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Properties

Label 11.7.b.a.10.1
Level $11$
Weight $7$
Character 11.10
Self dual yes
Analytic conductor $2.531$
Analytic rank $0$
Dimension $1$
CM discriminant -11
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [11,7,Mod(10,11)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(11, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.10");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 11.b (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: \(2.53059491982\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 10.1
Character \(\chi\) \(=\) 11.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+10.0000 q^{3} +64.0000 q^{4} +74.0000 q^{5} -629.000 q^{9} +O(q^{10})\) \(q+10.0000 q^{3} +64.0000 q^{4} +74.0000 q^{5} -629.000 q^{9} -1331.00 q^{11} +640.000 q^{12} +740.000 q^{15} +4096.00 q^{16} +4736.00 q^{20} -12670.0 q^{23} -10149.0 q^{25} -13580.0 q^{27} +56018.0 q^{31} -13310.0 q^{33} -40256.0 q^{36} +87050.0 q^{37} -85184.0 q^{44} -46546.0 q^{45} -206350. q^{47} +40960.0 q^{48} +117649. q^{49} +246890. q^{53} -98494.0 q^{55} +107642. q^{59} +47360.0 q^{60} +262144. q^{64} -428470. q^{67} -126700. q^{69} -341278. q^{71} -101490. q^{75} +303104. q^{80} +322741. q^{81} +1.39234e6 q^{89} -810880. q^{92} +560180. q^{93} -1.82419e6 q^{97} +837199. q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) 10.0000 0.370370 0.185185 − 0.982704i \(-0.440712\pi\)
0.185185 + 0.982704i \(0.440712\pi\)
\(4\) 64.0000 1.00000
\(5\) 74.0000 0.592000 0.296000 − 0.955188i \(-0.404347\pi\)
0.296000 + 0.955188i \(0.404347\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 0 0
\(9\) −629.000 −0.862826
\(10\) 0 0
\(11\) −1331.00 −1.00000
\(12\) 640.000 0.370370
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 740.000 0.219259
\(16\) 4096.00 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 4736.00 0.592000
\(21\) 0 0
\(22\) 0 0
\(23\) −12670.0 −1.04134 −0.520671 − 0.853758i \(-0.674318\pi\)
−0.520671 + 0.853758i \(0.674318\pi\)
\(24\) 0 0
\(25\) −10149.0 −0.649536
\(26\) 0 0
\(27\) −13580.0 −0.689935
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 56018.0 1.88037 0.940183 − 0.340669i \(-0.110654\pi\)
0.940183 + 0.340669i \(0.110654\pi\)
\(32\) 0 0
\(33\) −13310.0 −0.370370
\(34\) 0 0
\(35\) 0 0
\(36\) −40256.0 −0.862826
\(37\) 87050.0 1.71856 0.859278 − 0.511509i \(-0.170913\pi\)
0.859278 + 0.511509i \(0.170913\pi\)
\(38\) 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 \(\pi\)
\(44\) −85184.0 −1.00000
\(45\) −46546.0 −0.510793
\(46\) 0 0
\(47\) −206350. −1.98752 −0.993759 − 0.111552i \(-0.964418\pi\)
−0.993759 + 0.111552i \(0.964418\pi\)
\(48\) 40960.0 0.370370
\(49\) 117649. 1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 246890. 1.65835 0.829174 − 0.558990i \(-0.188811\pi\)
0.829174 + 0.558990i \(0.188811\pi\)
\(54\) 0 0
\(55\) −98494.0 −0.592000
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 107642. 0.524114 0.262057 − 0.965052i \(-0.415599\pi\)
0.262057 + 0.965052i \(0.415599\pi\)
\(60\) 47360.0 0.219259
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 262144. 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −428470. −1.42461 −0.712305 − 0.701870i \(-0.752349\pi\)
−0.712305 + 0.701870i \(0.752349\pi\)
\(68\) 0 0
\(69\) −126700. −0.385682
\(70\) 0 0
\(71\) −341278. −0.953528 −0.476764 − 0.879031i \(-0.658190\pi\)
−0.476764 + 0.879031i \(0.658190\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) −101490. −0.240569
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 303104. 0.592000
\(81\) 322741. 0.607294
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.39234e6 1.97503 0.987517 − 0.157511i \(-0.0503471\pi\)
0.987517 + 0.157511i \(0.0503471\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −810880. −1.04134
\(93\) 560180. 0.696432
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.82419e6 −1.99873 −0.999367 − 0.0355838i \(-0.988671\pi\)
−0.999367 + 0.0355838i \(0.988671\pi\)
\(98\) 0 0
\(99\) 837199. 0.862826
\(100\) −649536. −0.649536
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −811870. −0.742976 −0.371488 − 0.928438i \(-0.621152\pi\)
−0.371488 + 0.928438i \(0.621152\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −869120. −0.689935
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 870500. 0.636502
\(112\) 0 0
\(113\) 1.70237e6 1.17983 0.589914 − 0.807466i \(-0.299162\pi\)
0.589914 + 0.807466i \(0.299162\pi\)
\(114\) 0 0
\(115\) −937580. −0.616474
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.77156e6 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 3.58515e6 1.88037
\(125\) −1.90728e6 −0.976525
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) −851840. −0.370370
\(133\) 0 0
\(134\) 0 0
\(135\) −1.00492e6 −0.408442
\(136\) 0 0
\(137\) −3.68827e6 −1.43437 −0.717185 − 0.696883i \(-0.754570\pi\)
−0.717185 + 0.696883i \(0.754570\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) −2.06350e6 −0.736117
\(142\) 0 0
\(143\) 0 0
\(144\) −2.57638e6 −0.862826
\(145\) 0 0
\(146\) 0 0
\(147\) 1.17649e6 0.370370
\(148\) 5.57120e6 1.71856
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.14533e6 1.11318
\(156\) 0 0
\(157\) −5.96023e6 −1.54015 −0.770077 − 0.637951i \(-0.779782\pi\)
−0.770077 + 0.637951i \(0.779782\pi\)
\(158\) 0 0
\(159\) 2.46890e6 0.614203
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 5.23649e6 1.20914 0.604571 − 0.796551i \(-0.293344\pi\)
0.604571 + 0.796551i \(0.293344\pi\)
\(164\) 0 0
\(165\) −984940. −0.219259
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 4.82681e6 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
\(176\) −5.45178e6 −1.00000
\(177\) 1.07642e6 0.194116
\(178\) 0 0
\(179\) −7.40642e6 −1.29137 −0.645683 − 0.763606i \(-0.723427\pi\)
−0.645683 + 0.763606i \(0.723427\pi\)
\(180\) −2.97894e6 −0.510793
\(181\) −7.65698e6 −1.29128 −0.645642 − 0.763640i \(-0.723410\pi\)
−0.645642 + 0.763640i \(0.723410\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 6.44170e6 1.01738
\(186\) 0 0
\(187\) 0 0
\(188\) −1.32064e7 −1.98752
\(189\) 0 0
\(190\) 0 0
\(191\) 1.33127e7 1.91058 0.955289 − 0.295674i \(-0.0955443\pi\)
0.955289 + 0.295674i \(0.0955443\pi\)
\(192\) 2.62144e6 0.370370
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 7.52954e6 1.00000
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −237598. −0.0301497 −0.0150749 − 0.999886i \(-0.504799\pi\)
−0.0150749 + 0.999886i \(0.504799\pi\)
\(200\) 0 0
\(201\) −4.28470e6 −0.527633
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 7.96943e6 0.898496
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 1.58010e7 1.65835
\(213\) −3.41278e6 −0.353158
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −6.30362e6 −0.592000
\(221\) 0 0
\(222\) 0 0
\(223\) −2.17329e7 −1.95976 −0.979881 − 0.199583i \(-0.936041\pi\)
−0.979881 + 0.199583i \(0.936041\pi\)
\(224\) 0 0
\(225\) 6.38372e6 0.560436
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) −1.30619e7 −1.08768 −0.543838 − 0.839191i \(-0.683029\pi\)
−0.543838 + 0.839191i \(0.683029\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) −1.52699e7 −1.17661
\(236\) 6.88909e6 0.524114
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 3.03104e6 0.219259
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 1.31272e7 0.914859
\(244\) 0 0
\(245\) 8.70603e6 0.592000
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −3.12066e7 −1.97345 −0.986723 − 0.162412i \(-0.948073\pi\)
−0.986723 + 0.162412i \(0.948073\pi\)
\(252\) 0 0
\(253\) 1.68638e7 1.04134
\(254\) 0 0
\(255\) 0 0
\(256\) 1.67772e7 1.00000
\(257\) 3.07889e7 1.81382 0.906912 − 0.421320i \(-0.138433\pi\)
0.906912 + 0.421320i \(0.138433\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 1.82699e7 0.981743
\(266\) 0 0
\(267\) 1.39234e7 0.731494
\(268\) −2.74221e7 −1.42461
\(269\) −3.11461e7 −1.60010 −0.800050 − 0.599933i \(-0.795194\pi\)
−0.800050 + 0.599933i \(0.795194\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.35083e7 0.649536
\(276\) −8.10880e6 −0.385682
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) −3.52353e7 −1.62243
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) −2.18418e7 −0.953528
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2.41376e7 1.00000
\(290\) 0 0
\(291\) −1.82419e7 −0.740272
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 7.96551e6 0.310275
\(296\) 0 0
\(297\) 1.80750e7 0.689935
\(298\) 0 0
\(299\) 0 0
\(300\) −6.49536e6 −0.240569
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) −8.11870e6 −0.275176
\(310\) 0 0
\(311\) 2.94826e7 0.980131 0.490065 − 0.871686i \(-0.336973\pi\)
0.490065 + 0.871686i \(0.336973\pi\)
\(312\) 0 0
\(313\) 5.92757e7 1.93305 0.966527 − 0.256566i \(-0.0825910\pi\)
0.966527 + 0.256566i \(0.0825910\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.77820e7 −0.872139 −0.436069 − 0.899913i \(-0.643630\pi\)
−0.436069 + 0.899913i \(0.643630\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.93987e7 0.592000
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 2.06554e7 0.607294
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −6.59498e6 −0.181857 −0.0909284 − 0.995857i \(-0.528983\pi\)
−0.0909284 + 0.995857i \(0.528983\pi\)
\(332\) 0 0
\(333\) −5.47544e7 −1.48281
\(334\) 0 0
\(335\) −3.17068e7 −0.843369
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 1.70237e7 0.436973
\(340\) 0 0
\(341\) −7.45600e7 −1.88037
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −9.37580e6 −0.228324
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.04988e7 −0.238679 −0.119339 − 0.992854i \(-0.538078\pi\)
−0.119339 + 0.992854i \(0.538078\pi\)
\(354\) 0 0
\(355\) −2.52546e7 −0.564488
\(356\) 8.91096e7 1.97503
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 4.70459e7 1.00000
\(362\) 0 0
\(363\) 1.77156e7 0.370370
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −534670. −0.0108165 −0.00540826 − 0.999985i \(-0.501722\pi\)
−0.00540826 + 0.999985i \(0.501722\pi\)
\(368\) −5.18963e7 −1.04134
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 3.58515e7 0.696432
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) −1.90728e7 −0.361676
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 5.49601e7 1.00956 0.504778 − 0.863249i \(-0.331575\pi\)
0.504778 + 0.863249i \(0.331575\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9.81183e7 1.74644 0.873220 − 0.487326i \(-0.162028\pi\)
0.873220 + 0.487326i \(0.162028\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −1.16748e8 −1.99873
\(389\) 8.19292e7 1.39184 0.695921 − 0.718119i \(-0.254997\pi\)
0.695921 + 0.718119i \(0.254997\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 5.35807e7 0.862826
\(397\) −1.19506e8 −1.90993 −0.954964 − 0.296722i \(-0.904107\pi\)
−0.954964 + 0.296722i \(0.904107\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −4.15703e7 −0.649536
\(401\) −4.63343e7 −0.718571 −0.359285 − 0.933228i \(-0.616980\pi\)
−0.359285 + 0.933228i \(0.616980\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 2.38828e7 0.359518
\(406\) 0 0
\(407\) −1.15864e8 −1.71856
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) −3.68827e7 −0.531248
\(412\) −5.19597e7 −0.742976
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.20006e8 1.63140 0.815702 − 0.578472i \(-0.196351\pi\)
0.815702 + 0.578472i \(0.196351\pi\)
\(420\) 0 0
\(421\) −1.39800e7 −0.187353 −0.0936767 − 0.995603i \(-0.529862\pi\)
−0.0936767 + 0.995603i \(0.529862\pi\)
\(422\) 0 0
\(423\) 1.29794e8 1.71488
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −5.56237e7 −0.689935
\(433\) 1.40460e7 0.173018 0.0865088 − 0.996251i \(-0.472429\pi\)
0.0865088 + 0.996251i \(0.472429\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −7.40012e7 −0.862826
\(442\) 0 0
\(443\) 1.73871e8 1.99994 0.999969 − 0.00782546i \(-0.00249095\pi\)
0.999969 + 0.00782546i \(0.00249095\pi\)
\(444\) 5.57120e7 0.636502
\(445\) 1.03033e8 1.16922
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.34988e8 −1.49127 −0.745634 − 0.666355i \(-0.767853\pi\)
−0.745634 + 0.666355i \(0.767853\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 1.08952e8 1.17983
\(453\) 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
\(460\) −6.00051e7 −0.616474
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −2.24659e7 −0.226350 −0.113175 − 0.993575i \(-0.536102\pi\)
−0.113175 + 0.993575i \(0.536102\pi\)
\(464\) 0 0
\(465\) 4.14533e7 0.412288
\(466\) 0 0
\(467\) −1.86256e8 −1.82877 −0.914387 − 0.404842i \(-0.867327\pi\)
−0.914387 + 0.404842i \(0.867327\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −5.96023e7 −0.570427
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.55294e8 −1.43087
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1.13380e8 1.00000
\(485\) −1.34990e8 −1.18325
\(486\) 0 0
\(487\) 4.73532e7 0.409980 0.204990 − 0.978764i \(-0.434284\pi\)
0.204990 + 0.978764i \(0.434284\pi\)
\(488\) 0 0
\(489\) 5.23649e7 0.447831
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 6.19527e7 0.510793
\(496\) 2.29450e8 1.88037
\(497\) 0 0
\(498\) 0 0
\(499\) −2.31529e8 −1.86339 −0.931693 − 0.363246i \(-0.881669\pi\)
−0.931693 + 0.363246i \(0.881669\pi\)
\(500\) −1.22066e8 −0.976525
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 4.82681e7 0.370370
\(508\) 0 0
\(509\) 2.38464e8 1.80829 0.904147 − 0.427222i \(-0.140508\pi\)
0.904147 + 0.427222i \(0.140508\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −6.00784e7 −0.439842
\(516\) 0 0
\(517\) 2.74652e8 1.98752
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.19963e8 0.848273 0.424136 − 0.905598i \(-0.360578\pi\)
0.424136 + 0.905598i \(0.360578\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −5.45178e7 −0.370370
\(529\) 1.24930e7 0.0843918
\(530\) 0 0
\(531\) −6.77068e7 −0.452219
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −7.40642e7 −0.478284
\(538\) 0 0
\(539\) −1.56591e8 −1.00000
\(540\) −6.43149e7 −0.408442
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −7.65698e7 −0.478253
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) −2.36049e8 −1.43437
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 6.44170e7 0.376809
\(556\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) −1.32064e8 −0.736117
\(565\) 1.25975e8 0.698458
\(566\) 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
\(573\) 1.33127e8 0.707621
\(574\) 0 0
\(575\) 1.28588e8 0.676389
\(576\) −1.64889e8 −0.862826
\(577\) 1.20521e8 0.627387 0.313694 − 0.949524i \(-0.398434\pi\)
0.313694 + 0.949524i \(0.398434\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −3.28611e8 −1.65835
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2.74808e8 1.35867 0.679337 − 0.733827i \(-0.262268\pi\)
0.679337 + 0.733827i \(0.262268\pi\)
\(588\) 7.52954e7 0.370370
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 3.56557e8 1.71856
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.37598e6 −0.0111666
\(598\) 0 0
\(599\) −1.04546e8 −0.486439 −0.243219 − 0.969971i \(-0.578204\pi\)
−0.243219 + 0.969971i \(0.578204\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 2.69508e8 1.22919
\(604\) 0 0
\(605\) 1.31096e8 0.592000
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 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
\(617\) −4.56419e8 −1.94316 −0.971578 − 0.236719i \(-0.923928\pi\)
−0.971578 + 0.236719i \(0.923928\pi\)
\(618\) 0 0
\(619\) −4.70909e8 −1.98548 −0.992738 − 0.120296i \(-0.961616\pi\)
−0.992738 + 0.120296i \(0.961616\pi\)
\(620\) 2.65301e8 1.11318
\(621\) 1.72059e8 0.718458
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.74397e7 0.0714330
\(626\) 0 0
\(627\) 0 0
\(628\) −3.81455e8 −1.54015
\(629\) 0 0
\(630\) 0 0
\(631\) −3.35863e8 −1.33682 −0.668411 − 0.743792i \(-0.733025\pi\)
−0.668411 + 0.743792i \(0.733025\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 1.58010e8 0.614203
\(637\) 0 0
\(638\) 0 0
\(639\) 2.14664e8 0.822728
\(640\) 0 0
\(641\) −5.05681e8 −1.92001 −0.960004 − 0.279988i \(-0.909670\pi\)
−0.960004 + 0.279988i \(0.909670\pi\)
\(642\) 0 0
\(643\) −4.28307e8 −1.61110 −0.805550 − 0.592528i \(-0.798130\pi\)
−0.805550 + 0.592528i \(0.798130\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.29180e8 1.95385 0.976924 − 0.213588i \(-0.0685150\pi\)
0.976924 + 0.213588i \(0.0685150\pi\)
\(648\) 0 0
\(649\) −1.43272e8 −0.524114
\(650\) 0 0
\(651\) 0 0
\(652\) 3.35135e8 1.20914
\(653\) 5.15148e8 1.85009 0.925045 − 0.379858i \(-0.124027\pi\)
0.925045 + 0.379858i \(0.124027\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) −6.30362e7 −0.219259
\(661\) −2.14988e7 −0.0744407 −0.0372204 − 0.999307i \(-0.511850\pi\)
−0.0372204 + 0.999307i \(0.511850\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −2.17329e8 −0.725838
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 1.37823e8 0.448138
\(676\) 3.08916e8 1.00000
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 6.12540e8 1.92253 0.961263 − 0.275632i \(-0.0888872\pi\)
0.961263 + 0.275632i \(0.0888872\pi\)
\(684\) 0 0
\(685\) −2.72932e8 −0.849147
\(686\) 0 0
\(687\) −1.30619e8 −0.402843
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 2.59909e8 0.787747 0.393874 − 0.919165i \(-0.371135\pi\)
0.393874 + 0.919165i \(0.371135\pi\)
\(692\) 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
\(704\) −3.48914e8 −1.00000
\(705\) −1.52699e8 −0.435782
\(706\) 0 0
\(707\) 0 0
\(708\) 6.88909e7 0.194116
\(709\) 4.13069e8 1.15900 0.579501 − 0.814972i \(-0.303247\pi\)
0.579501 + 0.814972i \(0.303247\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −7.09748e8 −1.95810
\(714\) 0 0
\(715\) 0 0
\(716\) −4.74011e8 −1.29137
\(717\) 0 0
\(718\) 0 0
\(719\) −2.30639e8 −0.620507 −0.310253 − 0.950654i \(-0.600414\pi\)
−0.310253 + 0.950654i \(0.600414\pi\)
\(720\) −1.90652e8 −0.510793
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) −4.90047e8 −1.29128
\(725\) 0 0
\(726\) 0 0
\(727\) 3.39343e8 0.883154 0.441577 − 0.897223i \(-0.354419\pi\)
0.441577 + 0.897223i \(0.354419\pi\)
\(728\) 0 0
\(729\) −1.04006e8 −0.268457
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 8.70603e7 0.219259
\(736\) 0 0
\(737\) 5.70294e8 1.42461
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 4.12269e8 1.01738
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 7.25152e8 1.71202 0.856010 − 0.516959i \(-0.172936\pi\)
0.856010 + 0.516959i \(0.172936\pi\)
\(752\) −8.45210e8 −1.98752
\(753\) −3.12066e8 −0.730906
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.19997e8 0.276620 0.138310 − 0.990389i \(-0.455833\pi\)
0.138310 + 0.990389i \(0.455833\pi\)
\(758\) 0 0
\(759\) 1.68638e8 0.385682
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 8.52010e8 1.91058
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.67772e8 0.370370
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 3.07889e8 0.671787
\(772\) 0 0
\(773\) 1.15509e8 0.250079 0.125039 − 0.992152i \(-0.460094\pi\)
0.125039 + 0.992152i \(0.460094\pi\)
\(774\) 0 0
\(775\) −5.68527e8 −1.22137
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 4.54241e8 0.953528
\(782\) 0 0
\(783\) 0 0
\(784\) 4.81890e8 1.00000
\(785\) −4.41057e8 −0.911771
\(786\) 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
\(795\) 1.82699e8 0.363608
\(796\) −1.52063e7 −0.0301497
\(797\) −9.61458e8 −1.89913 −0.949566 − 0.313566i \(-0.898476\pi\)
−0.949566 + 0.313566i \(0.898476\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −8.75781e8 −1.70411
\(802\) 0 0
\(803\) 0 0
\(804\) −2.74221e8 −0.527633
\(805\) 0 0
\(806\) 0 0
\(807\) −3.11461e8 −0.592630
\(808\) 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
\(813\) 0 0
\(814\) 0 0
\(815\) 3.87500e8 0.715812
\(816\) 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
\(823\) −1.10378e9 −1.98008 −0.990042 − 0.140774i \(-0.955041\pi\)
−0.990042 + 0.140774i \(0.955041\pi\)
\(824\) 0 0
\(825\) 1.35083e8 0.240569
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 5.10044e8 0.898496
\(829\) 1.13909e9 1.99937 0.999687 − 0.0250094i \(-0.00796157\pi\)
0.999687 + 0.0250094i \(0.00796157\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −7.60724e8 −1.29733
\(838\) 0 0
\(839\) −6.91000e8 −1.17002 −0.585008 − 0.811027i \(-0.698909\pi\)
−0.585008 + 0.811027i \(0.698909\pi\)
\(840\) 0 0
\(841\) 5.94823e8 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 3.57184e8 0.592000
\(846\) 0 0
\(847\) 0 0
\(848\) 1.01126e9 1.65835
\(849\) 0 0
\(850\) 0 0
\(851\) −1.10292e9 −1.78960
\(852\) −2.18418e8 −0.353158
\(853\) 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
\(859\) 1.24193e9 1.95937 0.979687 − 0.200531i \(-0.0642667\pi\)
0.979687 + 0.200531i \(0.0642667\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 8.81245e8 1.37108 0.685542 − 0.728033i \(-0.259565\pi\)
0.685542 + 0.728033i \(0.259565\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 2.41376e8 0.370370
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 1.14742e9 1.72456
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) −4.03431e8 −0.592000
\(881\) −1.74446e8 −0.255113 −0.127557 − 0.991831i \(-0.540713\pi\)
−0.127557 + 0.991831i \(0.540713\pi\)
\(882\) 0 0
\(883\) −6.33169e8 −0.919681 −0.459841 − 0.888001i \(-0.652093\pi\)
−0.459841 + 0.888001i \(0.652093\pi\)
\(884\) 0 0
\(885\) 7.96551e7 0.114917
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −4.29568e8 −0.607294
\(892\) −1.39091e9 −1.95976
\(893\) 0 0
\(894\) 0 0
\(895\) −5.48075e8 −0.764489
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 4.08558e8 0.560436
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −5.66617e8 −0.764440
\(906\) 0 0
\(907\) −1.04047e9 −1.39446 −0.697231 − 0.716846i \(-0.745585\pi\)
−0.697231 + 0.716846i \(0.745585\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.19396e9 1.57920 0.789598 − 0.613624i \(-0.210289\pi\)
0.789598 + 0.613624i \(0.210289\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −8.35960e8 −1.08768
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −8.83470e8 −1.11626
\(926\) 0 0
\(927\) 5.10666e8 0.641059
\(928\) 0 0
\(929\) 1.60116e9 1.99705 0.998523 − 0.0543288i \(-0.0173019\pi\)
0.998523 + 0.0543288i \(0.0173019\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 2.94826e8 0.363011
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 5.92757e8 0.715946
\(940\) −9.77274e8 −1.17661
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 4.40902e8 0.524114
\(945\) 0 0
\(946\) 0 0
\(947\) −1.15771e9 −1.36318 −0.681588 − 0.731737i \(-0.738710\pi\)
−0.681588 + 0.731737i \(0.738710\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −2.77820e8 −0.323014
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 9.85137e8 1.13106
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 1.93987e8 0.219259
\(961\) 2.25051e9 2.53578
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −2.34196e8 −0.255812 −0.127906 − 0.991786i \(-0.540826\pi\)
−0.127906 + 0.991786i \(0.540826\pi\)
\(972\) 8.40143e8 0.914859
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.66963e9 1.79034 0.895171 − 0.445722i \(-0.147053\pi\)
0.895171 + 0.445722i \(0.147053\pi\)
\(978\) 0 0
\(979\) −1.85320e9 −1.97503
\(980\) 5.57186e8 0.592000
\(981\) 0 0
\(982\) 0 0
\(983\) −1.58473e9 −1.66838 −0.834191 − 0.551476i \(-0.814065\pi\)
−0.834191 + 0.551476i \(0.814065\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 7.01647e8 0.720938 0.360469 − 0.932771i \(-0.382617\pi\)
0.360469 + 0.932771i \(0.382617\pi\)
\(992\) 0 0
\(993\) −6.59498e7 −0.0673544
\(994\) 0 0
\(995\) −1.75823e7 −0.0178486
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0 0
\(999\) −1.18214e9 −1.18569
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 11.7.b.a.10.1 ✓ 1
3.2 odd 2 99.7.c.a.10.1 1
4.3 odd 2 176.7.h.a.65.1 1
11.10 odd 2 CM 11.7.b.a.10.1 ✓ 1
33.32 even 2 99.7.c.a.10.1 1
44.43 even 2 176.7.h.a.65.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.7.b.a.10.1 ✓ 1 1.1 even 1 trivial
11.7.b.a.10.1 ✓ 1 11.10 odd 2 CM
99.7.c.a.10.1 1 3.2 odd 2
99.7.c.a.10.1 1 33.32 even 2
176.7.h.a.65.1 1 4.3 odd 2
176.7.h.a.65.1 1 44.43 even 2