Properties

Label 2008.1.c.b.501.1
Level 2008
Weight 1
Character 2008.501
Self dual yes
Analytic conductor 1.002
Analytic rank 0
Dimension 3
Projective image \(D_{7}\)
CM discriminant -2008
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 2008 = 2^{3} \cdot 251 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2008.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(1.00212254537\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
Defining polynomial: \(x^{3} - x^{2} - 2 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(D_{7}\)
Projective field Galois closure of 7.1.8096384512.1
Artin image $D_7$
Artin field Galois closure of 7.1.8096384512.1

Embedding invariants

Embedding label 501.1
Root \(1.80194\) of defining polynomial
Character \(\chi\) \(=\) 2008.501

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} -1.80194 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} -1.80194 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.24698 q^{11} -1.80194 q^{14} +1.00000 q^{16} -0.445042 q^{17} +1.00000 q^{18} -0.445042 q^{19} +1.24698 q^{22} +1.24698 q^{23} +1.00000 q^{25} -1.80194 q^{28} -0.445042 q^{29} -0.445042 q^{31} +1.00000 q^{32} -0.445042 q^{34} +1.00000 q^{36} -1.80194 q^{37} -0.445042 q^{38} +1.24698 q^{41} -1.80194 q^{43} +1.24698 q^{44} +1.24698 q^{46} +2.24698 q^{49} +1.00000 q^{50} +1.24698 q^{53} -1.80194 q^{56} -0.445042 q^{58} -1.80194 q^{59} +1.24698 q^{61} -0.445042 q^{62} -1.80194 q^{63} +1.00000 q^{64} -0.445042 q^{68} +1.00000 q^{72} -1.80194 q^{73} -1.80194 q^{74} -0.445042 q^{76} -2.24698 q^{77} -0.445042 q^{79} +1.00000 q^{81} +1.24698 q^{82} -1.80194 q^{86} +1.24698 q^{88} -1.80194 q^{89} +1.24698 q^{92} +2.24698 q^{98} +1.24698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} + 3q^{4} - q^{7} + 3q^{8} + 3q^{9} + O(q^{10}) \) \( 3q + 3q^{2} + 3q^{4} - q^{7} + 3q^{8} + 3q^{9} - q^{11} - q^{14} + 3q^{16} - q^{17} + 3q^{18} - q^{19} - q^{22} - q^{23} + 3q^{25} - q^{28} - q^{29} - q^{31} + 3q^{32} - q^{34} + 3q^{36} - q^{37} - q^{38} - q^{41} - q^{43} - q^{44} - q^{46} + 2q^{49} + 3q^{50} - q^{53} - q^{56} - q^{58} - q^{59} - q^{61} - q^{62} - q^{63} + 3q^{64} - q^{68} + 3q^{72} - q^{73} - q^{74} - q^{76} - 2q^{77} - q^{79} + 3q^{81} - q^{82} - q^{86} - q^{88} - q^{89} - q^{92} + 2q^{98} - q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(503\) \(1005\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) 1.00000 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(8\) 1.00000 1.00000
\(9\) 1.00000 1.00000
\(10\) 0 0
\(11\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −1.80194 −1.80194
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(18\) 1.00000 1.00000
\(19\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.24698 1.24698
\(23\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(24\) 0 0
\(25\) 1.00000 1.00000
\(26\) 0 0
\(27\) 0 0
\(28\) −1.80194 −1.80194
\(29\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(30\) 0 0
\(31\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(32\) 1.00000 1.00000
\(33\) 0 0
\(34\) −0.445042 −0.445042
\(35\) 0 0
\(36\) 1.00000 1.00000
\(37\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(38\) −0.445042 −0.445042
\(39\) 0 0
\(40\) 0 0
\(41\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(42\) 0 0
\(43\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(44\) 1.24698 1.24698
\(45\) 0 0
\(46\) 1.24698 1.24698
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) 2.24698 2.24698
\(50\) 1.00000 1.00000
\(51\) 0 0
\(52\) 0 0
\(53\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.80194 −1.80194
\(57\) 0 0
\(58\) −0.445042 −0.445042
\(59\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(60\) 0 0
\(61\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(62\) −0.445042 −0.445042
\(63\) −1.80194 −1.80194
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −0.445042 −0.445042
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 1.00000 1.00000
\(73\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(74\) −1.80194 −1.80194
\(75\) 0 0
\(76\) −0.445042 −0.445042
\(77\) −2.24698 −2.24698
\(78\) 0 0
\(79\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(80\) 0 0
\(81\) 1.00000 1.00000
\(82\) 1.24698 1.24698
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.80194 −1.80194
\(87\) 0 0
\(88\) 1.24698 1.24698
\(89\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.24698 1.24698
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 2.24698 2.24698
\(99\) 1.24698 1.24698
\(100\) 1.00000 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 1.24698 1.24698
\(107\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(108\) 0 0
\(109\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.80194 −1.80194
\(113\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.445042 −0.445042
\(117\) 0 0
\(118\) −1.80194 −1.80194
\(119\) 0.801938 0.801938
\(120\) 0 0
\(121\) 0.554958 0.554958
\(122\) 1.24698 1.24698
\(123\) 0 0
\(124\) −0.445042 −0.445042
\(125\) 0 0
\(126\) −1.80194 −1.80194
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 1.00000 1.00000
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0.801938 0.801938
\(134\) 0 0
\(135\) 0 0
\(136\) −0.445042 −0.445042
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 1.00000
\(145\) 0 0
\(146\) −1.80194 −1.80194
\(147\) 0 0
\(148\) −1.80194 −1.80194
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) −0.445042 −0.445042
\(153\) −0.445042 −0.445042
\(154\) −2.24698 −2.24698
\(155\) 0 0
\(156\) 0 0
\(157\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(158\) −0.445042 −0.445042
\(159\) 0 0
\(160\) 0 0
\(161\) −2.24698 −2.24698
\(162\) 1.00000 1.00000
\(163\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(164\) 1.24698 1.24698
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) −0.445042 −0.445042
\(172\) −1.80194 −1.80194
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) −1.80194 −1.80194
\(176\) 1.24698 1.24698
\(177\) 0 0
\(178\) −1.80194 −1.80194
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1.24698 1.24698
\(185\) 0 0
\(186\) 0 0
\(187\) −0.554958 −0.554958
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 2.24698 2.24698
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 1.24698 1.24698
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 1.00000 1.00000
\(201\) 0 0
\(202\) 0 0
\(203\) 0.801938 0.801938
\(204\) 0 0
\(205\) 0 0
\(206\) 1.24698 1.24698
\(207\) 1.24698 1.24698
\(208\) 0 0
\(209\) −0.554958 −0.554958
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 1.24698 1.24698
\(213\) 0 0
\(214\) −0.445042 −0.445042
\(215\) 0 0
\(216\) 0 0
\(217\) 0.801938 0.801938
\(218\) −1.80194 −1.80194
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) −1.80194 −1.80194
\(225\) 1.00000 1.00000
\(226\) −1.80194 −1.80194
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.445042 −0.445042
\(233\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.80194 −1.80194
\(237\) 0 0
\(238\) 0.801938 0.801938
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(242\) 0.554958 0.554958
\(243\) 0 0
\(244\) 1.24698 1.24698
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −0.445042 −0.445042
\(249\) 0 0
\(250\) 0 0
\(251\) 1.00000 1.00000
\(252\) −1.80194 −1.80194
\(253\) 1.55496 1.55496
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 3.24698 3.24698
\(260\) 0 0
\(261\) −0.445042 −0.445042
\(262\) 0 0
\(263\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0.801938 0.801938
\(267\) 0 0
\(268\) 0 0
\(269\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(270\) 0 0
\(271\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(272\) −0.445042 −0.445042
\(273\) 0 0
\(274\) 0 0
\(275\) 1.24698 1.24698
\(276\) 0 0
\(277\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(278\) −1.80194 −1.80194
\(279\) −0.445042 −0.445042
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.24698 −2.24698
\(288\) 1.00000 1.00000
\(289\) −0.801938 −0.801938
\(290\) 0 0
\(291\) 0 0
\(292\) −1.80194 −1.80194
\(293\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.80194 −1.80194
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 3.24698 3.24698
\(302\) 0 0
\(303\) 0 0
\(304\) −0.445042 −0.445042
\(305\) 0 0
\(306\) −0.445042 −0.445042
\(307\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(308\) −2.24698 −2.24698
\(309\) 0 0
\(310\) 0 0
\(311\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 1.24698 1.24698
\(315\) 0 0
\(316\) −0.445042 −0.445042
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) −0.554958 −0.554958
\(320\) 0 0
\(321\) 0 0
\(322\) −2.24698 −2.24698
\(323\) 0.198062 0.198062
\(324\) 1.00000 1.00000
\(325\) 0 0
\(326\) −0.445042 −0.445042
\(327\) 0 0
\(328\) 1.24698 1.24698
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) −1.80194 −1.80194
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(338\) 1.00000 1.00000
\(339\) 0 0
\(340\) 0 0
\(341\) −0.554958 −0.554958
\(342\) −0.445042 −0.445042
\(343\) −2.24698 −2.24698
\(344\) −1.80194 −1.80194
\(345\) 0 0
\(346\) 0 0
\(347\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(348\) 0 0
\(349\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(350\) −1.80194 −1.80194
\(351\) 0 0
\(352\) 1.24698 1.24698
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1.80194 −1.80194
\(357\) 0 0
\(358\) 0 0
\(359\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(360\) 0 0
\(361\) −0.801938 −0.801938
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 1.24698 1.24698
\(369\) 1.24698 1.24698
\(370\) 0 0
\(371\) −2.24698 −2.24698
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) −0.554958 −0.554958
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.80194 −1.80194
\(388\) 0 0
\(389\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(390\) 0 0
\(391\) −0.554958 −0.554958
\(392\) 2.24698 2.24698
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 1.24698 1.24698
\(397\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0.801938 0.801938
\(407\) −2.24698 −2.24698
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.24698 1.24698
\(413\) 3.24698 3.24698
\(414\) 1.24698 1.24698
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) −0.554958 −0.554958
\(419\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(420\) 0 0
\(421\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 1.24698 1.24698
\(425\) −0.445042 −0.445042
\(426\) 0 0
\(427\) −2.24698 −2.24698
\(428\) −0.445042 −0.445042
\(429\) 0 0
\(430\) 0 0
\(431\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0.801938 0.801938
\(435\) 0 0
\(436\) −1.80194 −1.80194
\(437\) −0.554958 −0.554958
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 2.24698 2.24698
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −1.80194 −1.80194
\(449\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(450\) 1.00000 1.00000
\(451\) 1.55496 1.55496
\(452\) −1.80194 −1.80194
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) −1.80194 −1.80194
\(459\) 0 0
\(460\) 0 0
\(461\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) −0.445042 −0.445042
\(465\) 0 0
\(466\) 1.24698 1.24698
\(467\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.80194 −1.80194
\(473\) −2.24698 −2.24698
\(474\) 0 0
\(475\) −0.445042 −0.445042
\(476\) 0.801938 0.801938
\(477\) 1.24698 1.24698
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1.24698 1.24698
\(483\) 0 0
\(484\) 0.554958 0.554958
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 1.24698 1.24698
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0.198062 0.198062
\(494\) 0 0
\(495\) 0 0
\(496\) −0.445042 −0.445042
\(497\) 0 0
\(498\) 0 0
\(499\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 1.00000 1.00000
\(503\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(504\) −1.80194 −1.80194
\(505\) 0 0
\(506\) 1.55496 1.55496
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 3.24698 3.24698
\(512\) 1.00000 1.00000
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 3.24698 3.24698
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −0.445042 −0.445042
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −0.445042 −0.445042
\(527\) 0.198062 0.198062
\(528\) 0 0
\(529\) 0.554958 0.554958
\(530\) 0 0
\(531\) −1.80194 −1.80194
\(532\) 0.801938 0.801938
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 2.00000 2.00000
\(539\) 2.80194 2.80194
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 1.24698 1.24698
\(543\) 0 0
\(544\) −0.445042 −0.445042
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 1.24698 1.24698
\(550\) 1.24698 1.24698
\(551\) 0.198062 0.198062
\(552\) 0 0
\(553\) 0.801938 0.801938
\(554\) −0.445042 −0.445042
\(555\) 0 0
\(556\) −1.80194 −1.80194
\(557\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(558\) −0.445042 −0.445042
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 2.00000 2.00000
\(567\) −1.80194 −1.80194
\(568\) 0 0
\(569\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −2.24698 −2.24698
\(575\) 1.24698 1.24698
\(576\) 1.00000 1.00000
\(577\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(578\) −0.801938 −0.801938
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 1.55496 1.55496
\(584\) −1.80194 −1.80194
\(585\) 0 0
\(586\) −1.80194 −1.80194
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) 0.198062 0.198062
\(590\) 0 0
\(591\) 0 0
\(592\) −1.80194 −1.80194
\(593\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 3.24698 3.24698
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(608\) −0.445042 −0.445042
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.445042 −0.445042
\(613\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(614\) 1.24698 1.24698
\(615\) 0 0
\(616\) −2.24698 −2.24698
\(617\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −1.80194 −1.80194
\(623\) 3.24698 3.24698
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 1.24698 1.24698
\(629\) 0.801938 0.801938
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) −0.445042 −0.445042
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −0.554958 −0.554958
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(644\) −2.24698 −2.24698
\(645\) 0 0
\(646\) 0.198062 0.198062
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 1.00000 1.00000
\(649\) −2.24698 −2.24698
\(650\) 0 0
\(651\) 0 0
\(652\) −0.445042 −0.445042
\(653\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.24698 1.24698
\(657\) −1.80194 −1.80194
\(658\) 0 0
\(659\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(660\) 0 0
\(661\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −1.80194 −1.80194
\(667\) −0.554958 −0.554958
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.55496 1.55496
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) −0.445042 −0.445042
\(675\) 0 0
\(676\) 1.00000 1.00000
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) −0.554958 −0.554958
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −0.445042 −0.445042
\(685\) 0 0
\(686\) −2.24698 −2.24698
\(687\) 0 0
\(688\) −1.80194 −1.80194
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) −2.24698 −2.24698
\(694\) −1.80194 −1.80194
\(695\) 0 0
\(696\) 0 0
\(697\) −0.554958 −0.554958
\(698\) 2.00000 2.00000
\(699\) 0 0
\(700\) −1.80194 −1.80194
\(701\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(702\) 0 0
\(703\) 0.801938 0.801938
\(704\) 1.24698 1.24698
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) −0.445042 −0.445042
\(712\) −1.80194 −1.80194
\(713\) −0.554958 −0.554958
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 1.24698 1.24698
\(719\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(720\) 0 0
\(721\) −2.24698 −2.24698
\(722\) −0.801938 −0.801938
\(723\) 0 0
\(724\) 0 0
\(725\) −0.445042 −0.445042
\(726\) 0 0
\(727\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0.801938 0.801938
\(732\) 0 0
\(733\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 1.24698 1.24698
\(737\) 0 0
\(738\) 1.24698 1.24698
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −2.24698 −2.24698
\(743\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) −0.554958 −0.554958
\(749\) 0.801938 0.801938
\(750\) 0 0
\(751\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 2.00000 2.00000
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 3.24698 3.24698
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) −1.80194 −1.80194
\(775\) −0.445042 −0.445042
\(776\) 0 0
\(777\) 0 0
\(778\) −0.445042 −0.445042
\(779\) −0.554958 −0.554958
\(780\) 0 0
\(781\) 0 0
\(782\) −0.554958 −0.554958
\(783\) 0 0
\(784\) 2.24698 2.24698
\(785\) 0 0
\(786\) 0 0
\(787\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.24698 3.24698
\(792\) 1.24698 1.24698
\(793\) 0 0
\(794\) −0.445042 −0.445042
\(795\) 0 0
\(796\) 0 0
\(797\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.00000 1.00000
\(801\) −1.80194 −1.80194
\(802\) 0 0
\(803\) −2.24698 −2.24698
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0.801938 0.801938
\(813\) 0 0
\(814\) −2.24698 −2.24698
\(815\) 0 0
\(816\) 0 0
\(817\) 0.801938 0.801938
\(818\) 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 \(\pi\)
\(824\) 1.24698 1.24698
\(825\) 0 0
\(826\) 3.24698 3.24698
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 1.24698 1.24698
\(829\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.00000 −1.00000
\(834\) 0 0
\(835\) 0 0
\(836\) −0.554958 −0.554958
\(837\) 0 0
\(838\) 1.24698 1.24698
\(839\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(840\) 0 0
\(841\) −0.801938 −0.801938
\(842\) −0.445042 −0.445042
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −1.00000 −1.00000
\(848\) 1.24698 1.24698
\(849\) 0 0
\(850\) −0.445042 −0.445042
\(851\) −2.24698 −2.24698
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) −2.24698 −2.24698
\(855\) 0 0
\(856\) −0.445042 −0.445042
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −0.445042 −0.445042
\(863\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0.801938 0.801938
\(869\) −0.554958 −0.554958
\(870\) 0 0
\(871\) 0 0
\(872\) −1.80194 −1.80194
\(873\) 0 0
\(874\) −0.554958 −0.554958
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 2.24698 2.24698
\(883\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 1.24698 1.24698
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) −1.80194 −1.80194
\(897\) 0 0
\(898\) −0.445042 −0.445042
\(899\) 0.198062 0.198062
\(900\) 1.00000 1.00000
\(901\) −0.554958 −0.554958
\(902\) 1.55496 1.55496
\(903\) 0 0
\(904\) −1.80194 −1.80194
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 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
\(916\) −1.80194 −1.80194
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −1.80194 −1.80194
\(923\) 0 0
\(924\) 0 0
\(925\) −1.80194 −1.80194
\(926\) 0 0
\(927\) 1.24698 1.24698
\(928\) −0.445042 −0.445042
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) −1.00000 −1.00000
\(932\) 1.24698 1.24698
\(933\) 0 0
\(934\) −0.445042 −0.445042
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(942\) 0 0
\(943\) 1.55496 1.55496
\(944\) −1.80194 −1.80194
\(945\) 0 0
\(946\) −2.24698 −2.24698
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −0.445042 −0.445042
\(951\) 0 0
\(952\) 0.801938 0.801938
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 1.24698 1.24698
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −0.801938 −0.801938
\(962\) 0 0
\(963\) −0.445042 −0.445042
\(964\) 1.24698 1.24698
\(965\) 0 0
\(966\) 0 0
\(967\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(968\) 0.554958 0.554958
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 3.24698 3.24698
\(974\) 0 0
\(975\) 0 0
\(976\) 1.24698 1.24698
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) −2.24698 −2.24698
\(980\) 0 0
\(981\) −1.80194 −1.80194
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0.198062 0.198062
\(987\) 0 0
\(988\) 0 0
\(989\) −2.24698 −2.24698
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) −0.445042 −0.445042
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(998\) 1.24698 1.24698
\(999\) 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 2008.1.c.b.501.1 yes 3
8.5 even 2 2008.1.c.a.501.1 3
251.250 odd 2 2008.1.c.a.501.1 3
2008.501 odd 2 CM 2008.1.c.b.501.1 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2008.1.c.a.501.1 3 8.5 even 2
2008.1.c.a.501.1 3 251.250 odd 2
2008.1.c.b.501.1 yes 3 1.1 even 1 trivial
2008.1.c.b.501.1 yes 3 2008.501 odd 2 CM