↑

Properties

Label 363.3.b.b.122.1
Level $363$
Weight $3$
Character 363.122
Self dual yes
Analytic conductor $9.891$
Analytic rank $0$
Dimension $1$
CM discriminant -3
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [363,3,Mod(122,363)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(363, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("363.122");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 363.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: \(9.89103359628\)
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 122.1
Character \(\chi\) \(=\) 363.122

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.00000 q^{3} +4.00000 q^{4} +11.0000 q^{7} +9.00000 q^{9} +O(q^{10})\) \(q-3.00000 q^{3} +4.00000 q^{4} +11.0000 q^{7} +9.00000 q^{9} -12.0000 q^{12} -22.0000 q^{13} +16.0000 q^{16} +11.0000 q^{19} -33.0000 q^{21} +25.0000 q^{25} -27.0000 q^{27} +44.0000 q^{28} +59.0000 q^{31} +36.0000 q^{36} +47.0000 q^{37} +66.0000 q^{39} -22.0000 q^{43} -48.0000 q^{48} +72.0000 q^{49} -88.0000 q^{52} -33.0000 q^{57} -121.000 q^{61} +99.0000 q^{63} +64.0000 q^{64} -13.0000 q^{67} +143.000 q^{73} -75.0000 q^{75} +44.0000 q^{76} +11.0000 q^{79} +81.0000 q^{81} -132.000 q^{84} -242.000 q^{91} -177.000 q^{93} -169.000 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) −3.00000 −1.00000
\(4\) 4.00000 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) 11.0000 1.57143 0.785714 − 0.618590i \(-0.212296\pi\)
0.785714 + 0.618590i \(0.212296\pi\)
\(8\) 0 0
\(9\) 9.00000 1.00000
\(10\) 0 0
\(11\) 0 0
\(12\) −12.0000 −1.00000
\(13\) −22.0000 −1.69231 −0.846154 − 0.532939i \(-0.821088\pi\)
−0.846154 + 0.532939i \(0.821088\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 16.0000 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 11.0000 0.578947 0.289474 − 0.957186i \(-0.406520\pi\)
0.289474 + 0.957186i \(0.406520\pi\)
\(20\) 0 0
\(21\) −33.0000 −1.57143
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 25.0000 1.00000
\(26\) 0 0
\(27\) −27.0000 −1.00000
\(28\) 44.0000 1.57143
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 59.0000 1.90323 0.951613 − 0.307299i \(-0.0994253\pi\)
0.951613 + 0.307299i \(0.0994253\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 36.0000 1.00000
\(37\) 47.0000 1.27027 0.635135 − 0.772401i \(-0.280944\pi\)
0.635135 + 0.772401i \(0.280944\pi\)
\(38\) 0 0
\(39\) 66.0000 1.69231
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −22.0000 −0.511628 −0.255814 − 0.966726i \(-0.582343\pi\)
−0.255814 + 0.966726i \(0.582343\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −48.0000 −1.00000
\(49\) 72.0000 1.46939
\(50\) 0 0
\(51\) 0 0
\(52\) −88.0000 −1.69231
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −33.0000 −0.578947
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −121.000 −1.98361 −0.991803 − 0.127774i \(-0.959217\pi\)
−0.991803 + 0.127774i \(0.959217\pi\)
\(62\) 0 0
\(63\) 99.0000 1.57143
\(64\) 64.0000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −13.0000 −0.194030 −0.0970149 − 0.995283i \(-0.530929\pi\)
−0.0970149 + 0.995283i \(0.530929\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 143.000 1.95890 0.979452 − 0.201677i \(-0.0646392\pi\)
0.979452 + 0.201677i \(0.0646392\pi\)
\(74\) 0 0
\(75\) −75.0000 −1.00000
\(76\) 44.0000 0.578947
\(77\) 0 0
\(78\) 0 0
\(79\) 11.0000 0.139241 0.0696203 − 0.997574i \(-0.477821\pi\)
0.0696203 + 0.997574i \(0.477821\pi\)
\(80\) 0 0
\(81\) 81.0000 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −132.000 −1.57143
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −242.000 −2.65934
\(92\) 0 0
\(93\) −177.000 −1.90323
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −169.000 −1.74227 −0.871134 − 0.491045i \(-0.836615\pi\)
−0.871134 + 0.491045i \(0.836615\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 100.000 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −157.000 −1.52427 −0.762136 − 0.647417i \(-0.775849\pi\)
−0.762136 + 0.647417i \(0.775849\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −108.000 −1.00000
\(109\) 143.000 1.31193 0.655963 − 0.754793i \(-0.272263\pi\)
0.655963 + 0.754793i \(0.272263\pi\)
\(110\) 0 0
\(111\) −141.000 −1.27027
\(112\) 176.000 1.57143
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −198.000 −1.69231
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) 236.000 1.90323
\(125\) 0 0
\(126\) 0 0
\(127\) −253.000 −1.99213 −0.996063 − 0.0886483i \(-0.971745\pi\)
−0.996063 + 0.0886483i \(0.971745\pi\)
\(128\) 0 0
\(129\) 66.0000 0.511628
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 121.000 0.909774
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) −22.0000 −0.158273 −0.0791367 − 0.996864i \(-0.525216\pi\)
−0.0791367 + 0.996864i \(0.525216\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 144.000 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) −216.000 −1.46939
\(148\) 188.000 1.27027
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) −286.000 −1.89404 −0.947020 − 0.321175i \(-0.895922\pi\)
−0.947020 + 0.321175i \(0.895922\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 264.000 1.69231
\(157\) −193.000 −1.22930 −0.614650 − 0.788800i \(-0.710703\pi\)
−0.614650 + 0.788800i \(0.710703\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −37.0000 −0.226994 −0.113497 − 0.993538i \(-0.536205\pi\)
−0.113497 + 0.993538i \(0.536205\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 315.000 1.86391
\(170\) 0 0
\(171\) 99.0000 0.578947
\(172\) −88.0000 −0.511628
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 275.000 1.57143
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) −1.00000 −0.00552486 −0.00276243 − 0.999996i \(-0.500879\pi\)
−0.00276243 + 0.999996i \(0.500879\pi\)
\(182\) 0 0
\(183\) 363.000 1.98361
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −297.000 −1.57143
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −192.000 −1.00000
\(193\) 143.000 0.740933 0.370466 − 0.928846i \(-0.379198\pi\)
0.370466 + 0.928846i \(0.379198\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 288.000 1.46939
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −277.000 −1.39196 −0.695980 − 0.718061i \(-0.745030\pi\)
−0.695980 + 0.718061i \(0.745030\pi\)
\(200\) 0 0
\(201\) 39.0000 0.194030
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −352.000 −1.69231
\(209\) 0 0
\(210\) 0 0
\(211\) −253.000 −1.19905 −0.599526 − 0.800355i \(-0.704644\pi\)
−0.599526 + 0.800355i \(0.704644\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 649.000 2.99078
\(218\) 0 0
\(219\) −429.000 −1.95890
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 83.0000 0.372197 0.186099 − 0.982531i \(-0.440416\pi\)
0.186099 + 0.982531i \(0.440416\pi\)
\(224\) 0 0
\(225\) 225.000 1.00000
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) −132.000 −0.578947
\(229\) 26.0000 0.113537 0.0567686 − 0.998387i \(-0.481920\pi\)
0.0567686 + 0.998387i \(0.481920\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −33.0000 −0.139241
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −286.000 −1.18672 −0.593361 − 0.804936i \(-0.702199\pi\)
−0.593361 + 0.804936i \(0.702199\pi\)
\(242\) 0 0
\(243\) −243.000 −1.00000
\(244\) −484.000 −1.98361
\(245\) 0 0
\(246\) 0 0
\(247\) −242.000 −0.979757
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 396.000 1.57143
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 256.000 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 517.000 1.99614
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −52.0000 −0.194030
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 242.000 0.892989 0.446494 − 0.894786i \(-0.352672\pi\)
0.446494 + 0.894786i \(0.352672\pi\)
\(272\) 0 0
\(273\) 726.000 2.65934
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 407.000 1.46931 0.734657 − 0.678439i \(-0.237343\pi\)
0.734657 + 0.678439i \(0.237343\pi\)
\(278\) 0 0
\(279\) 531.000 1.90323
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −517.000 −1.82686 −0.913428 − 0.407001i \(-0.866574\pi\)
−0.913428 + 0.407001i \(0.866574\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 289.000 1.00000
\(290\) 0 0
\(291\) 507.000 1.74227
\(292\) 572.000 1.95890
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −300.000 −1.00000
\(301\) −242.000 −0.803987
\(302\) 0 0
\(303\) 0 0
\(304\) 176.000 0.578947
\(305\) 0 0
\(306\) 0 0
\(307\) −253.000 −0.824104 −0.412052 − 0.911160i \(-0.635188\pi\)
−0.412052 + 0.911160i \(0.635188\pi\)
\(308\) 0 0
\(309\) 471.000 1.52427
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) −142.000 −0.453674 −0.226837 − 0.973933i \(-0.572838\pi\)
−0.226837 + 0.973933i \(0.572838\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 44.0000 0.139241
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 324.000 1.00000
\(325\) −550.000 −1.69231
\(326\) 0 0
\(327\) −429.000 −1.31193
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 299.000 0.903323 0.451662 − 0.892189i \(-0.350831\pi\)
0.451662 + 0.892189i \(0.350831\pi\)
\(332\) 0 0
\(333\) 423.000 1.27027
\(334\) 0 0
\(335\) 0 0
\(336\) −528.000 −1.57143
\(337\) −649.000 −1.92582 −0.962908 − 0.269830i \(-0.913033\pi\)
−0.962908 + 0.269830i \(0.913033\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 253.000 0.737609
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 671.000 1.92264 0.961318 − 0.275441i \(-0.0888238\pi\)
0.961318 + 0.275441i \(0.0888238\pi\)
\(350\) 0 0
\(351\) 594.000 1.69231
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) −240.000 −0.664820
\(362\) 0 0
\(363\) 0 0
\(364\) −968.000 −2.65934
\(365\) 0 0
\(366\) 0 0
\(367\) −718.000 −1.95640 −0.978202 − 0.207657i \(-0.933416\pi\)
−0.978202 + 0.207657i \(0.933416\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −708.000 −1.90323
\(373\) −121.000 −0.324397 −0.162198 − 0.986758i \(-0.551858\pi\)
−0.162198 + 0.986758i \(0.551858\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −694.000 −1.83113 −0.915567 − 0.402165i \(-0.868258\pi\)
−0.915567 + 0.402165i \(0.868258\pi\)
\(380\) 0 0
\(381\) 759.000 1.99213
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −198.000 −0.511628
\(388\) −676.000 −1.74227
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 431.000 1.08564 0.542821 − 0.839848i \(-0.317356\pi\)
0.542821 + 0.839848i \(0.317356\pi\)
\(398\) 0 0
\(399\) −363.000 −0.909774
\(400\) 400.000 1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) −1298.00 −3.22084
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 143.000 0.349633 0.174817 − 0.984601i \(-0.444067\pi\)
0.174817 + 0.984601i \(0.444067\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −628.000 −1.52427
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 66.0000 0.158273
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −358.000 −0.850356 −0.425178 − 0.905110i \(-0.639789\pi\)
−0.425178 + 0.905110i \(0.639789\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1331.00 −3.11710
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −432.000 −1.00000
\(433\) 503.000 1.16166 0.580831 − 0.814024i \(-0.302728\pi\)
0.580831 + 0.814024i \(0.302728\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 572.000 1.31193
\(437\) 0 0
\(438\) 0 0
\(439\) 803.000 1.82916 0.914579 − 0.404408i \(-0.132522\pi\)
0.914579 + 0.404408i \(0.132522\pi\)
\(440\) 0 0
\(441\) 648.000 1.46939
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) −564.000 −1.27027
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 704.000 1.57143
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 858.000 1.89404
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −814.000 −1.78118 −0.890591 − 0.454805i \(-0.849709\pi\)
−0.890591 + 0.454805i \(0.849709\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −526.000 −1.13607 −0.568035 − 0.823005i \(-0.692296\pi\)
−0.568035 + 0.823005i \(0.692296\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) −792.000 −1.69231
\(469\) −143.000 −0.304904
\(470\) 0 0
\(471\) 579.000 1.22930
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 275.000 0.578947
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) −1034.00 −2.14969
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 962.000 1.97536 0.987680 − 0.156489i \(-0.0500176\pi\)
0.987680 + 0.156489i \(0.0500176\pi\)
\(488\) 0 0
\(489\) 111.000 0.226994
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 944.000 1.90323
\(497\) 0 0
\(498\) 0 0
\(499\) −877.000 −1.75752 −0.878758 − 0.477269i \(-0.841627\pi\)
−0.878758 + 0.477269i \(0.841627\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −945.000 −1.86391
\(508\) −1012.00 −1.99213
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 1573.00 3.07828
\(512\) 0 0
\(513\) −297.000 −0.578947
\(514\) 0 0
\(515\) 0 0
\(516\) 264.000 0.511628
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 803.000 1.53537 0.767686 − 0.640826i \(-0.221408\pi\)
0.767686 + 0.640826i \(0.221408\pi\)
\(524\) 0 0
\(525\) −825.000 −1.57143
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 529.000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 484.000 0.909774
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 1034.00 1.91128 0.955638 − 0.294545i \(-0.0951680\pi\)
0.955638 + 0.294545i \(0.0951680\pi\)
\(542\) 0 0
\(543\) 3.00000 0.00552486
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 506.000 0.925046 0.462523 − 0.886607i \(-0.346944\pi\)
0.462523 + 0.886607i \(0.346944\pi\)
\(548\) 0 0
\(549\) −1089.00 −1.98361
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 121.000 0.218807
\(554\) 0 0
\(555\) 0 0
\(556\) −88.0000 −0.158273
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 484.000 0.865832
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 891.000 1.57143
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 1067.00 1.86865 0.934326 − 0.356420i \(-0.116003\pi\)
0.934326 + 0.356420i \(0.116003\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 576.000 1.00000
\(577\) −1033.00 −1.79029 −0.895147 − 0.445770i \(-0.852930\pi\)
−0.895147 + 0.445770i \(0.852930\pi\)
\(578\) 0 0
\(579\) −429.000 −0.740933
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) −864.000 −1.46939
\(589\) 649.000 1.10187
\(590\) 0 0
\(591\) 0 0
\(592\) 752.000 1.27027
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 831.000 1.39196
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 1199.00 1.99501 0.997504 − 0.0706077i \(-0.0224939\pi\)
0.997504 + 0.0706077i \(0.0224939\pi\)
\(602\) 0 0
\(603\) −117.000 −0.194030
\(604\) −1144.00 −1.89404
\(605\) 0 0
\(606\) 0 0
\(607\) −814.000 −1.34102 −0.670511 − 0.741900i \(-0.733925\pi\)
−0.670511 + 0.741900i \(0.733925\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 143.000 0.233279 0.116639 − 0.993174i \(-0.462788\pi\)
0.116639 + 0.993174i \(0.462788\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −214.000 −0.345719 −0.172859 − 0.984947i \(-0.555301\pi\)
−0.172859 + 0.984947i \(0.555301\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 1056.00 1.69231
\(625\) 625.000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) −772.000 −1.22930
\(629\) 0 0
\(630\) 0 0
\(631\) 674.000 1.06815 0.534073 − 0.845438i \(-0.320661\pi\)
0.534073 + 0.845438i \(0.320661\pi\)
\(632\) 0 0
\(633\) 759.000 1.19905
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −1584.00 −2.48666
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 923.000 1.43546 0.717729 − 0.696322i \(-0.245181\pi\)
0.717729 + 0.696322i \(0.245181\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −1947.00 −2.99078
\(652\) −148.000 −0.226994
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 1287.00 1.95890
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −1201.00 −1.81694 −0.908472 − 0.417946i \(-0.862750\pi\)
−0.908472 + 0.417946i \(0.862750\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −249.000 −0.372197
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1177.00 −1.74889 −0.874443 − 0.485129i \(-0.838773\pi\)
−0.874443 + 0.485129i \(0.838773\pi\)
\(674\) 0 0
\(675\) −675.000 −1.00000
\(676\) 1260.00 1.86391
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) −1859.00 −2.73785
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 396.000 0.578947
\(685\) 0 0
\(686\) 0 0
\(687\) −78.0000 −0.113537
\(688\) −352.000 −0.511628
\(689\) 0 0
\(690\) 0 0
\(691\) 1019.00 1.47467 0.737337 − 0.675525i \(-0.236083\pi\)
0.737337 + 0.675525i \(0.236083\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 1100.00 1.57143
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 517.000 0.735420
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −934.000 −1.31735 −0.658674 − 0.752428i \(-0.728882\pi\)
−0.658674 + 0.752428i \(0.728882\pi\)
\(710\) 0 0
\(711\) 99.0000 0.139241
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) −1727.00 −2.39528
\(722\) 0 0
\(723\) 858.000 1.18672
\(724\) −4.00000 −0.00552486
\(725\) 0 0
\(726\) 0 0
\(727\) 482.000 0.662999 0.331499 − 0.943455i \(-0.392446\pi\)
0.331499 + 0.943455i \(0.392446\pi\)
\(728\) 0 0
\(729\) 729.000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 1452.00 1.98361
\(733\) 1034.00 1.41064 0.705321 − 0.708888i \(-0.250803\pi\)
0.705321 + 0.708888i \(0.250803\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 1331.00 1.80108 0.900541 − 0.434771i \(-0.143171\pi\)
0.900541 + 0.434771i \(0.143171\pi\)
\(740\) 0 0
\(741\) 726.000 0.979757
\(742\) 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
\(751\) −1381.00 −1.83888 −0.919441 − 0.393229i \(-0.871358\pi\)
−0.919441 + 0.393229i \(0.871358\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −1188.00 −1.57143
\(757\) 1511.00 1.99604 0.998018 − 0.0629213i \(-0.0200417\pi\)
0.998018 + 0.0629213i \(0.0200417\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 1573.00 2.06160
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −768.000 −1.00000
\(769\) 671.000 0.872562 0.436281 − 0.899811i \(-0.356295\pi\)
0.436281 + 0.899811i \(0.356295\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 572.000 0.740933
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 1475.00 1.90323
\(776\) 0 0
\(777\) −1551.00 −1.99614
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1152.00 1.46939
\(785\) 0 0
\(786\) 0 0
\(787\) 1562.00 1.98475 0.992376 − 0.123246i \(-0.0393305\pi\)
0.992376 + 0.123246i \(0.0393305\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 2662.00 3.35687
\(794\) 0 0
\(795\) 0 0
\(796\) −1108.00 −1.39196
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 156.000 0.194030
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) −253.000 −0.311961 −0.155980 − 0.987760i \(-0.549854\pi\)
−0.155980 + 0.987760i \(0.549854\pi\)
\(812\) 0 0
\(813\) −726.000 −0.892989
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −242.000 −0.296206
\(818\) 0 0
\(819\) −2178.00 −2.65934
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) −1621.00 −1.96962 −0.984812 − 0.173626i \(-0.944452\pi\)
−0.984812 + 0.173626i \(0.944452\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) −1609.00 −1.94089 −0.970446 − 0.241317i \(-0.922421\pi\)
−0.970446 + 0.241317i \(0.922421\pi\)
\(830\) 0 0
\(831\) −1221.00 −1.46931
\(832\) −1408.00 −1.69231
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −1593.00 −1.90323
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 841.000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) −1012.00 −1.19905
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 1551.00 1.82686
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −1177.00 −1.37984 −0.689918 − 0.723888i \(-0.742353\pi\)
−0.689918 + 0.723888i \(0.742353\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −1549.00 −1.80326 −0.901630 − 0.432509i \(-0.857629\pi\)
−0.901630 + 0.432509i \(0.857629\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −867.000 −1.00000
\(868\) 2596.00 2.99078
\(869\) 0 0
\(870\) 0 0
\(871\) 286.000 0.328358
\(872\) 0 0
\(873\) −1521.00 −1.74227
\(874\) 0 0
\(875\) 0 0
\(876\) −1716.00 −1.95890
\(877\) 1727.00 1.96921 0.984607 − 0.174785i \(-0.0559231\pi\)
0.984607 + 0.174785i \(0.0559231\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 1259.00 1.42582 0.712911 − 0.701255i \(-0.247377\pi\)
0.712911 + 0.701255i \(0.247377\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) −2783.00 −3.13048
\(890\) 0 0
\(891\) 0 0
\(892\) 332.000 0.372197
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 900.000 1.00000
\(901\) 0 0
\(902\) 0 0
\(903\) 726.000 0.803987
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −1453.00 −1.60198 −0.800992 − 0.598675i \(-0.795694\pi\)
−0.800992 + 0.598675i \(0.795694\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) −528.000 −0.578947
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 104.000 0.113537
\(917\) 0 0
\(918\) 0 0
\(919\) −1837.00 −1.99891 −0.999456 − 0.0329825i \(-0.989499\pi\)
−0.999456 + 0.0329825i \(0.989499\pi\)
\(920\) 0 0
\(921\) 759.000 0.824104
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1175.00 1.27027
\(926\) 0 0
\(927\) −1413.00 −1.52427
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 792.000 0.850698
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −649.000 −0.692636 −0.346318 − 0.938117i \(-0.612568\pi\)
−0.346318 + 0.938117i \(0.612568\pi\)
\(938\) 0 0
\(939\) 426.000 0.453674
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) −132.000 −0.139241
\(949\) −3146.00 −3.31507
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 2520.00 2.62227
\(962\) 0 0
\(963\) 0 0
\(964\) −1144.00 −1.18672
\(965\) 0 0
\(966\) 0 0
\(967\) −253.000 −0.261634 −0.130817 − 0.991407i \(-0.541760\pi\)
−0.130817 + 0.991407i \(0.541760\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) −972.000 −1.00000
\(973\) −242.000 −0.248715
\(974\) 0 0
\(975\) 1650.00 1.69231
\(976\) −1936.00 −1.98361
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 1287.00 1.31193
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −968.000 −0.979757
\(989\) 0 0
\(990\) 0 0
\(991\) −46.0000 −0.0464178 −0.0232089 − 0.999731i \(-0.507388\pi\)
−0.0232089 + 0.999731i \(0.507388\pi\)
\(992\) 0 0
\(993\) −897.000 −0.903323
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 407.000 0.408225 0.204112 − 0.978947i \(-0.434569\pi\)
0.204112 + 0.978947i \(0.434569\pi\)
\(998\) 0 0
\(999\) −1269.00 −1.27027
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 363.3.b.b.122.1 yes 1
3.2 odd 2 CM 363.3.b.b.122.1 yes 1
11.2 odd 10 363.3.h.b.323.1 4
11.3 even 5 363.3.h.a.251.1 4
11.4 even 5 363.3.h.a.269.1 4
11.5 even 5 363.3.h.a.245.1 4
11.6 odd 10 363.3.h.b.245.1 4
11.7 odd 10 363.3.h.b.269.1 4
11.8 odd 10 363.3.h.b.251.1 4
11.9 even 5 363.3.h.a.323.1 4
11.10 odd 2 363.3.b.a.122.1 ✓ 1
33.2 even 10 363.3.h.b.323.1 4
33.5 odd 10 363.3.h.a.245.1 4
33.8 even 10 363.3.h.b.251.1 4
33.14 odd 10 363.3.h.a.251.1 4
33.17 even 10 363.3.h.b.245.1 4
33.20 odd 10 363.3.h.a.323.1 4
33.26 odd 10 363.3.h.a.269.1 4
33.29 even 10 363.3.h.b.269.1 4
33.32 even 2 363.3.b.a.122.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
363.3.b.a.122.1 ✓ 1 11.10 odd 2
363.3.b.a.122.1 ✓ 1 33.32 even 2
363.3.b.b.122.1 yes 1 1.1 even 1 trivial
363.3.b.b.122.1 yes 1 3.2 odd 2 CM
363.3.h.a.245.1 4 11.5 even 5
363.3.h.a.245.1 4 33.5 odd 10
363.3.h.a.251.1 4 11.3 even 5
363.3.h.a.251.1 4 33.14 odd 10
363.3.h.a.269.1 4 11.4 even 5
363.3.h.a.269.1 4 33.26 odd 10
363.3.h.a.323.1 4 11.9 even 5
363.3.h.a.323.1 4 33.20 odd 10
363.3.h.b.245.1 4 11.6 odd 10
363.3.h.b.245.1 4 33.17 even 10
363.3.h.b.251.1 4 11.8 odd 10
363.3.h.b.251.1 4 33.8 even 10
363.3.h.b.269.1 4 11.7 odd 10
363.3.h.b.269.1 4 33.29 even 10
363.3.h.b.323.1 4 11.2 odd 10
363.3.h.b.323.1 4 33.2 even 10