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Properties

Label 4032.2.k.b.3905.3
Level $4032$
Weight $2$
Character 4032.3905
Analytic conductor $32.196$
Analytic rank $0$
Dimension $4$
CM discriminant -7
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4032,2,Mod(3905,4032)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4032.3905");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4032.k (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: no
Analytic conductor: \(32.1956820950\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{7})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 8x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2\cdot 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 3905.3
Root \(-2.57794i\) of defining polynomial
Character \(\chi\) \(=\) 4032.3905
Dual form 4032.2.k.b.3905.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.64575 q^{7} +O(q^{10})\) \(q+2.64575 q^{7} -6.57008i q^{11} -1.91520i q^{23} -5.00000 q^{25} -8.89753i q^{29} -10.5830 q^{37} -5.29150 q^{43} +7.00000 q^{49} -0.412247i q^{53} -4.00000 q^{67} +15.0554i q^{71} -17.3828i q^{77} -8.00000 q^{79} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 20 q^{25} + 28 q^{49} - 16 q^{67} - 32 q^{79}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(1793\) \(3781\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

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
\(4\) 0 0
\(5\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 2.64575 1.00000
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) − 6.57008i − 1.98096i −0.137675 − 0.990478i \(-0.543963\pi\)
0.137675 − 0.990478i \(-0.456037\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) − 1.91520i − 0.399346i −0.979863 − 0.199673i \(-0.936012\pi\)
0.979863 − 0.199673i \(-0.0639880\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) − 8.89753i − 1.65223i −0.563502 − 0.826115i \(-0.690546\pi\)
0.563502 − 0.826115i \(-0.309454\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −10.5830 −1.73984 −0.869918 − 0.493197i \(-0.835828\pi\)
−0.869918 + 0.493197i \(0.835828\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) −5.29150 −0.806947 −0.403473 − 0.914991i \(-0.632197\pi\)
−0.403473 + 0.914991i \(0.632197\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 7.00000 1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) − 0.412247i − 0.0566265i −0.999599 − 0.0283132i \(-0.990986\pi\)
0.999599 − 0.0283132i \(-0.00901359\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 − 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 15.0554i 1.78674i 0.449319 + 0.893372i \(0.351667\pi\)
−0.449319 + 0.893372i \(0.648333\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 17.3828i − 1.98096i
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 − 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 10.4005i 1.00545i 0.864446 + 0.502726i \(0.167670\pi\)
−0.864446 + 0.502726i \(0.832330\pi\)
\(108\) 0 0
\(109\) −10.5830 −1.01367 −0.506834 − 0.862044i \(-0.669184\pi\)
−0.506834 + 0.862044i \(0.669184\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 13.5524i − 1.27490i −0.770490 − 0.637452i \(-0.779988\pi\)
0.770490 − 0.637452i \(-0.220012\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −32.1660 −2.92418
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 − 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 22.0377i − 1.88281i −0.337282 − 0.941404i \(-0.609507\pi\)
0.337282 − 0.941404i \(-0.390493\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 8.07303i 0.661369i 0.943741 + 0.330684i \(0.107280\pi\)
−0.943741 + 0.330684i \(0.892720\pi\)
\(150\) 0 0
\(151\) 5.29150 0.430616 0.215308 − 0.976546i \(-0.430924\pi\)
0.215308 + 0.976546i \(0.430924\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) − 5.06713i − 0.399346i
\(162\) 0 0
\(163\) 20.0000 1.56652 0.783260 − 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) −13.2288 −1.00000
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 15.8799i 1.18692i 0.804865 + 0.593458i \(0.202238\pi\)
−0.804865 + 0.593458i \(0.797762\pi\)
\(180\) 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
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) − 24.3651i − 1.76300i −0.472184 − 0.881500i \(-0.656534\pi\)
0.472184 − 0.881500i \(-0.343466\pi\)
\(192\) 0 0
\(193\) −21.1660 −1.52356 −0.761781 − 0.647834i \(-0.775675\pi\)
−0.761781 + 0.647834i \(0.775675\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 25.8681i − 1.84303i −0.388348 − 0.921513i \(-0.626954\pi\)
0.388348 − 0.921513i \(-0.373046\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) − 23.5406i − 1.65223i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 26.4575 1.82141 0.910705 − 0.413057i \(-0.135539\pi\)
0.910705 + 0.413057i \(0.135539\pi\)
\(212\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 30.5230i − 1.99963i −0.0193169 − 0.999813i \(-0.506149\pi\)
0.0193169 − 0.999813i \(-0.493851\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) − 7.39458i − 0.478316i −0.970981 − 0.239158i \(-0.923129\pi\)
0.970981 − 0.239158i \(-0.0768713\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −12.5830 −0.791087
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) −28.0000 −1.73984
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) − 18.8858i − 1.16455i −0.812993 − 0.582273i \(-0.802164\pi\)
0.812993 − 0.582273i \(-0.197836\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 32.8504i 1.98096i
\(276\) 0 0
\(277\) 10.0000 0.600842 0.300421 − 0.953807i \(-0.402873\pi\)
0.300421 + 0.953807i \(0.402873\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3.41815i 0.203910i 0.994789 + 0.101955i \(0.0325097\pi\)
−0.994789 + 0.101955i \(0.967490\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −14.0000 −0.806947
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 16.5583i 0.930008i 0.885309 + 0.465004i \(0.153947\pi\)
−0.885309 + 0.465004i \(0.846053\pi\)
\(318\) 0 0
\(319\) −58.4575 −3.27299
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −5.29150 −0.290847 −0.145424 − 0.989369i \(-0.546455\pi\)
−0.145424 + 0.989369i \(0.546455\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −21.1660 −1.15299 −0.576493 − 0.817102i \(-0.695579\pi\)
−0.576493 + 0.817102i \(0.695579\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 18.5203 1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 29.0200i − 1.55788i −0.627100 − 0.778938i \(-0.715758\pi\)
0.627100 − 0.778938i \(-0.284242\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 20.5347i 1.08378i 0.840449 + 0.541891i \(0.182292\pi\)
−0.840449 + 0.541891i \(0.817708\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) − 1.09070i − 0.0566265i
\(372\) 0 0
\(373\) 22.0000 1.13912 0.569558 − 0.821951i \(-0.307114\pi\)
0.569558 + 0.821951i \(0.307114\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −37.0405 −1.90264 −0.951322 − 0.308199i \(-0.900274\pi\)
−0.951322 + 0.308199i \(0.900274\pi\)
\(380\) 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
\(387\) 0 0
\(388\) 0 0
\(389\) − 34.3534i − 1.74179i −0.491473 − 0.870893i \(-0.663542\pi\)
0.491473 − 0.870893i \(-0.336458\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 39.0083i − 1.94798i −0.226592 − 0.973990i \(-0.572758\pi\)
0.226592 − 0.973990i \(-0.427242\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 69.5312i 3.44654i
\(408\) 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
\(419\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −26.0000 −1.26716 −0.633581 − 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) − 41.3357i − 1.99107i −0.0943889 − 0.995535i \(-0.530090\pi\)
0.0943889 − 0.995535i \(-0.469910\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 12.0495i − 0.572487i −0.958157 − 0.286244i \(-0.907593\pi\)
0.958157 − 0.286244i \(-0.0924067\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 31.3475i 1.47938i 0.672948 + 0.739689i \(0.265028\pi\)
−0.672948 + 0.739689i \(0.734972\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 42.3320 1.98021 0.990104 − 0.140334i \(-0.0448177\pi\)
0.990104 + 0.140334i \(0.0448177\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 40.0000 1.85896 0.929479 − 0.368875i \(-0.120257\pi\)
0.929479 + 0.368875i \(0.120257\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) −10.5830 −0.488678
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 34.7656i 1.59852i
\(474\) 0 0
\(475\) 0 0
\(476\) 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
\(487\) 37.0405 1.67847 0.839233 − 0.543772i \(-0.183004\pi\)
0.839233 + 0.543772i \(0.183004\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 27.3710i 1.23524i 0.786478 + 0.617619i \(0.211903\pi\)
−0.786478 + 0.617619i \(0.788097\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 39.8328i 1.78674i
\(498\) 0 0
\(499\) 26.4575 1.18440 0.592200 − 0.805791i \(-0.298259\pi\)
0.592200 + 0.805791i \(0.298259\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 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
\(529\) 19.3320 0.840523
\(530\) 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
\(539\) − 45.9906i − 1.98096i
\(540\) 0 0
\(541\) 34.0000 1.46177 0.730887 − 0.682498i \(-0.239107\pi\)
0.730887 + 0.682498i \(0.239107\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 44.0000 1.88130 0.940652 − 0.339372i \(-0.110215\pi\)
0.940652 + 0.339372i \(0.110215\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −21.1660 −0.900070
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 25.0436i 1.06113i 0.847644 + 0.530566i \(0.178020\pi\)
−0.847644 + 0.530566i \(0.821980\pi\)
\(558\) 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
\(567\) 0 0
\(568\) 0 0
\(569\) 14.3769i 0.602711i 0.953512 + 0.301356i \(0.0974392\pi\)
−0.953512 + 0.301356i \(0.902561\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 − 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 9.57598i 0.399346i
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −2.70850 −0.112174
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 3.56418i 0.145629i 0.997346 + 0.0728143i \(0.0231980\pi\)
−0.997346 + 0.0728143i \(0.976802\pi\)
\(600\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −38.0000 −1.53481 −0.767403 − 0.641165i \(-0.778451\pi\)
−0.767403 + 0.641165i \(0.778451\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 48.3180i 1.94521i 0.232462 + 0.972605i \(0.425322\pi\)
−0.232462 + 0.972605i \(0.574678\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 − 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 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
\(641\) − 47.4935i − 1.87588i −0.346795 − 0.937941i \(-0.612730\pi\)
0.346795 − 0.937941i \(-0.387270\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) − 42.8387i − 1.67641i −0.545358 − 0.838203i \(-0.683606\pi\)
0.545358 − 0.838203i \(-0.316394\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 49.8210i 1.94075i 0.241604 + 0.970375i \(0.422327\pi\)
−0.241604 + 0.970375i \(0.577673\pi\)
\(660\) 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
\(667\) −17.0405 −0.659812
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 42.3320 1.63178 0.815890 − 0.578208i \(-0.196248\pi\)
0.815890 + 0.578208i \(0.196248\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 40.5112i − 1.55012i −0.631889 − 0.775059i \(-0.717720\pi\)
0.631889 − 0.775059i \(-0.282280\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 36.0024i 1.35979i 0.733309 + 0.679895i \(0.237975\pi\)
−0.733309 + 0.679895i \(0.762025\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 52.9150 1.98727 0.993633 − 0.112667i \(-0.0359394\pi\)
0.993633 + 0.112667i \(0.0359394\pi\)
\(710\) 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
\(723\) 0 0
\(724\) 0 0
\(725\) 44.4876i 1.65223i
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 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
\(737\) 26.2803i 0.968049i
\(738\) 0 0
\(739\) −52.0000 −1.91285 −0.956425 − 0.291977i \(-0.905687\pi\)
−0.956425 + 0.291977i \(0.905687\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 54.4759i 1.99853i 0.0383863 + 0.999263i \(0.487778\pi\)
−0.0383863 + 0.999263i \(0.512222\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 27.5171i 1.00545i
\(750\) 0 0
\(751\) −26.4575 −0.965448 −0.482724 − 0.875772i \(-0.660353\pi\)
−0.482724 + 0.875772i \(0.660353\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −10.5830 −0.384646 −0.192323 − 0.981332i \(-0.561602\pi\)
−0.192323 + 0.981332i \(0.561602\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) −28.0000 −1.01367
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 − 1.00000i \(-0.5\pi\)
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
\(781\) 98.9150 3.53946
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) − 35.8563i − 1.27490i
\(792\) 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
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 56.8033i 1.99710i 0.0538482 + 0.998549i \(0.482851\pi\)
−0.0538482 + 0.998549i \(0.517149\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 52.9729i 1.84877i 0.381464 + 0.924384i \(0.375420\pi\)
−0.381464 + 0.924384i \(0.624580\pi\)
\(822\) 0 0
\(823\) −32.0000 −1.11545 −0.557725 − 0.830026i \(-0.688326\pi\)
−0.557725 + 0.830026i \(0.688326\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 4.92110i 0.171123i 0.996333 + 0.0855616i \(0.0272685\pi\)
−0.996333 + 0.0855616i \(0.972732\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 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
\(841\) −50.1660 −1.72986
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −85.1033 −2.92418
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 20.2685i 0.694797i
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) − 46.8151i − 1.59360i −0.604240 − 0.796802i \(-0.706523\pi\)
0.604240 − 0.796802i \(-0.293477\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 52.5607i 1.78300i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −50.0000 −1.68838 −0.844190 − 0.536044i \(-0.819918\pi\)
−0.844190 + 0.536044i \(0.819918\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) 58.2065 1.95881 0.979403 − 0.201916i \(-0.0647168\pi\)
0.979403 + 0.201916i \(0.0647168\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 42.3320 1.41977
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 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
\(907\) −5.29150 −0.175701 −0.0878507 − 0.996134i \(-0.528000\pi\)
−0.0878507 + 0.996134i \(0.528000\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) − 29.8445i − 0.988793i −0.869236 − 0.494397i \(-0.835389\pi\)
0.869236 − 0.494397i \(-0.164611\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 37.0405 1.22185 0.610927 − 0.791687i \(-0.290797\pi\)
0.610927 + 0.791687i \(0.290797\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 52.9150 1.73984
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 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
\(947\) 55.3004i 1.79702i 0.438953 + 0.898510i \(0.355350\pi\)
−0.438953 + 0.898510i \(0.644650\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 55.9788i − 1.81333i −0.421849 − 0.906666i \(-0.638619\pi\)
0.421849 − 0.906666i \(-0.361381\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) − 58.3063i − 1.88281i
\(960\) 0 0
\(961\) 31.0000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 40.0000 1.28631 0.643157 − 0.765735i \(-0.277624\pi\)
0.643157 + 0.765735i \(0.277624\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 2.59365i − 0.0829783i −0.999139 − 0.0414892i \(-0.986790\pi\)
0.999139 − 0.0414892i \(-0.0132102\pi\)
\(978\) 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
\(989\) 10.1343i 0.322251i
\(990\) 0 0
\(991\) −58.2065 −1.84899 −0.924496 − 0.381193i \(-0.875513\pi\)
−0.924496 + 0.381193i \(0.875513\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 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 4032.2.k.b.3905.3 4
3.2 odd 2 inner 4032.2.k.b.3905.4 4
4.3 odd 2 4032.2.k.c.3905.2 4
7.6 odd 2 CM 4032.2.k.b.3905.3 4
8.3 odd 2 63.2.c.a.62.3 yes 4
8.5 even 2 1008.2.k.a.881.4 4
12.11 even 2 4032.2.k.c.3905.1 4
21.20 even 2 inner 4032.2.k.b.3905.4 4
24.5 odd 2 1008.2.k.a.881.3 4
24.11 even 2 63.2.c.a.62.2 ✓ 4
28.27 even 2 4032.2.k.c.3905.2 4
40.3 even 4 1575.2.g.d.1574.6 8
40.19 odd 2 1575.2.b.a.251.2 4
40.27 even 4 1575.2.g.d.1574.3 8
56.3 even 6 441.2.p.b.215.2 8
56.11 odd 6 441.2.p.b.215.2 8
56.13 odd 2 1008.2.k.a.881.4 4
56.19 even 6 441.2.p.b.80.3 8
56.27 even 2 63.2.c.a.62.3 yes 4
56.51 odd 6 441.2.p.b.80.3 8
72.11 even 6 567.2.o.f.377.2 8
72.43 odd 6 567.2.o.f.377.3 8
72.59 even 6 567.2.o.f.188.3 8
72.67 odd 6 567.2.o.f.188.2 8
84.83 odd 2 4032.2.k.c.3905.1 4
120.59 even 2 1575.2.b.a.251.3 4
120.83 odd 4 1575.2.g.d.1574.4 8
120.107 odd 4 1575.2.g.d.1574.5 8
168.11 even 6 441.2.p.b.215.3 8
168.59 odd 6 441.2.p.b.215.3 8
168.83 odd 2 63.2.c.a.62.2 ✓ 4
168.107 even 6 441.2.p.b.80.2 8
168.125 even 2 1008.2.k.a.881.3 4
168.131 odd 6 441.2.p.b.80.2 8
280.27 odd 4 1575.2.g.d.1574.3 8
280.83 odd 4 1575.2.g.d.1574.6 8
280.139 even 2 1575.2.b.a.251.2 4
504.83 odd 6 567.2.o.f.377.2 8
504.139 even 6 567.2.o.f.188.2 8
504.419 odd 6 567.2.o.f.188.3 8
504.475 even 6 567.2.o.f.377.3 8
840.83 even 4 1575.2.g.d.1574.4 8
840.419 odd 2 1575.2.b.a.251.3 4
840.587 even 4 1575.2.g.d.1574.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.c.a.62.2 ✓ 4 24.11 even 2
63.2.c.a.62.2 ✓ 4 168.83 odd 2
63.2.c.a.62.3 yes 4 8.3 odd 2
63.2.c.a.62.3 yes 4 56.27 even 2
441.2.p.b.80.2 8 168.107 even 6
441.2.p.b.80.2 8 168.131 odd 6
441.2.p.b.80.3 8 56.19 even 6
441.2.p.b.80.3 8 56.51 odd 6
441.2.p.b.215.2 8 56.3 even 6
441.2.p.b.215.2 8 56.11 odd 6
441.2.p.b.215.3 8 168.11 even 6
441.2.p.b.215.3 8 168.59 odd 6
567.2.o.f.188.2 8 72.67 odd 6
567.2.o.f.188.2 8 504.139 even 6
567.2.o.f.188.3 8 72.59 even 6
567.2.o.f.188.3 8 504.419 odd 6
567.2.o.f.377.2 8 72.11 even 6
567.2.o.f.377.2 8 504.83 odd 6
567.2.o.f.377.3 8 72.43 odd 6
567.2.o.f.377.3 8 504.475 even 6
1008.2.k.a.881.3 4 24.5 odd 2
1008.2.k.a.881.3 4 168.125 even 2
1008.2.k.a.881.4 4 8.5 even 2
1008.2.k.a.881.4 4 56.13 odd 2
1575.2.b.a.251.2 4 40.19 odd 2
1575.2.b.a.251.2 4 280.139 even 2
1575.2.b.a.251.3 4 120.59 even 2
1575.2.b.a.251.3 4 840.419 odd 2
1575.2.g.d.1574.3 8 40.27 even 4
1575.2.g.d.1574.3 8 280.27 odd 4
1575.2.g.d.1574.4 8 120.83 odd 4
1575.2.g.d.1574.4 8 840.83 even 4
1575.2.g.d.1574.5 8 120.107 odd 4
1575.2.g.d.1574.5 8 840.587 even 4
1575.2.g.d.1574.6 8 40.3 even 4
1575.2.g.d.1574.6 8 280.83 odd 4
4032.2.k.b.3905.3 4 1.1 even 1 trivial
4032.2.k.b.3905.3 4 7.6 odd 2 CM
4032.2.k.b.3905.4 4 3.2 odd 2 inner
4032.2.k.b.3905.4 4 21.20 even 2 inner
4032.2.k.c.3905.1 4 12.11 even 2
4032.2.k.c.3905.1 4 84.83 odd 2
4032.2.k.c.3905.2 4 4.3 odd 2
4032.2.k.c.3905.2 4 28.27 even 2