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Properties

Label 3.91.b.a.2.1
Level $3$
Weight $91$
Character 3.2
Self dual yes
Analytic conductor $153.888$
Analytic rank $0$
Dimension $1$
CM discriminant -3
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3,91,Mod(2,3)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 91, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 91);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 91 \)
Character orbit: \([\chi]\) \(=\) 3.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: \(153.887879814\)
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 2.1
Character \(\chi\) \(=\) 3.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.95431e21 q^{3} +1.23794e27 q^{4} +3.56705e37 q^{7} +8.72796e42 q^{9} +O(q^{10})\) \(q-2.95431e21 q^{3} +1.23794e27 q^{4} +3.56705e37 q^{7} +8.72796e42 q^{9} -3.65726e48 q^{12} -2.64771e50 q^{13} +1.53250e54 q^{16} +4.22972e57 q^{19} -1.05382e59 q^{21} +8.07794e62 q^{25} -2.57851e64 q^{27} +4.41579e64 q^{28} +2.09722e66 q^{31} +1.08047e70 q^{36} -3.20968e70 q^{37} +7.82215e71 q^{39} +5.12345e73 q^{43} -4.52747e75 q^{48} -1.01781e76 q^{49} -3.27770e77 q^{52} -1.24959e79 q^{57} -3.80103e80 q^{61} +3.11331e80 q^{63} +1.89714e81 q^{64} +2.81073e82 q^{67} -1.35665e84 q^{73} -2.38647e84 q^{75} +5.23614e84 q^{76} +3.03920e83 q^{79} +7.61773e85 q^{81} -1.30456e86 q^{84} -9.44450e87 q^{91} -6.19584e87 q^{93} +2.27256e89 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) −2.95431e21 −1.00000
\(4\) 1.23794e27 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) 3.56705e37 0.333348 0.166674 − 0.986012i \(-0.446697\pi\)
0.166674 + 0.986012i \(0.446697\pi\)
\(8\) 0 0
\(9\) 8.72796e42 1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) −3.65726e48 −1.00000
\(13\) −2.64771e50 −1.97433 −0.987163 − 0.159713i \(-0.948943\pi\)
−0.987163 + 0.159713i \(0.948943\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.53250e54 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 4.22972e57 1.20893 0.604463 − 0.796633i \(-0.293388\pi\)
0.604463 + 0.796633i \(0.293388\pi\)
\(20\) 0 0
\(21\) −1.05382e59 −0.333348
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 8.07794e62 1.00000
\(26\) 0 0
\(27\) −2.57851e64 −1.00000
\(28\) 4.41579e64 0.333348
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 2.09722e66 0.162318 0.0811592 − 0.996701i \(-0.474138\pi\)
0.0811592 + 0.996701i \(0.474138\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 1.08047e70 1.00000
\(37\) −3.20968e70 −0.865734 −0.432867 − 0.901458i \(-0.642498\pi\)
−0.432867 + 0.901458i \(0.642498\pi\)
\(38\) 0 0
\(39\) 7.82215e71 1.97433
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 5.12345e73 1.59765 0.798825 − 0.601563i \(-0.205455\pi\)
0.798825 + 0.601563i \(0.205455\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −4.52747e75 −1.00000
\(49\) −1.01781e76 −0.888879
\(50\) 0 0
\(51\) 0 0
\(52\) −3.27770e77 −1.97433
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.24959e79 −1.20893
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −3.80103e80 −1.73804 −0.869018 − 0.494781i \(-0.835248\pi\)
−0.869018 + 0.494781i \(0.835248\pi\)
\(62\) 0 0
\(63\) 3.11331e80 0.333348
\(64\) 1.89714e81 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 2.81073e82 1.88562 0.942808 − 0.333336i \(-0.108174\pi\)
0.942808 + 0.333336i \(0.108174\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −1.35665e84 −1.91840 −0.959202 − 0.282721i \(-0.908763\pi\)
−0.959202 + 0.282721i \(0.908763\pi\)
\(74\) 0 0
\(75\) −2.38647e84 −1.00000
\(76\) 5.23614e84 1.20893
\(77\) 0 0
\(78\) 0 0
\(79\) 3.03920e83 0.0122897 0.00614483 − 0.999981i \(-0.498044\pi\)
0.00614483 + 0.999981i \(0.498044\pi\)
\(80\) 0 0
\(81\) 7.61773e85 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −1.30456e86 −0.333348
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −9.44450e87 −0.658137
\(92\) 0 0
\(93\) −6.19584e87 −0.162318
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.27256e89 0.894925 0.447462 − 0.894303i \(-0.352328\pi\)
0.447462 + 0.894303i \(0.352328\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000e90 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −7.28383e90 −1.92612 −0.963062 − 0.269278i \(-0.913215\pi\)
−0.963062 + 0.269278i \(0.913215\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −3.19204e91 −1.00000
\(109\) 6.79539e91 1.40612 0.703060 − 0.711131i \(-0.251817\pi\)
0.703060 + 0.711131i \(0.251817\pi\)
\(110\) 0 0
\(111\) 9.48241e91 0.865734
\(112\) 5.46649e91 0.333348
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −2.31091e93 −1.97433
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.31302e93 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 2.59623e93 0.162318
\(125\) 0 0
\(126\) 0 0
\(127\) 6.17065e94 1.31572 0.657860 − 0.753140i \(-0.271462\pi\)
0.657860 + 0.753140i \(0.271462\pi\)
\(128\) 0 0
\(129\) −1.51363e95 −1.59765
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 1.50876e95 0.402992
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 2.24018e96 0.821517 0.410759 − 0.911744i \(-0.365264\pi\)
0.410759 + 0.911744i \(0.365264\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.33756e97 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 3.00693e97 0.888879
\(148\) −3.97339e97 −0.865734
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 1.23438e98 1.09015 0.545077 − 0.838386i \(-0.316501\pi\)
0.545077 + 0.838386i \(0.316501\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 9.68336e98 1.97433
\(157\) 1.30554e99 1.99667 0.998333 − 0.0577183i \(-0.0183825\pi\)
0.998333 + 0.0577183i \(0.0183825\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 6.49605e99 1.83741 0.918707 − 0.394940i \(-0.129235\pi\)
0.918707 + 0.394940i \(0.129235\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 5.21189e100 2.89797
\(170\) 0 0
\(171\) 3.69168e100 1.20893
\(172\) 6.34252e100 1.59765
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 2.88144e100 0.333348
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) −9.77128e100 −0.247979 −0.123990 − 0.992284i \(-0.539569\pi\)
−0.123990 + 0.992284i \(0.539569\pi\)
\(182\) 0 0
\(183\) 1.12294e102 1.73804
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −9.19768e101 −0.333348
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −5.60474e102 −1.00000
\(193\) −1.38770e103 −1.95983 −0.979915 − 0.199418i \(-0.936095\pi\)
−0.979915 + 0.199418i \(0.936095\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −1.25999e103 −0.888879
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 4.64156e102 0.165301 0.0826505 − 0.996579i \(-0.473661\pi\)
0.0826505 + 0.996579i \(0.473661\pi\)
\(200\) 0 0
\(201\) −8.30378e103 −1.88562
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −4.05760e104 −1.97433
\(209\) 0 0
\(210\) 0 0
\(211\) 4.77918e104 1.22080 0.610398 − 0.792095i \(-0.291009\pi\)
0.610398 + 0.792095i \(0.291009\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 7.48089e103 0.0541084
\(218\) 0 0
\(219\) 4.00798e105 1.91840
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 7.94567e105 1.68427 0.842135 − 0.539266i \(-0.181298\pi\)
0.842135 + 0.539266i \(0.181298\pi\)
\(224\) 0 0
\(225\) 7.05039e105 1.00000
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) −1.54692e106 −1.20893
\(229\) 1.72241e106 1.10545 0.552727 − 0.833362i \(-0.313587\pi\)
0.552727 + 0.833362i \(0.313587\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −8.97874e104 −0.0122897
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 9.49357e106 0.611875 0.305937 − 0.952052i \(-0.401030\pi\)
0.305937 + 0.952052i \(0.401030\pi\)
\(242\) 0 0
\(243\) −2.25052e107 −1.00000
\(244\) −4.70545e107 −1.73804
\(245\) 0 0
\(246\) 0 0
\(247\) −1.11991e108 −2.38681
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 3.85409e107 0.333348
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 2.34854e108 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −1.14491e108 −0.288590
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 3.47952e109 1.88562
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 5.59143e109 1.83614 0.918068 − 0.396423i \(-0.129748\pi\)
0.918068 + 0.396423i \(0.129748\pi\)
\(272\) 0 0
\(273\) 2.79020e109 0.658137
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −8.76166e109 −1.07398 −0.536991 − 0.843588i \(-0.680439\pi\)
−0.536991 + 0.843588i \(0.680439\pi\)
\(278\) 0 0
\(279\) 1.83045e109 0.162318
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −4.27940e110 −1.99983 −0.999915 − 0.0130390i \(-0.995849\pi\)
−0.999915 + 0.0130390i \(0.995849\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 5.50051e110 1.00000
\(290\) 0 0
\(291\) −6.71384e110 −0.894925
\(292\) −1.67946e111 −1.91840
\(293\) 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
\(300\) −2.95431e111 −1.00000
\(301\) 1.82756e111 0.532573
\(302\) 0 0
\(303\) 0 0
\(304\) 6.48203e111 1.20893
\(305\) 0 0
\(306\) 0 0
\(307\) −4.32375e111 −0.518363 −0.259181 − 0.965829i \(-0.583453\pi\)
−0.259181 + 0.965829i \(0.583453\pi\)
\(308\) 0 0
\(309\) 2.15187e112 1.92612
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 3.05300e112 1.53190 0.765952 − 0.642898i \(-0.222268\pi\)
0.765952 + 0.642898i \(0.222268\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 3.76234e110 0.0122897
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 9.43030e112 1.00000
\(325\) −2.13880e113 −1.97433
\(326\) 0 0
\(327\) −2.00757e113 −1.40612
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 3.87474e113 1.57030 0.785150 − 0.619305i \(-0.212586\pi\)
0.785150 + 0.619305i \(0.212586\pi\)
\(332\) 0 0
\(333\) −2.80140e113 −0.865734
\(334\) 0 0
\(335\) 0 0
\(336\) −1.61497e113 −0.333348
\(337\) −1.06697e114 −1.92667 −0.963334 − 0.268307i \(-0.913536\pi\)
−0.963334 + 0.268307i \(0.913536\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −7.71502e113 −0.629653
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 5.34756e114 1.99992 0.999958 − 0.00920366i \(-0.00292966\pi\)
0.999958 + 0.00920366i \(0.00292966\pi\)
\(350\) 0 0
\(351\) 6.82715e114 1.97433
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 5.64933e114 0.461501
\(362\) 0 0
\(363\) −1.56963e115 −1.00000
\(364\) −1.16917e115 −0.658137
\(365\) 0 0
\(366\) 0 0
\(367\) 5.14012e115 1.99986 0.999932 − 0.0117019i \(-0.00372493\pi\)
0.999932 + 0.0117019i \(0.00372493\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −7.67008e114 −0.162318
\(373\) −9.24042e115 −1.73298 −0.866492 − 0.499191i \(-0.833630\pi\)
−0.866492 + 0.499191i \(0.833630\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −2.13163e116 −1.94961 −0.974805 − 0.223059i \(-0.928396\pi\)
−0.974805 + 0.223059i \(0.928396\pi\)
\(380\) 0 0
\(381\) −1.82300e116 −1.31572
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 4.47173e116 1.59765
\(388\) 2.81329e116 0.894925
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1.12030e117 1.26987 0.634936 − 0.772565i \(-0.281026\pi\)
0.634936 + 0.772565i \(0.281026\pi\)
\(398\) 0 0
\(399\) −4.45735e116 −0.402992
\(400\) 1.23794e117 1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) −5.55282e116 −0.320470
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 6.72914e117 1.99715 0.998575 − 0.0533715i \(-0.0169968\pi\)
0.998575 + 0.0533715i \(0.0169968\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −9.01694e117 −1.92612
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −6.61819e117 −0.821517
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −1.95862e118 −1.58218 −0.791088 − 0.611702i \(-0.790485\pi\)
−0.791088 + 0.611702i \(0.790485\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.35585e118 −0.579370
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −3.95156e118 −1.00000
\(433\) 3.29841e118 0.752227 0.376114 − 0.926574i \(-0.377260\pi\)
0.376114 + 0.926574i \(0.377260\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 8.41229e118 1.40612
\(437\) 0 0
\(438\) 0 0
\(439\) 1.61836e119 1.98687 0.993437 − 0.114379i \(-0.0364879\pi\)
0.993437 + 0.114379i \(0.0364879\pi\)
\(440\) 0 0
\(441\) −8.88340e118 −0.888879
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 1.17386e119 0.865734
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 6.76718e118 0.333348
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −3.64676e119 −1.09015
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 7.30982e119 1.47122 0.735610 − 0.677405i \(-0.236895\pi\)
0.735610 + 0.677405i \(0.236895\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.58386e120 −1.77244 −0.886222 − 0.463261i \(-0.846679\pi\)
−0.886222 + 0.463261i \(0.846679\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) −2.86077e120 −1.97433
\(469\) 1.00260e120 0.628566
\(470\) 0 0
\(471\) −3.85697e120 −1.99667
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 3.41674e120 1.20893
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 8.49830e120 1.70924
\(482\) 0 0
\(483\) 0 0
\(484\) 6.57720e120 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) 1.22527e121 1.41068 0.705342 − 0.708868i \(-0.250794\pi\)
0.705342 + 0.708868i \(0.250794\pi\)
\(488\) 0 0
\(489\) −1.91914e121 −1.83741
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 3.21398e120 0.162318
\(497\) 0 0
\(498\) 0 0
\(499\) 4.78796e121 1.84343 0.921714 − 0.387869i \(-0.126789\pi\)
0.921714 + 0.387869i \(0.126789\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.53975e122 −2.89797
\(508\) 7.63889e121 1.31572
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) −4.83925e121 −0.639495
\(512\) 0 0
\(513\) −1.09064e122 −1.20893
\(514\) 0 0
\(515\) 0 0
\(516\) −1.87378e122 −1.59765
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 4.27289e122 1.98676 0.993380 − 0.114873i \(-0.0366460\pi\)
0.993380 + 0.114873i \(0.0366460\pi\)
\(524\) 0 0
\(525\) −8.51267e121 −0.333348
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 3.59340e122 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 1.86776e122 0.402992
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 1.24474e123 1.26242 0.631209 − 0.775613i \(-0.282559\pi\)
0.631209 + 0.775613i \(0.282559\pi\)
\(542\) 0 0
\(543\) 2.88674e122 0.247979
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.12114e123 0.692201 0.346100 − 0.938198i \(-0.387506\pi\)
0.346100 + 0.938198i \(0.387506\pi\)
\(548\) 0 0
\(549\) −3.31752e123 −1.73804
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 1.08410e121 0.00409673
\(554\) 0 0
\(555\) 0 0
\(556\) 2.77321e123 0.821517
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) −1.35654e124 −3.15428
\(560\) 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
\(567\) 2.71728e123 0.333348
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) −1.72302e124 −1.54051 −0.770256 − 0.637735i \(-0.779871\pi\)
−0.770256 + 0.637735i \(0.779871\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.65581e124 1.00000
\(577\) 1.29880e124 0.725491 0.362745 − 0.931888i \(-0.381840\pi\)
0.362745 + 0.931888i \(0.381840\pi\)
\(578\) 0 0
\(579\) 4.09971e124 1.95983
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 3.72240e124 0.888879
\(589\) 8.87065e123 0.196231
\(590\) 0 0
\(591\) 0 0
\(592\) −4.91882e124 −0.865734
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −1.37126e124 −0.165301
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) −2.23904e125 −1.99853 −0.999263 − 0.0383917i \(-0.987777\pi\)
−0.999263 + 0.0383917i \(0.987777\pi\)
\(602\) 0 0
\(603\) 2.45320e125 1.88562
\(604\) 1.52809e125 1.09015
\(605\) 0 0
\(606\) 0 0
\(607\) −3.49141e125 −1.99301 −0.996504 − 0.0835425i \(-0.973377\pi\)
−0.996504 + 0.0835425i \(0.973377\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −4.65472e125 −1.70676 −0.853379 − 0.521290i \(-0.825451\pi\)
−0.853379 + 0.521290i \(0.825451\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −8.44942e125 −1.99870 −0.999351 − 0.0360299i \(-0.988529\pi\)
−0.999351 + 0.0360299i \(0.988529\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 1.19874e126 1.97433
\(625\) 6.52530e125 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 1.61618e126 1.99667
\(629\) 0 0
\(630\) 0 0
\(631\) 4.39245e125 0.437911 0.218955 − 0.975735i \(-0.429735\pi\)
0.218955 + 0.975735i \(0.429735\pi\)
\(632\) 0 0
\(633\) −1.41192e126 −1.22080
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 2.69486e126 1.75494
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) −4.65760e126 −1.98915 −0.994576 − 0.104009i \(-0.966833\pi\)
−0.994576 + 0.104009i \(0.966833\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −2.21009e125 −0.0541084
\(652\) 8.04172e126 1.83741
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −1.18408e127 −1.91840
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −1.37981e127 −1.70120 −0.850599 − 0.525815i \(-0.823760\pi\)
−0.850599 + 0.525815i \(0.823760\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −2.34740e127 −1.68427
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 2.53481e127 1.39081 0.695404 − 0.718619i \(-0.255225\pi\)
0.695404 + 0.718619i \(0.255225\pi\)
\(674\) 0 0
\(675\) −2.08291e127 −1.00000
\(676\) 6.45201e127 2.89797
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 8.10632e126 0.298321
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 4.57008e127 1.20893
\(685\) 0 0
\(686\) 0 0
\(687\) −5.08855e127 −1.10545
\(688\) 7.85166e127 1.59765
\(689\) 0 0
\(690\) 0 0
\(691\) −4.53083e127 −0.757994 −0.378997 − 0.925398i \(-0.623731\pi\)
−0.378997 + 0.925398i \(0.623731\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 3.56705e127 0.333348
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) −1.35761e128 −1.04661
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −3.07454e128 −1.61696 −0.808480 − 0.588524i \(-0.799709\pi\)
−0.808480 + 0.588524i \(0.799709\pi\)
\(710\) 0 0
\(711\) 2.65260e126 0.0122897
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) −2.59818e128 −0.642069
\(722\) 0 0
\(723\) −2.80470e128 −0.611875
\(724\) −1.20963e128 −0.247979
\(725\) 0 0
\(726\) 0 0
\(727\) 5.66273e128 0.963779 0.481889 − 0.876232i \(-0.339951\pi\)
0.481889 + 0.876232i \(0.339951\pi\)
\(728\) 0 0
\(729\) 6.64873e128 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 1.39014e129 1.73804
\(733\) −1.05880e129 −1.24490 −0.622450 − 0.782659i \(-0.713863\pi\)
−0.622450 + 0.782659i \(0.713863\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 4.39730e128 0.358250 0.179125 − 0.983826i \(-0.442673\pi\)
0.179125 + 0.983826i \(0.442673\pi\)
\(740\) 0 0
\(741\) 3.30855e129 2.38681
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −3.99352e129 −1.57601 −0.788004 − 0.615671i \(-0.788885\pi\)
−0.788004 + 0.615671i \(0.788885\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −1.13862e129 −0.333348
\(757\) −6.90835e129 −1.90572 −0.952862 − 0.303405i \(-0.901876\pi\)
−0.952862 + 0.303405i \(0.901876\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 2.42395e129 0.468726
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −6.93833e129 −1.00000
\(769\) 1.46331e130 1.98907 0.994535 − 0.104404i \(-0.0332934\pi\)
0.994535 + 0.104404i \(0.0332934\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.71790e130 −1.95983
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 1.69412e129 0.162318
\(776\) 0 0
\(777\) 3.38242e129 0.288590
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −1.55979e130 −0.888879
\(785\) 0 0
\(786\) 0 0
\(787\) 3.12512e130 1.49970 0.749848 − 0.661610i \(-0.230127\pi\)
0.749848 + 0.661610i \(0.230127\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 1.00640e131 3.43145
\(794\) 0 0
\(795\) 0 0
\(796\) 5.74597e129 0.165301
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) −1.02796e131 −1.88562
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) −1.11501e131 −1.38465 −0.692324 − 0.721586i \(-0.743413\pi\)
−0.692324 + 0.721586i \(0.743413\pi\)
\(812\) 0 0
\(813\) −1.65188e131 −1.83614
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 2.16707e131 1.93144
\(818\) 0 0
\(819\) −8.24313e130 −0.658137
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) −3.16192e128 −0.00202748 −0.00101374 − 0.999999i \(-0.500323\pi\)
−0.00101374 + 0.999999i \(0.500323\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) 1.21288e130 0.0560871 0.0280435 − 0.999607i \(-0.491072\pi\)
0.0280435 + 0.999607i \(0.491072\pi\)
\(830\) 0 0
\(831\) 2.58847e131 1.07398
\(832\) −5.02306e131 −1.97433
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −5.40771e130 −0.162318
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 4.12876e131 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 5.91634e131 1.22080
\(845\) 0 0
\(846\) 0 0
\(847\) 1.89518e131 0.333348
\(848\) 0 0
\(849\) 1.26427e132 1.99983
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −4.55110e131 −0.582654 −0.291327 − 0.956624i \(-0.594097\pi\)
−0.291327 + 0.956624i \(0.594097\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −6.18642e131 −0.577760 −0.288880 − 0.957365i \(-0.593283\pi\)
−0.288880 + 0.957365i \(0.593283\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −1.62502e132 −1.00000
\(868\) 9.26089e130 0.0541084
\(869\) 0 0
\(870\) 0 0
\(871\) −7.44199e132 −3.72282
\(872\) 0 0
\(873\) 1.98348e132 0.894925
\(874\) 0 0
\(875\) 0 0
\(876\) 4.96164e132 1.91840
\(877\) −2.82772e131 −0.103862 −0.0519308 − 0.998651i \(-0.516538\pi\)
−0.0519308 + 0.998651i \(0.516538\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) −6.77377e132 −1.83062 −0.915311 − 0.402748i \(-0.868055\pi\)
−0.915311 + 0.402748i \(0.868055\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 2.20110e132 0.438592
\(890\) 0 0
\(891\) 0 0
\(892\) 9.83627e132 1.68427
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 8.72796e132 1.00000
\(901\) 0 0
\(902\) 0 0
\(903\) −5.39918e132 −0.532573
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 2.02944e133 1.64077 0.820385 − 0.571812i \(-0.193759\pi\)
0.820385 + 0.571812i \(0.193759\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) −1.91499e133 −1.20893
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 2.13225e133 1.10545
\(917\) 0 0
\(918\) 0 0
\(919\) −3.85283e132 −0.172418 −0.0862088 − 0.996277i \(-0.527475\pi\)
−0.0862088 + 0.996277i \(0.527475\pi\)
\(920\) 0 0
\(921\) 1.27737e133 0.518363
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −2.59276e133 −0.865734
\(926\) 0 0
\(927\) −6.35730e133 −1.92612
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) −4.30505e133 −1.07459
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 2.18817e133 0.409072 0.204536 − 0.978859i \(-0.434431\pi\)
0.204536 + 0.978859i \(0.434431\pi\)
\(938\) 0 0
\(939\) −9.01951e133 −1.53190
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) −1.11151e132 −0.0122897
\(949\) 3.59202e134 3.78756
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −1.62539e134 −0.973653
\(962\) 0 0
\(963\) 0 0
\(964\) 1.17525e134 0.611875
\(965\) 0 0
\(966\) 0 0
\(967\) 1.63666e134 0.740915 0.370457 − 0.928849i \(-0.379201\pi\)
0.370457 + 0.928849i \(0.379201\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) −2.78601e134 −1.00000
\(973\) 7.99083e133 0.273851
\(974\) 0 0
\(975\) 6.31869e134 1.97433
\(976\) −5.82506e134 −1.73804
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 5.93099e134 1.40612
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −1.38638e135 −2.38681
\(989\) 0 0
\(990\) 0 0
\(991\) −1.15132e135 −1.72934 −0.864670 − 0.502340i \(-0.832473\pi\)
−0.864670 + 0.502340i \(0.832473\pi\)
\(992\) 0 0
\(993\) −1.14472e135 −1.57030
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 3.03697e134 0.347663 0.173831 − 0.984775i \(-0.444385\pi\)
0.173831 + 0.984775i \(0.444385\pi\)
\(998\) 0 0
\(999\) 8.27621e134 0.865734
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 3.91.b.a.2.1 ✓ 1
3.2 odd 2 CM 3.91.b.a.2.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.91.b.a.2.1 ✓ 1 1.1 even 1 trivial
3.91.b.a.2.1 ✓ 1 3.2 odd 2 CM