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Properties

Label 1176.1.n.d.197.1
Level $1176$
Weight $1$
Character 1176.197
Self dual yes
Analytic conductor $0.587$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -24
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] = [1176,1,Mod(197,1176)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1176.197");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1176.n (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: \(0.586900454856\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 168)
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.1176.1
Artin image: $S_3$
Artin field: Galois closure of 3.1.1176.1

Embedding invariants

Embedding label 197.1
Character \(\chi\) \(=\) 1176.197

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} -1.00000 q^{20} -1.00000 q^{22} +1.00000 q^{24} +1.00000 q^{27} -1.00000 q^{29} -1.00000 q^{30} -1.00000 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{36} -1.00000 q^{40} -1.00000 q^{44} -1.00000 q^{45} +1.00000 q^{48} -1.00000 q^{53} +1.00000 q^{54} +1.00000 q^{55} -1.00000 q^{58} -1.00000 q^{59} -1.00000 q^{60} -1.00000 q^{62} +1.00000 q^{64} -1.00000 q^{66} +1.00000 q^{72} +2.00000 q^{73} -1.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -1.00000 q^{83} -1.00000 q^{87} -1.00000 q^{88} -1.00000 q^{90} -1.00000 q^{93} +1.00000 q^{96} -1.00000 q^{97} -1.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times\).

\(n\) \(295\) \(589\) \(785\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

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
\(3\) 1.00000 1.00000
\(4\) 1.00000 1.00000
\(5\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(6\) 1.00000 1.00000
\(7\) 0 0
\(8\) 1.00000 1.00000
\(9\) 1.00000 1.00000
\(10\) −1.00000 −1.00000
\(11\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) 1.00000 1.00000
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) −1.00000 −1.00000
\(16\) 1.00000 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 1.00000 1.00000
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −1.00000 −1.00000
\(21\) 0 0
\(22\) −1.00000 −1.00000
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 1.00000 1.00000
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000 1.00000
\(28\) 0 0
\(29\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) −1.00000 −1.00000
\(31\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 1.00000 1.00000
\(33\) −1.00000 −1.00000
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 1.00000
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 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 \(\pi\)
\(44\) −1.00000 −1.00000
\(45\) −1.00000 −1.00000
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 1.00000 1.00000
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 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
\(56\) 0 0
\(57\) 0 0
\(58\) −1.00000 −1.00000
\(59\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) −1.00000 −1.00000
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) −1.00000 −1.00000
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) −1.00000 −1.00000
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 1.00000 1.00000
\(73\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(74\) 0 0
\(75\) 0 0
\(76\) 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
\(83\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −1.00000 −1.00000
\(88\) −1.00000 −1.00000
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) −1.00000 −1.00000
\(91\) 0 0
\(92\) 0 0
\(93\) −1.00000 −1.00000
\(94\) 0 0
\(95\) 0 0
\(96\) 1.00000 1.00000
\(97\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(98\) 0 0
\(99\) −1.00000 −1.00000
\(100\) 0 0
\(101\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(102\) 0 0
\(103\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(104\) 0 0
\(105\) 0 0
\(106\) −1.00000 −1.00000
\(107\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) 1.00000 1.00000
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 1.00000 1.00000
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.00000 −1.00000
\(117\) 0 0
\(118\) −1.00000 −1.00000
\(119\) 0 0
\(120\) −1.00000 −1.00000
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) −1.00000 −1.00000
\(125\) 1.00000 1.00000
\(126\) 0 0
\(127\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(128\) 1.00000 1.00000
\(129\) 0 0
\(130\) 0 0
\(131\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(132\) −1.00000 −1.00000
\(133\) 0 0
\(134\) 0 0
\(135\) −1.00000 −1.00000
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 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
\(146\) 2.00000 2.00000
\(147\) 0 0
\(148\) 0 0
\(149\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(150\) 0 0
\(151\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 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
\(160\) −1.00000 −1.00000
\(161\) 0 0
\(162\) 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
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(174\) −1.00000 −1.00000
\(175\) 0 0
\(176\) −1.00000 −1.00000
\(177\) −1.00000 −1.00000
\(178\) 0 0
\(179\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(180\) −1.00000 −1.00000
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) −1.00000 −1.00000
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 1.00000 1.00000
\(193\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) −1.00000 −1.00000
\(195\) 0 0
\(196\) 0 0
\(197\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(198\) −1.00000 −1.00000
\(199\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(200\) 0 0
\(201\) 0 0
\(202\) 2.00000 2.00000
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 2.00000 2.00000
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) −1.00000 −1.00000
\(213\) 0 0
\(214\) −1.00000 −1.00000
\(215\) 0 0
\(216\) 1.00000 1.00000
\(217\) 0 0
\(218\) 0 0
\(219\) 2.00000 2.00000
\(220\) 1.00000 1.00000
\(221\) 0 0
\(222\) 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
\(227\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −1.00000 −1.00000
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.00000 −1.00000
\(237\) −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
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −1.00000 −1.00000
\(249\) −1.00000 −1.00000
\(250\) 1.00000 1.00000
\(251\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −1.00000 −1.00000
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −1.00000 −1.00000
\(262\) −1.00000 −1.00000
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) −1.00000 −1.00000
\(265\) 1.00000 1.00000
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) −1.00000 −1.00000
\(271\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) −1.00000 −1.00000
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 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
\(289\) 1.00000 1.00000
\(290\) 1.00000 1.00000
\(291\) −1.00000 −1.00000
\(292\) 2.00000 2.00000
\(293\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(294\) 0 0
\(295\) 1.00000 1.00000
\(296\) 0 0
\(297\) −1.00000 −1.00000
\(298\) 2.00000 2.00000
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) −1.00000 −1.00000
\(303\) 2.00000 2.00000
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 2.00000 2.00000
\(310\) 1.00000 1.00000
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −1.00000 −1.00000
\(317\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(318\) −1.00000 −1.00000
\(319\) 1.00000 1.00000
\(320\) −1.00000 −1.00000
\(321\) −1.00000 −1.00000
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 1.00000 1.00000
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −1.00000 −1.00000
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(338\) 1.00000 1.00000
\(339\) 0 0
\(340\) 0 0
\(341\) 1.00000 1.00000
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 2.00000 2.00000
\(347\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(348\) −1.00000 −1.00000
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.00000 −1.00000
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) −1.00000 −1.00000
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 2.00000 2.00000
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) −1.00000 −1.00000
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.00000 −2.00000
\(366\) 0 0
\(367\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −1.00000 −1.00000
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 1.00000 1.00000
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) −1.00000 −1.00000
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 1.00000 1.00000
\(385\) 0 0
\(386\) −1.00000 −1.00000
\(387\) 0 0
\(388\) −1.00000 −1.00000
\(389\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −1.00000 −1.00000
\(394\) 2.00000 2.00000
\(395\) 1.00000 1.00000
\(396\) −1.00000 −1.00000
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 2.00000 2.00000
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 2.00000 2.00000
\(405\) −1.00000 −1.00000
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 2.00000 2.00000
\(413\) 0 0
\(414\) 0 0
\(415\) 1.00000 1.00000
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −1.00000 −1.00000
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −1.00000 −1.00000
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 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
\(438\) 2.00000 2.00000
\(439\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 1.00000 1.00000
\(441\) 0 0
\(442\) 0 0
\(443\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −1.00000 −1.00000
\(447\) 2.00000 2.00000
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −1.00000 −1.00000
\(454\) −1.00000 −1.00000
\(455\) 0 0
\(456\) 0 0
\(457\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(462\) 0 0
\(463\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(464\) −1.00000 −1.00000
\(465\) 1.00000 1.00000
\(466\) 0 0
\(467\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.00000 −1.00000
\(473\) 0 0
\(474\) −1.00000 −1.00000
\(475\) 0 0
\(476\) 0 0
\(477\) −1.00000 −1.00000
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) −1.00000 −1.00000
\(481\) 0 0
\(482\) −1.00000 −1.00000
\(483\) 0 0
\(484\) 0 0
\(485\) 1.00000 1.00000
\(486\) 1.00000 1.00000
\(487\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 1.00000 1.00000
\(496\) −1.00000 −1.00000
\(497\) 0 0
\(498\) −1.00000 −1.00000
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 1.00000 1.00000
\(501\) 0 0
\(502\) −1.00000 −1.00000
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) −2.00000 −2.00000
\(506\) 0 0
\(507\) 1.00000 1.00000
\(508\) −1.00000 −1.00000
\(509\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 1.00000
\(513\) 0 0
\(514\) 0 0
\(515\) −2.00000 −2.00000
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 2.00000 2.00000
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −1.00000 −1.00000
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) −1.00000 −1.00000
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −1.00000 −1.00000
\(529\) 1.00000 1.00000
\(530\) 1.00000 1.00000
\(531\) −1.00000 −1.00000
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 1.00000 1.00000
\(536\) 0 0
\(537\) 2.00000 2.00000
\(538\) −1.00000 −1.00000
\(539\) 0 0
\(540\) −1.00000 −1.00000
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) −1.00000 −1.00000
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) −1.00000 −1.00000
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 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
\(577\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(578\) 1.00000 1.00000
\(579\) −1.00000 −1.00000
\(580\) 1.00000 1.00000
\(581\) 0 0
\(582\) −1.00000 −1.00000
\(583\) 1.00000 1.00000
\(584\) 2.00000 2.00000
\(585\) 0 0
\(586\) −1.00000 −1.00000
\(587\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 1.00000 1.00000
\(591\) 2.00000 2.00000
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) −1.00000 −1.00000
\(595\) 0 0
\(596\) 2.00000 2.00000
\(597\) 2.00000 2.00000
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1.00000 −1.00000
\(605\) 0 0
\(606\) 2.00000 2.00000
\(607\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 2.00000 2.00000
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 1.00000 1.00000
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −1.00000 −1.00000
\(626\) −1.00000 −1.00000
\(627\) 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
\(633\) 0 0
\(634\) −1.00000 −1.00000
\(635\) 1.00000 1.00000
\(636\) −1.00000 −1.00000
\(637\) 0 0
\(638\) 1.00000 1.00000
\(639\) 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
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 1.00000 1.00000
\(649\) 1.00000 1.00000
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(654\) 0 0
\(655\) 1.00000 1.00000
\(656\) 0 0
\(657\) 2.00000 2.00000
\(658\) 0 0
\(659\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(660\) 1.00000 1.00000
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −1.00000 −1.00000
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −1.00000 −1.00000
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(674\) −1.00000 −1.00000
\(675\) 0 0
\(676\) 1.00000 1.00000
\(677\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −1.00000 −1.00000
\(682\) 1.00000 1.00000
\(683\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 2.00000 2.00000
\(693\) 0 0
\(694\) 2.00000 2.00000
\(695\) 0 0
\(696\) −1.00000 −1.00000
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.00000 −1.00000
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) −1.00000 −1.00000
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) −1.00000 −1.00000
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 2.00000 2.00000
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) −1.00000 −1.00000
\(721\) 0 0
\(722\) 1.00000 1.00000
\(723\) −1.00000 −1.00000
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) −2.00000 −2.00000
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) −1.00000 −1.00000
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) −1.00000 −1.00000
\(745\) −2.00000 −2.00000
\(746\) 0 0
\(747\) −1.00000 −1.00000
\(748\) 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 \(0.666667\pi\)
\(752\) 0 0
\(753\) −1.00000 −1.00000
\(754\) 0 0
\(755\) 1.00000 1.00000
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) −1.00000 −1.00000
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.00000 1.00000
\(769\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.00000 −1.00000
\(773\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(774\) 0 0
\(775\) 0 0
\(776\) −1.00000 −1.00000
\(777\) 0 0
\(778\) 2.00000 2.00000
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −1.00000 −1.00000
\(784\) 0 0
\(785\) 0 0
\(786\) −1.00000 −1.00000
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 2.00000 2.00000
\(789\) 0 0
\(790\) 1.00000 1.00000
\(791\) 0 0
\(792\) −1.00000 −1.00000
\(793\) 0 0
\(794\) 0 0
\(795\) 1.00000 1.00000
\(796\) 2.00000 2.00000
\(797\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2.00000 −2.00000
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −1.00000 −1.00000
\(808\) 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
\(816\) 0 0
\(817\) 0 0
\(818\) −1.00000 −1.00000
\(819\) 0 0
\(820\) 0 0
\(821\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(822\) 0 0
\(823\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(824\) 2.00000 2.00000
\(825\) 0 0
\(826\) 0 0
\(827\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 1.00000 1.00000
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −1.00000 −1.00000
\(838\) 2.00000 2.00000
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 0 0
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.00000 −1.00000
\(846\) 0 0
\(847\) 0 0
\(848\) −1.00000 −1.00000
\(849\) 0 0
\(850\) 0 0
\(851\) 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
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 1.00000 1.00000
\(865\) −2.00000 −2.00000
\(866\) 2.00000 2.00000
\(867\) 1.00000 1.00000
\(868\) 0 0
\(869\) 1.00000 1.00000
\(870\) 1.00000 1.00000
\(871\) 0 0
\(872\) 0 0
\(873\) −1.00000 −1.00000
\(874\) 0 0
\(875\) 0 0
\(876\) 2.00000 2.00000
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) −1.00000 −1.00000
\(879\) −1.00000 −1.00000
\(880\) 1.00000 1.00000
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 1.00000 1.00000
\(886\) −1.00000 −1.00000
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1.00000 −1.00000
\(892\) −1.00000 −1.00000
\(893\) 0 0
\(894\) 2.00000 2.00000
\(895\) −2.00000 −2.00000
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 1.00000 1.00000
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) −1.00000 −1.00000
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) −1.00000 −1.00000
\(909\) 2.00000 2.00000
\(910\) 0 0
\(911\) 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
\(918\) 0 0
\(919\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(920\) 0 0
\(921\) 0 0
\(922\) 2.00000 2.00000
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 2.00000 2.00000
\(927\) 2.00000 2.00000
\(928\) −1.00000 −1.00000
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 1.00000 1.00000
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 2.00000 2.00000
\(935\) 0 0
\(936\) 0 0
\(937\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(938\) 0 0
\(939\) −1.00000 −1.00000
\(940\) 0 0
\(941\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −1.00000 −1.00000
\(945\) 0 0
\(946\) 0 0
\(947\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(948\) −1.00000 −1.00000
\(949\) 0 0
\(950\) 0 0
\(951\) −1.00000 −1.00000
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) −1.00000 −1.00000
\(955\) 0 0
\(956\) 0 0
\(957\) 1.00000 1.00000
\(958\) 0 0
\(959\) 0 0
\(960\) −1.00000 −1.00000
\(961\) 0 0
\(962\) 0 0
\(963\) −1.00000 −1.00000
\(964\) −1.00000 −1.00000
\(965\) 1.00000 1.00000
\(966\) 0 0
\(967\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 1.00000 1.00000
\(971\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(972\) 1.00000 1.00000
\(973\) 0 0
\(974\) −1.00000 −1.00000
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) −1.00000 −1.00000
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) −2.00000 −2.00000
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 1.00000 1.00000
\(991\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(992\) −1.00000 −1.00000
\(993\) 0 0
\(994\) 0 0
\(995\) −2.00000 −2.00000
\(996\) −1.00000 −1.00000
\(997\) 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 1176.1.n.d.197.1 1
3.2 odd 2 1176.1.n.a.197.1 1
7.2 even 3 168.1.s.a.53.1 ✓ 2
7.3 odd 6 1176.1.s.a.1157.1 2
7.4 even 3 168.1.s.a.149.1 yes 2
7.5 odd 6 1176.1.s.a.557.1 2
7.6 odd 2 1176.1.n.c.197.1 1
8.5 even 2 1176.1.n.a.197.1 1
21.2 odd 6 168.1.s.b.53.1 yes 2
21.5 even 6 1176.1.s.b.557.1 2
21.11 odd 6 168.1.s.b.149.1 yes 2
21.17 even 6 1176.1.s.b.1157.1 2
21.20 even 2 1176.1.n.b.197.1 1
24.5 odd 2 CM 1176.1.n.d.197.1 1
28.11 odd 6 672.1.ba.b.401.1 2
28.23 odd 6 672.1.ba.b.305.1 2
56.5 odd 6 1176.1.s.b.557.1 2
56.11 odd 6 672.1.ba.a.401.1 2
56.13 odd 2 1176.1.n.b.197.1 1
56.37 even 6 168.1.s.b.53.1 yes 2
56.45 odd 6 1176.1.s.b.1157.1 2
56.51 odd 6 672.1.ba.a.305.1 2
56.53 even 6 168.1.s.b.149.1 yes 2
84.11 even 6 672.1.ba.a.401.1 2
84.23 even 6 672.1.ba.a.305.1 2
168.5 even 6 1176.1.s.a.557.1 2
168.11 even 6 672.1.ba.b.401.1 2
168.53 odd 6 168.1.s.a.149.1 yes 2
168.101 even 6 1176.1.s.a.1157.1 2
168.107 even 6 672.1.ba.b.305.1 2
168.125 even 2 1176.1.n.c.197.1 1
168.149 odd 6 168.1.s.a.53.1 ✓ 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.1.s.a.53.1 ✓ 2 7.2 even 3
168.1.s.a.53.1 ✓ 2 168.149 odd 6
168.1.s.a.149.1 yes 2 7.4 even 3
168.1.s.a.149.1 yes 2 168.53 odd 6
168.1.s.b.53.1 yes 2 21.2 odd 6
168.1.s.b.53.1 yes 2 56.37 even 6
168.1.s.b.149.1 yes 2 21.11 odd 6
168.1.s.b.149.1 yes 2 56.53 even 6
672.1.ba.a.305.1 2 56.51 odd 6
672.1.ba.a.305.1 2 84.23 even 6
672.1.ba.a.401.1 2 56.11 odd 6
672.1.ba.a.401.1 2 84.11 even 6
672.1.ba.b.305.1 2 28.23 odd 6
672.1.ba.b.305.1 2 168.107 even 6
672.1.ba.b.401.1 2 28.11 odd 6
672.1.ba.b.401.1 2 168.11 even 6
1176.1.n.a.197.1 1 3.2 odd 2
1176.1.n.a.197.1 1 8.5 even 2
1176.1.n.b.197.1 1 21.20 even 2
1176.1.n.b.197.1 1 56.13 odd 2
1176.1.n.c.197.1 1 7.6 odd 2
1176.1.n.c.197.1 1 168.125 even 2
1176.1.n.d.197.1 1 1.1 even 1 trivial
1176.1.n.d.197.1 1 24.5 odd 2 CM
1176.1.s.a.557.1 2 7.5 odd 6
1176.1.s.a.557.1 2 168.5 even 6
1176.1.s.a.1157.1 2 7.3 odd 6
1176.1.s.a.1157.1 2 168.101 even 6
1176.1.s.b.557.1 2 21.5 even 6
1176.1.s.b.557.1 2 56.5 odd 6
1176.1.s.b.1157.1 2 21.17 even 6
1176.1.s.b.1157.1 2 56.45 odd 6