3} -2.23607i q^{5} -5.23607i q^{7} -1.47214 q^{9} +O(q^{10})\) \(q+1.23607 q^{3} -2.23607i q^{5} -5.23607i q^{7} -1.47214 q^{9} -2.76393i q^{15} -6.47214i q^{21} +7.70820i q^{23} -5.00000 q^{25} -5.52786 q^{27} -6.00000i q^{29} -11.7082 q^{35} -4.47214 q^{41} +6.76393 q^{43} +3.29180i q^{45} +0.291796i q^{47} -20.4164 q^{49} -13.4164i q^{61} +7.70820i q^{63} +14.1803 q^{67} +9.52786i q^{69} -6.18034 q^{75} -2.41641 q^{81} +4.29180 q^{83} -7.41641i q^{87} +6.00000 q^{89} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{3} + 12q^{9} + O(q^{10}) \) \( 4q - 4q^{3} + 12q^{9} - 20q^{25} - 40q^{27} - 20q^{35} + 36q^{43} - 28q^{49} + 12q^{67} + 20q^{75} + 44q^{81} + 44q^{83} + 24q^{89} + O(q^{100}) \)

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
\(3\) 1.23607 0.713644 0.356822 0.934172i \(-0.383860\pi\)
0.356822 + 0.934172i \(0.383860\pi\)
\(4\) 0 0
\(5\) − 2.23607i − 1.00000i
\(6\) 0 0
\(7\) − 5.23607i − 1.97905i −0.144370 0.989524i \(-0.546115\pi\)
0.144370 0.989524i \(-0.453885\pi\)
\(8\) 0 0
\(9\) −1.47214 −0.490712
\(10\) 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
\(15\) − 2.76393i − 0.713644i
\(16\) 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
\(21\) − 6.47214i − 1.41234i
\(22\) 0 0
\(23\) 7.70820i 1.60727i 0.595121 + 0.803636i \(0.297104\pi\)
−0.595121 + 0.803636i \(0.702896\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) −5.52786 −1.06384
\(28\) 0 0
\(29\) − 6.00000i − 1.11417i −0.830455 0.557086i \(-0.811919\pi\)
0.830455 0.557086i \(-0.188081\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −11.7082 −1.97905
\(36\) 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 \(-0.613552\pi\)
−0.349215 + 0.937043i \(0.613552\pi\)
\(42\) 0 0
\(43\) 6.76393 1.03149 0.515745 0.856742i \(-0.327515\pi\)
0.515745 + 0.856742i \(0.327515\pi\)
\(44\) 0 0
\(45\) 3.29180i 0.490712i
\(46\) 0 0
\(47\) 0.291796i 0.0425628i 0.999774 + 0.0212814i \(0.00677460\pi\)
−0.999774 + 0.0212814i \(0.993225\pi\)
\(48\) 0 0
\(49\) −20.4164 −2.91663
\(50\) 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
\(63\) 7.70820i 0.971142i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 14.1803 1.73240 0.866202 0.499694i \(-0.166554\pi\)
0.866202 + 0.499694i \(0.166554\pi\)
\(68\) 0 0
\(69\) 9.52786i 1.14702i
\(70\) 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
\(75\) −6.18034 −0.713644
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) −2.41641 −0.268490
\(82\) 0 0
\(83\) 4.29180 0.471086 0.235543 0.971864i \(-0.424313\pi\)
0.235543 + 0.971864i \(0.424313\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) − 7.41641i − 0.795122i
\(88\) 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 \(-0.646794\pi\)
0.444994 0.895533i \(-0.353206\pi\)
\(102\) 0 0
\(103\) − 2.18034i − 0.214835i −0.994214 0.107418i \(-0.965742\pi\)
0.994214 0.107418i \(-0.0342582\pi\)
\(104\) 0 0
\(105\) −14.4721 −1.41234
\(106\) 0 0
\(107\) 19.7082 1.90526 0.952632 0.304125i \(-0.0983642\pi\)
0.952632 + 0.304125i \(0.0983642\pi\)
\(108\) 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
\(115\) 17.2361 1.60727
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 11.0000 1.00000
\(122\) 0 0
\(123\) −5.52786 −0.498431
\(124\) 0 0
\(125\) 11.1803i 1.00000i
\(126\) 0 0
\(127\) − 12.6525i − 1.12273i −0.827570 0.561363i \(-0.810277\pi\)
0.827570 0.561363i \(-0.189723\pi\)
\(128\) 0 0
\(129\) 8.36068 0.736117
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 12.3607i 1.06384i
\(136\) 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
\(141\) 0.360680i 0.0303747i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −13.4164 −1.11417
\(146\) 0 0
\(147\) −25.2361 −2.08144
\(148\) 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
\(161\) 40.3607 3.18087
\(162\) 0 0
\(163\) −24.6525 −1.93093 −0.965465 0.260531i \(-0.916102\pi\)
−0.965465 + 0.260531i \(0.916102\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 23.7082i 1.83460i 0.398202 + 0.917298i \(0.369634\pi\)
−0.398202 + 0.917298i \(0.630366\pi\)
\(168\) 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
\(175\) 26.1803i 1.97905i
\(176\) 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 \(-0.976318\pi\)
0.997234 0.0743294i \(-0.0236816\pi\)
\(182\) 0 0
\(183\) − 16.5836i − 1.22589i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 28.9443i 2.10539i
\(190\) 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
\(201\) 17.5279 1.23632
\(202\) 0 0
\(203\) −31.4164 −2.20500
\(204\) 0 0
\(205\) 10.0000i 0.698430i
\(206\) 0 0
\(207\) − 11.3475i − 0.788707i
\(208\) 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
\(215\) − 15.1246i − 1.03149i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) − 18.7639i − 1.25653i −0.778001 0.628263i \(-0.783766\pi\)
0.778001 0.628263i \(-0.216234\pi\)
\(224\) 0 0
\(225\) 7.36068 0.490712
\(226\) 0 0
\(227\) 27.1246 1.80032 0.900162 0.435556i \(-0.143448\pi\)
0.900162 + 0.435556i \(0.143448\pi\)
\(228\) 0 0
\(229\) 14.0000i 0.925146i 0.886581 + 0.462573i \(0.153074\pi\)
−0.886581 + 0.462573i \(0.846926\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0.652476 0.0425628
\(236\) 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 \(-0.642232\pi\)
−0.432113 + 0.901819i \(0.642232\pi\)
\(242\) 0 0
\(243\) 13.5967 0.872232
\(244\) 0 0
\(245\) 45.6525i 2.91663i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 5.30495 0.336188
\(250\) 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
\(261\) 8.83282i 0.546738i
\(262\) 0 0
\(263\) − 31.1246i − 1.91923i −0.281324 0.959613i \(-0.590774\pi\)
0.281324 0.959613i \(-0.409226\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 7.41641 0.453877
\(268\) 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 \(-0.116517\pi\)
0.933748 + 0.357930i \(0.116517\pi\)
\(282\) 0 0
\(283\) 9.81966 0.583718 0.291859 0.956461i \(-0.405726\pi\)
0.291859 + 0.956461i \(0.405726\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 23.4164i 1.38223i
\(288\) 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
\(301\) − 35.4164i − 2.04137i
\(302\) 0 0
\(303\) − 22.2492i − 1.27818i
\(304\) 0 0
\(305\) −30.0000 −1.71780
\(306\) 0 0
\(307\) −21.5967 −1.23259 −0.616296 0.787515i \(-0.711367\pi\)
−0.616296 + 0.787515i \(0.711367\pi\)
\(308\) 0 0
\(309\) − 2.69505i − 0.153316i
\(310\) 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
\(315\) 17.2361 0.971142
\(316\) 0 0
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 24.3607 1.35968
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) − 16.5836i − 0.917075i
\(328\) 0 0
\(329\) 1.52786 0.0842339
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) − 31.7082i − 1.73240i
\(336\) 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
\(343\) 70.2492i 3.79310i
\(344\) 0 0
\(345\) 21.3050 1.14702
\(346\) 0 0
\(347\) −3.12461 −0.167738 −0.0838690 0.996477i \(-0.526728\pi\)
−0.0838690 + 0.996477i \(0.526728\pi\)
\(348\) 0 0
\(349\) 26.0000i 1.39175i 0.718164 + 0.695874i \(0.244983\pi\)
−0.718164 + 0.695874i \(0.755017\pi\)
\(350\) 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
\(363\) 13.5967 0.713644
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 29.2361i 1.52611i 0.646333 + 0.763055i \(0.276302\pi\)
−0.646333 + 0.763055i \(0.723698\pi\)
\(368\) 0 0
\(369\) 6.58359 0.342728
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 13.8197i 0.713644i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) − 15.6393i − 0.801227i
\(382\) 0 0
\(383\) 39.1246i 1.99917i 0.0287325 + 0.999587i \(0.490853\pi\)
−0.0287325 + 0.999587i \(0.509147\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −9.95743 −0.506164
\(388\) 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
\(405\) 5.40325i 0.268490i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −40.2492 −1.99020 −0.995098 0.0988936i \(-0.968470\pi\)
−0.995098 + 0.0988936i \(0.968470\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) − 9.59675i − 0.471086i
\(416\) 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
\(423\) − 0.429563i − 0.0208861i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −70.2492 −3.39960
\(428\) 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
\(435\) −16.5836 −0.795122
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 30.0557 1.43123
\(442\) 0 0
\(443\) 35.7082 1.69655 0.848274 0.529558i \(-0.177642\pi\)
0.848274 + 0.529558i \(0.177642\pi\)
\(444\) 0 0
\(445\) − 13.4164i − 0.635999i
\(446\) 0 0
\(447\) − 5.52786i − 0.261459i
\(448\) 0 0
\(449\) 22.3607 1.05527 0.527633 0.849473i \(-0.323080\pi\)
0.527633 + 0.849473i \(0.323080\pi\)
\(450\) 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 \(0.433211\pi\)
−0.208288 + 0.978068i \(0.566789\pi\)
\(462\) 0 0
\(463\) 20.0689i 0.932680i 0.884606 + 0.466340i \(0.154428\pi\)
−0.884606 + 0.466340i \(0.845572\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 43.1246 1.99557 0.997785 0.0665285i \(-0.0211923\pi\)
0.997785 + 0.0665285i \(0.0211923\pi\)
\(468\) 0 0
\(469\) − 74.2492i − 3.42851i
\(470\) 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
\(483\) 49.8885 2.27001
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) − 11.3475i − 0.514205i −0.966384 0.257103i \(-0.917232\pi\)
0.966384 0.257103i \(-0.0827679\pi\)
\(488\) 0 0
\(489\) −30.4721 −1.37800
\(490\) 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
\(501\) 29.3050i 1.30925i
\(502\) 0 0
\(503\) − 24.2918i − 1.08312i −0.840663 0.541559i \(-0.817834\pi\)
0.840663 0.541559i \(-0.182166\pi\)
\(504\) 0 0
\(505\) −40.2492 −1.79107
\(506\) 0 0
\(507\) −16.0689 −0.713644
\(508\) 0 0
\(509\) − 6.00000i − 0.265945i −0.991120 0.132973i \(-0.957548\pi\)
0.991120 0.132973i \(-0.0424523\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4.87539 −0.214835
\(516\) 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
\(523\) 45.5967 1.99381 0.996903 0.0786374i \(-0.0250569\pi\)
0.996903 + 0.0786374i \(0.0250569\pi\)
\(524\) 0 0
\(525\) 32.3607i 1.41234i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −36.4164 −1.58332
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) − 44.0689i − 1.90526i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) − 38.0000i − 1.63375i −0.576816 0.816874i \(-0.695705\pi\)
0.576816 0.816874i \(-0.304295\pi\)
\(542\) 0 0
\(543\) − 2.47214i − 0.106090i
\(544\) 0 0
\(545\) −30.0000 −1.28506
\(546\) 0 0
\(547\) −30.7639 −1.31537 −0.657685 0.753293i \(-0.728464\pi\)
−0.657685 + 0.753293i \(0.728464\pi\)
\(548\) 0 0
\(549\) 19.7508i 0.842943i
\(550\) 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
\(563\) −34.5410 −1.45573 −0.727865 0.685720i \(-0.759487\pi\)
−0.727865 + 0.685720i \(0.759487\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 12.6525i 0.531354i
\(568\) 0 0
\(569\) 31.3050 1.31237 0.656186 0.754599i \(-0.272169\pi\)
0.656186 + 0.754599i \(0.272169\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) − 38.5410i − 1.60727i
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 22.4721i − 0.932301i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 26.5410 1.09547 0.547733 0.836653i \(-0.315491\pi\)
0.547733 + 0.836653i \(0.315491\pi\)
\(588\) 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 \(-0.806528\pi\)
−0.820900 + 0.571072i \(0.806528\pi\)
\(602\) 0 0
\(603\) −20.8754 −0.850112
\(604\) 0 0
\(605\) − 24.5967i − 1.00000i
\(606\) 0 0
\(607\) − 21.8197i − 0.885633i −0.896612 0.442816i \(-0.853979\pi\)
0.896612 0.442816i \(-0.146021\pi\)
\(608\) 0 0
\(609\) −38.8328 −1.57359
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) 12.3607i 0.498431i
\(616\) 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
\(621\) − 42.6099i − 1.70988i
\(622\) 0 0
\(623\) − 31.4164i − 1.25867i
\(624\) 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
\(635\) −28.2918 −1.12273
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −49.1935 −1.94303 −0.971513 0.236986i \(-0.923841\pi\)
−0.971513 + 0.236986i \(0.923841\pi\)
\(642\) 0 0
\(643\) 8.06888 0.318206 0.159103 0.987262i \(-0.449140\pi\)
0.159103 + 0.987262i \(0.449140\pi\)
\(644\) 0 0
\(645\) − 18.6950i − 0.736117i
\(646\) 0 0
\(647\) 46.5410i 1.82972i 0.403775 + 0.914858i \(0.367698\pi\)
−0.403775 + 0.914858i \(0.632302\pi\)
\(648\) 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
\(667\) 46.2492 1.79078
\(668\) 0 0
\(669\) − 23.1935i − 0.896712i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 27.6393 1.06384
\(676\) 0 0
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 33.5279 1.28479
\(682\) 0 0
\(683\) −51.1246 −1.95623 −0.978114 0.208068i \(-0.933283\pi\)
−0.978114 + 0.208068i \(0.933283\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 17.3050i 0.660225i
\(688\) 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
\(705\) 0.806504 0.0303747
\(706\) 0 0
\(707\) −94.2492 −3.54461
\(708\) 0 0
\(709\) 46.0000i 1.72757i 0.503864 + 0.863783i \(0.331911\pi\)
−0.503864 + 0.863783i \(0.668089\pi\)
\(710\) 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
\(721\) −11.4164 −0.425169
\(722\) 0 0
\(723\) −16.5836 −0.616750
\(724\) 0 0
\(725\) 30.0000i 1.11417i
\(726\) 0 0
\(727\) − 41.0132i − 1.52109i −0.649283 0.760547i \(-0.724931\pi\)
0.649283 0.760547i \(-0.275069\pi\)
\(728\) 0 0
\(729\) 24.0557 0.890953
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) 56.4296i 2.08144i
\(736\) 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
\(743\) 14.5410i 0.533458i 0.963772 + 0.266729i \(0.0859429\pi\)
−0.963772 + 0.266729i \(0.914057\pi\)
\(744\) 0 0
\(745\) −10.0000 −0.366372
\(746\) 0 0
\(747\) −6.31811 −0.231167
\(748\) 0 0
\(749\) − 103.193i − 3.77061i
\(750\) 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
\(763\) −70.2492 −2.54319
\(764\) 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
\(783\) 33.1672i 1.18530i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 56.0689 1.99864 0.999320 0.0368739i \(-0.0117400\pi\)
0.999320 + 0.0368739i \(0.0117400\pi\)
\(788\) 0 0
\(789\) − 38.4721i − 1.36964i
\(790\) 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
\(801\) −8.83282 −0.312092
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) − 90.2492i − 3.18087i
\(806\) 0 0
\(807\) 27.6393i 0.972950i
\(808\) 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
\(815\) 55.1246i 1.93093i
\(816\) 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
\(823\) − 50.1803i − 1.74918i −0.484866 0.874588i \(-0.661132\pi\)
0.484866 0.874588i \(-0.338868\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 10.5410 0.366547 0.183274 0.983062i \(-0.441331\pi\)
0.183274 + 0.983062i \(0.441331\pi\)
\(828\) 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
\(835\) 53.0132 1.83460
\(836\) 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
\(843\) 38.6950 1.33273
\(844\) 0 0
\(845\) 29.0689i 1.00000i
\(846\) 0 0
\(847\) − 57.5967i − 1.97905i
\(848\) 0 0
\(849\) 12.1378 0.416567
\(850\) 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
\(861\) 28.9443i 0.986418i
\(862\) 0 0
\(863\) − 47.7082i − 1.62401i −0.583653 0.812003i \(-0.698377\pi\)
0.583653 0.812003i \(-0.301623\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 21.0132 0.713644
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 58.5410 1.97905
\(876\) 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 \(-0.0647913\pi\)
0.979356 + 0.202145i \(0.0647913\pi\)
\(882\) 0 0
\(883\) 23.3475 0.785707 0.392853 0.919601i \(-0.371488\pi\)
0.392853 + 0.919601i \(0.371488\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 16.8754i 0.566620i 0.959028 + 0.283310i \(0.0914325\pi\)
−0.959028 + 0.283310i \(0.908567\pi\)
\(888\) 0 0
\(889\) −66.2492 −2.22193
\(890\) 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
\(903\) − 43.7771i − 1.45681i
\(904\) 0 0
\(905\) −4.47214 −0.148659
\(906\) 0 0
\(907\) 39.4853 1.31109 0.655544 0.755157i \(-0.272439\pi\)
0.655544 + 0.755157i \(0.272439\pi\)
\(908\) 0 0
\(909\) 26.4984i 0.878898i
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −37.0820 −1.22589
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) −26.6950 −0.879632
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 3.20976i 0.105422i
\(928\) 0 0
\(929\) −49.1935 −1.61399 −0.806993 0.590561i \(-0.798907\pi\)
−0.806993 + 0.590561i \(0.798907\pi\)
\(930\) 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 \(0.240015\pi\)
−0.728937 + 0.684580i \(0.759985\pi\)
\(942\) 0 0
\(943\) − 34.4721i − 1.12257i
\(944\) 0 0
\(945\) 64.7214 2.10539
\(946\) 0 0
\(947\) 36.2918 1.17932 0.589662 0.807650i \(-0.299261\pi\)
0.589662 + 0.807650i \(0.299261\pi\)
\(948\) 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
\(963\) −29.0132 −0.934936
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 3.93112i 0.126416i 0.998000 + 0.0632081i \(0.0201332\pi\)
−0.998000 + 0.0632081i \(0.979867\pi\)
\(968\) 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
\(981\) 19.7508i 0.630594i
\(982\) 0 0
\(983\) 62.5410i 1.99475i 0.0724180 + 0.997374i \(0.476928\pi\)
−0.0724180 + 0.997374i \(0.523072\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 1.88854 0.0601130
\(988\) 0 0
\(989\) 52.1378i 1.65788i
\(990\) 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.129.3 4
4.3 odd 2 1280.2.f.h.129.1 4
5.4 even 2 1280.2.f.h.129.1 4
8.3 odd 2 inner 1280.2.f.g.129.4 4
8.5 even 2 1280.2.f.h.129.2 4
16.3 odd 4 160.2.c.b.129.2 4
16.5 even 4 320.2.c.d.129.2 4
16.11 odd 4 320.2.c.d.129.3 4
16.13 even 4 160.2.c.b.129.3 yes 4
20.19 odd 2 CM 1280.2.f.g.129.3 4
40.19 odd 2 1280.2.f.h.129.2 4
40.29 even 2 inner 1280.2.f.g.129.4 4
48.5 odd 4 2880.2.f.w.1729.2 4
48.11 even 4 2880.2.f.w.1729.1 4
48.29 odd 4 1440.2.f.i.289.4 4
48.35 even 4 1440.2.f.i.289.3 4
80.3 even 4 800.2.a.j.1.2 2
80.13 odd 4 800.2.a.n.1.1 2
80.19 odd 4 160.2.c.b.129.3 yes 4
80.27 even 4 1600.2.a.z.1.2 2
80.29 even 4 160.2.c.b.129.2 4
80.37 odd 4 1600.2.a.bd.1.1 2
80.43 even 4 1600.2.a.bd.1.1 2
80.53 odd 4 1600.2.a.z.1.2 2
80.59 odd 4 320.2.c.d.129.2 4
80.67 even 4 800.2.a.n.1.1 2
80.69 even 4 320.2.c.d.129.3 4
80.77 odd 4 800.2.a.j.1.2 2
240.29 odd 4 1440.2.f.i.289.3 4
240.59 even 4 2880.2.f.w.1729.2 4
240.77 even 4 7200.2.a.cb.1.1 2
240.83 odd 4 7200.2.a.cb.1.1 2
240.149 odd 4 2880.2.f.w.1729.1 4
240.173 even 4 7200.2.a.cr.1.2 2
240.179 even 4 1440.2.f.i.289.4 4
240.227 odd 4 7200.2.a.cr.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.2.c.b.129.2 4 16.3 odd 4
160.2.c.b.129.2 4 80.29 even 4
160.2.c.b.129.3 yes 4 16.13 even 4
160.2.c.b.129.3 yes 4 80.19 odd 4
320.2.c.d.129.2 4 16.5 even 4
320.2.c.d.129.2 4 80.59 odd 4
320.2.c.d.129.3 4 16.11 odd 4
320.2.c.d.129.3 4 80.69 even 4
800.2.a.j.1.2 2 80.3 even 4
800.2.a.j.1.2 2 80.77 odd 4
800.2.a.n.1.1 2 80.13 odd 4
800.2.a.n.1.1 2 80.67 even 4
1280.2.f.g.129.3 4 1.1 even 1 trivial
1280.2.f.g.129.3 4 20.19 odd 2 CM
1280.2.f.g.129.4 4 8.3 odd 2 inner
1280.2.f.g.129.4 4 40.29 even 2 inner
1280.2.f.h.129.1 4 4.3 odd 2
1280.2.f.h.129.1 4 5.4 even 2
1280.2.f.h.129.2 4 8.5 even 2
1280.2.f.h.129.2 4 40.19 odd 2
1440.2.f.i.289.3 4 48.35 even 4
1440.2.f.i.289.3 4 240.29 odd 4
1440.2.f.i.289.4 4 48.29 odd 4
1440.2.f.i.289.4 4 240.179 even 4
1600.2.a.z.1.2 2 80.27 even 4
1600.2.a.z.1.2 2 80.53 odd 4
1600.2.a.bd.1.1 2 80.37 odd 4
1600.2.a.bd.1.1 2 80.43 even 4
2880.2.f.w.1729.1 4 48.11 even 4
2880.2.f.w.1729.1 4 240.149 odd 4
2880.2.f.w.1729.2 4 48.5 odd 4
2880.2.f.w.1729.2 4 240.59 even 4
7200.2.a.cb.1.1 2 240.77 even 4
7200.2.a.cb.1.1 2 240.83 odd 4
7200.2.a.cr.1.2 2 240.173 even 4
7200.2.a.cr.1.2 2 240.227 odd 4