Properties

Label 121.4.a.a.1.1
Level $121$
Weight $4$
Character 121.1
Self dual yes
Analytic conductor $7.139$
Analytic rank $0$
Dimension $1$
CM discriminant -11
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [121,4,Mod(1,121)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(121, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("121.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 121 = 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 121.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: \(7.13923111069\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $N(\mathrm{U}(1))$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 121.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+8.00000 q^{3} -8.00000 q^{4} +18.0000 q^{5} +37.0000 q^{9} +O(q^{10})\) \(q+8.00000 q^{3} -8.00000 q^{4} +18.0000 q^{5} +37.0000 q^{9} -64.0000 q^{12} +144.000 q^{15} +64.0000 q^{16} -144.000 q^{20} -108.000 q^{23} +199.000 q^{25} +80.0000 q^{27} +340.000 q^{31} -296.000 q^{36} -434.000 q^{37} +666.000 q^{45} -36.0000 q^{47} +512.000 q^{48} -343.000 q^{49} -738.000 q^{53} -720.000 q^{59} -1152.00 q^{60} -512.000 q^{64} -416.000 q^{67} -864.000 q^{69} +612.000 q^{71} +1592.00 q^{75} +1152.00 q^{80} -359.000 q^{81} +1674.00 q^{89} +864.000 q^{92} +2720.00 q^{93} -34.0000 q^{97} +O(q^{100})\)

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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) 8.00000 1.53960 0.769800 0.638285i \(-0.220356\pi\)
0.769800 + 0.638285i \(0.220356\pi\)
\(4\) −8.00000 −1.00000
\(5\) 18.0000 1.60997 0.804984 0.593296i \(-0.202174\pi\)
0.804984 + 0.593296i \(0.202174\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 37.0000 1.37037
\(10\) 0 0
\(11\) 0 0
\(12\) −64.0000 −1.53960
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 144.000 2.47871
\(16\) 64.0000 1.00000
\(17\) 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 \(0.5\pi\)
\(20\) −144.000 −1.60997
\(21\) 0 0
\(22\) 0 0
\(23\) −108.000 −0.979111 −0.489556 0.871972i \(-0.662841\pi\)
−0.489556 + 0.871972i \(0.662841\pi\)
\(24\) 0 0
\(25\) 199.000 1.59200
\(26\) 0 0
\(27\) 80.0000 0.570222
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 340.000 1.96986 0.984932 0.172940i \(-0.0553268\pi\)
0.984932 + 0.172940i \(0.0553268\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −296.000 −1.37037
\(37\) −434.000 −1.92836 −0.964178 0.265257i \(-0.914543\pi\)
−0.964178 + 0.265257i \(0.914543\pi\)
\(38\) 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
\(45\) 666.000 2.20625
\(46\) 0 0
\(47\) −36.0000 −0.111726 −0.0558632 0.998438i \(-0.517791\pi\)
−0.0558632 + 0.998438i \(0.517791\pi\)
\(48\) 512.000 1.53960
\(49\) −343.000 −1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −738.000 −1.91268 −0.956341 0.292255i \(-0.905595\pi\)
−0.956341 + 0.292255i \(0.905595\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −720.000 −1.58875 −0.794373 0.607430i \(-0.792200\pi\)
−0.794373 + 0.607430i \(0.792200\pi\)
\(60\) −1152.00 −2.47871
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −512.000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −416.000 −0.758545 −0.379272 0.925285i \(-0.623826\pi\)
−0.379272 + 0.925285i \(0.623826\pi\)
\(68\) 0 0
\(69\) −864.000 −1.50744
\(70\) 0 0
\(71\) 612.000 1.02297 0.511486 0.859292i \(-0.329095\pi\)
0.511486 + 0.859292i \(0.329095\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 1592.00 2.45104
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 1152.00 1.60997
\(81\) −359.000 −0.492455
\(82\) 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
\(89\) 1674.00 1.99375 0.996874 0.0790026i \(-0.0251735\pi\)
0.996874 + 0.0790026i \(0.0251735\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 864.000 0.979111
\(93\) 2720.00 3.03280
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −34.0000 −0.0355895 −0.0177947 0.999842i \(-0.505665\pi\)
−0.0177947 + 0.999842i \(0.505665\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1592.00 −1.59200
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 1172.00 1.12117 0.560585 0.828097i \(-0.310576\pi\)
0.560585 + 0.828097i \(0.310576\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) −640.000 −0.570222
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) −3472.00 −2.96890
\(112\) 0 0
\(113\) 2142.00 1.78321 0.891604 0.452817i \(-0.149581\pi\)
0.891604 + 0.452817i \(0.149581\pi\)
\(114\) 0 0
\(115\) −1944.00 −1.57634
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) −2720.00 −1.96986
\(125\) 1332.00 0.953102
\(126\) 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
\(135\) 1440.00 0.918040
\(136\) 0 0
\(137\) 1206.00 0.752084 0.376042 0.926603i \(-0.377285\pi\)
0.376042 + 0.926603i \(0.377285\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −288.000 −0.172014
\(142\) 0 0
\(143\) 0 0
\(144\) 2368.00 1.37037
\(145\) 0 0
\(146\) 0 0
\(147\) −2744.00 −1.53960
\(148\) 3472.00 1.92836
\(149\) 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
\(155\) 6120.00 3.17142
\(156\) 0 0
\(157\) −1334.00 −0.678120 −0.339060 0.940765i \(-0.610109\pi\)
−0.339060 + 0.940765i \(0.610109\pi\)
\(158\) 0 0
\(159\) −5904.00 −2.94477
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 3728.00 1.79141 0.895704 0.444651i \(-0.146672\pi\)
0.895704 + 0.444651i \(0.146672\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −2197.00 −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
\(177\) −5760.00 −2.44603
\(178\) 0 0
\(179\) −2016.00 −0.841804 −0.420902 0.907106i \(-0.638286\pi\)
−0.420902 + 0.907106i \(0.638286\pi\)
\(180\) −5328.00 −2.20625
\(181\) −2050.00 −0.841852 −0.420926 0.907095i \(-0.638295\pi\)
−0.420926 + 0.907095i \(0.638295\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −7812.00 −3.10459
\(186\) 0 0
\(187\) 0 0
\(188\) 288.000 0.111726
\(189\) 0 0
\(190\) 0 0
\(191\) 5220.00 1.97752 0.988759 0.149518i \(-0.0477722\pi\)
0.988759 + 0.149518i \(0.0477722\pi\)
\(192\) −4096.00 −1.53960
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 2744.00 1.00000
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 3940.00 1.40351 0.701757 0.712417i \(-0.252399\pi\)
0.701757 + 0.712417i \(0.252399\pi\)
\(200\) 0 0
\(201\) −3328.00 −1.16786
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −3996.00 −1.34174
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 5904.00 1.91268
\(213\) 4896.00 1.57497
\(214\) 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
\(223\) 668.000 0.200595 0.100297 0.994958i \(-0.468021\pi\)
0.100297 + 0.994958i \(0.468021\pi\)
\(224\) 0 0
\(225\) 7363.00 2.18163
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 3310.00 0.955157 0.477579 0.878589i \(-0.341515\pi\)
0.477579 + 0.878589i \(0.341515\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) −648.000 −0.179876
\(236\) 5760.00 1.58875
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 9216.00 2.47871
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 0 0
\(243\) −5032.00 −1.32841
\(244\) 0 0
\(245\) −6174.00 −1.60997
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 648.000 0.162954 0.0814769 0.996675i \(-0.474036\pi\)
0.0814769 + 0.996675i \(0.474036\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 4096.00 1.00000
\(257\) −8046.00 −1.95290 −0.976451 0.215740i \(-0.930784\pi\)
−0.976451 + 0.215740i \(0.930784\pi\)
\(258\) 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
\(265\) −13284.0 −3.07936
\(266\) 0 0
\(267\) 13392.0 3.06958
\(268\) 3328.00 0.758545
\(269\) 2790.00 0.632377 0.316188 0.948696i \(-0.397597\pi\)
0.316188 + 0.948696i \(0.397597\pi\)
\(270\) 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
\(276\) 6912.00 1.50744
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 12580.0 2.69944
\(280\) 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 \(0.5\pi\)
\(284\) −4896.00 −1.02297
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −4913.00 −1.00000
\(290\) 0 0
\(291\) −272.000 −0.0547935
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) −12960.0 −2.55783
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −12736.0 −2.45104
\(301\) 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
\(309\) 9376.00 1.72616
\(310\) 0 0
\(311\) 9468.00 1.72631 0.863153 0.504943i \(-0.168486\pi\)
0.863153 + 0.504943i \(0.168486\pi\)
\(312\) 0 0
\(313\) −10982.0 −1.98319 −0.991596 0.129370i \(-0.958705\pi\)
−0.991596 + 0.129370i \(0.958705\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5994.00 1.06201 0.531004 0.847369i \(-0.321815\pi\)
0.531004 + 0.847369i \(0.321815\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −9216.00 −1.60997
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 2872.00 0.492455
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 8120.00 1.34839 0.674193 0.738555i \(-0.264492\pi\)
0.674193 + 0.738555i \(0.264492\pi\)
\(332\) 0 0
\(333\) −16058.0 −2.64256
\(334\) 0 0
\(335\) −7488.00 −1.22123
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0 0
\(339\) 17136.0 2.74543
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −15552.0 −2.42693
\(346\) 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
\(353\) 8802.00 1.32715 0.663574 0.748111i \(-0.269039\pi\)
0.663574 + 0.748111i \(0.269039\pi\)
\(354\) 0 0
\(355\) 11016.0 1.64695
\(356\) −13392.0 −1.99375
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −6859.00 −1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −9916.00 −1.41038 −0.705192 0.709016i \(-0.749139\pi\)
−0.705192 + 0.709016i \(0.749139\pi\)
\(368\) −6912.00 −0.979111
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −21760.0 −3.03280
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 10656.0 1.46740
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 12800.0 1.73481 0.867403 0.497605i \(-0.165787\pi\)
0.867403 + 0.497605i \(0.165787\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 14508.0 1.93557 0.967786 0.251774i \(-0.0810139\pi\)
0.967786 + 0.251774i \(0.0810139\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 272.000 0.0355895
\(389\) 14130.0 1.84170 0.920848 0.389923i \(-0.127498\pi\)
0.920848 + 0.389923i \(0.127498\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −2374.00 −0.300120 −0.150060 0.988677i \(-0.547947\pi\)
−0.150060 + 0.988677i \(0.547947\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 12736.0 1.59200
\(401\) −9090.00 −1.13200 −0.566001 0.824404i \(-0.691510\pi\)
−0.566001 + 0.824404i \(0.691510\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −6462.00 −0.792838
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) 9648.00 1.15791
\(412\) −9376.00 −1.12117
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −16344.0 −1.90562 −0.952812 0.303560i \(-0.901825\pi\)
−0.952812 + 0.303560i \(0.901825\pi\)
\(420\) 0 0
\(421\) −11630.0 −1.34635 −0.673173 0.739485i \(-0.735069\pi\)
−0.673173 + 0.739485i \(0.735069\pi\)
\(422\) 0 0
\(423\) −1332.00 −0.153107
\(424\) 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 \(0.5\pi\)
\(432\) 5120.00 0.570222
\(433\) −13282.0 −1.47412 −0.737058 0.675830i \(-0.763786\pi\)
−0.737058 + 0.675830i \(0.763786\pi\)
\(434\) 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
\(441\) −12691.0 −1.37037
\(442\) 0 0
\(443\) −18648.0 −1.99998 −0.999992 0.00391276i \(-0.998755\pi\)
−0.999992 + 0.00391276i \(0.998755\pi\)
\(444\) 27776.0 2.96890
\(445\) 30132.0 3.20987
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6786.00 0.713254 0.356627 0.934247i \(-0.383927\pi\)
0.356627 + 0.934247i \(0.383927\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −17136.0 −1.78321
\(453\) 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
\(460\) 15552.0 1.57634
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 13268.0 1.33178 0.665892 0.746048i \(-0.268051\pi\)
0.665892 + 0.746048i \(0.268051\pi\)
\(464\) 0 0
\(465\) 48960.0 4.88272
\(466\) 0 0
\(467\) 4176.00 0.413795 0.206897 0.978363i \(-0.433663\pi\)
0.206897 + 0.978363i \(0.433663\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −10672.0 −1.04403
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −27306.0 −2.62108
\(478\) 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
\(485\) −612.000 −0.0572979
\(486\) 0 0
\(487\) 16684.0 1.55241 0.776206 0.630480i \(-0.217142\pi\)
0.776206 + 0.630480i \(0.217142\pi\)
\(488\) 0 0
\(489\) 29824.0 2.75805
\(490\) 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
\(496\) 21760.0 1.96986
\(497\) 0 0
\(498\) 0 0
\(499\) 4120.00 0.369612 0.184806 0.982775i \(-0.440834\pi\)
0.184806 + 0.982775i \(0.440834\pi\)
\(500\) −10656.0 −0.953102
\(501\) 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
\(507\) −17576.0 −1.53960
\(508\) 0 0
\(509\) −22410.0 −1.95148 −0.975742 0.218922i \(-0.929746\pi\)
−0.975742 + 0.218922i \(0.929746\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 21096.0 1.80505
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 20070.0 1.68768 0.843841 0.536593i \(-0.180289\pi\)
0.843841 + 0.536593i \(0.180289\pi\)
\(522\) 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
\(529\) −503.000 −0.0413413
\(530\) 0 0
\(531\) −26640.0 −2.17717
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −16128.0 −1.29604
\(538\) 0 0
\(539\) 0 0
\(540\) −11520.0 −0.918040
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 0 0
\(543\) −16400.0 −1.29612
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) −9648.00 −0.752084
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −62496.0 −4.77983
\(556\) 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 \(0.5\pi\)
\(564\) 2304.00 0.172014
\(565\) 38556.0 2.87091
\(566\) 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
\(573\) 41760.0 3.04459
\(574\) 0 0
\(575\) −21492.0 −1.55874
\(576\) −18944.0 −1.37037
\(577\) −22466.0 −1.62092 −0.810461 0.585793i \(-0.800783\pi\)
−0.810461 + 0.585793i \(0.800783\pi\)
\(578\) 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
\(587\) −26064.0 −1.83267 −0.916334 0.400414i \(-0.868866\pi\)
−0.916334 + 0.400414i \(0.868866\pi\)
\(588\) 21952.0 1.53960
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −27776.0 −1.92836
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 31520.0 2.16085
\(598\) 0 0
\(599\) 18036.0 1.23027 0.615134 0.788422i \(-0.289102\pi\)
0.615134 + 0.788422i \(0.289102\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) 0 0
\(603\) −15392.0 −1.03949
\(604\) 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
\(617\) 3654.00 0.238419 0.119209 0.992869i \(-0.461964\pi\)
0.119209 + 0.992869i \(0.461964\pi\)
\(618\) 0 0
\(619\) 1856.00 0.120515 0.0602576 0.998183i \(-0.480808\pi\)
0.0602576 + 0.998183i \(0.480808\pi\)
\(620\) −48960.0 −3.17142
\(621\) −8640.00 −0.558311
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −899.000 −0.0575360
\(626\) 0 0
\(627\) 0 0
\(628\) 10672.0 0.678120
\(629\) 0 0
\(630\) 0 0
\(631\) −12908.0 −0.814357 −0.407179 0.913349i \(-0.633487\pi\)
−0.407179 + 0.913349i \(0.633487\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 47232.0 2.94477
\(637\) 0 0
\(638\) 0 0
\(639\) 22644.0 1.40185
\(640\) 0 0
\(641\) −4590.00 −0.282830 −0.141415 0.989950i \(-0.545165\pi\)
−0.141415 + 0.989950i \(0.545165\pi\)
\(642\) 0 0
\(643\) −10168.0 −0.623619 −0.311809 0.950145i \(-0.600935\pi\)
−0.311809 + 0.950145i \(0.600935\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 32724.0 1.98843 0.994214 0.107416i \(-0.0342575\pi\)
0.994214 + 0.107416i \(0.0342575\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −29824.0 −1.79141
\(653\) 32742.0 1.96216 0.981082 0.193591i \(-0.0620135\pi\)
0.981082 + 0.193591i \(0.0620135\pi\)
\(654\) 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
\(661\) −23582.0 −1.38765 −0.693823 0.720146i \(-0.744075\pi\)
−0.693823 + 0.720146i \(0.744075\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 5344.00 0.308836
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 15920.0 0.907794
\(676\) 17576.0 1.00000
\(677\) 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
\(683\) −35352.0 −1.98054 −0.990268 0.139170i \(-0.955556\pi\)
−0.990268 + 0.139170i \(0.955556\pi\)
\(684\) 0 0
\(685\) 21708.0 1.21083
\(686\) 0 0
\(687\) 26480.0 1.47056
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −30328.0 −1.66965 −0.834827 0.550512i \(-0.814433\pi\)
−0.834827 + 0.550512i \(0.814433\pi\)
\(692\) 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
\(705\) −5184.00 −0.276937
\(706\) 0 0
\(707\) 0 0
\(708\) 46080.0 2.44603
\(709\) −33554.0 −1.77736 −0.888679 0.458530i \(-0.848376\pi\)
−0.888679 + 0.458530i \(0.848376\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −36720.0 −1.92872
\(714\) 0 0
\(715\) 0 0
\(716\) 16128.0 0.841804
\(717\) 0 0
\(718\) 0 0
\(719\) 22644.0 1.17452 0.587259 0.809399i \(-0.300207\pi\)
0.587259 + 0.809399i \(0.300207\pi\)
\(720\) 42624.0 2.20625
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 16400.0 0.841852
\(725\) 0 0
\(726\) 0 0
\(727\) −33284.0 −1.69799 −0.848993 0.528405i \(-0.822790\pi\)
−0.848993 + 0.528405i \(0.822790\pi\)
\(728\) 0 0
\(729\) −30563.0 −1.55276
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) −49392.0 −2.47871
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 62496.0 3.10459
\(741\) 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
\(751\) 39652.0 1.92666 0.963330 0.268319i \(-0.0864680\pi\)
0.963330 + 0.268319i \(0.0864680\pi\)
\(752\) −2304.00 −0.111726
\(753\) 5184.00 0.250884
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 31426.0 1.50885 0.754424 0.656388i \(-0.227916\pi\)
0.754424 + 0.656388i \(0.227916\pi\)
\(758\) 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
\(764\) −41760.0 −1.97752
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 32768.0 1.53960
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) −64368.0 −3.00669
\(772\) 0 0
\(773\) 32238.0 1.50003 0.750013 0.661423i \(-0.230047\pi\)
0.750013 + 0.661423i \(0.230047\pi\)
\(774\) 0 0
\(775\) 67660.0 3.13602
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −21952.0 −1.00000
\(785\) −24012.0 −1.09175
\(786\) 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
\(795\) −106272. −4.74098
\(796\) −31520.0 −1.40351
\(797\) 7146.00 0.317596 0.158798 0.987311i \(-0.449238\pi\)
0.158798 + 0.987311i \(0.449238\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 61938.0 2.73217
\(802\) 0 0
\(803\) 0 0
\(804\) 26624.0 1.16786
\(805\) 0 0
\(806\) 0 0
\(807\) 22320.0 0.973607
\(808\) 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
\(815\) 67104.0 2.88411
\(816\) 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
\(823\) 3332.00 0.141125 0.0705627 0.997507i \(-0.477521\pi\)
0.0705627 + 0.997507i \(0.477521\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 31968.0 1.34174
\(829\) −47734.0 −1.99984 −0.999922 0.0125057i \(-0.996019\pi\)
−0.999922 + 0.0125057i \(0.996019\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 27200.0 1.12326
\(838\) 0 0
\(839\) 22140.0 0.911034 0.455517 0.890227i \(-0.349454\pi\)
0.455517 + 0.890227i \(0.349454\pi\)
\(840\) 0 0
\(841\) −24389.0 −1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −39546.0 −1.60997
\(846\) 0 0
\(847\) 0 0
\(848\) −47232.0 −1.91268
\(849\) 0 0
\(850\) 0 0
\(851\) 46872.0 1.88807
\(852\) −39168.0 −1.57497
\(853\) 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
\(859\) 50096.0 1.98982 0.994909 0.100779i \(-0.0321334\pi\)
0.994909 + 0.100779i \(0.0321334\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 46548.0 1.83605 0.918026 0.396521i \(-0.129783\pi\)
0.918026 + 0.396521i \(0.129783\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −39304.0 −1.53960
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −1258.00 −0.0487707
\(874\) 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
\(881\) 34542.0 1.32094 0.660471 0.750852i \(-0.270357\pi\)
0.660471 + 0.750852i \(0.270357\pi\)
\(882\) 0 0
\(883\) −27272.0 −1.03938 −0.519692 0.854354i \(-0.673953\pi\)
−0.519692 + 0.854354i \(0.673953\pi\)
\(884\) 0 0
\(885\) −103680. −3.93804
\(886\) 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
\(892\) −5344.00 −0.200595
\(893\) 0 0
\(894\) 0 0
\(895\) −36288.0 −1.35528
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −58904.0 −2.18163
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −36900.0 −1.35536
\(906\) 0 0
\(907\) −21256.0 −0.778163 −0.389082 0.921203i \(-0.627208\pi\)
−0.389082 + 0.921203i \(0.627208\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −52020.0 −1.89188 −0.945938 0.324347i \(-0.894856\pi\)
−0.945938 + 0.324347i \(0.894856\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −26480.0 −0.955157
\(917\) 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
\(925\) −86366.0 −3.06994
\(926\) 0 0
\(927\) 43364.0 1.53642
\(928\) 0 0
\(929\) −56610.0 −1.99926 −0.999631 0.0271744i \(-0.991349\pi\)
−0.999631 + 0.0271744i \(0.991349\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 75744.0 2.65782
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 0 0
\(939\) −87856.0 −3.05333
\(940\) 5184.00 0.179876
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −46080.0 −1.58875
\(945\) 0 0
\(946\) 0 0
\(947\) 23256.0 0.798013 0.399007 0.916948i \(-0.369355\pi\)
0.399007 + 0.916948i \(0.369355\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 47952.0 1.63507
\(952\) 0 0
\(953\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 0 0
\(955\) 93960.0 3.18374
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −73728.0 −2.47871
\(961\) 85809.0 2.88037
\(962\) 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
\(971\) 39960.0 1.32068 0.660339 0.750968i \(-0.270413\pi\)
0.660339 + 0.750968i \(0.270413\pi\)
\(972\) 40256.0 1.32841
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 59454.0 1.94688 0.973440 0.228942i \(-0.0735266\pi\)
0.973440 + 0.228942i \(0.0735266\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 49392.0 1.60997
\(981\) 0 0
\(982\) 0 0
\(983\) −17748.0 −0.575863 −0.287931 0.957651i \(-0.592968\pi\)
−0.287931 + 0.957651i \(0.592968\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 51460.0 1.64953 0.824763 0.565478i \(-0.191308\pi\)
0.824763 + 0.565478i \(0.191308\pi\)
\(992\) 0 0
\(993\) 64960.0 2.07598
\(994\) 0 0
\(995\) 70920.0 2.25961
\(996\) 0 0
\(997\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) 0 0
\(999\) −34720.0 −1.09959
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 121.4.a.a.1.1 1
3.2 odd 2 1089.4.a.f.1.1 1
4.3 odd 2 1936.4.a.a.1.1 1
11.2 odd 10 121.4.c.a.81.1 4
11.3 even 5 121.4.c.a.9.1 4
11.4 even 5 121.4.c.a.27.1 4
11.5 even 5 121.4.c.a.3.1 4
11.6 odd 10 121.4.c.a.3.1 4
11.7 odd 10 121.4.c.a.27.1 4
11.8 odd 10 121.4.c.a.9.1 4
11.9 even 5 121.4.c.a.81.1 4
11.10 odd 2 CM 121.4.a.a.1.1 1
33.32 even 2 1089.4.a.f.1.1 1
44.43 even 2 1936.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
121.4.a.a.1.1 1 1.1 even 1 trivial
121.4.a.a.1.1 1 11.10 odd 2 CM
121.4.c.a.3.1 4 11.5 even 5
121.4.c.a.3.1 4 11.6 odd 10
121.4.c.a.9.1 4 11.3 even 5
121.4.c.a.9.1 4 11.8 odd 10
121.4.c.a.27.1 4 11.4 even 5
121.4.c.a.27.1 4 11.7 odd 10
121.4.c.a.81.1 4 11.2 odd 10
121.4.c.a.81.1 4 11.9 even 5
1089.4.a.f.1.1 1 3.2 odd 2
1089.4.a.f.1.1 1 33.32 even 2
1936.4.a.a.1.1 1 4.3 odd 2
1936.4.a.a.1.1 1 44.43 even 2