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Properties

Label 256.12.a.a.1.1
Level $256$
Weight $12$
Character 256.1
Self dual yes
Analytic conductor $196.696$
Analytic rank $1$
Dimension $1$
CM discriminant -8
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [256,12,Mod(1,256)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(256, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("256.1");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 256 = 2^{8} \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 256.a (trivial)

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: \(196.695854223\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 64)
Fricke sign: \(-1\)
Sato-Tate group: $N(\mathrm{U}(1))$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 256.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-394.000 q^{3} -21911.0 q^{9} +O(q^{10})\) \(q-394.000 q^{3} -21911.0 q^{9} +141906. q^{11} +5.21558e6 q^{17} -1.21053e7 q^{19} -4.88281e7 q^{25} +7.84289e7 q^{27} -5.59110e7 q^{33} +1.17989e9 q^{41} -2.19226e8 q^{43} -1.97733e9 q^{49} -2.05494e9 q^{51} +4.76950e9 q^{57} +1.04966e10 q^{59} -2.11832e10 q^{67} +3.40413e10 q^{73} +1.92383e10 q^{75} -2.70195e10 q^{81} -1.02760e10 q^{83} +1.03092e11 q^{89} +6.98809e10 q^{97} -3.10930e9 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(3\) −394.000 −0.936115 −0.468058 − 0.883698i \(-0.655046\pi\)
−0.468058 + 0.883698i \(0.655046\pi\)
\(4\) 0 0
\(5\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) −21911.0 −0.123688
\(10\) 0 0
\(11\) 141906. 0.265669 0.132835 − 0.991138i \(-0.457592\pi\)
0.132835 + 0.991138i \(0.457592\pi\)
\(12\) 0 0
\(13\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.21558e6 0.890909 0.445455 − 0.895305i \(-0.353042\pi\)
0.445455 + 0.895305i \(0.353042\pi\)
\(18\) 0 0
\(19\) −1.21053e7 −1.12158 −0.560792 − 0.827957i \(-0.689503\pi\)
−0.560792 + 0.827957i \(0.689503\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −4.88281e7 −1.00000
\(26\) 0 0
\(27\) 7.84289e7 1.05190
\(28\) 0 0
\(29\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) −5.59110e7 −0.248697
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.17989e9 1.59048 0.795242 − 0.606292i \(-0.207344\pi\)
0.795242 + 0.606292i \(0.207344\pi\)
\(42\) 0 0
\(43\) −2.19226e8 −0.227413 −0.113707 − 0.993514i \(-0.536272\pi\)
−0.113707 + 0.993514i \(0.536272\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −1.97733e9 −1.00000
\(50\) 0 0
\(51\) −2.05494e9 −0.833994
\(52\) 0 0
\(53\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 4.76950e9 1.04993
\(58\) 0 0
\(59\) 1.04966e10 1.91146 0.955729 − 0.294250i \(-0.0950697\pi\)
0.955729 + 0.294250i \(0.0950697\pi\)
\(60\) 0 0
\(61\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −2.11832e10 −1.91681 −0.958406 − 0.285409i \(-0.907870\pi\)
−0.958406 + 0.285409i \(0.907870\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 3.40413e10 1.92190 0.960949 − 0.276727i \(-0.0892497\pi\)
0.960949 + 0.276727i \(0.0892497\pi\)
\(74\) 0 0
\(75\) 1.92383e10 0.936115
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) −2.70195e10 −0.861013
\(82\) 0 0
\(83\) −1.02760e10 −0.286348 −0.143174 − 0.989698i \(-0.545731\pi\)
−0.143174 + 0.989698i \(0.545731\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.03092e11 1.95695 0.978473 − 0.206373i \(-0.0661660\pi\)
0.978473 + 0.206373i \(0.0661660\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.98809e10 0.826255 0.413128 − 0.910673i \(-0.364436\pi\)
0.413128 + 0.910673i \(0.364436\pi\)
\(98\) 0 0
\(99\) −3.10930e9 −0.0328601
\(100\) 0 0
\(101\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.75654e10 0.190000 0.0949998 − 0.995477i \(-0.469715\pi\)
0.0949998 + 0.995477i \(0.469715\pi\)
\(108\) 0 0
\(109\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 3.89312e11 1.98777 0.993886 − 0.110415i \(-0.0352180\pi\)
0.993886 + 0.110415i \(0.0352180\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.65174e11 −0.929420
\(122\) 0 0
\(123\) −4.64876e11 −1.48888
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 8.63752e10 0.212885
\(130\) 0 0
\(131\) 4.45376e11 1.00864 0.504319 − 0.863518i \(-0.331744\pi\)
0.504319 + 0.863518i \(0.331744\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.23488e11 −0.572658 −0.286329 − 0.958131i \(-0.592435\pi\)
−0.286329 + 0.958131i \(0.592435\pi\)
\(138\) 0 0
\(139\) −7.53192e11 −1.23119 −0.615594 − 0.788064i \(-0.711084\pi\)
−0.615594 + 0.788064i \(0.711084\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 7.79067e11 0.936115
\(148\) 0 0
\(149\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) −1.14279e11 −0.110195
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −2.23132e12 −1.51890 −0.759452 − 0.650564i \(-0.774533\pi\)
−0.759452 + 0.650564i \(0.774533\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −1.79216e12 −1.00000
\(170\) 0 0
\(171\) 2.65240e11 0.138727
\(172\) 0 0
\(173\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −4.13568e12 −1.78934
\(178\) 0 0
\(179\) −4.74910e12 −1.93161 −0.965806 − 0.259267i \(-0.916519\pi\)
−0.965806 + 0.259267i \(0.916519\pi\)
\(180\) 0 0
\(181\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 7.40122e11 0.236687
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) −4.36196e12 −1.17251 −0.586255 − 0.810126i \(-0.699398\pi\)
−0.586255 + 0.810126i \(0.699398\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 8.34617e12 1.79436
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.71782e12 −0.297970
\(210\) 0 0
\(211\) −8.30112e12 −1.36642 −0.683208 − 0.730224i \(-0.739416\pi\)
−0.683208 + 0.730224i \(0.739416\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1.34123e13 −1.79912
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 1.06987e12 0.123688
\(226\) 0 0
\(227\) −9.28745e12 −1.02271 −0.511357 − 0.859368i \(-0.670857\pi\)
−0.511357 + 0.859368i \(0.670857\pi\)
\(228\) 0 0
\(229\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −9.66824e12 −0.922338 −0.461169 − 0.887312i \(-0.652570\pi\)
−0.461169 + 0.887312i \(0.652570\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 2.51654e13 1.99393 0.996967 − 0.0778240i \(-0.0247972\pi\)
0.996967 + 0.0778240i \(0.0247972\pi\)
\(242\) 0 0
\(243\) −3.24775e12 −0.245894
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 4.04874e12 0.268055
\(250\) 0 0
\(251\) −2.73190e13 −1.73085 −0.865425 − 0.501038i \(-0.832952\pi\)
−0.865425 + 0.501038i \(0.832952\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2.43828e13 1.35660 0.678300 − 0.734785i \(-0.262717\pi\)
0.678300 + 0.734785i \(0.262717\pi\)
\(258\) 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
\(267\) −4.06182e13 −1.83193
\(268\) 0 0
\(269\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6.92900e12 −0.265669
\(276\) 0 0
\(277\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −2.87168e12 −0.0977805 −0.0488902 − 0.998804i \(-0.515568\pi\)
−0.0488902 + 0.998804i \(0.515568\pi\)
\(282\) 0 0
\(283\) −6.10677e13 −1.99980 −0.999899 − 0.0142352i \(-0.995469\pi\)
−0.999899 + 0.0142352i \(0.995469\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −7.06964e12 −0.206281
\(290\) 0 0
\(291\) −2.75331e13 −0.773470
\(292\) 0 0
\(293\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.11295e13 0.279458
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −8.59952e13 −1.79975 −0.899877 − 0.436144i \(-0.856344\pi\)
−0.899877 + 0.436144i \(0.856344\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −1.07759e12 −0.0202749 −0.0101375 − 0.999949i \(-0.503227\pi\)
−0.0101375 + 0.999949i \(0.503227\pi\)
\(314\) 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
\(321\) −1.08608e13 −0.177862
\(322\) 0 0
\(323\) −6.31363e13 −0.999229
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 8.96723e13 1.24052 0.620261 − 0.784396i \(-0.287027\pi\)
0.620261 + 0.784396i \(0.287027\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.46423e14 −1.83504 −0.917521 − 0.397688i \(-0.869813\pi\)
−0.917521 + 0.397688i \(0.869813\pi\)
\(338\) 0 0
\(339\) −1.53389e14 −1.86078
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.83373e14 −1.95669 −0.978346 − 0.206978i \(-0.933637\pi\)
−0.978346 + 0.206978i \(0.933637\pi\)
\(348\) 0 0
\(349\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.39733e14 −1.35687 −0.678435 − 0.734661i \(-0.737341\pi\)
−0.678435 + 0.734661i \(0.737341\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 3.00486e13 0.257949
\(362\) 0 0
\(363\) 1.04479e14 0.870044
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) −2.58525e13 −0.196724
\(370\) 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
\(379\) −2.27902e14 −1.49704 −0.748518 − 0.663114i \(-0.769234\pi\)
−0.748518 + 0.663114i \(0.769234\pi\)
\(380\) 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
\(387\) 4.80347e12 0.0281284
\(388\) 0 0
\(389\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −1.75478e14 −0.944201
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4.13821e14 1.99305 0.996527 − 0.0832760i \(-0.0265383\pi\)
0.996527 + 0.0832760i \(0.0265383\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.98376e13 −0.0857058 −0.0428529 − 0.999081i \(-0.513645\pi\)
−0.0428529 + 0.999081i \(0.513645\pi\)
\(410\) 0 0
\(411\) 1.27454e14 0.536074
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 2.96757e14 1.15253
\(418\) 0 0
\(419\) 5.05818e14 1.91345 0.956726 − 0.290990i \(-0.0939848\pi\)
0.956726 + 0.290990i \(0.0939848\pi\)
\(420\) 0 0
\(421\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.54667e14 −0.890909
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 5.83180e13 0.184128 0.0920639 − 0.995753i \(-0.470654\pi\)
0.0920639 + 0.995753i \(0.470654\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 4.33252e13 0.123688
\(442\) 0 0
\(443\) −5.30538e14 −1.47739 −0.738697 − 0.674038i \(-0.764558\pi\)
−0.738697 + 0.674038i \(0.764558\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 7.57469e13 0.195889 0.0979445 − 0.995192i \(-0.468773\pi\)
0.0979445 + 0.995192i \(0.468773\pi\)
\(450\) 0 0
\(451\) 1.67433e14 0.422542
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6.71458e14 1.57572 0.787861 − 0.615852i \(-0.211188\pi\)
0.787861 + 0.615852i \(0.211188\pi\)
\(458\) 0 0
\(459\) 4.09052e14 0.937149
\(460\) 0 0
\(461\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8.00292e14 1.66727 0.833635 − 0.552316i \(-0.186256\pi\)
0.833635 + 0.552316i \(0.186256\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3.11095e13 −0.0604167
\(474\) 0 0
\(475\) 5.91080e14 1.12158
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) 8.79140e14 1.42187
\(490\) 0 0
\(491\) 1.14895e15 1.81699 0.908493 − 0.417900i \(-0.137234\pi\)
0.908493 + 0.417900i \(0.137234\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −4.92696e14 −0.712896 −0.356448 − 0.934315i \(-0.616012\pi\)
−0.356448 + 0.934315i \(0.616012\pi\)
\(500\) 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
\(507\) 7.06111e14 0.936115
\(508\) 0 0
\(509\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −9.49407e14 −1.17980
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.73964e15 −1.98541 −0.992707 − 0.120551i \(-0.961534\pi\)
−0.992707 + 0.120551i \(0.961534\pi\)
\(522\) 0 0
\(523\) 1.75066e15 1.95633 0.978164 − 0.207833i \(-0.0666409\pi\)
0.978164 + 0.207833i \(0.0666409\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −9.52810e14 −1.00000
\(530\) 0 0
\(531\) −2.29992e14 −0.236425
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1.87115e15 1.80821
\(538\) 0 0
\(539\) −2.80595e14 −0.265669
\(540\) 0 0
\(541\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 9.66838e14 0.844158 0.422079 − 0.906559i \(-0.361301\pi\)
0.422079 + 0.906559i \(0.361301\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −2.91608e14 −0.221566
\(562\) 0 0
\(563\) 2.54284e15 1.89462 0.947312 − 0.320312i \(-0.103788\pi\)
0.947312 + 0.320312i \(0.103788\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.88351e15 −1.32389 −0.661944 − 0.749554i \(-0.730268\pi\)
−0.661944 + 0.749554i \(0.730268\pi\)
\(570\) 0 0
\(571\) 2.47349e15 1.70534 0.852672 − 0.522446i \(-0.174980\pi\)
0.852672 + 0.522446i \(0.174980\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −2.15180e15 −1.40067 −0.700335 − 0.713815i \(-0.746966\pi\)
−0.700335 + 0.713815i \(0.746966\pi\)
\(578\) 0 0
\(579\) 1.71861e15 1.09761
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3.30619e15 −1.95803 −0.979013 − 0.203798i \(-0.934671\pi\)
−0.979013 + 0.203798i \(0.934671\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 3.04802e15 1.70693 0.853467 − 0.521147i \(-0.174496\pi\)
0.853467 + 0.521147i \(0.174496\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −2.82295e15 −1.46857 −0.734284 − 0.678842i \(-0.762482\pi\)
−0.734284 + 0.678842i \(0.762482\pi\)
\(602\) 0 0
\(603\) 4.64144e14 0.237087
\(604\) 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
\(613\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.33363e15 −1.50089 −0.750446 − 0.660932i \(-0.770161\pi\)
−0.750446 + 0.660932i \(0.770161\pi\)
\(618\) 0 0
\(619\) −1.05475e15 −0.466501 −0.233250 − 0.972417i \(-0.574936\pi\)
−0.233250 + 0.972417i \(0.574936\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 2.38419e15 1.00000
\(626\) 0 0
\(627\) 6.76820e14 0.278934
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 3.27064e15 1.27912
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 5.32742e15 1.94446 0.972228 − 0.234035i \(-0.0751931\pi\)
0.972228 + 0.234035i \(0.0751931\pi\)
\(642\) 0 0
\(643\) −1.53164e15 −0.549535 −0.274768 − 0.961511i \(-0.588601\pi\)
−0.274768 + 0.961511i \(0.588601\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 1.48954e15 0.507815
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −7.45879e14 −0.237716
\(658\) 0 0
\(659\) 4.57143e15 1.43279 0.716395 − 0.697695i \(-0.245791\pi\)
0.716395 + 0.697695i \(0.245791\pi\)
\(660\) 0 0
\(661\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 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
\(673\) −6.05904e15 −1.69169 −0.845845 − 0.533428i \(-0.820904\pi\)
−0.845845 + 0.533428i \(0.820904\pi\)
\(674\) 0 0
\(675\) −3.82953e15 −1.05190
\(676\) 0 0
\(677\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 3.65925e15 0.957378
\(682\) 0 0
\(683\) −5.78836e15 −1.49019 −0.745094 − 0.666959i \(-0.767596\pi\)
−0.745094 + 0.666959i \(0.767596\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −6.20853e15 −1.49920 −0.749600 − 0.661891i \(-0.769754\pi\)
−0.749600 + 0.661891i \(0.769754\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 6.15379e15 1.41698
\(698\) 0 0
\(699\) 3.80929e15 0.863415
\(700\) 0 0
\(701\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 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
\(719\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −9.91518e15 −1.86655
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 6.06604e15 1.09120
\(730\) 0 0
\(731\) −1.14339e15 −0.202605
\(732\) 0 0
\(733\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.00602e15 −0.509238
\(738\) 0 0
\(739\) −1.09294e16 −1.82411 −0.912054 − 0.410069i \(-0.865505\pi\)
−0.912054 + 0.410069i \(0.865505\pi\)
\(740\) 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
\(747\) 2.25157e14 0.0354179
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) 1.07637e16 1.62028
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −9.08212e15 −1.28995 −0.644973 − 0.764205i \(-0.723131\pi\)
−0.644973 + 0.764205i \(0.723131\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −1.45370e16 −1.94930 −0.974652 − 0.223727i \(-0.928178\pi\)
−0.974652 + 0.223727i \(0.928178\pi\)
\(770\) 0 0
\(771\) −9.60683e15 −1.26993
\(772\) 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
\(779\) −1.42829e16 −1.78386
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 7.63629e15 0.901616 0.450808 − 0.892621i \(-0.351136\pi\)
0.450808 + 0.892621i \(0.351136\pi\)
\(788\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −2.25884e15 −0.242051
\(802\) 0 0
\(803\) 4.83066e15 0.510589
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.80914e16 −1.83550 −0.917751 − 0.397156i \(-0.869997\pi\)
−0.917751 + 0.397156i \(0.869997\pi\)
\(810\) 0 0
\(811\) −1.96573e16 −1.96747 −0.983735 − 0.179624i \(-0.942512\pi\)
−0.983735 + 0.179624i \(0.942512\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 2.65380e15 0.255063
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 2.73003e15 0.248697
\(826\) 0 0
\(827\) −1.66664e16 −1.49817 −0.749084 − 0.662476i \(-0.769506\pi\)
−0.749084 + 0.662476i \(0.769506\pi\)
\(828\) 0 0
\(829\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.03129e16 −0.890909
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −1.22005e16 −1.00000
\(842\) 0 0
\(843\) 1.13144e15 0.0915338
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 2.40607e16 1.87204
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −9.21957e15 −0.681265 −0.340632 − 0.940197i \(-0.610641\pi\)
−0.340632 + 0.940197i \(0.610641\pi\)
\(858\) 0 0
\(859\) 7.44102e14 0.0542838 0.0271419 − 0.999632i \(-0.491359\pi\)
0.0271419 + 0.999632i \(0.491359\pi\)
\(860\) 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
\(867\) 2.78544e15 0.193103
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −1.53116e15 −0.102198
\(874\) 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
\(881\) 7.70775e15 0.489283 0.244642 − 0.969614i \(-0.421330\pi\)
0.244642 + 0.969614i \(0.421330\pi\)
\(882\) 0 0
\(883\) −1.15436e16 −0.723696 −0.361848 − 0.932237i \(-0.617854\pi\)
−0.361848 + 0.932237i \(0.617854\pi\)
\(884\) 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
\(891\) −3.83423e15 −0.228745
\(892\) 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
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 3.56914e16 1.93074 0.965369 − 0.260890i \(-0.0840160\pi\)
0.965369 + 0.260890i \(0.0840160\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) −1.45823e15 −0.0760739
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) 3.38821e16 1.68478
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −2.36437e16 −1.12106 −0.560531 − 0.828134i \(-0.689403\pi\)
−0.560531 + 0.828134i \(0.689403\pi\)
\(930\) 0 0
\(931\) 2.39362e16 1.12158
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 8.50916e15 0.384874 0.192437 − 0.981309i \(-0.438361\pi\)
0.192437 + 0.981309i \(0.438361\pi\)
\(938\) 0 0
\(939\) 4.24570e14 0.0189797
\(940\) 0 0
\(941\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2.95682e16 −1.26154 −0.630770 − 0.775970i \(-0.717261\pi\)
−0.630770 + 0.775970i \(0.717261\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 4.51561e16 1.86083 0.930413 − 0.366514i \(-0.119449\pi\)
0.930413 + 0.366514i \(0.119449\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −2.54085e16 −1.00000
\(962\) 0 0
\(963\) −6.03985e14 −0.0235007
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 0 0
\(969\) 2.48757e16 0.935393
\(970\) 0 0
\(971\) 4.63209e16 1.72215 0.861076 − 0.508477i \(-0.169791\pi\)
0.861076 + 0.508477i \(0.169791\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4.84738e16 1.74215 0.871077 − 0.491146i \(-0.163422\pi\)
0.871077 + 0.491146i \(0.163422\pi\)
\(978\) 0 0
\(979\) 1.46293e16 0.519900
\(980\) 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
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0 0
\(993\) −3.53309e16 −1.16127
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) 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 256.12.a.a.1.1 1
4.3 odd 2 256.12.a.d.1.1 1
8.3 odd 2 CM 256.12.a.a.1.1 1
8.5 even 2 256.12.a.d.1.1 1
16.3 odd 4 64.12.b.a.33.2 yes 2
16.5 even 4 64.12.b.a.33.2 yes 2
16.11 odd 4 64.12.b.a.33.1 ✓ 2
16.13 even 4 64.12.b.a.33.1 ✓ 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
64.12.b.a.33.1 ✓ 2 16.11 odd 4
64.12.b.a.33.1 ✓ 2 16.13 even 4
64.12.b.a.33.2 yes 2 16.3 odd 4
64.12.b.a.33.2 yes 2 16.5 even 4
256.12.a.a.1.1 1 1.1 even 1 trivial
256.12.a.a.1.1 1 8.3 odd 2 CM
256.12.a.d.1.1 1 4.3 odd 2
256.12.a.d.1.1 1 8.5 even 2