Properties

Label 768.2.c.j.767.4
Level $768$
Weight $2$
Character 768.767
Analytic conductor $6.133$
Analytic rank $0$
Dimension $4$
CM discriminant -24
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [768,2,Mod(767,768)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(768, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("768.767");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.c (of order \(2\), degree \(1\), not 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: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 4x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 384)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 767.4
Root \(1.93185i\) of defining polynomial
Character \(\chi\) \(=\) 768.767
Dual form 768.2.c.j.767.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.73205 q^{3} +2.82843i q^{5} -4.89898i q^{7} +3.00000 q^{9} +O(q^{10})\) \(q+1.73205 q^{3} +2.82843i q^{5} -4.89898i q^{7} +3.00000 q^{9} +3.46410 q^{11} +4.89898i q^{15} -8.48528i q^{21} -3.00000 q^{25} +5.19615 q^{27} -2.82843i q^{29} +4.89898i q^{31} +6.00000 q^{33} +13.8564 q^{35} +8.48528i q^{45} -17.0000 q^{49} +14.1421i q^{53} +9.79796i q^{55} +10.3923 q^{59} -14.6969i q^{63} -14.0000 q^{73} -5.19615 q^{75} -16.9706i q^{77} -14.6969i q^{79} +9.00000 q^{81} -17.3205 q^{83} -4.89898i q^{87} +8.48528i q^{93} +2.00000 q^{97} +10.3923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 12 q^{9} - 12 q^{25} + 24 q^{33} - 68 q^{49} - 56 q^{73} + 36 q^{81} + 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.73205 1.00000
\(4\) 0 0
\(5\) 2.82843i 1.26491i 0.774597 + 0.632456i \(0.217953\pi\)
−0.774597 + 0.632456i \(0.782047\pi\)
\(6\) 0 0
\(7\) − 4.89898i − 1.85164i −0.377964 0.925820i \(-0.623376\pi\)
0.377964 0.925820i \(-0.376624\pi\)
\(8\) 0 0
\(9\) 3.00000 1.00000
\(10\) 0 0
\(11\) 3.46410 1.04447 0.522233 0.852803i \(-0.325099\pi\)
0.522233 + 0.852803i \(0.325099\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 4.89898i 1.26491i
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) − 8.48528i − 1.85164i
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −3.00000 −0.600000
\(26\) 0 0
\(27\) 5.19615 1.00000
\(28\) 0 0
\(29\) − 2.82843i − 0.525226i −0.964901 0.262613i \(-0.915416\pi\)
0.964901 0.262613i \(-0.0845842\pi\)
\(30\) 0 0
\(31\) 4.89898i 0.879883i 0.898027 + 0.439941i \(0.145001\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) 0 0
\(33\) 6.00000 1.04447
\(34\) 0 0
\(35\) 13.8564 2.34216
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 8.48528i 1.26491i
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −17.0000 −2.42857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 14.1421i 1.94257i 0.237915 + 0.971286i \(0.423536\pi\)
−0.237915 + 0.971286i \(0.576464\pi\)
\(54\) 0 0
\(55\) 9.79796i 1.32116i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 10.3923 1.35296 0.676481 0.736460i \(-0.263504\pi\)
0.676481 + 0.736460i \(0.263504\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) − 14.6969i − 1.85164i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −14.0000 −1.63858 −0.819288 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 0 0
\(75\) −5.19615 −0.600000
\(76\) 0 0
\(77\) − 16.9706i − 1.93398i
\(78\) 0 0
\(79\) − 14.6969i − 1.65353i −0.562544 0.826767i \(-0.690177\pi\)
0.562544 0.826767i \(-0.309823\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −17.3205 −1.90117 −0.950586 0.310460i \(-0.899517\pi\)
−0.950586 + 0.310460i \(0.899517\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) − 4.89898i − 0.525226i
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 8.48528i 0.879883i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) 10.3923 1.04447
\(100\) 0 0
\(101\) − 19.7990i − 1.97007i −0.172345 0.985037i \(-0.555135\pi\)
0.172345 0.985037i \(-0.444865\pi\)
\(102\) 0 0
\(103\) 14.6969i 1.44813i 0.689730 + 0.724066i \(0.257729\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) 0 0
\(105\) 24.0000 2.34216
\(106\) 0 0
\(107\) −17.3205 −1.67444 −0.837218 0.546869i \(-0.815820\pi\)
−0.837218 + 0.546869i \(0.815820\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 5.65685i 0.505964i
\(126\) 0 0
\(127\) 4.89898i 0.434714i 0.976092 + 0.217357i \(0.0697436\pi\)
−0.976092 + 0.217357i \(0.930256\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 3.46410 0.302660 0.151330 0.988483i \(-0.451644\pi\)
0.151330 + 0.988483i \(0.451644\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 14.6969i 1.26491i
\(136\) 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
\(144\) 0 0
\(145\) 8.00000 0.664364
\(146\) 0 0
\(147\) −29.4449 −2.42857
\(148\) 0 0
\(149\) 2.82843i 0.231714i 0.993266 + 0.115857i \(0.0369614\pi\)
−0.993266 + 0.115857i \(0.963039\pi\)
\(150\) 0 0
\(151\) − 24.4949i − 1.99337i −0.0813788 0.996683i \(-0.525932\pi\)
0.0813788 0.996683i \(-0.474068\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −13.8564 −1.11297
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 24.4949i 1.94257i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 16.9706i 1.32116i
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 19.7990i 1.50529i 0.658427 + 0.752645i \(0.271222\pi\)
−0.658427 + 0.752645i \(0.728778\pi\)
\(174\) 0 0
\(175\) 14.6969i 1.11098i
\(176\) 0 0
\(177\) 18.0000 1.35296
\(178\) 0 0
\(179\) −24.2487 −1.81243 −0.906217 0.422813i \(-0.861043\pi\)
−0.906217 + 0.422813i \(0.861043\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) − 25.4558i − 1.85164i
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) −26.0000 −1.87152 −0.935760 0.352636i \(-0.885285\pi\)
−0.935760 + 0.352636i \(0.885285\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 14.1421i 1.00759i 0.863825 + 0.503793i \(0.168062\pi\)
−0.863825 + 0.503793i \(0.831938\pi\)
\(198\) 0 0
\(199\) − 24.4949i − 1.73640i −0.496217 0.868199i \(-0.665278\pi\)
0.496217 0.868199i \(-0.334722\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −13.8564 −0.972529
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 24.0000 1.62923
\(218\) 0 0
\(219\) −24.2487 −1.63858
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) − 14.6969i − 0.984180i −0.870544 0.492090i \(-0.836233\pi\)
0.870544 0.492090i \(-0.163767\pi\)
\(224\) 0 0
\(225\) −9.00000 −0.600000
\(226\) 0 0
\(227\) 10.3923 0.689761 0.344881 0.938647i \(-0.387919\pi\)
0.344881 + 0.938647i \(0.387919\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) − 29.3939i − 1.93398i
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) − 25.4558i − 1.65353i
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 0 0
\(243\) 15.5885 1.00000
\(244\) 0 0
\(245\) − 48.0833i − 3.07193i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −30.0000 −1.90117
\(250\) 0 0
\(251\) 31.1769 1.96787 0.983935 0.178529i \(-0.0571337\pi\)
0.983935 + 0.178529i \(0.0571337\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) − 8.48528i − 0.525226i
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −40.0000 −2.45718
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 31.1127i 1.89697i 0.316815 + 0.948487i \(0.397387\pi\)
−0.316815 + 0.948487i \(0.602613\pi\)
\(270\) 0 0
\(271\) 24.4949i 1.48796i 0.668202 + 0.743980i \(0.267064\pi\)
−0.668202 + 0.743980i \(0.732936\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −10.3923 −0.626680
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 14.6969i 0.879883i
\(280\) 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
\(288\) 0 0
\(289\) 17.0000 1.00000
\(290\) 0 0
\(291\) 3.46410 0.203069
\(292\) 0 0
\(293\) 14.1421i 0.826192i 0.910687 + 0.413096i \(0.135553\pi\)
−0.910687 + 0.413096i \(0.864447\pi\)
\(294\) 0 0
\(295\) 29.3939i 1.71138i
\(296\) 0 0
\(297\) 18.0000 1.04447
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) − 34.2929i − 1.97007i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 25.4558i 1.44813i
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 34.0000 1.92179 0.960897 0.276907i \(-0.0893093\pi\)
0.960897 + 0.276907i \(0.0893093\pi\)
\(314\) 0 0
\(315\) 41.5692 2.34216
\(316\) 0 0
\(317\) 31.1127i 1.74746i 0.486408 + 0.873732i \(0.338307\pi\)
−0.486408 + 0.873732i \(0.661693\pi\)
\(318\) 0 0
\(319\) − 9.79796i − 0.548580i
\(320\) 0 0
\(321\) −30.0000 −1.67444
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 22.0000 1.19842 0.599208 0.800593i \(-0.295482\pi\)
0.599208 + 0.800593i \(0.295482\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 16.9706i 0.919007i
\(342\) 0 0
\(343\) 48.9898i 2.64520i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −24.2487 −1.30174 −0.650870 0.759190i \(-0.725596\pi\)
−0.650870 + 0.759190i \(0.725596\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 0 0
\(363\) 1.73205 0.0909091
\(364\) 0 0
\(365\) − 39.5980i − 2.07265i
\(366\) 0 0
\(367\) 4.89898i 0.255725i 0.991792 + 0.127862i \(0.0408116\pi\)
−0.991792 + 0.127862i \(0.959188\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 69.2820 3.59694
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 9.79796i 0.505964i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 8.48528i 0.434714i
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 48.0000 2.44631
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) − 31.1127i − 1.57748i −0.614729 0.788738i \(-0.710735\pi\)
0.614729 0.788738i \(-0.289265\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 6.00000 0.302660
\(394\) 0 0
\(395\) 41.5692 2.09157
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 25.4558i 1.26491i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −10.0000 −0.494468 −0.247234 0.968956i \(-0.579522\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) − 50.9117i − 2.50520i
\(414\) 0 0
\(415\) − 48.9898i − 2.40481i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10.3923 0.507697 0.253849 0.967244i \(-0.418303\pi\)
0.253849 + 0.967244i \(0.418303\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 13.8564 0.664364
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) − 24.4949i − 1.16908i −0.811366 0.584539i \(-0.801275\pi\)
0.811366 0.584539i \(-0.198725\pi\)
\(440\) 0 0
\(441\) −51.0000 −2.42857
\(442\) 0 0
\(443\) 31.1769 1.48126 0.740630 0.671913i \(-0.234527\pi\)
0.740630 + 0.671913i \(0.234527\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 4.89898i 0.231714i
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) − 42.4264i − 1.99337i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 38.0000 1.77757 0.888783 0.458329i \(-0.151552\pi\)
0.888783 + 0.458329i \(0.151552\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 19.7990i 0.922131i 0.887366 + 0.461065i \(0.152533\pi\)
−0.887366 + 0.461065i \(0.847467\pi\)
\(462\) 0 0
\(463\) − 34.2929i − 1.59372i −0.604161 0.796862i \(-0.706492\pi\)
0.604161 0.796862i \(-0.293508\pi\)
\(464\) 0 0
\(465\) −24.0000 −1.11297
\(466\) 0 0
\(467\) −17.3205 −0.801498 −0.400749 0.916188i \(-0.631250\pi\)
−0.400749 + 0.916188i \(0.631250\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 42.4264i 1.94257i
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5.65685i 0.256865i
\(486\) 0 0
\(487\) − 44.0908i − 1.99795i −0.0453143 0.998973i \(-0.514429\pi\)
0.0453143 0.998973i \(-0.485571\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 38.1051 1.71966 0.859830 0.510581i \(-0.170569\pi\)
0.859830 + 0.510581i \(0.170569\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 29.3939i 1.32116i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 56.0000 2.49197
\(506\) 0 0
\(507\) −22.5167 −1.00000
\(508\) 0 0
\(509\) − 2.82843i − 0.125368i −0.998033 0.0626839i \(-0.980034\pi\)
0.998033 0.0626839i \(-0.0199660\pi\)
\(510\) 0 0
\(511\) 68.5857i 3.03405i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −41.5692 −1.83176
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 34.2929i 1.50529i
\(520\) 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
\(525\) 25.4558i 1.11098i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 31.1769 1.35296
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) − 48.9898i − 2.11801i
\(536\) 0 0
\(537\) −42.0000 −1.81243
\(538\) 0 0
\(539\) −58.8897 −2.53656
\(540\) 0 0
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 0 0
\(543\) 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
\(553\) −72.0000 −3.06175
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 14.1421i − 0.599222i −0.954062 0.299611i \(-0.903143\pi\)
0.954062 0.299611i \(-0.0968568\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 38.1051 1.60594 0.802970 0.596020i \(-0.203252\pi\)
0.802970 + 0.596020i \(0.203252\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) − 44.0908i − 1.85164i
\(568\) 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
\(576\) 0 0
\(577\) 38.0000 1.58196 0.790980 0.611842i \(-0.209571\pi\)
0.790980 + 0.611842i \(0.209571\pi\)
\(578\) 0 0
\(579\) −45.0333 −1.87152
\(580\) 0 0
\(581\) 84.8528i 3.52029i
\(582\) 0 0
\(583\) 48.9898i 2.02895i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −17.3205 −0.714894 −0.357447 0.933933i \(-0.616353\pi\)
−0.357447 + 0.933933i \(0.616353\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 24.4949i 1.00759i
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) − 42.4264i − 1.73640i
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.82843i 0.114992i
\(606\) 0 0
\(607\) 44.0908i 1.78959i 0.446476 + 0.894795i \(0.352679\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) 0 0
\(609\) −24.0000 −0.972529
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −31.0000 −1.24000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) − 4.89898i − 0.195025i −0.995234 0.0975126i \(-0.968911\pi\)
0.995234 0.0975126i \(-0.0310886\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −13.8564 −0.549875
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 36.0000 1.41312
\(650\) 0 0
\(651\) 41.5692 1.62923
\(652\) 0 0
\(653\) − 48.0833i − 1.88164i −0.338902 0.940822i \(-0.610055\pi\)
0.338902 0.940822i \(-0.389945\pi\)
\(654\) 0 0
\(655\) 9.79796i 0.382838i
\(656\) 0 0
\(657\) −42.0000 −1.63858
\(658\) 0 0
\(659\) −24.2487 −0.944596 −0.472298 0.881439i \(-0.656575\pi\)
−0.472298 + 0.881439i \(0.656575\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) − 25.4558i − 0.984180i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 0 0
\(675\) −15.5885 −0.600000
\(676\) 0 0
\(677\) 2.82843i 0.108705i 0.998522 + 0.0543526i \(0.0173095\pi\)
−0.998522 + 0.0543526i \(0.982690\pi\)
\(678\) 0 0
\(679\) − 9.79796i − 0.376011i
\(680\) 0 0
\(681\) 18.0000 0.689761
\(682\) 0 0
\(683\) −51.9615 −1.98825 −0.994126 0.108227i \(-0.965483\pi\)
−0.994126 + 0.108227i \(0.965483\pi\)
\(684\) 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 \(\pi\)
\(692\) 0 0
\(693\) − 50.9117i − 1.93398i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) − 36.7696i − 1.38877i −0.719605 0.694383i \(-0.755677\pi\)
0.719605 0.694383i \(-0.244323\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −96.9948 −3.64787
\(708\) 0 0
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 0 0
\(711\) − 44.0908i − 1.65353i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 72.0000 2.68142
\(722\) 0 0
\(723\) −17.3205 −0.644157
\(724\) 0 0
\(725\) 8.48528i 0.315135i
\(726\) 0 0
\(727\) 53.8888i 1.99862i 0.0370879 + 0.999312i \(0.488192\pi\)
−0.0370879 + 0.999312i \(0.511808\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) − 83.2827i − 3.07193i
\(736\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) −8.00000 −0.293097
\(746\) 0 0
\(747\) −51.9615 −1.90117
\(748\) 0 0
\(749\) 84.8528i 3.10045i
\(750\) 0 0
\(751\) − 53.8888i − 1.96643i −0.182453 0.983215i \(-0.558404\pi\)
0.182453 0.983215i \(-0.441596\pi\)
\(752\) 0 0
\(753\) 54.0000 1.96787
\(754\) 0 0
\(755\) 69.2820 2.52143
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −26.0000 −0.937584 −0.468792 0.883309i \(-0.655311\pi\)
−0.468792 + 0.883309i \(0.655311\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 19.7990i − 0.712120i −0.934463 0.356060i \(-0.884120\pi\)
0.934463 0.356060i \(-0.115880\pi\)
\(774\) 0 0
\(775\) − 14.6969i − 0.527930i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) − 14.6969i − 0.525226i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −69.2820 −2.45718
\(796\) 0 0
\(797\) 53.7401i 1.90357i 0.306762 + 0.951786i \(0.400754\pi\)
−0.306762 + 0.951786i \(0.599246\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −48.4974 −1.71144
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 53.8888i 1.89697i
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 42.4264i 1.48796i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 48.0833i 1.67812i 0.544041 + 0.839059i \(0.316894\pi\)
−0.544041 + 0.839059i \(0.683106\pi\)
\(822\) 0 0
\(823\) 34.2929i 1.19537i 0.801730 + 0.597687i \(0.203913\pi\)
−0.801730 + 0.597687i \(0.796087\pi\)
\(824\) 0 0
\(825\) −18.0000 −0.626680
\(826\) 0 0
\(827\) 10.3923 0.361376 0.180688 0.983540i \(-0.442168\pi\)
0.180688 + 0.983540i \(0.442168\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 25.4558i 0.879883i
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 21.0000 0.724138
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) − 36.7696i − 1.26491i
\(846\) 0 0
\(847\) − 4.89898i − 0.168331i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) −56.0000 −1.90406
\(866\) 0 0
\(867\) 29.4449 1.00000
\(868\) 0 0
\(869\) − 50.9117i − 1.72706i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 6.00000 0.203069
\(874\) 0 0
\(875\) 27.7128 0.936864
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) 24.4949i 0.826192i
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 50.9117i 1.71138i
\(886\) 0 0
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 24.0000 0.804934
\(890\) 0 0
\(891\) 31.1769 1.04447
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) − 68.5857i − 2.29257i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 13.8564 0.462137
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) − 59.3970i − 1.97007i
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) −60.0000 −1.98571
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 16.9706i − 0.560417i
\(918\) 0 0
\(919\) 34.2929i 1.13122i 0.824674 + 0.565608i \(0.191359\pi\)
−0.824674 + 0.565608i \(0.808641\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 44.0908i 1.44813i
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −58.0000 −1.89478 −0.947389 0.320085i \(-0.896288\pi\)
−0.947389 + 0.320085i \(0.896288\pi\)
\(938\) 0 0
\(939\) 58.8897 1.92179
\(940\) 0 0
\(941\) − 48.0833i − 1.56747i −0.621096 0.783735i \(-0.713312\pi\)
0.621096 0.783735i \(-0.286688\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 72.0000 2.34216
\(946\) 0 0
\(947\) −24.2487 −0.787977 −0.393989 0.919115i \(-0.628905\pi\)
−0.393989 + 0.919115i \(0.628905\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 53.8888i 1.74746i
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) − 16.9706i − 0.548580i
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 7.00000 0.225806
\(962\) 0 0
\(963\) −51.9615 −1.67444
\(964\) 0 0
\(965\) − 73.5391i − 2.36731i
\(966\) 0 0
\(967\) − 4.89898i − 0.157541i −0.996893 0.0787703i \(-0.974901\pi\)
0.996893 0.0787703i \(-0.0250994\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 3.46410 0.111168 0.0555842 0.998454i \(-0.482298\pi\)
0.0555842 + 0.998454i \(0.482298\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 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
\(982\) 0 0
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) −40.0000 −1.27451
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 24.4949i 0.778106i 0.921215 + 0.389053i \(0.127198\pi\)
−0.921215 + 0.389053i \(0.872802\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 69.2820 2.19639
\(996\) 0 0
\(997\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) 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 768.2.c.j.767.4 4
3.2 odd 2 inner 768.2.c.j.767.1 4
4.3 odd 2 inner 768.2.c.j.767.2 4
8.3 odd 2 inner 768.2.c.j.767.3 4
8.5 even 2 inner 768.2.c.j.767.1 4
12.11 even 2 inner 768.2.c.j.767.3 4
16.3 odd 4 384.2.f.a.191.2 yes 4
16.5 even 4 384.2.f.a.191.1 4
16.11 odd 4 384.2.f.a.191.3 yes 4
16.13 even 4 384.2.f.a.191.4 yes 4
24.5 odd 2 CM 768.2.c.j.767.4 4
24.11 even 2 inner 768.2.c.j.767.2 4
48.5 odd 4 384.2.f.a.191.4 yes 4
48.11 even 4 384.2.f.a.191.2 yes 4
48.29 odd 4 384.2.f.a.191.1 4
48.35 even 4 384.2.f.a.191.3 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
384.2.f.a.191.1 4 16.5 even 4
384.2.f.a.191.1 4 48.29 odd 4
384.2.f.a.191.2 yes 4 16.3 odd 4
384.2.f.a.191.2 yes 4 48.11 even 4
384.2.f.a.191.3 yes 4 16.11 odd 4
384.2.f.a.191.3 yes 4 48.35 even 4
384.2.f.a.191.4 yes 4 16.13 even 4
384.2.f.a.191.4 yes 4 48.5 odd 4
768.2.c.j.767.1 4 3.2 odd 2 inner
768.2.c.j.767.1 4 8.5 even 2 inner
768.2.c.j.767.2 4 4.3 odd 2 inner
768.2.c.j.767.2 4 24.11 even 2 inner
768.2.c.j.767.3 4 8.3 odd 2 inner
768.2.c.j.767.3 4 12.11 even 2 inner
768.2.c.j.767.4 4 1.1 even 1 trivial
768.2.c.j.767.4 4 24.5 odd 2 CM