Properties

Label 1183.1.d.a.846.2
Level $1183$
Weight $1$
Character 1183.846
Self dual yes
Analytic conductor $0.590$
Analytic rank $0$
Dimension $3$
Projective image $D_{7}$
CM discriminant -7
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1183.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.590393909945\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
Defining polynomial: \(x^{3} - x^{2} - 2 x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{7}\)
Projective field: Galois closure of 7.1.1655595487.1
Artin image: $D_7$
Artin field: Galois closure of 7.1.1655595487.1

Embedding invariants

Embedding label 846.2
Root \(0.445042\) of defining polynomial
Character \(\chi\) \(=\) 1183.846

$q$-expansion

\(f(q)\) \(=\) \(q-0.445042 q^{2} -0.801938 q^{4} +1.00000 q^{7} +0.801938 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.445042 q^{2} -0.801938 q^{4} +1.00000 q^{7} +0.801938 q^{8} +1.00000 q^{9} -1.80194 q^{11} -0.445042 q^{14} +0.445042 q^{16} -0.445042 q^{18} +0.801938 q^{22} +1.24698 q^{23} +1.00000 q^{25} -0.801938 q^{28} -0.445042 q^{29} -1.00000 q^{32} -0.801938 q^{36} +1.24698 q^{37} -0.445042 q^{43} +1.44504 q^{44} -0.554958 q^{46} +1.00000 q^{49} -0.445042 q^{50} +1.24698 q^{53} +0.801938 q^{56} +0.198062 q^{58} +1.00000 q^{63} +1.24698 q^{67} +1.24698 q^{71} +0.801938 q^{72} -0.554958 q^{74} -1.80194 q^{77} -1.80194 q^{79} +1.00000 q^{81} +0.198062 q^{86} -1.44504 q^{88} -1.00000 q^{92} -0.445042 q^{98} -1.80194 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - q^{2} + 2q^{4} + 3q^{7} - 2q^{8} + 3q^{9} + O(q^{10}) \) \( 3q - q^{2} + 2q^{4} + 3q^{7} - 2q^{8} + 3q^{9} - q^{11} - q^{14} + q^{16} - q^{18} - 2q^{22} - q^{23} + 3q^{25} + 2q^{28} - q^{29} - 3q^{32} + 2q^{36} - q^{37} - q^{43} + 4q^{44} - 2q^{46} + 3q^{49} - q^{50} - q^{53} - 2q^{56} + 5q^{58} + 3q^{63} - q^{67} - q^{71} - 2q^{72} - 2q^{74} - q^{77} - q^{79} + 3q^{81} + 5q^{86} - 4q^{88} - 3q^{92} - q^{98} - q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) −0.801938 −0.801938
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) 1.00000 1.00000
\(8\) 0.801938 0.801938
\(9\) 1.00000 1.00000
\(10\) 0 0
\(11\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) −0.445042 −0.445042
\(15\) 0 0
\(16\) 0.445042 0.445042
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) −0.445042 −0.445042
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.801938 0.801938
\(23\) 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
\(28\) −0.801938 −0.801938
\(29\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) −1.00000 −1.00000
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.801938 −0.801938
\(37\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(44\) 1.44504 1.44504
\(45\) 0 0
\(46\) −0.554958 −0.554958
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) 1.00000 1.00000
\(50\) −0.445042 −0.445042
\(51\) 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
\(56\) 0.801938 0.801938
\(57\) 0 0
\(58\) 0.198062 0.198062
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 1.00000 1.00000
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(72\) 0.801938 0.801938
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) −0.554958 −0.554958
\(75\) 0 0
\(76\) 0 0
\(77\) −1.80194 −1.80194
\(78\) 0 0
\(79\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(80\) 0 0
\(81\) 1.00000 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.198062 0.198062
\(87\) 0 0
\(88\) −1.44504 −1.44504
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1.00000 −1.00000
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −0.445042 −0.445042
\(99\) −1.80194 −1.80194
\(100\) −0.801938 −0.801938
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −0.554958 −0.554958
\(107\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(108\) 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
\(112\) 0.445042 0.445042
\(113\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.356896 0.356896
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 2.24698 2.24698
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −0.445042 −0.445042
\(127\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(128\) 1.00000 1.00000
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.554958 −0.554958
\(135\) 0 0
\(136\) 0 0
\(137\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.554958 −0.554958
\(143\) 0 0
\(144\) 0.445042 0.445042
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −1.00000 −1.00000
\(149\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(150\) 0 0
\(151\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0.801938 0.801938
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0.801938 0.801938
\(159\) 0 0
\(160\) 0 0
\(161\) 1.24698 1.24698
\(162\) −0.445042 −0.445042
\(163\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 0 0
\(172\) 0.356896 0.356896
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 1.00000 1.00000
\(176\) −0.801938 −0.801938
\(177\) 0 0
\(178\) 0 0
\(179\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1.00000 1.00000
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(192\) 0 0
\(193\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.801938 −0.801938
\(197\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(198\) 0.801938 0.801938
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0.801938 0.801938
\(201\) 0 0
\(202\) 0 0
\(203\) −0.445042 −0.445042
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.24698 1.24698
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(212\) −1.00000 −1.00000
\(213\) 0 0
\(214\) 0.801938 0.801938
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0.801938 0.801938
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) −1.00000 −1.00000
\(225\) 1.00000 1.00000
\(226\) 0.801938 0.801938
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.356896 −0.356896
\(233\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −1.00000 −1.00000
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −0.801938 −0.801938
\(253\) −2.24698 −2.24698
\(254\) 0.198062 0.198062
\(255\) 0 0
\(256\) −0.445042 −0.445042
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 1.24698 1.24698
\(260\) 0 0
\(261\) −0.445042 −0.445042
\(262\) 0 0
\(263\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −1.00000 −1.00000
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0.801938 0.801938
\(275\) −1.80194 −1.80194
\(276\) 0 0
\(277\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) −1.00000 −1.00000
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −1.00000
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.00000 1.00000
\(297\) 0 0
\(298\) 0.198062 0.198062
\(299\) 0 0
\(300\) 0 0
\(301\) −0.445042 −0.445042
\(302\) 0.198062 0.198062
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 1.44504 1.44504
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 1.44504 1.44504
\(317\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(318\) 0 0
\(319\) 0.801938 0.801938
\(320\) 0 0
\(321\) 0 0
\(322\) −0.554958 −0.554958
\(323\) 0 0
\(324\) −0.801938 −0.801938
\(325\) 0 0
\(326\) 0.198062 0.198062
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(332\) 0 0
\(333\) 1.24698 1.24698
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 1.00000
\(344\) −0.356896 −0.356896
\(345\) 0 0
\(346\) 0 0
\(347\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) −0.445042 −0.445042
\(351\) 0 0
\(352\) 1.80194 1.80194
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0.801938 0.801938
\(359\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0.554958 0.554958
\(369\) 0 0
\(370\) 0 0
\(371\) 1.24698 1.24698
\(372\) 0 0
\(373\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0.198062 0.198062
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0.198062 0.198062
\(387\) −0.445042 −0.445042
\(388\) 0 0
\(389\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.801938 0.801938
\(393\) 0 0
\(394\) −0.890084 −0.890084
\(395\) 0 0
\(396\) 1.44504 1.44504
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.445042 0.445042
\(401\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0.198062 0.198062
\(407\) −2.24698 −2.24698
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −0.554958 −0.554958
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(422\) −0.554958 −0.554958
\(423\) 0 0
\(424\) 1.00000 1.00000
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 1.44504 1.44504
\(429\) 0 0
\(430\) 0 0
\(431\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.44504 1.44504
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(450\) −0.445042 −0.445042
\(451\) 0 0
\(452\) 1.44504 1.44504
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(464\) −0.198062 −0.198062
\(465\) 0 0
\(466\) 0.198062 0.198062
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 1.24698 1.24698
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.801938 0.801938
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 1.24698 1.24698
\(478\) 0.198062 0.198062
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −1.80194 −1.80194
\(485\) 0 0
\(486\) 0 0
\(487\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.24698 1.24698
\(498\) 0 0
\(499\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0.801938 0.801938
\(505\) 0 0
\(506\) 1.00000 1.00000
\(507\) 0 0
\(508\) 0.356896 0.356896
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.801938 −0.801938
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −0.554958 −0.554958
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0.198062 0.198062
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0.801938 0.801938
\(527\) 0 0
\(528\) 0 0
\(529\) 0.554958 0.554958
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 1.00000 1.00000
\(537\) 0 0
\(538\) 0 0
\(539\) −1.80194 −1.80194
\(540\) 0 0
\(541\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(548\) 1.44504 1.44504
\(549\) 0 0
\(550\) 0.801938 0.801938
\(551\) 0 0
\(552\) 0 0
\(553\) −1.80194 −1.80194
\(554\) 0.801938 0.801938
\(555\) 0 0
\(556\) 0 0
\(557\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −0.890084 −0.890084
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1.00000 1.00000
\(568\) 1.00000 1.00000
\(569\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(570\) 0 0
\(571\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.24698 1.24698
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −0.445042 −0.445042
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −2.24698 −2.24698
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.554958 0.554958
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.356896 0.356896
\(597\) 0 0
\(598\) 0 0
\(599\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0.198062 0.198062
\(603\) 1.24698 1.24698
\(604\) 0.356896 0.356896
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −1.44504 −1.44504
\(617\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(632\) −1.44504 −1.44504
\(633\) 0 0
\(634\) 0.801938 0.801938
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −0.356896 −0.356896
\(639\) 1.24698 1.24698
\(640\) 0 0
\(641\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) −1.00000 −1.00000
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0.801938 0.801938
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.356896 0.356896
\(653\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 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 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) −0.554958 −0.554958
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −0.554958 −0.554958
\(667\) −0.554958 −0.554958
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(674\) 0.198062 0.198062
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.445042 −0.445042
\(687\) 0 0
\(688\) −0.198062 −0.198062
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) −1.80194 −1.80194
\(694\) −0.554958 −0.554958
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −0.801938 −0.801938
\(701\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(710\) 0 0
\(711\) −1.80194 −1.80194
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.44504 1.44504
\(717\) 0 0
\(718\) −0.554958 −0.554958
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.445042 −0.445042
\(723\) 0 0
\(724\) 0 0
\(725\) −0.445042 −0.445042
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −1.24698 −1.24698
\(737\) −2.24698 −2.24698
\(738\) 0 0
\(739\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.554958 −0.554958
\(743\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −0.554958 −0.554958
\(747\) 0 0
\(748\) 0 0
\(749\) −1.80194 −1.80194
\(750\) 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
\(757\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(758\) 0.198062 0.198062
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) −1.80194 −1.80194
\(764\) 0.356896 0.356896
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.356896 0.356896
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0.198062 0.198062
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.801938 0.801938
\(779\) 0 0
\(780\) 0 0
\(781\) −2.24698 −2.24698
\(782\) 0 0
\(783\) 0 0
\(784\) 0.445042 0.445042
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) −1.60388 −1.60388
\(789\) 0 0
\(790\) 0 0
\(791\) −1.80194 −1.80194
\(792\) −1.44504 −1.44504
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −1.00000 −1.00000
\(801\) 0 0
\(802\) 0.198062 0.198062
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0.356896 0.356896
\(813\) 0 0
\(814\) 1.00000 1.00000
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 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
\(823\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(828\) −1.00000 −1.00000
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) −0.801938 −0.801938
\(842\) −0.890084 −0.890084
\(843\) 0 0
\(844\) −1.00000 −1.00000
\(845\) 0 0
\(846\) 0 0
\(847\) 2.24698 2.24698
\(848\) 0.554958 0.554958
\(849\) 0 0
\(850\) 0 0
\(851\) 1.55496 1.55496
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −1.44504 −1.44504
\(857\) 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
\(862\) 0.801938 0.801938
\(863\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 3.24698 3.24698
\(870\) 0 0
\(871\) 0 0
\(872\) −1.44504 −1.44504
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −0.445042 −0.445042
\(883\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0.198062 0.198062
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) −0.445042 −0.445042
\(890\) 0 0
\(891\) −1.80194 −1.80194
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000 1.00000
\(897\) 0 0
\(898\) −0.554958 −0.554958
\(899\) 0 0
\(900\) −0.801938 −0.801938
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) −1.44504 −1.44504
\(905\) 0 0
\(906\) 0 0
\(907\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0.801938 0.801938
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1.24698 1.24698
\(926\) 0.801938 0.801938
\(927\) 0 0
\(928\) 0.445042 0.445042
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0.356896 0.356896
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) −0.554958 −0.554958
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) −0.356896 −0.356896
\(947\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(954\) −0.554958 −0.554958
\(955\) 0 0
\(956\) 0.356896 0.356896
\(957\) 0 0
\(958\) 0 0
\(959\) −1.80194 −1.80194
\(960\) 0 0
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) −1.80194 −1.80194
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(968\) 1.80194 1.80194
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0.801938 0.801938
\(975\) 0 0
\(976\) 0 0
\(977\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −1.80194 −1.80194
\(982\) −0.554958 −0.554958
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −0.554958 −0.554958
\(990\) 0 0
\(991\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) −0.554958 −0.554958
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0.198062 0.198062
\(999\) 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 1183.1.d.a.846.2 3
7.6 odd 2 CM 1183.1.d.a.846.2 3
13.2 odd 12 1183.1.t.a.1161.3 12
13.3 even 3 1183.1.n.b.867.2 6
13.4 even 6 1183.1.n.a.146.2 6
13.5 odd 4 1183.1.b.a.1182.4 6
13.6 odd 12 1183.1.t.a.699.4 12
13.7 odd 12 1183.1.t.a.699.3 12
13.8 odd 4 1183.1.b.a.1182.3 6
13.9 even 3 1183.1.n.b.146.2 6
13.10 even 6 1183.1.n.a.867.2 6
13.11 odd 12 1183.1.t.a.1161.4 12
13.12 even 2 1183.1.d.b.846.2 yes 3
91.6 even 12 1183.1.t.a.699.4 12
91.20 even 12 1183.1.t.a.699.3 12
91.34 even 4 1183.1.b.a.1182.3 6
91.41 even 12 1183.1.t.a.1161.3 12
91.48 odd 6 1183.1.n.b.146.2 6
91.55 odd 6 1183.1.n.b.867.2 6
91.62 odd 6 1183.1.n.a.867.2 6
91.69 odd 6 1183.1.n.a.146.2 6
91.76 even 12 1183.1.t.a.1161.4 12
91.83 even 4 1183.1.b.a.1182.4 6
91.90 odd 2 1183.1.d.b.846.2 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1183.1.b.a.1182.3 6 13.8 odd 4
1183.1.b.a.1182.3 6 91.34 even 4
1183.1.b.a.1182.4 6 13.5 odd 4
1183.1.b.a.1182.4 6 91.83 even 4
1183.1.d.a.846.2 3 1.1 even 1 trivial
1183.1.d.a.846.2 3 7.6 odd 2 CM
1183.1.d.b.846.2 yes 3 13.12 even 2
1183.1.d.b.846.2 yes 3 91.90 odd 2
1183.1.n.a.146.2 6 13.4 even 6
1183.1.n.a.146.2 6 91.69 odd 6
1183.1.n.a.867.2 6 13.10 even 6
1183.1.n.a.867.2 6 91.62 odd 6
1183.1.n.b.146.2 6 13.9 even 3
1183.1.n.b.146.2 6 91.48 odd 6
1183.1.n.b.867.2 6 13.3 even 3
1183.1.n.b.867.2 6 91.55 odd 6
1183.1.t.a.699.3 12 13.7 odd 12
1183.1.t.a.699.3 12 91.20 even 12
1183.1.t.a.699.4 12 13.6 odd 12
1183.1.t.a.699.4 12 91.6 even 12
1183.1.t.a.1161.3 12 13.2 odd 12
1183.1.t.a.1161.3 12 91.41 even 12
1183.1.t.a.1161.4 12 13.11 odd 12
1183.1.t.a.1161.4 12 91.76 even 12