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Properties

Label 1475.1.c.b.176.1
Level $1475$
Weight $1$
Character 1475.176
Self dual yes
Analytic conductor $0.736$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -59
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] = [1475,1,Mod(176,1475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1475, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1475.176");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1475 = 5^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1475.c (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: \(0.736120893634\)
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 6.2.435125.1

Embedding invariants

Embedding label 176.1
Character \(\chi\) \(=\) 1475.176

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{7} +O(q^{10})\) \(q+1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{12} +1.00000 q^{16} -2.00000 q^{17} -1.00000 q^{19} +1.00000 q^{21} -1.00000 q^{27} +1.00000 q^{28} -1.00000 q^{29} -1.00000 q^{41} +1.00000 q^{48} -2.00000 q^{51} +1.00000 q^{53} -1.00000 q^{57} +1.00000 q^{59} +1.00000 q^{64} -2.00000 q^{68} +2.00000 q^{71} -1.00000 q^{76} -1.00000 q^{79} -1.00000 q^{81} +1.00000 q^{84} -1.00000 q^{87} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1475\mathbb{Z}\right)^\times\).

\(n\) \(651\) \(827\)
\(\chi(n)\) \(-1\) \(1\)

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 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(4\) 1.00000 1.00000
\(5\) 0 0
\(6\) 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 \(\pi\)
\(12\) 1.00000 1.00000
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(18\) 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
\(28\) 1.00000 1.00000
\(29\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 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 \(\pi\)
\(48\) 1.00000 1.00000
\(49\) 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
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −2.00000 −2.00000
\(69\) 0 0
\(70\) 0 0
\(71\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −1.00000 −1.00000
\(77\) 0 0
\(78\) 0 0
\(79\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(80\) 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
\(87\) −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
\(95\) 0 0
\(96\) 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
\(105\) 0 0
\(106\) 0 0
\(107\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(108\) −1.00000 −1.00000
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.00000 1.00000
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.00000 −1.00000
\(117\) 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
\(125\) 0 0
\(126\) 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
\(135\) 0 0
\(136\) 0 0
\(137\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(138\) 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
\(145\) 0 0
\(146\) 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 \(\pi\)
−1.00000 \(\pi\)
\(164\) −1.00000 −1.00000
\(165\) 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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(182\) 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 \(\pi\)
\(192\) 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
\(197\) −2.00000 −2.00000 −1.00000 \(\pi\)
−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
\(201\) 0 0
\(202\) 0 0
\(203\) −1.00000 −1.00000
\(204\) −2.00000 −2.00000
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 1.00000 1.00000
\(213\) 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 \(\pi\)
\(228\) −1.00000 −1.00000
\(229\) 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
\(236\) 1.00000 1.00000
\(237\) −1.00000 −1.00000
\(238\) 0 0
\(239\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) 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
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(258\) 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
\(265\) 0 0
\(266\) 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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) −2.00000 −2.00000
\(273\) 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 \(\pi\)
\(284\) 2.00000 2.00000
\(285\) 0 0
\(286\) 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
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −1.00000 −1.00000
\(305\) 0 0
\(306\) 0 0
\(307\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −1.00000 −1.00000
\(317\) −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
\(324\) −1.00000 −1.00000
\(325\) 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
\(336\) 1.00000 1.00000
\(337\) 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 \(\pi\)
\(348\) −1.00000 −1.00000
\(349\) 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
\(355\) 0 0
\(356\) 0 0
\(357\) −2.00000 −2.00000
\(358\) 0 0
\(359\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(360\) 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
\(375\) 0 0
\(376\) 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 \(0\)
1.00000 \(0\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 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
\(405\) 0 0
\(406\) 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
\(428\) 1.00000 1.00000
\(429\) 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
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(440\) 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
\(448\) 1.00000 1.00000
\(449\) −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 \(0\)
1.00000 \(0\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) −1.00000 −1.00000
\(465\) 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
\(476\) −2.00000 −2.00000
\(477\) 0 0
\(478\) 0 0
\(479\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1.00000 1.00000
\(485\) 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 \(0.666667\pi\)
\(492\) −1.00000 −1.00000
\(493\) 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
\(508\) 1.00000 1.00000
\(509\) 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 \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(524\) 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
\(532\) −1.00000 −1.00000
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 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 \(\pi\)
−1.00000 \(\pi\)
\(548\) 1.00000 1.00000
\(549\) 0 0
\(550\) 0 0
\(551\) 1.00000 1.00000
\(552\) 0 0
\(553\) −1.00000 −1.00000
\(554\) 0 0
\(555\) 0 0
\(556\) 2.00000 2.00000
\(557\) 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 \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(578\) 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 \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −1.00000 −1.00000
\(598\) 0 0
\(599\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 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
\(609\) −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
\(615\) 0 0
\(616\) 0 0
\(617\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(618\) 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
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 1.00000 1.00000
\(637\) 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 \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(644\) 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
\(652\) −2.00000 −2.00000
\(653\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.00000 −1.00000
\(657\) 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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 1.00000 1.00000
\(669\) −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
\(676\) 1.00000 1.00000
\(677\) −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
\(685\) 0 0
\(686\) 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
\(695\) 0 0
\(696\) 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
\(708\) 1.00000 1.00000
\(709\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) 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
\(724\) −1.00000 −1.00000
\(725\) 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
\(756\) −1.00000 −1.00000
\(757\) 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
\(768\) 1.00000 1.00000
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 1.00000 1.00000
\(772\) 1.00000 1.00000
\(773\) 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 \(\pi\)
−1.00000 \(\pi\)
\(788\) −2.00000 −2.00000
\(789\) 1.00000 1.00000
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 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
\(804\) 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 \(\pi\)
\(812\) −1.00000 −1.00000
\(813\) −1.00000 −1.00000
\(814\) 0 0
\(815\) 0 0
\(816\) −2.00000 −2.00000
\(817\) 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 \(\pi\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) 0 0
\(831\) 1.00000 1.00000
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 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
\(845\) 0 0
\(846\) 0 0
\(847\) 1.00000 1.00000
\(848\) 1.00000 1.00000
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 2.00000 2.00000
\(853\) 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
\(875\) 0 0
\(876\) 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 \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 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
\(892\) −2.00000 −2.00000
\(893\) 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
\(905\) 0 0
\(906\) 0 0
\(907\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(912\) −1.00000 −1.00000
\(913\) 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
\(944\) 1.00000 1.00000
\(945\) 0 0
\(946\) 0 0
\(947\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(948\) −1.00000 −1.00000
\(949\) 0 0
\(950\) 0 0
\(951\) −2.00000 −2.00000
\(952\) 0 0
\(953\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −1.00000 −1.00000
\(957\) 0 0
\(958\) 0 0
\(959\) 1.00000 1.00000
\(960\) 0 0
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) −1.00000 −1.00000
\(965\) 0 0
\(966\) 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
\(985\) 0 0
\(986\) 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
\(995\) 0 0
\(996\) 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 1475.1.c.b.176.1 1
5.2 odd 4 1475.1.d.a.1474.1 2
5.3 odd 4 1475.1.d.a.1474.2 2
5.4 even 2 59.1.b.a.58.1 ✓ 1
15.14 odd 2 531.1.c.a.235.1 1
20.19 odd 2 944.1.h.a.353.1 1
35.4 even 6 2891.1.g.d.471.1 2
35.9 even 6 2891.1.g.d.2713.1 2
35.19 odd 6 2891.1.g.b.2713.1 2
35.24 odd 6 2891.1.g.b.471.1 2
35.34 odd 2 2891.1.c.e.589.1 1
40.19 odd 2 3776.1.h.a.2241.1 1
40.29 even 2 3776.1.h.b.2241.1 1
59.58 odd 2 CM 1475.1.c.b.176.1 1
295.4 even 58 3481.1.d.a.1105.1 28
295.9 even 58 3481.1.d.a.2869.1 28
295.14 odd 58 3481.1.d.a.3344.1 28
295.19 even 58 3481.1.d.a.2117.1 28
295.24 odd 58 3481.1.d.a.2374.1 28
295.29 even 58 3481.1.d.a.1106.1 28
295.34 odd 58 3481.1.d.a.1558.1 28
295.39 odd 58 3481.1.d.a.1311.1 28
295.44 odd 58 3481.1.d.a.2076.1 28
295.49 even 58 3481.1.d.a.1611.1 28
295.54 odd 58 3481.1.d.a.506.1 28
295.58 even 4 1475.1.d.a.1474.2 2
295.64 even 58 3481.1.d.a.506.1 28
295.69 odd 58 3481.1.d.a.1611.1 28
295.74 even 58 3481.1.d.a.2076.1 28
295.79 even 58 3481.1.d.a.1311.1 28
295.84 even 58 3481.1.d.a.1558.1 28
295.89 odd 58 3481.1.d.a.1106.1 28
295.94 even 58 3481.1.d.a.2374.1 28
295.99 odd 58 3481.1.d.a.2117.1 28
295.104 even 58 3481.1.d.a.3344.1 28
295.109 odd 58 3481.1.d.a.2869.1 28
295.114 odd 58 3481.1.d.a.1105.1 28
295.117 even 4 1475.1.d.a.1474.1 2
295.124 odd 58 3481.1.d.a.672.1 28
295.129 odd 58 3481.1.d.a.3183.1 28
295.134 even 58 3481.1.d.a.806.1 28
295.139 even 58 3481.1.d.a.2922.1 28
295.144 even 58 3481.1.d.a.2451.1 28
295.149 odd 58 3481.1.d.a.809.1 28
295.154 even 58 3481.1.d.a.946.1 28
295.159 even 58 3481.1.d.a.1505.1 28
295.164 even 58 3481.1.d.a.893.1 28
295.169 even 58 3481.1.d.a.3181.1 28
295.174 odd 58 3481.1.d.a.1702.1 28
295.179 odd 58 3481.1.d.a.3182.1 28
295.184 even 58 3481.1.d.a.1839.1 28
295.189 even 58 3481.1.d.a.2511.1 28
295.194 even 58 3481.1.d.a.3428.1 28
295.199 even 58 3481.1.d.a.1404.1 28
295.204 even 58 3481.1.d.a.805.1 28
295.209 odd 58 3481.1.d.a.805.1 28
295.214 odd 58 3481.1.d.a.1404.1 28
295.219 odd 58 3481.1.d.a.3428.1 28
295.224 odd 58 3481.1.d.a.2511.1 28
295.229 odd 58 3481.1.d.a.1839.1 28
295.234 even 58 3481.1.d.a.3182.1 28
295.239 even 58 3481.1.d.a.1702.1 28
295.244 odd 58 3481.1.d.a.3181.1 28
295.249 odd 58 3481.1.d.a.893.1 28
295.254 odd 58 3481.1.d.a.1505.1 28
295.259 odd 58 3481.1.d.a.946.1 28
295.264 even 58 3481.1.d.a.809.1 28
295.269 odd 58 3481.1.d.a.2451.1 28
295.274 odd 58 3481.1.d.a.2922.1 28
295.279 odd 58 3481.1.d.a.806.1 28
295.284 even 58 3481.1.d.a.3183.1 28
295.289 even 58 3481.1.d.a.672.1 28
295.294 odd 2 59.1.b.a.58.1 ✓ 1
885.884 even 2 531.1.c.a.235.1 1
1180.1179 even 2 944.1.h.a.353.1 1
2065.884 odd 6 2891.1.g.d.2713.1 2
2065.1179 even 6 2891.1.g.b.471.1 2
2065.1474 odd 6 2891.1.g.d.471.1 2
2065.1769 even 6 2891.1.g.b.2713.1 2
2065.2064 even 2 2891.1.c.e.589.1 1
2360.589 odd 2 3776.1.h.b.2241.1 1
2360.1179 even 2 3776.1.h.a.2241.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
59.1.b.a.58.1 ✓ 1 5.4 even 2
59.1.b.a.58.1 ✓ 1 295.294 odd 2
531.1.c.a.235.1 1 15.14 odd 2
531.1.c.a.235.1 1 885.884 even 2
944.1.h.a.353.1 1 20.19 odd 2
944.1.h.a.353.1 1 1180.1179 even 2
1475.1.c.b.176.1 1 1.1 even 1 trivial
1475.1.c.b.176.1 1 59.58 odd 2 CM
1475.1.d.a.1474.1 2 5.2 odd 4
1475.1.d.a.1474.1 2 295.117 even 4
1475.1.d.a.1474.2 2 5.3 odd 4
1475.1.d.a.1474.2 2 295.58 even 4
2891.1.c.e.589.1 1 35.34 odd 2
2891.1.c.e.589.1 1 2065.2064 even 2
2891.1.g.b.471.1 2 35.24 odd 6
2891.1.g.b.471.1 2 2065.1179 even 6
2891.1.g.b.2713.1 2 35.19 odd 6
2891.1.g.b.2713.1 2 2065.1769 even 6
2891.1.g.d.471.1 2 35.4 even 6
2891.1.g.d.471.1 2 2065.1474 odd 6
2891.1.g.d.2713.1 2 35.9 even 6
2891.1.g.d.2713.1 2 2065.884 odd 6
3481.1.d.a.506.1 28 295.54 odd 58
3481.1.d.a.506.1 28 295.64 even 58
3481.1.d.a.672.1 28 295.124 odd 58
3481.1.d.a.672.1 28 295.289 even 58
3481.1.d.a.805.1 28 295.204 even 58
3481.1.d.a.805.1 28 295.209 odd 58
3481.1.d.a.806.1 28 295.134 even 58
3481.1.d.a.806.1 28 295.279 odd 58
3481.1.d.a.809.1 28 295.149 odd 58
3481.1.d.a.809.1 28 295.264 even 58
3481.1.d.a.893.1 28 295.164 even 58
3481.1.d.a.893.1 28 295.249 odd 58
3481.1.d.a.946.1 28 295.154 even 58
3481.1.d.a.946.1 28 295.259 odd 58
3481.1.d.a.1105.1 28 295.4 even 58
3481.1.d.a.1105.1 28 295.114 odd 58
3481.1.d.a.1106.1 28 295.29 even 58
3481.1.d.a.1106.1 28 295.89 odd 58
3481.1.d.a.1311.1 28 295.39 odd 58
3481.1.d.a.1311.1 28 295.79 even 58
3481.1.d.a.1404.1 28 295.199 even 58
3481.1.d.a.1404.1 28 295.214 odd 58
3481.1.d.a.1505.1 28 295.159 even 58
3481.1.d.a.1505.1 28 295.254 odd 58
3481.1.d.a.1558.1 28 295.34 odd 58
3481.1.d.a.1558.1 28 295.84 even 58
3481.1.d.a.1611.1 28 295.49 even 58
3481.1.d.a.1611.1 28 295.69 odd 58
3481.1.d.a.1702.1 28 295.174 odd 58
3481.1.d.a.1702.1 28 295.239 even 58
3481.1.d.a.1839.1 28 295.184 even 58
3481.1.d.a.1839.1 28 295.229 odd 58
3481.1.d.a.2076.1 28 295.44 odd 58
3481.1.d.a.2076.1 28 295.74 even 58
3481.1.d.a.2117.1 28 295.19 even 58
3481.1.d.a.2117.1 28 295.99 odd 58
3481.1.d.a.2374.1 28 295.24 odd 58
3481.1.d.a.2374.1 28 295.94 even 58
3481.1.d.a.2451.1 28 295.144 even 58
3481.1.d.a.2451.1 28 295.269 odd 58
3481.1.d.a.2511.1 28 295.189 even 58
3481.1.d.a.2511.1 28 295.224 odd 58
3481.1.d.a.2869.1 28 295.9 even 58
3481.1.d.a.2869.1 28 295.109 odd 58
3481.1.d.a.2922.1 28 295.139 even 58
3481.1.d.a.2922.1 28 295.274 odd 58
3481.1.d.a.3181.1 28 295.169 even 58
3481.1.d.a.3181.1 28 295.244 odd 58
3481.1.d.a.3182.1 28 295.179 odd 58
3481.1.d.a.3182.1 28 295.234 even 58
3481.1.d.a.3183.1 28 295.129 odd 58
3481.1.d.a.3183.1 28 295.284 even 58
3481.1.d.a.3344.1 28 295.14 odd 58
3481.1.d.a.3344.1 28 295.104 even 58
3481.1.d.a.3428.1 28 295.194 even 58
3481.1.d.a.3428.1 28 295.219 odd 58
3776.1.h.a.2241.1 1 40.19 odd 2
3776.1.h.a.2241.1 1 2360.1179 even 2
3776.1.h.b.2241.1 1 40.29 even 2
3776.1.h.b.2241.1 1 2360.589 odd 2