↑

Properties

Label 3.85.b.a.2.1
Level $3$
Weight $85$
Character 3.2
Self dual yes
Analytic conductor $134.054$
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] = [3,85,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, 85, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 85);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 85 \)
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: \(134.054258054\)
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)
 
\(f(q)\) \(=\) \(q+1.09419e20 q^{3} +1.93428e25 q^{4} -6.02559e35 q^{7} +1.19725e40 q^{9} +O(q^{10})\) \(q+1.09419e20 q^{3} +1.93428e25 q^{4} -6.02559e35 q^{7} +1.19725e40 q^{9} +2.11647e45 q^{12} +5.49022e45 q^{13} +3.74144e50 q^{16} -9.92872e53 q^{19} -6.59314e55 q^{21} +5.16988e58 q^{25} +1.31002e60 q^{27} -1.16552e61 q^{28} +7.38353e62 q^{31} +2.31582e65 q^{36} +1.18339e66 q^{37} +6.00734e65 q^{39} +1.05064e68 q^{43} +4.09385e70 q^{48} +2.65750e71 q^{49} +1.06196e71 q^{52} -1.08639e74 q^{57} +1.19489e75 q^{61} -7.21415e75 q^{63} +7.23701e75 q^{64} +5.85050e76 q^{67} -2.27183e78 q^{73} +5.65683e78 q^{75} -1.92049e79 q^{76} +9.80021e79 q^{79} +1.43341e80 q^{81} -1.27530e81 q^{84} -3.30818e81 q^{91} +8.07898e82 q^{93} -5.05116e83 q^{97} +O(q^{100})\)

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 \(\pi\)
\(3\) 1.09419e20 1.00000
\(4\) 1.93428e25 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) −6.02559e35 −1.93144 −0.965722 − 0.259580i \(-0.916416\pi\)
−0.965722 + 0.259580i \(0.916416\pi\)
\(8\) 0 0
\(9\) 1.19725e40 1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 2.11647e45 1.00000
\(13\) 5.49022e45 0.0899433 0.0449717 − 0.998988i \(-0.485680\pi\)
0.0449717 + 0.998988i \(0.485680\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 3.74144e50 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) −9.92872e53 −1.94644 −0.973222 − 0.229865i \(-0.926171\pi\)
−0.973222 + 0.229865i \(0.926171\pi\)
\(20\) 0 0
\(21\) −6.59314e55 −1.93144
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 5.16988e58 1.00000
\(26\) 0 0
\(27\) 1.31002e60 1.00000
\(28\) −1.16552e61 −1.93144
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 7.38353e62 1.70244 0.851222 − 0.524805i \(-0.175862\pi\)
0.851222 + 0.524805i \(0.175862\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 2.31582e65 1.00000
\(37\) 1.18339e66 1.61680 0.808398 − 0.588637i \(-0.200335\pi\)
0.808398 + 0.588637i \(0.200335\pi\)
\(38\) 0 0
\(39\) 6.00734e65 0.0899433
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 1.05064e68 0.260482 0.130241 − 0.991482i \(-0.458425\pi\)
0.130241 + 0.991482i \(0.458425\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 4.09385e70 1.00000
\(49\) 2.65750e71 2.73047
\(50\) 0 0
\(51\) 0 0
\(52\) 1.06196e71 0.0899433
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.08639e74 −1.94644
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 1.19489e75 1.24015 0.620076 − 0.784542i \(-0.287102\pi\)
0.620076 + 0.784542i \(0.287102\pi\)
\(62\) 0 0
\(63\) −7.21415e75 −1.93144
\(64\) 7.23701e75 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 5.85050e76 1.18046 0.590230 − 0.807235i \(-0.299037\pi\)
0.590230 + 0.807235i \(0.299037\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −2.27183e78 −1.24973 −0.624863 − 0.780734i \(-0.714845\pi\)
−0.624863 + 0.780734i \(0.714845\pi\)
\(74\) 0 0
\(75\) 5.65683e78 1.00000
\(76\) −1.92049e79 −1.94644
\(77\) 0 0
\(78\) 0 0
\(79\) 9.80021e79 1.95388 0.976939 − 0.213518i \(-0.0684922\pi\)
0.976939 + 0.213518i \(0.0684922\pi\)
\(80\) 0 0
\(81\) 1.43341e80 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −1.27530e81 −1.93144
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −3.30818e81 −0.173720
\(92\) 0 0
\(93\) 8.07898e82 1.70244
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −5.05116e83 −1.81542 −0.907712 − 0.419593i \(-0.862173\pi\)
−0.907712 + 0.419593i \(0.862173\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000e84 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −1.84036e84 −0.531789 −0.265894 − 0.964002i \(-0.585667\pi\)
−0.265894 + 0.964002i \(0.585667\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 2.53395e85 1.00000
\(109\) −1.51284e85 −0.405396 −0.202698 − 0.979241i \(-0.564971\pi\)
−0.202698 + 0.979241i \(0.564971\pi\)
\(110\) 0 0
\(111\) 1.29485e86 1.61680
\(112\) −2.25444e86 −1.93144
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 6.57317e85 0.0899433
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 2.99906e87 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 1.42818e88 1.70244
\(125\) 0 0
\(126\) 0 0
\(127\) −3.81384e88 −1.66573 −0.832867 − 0.553473i \(-0.813302\pi\)
−0.832867 + 0.553473i \(0.813302\pi\)
\(128\) 0 0
\(129\) 1.14960e88 0.260482
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 5.98264e89 3.75945
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 1.99584e90 1.96564 0.982821 − 0.184563i \(-0.0590870\pi\)
0.982821 + 0.184563i \(0.0590870\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 4.47945e90 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 2.90781e91 2.73047
\(148\) 2.28901e91 1.61680
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 2.58821e91 0.786988 0.393494 − 0.919327i \(-0.371266\pi\)
0.393494 + 0.919327i \(0.371266\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 1.16199e91 0.0899433
\(157\) 3.00853e92 1.78061 0.890306 − 0.455363i \(-0.150490\pi\)
0.890306 + 0.455363i \(0.150490\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.05687e92 −0.129462 −0.0647308 − 0.997903i \(-0.520619\pi\)
−0.0647308 + 0.997903i \(0.520619\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) −3.69585e93 −0.991910
\(170\) 0 0
\(171\) −1.18872e94 −1.94644
\(172\) 2.03223e93 0.260482
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) −3.11516e94 −1.93144
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) −1.32008e95 −1.98655 −0.993277 − 0.115762i \(-0.963069\pi\)
−0.993277 + 0.115762i \(0.963069\pi\)
\(182\) 0 0
\(183\) 1.30744e95 1.24015
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −7.89365e95 −1.93144
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 7.91866e95 1.00000
\(193\) 1.91732e96 1.94665 0.973323 − 0.229437i \(-0.0736885\pi\)
0.973323 + 0.229437i \(0.0736885\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 5.14035e96 2.73047
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −4.34558e96 −1.21960 −0.609801 − 0.792554i \(-0.708751\pi\)
−0.609801 + 0.792554i \(0.708751\pi\)
\(200\) 0 0
\(201\) 6.40155e96 1.18046
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 2.05413e96 0.0899433
\(209\) 0 0
\(210\) 0 0
\(211\) 2.45220e97 0.588428 0.294214 − 0.955740i \(-0.404942\pi\)
0.294214 + 0.955740i \(0.404942\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −4.44901e98 −3.28817
\(218\) 0 0
\(219\) −2.48581e98 −1.24973
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 6.80263e96 0.0159909 0.00799544 − 0.999968i \(-0.497455\pi\)
0.00799544 + 0.999968i \(0.497455\pi\)
\(224\) 0 0
\(225\) 6.18965e98 1.00000
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) −2.10139e99 −1.94644
\(229\) 1.88796e99 1.45513 0.727565 − 0.686039i \(-0.240652\pi\)
0.727565 + 0.686039i \(0.240652\pi\)
\(230\) 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
\(237\) 1.07233e100 1.95388
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −5.31221e98 −0.0479247 −0.0239624 − 0.999713i \(-0.507628\pi\)
−0.0239624 + 0.999713i \(0.507628\pi\)
\(242\) 0 0
\(243\) 1.56842e100 1.00000
\(244\) 2.31125e100 1.24015
\(245\) 0 0
\(246\) 0 0
\(247\) −5.45109e99 −0.175070
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −1.39542e101 −1.93144
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.39984e101 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −7.13062e101 −3.12275
\(260\) 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
\(268\) 1.13165e102 1.18046
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −2.54299e102 −1.66201 −0.831006 − 0.556263i \(-0.812235\pi\)
−0.831006 + 0.556263i \(0.812235\pi\)
\(272\) 0 0
\(273\) −3.61978e101 −0.173720
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 7.63903e102 1.99016 0.995079 − 0.0990812i \(-0.0315903\pi\)
0.995079 + 0.0990812i \(0.0315903\pi\)
\(278\) 0 0
\(279\) 8.83994e102 1.70244
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 6.05314e102 0.641136 0.320568 − 0.947225i \(-0.396126\pi\)
0.320568 + 0.947225i \(0.396126\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2.27882e103 1.00000
\(290\) 0 0
\(291\) −5.52693e103 −1.81542
\(292\) −4.39435e103 −1.24973
\(293\) 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
\(300\) 1.09419e104 1.00000
\(301\) −6.33071e103 −0.503106
\(302\) 0 0
\(303\) 0 0
\(304\) −3.71478e104 −1.94644
\(305\) 0 0
\(306\) 0 0
\(307\) −3.05699e104 −1.06043 −0.530216 − 0.847863i \(-0.677889\pi\)
−0.530216 + 0.847863i \(0.677889\pi\)
\(308\) 0 0
\(309\) −2.01370e104 −0.531789
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 1.27742e105 1.96549 0.982746 − 0.184963i \(-0.0592164\pi\)
0.982746 + 0.184963i \(0.0592164\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 1.89564e105 1.95388
\(317\) 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
\(324\) 2.77262e105 1.00000
\(325\) 2.83838e104 0.0899433
\(326\) 0 0
\(327\) −1.65533e105 −0.405396
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −9.15607e105 −1.34565 −0.672827 − 0.739800i \(-0.734920\pi\)
−0.672827 + 0.739800i \(0.734920\pi\)
\(332\) 0 0
\(333\) 1.41681e106 1.61680
\(334\) 0 0
\(335\) 0 0
\(336\) −2.46679e106 −1.93144
\(337\) 1.33510e106 0.922693 0.461347 − 0.887220i \(-0.347366\pi\)
0.461347 + 0.887220i \(0.347366\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −1.01484e107 −3.34231
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 8.33738e106 1.32544 0.662722 − 0.748865i \(-0.269401\pi\)
0.662722 + 0.748865i \(0.269401\pi\)
\(350\) 0 0
\(351\) 7.19230e105 0.0899433
\(352\) 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
\(361\) 7.25598e107 2.78865
\(362\) 0 0
\(363\) 3.28154e107 1.00000
\(364\) −6.39895e106 −0.173720
\(365\) 0 0
\(366\) 0 0
\(367\) −8.34596e107 −1.60510 −0.802549 − 0.596586i \(-0.796523\pi\)
−0.802549 + 0.596586i \(0.796523\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 1.56270e108 1.70244
\(373\) −1.74175e108 −1.69517 −0.847586 − 0.530658i \(-0.821945\pi\)
−0.847586 + 0.530658i \(0.821945\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 4.17807e107 0.208032 0.104016 − 0.994576i \(-0.466831\pi\)
0.104016 + 0.994576i \(0.466831\pi\)
\(380\) 0 0
\(381\) −4.17306e108 −1.66573
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.25788e108 0.260482
\(388\) −9.77036e108 −1.81542
\(389\) 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
\(397\) −1.44338e109 −1.02371 −0.511857 − 0.859071i \(-0.671042\pi\)
−0.511857 + 0.859071i \(0.671042\pi\)
\(398\) 0 0
\(399\) 6.54615e109 3.75945
\(400\) 1.93428e109 1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 4.05372e108 0.153123
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −4.49365e109 −0.912474 −0.456237 − 0.889858i \(-0.650803\pi\)
−0.456237 + 0.889858i \(0.650803\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −3.55977e109 −0.531789
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 2.18383e110 1.96564
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −3.04974e110 −1.83829 −0.919146 − 0.393918i \(-0.871119\pi\)
−0.919146 + 0.393918i \(0.871119\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −7.19992e110 −2.39528
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 4.90137e110 1.00000
\(433\) −6.74241e110 −1.24831 −0.624156 − 0.781300i \(-0.714557\pi\)
−0.624156 + 0.781300i \(0.714557\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2.92626e110 −0.405396
\(437\) 0 0
\(438\) 0 0
\(439\) 3.96057e110 0.411385 0.205692 − 0.978617i \(-0.434055\pi\)
0.205692 + 0.978617i \(0.434055\pi\)
\(440\) 0 0
\(441\) 3.18170e111 2.73047
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 2.50461e111 1.61680
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −4.36072e111 −1.93144
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 2.83200e111 0.786988
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 5.79160e111 1.11255 0.556273 − 0.831000i \(-0.312231\pi\)
0.556273 + 0.831000i \(0.312231\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.74900e112 −1.94262 −0.971309 − 0.237819i \(-0.923567\pi\)
−0.971309 + 0.237819i \(0.923567\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 1.27144e111 0.0899433
\(469\) −3.52527e112 −2.27999
\(470\) 0 0
\(471\) 3.29191e112 1.78061
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −5.13303e112 −1.94644
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 6.49706e111 0.145420
\(482\) 0 0
\(483\) 0 0
\(484\) 5.80103e112 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) 1.42930e113 1.90067 0.950335 − 0.311229i \(-0.100741\pi\)
0.950335 + 0.311229i \(0.100741\pi\)
\(488\) 0 0
\(489\) −1.15641e112 −0.129462
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 2.76251e113 1.70244
\(497\) 0 0
\(498\) 0 0
\(499\) −1.91753e113 −0.917316 −0.458658 − 0.888613i \(-0.651670\pi\)
−0.458658 + 0.888613i \(0.651670\pi\)
\(500\) 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
\(507\) −4.04396e113 −0.991910
\(508\) −7.37703e113 −1.66573
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 1.36891e114 2.41378
\(512\) 0 0
\(513\) −1.30068e114 −1.94644
\(514\) 0 0
\(515\) 0 0
\(516\) 2.22364e113 0.260482
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −1.77398e114 −1.17999 −0.589993 − 0.807408i \(-0.700870\pi\)
−0.589993 + 0.807408i \(0.700870\pi\)
\(524\) 0 0
\(525\) −3.40857e114 −1.93144
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 2.42738e114 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 1.15721e115 3.75945
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 1.24536e115 1.99991 0.999957 − 0.00925115i \(-0.00294478\pi\)
0.999957 + 0.00925115i \(0.00294478\pi\)
\(542\) 0 0
\(543\) −1.44442e115 −1.98655
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −4.41833e114 −0.446468 −0.223234 − 0.974765i \(-0.571661\pi\)
−0.223234 + 0.974765i \(0.571661\pi\)
\(548\) 0 0
\(549\) 1.43058e115 1.24015
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −5.90520e115 −3.77380
\(554\) 0 0
\(555\) 0 0
\(556\) 3.86052e115 1.96564
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 5.76823e113 0.0234286
\(560\) 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
\(567\) −8.63715e115 −1.93144
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) −1.10589e116 −1.84076 −0.920379 − 0.391027i \(-0.872120\pi\)
−0.920379 + 0.391027i \(0.872120\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 8.66452e115 1.00000
\(577\) 1.58321e116 1.69885 0.849424 − 0.527712i \(-0.176950\pi\)
0.849424 + 0.527712i \(0.176950\pi\)
\(578\) 0 0
\(579\) 2.09791e116 1.94665
\(580\) 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 \(\pi\)
\(588\) 5.62452e116 2.73047
\(589\) −7.33090e116 −3.31371
\(590\) 0 0
\(591\) 0 0
\(592\) 4.42758e116 1.61680
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −4.75489e116 −1.21960
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) −1.01667e117 −1.96994 −0.984970 − 0.172728i \(-0.944742\pi\)
−0.984970 + 0.172728i \(0.944742\pi\)
\(602\) 0 0
\(603\) 7.00452e116 1.18046
\(604\) 5.00633e116 0.786988
\(605\) 0 0
\(606\) 0 0
\(607\) −1.33535e117 −1.70478 −0.852391 − 0.522904i \(-0.824849\pi\)
−0.852391 + 0.522904i \(0.824849\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −4.64971e116 −0.392723 −0.196361 − 0.980532i \(-0.562913\pi\)
−0.196361 + 0.980532i \(0.562913\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −1.88522e117 −1.05768 −0.528841 − 0.848721i \(-0.677373\pi\)
−0.528841 + 0.848721i \(0.677373\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 2.24761e116 0.0899433
\(625\) 2.67276e117 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 5.81935e117 1.78061
\(629\) 0 0
\(630\) 0 0
\(631\) −8.07537e116 −0.202269 −0.101134 − 0.994873i \(-0.532247\pi\)
−0.101134 + 0.994873i \(0.532247\pi\)
\(632\) 0 0
\(633\) 2.68318e117 0.588428
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1.45903e117 0.245588
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 1.04602e118 1.18762 0.593811 − 0.804604i \(-0.297623\pi\)
0.593811 + 0.804604i \(0.297623\pi\)
\(644\) 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
\(651\) −4.86807e118 −3.28817
\(652\) −2.04428e117 −0.129462
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −2.71995e118 −1.24973
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 4.14832e118 1.47710 0.738552 − 0.674196i \(-0.235510\pi\)
0.738552 + 0.674196i \(0.235510\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 7.44337e116 0.0159909
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −9.00816e118 −1.50662 −0.753309 − 0.657667i \(-0.771544\pi\)
−0.753309 + 0.657667i \(0.771544\pi\)
\(674\) 0 0
\(675\) 6.77265e118 1.00000
\(676\) −7.14881e118 −0.991910
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 3.04362e119 3.50639
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −2.29931e119 −1.94644
\(685\) 0 0
\(686\) 0 0
\(687\) 2.06578e119 1.45513
\(688\) 3.93090e118 0.260482
\(689\) 0 0
\(690\) 0 0
\(691\) 3.49635e119 1.92991 0.964956 − 0.262412i \(-0.0845179\pi\)
0.964956 + 0.262412i \(0.0845179\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −6.02559e119 −1.93144
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) −1.17495e120 −3.14700
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −3.71080e119 −0.695546 −0.347773 − 0.937579i \(-0.613062\pi\)
−0.347773 + 0.937579i \(0.613062\pi\)
\(710\) 0 0
\(711\) 1.17333e120 1.95388
\(712\) 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
\(721\) 1.10893e120 1.02712
\(722\) 0 0
\(723\) −5.81257e118 −0.0479247
\(724\) −2.55341e120 −1.98655
\(725\) 0 0
\(726\) 0 0
\(727\) 1.66012e119 0.108566 0.0542831 − 0.998526i \(-0.482713\pi\)
0.0542831 + 0.998526i \(0.482713\pi\)
\(728\) 0 0
\(729\) 1.71615e120 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 2.52895e120 1.24015
\(733\) −4.56801e119 −0.211524 −0.105762 − 0.994391i \(-0.533728\pi\)
−0.105762 + 0.994391i \(0.533728\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 6.07750e120 1.99829 0.999145 − 0.0413373i \(-0.0131618\pi\)
0.999145 + 0.0413373i \(0.0131618\pi\)
\(740\) 0 0
\(741\) −5.96452e119 −0.175070
\(742\) 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
\(751\) −3.59138e120 −0.600322 −0.300161 − 0.953888i \(-0.597040\pi\)
−0.300161 + 0.953888i \(0.597040\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −1.52685e121 −1.93144
\(757\) −1.46899e121 −1.75789 −0.878944 − 0.476925i \(-0.841751\pi\)
−0.878944 + 0.476925i \(0.841751\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 9.11575e120 0.783000
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.53169e121 1.00000
\(769\) −3.21526e121 −1.98751 −0.993755 − 0.111585i \(-0.964407\pi\)
−0.993755 + 0.111585i \(0.964407\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 3.70863e121 1.94665
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 3.81720e121 1.70244
\(776\) 0 0
\(777\) −7.80225e121 −3.12275
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 9.94289e121 2.73047
\(785\) 0 0
\(786\) 0 0
\(787\) 3.92661e121 0.918500 0.459250 − 0.888307i \(-0.348118\pi\)
0.459250 + 0.888307i \(0.348118\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 6.56021e120 0.111543
\(794\) 0 0
\(795\) 0 0
\(796\) −8.40557e121 −1.21960
\(797\) 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
\(804\) 1.23824e122 1.18046
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) −2.88901e122 −1.91369 −0.956847 − 0.290593i \(-0.906148\pi\)
−0.956847 + 0.290593i \(0.906148\pi\)
\(812\) 0 0
\(813\) −2.78251e122 −1.66201
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −1.04315e122 −0.507014
\(818\) 0 0
\(819\) −3.96072e121 −0.173720
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 2.80223e122 1.00164 0.500819 − 0.865552i \(-0.333032\pi\)
0.500819 + 0.865552i \(0.333032\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) −5.22554e122 −1.37671 −0.688353 − 0.725376i \(-0.741666\pi\)
−0.688353 + 0.725376i \(0.741666\pi\)
\(830\) 0 0
\(831\) 8.35855e122 1.99016
\(832\) 3.97327e121 0.0899433
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 9.67258e122 1.70244
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 6.94116e122 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 4.74325e122 0.588428
\(845\) 0 0
\(846\) 0 0
\(847\) −1.80711e123 −1.93144
\(848\) 0 0
\(849\) 6.62329e122 0.641136
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −2.13009e123 −1.69254 −0.846270 − 0.532754i \(-0.821157\pi\)
−0.846270 + 0.532754i \(0.821157\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 3.37171e123 1.99590 0.997948 − 0.0640362i \(-0.0203973\pi\)
0.997948 + 0.0640362i \(0.0203973\pi\)
\(860\) 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
\(867\) 2.49346e123 1.00000
\(868\) −8.60564e123 −3.28817
\(869\) 0 0
\(870\) 0 0
\(871\) 3.21205e122 0.106174
\(872\) 0 0
\(873\) −6.04751e123 −1.81542
\(874\) 0 0
\(875\) 0 0
\(876\) −4.80825e123 −1.24973
\(877\) 3.69268e123 0.914869 0.457435 − 0.889243i \(-0.348768\pi\)
0.457435 + 0.889243i \(0.348768\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 3.64706e123 0.678568 0.339284 − 0.940684i \(-0.389815\pi\)
0.339284 + 0.940684i \(0.389815\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 2.29806e124 3.21727
\(890\) 0 0
\(891\) 0 0
\(892\) 1.31582e122 0.0159909
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 1.19725e124 1.00000
\(901\) 0 0
\(902\) 0 0
\(903\) −6.92700e123 −0.503106
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −8.32998e123 −0.502502 −0.251251 − 0.967922i \(-0.580842\pi\)
−0.251251 + 0.967922i \(0.580842\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) −4.06467e124 −1.94644
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 3.65184e124 1.45513
\(917\) 0 0
\(918\) 0 0
\(919\) 1.06078e124 0.368446 0.184223 − 0.982884i \(-0.441023\pi\)
0.184223 + 0.982884i \(0.441023\pi\)
\(920\) 0 0
\(921\) −3.34493e124 −1.06043
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 6.11798e124 1.61680
\(926\) 0 0
\(927\) −2.20337e124 −0.531789
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) −2.63856e125 −5.31471
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 8.53436e124 1.31253 0.656263 − 0.754532i \(-0.272136\pi\)
0.656263 + 0.754532i \(0.272136\pi\)
\(938\) 0 0
\(939\) 1.39774e125 1.96549
\(940\) 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 \(\pi\)
\(948\) 2.07419e125 1.95388
\(949\) −1.24728e124 −0.112405
\(950\) 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
\(961\) 3.57068e125 1.89832
\(962\) 0 0
\(963\) 0 0
\(964\) −1.02753e124 −0.0479247
\(965\) 0 0
\(966\) 0 0
\(967\) −3.49712e125 −1.43153 −0.715763 − 0.698343i \(-0.753921\pi\)
−0.715763 + 0.698343i \(0.753921\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 3.03377e125 1.00000
\(973\) −1.20261e126 −3.79652
\(974\) 0 0
\(975\) 3.10572e124 0.0899433
\(976\) 4.47062e125 1.24015
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −1.81125e125 −0.405396
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −1.05439e125 −0.175070
\(989\) 0 0
\(990\) 0 0
\(991\) −7.67902e125 −1.12257 −0.561284 − 0.827624i \(-0.689692\pi\)
−0.561284 + 0.827624i \(0.689692\pi\)
\(992\) 0 0
\(993\) −1.00185e126 −1.34565
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 1.23906e126 1.40572 0.702858 − 0.711331i \(-0.251907\pi\)
0.702858 + 0.711331i \(0.251907\pi\)
\(998\) 0 0
\(999\) 1.55026e126 1.61680
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 3.85.b.a.2.1 ✓ 1
3.2 odd 2 CM 3.85.b.a.2.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.85.b.a.2.1 ✓ 1 1.1 even 1 trivial
3.85.b.a.2.1 ✓ 1 3.2 odd 2 CM