↑

Properties

Label 3776.1.h.a.2241.1
Level $3776$
Weight $1$
Character 3776.2241
Self dual yes
Analytic conductor $1.884$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -59
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3776,1,Mod(2241,3776)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3776, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3776.2241");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3776 = 2^{6} \cdot 59 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3776.h (of order \(2\), degree \(1\), not 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: \(1.88446948770\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 59)
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.59.1
Artin image: $D_6$
Artin field: Galois closure of 6.0.1782272.1

Embedding invariants

Embedding label 2241.1
Character \(\chi\) \(=\) 3776.2241

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q-1.00000 q^{3} +1.00000 q^{5} +1.00000 q^{7} -1.00000 q^{15} +2.00000 q^{17} -1.00000 q^{19} -1.00000 q^{21} +1.00000 q^{27} +1.00000 q^{29} +1.00000 q^{35} -1.00000 q^{41} -2.00000 q^{51} +1.00000 q^{53} +1.00000 q^{57} +1.00000 q^{59} -2.00000 q^{71} +1.00000 q^{79} -1.00000 q^{81} +2.00000 q^{85} -1.00000 q^{87} -1.00000 q^{95} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3776\mathbb{Z}\right)^\times\).

\(n\) \(709\) \(769\) \(1535\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(3\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(4\) 0 0
\(5\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(6\) 0 0
\(7\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) −1.00000 −1.00000
\(16\) 0 0
\(17\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(18\) 0 0
\(19\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(20\) 0 0
\(21\) −1.00000 −1.00000
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000 1.00000
\(28\) 0 0
\(29\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.00000 1.00000
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −2.00000 −2.00000
\(52\) 0 0
\(53\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.00000 1.00000
\(58\) 0 0
\(59\) 1.00000 1.00000
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 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 \(\pi\)
\(84\) 0 0
\(85\) 2.00000 2.00000
\(86\) 0 0
\(87\) −1.00000 −1.00000
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.00000 −1.00000
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) −1.00000 −1.00000
\(106\) 0 0
\(107\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.00000 2.00000
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) 1.00000 1.00000
\(124\) 0 0
\(125\) −1.00000 −1.00000
\(126\) 0 0
\(127\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) −1.00000 −1.00000
\(134\) 0 0
\(135\) 1.00000 1.00000
\(136\) 0 0
\(137\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 0 0
\(139\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 1.00000 1.00000
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) −1.00000 −1.00000
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(168\) 0 0
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1.00000 −1.00000
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 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 \(\pi\)
\(192\) 0 0
\(193\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.00000 1.00000
\(204\) 0 0
\(205\) −1.00000 −1.00000
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 2.00000 2.00000
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 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
\(239\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0 0
\(241\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −2.00000 −2.00000
\(256\) 0 0
\(257\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) 0 0
\(265\) 1.00000 1.00000
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 1.00000 1.00000
\(286\) 0 0
\(287\) −1.00000 −1.00000
\(288\) 0 0
\(289\) 3.00000 3.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(294\) 0 0
\(295\) 1.00000 1.00000
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 1.00000 1.00000
\(322\) 0 0
\(323\) −2.00000 −2.00000
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 0 0
\(333\) 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
\(340\) 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
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) −2.00000 −2.00000
\(356\) 0 0
\(357\) −2.00000 −2.00000
\(358\) 0 0
\(359\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) −1.00000 −1.00000
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.00000 1.00000
\(372\) 0 0
\(373\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 1.00000 1.00000
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(380\) 0 0
\(381\) −1.00000 −1.00000
\(382\) 0 0
\(383\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.00000 1.00000
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 1.00000 1.00000
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −1.00000 −1.00000
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 1.00000 1.00000
\(412\) 0 0
\(413\) 1.00000 1.00000
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −2.00000 −2.00000
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(434\) 0 0
\(435\) −1.00000 −1.00000
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 2.00000 2.00000
\(460\) 0 0
\(461\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(488\) 0 0
\(489\) −2.00000 −2.00000
\(490\) 0 0
\(491\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(492\) 0 0
\(493\) 2.00000 2.00000
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.00000 −2.00000
\(498\) 0 0
\(499\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0 0
\(501\) −1.00000 −1.00000
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −1.00000
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −1.00000 −1.00000
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(522\) 0 0
\(523\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 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
\(535\) −1.00000 −1.00000
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −1.00000 −1.00000
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.00000 −1.00000
\(552\) 0 0
\(553\) 1.00000 1.00000
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 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
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(578\) 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
\(591\) 2.00000 2.00000
\(592\) 0 0
\(593\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(594\) 0 0
\(595\) 2.00000 2.00000
\(596\) 0 0
\(597\) −1.00000 −1.00000
\(598\) 0 0
\(599\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.00000 1.00000
\(606\) 0 0
\(607\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(608\) 0 0
\(609\) −1.00000 −1.00000
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 1.00000 1.00000
\(616\) 0 0
\(617\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(618\) 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
\(624\) 0 0
\(625\) −1.00000 −1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.00000 1.00000
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(642\) 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
\(647\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.00000 −1.00000
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 2.00000 2.00000
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −2.00000 −2.00000 −1.00000 \(\pi\)
−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 \(\pi\)
\(684\) 0 0
\(685\) −1.00000 −1.00000
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.00000 2.00000
\(696\) 0 0
\(697\) −2.00000 −2.00000
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 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 \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −1.00000 −1.00000
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 1.00000 1.00000
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.00000 −1.00000
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 1.00000 1.00000
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 1.00000 1.00000
\(772\) 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
\(779\) 1.00000 1.00000
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 1.00000 1.00000
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(788\) 0 0
\(789\) −1.00000 −1.00000
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −1.00000 −1.00000
\(796\) 0 0
\(797\) 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
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) −1.00000 −1.00000
\(814\) 0 0
\(815\) 2.00000 2.00000
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(828\) 0 0
\(829\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(830\) 0 0
\(831\) −1.00000 −1.00000
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 1.00000 1.00000
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 0 0
\(842\) 0 0
\(843\) 1.00000 1.00000
\(844\) 0 0
\(845\) 1.00000 1.00000
\(846\) 0 0
\(847\) 1.00000 1.00000
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 1.00000 1.00000
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −3.00000 −3.00000
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.00000 −1.00000
\(876\) 0 0
\(877\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(878\) 0 0
\(879\) −1.00000 −1.00000
\(880\) 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
\(885\) −1.00000 −1.00000
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 1.00000 1.00000
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 2.00000 2.00000
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1.00000 1.00000
\(906\) 0 0
\(907\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 1.00000 1.00000
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −1.00000 −1.00000
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 1.00000 1.00000
\(946\) 0 0
\(947\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 2.00000 2.00000
\(952\) 0 0
\(953\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.00000 −1.00000
\(960\) 0 0
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1.00000 −1.00000
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0 0
\(969\) 2.00000 2.00000
\(970\) 0 0
\(971\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(972\) 0 0
\(973\) 2.00000 2.00000
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) −2.00000 −2.00000
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 1.00000 1.00000
\(994\) 0 0
\(995\) 1.00000 1.00000
\(996\) 0 0
\(997\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(998\) 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 3776.1.h.a.2241.1 1
4.3 odd 2 3776.1.h.b.2241.1 1
8.3 odd 2 59.1.b.a.58.1 ✓ 1
8.5 even 2 944.1.h.a.353.1 1
24.11 even 2 531.1.c.a.235.1 1
40.3 even 4 1475.1.d.a.1474.1 2
40.19 odd 2 1475.1.c.b.176.1 1
40.27 even 4 1475.1.d.a.1474.2 2
56.3 even 6 2891.1.g.b.471.1 2
56.11 odd 6 2891.1.g.d.471.1 2
56.19 even 6 2891.1.g.b.2713.1 2
56.27 even 2 2891.1.c.e.589.1 1
56.51 odd 6 2891.1.g.d.2713.1 2
59.58 odd 2 CM 3776.1.h.a.2241.1 1
236.235 even 2 3776.1.h.b.2241.1 1
472.3 odd 58 3481.1.d.a.1702.1 28
472.11 even 58 3481.1.d.a.3183.1 28
472.19 odd 58 3481.1.d.a.2117.1 28
472.27 odd 58 3481.1.d.a.805.1 28
472.35 odd 58 3481.1.d.a.2374.1 28
472.43 even 58 3481.1.d.a.806.1 28
472.51 odd 58 3481.1.d.a.3181.1 28
472.67 even 58 3481.1.d.a.3181.1 28
472.75 odd 58 3481.1.d.a.806.1 28
472.83 even 58 3481.1.d.a.2374.1 28
472.91 even 58 3481.1.d.a.805.1 28
472.99 even 58 3481.1.d.a.2117.1 28
472.107 odd 58 3481.1.d.a.3183.1 28
472.115 even 58 3481.1.d.a.1702.1 28
472.117 odd 2 944.1.h.a.353.1 1
472.123 odd 58 3481.1.d.a.506.1 28
472.131 even 58 3481.1.d.a.893.1 28
472.139 odd 58 3481.1.d.a.2922.1 28
472.147 odd 58 3481.1.d.a.1106.1 28
472.155 even 58 3481.1.d.a.1404.1 28
472.163 odd 58 3481.1.d.a.3344.1 28
472.171 odd 58 3481.1.d.a.672.1 28
472.179 even 58 3481.1.d.a.3182.1 28
472.187 even 58 3481.1.d.a.1611.1 28
472.195 even 58 3481.1.d.a.1505.1 28
472.203 odd 58 3481.1.d.a.2451.1 28
472.211 even 58 3481.1.d.a.1558.1 28
472.219 even 58 3481.1.d.a.3428.1 28
472.227 even 58 3481.1.d.a.2869.1 28
472.235 even 2 59.1.b.a.58.1 ✓ 1
472.243 odd 58 3481.1.d.a.1839.1 28
472.251 odd 58 3481.1.d.a.2076.1 28
472.259 even 58 3481.1.d.a.946.1 28
472.267 even 58 3481.1.d.a.809.1 28
472.275 even 58 3481.1.d.a.1311.1 28
472.283 even 58 3481.1.d.a.2511.1 28
472.291 even 58 3481.1.d.a.1105.1 28
472.299 odd 58 3481.1.d.a.1105.1 28
472.307 odd 58 3481.1.d.a.2511.1 28
472.315 odd 58 3481.1.d.a.1311.1 28
472.323 odd 58 3481.1.d.a.809.1 28
472.331 odd 58 3481.1.d.a.946.1 28
472.339 even 58 3481.1.d.a.2076.1 28
472.347 even 58 3481.1.d.a.1839.1 28
472.363 odd 58 3481.1.d.a.2869.1 28
472.371 odd 58 3481.1.d.a.3428.1 28
472.379 odd 58 3481.1.d.a.1558.1 28
472.387 even 58 3481.1.d.a.2451.1 28
472.395 odd 58 3481.1.d.a.1505.1 28
472.403 odd 58 3481.1.d.a.1611.1 28
472.411 odd 58 3481.1.d.a.3182.1 28
472.419 even 58 3481.1.d.a.672.1 28
472.427 even 58 3481.1.d.a.3344.1 28
472.435 odd 58 3481.1.d.a.1404.1 28
472.443 even 58 3481.1.d.a.1106.1 28
472.451 even 58 3481.1.d.a.2922.1 28
472.459 odd 58 3481.1.d.a.893.1 28
472.467 even 58 3481.1.d.a.506.1 28
1416.707 odd 2 531.1.c.a.235.1 1
2360.707 odd 4 1475.1.d.a.1474.2 2
2360.1179 even 2 1475.1.c.b.176.1 1
2360.2123 odd 4 1475.1.d.a.1474.1 2
3304.235 even 6 2891.1.g.d.471.1 2
3304.1179 odd 6 2891.1.g.b.471.1 2
3304.1651 odd 2 2891.1.c.e.589.1 1
3304.2123 even 6 2891.1.g.d.2713.1 2
3304.2595 odd 6 2891.1.g.b.2713.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
59.1.b.a.58.1 ✓ 1 8.3 odd 2
59.1.b.a.58.1 ✓ 1 472.235 even 2
531.1.c.a.235.1 1 24.11 even 2
531.1.c.a.235.1 1 1416.707 odd 2
944.1.h.a.353.1 1 8.5 even 2
944.1.h.a.353.1 1 472.117 odd 2
1475.1.c.b.176.1 1 40.19 odd 2
1475.1.c.b.176.1 1 2360.1179 even 2
1475.1.d.a.1474.1 2 40.3 even 4
1475.1.d.a.1474.1 2 2360.2123 odd 4
1475.1.d.a.1474.2 2 40.27 even 4
1475.1.d.a.1474.2 2 2360.707 odd 4
2891.1.c.e.589.1 1 56.27 even 2
2891.1.c.e.589.1 1 3304.1651 odd 2
2891.1.g.b.471.1 2 56.3 even 6
2891.1.g.b.471.1 2 3304.1179 odd 6
2891.1.g.b.2713.1 2 56.19 even 6
2891.1.g.b.2713.1 2 3304.2595 odd 6
2891.1.g.d.471.1 2 56.11 odd 6
2891.1.g.d.471.1 2 3304.235 even 6
2891.1.g.d.2713.1 2 56.51 odd 6
2891.1.g.d.2713.1 2 3304.2123 even 6
3481.1.d.a.506.1 28 472.123 odd 58
3481.1.d.a.506.1 28 472.467 even 58
3481.1.d.a.672.1 28 472.171 odd 58
3481.1.d.a.672.1 28 472.419 even 58
3481.1.d.a.805.1 28 472.27 odd 58
3481.1.d.a.805.1 28 472.91 even 58
3481.1.d.a.806.1 28 472.43 even 58
3481.1.d.a.806.1 28 472.75 odd 58
3481.1.d.a.809.1 28 472.267 even 58
3481.1.d.a.809.1 28 472.323 odd 58
3481.1.d.a.893.1 28 472.131 even 58
3481.1.d.a.893.1 28 472.459 odd 58
3481.1.d.a.946.1 28 472.259 even 58
3481.1.d.a.946.1 28 472.331 odd 58
3481.1.d.a.1105.1 28 472.291 even 58
3481.1.d.a.1105.1 28 472.299 odd 58
3481.1.d.a.1106.1 28 472.147 odd 58
3481.1.d.a.1106.1 28 472.443 even 58
3481.1.d.a.1311.1 28 472.275 even 58
3481.1.d.a.1311.1 28 472.315 odd 58
3481.1.d.a.1404.1 28 472.155 even 58
3481.1.d.a.1404.1 28 472.435 odd 58
3481.1.d.a.1505.1 28 472.195 even 58
3481.1.d.a.1505.1 28 472.395 odd 58
3481.1.d.a.1558.1 28 472.211 even 58
3481.1.d.a.1558.1 28 472.379 odd 58
3481.1.d.a.1611.1 28 472.187 even 58
3481.1.d.a.1611.1 28 472.403 odd 58
3481.1.d.a.1702.1 28 472.3 odd 58
3481.1.d.a.1702.1 28 472.115 even 58
3481.1.d.a.1839.1 28 472.243 odd 58
3481.1.d.a.1839.1 28 472.347 even 58
3481.1.d.a.2076.1 28 472.251 odd 58
3481.1.d.a.2076.1 28 472.339 even 58
3481.1.d.a.2117.1 28 472.19 odd 58
3481.1.d.a.2117.1 28 472.99 even 58
3481.1.d.a.2374.1 28 472.35 odd 58
3481.1.d.a.2374.1 28 472.83 even 58
3481.1.d.a.2451.1 28 472.203 odd 58
3481.1.d.a.2451.1 28 472.387 even 58
3481.1.d.a.2511.1 28 472.283 even 58
3481.1.d.a.2511.1 28 472.307 odd 58
3481.1.d.a.2869.1 28 472.227 even 58
3481.1.d.a.2869.1 28 472.363 odd 58
3481.1.d.a.2922.1 28 472.139 odd 58
3481.1.d.a.2922.1 28 472.451 even 58
3481.1.d.a.3181.1 28 472.51 odd 58
3481.1.d.a.3181.1 28 472.67 even 58
3481.1.d.a.3182.1 28 472.179 even 58
3481.1.d.a.3182.1 28 472.411 odd 58
3481.1.d.a.3183.1 28 472.11 even 58
3481.1.d.a.3183.1 28 472.107 odd 58
3481.1.d.a.3344.1 28 472.163 odd 58
3481.1.d.a.3344.1 28 472.427 even 58
3481.1.d.a.3428.1 28 472.219 even 58
3481.1.d.a.3428.1 28 472.371 odd 58
3776.1.h.a.2241.1 1 1.1 even 1 trivial
3776.1.h.a.2241.1 1 59.58 odd 2 CM
3776.1.h.b.2241.1 1 4.3 odd 2
3776.1.h.b.2241.1 1 236.235 even 2