Properties

Label 160.2.c.b.129.3
Level $160$
Weight $2$
Character 160.129
Analytic conductor $1.278$
Analytic rank $0$
Dimension $4$
CM discriminant -20
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 160.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.27760643234\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 129.3
Root \(0.618034i\) of defining polynomial
Character \(\chi\) \(=\) 160.129
Dual form 160.2.c.b.129.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.23607i q^{3} -2.23607 q^{5} +5.23607i q^{7} +1.47214 q^{9} +O(q^{10})\) \(q+1.23607i q^{3} -2.23607 q^{5} +5.23607i q^{7} +1.47214 q^{9} -2.76393i q^{15} -6.47214 q^{21} -7.70820i q^{23} +5.00000 q^{25} +5.52786i q^{27} +6.00000 q^{29} -11.7082i q^{35} +4.47214 q^{41} -6.76393i q^{43} -3.29180 q^{45} +0.291796i q^{47} -20.4164 q^{49} +13.4164 q^{61} +7.70820i q^{63} +14.1803i q^{67} +9.52786 q^{69} +6.18034i q^{75} -2.41641 q^{81} +4.29180i q^{83} +7.41641i q^{87} -6.00000 q^{89} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 12q^{9} + O(q^{10}) \) \( 4q - 12q^{9} - 8q^{21} + 20q^{25} + 24q^{29} - 40q^{45} - 28q^{49} + 56q^{69} + 44q^{81} - 24q^{89} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(101\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(3\) 1.23607i 0.713644i 0.934172 + 0.356822i \(0.116140\pi\)
−0.934172 + 0.356822i \(0.883860\pi\)
\(4\) 0 0
\(5\) −2.23607 −1.00000
\(6\) 0 0
\(7\) 5.23607i 1.97905i 0.144370 + 0.989524i \(0.453885\pi\)
−0.144370 + 0.989524i \(0.546115\pi\)
\(8\) 0 0
\(9\) 1.47214 0.490712
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) −6.47214 −1.41234
\(22\) 0 0
\(23\) − 7.70820i − 1.60727i −0.595121 0.803636i \(-0.702896\pi\)
0.595121 0.803636i \(-0.297104\pi\)
\(24\) 0 0
\(25\) 5.00000 1.00000
\(26\) 0 0
\(27\) 5.52786i 1.06384i
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 11.7082i − 1.97905i
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 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
\(43\) − 6.76393i − 1.03149i −0.856742 0.515745i \(-0.827515\pi\)
0.856742 0.515745i \(-0.172485\pi\)
\(44\) 0 0
\(45\) −3.29180 −0.490712
\(46\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 13.4164 1.71780 0.858898 0.512148i \(-0.171150\pi\)
0.858898 + 0.512148i \(0.171150\pi\)
\(62\) 0 0
\(63\) 7.70820i 0.971142i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 14.1803i 1.73240i 0.499694 + 0.866202i \(0.333446\pi\)
−0.499694 + 0.866202i \(0.666554\pi\)
\(68\) 0 0
\(69\) 9.52786 1.14702
\(70\) 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
\(75\) 6.18034i 0.713644i
\(76\) 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
\(83\) 4.29180i 0.471086i 0.971864 + 0.235543i \(0.0756868\pi\)
−0.971864 + 0.235543i \(0.924313\pi\)
\(84\) 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 \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 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
\(101\) −18.0000 −1.79107 −0.895533 0.444994i \(-0.853206\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) 0 0
\(103\) 2.18034i 0.214835i 0.994214 + 0.107418i \(0.0342582\pi\)
−0.994214 + 0.107418i \(0.965742\pi\)
\(104\) 0 0
\(105\) 14.4721 1.41234
\(106\) 0 0
\(107\) − 19.7082i − 1.90526i −0.304125 0.952632i \(-0.598364\pi\)
0.304125 0.952632i \(-0.401636\pi\)
\(108\) 0 0
\(109\) 13.4164 1.28506 0.642529 0.766261i \(-0.277885\pi\)
0.642529 + 0.766261i \(0.277885\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 17.2361i 1.60727i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 5.52786i 0.498431i
\(124\) 0 0
\(125\) −11.1803 −1.00000
\(126\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −0.360680 −0.0303747
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −13.4164 −1.11417
\(146\) 0 0
\(147\) − 25.2361i − 2.08144i
\(148\) 0 0
\(149\) −4.47214 −0.366372 −0.183186 0.983078i \(-0.558641\pi\)
−0.183186 + 0.983078i \(0.558641\pi\)
\(150\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 40.3607 3.18087
\(162\) 0 0
\(163\) − 24.6525i − 1.93093i −0.260531 0.965465i \(-0.583898\pi\)
0.260531 0.965465i \(-0.416102\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) − 23.7082i − 1.83460i −0.398202 0.917298i \(-0.630366\pi\)
0.398202 0.917298i \(-0.369634\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 26.1803i 1.97905i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 16.5836i 1.22589i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −28.9443 −2.10539
\(190\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 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
\(203\) 31.4164i 2.20500i
\(204\) 0 0
\(205\) −10.0000 −0.698430
\(206\) 0 0
\(207\) − 11.3475i − 0.788707i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 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
\(227\) 27.1246i 1.80032i 0.435556 + 0.900162i \(0.356552\pi\)
−0.435556 + 0.900162i \(0.643448\pi\)
\(228\) 0 0
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) − 0.652476i − 0.0425628i
\(236\) 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
\(243\) 13.5967i 0.872232i
\(244\) 0 0
\(245\) 45.6525 2.91663
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −5.30495 −0.336188
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 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
\(261\) 8.83282 0.546738
\(262\) 0 0
\(263\) 31.1246i 1.91923i 0.281324 + 0.959613i \(0.409226\pi\)
−0.281324 + 0.959613i \(0.590774\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) − 7.41641i − 0.453877i
\(268\) 0 0
\(269\) −22.3607 −1.36335 −0.681677 0.731653i \(-0.738749\pi\)
−0.681677 + 0.731653i \(0.738749\pi\)
\(270\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 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
\(283\) − 9.81966i − 0.583718i −0.956461 0.291859i \(-0.905726\pi\)
0.956461 0.291859i \(-0.0942738\pi\)
\(284\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 35.4164 2.04137
\(302\) 0 0
\(303\) − 22.2492i − 1.27818i
\(304\) 0 0
\(305\) −30.0000 −1.71780
\(306\) 0 0
\(307\) − 21.5967i − 1.23259i −0.787515 0.616296i \(-0.788633\pi\)
0.787515 0.616296i \(-0.211367\pi\)
\(308\) 0 0
\(309\) −2.69505 −0.153316
\(310\) 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
\(315\) − 17.2361i − 0.971142i
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 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
\(347\) 3.12461i 0.167738i 0.996477 + 0.0838690i \(0.0267277\pi\)
−0.996477 + 0.0838690i \(0.973272\pi\)
\(348\) 0 0
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 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
\(363\) − 13.5967i − 0.713644i
\(364\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) − 13.8197i − 0.713644i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 15.6393 0.801227
\(382\) 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
\(387\) − 9.95743i − 0.506164i
\(388\) 0 0
\(389\) 31.3050 1.58722 0.793612 0.608424i \(-0.208198\pi\)
0.793612 + 0.608424i \(0.208198\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 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
\(405\) 5.40325 0.268490
\(406\) 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
\(415\) − 9.59675i − 0.471086i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −40.2492 −1.96163 −0.980814 0.194948i \(-0.937546\pi\)
−0.980814 + 0.194948i \(0.937546\pi\)
\(422\) 0 0
\(423\) 0.429563i 0.0208861i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 70.2492i 3.39960i
\(428\) 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
\(435\) − 16.5836i − 0.795122i
\(436\) 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
\(443\) − 35.7082i − 1.69655i −0.529558 0.848274i \(-0.677642\pi\)
0.529558 0.848274i \(-0.322358\pi\)
\(444\) 0 0
\(445\) 13.4164 0.635999
\(446\) 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
\(461\) −42.0000 −1.95614 −0.978068 0.208288i \(-0.933211\pi\)
−0.978068 + 0.208288i \(0.933211\pi\)
\(462\) 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
\(467\) 43.1246i 1.99557i 0.0665285 + 0.997785i \(0.478808\pi\)
−0.0665285 + 0.997785i \(0.521192\pi\)
\(468\) 0 0
\(469\) −74.2492 −3.42851
\(470\) 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
\(483\) 49.8885i 2.27001i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 11.3475i 0.514205i 0.966384 + 0.257103i \(0.0827679\pi\)
−0.966384 + 0.257103i \(0.917232\pi\)
\(488\) 0 0
\(489\) 30.4721 1.37800
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 0 0
\(501\) 29.3050 1.30925
\(502\) 0 0
\(503\) 24.2918i 1.08312i 0.840663 + 0.541559i \(0.182166\pi\)
−0.840663 + 0.541559i \(0.817834\pi\)
\(504\) 0 0
\(505\) 40.2492 1.79107
\(506\) 0 0
\(507\) 16.0689i 0.713644i
\(508\) 0 0
\(509\) 6.00000 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 4.87539i − 0.214835i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 42.0000 1.84005 0.920027 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) 0 0
\(523\) − 45.5967i − 1.99381i −0.0786374 0.996903i \(-0.525057\pi\)
0.0786374 0.996903i \(-0.474943\pi\)
\(524\) 0 0
\(525\) −32.3607 −1.41234
\(526\) 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
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) 0 0
\(543\) − 2.47214i − 0.106090i
\(544\) 0 0
\(545\) −30.0000 −1.28506
\(546\) 0 0
\(547\) − 30.7639i − 1.31537i −0.753293 0.657685i \(-0.771536\pi\)
0.753293 0.657685i \(-0.228464\pi\)
\(548\) 0 0
\(549\) 19.7508 0.842943
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 34.5410i − 1.45573i −0.685720 0.727865i \(-0.740513\pi\)
0.685720 0.727865i \(-0.259487\pi\)
\(564\) 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 \(-0.727831\pi\)
−0.656186 + 0.754599i \(0.727831\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 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
\(581\) −22.4721 −0.932301
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 26.5410i − 1.09547i −0.836653 0.547733i \(-0.815491\pi\)
0.836653 0.547733i \(-0.184509\pi\)
\(588\) 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
\(603\) 20.8754i 0.850112i
\(604\) 0 0
\(605\) 24.5967 1.00000
\(606\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 42.6099 1.70988
\(622\) 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
\(635\) 28.2918i 1.12273i
\(636\) 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
\(643\) 8.06888i 0.318206i 0.987262 + 0.159103i \(0.0508601\pi\)
−0.987262 + 0.159103i \(0.949140\pi\)
\(644\) 0 0
\(645\) −18.6950 −0.736117
\(646\) 0 0
\(647\) − 46.5410i − 1.82972i −0.403775 0.914858i \(-0.632302\pi\)
0.403775 0.914858i \(-0.367698\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −40.2492 −1.56551 −0.782757 0.622328i \(-0.786187\pi\)
−0.782757 + 0.622328i \(0.786187\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) − 46.2492i − 1.79078i
\(668\) 0 0
\(669\) 23.1935 0.896712
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 27.6393i 1.06384i
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −33.5279 −1.28479
\(682\) 0 0
\(683\) 51.1246i 1.95623i 0.208068 + 0.978114i \(0.433283\pi\)
−0.208068 + 0.978114i \(0.566717\pi\)
\(684\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 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
\(701\) −22.3607 −0.844551 −0.422276 0.906467i \(-0.638769\pi\)
−0.422276 + 0.906467i \(0.638769\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0.806504 0.0303747
\(706\) 0 0
\(707\) − 94.2492i − 3.54461i
\(708\) 0 0
\(709\) 46.0000 1.72757 0.863783 0.503864i \(-0.168089\pi\)
0.863783 + 0.503864i \(0.168089\pi\)
\(710\) 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
\(723\) − 16.5836i − 0.616750i
\(724\) 0 0
\(725\) 30.0000 1.11417
\(726\) 0 0
\(727\) 41.0132i 1.52109i 0.649283 + 0.760547i \(0.275069\pi\)
−0.649283 + 0.760547i \(0.724931\pi\)
\(728\) 0 0
\(729\) −24.0557 −0.890953
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 56.4296i 2.08144i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) − 14.5410i − 0.533458i −0.963772 0.266729i \(-0.914057\pi\)
0.963772 0.266729i \(-0.0859429\pi\)
\(744\) 0 0
\(745\) 10.0000 0.366372
\(746\) 0 0
\(747\) 6.31811i 0.231167i
\(748\) 0 0
\(749\) 103.193 3.77061
\(750\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 42.0000 1.52250 0.761249 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 0 0
\(763\) 70.2492i 2.54319i
\(764\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 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
\(787\) 56.0689i 1.99864i 0.0368739 + 0.999320i \(0.488260\pi\)
−0.0368739 + 0.999320i \(0.511740\pi\)
\(788\) 0 0
\(789\) −38.4721 −1.36964
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −8.83282 −0.312092
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −90.2492 −3.18087
\(806\) 0 0
\(807\) − 27.6393i − 0.972950i
\(808\) 0 0
\(809\) −54.0000 −1.89854 −0.949269 0.314464i \(-0.898175\pi\)
−0.949269 + 0.314464i \(0.898175\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 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
\(821\) 31.3050 1.09255 0.546275 0.837606i \(-0.316045\pi\)
0.546275 + 0.837606i \(0.316045\pi\)
\(822\) 0 0
\(823\) 50.1803i 1.74918i 0.484866 + 0.874588i \(0.338868\pi\)
−0.484866 + 0.874588i \(0.661132\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 10.5410i − 0.366547i −0.983062 0.183274i \(-0.941331\pi\)
0.983062 0.183274i \(-0.0586694\pi\)
\(828\) 0 0
\(829\) 13.4164 0.465971 0.232986 0.972480i \(-0.425151\pi\)
0.232986 + 0.972480i \(0.425151\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 53.0132i 1.83460i
\(836\) 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
\(843\) − 38.6950i − 1.33273i
\(844\) 0 0
\(845\) −29.0689 −1.00000
\(846\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) 0 0
\(861\) −28.9443 −0.986418
\(862\) 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
\(867\) 21.0132i 0.713644i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) − 58.5410i − 1.97905i
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 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
\(883\) 23.3475i 0.785707i 0.919601 + 0.392853i \(0.128512\pi\)
−0.919601 + 0.392853i \(0.871488\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) − 16.8754i − 0.566620i −0.959028 0.283310i \(-0.908567\pi\)
0.959028 0.283310i \(-0.0914325\pi\)
\(888\) 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
\(907\) − 39.4853i − 1.31109i −0.755157 0.655544i \(-0.772439\pi\)
0.755157 0.655544i \(-0.227561\pi\)
\(908\) 0 0
\(909\) −26.4984 −0.878898
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) − 37.0820i − 1.22589i
\(916\) 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
\(941\) −42.0000 −1.36916 −0.684580 0.728937i \(-0.740015\pi\)
−0.684580 + 0.728937i \(0.740015\pi\)
\(942\) 0 0
\(943\) − 34.4721i − 1.12257i
\(944\) 0 0
\(945\) 64.7214 2.10539
\(946\) 0 0
\(947\) 36.2918i 1.17932i 0.807650 + 0.589662i \(0.200739\pi\)
−0.807650 + 0.589662i \(0.799261\pi\)
\(948\) 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
\(963\) − 29.0132i − 0.934936i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) − 3.93112i − 0.126416i −0.998000 0.0632081i \(-0.979867\pi\)
0.998000 0.0632081i \(-0.0201332\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 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
\(981\) 19.7508 0.630594
\(982\) 0 0
\(983\) − 62.5410i − 1.99475i −0.0724180 0.997374i \(-0.523072\pi\)
0.0724180 0.997374i \(-0.476928\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) − 1.88854i − 0.0601130i
\(988\) 0 0
\(989\) −52.1378 −1.65788
\(990\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 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 160.2.c.b.129.3 yes 4
3.2 odd 2 1440.2.f.i.289.4 4
4.3 odd 2 inner 160.2.c.b.129.2 4
5.2 odd 4 800.2.a.j.1.2 2
5.3 odd 4 800.2.a.n.1.1 2
5.4 even 2 inner 160.2.c.b.129.2 4
8.3 odd 2 320.2.c.d.129.3 4
8.5 even 2 320.2.c.d.129.2 4
12.11 even 2 1440.2.f.i.289.3 4
15.2 even 4 7200.2.a.cb.1.1 2
15.8 even 4 7200.2.a.cr.1.2 2
15.14 odd 2 1440.2.f.i.289.3 4
16.3 odd 4 1280.2.f.g.129.4 4
16.5 even 4 1280.2.f.g.129.3 4
16.11 odd 4 1280.2.f.h.129.1 4
16.13 even 4 1280.2.f.h.129.2 4
20.3 even 4 800.2.a.j.1.2 2
20.7 even 4 800.2.a.n.1.1 2
20.19 odd 2 CM 160.2.c.b.129.3 yes 4
24.5 odd 2 2880.2.f.w.1729.2 4
24.11 even 2 2880.2.f.w.1729.1 4
40.3 even 4 1600.2.a.bd.1.1 2
40.13 odd 4 1600.2.a.z.1.2 2
40.19 odd 2 320.2.c.d.129.2 4
40.27 even 4 1600.2.a.z.1.2 2
40.29 even 2 320.2.c.d.129.3 4
40.37 odd 4 1600.2.a.bd.1.1 2
60.23 odd 4 7200.2.a.cb.1.1 2
60.47 odd 4 7200.2.a.cr.1.2 2
60.59 even 2 1440.2.f.i.289.4 4
80.19 odd 4 1280.2.f.h.129.2 4
80.29 even 4 1280.2.f.g.129.4 4
80.59 odd 4 1280.2.f.g.129.3 4
80.69 even 4 1280.2.f.h.129.1 4
120.29 odd 2 2880.2.f.w.1729.1 4
120.59 even 2 2880.2.f.w.1729.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.2.c.b.129.2 4 4.3 odd 2 inner
160.2.c.b.129.2 4 5.4 even 2 inner
160.2.c.b.129.3 yes 4 1.1 even 1 trivial
160.2.c.b.129.3 yes 4 20.19 odd 2 CM
320.2.c.d.129.2 4 8.5 even 2
320.2.c.d.129.2 4 40.19 odd 2
320.2.c.d.129.3 4 8.3 odd 2
320.2.c.d.129.3 4 40.29 even 2
800.2.a.j.1.2 2 5.2 odd 4
800.2.a.j.1.2 2 20.3 even 4
800.2.a.n.1.1 2 5.3 odd 4
800.2.a.n.1.1 2 20.7 even 4
1280.2.f.g.129.3 4 16.5 even 4
1280.2.f.g.129.3 4 80.59 odd 4
1280.2.f.g.129.4 4 16.3 odd 4
1280.2.f.g.129.4 4 80.29 even 4
1280.2.f.h.129.1 4 16.11 odd 4
1280.2.f.h.129.1 4 80.69 even 4
1280.2.f.h.129.2 4 16.13 even 4
1280.2.f.h.129.2 4 80.19 odd 4
1440.2.f.i.289.3 4 12.11 even 2
1440.2.f.i.289.3 4 15.14 odd 2
1440.2.f.i.289.4 4 3.2 odd 2
1440.2.f.i.289.4 4 60.59 even 2
1600.2.a.z.1.2 2 40.13 odd 4
1600.2.a.z.1.2 2 40.27 even 4
1600.2.a.bd.1.1 2 40.3 even 4
1600.2.a.bd.1.1 2 40.37 odd 4
2880.2.f.w.1729.1 4 24.11 even 2
2880.2.f.w.1729.1 4 120.29 odd 2
2880.2.f.w.1729.2 4 24.5 odd 2
2880.2.f.w.1729.2 4 120.59 even 2
7200.2.a.cb.1.1 2 15.2 even 4
7200.2.a.cb.1.1 2 60.23 odd 4
7200.2.a.cr.1.2 2 15.8 even 4
7200.2.a.cr.1.2 2 60.47 odd 4