Properties

Label 900.3.f.b.199.2
Level $900$
Weight $3$
Character 900.199
Analytic conductor $24.523$
Analytic rank $0$
Dimension $2$
CM discriminant -4
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.5232237924\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 199.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 900.199
Dual form 900.3.f.b.199.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000i q^{2} -4.00000 q^{4} -8.00000i q^{8} +O(q^{10})\) \(q+2.00000i q^{2} -4.00000 q^{4} -8.00000i q^{8} -10.0000i q^{13} +16.0000 q^{16} +16.0000i q^{17} +20.0000 q^{26} +40.0000 q^{29} +32.0000i q^{32} -32.0000 q^{34} +70.0000i q^{37} +80.0000 q^{41} -49.0000 q^{49} +40.0000i q^{52} +56.0000i q^{53} +80.0000i q^{58} -22.0000 q^{61} -64.0000 q^{64} -64.0000i q^{68} +110.000i q^{73} -140.000 q^{74} +160.000i q^{82} +160.000 q^{89} +130.000i q^{97} -98.0000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 8q^{4} + O(q^{10}) \) \( 2q - 8q^{4} + 32q^{16} + 40q^{26} + 80q^{29} - 64q^{34} + 160q^{41} - 98q^{49} - 44q^{61} - 128q^{64} - 280q^{74} + 320q^{89} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(451\) \(577\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 1.00000i
\(3\) 0 0
\(4\) −4.00000 −1.00000
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) − 8.00000i − 1.00000i
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) − 10.0000i − 0.769231i −0.923077 0.384615i \(-0.874334\pi\)
0.923077 0.384615i \(-0.125666\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 16.0000 1.00000
\(17\) 16.0000i 0.941176i 0.882353 + 0.470588i \(0.155958\pi\)
−0.882353 + 0.470588i \(0.844042\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 20.0000 0.769231
\(27\) 0 0
\(28\) 0 0
\(29\) 40.0000 1.37931 0.689655 0.724138i \(-0.257762\pi\)
0.689655 + 0.724138i \(0.257762\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 32.0000i 1.00000i
\(33\) 0 0
\(34\) −32.0000 −0.941176
\(35\) 0 0
\(36\) 0 0
\(37\) 70.0000i 1.89189i 0.324324 + 0.945946i \(0.394863\pi\)
−0.324324 + 0.945946i \(0.605137\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 80.0000 1.95122 0.975610 0.219512i \(-0.0704466\pi\)
0.975610 + 0.219512i \(0.0704466\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −49.0000 −1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 40.0000i 0.769231i
\(53\) 56.0000i 1.05660i 0.849057 + 0.528302i \(0.177171\pi\)
−0.849057 + 0.528302i \(0.822829\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 80.0000i 1.37931i
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −22.0000 −0.360656 −0.180328 0.983607i \(-0.557716\pi\)
−0.180328 + 0.983607i \(0.557716\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −64.0000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) − 64.0000i − 0.941176i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 110.000i 1.50685i 0.657534 + 0.753425i \(0.271599\pi\)
−0.657534 + 0.753425i \(0.728401\pi\)
\(74\) −140.000 −1.89189
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 160.000i 1.95122i
\(83\) 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
\(89\) 160.000 1.79775 0.898876 0.438202i \(-0.144385\pi\)
0.898876 + 0.438202i \(0.144385\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 130.000i 1.34021i 0.742268 + 0.670103i \(0.233750\pi\)
−0.742268 + 0.670103i \(0.766250\pi\)
\(98\) − 98.0000i − 1.00000i
\(99\) 0 0
\(100\) 0 0
\(101\) −40.0000 −0.396040 −0.198020 0.980198i \(-0.563451\pi\)
−0.198020 + 0.980198i \(0.563451\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) −80.0000 −0.769231
\(105\) 0 0
\(106\) −112.000 −1.05660
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −182.000 −1.66972 −0.834862 0.550459i \(-0.814453\pi\)
−0.834862 + 0.550459i \(0.814453\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 224.000i 1.98230i 0.132743 + 0.991150i \(0.457621\pi\)
−0.132743 + 0.991150i \(0.542379\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −160.000 −1.37931
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 121.000 1.00000
\(122\) − 44.0000i − 0.360656i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) − 128.000i − 1.00000i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 128.000 0.941176
\(137\) − 176.000i − 1.28467i −0.766423 0.642336i \(-0.777965\pi\)
0.766423 0.642336i \(-0.222035\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) −220.000 −1.50685
\(147\) 0 0
\(148\) − 280.000i − 1.89189i
\(149\) 280.000 1.87919 0.939597 0.342282i \(-0.111200\pi\)
0.939597 + 0.342282i \(0.111200\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) − 170.000i − 1.08280i −0.840764 0.541401i \(-0.817894\pi\)
0.840764 0.541401i \(-0.182106\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) −320.000 −1.95122
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 69.0000 0.408284
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 104.000i 0.601156i 0.953757 + 0.300578i \(0.0971796\pi\)
−0.953757 + 0.300578i \(0.902820\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 320.000i 1.79775i
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 38.0000 0.209945 0.104972 0.994475i \(-0.466525\pi\)
0.104972 + 0.994475i \(0.466525\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) − 190.000i − 0.984456i −0.870466 0.492228i \(-0.836183\pi\)
0.870466 0.492228i \(-0.163817\pi\)
\(194\) −260.000 −1.34021
\(195\) 0 0
\(196\) 196.000 1.00000
\(197\) − 56.0000i − 0.284264i −0.989848 0.142132i \(-0.954604\pi\)
0.989848 0.142132i \(-0.0453957\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) − 80.0000i − 0.396040i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) − 160.000i − 0.769231i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) − 224.000i − 1.05660i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) − 364.000i − 1.66972i
\(219\) 0 0
\(220\) 0 0
\(221\) 160.000 0.723982
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −448.000 −1.98230
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 442.000 1.93013 0.965066 0.262009i \(-0.0843849\pi\)
0.965066 + 0.262009i \(0.0843849\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) − 320.000i − 1.37931i
\(233\) 416.000i 1.78541i 0.450644 + 0.892704i \(0.351194\pi\)
−0.450644 + 0.892704i \(0.648806\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −418.000 −1.73444 −0.867220 0.497925i \(-0.834095\pi\)
−0.867220 + 0.497925i \(0.834095\pi\)
\(242\) 242.000i 1.00000i
\(243\) 0 0
\(244\) 88.0000 0.360656
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 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
\(256\) 256.000 1.00000
\(257\) 64.0000i 0.249027i 0.992218 + 0.124514i \(0.0397370\pi\)
−0.992218 + 0.124514i \(0.960263\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 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
\(269\) 520.000 1.93309 0.966543 0.256506i \(-0.0825712\pi\)
0.966543 + 0.256506i \(0.0825712\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 256.000i 0.941176i
\(273\) 0 0
\(274\) 352.000 1.28467
\(275\) 0 0
\(276\) 0 0
\(277\) − 230.000i − 0.830325i −0.909747 0.415162i \(-0.863725\pi\)
0.909747 0.415162i \(-0.136275\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 320.000 1.13879 0.569395 0.822064i \(-0.307178\pi\)
0.569395 + 0.822064i \(0.307178\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 33.0000 0.114187
\(290\) 0 0
\(291\) 0 0
\(292\) − 440.000i − 1.50685i
\(293\) − 136.000i − 0.464164i −0.972696 0.232082i \(-0.925446\pi\)
0.972696 0.232082i \(-0.0745537\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 560.000 1.89189
\(297\) 0 0
\(298\) 560.000i 1.87919i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 50.0000i 0.159744i 0.996805 + 0.0798722i \(0.0254512\pi\)
−0.996805 + 0.0798722i \(0.974549\pi\)
\(314\) 340.000 1.08280
\(315\) 0 0
\(316\) 0 0
\(317\) 616.000i 1.94322i 0.236593 + 0.971609i \(0.423969\pi\)
−0.236593 + 0.971609i \(0.576031\pi\)
\(318\) 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
\(327\) 0 0
\(328\) − 640.000i − 1.95122i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) − 350.000i − 1.03858i −0.854599 0.519288i \(-0.826197\pi\)
0.854599 0.519288i \(-0.173803\pi\)
\(338\) 138.000i 0.408284i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −208.000 −0.601156
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 598.000 1.71347 0.856734 0.515759i \(-0.172490\pi\)
0.856734 + 0.515759i \(0.172490\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 544.000i − 1.54108i −0.637394 0.770538i \(-0.719988\pi\)
0.637394 0.770538i \(-0.280012\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −640.000 −1.79775
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 361.000 1.00000
\(362\) 76.0000i 0.209945i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) − 550.000i − 1.47453i −0.675603 0.737265i \(-0.736117\pi\)
0.675603 0.737265i \(-0.263883\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 400.000i − 1.06101i
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 380.000 0.984456
\(387\) 0 0
\(388\) − 520.000i − 1.34021i
\(389\) −680.000 −1.74807 −0.874036 0.485861i \(-0.838506\pi\)
−0.874036 + 0.485861i \(0.838506\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 392.000i 1.00000i
\(393\) 0 0
\(394\) 112.000 0.284264
\(395\) 0 0
\(396\) 0 0
\(397\) − 650.000i − 1.63728i −0.574307 0.818640i \(-0.694729\pi\)
0.574307 0.818640i \(-0.305271\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 80.0000 0.199501 0.0997506 0.995012i \(-0.468195\pi\)
0.0997506 + 0.995012i \(0.468195\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 160.000 0.396040
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −782.000 −1.91198 −0.955990 0.293399i \(-0.905214\pi\)
−0.955990 + 0.293399i \(0.905214\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 320.000 0.769231
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −58.0000 −0.137767 −0.0688836 0.997625i \(-0.521944\pi\)
−0.0688836 + 0.997625i \(0.521944\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 448.000 1.05660
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 290.000i 0.669746i 0.942263 + 0.334873i \(0.108693\pi\)
−0.942263 + 0.334873i \(0.891307\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 728.000 1.66972
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 320.000i 0.723982i
\(443\) 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
\(449\) −560.000 −1.24722 −0.623608 0.781737i \(-0.714334\pi\)
−0.623608 + 0.781737i \(0.714334\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) − 896.000i − 1.98230i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 850.000i 1.85996i 0.367615 + 0.929978i \(0.380174\pi\)
−0.367615 + 0.929978i \(0.619826\pi\)
\(458\) 884.000i 1.93013i
\(459\) 0 0
\(460\) 0 0
\(461\) −760.000 −1.64859 −0.824295 0.566161i \(-0.808428\pi\)
−0.824295 + 0.566161i \(0.808428\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 640.000 1.37931
\(465\) 0 0
\(466\) −832.000 −1.78541
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 700.000 1.45530
\(482\) − 836.000i − 1.73444i
\(483\) 0 0
\(484\) −484.000 −1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 176.000i 0.360656i
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 640.000i 1.29817i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 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
\(507\) 0 0
\(508\) 0 0
\(509\) −440.000 −0.864440 −0.432220 0.901768i \(-0.642270\pi\)
−0.432220 + 0.901768i \(0.642270\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000i 1.00000i
\(513\) 0 0
\(514\) −128.000 −0.249027
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −880.000 −1.68906 −0.844530 0.535509i \(-0.820120\pi\)
−0.844530 + 0.535509i \(0.820120\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 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
\(533\) − 800.000i − 1.50094i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 1040.00i 1.93309i
\(539\) 0 0
\(540\) 0 0
\(541\) −682.000 −1.26063 −0.630314 0.776340i \(-0.717074\pi\)
−0.630314 + 0.776340i \(0.717074\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −512.000 −0.941176
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 704.000i 1.28467i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 460.000 0.830325
\(555\) 0 0
\(556\) 0 0
\(557\) − 1064.00i − 1.91023i −0.296230 0.955117i \(-0.595729\pi\)
0.296230 0.955117i \(-0.404271\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 640.000i 1.13879i
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1040.00 −1.82777 −0.913884 0.405975i \(-0.866932\pi\)
−0.913884 + 0.405975i \(0.866932\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 1150.00i 1.99307i 0.0831889 + 0.996534i \(0.473490\pi\)
−0.0831889 + 0.996534i \(0.526510\pi\)
\(578\) 66.0000i 0.114187i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 880.000 1.50685
\(585\) 0 0
\(586\) 272.000 0.464164
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1120.00i 1.89189i
\(593\) − 736.000i − 1.24115i −0.784148 0.620573i \(-0.786900\pi\)
0.784148 0.620573i \(-0.213100\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1120.00 −1.87919
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) −1102.00 −1.83361 −0.916805 0.399334i \(-0.869241\pi\)
−0.916805 + 0.399334i \(0.869241\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) − 70.0000i − 0.114192i −0.998369 0.0570962i \(-0.981816\pi\)
0.998369 0.0570962i \(-0.0181842\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1216.00i 1.97083i 0.170178 + 0.985413i \(0.445566\pi\)
−0.170178 + 0.985413i \(0.554434\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) −100.000 −0.159744
\(627\) 0 0
\(628\) 680.000i 1.08280i
\(629\) −1120.00 −1.78060
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −1232.00 −1.94322
\(635\) 0 0
\(636\) 0 0
\(637\) 490.000i 0.769231i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −400.000 −0.624025 −0.312012 0.950078i \(-0.601003\pi\)
−0.312012 + 0.950078i \(0.601003\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 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
\(651\) 0 0
\(652\) 0 0
\(653\) − 1144.00i − 1.75191i −0.482389 0.875957i \(-0.660231\pi\)
0.482389 0.875957i \(-0.339769\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1280.00 1.95122
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 1178.00 1.78215 0.891074 0.453858i \(-0.149953\pi\)
0.891074 + 0.453858i \(0.149953\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 770.000i 1.14413i 0.820208 + 0.572065i \(0.193858\pi\)
−0.820208 + 0.572065i \(0.806142\pi\)
\(674\) 700.000 1.03858
\(675\) 0 0
\(676\) −276.000 −0.408284
\(677\) − 104.000i − 0.153619i −0.997046 0.0768095i \(-0.975527\pi\)
0.997046 0.0768095i \(-0.0244733\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 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
\(687\) 0 0
\(688\) 0 0
\(689\) 560.000 0.812772
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) − 416.000i − 0.601156i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 1280.00i 1.83644i
\(698\) 1196.00i 1.71347i
\(699\) 0 0
\(700\) 0 0
\(701\) −520.000 −0.741797 −0.370899 0.928673i \(-0.620950\pi\)
−0.370899 + 0.928673i \(0.620950\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 1088.00 1.54108
\(707\) 0 0
\(708\) 0 0
\(709\) −518.000 −0.730606 −0.365303 0.930889i \(-0.619035\pi\)
−0.365303 + 0.930889i \(0.619035\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) − 1280.00i − 1.79775i
\(713\) 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
\(721\) 0 0
\(722\) 722.000i 1.00000i
\(723\) 0 0
\(724\) −152.000 −0.209945
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) − 1450.00i − 1.97817i −0.147340 0.989086i \(-0.547071\pi\)
0.147340 0.989086i \(-0.452929\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 1100.00 1.47453
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 800.000 1.06101
\(755\) 0 0
\(756\) 0 0
\(757\) − 1190.00i − 1.57199i −0.618230 0.785997i \(-0.712150\pi\)
0.618230 0.785997i \(-0.287850\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1520.00 1.99737 0.998686 0.0512484i \(-0.0163200\pi\)
0.998686 + 0.0512484i \(0.0163200\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −962.000 −1.25098 −0.625488 0.780234i \(-0.715100\pi\)
−0.625488 + 0.780234i \(0.715100\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 760.000i 0.984456i
\(773\) 1496.00i 1.93532i 0.252264 + 0.967658i \(0.418825\pi\)
−0.252264 + 0.967658i \(0.581175\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 1040.00 1.34021
\(777\) 0 0
\(778\) − 1360.00i − 1.74807i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −784.000 −1.00000
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 224.000i 0.284264i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 220.000i 0.277427i
\(794\) 1300.00 1.63728
\(795\) 0 0
\(796\) 0 0
\(797\) 1144.00i 1.43538i 0.696361 + 0.717691i \(0.254801\pi\)
−0.696361 + 0.717691i \(0.745199\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 160.000i 0.199501i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 320.000i 0.396040i
\(809\) −560.000 −0.692213 −0.346106 0.938195i \(-0.612496\pi\)
−0.346106 + 0.938195i \(0.612496\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) − 1564.00i − 1.91198i
\(819\) 0 0
\(820\) 0 0
\(821\) 1400.00 1.70524 0.852619 0.522533i \(-0.175013\pi\)
0.852619 + 0.522533i \(0.175013\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 1258.00 1.51749 0.758745 0.651387i \(-0.225813\pi\)
0.758745 + 0.651387i \(0.225813\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 640.000i 0.769231i
\(833\) − 784.000i − 0.941176i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 759.000 0.902497
\(842\) − 116.000i − 0.137767i
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 896.000i 1.05660i
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 410.000i 0.480657i 0.970692 + 0.240328i \(0.0772551\pi\)
−0.970692 + 0.240328i \(0.922745\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 464.000i − 0.541424i −0.962660 0.270712i \(-0.912741\pi\)
0.962660 0.270712i \(-0.0872590\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 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
\(866\) −580.000 −0.669746
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 1456.00i 1.66972i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) − 1610.00i − 1.83580i −0.396807 0.917902i \(-0.629882\pi\)
0.396807 0.917902i \(-0.370118\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1600.00 −1.81612 −0.908059 0.418842i \(-0.862436\pi\)
−0.908059 + 0.418842i \(0.862436\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(884\) −640.000 −0.723982
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) − 1120.00i − 1.24722i
\(899\) 0 0
\(900\) 0 0
\(901\) −896.000 −0.994451
\(902\) 0 0
\(903\) 0 0
\(904\) 1792.00 1.98230
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −1700.00 −1.85996
\(915\) 0 0
\(916\) −1768.00 −1.93013
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) − 1520.00i − 1.64859i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 1280.00i 1.37931i
\(929\) 1840.00 1.98062 0.990312 0.138859i \(-0.0443435\pi\)
0.990312 + 0.138859i \(0.0443435\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) − 1664.00i − 1.78541i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 430.000i 0.458911i 0.973319 + 0.229456i \(0.0736946\pi\)
−0.973319 + 0.229456i \(0.926305\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1160.00 1.23273 0.616366 0.787460i \(-0.288604\pi\)
0.616366 + 0.787460i \(0.288604\pi\)
\(942\) 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
\(949\) 1100.00 1.15911
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 1456.00i − 1.52781i −0.645331 0.763903i \(-0.723280\pi\)
0.645331 0.763903i \(-0.276720\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 961.000 1.00000
\(962\) 1400.00i 1.45530i
\(963\) 0 0
\(964\) 1672.00 1.73444
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) − 968.000i − 1.00000i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −352.000 −0.360656
\(977\) 496.000i 0.507677i 0.967247 + 0.253838i \(0.0816931\pi\)
−0.967247 + 0.253838i \(0.918307\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −1280.00 −1.29817
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) − 1850.00i − 1.85557i −0.373119 0.927783i \(-0.621712\pi\)
0.373119 0.927783i \(-0.378288\pi\)
\(998\) 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 900.3.f.b.199.2 2
3.2 odd 2 900.3.f.a.199.1 2
4.3 odd 2 CM 900.3.f.b.199.2 2
5.2 odd 4 36.3.d.a.19.1 1
5.3 odd 4 900.3.c.c.451.1 1
5.4 even 2 inner 900.3.f.b.199.1 2
12.11 even 2 900.3.f.a.199.1 2
15.2 even 4 36.3.d.b.19.1 yes 1
15.8 even 4 900.3.c.b.451.1 1
15.14 odd 2 900.3.f.a.199.2 2
20.3 even 4 900.3.c.c.451.1 1
20.7 even 4 36.3.d.a.19.1 1
20.19 odd 2 inner 900.3.f.b.199.1 2
40.27 even 4 576.3.g.a.127.1 1
40.37 odd 4 576.3.g.a.127.1 1
45.2 even 12 324.3.f.e.271.1 2
45.7 odd 12 324.3.f.f.271.1 2
45.22 odd 12 324.3.f.f.55.1 2
45.32 even 12 324.3.f.e.55.1 2
60.23 odd 4 900.3.c.b.451.1 1
60.47 odd 4 36.3.d.b.19.1 yes 1
60.59 even 2 900.3.f.a.199.2 2
80.27 even 4 2304.3.b.d.127.2 2
80.37 odd 4 2304.3.b.d.127.2 2
80.67 even 4 2304.3.b.d.127.1 2
80.77 odd 4 2304.3.b.d.127.1 2
120.77 even 4 576.3.g.c.127.1 1
120.107 odd 4 576.3.g.c.127.1 1
180.7 even 12 324.3.f.f.271.1 2
180.47 odd 12 324.3.f.e.271.1 2
180.67 even 12 324.3.f.f.55.1 2
180.167 odd 12 324.3.f.e.55.1 2
240.77 even 4 2304.3.b.e.127.2 2
240.107 odd 4 2304.3.b.e.127.1 2
240.197 even 4 2304.3.b.e.127.1 2
240.227 odd 4 2304.3.b.e.127.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.3.d.a.19.1 1 5.2 odd 4
36.3.d.a.19.1 1 20.7 even 4
36.3.d.b.19.1 yes 1 15.2 even 4
36.3.d.b.19.1 yes 1 60.47 odd 4
324.3.f.e.55.1 2 45.32 even 12
324.3.f.e.55.1 2 180.167 odd 12
324.3.f.e.271.1 2 45.2 even 12
324.3.f.e.271.1 2 180.47 odd 12
324.3.f.f.55.1 2 45.22 odd 12
324.3.f.f.55.1 2 180.67 even 12
324.3.f.f.271.1 2 45.7 odd 12
324.3.f.f.271.1 2 180.7 even 12
576.3.g.a.127.1 1 40.27 even 4
576.3.g.a.127.1 1 40.37 odd 4
576.3.g.c.127.1 1 120.77 even 4
576.3.g.c.127.1 1 120.107 odd 4
900.3.c.b.451.1 1 15.8 even 4
900.3.c.b.451.1 1 60.23 odd 4
900.3.c.c.451.1 1 5.3 odd 4
900.3.c.c.451.1 1 20.3 even 4
900.3.f.a.199.1 2 3.2 odd 2
900.3.f.a.199.1 2 12.11 even 2
900.3.f.a.199.2 2 15.14 odd 2
900.3.f.a.199.2 2 60.59 even 2
900.3.f.b.199.1 2 5.4 even 2 inner
900.3.f.b.199.1 2 20.19 odd 2 inner
900.3.f.b.199.2 2 1.1 even 1 trivial
900.3.f.b.199.2 2 4.3 odd 2 CM
2304.3.b.d.127.1 2 80.67 even 4
2304.3.b.d.127.1 2 80.77 odd 4
2304.3.b.d.127.2 2 80.27 even 4
2304.3.b.d.127.2 2 80.37 odd 4
2304.3.b.e.127.1 2 240.107 odd 4
2304.3.b.e.127.1 2 240.197 even 4
2304.3.b.e.127.2 2 240.77 even 4
2304.3.b.e.127.2 2 240.227 odd 4