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Properties

Label 3311.1.h.d.3310.1
Level $3311$
Weight $1$
Character 3311.3310
Self dual yes
Analytic conductor $1.652$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -3311
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3311,1,Mod(3310,3311)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3311, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3311.3310");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3311 = 7 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3311.h (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: \(1.65240425683\)
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 3.1.3311.1
Artin image: $D_6$
Artin field: Galois closure of 6.0.120589931.1

Embedding invariants

Embedding label 3310.1
Character \(\chi\) \(=\) 3311.3310

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.00000 q^{10} +1.00000 q^{11} -2.00000 q^{13} -1.00000 q^{14} +1.00000 q^{15} -1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{21} +1.00000 q^{22} +2.00000 q^{23} +1.00000 q^{24} -2.00000 q^{26} +1.00000 q^{27} +1.00000 q^{29} +1.00000 q^{30} -1.00000 q^{33} +1.00000 q^{34} +1.00000 q^{35} +2.00000 q^{39} +1.00000 q^{40} +1.00000 q^{41} +1.00000 q^{42} -1.00000 q^{43} +2.00000 q^{46} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{51} -1.00000 q^{53} +1.00000 q^{54} -1.00000 q^{55} +1.00000 q^{56} +1.00000 q^{58} +1.00000 q^{64} +2.00000 q^{65} -1.00000 q^{66} -1.00000 q^{67} -2.00000 q^{69} +1.00000 q^{70} -1.00000 q^{77} +2.00000 q^{78} +1.00000 q^{80} -1.00000 q^{81} +1.00000 q^{82} +1.00000 q^{83} -1.00000 q^{85} -1.00000 q^{86} -1.00000 q^{87} -1.00000 q^{88} +2.00000 q^{89} +2.00000 q^{91} +1.00000 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3311\mathbb{Z}\right)^\times\).

\(n\) \(904\) \(1893\) \(2927\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(4\) 0 0
\(5\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(6\) −1.00000 −1.00000
\(7\) −1.00000 −1.00000
\(8\) −1.00000 −1.00000
\(9\) 0 0
\(10\) −1.00000 −1.00000
\(11\) 1.00000 1.00000
\(12\) 0 0
\(13\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(14\) −1.00000 −1.00000
\(15\) 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 \(0.333333\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 1.00000 1.00000
\(22\) 1.00000 1.00000
\(23\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(24\) 1.00000 1.00000
\(25\) 0 0
\(26\) −2.00000 −2.00000
\(27\) 1.00000 1.00000
\(28\) 0 0
\(29\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) 1.00000 1.00000
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) −1.00000 −1.00000
\(34\) 1.00000 1.00000
\(35\) 1.00000 1.00000
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 2.00000 2.00000
\(40\) 1.00000 1.00000
\(41\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(42\) 1.00000 1.00000
\(43\) −1.00000 −1.00000
\(44\) 0 0
\(45\) 0 0
\(46\) 2.00000 2.00000
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 1.00000 1.00000
\(49\) 1.00000 1.00000
\(50\) 0 0
\(51\) −1.00000 −1.00000
\(52\) 0 0
\(53\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 1.00000 1.00000
\(55\) −1.00000 −1.00000
\(56\) 1.00000 1.00000
\(57\) 0 0
\(58\) 1.00000 1.00000
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 2.00000 2.00000
\(66\) −1.00000 −1.00000
\(67\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) 0 0
\(69\) −2.00000 −2.00000
\(70\) 1.00000 1.00000
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.00000 −1.00000
\(78\) 2.00000 2.00000
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 1.00000 1.00000
\(81\) −1.00000 −1.00000
\(82\) 1.00000 1.00000
\(83\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(84\) 0 0
\(85\) −1.00000 −1.00000
\(86\) −1.00000 −1.00000
\(87\) −1.00000 −1.00000
\(88\) −1.00000 −1.00000
\(89\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(90\) 0 0
\(91\) 2.00000 2.00000
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 1.00000 1.00000
\(99\) 0 0
\(100\) 0 0
\(101\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(102\) −1.00000 −1.00000
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 2.00000 2.00000
\(105\) −1.00000 −1.00000
\(106\) −1.00000 −1.00000
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) −1.00000 −1.00000
\(111\) 0 0
\(112\) 1.00000 1.00000
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) −2.00000 −2.00000
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.00000 −1.00000
\(120\) −1.00000 −1.00000
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) −1.00000 −1.00000
\(124\) 0 0
\(125\) 1.00000 1.00000
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 1.00000 1.00000
\(129\) 1.00000 1.00000
\(130\) 2.00000 2.00000
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.00000 −1.00000
\(135\) −1.00000 −1.00000
\(136\) −1.00000 −1.00000
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) −2.00000 −2.00000
\(139\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.00000 −2.00000
\(144\) 0 0
\(145\) −1.00000 −1.00000
\(146\) 0 0
\(147\) −1.00000 −1.00000
\(148\) 0 0
\(149\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) 0 0
\(151\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −1.00000 −1.00000
\(155\) 0 0
\(156\) 0 0
\(157\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(158\) 0 0
\(159\) 1.00000 1.00000
\(160\) 0 0
\(161\) −2.00000 −2.00000
\(162\) −1.00000 −1.00000
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 1.00000 1.00000
\(166\) 1.00000 1.00000
\(167\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(168\) −1.00000 −1.00000
\(169\) 3.00000 3.00000
\(170\) −1.00000 −1.00000
\(171\) 0 0
\(172\) 0 0
\(173\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) −1.00000 −1.00000
\(175\) 0 0
\(176\) −1.00000 −1.00000
\(177\) 0 0
\(178\) 2.00000 2.00000
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 2.00000 2.00000
\(183\) 0 0
\(184\) −2.00000 −2.00000
\(185\) 0 0
\(186\) 0 0
\(187\) 1.00000 1.00000
\(188\) 0 0
\(189\) −1.00000 −1.00000
\(190\) 0 0
\(191\) 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
\(195\) −2.00000 −2.00000
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(200\) 0 0
\(201\) 1.00000 1.00000
\(202\) −2.00000 −2.00000
\(203\) −1.00000 −1.00000
\(204\) 0 0
\(205\) −1.00000 −1.00000
\(206\) 0 0
\(207\) 0 0
\(208\) 2.00000 2.00000
\(209\) 0 0
\(210\) −1.00000 −1.00000
\(211\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.00000 1.00000
\(216\) −1.00000 −1.00000
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.00000 −2.00000
\(222\) 0 0
\(223\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) −2.00000 −2.00000
\(231\) 1.00000 1.00000
\(232\) −1.00000 −1.00000
\(233\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) −1.00000 −1.00000
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) −1.00000 −1.00000
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 1.00000 1.00000
\(243\) 0 0
\(244\) 0 0
\(245\) −1.00000 −1.00000
\(246\) −1.00000 −1.00000
\(247\) 0 0
\(248\) 0 0
\(249\) −1.00000 −1.00000
\(250\) 1.00000 1.00000
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 2.00000 2.00000
\(254\) 0 0
\(255\) 1.00000 1.00000
\(256\) 0 0
\(257\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 1.00000 1.00000
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(264\) 1.00000 1.00000
\(265\) 1.00000 1.00000
\(266\) 0 0
\(267\) −2.00000 −2.00000
\(268\) 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 \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(272\) −1.00000 −1.00000
\(273\) −2.00000 −2.00000
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(278\) 1.00000 1.00000
\(279\) 0 0
\(280\) −1.00000 −1.00000
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −2.00000 −2.00000
\(287\) −1.00000 −1.00000
\(288\) 0 0
\(289\) 0 0
\(290\) −1.00000 −1.00000
\(291\) 0 0
\(292\) 0 0
\(293\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(294\) −1.00000 −1.00000
\(295\) 0 0
\(296\) 0 0
\(297\) 1.00000 1.00000
\(298\) 1.00000 1.00000
\(299\) −4.00000 −4.00000
\(300\) 0 0
\(301\) 1.00000 1.00000
\(302\) −2.00000 −2.00000
\(303\) 2.00000 2.00000
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) −2.00000 −2.00000
\(313\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) 2.00000 2.00000
\(315\) 0 0
\(316\) 0 0
\(317\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(318\) 1.00000 1.00000
\(319\) 1.00000 1.00000
\(320\) −1.00000 −1.00000
\(321\) 0 0
\(322\) −2.00000 −2.00000
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) −1.00000 −1.00000
\(329\) 0 0
\(330\) 1.00000 1.00000
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 1.00000 1.00000
\(335\) 1.00000 1.00000
\(336\) −1.00000 −1.00000
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 3.00000 3.00000
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −1.00000
\(344\) 1.00000 1.00000
\(345\) 2.00000 2.00000
\(346\) 1.00000 1.00000
\(347\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) −2.00000 −2.00000
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 1.00000 1.00000
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) −1.00000 −1.00000
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) −2.00000 −2.00000
\(369\) 0 0
\(370\) 0 0
\(371\) 1.00000 1.00000
\(372\) 0 0
\(373\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) 1.00000 1.00000
\(375\) −1.00000 −1.00000
\(376\) 0 0
\(377\) −2.00000 −2.00000
\(378\) −1.00000 −1.00000
\(379\) −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 \(0\)
1.00000 \(0\)
\(384\) −1.00000 −1.00000
\(385\) 1.00000 1.00000
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) −2.00000 −2.00000
\(391\) 2.00000 2.00000
\(392\) −1.00000 −1.00000
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 2.00000 2.00000
\(399\) 0 0
\(400\) 0 0
\(401\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(402\) 1.00000 1.00000
\(403\) 0 0
\(404\) 0 0
\(405\) 1.00000 1.00000
\(406\) −1.00000 −1.00000
\(407\) 0 0
\(408\) 1.00000 1.00000
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) −1.00000 −1.00000
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −1.00000 −1.00000
\(416\) 0 0
\(417\) −1.00000 −1.00000
\(418\) 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
\(424\) 1.00000 1.00000
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 2.00000 2.00000
\(430\) 1.00000 1.00000
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −1.00000 −1.00000
\(433\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(434\) 0 0
\(435\) 1.00000 1.00000
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(440\) 1.00000 1.00000
\(441\) 0 0
\(442\) −2.00000 −2.00000
\(443\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(444\) 0 0
\(445\) −2.00000 −2.00000
\(446\) −1.00000 −1.00000
\(447\) −1.00000 −1.00000
\(448\) −1.00000 −1.00000
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 1.00000 1.00000
\(452\) 0 0
\(453\) 2.00000 2.00000
\(454\) 0 0
\(455\) −2.00000 −2.00000
\(456\) 0 0
\(457\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(458\) 0 0
\(459\) 1.00000 1.00000
\(460\) 0 0
\(461\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(462\) 1.00000 1.00000
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) −1.00000 −1.00000
\(465\) 0 0
\(466\) 1.00000 1.00000
\(467\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(468\) 0 0
\(469\) 1.00000 1.00000
\(470\) 0 0
\(471\) −2.00000 −2.00000
\(472\) 0 0
\(473\) −1.00000 −1.00000
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 2.00000 2.00000
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −1.00000 −1.00000
\(491\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(492\) 0 0
\(493\) 1.00000 1.00000
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −1.00000 −1.00000
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) −1.00000 −1.00000
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 2.00000 2.00000
\(506\) 2.00000 2.00000
\(507\) −3.00000 −3.00000
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 1.00000 1.00000
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 0 0
\(514\) −1.00000 −1.00000
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −1.00000 −1.00000
\(520\) −2.00000 −2.00000
\(521\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −2.00000 −2.00000
\(527\) 0 0
\(528\) 1.00000 1.00000
\(529\) 3.00000 3.00000
\(530\) 1.00000 1.00000
\(531\) 0 0
\(532\) 0 0
\(533\) −2.00000 −2.00000
\(534\) −2.00000 −2.00000
\(535\) 0 0
\(536\) 1.00000 1.00000
\(537\) 0 0
\(538\) 0 0
\(539\) 1.00000 1.00000
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 1.00000 1.00000
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) −2.00000 −2.00000
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 2.00000 2.00000
\(553\) 0 0
\(554\) 1.00000 1.00000
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 2.00000 2.00000
\(560\) −1.00000 −1.00000
\(561\) −1.00000 −1.00000
\(562\) 0 0
\(563\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −2.00000 −2.00000
\(567\) 1.00000 1.00000
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −1.00000 −1.00000
\(575\) 0 0
\(576\) 0 0
\(577\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.00000 −1.00000
\(582\) 0 0
\(583\) −1.00000 −1.00000
\(584\) 0 0
\(585\) 0 0
\(586\) −2.00000 −2.00000
\(587\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 1.00000 1.00000
\(595\) 1.00000 1.00000
\(596\) 0 0
\(597\) −2.00000 −2.00000
\(598\) −4.00000 −4.00000
\(599\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 1.00000 1.00000
\(603\) 0 0
\(604\) 0 0
\(605\) −1.00000 −1.00000
\(606\) 2.00000 2.00000
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 1.00000 1.00000
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 1.00000 1.00000
\(615\) 1.00000 1.00000
\(616\) 1.00000 1.00000
\(617\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 2.00000 2.00000
\(622\) 0 0
\(623\) −2.00000 −2.00000
\(624\) −2.00000 −2.00000
\(625\) −1.00000 −1.00000
\(626\) −1.00000 −1.00000
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) −1.00000 −1.00000
\(634\) 2.00000 2.00000
\(635\) 0 0
\(636\) 0 0
\(637\) −2.00000 −2.00000
\(638\) 1.00000 1.00000
\(639\) 0 0
\(640\) −1.00000 −1.00000
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) −1.00000 −1.00000
\(646\) 0 0
\(647\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(648\) 1.00000 1.00000
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.00000 −1.00000
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 2.00000 2.00000
\(664\) −1.00000 −1.00000
\(665\) 0 0
\(666\) 0 0
\(667\) 2.00000 2.00000
\(668\) 0 0
\(669\) 1.00000 1.00000
\(670\) 1.00000 1.00000
\(671\) 0 0
\(672\) 0 0
\(673\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 1.00000 1.00000
\(681\) 0 0
\(682\) 0 0
\(683\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.00000 −1.00000
\(687\) 0 0
\(688\) 1.00000 1.00000
\(689\) 2.00000 2.00000
\(690\) 2.00000 2.00000
\(691\) −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
\(696\) 1.00000 1.00000
\(697\) 1.00000 1.00000
\(698\) 0 0
\(699\) −1.00000 −1.00000
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) −2.00000 −2.00000
\(703\) 0 0
\(704\) 1.00000 1.00000
\(705\) 0 0
\(706\) 0 0
\(707\) 2.00000 2.00000
\(708\) 0 0
\(709\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(710\) 0 0
\(711\) 0 0
\(712\) −2.00000 −2.00000
\(713\) 0 0
\(714\) 1.00000 1.00000
\(715\) 2.00000 2.00000
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.00000 1.00000
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) −1.00000 −1.00000
\(727\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(728\) −2.00000 −2.00000
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) −1.00000 −1.00000
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 1.00000 1.00000
\(736\) 0 0
\(737\) −1.00000 −1.00000
\(738\) 0 0
\(739\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 1.00000 1.00000
\(743\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(744\) 0 0
\(745\) −1.00000 −1.00000
\(746\) 1.00000 1.00000
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) −1.00000 −1.00000
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −2.00000 −2.00000
\(755\) 2.00000 2.00000
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) −1.00000 −1.00000
\(759\) −2.00000 −2.00000
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 2.00000 2.00000
\(767\) 0 0
\(768\) 0 0
\(769\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(770\) 1.00000 1.00000
\(771\) 1.00000 1.00000
\(772\) 0 0
\(773\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 2.00000 2.00000
\(783\) 1.00000 1.00000
\(784\) −1.00000 −1.00000
\(785\) −2.00000 −2.00000
\(786\) 0 0
\(787\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 2.00000 2.00000
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −1.00000 −1.00000
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 2.00000 2.00000
\(803\) 0 0
\(804\) 0 0
\(805\) 2.00000 2.00000
\(806\) 0 0
\(807\) 0 0
\(808\) 2.00000 2.00000
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 1.00000 1.00000
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) −1.00000 −1.00000
\(814\) 0 0
\(815\) 0 0
\(816\) 1.00000 1.00000
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) −1.00000 −1.00000
\(831\) −1.00000 −1.00000
\(832\) −2.00000 −2.00000
\(833\) 1.00000 1.00000
\(834\) −1.00000 −1.00000
\(835\) −1.00000 −1.00000
\(836\) 0 0
\(837\) 0 0
\(838\) −1.00000 −1.00000
\(839\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(840\) 1.00000 1.00000
\(841\) 0 0
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −3.00000 −3.00000
\(846\) 0 0
\(847\) −1.00000 −1.00000
\(848\) 1.00000 1.00000
\(849\) 2.00000 2.00000
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(858\) 2.00000 2.00000
\(859\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(860\) 0 0
\(861\) 1.00000 1.00000
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) −1.00000 −1.00000
\(866\) 2.00000 2.00000
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 1.00000 1.00000
\(871\) 2.00000 2.00000
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.00000 −1.00000
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) −2.00000 −2.00000
\(879\) 2.00000 2.00000
\(880\) 1.00000 1.00000
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(884\) 0 0
\(885\) 0 0
\(886\) −1.00000 −1.00000
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −2.00000 −2.00000
\(891\) −1.00000 −1.00000
\(892\) 0 0
\(893\) 0 0
\(894\) −1.00000 −1.00000
\(895\) 0 0
\(896\) −1.00000 −1.00000
\(897\) 4.00000 4.00000
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) −1.00000 −1.00000
\(902\) 1.00000 1.00000
\(903\) −1.00000 −1.00000
\(904\) 0 0
\(905\) 0 0
\(906\) 2.00000 2.00000
\(907\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) −2.00000 −2.00000
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 1.00000 1.00000
\(914\) 1.00000 1.00000
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 1.00000 1.00000
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 2.00000 2.00000
\(921\) −1.00000 −1.00000
\(922\) 1.00000 1.00000
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) −1.00000 −1.00000
\(935\) −1.00000 −1.00000
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 1.00000 1.00000
\(939\) 1.00000 1.00000
\(940\) 0 0
\(941\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(942\) −2.00000 −2.00000
\(943\) 2.00000 2.00000
\(944\) 0 0
\(945\) 1.00000 1.00000
\(946\) −1.00000 −1.00000
\(947\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −2.00000 −2.00000
\(952\) 1.00000 1.00000
\(953\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −1.00000 −1.00000
\(958\) −2.00000 −2.00000
\(959\) 0 0
\(960\) 1.00000 1.00000
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 2.00000 2.00000
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −1.00000 −1.00000
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) −1.00000 −1.00000
\(974\) −1.00000 −1.00000
\(975\) 0 0
\(976\) 0 0
\(977\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(978\) 0 0
\(979\) 2.00000 2.00000
\(980\) 0 0
\(981\) 0 0
\(982\) 1.00000 1.00000
\(983\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(984\) 1.00000 1.00000
\(985\) 0 0
\(986\) 1.00000 1.00000
\(987\) 0 0
\(988\) 0 0
\(989\) −2.00000 −2.00000
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −2.00000 −2.00000
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 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 3311.1.h.d.3310.1 yes 1
7.6 odd 2 3311.1.h.e.3310.1 yes 1
11.10 odd 2 3311.1.h.b.3310.1 ✓ 1
43.42 odd 2 3311.1.h.c.3310.1 yes 1
77.76 even 2 3311.1.h.c.3310.1 yes 1
301.300 even 2 3311.1.h.b.3310.1 ✓ 1
473.472 even 2 3311.1.h.e.3310.1 yes 1
3311.3310 odd 2 CM 3311.1.h.d.3310.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3311.1.h.b.3310.1 ✓ 1 11.10 odd 2
3311.1.h.b.3310.1 ✓ 1 301.300 even 2
3311.1.h.c.3310.1 yes 1 43.42 odd 2
3311.1.h.c.3310.1 yes 1 77.76 even 2
3311.1.h.d.3310.1 yes 1 1.1 even 1 trivial
3311.1.h.d.3310.1 yes 1 3311.3310 odd 2 CM
3311.1.h.e.3310.1 yes 1 7.6 odd 2
3311.1.h.e.3310.1 yes 1 473.472 even 2