Properties

Label 79.1.b.a.78.2
Level 79
Weight 1
Character 79.78
Self dual yes
Analytic conductor 0.039
Analytic rank 0
Dimension 2
Projective image \(D_{5}\)
CM discriminant -79
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 79 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 79.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.0394261359980\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \(x^{2} - x - 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(D_{5}\)
Projective field Galois closure of 5.1.6241.1
Artin image $D_5$
Artin field Galois closure of 5.1.6241.1

Embedding invariants

Embedding label 78.2
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 79.78

$q$-expansion

\(f(q)\) \(=\) \(q+0.618034 q^{2} -0.618034 q^{4} -1.61803 q^{5} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.618034 q^{2} -0.618034 q^{4} -1.61803 q^{5} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +0.618034 q^{11} +0.618034 q^{13} +0.618034 q^{18} -1.61803 q^{19} +1.00000 q^{20} +0.381966 q^{22} -1.61803 q^{23} +1.61803 q^{25} +0.381966 q^{26} +0.618034 q^{31} +1.00000 q^{32} -0.618034 q^{36} -1.00000 q^{38} +1.61803 q^{40} -0.381966 q^{44} -1.61803 q^{45} -1.00000 q^{46} +1.00000 q^{49} +1.00000 q^{50} -0.381966 q^{52} -1.00000 q^{55} +0.381966 q^{62} +0.618034 q^{64} -1.00000 q^{65} -1.61803 q^{67} -1.00000 q^{72} -1.61803 q^{73} +1.00000 q^{76} +1.00000 q^{79} +1.00000 q^{81} +2.00000 q^{83} -0.618034 q^{88} +0.618034 q^{89} -1.00000 q^{90} +1.00000 q^{92} +2.61803 q^{95} -1.61803 q^{97} +0.618034 q^{98} +0.618034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{4} - q^{5} - 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{4} - q^{5} - 2q^{8} + 2q^{9} - 2q^{10} - q^{11} - q^{13} - q^{18} - q^{19} + 2q^{20} + 3q^{22} - q^{23} + q^{25} + 3q^{26} - q^{31} + 2q^{32} + q^{36} - 2q^{38} + q^{40} - 3q^{44} - q^{45} - 2q^{46} + 2q^{49} + 2q^{50} - 3q^{52} - 2q^{55} + 3q^{62} - q^{64} - 2q^{65} - q^{67} - 2q^{72} - q^{73} + 2q^{76} + 2q^{79} + 2q^{81} + 4q^{83} + q^{88} - q^{89} - 2q^{90} + 2q^{92} + 3q^{95} - q^{97} - q^{98} - q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/79\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) −0.618034 −0.618034
\(5\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) −1.00000 −1.00000
\(9\) 1.00000 1.00000
\(10\) −1.00000 −1.00000
\(11\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(12\) 0 0
\(13\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0.618034 0.618034
\(19\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(20\) 1.00000 1.00000
\(21\) 0 0
\(22\) 0.381966 0.381966
\(23\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(24\) 0 0
\(25\) 1.61803 1.61803
\(26\) 0.381966 0.381966
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(32\) 1.00000 1.00000
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.618034 −0.618034
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) −1.00000 −1.00000
\(39\) 0 0
\(40\) 1.61803 1.61803
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −0.381966 −0.381966
\(45\) −1.61803 −1.61803
\(46\) −1.00000 −1.00000
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) 1.00000 1.00000
\(50\) 1.00000 1.00000
\(51\) 0 0
\(52\) −0.381966 −0.381966
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) −1.00000 −1.00000
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0.381966 0.381966
\(63\) 0 0
\(64\) 0.618034 0.618034
\(65\) −1.00000 −1.00000
\(66\) 0 0
\(67\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −1.00000 −1.00000
\(73\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 1.00000 1.00000
\(77\) 0 0
\(78\) 0 0
\(79\) 1.00000 1.00000
\(80\) 0 0
\(81\) 1.00000 1.00000
\(82\) 0 0
\(83\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −0.618034 −0.618034
\(89\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(90\) −1.00000 −1.00000
\(91\) 0 0
\(92\) 1.00000 1.00000
\(93\) 0 0
\(94\) 0 0
\(95\) 2.61803 2.61803
\(96\) 0 0
\(97\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(98\) 0.618034 0.618034
\(99\) 0.618034 0.618034
\(100\) −1.00000 −1.00000
\(101\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) −0.618034 −0.618034
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) −0.618034 −0.618034
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 2.61803 2.61803
\(116\) 0 0
\(117\) 0.618034 0.618034
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.618034 −0.618034
\(122\) 0 0
\(123\) 0 0
\(124\) −0.381966 −0.381966
\(125\) −1.00000 −1.00000
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −0.618034 −0.618034
\(129\) 0 0
\(130\) −0.618034 −0.618034
\(131\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.00000 −1.00000
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.381966 0.381966
\(144\) 0 0
\(145\) 0 0
\(146\) −1.00000 −1.00000
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(152\) 1.61803 1.61803
\(153\) 0 0
\(154\) 0 0
\(155\) −1.00000 −1.00000
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0.618034 0.618034
\(159\) 0 0
\(160\) −1.61803 −1.61803
\(161\) 0 0
\(162\) 0.618034 0.618034
\(163\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.23607 1.23607
\(167\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(168\) 0 0
\(169\) −0.618034 −0.618034
\(170\) 0 0
\(171\) −1.61803 −1.61803
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0.381966 0.381966
\(179\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(180\) 1.00000 1.00000
\(181\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1.61803 1.61803
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 1.61803 1.61803
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) −1.00000 −1.00000
\(195\) 0 0
\(196\) −0.618034 −0.618034
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0.381966 0.381966
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −1.61803 −1.61803
\(201\) 0 0
\(202\) 0.381966 0.381966
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.61803 −1.61803
\(208\) 0 0
\(209\) −1.00000 −1.00000
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0.618034 0.618034
\(221\) 0 0
\(222\) 0 0
\(223\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(224\) 0 0
\(225\) 1.61803 1.61803
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 1.61803 1.61803
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0.381966 0.381966
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(240\) 0 0
\(241\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(242\) −0.381966 −0.381966
\(243\) 0 0
\(244\) 0 0
\(245\) −1.61803 −1.61803
\(246\) 0 0
\(247\) −1.00000 −1.00000
\(248\) −0.618034 −0.618034
\(249\) 0 0
\(250\) −0.618034 −0.618034
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) −1.00000 −1.00000
\(254\) 0 0
\(255\) 0 0
\(256\) −1.00000 −1.00000
\(257\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0.618034 0.618034
\(261\) 0 0
\(262\) −1.00000 −1.00000
\(263\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 1.00000 1.00000
\(269\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.00000 1.00000
\(276\) 0 0
\(277\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(278\) 0 0
\(279\) 0.618034 0.618034
\(280\) 0 0
\(281\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(282\) 0 0
\(283\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0.236068 0.236068
\(287\) 0 0
\(288\) 1.00000 1.00000
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 1.00000 1.00000
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.00000 −1.00000
\(300\) 0 0
\(301\) 0 0
\(302\) −1.00000 −1.00000
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.618034 −0.618034
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −0.618034 −0.618034
\(317\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.00000 −1.00000
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.618034 −0.618034
\(325\) 1.00000 1.00000
\(326\) 0.381966 0.381966
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −1.23607 −1.23607
\(333\) 0 0
\(334\) 0.381966 0.381966
\(335\) 2.61803 2.61803
\(336\) 0 0
\(337\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(338\) −0.381966 −0.381966
\(339\) 0 0
\(340\) 0 0
\(341\) 0.381966 0.381966
\(342\) −1.00000 −1.00000
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.618034 0.618034
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.381966 −0.381966
\(357\) 0 0
\(358\) 1.23607 1.23607
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 1.61803 1.61803
\(361\) 1.61803 1.61803
\(362\) 0.381966 0.381966
\(363\) 0 0
\(364\) 0 0
\(365\) 2.61803 2.61803
\(366\) 0 0
\(367\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) −1.61803 −1.61803
\(381\) 0 0
\(382\) 0 0
\(383\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 1.00000 1.00000
\(389\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.00000 −1.00000
\(393\) 0 0
\(394\) 0 0
\(395\) −1.61803 −1.61803
\(396\) −0.381966 −0.381966
\(397\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0.381966 0.381966
\(404\) −0.381966 −0.381966
\(405\) −1.61803 −1.61803
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −1.00000 −1.00000
\(415\) −3.23607 −3.23607
\(416\) 0.618034 0.618034
\(417\) 0 0
\(418\) −0.618034 −0.618034
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(422\) 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
\(431\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(432\) 0 0
\(433\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.61803 2.61803
\(438\) 0 0
\(439\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(440\) 1.00000 1.00000
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) −1.00000 −1.00000
\(446\) 1.23607 1.23607
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 1.00000 1.00000
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −1.61803 −1.61803
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(468\) −0.381966 −0.381966
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −2.61803 −2.61803
\(476\) 0 0
\(477\) 0 0
\(478\) −1.00000 −1.00000
\(479\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.381966 0.381966
\(483\) 0 0
\(484\) 0.381966 0.381966
\(485\) 2.61803 2.61803
\(486\) 0 0
\(487\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −1.00000 −1.00000
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −0.618034 −0.618034
\(495\) −1.00000 −1.00000
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(500\) 0.618034 0.618034
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) −1.00000 −1.00000
\(506\) −0.618034 −0.618034
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0.381966 0.381966
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 1.00000 1.00000
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(524\) 1.00000 1.00000
\(525\) 0 0
\(526\) 0.381966 0.381966
\(527\) 0 0
\(528\) 0 0
\(529\) 1.61803 1.61803
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 1.61803 1.61803
\(537\) 0 0
\(538\) −1.00000 −1.00000
\(539\) 0.618034 0.618034
\(540\) 0 0
\(541\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0.618034 0.618034
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −1.00000 −1.00000
\(555\) 0 0
\(556\) 0 0
\(557\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(558\) 0.381966 0.381966
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −1.00000 −1.00000
\(563\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.381966 0.381966
\(567\) 0 0
\(568\) 0 0
\(569\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(570\) 0 0
\(571\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(572\) −0.236068 −0.236068
\(573\) 0 0
\(574\) 0 0
\(575\) −2.61803 −2.61803
\(576\) 0.618034 0.618034
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0.618034 0.618034
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 1.61803 1.61803
\(585\) −1.00000 −1.00000
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) −1.00000 −1.00000
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −0.618034 −0.618034
\(599\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) −1.61803 −1.61803
\(604\) 1.00000 1.00000
\(605\) 1.00000 1.00000
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) −1.61803 −1.61803
\(609\) 0 0
\(610\) 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
\(617\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0.618034 0.618034
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0.381966 0.381966
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) −1.00000 −1.00000
\(633\) 0 0
\(634\) 1.23607 1.23607
\(635\) 0 0
\(636\) 0 0
\(637\) 0.618034 0.618034
\(638\) 0 0
\(639\) 0 0
\(640\) 1.00000 1.00000
\(641\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(642\) 0 0
\(643\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) −1.00000 −1.00000
\(649\) 0 0
\(650\) 0.618034 0.618034
\(651\) 0 0
\(652\) −0.381966 −0.381966
\(653\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(654\) 0 0
\(655\) 2.61803 2.61803
\(656\) 0 0
\(657\) −1.61803 −1.61803
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −2.00000 −2.00000
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −0.381966 −0.381966
\(669\) 0 0
\(670\) 1.61803 1.61803
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) −1.00000 −1.00000
\(675\) 0 0
\(676\) 0.381966 0.381966
\(677\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0.236068 0.236068
\(683\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(684\) 1.00000 1.00000
\(685\) 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
\(694\) −1.00000 −1.00000
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.381966 0.381966
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 1.00000 1.00000
\(712\) −0.618034 −0.618034
\(713\) −1.00000 −1.00000
\(714\) 0 0
\(715\) −0.618034 −0.618034
\(716\) −1.23607 −1.23607
\(717\) 0 0
\(718\) 0 0
\(719\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.00000 1.00000
\(723\) 0 0
\(724\) −0.381966 −0.381966
\(725\) 0 0
\(726\) 0 0
\(727\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 1.61803 1.61803
\(731\) 0 0
\(732\) 0 0
\(733\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(734\) 0.381966 0.381966
\(735\) 0 0
\(736\) −1.61803 −1.61803
\(737\) −1.00000 −1.00000
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 2.00000 2.00000
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.61803 2.61803
\(756\) 0 0
\(757\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(758\) 0 0
\(759\) 0 0
\(760\) −2.61803 −2.61803
\(761\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0.381966 0.381966
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(774\) 0 0
\(775\) 1.00000 1.00000
\(776\) 1.61803 1.61803
\(777\) 0 0
\(778\) 0.381966 0.381966
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) −1.00000 −1.00000
\(791\) 0 0
\(792\) −0.618034 −0.618034
\(793\) 0 0
\(794\) 1.23607 1.23607
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.61803 1.61803
\(801\) 0.618034 0.618034
\(802\) 0 0
\(803\) −1.00000 −1.00000
\(804\) 0 0
\(805\) 0 0
\(806\) 0.236068 0.236068
\(807\) 0 0
\(808\) −0.618034 −0.618034
\(809\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(810\) −1.00000 −1.00000
\(811\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.00000 −1.00000
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 1.00000 1.00000
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) −2.00000 −2.00000
\(831\) 0 0
\(832\) 0.381966 0.381966
\(833\) 0 0
\(834\) 0 0
\(835\) −1.00000 −1.00000
\(836\) 0.618034 0.618034
\(837\) 0 0
\(838\) 0 0
\(839\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) −1.00000 −1.00000
\(843\) 0 0
\(844\) 0 0
\(845\) 1.00000 1.00000
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 2.61803 2.61803
\(856\) 0 0
\(857\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −1.00000 −1.00000
\(863\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(864\) 0 0
\(865\) 0 0
\(866\) −1.00000 −1.00000
\(867\) 0 0
\(868\) 0 0
\(869\) 0.618034 0.618034
\(870\) 0 0
\(871\) −1.00000 −1.00000
\(872\) 0 0
\(873\) −1.61803 −1.61803
\(874\) 1.61803 1.61803
\(875\) 0 0
\(876\) 0 0
\(877\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(878\) −1.00000 −1.00000
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0.618034 0.618034
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −0.618034 −0.618034
\(891\) 0.618034 0.618034
\(892\) −1.23607 −1.23607
\(893\) 0 0
\(894\) 0 0
\(895\) −3.23607 −3.23607
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −1.00000 −1.00000
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.00000 −1.00000
\(906\) 0 0
\(907\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(908\) 0 0
\(909\) 0.618034 0.618034
\(910\) 0 0
\(911\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(912\) 0 0
\(913\) 1.23607 1.23607
\(914\) 0.381966 0.381966
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(920\) −2.61803 −2.61803
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) −1.61803 −1.61803
\(932\) 0 0
\(933\) 0 0
\(934\) 0.381966 0.381966
\(935\) 0 0
\(936\) −0.618034 −0.618034
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) −1.00000 −1.00000
\(950\) −1.61803 −1.61803
\(951\) 0 0
\(952\) 0 0
\(953\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 1.00000 1.00000
\(957\) 0 0
\(958\) 1.23607 1.23607
\(959\) 0 0
\(960\) 0 0
\(961\) −0.618034 −0.618034
\(962\) 0 0
\(963\) 0 0
\(964\) −0.381966 −0.381966
\(965\) 0 0
\(966\) 0 0
\(967\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(968\) 0.618034 0.618034
\(969\) 0 0
\(970\) 1.61803 1.61803
\(971\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0.381966 0.381966
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0.381966 0.381966
\(980\) 1.00000 1.00000
\(981\) 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
\(988\) 0.618034 0.618034
\(989\) 0 0
\(990\) −0.618034 −0.618034
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0.618034 0.618034
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(998\) 0.381966 0.381966
\(999\) 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 79.1.b.a.78.2 2
3.2 odd 2 711.1.d.b.631.1 2
4.3 odd 2 1264.1.e.a.1105.1 2
5.2 odd 4 1975.1.c.a.1974.3 4
5.3 odd 4 1975.1.c.a.1974.2 4
5.4 even 2 1975.1.d.c.1026.1 2
7.2 even 3 3871.1.m.c.3791.1 4
7.3 odd 6 3871.1.m.b.1500.1 4
7.4 even 3 3871.1.m.c.1500.1 4
7.5 odd 6 3871.1.m.b.3791.1 4
7.6 odd 2 3871.1.c.c.2843.2 2
79.78 odd 2 CM 79.1.b.a.78.2 2
237.236 even 2 711.1.d.b.631.1 2
316.315 even 2 1264.1.e.a.1105.1 2
395.78 even 4 1975.1.c.a.1974.2 4
395.157 even 4 1975.1.c.a.1974.3 4
395.394 odd 2 1975.1.d.c.1026.1 2
553.157 even 6 3871.1.m.b.1500.1 4
553.236 even 6 3871.1.m.b.3791.1 4
553.394 odd 6 3871.1.m.c.3791.1 4
553.473 odd 6 3871.1.m.c.1500.1 4
553.552 even 2 3871.1.c.c.2843.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
79.1.b.a.78.2 2 1.1 even 1 trivial
79.1.b.a.78.2 2 79.78 odd 2 CM
711.1.d.b.631.1 2 3.2 odd 2
711.1.d.b.631.1 2 237.236 even 2
1264.1.e.a.1105.1 2 4.3 odd 2
1264.1.e.a.1105.1 2 316.315 even 2
1975.1.c.a.1974.2 4 5.3 odd 4
1975.1.c.a.1974.2 4 395.78 even 4
1975.1.c.a.1974.3 4 5.2 odd 4
1975.1.c.a.1974.3 4 395.157 even 4
1975.1.d.c.1026.1 2 5.4 even 2
1975.1.d.c.1026.1 2 395.394 odd 2
3871.1.c.c.2843.2 2 7.6 odd 2
3871.1.c.c.2843.2 2 553.552 even 2
3871.1.m.b.1500.1 4 7.3 odd 6
3871.1.m.b.1500.1 4 553.157 even 6
3871.1.m.b.3791.1 4 7.5 odd 6
3871.1.m.b.3791.1 4 553.236 even 6
3871.1.m.c.1500.1 4 7.4 even 3
3871.1.m.c.1500.1 4 553.473 odd 6
3871.1.m.c.3791.1 4 7.2 even 3
3871.1.m.c.3791.1 4 553.394 odd 6