Properties

Label 1815.1.g.e.1574.1
Level $1815$
Weight $1$
Character 1815.1574
Self dual yes
Analytic conductor $0.906$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -15
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1815,1,Mod(1574,1815)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1815.1574");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1815.g (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(0.905802997929\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.1815.1
Artin image: $D_6$
Artin field: Galois closure of 6.0.9882675.1

Embedding invariants

Embedding label 1574.1
Character \(\chi\) \(=\) 1815.1574

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{15} -1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +2.00000 q^{19} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{27} +1.00000 q^{30} -1.00000 q^{31} +1.00000 q^{34} +2.00000 q^{38} +1.00000 q^{40} -1.00000 q^{45} +1.00000 q^{46} +1.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} -1.00000 q^{51} +1.00000 q^{53} -1.00000 q^{54} -2.00000 q^{57} -1.00000 q^{61} -1.00000 q^{62} +1.00000 q^{64} -1.00000 q^{69} -1.00000 q^{72} -1.00000 q^{75} -1.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -2.00000 q^{83} -1.00000 q^{85} -1.00000 q^{90} +1.00000 q^{93} +1.00000 q^{94} -2.00000 q^{95} +1.00000 q^{98} +O(q^{100})\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times\).

\(n\) \(727\) \(1211\) \(1696\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(3\) −1.00000 −1.00000
\(4\) 0 0
\(5\) −1.00000 −1.00000
\(6\) −1.00000 −1.00000
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) −1.00000 −1.00000
\(9\) 1.00000 1.00000
\(10\) −1.00000 −1.00000
\(11\) 0 0
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 1.00000 1.00000
\(16\) −1.00000 −1.00000
\(17\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) 1.00000 1.00000
\(19\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) 1.00000 1.00000
\(25\) 1.00000 1.00000
\(26\) 0 0
\(27\) −1.00000 −1.00000
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 1.00000 1.00000
\(31\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 1.00000 1.00000
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 2.00000 2.00000
\(39\) 0 0
\(40\) 1.00000 1.00000
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) −1.00000 −1.00000
\(46\) 1.00000 1.00000
\(47\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(48\) 1.00000 1.00000
\(49\) 1.00000 1.00000
\(50\) 1.00000 1.00000
\(51\) −1.00000 −1.00000
\(52\) 0 0
\(53\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) −1.00000 −1.00000
\(55\) 0 0
\(56\) 0 0
\(57\) −2.00000 −2.00000
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) −1.00000 −1.00000
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) −1.00000 −1.00000
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −1.00000 −1.00000
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) −1.00000 −1.00000
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(80\) 1.00000 1.00000
\(81\) 1.00000 1.00000
\(82\) 0 0
\(83\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) −1.00000 −1.00000
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) −1.00000 −1.00000
\(91\) 0 0
\(92\) 0 0
\(93\) 1.00000 1.00000
\(94\) 1.00000 1.00000
\(95\) −2.00000 −2.00000
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 1.00000 1.00000
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) −1.00000 −1.00000
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 1.00000 1.00000
\(107\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(108\) 0 0
\(109\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(114\) −2.00000 −2.00000
\(115\) −1.00000 −1.00000
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −1.00000 −1.00000
\(121\) 0 0
\(122\) −1.00000 −1.00000
\(123\) 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
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.00000 1.00000
\(136\) −1.00000 −1.00000
\(137\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(138\) −1.00000 −1.00000
\(139\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 0 0
\(141\) −1.00000 −1.00000
\(142\) 0 0
\(143\) 0 0
\(144\) −1.00000 −1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) −1.00000 −1.00000
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) −1.00000 −1.00000
\(151\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(152\) −2.00000 −2.00000
\(153\) 1.00000 1.00000
\(154\) 0 0
\(155\) 1.00000 1.00000
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) −1.00000 −1.00000
\(159\) −1.00000 −1.00000
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000 1.00000
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −2.00000 −2.00000
\(167\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(168\) 0 0
\(169\) 1.00000 1.00000
\(170\) −1.00000 −1.00000
\(171\) 2.00000 2.00000
\(172\) 0 0
\(173\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(182\) 0 0
\(183\) 1.00000 1.00000
\(184\) −1.00000 −1.00000
\(185\) 0 0
\(186\) 1.00000 1.00000
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) −2.00000 −2.00000
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −1.00000 −1.00000
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(200\) −1.00000 −1.00000
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.00000 1.00000
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 1.00000 1.00000
\(215\) 0 0
\(216\) 1.00000 1.00000
\(217\) 0 0
\(218\) 2.00000 2.00000
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 1.00000 1.00000
\(226\) 1.00000 1.00000
\(227\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(228\) 0 0
\(229\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) −1.00000 −1.00000
\(231\) 0 0
\(232\) 0 0
\(233\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(234\) 0 0
\(235\) −1.00000 −1.00000
\(236\) 0 0
\(237\) 1.00000 1.00000
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) −1.00000 −1.00000
\(241\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) 0 0
\(243\) −1.00000 −1.00000
\(244\) 0 0
\(245\) −1.00000 −1.00000
\(246\) 0 0
\(247\) 0 0
\(248\) 1.00000 1.00000
\(249\) 2.00000 2.00000
\(250\) −1.00000 −1.00000
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 1.00000 1.00000
\(256\) 0 0
\(257\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) 0 0
\(265\) −1.00000 −1.00000
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 1.00000 1.00000
\(271\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) −1.00000 −1.00000
\(273\) 0 0
\(274\) 1.00000 1.00000
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) −1.00000 −1.00000
\(279\) −1.00000 −1.00000
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) −1.00000 −1.00000
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 2.00000 2.00000
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0 0
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(294\) −1.00000 −1.00000
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) −1.00000 −1.00000
\(303\) 0 0
\(304\) −2.00000 −2.00000
\(305\) 1.00000 1.00000
\(306\) 1.00000 1.00000
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 1.00000 1.00000
\(311\) 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
\(316\) 0 0
\(317\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(318\) −1.00000 −1.00000
\(319\) 0 0
\(320\) −1.00000 −1.00000
\(321\) −1.00000 −1.00000
\(322\) 0 0
\(323\) 2.00000 2.00000
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −2.00000 −2.00000
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 1.00000 1.00000
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 1.00000 1.00000
\(339\) −1.00000 −1.00000
\(340\) 0 0
\(341\) 0 0
\(342\) 2.00000 2.00000
\(343\) 0 0
\(344\) 0 0
\(345\) 1.00000 1.00000
\(346\) −2.00000 −2.00000
\(347\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(348\) 0 0
\(349\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 1.00000 1.00000
\(361\) 3.00000 3.00000
\(362\) 2.00000 2.00000
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 1.00000 1.00000
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) −1.00000 −1.00000
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 1.00000 1.00000
\(376\) −1.00000 −1.00000
\(377\) 0 0
\(378\) 0 0
\(379\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(384\) −1.00000 −1.00000
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 1.00000 1.00000
\(392\) −1.00000 −1.00000
\(393\) 0 0
\(394\) −2.00000 −2.00000
\(395\) 1.00000 1.00000
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) −1.00000 −1.00000
\(399\) 0 0
\(400\) −1.00000 −1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −1.00000 −1.00000
\(406\) 0 0
\(407\) 0 0
\(408\) 1.00000 1.00000
\(409\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) 0 0
\(411\) −1.00000 −1.00000
\(412\) 0 0
\(413\) 0 0
\(414\) 1.00000 1.00000
\(415\) 2.00000 2.00000
\(416\) 0 0
\(417\) 1.00000 1.00000
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) −1.00000 −1.00000
\(423\) 1.00000 1.00000
\(424\) −1.00000 −1.00000
\(425\) 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 \(\pi\)
\(432\) 1.00000 1.00000
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.00000 2.00000
\(438\) 0 0
\(439\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 1.00000 1.00000
\(451\) 0 0
\(452\) 0 0
\(453\) 1.00000 1.00000
\(454\) 1.00000 1.00000
\(455\) 0 0
\(456\) 2.00000 2.00000
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) −1.00000 −1.00000
\(459\) −1.00000 −1.00000
\(460\) 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
\(465\) −1.00000 −1.00000
\(466\) 1.00000 1.00000
\(467\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −1.00000 −1.00000
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 1.00000 1.00000
\(475\) 2.00000 2.00000
\(476\) 0 0
\(477\) 1.00000 1.00000
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.00000 −1.00000
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) −1.00000 −1.00000
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 1.00000 1.00000
\(489\) 0 0
\(490\) −1.00000 −1.00000
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.00000 1.00000
\(497\) 0 0
\(498\) 2.00000 2.00000
\(499\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(500\) 0 0
\(501\) −1.00000 −1.00000
\(502\) 0 0
\(503\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −1.00000
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 1.00000 1.00000
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) −2.00000 −2.00000
\(514\) 1.00000 1.00000
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 2.00000 2.00000
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 1.00000 1.00000
\(527\) −1.00000 −1.00000
\(528\) 0 0
\(529\) 0 0
\(530\) −1.00000 −1.00000
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −1.00000 −1.00000
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(542\) −1.00000 −1.00000
\(543\) −2.00000 −2.00000
\(544\) 0 0
\(545\) −2.00000 −2.00000
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) −1.00000 −1.00000
\(550\) 0 0
\(551\) 0 0
\(552\) 1.00000 1.00000
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(558\) −1.00000 −1.00000
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) −1.00000 −1.00000
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 2.00000 2.00000
\(571\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 1.00000
\(576\) 1.00000 1.00000
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 1.00000 1.00000
\(587\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(588\) 0 0
\(589\) −2.00000 −2.00000
\(590\) 0 0
\(591\) 2.00000 2.00000
\(592\) 0 0
\(593\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.00000 1.00000
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 1.00000 1.00000
\(601\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 1.00000 1.00000
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(620\) 0 0
\(621\) −1.00000 −1.00000
\(622\) 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
\(631\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(632\) 1.00000 1.00000
\(633\) 1.00000 1.00000
\(634\) 1.00000 1.00000
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −1.00000 −1.00000
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) −1.00000 −1.00000
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 2.00000 2.00000
\(647\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(648\) −1.00000 −1.00000
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(654\) −2.00000 −2.00000
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(662\) −1.00000 −1.00000
\(663\) 0 0
\(664\) 2.00000 2.00000
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) −1.00000 −1.00000
\(676\) 0 0
\(677\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(678\) −1.00000 −1.00000
\(679\) 0 0
\(680\) 1.00000 1.00000
\(681\) −1.00000 −1.00000
\(682\) 0 0
\(683\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) −1.00000 −1.00000
\(686\) 0 0
\(687\) 1.00000 1.00000
\(688\) 0 0
\(689\) 0 0
\(690\) 1.00000 1.00000
\(691\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 1.00000 1.00000
\(695\) 1.00000 1.00000
\(696\) 0 0
\(697\) 0 0
\(698\) −1.00000 −1.00000
\(699\) −1.00000 −1.00000
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 1.00000 1.00000
\(706\) 1.00000 1.00000
\(707\) 0 0
\(708\) 0 0
\(709\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) 0 0
\(711\) −1.00000 −1.00000
\(712\) 0 0
\(713\) −1.00000 −1.00000
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 1.00000 1.00000
\(721\) 0 0
\(722\) 3.00000 3.00000
\(723\) 1.00000 1.00000
\(724\) 0 0
\(725\) 0 0
\(726\) 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
\(735\) 1.00000 1.00000
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(744\) −1.00000 −1.00000
\(745\) 0 0
\(746\) 0 0
\(747\) −2.00000 −2.00000
\(748\) 0 0
\(749\) 0 0
\(750\) 1.00000 1.00000
\(751\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) −1.00000 −1.00000
\(753\) 0 0
\(754\) 0 0
\(755\) 1.00000 1.00000
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) −1.00000 −1.00000
\(759\) 0 0
\(760\) 2.00000 2.00000
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −1.00000 −1.00000
\(766\) −2.00000 −2.00000
\(767\) 0 0
\(768\) 0 0
\(769\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) 0 0
\(771\) −1.00000 −1.00000
\(772\) 0 0
\(773\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(774\) 0 0
\(775\) −1.00000 −1.00000
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 1.00000 1.00000
\(783\) 0 0
\(784\) −1.00000 −1.00000
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) −1.00000 −1.00000
\(790\) 1.00000 1.00000
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 1.00000 1.00000
\(796\) 0 0
\(797\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 1.00000 1.00000
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) −1.00000 −1.00000
\(811\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(812\) 0 0
\(813\) 1.00000 1.00000
\(814\) 0 0
\(815\) 0 0
\(816\) 1.00000 1.00000
\(817\) 0 0
\(818\) −1.00000 −1.00000
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) −1.00000 −1.00000
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) 2.00000 2.00000
\(831\) 0 0
\(832\) 0 0
\(833\) 1.00000 1.00000
\(834\) 1.00000 1.00000
\(835\) −1.00000 −1.00000
\(836\) 0 0
\(837\) 1.00000 1.00000
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) −1.00000 −1.00000
\(843\) 0 0
\(844\) 0 0
\(845\) −1.00000 −1.00000
\(846\) 1.00000 1.00000
\(847\) 0 0
\(848\) −1.00000 −1.00000
\(849\) 0 0
\(850\) 1.00000 1.00000
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) −2.00000 −2.00000
\(856\) −1.00000 −1.00000
\(857\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(858\) 0 0
\(859\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 2.00000 2.00000
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −2.00000 −2.00000
\(873\) 0 0
\(874\) 2.00000 2.00000
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) −1.00000 −1.00000
\(879\) −1.00000 −1.00000
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 1.00000 1.00000
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −2.00000 −2.00000
\(887\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2.00000 2.00000
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 1.00000 1.00000
\(902\) 0 0
\(903\) 0 0
\(904\) −1.00000 −1.00000
\(905\) −2.00000 −2.00000
\(906\) 1.00000 1.00000
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 2.00000 2.00000
\(913\) 0 0
\(914\) 0 0
\(915\) −1.00000 −1.00000
\(916\) 0 0
\(917\) 0 0
\(918\) −1.00000 −1.00000
\(919\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(920\) 1.00000 1.00000
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) −1.00000 −1.00000
\(931\) 2.00000 2.00000
\(932\) 0 0
\(933\) 0 0
\(934\) 1.00000 1.00000
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 2.00000 2.00000
\(951\) −1.00000 −1.00000
\(952\) 0 0
\(953\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(954\) 1.00000 1.00000
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 1.00000 1.00000
\(961\) 0 0
\(962\) 0 0
\(963\) 1.00000 1.00000
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0 0
\(969\) −2.00000 −2.00000
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 1.00000 1.00000
\(977\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 2.00000 2.00000
\(982\) 0 0
\(983\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(984\) 0 0
\(985\) 2.00000 2.00000
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(992\) 0 0
\(993\) 1.00000 1.00000
\(994\) 0 0
\(995\) 1.00000 1.00000
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 2.00000 2.00000
\(999\) 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 1815.1.g.e.1574.1 yes 1
3.2 odd 2 1815.1.g.b.1574.1 yes 1
5.4 even 2 1815.1.g.b.1574.1 yes 1
11.2 odd 10 1815.1.o.f.1049.1 4
11.3 even 5 1815.1.o.b.614.1 4
11.4 even 5 1815.1.o.b.269.1 4
11.5 even 5 1815.1.o.b.1334.1 4
11.6 odd 10 1815.1.o.f.1334.1 4
11.7 odd 10 1815.1.o.f.269.1 4
11.8 odd 10 1815.1.o.f.614.1 4
11.9 even 5 1815.1.o.b.1049.1 4
11.10 odd 2 1815.1.g.a.1574.1 1
15.14 odd 2 CM 1815.1.g.e.1574.1 yes 1
33.2 even 10 1815.1.o.a.1049.1 4
33.5 odd 10 1815.1.o.e.1334.1 4
33.8 even 10 1815.1.o.a.614.1 4
33.14 odd 10 1815.1.o.e.614.1 4
33.17 even 10 1815.1.o.a.1334.1 4
33.20 odd 10 1815.1.o.e.1049.1 4
33.26 odd 10 1815.1.o.e.269.1 4
33.29 even 10 1815.1.o.a.269.1 4
33.32 even 2 1815.1.g.f.1574.1 yes 1
55.4 even 10 1815.1.o.e.269.1 4
55.9 even 10 1815.1.o.e.1049.1 4
55.14 even 10 1815.1.o.e.614.1 4
55.19 odd 10 1815.1.o.a.614.1 4
55.24 odd 10 1815.1.o.a.1049.1 4
55.29 odd 10 1815.1.o.a.269.1 4
55.39 odd 10 1815.1.o.a.1334.1 4
55.49 even 10 1815.1.o.e.1334.1 4
55.54 odd 2 1815.1.g.f.1574.1 yes 1
165.14 odd 10 1815.1.o.b.614.1 4
165.29 even 10 1815.1.o.f.269.1 4
165.59 odd 10 1815.1.o.b.269.1 4
165.74 even 10 1815.1.o.f.614.1 4
165.104 odd 10 1815.1.o.b.1334.1 4
165.119 odd 10 1815.1.o.b.1049.1 4
165.134 even 10 1815.1.o.f.1049.1 4
165.149 even 10 1815.1.o.f.1334.1 4
165.164 even 2 1815.1.g.a.1574.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1815.1.g.a.1574.1 1 11.10 odd 2
1815.1.g.a.1574.1 1 165.164 even 2
1815.1.g.b.1574.1 yes 1 3.2 odd 2
1815.1.g.b.1574.1 yes 1 5.4 even 2
1815.1.g.e.1574.1 yes 1 1.1 even 1 trivial
1815.1.g.e.1574.1 yes 1 15.14 odd 2 CM
1815.1.g.f.1574.1 yes 1 33.32 even 2
1815.1.g.f.1574.1 yes 1 55.54 odd 2
1815.1.o.a.269.1 4 33.29 even 10
1815.1.o.a.269.1 4 55.29 odd 10
1815.1.o.a.614.1 4 33.8 even 10
1815.1.o.a.614.1 4 55.19 odd 10
1815.1.o.a.1049.1 4 33.2 even 10
1815.1.o.a.1049.1 4 55.24 odd 10
1815.1.o.a.1334.1 4 33.17 even 10
1815.1.o.a.1334.1 4 55.39 odd 10
1815.1.o.b.269.1 4 11.4 even 5
1815.1.o.b.269.1 4 165.59 odd 10
1815.1.o.b.614.1 4 11.3 even 5
1815.1.o.b.614.1 4 165.14 odd 10
1815.1.o.b.1049.1 4 11.9 even 5
1815.1.o.b.1049.1 4 165.119 odd 10
1815.1.o.b.1334.1 4 11.5 even 5
1815.1.o.b.1334.1 4 165.104 odd 10
1815.1.o.e.269.1 4 33.26 odd 10
1815.1.o.e.269.1 4 55.4 even 10
1815.1.o.e.614.1 4 33.14 odd 10
1815.1.o.e.614.1 4 55.14 even 10
1815.1.o.e.1049.1 4 33.20 odd 10
1815.1.o.e.1049.1 4 55.9 even 10
1815.1.o.e.1334.1 4 33.5 odd 10
1815.1.o.e.1334.1 4 55.49 even 10
1815.1.o.f.269.1 4 11.7 odd 10
1815.1.o.f.269.1 4 165.29 even 10
1815.1.o.f.614.1 4 11.8 odd 10
1815.1.o.f.614.1 4 165.74 even 10
1815.1.o.f.1049.1 4 11.2 odd 10
1815.1.o.f.1049.1 4 165.134 even 10
1815.1.o.f.1334.1 4 11.6 odd 10
1815.1.o.f.1334.1 4 165.149 even 10