Properties

Label 2575.1.c.b.2574.3
Level 2575
Weight 1
Character 2575.2574
Analytic conductor 1.285
Analytic rank 0
Dimension 4
Projective image \(D_{5}\)
CM discriminant -103
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 2575 = 5^{2} \cdot 103 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2575.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.28509240753\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 103)
Projective image \(D_{5}\)
Projective field Galois closure of 5.1.10609.1
Artin image $C_4\times D_5$
Artin field Galois closure of \(\mathbb{Q}[x]/(x^{20} - \cdots)\)

Embedding invariants

Embedding label 2574.3
Root \(1.61803i\) of defining polynomial
Character \(\chi\) \(=\) 2575.2574
Dual form 2575.1.c.b.2574.2

$q$-expansion

\(f(q)\) \(=\) \(q+0.618034i q^{2} +0.618034 q^{4} -1.61803i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+0.618034i q^{2} +0.618034 q^{4} -1.61803i q^{7} +1.00000i q^{8} -1.00000 q^{9} -0.618034i q^{13} +1.00000 q^{14} -1.61803i q^{17} -0.618034i q^{18} -0.618034 q^{19} -0.618034i q^{23} +0.381966 q^{26} -1.00000i q^{28} +1.61803 q^{29} +1.00000i q^{32} +1.00000 q^{34} -0.618034 q^{36} -0.381966i q^{38} +0.618034 q^{41} +0.381966 q^{46} -1.61803 q^{49} -0.381966i q^{52} +1.61803 q^{56} +1.00000i q^{58} +1.61803 q^{59} -1.61803 q^{61} +1.61803i q^{63} -0.618034 q^{64} -1.00000i q^{68} -1.00000i q^{72} -0.381966 q^{76} -0.618034 q^{79} +1.00000 q^{81} +0.381966i q^{82} +1.61803i q^{83} -1.00000 q^{91} -0.381966i q^{92} -1.61803i q^{97} -1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{4} - 4q^{9} + O(q^{10}) \) \( 4q - 2q^{4} - 4q^{9} + 4q^{14} + 2q^{19} + 6q^{26} + 2q^{29} + 4q^{34} + 2q^{36} - 2q^{41} + 6q^{46} - 2q^{49} + 2q^{56} + 2q^{59} - 2q^{61} + 2q^{64} - 6q^{76} + 2q^{79} + 4q^{81} - 4q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2575\mathbb{Z}\right)^\times\).

\(n\) \(726\) \(1752\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0.618034 0.618034
\(5\) 0 0
\(6\) 0 0
\(7\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(8\) 1.00000i 1.00000i
\(9\) −1.00000 −1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(14\) 1.00000 1.00000
\(15\) 0 0
\(16\) 0 0
\(17\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(18\) − 0.618034i − 0.618034i
\(19\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0.381966 0.381966
\(27\) 0 0
\(28\) − 1.00000i − 1.00000i
\(29\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 1.00000i 1.00000i
\(33\) 0 0
\(34\) 1.00000 1.00000
\(35\) 0 0
\(36\) −0.618034 −0.618034
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) − 0.381966i − 0.381966i
\(39\) 0 0
\(40\) 0 0
\(41\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0.381966 0.381966
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −1.61803 −1.61803
\(50\) 0 0
\(51\) 0 0
\(52\) − 0.381966i − 0.381966i
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.61803 1.61803
\(57\) 0 0
\(58\) 1.00000i 1.00000i
\(59\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(60\) 0 0
\(61\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(62\) 0 0
\(63\) 1.61803i 1.61803i
\(64\) −0.618034 −0.618034
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) − 1.00000i − 1.00000i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) − 1.00000i − 1.00000i
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −0.381966 −0.381966
\(77\) 0 0
\(78\) 0 0
\(79\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(80\) 0 0
\(81\) 1.00000 1.00000
\(82\) 0.381966i 0.381966i
\(83\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −1.00000 −1.00000
\(92\) − 0.381966i − 0.381966i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(98\) − 1.00000i − 1.00000i
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) − 1.00000i − 1.00000i
\(104\) 0.618034 0.618034
\(105\) 0 0
\(106\) 0 0
\(107\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 1.00000 1.00000
\(117\) 0.618034i 0.618034i
\(118\) 1.00000i 1.00000i
\(119\) −2.61803 −2.61803
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) − 1.00000i − 1.00000i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −1.00000 −1.00000
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0.618034i 0.618034i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(132\) 0 0
\(133\) 1.00000i 1.00000i
\(134\) 0 0
\(135\) 0 0
\(136\) 1.61803 1.61803
\(137\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(138\) 0 0
\(139\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(140\) 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
\(149\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) − 0.618034i − 0.618034i
\(153\) 1.61803i 1.61803i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) − 0.381966i − 0.381966i
\(159\) 0 0
\(160\) 0 0
\(161\) −1.00000 −1.00000
\(162\) 0.618034i 0.618034i
\(163\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(164\) 0.381966 0.381966
\(165\) 0 0
\(166\) −1.00000 −1.00000
\(167\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 0.618034 0.618034
\(170\) 0 0
\(171\) 0.618034 0.618034
\(172\) 0 0
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) − 0.618034i − 0.618034i
\(183\) 0 0
\(184\) 0.618034 0.618034
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 1.00000 1.00000
\(195\) 0 0
\(196\) −1.00000 −1.00000
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) − 2.61803i − 2.61803i
\(204\) 0 0
\(205\) 0 0
\(206\) 0.618034 0.618034
\(207\) 0.618034i 0.618034i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.23607 −1.23607
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.00000 −1.00000
\(222\) 0 0
\(223\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(224\) 1.61803 1.61803
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.61803i 1.61803i
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) −0.381966 −0.381966
\(235\) 0 0
\(236\) 1.00000 1.00000
\(237\) 0 0
\(238\) − 1.61803i − 1.61803i
\(239\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0.618034i 0.618034i
\(243\) 0 0
\(244\) −1.00000 −1.00000
\(245\) 0 0
\(246\) 0 0
\(247\) 0.381966i 0.381966i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 1.00000i 1.00000i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −1.00000 −1.00000
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −1.61803 −1.61803
\(262\) 0.381966i 0.381966i
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −0.618034 −0.618034
\(267\) 0 0
\(268\) 0 0
\(269\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −0.381966 −0.381966
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) − 1.23607i − 1.23607i
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) − 1.00000i − 1.00000i
\(288\) − 1.00000i − 1.00000i
\(289\) −1.61803 −1.61803
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) − 0.381966i − 0.381966i
\(299\) −0.381966 −0.381966
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) −1.00000 −1.00000
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(312\) 0 0
\(313\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −0.381966 −0.381966
\(317\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) − 0.618034i − 0.618034i
\(323\) 1.00000i 1.00000i
\(324\) 0.618034 0.618034
\(325\) 0 0
\(326\) −1.00000 −1.00000
\(327\) 0 0
\(328\) 0.618034i 0.618034i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 1.00000i 1.00000i
\(333\) 0 0
\(334\) −1.23607 −1.23607
\(335\) 0 0
\(336\) 0 0
\(337\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(338\) 0.381966i 0.381966i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0.381966i 0.381966i
\(343\) 1.00000i 1.00000i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 1.00000i 1.00000i
\(359\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) −0.618034 −0.618034
\(362\) 0 0
\(363\) 0 0
\(364\) −0.618034 −0.618034
\(365\) 0 0
\(366\) 0 0
\(367\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(368\) 0 0
\(369\) −0.618034 −0.618034
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 1.00000i − 1.00000i
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) − 1.00000i − 1.00000i
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) −1.00000 −1.00000
\(392\) − 1.61803i − 1.61803i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 1.61803 1.61803
\(407\) 0 0
\(408\) 0 0
\(409\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) − 0.618034i − 0.618034i
\(413\) − 2.61803i − 2.61803i
\(414\) −0.381966 −0.381966
\(415\) 0 0
\(416\) 0.618034 0.618034
\(417\) 0 0
\(418\) 0 0
\(419\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(420\) 0 0
\(421\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 2.61803i 2.61803i
\(428\) 1.23607i 1.23607i
\(429\) 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
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.381966i 0.381966i
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 1.61803 1.61803
\(442\) − 0.618034i − 0.618034i
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0.381966 0.381966
\(447\) 0 0
\(448\) 1.00000i 1.00000i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 1.00000i 1.00000i
\(459\) 0 0
\(460\) 0 0
\(461\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(468\) 0.381966i 0.381966i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 1.61803i 1.61803i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) −1.61803 −1.61803
\(477\) 0 0
\(478\) 1.00000i 1.00000i
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.618034 0.618034
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) − 1.61803i − 1.61803i
\(489\) 0 0
\(490\) 0 0
\(491\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(492\) 0 0
\(493\) − 2.61803i − 2.61803i
\(494\) −0.236068 −0.236068
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(504\) −1.61803 −1.61803
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) − 1.00000i − 1.00000i
\(523\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(524\) 0.381966 0.381966
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.618034 0.618034
\(530\) 0 0
\(531\) −1.61803 −1.61803
\(532\) 0.618034i 0.618034i
\(533\) − 0.381966i − 0.381966i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) − 0.381966i − 0.381966i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 1.61803 1.61803
\(545\) 0 0
\(546\) 0 0
\(547\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(548\) 0.381966i 0.381966i
\(549\) 1.61803 1.61803
\(550\) 0 0
\(551\) −1.00000 −1.00000
\(552\) 0 0
\(553\) 1.00000i 1.00000i
\(554\) 0 0
\(555\) 0 0
\(556\) −1.23607 −1.23607
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) − 1.61803i − 1.61803i
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0.618034 0.618034
\(575\) 0 0
\(576\) 0.618034 0.618034
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) − 1.00000i − 1.00000i
\(579\) 0 0
\(580\) 0 0
\(581\) 2.61803 2.61803
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.381966 −0.381966
\(597\) 0 0
\(598\) − 0.236068i − 0.236068i
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 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
\(607\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(608\) − 0.618034i − 0.618034i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 1.00000i 1.00000i
\(613\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) − 1.00000i − 1.00000i
\(623\) 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
\(631\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(632\) − 0.618034i − 0.618034i
\(633\) 0 0
\(634\) 1.00000 1.00000
\(635\) 0 0
\(636\) 0 0
\(637\) 1.00000i 1.00000i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(642\) 0 0
\(643\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(644\) −0.618034 −0.618034
\(645\) 0 0
\(646\) −0.618034 −0.618034
\(647\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(648\) 1.00000i 1.00000i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 1.00000i 1.00000i
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −1.61803 −1.61803
\(665\) 0 0
\(666\) 0 0
\(667\) − 1.00000i − 1.00000i
\(668\) 1.23607i 1.23607i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(674\) −0.381966 −0.381966
\(675\) 0 0
\(676\) 0.381966 0.381966
\(677\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(678\) 0 0
\(679\) −2.61803 −2.61803
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0.381966 0.381966
\(685\) 0 0
\(686\) −0.618034 −0.618034
\(687\) 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
\(694\) −0.381966 −0.381966
\(695\) 0 0
\(696\) 0 0
\(697\) − 1.00000i − 1.00000i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(710\) 0 0
\(711\) 0.618034 0.618034
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.00000 1.00000
\(717\) 0 0
\(718\) − 1.23607i − 1.23607i
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) −1.61803 −1.61803
\(722\) − 0.381966i − 0.381966i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) − 1.00000i − 1.00000i
\(729\) −1.00000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) −0.381966 −0.381966
\(735\) 0 0
\(736\) 0.618034 0.618034
\(737\) 0 0
\(738\) − 0.381966i − 0.381966i
\(739\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −1.00000 −1.00000
\(747\) − 1.61803i − 1.61803i
\(748\) 0 0
\(749\) 3.23607 3.23607
\(750\) 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
\(754\) 0.618034 0.618034
\(755\) 0 0
\(756\) 0 0
\(757\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) − 1.00000i − 1.00000i
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 1.61803 1.61803
\(777\) 0 0
\(778\) 0 0
\(779\) −0.381966 −0.381966
\(780\) 0 0
\(781\) 0 0
\(782\) − 0.618034i − 0.618034i
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 1.00000i 1.00000i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) − 1.00000i − 1.00000i
\(803\) 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 \(\pi\)
\(812\) − 1.61803i − 1.61803i
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 1.00000i 1.00000i
\(819\) 1.00000 1.00000
\(820\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 1.00000 1.00000
\(825\) 0 0
\(826\) 1.61803 1.61803
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0.381966i 0.381966i
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0.381966i 0.381966i
\(833\) 2.61803i 2.61803i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) − 0.381966i − 0.381966i
\(839\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(840\) 0 0
\(841\) 1.61803 1.61803
\(842\) 1.23607i 1.23607i
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) − 1.61803i − 1.61803i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(854\) −1.61803 −1.61803
\(855\) 0 0
\(856\) −2.00000 −2.00000
\(857\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) − 1.00000i − 1.00000i
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 1.61803i 1.61803i
\(874\) −0.236068 −0.236068
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 1.00000i 1.00000i
\(883\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(884\) −0.618034 −0.618034
\(885\) 0 0
\(886\) 0 0
\(887\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) − 0.381966i − 0.381966i
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000 1.00000
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 1.00000 1.00000
\(917\) − 1.00000i − 1.00000i
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 1.23607i 1.23607i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 1.00000i 1.00000i
\(928\) 1.61803i 1.61803i
\(929\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(930\) 0 0
\(931\) 1.00000 1.00000
\(932\) 0 0
\(933\) 0 0
\(934\) −0.381966 −0.381966
\(935\) 0 0
\(936\) −0.618034 −0.618034
\(937\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(942\) 0 0
\(943\) − 0.381966i − 0.381966i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) − 2.61803i − 2.61803i
\(953\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(954\) 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
\(963\) − 2.00000i − 2.00000i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 1.00000i 1.00000i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 3.23607i 3.23607i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) − 1.00000i − 1.00000i
\(983\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 1.61803 1.61803
\(987\) 0 0
\(988\) 0.236068i 0.236068i
\(989\) 0 0
\(990\) 0 0
\(991\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) 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 2575.1.c.b.2574.3 4
5.2 odd 4 2575.1.d.d.926.1 2
5.3 odd 4 103.1.b.a.102.2 2
5.4 even 2 inner 2575.1.c.b.2574.2 4
15.8 even 4 927.1.d.b.514.1 2
20.3 even 4 1648.1.c.a.1441.2 2
103.102 odd 2 CM 2575.1.c.b.2574.3 4
515.102 even 4 2575.1.d.d.926.1 2
515.308 even 4 103.1.b.a.102.2 2
515.514 odd 2 inner 2575.1.c.b.2574.2 4
1545.308 odd 4 927.1.d.b.514.1 2
2060.823 odd 4 1648.1.c.a.1441.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
103.1.b.a.102.2 2 5.3 odd 4
103.1.b.a.102.2 2 515.308 even 4
927.1.d.b.514.1 2 15.8 even 4
927.1.d.b.514.1 2 1545.308 odd 4
1648.1.c.a.1441.2 2 20.3 even 4
1648.1.c.a.1441.2 2 2060.823 odd 4
2575.1.c.b.2574.2 4 5.4 even 2 inner
2575.1.c.b.2574.2 4 515.514 odd 2 inner
2575.1.c.b.2574.3 4 1.1 even 1 trivial
2575.1.c.b.2574.3 4 103.102 odd 2 CM
2575.1.d.d.926.1 2 5.2 odd 4
2575.1.d.d.926.1 2 515.102 even 4