Properties

Label 768.2.f.d.383.1
Level $768$
Weight $2$
Character 768.383
Analytic conductor $6.133$
Analytic rank $0$
Dimension $4$
CM discriminant -3
Inner twists $8$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 383.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 768.383
Dual form 768.2.f.d.383.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.73205 q^{3} -3.46410i q^{7} +3.00000 q^{9} +O(q^{10})\) \(q-1.73205 q^{3} -3.46410i q^{7} +3.00000 q^{9} +2.00000i q^{13} -3.46410 q^{19} +6.00000i q^{21} -5.00000 q^{25} -5.19615 q^{27} -10.3923i q^{31} -10.0000i q^{37} -3.46410i q^{39} -10.3923 q^{43} -5.00000 q^{49} +6.00000 q^{57} -14.0000i q^{61} -10.3923i q^{63} -3.46410 q^{67} -10.0000 q^{73} +8.66025 q^{75} +17.3205i q^{79} +9.00000 q^{81} +6.92820 q^{91} +18.0000i q^{93} -14.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 12q^{9} + O(q^{10}) \) \( 4q + 12q^{9} - 20q^{25} - 20q^{49} + 24q^{57} - 40q^{73} + 36q^{81} - 56q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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
\(3\) −1.73205 −1.00000
\(4\) 0 0
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) − 3.46410i − 1.30931i −0.755929 0.654654i \(-0.772814\pi\)
0.755929 0.654654i \(-0.227186\pi\)
\(8\) 0 0
\(9\) 3.00000 1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) 2.00000i 0.554700i 0.960769 + 0.277350i \(0.0894562\pi\)
−0.960769 + 0.277350i \(0.910544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) −3.46410 −0.794719 −0.397360 0.917663i \(-0.630073\pi\)
−0.397360 + 0.917663i \(0.630073\pi\)
\(20\) 0 0
\(21\) 6.00000i 1.30931i
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) −5.19615 −1.00000
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) − 10.3923i − 1.86651i −0.359211 0.933257i \(-0.616954\pi\)
0.359211 0.933257i \(-0.383046\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) − 10.0000i − 1.64399i −0.569495 0.821995i \(-0.692861\pi\)
0.569495 0.821995i \(-0.307139\pi\)
\(38\) 0 0
\(39\) − 3.46410i − 0.554700i
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −10.3923 −1.58481 −0.792406 0.609994i \(-0.791172\pi\)
−0.792406 + 0.609994i \(0.791172\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −5.00000 −0.714286
\(50\) 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
\(57\) 6.00000 0.794719
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) − 14.0000i − 1.79252i −0.443533 0.896258i \(-0.646275\pi\)
0.443533 0.896258i \(-0.353725\pi\)
\(62\) 0 0
\(63\) − 10.3923i − 1.30931i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −3.46410 −0.423207 −0.211604 0.977356i \(-0.567869\pi\)
−0.211604 + 0.977356i \(0.567869\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 0 0
\(75\) 8.66025 1.00000
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 17.3205i 1.94871i 0.225018 + 0.974355i \(0.427756\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 6.92820 0.726273
\(92\) 0 0
\(93\) 18.0000i 1.86651i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −14.0000 −1.42148 −0.710742 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) − 3.46410i − 0.341328i −0.985329 0.170664i \(-0.945409\pi\)
0.985329 0.170664i \(-0.0545913\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) 2.00000i 0.191565i 0.995402 + 0.0957826i \(0.0305354\pi\)
−0.995402 + 0.0957826i \(0.969465\pi\)
\(110\) 0 0
\(111\) 17.3205i 1.64399i
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 6.00000i 0.554700i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 11.0000 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) − 10.3923i − 0.922168i −0.887357 0.461084i \(-0.847461\pi\)
0.887357 0.461084i \(-0.152539\pi\)
\(128\) 0 0
\(129\) 18.0000 1.58481
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 12.0000i 1.04053i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 17.3205 1.46911 0.734553 0.678551i \(-0.237392\pi\)
0.734553 + 0.678551i \(0.237392\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 8.66025 0.714286
\(148\) 0 0
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 24.2487i 1.97333i 0.162758 + 0.986666i \(0.447961\pi\)
−0.162758 + 0.986666i \(0.552039\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) − 14.0000i − 1.11732i −0.829396 0.558661i \(-0.811315\pi\)
0.829396 0.558661i \(-0.188685\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 24.2487 1.89931 0.949653 0.313304i \(-0.101436\pi\)
0.949653 + 0.313304i \(0.101436\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) 0 0
\(171\) −10.3923 −0.794719
\(172\) 0 0
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 17.3205i 1.30931i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) − 26.0000i − 1.93256i −0.257485 0.966282i \(-0.582894\pi\)
0.257485 0.966282i \(-0.417106\pi\)
\(182\) 0 0
\(183\) 24.2487i 1.79252i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 18.0000i 1.30931i
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 2.00000 0.143963 0.0719816 0.997406i \(-0.477068\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) − 3.46410i − 0.245564i −0.992434 0.122782i \(-0.960818\pi\)
0.992434 0.122782i \(-0.0391815\pi\)
\(200\) 0 0
\(201\) 6.00000 0.423207
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 24.2487 1.66935 0.834675 0.550743i \(-0.185655\pi\)
0.834675 + 0.550743i \(0.185655\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −36.0000 −2.44384
\(218\) 0 0
\(219\) 17.3205 1.17041
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) − 10.3923i − 0.695920i −0.937509 0.347960i \(-0.886874\pi\)
0.937509 0.347960i \(-0.113126\pi\)
\(224\) 0 0
\(225\) −15.0000 −1.00000
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 22.0000i 1.45380i 0.686743 + 0.726900i \(0.259040\pi\)
−0.686743 + 0.726900i \(0.740960\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) − 30.0000i − 1.94871i
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −14.0000 −0.901819 −0.450910 0.892570i \(-0.648900\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) 0 0
\(243\) −15.5885 −1.00000
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) − 6.92820i − 0.440831i
\(248\) 0 0
\(249\) 0 0
\(250\) 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
\(259\) −34.6410 −2.15249
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 17.3205i 1.05215i 0.850439 + 0.526073i \(0.176336\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) 0 0
\(273\) −12.0000 −0.726273
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) − 26.0000i − 1.56219i −0.624413 0.781094i \(-0.714662\pi\)
0.624413 0.781094i \(-0.285338\pi\)
\(278\) 0 0
\(279\) − 31.1769i − 1.86651i
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −10.3923 −0.617758 −0.308879 0.951101i \(-0.599954\pi\)
−0.308879 + 0.951101i \(0.599954\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 17.0000 1.00000
\(290\) 0 0
\(291\) 24.2487 1.42148
\(292\) 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
\(301\) 36.0000i 2.07501i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −31.1769 −1.77936 −0.889680 0.456584i \(-0.849073\pi\)
−0.889680 + 0.456584i \(0.849073\pi\)
\(308\) 0 0
\(309\) 6.00000i 0.341328i
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 22.0000 1.24351 0.621757 0.783210i \(-0.286419\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) − 10.0000i − 0.554700i
\(326\) 0 0
\(327\) − 3.46410i − 0.191565i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 17.3205 0.952021 0.476011 0.879440i \(-0.342082\pi\)
0.476011 + 0.879440i \(0.342082\pi\)
\(332\) 0 0
\(333\) − 30.0000i − 1.64399i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 34.0000 1.85210 0.926049 0.377403i \(-0.123183\pi\)
0.926049 + 0.377403i \(0.123183\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) − 6.92820i − 0.374088i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) − 14.0000i − 0.749403i −0.927146 0.374701i \(-0.877745\pi\)
0.927146 0.374701i \(-0.122255\pi\)
\(350\) 0 0
\(351\) − 10.3923i − 0.554700i
\(352\) 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
\(361\) −7.00000 −0.368421
\(362\) 0 0
\(363\) −19.0526 −1.00000
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) − 38.1051i − 1.98907i −0.104399 0.994535i \(-0.533292\pi\)
0.104399 0.994535i \(-0.466708\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 38.0000i 1.96757i 0.179364 + 0.983783i \(0.442596\pi\)
−0.179364 + 0.983783i \(0.557404\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −38.1051 −1.95733 −0.978664 0.205466i \(-0.934129\pi\)
−0.978664 + 0.205466i \(0.934129\pi\)
\(380\) 0 0
\(381\) 18.0000i 0.922168i
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −31.1769 −1.58481
\(388\) 0 0
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 34.0000i 1.70641i 0.521575 + 0.853206i \(0.325345\pi\)
−0.521575 + 0.853206i \(0.674655\pi\)
\(398\) 0 0
\(399\) − 20.7846i − 1.04053i
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 20.7846 1.03536
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 38.0000 1.87898 0.939490 0.342578i \(-0.111300\pi\)
0.939490 + 0.342578i \(0.111300\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −30.0000 −1.46911
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 22.0000i 1.07221i 0.844150 + 0.536107i \(0.180106\pi\)
−0.844150 + 0.536107i \(0.819894\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −48.4974 −2.34695
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) − 31.1769i − 1.48799i −0.668184 0.743996i \(-0.732928\pi\)
0.668184 0.743996i \(-0.267072\pi\)
\(440\) 0 0
\(441\) −15.0000 −0.714286
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) − 42.0000i − 1.97333i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) − 38.1051i − 1.77090i −0.464739 0.885448i \(-0.653852\pi\)
0.464739 0.885448i \(-0.346148\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 12.0000i 0.554109i
\(470\) 0 0
\(471\) 24.2487i 1.11732i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 17.3205 0.794719
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 20.0000 0.911922
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) − 3.46410i − 0.156973i −0.996915 0.0784867i \(-0.974991\pi\)
0.996915 0.0784867i \(-0.0250088\pi\)
\(488\) 0 0
\(489\) −42.0000 −1.89931
\(490\) 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
\(499\) −31.1769 −1.39567 −0.697835 0.716258i \(-0.745853\pi\)
−0.697835 + 0.716258i \(0.745853\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −15.5885 −0.692308
\(508\) 0 0
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 34.6410i 1.53243i
\(512\) 0 0
\(513\) 18.0000 0.794719
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 45.0333 1.96917 0.984585 0.174908i \(-0.0559627\pi\)
0.984585 + 0.174908i \(0.0559627\pi\)
\(524\) 0 0
\(525\) − 30.0000i − 1.30931i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) − 46.0000i − 1.97769i −0.148933 0.988847i \(-0.547584\pi\)
0.148933 0.988847i \(-0.452416\pi\)
\(542\) 0 0
\(543\) 45.0333i 1.93256i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 24.2487 1.03680 0.518400 0.855138i \(-0.326528\pi\)
0.518400 + 0.855138i \(0.326528\pi\)
\(548\) 0 0
\(549\) − 42.0000i − 1.79252i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 60.0000 2.55146
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) − 20.7846i − 0.879095i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) − 31.1769i − 1.30931i
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 45.0333 1.88459 0.942293 0.334790i \(-0.108665\pi\)
0.942293 + 0.334790i \(0.108665\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −46.0000 −1.91501 −0.957503 0.288425i \(-0.906868\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) 0 0
\(579\) −3.46410 −0.143963
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) 36.0000i 1.48335i
\(590\) 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
\(597\) 6.00000i 0.245564i
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 0 0
\(603\) −10.3923 −0.423207
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 45.0333i 1.82785i 0.405887 + 0.913923i \(0.366962\pi\)
−0.405887 + 0.913923i \(0.633038\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) − 10.0000i − 0.403896i −0.979396 0.201948i \(-0.935273\pi\)
0.979396 0.201948i \(-0.0647272\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −38.1051 −1.53157 −0.765787 0.643094i \(-0.777650\pi\)
−0.765787 + 0.643094i \(0.777650\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 24.2487i 0.965326i 0.875806 + 0.482663i \(0.160330\pi\)
−0.875806 + 0.482663i \(0.839670\pi\)
\(632\) 0 0
\(633\) −42.0000 −1.66935
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) − 10.0000i − 0.396214i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) −31.1769 −1.22950 −0.614749 0.788723i \(-0.710743\pi\)
−0.614749 + 0.788723i \(0.710743\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 62.3538 2.44384
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −30.0000 −1.17041
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 38.0000i 1.47803i 0.673690 + 0.739014i \(0.264708\pi\)
−0.673690 + 0.739014i \(0.735292\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 18.0000i 0.695920i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 50.0000 1.92736 0.963679 0.267063i \(-0.0860531\pi\)
0.963679 + 0.267063i \(0.0860531\pi\)
\(674\) 0 0
\(675\) 25.9808 1.00000
\(676\) 0 0
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 48.4974i 1.86116i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) − 38.1051i − 1.45380i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 51.9615 1.97671 0.988355 0.152167i \(-0.0486252\pi\)
0.988355 + 0.152167i \(0.0486252\pi\)
\(692\) 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
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 34.6410i 1.30651i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 22.0000i 0.826227i 0.910679 + 0.413114i \(0.135559\pi\)
−0.910679 + 0.413114i \(0.864441\pi\)
\(710\) 0 0
\(711\) 51.9615i 1.94871i
\(712\) 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
\(721\) −12.0000 −0.446903
\(722\) 0 0
\(723\) 24.2487 0.901819
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) − 31.1769i − 1.15629i −0.815935 0.578144i \(-0.803777\pi\)
0.815935 0.578144i \(-0.196223\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 50.0000i 1.84679i 0.383849 + 0.923396i \(0.374598\pi\)
−0.383849 + 0.923396i \(0.625402\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 51.9615 1.91144 0.955718 0.294285i \(-0.0950814\pi\)
0.955718 + 0.294285i \(0.0950814\pi\)
\(740\) 0 0
\(741\) 12.0000i 0.440831i
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 17.3205i 0.632034i 0.948753 + 0.316017i \(0.102346\pi\)
−0.948753 + 0.316017i \(0.897654\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) − 26.0000i − 0.944986i −0.881334 0.472493i \(-0.843354\pi\)
0.881334 0.472493i \(-0.156646\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 6.92820 0.250818
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 2.00000 0.0721218 0.0360609 0.999350i \(-0.488519\pi\)
0.0360609 + 0.999350i \(0.488519\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 51.9615i 1.86651i
\(776\) 0 0
\(777\) 60.0000 2.15249
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −3.46410 −0.123482 −0.0617409 0.998092i \(-0.519665\pi\)
−0.0617409 + 0.998092i \(0.519665\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 28.0000 0.994309
\(794\) 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
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) −10.3923 −0.364923 −0.182462 0.983213i \(-0.558407\pi\)
−0.182462 + 0.983213i \(0.558407\pi\)
\(812\) 0 0
\(813\) − 30.0000i − 1.05215i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 36.0000 1.25948
\(818\) 0 0
\(819\) 20.7846 0.726273
\(820\) 0 0
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) 24.2487i 0.845257i 0.906303 + 0.422628i \(0.138892\pi\)
−0.906303 + 0.422628i \(0.861108\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) − 46.0000i − 1.59765i −0.601566 0.798823i \(-0.705456\pi\)
0.601566 0.798823i \(-0.294544\pi\)
\(830\) 0 0
\(831\) 45.0333i 1.56219i
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 54.0000i 1.86651i
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) − 38.1051i − 1.30931i
\(848\) 0 0
\(849\) 18.0000 0.617758
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) − 58.0000i − 1.98588i −0.118609 0.992941i \(-0.537843\pi\)
0.118609 0.992941i \(-0.462157\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 17.3205 0.590968 0.295484 0.955348i \(-0.404519\pi\)
0.295484 + 0.955348i \(0.404519\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −29.4449 −1.00000
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) − 6.92820i − 0.234753i
\(872\) 0 0
\(873\) −42.0000 −1.42148
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 34.0000i 1.14810i 0.818821 + 0.574049i \(0.194628\pi\)
−0.818821 + 0.574049i \(0.805372\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) −58.8897 −1.98180 −0.990899 0.134611i \(-0.957022\pi\)
−0.990899 + 0.134611i \(0.957022\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) −36.0000 −1.20740
\(890\) 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
\(903\) − 62.3538i − 2.07501i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 45.0333 1.49531 0.747653 0.664089i \(-0.231180\pi\)
0.747653 + 0.664089i \(0.231180\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) − 31.1769i − 1.02843i −0.857661 0.514216i \(-0.828083\pi\)
0.857661 0.514216i \(-0.171917\pi\)
\(920\) 0 0
\(921\) 54.0000 1.77936
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 50.0000i 1.64399i
\(926\) 0 0
\(927\) − 10.3923i − 0.341328i
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 17.3205 0.567657
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −26.0000 −0.849383 −0.424691 0.905338i \(-0.639617\pi\)
−0.424691 + 0.905338i \(0.639617\pi\)
\(938\) 0 0
\(939\) −38.1051 −1.24351
\(940\) 0 0
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) − 20.0000i − 0.649227i
\(950\) 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
\(961\) −77.0000 −2.48387
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) − 58.8897i − 1.89377i −0.321578 0.946883i \(-0.604213\pi\)
0.321578 0.946883i \(-0.395787\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) − 60.0000i − 1.92351i
\(974\) 0 0
\(975\) 17.3205i 0.554700i
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 6.00000i 0.191565i
\(982\) 0 0
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 45.0333i 1.43053i 0.698853 + 0.715265i \(0.253694\pi\)
−0.698853 + 0.715265i \(0.746306\pi\)
\(992\) 0 0
\(993\) −30.0000 −0.952021
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) − 10.0000i − 0.316703i −0.987383 0.158352i \(-0.949382\pi\)
0.987383 0.158352i \(-0.0506179\pi\)
\(998\) 0 0
\(999\) 51.9615i 1.64399i
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 768.2.f.d.383.1 4
3.2 odd 2 CM 768.2.f.d.383.1 4
4.3 odd 2 inner 768.2.f.d.383.4 4
8.3 odd 2 inner 768.2.f.d.383.2 4
8.5 even 2 inner 768.2.f.d.383.3 4
12.11 even 2 inner 768.2.f.d.383.4 4
16.3 odd 4 48.2.c.a.47.2 yes 2
16.5 even 4 192.2.c.a.191.2 2
16.11 odd 4 192.2.c.a.191.1 2
16.13 even 4 48.2.c.a.47.1 2
24.5 odd 2 inner 768.2.f.d.383.3 4
24.11 even 2 inner 768.2.f.d.383.2 4
48.5 odd 4 192.2.c.a.191.2 2
48.11 even 4 192.2.c.a.191.1 2
48.29 odd 4 48.2.c.a.47.1 2
48.35 even 4 48.2.c.a.47.2 yes 2
80.3 even 4 1200.2.o.i.1199.1 4
80.13 odd 4 1200.2.o.i.1199.3 4
80.19 odd 4 1200.2.h.e.1151.1 2
80.29 even 4 1200.2.h.e.1151.2 2
80.67 even 4 1200.2.o.i.1199.4 4
80.77 odd 4 1200.2.o.i.1199.2 4
112.13 odd 4 2352.2.h.c.2255.2 2
112.83 even 4 2352.2.h.c.2255.1 2
144.13 even 12 1296.2.s.b.431.1 2
144.29 odd 12 1296.2.s.e.863.1 2
144.61 even 12 1296.2.s.e.863.1 2
144.67 odd 12 1296.2.s.e.431.1 2
144.77 odd 12 1296.2.s.b.431.1 2
144.83 even 12 1296.2.s.b.863.1 2
144.115 odd 12 1296.2.s.b.863.1 2
144.131 even 12 1296.2.s.e.431.1 2
240.29 odd 4 1200.2.h.e.1151.2 2
240.77 even 4 1200.2.o.i.1199.2 4
240.83 odd 4 1200.2.o.i.1199.1 4
240.173 even 4 1200.2.o.i.1199.3 4
240.179 even 4 1200.2.h.e.1151.1 2
240.227 odd 4 1200.2.o.i.1199.4 4
336.83 odd 4 2352.2.h.c.2255.1 2
336.125 even 4 2352.2.h.c.2255.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
48.2.c.a.47.1 2 16.13 even 4
48.2.c.a.47.1 2 48.29 odd 4
48.2.c.a.47.2 yes 2 16.3 odd 4
48.2.c.a.47.2 yes 2 48.35 even 4
192.2.c.a.191.1 2 16.11 odd 4
192.2.c.a.191.1 2 48.11 even 4
192.2.c.a.191.2 2 16.5 even 4
192.2.c.a.191.2 2 48.5 odd 4
768.2.f.d.383.1 4 1.1 even 1 trivial
768.2.f.d.383.1 4 3.2 odd 2 CM
768.2.f.d.383.2 4 8.3 odd 2 inner
768.2.f.d.383.2 4 24.11 even 2 inner
768.2.f.d.383.3 4 8.5 even 2 inner
768.2.f.d.383.3 4 24.5 odd 2 inner
768.2.f.d.383.4 4 4.3 odd 2 inner
768.2.f.d.383.4 4 12.11 even 2 inner
1200.2.h.e.1151.1 2 80.19 odd 4
1200.2.h.e.1151.1 2 240.179 even 4
1200.2.h.e.1151.2 2 80.29 even 4
1200.2.h.e.1151.2 2 240.29 odd 4
1200.2.o.i.1199.1 4 80.3 even 4
1200.2.o.i.1199.1 4 240.83 odd 4
1200.2.o.i.1199.2 4 80.77 odd 4
1200.2.o.i.1199.2 4 240.77 even 4
1200.2.o.i.1199.3 4 80.13 odd 4
1200.2.o.i.1199.3 4 240.173 even 4
1200.2.o.i.1199.4 4 80.67 even 4
1200.2.o.i.1199.4 4 240.227 odd 4
1296.2.s.b.431.1 2 144.13 even 12
1296.2.s.b.431.1 2 144.77 odd 12
1296.2.s.b.863.1 2 144.83 even 12
1296.2.s.b.863.1 2 144.115 odd 12
1296.2.s.e.431.1 2 144.67 odd 12
1296.2.s.e.431.1 2 144.131 even 12
1296.2.s.e.863.1 2 144.29 odd 12
1296.2.s.e.863.1 2 144.61 even 12
2352.2.h.c.2255.1 2 112.83 even 4
2352.2.h.c.2255.1 2 336.83 odd 4
2352.2.h.c.2255.2 2 112.13 odd 4
2352.2.h.c.2255.2 2 336.125 even 4