Properties

Label 59.1.b.a.58.1
Level $59$
Weight $1$
Character 59.58
Self dual yes
Analytic conductor $0.029$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -59
Inner twists $2$

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 59 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 59.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.0294448357453\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(D_{3}\)
Projective field Galois closure of 3.1.59.1
Artin image $S_3$
Artin field Galois closure of 3.1.59.1

Embedding invariants

Embedding label 58.1
Character \(\chi\) \(=\) 59.58

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{7} +O(q^{10})\) \(q-1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{7} -1.00000 q^{12} +1.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{19} -1.00000 q^{20} +1.00000 q^{21} +1.00000 q^{27} -1.00000 q^{28} -1.00000 q^{29} +1.00000 q^{35} -1.00000 q^{41} -1.00000 q^{48} -2.00000 q^{51} -1.00000 q^{53} +1.00000 q^{57} +1.00000 q^{59} +1.00000 q^{60} +1.00000 q^{64} +2.00000 q^{68} +2.00000 q^{71} -1.00000 q^{76} -1.00000 q^{79} -1.00000 q^{80} -1.00000 q^{81} +1.00000 q^{84} -2.00000 q^{85} +1.00000 q^{87} +1.00000 q^{95} +O(q^{100})\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/59\mathbb{Z}\right)^\times\).

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(4\) 1.00000 1.00000
\(5\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(6\) 0 0
\(7\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) 0 0
\(9\) 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
\(15\) 1.00000 1.00000
\(16\) 1.00000 1.00000
\(17\) 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 \(0.666667\pi\)
\(20\) −1.00000 −1.00000
\(21\) 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
\(35\) 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 \(\pi\)
\(48\) −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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.00000 1.00000
\(58\) 0 0
\(59\) 1.00000 1.00000
\(60\) 1.00000 1.00000
\(61\) 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 \(0.666667\pi\)
\(80\) −1.00000 −1.00000
\(81\) −1.00000 −1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 1.00000 1.00000
\(85\) −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 \(0.666667\pi\)
\(108\) 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
\(125\) 1.00000 1.00000
\(126\) 0 0
\(127\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(128\) 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 \(0\)
\(140\) 1.00000 1.00000
\(141\) 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 \(0\)
\(164\) −1.00000 −1.00000
\(165\) 0 0
\(166\) 0 0
\(167\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(168\) 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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(198\) 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
\(205\) 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 \(\pi\)
\(212\) −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 \(0\)
1.00000 \(0\)
\(224\) 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 \(0.666667\pi\)
\(240\) 1.00000 1.00000
\(241\) −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
\(256\) 1.00000 1.00000
\(257\) −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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 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 \(-0.666667\pi\)
−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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(278\) 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
\(285\) −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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(294\) 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
\(304\) −1.00000 −1.00000
\(305\) 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 \(-0.666667\pi\)
−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 \(0\)
1.00000 \(0\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.00000 −1.00000
\(321\) 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
\(340\) −2.00000 −2.00000
\(341\) 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
\(355\) −2.00000 −2.00000
\(356\) 0 0
\(357\) 2.00000 2.00000
\(358\) 0 0
\(359\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−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 \(0\)
1.00000 \(0\)
\(374\) 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 \(0.666667\pi\)
\(380\) 1.00000 1.00000
\(381\) 1.00000 1.00000
\(382\) 0 0
\(383\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(384\) 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
\(395\) 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 \(\pi\)
\(420\) −1.00000 −1.00000
\(421\) 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 \(-0.666667\pi\)
−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 \(0\)
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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 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 \(0.666667\pi\)
\(500\) 1.00000 1.00000
\(501\) 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 \(-0.666667\pi\)
−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
\(532\) 1.00000 1.00000
\(533\) 0 0
\(534\) 0 0
\(535\) 1.00000 1.00000
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) −1.00000 −1.00000
\(541\) 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 \(0\)
\(548\) −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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1.00000 1.00000
\(561\) 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
\(580\) 1.00000 1.00000
\(581\) 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 \(-0.666667\pi\)
−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
\(605\) −1.00000 −1.00000
\(606\) 0 0
\(607\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) 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 \(0\)
1.00000 \(0\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.00000 1.00000
\(636\) 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 \(-0.666667\pi\)
−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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(648\) 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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(654\) 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
\(665\) −1.00000 −1.00000
\(666\) 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 \(0\)
1.00000 \(0\)
\(678\) 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
\(708\) −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 \(0\)
1.00000 \(0\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 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
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(744\) 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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(758\) 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 \(0\)
1.00000 \(0\)
\(788\) 2.00000 2.00000
\(789\) 1.00000 1.00000
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −1.00000 −1.00000
\(796\) −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
\(815\) −2.00000 −2.00000
\(816\) −2.00000 −2.00000
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 1.00000 1.00000
\(821\) 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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) 0 0
\(831\) 1.00000 1.00000
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 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
\(848\) −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 \(-0.666667\pi\)
−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
\(859\) 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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(878\) 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
\(892\) 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
\(905\) 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 \(-0.666667\pi\)
−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
\(945\) 1.00000 1.00000
\(946\) 0 0
\(947\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(948\) 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 \(0\)
1.00000 \(0\)
\(954\) 0 0
\(955\) 0 0
\(956\) −1.00000 −1.00000
\(957\) 0 0
\(958\) 0 0
\(959\) 1.00000 1.00000
\(960\) 1.00000 1.00000
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) −1.00000 −1.00000
\(965\) 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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(998\) 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 59.1.b.a.58.1 1
3.2 odd 2 531.1.c.a.235.1 1
4.3 odd 2 944.1.h.a.353.1 1
5.2 odd 4 1475.1.d.a.1474.2 2
5.3 odd 4 1475.1.d.a.1474.1 2
5.4 even 2 1475.1.c.b.176.1 1
7.2 even 3 2891.1.g.d.2713.1 2
7.3 odd 6 2891.1.g.b.471.1 2
7.4 even 3 2891.1.g.d.471.1 2
7.5 odd 6 2891.1.g.b.2713.1 2
7.6 odd 2 2891.1.c.e.589.1 1
8.3 odd 2 3776.1.h.a.2241.1 1
8.5 even 2 3776.1.h.b.2241.1 1
59.2 odd 58 3481.1.d.a.3182.1 28
59.3 even 29 3481.1.d.a.1702.1 28
59.4 even 29 3481.1.d.a.1105.1 28
59.5 even 29 3481.1.d.a.506.1 28
59.6 odd 58 3481.1.d.a.672.1 28
59.7 even 29 3481.1.d.a.1839.1 28
59.8 odd 58 3481.1.d.a.3181.1 28
59.9 even 29 3481.1.d.a.2869.1 28
59.10 odd 58 3481.1.d.a.1611.1 28
59.11 odd 58 3481.1.d.a.3183.1 28
59.12 even 29 3481.1.d.a.2511.1 28
59.13 odd 58 3481.1.d.a.893.1 28
59.14 odd 58 3481.1.d.a.3344.1 28
59.15 even 29 3481.1.d.a.2076.1 28
59.16 even 29 3481.1.d.a.806.1 28
59.17 even 29 3481.1.d.a.3428.1 28
59.18 odd 58 3481.1.d.a.1505.1 28
59.19 even 29 3481.1.d.a.2117.1 28
59.20 even 29 3481.1.d.a.1311.1 28
59.21 even 29 3481.1.d.a.2922.1 28
59.22 even 29 3481.1.d.a.1404.1 28
59.23 odd 58 3481.1.d.a.946.1 28
59.24 odd 58 3481.1.d.a.2374.1 28
59.25 even 29 3481.1.d.a.1558.1 28
59.26 even 29 3481.1.d.a.2451.1 28
59.27 even 29 3481.1.d.a.805.1 28
59.28 even 29 3481.1.d.a.809.1 28
59.29 even 29 3481.1.d.a.1106.1 28
59.30 odd 58 3481.1.d.a.1106.1 28
59.31 odd 58 3481.1.d.a.809.1 28
59.32 odd 58 3481.1.d.a.805.1 28
59.33 odd 58 3481.1.d.a.2451.1 28
59.34 odd 58 3481.1.d.a.1558.1 28
59.35 even 29 3481.1.d.a.2374.1 28
59.36 even 29 3481.1.d.a.946.1 28
59.37 odd 58 3481.1.d.a.1404.1 28
59.38 odd 58 3481.1.d.a.2922.1 28
59.39 odd 58 3481.1.d.a.1311.1 28
59.40 odd 58 3481.1.d.a.2117.1 28
59.41 even 29 3481.1.d.a.1505.1 28
59.42 odd 58 3481.1.d.a.3428.1 28
59.43 odd 58 3481.1.d.a.806.1 28
59.44 odd 58 3481.1.d.a.2076.1 28
59.45 even 29 3481.1.d.a.3344.1 28
59.46 even 29 3481.1.d.a.893.1 28
59.47 odd 58 3481.1.d.a.2511.1 28
59.48 even 29 3481.1.d.a.3183.1 28
59.49 even 29 3481.1.d.a.1611.1 28
59.50 odd 58 3481.1.d.a.2869.1 28
59.51 even 29 3481.1.d.a.3181.1 28
59.52 odd 58 3481.1.d.a.1839.1 28
59.53 even 29 3481.1.d.a.672.1 28
59.54 odd 58 3481.1.d.a.506.1 28
59.55 odd 58 3481.1.d.a.1105.1 28
59.56 odd 58 3481.1.d.a.1702.1 28
59.57 even 29 3481.1.d.a.3182.1 28
59.58 odd 2 CM 59.1.b.a.58.1 1
177.176 even 2 531.1.c.a.235.1 1
236.235 even 2 944.1.h.a.353.1 1
295.58 even 4 1475.1.d.a.1474.1 2
295.117 even 4 1475.1.d.a.1474.2 2
295.294 odd 2 1475.1.c.b.176.1 1
413.58 odd 6 2891.1.g.d.2713.1 2
413.117 even 6 2891.1.g.b.2713.1 2
413.235 odd 6 2891.1.g.d.471.1 2
413.353 even 6 2891.1.g.b.471.1 2
413.412 even 2 2891.1.c.e.589.1 1
472.117 odd 2 3776.1.h.b.2241.1 1
472.235 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 1.1 even 1 trivial
59.1.b.a.58.1 1 59.58 odd 2 CM
531.1.c.a.235.1 1 3.2 odd 2
531.1.c.a.235.1 1 177.176 even 2
944.1.h.a.353.1 1 4.3 odd 2
944.1.h.a.353.1 1 236.235 even 2
1475.1.c.b.176.1 1 5.4 even 2
1475.1.c.b.176.1 1 295.294 odd 2
1475.1.d.a.1474.1 2 5.3 odd 4
1475.1.d.a.1474.1 2 295.58 even 4
1475.1.d.a.1474.2 2 5.2 odd 4
1475.1.d.a.1474.2 2 295.117 even 4
2891.1.c.e.589.1 1 7.6 odd 2
2891.1.c.e.589.1 1 413.412 even 2
2891.1.g.b.471.1 2 7.3 odd 6
2891.1.g.b.471.1 2 413.353 even 6
2891.1.g.b.2713.1 2 7.5 odd 6
2891.1.g.b.2713.1 2 413.117 even 6
2891.1.g.d.471.1 2 7.4 even 3
2891.1.g.d.471.1 2 413.235 odd 6
2891.1.g.d.2713.1 2 7.2 even 3
2891.1.g.d.2713.1 2 413.58 odd 6
3481.1.d.a.506.1 28 59.5 even 29
3481.1.d.a.506.1 28 59.54 odd 58
3481.1.d.a.672.1 28 59.6 odd 58
3481.1.d.a.672.1 28 59.53 even 29
3481.1.d.a.805.1 28 59.27 even 29
3481.1.d.a.805.1 28 59.32 odd 58
3481.1.d.a.806.1 28 59.16 even 29
3481.1.d.a.806.1 28 59.43 odd 58
3481.1.d.a.809.1 28 59.28 even 29
3481.1.d.a.809.1 28 59.31 odd 58
3481.1.d.a.893.1 28 59.13 odd 58
3481.1.d.a.893.1 28 59.46 even 29
3481.1.d.a.946.1 28 59.23 odd 58
3481.1.d.a.946.1 28 59.36 even 29
3481.1.d.a.1105.1 28 59.4 even 29
3481.1.d.a.1105.1 28 59.55 odd 58
3481.1.d.a.1106.1 28 59.29 even 29
3481.1.d.a.1106.1 28 59.30 odd 58
3481.1.d.a.1311.1 28 59.20 even 29
3481.1.d.a.1311.1 28 59.39 odd 58
3481.1.d.a.1404.1 28 59.22 even 29
3481.1.d.a.1404.1 28 59.37 odd 58
3481.1.d.a.1505.1 28 59.18 odd 58
3481.1.d.a.1505.1 28 59.41 even 29
3481.1.d.a.1558.1 28 59.25 even 29
3481.1.d.a.1558.1 28 59.34 odd 58
3481.1.d.a.1611.1 28 59.10 odd 58
3481.1.d.a.1611.1 28 59.49 even 29
3481.1.d.a.1702.1 28 59.3 even 29
3481.1.d.a.1702.1 28 59.56 odd 58
3481.1.d.a.1839.1 28 59.7 even 29
3481.1.d.a.1839.1 28 59.52 odd 58
3481.1.d.a.2076.1 28 59.15 even 29
3481.1.d.a.2076.1 28 59.44 odd 58
3481.1.d.a.2117.1 28 59.19 even 29
3481.1.d.a.2117.1 28 59.40 odd 58
3481.1.d.a.2374.1 28 59.24 odd 58
3481.1.d.a.2374.1 28 59.35 even 29
3481.1.d.a.2451.1 28 59.26 even 29
3481.1.d.a.2451.1 28 59.33 odd 58
3481.1.d.a.2511.1 28 59.12 even 29
3481.1.d.a.2511.1 28 59.47 odd 58
3481.1.d.a.2869.1 28 59.9 even 29
3481.1.d.a.2869.1 28 59.50 odd 58
3481.1.d.a.2922.1 28 59.21 even 29
3481.1.d.a.2922.1 28 59.38 odd 58
3481.1.d.a.3181.1 28 59.8 odd 58
3481.1.d.a.3181.1 28 59.51 even 29
3481.1.d.a.3182.1 28 59.2 odd 58
3481.1.d.a.3182.1 28 59.57 even 29
3481.1.d.a.3183.1 28 59.11 odd 58
3481.1.d.a.3183.1 28 59.48 even 29
3481.1.d.a.3344.1 28 59.14 odd 58
3481.1.d.a.3344.1 28 59.45 even 29
3481.1.d.a.3428.1 28 59.17 even 29
3481.1.d.a.3428.1 28 59.42 odd 58
3776.1.h.a.2241.1 1 8.3 odd 2
3776.1.h.a.2241.1 1 472.235 even 2
3776.1.h.b.2241.1 1 8.5 even 2
3776.1.h.b.2241.1 1 472.117 odd 2