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Properties

Label 11.3.b.a.10.1
Level $11$
Weight $3$
Character 11.10
Self dual yes
Analytic conductor $0.300$
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] = [11,3,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, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.10");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 3 \)
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: \(0.299728290796\)
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)
 
\(f(q)\) \(=\) \(q-5.00000 q^{3} +4.00000 q^{4} -1.00000 q^{5} +16.0000 q^{9} +O(q^{10})\) \(q-5.00000 q^{3} +4.00000 q^{4} -1.00000 q^{5} +16.0000 q^{9} -11.0000 q^{11} -20.0000 q^{12} +5.00000 q^{15} +16.0000 q^{16} -4.00000 q^{20} +35.0000 q^{23} -24.0000 q^{25} -35.0000 q^{27} -37.0000 q^{31} +55.0000 q^{33} +64.0000 q^{36} -25.0000 q^{37} -44.0000 q^{44} -16.0000 q^{45} +50.0000 q^{47} -80.0000 q^{48} +49.0000 q^{49} -70.0000 q^{53} +11.0000 q^{55} +107.000 q^{59} +20.0000 q^{60} +64.0000 q^{64} +35.0000 q^{67} -175.000 q^{69} -133.000 q^{71} +120.000 q^{75} -16.0000 q^{80} +31.0000 q^{81} -97.0000 q^{89} +140.000 q^{92} +185.000 q^{93} +95.0000 q^{97} -176.000 q^{99} +O(q^{100})\)

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 \(\pi\)
\(3\) −5.00000 −1.66667 −0.833333 − 0.552771i \(-0.813571\pi\)
−0.833333 + 0.552771i \(0.813571\pi\)
\(4\) 4.00000 1.00000
\(5\) −1.00000 −0.200000 −0.100000 − 0.994987i \(-0.531884\pi\)
−0.100000 + 0.994987i \(0.531884\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 0 0
\(9\) 16.0000 1.77778
\(10\) 0 0
\(11\) −11.0000 −1.00000
\(12\) −20.0000 −1.66667
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 5.00000 0.333333
\(16\) 16.0000 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −4.00000 −0.200000
\(21\) 0 0
\(22\) 0 0
\(23\) 35.0000 1.52174 0.760870 − 0.648905i \(-0.224773\pi\)
0.760870 + 0.648905i \(0.224773\pi\)
\(24\) 0 0
\(25\) −24.0000 −0.960000
\(26\) 0 0
\(27\) −35.0000 −1.29630
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −37.0000 −1.19355 −0.596774 − 0.802409i \(-0.703551\pi\)
−0.596774 + 0.802409i \(0.703551\pi\)
\(32\) 0 0
\(33\) 55.0000 1.66667
\(34\) 0 0
\(35\) 0 0
\(36\) 64.0000 1.77778
\(37\) −25.0000 −0.675676 −0.337838 − 0.941204i \(-0.609696\pi\)
−0.337838 + 0.941204i \(0.609696\pi\)
\(38\) 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 \(\pi\)
\(44\) −44.0000 −1.00000
\(45\) −16.0000 −0.355556
\(46\) 0 0
\(47\) 50.0000 1.06383 0.531915 − 0.846798i \(-0.321473\pi\)
0.531915 + 0.846798i \(0.321473\pi\)
\(48\) −80.0000 −1.66667
\(49\) 49.0000 1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −70.0000 −1.32075 −0.660377 − 0.750934i \(-0.729604\pi\)
−0.660377 + 0.750934i \(0.729604\pi\)
\(54\) 0 0
\(55\) 11.0000 0.200000
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 107.000 1.81356 0.906780 − 0.421605i \(-0.138533\pi\)
0.906780 + 0.421605i \(0.138533\pi\)
\(60\) 20.0000 0.333333
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 64.0000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 35.0000 0.522388 0.261194 − 0.965286i \(-0.415884\pi\)
0.261194 + 0.965286i \(0.415884\pi\)
\(68\) 0 0
\(69\) −175.000 −2.53623
\(70\) 0 0
\(71\) −133.000 −1.87324 −0.936620 − 0.350348i \(-0.886063\pi\)
−0.936620 + 0.350348i \(0.886063\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 120.000 1.60000
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −16.0000 −0.200000
\(81\) 31.0000 0.382716
\(82\) 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
\(89\) −97.0000 −1.08989 −0.544944 − 0.838473i \(-0.683449\pi\)
−0.544944 + 0.838473i \(0.683449\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 140.000 1.52174
\(93\) 185.000 1.98925
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 95.0000 0.979381 0.489691 − 0.871896i \(-0.337110\pi\)
0.489691 + 0.871896i \(0.337110\pi\)
\(98\) 0 0
\(99\) −176.000 −1.77778
\(100\) −96.0000 −0.960000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −190.000 −1.84466 −0.922330 − 0.386403i \(-0.873717\pi\)
−0.922330 + 0.386403i \(0.873717\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −140.000 −1.29630
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 125.000 1.12613
\(112\) 0 0
\(113\) 215.000 1.90265 0.951327 − 0.308182i \(-0.0997206\pi\)
0.951327 + 0.308182i \(0.0997206\pi\)
\(114\) 0 0
\(115\) −35.0000 −0.304348
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 121.000 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) −148.000 −1.19355
\(125\) 49.0000 0.392000
\(126\) 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 \(\pi\)
\(132\) 220.000 1.66667
\(133\) 0 0
\(134\) 0 0
\(135\) 35.0000 0.259259
\(136\) 0 0
\(137\) −265.000 −1.93431 −0.967153 − 0.254194i \(-0.918190\pi\)
−0.967153 + 0.254194i \(0.918190\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) −250.000 −1.77305
\(142\) 0 0
\(143\) 0 0
\(144\) 256.000 1.77778
\(145\) 0 0
\(146\) 0 0
\(147\) −245.000 −1.66667
\(148\) −100.000 −0.675676
\(149\) 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
\(155\) 37.0000 0.238710
\(156\) 0 0
\(157\) 215.000 1.36943 0.684713 − 0.728812i \(-0.259927\pi\)
0.684713 + 0.728812i \(0.259927\pi\)
\(158\) 0 0
\(159\) 350.000 2.20126
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −70.0000 −0.429448 −0.214724 − 0.976675i \(-0.568885\pi\)
−0.214724 + 0.976675i \(0.568885\pi\)
\(164\) 0 0
\(165\) −55.0000 −0.333333
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 169.000 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
\(176\) −176.000 −1.00000
\(177\) −535.000 −3.02260
\(178\) 0 0
\(179\) 83.0000 0.463687 0.231844 − 0.972753i \(-0.425524\pi\)
0.231844 + 0.972753i \(0.425524\pi\)
\(180\) −64.0000 −0.355556
\(181\) 263.000 1.45304 0.726519 − 0.687146i \(-0.241137\pi\)
0.726519 + 0.687146i \(0.241137\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 25.0000 0.135135
\(186\) 0 0
\(187\) 0 0
\(188\) 200.000 1.06383
\(189\) 0 0
\(190\) 0 0
\(191\) −157.000 −0.821990 −0.410995 − 0.911638i \(-0.634819\pi\)
−0.410995 + 0.911638i \(0.634819\pi\)
\(192\) −320.000 −1.66667
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 196.000 1.00000
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 2.00000 0.0100503 0.00502513 − 0.999987i \(-0.498400\pi\)
0.00502513 + 0.999987i \(0.498400\pi\)
\(200\) 0 0
\(201\) −175.000 −0.870647
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 560.000 2.70531
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) −280.000 −1.32075
\(213\) 665.000 3.12207
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 44.0000 0.200000
\(221\) 0 0
\(222\) 0 0
\(223\) −445.000 −1.99552 −0.997758 − 0.0669274i \(-0.978680\pi\)
−0.997758 + 0.0669274i \(0.978680\pi\)
\(224\) 0 0
\(225\) −384.000 −1.70667
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) −433.000 −1.89083 −0.945415 − 0.325869i \(-0.894343\pi\)
−0.945415 + 0.325869i \(0.894343\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) −50.0000 −0.212766
\(236\) 428.000 1.81356
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 80.0000 0.333333
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 160.000 0.658436
\(244\) 0 0
\(245\) −49.0000 −0.200000
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 227.000 0.904382 0.452191 − 0.891921i \(-0.350642\pi\)
0.452191 + 0.891921i \(0.350642\pi\)
\(252\) 0 0
\(253\) −385.000 −1.52174
\(254\) 0 0
\(255\) 0 0
\(256\) 256.000 1.00000
\(257\) −190.000 −0.739300 −0.369650 − 0.929171i \(-0.620522\pi\)
−0.369650 + 0.929171i \(0.620522\pi\)
\(258\) 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
\(265\) 70.0000 0.264151
\(266\) 0 0
\(267\) 485.000 1.81648
\(268\) 140.000 0.522388
\(269\) 362.000 1.34572 0.672862 − 0.739768i \(-0.265065\pi\)
0.672862 + 0.739768i \(0.265065\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 264.000 0.960000
\(276\) −700.000 −2.53623
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) −592.000 −2.12186
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) −532.000 −1.87324
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 289.000 1.00000
\(290\) 0 0
\(291\) −475.000 −1.63230
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) −107.000 −0.362712
\(296\) 0 0
\(297\) 385.000 1.29630
\(298\) 0 0
\(299\) 0 0
\(300\) 480.000 1.60000
\(301\) 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
\(309\) 950.000 3.07443
\(310\) 0 0
\(311\) −478.000 −1.53698 −0.768489 − 0.639863i \(-0.778991\pi\)
−0.768489 + 0.639863i \(0.778991\pi\)
\(312\) 0 0
\(313\) −265.000 −0.846645 −0.423323 − 0.905979i \(-0.639136\pi\)
−0.423323 + 0.905979i \(0.639136\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 95.0000 0.299685 0.149842 − 0.988710i \(-0.452123\pi\)
0.149842 + 0.988710i \(0.452123\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −64.0000 −0.200000
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 124.000 0.382716
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 563.000 1.70091 0.850453 − 0.526051i \(-0.176328\pi\)
0.850453 + 0.526051i \(0.176328\pi\)
\(332\) 0 0
\(333\) −400.000 −1.20120
\(334\) 0 0
\(335\) −35.0000 −0.104478
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) −1075.00 −3.17109
\(340\) 0 0
\(341\) 407.000 1.19355
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 175.000 0.507246
\(346\) 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
\(353\) −625.000 −1.77054 −0.885269 − 0.465079i \(-0.846026\pi\)
−0.885269 + 0.465079i \(0.846026\pi\)
\(354\) 0 0
\(355\) 133.000 0.374648
\(356\) −388.000 −1.08989
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 361.000 1.00000
\(362\) 0 0
\(363\) −605.000 −1.66667
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 635.000 1.73025 0.865123 − 0.501560i \(-0.167241\pi\)
0.865123 + 0.501560i \(0.167241\pi\)
\(368\) 560.000 1.52174
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 740.000 1.98925
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) −245.000 −0.653333
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −133.000 −0.350923 −0.175462 − 0.984486i \(-0.556142\pi\)
−0.175462 + 0.984486i \(0.556142\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 755.000 1.97128 0.985640 − 0.168862i \(-0.0540093\pi\)
0.985640 + 0.168862i \(0.0540093\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 380.000 0.979381
\(389\) −553.000 −1.42159 −0.710797 − 0.703397i \(-0.751666\pi\)
−0.710797 + 0.703397i \(0.751666\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −704.000 −1.77778
\(397\) −790.000 −1.98992 −0.994962 − 0.100251i \(-0.968036\pi\)
−0.994962 + 0.100251i \(0.968036\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −384.000 −0.960000
\(401\) 98.0000 0.244389 0.122195 − 0.992506i \(-0.461007\pi\)
0.122195 + 0.992506i \(0.461007\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −31.0000 −0.0765432
\(406\) 0 0
\(407\) 275.000 0.675676
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 1325.00 3.22384
\(412\) −760.000 −1.84466
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −262.000 −0.625298 −0.312649 − 0.949869i \(-0.601216\pi\)
−0.312649 + 0.949869i \(0.601216\pi\)
\(420\) 0 0
\(421\) −742.000 −1.76247 −0.881235 − 0.472678i \(-0.843287\pi\)
−0.881235 + 0.472678i \(0.843287\pi\)
\(422\) 0 0
\(423\) 800.000 1.89125
\(424\) 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 \(\pi\)
\(432\) −560.000 −1.29630
\(433\) −25.0000 −0.0577367 −0.0288684 − 0.999583i \(-0.509190\pi\)
−0.0288684 + 0.999583i \(0.509190\pi\)
\(434\) 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
\(441\) 784.000 1.77778
\(442\) 0 0
\(443\) −445.000 −1.00451 −0.502257 − 0.864718i \(-0.667497\pi\)
−0.502257 + 0.864718i \(0.667497\pi\)
\(444\) 500.000 1.12613
\(445\) 97.0000 0.217978
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 623.000 1.38753 0.693764 − 0.720202i \(-0.255951\pi\)
0.693764 + 0.720202i \(0.255951\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 860.000 1.90265
\(453\) 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
\(460\) −140.000 −0.304348
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 35.0000 0.0755940 0.0377970 − 0.999285i \(-0.487966\pi\)
0.0377970 + 0.999285i \(0.487966\pi\)
\(464\) 0 0
\(465\) −185.000 −0.397849
\(466\) 0 0
\(467\) −925.000 −1.98073 −0.990364 − 0.138489i \(-0.955776\pi\)
−0.990364 + 0.138489i \(0.955776\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1075.00 −2.28238
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1120.00 −2.34801
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 484.000 1.00000
\(485\) −95.0000 −0.195876
\(486\) 0 0
\(487\) 875.000 1.79671 0.898357 − 0.439266i \(-0.144761\pi\)
0.898357 + 0.439266i \(0.144761\pi\)
\(488\) 0 0
\(489\) 350.000 0.715746
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 176.000 0.355556
\(496\) −592.000 −1.19355
\(497\) 0 0
\(498\) 0 0
\(499\) 602.000 1.20641 0.603206 − 0.797585i \(-0.293890\pi\)
0.603206 + 0.797585i \(0.293890\pi\)
\(500\) 196.000 0.392000
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −845.000 −1.66667
\(508\) 0 0
\(509\) 1007.00 1.97839 0.989194 − 0.146609i \(-0.0468360\pi\)
0.989194 + 0.146609i \(0.0468360\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 190.000 0.368932
\(516\) 0 0
\(517\) −550.000 −1.06383
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −817.000 −1.56814 −0.784069 − 0.620674i \(-0.786859\pi\)
−0.784069 + 0.620674i \(0.786859\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 880.000 1.66667
\(529\) 696.000 1.31569
\(530\) 0 0
\(531\) 1712.00 3.22411
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −415.000 −0.772812
\(538\) 0 0
\(539\) −539.000 −1.00000
\(540\) 140.000 0.259259
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −1315.00 −2.42173
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) −1060.00 −1.93431
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −125.000 −0.225225
\(556\) 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 \(\pi\)
\(564\) −1000.00 −1.77305
\(565\) −215.000 −0.380531
\(566\) 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
\(573\) 785.000 1.36998
\(574\) 0 0
\(575\) −840.000 −1.46087
\(576\) 1024.00 1.77778
\(577\) 1055.00 1.82842 0.914211 − 0.405238i \(-0.132811\pi\)
0.914211 + 0.405238i \(0.132811\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 770.000 1.32075
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1130.00 1.92504 0.962521 − 0.271206i \(-0.0874225\pi\)
0.962521 + 0.271206i \(0.0874225\pi\)
\(588\) −980.000 −1.66667
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −400.000 −0.675676
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −10.0000 −0.0167504
\(598\) 0 0
\(599\) 98.0000 0.163606 0.0818030 − 0.996649i \(-0.473932\pi\)
0.0818030 + 0.996649i \(0.473932\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 560.000 0.928690
\(604\) 0 0
\(605\) −121.000 −0.200000
\(606\) 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
\(617\) 530.000 0.858995 0.429498 − 0.903068i \(-0.358691\pi\)
0.429498 + 0.903068i \(0.358691\pi\)
\(618\) 0 0
\(619\) −1237.00 −1.99838 −0.999192 − 0.0401853i \(-0.987205\pi\)
−0.999192 + 0.0401853i \(0.987205\pi\)
\(620\) 148.000 0.238710
\(621\) −1225.00 −1.97262
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 551.000 0.881600
\(626\) 0 0
\(627\) 0 0
\(628\) 860.000 1.36943
\(629\) 0 0
\(630\) 0 0
\(631\) −1213.00 −1.92235 −0.961173 − 0.275947i \(-0.911008\pi\)
−0.961173 + 0.275947i \(0.911008\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 1400.00 2.20126
\(637\) 0 0
\(638\) 0 0
\(639\) −2128.00 −3.33020
\(640\) 0 0
\(641\) 743.000 1.15913 0.579563 − 0.814927i \(-0.303223\pi\)
0.579563 + 0.814927i \(0.303223\pi\)
\(642\) 0 0
\(643\) 395.000 0.614308 0.307154 − 0.951660i \(-0.400623\pi\)
0.307154 + 0.951660i \(0.400623\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −565.000 −0.873261 −0.436631 − 0.899641i \(-0.643828\pi\)
−0.436631 + 0.899641i \(0.643828\pi\)
\(648\) 0 0
\(649\) −1177.00 −1.81356
\(650\) 0 0
\(651\) 0 0
\(652\) −280.000 −0.429448
\(653\) 1295.00 1.98315 0.991577 − 0.129516i \(-0.0413424\pi\)
0.991577 + 0.129516i \(0.0413424\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) −220.000 −0.333333
\(661\) −1153.00 −1.74433 −0.872163 − 0.489215i \(-0.837283\pi\)
−0.872163 + 0.489215i \(0.837283\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 2225.00 3.32586
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 840.000 1.24444
\(676\) 676.000 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
\(683\) −790.000 −1.15666 −0.578331 − 0.815802i \(-0.696296\pi\)
−0.578331 + 0.815802i \(0.696296\pi\)
\(684\) 0 0
\(685\) 265.000 0.386861
\(686\) 0 0
\(687\) 2165.00 3.15138
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −1093.00 −1.58177 −0.790883 − 0.611968i \(-0.790378\pi\)
−0.790883 + 0.611968i \(0.790378\pi\)
\(692\) 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
\(704\) −704.000 −1.00000
\(705\) 250.000 0.354610
\(706\) 0 0
\(707\) 0 0
\(708\) −2140.00 −3.02260
\(709\) −1057.00 −1.49083 −0.745416 − 0.666599i \(-0.767749\pi\)
−0.745416 + 0.666599i \(0.767749\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1295.00 −1.81627
\(714\) 0 0
\(715\) 0 0
\(716\) 332.000 0.463687
\(717\) 0 0
\(718\) 0 0
\(719\) 1163.00 1.61752 0.808762 − 0.588136i \(-0.200138\pi\)
0.808762 + 0.588136i \(0.200138\pi\)
\(720\) −256.000 −0.355556
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 1052.00 1.45304
\(725\) 0 0
\(726\) 0 0
\(727\) 1355.00 1.86382 0.931912 − 0.362685i \(-0.118140\pi\)
0.931912 + 0.362685i \(0.118140\pi\)
\(728\) 0 0
\(729\) −1079.00 −1.48011
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 245.000 0.333333
\(736\) 0 0
\(737\) −385.000 −0.522388
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 100.000 0.135135
\(741\) 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
\(751\) −973.000 −1.29561 −0.647803 − 0.761808i \(-0.724312\pi\)
−0.647803 + 0.761808i \(0.724312\pi\)
\(752\) 800.000 1.06383
\(753\) −1135.00 −1.50730
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −70.0000 −0.0924703 −0.0462351 − 0.998931i \(-0.514722\pi\)
−0.0462351 + 0.998931i \(0.514722\pi\)
\(758\) 0 0
\(759\) 1925.00 2.53623
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −628.000 −0.821990
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −1280.00 −1.66667
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 950.000 1.23217
\(772\) 0 0
\(773\) 1370.00 1.77232 0.886158 − 0.463384i \(-0.153365\pi\)
0.886158 + 0.463384i \(0.153365\pi\)
\(774\) 0 0
\(775\) 888.000 1.14581
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 1463.00 1.87324
\(782\) 0 0
\(783\) 0 0
\(784\) 784.000 1.00000
\(785\) −215.000 −0.273885
\(786\) 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
\(795\) −350.000 −0.440252
\(796\) 8.00000 0.0100503
\(797\) −1585.00 −1.98871 −0.994354 − 0.106115i \(-0.966159\pi\)
−0.994354 + 0.106115i \(0.966159\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −1552.00 −1.93758
\(802\) 0 0
\(803\) 0 0
\(804\) −700.000 −0.870647
\(805\) 0 0
\(806\) 0 0
\(807\) −1810.00 −2.24287
\(808\) 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
\(815\) 70.0000 0.0858896
\(816\) 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
\(823\) 755.000 0.917375 0.458688 − 0.888598i \(-0.348320\pi\)
0.458688 + 0.888598i \(0.348320\pi\)
\(824\) 0 0
\(825\) −1320.00 −1.60000
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 2240.00 2.70531
\(829\) −817.000 −0.985525 −0.492762 − 0.870164i \(-0.664013\pi\)
−0.492762 + 0.870164i \(0.664013\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1295.00 1.54719
\(838\) 0 0
\(839\) 347.000 0.413588 0.206794 − 0.978385i \(-0.433697\pi\)
0.206794 + 0.978385i \(0.433697\pi\)
\(840\) 0 0
\(841\) 841.000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −169.000 −0.200000
\(846\) 0 0
\(847\) 0 0
\(848\) −1120.00 −1.32075
\(849\) 0 0
\(850\) 0 0
\(851\) −875.000 −1.02820
\(852\) 2660.00 3.12207
\(853\) 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
\(859\) −757.000 −0.881257 −0.440629 − 0.897689i \(-0.645244\pi\)
−0.440629 + 0.897689i \(0.645244\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −430.000 −0.498262 −0.249131 − 0.968470i \(-0.580145\pi\)
−0.249131 + 0.968470i \(0.580145\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −1445.00 −1.66667
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 1520.00 1.74112
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 176.000 0.200000
\(881\) 1487.00 1.68785 0.843927 − 0.536457i \(-0.180238\pi\)
0.843927 + 0.536457i \(0.180238\pi\)
\(882\) 0 0
\(883\) 1370.00 1.55153 0.775764 − 0.631023i \(-0.217364\pi\)
0.775764 + 0.631023i \(0.217364\pi\)
\(884\) 0 0
\(885\) 535.000 0.604520
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −341.000 −0.382716
\(892\) −1780.00 −1.99552
\(893\) 0 0
\(894\) 0 0
\(895\) −83.0000 −0.0927374
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −1536.00 −1.70667
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −263.000 −0.290608
\(906\) 0 0
\(907\) −1750.00 −1.92944 −0.964719 − 0.263282i \(-0.915195\pi\)
−0.964719 + 0.263282i \(0.915195\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1778.00 1.95170 0.975851 − 0.218439i \(-0.0700963\pi\)
0.975851 + 0.218439i \(0.0700963\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −1732.00 −1.89083
\(917\) 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
\(925\) 600.000 0.648649
\(926\) 0 0
\(927\) −3040.00 −3.27940
\(928\) 0 0
\(929\) −958.000 −1.03122 −0.515608 − 0.856824i \(-0.672434\pi\)
−0.515608 + 0.856824i \(0.672434\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 2390.00 2.56163
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 1325.00 1.41108
\(940\) −200.000 −0.212766
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 1712.00 1.81356
\(945\) 0 0
\(946\) 0 0
\(947\) 1355.00 1.43083 0.715417 − 0.698698i \(-0.246237\pi\)
0.715417 + 0.698698i \(0.246237\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −475.000 −0.499474
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 157.000 0.164398
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 320.000 0.333333
\(961\) 408.000 0.424558
\(962\) 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
\(971\) 83.0000 0.0854789 0.0427394 − 0.999086i \(-0.486391\pi\)
0.0427394 + 0.999086i \(0.486391\pi\)
\(972\) 640.000 0.658436
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −1225.00 −1.25384 −0.626919 − 0.779084i \(-0.715684\pi\)
−0.626919 + 0.779084i \(0.715684\pi\)
\(978\) 0 0
\(979\) 1067.00 1.08989
\(980\) −196.000 −0.200000
\(981\) 0 0
\(982\) 0 0
\(983\) 635.000 0.645982 0.322991 − 0.946402i \(-0.395312\pi\)
0.322991 + 0.946402i \(0.395312\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −1582.00 −1.59637 −0.798184 − 0.602414i \(-0.794206\pi\)
−0.798184 + 0.602414i \(0.794206\pi\)
\(992\) 0 0
\(993\) −2815.00 −2.83484
\(994\) 0 0
\(995\) −2.00000 −0.00201005
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0 0
\(999\) 875.000 0.875876
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 11.3.b.a.10.1 ✓ 1
3.2 odd 2 99.3.c.a.10.1 1
4.3 odd 2 176.3.h.a.65.1 1
5.2 odd 4 275.3.d.a.274.2 2
5.3 odd 4 275.3.d.a.274.1 2
5.4 even 2 275.3.c.a.76.1 1
7.6 odd 2 539.3.c.a.197.1 1
8.3 odd 2 704.3.h.a.65.1 1
8.5 even 2 704.3.h.b.65.1 1
11.2 odd 10 121.3.d.b.40.1 4
11.3 even 5 121.3.d.b.112.1 4
11.4 even 5 121.3.d.b.94.1 4
11.5 even 5 121.3.d.b.118.1 4
11.6 odd 10 121.3.d.b.118.1 4
11.7 odd 10 121.3.d.b.94.1 4
11.8 odd 10 121.3.d.b.112.1 4
11.9 even 5 121.3.d.b.40.1 4
11.10 odd 2 CM 11.3.b.a.10.1 ✓ 1
12.11 even 2 1584.3.j.a.1297.1 1
33.32 even 2 99.3.c.a.10.1 1
44.43 even 2 176.3.h.a.65.1 1
55.32 even 4 275.3.d.a.274.2 2
55.43 even 4 275.3.d.a.274.1 2
55.54 odd 2 275.3.c.a.76.1 1
77.76 even 2 539.3.c.a.197.1 1
88.21 odd 2 704.3.h.b.65.1 1
88.43 even 2 704.3.h.a.65.1 1
132.131 odd 2 1584.3.j.a.1297.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.3.b.a.10.1 ✓ 1 1.1 even 1 trivial
11.3.b.a.10.1 ✓ 1 11.10 odd 2 CM
99.3.c.a.10.1 1 3.2 odd 2
99.3.c.a.10.1 1 33.32 even 2
121.3.d.b.40.1 4 11.2 odd 10
121.3.d.b.40.1 4 11.9 even 5
121.3.d.b.94.1 4 11.4 even 5
121.3.d.b.94.1 4 11.7 odd 10
121.3.d.b.112.1 4 11.3 even 5
121.3.d.b.112.1 4 11.8 odd 10
121.3.d.b.118.1 4 11.5 even 5
121.3.d.b.118.1 4 11.6 odd 10
176.3.h.a.65.1 1 4.3 odd 2
176.3.h.a.65.1 1 44.43 even 2
275.3.c.a.76.1 1 5.4 even 2
275.3.c.a.76.1 1 55.54 odd 2
275.3.d.a.274.1 2 5.3 odd 4
275.3.d.a.274.1 2 55.43 even 4
275.3.d.a.274.2 2 5.2 odd 4
275.3.d.a.274.2 2 55.32 even 4
539.3.c.a.197.1 1 7.6 odd 2
539.3.c.a.197.1 1 77.76 even 2
704.3.h.a.65.1 1 8.3 odd 2
704.3.h.a.65.1 1 88.43 even 2
704.3.h.b.65.1 1 8.5 even 2
704.3.h.b.65.1 1 88.21 odd 2
1584.3.j.a.1297.1 1 12.11 even 2
1584.3.j.a.1297.1 1 132.131 odd 2