Properties

Label 1200.3.c.c.449.2
Level $1200$
Weight $3$
Character 1200.449
Analytic conductor $32.698$
Analytic rank $0$
Dimension $2$
CM discriminant -3
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1200.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(32.6976317232\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 12)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 449.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1200.449
Dual form 1200.3.c.c.449.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.00000i q^{3} +2.00000i q^{7} -9.00000 q^{9} +O(q^{10})\) \(q+3.00000i q^{3} +2.00000i q^{7} -9.00000 q^{9} -22.0000i q^{13} +26.0000 q^{19} -6.00000 q^{21} -27.0000i q^{27} +46.0000 q^{31} -26.0000i q^{37} +66.0000 q^{39} +22.0000i q^{43} +45.0000 q^{49} +78.0000i q^{57} +74.0000 q^{61} -18.0000i q^{63} +122.000i q^{67} -46.0000i q^{73} -142.000 q^{79} +81.0000 q^{81} +44.0000 q^{91} +138.000i q^{93} -2.00000i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 18q^{9} + O(q^{10}) \) \( 2q - 18q^{9} + 52q^{19} - 12q^{21} + 92q^{31} + 132q^{39} + 90q^{49} + 148q^{61} - 284q^{79} + 162q^{81} + 88q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).

\(n\) \(401\) \(577\) \(751\) \(901\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(1\)

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
\(6\) 0 0
\(7\) 2.00000i 0.285714i 0.989743 + 0.142857i \(0.0456289\pi\)
−0.989743 + 0.142857i \(0.954371\pi\)
\(8\) 0 0
\(9\) −9.00000 −1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 26.0000 1.36842 0.684211 0.729285i \(-0.260147\pi\)
0.684211 + 0.729285i \(0.260147\pi\)
\(20\) 0 0
\(21\) −6.00000 −0.285714
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) − 27.0000i − 1.00000i
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 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 \(0.0823435\pi\)
−0.966726 + 0.255814i \(0.917657\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 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
\(57\) 78.0000i 1.36842i
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 74.0000 1.21311 0.606557 0.795040i \(-0.292550\pi\)
0.606557 + 0.795040i \(0.292550\pi\)
\(62\) 0 0
\(63\) − 18.0000i − 0.285714i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 122.000i 1.82090i 0.413624 + 0.910448i \(0.364263\pi\)
−0.413624 + 0.910448i \(0.635737\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) − 46.0000i − 0.630137i −0.949069 0.315068i \(-0.897973\pi\)
0.949069 0.315068i \(-0.102027\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −142.000 −1.79747 −0.898734 0.438494i \(-0.855512\pi\)
−0.898734 + 0.438494i \(0.855512\pi\)
\(80\) 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
\(91\) 44.0000 0.483516
\(92\) 0 0
\(93\) 138.000i 1.48387i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) − 2.00000i − 0.0206186i −0.999947 0.0103093i \(-0.996718\pi\)
0.999947 0.0103093i \(-0.00328160\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) − 194.000i − 1.88350i −0.336321 0.941748i \(-0.609183\pi\)
0.336321 0.941748i \(-0.390817\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 214.000 1.96330 0.981651 0.190684i \(-0.0610707\pi\)
0.981651 + 0.190684i \(0.0610707\pi\)
\(110\) 0 0
\(111\) 78.0000 0.702703
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 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
\(127\) 146.000i 1.14961i 0.818292 + 0.574803i \(0.194921\pi\)
−0.818292 + 0.574803i \(0.805079\pi\)
\(128\) 0 0
\(129\) −66.0000 −0.511628
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 52.0000i 0.390977i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) −22.0000 −0.158273 −0.0791367 0.996864i \(-0.525216\pi\)
−0.0791367 + 0.996864i \(0.525216\pi\)
\(140\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 286.000 1.89404 0.947020 0.321175i \(-0.104078\pi\)
0.947020 + 0.321175i \(0.104078\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 118.000i 0.751592i 0.926702 + 0.375796i \(0.122631\pi\)
−0.926702 + 0.375796i \(0.877369\pi\)
\(158\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −315.000 −1.86391
\(170\) 0 0
\(171\) −234.000 −1.36842
\(172\) 0 0
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 314.000 1.73481 0.867403 0.497606i \(-0.165787\pi\)
0.867403 + 0.497606i \(0.165787\pi\)
\(182\) 0 0
\(183\) 222.000i 1.21311i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 54.0000 0.285714
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) − 382.000i − 1.97927i −0.143590 0.989637i \(-0.545865\pi\)
0.143590 0.989637i \(-0.454135\pi\)
\(194\) 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
\(211\) 166.000 0.786730 0.393365 0.919382i \(-0.371311\pi\)
0.393365 + 0.919382i \(0.371311\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 92.0000i 0.423963i
\(218\) 0 0
\(219\) 138.000 0.630137
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) − 338.000i − 1.51570i −0.652432 0.757848i \(-0.726251\pi\)
0.652432 0.757848i \(-0.273749\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) −26.0000 −0.113537 −0.0567686 0.998387i \(-0.518080\pi\)
−0.0567686 + 0.998387i \(0.518080\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 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
\(247\) − 572.000i − 2.31579i
\(248\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 52.0000 0.200772
\(260\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −242.000 −0.892989 −0.446494 0.894786i \(-0.647328\pi\)
−0.446494 + 0.894786i \(0.647328\pi\)
\(272\) 0 0
\(273\) 132.000i 0.483516i
\(274\) 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 \(-0.699908\pi\)
0.587551 0.809187i \(-0.300092\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −289.000 −1.00000
\(290\) 0 0
\(291\) 6.00000 0.0206186
\(292\) 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
\(301\) −44.0000 −0.146179
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) − 358.000i − 1.16612i −0.812428 0.583062i \(-0.801855\pi\)
0.812428 0.583062i \(-0.198145\pi\)
\(308\) 0 0
\(309\) 582.000 1.88350
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) − 142.000i − 0.453674i −0.973933 0.226837i \(-0.927162\pi\)
0.973933 0.226837i \(-0.0728385\pi\)
\(314\) 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
\(325\) 0 0
\(326\) 0 0
\(327\) 642.000i 1.96330i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −362.000 −1.09366 −0.546828 0.837245i \(-0.684165\pi\)
−0.546828 + 0.837245i \(0.684165\pi\)
\(332\) 0 0
\(333\) 234.000i 0.702703i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) − 482.000i − 1.43027i −0.698988 0.715134i \(-0.746366\pi\)
0.698988 0.715134i \(-0.253634\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 188.000i 0.548105i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 502.000 1.43840 0.719198 0.694805i \(-0.244510\pi\)
0.719198 + 0.694805i \(0.244510\pi\)
\(350\) 0 0
\(351\) −594.000 −1.69231
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 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
\(367\) − 718.000i − 1.95640i −0.207657 0.978202i \(-0.566584\pi\)
0.207657 0.978202i \(-0.433416\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 698.000i 1.87131i 0.352911 + 0.935657i \(0.385192\pi\)
−0.352911 + 0.935657i \(0.614808\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −694.000 −1.83113 −0.915567 0.402165i \(-0.868258\pi\)
−0.915567 + 0.402165i \(0.868258\pi\)
\(380\) 0 0
\(381\) −438.000 −1.14961
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) − 198.000i − 0.511628i
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 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 \(-0.849311\pi\)
0.890021 0.455919i \(-0.150689\pi\)
\(398\) 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
\(417\) − 66.0000i − 0.158273i
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −358.000 −0.850356 −0.425178 0.905110i \(-0.639789\pi\)
−0.425178 + 0.905110i \(0.639789\pi\)
\(422\) 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
\(433\) − 862.000i − 1.99076i −0.0960028 0.995381i \(-0.530606\pi\)
0.0960028 0.995381i \(-0.469394\pi\)
\(434\) 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
\(457\) 814.000i 1.78118i 0.454805 + 0.890591i \(0.349709\pi\)
−0.454805 + 0.890591i \(0.650291\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 526.000i 1.13607i 0.823005 + 0.568035i \(0.192296\pi\)
−0.823005 + 0.568035i \(0.807704\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) −244.000 −0.520256
\(470\) 0 0
\(471\) −354.000 −0.751592
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−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
\(487\) 962.000i 1.97536i 0.156489 + 0.987680i \(0.449982\pi\)
−0.156489 + 0.987680i \(0.550018\pi\)
\(488\) 0 0
\(489\) −786.000 −1.60736
\(490\) 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
\(499\) 26.0000 0.0521042 0.0260521 0.999661i \(-0.491706\pi\)
0.0260521 + 0.999661i \(0.491706\pi\)
\(500\) 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
\(507\) − 945.000i − 1.86391i
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 92.0000 0.180039
\(512\) 0 0
\(513\) − 702.000i − 1.36842i
\(514\) 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 \(0.388075\pi\)
−0.344423 + 0.938815i \(0.611925\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 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
\(541\) 1034.00 1.91128 0.955638 0.294545i \(-0.0951680\pi\)
0.955638 + 0.294545i \(0.0951680\pi\)
\(542\) 0 0
\(543\) 942.000i 1.73481i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 506.000i 0.925046i 0.886607 + 0.462523i \(0.153056\pi\)
−0.886607 + 0.462523i \(0.846944\pi\)
\(548\) 0 0
\(549\) −666.000 −1.21311
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) − 284.000i − 0.513562i
\(554\) 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
\(567\) 162.000i 0.285714i
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 886.000 1.55166 0.775832 0.630940i \(-0.217330\pi\)
0.775832 + 0.630940i \(0.217330\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) − 962.000i − 1.66724i −0.552335 0.833622i \(-0.686263\pi\)
0.552335 0.833622i \(-0.313737\pi\)
\(578\) 0 0
\(579\) 1146.00 1.97927
\(580\) 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
\(589\) 1196.00 2.03056
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 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 \(-0.644173\pi\)
−0.437604 + 0.899168i \(0.644173\pi\)
\(602\) 0 0
\(603\) − 1098.00i − 1.82090i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) − 814.000i − 1.34102i −0.741900 0.670511i \(-0.766075\pi\)
0.741900 0.670511i \(-0.233925\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) − 1126.00i − 1.83687i −0.395574 0.918434i \(-0.629454\pi\)
0.395574 0.918434i \(-0.370546\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) −214.000 −0.345719 −0.172859 0.984947i \(-0.555301\pi\)
−0.172859 + 0.984947i \(0.555301\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −674.000 −1.06815 −0.534073 0.845438i \(-0.679339\pi\)
−0.534073 + 0.845438i \(0.679339\pi\)
\(632\) 0 0
\(633\) 498.000i 0.786730i
\(634\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −276.000 −0.423963
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 414.000i 0.630137i
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 122.000 0.184569 0.0922844 0.995733i \(-0.470583\pi\)
0.0922844 + 0.995733i \(0.470583\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 1014.00 1.51570
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1154.00i 1.71471i 0.514725 + 0.857355i \(0.327894\pi\)
−0.514725 + 0.857355i \(0.672106\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 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
\(687\) − 78.0000i − 0.113537i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 1318.00 1.90738 0.953690 0.300790i \(-0.0972504\pi\)
0.953690 + 0.300790i \(0.0972504\pi\)
\(692\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) − 676.000i − 0.961593i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 934.000 1.31735 0.658674 0.752428i \(-0.271118\pi\)
0.658674 + 0.752428i \(0.271118\pi\)
\(710\) 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
\(727\) 482.000i 0.662999i 0.943455 + 0.331499i \(0.107554\pi\)
−0.943455 + 0.331499i \(0.892446\pi\)
\(728\) 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
\(739\) −1222.00 −1.65359 −0.826793 0.562506i \(-0.809837\pi\)
−0.826793 + 0.562506i \(0.809837\pi\)
\(740\) 0 0
\(741\) 1716.00 2.31579
\(742\) 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
\(751\) −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 \(-0.0229621\pi\)
0.997399 + 0.0720749i \(0.0229621\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 156.000i 0.200772i
\(778\) 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 \(0.460669\pi\)
−0.123246 + 0.992376i \(0.539331\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) − 1628.00i − 2.05296i
\(794\) 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
\(811\) −1514.00 −1.86683 −0.933416 0.358797i \(-0.883187\pi\)
−0.933416 + 0.358797i \(0.883187\pi\)
\(812\) 0 0
\(813\) − 726.000i − 0.892989i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 572.000i 0.700122i
\(818\) 0 0
\(819\) −396.000 −0.483516
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) − 1058.00i − 1.28554i −0.766059 0.642770i \(-0.777785\pi\)
0.766059 0.642770i \(-0.222215\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) −458.000 −0.552473 −0.276236 0.961090i \(-0.589087\pi\)
−0.276236 + 0.961090i \(0.589087\pi\)
\(830\) 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
\(847\) 242.000i 0.285714i
\(848\) 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 \(0.424313\pi\)
−0.235543 + 0.971864i \(0.575687\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) 1418.00 1.65076 0.825378 0.564580i \(-0.190962\pi\)
0.825378 + 0.564580i \(0.190962\pi\)
\(860\) 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
\(867\) − 867.000i − 1.00000i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 2684.00 3.08152
\(872\) 0 0
\(873\) 18.0000i 0.0206186i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 598.000i 0.681870i 0.940087 + 0.340935i \(0.110744\pi\)
−0.940087 + 0.340935i \(0.889256\pi\)
\(878\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 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
\(903\) − 132.000i − 0.146179i
\(904\) 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
\(925\) 0 0
\(926\) 0 0
\(927\) 1746.00i 1.88350i
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 1170.00 1.25671
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 1198.00i 1.27855i 0.768979 + 0.639274i \(0.220765\pi\)
−0.768979 + 0.639274i \(0.779235\pi\)
\(938\) 0 0
\(939\) 426.000 0.453674
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 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
\(949\) −1012.00 −1.06639
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 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
\(967\) − 1534.00i − 1.58635i −0.608994 0.793175i \(-0.708427\pi\)
0.608994 0.793175i \(-0.291573\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) − 44.0000i − 0.0452210i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −1926.00 −1.96330
\(982\) 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
\(991\) 46.0000 0.0464178 0.0232089 0.999731i \(-0.492612\pi\)
0.0232089 + 0.999731i \(0.492612\pi\)
\(992\) 0 0
\(993\) − 1086.00i − 1.09366i
\(994\) 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 1200.3.c.c.449.2 2
3.2 odd 2 CM 1200.3.c.c.449.2 2
4.3 odd 2 300.3.b.a.149.1 2
5.2 odd 4 48.3.e.a.17.1 1
5.3 odd 4 1200.3.l.b.401.1 1
5.4 even 2 inner 1200.3.c.c.449.1 2
12.11 even 2 300.3.b.a.149.1 2
15.2 even 4 48.3.e.a.17.1 1
15.8 even 4 1200.3.l.b.401.1 1
15.14 odd 2 inner 1200.3.c.c.449.1 2
20.3 even 4 300.3.g.b.101.1 1
20.7 even 4 12.3.c.a.5.1 1
20.19 odd 2 300.3.b.a.149.2 2
40.27 even 4 192.3.e.b.65.1 1
40.37 odd 4 192.3.e.a.65.1 1
45.2 even 12 1296.3.q.b.1025.1 2
45.7 odd 12 1296.3.q.b.1025.1 2
45.22 odd 12 1296.3.q.b.593.1 2
45.32 even 12 1296.3.q.b.593.1 2
60.23 odd 4 300.3.g.b.101.1 1
60.47 odd 4 12.3.c.a.5.1 1
60.59 even 2 300.3.b.a.149.2 2
80.27 even 4 768.3.h.a.641.2 2
80.37 odd 4 768.3.h.b.641.1 2
80.67 even 4 768.3.h.a.641.1 2
80.77 odd 4 768.3.h.b.641.2 2
120.77 even 4 192.3.e.a.65.1 1
120.107 odd 4 192.3.e.b.65.1 1
140.27 odd 4 588.3.c.c.197.1 1
140.47 odd 12 588.3.p.b.557.1 2
140.67 even 12 588.3.p.c.569.1 2
140.87 odd 12 588.3.p.b.569.1 2
140.107 even 12 588.3.p.c.557.1 2
180.7 even 12 324.3.g.b.53.1 2
180.47 odd 12 324.3.g.b.53.1 2
180.67 even 12 324.3.g.b.269.1 2
180.167 odd 12 324.3.g.b.269.1 2
220.87 odd 4 1452.3.e.b.485.1 1
240.77 even 4 768.3.h.b.641.2 2
240.107 odd 4 768.3.h.a.641.2 2
240.197 even 4 768.3.h.b.641.1 2
240.227 odd 4 768.3.h.a.641.1 2
420.47 even 12 588.3.p.b.557.1 2
420.107 odd 12 588.3.p.c.557.1 2
420.167 even 4 588.3.c.c.197.1 1
420.227 even 12 588.3.p.b.569.1 2
420.347 odd 12 588.3.p.c.569.1 2
660.527 even 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 20.7 even 4
12.3.c.a.5.1 1 60.47 odd 4
48.3.e.a.17.1 1 5.2 odd 4
48.3.e.a.17.1 1 15.2 even 4
192.3.e.a.65.1 1 40.37 odd 4
192.3.e.a.65.1 1 120.77 even 4
192.3.e.b.65.1 1 40.27 even 4
192.3.e.b.65.1 1 120.107 odd 4
300.3.b.a.149.1 2 4.3 odd 2
300.3.b.a.149.1 2 12.11 even 2
300.3.b.a.149.2 2 20.19 odd 2
300.3.b.a.149.2 2 60.59 even 2
300.3.g.b.101.1 1 20.3 even 4
300.3.g.b.101.1 1 60.23 odd 4
324.3.g.b.53.1 2 180.7 even 12
324.3.g.b.53.1 2 180.47 odd 12
324.3.g.b.269.1 2 180.67 even 12
324.3.g.b.269.1 2 180.167 odd 12
588.3.c.c.197.1 1 140.27 odd 4
588.3.c.c.197.1 1 420.167 even 4
588.3.p.b.557.1 2 140.47 odd 12
588.3.p.b.557.1 2 420.47 even 12
588.3.p.b.569.1 2 140.87 odd 12
588.3.p.b.569.1 2 420.227 even 12
588.3.p.c.557.1 2 140.107 even 12
588.3.p.c.557.1 2 420.107 odd 12
588.3.p.c.569.1 2 140.67 even 12
588.3.p.c.569.1 2 420.347 odd 12
768.3.h.a.641.1 2 80.67 even 4
768.3.h.a.641.1 2 240.227 odd 4
768.3.h.a.641.2 2 80.27 even 4
768.3.h.a.641.2 2 240.107 odd 4
768.3.h.b.641.1 2 80.37 odd 4
768.3.h.b.641.1 2 240.197 even 4
768.3.h.b.641.2 2 80.77 odd 4
768.3.h.b.641.2 2 240.77 even 4
1200.3.c.c.449.1 2 5.4 even 2 inner
1200.3.c.c.449.1 2 15.14 odd 2 inner
1200.3.c.c.449.2 2 1.1 even 1 trivial
1200.3.c.c.449.2 2 3.2 odd 2 CM
1200.3.l.b.401.1 1 5.3 odd 4
1200.3.l.b.401.1 1 15.8 even 4
1296.3.q.b.593.1 2 45.22 odd 12
1296.3.q.b.593.1 2 45.32 even 12
1296.3.q.b.1025.1 2 45.2 even 12
1296.3.q.b.1025.1 2 45.7 odd 12
1452.3.e.b.485.1 1 220.87 odd 4
1452.3.e.b.485.1 1 660.527 even 4