Properties

Label 1083.1.b.a.362.1
Level $1083$
Weight $1$
Character 1083.362
Self dual yes
Analytic conductor $0.540$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -3
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] = [1083,1,Mod(362,1083)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1083, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1083.362");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1083 = 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1083.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: \(0.540487408682\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 57)
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.1083.1
Artin image: $D_6$
Artin field: Galois closure of 6.0.22284891.1

Embedding invariants

Embedding label 362.1
Character \(\chi\) \(=\) 1083.362

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{9} -1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{16} +1.00000 q^{21} +1.00000 q^{25} -1.00000 q^{27} -1.00000 q^{28} +1.00000 q^{31} +1.00000 q^{36} +1.00000 q^{37} -1.00000 q^{39} -1.00000 q^{43} -1.00000 q^{48} +1.00000 q^{52} -1.00000 q^{61} -1.00000 q^{63} +1.00000 q^{64} +1.00000 q^{67} -1.00000 q^{73} -1.00000 q^{75} +1.00000 q^{79} +1.00000 q^{81} +1.00000 q^{84} -1.00000 q^{91} -1.00000 q^{93} -2.00000 q^{97} +O(q^{100})\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1083\mathbb{Z}\right)^\times\).

\(n\) \(362\) \(724\)
\(\chi(n)\) \(-1\) \(1\)

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 \(\pi\)
\(3\) −1.00000 −1.00000
\(4\) 1.00000 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) 0 0
\(9\) 1.00000 1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) −1.00000 −1.00000
\(13\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0
\(20\) 0 0
\(21\) 1.00000 1.00000
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 1.00000 1.00000
\(26\) 0 0
\(27\) −1.00000 −1.00000
\(28\) −1.00000 −1.00000
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 1.00000
\(37\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) 0 0
\(39\) −1.00000 −1.00000
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −1.00000 −1.00000
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 1.00000 1.00000
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 0 0
\(63\) −1.00000 −1.00000
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) 0 0
\(75\) −1.00000 −1.00000
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(80\) 0 0
\(81\) 1.00000 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 1.00000 1.00000
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −1.00000 −1.00000
\(92\) 0 0
\(93\) −1.00000 −1.00000
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −1.00000 −1.00000
\(109\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) −1.00000 −1.00000
\(112\) −1.00000 −1.00000
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.00000 1.00000
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 1.00000 1.00000
\(125\) 0 0
\(126\) 0 0
\(127\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) 1.00000 1.00000
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 1.00000 1.00000
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −1.00000 −1.00000
\(157\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 0 0
\(172\) −1.00000 −1.00000
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) −1.00000 −1.00000
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 1.00000 1.00000
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 1.00000 1.00000
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −1.00000 −1.00000
\(193\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(200\) 0 0
\(201\) −1.00000 −1.00000
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 1.00000 1.00000
\(209\) 0 0
\(210\) 0 0
\(211\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −1.00000 −1.00000
\(218\) 0 0
\(219\) 1.00000 1.00000
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(224\) 0 0
\(225\) 1.00000 1.00000
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) 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
\(237\) −1.00000 −1.00000
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(242\) 0 0
\(243\) −1.00000 −1.00000
\(244\) −1.00000 −1.00000
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −1.00000 −1.00000
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −1.00000 −1.00000
\(260\) 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
\(268\) 1.00000 1.00000
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(272\) 0 0
\(273\) 1.00000 1.00000
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(278\) 0 0
\(279\) 1.00000 1.00000
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) 2.00000 2.00000
\(292\) −1.00000 −1.00000
\(293\) 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
\(300\) −1.00000 −1.00000
\(301\) 1.00000 1.00000
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) −1.00000 −1.00000
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(314\) 0 0
\(315\) 0 0
\(316\) 1.00000 1.00000
\(317\) 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
\(324\) 1.00000 1.00000
\(325\) 1.00000 1.00000
\(326\) 0 0
\(327\) 2.00000 2.00000
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) 0 0
\(333\) 1.00000 1.00000
\(334\) 0 0
\(335\) 0 0
\(336\) 1.00000 1.00000
\(337\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 0 0
\(351\) −1.00000 −1.00000
\(352\) 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
\(361\) 0 0
\(362\) 0 0
\(363\) −1.00000 −1.00000
\(364\) −1.00000 −1.00000
\(365\) 0 0
\(366\) 0 0
\(367\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −1.00000 −1.00000
\(373\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(380\) 0 0
\(381\) 2.00000 2.00000
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.00000 −1.00000
\(388\) −2.00000 −2.00000
\(389\) 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
\(397\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 1.00000 1.00000
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.00000 1.00000
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.00000 1.00000
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.00000 1.00000
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −1.00000 −1.00000
\(433\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2.00000 −2.00000
\(437\) 0 0
\(438\) 0 0
\(439\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) −1.00000 −1.00000
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −1.00000 −1.00000
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 2.00000 2.00000
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 1.00000 1.00000
\(469\) −1.00000 −1.00000
\(470\) 0 0
\(471\) 1.00000 1.00000
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 1.00000 1.00000
\(482\) 0 0
\(483\) 0 0
\(484\) 1.00000 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 1.00000 1.00000
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.00000 1.00000
\(497\) 0 0
\(498\) 0 0
\(499\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 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
\(507\) 0 0
\(508\) −2.00000 −2.00000
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 1.00000 1.00000
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 1.00000 1.00000
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(524\) 0 0
\(525\) 1.00000 1.00000
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) 0 0
\(543\) 2.00000 2.00000
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(548\) 0 0
\(549\) −1.00000 −1.00000
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −1.00000 −1.00000
\(554\) 0 0
\(555\) 0 0
\(556\) −1.00000 −1.00000
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) −1.00000 −1.00000
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −1.00000 −1.00000
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 1.00000
\(577\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(578\) 0 0
\(579\) −1.00000 −1.00000
\(580\) 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 \(\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1.00000 1.00000
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.00000 1.00000
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(602\) 0 0
\(603\) 1.00000 1.00000
\(604\) −2.00000 −2.00000
\(605\) 0 0
\(606\) 0 0
\(607\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −1.00000 −1.00000
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) −1.00000 −1.00000
\(629\) 0 0
\(630\) 0 0
\(631\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(632\) 0 0
\(633\) −1.00000 −1.00000
\(634\) 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
\(643\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(644\) 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
\(651\) 1.00000 1.00000
\(652\) −1.00000 −1.00000
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −1.00000 −1.00000
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −1.00000 −1.00000
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(674\) 0 0
\(675\) −1.00000 −1.00000
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 2.00000 2.00000
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 1.00000 1.00000
\(688\) −1.00000 −1.00000
\(689\) 0 0
\(690\) 0 0
\(691\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −1.00000 −1.00000
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) 0 0
\(711\) 1.00000 1.00000
\(712\) 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
\(721\) −1.00000 −1.00000
\(722\) 0 0
\(723\) −1.00000 −1.00000
\(724\) −2.00000 −2.00000
\(725\) 0 0
\(726\) 0 0
\(727\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 1.00000 1.00000
\(733\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 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
\(751\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.00000 1.00000
\(757\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 2.00000 2.00000
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −1.00000 −1.00000
\(769\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.00000 1.00000
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 1.00000 1.00000
\(776\) 0 0
\(777\) 1.00000 1.00000
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −1.00000 −1.00000
\(794\) 0 0
\(795\) 0 0
\(796\) −1.00000 −1.00000
\(797\) 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
\(804\) −1.00000 −1.00000
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) −2.00000 −2.00000
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) −1.00000 −1.00000
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(830\) 0 0
\(831\) −2.00000 −2.00000
\(832\) 1.00000 1.00000
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −1.00000 −1.00000
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 1.00000 1.00000
\(845\) 0 0
\(846\) 0 0
\(847\) −1.00000 −1.00000
\(848\) 0 0
\(849\) −2.00000 −2.00000
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(860\) 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
\(867\) −1.00000 −1.00000
\(868\) −1.00000 −1.00000
\(869\) 0 0
\(870\) 0 0
\(871\) 1.00000 1.00000
\(872\) 0 0
\(873\) −2.00000 −2.00000
\(874\) 0 0
\(875\) 0 0
\(876\) 1.00000 1.00000
\(877\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 2.00000 2.00000
\(890\) 0 0
\(891\) 0 0
\(892\) 1.00000 1.00000
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 1.00000 1.00000
\(901\) 0 0
\(902\) 0 0
\(903\) −1.00000 −1.00000
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −1.00000 −1.00000
\(917\) 0 0
\(918\) 0 0
\(919\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(920\) 0 0
\(921\) 2.00000 2.00000
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1.00000 1.00000
\(926\) 0 0
\(927\) 1.00000 1.00000
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(938\) 0 0
\(939\) −2.00000 −2.00000
\(940\) 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 \(\pi\)
\(948\) −1.00000 −1.00000
\(949\) −1.00000 −1.00000
\(950\) 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
\(961\) 0 0
\(962\) 0 0
\(963\) 0 0
\(964\) 1.00000 1.00000
\(965\) 0 0
\(966\) 0 0
\(967\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) −1.00000 −1.00000
\(973\) 1.00000 1.00000
\(974\) 0 0
\(975\) −1.00000 −1.00000
\(976\) −1.00000 −1.00000
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −2.00000 −2.00000
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(992\) 0 0
\(993\) −1.00000 −1.00000
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(998\) 0 0
\(999\) −1.00000 −1.00000
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 1083.1.b.a.362.1 1
3.2 odd 2 CM 1083.1.b.a.362.1 1
19.2 odd 18 1083.1.l.a.821.1 6
19.3 odd 18 1083.1.l.a.389.1 6
19.4 even 9 1083.1.l.b.776.1 6
19.5 even 9 1083.1.l.b.956.1 6
19.6 even 9 1083.1.l.b.245.1 6
19.7 even 3 1083.1.h.a.68.1 2
19.8 odd 6 57.1.h.a.26.1 yes 2
19.9 even 9 1083.1.l.b.62.1 6
19.10 odd 18 1083.1.l.a.62.1 6
19.11 even 3 1083.1.h.a.653.1 2
19.12 odd 6 57.1.h.a.11.1 2
19.13 odd 18 1083.1.l.a.245.1 6
19.14 odd 18 1083.1.l.a.956.1 6
19.15 odd 18 1083.1.l.a.776.1 6
19.16 even 9 1083.1.l.b.389.1 6
19.17 even 9 1083.1.l.b.821.1 6
19.18 odd 2 1083.1.b.b.362.1 1
57.2 even 18 1083.1.l.a.821.1 6
57.5 odd 18 1083.1.l.b.956.1 6
57.8 even 6 57.1.h.a.26.1 yes 2
57.11 odd 6 1083.1.h.a.653.1 2
57.14 even 18 1083.1.l.a.956.1 6
57.17 odd 18 1083.1.l.b.821.1 6
57.23 odd 18 1083.1.l.b.776.1 6
57.26 odd 6 1083.1.h.a.68.1 2
57.29 even 18 1083.1.l.a.62.1 6
57.32 even 18 1083.1.l.a.245.1 6
57.35 odd 18 1083.1.l.b.389.1 6
57.41 even 18 1083.1.l.a.389.1 6
57.44 odd 18 1083.1.l.b.245.1 6
57.47 odd 18 1083.1.l.b.62.1 6
57.50 even 6 57.1.h.a.11.1 2
57.53 even 18 1083.1.l.a.776.1 6
57.56 even 2 1083.1.b.b.362.1 1
76.27 even 6 912.1.bl.a.881.1 2
76.31 even 6 912.1.bl.a.353.1 2
95.8 even 12 1425.1.o.a.824.2 4
95.12 even 12 1425.1.o.a.524.2 4
95.27 even 12 1425.1.o.a.824.1 4
95.69 odd 6 1425.1.t.a.1151.1 2
95.84 odd 6 1425.1.t.a.26.1 2
95.88 even 12 1425.1.o.a.524.1 4
133.12 even 6 2793.1.n.b.410.1 2
133.27 even 6 2793.1.bf.a.197.1 2
133.31 even 6 2793.1.bi.a.1892.1 2
133.46 odd 6 2793.1.n.a.1451.1 2
133.65 odd 6 2793.1.bi.b.2762.1 2
133.69 even 6 2793.1.bf.a.638.1 2
133.88 odd 6 2793.1.bi.b.1892.1 2
133.103 even 6 2793.1.bi.a.2762.1 2
133.107 odd 6 2793.1.n.a.410.1 2
133.122 even 6 2793.1.n.b.1451.1 2
152.27 even 6 3648.1.bl.a.1793.1 2
152.69 odd 6 3648.1.bl.b.2177.1 2
152.107 even 6 3648.1.bl.a.2177.1 2
152.141 odd 6 3648.1.bl.b.1793.1 2
171.31 odd 6 1539.1.n.a.1322.1 2
171.50 even 6 1539.1.n.a.1322.1 2
171.65 even 6 1539.1.n.a.539.1 2
171.88 odd 6 1539.1.j.a.296.1 2
171.103 odd 6 1539.1.j.a.26.1 2
171.122 even 6 1539.1.j.a.26.1 2
171.160 odd 6 1539.1.n.a.539.1 2
171.164 even 6 1539.1.j.a.296.1 2
228.107 odd 6 912.1.bl.a.353.1 2
228.179 odd 6 912.1.bl.a.881.1 2
285.8 odd 12 1425.1.o.a.824.2 4
285.107 odd 12 1425.1.o.a.524.2 4
285.122 odd 12 1425.1.o.a.824.1 4
285.164 even 6 1425.1.t.a.1151.1 2
285.179 even 6 1425.1.t.a.26.1 2
285.278 odd 12 1425.1.o.a.524.1 4
399.65 even 6 2793.1.bi.b.2762.1 2
399.107 even 6 2793.1.n.a.410.1 2
399.122 odd 6 2793.1.n.b.1451.1 2
399.164 odd 6 2793.1.bi.a.1892.1 2
399.179 even 6 2793.1.n.a.1451.1 2
399.221 even 6 2793.1.bi.b.1892.1 2
399.236 odd 6 2793.1.bi.a.2762.1 2
399.278 odd 6 2793.1.n.b.410.1 2
399.293 odd 6 2793.1.bf.a.197.1 2
399.335 odd 6 2793.1.bf.a.638.1 2
456.107 odd 6 3648.1.bl.a.2177.1 2
456.179 odd 6 3648.1.bl.a.1793.1 2
456.221 even 6 3648.1.bl.b.2177.1 2
456.293 even 6 3648.1.bl.b.1793.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
57.1.h.a.11.1 2 19.12 odd 6
57.1.h.a.11.1 2 57.50 even 6
57.1.h.a.26.1 yes 2 19.8 odd 6
57.1.h.a.26.1 yes 2 57.8 even 6
912.1.bl.a.353.1 2 76.31 even 6
912.1.bl.a.353.1 2 228.107 odd 6
912.1.bl.a.881.1 2 76.27 even 6
912.1.bl.a.881.1 2 228.179 odd 6
1083.1.b.a.362.1 1 1.1 even 1 trivial
1083.1.b.a.362.1 1 3.2 odd 2 CM
1083.1.b.b.362.1 1 19.18 odd 2
1083.1.b.b.362.1 1 57.56 even 2
1083.1.h.a.68.1 2 19.7 even 3
1083.1.h.a.68.1 2 57.26 odd 6
1083.1.h.a.653.1 2 19.11 even 3
1083.1.h.a.653.1 2 57.11 odd 6
1083.1.l.a.62.1 6 19.10 odd 18
1083.1.l.a.62.1 6 57.29 even 18
1083.1.l.a.245.1 6 19.13 odd 18
1083.1.l.a.245.1 6 57.32 even 18
1083.1.l.a.389.1 6 19.3 odd 18
1083.1.l.a.389.1 6 57.41 even 18
1083.1.l.a.776.1 6 19.15 odd 18
1083.1.l.a.776.1 6 57.53 even 18
1083.1.l.a.821.1 6 19.2 odd 18
1083.1.l.a.821.1 6 57.2 even 18
1083.1.l.a.956.1 6 19.14 odd 18
1083.1.l.a.956.1 6 57.14 even 18
1083.1.l.b.62.1 6 19.9 even 9
1083.1.l.b.62.1 6 57.47 odd 18
1083.1.l.b.245.1 6 19.6 even 9
1083.1.l.b.245.1 6 57.44 odd 18
1083.1.l.b.389.1 6 19.16 even 9
1083.1.l.b.389.1 6 57.35 odd 18
1083.1.l.b.776.1 6 19.4 even 9
1083.1.l.b.776.1 6 57.23 odd 18
1083.1.l.b.821.1 6 19.17 even 9
1083.1.l.b.821.1 6 57.17 odd 18
1083.1.l.b.956.1 6 19.5 even 9
1083.1.l.b.956.1 6 57.5 odd 18
1425.1.o.a.524.1 4 95.88 even 12
1425.1.o.a.524.1 4 285.278 odd 12
1425.1.o.a.524.2 4 95.12 even 12
1425.1.o.a.524.2 4 285.107 odd 12
1425.1.o.a.824.1 4 95.27 even 12
1425.1.o.a.824.1 4 285.122 odd 12
1425.1.o.a.824.2 4 95.8 even 12
1425.1.o.a.824.2 4 285.8 odd 12
1425.1.t.a.26.1 2 95.84 odd 6
1425.1.t.a.26.1 2 285.179 even 6
1425.1.t.a.1151.1 2 95.69 odd 6
1425.1.t.a.1151.1 2 285.164 even 6
1539.1.j.a.26.1 2 171.103 odd 6
1539.1.j.a.26.1 2 171.122 even 6
1539.1.j.a.296.1 2 171.88 odd 6
1539.1.j.a.296.1 2 171.164 even 6
1539.1.n.a.539.1 2 171.65 even 6
1539.1.n.a.539.1 2 171.160 odd 6
1539.1.n.a.1322.1 2 171.31 odd 6
1539.1.n.a.1322.1 2 171.50 even 6
2793.1.n.a.410.1 2 133.107 odd 6
2793.1.n.a.410.1 2 399.107 even 6
2793.1.n.a.1451.1 2 133.46 odd 6
2793.1.n.a.1451.1 2 399.179 even 6
2793.1.n.b.410.1 2 133.12 even 6
2793.1.n.b.410.1 2 399.278 odd 6
2793.1.n.b.1451.1 2 133.122 even 6
2793.1.n.b.1451.1 2 399.122 odd 6
2793.1.bf.a.197.1 2 133.27 even 6
2793.1.bf.a.197.1 2 399.293 odd 6
2793.1.bf.a.638.1 2 133.69 even 6
2793.1.bf.a.638.1 2 399.335 odd 6
2793.1.bi.a.1892.1 2 133.31 even 6
2793.1.bi.a.1892.1 2 399.164 odd 6
2793.1.bi.a.2762.1 2 133.103 even 6
2793.1.bi.a.2762.1 2 399.236 odd 6
2793.1.bi.b.1892.1 2 133.88 odd 6
2793.1.bi.b.1892.1 2 399.221 even 6
2793.1.bi.b.2762.1 2 133.65 odd 6
2793.1.bi.b.2762.1 2 399.65 even 6
3648.1.bl.a.1793.1 2 152.27 even 6
3648.1.bl.a.1793.1 2 456.179 odd 6
3648.1.bl.a.2177.1 2 152.107 even 6
3648.1.bl.a.2177.1 2 456.107 odd 6
3648.1.bl.b.1793.1 2 152.141 odd 6
3648.1.bl.b.1793.1 2 456.293 even 6
3648.1.bl.b.2177.1 2 152.69 odd 6
3648.1.bl.b.2177.1 2 456.221 even 6