Properties

Label 768.3.h.b.641.2
Level $768$
Weight $3$
Character 768.641
Analytic conductor $20.926$
Analytic rank $0$
Dimension $2$
CM discriminant -3
Inner twists $4$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(20.9264843029\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 12)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 641.2
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 768.641
Dual form 768.3.h.b.641.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.00000i q^{3} +2.00000 q^{7} -9.00000 q^{9} +O(q^{10})\) \(q+3.00000i q^{3} +2.00000 q^{7} -9.00000 q^{9} -22.0000i q^{13} -26.0000i q^{19} +6.00000i q^{21} -25.0000 q^{25} -27.0000i q^{27} +46.0000 q^{31} -26.0000i q^{37} +66.0000 q^{39} -22.0000i q^{43} -45.0000 q^{49} +78.0000 q^{57} +74.0000i q^{61} -18.0000 q^{63} -122.000i q^{67} +46.0000 q^{73} -75.0000i q^{75} +142.000 q^{79} +81.0000 q^{81} -44.0000i q^{91} +138.000i q^{93} +2.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 4q^{7} - 18q^{9} + O(q^{10}) \) \( 2q + 4q^{7} - 18q^{9} - 50q^{25} + 92q^{31} + 132q^{39} - 90q^{49} + 156q^{57} - 36q^{63} + 92q^{73} + 284q^{79} + 162q^{81} + 4q^{97} + O(q^{100}) \)

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
\(3\) 3.00000i 1.00000i
\(4\) 0 0
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 2.00000 0.285714 0.142857 0.989743i \(-0.454371\pi\)
0.142857 + 0.989743i \(0.454371\pi\)
\(8\) 0 0
\(9\) −9.00000 −1.00000
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) − 22.0000i − 1.69231i −0.532939 0.846154i \(-0.678912\pi\)
0.532939 0.846154i \(-0.321088\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) − 26.0000i − 1.36842i −0.729285 0.684211i \(-0.760147\pi\)
0.729285 0.684211i \(-0.239853\pi\)
\(20\) 0 0
\(21\) 6.00000i 0.285714i
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) −25.0000 −1.00000
\(26\) 0 0
\(27\) − 27.0000i − 1.00000i
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 46.0000 1.48387 0.741935 0.670471i \(-0.233908\pi\)
0.741935 + 0.670471i \(0.233908\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) − 26.0000i − 0.702703i −0.936244 0.351351i \(-0.885722\pi\)
0.936244 0.351351i \(-0.114278\pi\)
\(38\) 0 0
\(39\) 66.0000 1.69231
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) − 22.0000i − 0.511628i −0.966726 0.255814i \(-0.917657\pi\)
0.966726 0.255814i \(-0.0823435\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) −45.0000 −0.918367
\(50\) 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
\(57\) 78.0000 1.36842
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 74.0000i 1.21311i 0.795040 + 0.606557i \(0.207450\pi\)
−0.795040 + 0.606557i \(0.792550\pi\)
\(62\) 0 0
\(63\) −18.0000 −0.285714
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) − 122.000i − 1.82090i −0.413624 0.910448i \(-0.635737\pi\)
0.413624 0.910448i \(-0.364263\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 46.0000 0.630137 0.315068 0.949069i \(-0.397973\pi\)
0.315068 + 0.949069i \(0.397973\pi\)
\(74\) 0 0
\(75\) − 75.0000i − 1.00000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 142.000 1.79747 0.898734 0.438494i \(-0.144488\pi\)
0.898734 + 0.438494i \(0.144488\pi\)
\(80\) 0 0
\(81\) 81.0000 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 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
\(91\) − 44.0000i − 0.483516i
\(92\) 0 0
\(93\) 138.000i 1.48387i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.00000 0.0206186 0.0103093 0.999947i \(-0.496718\pi\)
0.0103093 + 0.999947i \(0.496718\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 194.000 1.88350 0.941748 0.336321i \(-0.109183\pi\)
0.941748 + 0.336321i \(0.109183\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) − 214.000i − 1.96330i −0.190684 0.981651i \(-0.561071\pi\)
0.190684 0.981651i \(-0.438929\pi\)
\(110\) 0 0
\(111\) 78.0000 0.702703
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 198.000i 1.69231i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −121.000 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −146.000 −1.14961 −0.574803 0.818292i \(-0.694921\pi\)
−0.574803 + 0.818292i \(0.694921\pi\)
\(128\) 0 0
\(129\) 66.0000 0.511628
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) − 52.0000i − 0.390977i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) − 22.0000i − 0.158273i −0.996864 0.0791367i \(-0.974784\pi\)
0.996864 0.0791367i \(-0.0252164\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) − 135.000i − 0.918367i
\(148\) 0 0
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) −286.000 −1.89404 −0.947020 0.321175i \(-0.895922\pi\)
−0.947020 + 0.321175i \(0.895922\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) − 118.000i − 0.751592i −0.926702 0.375796i \(-0.877369\pi\)
0.926702 0.375796i \(-0.122631\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 262.000i 1.60736i 0.595060 + 0.803681i \(0.297128\pi\)
−0.595060 + 0.803681i \(0.702872\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) −315.000 −1.86391
\(170\) 0 0
\(171\) 234.000i 1.36842i
\(172\) 0 0
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) −50.0000 −0.285714
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) − 314.000i − 1.73481i −0.497606 0.867403i \(-0.665787\pi\)
0.497606 0.867403i \(-0.334213\pi\)
\(182\) 0 0
\(183\) −222.000 −1.21311
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) − 54.0000i − 0.285714i
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) −382.000 −1.97927 −0.989637 0.143590i \(-0.954135\pi\)
−0.989637 + 0.143590i \(0.954135\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 386.000 1.93970 0.969849 0.243706i \(-0.0783631\pi\)
0.969849 + 0.243706i \(0.0783631\pi\)
\(200\) 0 0
\(201\) 366.000 1.82090
\(202\) 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
\(211\) 166.000i 0.786730i 0.919382 + 0.393365i \(0.128689\pi\)
−0.919382 + 0.393365i \(0.871311\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 92.0000 0.423963
\(218\) 0 0
\(219\) 138.000i 0.630137i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −338.000 −1.51570 −0.757848 0.652432i \(-0.773749\pi\)
−0.757848 + 0.652432i \(0.773749\pi\)
\(224\) 0 0
\(225\) 225.000 1.00000
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) − 26.0000i − 0.113537i −0.998387 0.0567686i \(-0.981920\pi\)
0.998387 0.0567686i \(-0.0180797\pi\)
\(230\) 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
\(237\) 426.000i 1.79747i
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −286.000 −1.18672 −0.593361 0.804936i \(-0.702199\pi\)
−0.593361 + 0.804936i \(0.702199\pi\)
\(242\) 0 0
\(243\) 243.000i 1.00000i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −572.000 −2.31579
\(248\) 0 0
\(249\) 0 0
\(250\) 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
\(259\) − 52.0000i − 0.200772i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 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
\(271\) −242.000 −0.892989 −0.446494 0.894786i \(-0.647328\pi\)
−0.446494 + 0.894786i \(0.647328\pi\)
\(272\) 0 0
\(273\) 132.000 0.483516
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) − 122.000i − 0.440433i −0.975451 0.220217i \(-0.929324\pi\)
0.975451 0.220217i \(-0.0706764\pi\)
\(278\) 0 0
\(279\) −414.000 −1.48387
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 458.000i 1.61837i 0.587551 + 0.809187i \(0.300092\pi\)
−0.587551 + 0.809187i \(0.699908\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 289.000 1.00000
\(290\) 0 0
\(291\) 6.00000i 0.0206186i
\(292\) 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
\(301\) − 44.0000i − 0.146179i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 358.000i 1.16612i 0.812428 + 0.583062i \(0.198145\pi\)
−0.812428 + 0.583062i \(0.801855\pi\)
\(308\) 0 0
\(309\) 582.000i 1.88350i
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 142.000 0.453674 0.226837 0.973933i \(-0.427162\pi\)
0.226837 + 0.973933i \(0.427162\pi\)
\(314\) 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
\(325\) 550.000i 1.69231i
\(326\) 0 0
\(327\) 642.000 1.96330
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 362.000i 1.09366i 0.837245 + 0.546828i \(0.184165\pi\)
−0.837245 + 0.546828i \(0.815835\pi\)
\(332\) 0 0
\(333\) 234.000i 0.702703i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 482.000 1.43027 0.715134 0.698988i \(-0.246366\pi\)
0.715134 + 0.698988i \(0.246366\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −188.000 −0.548105
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) − 502.000i − 1.43840i −0.694805 0.719198i \(-0.744510\pi\)
0.694805 0.719198i \(-0.255490\pi\)
\(350\) 0 0
\(351\) −594.000 −1.69231
\(352\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) −315.000 −0.872576
\(362\) 0 0
\(363\) − 363.000i − 1.00000i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 718.000 1.95640 0.978202 0.207657i \(-0.0665839\pi\)
0.978202 + 0.207657i \(0.0665839\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) − 698.000i − 1.87131i −0.352911 0.935657i \(-0.614808\pi\)
0.352911 0.935657i \(-0.385192\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) − 694.000i − 1.83113i −0.402165 0.915567i \(-0.631742\pi\)
0.402165 0.915567i \(-0.368258\pi\)
\(380\) 0 0
\(381\) − 438.000i − 1.14961i
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 198.000i 0.511628i
\(388\) 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
\(397\) 362.000i 0.911839i 0.890021 + 0.455919i \(0.150689\pi\)
−0.890021 + 0.455919i \(0.849311\pi\)
\(398\) 0 0
\(399\) 156.000 0.390977
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) − 1012.00i − 2.51117i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −626.000 −1.53056 −0.765281 0.643696i \(-0.777400\pi\)
−0.765281 + 0.643696i \(0.777400\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 66.0000 0.158273
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 358.000i 0.850356i 0.905110 + 0.425178i \(0.139789\pi\)
−0.905110 + 0.425178i \(0.860211\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 148.000i 0.346604i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) −862.000 −1.99076 −0.995381 0.0960028i \(-0.969394\pi\)
−0.995381 + 0.0960028i \(0.969394\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −94.0000 −0.214123 −0.107062 0.994252i \(-0.534144\pi\)
−0.107062 + 0.994252i \(0.534144\pi\)
\(440\) 0 0
\(441\) 405.000 0.918367
\(442\) 0 0
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 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
\(453\) − 858.000i − 1.89404i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 814.000 1.78118 0.890591 0.454805i \(-0.150291\pi\)
0.890591 + 0.454805i \(0.150291\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 526.000 1.13607 0.568035 0.823005i \(-0.307704\pi\)
0.568035 + 0.823005i \(0.307704\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) − 244.000i − 0.520256i
\(470\) 0 0
\(471\) 354.000 0.751592
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 650.000i 1.36842i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) −572.000 −1.18919
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 962.000 1.97536 0.987680 0.156489i \(-0.0500176\pi\)
0.987680 + 0.156489i \(0.0500176\pi\)
\(488\) 0 0
\(489\) −786.000 −1.60736
\(490\) 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
\(499\) − 26.0000i − 0.0521042i −0.999661 0.0260521i \(-0.991706\pi\)
0.999661 0.0260521i \(-0.00829358\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) − 945.000i − 1.86391i
\(508\) 0 0
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 92.0000 0.180039
\(512\) 0 0
\(513\) −702.000 −1.36842
\(514\) 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
\(523\) − 982.000i − 1.87763i −0.344423 0.938815i \(-0.611925\pi\)
0.344423 0.938815i \(-0.388075\pi\)
\(524\) 0 0
\(525\) − 150.000i − 0.285714i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 529.000 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
\(541\) 1034.00i 1.91128i 0.294545 + 0.955638i \(0.404832\pi\)
−0.294545 + 0.955638i \(0.595168\pi\)
\(542\) 0 0
\(543\) 942.000 1.73481
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) − 506.000i − 0.925046i −0.886607 0.462523i \(-0.846944\pi\)
0.886607 0.462523i \(-0.153056\pi\)
\(548\) 0 0
\(549\) − 666.000i − 1.21311i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 284.000 0.513562
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) −484.000 −0.865832
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 162.000 0.285714
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) − 886.000i − 1.55166i −0.630940 0.775832i \(-0.717330\pi\)
0.630940 0.775832i \(-0.282670\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 962.000 1.66724 0.833622 0.552335i \(-0.186263\pi\)
0.833622 + 0.552335i \(0.186263\pi\)
\(578\) 0 0
\(579\) − 1146.00i − 1.97927i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) − 1196.00i − 2.03056i
\(590\) 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
\(597\) 1158.00i 1.93970i
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 526.000 0.875208 0.437604 0.899168i \(-0.355827\pi\)
0.437604 + 0.899168i \(0.355827\pi\)
\(602\) 0 0
\(603\) 1098.00i 1.82090i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 814.000 1.34102 0.670511 0.741900i \(-0.266075\pi\)
0.670511 + 0.741900i \(0.266075\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 1126.00i 1.83687i 0.395574 + 0.918434i \(0.370546\pi\)
−0.395574 + 0.918434i \(0.629454\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) − 214.000i − 0.345719i −0.984947 0.172859i \(-0.944699\pi\)
0.984947 0.172859i \(-0.0553006\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 625.000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 674.000 1.06815 0.534073 0.845438i \(-0.320661\pi\)
0.534073 + 0.845438i \(0.320661\pi\)
\(632\) 0 0
\(633\) −498.000 −0.786730
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 990.000i 1.55416i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) − 314.000i − 0.488336i −0.969733 0.244168i \(-0.921485\pi\)
0.969733 0.244168i \(-0.0785148\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 276.000i 0.423963i
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −414.000 −0.630137
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) − 122.000i − 0.184569i −0.995733 0.0922844i \(-0.970583\pi\)
0.995733 0.0922844i \(-0.0294169\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) − 1014.00i − 1.51570i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1154.00 1.71471 0.857355 0.514725i \(-0.172106\pi\)
0.857355 + 0.514725i \(0.172106\pi\)
\(674\) 0 0
\(675\) 675.000i 1.00000i
\(676\) 0 0
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 4.00000 0.00589102
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 78.0000 0.113537
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 1318.00i 1.90738i 0.300790 + 0.953690i \(0.402750\pi\)
−0.300790 + 0.953690i \(0.597250\pi\)
\(692\) 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
\(703\) −676.000 −0.961593
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 934.000i 1.31735i 0.752428 + 0.658674i \(0.228882\pi\)
−0.752428 + 0.658674i \(0.771118\pi\)
\(710\) 0 0
\(711\) −1278.00 −1.79747
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 388.000 0.538141
\(722\) 0 0
\(723\) − 858.000i − 1.18672i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 482.000 0.662999 0.331499 0.943455i \(-0.392446\pi\)
0.331499 + 0.943455i \(0.392446\pi\)
\(728\) 0 0
\(729\) −729.000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 1034.00i 1.41064i 0.708888 + 0.705321i \(0.249197\pi\)
−0.708888 + 0.705321i \(0.750803\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 1222.00i 1.65359i 0.562506 + 0.826793i \(0.309837\pi\)
−0.562506 + 0.826793i \(0.690163\pi\)
\(740\) 0 0
\(741\) − 1716.00i − 2.31579i
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −1202.00 −1.60053 −0.800266 0.599645i \(-0.795309\pi\)
−0.800266 + 0.599645i \(0.795309\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 838.000i 1.10700i 0.832849 + 0.553501i \(0.186708\pi\)
−0.832849 + 0.553501i \(0.813292\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) − 428.000i − 0.560944i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −1534.00 −1.99480 −0.997399 0.0720749i \(-0.977038\pi\)
−0.997399 + 0.0720749i \(0.977038\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) −1150.00 −1.48387
\(776\) 0 0
\(777\) 156.000 0.200772
\(778\) 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
\(787\) − 1562.00i − 1.98475i −0.123246 0.992376i \(-0.539331\pi\)
0.123246 0.992376i \(-0.460669\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 1628.00 2.05296
\(794\) 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
\(811\) 1514.00i 1.86683i 0.358797 + 0.933416i \(0.383187\pi\)
−0.358797 + 0.933416i \(0.616813\pi\)
\(812\) 0 0
\(813\) − 726.000i − 0.892989i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −572.000 −0.700122
\(818\) 0 0
\(819\) 396.000i 0.483516i
\(820\) 0 0
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) 1058.00 1.28554 0.642770 0.766059i \(-0.277785\pi\)
0.642770 + 0.766059i \(0.277785\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 458.000i 0.552473i 0.961090 + 0.276236i \(0.0890873\pi\)
−0.961090 + 0.276236i \(0.910913\pi\)
\(830\) 0 0
\(831\) 366.000 0.440433
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) − 1242.00i − 1.48387i
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) −841.000 −1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −242.000 −0.285714
\(848\) 0 0
\(849\) −1374.00 −1.61837
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) − 1658.00i − 1.94373i −0.235543 0.971864i \(-0.575687\pi\)
0.235543 0.971864i \(-0.424313\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 1418.00i 1.65076i 0.564580 + 0.825378i \(0.309038\pi\)
−0.564580 + 0.825378i \(0.690962\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 867.000i 1.00000i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −2684.00 −3.08152
\(872\) 0 0
\(873\) −18.0000 −0.0206186
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) − 598.000i − 0.681870i −0.940087 0.340935i \(-0.889256\pi\)
0.940087 0.340935i \(-0.110744\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 1702.00i 1.92752i 0.266771 + 0.963760i \(0.414043\pi\)
−0.266771 + 0.963760i \(0.585957\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) −292.000 −0.328459
\(890\) 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
\(903\) 132.000 0.146179
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) − 214.000i − 0.235943i −0.993017 0.117971i \(-0.962361\pi\)
0.993017 0.117971i \(-0.0376391\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 866.000 0.942329 0.471164 0.882045i \(-0.343834\pi\)
0.471164 + 0.882045i \(0.343834\pi\)
\(920\) 0 0
\(921\) −1074.00 −1.16612
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 650.000i 0.702703i
\(926\) 0 0
\(927\) −1746.00 −1.88350
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 1170.00i 1.25671i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 1198.00 1.27855 0.639274 0.768979i \(-0.279235\pi\)
0.639274 + 0.768979i \(0.279235\pi\)
\(938\) 0 0
\(939\) 426.000i 0.453674i
\(940\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 0 0
\(949\) − 1012.00i − 1.06639i
\(950\) 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
\(961\) 1155.00 1.20187
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −1534.00 −1.58635 −0.793175 0.608994i \(-0.791573\pi\)
−0.793175 + 0.608994i \(0.791573\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) − 44.0000i − 0.0452210i
\(974\) 0 0
\(975\) −1650.00 −1.69231
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 1926.00i 1.96330i
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 46.0000 0.0464178 0.0232089 0.999731i \(-0.492612\pi\)
0.0232089 + 0.999731i \(0.492612\pi\)
\(992\) 0 0
\(993\) −1086.00 −1.09366
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 1894.00i 1.89970i 0.312707 + 0.949850i \(0.398764\pi\)
−0.312707 + 0.949850i \(0.601236\pi\)
\(998\) 0 0
\(999\) −702.000 −0.702703
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 768.3.h.b.641.2 2
3.2 odd 2 CM 768.3.h.b.641.2 2
4.3 odd 2 768.3.h.a.641.1 2
8.3 odd 2 768.3.h.a.641.2 2
8.5 even 2 inner 768.3.h.b.641.1 2
12.11 even 2 768.3.h.a.641.1 2
16.3 odd 4 192.3.e.b.65.1 1
16.5 even 4 48.3.e.a.17.1 1
16.11 odd 4 12.3.c.a.5.1 1
16.13 even 4 192.3.e.a.65.1 1
24.5 odd 2 inner 768.3.h.b.641.1 2
24.11 even 2 768.3.h.a.641.2 2
48.5 odd 4 48.3.e.a.17.1 1
48.11 even 4 12.3.c.a.5.1 1
48.29 odd 4 192.3.e.a.65.1 1
48.35 even 4 192.3.e.b.65.1 1
80.27 even 4 300.3.b.a.149.2 2
80.37 odd 4 1200.3.c.c.449.1 2
80.43 even 4 300.3.b.a.149.1 2
80.53 odd 4 1200.3.c.c.449.2 2
80.59 odd 4 300.3.g.b.101.1 1
80.69 even 4 1200.3.l.b.401.1 1
112.11 odd 12 588.3.p.c.569.1 2
112.27 even 4 588.3.c.c.197.1 1
112.59 even 12 588.3.p.b.569.1 2
112.75 even 12 588.3.p.b.557.1 2
112.107 odd 12 588.3.p.c.557.1 2
144.5 odd 12 1296.3.q.b.593.1 2
144.11 even 12 324.3.g.b.53.1 2
144.43 odd 12 324.3.g.b.53.1 2
144.59 even 12 324.3.g.b.269.1 2
144.85 even 12 1296.3.q.b.593.1 2
144.101 odd 12 1296.3.q.b.1025.1 2
144.133 even 12 1296.3.q.b.1025.1 2
144.139 odd 12 324.3.g.b.269.1 2
176.43 even 4 1452.3.e.b.485.1 1
240.53 even 4 1200.3.c.c.449.2 2
240.59 even 4 300.3.g.b.101.1 1
240.107 odd 4 300.3.b.a.149.2 2
240.149 odd 4 1200.3.l.b.401.1 1
240.197 even 4 1200.3.c.c.449.1 2
240.203 odd 4 300.3.b.a.149.1 2
336.11 even 12 588.3.p.c.569.1 2
336.59 odd 12 588.3.p.b.569.1 2
336.107 even 12 588.3.p.c.557.1 2
336.251 odd 4 588.3.c.c.197.1 1
336.299 odd 12 588.3.p.b.557.1 2
528.395 odd 4 1452.3.e.b.485.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
12.3.c.a.5.1 1 16.11 odd 4
12.3.c.a.5.1 1 48.11 even 4
48.3.e.a.17.1 1 16.5 even 4
48.3.e.a.17.1 1 48.5 odd 4
192.3.e.a.65.1 1 16.13 even 4
192.3.e.a.65.1 1 48.29 odd 4
192.3.e.b.65.1 1 16.3 odd 4
192.3.e.b.65.1 1 48.35 even 4
300.3.b.a.149.1 2 80.43 even 4
300.3.b.a.149.1 2 240.203 odd 4
300.3.b.a.149.2 2 80.27 even 4
300.3.b.a.149.2 2 240.107 odd 4
300.3.g.b.101.1 1 80.59 odd 4
300.3.g.b.101.1 1 240.59 even 4
324.3.g.b.53.1 2 144.11 even 12
324.3.g.b.53.1 2 144.43 odd 12
324.3.g.b.269.1 2 144.59 even 12
324.3.g.b.269.1 2 144.139 odd 12
588.3.c.c.197.1 1 112.27 even 4
588.3.c.c.197.1 1 336.251 odd 4
588.3.p.b.557.1 2 112.75 even 12
588.3.p.b.557.1 2 336.299 odd 12
588.3.p.b.569.1 2 112.59 even 12
588.3.p.b.569.1 2 336.59 odd 12
588.3.p.c.557.1 2 112.107 odd 12
588.3.p.c.557.1 2 336.107 even 12
588.3.p.c.569.1 2 112.11 odd 12
588.3.p.c.569.1 2 336.11 even 12
768.3.h.a.641.1 2 4.3 odd 2
768.3.h.a.641.1 2 12.11 even 2
768.3.h.a.641.2 2 8.3 odd 2
768.3.h.a.641.2 2 24.11 even 2
768.3.h.b.641.1 2 8.5 even 2 inner
768.3.h.b.641.1 2 24.5 odd 2 inner
768.3.h.b.641.2 2 1.1 even 1 trivial
768.3.h.b.641.2 2 3.2 odd 2 CM
1200.3.c.c.449.1 2 80.37 odd 4
1200.3.c.c.449.1 2 240.197 even 4
1200.3.c.c.449.2 2 80.53 odd 4
1200.3.c.c.449.2 2 240.53 even 4
1200.3.l.b.401.1 1 80.69 even 4
1200.3.l.b.401.1 1 240.149 odd 4
1296.3.q.b.593.1 2 144.5 odd 12
1296.3.q.b.593.1 2 144.85 even 12
1296.3.q.b.1025.1 2 144.101 odd 12
1296.3.q.b.1025.1 2 144.133 even 12
1452.3.e.b.485.1 1 176.43 even 4
1452.3.e.b.485.1 1 528.395 odd 4