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Properties

Label 1216.3.e.a.1025.1
Level $1216$
Weight $3$
Character 1216.1025
Self dual yes
Analytic conductor $33.134$
Analytic rank $0$
Dimension $1$
CM discriminant -19
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1216,3,Mod(1025,1216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1216.1025");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1216.e (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(33.1336001462\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 19)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 1025.1
Character \(\chi\) \(=\) 1216.1025

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+9.00000 q^{5} -5.00000 q^{7} +9.00000 q^{9} -3.00000 q^{11} +15.0000 q^{17} +19.0000 q^{19} -30.0000 q^{23} +56.0000 q^{25} -45.0000 q^{35} +85.0000 q^{43} +81.0000 q^{45} +75.0000 q^{47} -24.0000 q^{49} -27.0000 q^{55} -103.000 q^{61} -45.0000 q^{63} -25.0000 q^{73} +15.0000 q^{77} +81.0000 q^{81} -90.0000 q^{83} +135.000 q^{85} +171.000 q^{95} -27.0000 q^{99} +O(q^{100})\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(705\) \(837\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) 0 0
\(5\) 9.00000 1.80000 0.900000 − 0.435890i \(-0.143566\pi\)
0.900000 + 0.435890i \(0.143566\pi\)
\(6\) 0 0
\(7\) −5.00000 −0.714286 −0.357143 − 0.934050i \(-0.616249\pi\)
−0.357143 + 0.934050i \(0.616249\pi\)
\(8\) 0 0
\(9\) 9.00000 1.00000
\(10\) 0 0
\(11\) −3.00000 −0.272727 −0.136364 − 0.990659i \(-0.543542\pi\)
−0.136364 + 0.990659i \(0.543542\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 15.0000 0.882353 0.441176 − 0.897420i \(-0.354561\pi\)
0.441176 + 0.897420i \(0.354561\pi\)
\(18\) 0 0
\(19\) 19.0000 1.00000
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −30.0000 −1.30435 −0.652174 − 0.758069i \(-0.726143\pi\)
−0.652174 + 0.758069i \(0.726143\pi\)
\(24\) 0 0
\(25\) 56.0000 2.24000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 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
\(35\) −45.0000 −1.28571
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 85.0000 1.97674 0.988372 − 0.152055i \(-0.0485890\pi\)
0.988372 + 0.152055i \(0.0485890\pi\)
\(44\) 0 0
\(45\) 81.0000 1.80000
\(46\) 0 0
\(47\) 75.0000 1.59574 0.797872 − 0.602826i \(-0.205959\pi\)
0.797872 + 0.602826i \(0.205959\pi\)
\(48\) 0 0
\(49\) −24.0000 −0.489796
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) −27.0000 −0.490909
\(56\) 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 \(-0.819961\pi\)
−0.844262 + 0.535930i \(0.819961\pi\)
\(62\) 0 0
\(63\) −45.0000 −0.714286
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −25.0000 −0.342466 −0.171233 − 0.985231i \(-0.554775\pi\)
−0.171233 + 0.985231i \(0.554775\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 15.0000 0.194805
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 81.0000 1.00000
\(82\) 0 0
\(83\) −90.0000 −1.08434 −0.542169 − 0.840270i \(-0.682397\pi\)
−0.542169 + 0.840270i \(0.682397\pi\)
\(84\) 0 0
\(85\) 135.000 1.58824
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 171.000 1.80000
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) −27.0000 −0.272727
\(100\) 0 0
\(101\) 102.000 1.00990 0.504950 − 0.863148i \(-0.331511\pi\)
0.504950 + 0.863148i \(0.331511\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) −270.000 −2.34783
\(116\) 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
\(125\) 279.000 2.23200
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 213.000 1.62595 0.812977 − 0.582296i \(-0.197845\pi\)
0.812977 + 0.582296i \(0.197845\pi\)
\(132\) 0 0
\(133\) −95.0000 −0.714286
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 255.000 1.86131 0.930657 − 0.365893i \(-0.119236\pi\)
0.930657 + 0.365893i \(0.119236\pi\)
\(138\) 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
\(144\) 0 0
\(145\) 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
\(153\) 135.000 0.882353
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −10.0000 −0.0636943 −0.0318471 − 0.999493i \(-0.510139\pi\)
−0.0318471 + 0.999493i \(0.510139\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 150.000 0.931677
\(162\) 0 0
\(163\) −250.000 −1.53374 −0.766871 − 0.641801i \(-0.778187\pi\)
−0.766871 + 0.641801i \(0.778187\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 169.000 1.00000
\(170\) 0 0
\(171\) 171.000 1.00000
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) −280.000 −1.60000
\(176\) 0 0
\(177\) 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
\(187\) −45.0000 −0.240642
\(188\) 0 0
\(189\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −90.0000 −0.456853 −0.228426 − 0.973561i \(-0.573358\pi\)
−0.228426 + 0.973561i \(0.573358\pi\)
\(198\) 0 0
\(199\) 227.000 1.14070 0.570352 − 0.821401i \(-0.306807\pi\)
0.570352 + 0.821401i \(0.306807\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −270.000 −1.30435
\(208\) 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
\(215\) 765.000 3.55814
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 504.000 2.24000
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 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
\(233\) −465.000 −1.99571 −0.997854 − 0.0654770i \(-0.979143\pi\)
−0.997854 + 0.0654770i \(0.979143\pi\)
\(234\) 0 0
\(235\) 675.000 2.87234
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −453.000 −1.89540 −0.947699 − 0.319166i \(-0.896597\pi\)
−0.947699 + 0.319166i \(0.896597\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −216.000 −0.881633
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −27.0000 −0.107570 −0.0537849 − 0.998553i \(-0.517129\pi\)
−0.0537849 + 0.998553i \(0.517129\pi\)
\(252\) 0 0
\(253\) 90.0000 0.355731
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −405.000 −1.53992 −0.769962 − 0.638090i \(-0.779725\pi\)
−0.769962 + 0.638090i \(0.779725\pi\)
\(264\) 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 \(0.584380\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −168.000 −0.610909
\(276\) 0 0
\(277\) −535.000 −1.93141 −0.965704 − 0.259646i \(-0.916394\pi\)
−0.965704 + 0.259646i \(0.916394\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −395.000 −1.39576 −0.697880 − 0.716215i \(-0.745873\pi\)
−0.697880 + 0.716215i \(0.745873\pi\)
\(284\) 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
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 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
\(304\) 0 0
\(305\) −927.000 −3.03934
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 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
\(313\) −590.000 −1.88498 −0.942492 − 0.334229i \(-0.891524\pi\)
−0.942492 + 0.334229i \(0.891524\pi\)
\(314\) 0 0
\(315\) −405.000 −1.28571
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 285.000 0.882353
\(324\) 0 0
\(325\) 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 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 365.000 1.06414
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −675.000 −1.94524 −0.972622 − 0.232391i \(-0.925345\pi\)
−0.972622 + 0.232391i \(0.925345\pi\)
\(348\) 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
\(353\) −510.000 −1.44476 −0.722380 − 0.691497i \(-0.756952\pi\)
−0.722380 + 0.691497i \(0.756952\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 243.000 0.676880 0.338440 − 0.940988i \(-0.390101\pi\)
0.338440 + 0.940988i \(0.390101\pi\)
\(360\) 0 0
\(361\) 361.000 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −225.000 −0.616438
\(366\) 0 0
\(367\) 50.0000 0.136240 0.0681199 − 0.997677i \(-0.478300\pi\)
0.0681199 + 0.997677i \(0.478300\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 135.000 0.350649
\(386\) 0 0
\(387\) 765.000 1.97674
\(388\) 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
\(396\) 0 0
\(397\) 745.000 1.87657 0.938287 − 0.345857i \(-0.112412\pi\)
0.938287 + 0.345857i \(0.112412\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 729.000 1.80000
\(406\) 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
\(415\) −810.000 −1.95181
\(416\) 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
\(423\) 675.000 1.59574
\(424\) 0 0
\(425\) 840.000 1.97647
\(426\) 0 0
\(427\) 515.000 1.20609
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −570.000 −1.30435
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −216.000 −0.489796
\(442\) 0 0
\(443\) 45.0000 0.101580 0.0507901 − 0.998709i \(-0.483826\pi\)
0.0507901 + 0.998709i \(0.483826\pi\)
\(444\) 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
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −625.000 −1.36761 −0.683807 − 0.729663i \(-0.739677\pi\)
−0.683807 + 0.729663i \(0.739677\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −447.000 −0.969631 −0.484816 − 0.874616i \(-0.661113\pi\)
−0.484816 + 0.874616i \(0.661113\pi\)
\(462\) 0 0
\(463\) 755.000 1.63067 0.815335 − 0.578990i \(-0.196553\pi\)
0.815335 + 0.578990i \(0.196553\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −915.000 −1.95931 −0.979657 − 0.200677i \(-0.935686\pi\)
−0.979657 + 0.200677i \(0.935686\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −255.000 −0.539112
\(474\) 0 0
\(475\) 1064.00 2.24000
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −942.000 −1.96660 −0.983299 − 0.182000i \(-0.941743\pi\)
−0.983299 + 0.182000i \(0.941743\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 918.000 1.86965 0.934827 − 0.355104i \(-0.115554\pi\)
0.934827 + 0.355104i \(0.115554\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −243.000 −0.490909
\(496\) 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
\(503\) 930.000 1.84891 0.924453 − 0.381295i \(-0.124522\pi\)
0.924453 + 0.381295i \(0.124522\pi\)
\(504\) 0 0
\(505\) 918.000 1.81782
\(506\) 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
\(517\) −225.000 −0.435203
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 371.000 0.701323
\(530\) 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
\(539\) 72.0000 0.133581
\(540\) 0 0
\(541\) 457.000 0.844732 0.422366 − 0.906425i \(-0.361200\pi\)
0.422366 + 0.906425i \(0.361200\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) −927.000 −1.68852
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1095.00 −1.96589 −0.982944 − 0.183903i \(-0.941127\pi\)
−0.982944 + 0.183903i \(0.941127\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −405.000 −0.714286
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) −458.000 −0.802102 −0.401051 − 0.916056i \(-0.631355\pi\)
−0.401051 + 0.916056i \(0.631355\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1680.00 −2.92174
\(576\) 0 0
\(577\) −1145.00 −1.98440 −0.992201 − 0.124648i \(-0.960220\pi\)
−0.992201 + 0.124648i \(0.960220\pi\)
\(578\) 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
\(587\) 1125.00 1.91652 0.958262 − 0.285890i \(-0.0922893\pi\)
0.958262 + 0.285890i \(0.0922893\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −30.0000 −0.0505902 −0.0252951 − 0.999680i \(-0.508053\pi\)
−0.0252951 + 0.999680i \(0.508053\pi\)
\(594\) 0 0
\(595\) −675.000 −1.13445
\(596\) 0 0
\(597\) 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
\(605\) −1008.00 −1.66612
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −295.000 −0.481240 −0.240620 − 0.970619i \(-0.577351\pi\)
−0.240620 + 0.970619i \(0.577351\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1065.00 −1.72609 −0.863047 − 0.505124i \(-0.831447\pi\)
−0.863047 + 0.505124i \(0.831447\pi\)
\(618\) 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
\(625\) 1111.00 1.77760
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 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
\(643\) −1115.00 −1.73406 −0.867030 − 0.498257i \(-0.833974\pi\)
−0.867030 + 0.498257i \(0.833974\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1005.00 −1.55332 −0.776662 − 0.629918i \(-0.783088\pi\)
−0.776662 + 0.629918i \(0.783088\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −375.000 −0.574273 −0.287136 − 0.957890i \(-0.592703\pi\)
−0.287136 + 0.957890i \(0.592703\pi\)
\(654\) 0 0
\(655\) 1917.00 2.92672
\(656\) 0 0
\(657\) −225.000 −0.342466
\(658\) 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
\(665\) −855.000 −1.28571
\(666\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 2295.00 3.35036
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 157.000 0.227207 0.113603 − 0.993526i \(-0.463761\pi\)
0.113603 + 0.993526i \(0.463761\pi\)
\(692\) 0 0
\(693\) 135.000 0.194805
\(694\) 0 0
\(695\) 1773.00 2.55108
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1098.00 −1.56633 −0.783167 − 0.621812i \(-0.786397\pi\)
−0.783167 + 0.621812i \(0.786397\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −510.000 −0.721358
\(708\) 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 \(-0.266431\pi\)
0.669680 + 0.742650i \(0.266431\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −85.0000 −0.116919 −0.0584594 − 0.998290i \(-0.518619\pi\)
−0.0584594 + 0.998290i \(0.518619\pi\)
\(728\) 0 0
\(729\) 729.000 1.00000
\(730\) 0 0
\(731\) 1275.00 1.74419
\(732\) 0 0
\(733\) 1270.00 1.73261 0.866303 − 0.499519i \(-0.166490\pi\)
0.866303 + 0.499519i \(0.166490\pi\)
\(734\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 1593.00 2.13826
\(746\) 0 0
\(747\) −810.000 −1.08434
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 785.000 1.03699 0.518494 − 0.855081i \(-0.326493\pi\)
0.518494 + 0.855081i \(0.326493\pi\)
\(758\) 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
\(764\) 0 0
\(765\) 1215.00 1.58824
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 1063.00 1.38231 0.691157 − 0.722704i \(-0.257101\pi\)
0.691157 + 0.722704i \(0.257101\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 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
\(784\) 0 0
\(785\) −90.0000 −0.114650
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 1125.00 1.40801
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 75.0000 0.0933998
\(804\) 0 0
\(805\) 1350.00 1.67702
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1593.00 −1.96910 −0.984549 − 0.175110i \(-0.943972\pi\)
−0.984549 + 0.175110i \(0.943972\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −2250.00 −2.76074
\(816\) 0 0
\(817\) 1615.00 1.97674
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1167.00 −1.42144 −0.710719 − 0.703476i \(-0.751630\pi\)
−0.710719 + 0.703476i \(0.751630\pi\)
\(822\) 0 0
\(823\) −1565.00 −1.90158 −0.950790 − 0.309837i \(-0.899726\pi\)
−0.950790 + 0.309837i \(0.899726\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −360.000 −0.432173
\(834\) 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
\(841\) 841.000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1521.00 1.80000
\(846\) 0 0
\(847\) 560.000 0.661157
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 1030.00 1.20750 0.603751 − 0.797173i \(-0.293672\pi\)
0.603751 + 0.797173i \(0.293672\pi\)
\(854\) 0 0
\(855\) 1539.00 1.80000
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 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
\(875\) −1395.00 −1.59429
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 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
\(883\) −835.000 −0.945640 −0.472820 − 0.881159i \(-0.656764\pi\)
−0.472820 + 0.881159i \(0.656764\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −243.000 −0.272727
\(892\) 0 0
\(893\) 1425.00 1.59574
\(894\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) 918.000 1.00990
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 270.000 0.295728
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1065.00 −1.16140
\(918\) 0 0
\(919\) 1762.00 1.91730 0.958651 − 0.284585i \(-0.0918559\pi\)
0.958651 + 0.284585i \(0.0918559\pi\)
\(920\) 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 \(-0.387698\pi\)
0.345533 + 0.938407i \(0.387698\pi\)
\(930\) 0 0
\(931\) −456.000 −0.489796
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −405.000 −0.433155
\(936\) 0 0
\(937\) 335.000 0.357524 0.178762 − 0.983892i \(-0.442791\pi\)
0.178762 + 0.983892i \(0.442791\pi\)
\(938\) 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
\(947\) 1830.00 1.93242 0.966209 − 0.257760i \(-0.0829843\pi\)
0.966209 + 0.257760i \(0.0829843\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) −837.000 −0.876440
\(956\) 0 0
\(957\) 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
\(967\) −1790.00 −1.85109 −0.925543 − 0.378643i \(-0.876391\pi\)
−0.925543 + 0.378643i \(0.876391\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) −985.000 −1.01233
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) −810.000 −0.822335
\(986\) 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
\(995\) 2043.00 2.05327
\(996\) 0 0
\(997\) −1975.00 −1.98094 −0.990471 − 0.137718i \(-0.956023\pi\)
−0.990471 + 0.137718i \(0.956023\pi\)
\(998\) 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 1216.3.e.a.1025.1 1
4.3 odd 2 1216.3.e.b.1025.1 1
8.3 odd 2 304.3.e.a.113.1 1
8.5 even 2 19.3.b.a.18.1 ✓ 1
19.18 odd 2 CM 1216.3.e.a.1025.1 1
24.5 odd 2 171.3.c.a.37.1 1
24.11 even 2 2736.3.o.a.721.1 1
40.13 odd 4 475.3.d.a.474.2 2
40.29 even 2 475.3.c.a.151.1 1
40.37 odd 4 475.3.d.a.474.1 2
76.75 even 2 1216.3.e.b.1025.1 1
152.5 even 18 361.3.f.a.127.1 6
152.13 odd 18 361.3.f.a.116.1 6
152.21 odd 18 361.3.f.a.262.1 6
152.29 odd 18 361.3.f.a.299.1 6
152.37 odd 2 19.3.b.a.18.1 ✓ 1
152.45 even 6 361.3.d.a.293.1 2
152.53 odd 18 361.3.f.a.307.1 6
152.61 even 18 361.3.f.a.307.1 6
152.69 odd 6 361.3.d.a.293.1 2
152.75 even 2 304.3.e.a.113.1 1
152.85 even 18 361.3.f.a.299.1 6
152.93 even 18 361.3.f.a.262.1 6
152.101 even 18 361.3.f.a.116.1 6
152.109 odd 18 361.3.f.a.127.1 6
152.117 odd 18 361.3.f.a.333.1 6
152.125 even 6 361.3.d.a.69.1 2
152.141 odd 6 361.3.d.a.69.1 2
152.149 even 18 361.3.f.a.333.1 6
456.227 odd 2 2736.3.o.a.721.1 1
456.341 even 2 171.3.c.a.37.1 1
760.37 even 4 475.3.d.a.474.1 2
760.189 odd 2 475.3.c.a.151.1 1
760.493 even 4 475.3.d.a.474.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
19.3.b.a.18.1 ✓ 1 8.5 even 2
19.3.b.a.18.1 ✓ 1 152.37 odd 2
171.3.c.a.37.1 1 24.5 odd 2
171.3.c.a.37.1 1 456.341 even 2
304.3.e.a.113.1 1 8.3 odd 2
304.3.e.a.113.1 1 152.75 even 2
361.3.d.a.69.1 2 152.125 even 6
361.3.d.a.69.1 2 152.141 odd 6
361.3.d.a.293.1 2 152.45 even 6
361.3.d.a.293.1 2 152.69 odd 6
361.3.f.a.116.1 6 152.13 odd 18
361.3.f.a.116.1 6 152.101 even 18
361.3.f.a.127.1 6 152.5 even 18
361.3.f.a.127.1 6 152.109 odd 18
361.3.f.a.262.1 6 152.21 odd 18
361.3.f.a.262.1 6 152.93 even 18
361.3.f.a.299.1 6 152.29 odd 18
361.3.f.a.299.1 6 152.85 even 18
361.3.f.a.307.1 6 152.53 odd 18
361.3.f.a.307.1 6 152.61 even 18
361.3.f.a.333.1 6 152.117 odd 18
361.3.f.a.333.1 6 152.149 even 18
475.3.c.a.151.1 1 40.29 even 2
475.3.c.a.151.1 1 760.189 odd 2
475.3.d.a.474.1 2 40.37 odd 4
475.3.d.a.474.1 2 760.37 even 4
475.3.d.a.474.2 2 40.13 odd 4
475.3.d.a.474.2 2 760.493 even 4
1216.3.e.a.1025.1 1 1.1 even 1 trivial
1216.3.e.a.1025.1 1 19.18 odd 2 CM
1216.3.e.b.1025.1 1 4.3 odd 2
1216.3.e.b.1025.1 1 76.75 even 2
2736.3.o.a.721.1 1 24.11 even 2
2736.3.o.a.721.1 1 456.227 odd 2