Properties

Label 2888.1.f.c.723.1
Level $2888$
Weight $1$
Character 2888.723
Self dual yes
Analytic conductor $1.441$
Analytic rank $0$
Dimension $3$
Projective image $D_{9}$
CM discriminant -8
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2888 = 2^{3} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2888.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(1.44129975648\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{18})^+\)
Defining polynomial: \( x^{3} - 3x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 152)
Projective image: \(D_{9}\)
Projective field: Galois closure of 9.1.69564674215936.1

Embedding invariants

Embedding label 723.1
Root \(-1.53209\) of defining polynomial
Character \(\chi\) \(=\) 2888.723

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.53209 q^{3} +1.00000 q^{4} +1.53209 q^{6} -1.00000 q^{8} +1.34730 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.53209 q^{3} +1.00000 q^{4} +1.53209 q^{6} -1.00000 q^{8} +1.34730 q^{9} -1.87939 q^{11} -1.53209 q^{12} +1.00000 q^{16} -1.00000 q^{17} -1.34730 q^{18} +1.87939 q^{22} +1.53209 q^{24} +1.00000 q^{25} -0.532089 q^{27} -1.00000 q^{32} +2.87939 q^{33} +1.00000 q^{34} +1.34730 q^{36} -0.347296 q^{41} -1.00000 q^{43} -1.87939 q^{44} -1.53209 q^{48} +1.00000 q^{49} -1.00000 q^{50} +1.53209 q^{51} +0.532089 q^{54} +1.87939 q^{59} +1.00000 q^{64} -2.87939 q^{66} -0.347296 q^{67} -1.00000 q^{68} -1.34730 q^{72} -1.87939 q^{73} -1.53209 q^{75} -0.532089 q^{81} +0.347296 q^{82} +0.347296 q^{83} +1.00000 q^{86} +1.87939 q^{88} +1.00000 q^{89} +1.53209 q^{96} -0.347296 q^{97} -1.00000 q^{98} -2.53209 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{2} + 3 q^{4} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{2} + 3 q^{4} - 3 q^{8} + 3 q^{9} + 3 q^{16} - 3 q^{17} - 3 q^{18} + 3 q^{25} + 3 q^{27} - 3 q^{32} + 3 q^{33} + 3 q^{34} + 3 q^{36} - 3 q^{43} + 3 q^{49} - 3 q^{50} - 3 q^{54} + 3 q^{64} - 3 q^{66} - 3 q^{68} - 3 q^{72} + 3 q^{81} + 3 q^{86} + 3 q^{89} - 3 q^{98} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times\).

\(n\) \(1445\) \(2167\) \(2529\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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
\(3\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(4\) 1.00000 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 1.53209 1.53209
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) −1.00000 −1.00000
\(9\) 1.34730 1.34730
\(10\) 0 0
\(11\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(12\) −1.53209 −1.53209
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) −1.34730 −1.34730
\(19\) 0 0
\(20\) 0 0
\(21\) 0 0
\(22\) 1.87939 1.87939
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 1.53209 1.53209
\(25\) 1.00000 1.00000
\(26\) 0 0
\(27\) −0.532089 −0.532089
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) −1.00000 −1.00000
\(33\) 2.87939 2.87939
\(34\) 1.00000 1.00000
\(35\) 0 0
\(36\) 1.34730 1.34730
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(42\) 0 0
\(43\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(44\) −1.87939 −1.87939
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −1.53209 −1.53209
\(49\) 1.00000 1.00000
\(50\) −1.00000 −1.00000
\(51\) 1.53209 1.53209
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0.532089 0.532089
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) −2.87939 −2.87939
\(67\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(68\) −1.00000 −1.00000
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −1.34730 −1.34730
\(73\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(74\) 0 0
\(75\) −1.53209 −1.53209
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) −0.532089 −0.532089
\(82\) 0.347296 0.347296
\(83\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.00000 1.00000
\(87\) 0 0
\(88\) 1.87939 1.87939
\(89\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 1.53209 1.53209
\(97\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(98\) −1.00000 −1.00000
\(99\) −2.53209 −2.53209
\(100\) 1.00000 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) −1.53209 −1.53209
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(108\) −0.532089 −0.532089
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −1.87939 −1.87939
\(119\) 0 0
\(120\) 0 0
\(121\) 2.53209 2.53209
\(122\) 0 0
\(123\) 0.532089 0.532089
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −1.00000 −1.00000
\(129\) 1.53209 1.53209
\(130\) 0 0
\(131\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(132\) 2.87939 2.87939
\(133\) 0 0
\(134\) 0.347296 0.347296
\(135\) 0 0
\(136\) 1.00000 1.00000
\(137\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(138\) 0 0
\(139\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.34730 1.34730
\(145\) 0 0
\(146\) 1.87939 1.87939
\(147\) −1.53209 −1.53209
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 1.53209 1.53209
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) −1.34730 −1.34730
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.532089 0.532089
\(163\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(164\) −0.347296 −0.347296
\(165\) 0 0
\(166\) −0.347296 −0.347296
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) −1.00000 −1.00000
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.87939 −1.87939
\(177\) −2.87939 −2.87939
\(178\) −1.00000 −1.00000
\(179\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(180\) 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
\(187\) 1.87939 1.87939
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −1.53209 −1.53209
\(193\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) 0.347296 0.347296
\(195\) 0 0
\(196\) 1.00000 1.00000
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 2.53209 2.53209
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −1.00000 −1.00000
\(201\) 0.532089 0.532089
\(202\) 0 0
\(203\) 0 0
\(204\) 1.53209 1.53209
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.00000 −1.00000
\(215\) 0 0
\(216\) 0.532089 0.532089
\(217\) 0 0
\(218\) 0 0
\(219\) 2.87939 2.87939
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 1.34730 1.34730
\(226\) −1.87939 −1.87939
\(227\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.87939 1.87939
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(242\) −2.53209 −2.53209
\(243\) 1.34730 1.34730
\(244\) 0 0
\(245\) 0 0
\(246\) −0.532089 −0.532089
\(247\) 0 0
\(248\) 0 0
\(249\) −0.532089 −0.532089
\(250\) 0 0
\(251\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(258\) −1.53209 −1.53209
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −1.53209 −1.53209
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) −2.87939 −2.87939
\(265\) 0 0
\(266\) 0 0
\(267\) −1.53209 −1.53209
\(268\) −0.347296 −0.347296
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −1.00000 −1.00000
\(273\) 0 0
\(274\) −1.53209 −1.53209
\(275\) −1.87939 −1.87939
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) −0.347296 −0.347296
\(279\) 0 0
\(280\) 0 0
\(281\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(282\) 0 0
\(283\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.34730 −1.34730
\(289\) 0 0
\(290\) 0 0
\(291\) 0.532089 0.532089
\(292\) −1.87939 −1.87939
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 1.53209 1.53209
\(295\) 0 0
\(296\) 0 0
\(297\) 1.00000 1.00000
\(298\) 0 0
\(299\) 0 0
\(300\) −1.53209 −1.53209
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 1.34730 1.34730
\(307\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −1.53209 −1.53209
\(322\) 0 0
\(323\) 0 0
\(324\) −0.532089 −0.532089
\(325\) 0 0
\(326\) −1.53209 −1.53209
\(327\) 0 0
\(328\) 0.347296 0.347296
\(329\) 0 0
\(330\) 0 0
\(331\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(332\) 0.347296 0.347296
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(338\) −1.00000 −1.00000
\(339\) −2.87939 −2.87939
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 1.00000 1.00000
\(345\) 0 0
\(346\) 0 0
\(347\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.87939 1.87939
\(353\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(354\) 2.87939 2.87939
\(355\) 0 0
\(356\) 1.00000 1.00000
\(357\) 0 0
\(358\) 0.347296 0.347296
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) −3.87939 −3.87939
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) −0.467911 −0.467911
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) −1.87939 −1.87939
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 1.53209 1.53209
\(385\) 0 0
\(386\) −1.00000 −1.00000
\(387\) −1.34730 −1.34730
\(388\) −0.347296 −0.347296
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.00000 −1.00000
\(393\) −2.34730 −2.34730
\(394\) 0 0
\(395\) 0 0
\(396\) −2.53209 −2.53209
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(402\) −0.532089 −0.532089
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −1.53209 −1.53209
\(409\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(410\) 0 0
\(411\) −2.34730 −2.34730
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.532089 −0.532089
\(418\) 0 0
\(419\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) −1.00000 −1.00000
\(423\) 0 0
\(424\) 0 0
\(425\) −1.00000 −1.00000
\(426\) 0 0
\(427\) 0 0
\(428\) 1.00000 1.00000
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −0.532089 −0.532089
\(433\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −2.87939 −2.87939
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 1.34730 1.34730
\(442\) 0 0
\(443\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(450\) −1.34730 −1.34730
\(451\) 0.652704 0.652704
\(452\) 1.87939 1.87939
\(453\) 0 0
\(454\) 0.347296 0.347296
\(455\) 0 0
\(456\) 0 0
\(457\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(458\) 0 0
\(459\) 0.532089 0.532089
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −1.53209 −1.53209
\(467\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.87939 −1.87939
\(473\) 1.87939 1.87939
\(474\) 0 0
\(475\) 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
\(482\) 1.53209 1.53209
\(483\) 0 0
\(484\) 2.53209 2.53209
\(485\) 0 0
\(486\) −1.34730 −1.34730
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) −2.34730 −2.34730
\(490\) 0 0
\(491\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(492\) 0.532089 0.532089
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.532089 0.532089
\(499\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −1.53209 −1.53209
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.53209 −1.53209
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 0 0
\(514\) 1.53209 1.53209
\(515\) 0 0
\(516\) 1.53209 1.53209
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(522\) 0 0
\(523\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(524\) 1.53209 1.53209
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 2.87939 2.87939
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 2.53209 2.53209
\(532\) 0 0
\(533\) 0 0
\(534\) 1.53209 1.53209
\(535\) 0 0
\(536\) 0.347296 0.347296
\(537\) 0.532089 0.532089
\(538\) 0 0
\(539\) −1.87939 −1.87939
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 1.00000 1.00000
\(545\) 0 0
\(546\) 0 0
\(547\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(548\) 1.53209 1.53209
\(549\) 0 0
\(550\) 1.87939 1.87939
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0.347296 0.347296
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −2.87939 −2.87939
\(562\) 1.53209 1.53209
\(563\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 1.87939 1.87939
\(567\) 0 0
\(568\) 0 0
\(569\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(570\) 0 0
\(571\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.34730 1.34730
\(577\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(578\) 0 0
\(579\) −1.53209 −1.53209
\(580\) 0 0
\(581\) 0 0
\(582\) −0.532089 −0.532089
\(583\) 0 0
\(584\) 1.87939 1.87939
\(585\) 0 0
\(586\) 0 0
\(587\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(588\) −1.53209 −1.53209
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(594\) −1.00000 −1.00000
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 1.53209 1.53209
\(601\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(602\) 0 0
\(603\) −0.467911 −0.467911
\(604\) 0 0
\(605\) 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
\(612\) −1.34730 −1.34730
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) −1.87939 −1.87939
\(615\) 0 0
\(616\) 0 0
\(617\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(618\) 0 0
\(619\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) −1.53209 −1.53209
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) −1.53209 −1.53209
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(642\) 1.53209 1.53209
\(643\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0.532089 0.532089
\(649\) −3.53209 −3.53209
\(650\) 0 0
\(651\) 0 0
\(652\) 1.53209 1.53209
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.347296 −0.347296
\(657\) −2.53209 −2.53209
\(658\) 0 0
\(659\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) −1.87939 −1.87939
\(663\) 0 0
\(664\) −0.347296 −0.347296
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(674\) 1.53209 1.53209
\(675\) −0.532089 −0.532089
\(676\) 1.00000 1.00000
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 2.87939 2.87939
\(679\) 0 0
\(680\) 0 0
\(681\) 0.532089 0.532089
\(682\) 0 0
\(683\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −1.00000 −1.00000
\(689\) 0 0
\(690\) 0 0
\(691\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.347296 −0.347296
\(695\) 0 0
\(696\) 0 0
\(697\) 0.347296 0.347296
\(698\) 0 0
\(699\) −2.34730 −2.34730
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.87939 −1.87939
\(705\) 0 0
\(706\) −0.347296 −0.347296
\(707\) 0 0
\(708\) −2.87939 −2.87939
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.00000 −1.00000
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.347296 −0.347296
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 2.34730 2.34730
\(724\) 0 0
\(725\) 0 0
\(726\) 3.87939 3.87939
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −1.53209 −1.53209
\(730\) 0 0
\(731\) 1.00000 1.00000
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.652704 0.652704
\(738\) 0.467911 0.467911
\(739\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.467911 0.467911
\(748\) 1.87939 1.87939
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) −2.34730 −2.34730
\(754\) 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
\(761\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −1.53209 −1.53209
\(769\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) 0 0
\(771\) 2.34730 2.34730
\(772\) 1.00000 1.00000
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 1.34730 1.34730
\(775\) 0 0
\(776\) 0.347296 0.347296
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 1.00000
\(785\) 0 0
\(786\) 2.34730 2.34730
\(787\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 2.53209 2.53209
\(793\) 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
\(801\) 1.34730 1.34730
\(802\) −1.87939 −1.87939
\(803\) 3.53209 3.53209
\(804\) 0.532089 0.532089
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(810\) 0 0
\(811\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 1.53209 1.53209
\(817\) 0 0
\(818\) −1.87939 −1.87939
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 2.34730 2.34730
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 2.87939 2.87939
\(826\) 0 0
\(827\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.00000 −1.00000
\(834\) 0.532089 0.532089
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 1.00000 1.00000
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 2.34730 2.34730
\(844\) 1.00000 1.00000
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 2.87939 2.87939
\(850\) 1.00000 1.00000
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −1.00000 −1.00000
\(857\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(858\) 0 0
\(859\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0.532089 0.532089
\(865\) 0 0
\(866\) 2.00000 2.00000
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −0.467911 −0.467911
\(874\) 0 0
\(875\) 0 0
\(876\) 2.87939 2.87939
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(882\) −1.34730 −1.34730
\(883\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −1.53209 −1.53209
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 1.00000 1.00000
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 1.53209 1.53209
\(899\) 0 0
\(900\) 1.34730 1.34730
\(901\) 0 0
\(902\) −0.652704 −0.652704
\(903\) 0 0
\(904\) −1.87939 −1.87939
\(905\) 0 0
\(906\) 0 0
\(907\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(908\) −0.347296 −0.347296
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) −0.652704 −0.652704
\(914\) −0.347296 −0.347296
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) −0.532089 −0.532089
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) −2.87939 −2.87939
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 1.53209 1.53209
\(933\) 0 0
\(934\) −0.347296 −0.347296
\(935\) 0 0
\(936\) 0 0
\(937\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(938\) 0 0
\(939\) −2.34730 −2.34730
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 1.87939 1.87939
\(945\) 0 0
\(946\) −1.87939 −1.87939
\(947\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(954\) 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
\(963\) 1.34730 1.34730
\(964\) −1.53209 −1.53209
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −2.53209 −2.53209
\(969\) 0 0
\(970\) 0 0
\(971\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(972\) 1.34730 1.34730
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(978\) 2.34730 2.34730
\(979\) −1.87939 −1.87939
\(980\) 0 0
\(981\) 0 0
\(982\) 1.00000 1.00000
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) −0.532089 −0.532089
\(985\) 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
\(993\) −2.87939 −2.87939
\(994\) 0 0
\(995\) 0 0
\(996\) −0.532089 −0.532089
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 1.87939 1.87939
\(999\) 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 2888.1.f.c.723.1 3
8.3 odd 2 CM 2888.1.f.c.723.1 3
19.2 odd 18 2888.1.u.b.99.1 6
19.3 odd 18 2888.1.u.g.2555.1 6
19.4 even 9 2888.1.u.e.1859.1 6
19.5 even 9 2888.1.u.e.595.1 6
19.6 even 9 2888.1.u.a.2411.1 6
19.7 even 3 2888.1.k.c.2595.3 6
19.8 odd 6 2888.1.k.b.2819.1 6
19.9 even 9 2888.1.u.f.1867.1 6
19.10 odd 18 2888.1.u.b.1867.1 6
19.11 even 3 2888.1.k.c.2819.3 6
19.12 odd 6 2888.1.k.b.2595.1 6
19.13 odd 18 2888.1.u.g.2411.1 6
19.14 odd 18 152.1.u.a.139.1 yes 6
19.15 odd 18 152.1.u.a.35.1 6
19.16 even 9 2888.1.u.a.2555.1 6
19.17 even 9 2888.1.u.f.99.1 6
19.18 odd 2 2888.1.f.d.723.3 3
57.14 even 18 1368.1.eh.a.595.1 6
57.53 even 18 1368.1.eh.a.1099.1 6
76.15 even 18 608.1.bg.a.111.1 6
76.71 even 18 608.1.bg.a.367.1 6
95.14 odd 18 3800.1.cv.c.1051.1 6
95.33 even 36 3800.1.cq.b.899.1 12
95.34 odd 18 3800.1.cv.c.1251.1 6
95.52 even 36 3800.1.cq.b.899.2 12
95.53 even 36 3800.1.cq.b.1099.2 12
95.72 even 36 3800.1.cq.b.1099.1 12
152.3 even 18 2888.1.u.g.2555.1 6
152.11 odd 6 2888.1.k.c.2819.3 6
152.27 even 6 2888.1.k.b.2819.1 6
152.35 odd 18 2888.1.u.a.2555.1 6
152.43 odd 18 2888.1.u.e.595.1 6
152.51 even 18 2888.1.u.g.2411.1 6
152.53 odd 18 608.1.bg.a.111.1 6
152.59 even 18 2888.1.u.b.99.1 6
152.67 even 18 2888.1.u.b.1867.1 6
152.75 even 2 2888.1.f.d.723.3 3
152.83 odd 6 2888.1.k.c.2595.3 6
152.91 even 18 152.1.u.a.35.1 6
152.99 odd 18 2888.1.u.e.1859.1 6
152.107 even 6 2888.1.k.b.2595.1 6
152.109 odd 18 608.1.bg.a.367.1 6
152.123 odd 18 2888.1.u.f.1867.1 6
152.131 odd 18 2888.1.u.f.99.1 6
152.139 odd 18 2888.1.u.a.2411.1 6
152.147 even 18 152.1.u.a.139.1 yes 6
456.299 odd 18 1368.1.eh.a.595.1 6
456.395 odd 18 1368.1.eh.a.1099.1 6
760.147 odd 36 3800.1.cq.b.899.2 12
760.243 odd 36 3800.1.cq.b.1099.2 12
760.299 even 18 3800.1.cv.c.1051.1 6
760.547 odd 36 3800.1.cq.b.1099.1 12
760.603 odd 36 3800.1.cq.b.899.1 12
760.699 even 18 3800.1.cv.c.1251.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
152.1.u.a.35.1 6 19.15 odd 18
152.1.u.a.35.1 6 152.91 even 18
152.1.u.a.139.1 yes 6 19.14 odd 18
152.1.u.a.139.1 yes 6 152.147 even 18
608.1.bg.a.111.1 6 76.15 even 18
608.1.bg.a.111.1 6 152.53 odd 18
608.1.bg.a.367.1 6 76.71 even 18
608.1.bg.a.367.1 6 152.109 odd 18
1368.1.eh.a.595.1 6 57.14 even 18
1368.1.eh.a.595.1 6 456.299 odd 18
1368.1.eh.a.1099.1 6 57.53 even 18
1368.1.eh.a.1099.1 6 456.395 odd 18
2888.1.f.c.723.1 3 1.1 even 1 trivial
2888.1.f.c.723.1 3 8.3 odd 2 CM
2888.1.f.d.723.3 3 19.18 odd 2
2888.1.f.d.723.3 3 152.75 even 2
2888.1.k.b.2595.1 6 19.12 odd 6
2888.1.k.b.2595.1 6 152.107 even 6
2888.1.k.b.2819.1 6 19.8 odd 6
2888.1.k.b.2819.1 6 152.27 even 6
2888.1.k.c.2595.3 6 19.7 even 3
2888.1.k.c.2595.3 6 152.83 odd 6
2888.1.k.c.2819.3 6 19.11 even 3
2888.1.k.c.2819.3 6 152.11 odd 6
2888.1.u.a.2411.1 6 19.6 even 9
2888.1.u.a.2411.1 6 152.139 odd 18
2888.1.u.a.2555.1 6 19.16 even 9
2888.1.u.a.2555.1 6 152.35 odd 18
2888.1.u.b.99.1 6 19.2 odd 18
2888.1.u.b.99.1 6 152.59 even 18
2888.1.u.b.1867.1 6 19.10 odd 18
2888.1.u.b.1867.1 6 152.67 even 18
2888.1.u.e.595.1 6 19.5 even 9
2888.1.u.e.595.1 6 152.43 odd 18
2888.1.u.e.1859.1 6 19.4 even 9
2888.1.u.e.1859.1 6 152.99 odd 18
2888.1.u.f.99.1 6 19.17 even 9
2888.1.u.f.99.1 6 152.131 odd 18
2888.1.u.f.1867.1 6 19.9 even 9
2888.1.u.f.1867.1 6 152.123 odd 18
2888.1.u.g.2411.1 6 19.13 odd 18
2888.1.u.g.2411.1 6 152.51 even 18
2888.1.u.g.2555.1 6 19.3 odd 18
2888.1.u.g.2555.1 6 152.3 even 18
3800.1.cq.b.899.1 12 95.33 even 36
3800.1.cq.b.899.1 12 760.603 odd 36
3800.1.cq.b.899.2 12 95.52 even 36
3800.1.cq.b.899.2 12 760.147 odd 36
3800.1.cq.b.1099.1 12 95.72 even 36
3800.1.cq.b.1099.1 12 760.547 odd 36
3800.1.cq.b.1099.2 12 95.53 even 36
3800.1.cq.b.1099.2 12 760.243 odd 36
3800.1.cv.c.1051.1 6 95.14 odd 18
3800.1.cv.c.1051.1 6 760.299 even 18
3800.1.cv.c.1251.1 6 95.34 odd 18
3800.1.cv.c.1251.1 6 760.699 even 18