↑

Properties

Label 3.133.b.a.2.1
Level $3$
Weight $133$
Character 3.2
Self dual yes
Analytic conductor $331.023$
Analytic rank $0$
Dimension $1$
CM discriminant -3
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3,133,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, 133, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 133);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 133 \)
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: \(331.022639340\)
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)
 
\(f(q)\) \(=\) \(q+3.09032e31 q^{3} +5.44452e39 q^{4} +1.19458e56 q^{7} +9.55005e62 q^{9} +O(q^{10})\) \(q+3.09032e31 q^{3} +5.44452e39 q^{4} +1.19458e56 q^{7} +9.55005e62 q^{9} +1.68253e71 q^{12} +5.45979e73 q^{13} +2.96428e79 q^{16} -4.30412e84 q^{19} +3.69164e87 q^{21} +1.83671e92 q^{25} +2.95127e94 q^{27} +6.50393e95 q^{28} -1.04272e98 q^{31} +5.19954e102 q^{36} -8.41135e102 q^{37} +1.68725e105 q^{39} +2.62526e107 q^{43} +9.16055e110 q^{48} +1.06981e112 q^{49} +2.97259e113 q^{52} -1.33011e116 q^{57} -7.69110e117 q^{61} +1.14083e119 q^{63} +1.61391e119 q^{64} -6.58102e120 q^{67} +1.27814e123 q^{73} +5.67601e123 q^{75} -2.34338e124 q^{76} +3.97525e124 q^{79} +9.12034e125 q^{81} +2.00992e127 q^{84} +6.52217e129 q^{91} -3.22234e129 q^{93} -2.08236e131 q^{97} +O(q^{100})\)

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 \(\pi\)
\(3\) 3.09032e31 1.00000
\(4\) 5.44452e39 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) 1.19458e56 1.99869 0.999346 − 0.0361537i \(-0.0115106\pi\)
0.999346 + 0.0361537i \(0.0115106\pi\)
\(8\) 0 0
\(9\) 9.55005e62 1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 1.68253e71 1.00000
\(13\) 5.45979e73 1.64784 0.823919 − 0.566708i \(-0.191783\pi\)
0.823919 + 0.566708i \(0.191783\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.96428e79 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) −4.30412e84 −1.72245 −0.861225 − 0.508224i \(-0.830302\pi\)
−0.861225 + 0.508224i \(0.830302\pi\)
\(20\) 0 0
\(21\) 3.69164e87 1.99869
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 1.83671e92 1.00000
\(26\) 0 0
\(27\) 2.95127e94 1.00000
\(28\) 6.50393e95 1.99869
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −1.04272e98 −0.387523 −0.193761 − 0.981049i \(-0.562069\pi\)
−0.193761 + 0.981049i \(0.562069\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 5.19954e102 1.00000
\(37\) −8.41135e102 −0.265187 −0.132593 − 0.991171i \(-0.542330\pi\)
−0.132593 + 0.991171i \(0.542330\pi\)
\(38\) 0 0
\(39\) 1.68725e105 1.64784
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 2.62526e107 0.407619 0.203809 − 0.979011i \(-0.434668\pi\)
0.203809 + 0.979011i \(0.434668\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 9.16055e110 1.00000
\(49\) 1.06981e112 2.99477
\(50\) 0 0
\(51\) 0 0
\(52\) 2.97259e113 1.64784
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.33011e116 −1.72245
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −7.69110e117 −1.13297 −0.566486 − 0.824071i \(-0.691697\pi\)
−0.566486 + 0.824071i \(0.691697\pi\)
\(62\) 0 0
\(63\) 1.14083e119 1.99869
\(64\) 1.61391e119 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −6.58102e120 −1.98315 −0.991577 − 0.129522i \(-0.958656\pi\)
−0.991577 + 0.129522i \(0.958656\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 1.27814e123 1.34051 0.670253 − 0.742132i \(-0.266185\pi\)
0.670253 + 0.742132i \(0.266185\pi\)
\(74\) 0 0
\(75\) 5.67601e123 1.00000
\(76\) −2.34338e124 −1.72245
\(77\) 0 0
\(78\) 0 0
\(79\) 3.97525e124 0.226974 0.113487 − 0.993539i \(-0.463798\pi\)
0.113487 + 0.993539i \(0.463798\pi\)
\(80\) 0 0
\(81\) 9.12034e125 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 2.00992e127 1.99869
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 6.52217e129 3.29352
\(92\) 0 0
\(93\) −3.22234e129 −0.387523
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −2.08236e131 −1.55461 −0.777306 − 0.629123i \(-0.783414\pi\)
−0.777306 + 0.629123i \(0.783414\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000e132 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −1.12235e133 −1.59541 −0.797703 − 0.603051i \(-0.793951\pi\)
−0.797703 + 0.603051i \(0.793951\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 1.60682e134 1.00000
\(109\) 5.87706e134 1.99072 0.995362 − 0.0961999i \(-0.0306688\pi\)
0.995362 + 0.0961999i \(0.0306688\pi\)
\(110\) 0 0
\(111\) −2.59937e134 −0.265187
\(112\) 3.54108e135 1.99869
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 5.21412e136 1.64784
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 2.90961e137 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) −5.67712e137 −0.387523
\(125\) 0 0
\(126\) 0 0
\(127\) 1.29321e139 1.82232 0.911159 − 0.412056i \(-0.135189\pi\)
0.911159 + 0.412056i \(0.135189\pi\)
\(128\) 0 0
\(129\) 8.11288e138 0.407619
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) −5.14163e140 −3.44265
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) −2.71198e141 −0.986983 −0.493492 − 0.869751i \(-0.664280\pi\)
−0.493492 + 0.869751i \(0.664280\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 2.83090e142 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 3.30604e143 2.99477
\(148\) −4.57957e142 −0.265187
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) −1.19048e144 −1.83334 −0.916669 − 0.399647i \(-0.869133\pi\)
−0.916669 + 0.399647i \(0.869133\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 9.18624e144 1.64784
\(157\) −1.62683e145 −1.91410 −0.957052 − 0.289917i \(-0.906372\pi\)
−0.957052 + 0.289917i \(0.906372\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −6.87069e145 −0.680171 −0.340086 − 0.940394i \(-0.610456\pi\)
−0.340086 + 0.940394i \(0.610456\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 1.88313e147 1.71537
\(170\) 0 0
\(171\) −4.11045e147 −1.72245
\(172\) 1.42933e147 0.407619
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 2.19410e148 1.99869
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) −1.99782e149 −1.96685 −0.983426 − 0.181312i \(-0.941966\pi\)
−0.983426 + 0.181312i \(0.941966\pi\)
\(182\) 0 0
\(183\) −2.37679e149 −1.13297
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 3.52554e150 1.99869
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 4.98748e150 1.00000
\(193\) −1.40036e151 −1.99278 −0.996388 − 0.0849119i \(-0.972939\pi\)
−0.996388 + 0.0849119i \(0.972939\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 5.82458e151 2.99477
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −9.09098e151 −1.71517 −0.857586 − 0.514340i \(-0.828037\pi\)
−0.857586 + 0.514340i \(0.828037\pi\)
\(200\) 0 0
\(201\) −2.03374e152 −1.98315
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 1.61843e153 1.64784
\(209\) 0 0
\(210\) 0 0
\(211\) −1.03515e152 −0.0409602 −0.0204801 − 0.999790i \(-0.506519\pi\)
−0.0204801 + 0.999790i \(0.506519\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −1.24562e154 −0.774539
\(218\) 0 0
\(219\) 3.94985e154 1.34051
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.90254e155 −1.95529 −0.977647 − 0.210254i \(-0.932571\pi\)
−0.977647 + 0.210254i \(0.932571\pi\)
\(224\) 0 0
\(225\) 1.75407e155 1.00000
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) −7.24180e155 −1.72245
\(229\) 9.21855e155 1.64256 0.821279 − 0.570527i \(-0.193261\pi\)
0.821279 + 0.570527i \(0.193261\pi\)
\(230\) 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
\(237\) 1.22848e156 0.226974
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 1.52733e157 0.934995 0.467497 − 0.883994i \(-0.345156\pi\)
0.467497 + 0.883994i \(0.345156\pi\)
\(242\) 0 0
\(243\) 2.81847e157 1.00000
\(244\) −4.18743e157 −1.13297
\(245\) 0 0
\(246\) 0 0
\(247\) −2.34996e158 −2.83832
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 6.21129e158 1.99869
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 8.78694e158 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −1.00481e159 −0.530027
\(260\) 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
\(268\) −3.58305e160 −1.98315
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −4.86801e160 −1.29234 −0.646172 − 0.763192i \(-0.723631\pi\)
−0.646172 + 0.763192i \(0.723631\pi\)
\(272\) 0 0
\(273\) 2.01556e161 3.29352
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.58070e161 0.988972 0.494486 − 0.869186i \(-0.335356\pi\)
0.494486 + 0.869186i \(0.335356\pi\)
\(278\) 0 0
\(279\) −9.95806e160 −0.387523
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −1.07847e162 −1.64022 −0.820109 − 0.572207i \(-0.806087\pi\)
−0.820109 + 0.572207i \(0.806087\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2.62578e162 1.00000
\(290\) 0 0
\(291\) −6.43516e162 −1.55461
\(292\) 6.95884e162 1.34051
\(293\) 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
\(300\) 3.09032e163 1.00000
\(301\) 3.13609e163 0.814705
\(302\) 0 0
\(303\) 0 0
\(304\) −1.27586e164 −1.72245
\(305\) 0 0
\(306\) 0 0
\(307\) 2.74869e164 1.94086 0.970429 − 0.241388i \(-0.0776027\pi\)
0.970429 + 0.241388i \(0.0776027\pi\)
\(308\) 0 0
\(309\) −3.46841e164 −1.59541
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 8.35633e164 1.64471 0.822355 − 0.568975i \(-0.192660\pi\)
0.822355 + 0.568975i \(0.192660\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 2.16433e164 0.226974
\(317\) 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
\(324\) 4.96559e165 1.00000
\(325\) 1.00280e166 1.64784
\(326\) 0 0
\(327\) 1.81620e166 1.99072
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −3.59837e166 −1.76790 −0.883950 − 0.467581i \(-0.845126\pi\)
−0.883950 + 0.467581i \(0.845126\pi\)
\(332\) 0 0
\(333\) −8.03288e165 −0.265187
\(334\) 0 0
\(335\) 0 0
\(336\) 1.09430e167 1.99869
\(337\) 9.11575e166 1.36842 0.684210 − 0.729285i \(-0.260147\pi\)
0.684210 + 0.729285i \(0.260147\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 8.51238e167 3.98694
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 1.21781e168 1.81594 0.907972 − 0.419031i \(-0.137630\pi\)
0.907972 + 0.419031i \(0.137630\pi\)
\(350\) 0 0
\(351\) 1.61133e168 1.64784
\(352\) 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
\(361\) 1.22813e169 1.96683
\(362\) 0 0
\(363\) 8.99161e168 1.00000
\(364\) 3.55101e169 3.29352
\(365\) 0 0
\(366\) 0 0
\(367\) 1.20577e169 0.650588 0.325294 − 0.945613i \(-0.394537\pi\)
0.325294 + 0.945613i \(0.394537\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −1.75441e169 −0.387523
\(373\) 2.60074e169 0.481187 0.240593 − 0.970626i \(-0.422658\pi\)
0.240593 + 0.970626i \(0.422658\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.78177e170 −1.14991 −0.574954 − 0.818185i \(-0.694980\pi\)
−0.574954 + 0.818185i \(0.694980\pi\)
\(380\) 0 0
\(381\) 3.99643e170 1.82232
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.50714e170 0.407619
\(388\) −1.13375e171 −1.55461
\(389\) 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
\(397\) −6.52841e171 −1.97076 −0.985381 − 0.170365i \(-0.945505\pi\)
−0.985381 + 0.170365i \(0.945505\pi\)
\(398\) 0 0
\(399\) −1.58893e172 −3.44265
\(400\) 5.44452e171 1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) −5.69304e171 −0.638574
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −2.67765e172 −1.13244 −0.566221 − 0.824253i \(-0.691595\pi\)
−0.566221 + 0.824253i \(0.691595\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −6.11065e172 −1.59541
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −8.38087e172 −0.986983
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 2.41809e173 1.51654 0.758270 − 0.651940i \(-0.226045\pi\)
0.758270 + 0.651940i \(0.226045\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −9.18766e173 −2.26446
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 8.74837e173 1.00000
\(433\) 2.03411e174 1.99606 0.998030 − 0.0627329i \(-0.0199816\pi\)
0.998030 + 0.0627329i \(0.0199816\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 3.19977e174 1.99072
\(437\) 0 0
\(438\) 0 0
\(439\) −3.53446e174 −1.39851 −0.699254 − 0.714873i \(-0.746484\pi\)
−0.699254 + 0.714873i \(0.746484\pi\)
\(440\) 0 0
\(441\) 1.02167e175 2.99477
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) −1.41523e174 −0.265187
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 1.92795e175 1.99869
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −3.67895e175 −1.83334
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6.94003e175 1.93594 0.967971 − 0.251063i \(-0.0807800\pi\)
0.967971 + 0.251063i \(0.0807800\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 9.59944e175 1.13214 0.566071 − 0.824357i \(-0.308463\pi\)
0.566071 + 0.824357i \(0.308463\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 2.83884e176 1.64784
\(469\) −7.86158e176 −3.96371
\(470\) 0 0
\(471\) −5.02742e176 −1.91410
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −7.90542e176 −1.72245
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) −4.59242e176 −0.436985
\(482\) 0 0
\(483\) 0 0
\(484\) 1.58414e177 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) −2.78590e177 −1.16965 −0.584823 − 0.811161i \(-0.698836\pi\)
−0.584823 + 0.811161i \(0.698836\pi\)
\(488\) 0 0
\(489\) −2.12326e177 −0.680171
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −3.09092e177 −0.387523
\(497\) 0 0
\(498\) 0 0
\(499\) 3.52186e177 0.296576 0.148288 − 0.988944i \(-0.452624\pi\)
0.148288 + 0.988944i \(0.452624\pi\)
\(500\) 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
\(507\) 5.81946e178 1.71537
\(508\) 7.04091e178 1.82232
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 1.52684e179 2.67926
\(512\) 0 0
\(513\) −1.27026e179 −1.72245
\(514\) 0 0
\(515\) 0 0
\(516\) 4.41707e178 0.407619
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −1.83194e179 −0.694705 −0.347352 − 0.937735i \(-0.612919\pi\)
−0.347352 + 0.937735i \(0.612919\pi\)
\(524\) 0 0
\(525\) 6.78047e179 1.99869
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 5.59853e179 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) −2.79937e180 −3.44265
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 3.12377e180 1.26958 0.634790 − 0.772685i \(-0.281087\pi\)
0.634790 + 0.772685i \(0.281087\pi\)
\(542\) 0 0
\(543\) −6.17391e180 −1.96685
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −9.67499e180 −1.89883 −0.949417 − 0.314017i \(-0.898325\pi\)
−0.949417 + 0.314017i \(0.898325\pi\)
\(548\) 0 0
\(549\) −7.34503e180 −1.13297
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 4.74877e180 0.453652
\(554\) 0 0
\(555\) 0 0
\(556\) −1.47654e181 −0.986983
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 1.43334e181 0.671689
\(560\) 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
\(567\) 1.08950e182 1.99869
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 8.17039e181 0.942453 0.471226 − 0.882012i \(-0.343811\pi\)
0.471226 + 0.882012i \(0.343811\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.54129e182 1.00000
\(577\) 2.08951e182 1.20904 0.604521 − 0.796589i \(-0.293365\pi\)
0.604521 + 0.796589i \(0.293365\pi\)
\(578\) 0 0
\(579\) −4.32757e182 −1.99278
\(580\) 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 \(\pi\)
\(588\) 1.79998e183 2.99477
\(589\) 4.48800e182 0.667488
\(590\) 0 0
\(591\) 0 0
\(592\) −2.49336e182 −0.265187
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.80940e183 −1.71517
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) −2.46266e182 −0.0967583 −0.0483792 − 0.998829i \(-0.515406\pi\)
−0.0483792 + 0.998829i \(0.515406\pi\)
\(602\) 0 0
\(603\) −6.28491e183 −1.98315
\(604\) −6.48157e183 −1.83334
\(605\) 0 0
\(606\) 0 0
\(607\) 1.86623e183 0.380638 0.190319 − 0.981722i \(-0.439048\pi\)
0.190319 + 0.981722i \(0.439048\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −2.58575e183 −0.275547 −0.137773 − 0.990464i \(-0.543995\pi\)
−0.137773 + 0.990464i \(0.543995\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −1.61896e184 −0.907098 −0.453549 − 0.891231i \(-0.649842\pi\)
−0.453549 + 0.891231i \(0.649842\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 5.00147e184 1.64784
\(625\) 3.37350e184 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) −8.85731e184 −1.91410
\(629\) 0 0
\(630\) 0 0
\(631\) −1.10377e185 −1.74157 −0.870785 − 0.491665i \(-0.836389\pi\)
−0.870785 + 0.491665i \(0.836389\pi\)
\(632\) 0 0
\(633\) −3.19894e183 −0.0409602
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 5.84091e185 4.93490
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 3.69607e185 1.68196 0.840981 − 0.541064i \(-0.181978\pi\)
0.840981 + 0.541064i \(0.181978\pi\)
\(644\) 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
\(651\) −3.84936e185 −0.774539
\(652\) −3.74076e185 −0.680171
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 1.22063e186 1.34051
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −2.67272e186 −1.96634 −0.983168 − 0.182703i \(-0.941515\pi\)
−0.983168 + 0.182703i \(0.941515\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −5.87944e186 −1.95529
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −3.82022e186 −0.857223 −0.428612 − 0.903489i \(-0.640997\pi\)
−0.428612 + 0.903489i \(0.640997\pi\)
\(674\) 0 0
\(675\) 5.42062e186 1.00000
\(676\) 1.02527e187 1.71537
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) −2.48756e187 −3.10719
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −2.23794e187 −1.72245
\(685\) 0 0
\(686\) 0 0
\(687\) 2.84882e187 1.64256
\(688\) 7.78200e186 0.407619
\(689\) 0 0
\(690\) 0 0
\(691\) 1.28821e187 0.506332 0.253166 − 0.967423i \(-0.418528\pi\)
0.253166 + 0.967423i \(0.418528\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 1.19458e188 1.99869
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 3.62034e187 0.456771
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 2.62439e188 1.88963 0.944816 − 0.327601i \(-0.106240\pi\)
0.944816 + 0.327601i \(0.106240\pi\)
\(710\) 0 0
\(711\) 3.79639e187 0.226974
\(712\) 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
\(721\) −1.34074e189 −3.18872
\(722\) 0 0
\(723\) 4.71994e188 0.934995
\(724\) −1.08772e189 −1.96685
\(725\) 0 0
\(726\) 0 0
\(727\) 1.38397e189 1.90482 0.952412 − 0.304814i \(-0.0985944\pi\)
0.952412 + 0.304814i \(0.0985944\pi\)
\(728\) 0 0
\(729\) 8.70997e188 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) −1.29405e189 −1.13297
\(733\) −4.14306e188 −0.331481 −0.165741 − 0.986169i \(-0.553001\pi\)
−0.165741 + 0.986169i \(0.553001\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −6.79628e188 −0.317496 −0.158748 − 0.987319i \(-0.550746\pi\)
−0.158748 + 0.987319i \(0.550746\pi\)
\(740\) 0 0
\(741\) −7.26211e189 −2.83832
\(742\) 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
\(751\) 3.75149e188 0.0605296 0.0302648 − 0.999542i \(-0.490365\pi\)
0.0302648 + 0.999542i \(0.490365\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.91948e190 1.99869
\(757\) −1.10767e190 −1.05701 −0.528507 − 0.848929i \(-0.677248\pi\)
−0.528507 + 0.848929i \(0.677248\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 7.02064e190 3.97885
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 2.71544e190 1.00000
\(769\) 2.88000e189 0.0973316 0.0486658 − 0.998815i \(-0.484503\pi\)
0.0486658 + 0.998815i \(0.484503\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7.62431e190 −1.99278
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) −1.91518e190 −0.387523
\(776\) 0 0
\(777\) −3.10517e190 −0.530027
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 3.17120e191 2.99477
\(785\) 0 0
\(786\) 0 0
\(787\) −8.07913e190 −0.592969 −0.296485 − 0.955038i \(-0.595814\pi\)
−0.296485 + 0.955038i \(0.595814\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −4.19917e191 −1.86695
\(794\) 0 0
\(795\) 0 0
\(796\) −4.94960e191 −1.71517
\(797\) 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
\(804\) −1.10727e192 −1.98315
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 1.21116e192 1.22413 0.612064 − 0.790808i \(-0.290340\pi\)
0.612064 + 0.790808i \(0.290340\pi\)
\(812\) 0 0
\(813\) −1.50437e192 −1.29234
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −1.12994e192 −0.702103
\(818\) 0 0
\(819\) 6.22871e192 3.29352
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 2.60177e192 0.997424 0.498712 − 0.866768i \(-0.333807\pi\)
0.498712 + 0.866768i \(0.333807\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) −7.83210e192 −1.85900 −0.929499 − 0.368824i \(-0.879761\pi\)
−0.929499 + 0.368824i \(0.879761\pi\)
\(830\) 0 0
\(831\) 4.88486e192 0.988972
\(832\) 8.81158e192 1.64784
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −3.07735e192 −0.387523
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.08777e193 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) −5.63590e191 −0.0409602
\(845\) 0 0
\(846\) 0 0
\(847\) 3.47577e193 1.99869
\(848\) 0 0
\(849\) −3.33280e193 −1.64022
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −5.54140e193 −1.99978 −0.999892 − 0.0146869i \(-0.995325\pi\)
−0.999892 + 0.0146869i \(0.995325\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −2.81135e193 −0.638801 −0.319400 − 0.947620i \(-0.603481\pi\)
−0.319400 + 0.947620i \(0.603481\pi\)
\(860\) 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
\(867\) 8.11448e193 1.00000
\(868\) −6.78180e193 −0.774539
\(869\) 0 0
\(870\) 0 0
\(871\) −3.59310e194 −3.26791
\(872\) 0 0
\(873\) −1.98867e194 −1.55461
\(874\) 0 0
\(875\) 0 0
\(876\) 2.15050e194 1.34051
\(877\) 1.95276e194 1.12895 0.564476 − 0.825450i \(-0.309078\pi\)
0.564476 + 0.825450i \(0.309078\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 2.80782e194 1.03505 0.517527 − 0.855667i \(-0.326853\pi\)
0.517527 + 0.855667i \(0.326853\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 1.54485e195 3.64225
\(890\) 0 0
\(891\) 0 0
\(892\) −1.03584e195 −1.95529
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 9.55005e194 1.00000
\(901\) 0 0
\(902\) 0 0
\(903\) 9.69151e194 0.814705
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −1.58228e194 −0.0993578 −0.0496789 − 0.998765i \(-0.515820\pi\)
−0.0496789 + 0.998765i \(0.515820\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) −3.94281e195 −1.72245
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 5.01905e195 1.64256
\(917\) 0 0
\(918\) 0 0
\(919\) −4.32204e195 −1.13989 −0.569947 − 0.821681i \(-0.693036\pi\)
−0.569947 + 0.821681i \(0.693036\pi\)
\(920\) 0 0
\(921\) 8.49433e195 1.94086
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −1.54492e195 −0.265187
\(926\) 0 0
\(927\) −1.07185e196 −1.59541
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) −4.60457e196 −5.15834
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 5.99269e195 0.439348 0.219674 − 0.975573i \(-0.429501\pi\)
0.219674 + 0.975573i \(0.429501\pi\)
\(938\) 0 0
\(939\) 2.58237e196 1.64471
\(940\) 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 \(\pi\)
\(948\) 6.68848e195 0.226974
\(949\) 6.97836e196 2.20894
\(950\) 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
\(961\) −6.15281e196 −0.849826
\(962\) 0 0
\(963\) 0 0
\(964\) 8.31560e196 0.934995
\(965\) 0 0
\(966\) 0 0
\(967\) 1.57365e197 1.44132 0.720661 − 0.693288i \(-0.243839\pi\)
0.720661 + 0.693288i \(0.243839\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 1.53452e197 1.00000
\(973\) −3.23969e197 −1.97268
\(974\) 0 0
\(975\) 3.09898e197 1.64784
\(976\) −2.27985e197 −1.13297
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 5.61262e197 1.99072
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −1.27944e198 −2.83832
\(989\) 0 0
\(990\) 0 0
\(991\) −4.27983e196 −0.0777258 −0.0388629 − 0.999245i \(-0.512374\pi\)
−0.0388629 + 0.999245i \(0.512374\pi\)
\(992\) 0 0
\(993\) −1.11201e198 −1.76790
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −8.85703e197 −1.07996 −0.539980 − 0.841678i \(-0.681568\pi\)
−0.539980 + 0.841678i \(0.681568\pi\)
\(998\) 0 0
\(999\) −2.48241e197 −0.265187
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 3.133.b.a.2.1 ✓ 1
3.2 odd 2 CM 3.133.b.a.2.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.133.b.a.2.1 ✓ 1 1.1 even 1 trivial
3.133.b.a.2.1 ✓ 1 3.2 odd 2 CM