Properties

Label 320.2.c.d.129.1
Level $320$
Weight $2$
Character 320.129
Analytic conductor $2.555$
Analytic rank $0$
Dimension $4$
CM discriminant -20
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.55521286468\)
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: no (minimal twist has level 160)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 129.1
Root \(-1.61803i\) of defining polynomial
Character \(\chi\) \(=\) 320.129
Dual form 320.2.c.d.129.4

$q$-expansion

\(f(q)\) \(=\) \(q-3.23607i q^{3} -2.23607 q^{5} -0.763932i q^{7} -7.47214 q^{9} +O(q^{10})\) \(q-3.23607i q^{3} -2.23607 q^{5} -0.763932i q^{7} -7.47214 q^{9} +7.23607i q^{15} -2.47214 q^{21} -5.70820i q^{23} +5.00000 q^{25} +14.4721i q^{27} -6.00000 q^{29} +1.70820i q^{35} -4.47214 q^{41} -11.2361i q^{43} +16.7082 q^{45} -13.7082i q^{47} +6.41641 q^{49} +13.4164 q^{61} +5.70820i q^{63} -8.18034i q^{67} -18.4721 q^{69} -16.1803i q^{75} +24.4164 q^{81} +17.7082i q^{83} +19.4164i q^{87} -6.00000 q^{89} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 12q^{9} + O(q^{10}) \) \( 4q - 12q^{9} + 8q^{21} + 20q^{25} - 24q^{29} + 40q^{45} - 28q^{49} - 56q^{69} + 44q^{81} - 24q^{89} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(3\) − 3.23607i − 1.86834i −0.356822 0.934172i \(-0.616140\pi\)
0.356822 0.934172i \(-0.383860\pi\)
\(4\) 0 0
\(5\) −2.23607 −1.00000
\(6\) 0 0
\(7\) − 0.763932i − 0.288739i −0.989524 0.144370i \(-0.953885\pi\)
0.989524 0.144370i \(-0.0461154\pi\)
\(8\) 0 0
\(9\) −7.47214 −2.49071
\(10\) 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
\(15\) 7.23607i 1.86834i
\(16\) 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
\(21\) −2.47214 −0.539464
\(22\) 0 0
\(23\) − 5.70820i − 1.19024i −0.803636 0.595121i \(-0.797104\pi\)
0.803636 0.595121i \(-0.202896\pi\)
\(24\) 0 0
\(25\) 5.00000 1.00000
\(26\) 0 0
\(27\) 14.4721i 2.78516i
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.70820i 0.288739i
\(36\) 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 \(-0.613552\pi\)
−0.349215 + 0.937043i \(0.613552\pi\)
\(42\) 0 0
\(43\) − 11.2361i − 1.71348i −0.515745 0.856742i \(-0.672485\pi\)
0.515745 0.856742i \(-0.327515\pi\)
\(44\) 0 0
\(45\) 16.7082 2.49071
\(46\) 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 1.00000 \(0\)
−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
\(63\) 5.70820i 0.719166i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) − 8.18034i − 0.999388i −0.866202 0.499694i \(-0.833446\pi\)
0.866202 0.499694i \(-0.166554\pi\)
\(68\) 0 0
\(69\) −18.4721 −2.22378
\(70\) 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
\(75\) − 16.1803i − 1.86834i
\(76\) 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
\(83\) 17.7082i 1.94373i 0.235543 + 0.971864i \(0.424313\pi\)
−0.235543 + 0.971864i \(0.575687\pi\)
\(84\) 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 \(-0.603011\pi\)
−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 \(-0.146794\pi\)
0.895533 + 0.444994i \(0.146794\pi\)
\(102\) 0 0
\(103\) 20.1803i 1.98843i 0.107418 + 0.994214i \(0.465742\pi\)
−0.107418 + 0.994214i \(0.534258\pi\)
\(104\) 0 0
\(105\) 5.52786 0.539464
\(106\) 0 0
\(107\) − 6.29180i − 0.608251i −0.952632 0.304125i \(-0.901636\pi\)
0.952632 0.304125i \(-0.0983642\pi\)
\(108\) 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
\(115\) 12.7639i 1.19024i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 14.4721i 1.30491i
\(124\) 0 0
\(125\) −11.1803 −1.00000
\(126\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −44.3607 −3.73584
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 13.4164 1.11417
\(146\) 0 0
\(147\) − 20.7639i − 1.71258i
\(148\) 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
\(161\) −4.36068 −0.343670
\(162\) 0 0
\(163\) 6.65248i 0.521062i 0.965465 + 0.260531i \(0.0838976\pi\)
−0.965465 + 0.260531i \(0.916102\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 10.2918i 0.796403i 0.917298 + 0.398202i \(0.130366\pi\)
−0.917298 + 0.398202i \(0.869634\pi\)
\(168\) 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
\(175\) − 3.81966i − 0.288739i
\(176\) 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 \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) − 43.4164i − 3.20943i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 11.0557 0.804186
\(190\) 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
\(201\) −26.4721 −1.86720
\(202\) 0 0
\(203\) 4.58359i 0.321705i
\(204\) 0 0
\(205\) 10.0000 0.698430
\(206\) 0 0
\(207\) 42.6525i 2.96455i
\(208\) 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
\(215\) 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
\(227\) − 13.1246i − 0.871111i −0.900162 0.435556i \(-0.856552\pi\)
0.900162 0.435556i \(-0.143448\pi\)
\(228\) 0 0
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 30.6525i 1.99955i
\(236\) 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
\(243\) − 35.5967i − 2.28353i
\(244\) 0 0
\(245\) −14.3475 −0.916630
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 57.3050 3.63155
\(250\) 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
\(261\) 44.8328 2.77508
\(262\) 0 0
\(263\) 9.12461i 0.562648i 0.959613 + 0.281324i \(0.0907735\pi\)
−0.959613 + 0.281324i \(0.909226\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 19.4164i 1.18826i
\(268\) 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 \(-0.116517\pi\)
0.933748 + 0.357930i \(0.116517\pi\)
\(282\) 0 0
\(283\) − 32.1803i − 1.91292i −0.291859 0.956461i \(-0.594274\pi\)
0.291859 0.956461i \(-0.405726\pi\)
\(284\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −8.58359 −0.494750
\(302\) 0 0
\(303\) − 58.2492i − 3.34633i
\(304\) 0 0
\(305\) −30.0000 −1.71780
\(306\) 0 0
\(307\) 27.5967i 1.57503i 0.616296 + 0.787515i \(0.288633\pi\)
−0.616296 + 0.787515i \(0.711367\pi\)
\(308\) 0 0
\(309\) 65.3050 3.71507
\(310\) 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
\(315\) − 12.7639i − 0.719166i
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 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
\(347\) − 37.1246i − 1.99295i −0.0838690 0.996477i \(-0.526728\pi\)
0.0838690 0.996477i \(-0.473272\pi\)
\(348\) 0 0
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 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
\(363\) 35.5967i 1.86834i
\(364\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 36.1803i 1.86834i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) −60.3607 −3.09237
\(382\) 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
\(387\) 83.9574i 4.26780i
\(388\) 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
\(405\) −54.5967 −2.71293
\(406\) 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
\(415\) − 39.5967i − 1.94373i
\(416\) 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
\(423\) 102.430i 4.98030i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) − 10.2492i − 0.495995i
\(428\) 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
\(435\) − 43.4164i − 2.08166i
\(436\) 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
\(443\) − 22.2918i − 1.05912i −0.848274 0.529558i \(-0.822358\pi\)
0.848274 0.529558i \(-0.177642\pi\)
\(444\) 0 0
\(445\) 13.4164 0.635999
\(446\) 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
\(461\) 42.0000 1.95614 0.978068 0.208288i \(-0.0667892\pi\)
0.978068 + 0.208288i \(0.0667892\pi\)
\(462\) 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
\(467\) 2.87539i 0.133057i 0.997785 + 0.0665285i \(0.0211923\pi\)
−0.997785 + 0.0665285i \(0.978808\pi\)
\(468\) 0 0
\(469\) −6.24922 −0.288562
\(470\) 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
\(483\) 14.1115i 0.642093i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) − 42.6525i − 1.93277i −0.257103 0.966384i \(-0.582768\pi\)
0.257103 0.966384i \(-0.417232\pi\)
\(488\) 0 0
\(489\) 21.5279 0.973524
\(490\) 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
\(501\) 33.3050 1.48796
\(502\) 0 0
\(503\) − 37.7082i − 1.68133i −0.541559 0.840663i \(-0.682166\pi\)
0.541559 0.840663i \(-0.317834\pi\)
\(504\) 0 0
\(505\) −40.2492 −1.79107
\(506\) 0 0
\(507\) − 42.0689i − 1.86834i
\(508\) 0 0
\(509\) −6.00000 −0.265945 −0.132973 0.991120i \(-0.542452\pi\)
−0.132973 + 0.991120i \(0.542452\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 45.1246i − 1.98843i
\(516\) 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
\(523\) 3.59675i 0.157275i 0.996903 + 0.0786374i \(0.0250569\pi\)
−0.996903 + 0.0786374i \(0.974943\pi\)
\(524\) 0 0
\(525\) −12.3607 −0.539464
\(526\) 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
\(541\) −38.0000 −1.63375 −0.816874 0.576816i \(-0.804295\pi\)
−0.816874 + 0.576816i \(0.804295\pi\)
\(542\) 0 0
\(543\) − 6.47214i − 0.277746i
\(544\) 0 0
\(545\) −30.0000 −1.28506
\(546\) 0 0
\(547\) − 35.2361i − 1.50659i −0.657685 0.753293i \(-0.728464\pi\)
0.657685 0.753293i \(-0.271536\pi\)
\(548\) 0 0
\(549\) −100.249 −4.27853
\(550\) 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
\(563\) 32.5410i 1.37144i 0.727865 + 0.685720i \(0.240513\pi\)
−0.727865 + 0.685720i \(0.759487\pi\)
\(564\) 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 \(-0.272169\pi\)
0.656186 + 0.754599i \(0.272169\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) − 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
\(581\) 13.5279 0.561230
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 40.5410i 1.67331i 0.547733 + 0.836653i \(0.315491\pi\)
−0.547733 + 0.836653i \(0.684509\pi\)
\(588\) 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
\(603\) 61.1246i 2.48919i
\(604\) 0 0
\(605\) 24.5967 1.00000
\(606\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 82.6099 3.31502
\(622\) 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
\(635\) 41.7082i 1.65514i
\(636\) 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
\(643\) − 50.0689i − 1.97452i −0.159103 0.987262i \(-0.550860\pi\)
0.159103 0.987262i \(-0.449140\pi\)
\(644\) 0 0
\(645\) 81.3050 3.20138
\(646\) 0 0
\(647\) − 20.5410i − 0.807551i −0.914858 0.403775i \(-0.867698\pi\)
0.914858 0.403775i \(-0.132302\pi\)
\(648\) 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
\(667\) 34.2492i 1.32614i
\(668\) 0 0
\(669\) 75.1935 2.90715
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 72.3607i 2.78516i
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −42.4721 −1.62754
\(682\) 0 0
\(683\) 10.8754i 0.416135i 0.978114 + 0.208068i \(0.0667174\pi\)
−0.978114 + 0.208068i \(0.933283\pi\)
\(684\) 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 1.00000i \(-0.5\pi\)
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
\(705\) 99.1935 3.73584
\(706\) 0 0
\(707\) − 13.7508i − 0.517151i
\(708\) 0 0
\(709\) −46.0000 −1.72757 −0.863783 0.503864i \(-0.831911\pi\)
−0.863783 + 0.503864i \(0.831911\pi\)
\(710\) 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
\(723\) − 43.4164i − 1.61467i
\(724\) 0 0
\(725\) −30.0000 −1.11417
\(726\) 0 0
\(727\) 35.0132i 1.29857i 0.760547 + 0.649283i \(0.224931\pi\)
−0.760547 + 0.649283i \(0.775069\pi\)
\(728\) 0 0
\(729\) −41.9443 −1.55349
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 46.4296i 1.71258i
\(736\) 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
\(743\) − 52.5410i − 1.92754i −0.266729 0.963772i \(-0.585943\pi\)
0.266729 0.963772i \(-0.414057\pi\)
\(744\) 0 0
\(745\) 10.0000 0.366372
\(746\) 0 0
\(747\) − 132.318i − 4.84127i
\(748\) 0 0
\(749\) −4.80650 −0.175626
\(750\) 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
\(763\) − 10.2492i − 0.371047i
\(764\) 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
\(783\) − 86.8328i − 3.10315i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) − 2.06888i − 0.0737477i −0.999320 0.0368739i \(-0.988260\pi\)
0.999320 0.0368739i \(-0.0117400\pi\)
\(788\) 0 0
\(789\) 29.5279 1.05122
\(790\) 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
\(801\) 44.8328 1.58409
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 9.75078 0.343670
\(806\) 0 0
\(807\) 72.3607i 2.54722i
\(808\) 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
\(815\) − 14.8754i − 0.521062i
\(816\) 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
\(823\) − 27.8197i − 0.969732i −0.874588 0.484866i \(-0.838868\pi\)
0.874588 0.484866i \(-0.161132\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 56.5410i 1.96612i 0.183274 + 0.983062i \(0.441331\pi\)
−0.183274 + 0.983062i \(0.558669\pi\)
\(828\) 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
\(835\) − 23.0132i − 0.796403i
\(836\) 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
\(843\) − 101.305i − 3.48913i
\(844\) 0 0
\(845\) −29.0689 −1.00000
\(846\) 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 1.00000 \(0\)
−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
\(861\) 11.0557 0.376778
\(862\) 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
\(867\) − 55.0132i − 1.86834i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 8.54102i 0.288739i
\(876\) 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 \(-0.935209\pi\)
−0.979356 + 0.202145i \(0.935209\pi\)
\(882\) 0 0
\(883\) 54.6525i 1.83920i 0.392853 + 0.919601i \(0.371488\pi\)
−0.392853 + 0.919601i \(0.628512\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 57.1246i 1.91806i 0.283310 + 0.959028i \(0.408567\pi\)
−0.283310 + 0.959028i \(0.591433\pi\)
\(888\) 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
\(907\) 45.4853i 1.51031i 0.655544 + 0.755157i \(0.272439\pi\)
−0.655544 + 0.755157i \(0.727561\pi\)
\(908\) 0 0
\(909\) −134.498 −4.46103
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 97.0820i 3.20943i
\(916\) 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
\(941\) 42.0000 1.36916 0.684580 0.728937i \(-0.259985\pi\)
0.684580 + 0.728937i \(0.259985\pi\)
\(942\) 0 0
\(943\) 25.5279i 0.831302i
\(944\) 0 0
\(945\) −24.7214 −0.804186
\(946\) 0 0
\(947\) 49.7082i 1.61530i 0.589662 + 0.807650i \(0.299261\pi\)
−0.589662 + 0.807650i \(0.700739\pi\)
\(948\) 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
\(963\) 47.0132i 1.51498i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 62.0689i 1.99600i 0.0632081 + 0.998000i \(0.479867\pi\)
−0.0632081 + 0.998000i \(0.520133\pi\)
\(968\) 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
\(981\) −100.249 −3.20071
\(982\) 0 0
\(983\) − 4.54102i − 0.144836i −0.997374 0.0724180i \(-0.976928\pi\)
0.997374 0.0724180i \(-0.0230716\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 33.8885i 1.07868i
\(988\) 0 0
\(989\) −64.1378 −2.03946
\(990\) 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 320.2.c.d.129.1 4
3.2 odd 2 2880.2.f.w.1729.3 4
4.3 odd 2 inner 320.2.c.d.129.4 4
5.2 odd 4 1600.2.a.z.1.1 2
5.3 odd 4 1600.2.a.bd.1.2 2
5.4 even 2 inner 320.2.c.d.129.4 4
8.3 odd 2 160.2.c.b.129.1 4
8.5 even 2 160.2.c.b.129.4 yes 4
12.11 even 2 2880.2.f.w.1729.4 4
15.14 odd 2 2880.2.f.w.1729.4 4
16.3 odd 4 1280.2.f.g.129.2 4
16.5 even 4 1280.2.f.g.129.1 4
16.11 odd 4 1280.2.f.h.129.3 4
16.13 even 4 1280.2.f.h.129.4 4
20.3 even 4 1600.2.a.z.1.1 2
20.7 even 4 1600.2.a.bd.1.2 2
20.19 odd 2 CM 320.2.c.d.129.1 4
24.5 odd 2 1440.2.f.i.289.1 4
24.11 even 2 1440.2.f.i.289.2 4
40.3 even 4 800.2.a.n.1.2 2
40.13 odd 4 800.2.a.j.1.1 2
40.19 odd 2 160.2.c.b.129.4 yes 4
40.27 even 4 800.2.a.j.1.1 2
40.29 even 2 160.2.c.b.129.1 4
40.37 odd 4 800.2.a.n.1.2 2
60.59 even 2 2880.2.f.w.1729.3 4
80.19 odd 4 1280.2.f.h.129.4 4
80.29 even 4 1280.2.f.g.129.2 4
80.59 odd 4 1280.2.f.g.129.1 4
80.69 even 4 1280.2.f.h.129.3 4
120.29 odd 2 1440.2.f.i.289.2 4
120.53 even 4 7200.2.a.cb.1.2 2
120.59 even 2 1440.2.f.i.289.1 4
120.77 even 4 7200.2.a.cr.1.1 2
120.83 odd 4 7200.2.a.cr.1.1 2
120.107 odd 4 7200.2.a.cb.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.2.c.b.129.1 4 8.3 odd 2
160.2.c.b.129.1 4 40.29 even 2
160.2.c.b.129.4 yes 4 8.5 even 2
160.2.c.b.129.4 yes 4 40.19 odd 2
320.2.c.d.129.1 4 1.1 even 1 trivial
320.2.c.d.129.1 4 20.19 odd 2 CM
320.2.c.d.129.4 4 4.3 odd 2 inner
320.2.c.d.129.4 4 5.4 even 2 inner
800.2.a.j.1.1 2 40.13 odd 4
800.2.a.j.1.1 2 40.27 even 4
800.2.a.n.1.2 2 40.3 even 4
800.2.a.n.1.2 2 40.37 odd 4
1280.2.f.g.129.1 4 16.5 even 4
1280.2.f.g.129.1 4 80.59 odd 4
1280.2.f.g.129.2 4 16.3 odd 4
1280.2.f.g.129.2 4 80.29 even 4
1280.2.f.h.129.3 4 16.11 odd 4
1280.2.f.h.129.3 4 80.69 even 4
1280.2.f.h.129.4 4 16.13 even 4
1280.2.f.h.129.4 4 80.19 odd 4
1440.2.f.i.289.1 4 24.5 odd 2
1440.2.f.i.289.1 4 120.59 even 2
1440.2.f.i.289.2 4 24.11 even 2
1440.2.f.i.289.2 4 120.29 odd 2
1600.2.a.z.1.1 2 5.2 odd 4
1600.2.a.z.1.1 2 20.3 even 4
1600.2.a.bd.1.2 2 5.3 odd 4
1600.2.a.bd.1.2 2 20.7 even 4
2880.2.f.w.1729.3 4 3.2 odd 2
2880.2.f.w.1729.3 4 60.59 even 2
2880.2.f.w.1729.4 4 12.11 even 2
2880.2.f.w.1729.4 4 15.14 odd 2
7200.2.a.cb.1.2 2 120.53 even 4
7200.2.a.cb.1.2 2 120.107 odd 4
7200.2.a.cr.1.1 2 120.77 even 4
7200.2.a.cr.1.1 2 120.83 odd 4