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Properties

Label 3.103.b.a.2.1
Level $3$
Weight $103$
Character 3.2
Self dual yes
Analytic conductor $197.659$
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] = [3,103,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, 103, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 103);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 103 \)
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: \(197.658631240\)
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)
 
\(f(q)\) \(=\) \(q-2.15369e24 q^{3} +5.07060e30 q^{4} -2.15536e43 q^{7} +4.63840e48 q^{9} +O(q^{10})\) \(q-2.15369e24 q^{3} +5.07060e30 q^{4} -2.15536e43 q^{7} +4.63840e48 q^{9} -1.09205e55 q^{12} +1.19680e57 q^{13} +2.57110e61 q^{16} -2.19643e65 q^{19} +4.64198e67 q^{21} +1.97215e71 q^{25} -9.98969e72 q^{27} -1.09290e74 q^{28} -2.23706e76 q^{31} +2.35195e79 q^{36} +9.77863e79 q^{37} -2.57754e81 q^{39} +2.37810e83 q^{43} -5.53736e85 q^{48} +3.06067e86 q^{49} +6.06849e87 q^{52} +4.73044e89 q^{57} -2.18276e91 q^{61} -9.99740e91 q^{63} +1.30370e92 q^{64} -2.61744e93 q^{67} -1.27653e95 q^{73} -4.24741e95 q^{75} -1.11372e96 q^{76} +4.81357e96 q^{79} +2.15147e97 q^{81} +2.35376e98 q^{84} -2.57953e100 q^{91} +4.81794e100 q^{93} -2.12323e101 q^{97} +O(q^{100})\)

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 \(\pi\)
\(3\) −2.15369e24 −1.00000
\(4\) 5.07060e30 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) −2.15536e43 −1.71206 −0.856030 − 0.516926i \(-0.827076\pi\)
−0.856030 + 0.516926i \(0.827076\pi\)
\(8\) 0 0
\(9\) 4.63840e48 1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) −1.09205e55 −1.00000
\(13\) 1.19680e57 1.84888 0.924442 − 0.381322i \(-0.124531\pi\)
0.924442 + 0.381322i \(0.124531\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.57110e61 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) −2.19643e65 −1.33439 −0.667197 − 0.744881i \(-0.732506\pi\)
−0.667197 + 0.744881i \(0.732506\pi\)
\(20\) 0 0
\(21\) 4.64198e67 1.71206
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 1.97215e71 1.00000
\(26\) 0 0
\(27\) −9.98969e72 −1.00000
\(28\) −1.09290e74 −1.71206
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −2.23706e76 −1.95088 −0.975442 − 0.220257i \(-0.929311\pi\)
−0.975442 + 0.220257i \(0.929311\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 2.35195e79 1.00000
\(37\) 9.77863e79 1.02799 0.513997 − 0.857792i \(-0.328164\pi\)
0.513997 + 0.857792i \(0.328164\pi\)
\(38\) 0 0
\(39\) −2.57754e81 −1.84888
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 2.37810e83 1.17311 0.586554 − 0.809910i \(-0.300484\pi\)
0.586554 + 0.809910i \(0.300484\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −5.53736e85 −1.00000
\(49\) 3.06067e86 1.93115
\(50\) 0 0
\(51\) 0 0
\(52\) 6.06849e87 1.84888
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 4.73044e89 1.33439
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −2.18276e91 −1.93725 −0.968624 − 0.248532i \(-0.920052\pi\)
−0.968624 + 0.248532i \(0.920052\pi\)
\(62\) 0 0
\(63\) −9.99740e91 −1.71206
\(64\) 1.30370e92 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −2.61744e93 −1.94116 −0.970580 − 0.240777i \(-0.922598\pi\)
−0.970580 + 0.240777i \(0.922598\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −1.27653e95 −1.19280 −0.596398 − 0.802689i \(-0.703402\pi\)
−0.596398 + 0.802689i \(0.703402\pi\)
\(74\) 0 0
\(75\) −4.24741e95 −1.00000
\(76\) −1.11372e96 −1.33439
\(77\) 0 0
\(78\) 0 0
\(79\) 4.81357e96 0.800729 0.400365 − 0.916356i \(-0.368883\pi\)
0.400365 + 0.916356i \(0.368883\pi\)
\(80\) 0 0
\(81\) 2.15147e97 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 2.35376e98 1.71206
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −2.57953e100 −3.16540
\(92\) 0 0
\(93\) 4.81794e100 1.95088
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −2.12323e101 −1.00378 −0.501890 − 0.864931i \(-0.667362\pi\)
−0.501890 + 0.864931i \(0.667362\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000e102 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 1.92320e102 0.425919 0.212959 − 0.977061i \(-0.431690\pi\)
0.212959 + 0.977061i \(0.431690\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −5.06537e103 −1.00000
\(109\) 1.51705e104 1.87176 0.935879 − 0.352322i \(-0.114608\pi\)
0.935879 + 0.352322i \(0.114608\pi\)
\(110\) 0 0
\(111\) −2.10602e104 −1.02799
\(112\) −5.54164e104 −1.71206
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 5.55122e105 1.84888
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.66745e106 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) −1.13432e107 −1.95088
\(125\) 0 0
\(126\) 0 0
\(127\) 7.25443e106 0.368649 0.184325 − 0.982865i \(-0.440990\pi\)
0.184325 + 0.982865i \(0.440990\pi\)
\(128\) 0 0
\(129\) −5.12169e107 −1.17311
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 4.73410e108 2.28456
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) −3.07784e109 −1.56492 −0.782458 − 0.622704i \(-0.786034\pi\)
−0.782458 + 0.622704i \(0.786034\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.19258e110 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) −6.59175e110 −1.93115
\(148\) 4.95836e110 1.02799
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 1.52304e111 1.13471 0.567357 − 0.823472i \(-0.307966\pi\)
0.567357 + 0.823472i \(0.307966\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −1.30697e112 −1.84888
\(157\) 1.40284e112 1.43260 0.716302 − 0.697790i \(-0.245833\pi\)
0.716302 + 0.697790i \(0.245833\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −6.15149e112 −0.927711 −0.463855 − 0.885911i \(-0.653534\pi\)
−0.463855 + 0.885911i \(0.653534\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 1.01332e114 2.41837
\(170\) 0 0
\(171\) −1.01879e114 −1.33439
\(172\) 1.20584e114 1.17311
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) −4.25069e114 −1.71206
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 3.89101e114 0.280837 0.140419 − 0.990092i \(-0.455155\pi\)
0.140419 + 0.990092i \(0.455155\pi\)
\(182\) 0 0
\(183\) 4.70100e115 1.93725
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 2.15313e116 1.71206
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −2.80778e116 −1.00000
\(193\) −3.54423e116 −0.968500 −0.484250 − 0.874930i \(-0.660907\pi\)
−0.484250 + 0.874930i \(0.660907\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.55194e117 1.93115
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 3.48747e117 1.99988 0.999940 − 0.0109420i \(-0.00348302\pi\)
0.999940 + 0.0109420i \(0.00348302\pi\)
\(200\) 0 0
\(201\) 5.63716e117 1.94116
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 3.07709e118 1.84888
\(209\) 0 0
\(210\) 0 0
\(211\) 6.77382e118 1.96078 0.980389 − 0.197074i \(-0.0631440\pi\)
0.980389 + 0.197074i \(0.0631440\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 4.82166e119 3.34003
\(218\) 0 0
\(219\) 2.74926e119 1.19280
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.41103e119 0.243214 0.121607 − 0.992578i \(-0.461195\pi\)
0.121607 + 0.992578i \(0.461195\pi\)
\(224\) 0 0
\(225\) 9.14763e119 1.00000
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 2.39862e120 1.33439
\(229\) −1.08936e120 −0.484800 −0.242400 − 0.970176i \(-0.577935\pi\)
−0.242400 + 0.970176i \(0.577935\pi\)
\(230\) 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
\(237\) −1.03670e121 −0.800729
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 5.05173e121 1.66177 0.830886 − 0.556443i \(-0.187834\pi\)
0.830886 + 0.556443i \(0.187834\pi\)
\(242\) 0 0
\(243\) −4.63362e121 −1.00000
\(244\) −1.10679e122 −1.93725
\(245\) 0 0
\(246\) 0 0
\(247\) −2.62869e122 −2.46714
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −5.06929e122 −1.71206
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 6.61056e122 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −2.10764e123 −1.75999
\(260\) 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
\(268\) −1.32720e124 −1.94116
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 2.41024e124 1.99814 0.999072 − 0.0430734i \(-0.0137149\pi\)
0.999072 + 0.0430734i \(0.0137149\pi\)
\(272\) 0 0
\(273\) 5.55551e124 3.16540
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 6.97690e124 1.89319 0.946596 − 0.322423i \(-0.104497\pi\)
0.946596 + 0.322423i \(0.104497\pi\)
\(278\) 0 0
\(279\) −1.03764e125 −1.95088
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 1.79757e125 1.63523 0.817615 − 0.575766i \(-0.195296\pi\)
0.817615 + 0.575766i \(0.195296\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 3.20472e125 1.00000
\(290\) 0 0
\(291\) 4.57279e125 1.00378
\(292\) −6.47280e125 −1.19280
\(293\) 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
\(300\) −2.15369e126 −1.00000
\(301\) −5.12565e126 −2.00843
\(302\) 0 0
\(303\) 0 0
\(304\) −5.64725e126 −1.33439
\(305\) 0 0
\(306\) 0 0
\(307\) 4.54143e126 0.650332 0.325166 − 0.945657i \(-0.394580\pi\)
0.325166 + 0.945657i \(0.394580\pi\)
\(308\) 0 0
\(309\) −4.14199e126 −0.425919
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) −2.92674e127 −1.56179 −0.780896 − 0.624661i \(-0.785237\pi\)
−0.780896 + 0.624661i \(0.785237\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 2.44077e127 0.800729
\(317\) 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
\(324\) 1.09093e128 1.00000
\(325\) 2.36027e128 1.84888
\(326\) 0 0
\(327\) −3.26727e128 −1.87176
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 6.12292e128 1.88682 0.943411 − 0.331626i \(-0.107597\pi\)
0.943411 + 0.331626i \(0.107597\pi\)
\(332\) 0 0
\(333\) 4.53572e128 1.02799
\(334\) 0 0
\(335\) 0 0
\(336\) 1.19350e129 1.71206
\(337\) −3.27299e128 −0.403478 −0.201739 − 0.979439i \(-0.564659\pi\)
−0.201739 + 0.979439i \(0.564659\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −3.18082e129 −1.59419
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −9.09794e128 −0.188298 −0.0941491 − 0.995558i \(-0.530013\pi\)
−0.0941491 + 0.995558i \(0.530013\pi\)
\(350\) 0 0
\(351\) −1.19556e130 −1.84888
\(352\) 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
\(361\) 2.11495e130 0.780608
\(362\) 0 0
\(363\) −3.59119e130 −1.00000
\(364\) −1.30798e131 −3.16540
\(365\) 0 0
\(366\) 0 0
\(367\) 4.03942e130 0.643206 0.321603 − 0.946875i \(-0.395778\pi\)
0.321603 + 0.946875i \(0.395778\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 2.44299e131 1.95088
\(373\) 2.57998e131 1.79666 0.898330 − 0.439322i \(-0.144781\pi\)
0.898330 + 0.439322i \(0.144781\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 4.11293e131 1.26926 0.634632 − 0.772814i \(-0.281152\pi\)
0.634632 + 0.772814i \(0.281152\pi\)
\(380\) 0 0
\(381\) −1.56238e131 −0.368649
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.10306e132 1.17311
\(388\) −1.07661e132 −1.00378
\(389\) 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
\(397\) 5.77173e132 1.67105 0.835526 − 0.549451i \(-0.185163\pi\)
0.835526 + 0.549451i \(0.185163\pi\)
\(398\) 0 0
\(399\) −1.01958e133 −2.28456
\(400\) 5.07060e132 1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) −2.67731e133 −3.60696
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.40910e133 −0.893416 −0.446708 − 0.894680i \(-0.647404\pi\)
−0.446708 + 0.894680i \(0.647404\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 9.75180e132 0.425919
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 6.62872e133 1.56492
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −5.44365e133 −0.789775 −0.394887 − 0.918730i \(-0.629216\pi\)
−0.394887 + 0.918730i \(0.629216\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 4.70463e134 3.31669
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −2.56845e134 −1.00000
\(433\) −1.09898e134 −0.380284 −0.190142 − 0.981757i \(-0.560895\pi\)
−0.190142 + 0.981757i \(0.560895\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 7.69238e134 1.87176
\(437\) 0 0
\(438\) 0 0
\(439\) −8.46620e134 −1.45210 −0.726052 − 0.687639i \(-0.758647\pi\)
−0.726052 + 0.687639i \(0.758647\pi\)
\(440\) 0 0
\(441\) 1.41966e135 1.93115
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) −1.06788e135 −1.02799
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −2.80995e135 −1.71206
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −3.28016e135 −1.13471
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −4.48135e135 −0.990108 −0.495054 − 0.868862i \(-0.664852\pi\)
−0.495054 + 0.868862i \(0.664852\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.00284e136 −1.13921 −0.569603 − 0.821920i \(-0.692903\pi\)
−0.569603 + 0.821920i \(0.692903\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 2.81480e136 1.84888
\(469\) 5.64151e136 3.32338
\(470\) 0 0
\(471\) −3.02129e136 −1.43260
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −4.33170e136 −1.33439
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 1.17030e137 1.90064
\(482\) 0 0
\(483\) 0 0
\(484\) 8.45500e136 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) −3.68993e136 −0.318450 −0.159225 − 0.987242i \(-0.550899\pi\)
−0.159225 + 0.987242i \(0.550899\pi\)
\(488\) 0 0
\(489\) 1.32484e137 0.927711
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −5.75171e137 −1.95088
\(497\) 0 0
\(498\) 0 0
\(499\) −7.78603e137 −1.94173 −0.970863 − 0.239634i \(-0.922973\pi\)
−0.970863 + 0.239634i \(0.922973\pi\)
\(500\) 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
\(507\) −2.18237e138 −2.41837
\(508\) 3.67843e137 0.368649
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 2.75139e138 2.04214
\(512\) 0 0
\(513\) 2.19417e138 1.33439
\(514\) 0 0
\(515\) 0 0
\(516\) −2.59701e138 −1.17311
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −5.35579e138 −1.21685 −0.608426 − 0.793611i \(-0.708199\pi\)
−0.608426 + 0.793611i \(0.708199\pi\)
\(524\) 0 0
\(525\) 9.15469e138 1.71206
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 7.87480e138 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 2.40047e139 2.28456
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −4.43013e139 −1.79208 −0.896038 − 0.443977i \(-0.853567\pi\)
−0.896038 + 0.443977i \(0.853567\pi\)
\(542\) 0 0
\(543\) −8.38004e138 −0.280837
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 4.97073e139 1.14569 0.572845 − 0.819664i \(-0.305840\pi\)
0.572845 + 0.819664i \(0.305840\pi\)
\(548\) 0 0
\(549\) −1.01245e140 −1.93725
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −1.03750e140 −1.37090
\(554\) 0 0
\(555\) 0 0
\(556\) −1.56065e140 −1.56492
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 2.84610e140 2.16894
\(560\) 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
\(567\) −4.63719e140 −1.71206
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 7.48556e140 1.93100 0.965501 − 0.260400i \(-0.0838543\pi\)
0.965501 + 0.260400i \(0.0838543\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 6.04709e140 1.00000
\(577\) −2.41537e138 −0.00365610 −0.00182805 − 0.999998i \(-0.500582\pi\)
−0.00182805 + 0.999998i \(0.500582\pi\)
\(578\) 0 0
\(579\) 7.63320e140 0.968500
\(580\) 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 \(\pi\)
\(588\) −3.34241e141 −1.93115
\(589\) 4.91355e141 2.60325
\(590\) 0 0
\(591\) 0 0
\(592\) 2.51418e141 1.02799
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −7.51095e141 −1.99988
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) −9.45025e141 −1.78997 −0.894984 − 0.446098i \(-0.852813\pi\)
−0.894984 + 0.446098i \(0.852813\pi\)
\(602\) 0 0
\(603\) −1.21407e142 −1.94116
\(604\) 7.72272e141 1.13471
\(605\) 0 0
\(606\) 0 0
\(607\) −3.81361e141 −0.435224 −0.217612 − 0.976035i \(-0.569827\pi\)
−0.217612 + 0.976035i \(0.569827\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 9.13136e141 0.631032 0.315516 − 0.948920i \(-0.397822\pi\)
0.315516 + 0.948920i \(0.397822\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 2.54426e142 1.06989 0.534944 − 0.844887i \(-0.320333\pi\)
0.534944 + 0.844887i \(0.320333\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −6.62710e142 −1.84888
\(625\) 3.88938e142 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 7.11325e142 1.43260
\(629\) 0 0
\(630\) 0 0
\(631\) 5.61723e142 0.887207 0.443604 − 0.896223i \(-0.353700\pi\)
0.443604 + 0.896223i \(0.353700\pi\)
\(632\) 0 0
\(633\) −1.45887e143 −1.96078
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 3.66300e143 3.57048
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) −4.42516e141 −0.0267405 −0.0133702 − 0.999911i \(-0.504256\pi\)
−0.0133702 + 0.999911i \(0.504256\pi\)
\(644\) 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
\(651\) −1.03844e144 −3.34003
\(652\) −3.11918e143 −0.927711
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −5.92107e143 −1.19280
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 1.35302e144 2.00000 1.00000 0.000822471i \(-0.000261801\pi\)
1.00000 0.000822471i \(0.000261801\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −3.03893e143 −0.243214
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −2.59198e144 −1.53061 −0.765304 − 0.643669i \(-0.777411\pi\)
−0.765304 + 0.643669i \(0.777411\pi\)
\(674\) 0 0
\(675\) −1.97012e144 −1.00000
\(676\) 5.13813e144 2.41837
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 4.57632e144 1.71853
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −5.16589e144 −1.33439
\(685\) 0 0
\(686\) 0 0
\(687\) 2.34615e144 0.484800
\(688\) 6.11433e144 1.17311
\(689\) 0 0
\(690\) 0 0
\(691\) 1.29102e145 1.98405 0.992025 − 0.126045i \(-0.0402283\pi\)
0.992025 + 0.126045i \(0.0402283\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −2.15536e145 −1.71206
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) −2.14781e145 −1.37175
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −4.13439e145 −1.71180 −0.855900 − 0.517141i \(-0.826996\pi\)
−0.855900 + 0.517141i \(0.826996\pi\)
\(710\) 0 0
\(711\) 2.23273e145 0.800729
\(712\) 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
\(721\) −4.14519e145 −0.729199
\(722\) 0 0
\(723\) −1.08799e146 −1.66177
\(724\) 1.97297e145 0.280837
\(725\) 0 0
\(726\) 0 0
\(727\) 1.73309e146 1.99786 0.998931 − 0.0462356i \(-0.0147225\pi\)
0.998931 + 0.0462356i \(0.0147225\pi\)
\(728\) 0 0
\(729\) 9.97939e145 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 2.38369e146 1.93725
\(733\) −2.08955e146 −1.58398 −0.791992 − 0.610532i \(-0.790956\pi\)
−0.791992 + 0.610532i \(0.790956\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −2.33298e146 −1.16693 −0.583465 − 0.812138i \(-0.698304\pi\)
−0.583465 + 0.812138i \(0.698304\pi\)
\(740\) 0 0
\(741\) 5.66138e146 2.46714
\(742\) 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
\(751\) 1.72436e146 0.379308 0.189654 − 0.981851i \(-0.439263\pi\)
0.189654 + 0.981851i \(0.439263\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.09177e147 1.71206
\(757\) −1.36104e147 −1.99517 −0.997585 − 0.0694571i \(-0.977873\pi\)
−0.997585 + 0.0694571i \(0.977873\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) −3.26979e147 −3.20456
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −1.42371e147 −1.00000
\(769\) 2.61386e147 1.71807 0.859033 − 0.511921i \(-0.171066\pi\)
0.859033 + 0.511921i \(0.171066\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.79714e147 −0.968500
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) −4.41182e147 −1.95088
\(776\) 0 0
\(777\) 4.53922e147 1.75999
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 7.86929e147 1.93115
\(785\) 0 0
\(786\) 0 0
\(787\) 9.90074e147 1.99966 0.999831 − 0.0183978i \(-0.00585652\pi\)
0.999831 + 0.0183978i \(0.00585652\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −2.61233e148 −3.58175
\(794\) 0 0
\(795\) 0 0
\(796\) 1.76836e148 1.99988
\(797\) 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
\(804\) 2.85838e148 1.94116
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 4.54155e148 1.98217 0.991085 − 0.133231i \(-0.0425351\pi\)
0.991085 + 0.133231i \(0.0425351\pi\)
\(812\) 0 0
\(813\) −5.19092e148 −1.99814
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −5.22333e148 −1.56539
\(818\) 0 0
\(819\) −1.19649e149 −3.16540
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 8.38810e148 1.73090 0.865450 − 0.500995i \(-0.167032\pi\)
0.865450 + 0.500995i \(0.167032\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) −1.39076e149 −1.98139 −0.990697 − 0.136083i \(-0.956549\pi\)
−0.990697 + 0.136083i \(0.956549\pi\)
\(830\) 0 0
\(831\) −1.50261e149 −1.89319
\(832\) 1.56027e149 1.84888
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 2.23475e149 1.95088
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.46082e149 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 3.43473e149 1.96078
\(845\) 0 0
\(846\) 0 0
\(847\) −3.59396e149 −1.71206
\(848\) 0 0
\(849\) −3.87142e149 −1.63523
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 5.44517e149 1.80972 0.904859 − 0.425712i \(-0.139976\pi\)
0.904859 + 0.425712i \(0.139976\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 5.87092e149 1.36475 0.682377 − 0.731000i \(-0.260946\pi\)
0.682377 + 0.731000i \(0.260946\pi\)
\(860\) 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
\(867\) −6.90198e149 −1.00000
\(868\) 2.44487e150 3.34003
\(869\) 0 0
\(870\) 0 0
\(871\) −3.13254e150 −3.58898
\(872\) 0 0
\(873\) −9.84838e149 −1.00378
\(874\) 0 0
\(875\) 0 0
\(876\) 1.39404e150 1.19280
\(877\) −2.21473e150 −1.78790 −0.893948 − 0.448170i \(-0.852076\pi\)
−0.893948 + 0.448170i \(0.852076\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) −1.25230e150 −0.714023 −0.357011 − 0.934100i \(-0.616204\pi\)
−0.357011 + 0.934100i \(0.616204\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) −1.56359e150 −0.631150
\(890\) 0 0
\(891\) 0 0
\(892\) 7.15477e149 0.243214
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 4.63840e150 1.00000
\(901\) 0 0
\(902\) 0 0
\(903\) 1.10391e151 2.00843
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −3.44201e150 −0.499851 −0.249926 − 0.968265i \(-0.580406\pi\)
−0.249926 + 0.968265i \(0.580406\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 1.21624e151 1.33439
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −5.52372e150 −0.484800
\(917\) 0 0
\(918\) 0 0
\(919\) 2.99875e150 0.222766 0.111383 − 0.993778i \(-0.464472\pi\)
0.111383 + 0.993778i \(0.464472\pi\)
\(920\) 0 0
\(921\) −9.78085e150 −0.650332
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1.92850e151 1.02799
\(926\) 0 0
\(927\) 8.92059e150 0.425919
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) −6.72255e151 −2.57692
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −5.26261e151 −1.45372 −0.726862 − 0.686783i \(-0.759022\pi\)
−0.726862 + 0.686783i \(0.759022\pi\)
\(938\) 0 0
\(939\) 6.30331e151 1.56179
\(940\) 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 \(\pi\)
\(948\) −5.25667e151 −0.800729
\(949\) −1.52775e152 −2.20534
\(950\) 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
\(961\) 3.68954e152 2.80595
\(962\) 0 0
\(963\) 0 0
\(964\) 2.56153e152 1.66177
\(965\) 0 0
\(966\) 0 0
\(967\) 1.43212e152 0.792918 0.396459 − 0.918052i \(-0.370239\pi\)
0.396459 + 0.918052i \(0.370239\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) −2.34952e152 −1.00000
\(973\) 6.63384e152 2.67923
\(974\) 0 0
\(975\) −5.08329e152 −1.84888
\(976\) −5.61211e152 −1.93725
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 7.03670e152 1.87176
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −1.33290e153 −2.46714
\(989\) 0 0
\(990\) 0 0
\(991\) 1.16792e153 1.85206 0.926031 − 0.377446i \(-0.123198\pi\)
0.926031 + 0.377446i \(0.123198\pi\)
\(992\) 0 0
\(993\) −1.31869e153 −1.88682
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 1.49569e153 1.74336 0.871681 − 0.490073i \(-0.163030\pi\)
0.871681 + 0.490073i \(0.163030\pi\)
\(998\) 0 0
\(999\) −9.76855e152 −1.02799
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 3.103.b.a.2.1 ✓ 1
3.2 odd 2 CM 3.103.b.a.2.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.103.b.a.2.1 ✓ 1 1.1 even 1 trivial
3.103.b.a.2.1 ✓ 1 3.2 odd 2 CM