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Properties

Label 19.9.b.a.18.1
Level $19$
Weight $9$
Character 19.18
Self dual yes
Analytic conductor $7.740$
Analytic rank $0$
Dimension $1$
CM discriminant -19
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [19,9,Mod(18,19)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(19, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("19.18");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 19.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: \(7.74019359116\)
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 18.1
Character \(\chi\) \(=\) 19.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+256.000 q^{4} -289.000 q^{5} +527.000 q^{7} +6561.00 q^{9} +O(q^{10})\) \(q+256.000 q^{4} -289.000 q^{5} +527.000 q^{7} +6561.00 q^{9} +25007.0 q^{11} +65536.0 q^{16} -42433.0 q^{17} +130321. q^{19} -73984.0 q^{20} -534718. q^{23} -307104. q^{25} +134912. q^{28} -152303. q^{35} +1.67962e6 q^{36} +5.60213e6 q^{43} +6.40179e6 q^{44} -1.89613e6 q^{45} -8.30251e6 q^{47} -5.48707e6 q^{49} -7.22702e6 q^{55} -1.76618e7 q^{61} +3.45765e6 q^{63} +1.67772e7 q^{64} -1.08628e7 q^{68} +4.38646e7 q^{73} +3.33622e7 q^{76} +1.31787e7 q^{77} -1.89399e7 q^{80} +4.30467e7 q^{81} -6.26770e7 q^{83} +1.22631e7 q^{85} -1.36888e8 q^{92} -3.76628e7 q^{95} +1.64071e8 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/19\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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 \(\pi\)
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) 256.000 1.00000
\(5\) −289.000 −0.462400 −0.231200 − 0.972906i \(-0.574265\pi\)
−0.231200 + 0.972906i \(0.574265\pi\)
\(6\) 0 0
\(7\) 527.000 0.219492 0.109746 − 0.993960i \(-0.464996\pi\)
0.109746 + 0.993960i \(0.464996\pi\)
\(8\) 0 0
\(9\) 6561.00 1.00000
\(10\) 0 0
\(11\) 25007.0 1.70801 0.854006 − 0.520263i \(-0.174166\pi\)
0.854006 + 0.520263i \(0.174166\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 65536.0 1.00000
\(17\) −42433.0 −0.508052 −0.254026 − 0.967197i \(-0.581755\pi\)
−0.254026 + 0.967197i \(0.581755\pi\)
\(18\) 0 0
\(19\) 130321. 1.00000
\(20\) −73984.0 −0.462400
\(21\) 0 0
\(22\) 0 0
\(23\) −534718. −1.91079 −0.955396 − 0.295327i \(-0.904571\pi\)
−0.955396 + 0.295327i \(0.904571\pi\)
\(24\) 0 0
\(25\) −307104. −0.786186
\(26\) 0 0
\(27\) 0 0
\(28\) 134912. 0.219492
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −152303. −0.101493
\(36\) 1.67962e6 1.00000
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 5.60213e6 1.63862 0.819312 − 0.573348i \(-0.194356\pi\)
0.819312 + 0.573348i \(0.194356\pi\)
\(44\) 6.40179e6 1.70801
\(45\) −1.89613e6 −0.462400
\(46\) 0 0
\(47\) −8.30251e6 −1.70145 −0.850723 − 0.525614i \(-0.823835\pi\)
−0.850723 + 0.525614i \(0.823835\pi\)
\(48\) 0 0
\(49\) −5.48707e6 −0.951823
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) −7.22702e6 −0.789785
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −1.76618e7 −1.27560 −0.637801 − 0.770201i \(-0.720156\pi\)
−0.637801 + 0.770201i \(0.720156\pi\)
\(62\) 0 0
\(63\) 3.45765e6 0.219492
\(64\) 1.67772e7 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −1.08628e7 −0.508052
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 4.38646e7 1.54462 0.772312 − 0.635243i \(-0.219100\pi\)
0.772312 + 0.635243i \(0.219100\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 3.33622e7 1.00000
\(77\) 1.31787e7 0.374895
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −1.89399e7 −0.462400
\(81\) 4.30467e7 1.00000
\(82\) 0 0
\(83\) −6.26770e7 −1.32067 −0.660337 − 0.750970i \(-0.729586\pi\)
−0.660337 + 0.750970i \(0.729586\pi\)
\(84\) 0 0
\(85\) 1.22631e7 0.234923
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1.36888e8 −1.91079
\(93\) 0 0
\(94\) 0 0
\(95\) −3.76628e7 −0.462400
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 1.64071e8 1.70801
\(100\) −7.86186e7 −0.786186
\(101\) −1.08161e8 −1.03940 −0.519702 − 0.854348i \(-0.673957\pi\)
−0.519702 + 0.854348i \(0.673957\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 3.45375e7 0.219492
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 1.54534e8 0.883550
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.23622e7 −0.111513
\(120\) 0 0
\(121\) 4.10991e8 1.91730
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 2.01644e8 0.825933
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −4.66964e8 −1.58562 −0.792808 − 0.609472i \(-0.791382\pi\)
−0.792808 + 0.609472i \(0.791382\pi\)
\(132\) 0 0
\(133\) 6.86792e7 0.219492
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.09844e7 0.144729 0.0723645 − 0.997378i \(-0.476946\pi\)
0.0723645 + 0.997378i \(0.476946\pi\)
\(138\) 0 0
\(139\) −7.46574e8 −1.99993 −0.999963 − 0.00864336i \(-0.997249\pi\)
−0.999963 + 0.00864336i \(0.997249\pi\)
\(140\) −3.89896e7 −0.101493
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 4.29982e8 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −8.14865e8 −1.65326 −0.826629 − 0.562747i \(-0.809745\pi\)
−0.826629 + 0.562747i \(0.809745\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) −2.78403e8 −0.508052
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1.20530e9 1.98379 0.991894 − 0.127066i \(-0.0405559\pi\)
0.991894 + 0.127066i \(0.0405559\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −2.81796e8 −0.419403
\(162\) 0 0
\(163\) −1.32418e9 −1.87584 −0.937919 − 0.346854i \(-0.887250\pi\)
−0.937919 + 0.346854i \(0.887250\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 8.15731e8 1.00000
\(170\) 0 0
\(171\) 8.55036e8 1.00000
\(172\) 1.43414e9 1.63862
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) −1.61844e8 −0.172561
\(176\) 1.63886e9 1.70801
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) −4.85409e8 −0.462400
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −1.06112e9 −0.867759
\(188\) −2.12544e9 −1.70145
\(189\) 0 0
\(190\) 0 0
\(191\) 1.47444e9 1.10788 0.553939 − 0.832557i \(-0.313124\pi\)
0.553939 + 0.832557i \(0.313124\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −1.40469e9 −0.951823
\(197\) 1.82048e9 1.20870 0.604352 − 0.796717i \(-0.293432\pi\)
0.604352 + 0.796717i \(0.293432\pi\)
\(198\) 0 0
\(199\) −2.37068e9 −1.51168 −0.755842 − 0.654754i \(-0.772772\pi\)
−0.755842 + 0.654754i \(0.772772\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −3.50828e9 −1.91079
\(208\) 0 0
\(209\) 3.25894e9 1.70801
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.61901e9 −0.757699
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −1.85012e9 −0.789785
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) −2.01491e9 −0.786186
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 5.43958e9 1.97799 0.988993 − 0.147960i \(-0.0472708\pi\)
0.988993 + 0.147960i \(0.0472708\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5.69329e9 1.93170 0.965849 − 0.259105i \(-0.0834276\pi\)
0.965849 + 0.259105i \(0.0834276\pi\)
\(234\) 0 0
\(235\) 2.39943e9 0.786749
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.74938e9 0.536157 0.268079 − 0.963397i \(-0.413611\pi\)
0.268079 + 0.963397i \(0.413611\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −4.52142e9 −1.27560
\(245\) 1.58576e9 0.440123
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 7.75507e9 1.95385 0.976924 − 0.213585i \(-0.0685141\pi\)
0.976924 + 0.213585i \(0.0685141\pi\)
\(252\) 8.85158e8 0.219492
\(253\) −1.33717e10 −3.26366
\(254\) 0 0
\(255\) 0 0
\(256\) 4.29497e9 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −8.90888e9 −1.86209 −0.931044 − 0.364908i \(-0.881101\pi\)
−0.931044 + 0.364908i \(0.881101\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 5.27029e9 0.977141 0.488571 − 0.872524i \(-0.337518\pi\)
0.488571 + 0.872524i \(0.337518\pi\)
\(272\) −2.78089e9 −0.508052
\(273\) 0 0
\(274\) 0 0
\(275\) −7.67975e9 −1.34282
\(276\) 0 0
\(277\) 5.85240e9 0.994065 0.497032 − 0.867732i \(-0.334423\pi\)
0.497032 + 0.867732i \(0.334423\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −1.28112e10 −1.99731 −0.998656 − 0.0518374i \(-0.983492\pi\)
−0.998656 + 0.0518374i \(0.983492\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −5.17520e9 −0.741883
\(290\) 0 0
\(291\) 0 0
\(292\) 1.12293e10 1.54462
\(293\) 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
\(300\) 0 0
\(301\) 2.95232e9 0.359665
\(302\) 0 0
\(303\) 0 0
\(304\) 8.54072e9 1.00000
\(305\) 5.10426e9 0.589839
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 3.37374e9 0.374895
\(309\) 0 0
\(310\) 0 0
\(311\) 1.02469e10 1.09535 0.547673 − 0.836693i \(-0.315514\pi\)
0.547673 + 0.836693i \(0.315514\pi\)
\(312\) 0 0
\(313\) 3.95742e9 0.412321 0.206160 − 0.978518i \(-0.433903\pi\)
0.206160 + 0.978518i \(0.433903\pi\)
\(314\) 0 0
\(315\) −9.99260e8 −0.101493
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −4.84862e9 −0.462400
\(321\) 0 0
\(322\) 0 0
\(323\) −5.52991e9 −0.508052
\(324\) 1.10200e10 1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4.37542e9 −0.373454
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −1.60453e10 −1.32067
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 3.13936e9 0.234923
\(341\) 0 0
\(342\) 0 0
\(343\) −5.92974e9 −0.428409
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.71454e10 1.18258 0.591289 − 0.806460i \(-0.298619\pi\)
0.591289 + 0.806460i \(0.298619\pi\)
\(348\) 0 0
\(349\) −2.85063e10 −1.92150 −0.960748 − 0.277423i \(-0.910520\pi\)
−0.960748 + 0.277423i \(0.910520\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3.09364e10 −1.99237 −0.996187 − 0.0872459i \(-0.972193\pi\)
−0.996187 + 0.0872459i \(0.972193\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.26623e9 0.377250 0.188625 − 0.982049i \(-0.439597\pi\)
0.188625 + 0.982049i \(0.439597\pi\)
\(360\) 0 0
\(361\) 1.69836e10 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.26769e10 −0.714234
\(366\) 0 0
\(367\) 3.49416e10 1.92610 0.963050 − 0.269324i \(-0.0868002\pi\)
0.963050 + 0.269324i \(0.0868002\pi\)
\(368\) −3.50433e10 −1.91079
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) −9.64167e9 −0.462400
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) −3.80864e9 −0.173351
\(386\) 0 0
\(387\) 3.67556e10 1.63862
\(388\) 0 0
\(389\) 3.21750e10 1.40514 0.702570 − 0.711614i \(-0.252036\pi\)
0.702570 + 0.711614i \(0.252036\pi\)
\(390\) 0 0
\(391\) 2.26897e10 0.970782
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 4.20022e10 1.70801
\(397\) 7.82620e9 0.315057 0.157528 − 0.987514i \(-0.449647\pi\)
0.157528 + 0.987514i \(0.449647\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −2.01264e10 −0.786186
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −2.76892e10 −1.03940
\(405\) −1.24405e10 −0.462400
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 1.81136e10 0.610680
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −8.96298e9 −0.290801 −0.145401 − 0.989373i \(-0.546447\pi\)
−0.145401 + 0.989373i \(0.546447\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) −5.44728e10 −1.70145
\(424\) 0 0
\(425\) 1.30313e10 0.399423
\(426\) 0 0
\(427\) −9.30776e9 −0.279984
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6.96850e10 −1.91079
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −3.60007e10 −0.951823
\(442\) 0 0
\(443\) 7.54418e10 1.95883 0.979416 − 0.201851i \(-0.0646958\pi\)
0.979416 + 0.201851i \(0.0646958\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 8.84159e9 0.219492
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −8.65029e10 −1.98320 −0.991598 − 0.129357i \(-0.958709\pi\)
−0.991598 + 0.129357i \(0.958709\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 3.95606e10 0.883550
\(461\) −3.96004e10 −0.876792 −0.438396 − 0.898782i \(-0.644453\pi\)
−0.438396 + 0.898782i \(0.644453\pi\)
\(462\) 0 0
\(463\) −7.19461e10 −1.56561 −0.782805 − 0.622267i \(-0.786212\pi\)
−0.782805 + 0.622267i \(0.786212\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.57131e10 1.38161 0.690803 − 0.723043i \(-0.257257\pi\)
0.690803 + 0.723043i \(0.257257\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.40092e11 2.79879
\(474\) 0 0
\(475\) −4.00221e10 −0.786186
\(476\) −5.72472e9 −0.111513
\(477\) 0 0
\(478\) 0 0
\(479\) 7.83105e10 1.48757 0.743786 − 0.668418i \(-0.233028\pi\)
0.743786 + 0.668418i \(0.233028\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1.05214e11 1.91730
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.37649e10 0.236835 0.118417 − 0.992964i \(-0.462218\pi\)
0.118417 + 0.992964i \(0.462218\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −4.74165e10 −0.789785
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −7.36149e10 −1.18731 −0.593654 − 0.804720i \(-0.702315\pi\)
−0.593654 + 0.804720i \(0.702315\pi\)
\(500\) 5.16208e10 0.825933
\(501\) 0 0
\(502\) 0 0
\(503\) 7.69182e8 0.0120159 0.00600796 − 0.999982i \(-0.498088\pi\)
0.00600796 + 0.999982i \(0.498088\pi\)
\(504\) 0 0
\(505\) 3.12585e10 0.480620
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 2.31166e10 0.339032
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −2.07621e11 −2.90609
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) −1.19543e11 −1.58562
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 2.07612e11 2.65113
\(530\) 0 0
\(531\) 0 0
\(532\) 1.75819e10 0.219492
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.37215e11 −1.62573
\(540\) 0 0
\(541\) −2.95623e10 −0.345103 −0.172552 − 0.985000i \(-0.555201\pi\)
−0.172552 + 0.985000i \(0.555201\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 1.30520e10 0.144729
\(549\) −1.15879e11 −1.27560
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −1.91123e11 −1.99993
\(557\) 1.42185e11 1.47717 0.738587 − 0.674158i \(-0.235493\pi\)
0.738587 + 0.674158i \(0.235493\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −9.98133e9 −0.101493
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 2.26856e10 0.219492
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) −1.69603e10 −0.159547 −0.0797734 − 0.996813i \(-0.525420\pi\)
−0.0797734 + 0.996813i \(0.525420\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.64214e11 1.50224
\(576\) 1.10075e11 1.00000
\(577\) 1.94557e11 1.75527 0.877634 − 0.479331i \(-0.159120\pi\)
0.877634 + 0.479331i \(0.159120\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3.30308e10 −0.289877
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.48817e10 0.799153 0.399576 − 0.916700i \(-0.369157\pi\)
0.399576 + 0.916700i \(0.369157\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2.46049e11 1.98977 0.994885 − 0.101019i \(-0.0322102\pi\)
0.994885 + 0.101019i \(0.0322102\pi\)
\(594\) 0 0
\(595\) 6.46267e9 0.0515637
\(596\) −2.08606e11 −1.65326
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.18776e11 −0.886561
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −7.12711e10 −0.508052
\(613\) 1.59173e11 1.12727 0.563634 − 0.826025i \(-0.309403\pi\)
0.563634 + 0.826025i \(0.309403\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.50833e11 −1.04077 −0.520387 − 0.853930i \(-0.674212\pi\)
−0.520387 + 0.853930i \(0.674212\pi\)
\(618\) 0 0
\(619\) −1.85990e11 −1.26685 −0.633426 − 0.773803i \(-0.718352\pi\)
−0.633426 + 0.773803i \(0.718352\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 6.16875e10 0.404275
\(626\) 0 0
\(627\) 0 0
\(628\) 3.08556e11 1.98379
\(629\) 0 0
\(630\) 0 0
\(631\) −2.39197e11 −1.50882 −0.754412 − 0.656401i \(-0.772078\pi\)
−0.754412 + 0.656401i \(0.772078\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) −1.68552e11 −0.986030 −0.493015 − 0.870021i \(-0.664105\pi\)
−0.493015 + 0.870021i \(0.664105\pi\)
\(644\) −7.21399e10 −0.419403
\(645\) 0 0
\(646\) 0 0
\(647\) −3.20605e11 −1.82959 −0.914793 − 0.403923i \(-0.867646\pi\)
−0.914793 + 0.403923i \(0.867646\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −3.38989e11 −1.87584
\(653\) 1.43570e11 0.789605 0.394802 − 0.918766i \(-0.370813\pi\)
0.394802 + 0.918766i \(0.370813\pi\)
\(654\) 0 0
\(655\) 1.34952e11 0.733189
\(656\) 0 0
\(657\) 2.87796e11 1.54462
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.98483e10 −0.101493
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.41668e11 −2.17874
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 2.08827e11 1.00000
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 2.18889e11 1.00000
\(685\) −1.47345e10 −0.0669227
\(686\) 0 0
\(687\) 0 0
\(688\) 3.67141e11 1.63862
\(689\) 0 0
\(690\) 0 0
\(691\) 4.09506e11 1.79617 0.898086 − 0.439819i \(-0.144957\pi\)
0.898086 + 0.439819i \(0.144957\pi\)
\(692\) 0 0
\(693\) 8.64654e10 0.374895
\(694\) 0 0
\(695\) 2.15760e11 0.924765
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −4.14320e10 −0.172561
\(701\) −4.33309e11 −1.79443 −0.897213 − 0.441597i \(-0.854412\pi\)
−0.897213 + 0.441597i \(0.854412\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 4.19548e11 1.70801
\(705\) 0 0
\(706\) 0 0
\(707\) −5.70007e10 −0.228141
\(708\) 0 0
\(709\) 3.00992e10 0.119116 0.0595581 − 0.998225i \(-0.481031\pi\)
0.0595581 + 0.998225i \(0.481031\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −5.23144e11 −1.95752 −0.978758 − 0.205017i \(-0.934275\pi\)
−0.978758 + 0.205017i \(0.934275\pi\)
\(720\) −1.24265e11 −0.462400
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 5.43464e11 1.94551 0.972753 − 0.231842i \(-0.0744753\pi\)
0.972753 + 0.231842i \(0.0744753\pi\)
\(728\) 0 0
\(729\) 2.82430e11 1.00000
\(730\) 0 0
\(731\) −2.37715e11 −0.832506
\(732\) 0 0
\(733\) −2.87568e11 −0.996151 −0.498076 − 0.867134i \(-0.665960\pi\)
−0.498076 + 0.867134i \(0.665960\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 3.24050e10 0.108651 0.0543256 − 0.998523i \(-0.482699\pi\)
0.0543256 + 0.998523i \(0.482699\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 2.35496e11 0.764467
\(746\) 0 0
\(747\) −4.11224e11 −1.32067
\(748\) −2.71647e11 −0.867759
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) −5.44113e11 −1.70145
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −3.76005e11 −1.14501 −0.572506 − 0.819901i \(-0.694029\pi\)
−0.572506 + 0.819901i \(0.694029\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 5.40926e11 1.61287 0.806434 − 0.591324i \(-0.201394\pi\)
0.806434 + 0.591324i \(0.201394\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 3.77455e11 1.10788
\(765\) 8.04584e10 0.234923
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −6.96633e11 −1.99204 −0.996021 − 0.0891173i \(-0.971595\pi\)
−0.996021 + 0.0891173i \(0.971595\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −3.59601e11 −0.951823
\(785\) −3.48331e11 −0.917304
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 4.66042e11 1.20870
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −6.06895e11 −1.51168
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 3.52301e11 0.864423
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.09692e12 2.63824
\(804\) 0 0
\(805\) 8.14392e10 0.193932
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 6.52981e11 1.52443 0.762213 − 0.647326i \(-0.224113\pi\)
0.762213 + 0.647326i \(0.224113\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 3.82687e11 0.867388
\(816\) 0 0
\(817\) 7.30075e11 1.63862
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −9.08472e11 −1.99958 −0.999790 − 0.0204828i \(-0.993480\pi\)
−0.999790 + 0.0204828i \(0.993480\pi\)
\(822\) 0 0
\(823\) 2.80528e11 0.611472 0.305736 − 0.952116i \(-0.401098\pi\)
0.305736 + 0.952116i \(0.401098\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) −8.98121e11 −1.91079
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.32833e11 0.483576
\(834\) 0 0
\(835\) 0 0
\(836\) 8.34288e11 1.70801
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 5.00246e11 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −2.35746e11 −0.462400
\(846\) 0 0
\(847\) 2.16592e11 0.420833
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −9.03343e11 −1.70630 −0.853152 − 0.521662i \(-0.825312\pi\)
−0.853152 + 0.521662i \(0.825312\pi\)
\(854\) 0 0
\(855\) −2.47105e11 −0.462400
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −5.21495e11 −0.957807 −0.478903 − 0.877868i \(-0.658966\pi\)
−0.478903 + 0.877868i \(0.658966\pi\)
\(860\) −4.14468e11 −0.757699
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1.06266e11 0.181285
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) −4.73630e11 −0.789785
\(881\) 3.92725e11 0.651907 0.325953 − 0.945386i \(-0.394315\pi\)
0.325953 + 0.945386i \(0.394315\pi\)
\(882\) 0 0
\(883\) −4.72522e11 −0.777283 −0.388642 − 0.921389i \(-0.627056\pi\)
−0.388642 + 0.921389i \(0.627056\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 1.07647e12 1.70801
\(892\) 0 0
\(893\) −1.08199e12 −1.70145
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −5.15817e11 −0.786186
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) −7.09643e11 −1.03940
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) −1.56736e12 −2.25573
\(914\) 0 0
\(915\) 0 0
\(916\) 1.39253e12 1.97799
\(917\) −2.46090e11 −0.348030
\(918\) 0 0
\(919\) 5.77136e11 0.809126 0.404563 − 0.914510i \(-0.367424\pi\)
0.404563 + 0.914510i \(0.367424\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 2.36701e11 0.317788 0.158894 − 0.987296i \(-0.449207\pi\)
0.158894 + 0.987296i \(0.449207\pi\)
\(930\) 0 0
\(931\) −7.15081e11 −0.951823
\(932\) 1.45748e12 1.93170
\(933\) 0 0
\(934\) 0 0
\(935\) 3.06664e11 0.401252
\(936\) 0 0
\(937\) 1.16013e12 1.50505 0.752523 − 0.658566i \(-0.228837\pi\)
0.752523 + 0.658566i \(0.228837\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 6.14253e11 0.786749
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 8.10369e11 1.00759 0.503794 − 0.863824i \(-0.331937\pi\)
0.503794 + 0.863824i \(0.331937\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) −4.26112e11 −0.512283
\(956\) 4.47841e11 0.536157
\(957\) 0 0
\(958\) 0 0
\(959\) 2.68688e10 0.0317668
\(960\) 0 0
\(961\) 8.52891e11 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 3.05650e10 0.0349558 0.0174779 − 0.999847i \(-0.494436\pi\)
0.0174779 + 0.999847i \(0.494436\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) −3.93445e11 −0.438967
\(974\) 0 0
\(975\) 0 0
\(976\) −1.15748e12 −1.27560
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 4.05956e11 0.440123
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) −5.26117e11 −0.558905
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −2.99556e12 −3.13107
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 6.85128e11 0.699003
\(996\) 0 0
\(997\) 1.68196e12 1.70229 0.851147 − 0.524928i \(-0.175908\pi\)
0.851147 + 0.524928i \(0.175908\pi\)
\(998\) 0 0
\(999\) 0 0
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 19.9.b.a.18.1 ✓ 1
3.2 odd 2 171.9.c.a.37.1 1
4.3 odd 2 304.9.e.a.113.1 1
19.18 odd 2 CM 19.9.b.a.18.1 ✓ 1
57.56 even 2 171.9.c.a.37.1 1
76.75 even 2 304.9.e.a.113.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
19.9.b.a.18.1 ✓ 1 1.1 even 1 trivial
19.9.b.a.18.1 ✓ 1 19.18 odd 2 CM
171.9.c.a.37.1 1 3.2 odd 2
171.9.c.a.37.1 1 57.56 even 2
304.9.e.a.113.1 1 4.3 odd 2
304.9.e.a.113.1 1 76.75 even 2