Properties

Label 8.3.d.a.3.1
Level $8$
Weight $3$
Character 8.3
Self dual yes
Analytic conductor $0.218$
Analytic rank $0$
Dimension $1$
CM discriminant -8
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] = [8,3,Mod(3,8)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8, 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("8.3");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 8.d (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: \(0.217984211488\)
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 3.1
Character \(\chi\) \(=\) 8.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} -2.00000 q^{3} +4.00000 q^{4} +4.00000 q^{6} -8.00000 q^{8} -5.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -2.00000 q^{3} +4.00000 q^{4} +4.00000 q^{6} -8.00000 q^{8} -5.00000 q^{9} +14.0000 q^{11} -8.00000 q^{12} +16.0000 q^{16} +2.00000 q^{17} +10.0000 q^{18} -34.0000 q^{19} -28.0000 q^{22} +16.0000 q^{24} +25.0000 q^{25} +28.0000 q^{27} -32.0000 q^{32} -28.0000 q^{33} -4.00000 q^{34} -20.0000 q^{36} +68.0000 q^{38} -46.0000 q^{41} +14.0000 q^{43} +56.0000 q^{44} -32.0000 q^{48} +49.0000 q^{49} -50.0000 q^{50} -4.00000 q^{51} -56.0000 q^{54} +68.0000 q^{57} -82.0000 q^{59} +64.0000 q^{64} +56.0000 q^{66} +62.0000 q^{67} +8.00000 q^{68} +40.0000 q^{72} -142.000 q^{73} -50.0000 q^{75} -136.000 q^{76} -11.0000 q^{81} +92.0000 q^{82} +158.000 q^{83} -28.0000 q^{86} -112.000 q^{88} +146.000 q^{89} +64.0000 q^{96} -94.0000 q^{97} -98.0000 q^{98} -70.0000 q^{99} +O(q^{100})\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(-1\)

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
\(3\) −2.00000 −0.666667 −0.333333 0.942809i \(-0.608173\pi\)
−0.333333 + 0.942809i \(0.608173\pi\)
\(4\) 4.00000 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 4.00000 0.666667
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) −8.00000 −1.00000
\(9\) −5.00000 −0.555556
\(10\) 0 0
\(11\) 14.0000 1.27273 0.636364 0.771389i \(-0.280438\pi\)
0.636364 + 0.771389i \(0.280438\pi\)
\(12\) −8.00000 −0.666667
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 16.0000 1.00000
\(17\) 2.00000 0.117647 0.0588235 0.998268i \(-0.481265\pi\)
0.0588235 + 0.998268i \(0.481265\pi\)
\(18\) 10.0000 0.555556
\(19\) −34.0000 −1.78947 −0.894737 0.446594i \(-0.852637\pi\)
−0.894737 + 0.446594i \(0.852637\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −28.0000 −1.27273
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 16.0000 0.666667
\(25\) 25.0000 1.00000
\(26\) 0 0
\(27\) 28.0000 1.03704
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) −32.0000 −1.00000
\(33\) −28.0000 −0.848485
\(34\) −4.00000 −0.117647
\(35\) 0 0
\(36\) −20.0000 −0.555556
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 68.0000 1.78947
\(39\) 0 0
\(40\) 0 0
\(41\) −46.0000 −1.12195 −0.560976 0.827832i \(-0.689574\pi\)
−0.560976 + 0.827832i \(0.689574\pi\)
\(42\) 0 0
\(43\) 14.0000 0.325581 0.162791 0.986661i \(-0.447950\pi\)
0.162791 + 0.986661i \(0.447950\pi\)
\(44\) 56.0000 1.27273
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −32.0000 −0.666667
\(49\) 49.0000 1.00000
\(50\) −50.0000 −1.00000
\(51\) −4.00000 −0.0784314
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) −56.0000 −1.03704
\(55\) 0 0
\(56\) 0 0
\(57\) 68.0000 1.19298
\(58\) 0 0
\(59\) −82.0000 −1.38983 −0.694915 0.719092i \(-0.744558\pi\)
−0.694915 + 0.719092i \(0.744558\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 64.0000 1.00000
\(65\) 0 0
\(66\) 56.0000 0.848485
\(67\) 62.0000 0.925373 0.462687 0.886522i \(-0.346886\pi\)
0.462687 + 0.886522i \(0.346886\pi\)
\(68\) 8.00000 0.117647
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 40.0000 0.555556
\(73\) −142.000 −1.94521 −0.972603 0.232473i \(-0.925318\pi\)
−0.972603 + 0.232473i \(0.925318\pi\)
\(74\) 0 0
\(75\) −50.0000 −0.666667
\(76\) −136.000 −1.78947
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) −11.0000 −0.135802
\(82\) 92.0000 1.12195
\(83\) 158.000 1.90361 0.951807 0.306697i \(-0.0992238\pi\)
0.951807 + 0.306697i \(0.0992238\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −28.0000 −0.325581
\(87\) 0 0
\(88\) −112.000 −1.27273
\(89\) 146.000 1.64045 0.820225 0.572041i \(-0.193848\pi\)
0.820225 + 0.572041i \(0.193848\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 64.0000 0.666667
\(97\) −94.0000 −0.969072 −0.484536 0.874771i \(-0.661012\pi\)
−0.484536 + 0.874771i \(0.661012\pi\)
\(98\) −98.0000 −1.00000
\(99\) −70.0000 −0.707071
\(100\) 100.000 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 8.00000 0.0784314
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −178.000 −1.66355 −0.831776 0.555112i \(-0.812675\pi\)
−0.831776 + 0.555112i \(0.812675\pi\)
\(108\) 112.000 1.03704
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 98.0000 0.867257 0.433628 0.901092i \(-0.357233\pi\)
0.433628 + 0.901092i \(0.357233\pi\)
\(114\) −136.000 −1.19298
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 164.000 1.38983
\(119\) 0 0
\(120\) 0 0
\(121\) 75.0000 0.619835
\(122\) 0 0
\(123\) 92.0000 0.747967
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −128.000 −1.00000
\(129\) −28.0000 −0.217054
\(130\) 0 0
\(131\) 62.0000 0.473282 0.236641 0.971597i \(-0.423953\pi\)
0.236641 + 0.971597i \(0.423953\pi\)
\(132\) −112.000 −0.848485
\(133\) 0 0
\(134\) −124.000 −0.925373
\(135\) 0 0
\(136\) −16.0000 −0.117647
\(137\) −238.000 −1.73723 −0.868613 0.495491i \(-0.834988\pi\)
−0.868613 + 0.495491i \(0.834988\pi\)
\(138\) 0 0
\(139\) 206.000 1.48201 0.741007 0.671497i \(-0.234348\pi\)
0.741007 + 0.671497i \(0.234348\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −80.0000 −0.555556
\(145\) 0 0
\(146\) 284.000 1.94521
\(147\) −98.0000 −0.666667
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 100.000 0.666667
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 272.000 1.78947
\(153\) −10.0000 −0.0653595
\(154\) 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
\(161\) 0 0
\(162\) 22.0000 0.135802
\(163\) −322.000 −1.97546 −0.987730 0.156171i \(-0.950085\pi\)
−0.987730 + 0.156171i \(0.950085\pi\)
\(164\) −184.000 −1.12195
\(165\) 0 0
\(166\) −316.000 −1.90361
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 169.000 1.00000
\(170\) 0 0
\(171\) 170.000 0.994152
\(172\) 56.0000 0.325581
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 224.000 1.27273
\(177\) 164.000 0.926554
\(178\) −292.000 −1.64045
\(179\) −34.0000 −0.189944 −0.0949721 0.995480i \(-0.530276\pi\)
−0.0949721 + 0.995480i \(0.530276\pi\)
\(180\) 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
\(187\) 28.0000 0.149733
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −128.000 −0.666667
\(193\) 98.0000 0.507772 0.253886 0.967234i \(-0.418291\pi\)
0.253886 + 0.967234i \(0.418291\pi\)
\(194\) 188.000 0.969072
\(195\) 0 0
\(196\) 196.000 1.00000
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 140.000 0.707071
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −200.000 −1.00000
\(201\) −124.000 −0.616915
\(202\) 0 0
\(203\) 0 0
\(204\) −16.0000 −0.0784314
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −476.000 −2.27751
\(210\) 0 0
\(211\) −226.000 −1.07109 −0.535545 0.844507i \(-0.679894\pi\)
−0.535545 + 0.844507i \(0.679894\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 356.000 1.66355
\(215\) 0 0
\(216\) −224.000 −1.03704
\(217\) 0 0
\(218\) 0 0
\(219\) 284.000 1.29680
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) −125.000 −0.555556
\(226\) −196.000 −0.867257
\(227\) 446.000 1.96476 0.982379 0.186900i \(-0.0598442\pi\)
0.982379 + 0.186900i \(0.0598442\pi\)
\(228\) 272.000 1.19298
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 434.000 1.86266 0.931330 0.364175i \(-0.118649\pi\)
0.931330 + 0.364175i \(0.118649\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −328.000 −1.38983
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 194.000 0.804979 0.402490 0.915425i \(-0.368145\pi\)
0.402490 + 0.915425i \(0.368145\pi\)
\(242\) −150.000 −0.619835
\(243\) −230.000 −0.946502
\(244\) 0 0
\(245\) 0 0
\(246\) −184.000 −0.747967
\(247\) 0 0
\(248\) 0 0
\(249\) −316.000 −1.26908
\(250\) 0 0
\(251\) −466.000 −1.85657 −0.928287 0.371865i \(-0.878718\pi\)
−0.928287 + 0.371865i \(0.878718\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 256.000 1.00000
\(257\) 386.000 1.50195 0.750973 0.660333i \(-0.229585\pi\)
0.750973 + 0.660333i \(0.229585\pi\)
\(258\) 56.0000 0.217054
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −124.000 −0.473282
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 224.000 0.848485
\(265\) 0 0
\(266\) 0 0
\(267\) −292.000 −1.09363
\(268\) 248.000 0.925373
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 32.0000 0.117647
\(273\) 0 0
\(274\) 476.000 1.73723
\(275\) 350.000 1.27273
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) −412.000 −1.48201
\(279\) 0 0
\(280\) 0 0
\(281\) −238.000 −0.846975 −0.423488 0.905902i \(-0.639194\pi\)
−0.423488 + 0.905902i \(0.639194\pi\)
\(282\) 0 0
\(283\) −82.0000 −0.289753 −0.144876 0.989450i \(-0.546278\pi\)
−0.144876 + 0.989450i \(0.546278\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 160.000 0.555556
\(289\) −285.000 −0.986159
\(290\) 0 0
\(291\) 188.000 0.646048
\(292\) −568.000 −1.94521
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 196.000 0.666667
\(295\) 0 0
\(296\) 0 0
\(297\) 392.000 1.31987
\(298\) 0 0
\(299\) 0 0
\(300\) −200.000 −0.666667
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −544.000 −1.78947
\(305\) 0 0
\(306\) 20.0000 0.0653595
\(307\) 542.000 1.76547 0.882736 0.469869i \(-0.155699\pi\)
0.882736 + 0.469869i \(0.155699\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) −526.000 −1.68051 −0.840256 0.542191i \(-0.817595\pi\)
−0.840256 + 0.542191i \(0.817595\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 356.000 1.10903
\(322\) 0 0
\(323\) −68.0000 −0.210526
\(324\) −44.0000 −0.135802
\(325\) 0 0
\(326\) 644.000 1.97546
\(327\) 0 0
\(328\) 368.000 1.12195
\(329\) 0 0
\(330\) 0 0
\(331\) 14.0000 0.0422961 0.0211480 0.999776i \(-0.493268\pi\)
0.0211480 + 0.999776i \(0.493268\pi\)
\(332\) 632.000 1.90361
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −478.000 −1.41840 −0.709199 0.705009i \(-0.750943\pi\)
−0.709199 + 0.705009i \(0.750943\pi\)
\(338\) −338.000 −1.00000
\(339\) −196.000 −0.578171
\(340\) 0 0
\(341\) 0 0
\(342\) −340.000 −0.994152
\(343\) 0 0
\(344\) −112.000 −0.325581
\(345\) 0 0
\(346\) 0 0
\(347\) −658.000 −1.89625 −0.948127 0.317892i \(-0.897025\pi\)
−0.948127 + 0.317892i \(0.897025\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −448.000 −1.27273
\(353\) 194.000 0.549575 0.274788 0.961505i \(-0.411392\pi\)
0.274788 + 0.961505i \(0.411392\pi\)
\(354\) −328.000 −0.926554
\(355\) 0 0
\(356\) 584.000 1.64045
\(357\) 0 0
\(358\) 68.0000 0.189944
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 795.000 2.20222
\(362\) 0 0
\(363\) −150.000 −0.413223
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 230.000 0.623306
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) −56.0000 −0.149733
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 686.000 1.81003 0.905013 0.425383i \(-0.139861\pi\)
0.905013 + 0.425383i \(0.139861\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 256.000 0.666667
\(385\) 0 0
\(386\) −196.000 −0.507772
\(387\) −70.0000 −0.180879
\(388\) −376.000 −0.969072
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −392.000 −1.00000
\(393\) −124.000 −0.315522
\(394\) 0 0
\(395\) 0 0
\(396\) −280.000 −0.707071
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 400.000 1.00000
\(401\) −766.000 −1.91022 −0.955112 0.296244i \(-0.904266\pi\)
−0.955112 + 0.296244i \(0.904266\pi\)
\(402\) 248.000 0.616915
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 32.0000 0.0784314
\(409\) −334.000 −0.816626 −0.408313 0.912842i \(-0.633883\pi\)
−0.408313 + 0.912842i \(0.633883\pi\)
\(410\) 0 0
\(411\) 476.000 1.15815
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −412.000 −0.988010
\(418\) 952.000 2.27751
\(419\) −514.000 −1.22673 −0.613365 0.789799i \(-0.710185\pi\)
−0.613365 + 0.789799i \(0.710185\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 452.000 1.07109
\(423\) 0 0
\(424\) 0 0
\(425\) 50.0000 0.117647
\(426\) 0 0
\(427\) 0 0
\(428\) −712.000 −1.66355
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 448.000 1.03704
\(433\) 578.000 1.33487 0.667436 0.744667i \(-0.267392\pi\)
0.667436 + 0.744667i \(0.267392\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −568.000 −1.29680
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −245.000 −0.555556
\(442\) 0 0
\(443\) 878.000 1.98194 0.990971 0.134079i \(-0.0428076\pi\)
0.990971 + 0.134079i \(0.0428076\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 866.000 1.92873 0.964365 0.264574i \(-0.0852315\pi\)
0.964365 + 0.264574i \(0.0852315\pi\)
\(450\) 250.000 0.555556
\(451\) −644.000 −1.42794
\(452\) 392.000 0.867257
\(453\) 0 0
\(454\) −892.000 −1.96476
\(455\) 0 0
\(456\) −544.000 −1.19298
\(457\) −238.000 −0.520788 −0.260394 0.965502i \(-0.583852\pi\)
−0.260394 + 0.965502i \(0.583852\pi\)
\(458\) 0 0
\(459\) 56.0000 0.122004
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −868.000 −1.86266
\(467\) −34.0000 −0.0728051 −0.0364026 0.999337i \(-0.511590\pi\)
−0.0364026 + 0.999337i \(0.511590\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 656.000 1.38983
\(473\) 196.000 0.414376
\(474\) 0 0
\(475\) −850.000 −1.78947
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −388.000 −0.804979
\(483\) 0 0
\(484\) 300.000 0.619835
\(485\) 0 0
\(486\) 460.000 0.946502
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 644.000 1.31697
\(490\) 0 0
\(491\) 782.000 1.59267 0.796334 0.604857i \(-0.206770\pi\)
0.796334 + 0.604857i \(0.206770\pi\)
\(492\) 368.000 0.747967
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 632.000 1.26908
\(499\) −802.000 −1.60721 −0.803607 0.595160i \(-0.797089\pi\)
−0.803607 + 0.595160i \(0.797089\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 932.000 1.85657
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −338.000 −0.666667
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −512.000 −1.00000
\(513\) −952.000 −1.85575
\(514\) −772.000 −1.50195
\(515\) 0 0
\(516\) −112.000 −0.217054
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1006.00 −1.93090 −0.965451 0.260584i \(-0.916085\pi\)
−0.965451 + 0.260584i \(0.916085\pi\)
\(522\) 0 0
\(523\) 398.000 0.760994 0.380497 0.924782i \(-0.375753\pi\)
0.380497 + 0.924782i \(0.375753\pi\)
\(524\) 248.000 0.473282
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −448.000 −0.848485
\(529\) 529.000 1.00000
\(530\) 0 0
\(531\) 410.000 0.772128
\(532\) 0 0
\(533\) 0 0
\(534\) 584.000 1.09363
\(535\) 0 0
\(536\) −496.000 −0.925373
\(537\) 68.0000 0.126629
\(538\) 0 0
\(539\) 686.000 1.27273
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −64.0000 −0.117647
\(545\) 0 0
\(546\) 0 0
\(547\) 1022.00 1.86837 0.934186 0.356785i \(-0.116127\pi\)
0.934186 + 0.356785i \(0.116127\pi\)
\(548\) −952.000 −1.73723
\(549\) 0 0
\(550\) −700.000 −1.27273
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 824.000 1.48201
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −56.0000 −0.0998217
\(562\) 476.000 0.846975
\(563\) −226.000 −0.401421 −0.200710 0.979651i \(-0.564325\pi\)
−0.200710 + 0.979651i \(0.564325\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 164.000 0.289753
\(567\) 0 0
\(568\) 0 0
\(569\) 626.000 1.10018 0.550088 0.835107i \(-0.314594\pi\)
0.550088 + 0.835107i \(0.314594\pi\)
\(570\) 0 0
\(571\) −658.000 −1.15236 −0.576182 0.817321i \(-0.695458\pi\)
−0.576182 + 0.817321i \(0.695458\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −320.000 −0.555556
\(577\) 2.00000 0.00346620 0.00173310 0.999998i \(-0.499448\pi\)
0.00173310 + 0.999998i \(0.499448\pi\)
\(578\) 570.000 0.986159
\(579\) −196.000 −0.338515
\(580\) 0 0
\(581\) 0 0
\(582\) −376.000 −0.646048
\(583\) 0 0
\(584\) 1136.00 1.94521
\(585\) 0 0
\(586\) 0 0
\(587\) −1138.00 −1.93867 −0.969336 0.245741i \(-0.920969\pi\)
−0.969336 + 0.245741i \(0.920969\pi\)
\(588\) −392.000 −0.666667
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −862.000 −1.45363 −0.726813 0.686836i \(-0.758999\pi\)
−0.726813 + 0.686836i \(0.758999\pi\)
\(594\) −784.000 −1.31987
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 400.000 0.666667
\(601\) 914.000 1.52080 0.760399 0.649456i \(-0.225003\pi\)
0.760399 + 0.649456i \(0.225003\pi\)
\(602\) 0 0
\(603\) −310.000 −0.514096
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 1088.00 1.78947
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −40.0000 −0.0653595
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) −1084.00 −1.76547
\(615\) 0 0
\(616\) 0 0
\(617\) −334.000 −0.541329 −0.270665 0.962674i \(-0.587243\pi\)
−0.270665 + 0.962674i \(0.587243\pi\)
\(618\) 0 0
\(619\) −562.000 −0.907916 −0.453958 0.891023i \(-0.649988\pi\)
−0.453958 + 0.891023i \(0.649988\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 625.000 1.00000
\(626\) 1052.00 1.68051
\(627\) 952.000 1.51834
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 452.000 0.714060
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 482.000 0.751950 0.375975 0.926630i \(-0.377308\pi\)
0.375975 + 0.926630i \(0.377308\pi\)
\(642\) −712.000 −1.10903
\(643\) 1214.00 1.88802 0.944012 0.329910i \(-0.107018\pi\)
0.944012 + 0.329910i \(0.107018\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 136.000 0.210526
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 88.0000 0.135802
\(649\) −1148.00 −1.76888
\(650\) 0 0
\(651\) 0 0
\(652\) −1288.00 −1.97546
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −736.000 −1.12195
\(657\) 710.000 1.08067
\(658\) 0 0
\(659\) −994.000 −1.50835 −0.754173 0.656676i \(-0.771962\pi\)
−0.754173 + 0.656676i \(0.771962\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) −28.0000 −0.0422961
\(663\) 0 0
\(664\) −1264.00 −1.90361
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1246.00 −1.85141 −0.925706 0.378244i \(-0.876528\pi\)
−0.925706 + 0.378244i \(0.876528\pi\)
\(674\) 956.000 1.41840
\(675\) 700.000 1.03704
\(676\) 676.000 1.00000
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 392.000 0.578171
\(679\) 0 0
\(680\) 0 0
\(681\) −892.000 −1.30984
\(682\) 0 0
\(683\) 398.000 0.582723 0.291362 0.956613i \(-0.405892\pi\)
0.291362 + 0.956613i \(0.405892\pi\)
\(684\) 680.000 0.994152
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 224.000 0.325581
\(689\) 0 0
\(690\) 0 0
\(691\) 734.000 1.06223 0.531114 0.847300i \(-0.321773\pi\)
0.531114 + 0.847300i \(0.321773\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 1316.00 1.89625
\(695\) 0 0
\(696\) 0 0
\(697\) −92.0000 −0.131994
\(698\) 0 0
\(699\) −868.000 −1.24177
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 896.000 1.27273
\(705\) 0 0
\(706\) −388.000 −0.549575
\(707\) 0 0
\(708\) 656.000 0.926554
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1168.00 −1.64045
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −136.000 −0.189944
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1590.00 −2.20222
\(723\) −388.000 −0.536653
\(724\) 0 0
\(725\) 0 0
\(726\) 300.000 0.413223
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 559.000 0.766804
\(730\) 0 0
\(731\) 28.0000 0.0383037
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 868.000 1.17775
\(738\) −460.000 −0.623306
\(739\) −322.000 −0.435724 −0.217862 0.975980i \(-0.569908\pi\)
−0.217862 + 0.975980i \(0.569908\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −790.000 −1.05756
\(748\) 112.000 0.149733
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 932.000 1.23772
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) −1372.00 −1.81003
\(759\) 0 0
\(760\) 0 0
\(761\) 1394.00 1.83180 0.915900 0.401406i \(-0.131478\pi\)
0.915900 + 0.401406i \(0.131478\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −512.000 −0.666667
\(769\) −1054.00 −1.37061 −0.685306 0.728256i \(-0.740331\pi\)
−0.685306 + 0.728256i \(0.740331\pi\)
\(770\) 0 0
\(771\) −772.000 −1.00130
\(772\) 392.000 0.507772
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 140.000 0.180879
\(775\) 0 0
\(776\) 752.000 0.969072
\(777\) 0 0
\(778\) 0 0
\(779\) 1564.00 2.00770
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 784.000 1.00000
\(785\) 0 0
\(786\) 248.000 0.315522
\(787\) 926.000 1.17662 0.588310 0.808635i \(-0.299793\pi\)
0.588310 + 0.808635i \(0.299793\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 560.000 0.707071
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −800.000 −1.00000
\(801\) −730.000 −0.911361
\(802\) 1532.00 1.91022
\(803\) −1988.00 −2.47572
\(804\) −496.000 −0.616915
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1582.00 −1.95550 −0.977750 0.209772i \(-0.932728\pi\)
−0.977750 + 0.209772i \(0.932728\pi\)
\(810\) 0 0
\(811\) −178.000 −0.219482 −0.109741 0.993960i \(-0.535002\pi\)
−0.109741 + 0.993960i \(0.535002\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) −64.0000 −0.0784314
\(817\) −476.000 −0.582619
\(818\) 668.000 0.816626
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) −952.000 −1.15815
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) −700.000 −0.848485
\(826\) 0 0
\(827\) 1262.00 1.52600 0.762999 0.646400i \(-0.223726\pi\)
0.762999 + 0.646400i \(0.223726\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 98.0000 0.117647
\(834\) 824.000 0.988010
\(835\) 0 0
\(836\) −1904.00 −2.27751
\(837\) 0 0
\(838\) 1028.00 1.22673
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 841.000 1.00000
\(842\) 0 0
\(843\) 476.000 0.564650
\(844\) −904.000 −1.07109
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 164.000 0.193168
\(850\) −100.000 −0.117647
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 1424.00 1.66355
\(857\) 1202.00 1.40257 0.701284 0.712882i \(-0.252611\pi\)
0.701284 + 0.712882i \(0.252611\pi\)
\(858\) 0 0
\(859\) 1646.00 1.91618 0.958091 0.286465i \(-0.0924801\pi\)
0.958091 + 0.286465i \(0.0924801\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) −896.000 −1.03704
\(865\) 0 0
\(866\) −1156.00 −1.33487
\(867\) 570.000 0.657439
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 470.000 0.538373
\(874\) 0 0
\(875\) 0 0
\(876\) 1136.00 1.29680
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1438.00 −1.63224 −0.816118 0.577885i \(-0.803878\pi\)
−0.816118 + 0.577885i \(0.803878\pi\)
\(882\) 490.000 0.555556
\(883\) −1762.00 −1.99547 −0.997735 0.0672672i \(-0.978572\pi\)
−0.997735 + 0.0672672i \(0.978572\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −1756.00 −1.98194
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −154.000 −0.172840
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −1732.00 −1.92873
\(899\) 0 0
\(900\) −500.000 −0.555556
\(901\) 0 0
\(902\) 1288.00 1.42794
\(903\) 0 0
\(904\) −784.000 −0.867257
\(905\) 0 0
\(906\) 0 0
\(907\) −1714.00 −1.88975 −0.944873 0.327436i \(-0.893815\pi\)
−0.944873 + 0.327436i \(0.893815\pi\)
\(908\) 1784.00 1.96476
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 1088.00 1.19298
\(913\) 2212.00 2.42278
\(914\) 476.000 0.520788
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) −112.000 −0.122004
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) −1084.00 −1.17698
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1058.00 1.13886 0.569429 0.822040i \(-0.307164\pi\)
0.569429 + 0.822040i \(0.307164\pi\)
\(930\) 0 0
\(931\) −1666.00 −1.78947
\(932\) 1736.00 1.86266
\(933\) 0 0
\(934\) 68.0000 0.0728051
\(935\) 0 0
\(936\) 0 0
\(937\) −718.000 −0.766275 −0.383138 0.923691i \(-0.625157\pi\)
−0.383138 + 0.923691i \(0.625157\pi\)
\(938\) 0 0
\(939\) 1052.00 1.12034
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −1312.00 −1.38983
\(945\) 0 0
\(946\) −392.000 −0.414376
\(947\) −994.000 −1.04963 −0.524815 0.851216i \(-0.675866\pi\)
−0.524815 + 0.851216i \(0.675866\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 1700.00 1.78947
\(951\) 0 0
\(952\) 0 0
\(953\) −142.000 −0.149003 −0.0745016 0.997221i \(-0.523737\pi\)
−0.0745016 + 0.997221i \(0.523737\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 961.000 1.00000
\(962\) 0 0
\(963\) 890.000 0.924195
\(964\) 776.000 0.804979
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −600.000 −0.619835
\(969\) 136.000 0.140351
\(970\) 0 0
\(971\) 974.000 1.00309 0.501545 0.865132i \(-0.332765\pi\)
0.501545 + 0.865132i \(0.332765\pi\)
\(972\) −920.000 −0.946502
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −1918.00 −1.96315 −0.981576 0.191071i \(-0.938804\pi\)
−0.981576 + 0.191071i \(0.938804\pi\)
\(978\) −1288.00 −1.31697
\(979\) 2044.00 2.08784
\(980\) 0 0
\(981\) 0 0
\(982\) −1564.00 −1.59267
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) −736.000 −0.747967
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) −28.0000 −0.0281974
\(994\) 0 0
\(995\) 0 0
\(996\) −1264.00 −1.26908
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 1604.00 1.60721
\(999\) 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 8.3.d.a.3.1 1
3.2 odd 2 72.3.b.a.19.1 1
4.3 odd 2 32.3.d.a.15.1 1
5.2 odd 4 200.3.e.a.99.1 2
5.3 odd 4 200.3.e.a.99.2 2
5.4 even 2 200.3.g.a.51.1 1
7.2 even 3 392.3.k.d.67.1 2
7.3 odd 6 392.3.k.b.275.1 2
7.4 even 3 392.3.k.d.275.1 2
7.5 odd 6 392.3.k.b.67.1 2
7.6 odd 2 392.3.g.a.99.1 1
8.3 odd 2 CM 8.3.d.a.3.1 1
8.5 even 2 32.3.d.a.15.1 1
12.11 even 2 288.3.b.a.271.1 1
16.3 odd 4 256.3.c.e.255.2 2
16.5 even 4 256.3.c.e.255.2 2
16.11 odd 4 256.3.c.e.255.1 2
16.13 even 4 256.3.c.e.255.1 2
20.3 even 4 800.3.e.a.399.2 2
20.7 even 4 800.3.e.a.399.1 2
20.19 odd 2 800.3.g.a.751.1 1
24.5 odd 2 288.3.b.a.271.1 1
24.11 even 2 72.3.b.a.19.1 1
28.27 even 2 1568.3.g.a.687.1 1
40.3 even 4 200.3.e.a.99.2 2
40.13 odd 4 800.3.e.a.399.2 2
40.19 odd 2 200.3.g.a.51.1 1
40.27 even 4 200.3.e.a.99.1 2
40.29 even 2 800.3.g.a.751.1 1
40.37 odd 4 800.3.e.a.399.1 2
48.5 odd 4 2304.3.g.j.1279.1 2
48.11 even 4 2304.3.g.j.1279.2 2
48.29 odd 4 2304.3.g.j.1279.2 2
48.35 even 4 2304.3.g.j.1279.1 2
56.3 even 6 392.3.k.b.275.1 2
56.11 odd 6 392.3.k.d.275.1 2
56.13 odd 2 1568.3.g.a.687.1 1
56.19 even 6 392.3.k.b.67.1 2
56.27 even 2 392.3.g.a.99.1 1
56.51 odd 6 392.3.k.d.67.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.3.d.a.3.1 1 1.1 even 1 trivial
8.3.d.a.3.1 1 8.3 odd 2 CM
32.3.d.a.15.1 1 4.3 odd 2
32.3.d.a.15.1 1 8.5 even 2
72.3.b.a.19.1 1 3.2 odd 2
72.3.b.a.19.1 1 24.11 even 2
200.3.e.a.99.1 2 5.2 odd 4
200.3.e.a.99.1 2 40.27 even 4
200.3.e.a.99.2 2 5.3 odd 4
200.3.e.a.99.2 2 40.3 even 4
200.3.g.a.51.1 1 5.4 even 2
200.3.g.a.51.1 1 40.19 odd 2
256.3.c.e.255.1 2 16.11 odd 4
256.3.c.e.255.1 2 16.13 even 4
256.3.c.e.255.2 2 16.3 odd 4
256.3.c.e.255.2 2 16.5 even 4
288.3.b.a.271.1 1 12.11 even 2
288.3.b.a.271.1 1 24.5 odd 2
392.3.g.a.99.1 1 7.6 odd 2
392.3.g.a.99.1 1 56.27 even 2
392.3.k.b.67.1 2 7.5 odd 6
392.3.k.b.67.1 2 56.19 even 6
392.3.k.b.275.1 2 7.3 odd 6
392.3.k.b.275.1 2 56.3 even 6
392.3.k.d.67.1 2 7.2 even 3
392.3.k.d.67.1 2 56.51 odd 6
392.3.k.d.275.1 2 7.4 even 3
392.3.k.d.275.1 2 56.11 odd 6
800.3.e.a.399.1 2 20.7 even 4
800.3.e.a.399.1 2 40.37 odd 4
800.3.e.a.399.2 2 20.3 even 4
800.3.e.a.399.2 2 40.13 odd 4
800.3.g.a.751.1 1 20.19 odd 2
800.3.g.a.751.1 1 40.29 even 2
1568.3.g.a.687.1 1 28.27 even 2
1568.3.g.a.687.1 1 56.13 odd 2
2304.3.g.j.1279.1 2 48.5 odd 4
2304.3.g.j.1279.1 2 48.35 even 4
2304.3.g.j.1279.2 2 48.11 even 4
2304.3.g.j.1279.2 2 48.29 odd 4