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Properties

Label 244.1.c.b.243.1
Level $244$
Weight $1$
Character 244.243
Self dual yes
Analytic conductor $0.122$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -244
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] = [244,1,Mod(243,244)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(244, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("244.243");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 244 = 2^{2} \cdot 61 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 244.c (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: \(0.121771863082\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.244.1
Artin image: $S_3$
Artin field: Galois closure of 3.1.244.1

Embedding invariants

Embedding label 243.1
Character \(\chi\) \(=\) 244.243

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +1.00000 q^{18} -1.00000 q^{20} -1.00000 q^{22} -1.00000 q^{23} -1.00000 q^{26} -1.00000 q^{28} +2.00000 q^{31} +1.00000 q^{32} +1.00000 q^{35} +1.00000 q^{36} -1.00000 q^{40} -1.00000 q^{41} +2.00000 q^{43} -1.00000 q^{44} -1.00000 q^{45} -1.00000 q^{46} -1.00000 q^{52} +1.00000 q^{55} -1.00000 q^{56} -1.00000 q^{59} +1.00000 q^{61} +2.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} +1.00000 q^{65} -1.00000 q^{67} +1.00000 q^{70} +2.00000 q^{71} +1.00000 q^{72} -1.00000 q^{73} +1.00000 q^{77} -1.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -1.00000 q^{82} +2.00000 q^{86} -1.00000 q^{88} -1.00000 q^{90} +1.00000 q^{91} -1.00000 q^{92} +2.00000 q^{97} -1.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/244\mathbb{Z}\right)^\times\).

\(n\) \(123\) \(185\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) 1.00000 1.00000
\(5\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(6\) 0 0
\(7\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) 1.00000 1.00000
\(9\) 1.00000 1.00000
\(10\) −1.00000 −1.00000
\(11\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) 0 0
\(13\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(14\) −1.00000 −1.00000
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 1.00000 1.00000
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −1.00000 −1.00000
\(21\) 0 0
\(22\) −1.00000 −1.00000
\(23\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −1.00000 −1.00000
\(27\) 0 0
\(28\) −1.00000 −1.00000
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(32\) 1.00000 1.00000
\(33\) 0 0
\(34\) 0 0
\(35\) 1.00000 1.00000
\(36\) 1.00000 1.00000
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −1.00000 −1.00000
\(41\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 0 0
\(43\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(44\) −1.00000 −1.00000
\(45\) −1.00000 −1.00000
\(46\) −1.00000 −1.00000
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) −1.00000 −1.00000
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 1.00000 1.00000
\(56\) −1.00000 −1.00000
\(57\) 0 0
\(58\) 0 0
\(59\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 1.00000 1.00000
\(62\) 2.00000 2.00000
\(63\) −1.00000 −1.00000
\(64\) 1.00000 1.00000
\(65\) 1.00000 1.00000
\(66\) 0 0
\(67\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 1.00000 1.00000
\(71\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(72\) 1.00000 1.00000
\(73\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.00000 1.00000
\(78\) 0 0
\(79\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(80\) −1.00000 −1.00000
\(81\) 1.00000 1.00000
\(82\) −1.00000 −1.00000
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 2.00000 2.00000
\(87\) 0 0
\(88\) −1.00000 −1.00000
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) −1.00000 −1.00000
\(91\) 1.00000 1.00000
\(92\) −1.00000 −1.00000
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(98\) 0 0
\(99\) −1.00000 −1.00000
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) −1.00000 −1.00000
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(110\) 1.00000 1.00000
\(111\) 0 0
\(112\) −1.00000 −1.00000
\(113\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(114\) 0 0
\(115\) 1.00000 1.00000
\(116\) 0 0
\(117\) −1.00000 −1.00000
\(118\) −1.00000 −1.00000
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) 1.00000 1.00000
\(123\) 0 0
\(124\) 2.00000 2.00000
\(125\) 1.00000 1.00000
\(126\) −1.00000 −1.00000
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 1.00000 1.00000
\(129\) 0 0
\(130\) 1.00000 1.00000
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.00000 −1.00000
\(135\) 0 0
\(136\) 0 0
\(137\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 0 0
\(139\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 1.00000 1.00000
\(141\) 0 0
\(142\) 2.00000 2.00000
\(143\) 1.00000 1.00000
\(144\) 1.00000 1.00000
\(145\) 0 0
\(146\) −1.00000 −1.00000
\(147\) 0 0
\(148\) 0 0
\(149\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(150\) 0 0
\(151\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 1.00000 1.00000
\(155\) −2.00000 −2.00000
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) −1.00000 −1.00000
\(159\) 0 0
\(160\) −1.00000 −1.00000
\(161\) 1.00000 1.00000
\(162\) 1.00000 1.00000
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) −1.00000 −1.00000
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 0 0
\(172\) 2.00000 2.00000
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.00000 −1.00000
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) −1.00000 −1.00000
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 1.00000 1.00000
\(183\) 0 0
\(184\) −1.00000 −1.00000
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 2.00000 2.00000
\(195\) 0 0
\(196\) 0 0
\(197\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(198\) −1.00000 −1.00000
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 1.00000 1.00000
\(206\) 0 0
\(207\) −1.00000 −1.00000
\(208\) −1.00000 −1.00000
\(209\) 0 0
\(210\) 0 0
\(211\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.00000 −2.00000
\(216\) 0 0
\(217\) −2.00000 −2.00000
\(218\) −1.00000 −1.00000
\(219\) 0 0
\(220\) 1.00000 1.00000
\(221\) 0 0
\(222\) 0 0
\(223\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(224\) −1.00000 −1.00000
\(225\) 0 0
\(226\) −1.00000 −1.00000
\(227\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(228\) 0 0
\(229\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) 1.00000 1.00000
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) −1.00000 −1.00000
\(235\) 0 0
\(236\) −1.00000 −1.00000
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 1.00000 1.00000
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 2.00000 2.00000
\(249\) 0 0
\(250\) 1.00000 1.00000
\(251\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(252\) −1.00000 −1.00000
\(253\) 1.00000 1.00000
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1.00000 1.00000
\(261\) 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
\(268\) −1.00000 −1.00000
\(269\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −1.00000 −1.00000
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) −1.00000 −1.00000
\(279\) 2.00000 2.00000
\(280\) 1.00000 1.00000
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 2.00000 2.00000
\(285\) 0 0
\(286\) 1.00000 1.00000
\(287\) 1.00000 1.00000
\(288\) 1.00000 1.00000
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) −1.00000 −1.00000
\(293\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(294\) 0 0
\(295\) 1.00000 1.00000
\(296\) 0 0
\(297\) 0 0
\(298\) −1.00000 −1.00000
\(299\) 1.00000 1.00000
\(300\) 0 0
\(301\) −2.00000 −2.00000
\(302\) −1.00000 −1.00000
\(303\) 0 0
\(304\) 0 0
\(305\) −1.00000 −1.00000
\(306\) 0 0
\(307\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(308\) 1.00000 1.00000
\(309\) 0 0
\(310\) −2.00000 −2.00000
\(311\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 1.00000 1.00000
\(316\) −1.00000 −1.00000
\(317\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.00000 −1.00000
\(321\) 0 0
\(322\) 1.00000 1.00000
\(323\) 0 0
\(324\) 1.00000 1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) −1.00000 −1.00000
\(329\) 0 0
\(330\) 0 0
\(331\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.00000 1.00000
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.00000 −2.00000
\(342\) 0 0
\(343\) 1.00000 1.00000
\(344\) 2.00000 2.00000
\(345\) 0 0
\(346\) 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
\(352\) −1.00000 −1.00000
\(353\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(354\) 0 0
\(355\) −2.00000 −2.00000
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(360\) −1.00000 −1.00000
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 1.00000 1.00000
\(365\) 1.00000 1.00000
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) −1.00000 −1.00000
\(369\) −1.00000 −1.00000
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −1.00000 −1.00000
\(383\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(384\) 0 0
\(385\) −1.00000 −1.00000
\(386\) 0 0
\(387\) 2.00000 2.00000
\(388\) 2.00000 2.00000
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) −1.00000 −1.00000
\(395\) 1.00000 1.00000
\(396\) −1.00000 −1.00000
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) −2.00000 −2.00000
\(404\) 0 0
\(405\) −1.00000 −1.00000
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 1.00000 1.00000
\(411\) 0 0
\(412\) 0 0
\(413\) 1.00000 1.00000
\(414\) −1.00000 −1.00000
\(415\) 0 0
\(416\) −1.00000 −1.00000
\(417\) 0 0
\(418\) 0 0
\(419\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 2.00000 2.00000
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.00000 −1.00000
\(428\) 0 0
\(429\) 0 0
\(430\) −2.00000 −2.00000
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) −2.00000 −2.00000
\(435\) 0 0
\(436\) −1.00000 −1.00000
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 1.00000 1.00000
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −1.00000 −1.00000
\(447\) 0 0
\(448\) −1.00000 −1.00000
\(449\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(450\) 0 0
\(451\) 1.00000 1.00000
\(452\) −1.00000 −1.00000
\(453\) 0 0
\(454\) −1.00000 −1.00000
\(455\) −1.00000 −1.00000
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) −1.00000 −1.00000
\(459\) 0 0
\(460\) 1.00000 1.00000
\(461\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(468\) −1.00000 −1.00000
\(469\) 1.00000 1.00000
\(470\) 0 0
\(471\) 0 0
\(472\) −1.00000 −1.00000
\(473\) −2.00000 −2.00000
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.00000 −1.00000
\(483\) 0 0
\(484\) 0 0
\(485\) −2.00000 −2.00000
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 1.00000 1.00000
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 1.00000 1.00000
\(496\) 2.00000 2.00000
\(497\) −2.00000 −2.00000
\(498\) 0 0
\(499\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 1.00000 1.00000
\(501\) 0 0
\(502\) 2.00000 2.00000
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) −1.00000 −1.00000
\(505\) 0 0
\(506\) 1.00000 1.00000
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 1.00000 1.00000
\(512\) 1.00000 1.00000
\(513\) 0 0
\(514\) 2.00000 2.00000
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 1.00000 1.00000
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) −1.00000 −1.00000
\(532\) 0 0
\(533\) 1.00000 1.00000
\(534\) 0 0
\(535\) 0 0
\(536\) −1.00000 −1.00000
\(537\) 0 0
\(538\) 2.00000 2.00000
\(539\) 0 0
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.00000 1.00000
\(546\) 0 0
\(547\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) −1.00000 −1.00000
\(549\) 1.00000 1.00000
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 1.00000 1.00000
\(554\) 0 0
\(555\) 0 0
\(556\) −1.00000 −1.00000
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 2.00000 2.00000
\(559\) −2.00000 −2.00000
\(560\) 1.00000 1.00000
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 1.00000 1.00000
\(566\) 0 0
\(567\) −1.00000 −1.00000
\(568\) 2.00000 2.00000
\(569\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 1.00000 1.00000
\(573\) 0 0
\(574\) 1.00000 1.00000
\(575\) 0 0
\(576\) 1.00000 1.00000
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 1.00000 1.00000
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −1.00000 −1.00000
\(585\) 1.00000 1.00000
\(586\) 2.00000 2.00000
\(587\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(588\) 0 0
\(589\) 0 0
\(590\) 1.00000 1.00000
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.00000 −1.00000
\(597\) 0 0
\(598\) 1.00000 1.00000
\(599\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0 0
\(601\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) −2.00000 −2.00000
\(603\) −1.00000 −1.00000
\(604\) −1.00000 −1.00000
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −1.00000 −1.00000
\(611\) 0 0
\(612\) 0 0
\(613\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(614\) −1.00000 −1.00000
\(615\) 0 0
\(616\) 1.00000 1.00000
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) −2.00000 −2.00000
\(621\) 0 0
\(622\) −1.00000 −1.00000
\(623\) 0 0
\(624\) 0 0
\(625\) −1.00000 −1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 1.00000 1.00000
\(631\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(632\) −1.00000 −1.00000
\(633\) 0 0
\(634\) 2.00000 2.00000
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 2.00000 2.00000
\(640\) −1.00000 −1.00000
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(644\) 1.00000 1.00000
\(645\) 0 0
\(646\) 0 0
\(647\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(648\) 1.00000 1.00000
\(649\) 1.00000 1.00000
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.00000 −1.00000
\(657\) −1.00000 −1.00000
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) −1.00000 −1.00000
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 1.00000 1.00000
\(671\) −1.00000 −1.00000
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) −2.00000 −2.00000
\(680\) 0 0
\(681\) 0 0
\(682\) −2.00000 −2.00000
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 1.00000 1.00000
\(686\) 1.00000 1.00000
\(687\) 0 0
\(688\) 2.00000 2.00000
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 1.00000 1.00000
\(694\) 0 0
\(695\) 1.00000 1.00000
\(696\) 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
\(704\) −1.00000 −1.00000
\(705\) 0 0
\(706\) −1.00000 −1.00000
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) −2.00000 −2.00000
\(711\) −1.00000 −1.00000
\(712\) 0 0
\(713\) −2.00000 −2.00000
\(714\) 0 0
\(715\) −1.00000 −1.00000
\(716\) 0 0
\(717\) 0 0
\(718\) 2.00000 2.00000
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) −1.00000 −1.00000
\(721\) 0 0
\(722\) 1.00000 1.00000
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 1.00000 1.00000
\(729\) 1.00000 1.00000
\(730\) 1.00000 1.00000
\(731\) 0 0
\(732\) 0 0
\(733\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −1.00000 −1.00000
\(737\) 1.00000 1.00000
\(738\) −1.00000 −1.00000
\(739\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(744\) 0 0
\(745\) 1.00000 1.00000
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.00000 1.00000
\(756\) 0 0
\(757\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 1.00000 1.00000
\(764\) −1.00000 −1.00000
\(765\) 0 0
\(766\) −1.00000 −1.00000
\(767\) 1.00000 1.00000
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) −1.00000 −1.00000
\(771\) 0 0
\(772\) 0 0
\(773\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(774\) 2.00000 2.00000
\(775\) 0 0
\(776\) 2.00000 2.00000
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −2.00000 −2.00000
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(788\) −1.00000 −1.00000
\(789\) 0 0
\(790\) 1.00000 1.00000
\(791\) 1.00000 1.00000
\(792\) −1.00000 −1.00000
\(793\) −1.00000 −1.00000
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.00000 1.00000
\(804\) 0 0
\(805\) −1.00000 −1.00000
\(806\) −2.00000 −2.00000
\(807\) 0 0
\(808\) 0 0
\(809\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(810\) −1.00000 −1.00000
\(811\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 1.00000 1.00000
\(820\) 1.00000 1.00000
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(824\) 0 0
\(825\) 0 0
\(826\) 1.00000 1.00000
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) −1.00000 −1.00000
\(829\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.00000 −1.00000
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 2.00000 2.00000
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 2.00000 2.00000
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(854\) −1.00000 −1.00000
\(855\) 0 0
\(856\) 0 0
\(857\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) −2.00000 −2.00000
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) −2.00000 −2.00000
\(869\) 1.00000 1.00000
\(870\) 0 0
\(871\) 1.00000 1.00000
\(872\) −1.00000 −1.00000
\(873\) 2.00000 2.00000
\(874\) 0 0
\(875\) −1.00000 −1.00000
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 1.00000 1.00000
\(881\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(882\) 0 0
\(883\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1.00000 −1.00000
\(892\) −1.00000 −1.00000
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) −1.00000 −1.00000
\(897\) 0 0
\(898\) −1.00000 −1.00000
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 1.00000 1.00000
\(903\) 0 0
\(904\) −1.00000 −1.00000
\(905\) 0 0
\(906\) 0 0
\(907\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(908\) −1.00000 −1.00000
\(909\) 0 0
\(910\) −1.00000 −1.00000
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −1.00000 −1.00000
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 1.00000 1.00000
\(921\) 0 0
\(922\) 2.00000 2.00000
\(923\) −2.00000 −2.00000
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) −1.00000 −1.00000
\(935\) 0 0
\(936\) −1.00000 −1.00000
\(937\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(938\) 1.00000 1.00000
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 1.00000 1.00000
\(944\) −1.00000 −1.00000
\(945\) 0 0
\(946\) −2.00000 −2.00000
\(947\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(948\) 0 0
\(949\) 1.00000 1.00000
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 1.00000 1.00000
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1.00000 1.00000
\(960\) 0 0
\(961\) 3.00000 3.00000
\(962\) 0 0
\(963\) 0 0
\(964\) −1.00000 −1.00000
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −2.00000 −2.00000
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 1.00000 1.00000
\(974\) 0 0
\(975\) 0 0
\(976\) 1.00000 1.00000
\(977\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −1.00000 −1.00000
\(982\) 0 0
\(983\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(984\) 0 0
\(985\) 1.00000 1.00000
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −2.00000 −2.00000
\(990\) 1.00000 1.00000
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 2.00000 2.00000
\(993\) 0 0
\(994\) −2.00000 −2.00000
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) −1.00000 −1.00000
\(999\) 0 0
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 244.1.c.b.243.1 yes 1
3.2 odd 2 2196.1.h.b.487.1 1
4.3 odd 2 244.1.c.a.243.1 ✓ 1
8.3 odd 2 3904.1.e.b.3903.1 1
8.5 even 2 3904.1.e.a.3903.1 1
12.11 even 2 2196.1.h.d.487.1 1
61.60 even 2 244.1.c.a.243.1 ✓ 1
183.182 odd 2 2196.1.h.d.487.1 1
244.243 odd 2 CM 244.1.c.b.243.1 yes 1
488.243 odd 2 3904.1.e.a.3903.1 1
488.365 even 2 3904.1.e.b.3903.1 1
732.731 even 2 2196.1.h.b.487.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
244.1.c.a.243.1 ✓ 1 4.3 odd 2
244.1.c.a.243.1 ✓ 1 61.60 even 2
244.1.c.b.243.1 yes 1 1.1 even 1 trivial
244.1.c.b.243.1 yes 1 244.243 odd 2 CM
2196.1.h.b.487.1 1 3.2 odd 2
2196.1.h.b.487.1 1 732.731 even 2
2196.1.h.d.487.1 1 12.11 even 2
2196.1.h.d.487.1 1 183.182 odd 2
3904.1.e.a.3903.1 1 8.5 even 2
3904.1.e.a.3903.1 1 488.243 odd 2
3904.1.e.b.3903.1 1 8.3 odd 2
3904.1.e.b.3903.1 1 488.365 even 2