Properties

Label 475.3.d.a.474.2
Level $475$
Weight $3$
Character 475.474
Analytic conductor $12.943$
Analytic rank $0$
Dimension $2$
CM discriminant -19
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 475.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.9428125571\)
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: \( 5 \)
Twist minimal: no (minimal twist has level 19)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 474.2
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 475.474
Dual form 475.3.d.a.474.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{4} +5.00000i q^{7} -9.00000 q^{9} +O(q^{10})\) \(q-4.00000 q^{4} +5.00000i q^{7} -9.00000 q^{9} +3.00000 q^{11} +16.0000 q^{16} -15.0000i q^{17} +19.0000 q^{19} -30.0000i q^{23} -20.0000i q^{28} +36.0000 q^{36} -85.0000i q^{43} -12.0000 q^{44} -75.0000i q^{47} +24.0000 q^{49} +103.000 q^{61} -45.0000i q^{63} -64.0000 q^{64} +60.0000i q^{68} -25.0000i q^{73} -76.0000 q^{76} +15.0000i q^{77} +81.0000 q^{81} +90.0000i q^{83} +120.000i q^{92} -27.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 8 q^{4} - 18 q^{9} + O(q^{10}) \) \( 2 q - 8 q^{4} - 18 q^{9} + 6 q^{11} + 32 q^{16} + 38 q^{19} + 72 q^{36} - 24 q^{44} + 48 q^{49} + 206 q^{61} - 128 q^{64} - 152 q^{76} + 162 q^{81} - 54 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(-1\)

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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) −4.00000 −1.00000
\(5\) 0 0
\(6\) 0 0
\(7\) 5.00000i 0.714286i 0.934050 + 0.357143i \(0.116249\pi\)
−0.934050 + 0.357143i \(0.883751\pi\)
\(8\) 0 0
\(9\) −9.00000 −1.00000
\(10\) 0 0
\(11\) 3.00000 0.272727 0.136364 0.990659i \(-0.456458\pi\)
0.136364 + 0.990659i \(0.456458\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 16.0000 1.00000
\(17\) − 15.0000i − 0.882353i −0.897420 0.441176i \(-0.854561\pi\)
0.897420 0.441176i \(-0.145439\pi\)
\(18\) 0 0
\(19\) 19.0000 1.00000
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) − 30.0000i − 1.30435i −0.758069 0.652174i \(-0.773857\pi\)
0.758069 0.652174i \(-0.226143\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) − 20.0000i − 0.714286i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 36.0000 1.00000
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) − 85.0000i − 1.97674i −0.152055 0.988372i \(-0.548589\pi\)
0.152055 0.988372i \(-0.451411\pi\)
\(44\) −12.0000 −0.272727
\(45\) 0 0
\(46\) 0 0
\(47\) − 75.0000i − 1.59574i −0.602826 0.797872i \(-0.705959\pi\)
0.602826 0.797872i \(-0.294041\pi\)
\(48\) 0 0
\(49\) 24.0000 0.489796
\(50\) 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
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 103.000 1.68852 0.844262 0.535930i \(-0.180039\pi\)
0.844262 + 0.535930i \(0.180039\pi\)
\(62\) 0 0
\(63\) − 45.0000i − 0.714286i
\(64\) −64.0000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 60.0000i 0.882353i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) − 25.0000i − 0.342466i −0.985231 0.171233i \(-0.945225\pi\)
0.985231 0.171233i \(-0.0547750\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −76.0000 −1.00000
\(77\) 15.0000i 0.194805i
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 81.0000 1.00000
\(82\) 0 0
\(83\) 90.0000i 1.08434i 0.840270 + 0.542169i \(0.182397\pi\)
−0.840270 + 0.542169i \(0.817603\pi\)
\(84\) 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
\(91\) 0 0
\(92\) 120.000i 1.30435i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 0 0
\(99\) −27.0000 −0.272727
\(100\) 0 0
\(101\) −102.000 −1.00990 −0.504950 0.863148i \(-0.668489\pi\)
−0.504950 + 0.863148i \(0.668489\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 80.0000i 0.714286i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 75.0000 0.630252
\(120\) 0 0
\(121\) −112.000 −0.925620
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −213.000 −1.62595 −0.812977 0.582296i \(-0.802155\pi\)
−0.812977 + 0.582296i \(0.802155\pi\)
\(132\) 0 0
\(133\) 95.0000i 0.714286i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 255.000i − 1.86131i −0.365893 0.930657i \(-0.619236\pi\)
0.365893 0.930657i \(-0.380764\pi\)
\(138\) 0 0
\(139\) 197.000 1.41727 0.708633 0.705577i \(-0.249312\pi\)
0.708633 + 0.705577i \(0.249312\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −144.000 −1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 177.000 1.18792 0.593960 0.804495i \(-0.297564\pi\)
0.593960 + 0.804495i \(0.297564\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 135.000i 0.882353i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) − 10.0000i − 0.0636943i −0.999493 0.0318471i \(-0.989861\pi\)
0.999493 0.0318471i \(-0.0101390\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 150.000 0.931677
\(162\) 0 0
\(163\) 250.000i 1.53374i 0.641801 + 0.766871i \(0.278187\pi\)
−0.641801 + 0.766871i \(0.721813\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −169.000 −1.00000
\(170\) 0 0
\(171\) −171.000 −1.00000
\(172\) 340.000i 1.97674i
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 48.0000 0.272727
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) − 45.0000i − 0.240642i
\(188\) 300.000i 1.59574i
\(189\) 0 0
\(190\) 0 0
\(191\) −93.0000 −0.486911 −0.243455 0.969912i \(-0.578281\pi\)
−0.243455 + 0.969912i \(0.578281\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −96.0000 −0.489796
\(197\) − 90.0000i − 0.456853i −0.973561 0.228426i \(-0.926642\pi\)
0.973561 0.228426i \(-0.0733580\pi\)
\(198\) 0 0
\(199\) −227.000 −1.14070 −0.570352 0.821401i \(-0.693193\pi\)
−0.570352 + 0.821401i \(0.693193\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 270.000i 1.30435i
\(208\) 0 0
\(209\) 57.0000 0.272727
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 17.0000 0.0742358 0.0371179 0.999311i \(-0.488182\pi\)
0.0371179 + 0.999311i \(0.488182\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 465.000i − 1.99571i −0.0654770 0.997854i \(-0.520857\pi\)
0.0654770 0.997854i \(-0.479143\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 453.000 1.89540 0.947699 0.319166i \(-0.103403\pi\)
0.947699 + 0.319166i \(0.103403\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −412.000 −1.68852
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 27.0000 0.107570 0.0537849 0.998553i \(-0.482871\pi\)
0.0537849 + 0.998553i \(0.482871\pi\)
\(252\) 180.000i 0.714286i
\(253\) − 90.0000i − 0.355731i
\(254\) 0 0
\(255\) 0 0
\(256\) 256.000 1.00000
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) − 405.000i − 1.53992i −0.638090 0.769962i \(-0.720275\pi\)
0.638090 0.769962i \(-0.279725\pi\)
\(264\) 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
\(271\) −142.000 −0.523985 −0.261993 0.965070i \(-0.584380\pi\)
−0.261993 + 0.965070i \(0.584380\pi\)
\(272\) − 240.000i − 0.882353i
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) − 535.000i − 1.93141i −0.259646 0.965704i \(-0.583606\pi\)
0.259646 0.965704i \(-0.416394\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 395.000i 1.39576i 0.716215 + 0.697880i \(0.245873\pi\)
−0.716215 + 0.697880i \(0.754127\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 64.0000 0.221453
\(290\) 0 0
\(291\) 0 0
\(292\) 100.000i 0.342466i
\(293\) 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
\(301\) 425.000 1.41196
\(302\) 0 0
\(303\) 0 0
\(304\) 304.000 1.00000
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) − 60.0000i − 0.194805i
\(309\) 0 0
\(310\) 0 0
\(311\) 603.000 1.93891 0.969453 0.245276i \(-0.0788785\pi\)
0.969453 + 0.245276i \(0.0788785\pi\)
\(312\) 0 0
\(313\) − 590.000i − 1.88498i −0.334229 0.942492i \(-0.608476\pi\)
0.334229 0.942492i \(-0.391524\pi\)
\(314\) 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
\(323\) − 285.000i − 0.882353i
\(324\) −324.000 −1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 375.000 1.13982
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) − 360.000i − 1.08434i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 365.000i 1.06414i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 675.000i − 1.94524i −0.232391 0.972622i \(-0.574655\pi\)
0.232391 0.972622i \(-0.425345\pi\)
\(348\) 0 0
\(349\) −527.000 −1.51003 −0.755014 0.655708i \(-0.772370\pi\)
−0.755014 + 0.655708i \(0.772370\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 510.000i − 1.44476i −0.691497 0.722380i \(-0.743048\pi\)
0.691497 0.722380i \(-0.256952\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −243.000 −0.676880 −0.338440 0.940988i \(-0.609899\pi\)
−0.338440 + 0.940988i \(0.609899\pi\)
\(360\) 0 0
\(361\) 361.000 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) − 50.0000i − 0.136240i −0.997677 0.0681199i \(-0.978300\pi\)
0.997677 0.0681199i \(-0.0217000\pi\)
\(368\) − 480.000i − 1.30435i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 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
\(386\) 0 0
\(387\) 765.000i 1.97674i
\(388\) 0 0
\(389\) 153.000 0.393316 0.196658 0.980472i \(-0.436991\pi\)
0.196658 + 0.980472i \(0.436991\pi\)
\(390\) 0 0
\(391\) −450.000 −1.15090
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 108.000 0.272727
\(397\) 745.000i 1.87657i 0.345857 + 0.938287i \(0.387588\pi\)
−0.345857 + 0.938287i \(0.612412\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 408.000 1.00990
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −762.000 −1.81862 −0.909308 0.416124i \(-0.863388\pi\)
−0.909308 + 0.416124i \(0.863388\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 675.000i 1.59574i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 515.000i 1.20609i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 570.000i − 1.30435i
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −216.000 −0.489796
\(442\) 0 0
\(443\) − 45.0000i − 0.101580i −0.998709 0.0507901i \(-0.983826\pi\)
0.998709 0.0507901i \(-0.0161739\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) − 320.000i − 0.714286i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 625.000i 1.36761i 0.729663 + 0.683807i \(0.239677\pi\)
−0.729663 + 0.683807i \(0.760323\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 447.000 0.969631 0.484816 0.874616i \(-0.338887\pi\)
0.484816 + 0.874616i \(0.338887\pi\)
\(462\) 0 0
\(463\) 755.000i 1.63067i 0.578990 + 0.815335i \(0.303447\pi\)
−0.578990 + 0.815335i \(0.696553\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 915.000i − 1.95931i −0.200677 0.979657i \(-0.564314\pi\)
0.200677 0.979657i \(-0.435686\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) − 255.000i − 0.539112i
\(474\) 0 0
\(475\) 0 0
\(476\) −300.000 −0.630252
\(477\) 0 0
\(478\) 0 0
\(479\) 942.000 1.96660 0.983299 0.182000i \(-0.0582571\pi\)
0.983299 + 0.182000i \(0.0582571\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 448.000 0.925620
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −918.000 −1.86965 −0.934827 0.355104i \(-0.884446\pi\)
−0.934827 + 0.355104i \(0.884446\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −523.000 −1.04810 −0.524048 0.851689i \(-0.675579\pi\)
−0.524048 + 0.851689i \(0.675579\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 930.000i 1.84891i 0.381295 + 0.924453i \(0.375478\pi\)
−0.381295 + 0.924453i \(0.624522\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 125.000 0.244618
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) − 225.000i − 0.435203i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 852.000 1.62595
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −371.000 −0.701323
\(530\) 0 0
\(531\) 0 0
\(532\) − 380.000i − 0.714286i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 72.0000 0.133581
\(540\) 0 0
\(541\) −457.000 −0.844732 −0.422366 0.906425i \(-0.638800\pi\)
−0.422366 + 0.906425i \(0.638800\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 1020.00i 1.86131i
\(549\) −927.000 −1.68852
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −788.000 −1.41727
\(557\) − 1095.00i − 1.96589i −0.183903 0.982944i \(-0.558873\pi\)
0.183903 0.982944i \(-0.441127\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 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
\(567\) 405.000i 0.714286i
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 458.000 0.802102 0.401051 0.916056i \(-0.368645\pi\)
0.401051 + 0.916056i \(0.368645\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 576.000 1.00000
\(577\) 1145.00i 1.98440i 0.124648 + 0.992201i \(0.460220\pi\)
−0.124648 + 0.992201i \(0.539780\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −450.000 −0.774527
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1125.00i 1.91652i 0.285890 + 0.958262i \(0.407711\pi\)
−0.285890 + 0.958262i \(0.592289\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 30.0000i − 0.0505902i −0.999680 0.0252951i \(-0.991947\pi\)
0.999680 0.0252951i \(-0.00805254\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −708.000 −1.18792
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 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
\(612\) − 540.000i − 0.882353i
\(613\) 295.000i 0.481240i 0.970619 + 0.240620i \(0.0773507\pi\)
−0.970619 + 0.240620i \(0.922649\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1065.00i 1.72609i 0.505124 + 0.863047i \(0.331447\pi\)
−0.505124 + 0.863047i \(0.668553\pi\)
\(618\) 0 0
\(619\) 662.000 1.06947 0.534733 0.845021i \(-0.320412\pi\)
0.534733 + 0.845021i \(0.320412\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 40.0000i 0.0636943i
\(629\) 0 0
\(630\) 0 0
\(631\) −1037.00 −1.64342 −0.821712 0.569904i \(-0.806981\pi\)
−0.821712 + 0.569904i \(0.806981\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 1115.00i 1.73406i 0.498257 + 0.867030i \(0.333974\pi\)
−0.498257 + 0.867030i \(0.666026\pi\)
\(644\) −600.000 −0.931677
\(645\) 0 0
\(646\) 0 0
\(647\) 1005.00i 1.55332i 0.629918 + 0.776662i \(0.283088\pi\)
−0.629918 + 0.776662i \(0.716912\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) − 1000.00i − 1.53374i
\(653\) 375.000i 0.574273i 0.957890 + 0.287136i \(0.0927033\pi\)
−0.957890 + 0.287136i \(0.907297\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 225.000i 0.342466i
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 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
\(671\) 309.000 0.460507
\(672\) 0 0
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 676.000 1.00000
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 684.000 1.00000
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) − 1360.00i − 1.97674i
\(689\) 0 0
\(690\) 0 0
\(691\) −157.000 −0.227207 −0.113603 0.993526i \(-0.536239\pi\)
−0.113603 + 0.993526i \(0.536239\pi\)
\(692\) 0 0
\(693\) − 135.000i − 0.194805i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1098.00 1.56633 0.783167 0.621812i \(-0.213603\pi\)
0.783167 + 0.621812i \(0.213603\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −192.000 −0.272727
\(705\) 0 0
\(706\) 0 0
\(707\) − 510.000i − 0.721358i
\(708\) 0 0
\(709\) 1318.00 1.85896 0.929478 0.368877i \(-0.120258\pi\)
0.929478 + 0.368877i \(0.120258\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −963.000 −1.33936 −0.669680 0.742650i \(-0.733569\pi\)
−0.669680 + 0.742650i \(0.733569\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 85.0000i 0.116919i 0.998290 + 0.0584594i \(0.0186188\pi\)
−0.998290 + 0.0584594i \(0.981381\pi\)
\(728\) 0 0
\(729\) −729.000 −1.00000
\(730\) 0 0
\(731\) −1275.00 −1.74419
\(732\) 0 0
\(733\) − 1270.00i − 1.73261i −0.499519 0.866303i \(-0.666490\pi\)
0.499519 0.866303i \(-0.333510\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −547.000 −0.740189 −0.370095 0.928994i \(-0.620675\pi\)
−0.370095 + 0.928994i \(0.620675\pi\)
\(740\) 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
\(746\) 0 0
\(747\) − 810.000i − 1.08434i
\(748\) 180.000i 0.240642i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) − 1200.00i − 1.59574i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 785.000i 1.03699i 0.855081 + 0.518494i \(0.173507\pi\)
−0.855081 + 0.518494i \(0.826493\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1503.00 1.97503 0.987516 0.157516i \(-0.0503486\pi\)
0.987516 + 0.157516i \(0.0503486\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 372.000 0.486911
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −1063.00 −1.38231 −0.691157 0.722704i \(-0.742899\pi\)
−0.691157 + 0.722704i \(0.742899\pi\)
\(770\) 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
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 384.000 0.489796
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 360.000i 0.456853i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 908.000 1.14070
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) −1125.00 −1.40801
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 75.0000i − 0.0933998i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1593.00 1.96910 0.984549 0.175110i \(-0.0560282\pi\)
0.984549 + 0.175110i \(0.0560282\pi\)
\(810\) 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
\(817\) − 1615.00i − 1.97674i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1167.00 1.42144 0.710719 0.703476i \(-0.248370\pi\)
0.710719 + 0.703476i \(0.248370\pi\)
\(822\) 0 0
\(823\) − 1565.00i − 1.90158i −0.309837 0.950790i \(-0.600274\pi\)
0.309837 0.950790i \(-0.399726\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) − 1080.00i − 1.30435i
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) − 360.000i − 0.432173i
\(834\) 0 0
\(835\) 0 0
\(836\) −228.000 −0.272727
\(837\) 0 0
\(838\) 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
\(847\) − 560.000i − 0.661157i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) − 1030.00i − 1.20750i −0.797173 0.603751i \(-0.793672\pi\)
0.797173 0.603751i \(-0.206328\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) 1493.00 1.73807 0.869034 0.494753i \(-0.164741\pi\)
0.869034 + 0.494753i \(0.164741\pi\)
\(860\) 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
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −537.000 −0.609535 −0.304767 0.952427i \(-0.598579\pi\)
−0.304767 + 0.952427i \(0.598579\pi\)
\(882\) 0 0
\(883\) 835.000i 0.945640i 0.881159 + 0.472820i \(0.156764\pi\)
−0.881159 + 0.472820i \(0.843236\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 243.000 0.272727
\(892\) 0 0
\(893\) − 1425.00i − 1.59574i
\(894\) 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
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 0 0
\(909\) 918.000 1.00990
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 270.000i 0.295728i
\(914\) 0 0
\(915\) 0 0
\(916\) −68.0000 −0.0742358
\(917\) − 1065.00i − 1.16140i
\(918\) 0 0
\(919\) −1762.00 −1.91730 −0.958651 0.284585i \(-0.908144\pi\)
−0.958651 + 0.284585i \(0.908144\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −642.000 −0.691066 −0.345533 0.938407i \(-0.612302\pi\)
−0.345533 + 0.938407i \(0.612302\pi\)
\(930\) 0 0
\(931\) 456.000 0.489796
\(932\) 1860.00i 1.99571i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) − 335.000i − 0.357524i −0.983892 0.178762i \(-0.942791\pi\)
0.983892 0.178762i \(-0.0572092\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 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
\(947\) 1830.00i 1.93242i 0.257760 + 0.966209i \(0.417016\pi\)
−0.257760 + 0.966209i \(0.582984\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 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
\(956\) −1812.00 −1.89540
\(957\) 0 0
\(958\) 0 0
\(959\) 1275.00 1.32951
\(960\) 0 0
\(961\) 961.000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 1790.00i 1.85109i 0.378643 + 0.925543i \(0.376391\pi\)
−0.378643 + 0.925543i \(0.623609\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 985.000i 1.01233i
\(974\) 0 0
\(975\) 0 0
\(976\) 1648.00 1.68852
\(977\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) 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
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −2550.00 −2.57836
\(990\) 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
\(997\) − 1975.00i − 1.98094i −0.137718 0.990471i \(-0.543977\pi\)
0.137718 0.990471i \(-0.456023\pi\)
\(998\) 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 475.3.d.a.474.2 2
5.2 odd 4 19.3.b.a.18.1 1
5.3 odd 4 475.3.c.a.151.1 1
5.4 even 2 inner 475.3.d.a.474.1 2
15.2 even 4 171.3.c.a.37.1 1
19.18 odd 2 CM 475.3.d.a.474.2 2
20.7 even 4 304.3.e.a.113.1 1
40.27 even 4 1216.3.e.b.1025.1 1
40.37 odd 4 1216.3.e.a.1025.1 1
60.47 odd 4 2736.3.o.a.721.1 1
95.2 even 36 361.3.f.a.262.1 6
95.7 odd 12 361.3.d.a.293.1 2
95.12 even 12 361.3.d.a.293.1 2
95.17 odd 36 361.3.f.a.262.1 6
95.18 even 4 475.3.c.a.151.1 1
95.22 even 36 361.3.f.a.333.1 6
95.27 even 12 361.3.d.a.69.1 2
95.32 even 36 361.3.f.a.116.1 6
95.37 even 4 19.3.b.a.18.1 1
95.42 odd 36 361.3.f.a.307.1 6
95.47 odd 36 361.3.f.a.299.1 6
95.52 even 36 361.3.f.a.127.1 6
95.62 odd 36 361.3.f.a.127.1 6
95.67 even 36 361.3.f.a.299.1 6
95.72 even 36 361.3.f.a.307.1 6
95.82 odd 36 361.3.f.a.116.1 6
95.87 odd 12 361.3.d.a.69.1 2
95.92 odd 36 361.3.f.a.333.1 6
95.94 odd 2 inner 475.3.d.a.474.1 2
285.227 odd 4 171.3.c.a.37.1 1
380.227 odd 4 304.3.e.a.113.1 1
760.37 even 4 1216.3.e.a.1025.1 1
760.227 odd 4 1216.3.e.b.1025.1 1
1140.227 even 4 2736.3.o.a.721.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
19.3.b.a.18.1 1 5.2 odd 4
19.3.b.a.18.1 1 95.37 even 4
171.3.c.a.37.1 1 15.2 even 4
171.3.c.a.37.1 1 285.227 odd 4
304.3.e.a.113.1 1 20.7 even 4
304.3.e.a.113.1 1 380.227 odd 4
361.3.d.a.69.1 2 95.27 even 12
361.3.d.a.69.1 2 95.87 odd 12
361.3.d.a.293.1 2 95.7 odd 12
361.3.d.a.293.1 2 95.12 even 12
361.3.f.a.116.1 6 95.32 even 36
361.3.f.a.116.1 6 95.82 odd 36
361.3.f.a.127.1 6 95.52 even 36
361.3.f.a.127.1 6 95.62 odd 36
361.3.f.a.262.1 6 95.2 even 36
361.3.f.a.262.1 6 95.17 odd 36
361.3.f.a.299.1 6 95.47 odd 36
361.3.f.a.299.1 6 95.67 even 36
361.3.f.a.307.1 6 95.42 odd 36
361.3.f.a.307.1 6 95.72 even 36
361.3.f.a.333.1 6 95.22 even 36
361.3.f.a.333.1 6 95.92 odd 36
475.3.c.a.151.1 1 5.3 odd 4
475.3.c.a.151.1 1 95.18 even 4
475.3.d.a.474.1 2 5.4 even 2 inner
475.3.d.a.474.1 2 95.94 odd 2 inner
475.3.d.a.474.2 2 1.1 even 1 trivial
475.3.d.a.474.2 2 19.18 odd 2 CM
1216.3.e.a.1025.1 1 40.37 odd 4
1216.3.e.a.1025.1 1 760.37 even 4
1216.3.e.b.1025.1 1 40.27 even 4
1216.3.e.b.1025.1 1 760.227 odd 4
2736.3.o.a.721.1 1 60.47 odd 4
2736.3.o.a.721.1 1 1140.227 even 4