Properties

Label 1792.2.f.l.1791.8
Level $1792$
Weight $2$
Character 1792.1791
Analytic conductor $14.309$
Analytic rank $0$
Dimension $8$
CM discriminant -56
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1792,2,Mod(1791,1792)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1792, 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("1792.1791");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.f (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: \(14.3091920422\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.2517630976.5
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{6} + 11x^{4} + 4x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: no (minimal twist has level 896)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 1791.8
Root \(0.435132 + 0.629640i\) of defining polynomial
Character \(\chi\) \(=\) 1792.1791
Dual form 1792.2.f.l.1791.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.97127 q^{3} +4.29945i q^{5} +2.64575i q^{7} +5.82843 q^{9} +O(q^{10})\) \(q+2.97127 q^{3} +4.29945i q^{5} +2.64575i q^{7} +5.82843 q^{9} -0.737669i q^{13} +12.7748i q^{15} +5.43275 q^{19} +7.86123i q^{21} -7.48331i q^{23} -13.4853 q^{25} +8.40401 q^{27} -11.3753 q^{35} -2.19181i q^{39} +25.0590i q^{45} -7.00000 q^{49} +16.1421 q^{57} +6.45232 q^{59} -11.4230i q^{61} +15.4206i q^{63} +3.17157 q^{65} -22.2349i q^{69} +15.8745i q^{71} -40.0684 q^{75} +5.29150i q^{79} +7.48528 q^{81} -13.8368 q^{83} +1.95169 q^{91} +23.3578i q^{95} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 24 q^{9} - 40 q^{25} - 56 q^{49} + 16 q^{57} + 48 q^{65} - 8 q^{81}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).

\(n\) \(1023\) \(1025\) \(1541\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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
\(3\) 2.97127 1.71546 0.857731 0.514099i \(-0.171874\pi\)
0.857731 + 0.514099i \(0.171874\pi\)
\(4\) 0 0
\(5\) 4.29945i 1.92277i 0.275202 + 0.961387i \(0.411255\pi\)
−0.275202 + 0.961387i \(0.588745\pi\)
\(6\) 0 0
\(7\) 2.64575i 1.00000i
\(8\) 0 0
\(9\) 5.82843 1.94281
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) − 0.737669i − 0.204593i −0.994754 0.102296i \(-0.967381\pi\)
0.994754 0.102296i \(-0.0326190\pi\)
\(14\) 0 0
\(15\) 12.7748i 3.29844i
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 5.43275 1.24636 0.623179 0.782080i \(-0.285841\pi\)
0.623179 + 0.782080i \(0.285841\pi\)
\(20\) 0 0
\(21\) 7.86123i 1.71546i
\(22\) 0 0
\(23\) − 7.48331i − 1.56038i −0.625543 0.780189i \(-0.715123\pi\)
0.625543 0.780189i \(-0.284877\pi\)
\(24\) 0 0
\(25\) −13.4853 −2.69706
\(26\) 0 0
\(27\) 8.40401 1.61735
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −11.3753 −1.92277
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) − 2.19181i − 0.350971i
\(40\) 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
\(45\) 25.0590i 3.73558i
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 16.1421 2.13808
\(58\) 0 0
\(59\) 6.45232 0.840021 0.420010 0.907519i \(-0.362026\pi\)
0.420010 + 0.907519i \(0.362026\pi\)
\(60\) 0 0
\(61\) − 11.4230i − 1.46257i −0.682073 0.731284i \(-0.738922\pi\)
0.682073 0.731284i \(-0.261078\pi\)
\(62\) 0 0
\(63\) 15.4206i 1.94281i
\(64\) 0 0
\(65\) 3.17157 0.393385
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) − 22.2349i − 2.67677i
\(70\) 0 0
\(71\) 15.8745i 1.88396i 0.335673 + 0.941979i \(0.391036\pi\)
−0.335673 + 0.941979i \(0.608964\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) −40.0684 −4.62670
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 5.29150i 0.595341i 0.954669 + 0.297670i \(0.0962096\pi\)
−0.954669 + 0.297670i \(0.903790\pi\)
\(80\) 0 0
\(81\) 7.48528 0.831698
\(82\) 0 0
\(83\) −13.8368 −1.51878 −0.759391 0.650635i \(-0.774503\pi\)
−0.759391 + 0.650635i \(0.774503\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 1.95169 0.204593
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 23.3578i 2.39646i
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) − 6.38589i − 0.635420i −0.948188 0.317710i \(-0.897086\pi\)
0.948188 0.317710i \(-0.102914\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) −33.7990 −3.29844
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −14.1421 −1.33038 −0.665190 0.746674i \(-0.731650\pi\)
−0.665190 + 0.746674i \(0.731650\pi\)
\(114\) 0 0
\(115\) 32.1741 3.00025
\(116\) 0 0
\(117\) − 4.29945i − 0.397484i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 11.0000 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 36.4821i − 3.26305i
\(126\) 0 0
\(127\) − 22.4499i − 1.99211i −0.0887357 0.996055i \(-0.528283\pi\)
0.0887357 0.996055i \(-0.471717\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −3.99084 −0.348682 −0.174341 0.984685i \(-0.555779\pi\)
−0.174341 + 0.984685i \(0.555779\pi\)
\(132\) 0 0
\(133\) 14.3737i 1.24636i
\(134\) 0 0
\(135\) 36.1326i 3.10980i
\(136\) 0 0
\(137\) 18.0000 1.53784 0.768922 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) 0 0
\(139\) 23.2603 1.97292 0.986458 0.164012i \(-0.0524434\pi\)
0.986458 + 0.164012i \(0.0524434\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −20.7989 −1.71546
\(148\) 0 0
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 22.4499i 1.82695i 0.406894 + 0.913475i \(0.366612\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) − 25.0590i − 1.99993i −0.00842626 0.999964i \(-0.502682\pi\)
0.00842626 0.999964i \(-0.497318\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 19.7990 1.56038
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 12.4558 0.958142
\(170\) 0 0
\(171\) 31.6644 2.42143
\(172\) 0 0
\(173\) − 10.8119i − 0.822014i −0.911632 0.411007i \(-0.865177\pi\)
0.911632 0.411007i \(-0.134823\pi\)
\(174\) 0 0
\(175\) − 35.6787i − 2.69706i
\(176\) 0 0
\(177\) 19.1716 1.44102
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) − 9.94768i − 0.739405i −0.929150 0.369703i \(-0.879460\pi\)
0.929150 0.369703i \(-0.120540\pi\)
\(182\) 0 0
\(183\) − 33.9408i − 2.50898i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 22.2349i 1.61735i
\(190\) 0 0
\(191\) 15.8745i 1.14864i 0.818631 + 0.574320i \(0.194733\pi\)
−0.818631 + 0.574320i \(0.805267\pi\)
\(192\) 0 0
\(193\) 8.48528 0.610784 0.305392 0.952227i \(-0.401213\pi\)
0.305392 + 0.952227i \(0.401213\pi\)
\(194\) 0 0
\(195\) 9.42359 0.674837
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) − 43.6160i − 3.03152i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 47.1674i 3.23186i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) −78.5980 −5.23987
\(226\) 0 0
\(227\) 29.2029 1.93826 0.969132 0.246544i \(-0.0792950\pi\)
0.969132 + 0.246544i \(0.0792950\pi\)
\(228\) 0 0
\(229\) − 26.5344i − 1.75344i −0.481000 0.876720i \(-0.659726\pi\)
0.481000 0.876720i \(-0.340274\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 15.7225i 1.02128i
\(238\) 0 0
\(239\) 7.48331i 0.484055i 0.970269 + 0.242028i \(0.0778125\pi\)
−0.970269 + 0.242028i \(0.922188\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) −2.97127 −0.190607
\(244\) 0 0
\(245\) − 30.0962i − 1.92277i
\(246\) 0 0
\(247\) − 4.00757i − 0.254995i
\(248\) 0 0
\(249\) −41.1127 −2.60541
\(250\) 0 0
\(251\) −31.6644 −1.99864 −0.999318 0.0369181i \(-0.988246\pi\)
−0.999318 + 0.0369181i \(0.988246\pi\)
\(252\) 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
\(261\) 0 0
\(262\) 0 0
\(263\) 15.8745i 0.978864i 0.872041 + 0.489432i \(0.162796\pi\)
−0.872041 + 0.489432i \(0.837204\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 19.4108i 1.18350i 0.806122 + 0.591749i \(0.201562\pi\)
−0.806122 + 0.591749i \(0.798438\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 5.79899 0.350971
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −30.0000 −1.78965 −0.894825 0.446417i \(-0.852700\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) 0 0
\(283\) 15.8759 0.943725 0.471863 0.881672i \(-0.343582\pi\)
0.471863 + 0.881672i \(0.343582\pi\)
\(284\) 0 0
\(285\) 69.4023i 4.11104i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 17.0000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 32.1826i 1.88013i 0.340998 + 0.940064i \(0.389235\pi\)
−0.340998 + 0.940064i \(0.610765\pi\)
\(294\) 0 0
\(295\) 27.7414i 1.61517i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −5.52021 −0.319242
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) − 18.9742i − 1.09004i
\(304\) 0 0
\(305\) 49.1127 2.81218
\(306\) 0 0
\(307\) 12.8172 0.731515 0.365758 0.930710i \(-0.380810\pi\)
0.365758 + 0.930710i \(0.380810\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) −66.3000 −3.73558
\(316\) 0 0
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 9.94768i 0.551798i
\(326\) 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
\(337\) −25.4558 −1.38667 −0.693334 0.720616i \(-0.743859\pi\)
−0.693334 + 0.720616i \(0.743859\pi\)
\(338\) 0 0
\(339\) −42.0201 −2.28222
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) − 18.5203i − 1.00000i
\(344\) 0 0
\(345\) 95.5980 5.14682
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 37.2197i 1.99233i 0.0875167 + 0.996163i \(0.472107\pi\)
−0.0875167 + 0.996163i \(0.527893\pi\)
\(350\) 0 0
\(351\) − 6.19938i − 0.330898i
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) −68.2517 −3.62242
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) − 37.4166i − 1.97477i −0.158334 0.987386i \(-0.550612\pi\)
0.158334 0.987386i \(-0.449388\pi\)
\(360\) 0 0
\(361\) 10.5147 0.553406
\(362\) 0 0
\(363\) 32.6839 1.71546
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) − 108.398i − 5.59764i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) − 66.7048i − 3.41739i
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −11.8579 −0.598150
\(394\) 0 0
\(395\) −22.7506 −1.14470
\(396\) 0 0
\(397\) − 35.7444i − 1.79396i −0.442072 0.896980i \(-0.645756\pi\)
0.442072 0.896980i \(-0.354244\pi\)
\(398\) 0 0
\(399\) 42.7081i 2.13808i
\(400\) 0 0
\(401\) −36.7696 −1.83618 −0.918092 0.396368i \(-0.870271\pi\)
−0.918092 + 0.396368i \(0.870271\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 32.1826i 1.59917i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 53.4828 2.63811
\(412\) 0 0
\(413\) 17.0712i 0.840021i
\(414\) 0 0
\(415\) − 59.4905i − 2.92027i
\(416\) 0 0
\(417\) 69.1127 3.38446
\(418\) 0 0
\(419\) 36.5873 1.78741 0.893704 0.448658i \(-0.148098\pi\)
0.893704 + 0.448658i \(0.148098\pi\)
\(420\) 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
\(427\) 30.2225 1.46257
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 37.4166i 1.80229i 0.433515 + 0.901146i \(0.357273\pi\)
−0.433515 + 0.901146i \(0.642727\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 40.6549i − 1.94479i
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −40.7990 −1.94281
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 66.7048i 3.13406i
\(454\) 0 0
\(455\) 8.39119i 0.393385i
\(456\) 0 0
\(457\) −42.4264 −1.98462 −0.992312 0.123763i \(-0.960504\pi\)
−0.992312 + 0.123763i \(0.960504\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 25.6701i − 1.19558i −0.801654 0.597789i \(-0.796046\pi\)
0.801654 0.597789i \(-0.203954\pi\)
\(462\) 0 0
\(463\) − 26.4575i − 1.22958i −0.788689 0.614792i \(-0.789240\pi\)
0.788689 0.614792i \(-0.210760\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −21.2212 −0.982000 −0.491000 0.871160i \(-0.663368\pi\)
−0.491000 + 0.871160i \(0.663368\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) − 74.4571i − 3.43080i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −73.2621 −3.36150
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 58.8281 2.67677
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 22.4499i 1.01730i 0.860972 + 0.508652i \(0.169856\pi\)
−0.860972 + 0.508652i \(0.830144\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −42.0000 −1.88396
\(498\) 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
\(505\) 27.4558 1.22177
\(506\) 0 0
\(507\) 37.0096 1.64366
\(508\) 0 0
\(509\) 8.72547i 0.386750i 0.981125 + 0.193375i \(0.0619433\pi\)
−0.981125 + 0.193375i \(0.938057\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 45.6569 2.01580
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) − 32.1251i − 1.41013i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 9.33612 0.408240 0.204120 0.978946i \(-0.434567\pi\)
0.204120 + 0.978946i \(0.434567\pi\)
\(524\) 0 0
\(525\) − 106.011i − 4.62670i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −33.0000 −1.43478
\(530\) 0 0
\(531\) 37.6069 1.63200
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 0 0
\(543\) − 29.5572i − 1.26842i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) − 66.5782i − 2.84149i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −14.0000 −0.595341
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 39.0488 1.64571 0.822855 0.568251i \(-0.192380\pi\)
0.822855 + 0.568251i \(0.192380\pi\)
\(564\) 0 0
\(565\) − 60.8034i − 2.55802i
\(566\) 0 0
\(567\) 19.8042i 0.831698i
\(568\) 0 0
\(569\) 2.82843 0.118574 0.0592869 0.998241i \(-0.481117\pi\)
0.0592869 + 0.998241i \(0.481117\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 47.1674i 1.97045i
\(574\) 0 0
\(575\) 100.915i 4.20843i
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 25.2120 1.04778
\(580\) 0 0
\(581\) − 36.6086i − 1.51878i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 18.4853 0.764272
\(586\) 0 0
\(587\) −3.39359 −0.140068 −0.0700342 0.997545i \(-0.522311\pi\)
−0.0700342 + 0.997545i \(0.522311\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 47.6235i 1.94584i 0.231133 + 0.972922i \(0.425757\pi\)
−0.231133 + 0.972922i \(0.574243\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 47.2940i 1.92277i
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 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
\(617\) 14.1421 0.569341 0.284670 0.958625i \(-0.408116\pi\)
0.284670 + 0.958625i \(0.408116\pi\)
\(618\) 0 0
\(619\) −48.4724 −1.94827 −0.974135 0.225968i \(-0.927446\pi\)
−0.974135 + 0.225968i \(0.927446\pi\)
\(620\) 0 0
\(621\) − 62.8899i − 2.52368i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 89.4264 3.57706
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) − 37.0405i − 1.47456i −0.675587 0.737280i \(-0.736110\pi\)
0.675587 0.737280i \(-0.263890\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 96.5224 3.83038
\(636\) 0 0
\(637\) 5.16368i 0.204593i
\(638\) 0 0
\(639\) 92.5234i 3.66017i
\(640\) 0 0
\(641\) −48.0833 −1.89917 −0.949587 0.313503i \(-0.898498\pi\)
−0.949587 + 0.313503i \(0.898498\pi\)
\(642\) 0 0
\(643\) −44.9913 −1.77428 −0.887142 0.461496i \(-0.847313\pi\)
−0.887142 + 0.461496i \(0.847313\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) − 17.1584i − 0.670436i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) − 50.8557i − 1.97806i −0.147717 0.989030i \(-0.547193\pi\)
0.147717 0.989030i \(-0.452807\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −61.7990 −2.39646
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −26.0000 −1.00223 −0.501113 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) 0 0
\(675\) −113.330 −4.36209
\(676\) 0 0
\(677\) 42.8679i 1.64755i 0.566918 + 0.823775i \(0.308136\pi\)
−0.566918 + 0.823775i \(0.691864\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 86.7696 3.32502
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 77.3901i 2.95692i
\(686\) 0 0
\(687\) − 78.8407i − 3.00796i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 33.7035 1.28214 0.641071 0.767482i \(-0.278490\pi\)
0.641071 + 0.767482i \(0.278490\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 100.007i 3.79347i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 17.8276 0.674302
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 16.8955 0.635420
\(708\) 0 0
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 0 0
\(711\) 30.8411i 1.15663i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 22.2349i 0.830379i
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) −31.2843 −1.15868
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 6.99700i 0.258440i 0.991616 + 0.129220i \(0.0412474\pi\)
−0.991616 + 0.129220i \(0.958753\pi\)
\(734\) 0 0
\(735\) − 89.4237i − 3.29844i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) − 11.9076i − 0.437435i
\(742\) 0 0
\(743\) − 7.48331i − 0.274536i −0.990534 0.137268i \(-0.956168\pi\)
0.990534 0.137268i \(-0.0438322\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −80.6465 −2.95070
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) − 22.4499i − 0.819210i −0.912263 0.409605i \(-0.865667\pi\)
0.912263 0.409605i \(-0.134333\pi\)
\(752\) 0 0
\(753\) −94.0833 −3.42858
\(754\) 0 0
\(755\) −96.5224 −3.51281
\(756\) 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
\(767\) − 4.75968i − 0.171862i
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 25.9233i − 0.932395i −0.884681 0.466198i \(-0.845624\pi\)
0.884681 0.466198i \(-0.154376\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 107.740 3.84541
\(786\) 0 0
\(787\) −8.49148 −0.302688 −0.151344 0.988481i \(-0.548360\pi\)
−0.151344 + 0.988481i \(0.548360\pi\)
\(788\) 0 0
\(789\) 47.1674i 1.67920i
\(790\) 0 0
\(791\) − 37.4166i − 1.33038i
\(792\) 0 0
\(793\) −8.42641 −0.299230
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 45.2075i − 1.60133i −0.599111 0.800666i \(-0.704479\pi\)
0.599111 0.800666i \(-0.295521\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 85.1248i 3.00025i
\(806\) 0 0
\(807\) 57.6747i 2.03025i
\(808\) 0 0
\(809\) −31.1127 −1.09386 −0.546932 0.837177i \(-0.684204\pi\)
−0.546932 + 0.837177i \(0.684204\pi\)
\(810\) 0 0
\(811\) −55.4345 −1.94657 −0.973284 0.229604i \(-0.926257\pi\)
−0.973284 + 0.229604i \(0.926257\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 11.3753 0.397484
\(820\) 0 0
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) − 26.4575i − 0.922251i −0.887335 0.461125i \(-0.847446\pi\)
0.887335 0.461125i \(-0.152554\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) − 41.6457i − 1.44642i −0.690630 0.723208i \(-0.742667\pi\)
0.690630 0.723208i \(-0.257333\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) −89.1380 −3.07008
\(844\) 0 0
\(845\) 53.5533i 1.84229i
\(846\) 0 0
\(847\) 29.1033i 1.00000i
\(848\) 0 0
\(849\) 47.1716 1.61892
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 46.4297i 1.58972i 0.606790 + 0.794862i \(0.292457\pi\)
−0.606790 + 0.794862i \(0.707543\pi\)
\(854\) 0 0
\(855\) 136.139i 4.65587i
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 22.8380 0.779223 0.389612 0.920979i \(-0.372609\pi\)
0.389612 + 0.920979i \(0.372609\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 15.8745i 0.540375i 0.962808 + 0.270187i \(0.0870856\pi\)
−0.962808 + 0.270187i \(0.912914\pi\)
\(864\) 0 0
\(865\) 46.4853 1.58055
\(866\) 0 0
\(867\) 50.5115 1.71546
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 96.5224 3.26305
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) 95.6231i 3.22529i
\(880\) 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
\(885\) 82.4272i 2.77076i
\(886\) 0 0
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 59.3970 1.99211
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −16.4020 −0.547648
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 42.7696 1.42171
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) − 37.2197i − 1.23450i
\(910\) 0 0
\(911\) − 52.3832i − 1.73553i −0.496972 0.867766i \(-0.665555\pi\)
0.496972 0.867766i \(-0.334445\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 145.927 4.82420
\(916\) 0 0
\(917\) − 10.5588i − 0.348682i
\(918\) 0 0
\(919\) 58.2065i 1.92006i 0.279904 + 0.960028i \(0.409697\pi\)
−0.279904 + 0.960028i \(0.590303\pi\)
\(920\) 0 0
\(921\) 38.0833 1.25489
\(922\) 0 0
\(923\) 11.7101 0.385444
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) −38.0292 −1.24636
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 27.7566i 0.904839i 0.891805 + 0.452419i \(0.149439\pi\)
−0.891805 + 0.452419i \(0.850561\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) −95.5980 −3.10980
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 54.0000 1.74923 0.874616 0.484817i \(-0.161114\pi\)
0.874616 + 0.484817i \(0.161114\pi\)
\(954\) 0 0
\(955\) −68.2517 −2.20857
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 47.6235i 1.53784i
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 36.4821i 1.17440i
\(966\) 0 0
\(967\) 22.4499i 0.721942i 0.932577 + 0.360971i \(0.117555\pi\)
−0.932577 + 0.360971i \(0.882445\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −43.9717 −1.41112 −0.705560 0.708650i \(-0.749305\pi\)
−0.705560 + 0.708650i \(0.749305\pi\)
\(972\) 0 0
\(973\) 61.5411i 1.97292i
\(974\) 0 0
\(975\) 29.5572i 0.946588i
\(976\) 0 0
\(977\) 18.0000 0.575871 0.287936 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) 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
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) − 37.0405i − 1.17663i −0.808632 0.588315i \(-0.799791\pi\)
0.808632 0.588315i \(-0.200209\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 63.0164i 1.99575i 0.0651544 + 0.997875i \(0.479246\pi\)
−0.0651544 + 0.997875i \(0.520754\pi\)
\(998\) 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 1792.2.f.l.1791.8 8
4.3 odd 2 inner 1792.2.f.l.1791.2 8
7.6 odd 2 inner 1792.2.f.l.1791.1 8
8.3 odd 2 inner 1792.2.f.l.1791.7 8
8.5 even 2 inner 1792.2.f.l.1791.1 8
16.3 odd 4 896.2.e.g.447.2 yes 8
16.5 even 4 896.2.e.g.447.1 8
16.11 odd 4 896.2.e.g.447.7 yes 8
16.13 even 4 896.2.e.g.447.8 yes 8
28.27 even 2 inner 1792.2.f.l.1791.7 8
56.13 odd 2 CM 1792.2.f.l.1791.8 8
56.27 even 2 inner 1792.2.f.l.1791.2 8
112.13 odd 4 896.2.e.g.447.1 8
112.27 even 4 896.2.e.g.447.2 yes 8
112.69 odd 4 896.2.e.g.447.8 yes 8
112.83 even 4 896.2.e.g.447.7 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
896.2.e.g.447.1 8 16.5 even 4
896.2.e.g.447.1 8 112.13 odd 4
896.2.e.g.447.2 yes 8 16.3 odd 4
896.2.e.g.447.2 yes 8 112.27 even 4
896.2.e.g.447.7 yes 8 16.11 odd 4
896.2.e.g.447.7 yes 8 112.83 even 4
896.2.e.g.447.8 yes 8 16.13 even 4
896.2.e.g.447.8 yes 8 112.69 odd 4
1792.2.f.l.1791.1 8 7.6 odd 2 inner
1792.2.f.l.1791.1 8 8.5 even 2 inner
1792.2.f.l.1791.2 8 4.3 odd 2 inner
1792.2.f.l.1791.2 8 56.27 even 2 inner
1792.2.f.l.1791.7 8 8.3 odd 2 inner
1792.2.f.l.1791.7 8 28.27 even 2 inner
1792.2.f.l.1791.8 8 1.1 even 1 trivial
1792.2.f.l.1791.8 8 56.13 odd 2 CM