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Properties

Label 3.97.b.a.2.1
Level $3$
Weight $97$
Character 3.2
Self dual yes
Analytic conductor $175.089$
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] = [3,97,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, 97, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 97);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 97 \)
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: \(175.089337542\)
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)
 
\(f(q)\) \(=\) \(q+7.97664e22 q^{3} +7.92282e28 q^{4} +6.06887e40 q^{7} +6.36269e45 q^{9} +O(q^{10})\) \(q+7.97664e22 q^{3} +7.92282e28 q^{4} +6.06887e40 q^{7} +6.36269e45 q^{9} +6.31975e51 q^{12} -1.60474e53 q^{13} +6.27710e57 q^{16} +1.95165e60 q^{19} +4.84092e63 q^{21} +1.26218e67 q^{25} +5.07529e68 q^{27} +4.80825e69 q^{28} -5.81297e71 q^{31} +5.04104e74 q^{36} -1.73023e74 q^{37} -1.28005e76 q^{39} +5.04266e78 q^{43} +5.00702e80 q^{48} +2.33598e81 q^{49} -1.27141e82 q^{52} +1.55676e83 q^{57} +9.84005e85 q^{61} +3.86143e86 q^{63} +4.97323e86 q^{64} -4.33240e86 q^{67} -5.21829e89 q^{73} +1.00679e90 q^{75} +1.54625e89 q^{76} -2.38853e91 q^{79} +4.04838e91 q^{81} +3.83537e92 q^{84} -9.73897e93 q^{91} -4.63680e94 q^{93} +4.07920e95 q^{97} +O(q^{100})\)

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 \(\pi\)
\(3\) 7.97664e22 1.00000
\(4\) 7.92282e28 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) 6.06887e40 1.65349 0.826746 − 0.562576i \(-0.190190\pi\)
0.826746 + 0.562576i \(0.190190\pi\)
\(8\) 0 0
\(9\) 6.36269e45 1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 6.31975e51 1.00000
\(13\) −1.60474e53 −0.544659 −0.272329 − 0.962204i \(-0.587794\pi\)
−0.272329 + 0.962204i \(0.587794\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 6.27710e57 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 1.95165e60 0.0813257 0.0406629 − 0.999173i \(-0.487053\pi\)
0.0406629 + 0.999173i \(0.487053\pi\)
\(20\) 0 0
\(21\) 4.84092e63 1.65349
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 1.26218e67 1.00000
\(26\) 0 0
\(27\) 5.07529e68 1.00000
\(28\) 4.80825e69 1.65349
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −5.81297e71 −1.51021 −0.755104 − 0.655605i \(-0.772414\pi\)
−0.755104 + 0.655605i \(0.772414\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 5.04104e74 1.00000
\(37\) −1.73023e74 −0.0921340 −0.0460670 − 0.998938i \(-0.514669\pi\)
−0.0460670 + 0.998938i \(0.514669\pi\)
\(38\) 0 0
\(39\) −1.28005e76 −0.544659
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 5.04266e78 1.97776 0.988880 − 0.148717i \(-0.0475144\pi\)
0.988880 + 0.148717i \(0.0475144\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 5.00702e80 1.00000
\(49\) 2.33598e81 1.73403
\(50\) 0 0
\(51\) 0 0
\(52\) −1.27141e82 −0.544659
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.55676e83 0.0813257
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 9.84005e85 1.98228 0.991141 − 0.132816i \(-0.0424019\pi\)
0.991141 + 0.132816i \(0.0424019\pi\)
\(62\) 0 0
\(63\) 3.86143e86 1.65349
\(64\) 4.97323e86 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −4.33240e86 −0.0966357 −0.0483179 − 0.998832i \(-0.515386\pi\)
−0.0483179 + 0.998832i \(0.515386\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −5.21829e89 −1.89684 −0.948421 − 0.317014i \(-0.897320\pi\)
−0.948421 + 0.317014i \(0.897320\pi\)
\(74\) 0 0
\(75\) 1.00679e90 1.00000
\(76\) 1.54625e89 0.0813257
\(77\) 0 0
\(78\) 0 0
\(79\) −2.38853e91 −1.95898 −0.979489 − 0.201496i \(-0.935420\pi\)
−0.979489 + 0.201496i \(0.935420\pi\)
\(80\) 0 0
\(81\) 4.04838e91 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 3.83537e92 1.65349
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −9.73897e93 −0.900588
\(92\) 0 0
\(93\) −4.63680e94 −1.51021
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 4.07920e95 1.76008 0.880038 − 0.474903i \(-0.157517\pi\)
0.880038 + 0.474903i \(0.157517\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000e96 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −6.01099e96 −1.45465 −0.727327 − 0.686292i \(-0.759237\pi\)
−0.727327 + 0.686292i \(0.759237\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 4.02106e97 1.00000
\(109\) −1.22274e98 −1.95373 −0.976864 − 0.213863i \(-0.931395\pi\)
−0.976864 + 0.213863i \(0.931395\pi\)
\(110\) 0 0
\(111\) −1.38014e97 −0.0921340
\(112\) 3.80949e98 1.65349
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.02105e99 −0.544659
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 9.41234e99 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) −4.60551e100 −1.51021
\(125\) 0 0
\(126\) 0 0
\(127\) −8.38629e100 −0.872954 −0.436477 − 0.899715i \(-0.643774\pi\)
−0.436477 + 0.899715i \(0.643774\pi\)
\(128\) 0 0
\(129\) 4.02235e101 1.97776
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 1.18443e101 0.134471
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) −1.15623e103 −1.57883 −0.789413 − 0.613863i \(-0.789615\pi\)
−0.789413 + 0.613863i \(0.789615\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 3.99392e103 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 1.86333e104 1.73403
\(148\) −1.37083e103 −0.0921340
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) −7.79623e104 −1.99982 −0.999910 − 0.0134055i \(-0.995733\pi\)
−0.999910 + 0.0134055i \(0.995733\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −1.01416e105 −0.544659
\(157\) 4.74116e105 1.87370 0.936852 − 0.349726i \(-0.113725\pi\)
0.936852 + 0.349726i \(0.113725\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.08110e106 1.35922 0.679608 − 0.733575i \(-0.262150\pi\)
0.679608 + 0.733575i \(0.262150\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) −6.10564e106 −0.703347
\(170\) 0 0
\(171\) 1.24177e106 0.0813257
\(172\) 3.99520e107 1.97776
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 7.65999e107 1.65349
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 4.63204e108 1.98244 0.991222 − 0.132209i \(-0.0422069\pi\)
0.991222 + 0.132209i \(0.0422069\pi\)
\(182\) 0 0
\(183\) 7.84906e108 1.98228
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 3.08013e109 1.65349
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 3.96697e109 1.00000
\(193\) 8.20815e109 1.61248 0.806240 − 0.591588i \(-0.201499\pi\)
0.806240 + 0.591588i \(0.201499\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.85076e110 1.73403
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 3.23972e110 1.46406 0.732032 − 0.681271i \(-0.238572\pi\)
0.732032 + 0.681271i \(0.238572\pi\)
\(200\) 0 0
\(201\) −3.45580e109 −0.0966357
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −1.00731e111 −0.544659
\(209\) 0 0
\(210\) 0 0
\(211\) 6.24604e111 1.69843 0.849213 − 0.528050i \(-0.177077\pi\)
0.849213 + 0.528050i \(0.177077\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −3.52782e112 −2.49712
\(218\) 0 0
\(219\) −4.16245e112 −1.89684
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −9.46808e112 −1.80979 −0.904896 − 0.425633i \(-0.860051\pi\)
−0.904896 + 0.425633i \(0.860051\pi\)
\(224\) 0 0
\(225\) 8.03084e112 1.00000
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 1.23339e112 0.0813257
\(229\) −3.42424e113 −1.83004 −0.915021 − 0.403406i \(-0.867826\pi\)
−0.915021 + 0.403406i \(0.867826\pi\)
\(230\) 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
\(237\) −1.90524e114 −1.95898
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 2.61417e114 1.20369 0.601846 − 0.798612i \(-0.294432\pi\)
0.601846 + 0.798612i \(0.294432\pi\)
\(242\) 0 0
\(243\) 3.22925e114 1.00000
\(244\) 7.79609e114 1.98228
\(245\) 0 0
\(246\) 0 0
\(247\) −3.13189e113 −0.0442948
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 3.05934e115 1.65349
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 3.94020e115 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −1.05005e115 −0.152343
\(260\) 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
\(268\) −3.43248e115 −0.0966357
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −1.18150e117 −1.94943 −0.974716 − 0.223449i \(-0.928268\pi\)
−0.974716 + 0.223449i \(0.928268\pi\)
\(272\) 0 0
\(273\) −7.76843e116 −0.900588
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.14935e117 −0.662864 −0.331432 − 0.943479i \(-0.607532\pi\)
−0.331432 + 0.943479i \(0.607532\pi\)
\(278\) 0 0
\(279\) −3.69861e117 −1.51021
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 2.86892e117 0.591519 0.295760 − 0.955262i \(-0.404427\pi\)
0.295760 + 0.955262i \(0.404427\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.32769e118 1.00000
\(290\) 0 0
\(291\) 3.25383e118 1.76008
\(292\) −4.13436e118 −1.89684
\(293\) 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
\(300\) 7.97664e118 1.00000
\(301\) 3.06032e119 3.27021
\(302\) 0 0
\(303\) 0 0
\(304\) 1.22507e118 0.0813257
\(305\) 0 0
\(306\) 0 0
\(307\) 1.66528e118 0.0689992 0.0344996 − 0.999405i \(-0.489016\pi\)
0.0344996 + 0.999405i \(0.489016\pi\)
\(308\) 0 0
\(309\) −4.79476e119 −1.45465
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) −1.44091e118 −0.0235782 −0.0117891 − 0.999931i \(-0.503753\pi\)
−0.0117891 + 0.999931i \(0.503753\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −1.89239e120 −1.95898
\(317\) 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
\(324\) 3.20745e120 1.00000
\(325\) −2.02547e120 −0.544659
\(326\) 0 0
\(327\) −9.75340e120 −1.95373
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.56805e121 −1.75234 −0.876168 − 0.482005i \(-0.839909\pi\)
−0.876168 + 0.482005i \(0.839909\pi\)
\(332\) 0 0
\(333\) −1.10089e120 −0.0921340
\(334\) 0 0
\(335\) 0 0
\(336\) 3.03870e121 1.65349
\(337\) 3.61826e121 1.70712 0.853561 − 0.520993i \(-0.174438\pi\)
0.853561 + 0.520993i \(0.174438\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 6.00117e121 1.21372
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 1.53762e122 1.35279 0.676394 − 0.736540i \(-0.263542\pi\)
0.676394 + 0.736540i \(0.263542\pi\)
\(350\) 0 0
\(351\) −8.14453e121 −0.544659
\(352\) 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
\(361\) −5.72089e122 −0.993386
\(362\) 0 0
\(363\) 7.50789e122 1.00000
\(364\) −7.71601e122 −0.900588
\(365\) 0 0
\(366\) 0 0
\(367\) −2.07418e123 −1.63258 −0.816291 − 0.577641i \(-0.803973\pi\)
−0.816291 + 0.577641i \(0.803973\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −3.67365e123 −1.51021
\(373\) 1.87633e122 0.0678088 0.0339044 − 0.999425i \(-0.489206\pi\)
0.0339044 + 0.999425i \(0.489206\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 6.26398e123 1.05237 0.526185 − 0.850370i \(-0.323622\pi\)
0.526185 + 0.850370i \(0.323622\pi\)
\(380\) 0 0
\(381\) −6.68944e123 −0.872954
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3.20848e124 1.97776
\(388\) 3.23187e124 1.76008
\(389\) 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
\(397\) −8.20995e124 −1.48729 −0.743646 − 0.668573i \(-0.766905\pi\)
−0.743646 + 0.668573i \(0.766905\pi\)
\(398\) 0 0
\(399\) 9.44776e123 0.134471
\(400\) 7.92282e124 1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 9.32832e124 0.822548
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −2.52881e125 −1.09698 −0.548488 − 0.836158i \(-0.684797\pi\)
−0.548488 + 0.836158i \(0.684797\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4.76240e125 −1.45465
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −9.22284e125 −1.57883
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −1.13162e126 −1.22507 −0.612536 − 0.790442i \(-0.709851\pi\)
−0.612536 + 0.790442i \(0.709851\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 5.97180e126 3.27769
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 3.18581e126 1.00000
\(433\) −6.90541e125 −0.193986 −0.0969930 − 0.995285i \(-0.530922\pi\)
−0.0969930 + 0.995285i \(0.530922\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −9.68758e126 −1.95373
\(437\) 0 0
\(438\) 0 0
\(439\) 5.82596e126 0.845416 0.422708 − 0.906266i \(-0.361080\pi\)
0.422708 + 0.906266i \(0.361080\pi\)
\(440\) 0 0
\(441\) 1.48631e127 1.73403
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) −1.09346e126 −0.0921340
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 3.01819e127 1.65349
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −6.21877e127 −1.99982
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −7.42087e127 −1.56487 −0.782434 − 0.622734i \(-0.786022\pi\)
−0.782434 + 0.622734i \(0.786022\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.32982e128 −1.49935 −0.749677 − 0.661804i \(-0.769791\pi\)
−0.749677 + 0.661804i \(0.769791\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) −8.08957e127 −0.544659
\(469\) −2.62928e127 −0.159786
\(470\) 0 0
\(471\) 3.78185e128 1.87370
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 2.46332e127 0.0813257
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 2.77657e127 0.0501816
\(482\) 0 0
\(483\) 0 0
\(484\) 7.45723e128 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) 6.14938e128 0.612973 0.306487 − 0.951875i \(-0.400847\pi\)
0.306487 + 0.951875i \(0.400847\pi\)
\(488\) 0 0
\(489\) 1.66002e129 1.35922
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −3.64886e129 −1.51021
\(497\) 0 0
\(498\) 0 0
\(499\) 2.03128e129 0.629425 0.314713 − 0.949187i \(-0.398092\pi\)
0.314713 + 0.949187i \(0.398092\pi\)
\(500\) 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
\(507\) −4.87026e129 −0.703347
\(508\) −6.64430e129 −0.872954
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) −3.16691e130 −3.13641
\(512\) 0 0
\(513\) 9.90516e128 0.0813257
\(514\) 0 0
\(515\) 0 0
\(516\) 3.18683e130 1.97776
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −2.40074e130 −0.780304 −0.390152 − 0.920750i \(-0.627578\pi\)
−0.390152 + 0.920750i \(0.627578\pi\)
\(524\) 0 0
\(525\) 6.11010e130 1.65349
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 5.31952e130 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 9.38401e129 0.134471
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −6.62592e130 −0.424402 −0.212201 − 0.977226i \(-0.568063\pi\)
−0.212201 + 0.977226i \(0.568063\pi\)
\(542\) 0 0
\(543\) 3.69482e131 1.98244
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −2.45620e131 −0.926558 −0.463279 − 0.886212i \(-0.653327\pi\)
−0.463279 + 0.886212i \(0.653327\pi\)
\(548\) 0 0
\(549\) 6.26092e131 1.98228
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −1.44957e132 −3.23915
\(554\) 0 0
\(555\) 0 0
\(556\) −9.16060e131 −1.57883
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) −8.09216e131 −1.07720
\(560\) 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
\(567\) 2.45691e132 1.65349
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 8.84657e131 0.424856 0.212428 − 0.977177i \(-0.431863\pi\)
0.212428 + 0.977177i \(0.431863\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 3.16431e132 1.00000
\(577\) −6.75881e132 −1.96531 −0.982656 − 0.185440i \(-0.940629\pi\)
−0.982656 + 0.185440i \(0.940629\pi\)
\(578\) 0 0
\(579\) 6.54735e132 1.61248
\(580\) 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 \(\pi\)
\(588\) 1.47628e133 1.73403
\(589\) −1.13449e132 −0.122819
\(590\) 0 0
\(591\) 0 0
\(592\) −1.08608e132 −0.0921340
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 2.58421e133 1.46406
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) −4.71243e133 −1.93763 −0.968813 − 0.247792i \(-0.920295\pi\)
−0.968813 + 0.247792i \(0.920295\pi\)
\(602\) 0 0
\(603\) −2.75657e132 −0.0966357
\(604\) −6.17681e133 −1.99982
\(605\) 0 0
\(606\) 0 0
\(607\) −5.90377e133 −1.50686 −0.753429 − 0.657529i \(-0.771602\pi\)
−0.753429 + 0.657529i \(0.771602\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 9.83463e133 1.56551 0.782754 − 0.622331i \(-0.213814\pi\)
0.782754 + 0.622331i \(0.213814\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −9.35173e133 −0.932697 −0.466349 − 0.884601i \(-0.654431\pi\)
−0.466349 + 0.884601i \(0.654431\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −8.03498e133 −0.544659
\(625\) 1.59309e134 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 3.75633e134 1.87370
\(629\) 0 0
\(630\) 0 0
\(631\) −1.68166e134 −0.667313 −0.333657 − 0.942695i \(-0.608283\pi\)
−0.333657 + 0.942695i \(0.608283\pi\)
\(632\) 0 0
\(633\) 4.98224e134 1.69843
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −3.74865e134 −0.944457
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 9.30521e134 1.49486 0.747428 − 0.664343i \(-0.231288\pi\)
0.747428 + 0.664343i \(0.231288\pi\)
\(644\) 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
\(651\) −2.81401e135 −2.49712
\(652\) 1.64882e135 1.35922
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −3.32023e135 −1.89684
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −1.27859e135 −0.545837 −0.272918 − 0.962037i \(-0.587989\pi\)
−0.272918 + 0.962037i \(0.587989\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −7.55235e135 −1.80979
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 7.57814e135 1.36408 0.682040 − 0.731315i \(-0.261093\pi\)
0.682040 + 0.731315i \(0.261093\pi\)
\(674\) 0 0
\(675\) 6.40591e135 1.00000
\(676\) −4.83739e135 −0.703347
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 2.47561e136 2.91027
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 9.83832e134 0.0813257
\(685\) 0 0
\(686\) 0 0
\(687\) −2.73139e136 −1.83004
\(688\) 3.16533e136 1.97776
\(689\) 0 0
\(690\) 0 0
\(691\) −1.98669e136 −1.00736 −0.503679 − 0.863891i \(-0.668020\pi\)
−0.503679 + 0.863891i \(0.668020\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 6.06887e136 1.65349
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) −3.37679e134 −0.00749287
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.35410e137 −1.99816 −0.999082 − 0.0428490i \(-0.986357\pi\)
−0.999082 + 0.0428490i \(0.986357\pi\)
\(710\) 0 0
\(711\) −1.51974e137 −1.95898
\(712\) 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
\(721\) −3.64799e137 −2.40526
\(722\) 0 0
\(723\) 2.08523e137 1.20369
\(724\) 3.66988e137 1.98244
\(725\) 0 0
\(726\) 0 0
\(727\) −3.93875e137 −1.74464 −0.872321 − 0.488934i \(-0.837386\pi\)
−0.872321 + 0.488934i \(0.837386\pi\)
\(728\) 0 0
\(729\) 2.57585e137 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 6.21867e137 1.98228
\(733\) 6.65011e137 1.98535 0.992677 − 0.120802i \(-0.0385465\pi\)
0.992677 + 0.120802i \(0.0385465\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −9.11943e137 −1.84092 −0.920459 − 0.390839i \(-0.872185\pi\)
−0.920459 + 0.390839i \(0.872185\pi\)
\(740\) 0 0
\(741\) −2.49819e136 −0.0442948
\(742\) 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
\(751\) 1.83093e138 1.70590 0.852950 − 0.521992i \(-0.174811\pi\)
0.852950 + 0.521992i \(0.174811\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 2.44033e138 1.65349
\(757\) −3.12270e138 −1.98577 −0.992883 − 0.119092i \(-0.962002\pi\)
−0.992883 + 0.119092i \(0.962002\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) −7.42068e138 −3.23047
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 3.14296e138 1.00000
\(769\) −6.34926e138 −1.89784 −0.948918 − 0.315522i \(-0.897820\pi\)
−0.948918 + 0.315522i \(0.897820\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.50317e138 1.61248
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) −7.33700e138 −1.51021
\(776\) 0 0
\(777\) −8.37589e137 −0.152343
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.46632e139 1.73403
\(785\) 0 0
\(786\) 0 0
\(787\) 1.90674e139 1.87718 0.938588 − 0.345041i \(-0.112135\pi\)
0.938588 + 0.345041i \(0.112135\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −1.57907e139 −1.07967
\(794\) 0 0
\(795\) 0 0
\(796\) 2.56677e139 1.46406
\(797\) 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
\(804\) −2.73797e138 −0.0966357
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 2.83436e139 0.659864 0.329932 − 0.944005i \(-0.392974\pi\)
0.329932 + 0.944005i \(0.392974\pi\)
\(812\) 0 0
\(813\) −9.42441e139 −1.94943
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 9.84147e138 0.160843
\(818\) 0 0
\(819\) −6.19660e139 −0.900588
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) −8.67716e139 −0.998127 −0.499063 − 0.866566i \(-0.666322\pi\)
−0.499063 + 0.866566i \(0.666322\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) 1.59325e140 1.29320 0.646602 − 0.762828i \(-0.276190\pi\)
0.646602 + 0.762828i \(0.276190\pi\)
\(830\) 0 0
\(831\) −9.16798e139 −0.662864
\(832\) −7.98076e139 −0.544659
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −2.95025e140 −1.51021
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 2.45588e140 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 4.94862e140 1.69843
\(845\) 0 0
\(846\) 0 0
\(847\) 5.71223e140 1.65349
\(848\) 0 0
\(849\) 2.28843e140 0.591519
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 3.93334e140 0.811350 0.405675 − 0.914017i \(-0.367036\pi\)
0.405675 + 0.914017i \(0.367036\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −1.17659e141 −1.73361 −0.866807 − 0.498644i \(-0.833832\pi\)
−0.866807 + 0.498644i \(0.833832\pi\)
\(860\) 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
\(867\) 1.05905e141 1.00000
\(868\) −2.79502e141 −2.49712
\(869\) 0 0
\(870\) 0 0
\(871\) 6.95238e139 0.0526335
\(872\) 0 0
\(873\) 2.59546e141 1.76008
\(874\) 0 0
\(875\) 0 0
\(876\) −3.29783e141 −1.89684
\(877\) −2.00982e141 −1.09440 −0.547201 − 0.837001i \(-0.684307\pi\)
−0.547201 + 0.837001i \(0.684307\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 4.70147e141 1.84553 0.922763 − 0.385368i \(-0.125925\pi\)
0.922763 + 0.385368i \(0.125925\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) −5.08953e141 −1.44342
\(890\) 0 0
\(891\) 0 0
\(892\) −7.50139e141 −1.80979
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 6.36269e141 1.00000
\(901\) 0 0
\(902\) 0 0
\(903\) 2.44111e142 3.27021
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 1.51569e142 1.64233 0.821167 − 0.570688i \(-0.193323\pi\)
0.821167 + 0.570688i \(0.193323\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 9.77193e140 0.0813257
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −2.71296e142 −1.83004
\(917\) 0 0
\(918\) 0 0
\(919\) −4.38765e140 −0.0252981 −0.0126490 − 0.999920i \(-0.504026\pi\)
−0.0126490 + 0.999920i \(0.504026\pi\)
\(920\) 0 0
\(921\) 1.32833e141 0.0689992
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −2.18385e141 −0.0921340
\(926\) 0 0
\(927\) −3.82461e142 −1.45465
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 4.55901e141 0.141022
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −2.63344e142 −0.598442 −0.299221 − 0.954184i \(-0.596727\pi\)
−0.299221 + 0.954184i \(0.596727\pi\)
\(938\) 0 0
\(939\) −1.14937e141 −0.0235782
\(940\) 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 \(\pi\)
\(948\) −1.50949e143 −1.95898
\(949\) 8.37401e142 1.03313
\(950\) 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
\(961\) 1.89749e143 1.28073
\(962\) 0 0
\(963\) 0 0
\(964\) 2.07116e143 1.20369
\(965\) 0 0
\(966\) 0 0
\(967\) 3.99446e143 1.99980 0.999901 − 0.0140771i \(-0.00448102\pi\)
0.999901 + 0.0140771i \(0.00448102\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 2.55847e143 1.00000
\(973\) −7.01702e143 −2.61057
\(974\) 0 0
\(975\) −1.61564e143 −0.544659
\(976\) 6.17670e143 1.98228
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −7.77994e143 −1.95373
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −2.48134e142 −0.0442948
\(989\) 0 0
\(990\) 0 0
\(991\) 5.71434e143 0.881924 0.440962 − 0.897526i \(-0.354637\pi\)
0.440962 + 0.897526i \(0.354637\pi\)
\(992\) 0 0
\(993\) −1.25078e144 −1.75234
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1.56505e144 −1.80784 −0.903919 − 0.427705i \(-0.859322\pi\)
−0.903919 + 0.427705i \(0.859322\pi\)
\(998\) 0 0
\(999\) −8.78139e142 −0.0921340
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 3.97.b.a.2.1 ✓ 1
3.2 odd 2 CM 3.97.b.a.2.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.97.b.a.2.1 ✓ 1 1.1 even 1 trivial
3.97.b.a.2.1 ✓ 1 3.2 odd 2 CM