Properties

Label 1444.1.b.a.723.2
Level $1444$
Weight $1$
Character 1444.723
Self dual yes
Analytic conductor $0.721$
Analytic rank $0$
Dimension $2$
Projective image $D_{5}$
CM discriminant -4
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1444 = 2^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1444.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.720649878242\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \(x^{2} - x - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{5}\)
Projective field: Galois closure of 5.1.2085136.1

Embedding invariants

Embedding label 723.2
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 1444.723

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +0.618034 q^{5} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} +0.618034 q^{5} -1.00000 q^{8} +1.00000 q^{9} -0.618034 q^{10} +1.61803 q^{13} +1.00000 q^{16} -1.61803 q^{17} -1.00000 q^{18} +0.618034 q^{20} -0.618034 q^{25} -1.61803 q^{26} +1.61803 q^{29} -1.00000 q^{32} +1.61803 q^{34} +1.00000 q^{36} -0.618034 q^{37} -0.618034 q^{40} -0.618034 q^{41} +0.618034 q^{45} +1.00000 q^{49} +0.618034 q^{50} +1.61803 q^{52} -0.618034 q^{53} -1.61803 q^{58} -1.61803 q^{61} +1.00000 q^{64} +1.00000 q^{65} -1.61803 q^{68} -1.00000 q^{72} +0.618034 q^{73} +0.618034 q^{74} +0.618034 q^{80} +1.00000 q^{81} +0.618034 q^{82} -1.00000 q^{85} -0.618034 q^{89} -0.618034 q^{90} +1.61803 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} + 2q^{4} - q^{5} - 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q - 2q^{2} + 2q^{4} - q^{5} - 2q^{8} + 2q^{9} + q^{10} + q^{13} + 2q^{16} - q^{17} - 2q^{18} - q^{20} + q^{25} - q^{26} + q^{29} - 2q^{32} + q^{34} + 2q^{36} + q^{37} + q^{40} + q^{41} - q^{45} + 2q^{49} - q^{50} + q^{52} + q^{53} - q^{58} - q^{61} + 2q^{64} + 2q^{65} - q^{68} - 2q^{72} - q^{73} - q^{74} - q^{80} + 2q^{81} - q^{82} - 2q^{85} + q^{89} + q^{90} + q^{97} - 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1444\mathbb{Z}\right)^\times\).

\(n\) \(723\) \(1085\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −1.00000
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) 1.00000 1.00000
\(5\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) −1.00000 −1.00000
\(9\) 1.00000 1.00000
\(10\) −0.618034 −0.618034
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(18\) −1.00000 −1.00000
\(19\) 0 0
\(20\) 0.618034 0.618034
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) −0.618034 −0.618034
\(26\) −1.61803 −1.61803
\(27\) 0 0
\(28\) 0 0
\(29\) 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 \(\pi\)
\(32\) −1.00000 −1.00000
\(33\) 0 0
\(34\) 1.61803 1.61803
\(35\) 0 0
\(36\) 1.00000 1.00000
\(37\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.618034 −0.618034
\(41\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0.618034 0.618034
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) 1.00000 1.00000
\(50\) 0.618034 0.618034
\(51\) 0 0
\(52\) 1.61803 1.61803
\(53\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −1.61803 −1.61803
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 1.00000 1.00000
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −1.61803 −1.61803
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −1.00000 −1.00000
\(73\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(74\) 0.618034 0.618034
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0.618034 0.618034
\(81\) 1.00000 1.00000
\(82\) 0.618034 0.618034
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) −1.00000 −1.00000
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(90\) −0.618034 −0.618034
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(98\) −1.00000 −1.00000
\(99\) 0 0
\(100\) −0.618034 −0.618034
\(101\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) −1.61803 −1.61803
\(105\) 0 0
\(106\) 0.618034 0.618034
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 1.61803 1.61803
\(117\) 1.61803 1.61803
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 1.61803 1.61803
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −1.00000
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −1.00000 −1.00000
\(129\) 0 0
\(130\) −1.00000 −1.00000
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 1.61803 1.61803
\(137\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 1.00000
\(145\) 1.00000 1.00000
\(146\) −0.618034 −0.618034
\(147\) 0 0
\(148\) −0.618034 −0.618034
\(149\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) −1.61803 −1.61803
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −0.618034 −0.618034
\(161\) 0 0
\(162\) −1.00000 −1.00000
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) −0.618034 −0.618034
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 1.61803 1.61803
\(170\) 1.00000 1.00000
\(171\) 0 0
\(172\) 0 0
\(173\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0.618034 0.618034
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0.618034 0.618034
\(181\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.381966 −0.381966
\(186\) 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
\(193\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(194\) −1.61803 −1.61803
\(195\) 0 0
\(196\) 1.00000 1.00000
\(197\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0.618034 0.618034
\(201\) 0 0
\(202\) −0.618034 −0.618034
\(203\) 0 0
\(204\) 0 0
\(205\) −0.381966 −0.381966
\(206\) 0 0
\(207\) 0 0
\(208\) 1.61803 1.61803
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) −0.618034 −0.618034
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0.618034 0.618034
\(219\) 0 0
\(220\) 0 0
\(221\) −2.61803 −2.61803
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) −0.618034 −0.618034
\(226\) −1.61803 −1.61803
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −1.61803 −1.61803
\(233\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(234\) −1.61803 −1.61803
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(242\) −1.00000 −1.00000
\(243\) 0 0
\(244\) −1.61803 −1.61803
\(245\) 0.618034 0.618034
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 1.00000 1.00000
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1.00000 1.00000
\(261\) 1.61803 1.61803
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) −0.381966 −0.381966
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −1.61803 −1.61803
\(273\) 0 0
\(274\) −0.618034 −0.618034
\(275\) 0 0
\(276\) 0 0
\(277\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −1.00000
\(289\) 1.61803 1.61803
\(290\) −1.00000 −1.00000
\(291\) 0 0
\(292\) 0.618034 0.618034
\(293\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.618034 0.618034
\(297\) 0 0
\(298\) 1.61803 1.61803
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.00000 −1.00000
\(306\) 1.61803 1.61803
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(314\) 1.61803 1.61803
\(315\) 0 0
\(316\) 0 0
\(317\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.618034 0.618034
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 1.00000
\(325\) −1.00000 −1.00000
\(326\) 0 0
\(327\) 0 0
\(328\) 0.618034 0.618034
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) −0.618034 −0.618034
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(338\) −1.61803 −1.61803
\(339\) 0 0
\(340\) −1.00000 −1.00000
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0.618034 0.618034
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.618034 −0.618034
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) −0.618034 −0.618034
\(361\) 0 0
\(362\) 2.00000 2.00000
\(363\) 0 0
\(364\) 0 0
\(365\) 0.381966 0.381966
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) −0.618034 −0.618034
\(370\) 0.381966 0.381966
\(371\) 0 0
\(372\) 0 0
\(373\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.61803 2.61803
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2.00000 2.00000
\(387\) 0 0
\(388\) 1.61803 1.61803
\(389\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.00000 −1.00000
\(393\) 0 0
\(394\) 1.61803 1.61803
\(395\) 0 0
\(396\) 0 0
\(397\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.618034 −0.618034
\(401\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.618034 0.618034
\(405\) 0.618034 0.618034
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(410\) 0.381966 0.381966
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −1.61803 −1.61803
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0.618034 0.618034
\(425\) 1.00000 1.00000
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.618034 −0.618034
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 1.00000 1.00000
\(442\) 2.61803 2.61803
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) −0.381966 −0.381966
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(450\) 0.618034 0.618034
\(451\) 0 0
\(452\) 1.61803 1.61803
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(458\) −0.618034 −0.618034
\(459\) 0 0
\(460\) 0 0
\(461\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 1.61803 1.61803
\(465\) 0 0
\(466\) 1.61803 1.61803
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 1.61803 1.61803
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.618034 −0.618034
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) −1.00000 −1.00000
\(482\) 2.00000 2.00000
\(483\) 0 0
\(484\) 1.00000 1.00000
\(485\) 1.00000 1.00000
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 1.61803 1.61803
\(489\) 0 0
\(490\) −0.618034 −0.618034
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) −2.61803 −2.61803
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) −1.00000 −1.00000
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0.381966 0.381966
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 0 0
\(514\) 0.618034 0.618034
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −1.00000 −1.00000
\(521\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(522\) −1.61803 −1.61803
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0.381966 0.381966
\(531\) 0 0
\(532\) 0 0
\(533\) −1.00000 −1.00000
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −1.61803 −1.61803
\(539\) 0 0
\(540\) 0 0
\(541\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 1.61803 1.61803
\(545\) −0.381966 −0.381966
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0.618034 0.618034
\(549\) −1.61803 −1.61803
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −0.618034 −0.618034
\(555\) 0 0
\(556\) 0 0
\(557\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −1.61803 −1.61803
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 1.00000 1.00000
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 1.00000
\(577\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(578\) −1.61803 −1.61803
\(579\) 0 0
\(580\) 1.00000 1.00000
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −0.618034 −0.618034
\(585\) 1.00000 1.00000
\(586\) 2.00000 2.00000
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −0.618034 −0.618034
\(593\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.61803 −1.61803
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.618034 0.618034
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 1.00000 1.00000
\(611\) 0 0
\(612\) −1.61803 −1.61803
\(613\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 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
\(625\) 0 0
\(626\) −0.618034 −0.618034
\(627\) 0 0
\(628\) −1.61803 −1.61803
\(629\) 1.00000 1.00000
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0.618034 0.618034
\(635\) 0 0
\(636\) 0 0
\(637\) 1.61803 1.61803
\(638\) 0 0
\(639\) 0 0
\(640\) −0.618034 −0.618034
\(641\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) −1.00000 −1.00000
\(649\) 0 0
\(650\) 1.00000 1.00000
\(651\) 0 0
\(652\) 0 0
\(653\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.618034 −0.618034
\(657\) 0.618034 0.618034
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0.618034 0.618034
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(674\) 0.618034 0.618034
\(675\) 0 0
\(676\) 1.61803 1.61803
\(677\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 1.00000 1.00000
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0.381966 0.381966
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.00000 −1.00000
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) −0.618034 −0.618034
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 1.00000 1.00000
\(698\) 1.61803 1.61803
\(699\) 0 0
\(700\) 0 0
\(701\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 1.61803 1.61803
\(707\) 0 0
\(708\) 0 0
\(709\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.618034 0.618034
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0.618034 0.618034
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) −2.00000 −2.00000
\(725\) −1.00000 −1.00000
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) −0.381966 −0.381966
\(731\) 0 0
\(732\) 0 0
\(733\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0.618034 0.618034
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) −0.381966 −0.381966
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) −1.00000 −1.00000
\(746\) −1.61803 −1.61803
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −2.61803 −2.61803
\(755\) 0 0
\(756\) 0 0
\(757\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −1.00000 −1.00000
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.00000 −2.00000
\(773\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −1.61803 −1.61803
\(777\) 0 0
\(778\) 1.61803 1.61803
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 1.00000
\(785\) −1.00000 −1.00000
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) −1.61803 −1.61803
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −2.61803 −2.61803
\(794\) −2.00000 −2.00000
\(795\) 0 0
\(796\) 0 0
\(797\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.618034 0.618034
\(801\) −0.618034 −0.618034
\(802\) 2.00000 2.00000
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) −0.618034 −0.618034
\(809\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(810\) −0.618034 −0.618034
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0.618034 0.618034
\(819\) 0 0
\(820\) −0.381966 −0.381966
\(821\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 1.61803 1.61803
\(833\) −1.61803 −1.61803
\(834\) 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
\(841\) 1.61803 1.61803
\(842\) 0.618034 0.618034
\(843\) 0 0
\(844\) 0 0
\(845\) 1.00000 1.00000
\(846\) 0 0
\(847\) 0 0
\(848\) −0.618034 −0.618034
\(849\) 0 0
\(850\) −1.00000 −1.00000
\(851\) 0 0
\(852\) 0 0
\(853\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) −0.381966 −0.381966
\(866\) 0.618034 0.618034
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0.618034 0.618034
\(873\) 1.61803 1.61803
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(882\) −1.00000 −1.00000
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) −2.61803 −2.61803
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0.381966 0.381966
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −1.61803 −1.61803
\(899\) 0 0
\(900\) −0.618034 −0.618034
\(901\) 1.00000 1.00000
\(902\) 0 0
\(903\) 0 0
\(904\) −1.61803 −1.61803
\(905\) −1.23607 −1.23607
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) 0.618034 0.618034
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −0.618034 −0.618034
\(915\) 0 0
\(916\) 0.618034 0.618034
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −2.00000 −2.00000
\(923\) 0 0
\(924\) 0 0
\(925\) 0.381966 0.381966
\(926\) 0 0
\(927\) 0 0
\(928\) −1.61803 −1.61803
\(929\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −1.61803 −1.61803
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) −1.61803 −1.61803
\(937\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 1.00000 1.00000
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(954\) 0.618034 0.618034
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 1.00000 1.00000
\(962\) 1.00000 1.00000
\(963\) 0 0
\(964\) −2.00000 −2.00000
\(965\) −1.23607 −1.23607
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −1.00000 −1.00000
\(969\) 0 0
\(970\) −1.00000 −1.00000
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −1.61803 −1.61803
\(977\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0.618034 0.618034
\(981\) −0.618034 −0.618034
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) −1.00000 −1.00000
\(986\) 2.61803 2.61803
\(987\) 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
\(996\) 0 0
\(997\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(998\) 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 1444.1.b.a.723.2 2
4.3 odd 2 CM 1444.1.b.a.723.2 2
19.2 odd 18 1444.1.l.a.99.2 12
19.3 odd 18 1444.1.l.a.1111.1 12
19.4 even 9 1444.1.l.b.415.2 12
19.5 even 9 1444.1.l.b.595.2 12
19.6 even 9 1444.1.l.b.967.1 12
19.7 even 3 1444.1.g.b.1151.1 4
19.8 odd 6 1444.1.g.a.1375.1 4
19.9 even 9 1444.1.l.b.423.2 12
19.10 odd 18 1444.1.l.a.423.2 12
19.11 even 3 1444.1.g.b.1375.1 4
19.12 odd 6 1444.1.g.a.1151.1 4
19.13 odd 18 1444.1.l.a.967.1 12
19.14 odd 18 1444.1.l.a.595.2 12
19.15 odd 18 1444.1.l.a.415.2 12
19.16 even 9 1444.1.l.b.1111.1 12
19.17 even 9 1444.1.l.b.99.2 12
19.18 odd 2 1444.1.b.b.723.2 yes 2
76.3 even 18 1444.1.l.a.1111.1 12
76.7 odd 6 1444.1.g.b.1151.1 4
76.11 odd 6 1444.1.g.b.1375.1 4
76.15 even 18 1444.1.l.a.415.2 12
76.23 odd 18 1444.1.l.b.415.2 12
76.27 even 6 1444.1.g.a.1375.1 4
76.31 even 6 1444.1.g.a.1151.1 4
76.35 odd 18 1444.1.l.b.1111.1 12
76.43 odd 18 1444.1.l.b.595.2 12
76.47 odd 18 1444.1.l.b.423.2 12
76.51 even 18 1444.1.l.a.967.1 12
76.55 odd 18 1444.1.l.b.99.2 12
76.59 even 18 1444.1.l.a.99.2 12
76.63 odd 18 1444.1.l.b.967.1 12
76.67 even 18 1444.1.l.a.423.2 12
76.71 even 18 1444.1.l.a.595.2 12
76.75 even 2 1444.1.b.b.723.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1444.1.b.a.723.2 2 1.1 even 1 trivial
1444.1.b.a.723.2 2 4.3 odd 2 CM
1444.1.b.b.723.2 yes 2 19.18 odd 2
1444.1.b.b.723.2 yes 2 76.75 even 2
1444.1.g.a.1151.1 4 19.12 odd 6
1444.1.g.a.1151.1 4 76.31 even 6
1444.1.g.a.1375.1 4 19.8 odd 6
1444.1.g.a.1375.1 4 76.27 even 6
1444.1.g.b.1151.1 4 19.7 even 3
1444.1.g.b.1151.1 4 76.7 odd 6
1444.1.g.b.1375.1 4 19.11 even 3
1444.1.g.b.1375.1 4 76.11 odd 6
1444.1.l.a.99.2 12 19.2 odd 18
1444.1.l.a.99.2 12 76.59 even 18
1444.1.l.a.415.2 12 19.15 odd 18
1444.1.l.a.415.2 12 76.15 even 18
1444.1.l.a.423.2 12 19.10 odd 18
1444.1.l.a.423.2 12 76.67 even 18
1444.1.l.a.595.2 12 19.14 odd 18
1444.1.l.a.595.2 12 76.71 even 18
1444.1.l.a.967.1 12 19.13 odd 18
1444.1.l.a.967.1 12 76.51 even 18
1444.1.l.a.1111.1 12 19.3 odd 18
1444.1.l.a.1111.1 12 76.3 even 18
1444.1.l.b.99.2 12 19.17 even 9
1444.1.l.b.99.2 12 76.55 odd 18
1444.1.l.b.415.2 12 19.4 even 9
1444.1.l.b.415.2 12 76.23 odd 18
1444.1.l.b.423.2 12 19.9 even 9
1444.1.l.b.423.2 12 76.47 odd 18
1444.1.l.b.595.2 12 19.5 even 9
1444.1.l.b.595.2 12 76.43 odd 18
1444.1.l.b.967.1 12 19.6 even 9
1444.1.l.b.967.1 12 76.63 odd 18
1444.1.l.b.1111.1 12 19.16 even 9
1444.1.l.b.1111.1 12 76.35 odd 18