Properties

Label 176.2.e.a.175.2
Level $176$
Weight $2$
Character 176.175
Analytic conductor $1.405$
Analytic rank $0$
Dimension $2$
CM discriminant -11
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [176,2,Mod(175,176)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(176, 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("176.175");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 176 = 2^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 176.e (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: no
Analytic conductor: \(1.40536707557\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-11}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 175.2
Root \(0.500000 - 1.65831i\) of defining polynomial
Character \(\chi\) \(=\) 176.175
Dual form 176.2.e.a.175.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.31662i q^{3} +3.00000 q^{5} -8.00000 q^{9} +O(q^{10})\) \(q+3.31662i q^{3} +3.00000 q^{5} -8.00000 q^{9} -3.31662i q^{11} +9.94987i q^{15} +3.31662i q^{23} +4.00000 q^{25} -16.5831i q^{27} -9.94987i q^{31} +11.0000 q^{33} +7.00000 q^{37} -24.0000 q^{45} +6.63325i q^{47} -7.00000 q^{49} +6.00000 q^{53} -9.94987i q^{55} +3.31662i q^{59} -9.94987i q^{67} -11.0000 q^{69} +16.5831i q^{71} +13.2665i q^{75} +31.0000 q^{81} -9.00000 q^{89} +33.0000 q^{93} -17.0000 q^{97} +26.5330i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 6 q^{5} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 6 q^{5} - 16 q^{9} + 8 q^{25} + 22 q^{33} + 14 q^{37} - 48 q^{45} - 14 q^{49} + 12 q^{53} - 22 q^{69} + 62 q^{81} - 18 q^{89} + 66 q^{93} - 34 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/176\mathbb{Z}\right)^\times\).

\(n\) \(111\) \(133\) \(145\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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
\(3\) 3.31662i 1.91485i 0.288675 + 0.957427i \(0.406785\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 0 0
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) −8.00000 −2.66667
\(10\) 0 0
\(11\) − 3.31662i − 1.00000i
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 9.94987i 2.56905i
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.31662i 0.691564i 0.938315 + 0.345782i \(0.112386\pi\)
−0.938315 + 0.345782i \(0.887614\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) 0 0
\(27\) − 16.5831i − 3.19142i
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) − 9.94987i − 1.78705i −0.449013 0.893525i \(-0.648224\pi\)
0.449013 0.893525i \(-0.351776\pi\)
\(32\) 0 0
\(33\) 11.0000 1.91485
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 7.00000 1.15079 0.575396 0.817875i \(-0.304848\pi\)
0.575396 + 0.817875i \(0.304848\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) −24.0000 −3.57771
\(46\) 0 0
\(47\) 6.63325i 0.967559i 0.875190 + 0.483779i \(0.160736\pi\)
−0.875190 + 0.483779i \(0.839264\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) − 9.94987i − 1.34164i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.31662i 0.431788i 0.976417 + 0.215894i \(0.0692665\pi\)
−0.976417 + 0.215894i \(0.930733\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) − 9.94987i − 1.21557i −0.794101 0.607785i \(-0.792058\pi\)
0.794101 0.607785i \(-0.207942\pi\)
\(68\) 0 0
\(69\) −11.0000 −1.32424
\(70\) 0 0
\(71\) 16.5831i 1.96805i 0.178017 + 0.984027i \(0.443032\pi\)
−0.178017 + 0.984027i \(0.556968\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 13.2665i 1.53188i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 31.0000 3.44444
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −9.00000 −0.953998 −0.476999 0.878904i \(-0.658275\pi\)
−0.476999 + 0.878904i \(0.658275\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 33.0000 3.42194
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −17.0000 −1.72609 −0.863044 0.505128i \(-0.831445\pi\)
−0.863044 + 0.505128i \(0.831445\pi\)
\(98\) 0 0
\(99\) 26.5330i 2.66667i
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) − 19.8997i − 1.96078i −0.197066 0.980390i \(-0.563141\pi\)
0.197066 0.980390i \(-0.436859\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 23.2164i 2.20360i
\(112\) 0 0
\(113\) −21.0000 −1.97551 −0.987757 0.156001i \(-0.950140\pi\)
−0.987757 + 0.156001i \(0.950140\pi\)
\(114\) 0 0
\(115\) 9.94987i 0.927831i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) − 49.7494i − 4.28174i
\(136\) 0 0
\(137\) 3.00000 0.256307 0.128154 0.991754i \(-0.459095\pi\)
0.128154 + 0.991754i \(0.459095\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −22.0000 −1.85273
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) − 23.2164i − 1.91485i
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 29.8496i − 2.39758i
\(156\) 0 0
\(157\) 23.0000 1.83560 0.917800 0.397043i \(-0.129964\pi\)
0.917800 + 0.397043i \(0.129964\pi\)
\(158\) 0 0
\(159\) 19.8997i 1.57815i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 19.8997i 1.55867i 0.626608 + 0.779334i \(0.284443\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 0 0
\(165\) 33.0000 2.56905
\(166\) 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
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −11.0000 −0.826811
\(178\) 0 0
\(179\) 16.5831i 1.23948i 0.784807 + 0.619740i \(0.212762\pi\)
−0.784807 + 0.619740i \(0.787238\pi\)
\(180\) 0 0
\(181\) −25.0000 −1.85824 −0.929118 0.369784i \(-0.879432\pi\)
−0.929118 + 0.369784i \(0.879432\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 21.0000 1.54395
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) − 23.2164i − 1.67988i −0.542681 0.839939i \(-0.682591\pi\)
0.542681 0.839939i \(-0.317409\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) − 19.8997i − 1.41066i −0.708881 0.705328i \(-0.750800\pi\)
0.708881 0.705328i \(-0.249200\pi\)
\(200\) 0 0
\(201\) 33.0000 2.32764
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) − 26.5330i − 1.84417i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 0 0
\(213\) −55.0000 −3.76854
\(214\) 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
\(223\) 29.8496i 1.99888i 0.0334825 + 0.999439i \(0.489340\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) 0 0
\(225\) −32.0000 −2.13333
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) −5.00000 −0.330409 −0.165205 0.986259i \(-0.552828\pi\)
−0.165205 + 0.986259i \(0.552828\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 19.8997i 1.29812i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 53.0660i 3.40419i
\(244\) 0 0
\(245\) −21.0000 −1.34164
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 16.5831i 1.04672i 0.852112 + 0.523359i \(0.175321\pi\)
−0.852112 + 0.523359i \(0.824679\pi\)
\(252\) 0 0
\(253\) 11.0000 0.691564
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 18.0000 1.10573
\(266\) 0 0
\(267\) − 29.8496i − 1.82677i
\(268\) 0 0
\(269\) 30.0000 1.82913 0.914566 0.404436i \(-0.132532\pi\)
0.914566 + 0.404436i \(0.132532\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) − 13.2665i − 0.800000i
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 79.5990i 4.76547i
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 17.0000 1.00000
\(290\) 0 0
\(291\) − 56.3826i − 3.30521i
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 9.94987i 0.579304i
\(296\) 0 0
\(297\) −55.0000 −3.19142
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 66.0000 3.75461
\(310\) 0 0
\(311\) 33.1662i 1.88069i 0.340229 + 0.940343i \(0.389495\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 0 0
\(313\) 19.0000 1.07394 0.536972 0.843600i \(-0.319568\pi\)
0.536972 + 0.843600i \(0.319568\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 27.0000 1.51647 0.758236 0.651981i \(-0.226062\pi\)
0.758236 + 0.651981i \(0.226062\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 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
\(331\) − 9.94987i − 0.546895i −0.961887 0.273447i \(-0.911836\pi\)
0.961887 0.273447i \(-0.0881639\pi\)
\(332\) 0 0
\(333\) −56.0000 −3.06878
\(334\) 0 0
\(335\) − 29.8496i − 1.63086i
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) − 69.6491i − 3.78282i
\(340\) 0 0
\(341\) −33.0000 −1.78705
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −33.0000 −1.77666
\(346\) 0 0
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9.00000 −0.479022 −0.239511 0.970894i \(-0.576987\pi\)
−0.239511 + 0.970894i \(0.576987\pi\)
\(354\) 0 0
\(355\) 49.7494i 2.64042i
\(356\) 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
\(363\) − 36.4829i − 1.91485i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) − 9.94987i − 0.519379i −0.965692 0.259690i \(-0.916380\pi\)
0.965692 0.259690i \(-0.0836203\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) − 9.94987i − 0.513809i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 29.8496i 1.53327i 0.642082 + 0.766636i \(0.278071\pi\)
−0.642082 + 0.766636i \(0.721929\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3.31662i 0.169472i 0.996403 + 0.0847358i \(0.0270046\pi\)
−0.996403 + 0.0847358i \(0.972995\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 15.0000 0.760530 0.380265 0.924878i \(-0.375833\pi\)
0.380265 + 0.924878i \(0.375833\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −2.00000 −0.100377 −0.0501886 0.998740i \(-0.515982\pi\)
−0.0501886 + 0.998740i \(0.515982\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −30.0000 −1.49813 −0.749064 0.662497i \(-0.769497\pi\)
−0.749064 + 0.662497i \(0.769497\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 93.0000 4.62121
\(406\) 0 0
\(407\) − 23.2164i − 1.15079i
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 9.94987i 0.490791i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 33.1662i − 1.62028i −0.586238 0.810139i \(-0.699392\pi\)
0.586238 0.810139i \(-0.300608\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 0 0
\(423\) − 53.0660i − 2.58016i
\(424\) 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
\(433\) −29.0000 −1.39365 −0.696826 0.717241i \(-0.745405\pi\)
−0.696826 + 0.717241i \(0.745405\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 56.0000 2.66667
\(442\) 0 0
\(443\) − 36.4829i − 1.73335i −0.498870 0.866677i \(-0.666252\pi\)
0.498870 0.866677i \(-0.333748\pi\)
\(444\) 0 0
\(445\) −27.0000 −1.27992
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 39.0000 1.84052 0.920262 0.391303i \(-0.127976\pi\)
0.920262 + 0.391303i \(0.127976\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 29.8496i 1.38723i 0.720346 + 0.693615i \(0.243983\pi\)
−0.720346 + 0.693615i \(0.756017\pi\)
\(464\) 0 0
\(465\) 99.0000 4.59102
\(466\) 0 0
\(467\) 43.1161i 1.99518i 0.0694117 + 0.997588i \(0.477888\pi\)
−0.0694117 + 0.997588i \(0.522112\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 76.2824i 3.51491i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −48.0000 −2.19777
\(478\) 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
\(485\) −51.0000 −2.31579
\(486\) 0 0
\(487\) − 9.94987i − 0.450872i −0.974258 0.225436i \(-0.927619\pi\)
0.974258 0.225436i \(-0.0723806\pi\)
\(488\) 0 0
\(489\) −66.0000 −2.98462
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 79.5990i 3.57771i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 19.8997i 0.890835i 0.895323 + 0.445418i \(0.146945\pi\)
−0.895323 + 0.445418i \(0.853055\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 43.1161i 1.91485i
\(508\) 0 0
\(509\) −45.0000 −1.99459 −0.997295 0.0735034i \(-0.976582\pi\)
−0.997295 + 0.0735034i \(0.976582\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 59.6992i − 2.63066i
\(516\) 0 0
\(517\) 22.0000 0.967559
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 15.0000 0.657162 0.328581 0.944476i \(-0.393430\pi\)
0.328581 + 0.944476i \(0.393430\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 12.0000 0.521739
\(530\) 0 0
\(531\) − 26.5330i − 1.15143i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −55.0000 −2.37343
\(538\) 0 0
\(539\) 23.2164i 1.00000i
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) − 82.9156i − 3.55825i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 69.6491i 2.95644i
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) −63.0000 −2.65043
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 77.0000 3.21672
\(574\) 0 0
\(575\) 13.2665i 0.553251i
\(576\) 0 0
\(577\) 47.0000 1.95664 0.978318 0.207109i \(-0.0664056\pi\)
0.978318 + 0.207109i \(0.0664056\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) − 19.8997i − 0.824163i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 6.63325i − 0.273784i −0.990586 0.136892i \(-0.956289\pi\)
0.990586 0.136892i \(-0.0437113\pi\)
\(588\) 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
\(597\) 66.0000 2.70120
\(598\) 0 0
\(599\) 33.1662i 1.35514i 0.735460 + 0.677568i \(0.236966\pi\)
−0.735460 + 0.677568i \(0.763034\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 79.5990i 3.24152i
\(604\) 0 0
\(605\) −33.0000 −1.34164
\(606\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 42.0000 1.69086 0.845428 0.534089i \(-0.179345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(618\) 0 0
\(619\) − 49.7494i − 1.99960i −0.0200967 0.999798i \(-0.506397\pi\)
0.0200967 0.999798i \(-0.493603\pi\)
\(620\) 0 0
\(621\) 55.0000 2.20707
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) − 49.7494i − 1.98049i −0.139333 0.990246i \(-0.544496\pi\)
0.139333 0.990246i \(-0.455504\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) − 132.665i − 5.24815i
\(640\) 0 0
\(641\) −45.0000 −1.77739 −0.888697 0.458496i \(-0.848388\pi\)
−0.888697 + 0.458496i \(0.848388\pi\)
\(642\) 0 0
\(643\) 29.8496i 1.17715i 0.808441 + 0.588577i \(0.200312\pi\)
−0.808441 + 0.588577i \(0.799688\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 43.1161i 1.69507i 0.530740 + 0.847535i \(0.321914\pi\)
−0.530740 + 0.847535i \(0.678086\pi\)
\(648\) 0 0
\(649\) 11.0000 0.431788
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 51.0000 1.99578 0.997892 0.0648948i \(-0.0206712\pi\)
0.997892 + 0.0648948i \(0.0206712\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −13.0000 −0.505641 −0.252821 0.967513i \(-0.581358\pi\)
−0.252821 + 0.967513i \(0.581358\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −99.0000 −3.82756
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) − 66.3325i − 2.55314i
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 46.4327i 1.77670i 0.459167 + 0.888350i \(0.348148\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) 0 0
\(685\) 9.00000 0.343872
\(686\) 0 0
\(687\) − 16.5831i − 0.632686i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) − 49.7494i − 1.89256i −0.323355 0.946278i \(-0.604811\pi\)
0.323355 0.946278i \(-0.395189\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −66.0000 −2.48570
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 19.0000 0.713560 0.356780 0.934188i \(-0.383875\pi\)
0.356780 + 0.934188i \(0.383875\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 33.0000 1.23586
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 16.5831i 0.618446i 0.950990 + 0.309223i \(0.100069\pi\)
−0.950990 + 0.309223i \(0.899931\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) − 9.94987i − 0.369020i −0.982831 0.184510i \(-0.940930\pi\)
0.982831 0.184510i \(-0.0590699\pi\)
\(728\) 0 0
\(729\) −83.0000 −3.07407
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) − 69.6491i − 2.56905i
\(736\) 0 0
\(737\) −33.0000 −1.21557
\(738\) 0 0
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) − 49.7494i − 1.81538i −0.419641 0.907690i \(-0.637844\pi\)
0.419641 0.907690i \(-0.362156\pi\)
\(752\) 0 0
\(753\) −55.0000 −2.00431
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 0 0
\(759\) 36.4829i 1.32424i
\(760\) 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
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 59.6992i 2.15002i
\(772\) 0 0
\(773\) 54.0000 1.94225 0.971123 0.238581i \(-0.0766824\pi\)
0.971123 + 0.238581i \(0.0766824\pi\)
\(774\) 0 0
\(775\) − 39.7995i − 1.42964i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 55.0000 1.96805
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 69.0000 2.46272
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 59.6992i 2.11731i
\(796\) 0 0
\(797\) 3.00000 0.106265 0.0531327 0.998587i \(-0.483079\pi\)
0.0531327 + 0.998587i \(0.483079\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 72.0000 2.54399
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 99.4987i 3.50252i
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 59.6992i 2.09117i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 29.8496i 1.04049i 0.854016 + 0.520246i \(0.174160\pi\)
−0.854016 + 0.520246i \(0.825840\pi\)
\(824\) 0 0
\(825\) 44.0000 1.53188
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) −29.0000 −1.00721 −0.503606 0.863934i \(-0.667994\pi\)
−0.503606 + 0.863934i \(0.667994\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −165.000 −5.70323
\(838\) 0 0
\(839\) − 36.4829i − 1.25953i −0.776786 0.629764i \(-0.783151\pi\)
0.776786 0.629764i \(-0.216849\pi\)
\(840\) 0 0
\(841\) 29.0000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 39.0000 1.34164
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 23.2164i 0.795847i
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) − 49.7494i − 1.69743i −0.528853 0.848713i \(-0.677378\pi\)
0.528853 0.848713i \(-0.322622\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) − 46.4327i − 1.58059i −0.612727 0.790295i \(-0.709928\pi\)
0.612727 0.790295i \(-0.290072\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 56.3826i 1.91485i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 136.000 4.60290
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −57.0000 −1.92038 −0.960189 0.279350i \(-0.909881\pi\)
−0.960189 + 0.279350i \(0.909881\pi\)
\(882\) 0 0
\(883\) 19.8997i 0.669680i 0.942275 + 0.334840i \(0.108682\pi\)
−0.942275 + 0.334840i \(0.891318\pi\)
\(884\) 0 0
\(885\) −33.0000 −1.10928
\(886\) 0 0
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) − 102.815i − 3.44444i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 49.7494i 1.66294i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −75.0000 −2.49308
\(906\) 0 0
\(907\) − 59.6992i − 1.98228i −0.132818 0.991140i \(-0.542403\pi\)
0.132818 0.991140i \(-0.457597\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 6.63325i 0.219769i 0.993944 + 0.109885i \(0.0350482\pi\)
−0.993944 + 0.109885i \(0.964952\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 28.0000 0.920634
\(926\) 0 0
\(927\) 159.198i 5.22875i
\(928\) 0 0
\(929\) −30.0000 −0.984268 −0.492134 0.870519i \(-0.663783\pi\)
−0.492134 + 0.870519i \(0.663783\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −110.000 −3.60124
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 63.0159i 2.05645i
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 23.2164i − 0.754431i −0.926126 0.377215i \(-0.876882\pi\)
0.926126 0.377215i \(-0.123118\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 89.5489i 2.90382i
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) − 69.6491i − 2.25379i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −68.0000 −2.19355
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 43.1161i 1.38366i 0.722059 + 0.691831i \(0.243196\pi\)
−0.722059 + 0.691831i \(0.756804\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 27.0000 0.863807 0.431903 0.901920i \(-0.357842\pi\)
0.431903 + 0.901920i \(0.357842\pi\)
\(978\) 0 0
\(979\) 29.8496i 0.953998i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) − 36.4829i − 1.16362i −0.813324 0.581811i \(-0.802344\pi\)
0.813324 0.581811i \(-0.197656\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 59.6992i 1.89641i 0.317660 + 0.948205i \(0.397103\pi\)
−0.317660 + 0.948205i \(0.602897\pi\)
\(992\) 0 0
\(993\) 33.0000 1.04722
\(994\) 0 0
\(995\) − 59.6992i − 1.89259i
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0 0
\(999\) − 116.082i − 3.67267i
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 176.2.e.a.175.2 yes 2
3.2 odd 2 1584.2.o.a.703.2 2
4.3 odd 2 inner 176.2.e.a.175.1 2
8.3 odd 2 704.2.e.a.703.2 2
8.5 even 2 704.2.e.a.703.1 2
11.10 odd 2 CM 176.2.e.a.175.2 yes 2
12.11 even 2 1584.2.o.a.703.1 2
16.3 odd 4 2816.2.g.a.1407.3 4
16.5 even 4 2816.2.g.a.1407.4 4
16.11 odd 4 2816.2.g.a.1407.2 4
16.13 even 4 2816.2.g.a.1407.1 4
33.32 even 2 1584.2.o.a.703.2 2
44.43 even 2 inner 176.2.e.a.175.1 2
88.21 odd 2 704.2.e.a.703.1 2
88.43 even 2 704.2.e.a.703.2 2
132.131 odd 2 1584.2.o.a.703.1 2
176.21 odd 4 2816.2.g.a.1407.4 4
176.43 even 4 2816.2.g.a.1407.2 4
176.109 odd 4 2816.2.g.a.1407.1 4
176.131 even 4 2816.2.g.a.1407.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
176.2.e.a.175.1 2 4.3 odd 2 inner
176.2.e.a.175.1 2 44.43 even 2 inner
176.2.e.a.175.2 yes 2 1.1 even 1 trivial
176.2.e.a.175.2 yes 2 11.10 odd 2 CM
704.2.e.a.703.1 2 8.5 even 2
704.2.e.a.703.1 2 88.21 odd 2
704.2.e.a.703.2 2 8.3 odd 2
704.2.e.a.703.2 2 88.43 even 2
1584.2.o.a.703.1 2 12.11 even 2
1584.2.o.a.703.1 2 132.131 odd 2
1584.2.o.a.703.2 2 3.2 odd 2
1584.2.o.a.703.2 2 33.32 even 2
2816.2.g.a.1407.1 4 16.13 even 4
2816.2.g.a.1407.1 4 176.109 odd 4
2816.2.g.a.1407.2 4 16.11 odd 4
2816.2.g.a.1407.2 4 176.43 even 4
2816.2.g.a.1407.3 4 16.3 odd 4
2816.2.g.a.1407.3 4 176.131 even 4
2816.2.g.a.1407.4 4 16.5 even 4
2816.2.g.a.1407.4 4 176.21 odd 4