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Properties

Label 52.3.b.b.51.1
Level $52$
Weight $3$
Character 52.51
Self dual yes
Analytic conductor $1.417$
Analytic rank $0$
Dimension $1$
CM discriminant -52
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] = [52,3,Mod(51,52)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(52, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("52.51");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 52 = 2^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 52.b (of order \(2\), degree \(1\), 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: \(1.41689737467\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 51.1
Character \(\chi\) \(=\) 52.51

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} +4.00000 q^{4} -12.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +4.00000 q^{4} -12.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -4.00000 q^{11} -13.0000 q^{13} -24.0000 q^{14} +16.0000 q^{16} -18.0000 q^{17} +18.0000 q^{18} +12.0000 q^{19} -8.00000 q^{22} +25.0000 q^{25} -26.0000 q^{26} -48.0000 q^{28} +6.00000 q^{29} +36.0000 q^{31} +32.0000 q^{32} -36.0000 q^{34} +36.0000 q^{36} +24.0000 q^{38} -16.0000 q^{44} +68.0000 q^{47} +95.0000 q^{49} +50.0000 q^{50} -52.0000 q^{52} -102.000 q^{53} -96.0000 q^{56} +12.0000 q^{58} -116.000 q^{59} -86.0000 q^{61} +72.0000 q^{62} -108.000 q^{63} +64.0000 q^{64} +108.000 q^{67} -72.0000 q^{68} -92.0000 q^{71} +72.0000 q^{72} +48.0000 q^{76} +48.0000 q^{77} +81.0000 q^{81} -68.0000 q^{83} -32.0000 q^{88} +156.000 q^{91} +136.000 q^{94} +190.000 q^{98} -36.0000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/52\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 1.00000
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) 4.00000 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) −12.0000 −1.71429 −0.857143 − 0.515079i \(-0.827763\pi\)
−0.857143 + 0.515079i \(0.827763\pi\)
\(8\) 8.00000 1.00000
\(9\) 9.00000 1.00000
\(10\) 0 0
\(11\) −4.00000 −0.363636 −0.181818 − 0.983332i \(-0.558198\pi\)
−0.181818 + 0.983332i \(0.558198\pi\)
\(12\) 0 0
\(13\) −13.0000 −1.00000
\(14\) −24.0000 −1.71429
\(15\) 0 0
\(16\) 16.0000 1.00000
\(17\) −18.0000 −1.05882 −0.529412 − 0.848365i \(-0.677587\pi\)
−0.529412 + 0.848365i \(0.677587\pi\)
\(18\) 18.0000 1.00000
\(19\) 12.0000 0.631579 0.315789 − 0.948829i \(-0.397731\pi\)
0.315789 + 0.948829i \(0.397731\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −8.00000 −0.363636
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 25.0000 1.00000
\(26\) −26.0000 −1.00000
\(27\) 0 0
\(28\) −48.0000 −1.71429
\(29\) 6.00000 0.206897 0.103448 − 0.994635i \(-0.467012\pi\)
0.103448 + 0.994635i \(0.467012\pi\)
\(30\) 0 0
\(31\) 36.0000 1.16129 0.580645 − 0.814157i \(-0.302800\pi\)
0.580645 + 0.814157i \(0.302800\pi\)
\(32\) 32.0000 1.00000
\(33\) 0 0
\(34\) −36.0000 −1.05882
\(35\) 0 0
\(36\) 36.0000 1.00000
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 24.0000 0.631579
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −16.0000 −0.363636
\(45\) 0 0
\(46\) 0 0
\(47\) 68.0000 1.44681 0.723404 − 0.690425i \(-0.242576\pi\)
0.723404 + 0.690425i \(0.242576\pi\)
\(48\) 0 0
\(49\) 95.0000 1.93878
\(50\) 50.0000 1.00000
\(51\) 0 0
\(52\) −52.0000 −1.00000
\(53\) −102.000 −1.92453 −0.962264 − 0.272117i \(-0.912276\pi\)
−0.962264 + 0.272117i \(0.912276\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −96.0000 −1.71429
\(57\) 0 0
\(58\) 12.0000 0.206897
\(59\) −116.000 −1.96610 −0.983051 − 0.183333i \(-0.941311\pi\)
−0.983051 + 0.183333i \(0.941311\pi\)
\(60\) 0 0
\(61\) −86.0000 −1.40984 −0.704918 − 0.709289i \(-0.749016\pi\)
−0.704918 + 0.709289i \(0.749016\pi\)
\(62\) 72.0000 1.16129
\(63\) −108.000 −1.71429
\(64\) 64.0000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 108.000 1.61194 0.805970 − 0.591956i \(-0.201644\pi\)
0.805970 + 0.591956i \(0.201644\pi\)
\(68\) −72.0000 −1.05882
\(69\) 0 0
\(70\) 0 0
\(71\) −92.0000 −1.29577 −0.647887 − 0.761736i \(-0.724347\pi\)
−0.647887 + 0.761736i \(0.724347\pi\)
\(72\) 72.0000 1.00000
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 48.0000 0.631579
\(77\) 48.0000 0.623377
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 81.0000 1.00000
\(82\) 0 0
\(83\) −68.0000 −0.819277 −0.409639 − 0.912248i \(-0.634345\pi\)
−0.409639 + 0.912248i \(0.634345\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −32.0000 −0.363636
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 156.000 1.71429
\(92\) 0 0
\(93\) 0 0
\(94\) 136.000 1.44681
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 190.000 1.93878
\(99\) −36.0000 −0.363636
\(100\) 100.000 1.00000
\(101\) −6.00000 −0.0594059 −0.0297030 − 0.999559i \(-0.509456\pi\)
−0.0297030 + 0.999559i \(0.509456\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) −104.000 −1.00000
\(105\) 0 0
\(106\) −204.000 −1.92453
\(107\) 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
\(112\) −192.000 −1.71429
\(113\) 174.000 1.53982 0.769912 − 0.638151i \(-0.220300\pi\)
0.769912 + 0.638151i \(0.220300\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 24.0000 0.206897
\(117\) −117.000 −1.00000
\(118\) −232.000 −1.96610
\(119\) 216.000 1.81513
\(120\) 0 0
\(121\) −105.000 −0.867769
\(122\) −172.000 −1.40984
\(123\) 0 0
\(124\) 144.000 1.16129
\(125\) 0 0
\(126\) −216.000 −1.71429
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 128.000 1.00000
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) −144.000 −1.08271
\(134\) 216.000 1.61194
\(135\) 0 0
\(136\) −144.000 −1.05882
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −184.000 −1.29577
\(143\) 52.0000 0.363636
\(144\) 144.000 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 276.000 1.82781 0.913907 − 0.405923i \(-0.133050\pi\)
0.913907 + 0.405923i \(0.133050\pi\)
\(152\) 96.0000 0.631579
\(153\) −162.000 −1.05882
\(154\) 96.0000 0.623377
\(155\) 0 0
\(156\) 0 0
\(157\) 262.000 1.66879 0.834395 − 0.551167i \(-0.185817\pi\)
0.834395 + 0.551167i \(0.185817\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 162.000 1.00000
\(163\) −324.000 −1.98773 −0.993865 − 0.110600i \(-0.964723\pi\)
−0.993865 + 0.110600i \(0.964723\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −136.000 −0.819277
\(167\) −316.000 −1.89222 −0.946108 − 0.323852i \(-0.895022\pi\)
−0.946108 + 0.323852i \(0.895022\pi\)
\(168\) 0 0
\(169\) 169.000 1.00000
\(170\) 0 0
\(171\) 108.000 0.631579
\(172\) 0 0
\(173\) 138.000 0.797688 0.398844 − 0.917019i \(-0.369412\pi\)
0.398844 + 0.917019i \(0.369412\pi\)
\(174\) 0 0
\(175\) −300.000 −1.71429
\(176\) −64.0000 −0.363636
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) −106.000 −0.585635 −0.292818 − 0.956168i \(-0.594593\pi\)
−0.292818 + 0.956168i \(0.594593\pi\)
\(182\) 312.000 1.71429
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 72.0000 0.385027
\(188\) 272.000 1.44681
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 380.000 1.93878
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −72.0000 −0.363636
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 200.000 1.00000
\(201\) 0 0
\(202\) −12.0000 −0.0594059
\(203\) −72.0000 −0.354680
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −208.000 −1.00000
\(209\) −48.0000 −0.229665
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) −408.000 −1.92453
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −432.000 −1.99078
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 234.000 1.05882
\(222\) 0 0
\(223\) −204.000 −0.914798 −0.457399 − 0.889262i \(-0.651219\pi\)
−0.457399 + 0.889262i \(0.651219\pi\)
\(224\) −384.000 −1.71429
\(225\) 225.000 1.00000
\(226\) 348.000 1.53982
\(227\) 428.000 1.88546 0.942731 − 0.333553i \(-0.108248\pi\)
0.942731 + 0.333553i \(0.108248\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 48.0000 0.206897
\(233\) −366.000 −1.57082 −0.785408 − 0.618979i \(-0.787547\pi\)
−0.785408 + 0.618979i \(0.787547\pi\)
\(234\) −234.000 −1.00000
\(235\) 0 0
\(236\) −464.000 −1.96610
\(237\) 0 0
\(238\) 432.000 1.81513
\(239\) 244.000 1.02092 0.510460 − 0.859901i \(-0.329475\pi\)
0.510460 + 0.859901i \(0.329475\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −210.000 −0.867769
\(243\) 0 0
\(244\) −344.000 −1.40984
\(245\) 0 0
\(246\) 0 0
\(247\) −156.000 −0.631579
\(248\) 288.000 1.16129
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −432.000 −1.71429
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 256.000 1.00000
\(257\) −318.000 −1.23735 −0.618677 − 0.785645i \(-0.712331\pi\)
−0.618677 + 0.785645i \(0.712331\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 54.0000 0.206897
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −288.000 −1.08271
\(267\) 0 0
\(268\) 432.000 1.61194
\(269\) 486.000 1.80669 0.903346 − 0.428913i \(-0.141103\pi\)
0.903346 + 0.428913i \(0.141103\pi\)
\(270\) 0 0
\(271\) 516.000 1.90406 0.952030 − 0.306006i \(-0.0989928\pi\)
0.952030 + 0.306006i \(0.0989928\pi\)
\(272\) −288.000 −1.05882
\(273\) 0 0
\(274\) 0 0
\(275\) −100.000 −0.363636
\(276\) 0 0
\(277\) 346.000 1.24910 0.624549 − 0.780986i \(-0.285283\pi\)
0.624549 + 0.780986i \(0.285283\pi\)
\(278\) 0 0
\(279\) 324.000 1.16129
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) −368.000 −1.29577
\(285\) 0 0
\(286\) 104.000 0.363636
\(287\) 0 0
\(288\) 288.000 1.00000
\(289\) 35.0000 0.121107
\(290\) 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
\(301\) 0 0
\(302\) 552.000 1.82781
\(303\) 0 0
\(304\) 192.000 0.631579
\(305\) 0 0
\(306\) −324.000 −1.05882
\(307\) −36.0000 −0.117264 −0.0586319 − 0.998280i \(-0.518674\pi\)
−0.0586319 + 0.998280i \(0.518674\pi\)
\(308\) 192.000 0.623377
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 158.000 0.504792 0.252396 − 0.967624i \(-0.418781\pi\)
0.252396 + 0.967624i \(0.418781\pi\)
\(314\) 524.000 1.66879
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) −24.0000 −0.0752351
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −216.000 −0.668731
\(324\) 324.000 1.00000
\(325\) −325.000 −1.00000
\(326\) −648.000 −1.98773
\(327\) 0 0
\(328\) 0 0
\(329\) −816.000 −2.48024
\(330\) 0 0
\(331\) −612.000 −1.84894 −0.924471 − 0.381252i \(-0.875493\pi\)
−0.924471 + 0.381252i \(0.875493\pi\)
\(332\) −272.000 −0.819277
\(333\) 0 0
\(334\) −632.000 −1.89222
\(335\) 0 0
\(336\) 0 0
\(337\) 622.000 1.84570 0.922849 − 0.385163i \(-0.125855\pi\)
0.922849 + 0.385163i \(0.125855\pi\)
\(338\) 338.000 1.00000
\(339\) 0 0
\(340\) 0 0
\(341\) −144.000 −0.422287
\(342\) 216.000 0.631579
\(343\) −552.000 −1.60933
\(344\) 0 0
\(345\) 0 0
\(346\) 276.000 0.797688
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) −600.000 −1.71429
\(351\) 0 0
\(352\) −128.000 −0.363636
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −556.000 −1.54875 −0.774373 − 0.632729i \(-0.781935\pi\)
−0.774373 + 0.632729i \(0.781935\pi\)
\(360\) 0 0
\(361\) −217.000 −0.601108
\(362\) −212.000 −0.585635
\(363\) 0 0
\(364\) 624.000 1.71429
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1224.00 3.29919
\(372\) 0 0
\(373\) 278.000 0.745308 0.372654 − 0.927970i \(-0.378448\pi\)
0.372654 + 0.927970i \(0.378448\pi\)
\(374\) 144.000 0.385027
\(375\) 0 0
\(376\) 544.000 1.44681
\(377\) −78.0000 −0.206897
\(378\) 0 0
\(379\) −516.000 −1.36148 −0.680739 − 0.732526i \(-0.738341\pi\)
−0.680739 + 0.732526i \(0.738341\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 116.000 0.302872 0.151436 − 0.988467i \(-0.451610\pi\)
0.151436 + 0.988467i \(0.451610\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −522.000 −1.34190 −0.670951 − 0.741502i \(-0.734114\pi\)
−0.670951 + 0.741502i \(0.734114\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 760.000 1.93878
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −144.000 −0.363636
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 400.000 1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) −468.000 −1.16129
\(404\) −24.0000 −0.0594059
\(405\) 0 0
\(406\) −144.000 −0.354680
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1392.00 3.37046
\(414\) 0 0
\(415\) 0 0
\(416\) −416.000 −1.00000
\(417\) 0 0
\(418\) −96.0000 −0.229665
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 612.000 1.44681
\(424\) −816.000 −1.92453
\(425\) −450.000 −1.05882
\(426\) 0 0
\(427\) 1032.00 2.41686
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −412.000 −0.955916 −0.477958 − 0.878383i \(-0.658623\pi\)
−0.477958 + 0.878383i \(0.658623\pi\)
\(432\) 0 0
\(433\) 34.0000 0.0785219 0.0392610 − 0.999229i \(-0.487500\pi\)
0.0392610 + 0.999229i \(0.487500\pi\)
\(434\) −864.000 −1.99078
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 855.000 1.93878
\(442\) 468.000 1.05882
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −408.000 −0.914798
\(447\) 0 0
\(448\) −768.000 −1.71429
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 450.000 1.00000
\(451\) 0 0
\(452\) 696.000 1.53982
\(453\) 0 0
\(454\) 856.000 1.88546
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −348.000 −0.751620 −0.375810 − 0.926697i \(-0.622635\pi\)
−0.375810 + 0.926697i \(0.622635\pi\)
\(464\) 96.0000 0.206897
\(465\) 0 0
\(466\) −732.000 −1.57082
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) −468.000 −1.00000
\(469\) −1296.00 −2.76333
\(470\) 0 0
\(471\) 0 0
\(472\) −928.000 −1.96610
\(473\) 0 0
\(474\) 0 0
\(475\) 300.000 0.631579
\(476\) 864.000 1.81513
\(477\) −918.000 −1.92453
\(478\) 488.000 1.02092
\(479\) 724.000 1.51148 0.755741 − 0.654870i \(-0.227277\pi\)
0.755741 + 0.654870i \(0.227277\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −420.000 −0.867769
\(485\) 0 0
\(486\) 0 0
\(487\) 948.000 1.94661 0.973306 − 0.229511i \(-0.0737128\pi\)
0.973306 + 0.229511i \(0.0737128\pi\)
\(488\) −688.000 −1.40984
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) −108.000 −0.219067
\(494\) −312.000 −0.631579
\(495\) 0 0
\(496\) 576.000 1.16129
\(497\) 1104.00 2.22133
\(498\) 0 0
\(499\) −276.000 −0.553106 −0.276553 − 0.960999i \(-0.589192\pi\)
−0.276553 + 0.960999i \(0.589192\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) −864.000 −1.71429
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 1.00000
\(513\) 0 0
\(514\) −636.000 −1.23735
\(515\) 0 0
\(516\) 0 0
\(517\) −272.000 −0.526112
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −258.000 −0.495202 −0.247601 − 0.968862i \(-0.579642\pi\)
−0.247601 + 0.968862i \(0.579642\pi\)
\(522\) 108.000 0.206897
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −648.000 −1.22960
\(528\) 0 0
\(529\) 529.000 1.00000
\(530\) 0 0
\(531\) −1044.00 −1.96610
\(532\) −576.000 −1.08271
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 864.000 1.61194
\(537\) 0 0
\(538\) 972.000 1.80669
\(539\) −380.000 −0.705009
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 1032.00 1.90406
\(543\) 0 0
\(544\) −576.000 −1.05882
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) −774.000 −1.40984
\(550\) −200.000 −0.363636
\(551\) 72.0000 0.130672
\(552\) 0 0
\(553\) 0 0
\(554\) 692.000 1.24910
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 648.000 1.16129
\(559\) 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
\(567\) −972.000 −1.71429
\(568\) −736.000 −1.29577
\(569\) 306.000 0.537786 0.268893 − 0.963170i \(-0.413342\pi\)
0.268893 + 0.963170i \(0.413342\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 208.000 0.363636
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 576.000 1.00000
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 70.0000 0.121107
\(579\) 0 0
\(580\) 0 0
\(581\) 816.000 1.40448
\(582\) 0 0
\(583\) 408.000 0.699828
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −932.000 −1.58773 −0.793867 − 0.608091i \(-0.791935\pi\)
−0.793867 + 0.608091i \(0.791935\pi\)
\(588\) 0 0
\(589\) 432.000 0.733447
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 734.000 1.22130 0.610649 − 0.791901i \(-0.290909\pi\)
0.610649 + 0.791901i \(0.290909\pi\)
\(602\) 0 0
\(603\) 972.000 1.61194
\(604\) 1104.00 1.82781
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 384.000 0.631579
\(609\) 0 0
\(610\) 0 0
\(611\) −884.000 −1.44681
\(612\) −648.000 −1.05882
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) −72.0000 −0.117264
\(615\) 0 0
\(616\) 384.000 0.623377
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 1212.00 1.95800 0.978998 − 0.203868i \(-0.0653513\pi\)
0.978998 + 0.203868i \(0.0653513\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 625.000 1.00000
\(626\) 316.000 0.504792
\(627\) 0 0
\(628\) 1048.00 1.66879
\(629\) 0 0
\(630\) 0 0
\(631\) −12.0000 −0.0190174 −0.00950872 − 0.999955i \(-0.503027\pi\)
−0.00950872 + 0.999955i \(0.503027\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −1235.00 −1.93878
\(638\) −48.0000 −0.0752351
\(639\) −828.000 −1.29577
\(640\) 0 0
\(641\) −1266.00 −1.97504 −0.987520 − 0.157497i \(-0.949658\pi\)
−0.987520 + 0.157497i \(0.949658\pi\)
\(642\) 0 0
\(643\) 636.000 0.989114 0.494557 − 0.869145i \(-0.335330\pi\)
0.494557 + 0.869145i \(0.335330\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −432.000 −0.668731
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 648.000 1.00000
\(649\) 464.000 0.714946
\(650\) −650.000 −1.00000
\(651\) 0 0
\(652\) −1296.00 −1.98773
\(653\) −1242.00 −1.90199 −0.950995 − 0.309205i \(-0.899937\pi\)
−0.950995 + 0.309205i \(0.899937\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) −1632.00 −2.48024
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) −1224.00 −1.84894
\(663\) 0 0
\(664\) −544.000 −0.819277
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −1264.00 −1.89222
\(669\) 0 0
\(670\) 0 0
\(671\) 344.000 0.512668
\(672\) 0 0
\(673\) −1202.00 −1.78603 −0.893016 − 0.450024i \(-0.851415\pi\)
−0.893016 + 0.450024i \(0.851415\pi\)
\(674\) 1244.00 1.84570
\(675\) 0 0
\(676\) 676.000 1.00000
\(677\) 1146.00 1.69276 0.846381 − 0.532578i \(-0.178777\pi\)
0.846381 + 0.532578i \(0.178777\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) −288.000 −0.422287
\(683\) 92.0000 0.134700 0.0673499 − 0.997729i \(-0.478546\pi\)
0.0673499 + 0.997729i \(0.478546\pi\)
\(684\) 432.000 0.631579
\(685\) 0 0
\(686\) −1104.00 −1.60933
\(687\) 0 0
\(688\) 0 0
\(689\) 1326.00 1.92453
\(690\) 0 0
\(691\) 1356.00 1.96237 0.981187 − 0.193061i \(-0.0618416\pi\)
0.981187 + 0.193061i \(0.0618416\pi\)
\(692\) 552.000 0.797688
\(693\) 432.000 0.623377
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −1200.00 −1.71429
\(701\) −1146.00 −1.63481 −0.817404 − 0.576065i \(-0.804587\pi\)
−0.817404 + 0.576065i \(0.804587\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −256.000 −0.363636
\(705\) 0 0
\(706\) 0 0
\(707\) 72.0000 0.101839
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) −1112.00 −1.54875
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −434.000 −0.601108
\(723\) 0 0
\(724\) −424.000 −0.585635
\(725\) 150.000 0.206897
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 1248.00 1.71429
\(729\) 729.000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −432.000 −0.586160
\(738\) 0 0
\(739\) 204.000 0.276049 0.138024 − 0.990429i \(-0.455925\pi\)
0.138024 + 0.990429i \(0.455925\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 2448.00 3.29919
\(743\) 1252.00 1.68506 0.842530 − 0.538649i \(-0.181065\pi\)
0.842530 + 0.538649i \(0.181065\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 556.000 0.745308
\(747\) −612.000 −0.819277
\(748\) 288.000 0.385027
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 1088.00 1.44681
\(753\) 0 0
\(754\) −156.000 −0.206897
\(755\) 0 0
\(756\) 0 0
\(757\) −358.000 −0.472919 −0.236460 − 0.971641i \(-0.575987\pi\)
−0.236460 + 0.971641i \(0.575987\pi\)
\(758\) −1032.00 −1.36148
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 232.000 0.302872
\(767\) 1508.00 1.96610
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 900.000 1.16129
\(776\) 0 0
\(777\) 0 0
\(778\) −1044.00 −1.34190
\(779\) 0 0
\(780\) 0 0
\(781\) 368.000 0.471191
\(782\) 0 0
\(783\) 0 0
\(784\) 1520.00 1.93878
\(785\) 0 0
\(786\) 0 0
\(787\) −1572.00 −1.99746 −0.998729 − 0.0503953i \(-0.983952\pi\)
−0.998729 + 0.0503953i \(0.983952\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −2088.00 −2.63970
\(792\) −288.000 −0.363636
\(793\) 1118.00 1.40984
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1542.00 1.93476 0.967378 − 0.253339i \(-0.0815287\pi\)
0.967378 + 0.253339i \(0.0815287\pi\)
\(798\) 0 0
\(799\) −1224.00 −1.53191
\(800\) 800.000 1.00000
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) −936.000 −1.16129
\(807\) 0 0
\(808\) −48.0000 −0.0594059
\(809\) 318.000 0.393078 0.196539 − 0.980496i \(-0.437030\pi\)
0.196539 + 0.980496i \(0.437030\pi\)
\(810\) 0 0
\(811\) −1524.00 −1.87916 −0.939581 − 0.342327i \(-0.888785\pi\)
−0.939581 + 0.342327i \(0.888785\pi\)
\(812\) −288.000 −0.354680
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 1404.00 1.71429
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 2784.00 3.37046
\(827\) −1492.00 −1.80411 −0.902056 − 0.431620i \(-0.857942\pi\)
−0.902056 + 0.431620i \(0.857942\pi\)
\(828\) 0 0
\(829\) −214.000 −0.258142 −0.129071 − 0.991635i \(-0.541200\pi\)
−0.129071 + 0.991635i \(0.541200\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −832.000 −1.00000
\(833\) −1710.00 −2.05282
\(834\) 0 0
\(835\) 0 0
\(836\) −192.000 −0.229665
\(837\) 0 0
\(838\) 0 0
\(839\) −428.000 −0.510131 −0.255066 − 0.966924i \(-0.582097\pi\)
−0.255066 + 0.966924i \(0.582097\pi\)
\(840\) 0 0
\(841\) −805.000 −0.957194
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 1224.00 1.44681
\(847\) 1260.00 1.48760
\(848\) −1632.00 −1.92453
\(849\) 0 0
\(850\) −900.000 −1.05882
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 2064.00 2.41686
\(855\) 0 0
\(856\) 0 0
\(857\) −1614.00 −1.88331 −0.941657 − 0.336574i \(-0.890732\pi\)
−0.941657 + 0.336574i \(0.890732\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −824.000 −0.955916
\(863\) 452.000 0.523754 0.261877 − 0.965101i \(-0.415658\pi\)
0.261877 + 0.965101i \(0.415658\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 68.0000 0.0785219
\(867\) 0 0
\(868\) −1728.00 −1.99078
\(869\) 0 0
\(870\) 0 0
\(871\) −1404.00 −1.61194
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1566.00 −1.77753 −0.888763 − 0.458367i \(-0.848434\pi\)
−0.888763 + 0.458367i \(0.848434\pi\)
\(882\) 1710.00 1.93878
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 936.000 1.05882
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −324.000 −0.363636
\(892\) −816.000 −0.914798
\(893\) 816.000 0.913774
\(894\) 0 0
\(895\) 0 0
\(896\) −1536.00 −1.71429
\(897\) 0 0
\(898\) 0 0
\(899\) 216.000 0.240267
\(900\) 900.000 1.00000
\(901\) 1836.00 2.03774
\(902\) 0 0
\(903\) 0 0
\(904\) 1392.00 1.53982
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 1712.00 1.88546
\(909\) −54.0000 −0.0594059
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 272.000 0.297919
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1196.00 1.29577
\(924\) 0 0
\(925\) 0 0
\(926\) −696.000 −0.751620
\(927\) 0 0
\(928\) 192.000 0.206897
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 1140.00 1.22449
\(932\) −1464.00 −1.57082
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) −936.000 −1.00000
\(937\) 1042.00 1.11206 0.556030 − 0.831162i \(-0.312324\pi\)
0.556030 + 0.831162i \(0.312324\pi\)
\(938\) −2592.00 −2.76333
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −1856.00 −1.96610
\(945\) 0 0
\(946\) 0 0
\(947\) −212.000 −0.223865 −0.111932 − 0.993716i \(-0.535704\pi\)
−0.111932 + 0.993716i \(0.535704\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 600.000 0.631579
\(951\) 0 0
\(952\) 1728.00 1.81513
\(953\) −1422.00 −1.49213 −0.746065 − 0.665873i \(-0.768059\pi\)
−0.746065 + 0.665873i \(0.768059\pi\)
\(954\) −1836.00 −1.92453
\(955\) 0 0
\(956\) 976.000 1.02092
\(957\) 0 0
\(958\) 1448.00 1.51148
\(959\) 0 0
\(960\) 0 0
\(961\) 335.000 0.348595
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −1212.00 −1.25336 −0.626680 − 0.779276i \(-0.715587\pi\)
−0.626680 + 0.779276i \(0.715587\pi\)
\(968\) −840.000 −0.867769
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 1896.00 1.94661
\(975\) 0 0
\(976\) −1376.00 −1.40984
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1732.00 1.76195 0.880977 − 0.473160i \(-0.156887\pi\)
0.880977 + 0.473160i \(0.156887\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −216.000 −0.219067
\(987\) 0 0
\(988\) −624.000 −0.631579
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 1152.00 1.16129
\(993\) 0 0
\(994\) 2208.00 2.22133
\(995\) 0 0
\(996\) 0 0
\(997\) 122.000 0.122367 0.0611836 − 0.998127i \(-0.480512\pi\)
0.0611836 + 0.998127i \(0.480512\pi\)
\(998\) −552.000 −0.553106
\(999\) 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 52.3.b.b.51.1 yes 1
3.2 odd 2 468.3.e.a.415.1 1
4.3 odd 2 52.3.b.a.51.1 ✓ 1
8.3 odd 2 832.3.c.b.831.1 1
8.5 even 2 832.3.c.a.831.1 1
12.11 even 2 468.3.e.b.415.1 1
13.12 even 2 52.3.b.a.51.1 ✓ 1
39.38 odd 2 468.3.e.b.415.1 1
52.51 odd 2 CM 52.3.b.b.51.1 yes 1
104.51 odd 2 832.3.c.a.831.1 1
104.77 even 2 832.3.c.b.831.1 1
156.155 even 2 468.3.e.a.415.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
52.3.b.a.51.1 ✓ 1 4.3 odd 2
52.3.b.a.51.1 ✓ 1 13.12 even 2
52.3.b.b.51.1 yes 1 1.1 even 1 trivial
52.3.b.b.51.1 yes 1 52.51 odd 2 CM
468.3.e.a.415.1 1 3.2 odd 2
468.3.e.a.415.1 1 156.155 even 2
468.3.e.b.415.1 1 12.11 even 2
468.3.e.b.415.1 1 39.38 odd 2
832.3.c.a.831.1 1 8.5 even 2
832.3.c.a.831.1 1 104.51 odd 2
832.3.c.b.831.1 1 8.3 odd 2
832.3.c.b.831.1 1 104.77 even 2