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Properties

Label 3.121.b.a.2.1
Level $3$
Weight $121$
Character 3.2
Self dual yes
Analytic conductor $273.574$
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] = [3,121,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, 121, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 121);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 121 \)
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: \(273.573528174\)
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)
 
\(f(q)\) \(=\) \(q+4.23912e28 q^{3} +1.32923e36 q^{4} -6.90246e50 q^{7} +1.79701e57 q^{9} +O(q^{10})\) \(q+4.23912e28 q^{3} +1.32923e36 q^{4} -6.90246e50 q^{7} +1.79701e57 q^{9} +5.63475e64 q^{12} -9.23141e66 q^{13} +1.76685e72 q^{16} +3.56121e76 q^{19} -2.92603e79 q^{21} +7.52316e83 q^{25} +7.61773e85 q^{27} -9.17495e86 q^{28} +6.02807e89 q^{31} +2.38864e93 q^{36} -2.22601e94 q^{37} -3.91330e95 q^{39} -2.00232e98 q^{43} +7.48987e100 q^{48} +2.18354e101 q^{49} -1.22706e103 q^{52} +1.50964e105 q^{57} +4.36773e106 q^{61} -1.24038e108 q^{63} +2.34854e108 q^{64} +6.59659e109 q^{67} +1.16918e112 q^{73} +3.18916e112 q^{75} +4.73366e112 q^{76} -7.30686e113 q^{79} +3.22925e114 q^{81} -3.88937e115 q^{84} +6.37194e117 q^{91} +2.55537e118 q^{93} +2.62022e119 q^{97} +O(q^{100})\)

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 \(\pi\)
\(3\) 4.23912e28 1.00000
\(4\) 1.32923e36 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) −6.90246e50 −1.35869 −0.679347 − 0.733817i \(-0.737737\pi\)
−0.679347 + 0.733817i \(0.737737\pi\)
\(8\) 0 0
\(9\) 1.79701e57 1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 5.63475e64 1.00000
\(13\) −9.23141e66 −1.34483 −0.672414 − 0.740175i \(-0.734743\pi\)
−0.672414 + 0.740175i \(0.734743\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.76685e72 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 3.56121e76 0.670473 0.335237 − 0.942134i \(-0.391184\pi\)
0.335237 + 0.942134i \(0.391184\pi\)
\(20\) 0 0
\(21\) −2.92603e79 −1.35869
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 7.52316e83 1.00000
\(26\) 0 0
\(27\) 7.61773e85 1.00000
\(28\) −9.17495e86 −1.35869
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 6.02807e89 1.98828 0.994138 − 0.108120i \(-0.0344830\pi\)
0.994138 + 0.108120i \(0.0344830\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 2.38864e93 1.00000
\(37\) −2.22601e94 −1.80063 −0.900315 − 0.435239i \(-0.856664\pi\)
−0.900315 + 0.435239i \(0.856664\pi\)
\(38\) 0 0
\(39\) −3.91330e95 −1.34483
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −2.00232e98 −1.96529 −0.982643 − 0.185508i \(-0.940607\pi\)
−0.982643 + 0.185508i \(0.940607\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 7.48987e100 1.00000
\(49\) 2.18354e101 0.846050
\(50\) 0 0
\(51\) 0 0
\(52\) −1.22706e103 −1.34483
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.50964e105 0.670473
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 4.36773e106 0.331487 0.165743 − 0.986169i \(-0.446998\pi\)
0.165743 + 0.986169i \(0.446998\pi\)
\(62\) 0 0
\(63\) −1.24038e108 −1.35869
\(64\) 2.34854e108 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 6.59659e109 1.79817 0.899086 − 0.437773i \(-0.144233\pi\)
0.899086 + 0.437773i \(0.144233\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 1.16918e112 1.85571 0.927856 − 0.372938i \(-0.121650\pi\)
0.927856 + 0.372938i \(0.121650\pi\)
\(74\) 0 0
\(75\) 3.18916e112 1.00000
\(76\) 4.73366e112 0.670473
\(77\) 0 0
\(78\) 0 0
\(79\) −7.30686e113 −1.01416 −0.507079 − 0.861900i \(-0.669275\pi\)
−0.507079 + 0.861900i \(0.669275\pi\)
\(80\) 0 0
\(81\) 3.22925e114 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −3.88937e115 −1.35869
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 6.37194e117 1.82721
\(92\) 0 0
\(93\) 2.55537e118 1.98828
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.62022e119 1.62942 0.814710 − 0.579869i \(-0.196896\pi\)
0.814710 + 0.579869i \(0.196896\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000e120 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −1.87814e120 −0.318783 −0.159391 − 0.987215i \(-0.550953\pi\)
−0.159391 + 0.987215i \(0.550953\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 1.01257e122 1.00000
\(109\) 1.73706e122 0.986790 0.493395 − 0.869805i \(-0.335756\pi\)
0.493395 + 0.869805i \(0.335756\pi\)
\(110\) 0 0
\(111\) −9.43633e122 −1.80063
\(112\) −1.21956e123 −1.35869
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.65889e124 −1.34483
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 9.27091e124 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 8.01268e125 1.98828
\(125\) 0 0
\(126\) 0 0
\(127\) 1.94748e126 1.15146 0.575731 − 0.817639i \(-0.304717\pi\)
0.575731 + 0.817639i \(0.304717\pi\)
\(128\) 0 0
\(129\) −8.48806e126 −1.96529
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) −2.45811e127 −0.910968
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 3.10650e127 0.0815424 0.0407712 − 0.999169i \(-0.487019\pi\)
0.0407712 + 0.999169i \(0.487019\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 3.17504e129 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 9.25627e129 0.846050
\(148\) −2.95888e130 −1.80063
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 7.87569e130 1.43771 0.718856 − 0.695159i \(-0.244666\pi\)
0.718856 + 0.695159i \(0.244666\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −5.20167e131 −1.34483
\(157\) −4.90221e131 −0.863800 −0.431900 − 0.901922i \(-0.642157\pi\)
−0.431900 + 0.901922i \(0.642157\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 9.23161e132 1.71404 0.857021 − 0.515282i \(-0.172313\pi\)
0.857021 + 0.515282i \(0.172313\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 3.80992e133 0.808562
\(170\) 0 0
\(171\) 6.39953e133 0.670473
\(172\) −2.66154e134 −1.96529
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) −5.19284e134 −1.35869
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 5.69838e135 1.97259 0.986296 − 0.164988i \(-0.0527586\pi\)
0.986296 + 0.164988i \(0.0527586\pi\)
\(182\) 0 0
\(183\) 1.85153e135 0.331487
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −5.25811e136 −1.35869
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 9.95574e136 1.00000
\(193\) −1.93417e137 −1.42251 −0.711256 − 0.702933i \(-0.751874\pi\)
−0.711256 + 0.702933i \(0.751874\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 2.90242e137 0.846050
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −1.01103e138 −1.18462 −0.592312 − 0.805709i \(-0.701785\pi\)
−0.592312 + 0.805709i \(0.701785\pi\)
\(200\) 0 0
\(201\) 2.79637e138 1.79817
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −1.63105e139 −1.34483
\(209\) 0 0
\(210\) 0 0
\(211\) 3.66958e139 1.28135 0.640676 − 0.767811i \(-0.278654\pi\)
0.640676 + 0.767811i \(0.278654\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −4.16085e140 −2.70146
\(218\) 0 0
\(219\) 4.95630e140 1.85571
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 3.69720e140 0.467284 0.233642 − 0.972323i \(-0.424936\pi\)
0.233642 + 0.972323i \(0.424936\pi\)
\(224\) 0 0
\(225\) 1.35192e141 1.00000
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 2.00665e141 0.670473
\(229\) −7.50876e141 −1.92947 −0.964737 − 0.263215i \(-0.915217\pi\)
−0.964737 + 0.263215i \(0.915217\pi\)
\(230\) 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
\(237\) −3.09746e142 −1.01416
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 1.52620e143 1.83058 0.915292 − 0.402791i \(-0.131960\pi\)
0.915292 + 0.402791i \(0.131960\pi\)
\(242\) 0 0
\(243\) 1.36891e143 1.00000
\(244\) 5.80571e142 0.331487
\(245\) 0 0
\(246\) 0 0
\(247\) −3.28750e143 −0.901671
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −1.64875e144 −1.35869
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 3.12175e144 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 1.53650e145 2.44651
\(260\) 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
\(268\) 8.76837e145 1.79817
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −1.66568e146 −1.75160 −0.875799 − 0.482677i \(-0.839665\pi\)
−0.875799 + 0.482677i \(0.839665\pi\)
\(272\) 0 0
\(273\) 2.70114e146 1.82721
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 5.14960e146 1.45542 0.727709 − 0.685886i \(-0.240585\pi\)
0.727709 + 0.685886i \(0.240585\pi\)
\(278\) 0 0
\(279\) 1.08325e147 1.98828
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 2.55947e147 1.99970 0.999849 − 0.0173849i \(-0.00553408\pi\)
0.999849 + 0.0173849i \(0.00553408\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 4.50682e147 1.00000
\(290\) 0 0
\(291\) 1.11074e148 1.62942
\(292\) 1.55411e148 1.85571
\(293\) 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
\(300\) 4.23912e148 1.00000
\(301\) 1.38209e149 2.67022
\(302\) 0 0
\(303\) 0 0
\(304\) 6.29211e148 0.670473
\(305\) 0 0
\(306\) 0 0
\(307\) 3.17862e149 1.87904 0.939521 − 0.342490i \(-0.111270\pi\)
0.939521 + 0.342490i \(0.111270\pi\)
\(308\) 0 0
\(309\) −7.96166e148 −0.318783
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 4.28220e149 0.792513 0.396256 − 0.918140i \(-0.370309\pi\)
0.396256 + 0.918140i \(0.370309\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −9.71248e149 −1.01416
\(317\) 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
\(324\) 4.29240e150 1.00000
\(325\) −6.94494e150 −1.34483
\(326\) 0 0
\(327\) 7.36360e150 0.986790
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −3.05741e151 −1.97549 −0.987744 − 0.156080i \(-0.950114\pi\)
−0.987744 + 0.156080i \(0.950114\pi\)
\(332\) 0 0
\(333\) −4.00017e151 −1.80063
\(334\) 0 0
\(335\) 0 0
\(336\) −5.16985e151 −1.35869
\(337\) −7.04359e151 −1.54882 −0.774408 − 0.632687i \(-0.781952\pi\)
−0.774408 + 0.632687i \(0.781952\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 2.74252e151 0.209171
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −3.78990e152 −1.02118 −0.510590 − 0.859824i \(-0.670573\pi\)
−0.510590 + 0.859824i \(0.670573\pi\)
\(350\) 0 0
\(351\) −7.03224e152 −1.34483
\(352\) 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
\(361\) −1.55297e153 −0.550465
\(362\) 0 0
\(363\) 3.93004e153 1.00000
\(364\) 8.46977e153 1.82721
\(365\) 0 0
\(366\) 0 0
\(367\) 1.51684e154 1.99976 0.999878 − 0.0156023i \(-0.00496657\pi\)
0.999878 + 0.0156023i \(0.00496657\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 3.39667e154 1.98828
\(373\) −3.77006e154 −1.87853 −0.939266 − 0.343189i \(-0.888493\pi\)
−0.939266 + 0.343189i \(0.888493\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 9.98959e154 1.91071 0.955355 − 0.295459i \(-0.0954725\pi\)
0.955355 + 0.295459i \(0.0954725\pi\)
\(380\) 0 0
\(381\) 8.25560e154 1.15146
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −3.59819e155 −1.96529
\(388\) 3.48286e155 1.62942
\(389\) 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
\(397\) −1.67796e156 −1.98313 −0.991567 − 0.129597i \(-0.958632\pi\)
−0.991567 + 0.129597i \(0.958632\pi\)
\(398\) 0 0
\(399\) −1.04202e156 −0.910968
\(400\) 1.32923e156 1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) −5.56476e156 −2.67389
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −4.41608e156 −0.874256 −0.437128 − 0.899399i \(-0.644004\pi\)
−0.437128 + 0.899399i \(0.644004\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −2.49648e156 −0.318783
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.31688e156 0.0815424
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 1.98549e157 0.693334 0.346667 − 0.937988i \(-0.387313\pi\)
0.346667 + 0.937988i \(0.387313\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −3.01481e157 −0.450389
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 1.34594e158 1.00000
\(433\) 2.69267e158 1.74144 0.870720 − 0.491779i \(-0.163653\pi\)
0.870720 + 0.491779i \(0.163653\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.30895e158 0.986790
\(437\) 0 0
\(438\) 0 0
\(439\) 6.97925e158 1.97669 0.988343 − 0.152246i \(-0.0486505\pi\)
0.988343 + 0.152246i \(0.0486505\pi\)
\(440\) 0 0
\(441\) 3.92384e158 0.846050
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) −1.25430e159 −1.80063
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −1.62107e159 −1.35869
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 3.33860e159 1.43771
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −7.85864e159 −1.99699 −0.998494 − 0.0548646i \(-0.982527\pi\)
−0.998494 + 0.0548646i \(0.982527\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 2.03734e159 0.236703 0.118351 − 0.992972i \(-0.462239\pi\)
0.118351 + 0.992972i \(0.462239\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) −2.20505e160 −1.34483
\(469\) −4.55327e160 −2.44316
\(470\) 0 0
\(471\) −2.07811e160 −0.863800
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 2.67916e160 0.670473
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 2.05492e161 2.42154
\(482\) 0 0
\(483\) 0 0
\(484\) 1.23231e161 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) −3.57080e161 −1.99999 −0.999994 − 0.00332444i \(-0.998942\pi\)
−0.999994 + 0.00332444i \(0.998942\pi\)
\(488\) 0 0
\(489\) 3.91339e161 1.71404
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.06507e162 1.98828
\(497\) 0 0
\(498\) 0 0
\(499\) 1.15273e160 0.0149863 0.00749313 − 0.999972i \(-0.497615\pi\)
0.00749313 + 0.999972i \(0.497615\pi\)
\(500\) 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
\(507\) 1.61507e162 0.808562
\(508\) 2.58865e162 1.15146
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) −8.07024e162 −2.52135
\(512\) 0 0
\(513\) 2.71284e162 0.670473
\(514\) 0 0
\(515\) 0 0
\(516\) −1.12826e163 −1.96529
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −1.61465e163 −1.25307 −0.626536 − 0.779392i \(-0.715528\pi\)
−0.626536 + 0.779392i \(0.715528\pi\)
\(524\) 0 0
\(525\) −2.20130e163 −1.35869
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 2.55470e163 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) −3.26739e163 −0.910968
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 1.20337e164 1.22621 0.613103 − 0.790003i \(-0.289921\pi\)
0.613103 + 0.790003i \(0.289921\pi\)
\(542\) 0 0
\(543\) 2.41561e164 1.97259
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −3.19047e164 −1.67732 −0.838658 − 0.544659i \(-0.816659\pi\)
−0.838658 + 0.544659i \(0.816659\pi\)
\(548\) 0 0
\(549\) 7.84886e163 0.331487
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 5.04353e164 1.37793
\(554\) 0 0
\(555\) 0 0
\(556\) 4.12925e163 0.0815424
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 1.84842e165 2.64297
\(560\) 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
\(567\) −2.22898e165 −1.35869
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) −4.96350e165 −1.98436 −0.992182 − 0.124799i \(-0.960171\pi\)
−0.992182 + 0.124799i \(0.960171\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 4.22036e165 1.00000
\(577\) −7.97417e165 −1.70269 −0.851347 − 0.524602i \(-0.824214\pi\)
−0.851347 + 0.524602i \(0.824214\pi\)
\(578\) 0 0
\(579\) −8.19917e165 −1.42251
\(580\) 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 \(\pi\)
\(588\) 1.23037e166 0.846050
\(589\) 2.14672e166 1.33309
\(590\) 0 0
\(591\) 0 0
\(592\) −3.93303e166 −1.80063
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −4.28588e166 −1.18462
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) −4.91508e166 −0.910045 −0.455022 − 0.890480i \(-0.650369\pi\)
−0.455022 + 0.890480i \(0.650369\pi\)
\(602\) 0 0
\(603\) 1.18541e167 1.79817
\(604\) 1.04686e167 1.43771
\(605\) 0 0
\(606\) 0 0
\(607\) 1.94825e167 1.98758 0.993788 − 0.111289i \(-0.0354979\pi\)
0.993788 + 0.111289i \(0.0354979\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 2.63311e167 1.48881 0.744407 − 0.667726i \(-0.232732\pi\)
0.744407 + 0.667726i \(0.232732\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −3.43306e167 −1.08204 −0.541020 − 0.841010i \(-0.681962\pi\)
−0.541020 + 0.841010i \(0.681962\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −6.91420e167 −1.34483
\(625\) 5.65980e167 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) −6.51616e167 −0.863800
\(629\) 0 0
\(630\) 0 0
\(631\) −1.46539e168 −1.45946 −0.729728 − 0.683738i \(-0.760353\pi\)
−0.729728 + 0.683738i \(0.760353\pi\)
\(632\) 0 0
\(633\) 1.55558e168 1.28135
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −2.01571e168 −1.13779
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) −3.82510e168 −1.23022 −0.615112 − 0.788439i \(-0.710889\pi\)
−0.615112 + 0.788439i \(0.710889\pi\)
\(644\) 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
\(651\) −1.76383e169 −2.70146
\(652\) 1.22709e169 1.71404
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 2.10103e169 1.85571
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 2.41074e169 1.47932 0.739660 − 0.672980i \(-0.234986\pi\)
0.739660 + 0.672980i \(0.234986\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 1.56728e169 0.467284
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 4.97694e169 1.03767 0.518834 − 0.854875i \(-0.326366\pi\)
0.518834 + 0.854875i \(0.326366\pi\)
\(674\) 0 0
\(675\) 5.73095e169 1.00000
\(676\) 5.06425e169 0.808562
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) −1.80859e170 −2.21388
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 8.50644e169 0.670473
\(685\) 0 0
\(686\) 0 0
\(687\) −3.18305e170 −1.92947
\(688\) −3.53779e170 −1.96529
\(689\) 0 0
\(690\) 0 0
\(691\) 4.06039e170 1.73734 0.868671 − 0.495389i \(-0.164974\pi\)
0.868671 + 0.495389i \(0.164974\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −6.90246e170 −1.35869
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) −7.92731e170 −1.20727
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1.46126e171 1.33645 0.668225 − 0.743959i \(-0.267054\pi\)
0.668225 + 0.743959i \(0.267054\pi\)
\(710\) 0 0
\(711\) −1.31305e171 −1.01416
\(712\) 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
\(721\) 1.29638e171 0.433129
\(722\) 0 0
\(723\) 6.46975e171 1.83058
\(724\) 7.57445e171 1.97259
\(725\) 0 0
\(726\) 0 0
\(727\) 1.43980e171 0.292574 0.146287 − 0.989242i \(-0.453268\pi\)
0.146287 + 0.989242i \(0.453268\pi\)
\(728\) 0 0
\(729\) 5.80299e171 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 2.46111e171 0.331487
\(733\) −1.59321e172 −1.97713 −0.988565 − 0.150794i \(-0.951817\pi\)
−0.988565 + 0.150794i \(0.951817\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −7.35141e171 −0.559377 −0.279688 − 0.960091i \(-0.590231\pi\)
−0.279688 + 0.960091i \(0.590231\pi\)
\(740\) 0 0
\(741\) −1.39361e172 −0.901671
\(742\) 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
\(751\) 4.37917e172 1.26764 0.633819 − 0.773481i \(-0.281486\pi\)
0.633819 + 0.773481i \(0.281486\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −6.98923e172 −1.35869
\(757\) −8.95859e172 −1.60874 −0.804372 − 0.594126i \(-0.797498\pi\)
−0.804372 + 0.594126i \(0.797498\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) −1.19900e173 −1.34075
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.32335e173 1.00000
\(769\) −1.07242e173 −0.749524 −0.374762 − 0.927121i \(-0.622276\pi\)
−0.374762 + 0.927121i \(0.622276\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.57095e173 −1.42251
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 4.53502e173 1.98828
\(776\) 0 0
\(777\) 6.51339e173 2.44651
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 3.85798e173 0.846050
\(785\) 0 0
\(786\) 0 0
\(787\) 4.88863e173 0.852518 0.426259 − 0.904601i \(-0.359831\pi\)
0.426259 + 0.904601i \(0.359831\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −4.03203e173 −0.445793
\(794\) 0 0
\(795\) 0 0
\(796\) −1.34389e174 −1.18462
\(797\) 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
\(804\) 3.71701e174 1.79817
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) −6.95210e174 −1.99924 −0.999619 − 0.0275868i \(-0.991218\pi\)
−0.999619 + 0.0275868i \(0.991218\pi\)
\(812\) 0 0
\(813\) −7.06101e174 −1.75160
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −7.13068e174 −1.31767
\(818\) 0 0
\(819\) 1.14504e175 1.82721
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) −8.41405e174 −1.00234 −0.501170 − 0.865349i \(-0.667097\pi\)
−0.501170 + 0.865349i \(0.667097\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) −1.21303e175 −0.934544 −0.467272 − 0.884114i \(-0.654763\pi\)
−0.467272 + 0.884114i \(0.654763\pi\)
\(830\) 0 0
\(831\) 2.18298e175 1.45542
\(832\) −2.16804e175 −1.34483
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 4.59202e175 1.98828
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 3.07440e175 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 4.87770e175 1.28135
\(845\) 0 0
\(846\) 0 0
\(847\) −6.39921e175 −1.35869
\(848\) 0 0
\(849\) 1.08499e176 1.99970
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −1.85717e175 −0.258172 −0.129086 − 0.991633i \(-0.541204\pi\)
−0.129086 + 0.991633i \(0.541204\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −2.90218e175 −0.264932 −0.132466 − 0.991188i \(-0.542290\pi\)
−0.132466 + 0.991188i \(0.542290\pi\)
\(860\) 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
\(867\) 1.91049e176 1.00000
\(868\) −5.53072e176 −2.70146
\(869\) 0 0
\(870\) 0 0
\(871\) −6.08958e176 −2.41823
\(872\) 0 0
\(873\) 4.70855e176 1.62942
\(874\) 0 0
\(875\) 0 0
\(876\) 6.58805e176 1.85571
\(877\) −3.33679e176 −0.877715 −0.438857 − 0.898557i \(-0.644617\pi\)
−0.438857 + 0.898557i \(0.644617\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) −1.00752e177 −1.76040 −0.880202 − 0.474599i \(-0.842593\pi\)
−0.880202 + 0.474599i \(0.842593\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) −1.34424e177 −1.56449
\(890\) 0 0
\(891\) 0 0
\(892\) 4.91442e176 0.467284
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 1.79701e177 1.00000
\(901\) 0 0
\(902\) 0 0
\(903\) 5.85885e177 2.67022
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 3.93787e177 1.37665 0.688327 − 0.725401i \(-0.258346\pi\)
0.688327 + 0.725401i \(0.258346\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 2.66730e177 0.670473
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −9.98085e177 −1.92947
\(917\) 0 0
\(918\) 0 0
\(919\) −5.00054e177 −0.794486 −0.397243 − 0.917713i \(-0.630033\pi\)
−0.397243 + 0.917713i \(0.630033\pi\)
\(920\) 0 0
\(921\) 1.34746e178 1.87904
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −1.67467e178 −1.80063
\(926\) 0 0
\(927\) −3.37504e177 −0.318783
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 7.77604e177 0.567254
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −2.88670e178 −1.43227 −0.716137 − 0.697960i \(-0.754091\pi\)
−0.716137 + 0.697960i \(0.754091\pi\)
\(938\) 0 0
\(939\) 1.81527e178 0.792513
\(940\) 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 \(\pi\)
\(948\) −4.11723e178 −1.01416
\(949\) −1.07932e179 −2.49561
\(950\) 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
\(961\) 2.71458e179 2.95324
\(962\) 0 0
\(963\) 0 0
\(964\) 2.02867e179 1.83058
\(965\) 0 0
\(966\) 0 0
\(967\) −4.69930e177 −0.0351920 −0.0175960 − 0.999845i \(-0.505601\pi\)
−0.0175960 + 0.999845i \(0.505601\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 1.81960e179 1.00000
\(973\) −2.14425e178 −0.110791
\(974\) 0 0
\(975\) −2.94404e179 −1.34483
\(976\) 7.71712e178 0.331487
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 3.12151e179 0.986790
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −4.36983e179 −0.901671
\(989\) 0 0
\(990\) 0 0
\(991\) 2.06019e179 0.354396 0.177198 − 0.984175i \(-0.443297\pi\)
0.177198 + 0.984175i \(0.443297\pi\)
\(992\) 0 0
\(993\) −1.29607e180 −1.97549
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 1.62498e180 1.94598 0.972988 − 0.230857i \(-0.0741530\pi\)
0.972988 + 0.230857i \(0.0741530\pi\)
\(998\) 0 0
\(999\) −1.69572e180 −1.80063
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 3.121.b.a.2.1 ✓ 1
3.2 odd 2 CM 3.121.b.a.2.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.121.b.a.2.1 ✓ 1 1.1 even 1 trivial
3.121.b.a.2.1 ✓ 1 3.2 odd 2 CM