Properties

Label 1775.1.c.a.1774.5
Level $1775$
Weight $1$
Character 1775.1774
Analytic conductor $0.886$
Analytic rank $0$
Dimension $6$
Projective image $D_{7}$
CM discriminant -71
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1775 = 5^{2} \cdot 71 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1775.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.885840397424\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.153664.1
Defining polynomial: \( x^{6} + 5x^{4} + 6x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 71)
Projective image: \(D_{7}\)
Projective field: Galois closure of 7.1.357911.1
Artin image: $C_4\times D_7$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{28} - \cdots)\)

Embedding invariants

Embedding label 1774.5
Root \(-1.24698i\) of defining polynomial
Character \(\chi\) \(=\) 1775.1774
Dual form 1775.1.c.a.1774.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.24698i q^{2} +1.80194i q^{3} -0.554958 q^{4} -2.24698 q^{6} +0.554958i q^{8} -2.24698 q^{9} +O(q^{10})\) \(q+1.24698i q^{2} +1.80194i q^{3} -0.554958 q^{4} -2.24698 q^{6} +0.554958i q^{8} -2.24698 q^{9} -1.00000i q^{12} -1.24698 q^{16} -2.80194i q^{18} -1.24698 q^{19} -1.00000 q^{24} -2.24698i q^{27} +1.80194 q^{29} -1.00000i q^{32} +1.24698 q^{36} +1.24698i q^{37} -1.55496i q^{38} +0.445042i q^{43} -2.24698i q^{48} -1.00000 q^{49} +2.80194 q^{54} -2.24698i q^{57} +2.24698i q^{58} +1.00000 q^{71} -1.24698i q^{72} +0.445042i q^{73} -1.55496 q^{74} +0.692021 q^{76} +0.445042 q^{79} +1.80194 q^{81} -1.24698i q^{83} -0.554958 q^{86} +3.24698i q^{87} +1.80194 q^{89} +1.80194 q^{96} -1.24698i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 2 q^{16} + 2 q^{19} - 6 q^{24} + 2 q^{29} - 2 q^{36} - 6 q^{49} + 8 q^{54} + 6 q^{71} - 10 q^{74} - 6 q^{76} + 2 q^{79} + 2 q^{81} - 4 q^{86} + 2 q^{89} + 2 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1775\mathbb{Z}\right)^\times\).

\(n\) \(427\) \(1001\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.24698i 1.24698i 0.781831 + 0.623490i \(0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(3\) 1.80194i 1.80194i 0.433884 + 0.900969i \(0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(4\) −0.554958 −0.554958
\(5\) 0 0
\(6\) −2.24698 −2.24698
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0.554958i 0.554958i
\(9\) −2.24698 −2.24698
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) − 1.00000i − 1.00000i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.24698 −1.24698
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) − 2.80194i − 2.80194i
\(19\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −1.00000 −1.00000
\(25\) 0 0
\(26\) 0 0
\(27\) − 2.24698i − 2.24698i
\(28\) 0 0
\(29\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) − 1.00000i − 1.00000i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 1.24698 1.24698
\(37\) 1.24698i 1.24698i 0.781831 + 0.623490i \(0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(38\) − 1.55496i − 1.55496i
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0.445042i 0.445042i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) − 2.24698i − 2.24698i
\(49\) −1.00000 −1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 2.80194 2.80194
\(55\) 0 0
\(56\) 0 0
\(57\) − 2.24698i − 2.24698i
\(58\) 2.24698i 2.24698i
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.00000 1.00000
\(72\) − 1.24698i − 1.24698i
\(73\) 0.445042i 0.445042i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(74\) −1.55496 −1.55496
\(75\) 0 0
\(76\) 0.692021 0.692021
\(77\) 0 0
\(78\) 0 0
\(79\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(80\) 0 0
\(81\) 1.80194 1.80194
\(82\) 0 0
\(83\) − 1.24698i − 1.24698i −0.781831 0.623490i \(-0.785714\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.554958 −0.554958
\(87\) 3.24698i 3.24698i
\(88\) 0 0
\(89\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 1.80194 1.80194
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) − 1.24698i − 1.24698i
\(99\) 0 0
\(100\) 0 0
\(101\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(102\) 0 0
\(103\) 1.80194i 1.80194i 0.433884 + 0.900969i \(0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 1.24698i 1.24698i
\(109\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(110\) 0 0
\(111\) −2.24698 −2.24698
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 2.80194 2.80194
\(115\) 0 0
\(116\) −1.00000 −1.00000
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) − 1.00000i − 1.00000i
\(129\) −0.801938 −0.801938
\(130\) 0 0
\(131\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.24698i 1.24698i
\(143\) 0 0
\(144\) 2.80194 2.80194
\(145\) 0 0
\(146\) −0.554958 −0.554958
\(147\) − 1.80194i − 1.80194i
\(148\) − 0.692021i − 0.692021i
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(152\) − 0.692021i − 0.692021i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) − 1.80194i − 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(158\) 0.554958i 0.554958i
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 2.24698i 2.24698i
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.55496 1.55496
\(167\) − 0.445042i − 0.445042i −0.974928 0.222521i \(-0.928571\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(168\) 0 0
\(169\) −1.00000 −1.00000
\(170\) 0 0
\(171\) 2.80194 2.80194
\(172\) − 0.246980i − 0.246980i
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) −4.04892 −4.04892
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 2.24698i 2.24698i
\(179\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.554958 0.554958
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 1.55496i 1.55496i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −2.24698 −2.24698
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 1.80194i 1.80194i
\(214\) −2.49396 −2.49396
\(215\) 0 0
\(216\) 1.24698 1.24698
\(217\) 0 0
\(218\) 2.24698i 2.24698i
\(219\) −0.801938 −0.801938
\(220\) 0 0
\(221\) 0 0
\(222\) − 2.80194i − 2.80194i
\(223\) − 1.24698i − 1.24698i −0.781831 0.623490i \(-0.785714\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 1.24698i 1.24698i
\(229\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.00000i 1.00000i
\(233\) − 1.24698i − 1.24698i −0.781831 0.623490i \(-0.785714\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0.801938i 0.801938i
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 1.24698i 1.24698i
\(243\) 1.00000i 1.00000i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 2.24698 2.24698
\(250\) 0 0
\(251\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.24698 1.24698
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) − 1.00000i − 1.00000i
\(259\) 0 0
\(260\) 0 0
\(261\) −4.04892 −4.04892
\(262\) − 0.554958i − 0.554958i
\(263\) 0.445042i 0.445042i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 3.24698i 3.24698i
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.24698i 1.24698i 0.781831 + 0.623490i \(0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(278\) 0 0
\(279\) 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 \(0.5\pi\)
\(284\) −0.554958 −0.554958
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 2.24698i 2.24698i
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) − 0.246980i − 0.246980i
\(293\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(294\) 2.24698 2.24698
\(295\) 0 0
\(296\) −0.692021 −0.692021
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) − 2.24698i − 2.24698i
\(303\) 2.24698i 2.24698i
\(304\) 1.55496 1.55496
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) −3.24698 −3.24698
\(310\) 0 0
\(311\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(312\) 0 0
\(313\) − 1.24698i − 1.24698i −0.781831 0.623490i \(-0.785714\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(314\) 2.24698 2.24698
\(315\) 0 0
\(316\) −0.246980 −0.246980
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −3.60388 −3.60388
\(322\) 0 0
\(323\) 0 0
\(324\) −1.00000 −1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) 3.24698i 3.24698i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0.692021i 0.692021i
\(333\) − 2.80194i − 2.80194i
\(334\) 0.554958 0.554958
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) − 1.24698i − 1.24698i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 3.49396i 3.49396i
\(343\) 0 0
\(344\) −0.246980 −0.246980
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) − 1.80194i − 1.80194i
\(349\) 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
\(356\) −1.00000 −1.00000
\(357\) 0 0
\(358\) 0.554958i 0.554958i
\(359\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(360\) 0 0
\(361\) 0.554958 0.554958
\(362\) 0 0
\(363\) 1.80194i 1.80194i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) − 0.445042i − 0.445042i −0.974928 0.222521i \(-0.928571\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0.445042i 0.445042i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) − 2.24698i − 2.24698i
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 1.80194 1.80194
\(385\) 0 0
\(386\) 0 0
\(387\) − 1.00000i − 1.00000i
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) − 0.554958i − 0.554958i
\(393\) − 0.801938i − 0.801938i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) − 1.55496i − 1.55496i
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.692021 −0.692021
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) − 1.00000i − 1.00000i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) −2.24698 −2.24698
\(427\) 0 0
\(428\) − 1.10992i − 1.10992i
\(429\) 0 0
\(430\) 0 0
\(431\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(432\) 2.80194i 2.80194i
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.00000 −1.00000
\(437\) 0 0
\(438\) − 1.00000i − 1.00000i
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 2.24698 2.24698
\(442\) 0 0
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 1.24698 1.24698
\(445\) 0 0
\(446\) 1.55496 1.55496
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) − 3.24698i − 3.24698i
\(454\) 0 0
\(455\) 0 0
\(456\) 1.24698 1.24698
\(457\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0.554958i 0.554958i
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) − 1.24698i − 1.24698i −0.781831 0.623490i \(-0.785714\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(464\) −2.24698 −2.24698
\(465\) 0 0
\(466\) 1.55496 1.55496
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 3.24698 3.24698
\(472\) 0 0
\(473\) 0 0
\(474\) −1.00000 −1.00000
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.554958 −0.554958
\(485\) 0 0
\(486\) −1.24698 −1.24698
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 2.80194i 2.80194i
\(499\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(500\) 0 0
\(501\) 0.801938 0.801938
\(502\) 1.55496i 1.55496i
\(503\) 1.80194i 1.80194i 0.433884 + 0.900969i \(0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) − 1.80194i − 1.80194i
\(508\) 0 0
\(509\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.554958i 0.554958i
\(513\) 2.80194i 2.80194i
\(514\) 0 0
\(515\) 0 0
\(516\) 0.445042 0.445042
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(522\) − 5.04892i − 5.04892i
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 0.246980 0.246980
\(525\) 0 0
\(526\) −0.554958 −0.554958
\(527\) 0 0
\(528\) 0 0
\(529\) −1.00000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −4.04892 −4.04892
\(535\) 0 0
\(536\) 0 0
\(537\) 0.801938i 0.801938i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) − 2.24698i − 2.24698i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.24698i 1.24698i 0.781831 + 0.623490i \(0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.24698 −2.24698
\(552\) 0 0
\(553\) 0 0
\(554\) −1.55496 −1.55496
\(555\) 0 0
\(556\) 0 0
\(557\) − 1.80194i − 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(558\) 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
\(567\) 0 0
\(568\) 0.554958i 0.554958i
\(569\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(570\) 0 0
\(571\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(572\) 0 0
\(573\) − 3.24698i − 3.24698i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) − 0.445042i − 0.445042i −0.974928 0.222521i \(-0.928571\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(578\) − 1.24698i − 1.24698i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −0.246980 −0.246980
\(585\) 0 0
\(586\) 2.49396 2.49396
\(587\) − 1.80194i − 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(588\) 1.00000i 1.00000i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) − 1.55496i − 1.55496i
\(593\) 1.80194i 1.80194i 0.433884 + 0.900969i \(0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) − 2.24698i − 2.24698i
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.00000 1.00000
\(605\) 0 0
\(606\) −2.80194 −2.80194
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 1.24698i 1.24698i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 1.80194i 1.80194i 0.433884 + 0.900969i \(0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 0.445042i − 0.445042i −0.974928 0.222521i \(-0.928571\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(618\) − 4.04892i − 4.04892i
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 1.55496i 1.55496i
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 1.55496 1.55496
\(627\) 0 0
\(628\) 1.00000i 1.00000i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0.246980i 0.246980i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −2.24698 −2.24698
\(640\) 0 0
\(641\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(642\) − 4.49396i − 4.49396i
\(643\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 1.00000i 1.00000i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) −4.04892 −4.04892
\(655\) 0 0
\(656\) 0 0
\(657\) − 1.00000i − 1.00000i
\(658\) 0 0
\(659\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.692021 0.692021
\(665\) 0 0
\(666\) 3.49396 3.49396
\(667\) 0 0
\(668\) 0.246980i 0.246980i
\(669\) 2.24698 2.24698
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0.554958 0.554958
\(677\) − 1.80194i − 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) −1.55496 −1.55496
\(685\) 0 0
\(686\) 0 0
\(687\) 0.801938i 0.801938i
\(688\) − 0.554958i − 0.554958i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) −1.80194 −1.80194
\(697\) 0 0
\(698\) 0 0
\(699\) 2.24698 2.24698
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) − 1.55496i − 1.55496i
\(704\) 0 0
\(705\) 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
\(712\) 1.00000i 1.00000i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.246980 −0.246980
\(717\) 0 0
\(718\) 0.554958i 0.554958i
\(719\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.692021i 0.692021i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) −2.24698 −2.24698
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0.554958 0.554958
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(740\) 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
\(746\) −0.554958 −0.554958
\(747\) 2.80194i 2.80194i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 2.24698i 2.24698i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 2.24698i 2.24698i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 1.00000 1.00000
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 2.24698i 2.24698i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 1.24698 1.24698
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) − 4.04892i − 4.04892i
\(784\) 1.24698 1.24698
\(785\) 0 0
\(786\) 1.00000 1.00000
\(787\) − 1.80194i − 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(788\) 0 0
\(789\) −0.801938 −0.801938
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0.692021 0.692021
\(797\) 1.24698i 1.24698i 0.781831 + 0.623490i \(0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −4.04892 −4.04892
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0.692021i 0.692021i
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(812\) 0 0
\(813\) − 3.24698i − 3.24698i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) − 0.554958i − 0.554958i
\(818\) 2.24698i 2.24698i
\(819\) 0 0
\(820\) 0 0
\(821\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) −1.00000 −1.00000
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(830\) 0 0
\(831\) −2.24698 −2.24698
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 2.24698i 2.24698i
\(839\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(840\) 0 0
\(841\) 2.24698 2.24698
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) − 1.00000i − 1.00000i
\(853\) 1.80194i 1.80194i 0.433884 + 0.900969i \(0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −1.10992 −1.10992
\(857\) − 1.80194i − 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 1.55496i 1.55496i
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) −2.24698 −2.24698
\(865\) 0 0
\(866\) 0 0
\(867\) − 1.80194i − 1.80194i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 1.00000i 1.00000i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0.445042 0.445042
\(877\) − 0.445042i − 0.445042i −0.974928 0.222521i \(-0.928571\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(878\) 0 0
\(879\) 3.60388 3.60388
\(880\) 0 0
\(881\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(882\) 2.80194i 2.80194i
\(883\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) − 1.24698i − 1.24698i
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0.692021i 0.692021i
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 4.04892 4.04892
\(907\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 0 0
\(909\) −2.80194 −2.80194
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 2.80194i 2.80194i
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −0.246980 −0.246980
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 1.55496 1.55496
\(927\) − 4.04892i − 4.04892i
\(928\) − 1.80194i − 1.80194i
\(929\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(930\) 0 0
\(931\) 1.24698 1.24698
\(932\) 0.692021i 0.692021i
\(933\) 2.24698i 2.24698i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 0 0
\(939\) 2.24698 2.24698
\(940\) 0 0
\(941\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(942\) 4.04892i 4.04892i
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 0.445042i − 0.445042i −0.974928 0.222521i \(-0.928571\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(948\) − 0.445042i − 0.445042i
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0.445042i 0.445042i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) − 4.49396i − 4.49396i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 0.554958i 0.554958i
\(969\) 0 0
\(970\) 0 0
\(971\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(972\) − 0.554958i − 0.554958i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 1.80194i − 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −4.04892 −4.04892
\(982\) 0 0
\(983\) − 1.24698i − 1.24698i −0.781831 0.623490i \(-0.785714\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) −1.24698 −1.24698
\(997\) − 0.445042i − 0.445042i −0.974928 0.222521i \(-0.928571\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(998\) 2.24698i 2.24698i
\(999\) 2.80194 2.80194
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 1775.1.c.a.1774.5 6
5.2 odd 4 1775.1.d.b.851.1 3
5.3 odd 4 71.1.b.a.70.3 3
5.4 even 2 inner 1775.1.c.a.1774.2 6
15.8 even 4 639.1.d.a.496.1 3
20.3 even 4 1136.1.h.a.993.3 3
35.3 even 12 3479.1.g.d.1206.1 6
35.13 even 4 3479.1.d.e.638.3 3
35.18 odd 12 3479.1.g.e.1206.1 6
35.23 odd 12 3479.1.g.e.851.1 6
35.33 even 12 3479.1.g.d.851.1 6
71.70 odd 2 CM 1775.1.c.a.1774.5 6
355.212 even 4 1775.1.d.b.851.1 3
355.283 even 4 71.1.b.a.70.3 3
355.354 odd 2 inner 1775.1.c.a.1774.2 6
1065.638 odd 4 639.1.d.a.496.1 3
1420.283 odd 4 1136.1.h.a.993.3 3
2485.283 odd 12 3479.1.g.d.1206.1 6
2485.993 odd 4 3479.1.d.e.638.3 3
2485.1348 even 12 3479.1.g.e.1206.1 6
2485.1703 even 12 3479.1.g.e.851.1 6
2485.2413 odd 12 3479.1.g.d.851.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
71.1.b.a.70.3 3 5.3 odd 4
71.1.b.a.70.3 3 355.283 even 4
639.1.d.a.496.1 3 15.8 even 4
639.1.d.a.496.1 3 1065.638 odd 4
1136.1.h.a.993.3 3 20.3 even 4
1136.1.h.a.993.3 3 1420.283 odd 4
1775.1.c.a.1774.2 6 5.4 even 2 inner
1775.1.c.a.1774.2 6 355.354 odd 2 inner
1775.1.c.a.1774.5 6 1.1 even 1 trivial
1775.1.c.a.1774.5 6 71.70 odd 2 CM
1775.1.d.b.851.1 3 5.2 odd 4
1775.1.d.b.851.1 3 355.212 even 4
3479.1.d.e.638.3 3 35.13 even 4
3479.1.d.e.638.3 3 2485.993 odd 4
3479.1.g.d.851.1 6 35.33 even 12
3479.1.g.d.851.1 6 2485.2413 odd 12
3479.1.g.d.1206.1 6 35.3 even 12
3479.1.g.d.1206.1 6 2485.283 odd 12
3479.1.g.e.851.1 6 35.23 odd 12
3479.1.g.e.851.1 6 2485.1703 even 12
3479.1.g.e.1206.1 6 35.18 odd 12
3479.1.g.e.1206.1 6 2485.1348 even 12