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Properties

Label 484.2.a.d.1.2
Level $484$
Weight $2$
Character 484.1
Self dual yes
Analytic conductor $3.865$
Analytic rank $0$
Dimension $2$
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] = [484,2,Mod(1,484)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(484, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("484.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 484 = 2^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 484.a (trivial)

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: \(3.86475945783\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{33}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $N(\mathrm{U}(1))$

Embedding invariants

Embedding label 1.2
Root \(3.37228\) of defining polynomial
Character \(\chi\) \(=\) 484.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.37228 q^{3} -1.37228 q^{5} +8.37228 q^{9} -4.62772 q^{15} +7.37228 q^{23} -3.11684 q^{25} +18.1168 q^{27} -6.11684 q^{31} -12.1168 q^{37} -11.4891 q^{45} -12.0000 q^{47} -7.00000 q^{49} +6.00000 q^{53} +4.62772 q^{59} +2.11684 q^{67} +24.8614 q^{69} -12.8614 q^{71} -10.5109 q^{75} +35.9783 q^{81} +18.8614 q^{89} -20.6277 q^{93} +0.116844 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} + 3 q^{5} + 11 q^{9} - 15 q^{15} + 9 q^{23} + 11 q^{25} + 19 q^{27} + 5 q^{31} - 7 q^{37} - 24 q^{47} - 14 q^{49} + 12 q^{53} + 15 q^{59} - 13 q^{67} + 21 q^{69} + 3 q^{71} - 44 q^{75} + 26 q^{81}+ \cdots - 17 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 3.37228 1.94699 0.973494 − 0.228714i \(-0.0734519\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) 0 0
\(5\) −1.37228 −0.613703 −0.306851 − 0.951757i \(-0.599275\pi\)
−0.306851 + 0.951757i \(0.599275\pi\)
\(6\) 0 0
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 8.37228 2.79076
\(10\) 0 0
\(11\) 0 0
\(12\) 0 0
\(13\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) −4.62772 −1.19487
\(16\) 0 0
\(17\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.37228 1.53723 0.768613 − 0.639713i \(-0.220947\pi\)
0.768613 + 0.639713i \(0.220947\pi\)
\(24\) 0 0
\(25\) −3.11684 −0.623369
\(26\) 0 0
\(27\) 18.1168 3.48659
\(28\) 0 0
\(29\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) −6.11684 −1.09862 −0.549309 − 0.835619i \(-0.685109\pi\)
−0.549309 + 0.835619i \(0.685109\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −12.1168 −1.99200 −0.995998 − 0.0893706i \(-0.971514\pi\)
−0.995998 + 0.0893706i \(0.971514\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) −11.4891 −1.71270
\(46\) 0 0
\(47\) −12.0000 −1.75038 −0.875190 − 0.483779i \(-0.839264\pi\)
−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
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.62772 0.602478 0.301239 − 0.953549i \(-0.402600\pi\)
0.301239 + 0.953549i \(0.402600\pi\)
\(60\) 0 0
\(61\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 2.11684 0.258614 0.129307 − 0.991605i \(-0.458725\pi\)
0.129307 + 0.991605i \(0.458725\pi\)
\(68\) 0 0
\(69\) 24.8614 2.99296
\(70\) 0 0
\(71\) −12.8614 −1.52637 −0.763184 − 0.646181i \(-0.776365\pi\)
−0.763184 + 0.646181i \(0.776365\pi\)
\(72\) 0 0
\(73\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) −10.5109 −1.21369
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 35.9783 3.99758
\(82\) 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
\(89\) 18.8614 1.99931 0.999653 − 0.0263586i \(-0.00839118\pi\)
0.999653 + 0.0263586i \(0.00839118\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −20.6277 −2.13899
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.116844 0.0118637 0.00593185 − 0.999982i \(-0.498112\pi\)
0.00593185 + 0.999982i \(0.498112\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) −4.00000 −0.394132 −0.197066 − 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) −40.8614 −3.87839
\(112\) 0 0
\(113\) −13.3723 −1.25796 −0.628979 − 0.777422i \(-0.716527\pi\)
−0.628979 + 0.777422i \(0.716527\pi\)
\(114\) 0 0
\(115\) −10.1168 −0.943401
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.1386 0.996266
\(126\) 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
\(135\) −24.8614 −2.13973
\(136\) 0 0
\(137\) 21.6060 1.84592 0.922961 − 0.384893i \(-0.125762\pi\)
0.922961 + 0.384893i \(0.125762\pi\)
\(138\) 0 0
\(139\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −40.4674 −3.40797
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −23.6060 −1.94699
\(148\) 0 0
\(149\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 8.39403 0.674225
\(156\) 0 0
\(157\) 20.1168 1.60550 0.802749 − 0.596316i \(-0.203370\pi\)
0.802749 + 0.596316i \(0.203370\pi\)
\(158\) 0 0
\(159\) 20.2337 1.60464
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −16.0000 −1.25322 −0.626608 − 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 15.6060 1.17302
\(178\) 0 0
\(179\) −24.8614 −1.85823 −0.929114 − 0.369792i \(-0.879429\pi\)
−0.929114 + 0.369792i \(0.879429\pi\)
\(180\) 0 0
\(181\) 3.88316 0.288633 0.144316 − 0.989532i \(-0.453902\pi\)
0.144316 + 0.989532i \(0.453902\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 16.6277 1.22249
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 27.6060 1.99750 0.998749 − 0.0500060i \(-0.0159241\pi\)
0.998749 + 0.0500060i \(0.0159241\pi\)
\(192\) 0 0
\(193\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) −20.0000 −1.41776 −0.708881 − 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) 0 0
\(201\) 7.13859 0.503518
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 61.7228 4.29003
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 0 0
\(213\) −43.3723 −2.97182
\(214\) 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
\(223\) 26.3505 1.76456 0.882281 − 0.470723i \(-0.156007\pi\)
0.882281 + 0.470723i \(0.156007\pi\)
\(224\) 0 0
\(225\) −26.0951 −1.73967
\(226\) 0 0
\(227\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 28.3505 1.87346 0.936728 − 0.350058i \(-0.113838\pi\)
0.936728 + 0.350058i \(0.113838\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) 16.4674 1.07421
\(236\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 0 0
\(243\) 66.9783 4.29666
\(244\) 0 0
\(245\) 9.60597 0.613703
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.861407 −0.0543715 −0.0271858 − 0.999630i \(-0.508655\pi\)
−0.0271858 + 0.999630i \(0.508655\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 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
\(265\) −8.23369 −0.505791
\(266\) 0 0
\(267\) 63.6060 3.89262
\(268\) 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
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) −51.2119 −3.06598
\(280\) 0 0
\(281\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 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
\(291\) 0.394031 0.0230985
\(292\) 0 0
\(293\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) −6.35053 −0.369742
\(296\) 0 0
\(297\) 0 0
\(298\) 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
\(309\) −13.4891 −0.767370
\(310\) 0 0
\(311\) −12.0000 −0.680458 −0.340229 − 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 0 0
\(313\) 16.3505 0.924187 0.462093 − 0.886831i \(-0.347098\pi\)
0.462093 + 0.886831i \(0.347098\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 33.6060 1.88750 0.943750 − 0.330661i \(-0.107272\pi\)
0.943750 + 0.330661i \(0.107272\pi\)
\(318\) 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
\(331\) −26.1168 −1.43551 −0.717756 − 0.696295i \(-0.754831\pi\)
−0.717756 + 0.696295i \(0.754831\pi\)
\(332\) 0 0
\(333\) −101.446 −5.55919
\(334\) 0 0
\(335\) −2.90491 −0.158712
\(336\) 0 0
\(337\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0 0
\(339\) −45.0951 −2.44923
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −34.1168 −1.83679
\(346\) 0 0
\(347\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −27.0951 −1.44213 −0.721063 − 0.692869i \(-0.756346\pi\)
−0.721063 + 0.692869i \(0.756346\pi\)
\(354\) 0 0
\(355\) 17.6495 0.936737
\(356\) 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
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 9.88316 0.515897 0.257948 − 0.966159i \(-0.416954\pi\)
0.257948 + 0.966159i \(0.416954\pi\)
\(368\) 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
\(375\) 37.5625 1.93972
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 38.3505 1.96993 0.984967 − 0.172741i \(-0.0552624\pi\)
0.984967 + 0.172741i \(0.0552624\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −16.6277 −0.849637 −0.424818 − 0.905279i \(-0.639662\pi\)
−0.424818 + 0.905279i \(0.639662\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 39.0951 1.98220 0.991100 − 0.133120i \(-0.0424994\pi\)
0.991100 + 0.133120i \(0.0424994\pi\)
\(390\) 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 \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 30.0000 1.49813 0.749064 − 0.662497i \(-0.230503\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −49.3723 −2.45333
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) 72.8614 3.59399
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 − 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 − 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 0 0
\(423\) −100.467 −4.88489
\(424\) 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
\(433\) −40.3505 −1.93912 −0.969561 − 0.244848i \(-0.921262\pi\)
−0.969561 + 0.244848i \(0.921262\pi\)
\(434\) 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
\(441\) −58.6060 −2.79076
\(442\) 0 0
\(443\) 21.0951 1.00226 0.501129 − 0.865373i \(-0.332918\pi\)
0.501129 + 0.865373i \(0.332918\pi\)
\(444\) 0 0
\(445\) −25.8832 −1.22698
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −5.13859 −0.242505 −0.121253 − 0.992622i \(-0.538691\pi\)
−0.121253 + 0.992622i \(0.538691\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) −10.3505 −0.481030 −0.240515 − 0.970645i \(-0.577316\pi\)
−0.240515 + 0.970645i \(0.577316\pi\)
\(464\) 0 0
\(465\) 28.3070 1.31271
\(466\) 0 0
\(467\) −35.8397 −1.65846 −0.829231 − 0.558906i \(-0.811221\pi\)
−0.829231 + 0.558906i \(0.811221\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 67.8397 3.12589
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 50.2337 2.30004
\(478\) 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
\(485\) −0.160343 −0.00728079
\(486\) 0 0
\(487\) −30.1168 −1.36472 −0.682362 − 0.731014i \(-0.739047\pi\)
−0.682362 + 0.731014i \(0.739047\pi\)
\(488\) 0 0
\(489\) −53.9565 −2.44000
\(490\) 0 0
\(491\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 40.0000 1.79065 0.895323 − 0.445418i \(-0.146945\pi\)
0.895323 + 0.445418i \(0.146945\pi\)
\(500\) 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
\(507\) −43.8397 −1.94699
\(508\) 0 0
\(509\) 25.3723 1.12461 0.562303 − 0.826931i \(-0.309915\pi\)
0.562303 + 0.826931i \(0.309915\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5.48913 0.241880
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −29.8397 −1.30730 −0.653650 − 0.756797i \(-0.726763\pi\)
−0.653650 + 0.756797i \(0.726763\pi\)
\(522\) 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
\(529\) 31.3505 1.36307
\(530\) 0 0
\(531\) 38.7446 1.68137
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −83.8397 −3.61795
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 0 0
\(543\) 13.0951 0.561964
\(544\) 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
\(555\) 56.0733 2.38018
\(556\) 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
\(563\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 18.3505 0.772013
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 93.0951 3.88910
\(574\) 0 0
\(575\) −22.9783 −0.958259
\(576\) 0 0
\(577\) 32.1168 1.33704 0.668521 − 0.743693i \(-0.266928\pi\)
0.668521 + 0.743693i \(0.266928\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −48.0000 −1.98117 −0.990586 − 0.136892i \(-0.956289\pi\)
−0.990586 + 0.136892i \(0.956289\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −67.4456 −2.76037
\(598\) 0 0
\(599\) −36.0000 −1.47092 −0.735460 − 0.677568i \(-0.763034\pi\)
−0.735460 + 0.677568i \(0.763034\pi\)
\(600\) 0 0
\(601\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) 0 0
\(603\) 17.7228 0.721729
\(604\) 0 0
\(605\) 0 0
\(606\) 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
\(617\) −42.0000 −1.69086 −0.845428 − 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(618\) 0 0
\(619\) −42.5842 −1.71160 −0.855802 − 0.517303i \(-0.826936\pi\)
−0.855802 + 0.517303i \(0.826936\pi\)
\(620\) 0 0
\(621\) 133.562 5.35968
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.298936 0.0119574
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −46.5842 −1.85449 −0.927244 − 0.374457i \(-0.877829\pi\)
−0.927244 + 0.374457i \(0.877829\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −107.679 −4.25973
\(640\) 0 0
\(641\) 2.39403 0.0945585 0.0472793 − 0.998882i \(-0.484945\pi\)
0.0472793 + 0.998882i \(0.484945\pi\)
\(642\) 0 0
\(643\) −46.3505 −1.82789 −0.913943 − 0.405842i \(-0.866978\pi\)
−0.913943 + 0.405842i \(0.866978\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −23.8397 −0.937234 −0.468617 − 0.883402i \(-0.655247\pi\)
−0.468617 + 0.883402i \(0.655247\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −22.6277 −0.885491 −0.442746 − 0.896647i \(-0.645995\pi\)
−0.442746 + 0.896647i \(0.645995\pi\)
\(654\) 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
\(661\) 36.5842 1.42296 0.711481 − 0.702706i \(-0.248025\pi\)
0.711481 + 0.702706i \(0.248025\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 88.8614 3.43558
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) −56.4674 −2.17343
\(676\) 0 0
\(677\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 24.0000 0.918334 0.459167 − 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(684\) 0 0
\(685\) −29.6495 −1.13285
\(686\) 0 0
\(687\) 95.6060 3.64760
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 34.5842 1.31565 0.657823 − 0.753173i \(-0.271478\pi\)
0.657823 + 0.753173i \(0.271478\pi\)
\(692\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 55.5326 2.09148
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −52.5842 −1.97484 −0.987421 − 0.158114i \(-0.949459\pi\)
−0.987421 + 0.158114i \(0.949459\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −45.0951 −1.68882
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −11.1386 −0.415399 −0.207700 − 0.978193i \(-0.566598\pi\)
−0.207700 + 0.978193i \(0.566598\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 17.8832 0.663250 0.331625 − 0.943411i \(-0.392403\pi\)
0.331625 + 0.943411i \(0.392403\pi\)
\(728\) 0 0
\(729\) 117.935 4.36795
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) 32.3940 1.19487
\(736\) 0 0
\(737\) 0 0
\(738\) 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
\(751\) 54.5842 1.99181 0.995903 − 0.0904254i \(-0.0288227\pi\)
0.995903 + 0.0904254i \(0.0288227\pi\)
\(752\) 0 0
\(753\) −2.90491 −0.105861
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −38.0000 −1.38113 −0.690567 − 0.723269i \(-0.742639\pi\)
−0.690567 + 0.723269i \(0.742639\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) 60.7011 2.18610
\(772\) 0 0
\(773\) 54.0000 1.94225 0.971123 − 0.238581i \(-0.0766824\pi\)
0.971123 + 0.238581i \(0.0766824\pi\)
\(774\) 0 0
\(775\) 19.0652 0.684844
\(776\) 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
\(785\) −27.6060 −0.985299
\(786\) 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
\(795\) −27.7663 −0.984770
\(796\) 0 0
\(797\) −47.3288 −1.67647 −0.838236 − 0.545308i \(-0.816413\pi\)
−0.838236 + 0.545308i \(0.816413\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 157.913 5.57958
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 101.168 3.56130
\(808\) 0 0
\(809\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) 0 0
\(811\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 21.9565 0.769103
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) 50.3505 1.75511 0.877555 − 0.479477i \(-0.159174\pi\)
0.877555 + 0.479477i \(0.159174\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 28.5842 0.992771 0.496385 − 0.868102i \(-0.334660\pi\)
0.496385 + 0.868102i \(0.334660\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −110.818 −3.83043
\(838\) 0 0
\(839\) −9.09509 −0.313998 −0.156999 − 0.987599i \(-0.550182\pi\)
−0.156999 + 0.987599i \(0.550182\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 17.8397 0.613703
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −89.3288 −3.06215
\(852\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) 58.5842 1.99887 0.999434 − 0.0336436i \(-0.0107111\pi\)
0.999434 + 0.0336436i \(0.0107111\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −36.0000 −1.22545 −0.612727 − 0.790295i \(-0.709928\pi\)
−0.612727 + 0.790295i \(0.709928\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −57.3288 −1.94699
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0.978251 0.0331088
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −42.8614 −1.44404 −0.722019 − 0.691873i \(-0.756786\pi\)
−0.722019 + 0.691873i \(0.756786\pi\)
\(882\) 0 0
\(883\) −56.0000 −1.88455 −0.942275 − 0.334840i \(-0.891318\pi\)
−0.942275 + 0.334840i \(0.891318\pi\)
\(884\) 0 0
\(885\) −21.4158 −0.719884
\(886\) 0 0
\(887\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 34.1168 1.14040
\(896\) 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
\(905\) −5.32878 −0.177135
\(906\) 0 0
\(907\) 8.00000 0.265636 0.132818 − 0.991140i \(-0.457597\pi\)
0.132818 + 0.991140i \(0.457597\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −60.0000 −1.98789 −0.993944 − 0.109885i \(-0.964952\pi\)
−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
\(925\) 37.7663 1.24175
\(926\) 0 0
\(927\) −33.4891 −1.09993
\(928\) 0 0
\(929\) 30.0000 0.984268 0.492134 − 0.870519i \(-0.336217\pi\)
0.492134 + 0.870519i \(0.336217\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −40.4674 −1.32484
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 0 0
\(939\) 55.1386 1.79938
\(940\) 0 0
\(941\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −8.39403 −0.272769 −0.136385 − 0.990656i \(-0.543548\pi\)
−0.136385 + 0.990656i \(0.543548\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 113.329 3.67494
\(952\) 0 0
\(953\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 0 0
\(955\) −37.8832 −1.22587
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 6.41578 0.206961
\(962\) 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
\(971\) 59.8397 1.92035 0.960173 − 0.279406i \(-0.0901376\pi\)
0.960173 + 0.279406i \(0.0901376\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −35.3288 −1.13027 −0.565134 − 0.824999i \(-0.691176\pi\)
−0.565134 + 0.824999i \(0.691176\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −57.0951 −1.82105 −0.910525 − 0.413453i \(-0.864323\pi\)
−0.910525 + 0.413453i \(0.864323\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −20.0000 −0.635321 −0.317660 − 0.948205i \(-0.602897\pi\)
−0.317660 + 0.948205i \(0.602897\pi\)
\(992\) 0 0
\(993\) −88.0733 −2.79492
\(994\) 0 0
\(995\) 27.4456 0.870085
\(996\) 0 0
\(997\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) 0 0
\(999\) −219.519 −6.94527
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 484.2.a.d.1.2 ✓ 2
3.2 odd 2 4356.2.a.n.1.2 2
4.3 odd 2 1936.2.a.s.1.1 2
8.3 odd 2 7744.2.a.cn.1.2 2
8.5 even 2 7744.2.a.bx.1.1 2
11.2 odd 10 484.2.e.g.81.2 8
11.3 even 5 484.2.e.g.9.1 8
11.4 even 5 484.2.e.g.269.1 8
11.5 even 5 484.2.e.g.245.2 8
11.6 odd 10 484.2.e.g.245.2 8
11.7 odd 10 484.2.e.g.269.1 8
11.8 odd 10 484.2.e.g.9.1 8
11.9 even 5 484.2.e.g.81.2 8
11.10 odd 2 CM 484.2.a.d.1.2 ✓ 2
33.32 even 2 4356.2.a.n.1.2 2
44.43 even 2 1936.2.a.s.1.1 2
88.21 odd 2 7744.2.a.bx.1.1 2
88.43 even 2 7744.2.a.cn.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
484.2.a.d.1.2 ✓ 2 1.1 even 1 trivial
484.2.a.d.1.2 ✓ 2 11.10 odd 2 CM
484.2.e.g.9.1 8 11.3 even 5
484.2.e.g.9.1 8 11.8 odd 10
484.2.e.g.81.2 8 11.2 odd 10
484.2.e.g.81.2 8 11.9 even 5
484.2.e.g.245.2 8 11.5 even 5
484.2.e.g.245.2 8 11.6 odd 10
484.2.e.g.269.1 8 11.4 even 5
484.2.e.g.269.1 8 11.7 odd 10
1936.2.a.s.1.1 2 4.3 odd 2
1936.2.a.s.1.1 2 44.43 even 2
4356.2.a.n.1.2 2 3.2 odd 2
4356.2.a.n.1.2 2 33.32 even 2
7744.2.a.bx.1.1 2 8.5 even 2
7744.2.a.bx.1.1 2 88.21 odd 2
7744.2.a.cn.1.2 2 8.3 odd 2
7744.2.a.cn.1.2 2 88.43 even 2