Properties

Label 1792.2.e.b.895.2
Level $1792$
Weight $2$
Character 1792.895
Analytic conductor $14.309$
Analytic rank $0$
Dimension $4$
CM discriminant -7
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1792,2,Mod(895,1792)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1792.895");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.e (of order \(2\), degree \(1\), not 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: no
Analytic conductor: \(14.3091920422\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{7})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 3x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 28)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 895.2
Root \(-1.32288 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1792.895
Dual form 1792.2.e.b.895.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.64575i q^{7} +3.00000 q^{9} +O(q^{10})\) \(q-2.64575i q^{7} +3.00000 q^{9} +5.29150 q^{11} -5.29150i q^{23} -5.00000 q^{25} +2.00000i q^{29} +6.00000i q^{37} +5.29150 q^{43} -7.00000 q^{49} -10.0000i q^{53} -7.93725i q^{63} +15.8745 q^{67} -5.29150i q^{71} -14.0000i q^{77} -15.8745i q^{79} +9.00000 q^{81} +15.8745 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 12 q^{9} - 20 q^{25} - 28 q^{49} + 36 q^{81}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).

\(n\) \(1023\) \(1025\) \(1541\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) 0 0
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) − 2.64575i − 1.00000i
\(8\) 0 0
\(9\) 3.00000 1.00000
\(10\) 0 0
\(11\) 5.29150 1.59545 0.797724 0.603023i \(-0.206037\pi\)
0.797724 + 0.603023i \(0.206037\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) − 5.29150i − 1.10335i −0.834058 0.551677i \(-0.813988\pi\)
0.834058 0.551677i \(-0.186012\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.00000i 0.371391i 0.982607 + 0.185695i \(0.0594537\pi\)
−0.982607 + 0.185695i \(0.940546\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6.00000i 0.986394i 0.869918 + 0.493197i \(0.164172\pi\)
−0.869918 + 0.493197i \(0.835828\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 5.29150 0.806947 0.403473 0.914991i \(-0.367803\pi\)
0.403473 + 0.914991i \(0.367803\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) − 10.0000i − 1.37361i −0.726844 0.686803i \(-0.759014\pi\)
0.726844 0.686803i \(-0.240986\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) − 7.93725i − 1.00000i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 15.8745 1.93938 0.969690 0.244339i \(-0.0785709\pi\)
0.969690 + 0.244339i \(0.0785709\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) − 5.29150i − 0.627986i −0.949425 0.313993i \(-0.898333\pi\)
0.949425 0.313993i \(-0.101667\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 14.0000i − 1.59545i
\(78\) 0 0
\(79\) − 15.8745i − 1.78602i −0.450035 0.893011i \(-0.648589\pi\)
0.450035 0.893011i \(-0.351411\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 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
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 15.8745 1.59545
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.29150 0.511549 0.255774 0.966736i \(-0.417670\pi\)
0.255774 + 0.966736i \(0.417670\pi\)
\(108\) 0 0
\(109\) 18.0000i 1.72409i 0.506834 + 0.862044i \(0.330816\pi\)
−0.506834 + 0.862044i \(0.669184\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 17.0000 1.54545
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) − 15.8745i − 1.40863i −0.709885 0.704317i \(-0.751253\pi\)
0.709885 0.704317i \(-0.248747\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −10.0000 −0.854358 −0.427179 0.904167i \(-0.640493\pi\)
−0.427179 + 0.904167i \(0.640493\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 22.0000i 1.80231i 0.433497 + 0.901155i \(0.357280\pi\)
−0.433497 + 0.901155i \(0.642720\pi\)
\(150\) 0 0
\(151\) − 5.29150i − 0.430616i −0.976546 0.215308i \(-0.930924\pi\)
0.976546 0.215308i \(-0.0690756\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −14.0000 −1.10335
\(162\) 0 0
\(163\) 15.8745 1.24339 0.621694 0.783260i \(-0.286445\pi\)
0.621694 + 0.783260i \(0.286445\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 13.2288i 1.00000i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −26.4575 −1.97753 −0.988764 0.149487i \(-0.952238\pi\)
−0.988764 + 0.149487i \(0.952238\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 26.4575i 1.91440i 0.289430 + 0.957199i \(0.406534\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 0 0
\(193\) 18.0000 1.29567 0.647834 0.761781i \(-0.275675\pi\)
0.647834 + 0.761781i \(0.275675\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 26.0000i − 1.85242i −0.377004 0.926212i \(-0.623046\pi\)
0.377004 0.926212i \(-0.376954\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 5.29150 0.371391
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) − 15.8745i − 1.10335i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −26.4575 −1.82141 −0.910705 0.413057i \(-0.864461\pi\)
−0.910705 + 0.413057i \(0.864461\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 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
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) −15.0000 −1.00000
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 22.0000 1.44127 0.720634 0.693316i \(-0.243851\pi\)
0.720634 + 0.693316i \(0.243851\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 26.4575i 1.71139i 0.517477 + 0.855697i \(0.326871\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) − 28.0000i − 1.76034i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 15.8745 0.986394
\(260\) 0 0
\(261\) 6.00000i 0.371391i
\(262\) 0 0
\(263\) − 5.29150i − 0.326288i −0.986602 0.163144i \(-0.947836\pi\)
0.986602 0.163144i \(-0.0521635\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −26.4575 −1.59545
\(276\) 0 0
\(277\) − 10.0000i − 0.600842i −0.953807 0.300421i \(-0.902873\pi\)
0.953807 0.300421i \(-0.0971271\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −26.0000 −1.55103 −0.775515 0.631329i \(-0.782510\pi\)
−0.775515 + 0.631329i \(0.782510\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 17.0000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) − 14.0000i − 0.806947i
\(302\) 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
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 34.0000i 1.90963i 0.297200 + 0.954815i \(0.403947\pi\)
−0.297200 + 0.954815i \(0.596053\pi\)
\(318\) 0 0
\(319\) 10.5830i 0.592535i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 5.29150 0.290847 0.145424 0.989369i \(-0.453545\pi\)
0.145424 + 0.989369i \(0.453545\pi\)
\(332\) 0 0
\(333\) 18.0000i 0.986394i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −30.0000 −1.63420 −0.817102 0.576493i \(-0.804421\pi\)
−0.817102 + 0.576493i \(0.804421\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 18.5203i 1.00000i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −37.0405 −1.98844 −0.994220 0.107366i \(-0.965758\pi\)
−0.994220 + 0.107366i \(0.965758\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 37.0405i 1.95492i 0.211112 + 0.977462i \(0.432292\pi\)
−0.211112 + 0.977462i \(0.567708\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −26.4575 −1.37361
\(372\) 0 0
\(373\) 22.0000i 1.13912i 0.821951 + 0.569558i \(0.192886\pi\)
−0.821951 + 0.569558i \(0.807114\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −37.0405 −1.90264 −0.951322 0.308199i \(-0.900274\pi\)
−0.951322 + 0.308199i \(0.900274\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 15.8745 0.806947
\(388\) 0 0
\(389\) 38.0000i 1.92668i 0.268290 + 0.963338i \(0.413542\pi\)
−0.268290 + 0.963338i \(0.586458\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 34.0000 1.69788 0.848939 0.528490i \(-0.177242\pi\)
0.848939 + 0.528490i \(0.177242\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 31.7490i 1.57374i
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) − 26.0000i − 1.26716i −0.773676 0.633581i \(-0.781584\pi\)
0.773676 0.633581i \(-0.218416\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 26.4575i 1.27441i 0.770693 + 0.637207i \(0.219910\pi\)
−0.770693 + 0.637207i \(0.780090\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 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
\(441\) −21.0000 −1.00000
\(442\) 0 0
\(443\) −37.0405 −1.75985 −0.879924 0.475114i \(-0.842407\pi\)
−0.879924 + 0.475114i \(0.842407\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6.00000 0.280668 0.140334 0.990104i \(-0.455182\pi\)
0.140334 + 0.990104i \(0.455182\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) − 15.8745i − 0.737751i −0.929479 0.368875i \(-0.879743\pi\)
0.929479 0.368875i \(-0.120257\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) − 42.0000i − 1.93938i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 28.0000 1.28744
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) − 30.0000i − 1.37361i
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 37.0405i 1.67847i 0.543772 + 0.839233i \(0.316996\pi\)
−0.543772 + 0.839233i \(0.683004\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5.29150 0.238802 0.119401 0.992846i \(-0.461903\pi\)
0.119401 + 0.992846i \(0.461903\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −14.0000 −0.627986
\(498\) 0 0
\(499\) −26.4575 −1.18440 −0.592200 0.805791i \(-0.701741\pi\)
−0.592200 + 0.805791i \(0.701741\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −5.00000 −0.217391
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −37.0405 −1.59545
\(540\) 0 0
\(541\) 34.0000i 1.46177i 0.682498 + 0.730887i \(0.260893\pi\)
−0.682498 + 0.730887i \(0.739107\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 15.8745 0.678745 0.339372 0.940652i \(-0.389785\pi\)
0.339372 + 0.940652i \(0.389785\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −42.0000 −1.78602
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 46.0000i − 1.94908i −0.224208 0.974541i \(-0.571980\pi\)
0.224208 0.974541i \(-0.428020\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) − 23.8118i − 1.00000i
\(568\) 0 0
\(569\) 22.0000 0.922288 0.461144 0.887325i \(-0.347439\pi\)
0.461144 + 0.887325i \(0.347439\pi\)
\(570\) 0 0
\(571\) 47.6235 1.99298 0.996491 0.0836974i \(-0.0266729\pi\)
0.996491 + 0.0836974i \(0.0266729\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 26.4575i 1.10335i
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) − 52.9150i − 2.19152i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 37.0405i 1.51343i 0.653742 + 0.756717i \(0.273198\pi\)
−0.653742 + 0.756717i \(0.726802\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 47.6235 1.93938
\(604\) 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
\(613\) 38.0000i 1.53481i 0.641165 + 0.767403i \(0.278451\pi\)
−0.641165 + 0.767403i \(0.721549\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −26.0000 −1.04672 −0.523360 0.852111i \(-0.675322\pi\)
−0.523360 + 0.852111i \(0.675322\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) − 47.6235i − 1.89586i −0.318475 0.947931i \(-0.603171\pi\)
0.318475 0.947931i \(-0.396829\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) − 15.8745i − 0.627986i
\(640\) 0 0
\(641\) −46.0000 −1.81689 −0.908445 0.418004i \(-0.862730\pi\)
−0.908445 + 0.418004i \(0.862730\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 50.0000i 1.95665i 0.207072 + 0.978326i \(0.433606\pi\)
−0.207072 + 0.978326i \(0.566394\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −26.4575 −1.03064 −0.515319 0.856998i \(-0.672327\pi\)
−0.515319 + 0.856998i \(0.672327\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 10.5830 0.409776
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −30.0000 −1.15642 −0.578208 0.815890i \(-0.696248\pi\)
−0.578208 + 0.815890i \(0.696248\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 5.29150 0.202474 0.101237 0.994862i \(-0.467720\pi\)
0.101237 + 0.994862i \(0.467720\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) − 42.0000i − 1.59545i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 2.00000i 0.0755390i 0.999286 + 0.0377695i \(0.0120253\pi\)
−0.999286 + 0.0377695i \(0.987975\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 6.00000i 0.225335i 0.993633 + 0.112667i \(0.0359394\pi\)
−0.993633 + 0.112667i \(0.964061\pi\)
\(710\) 0 0
\(711\) − 47.6235i − 1.78602i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) − 10.0000i − 0.371391i
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 84.0000 3.09418
\(738\) 0 0
\(739\) 15.8745 0.583953 0.291977 0.956425i \(-0.405687\pi\)
0.291977 + 0.956425i \(0.405687\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 37.0405i 1.35888i 0.733729 + 0.679442i \(0.237778\pi\)
−0.733729 + 0.679442i \(0.762222\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 14.0000i − 0.511549i
\(750\) 0 0
\(751\) 26.4575i 0.965448i 0.875772 + 0.482724i \(0.160353\pi\)
−0.875772 + 0.482724i \(0.839647\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 54.0000i 1.96266i 0.192323 + 0.981332i \(0.438398\pi\)
−0.192323 + 0.981332i \(0.561602\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 47.6235 1.72409
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) − 28.0000i − 1.00192i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) − 5.29150i − 0.188144i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 38.0000 1.33601 0.668004 0.744157i \(-0.267149\pi\)
0.668004 + 0.744157i \(0.267149\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 22.0000i 0.767805i 0.923374 + 0.383903i \(0.125420\pi\)
−0.923374 + 0.383903i \(0.874580\pi\)
\(822\) 0 0
\(823\) − 47.6235i − 1.66005i −0.557725 0.830026i \(-0.688326\pi\)
0.557725 0.830026i \(-0.311674\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −37.0405 −1.28803 −0.644013 0.765015i \(-0.722732\pi\)
−0.644013 + 0.765015i \(0.722732\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 25.0000 0.862069
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) − 44.9778i − 1.54545i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 31.7490 1.08834
\(852\) 0 0
\(853\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) − 58.2065i − 1.98137i −0.136162 0.990687i \(-0.543477\pi\)
0.136162 0.990687i \(-0.456523\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 84.0000i − 2.84950i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 50.0000i 1.68838i 0.536044 + 0.844190i \(0.319918\pi\)
−0.536044 + 0.844190i \(0.680082\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 58.2065 1.95881 0.979403 0.201916i \(-0.0647168\pi\)
0.979403 + 0.201916i \(0.0647168\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) −42.0000 −1.40863
\(890\) 0 0
\(891\) 47.6235 1.59545
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 5.29150 0.175701 0.0878507 0.996134i \(-0.472000\pi\)
0.0878507 + 0.996134i \(0.472000\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) − 58.2065i − 1.92847i −0.265052 0.964234i \(-0.585389\pi\)
0.265052 0.964234i \(-0.414611\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 37.0405i 1.22185i 0.791687 + 0.610927i \(0.209203\pi\)
−0.791687 + 0.610927i \(0.790797\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) − 30.0000i − 0.986394i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 58.2065 1.89146 0.945729 0.324956i \(-0.105350\pi\)
0.945729 + 0.324956i \(0.105350\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −58.0000 −1.87880 −0.939402 0.342817i \(-0.888619\pi\)
−0.939402 + 0.342817i \(0.888619\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 26.4575i 0.854358i
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 15.8745 0.511549
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) − 47.6235i − 1.53147i −0.643157 0.765735i \(-0.722376\pi\)
0.643157 0.765735i \(-0.277624\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −46.0000 −1.47167 −0.735835 0.677161i \(-0.763210\pi\)
−0.735835 + 0.677161i \(0.763210\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 54.0000i 1.72409i
\(982\) 0 0
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 28.0000i − 0.890348i
\(990\) 0 0
\(991\) − 58.2065i − 1.84899i −0.381193 0.924496i \(-0.624487\pi\)
0.381193 0.924496i \(-0.375513\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) 0 0
\(999\) 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 1792.2.e.b.895.2 4
4.3 odd 2 inner 1792.2.e.b.895.3 4
7.6 odd 2 CM 1792.2.e.b.895.2 4
8.3 odd 2 inner 1792.2.e.b.895.4 4
8.5 even 2 inner 1792.2.e.b.895.1 4
16.3 odd 4 28.2.d.a.27.2 yes 2
16.5 even 4 448.2.f.b.447.2 2
16.11 odd 4 448.2.f.b.447.1 2
16.13 even 4 28.2.d.a.27.1 2
28.27 even 2 inner 1792.2.e.b.895.3 4
48.5 odd 4 4032.2.b.e.3583.2 2
48.11 even 4 4032.2.b.e.3583.1 2
48.29 odd 4 252.2.b.a.55.2 2
48.35 even 4 252.2.b.a.55.1 2
56.13 odd 2 inner 1792.2.e.b.895.1 4
56.27 even 2 inner 1792.2.e.b.895.4 4
80.3 even 4 700.2.c.d.699.4 4
80.13 odd 4 700.2.c.d.699.2 4
80.19 odd 4 700.2.g.a.251.1 2
80.29 even 4 700.2.g.a.251.2 2
80.67 even 4 700.2.c.d.699.1 4
80.77 odd 4 700.2.c.d.699.3 4
112.3 even 12 196.2.f.b.19.1 4
112.13 odd 4 28.2.d.a.27.1 2
112.19 even 12 196.2.f.b.31.2 4
112.27 even 4 448.2.f.b.447.1 2
112.45 odd 12 196.2.f.b.19.2 4
112.51 odd 12 196.2.f.b.31.2 4
112.61 odd 12 196.2.f.b.31.1 4
112.67 odd 12 196.2.f.b.19.1 4
112.69 odd 4 448.2.f.b.447.2 2
112.83 even 4 28.2.d.a.27.2 yes 2
112.93 even 12 196.2.f.b.31.1 4
112.109 even 12 196.2.f.b.19.2 4
336.83 odd 4 252.2.b.a.55.1 2
336.125 even 4 252.2.b.a.55.2 2
336.251 odd 4 4032.2.b.e.3583.1 2
336.293 even 4 4032.2.b.e.3583.2 2
560.13 even 4 700.2.c.d.699.2 4
560.83 odd 4 700.2.c.d.699.4 4
560.237 even 4 700.2.c.d.699.3 4
560.307 odd 4 700.2.c.d.699.1 4
560.349 odd 4 700.2.g.a.251.2 2
560.419 even 4 700.2.g.a.251.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.2.d.a.27.1 2 16.13 even 4
28.2.d.a.27.1 2 112.13 odd 4
28.2.d.a.27.2 yes 2 16.3 odd 4
28.2.d.a.27.2 yes 2 112.83 even 4
196.2.f.b.19.1 4 112.3 even 12
196.2.f.b.19.1 4 112.67 odd 12
196.2.f.b.19.2 4 112.45 odd 12
196.2.f.b.19.2 4 112.109 even 12
196.2.f.b.31.1 4 112.61 odd 12
196.2.f.b.31.1 4 112.93 even 12
196.2.f.b.31.2 4 112.19 even 12
196.2.f.b.31.2 4 112.51 odd 12
252.2.b.a.55.1 2 48.35 even 4
252.2.b.a.55.1 2 336.83 odd 4
252.2.b.a.55.2 2 48.29 odd 4
252.2.b.a.55.2 2 336.125 even 4
448.2.f.b.447.1 2 16.11 odd 4
448.2.f.b.447.1 2 112.27 even 4
448.2.f.b.447.2 2 16.5 even 4
448.2.f.b.447.2 2 112.69 odd 4
700.2.c.d.699.1 4 80.67 even 4
700.2.c.d.699.1 4 560.307 odd 4
700.2.c.d.699.2 4 80.13 odd 4
700.2.c.d.699.2 4 560.13 even 4
700.2.c.d.699.3 4 80.77 odd 4
700.2.c.d.699.3 4 560.237 even 4
700.2.c.d.699.4 4 80.3 even 4
700.2.c.d.699.4 4 560.83 odd 4
700.2.g.a.251.1 2 80.19 odd 4
700.2.g.a.251.1 2 560.419 even 4
700.2.g.a.251.2 2 80.29 even 4
700.2.g.a.251.2 2 560.349 odd 4
1792.2.e.b.895.1 4 8.5 even 2 inner
1792.2.e.b.895.1 4 56.13 odd 2 inner
1792.2.e.b.895.2 4 1.1 even 1 trivial
1792.2.e.b.895.2 4 7.6 odd 2 CM
1792.2.e.b.895.3 4 4.3 odd 2 inner
1792.2.e.b.895.3 4 28.27 even 2 inner
1792.2.e.b.895.4 4 8.3 odd 2 inner
1792.2.e.b.895.4 4 56.27 even 2 inner
4032.2.b.e.3583.1 2 48.11 even 4
4032.2.b.e.3583.1 2 336.251 odd 4
4032.2.b.e.3583.2 2 48.5 odd 4
4032.2.b.e.3583.2 2 336.293 even 4