Properties

Label 1760.2.c.b.879.7
Level $1760$
Weight $2$
Character 1760.879
Analytic conductor $14.054$
Analytic rank $0$
Dimension $8$
CM discriminant -55
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1760,2,Mod(879,1760)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1760, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 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("1760.879");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1760 = 2^{5} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1760.c (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: \(14.0536707557\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.599695360000.19
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{4} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 440)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 879.7
Root \(0.413333 - 1.35246i\) of defining polynomial
Character \(\chi\) \(=\) 1760.879
Dual form 1760.2.c.b.879.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.23607i q^{5} +0.856447i q^{7} +3.00000 q^{9} -3.31662 q^{11} +6.26630i q^{13} -6.87506 q^{17} -5.00000 q^{25} -8.94427i q^{31} -1.91507 q^{35} -8.52839 q^{43} +6.70820i q^{45} +6.26650 q^{49} -7.41620i q^{55} +4.00000 q^{59} +2.56934i q^{63} -14.0119 q^{65} +14.8324i q^{71} -0.261743 q^{73} -2.84051i q^{77} +9.00000 q^{81} -12.3585 q^{83} -15.3731i q^{85} -13.2665 q^{89} -5.36675 q^{91} -9.94987 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 24 q^{9} - 40 q^{25} - 56 q^{49} + 32 q^{59} + 72 q^{81} - 96 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1760\mathbb{Z}\right)^\times\).

\(n\) \(321\) \(991\) \(1057\) \(1541\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(-1\)

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
\(5\) 2.23607i 1.00000i
\(6\) 0 0
\(7\) 0.856447i 0.323706i 0.986815 + 0.161853i \(0.0517471\pi\)
−0.986815 + 0.161853i \(0.948253\pi\)
\(8\) 0 0
\(9\) 3.00000 1.00000
\(10\) 0 0
\(11\) −3.31662 −1.00000
\(12\) 0 0
\(13\) 6.26630i 1.73796i 0.494848 + 0.868979i \(0.335224\pi\)
−0.494848 + 0.868979i \(0.664776\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.87506 −1.66745 −0.833724 0.552182i \(-0.813796\pi\)
−0.833724 + 0.552182i \(0.813796\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) − 8.94427i − 1.60644i −0.595683 0.803219i \(-0.703119\pi\)
0.595683 0.803219i \(-0.296881\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.91507 −0.323706
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −8.52839 −1.30057 −0.650284 0.759691i \(-0.725350\pi\)
−0.650284 + 0.759691i \(0.725350\pi\)
\(44\) 0 0
\(45\) 6.70820i 1.00000i
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 6.26650 0.895214
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) − 7.41620i − 1.00000i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 2.56934i 0.323706i
\(64\) 0 0
\(65\) −14.0119 −1.73796
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 14.8324i 1.76028i 0.474713 + 0.880141i \(0.342552\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) −0.261743 −0.0306347 −0.0153173 0.999883i \(-0.504876\pi\)
−0.0153173 + 0.999883i \(0.504876\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 2.84051i − 0.323706i
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −12.3585 −1.35653 −0.678263 0.734819i \(-0.737267\pi\)
−0.678263 + 0.734819i \(0.737267\pi\)
\(84\) 0 0
\(85\) − 15.3731i − 1.66745i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −13.2665 −1.40625 −0.703123 0.711068i \(-0.748212\pi\)
−0.703123 + 0.711068i \(0.748212\pi\)
\(90\) 0 0
\(91\) −5.36675 −0.562588
\(92\) 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
\(99\) −9.94987 −1.00000
\(100\) 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
\(107\) −18.9719 −1.83408 −0.917039 0.398796i \(-0.869428\pi\)
−0.917039 + 0.398796i \(0.869428\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 18.7989i 1.73796i
\(118\) 0 0
\(119\) − 5.88813i − 0.539764i
\(120\) 0 0
\(121\) 11.0000 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 11.1803i − 1.00000i
\(126\) 0 0
\(127\) 22.4959i 1.99618i 0.0617417 + 0.998092i \(0.480334\pi\)
−0.0617417 + 0.998092i \(0.519666\pi\)
\(128\) 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
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) − 20.7830i − 1.73796i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) −20.6252 −1.66745
\(154\) 0 0
\(155\) 20.0000 1.60644
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 24.2087i 1.87333i 0.350228 + 0.936665i \(0.386104\pi\)
−0.350228 + 0.936665i \(0.613896\pi\)
\(168\) 0 0
\(169\) −26.2665 −2.02050
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 9.69209i − 0.736876i −0.929652 0.368438i \(-0.879893\pi\)
0.929652 0.368438i \(-0.120107\pi\)
\(174\) 0 0
\(175\) − 4.28223i − 0.323706i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 19.8997 1.48738 0.743689 0.668526i \(-0.233075\pi\)
0.743689 + 0.668526i \(0.233075\pi\)
\(180\) 0 0
\(181\) − 4.47214i − 0.332411i −0.986091 0.166206i \(-0.946848\pi\)
0.986091 0.166206i \(-0.0531515\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 22.8020 1.66745
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 26.8328i 1.94155i 0.239983 + 0.970777i \(0.422858\pi\)
−0.239983 + 0.970777i \(0.577142\pi\)
\(192\) 0 0
\(193\) 27.7620 1.99835 0.999176 0.0405839i \(-0.0129218\pi\)
0.999176 + 0.0405839i \(0.0129218\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 27.9057i 1.98820i 0.108471 + 0.994100i \(0.465405\pi\)
−0.108471 + 0.994100i \(0.534595\pi\)
\(198\) 0 0
\(199\) 14.8324i 1.05144i 0.850657 + 0.525720i \(0.176204\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) − 19.0701i − 1.30057i
\(216\) 0 0
\(217\) 7.66029 0.520014
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) − 43.0812i − 2.89796i
\(222\) 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
\(227\) 29.4153 1.95236 0.976182 0.216954i \(-0.0696120\pi\)
0.976182 + 0.216954i \(0.0696120\pi\)
\(228\) 0 0
\(229\) 29.6648i 1.96030i 0.198246 + 0.980152i \(0.436476\pi\)
−0.198246 + 0.980152i \(0.563524\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −7.39855 −0.484695 −0.242348 0.970190i \(-0.577917\pi\)
−0.242348 + 0.970190i \(0.577917\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 14.0123i 0.895214i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −28.0000 −1.76734 −0.883672 0.468106i \(-0.844936\pi\)
−0.883672 + 0.468106i \(0.844936\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) − 25.9216i − 1.59840i −0.601067 0.799198i \(-0.705258\pi\)
0.601067 0.799198i \(-0.294742\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 29.6648i − 1.80869i −0.426798 0.904347i \(-0.640358\pi\)
0.426798 0.904347i \(-0.359642\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 16.5831 1.00000
\(276\) 0 0
\(277\) 11.9473i 0.717845i 0.933367 + 0.358923i \(0.116856\pi\)
−0.933367 + 0.358923i \(0.883144\pi\)
\(278\) 0 0
\(279\) − 26.8328i − 1.60644i
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 4.69825 0.279282 0.139641 0.990202i \(-0.455405\pi\)
0.139641 + 0.990202i \(0.455405\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 30.2665 1.78038
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 24.4799i − 1.43013i −0.699057 0.715066i \(-0.746397\pi\)
0.699057 0.715066i \(-0.253603\pi\)
\(294\) 0 0
\(295\) 8.94427i 0.520756i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) − 7.30411i − 0.421002i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −15.1417 −0.864183 −0.432092 0.901830i \(-0.642224\pi\)
−0.432092 + 0.901830i \(0.642224\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) − 14.8324i − 0.841068i −0.907277 0.420534i \(-0.861843\pi\)
0.907277 0.420534i \(-0.138157\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) −5.74522 −0.323706
\(316\) 0 0
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) − 31.3315i − 1.73796i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −6.63325 −0.364596 −0.182298 0.983243i \(-0.558354\pi\)
−0.182298 + 0.983243i \(0.558354\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 34.8988 1.90106 0.950529 0.310634i \(-0.100541\pi\)
0.950529 + 0.310634i \(0.100541\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 29.6648i 1.60644i
\(342\) 0 0
\(343\) 11.3620i 0.613493i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 33.2455 1.78471 0.892355 0.451334i \(-0.149052\pi\)
0.892355 + 0.451334i \(0.149052\pi\)
\(348\) 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
\(355\) −33.1662 −1.76028
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) − 0.585274i − 0.0306347i
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) − 22.2247i − 1.15075i −0.817890 0.575375i \(-0.804856\pi\)
0.817890 0.575375i \(-0.195144\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 36.0000 1.84920 0.924598 0.380945i \(-0.124401\pi\)
0.924598 + 0.380945i \(0.124401\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 6.35158 0.323706
\(386\) 0 0
\(387\) −25.5852 −1.30057
\(388\) 0 0
\(389\) 29.6648i 1.50406i 0.659126 + 0.752032i \(0.270926\pi\)
−0.659126 + 0.752032i \(0.729074\pi\)
\(390\) 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
\(401\) −39.7995 −1.98749 −0.993746 0.111664i \(-0.964382\pi\)
−0.993746 + 0.111664i \(0.964382\pi\)
\(402\) 0 0
\(403\) 56.0475 2.79192
\(404\) 0 0
\(405\) 20.1246i 1.00000i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3.42579i 0.168572i
\(414\) 0 0
\(415\) − 27.6345i − 1.35653i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −19.8997 −0.972166 −0.486083 0.873913i \(-0.661575\pi\)
−0.486083 + 0.873913i \(0.661575\pi\)
\(420\) 0 0
\(421\) 31.3050i 1.52571i 0.646570 + 0.762855i \(0.276203\pi\)
−0.646570 + 0.762855i \(0.723797\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 34.3753 1.66745
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 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
\(441\) 18.7995 0.895214
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) − 29.6648i − 1.40625i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 13.2665 0.626085 0.313042 0.949739i \(-0.398652\pi\)
0.313042 + 0.949739i \(0.398652\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) − 12.0004i − 0.562588i
\(456\) 0 0
\(457\) 41.5121 1.94186 0.970928 0.239373i \(-0.0769419\pi\)
0.970928 + 0.239373i \(0.0769419\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 28.2855 1.30057
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 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
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) − 22.2486i − 1.00000i
\(496\) 0 0
\(497\) −12.7032 −0.569814
\(498\) 0 0
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 44.1353i 1.96789i 0.178461 + 0.983947i \(0.442888\pi\)
−0.178461 + 0.983947i \(0.557112\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) − 29.6648i − 1.31487i −0.753512 0.657434i \(-0.771642\pi\)
0.753512 0.657434i \(-0.228358\pi\)
\(510\) 0 0
\(511\) − 0.224169i − 0.00991664i
\(512\) 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
\(521\) 39.7995 1.74365 0.871824 0.489820i \(-0.162937\pi\)
0.871824 + 0.489820i \(0.162937\pi\)
\(522\) 0 0
\(523\) 36.0286 1.57542 0.787711 0.616044i \(-0.211266\pi\)
0.787711 + 0.616044i \(0.211266\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 61.4924i 2.67865i
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) − 42.4224i − 1.83408i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −20.7836 −0.895214
\(540\) 0 0
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 26.6322 1.13871 0.569354 0.822092i \(-0.307193\pi\)
0.569354 + 0.822092i \(0.307193\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 13.1179i 0.555822i 0.960607 + 0.277911i \(0.0896420\pi\)
−0.960607 + 0.277911i \(0.910358\pi\)
\(558\) 0 0
\(559\) − 53.4415i − 2.26033i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −43.6889 −1.84127 −0.920635 0.390425i \(-0.872328\pi\)
−0.920635 + 0.390425i \(0.872328\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 7.70802i 0.323706i
\(568\) 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
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 10.5844i − 0.439116i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −42.0356 −1.73796
\(586\) 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
\(593\) −48.6489 −1.99777 −0.998886 0.0471872i \(-0.984974\pi\)
−0.998886 + 0.0471872i \(0.984974\pi\)
\(594\) 0 0
\(595\) 13.1662 0.539764
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 44.7214i 1.82727i 0.406541 + 0.913633i \(0.366735\pi\)
−0.406541 + 0.913633i \(0.633265\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 24.5967i 1.00000i
\(606\) 0 0
\(607\) − 47.5610i − 1.93044i −0.261433 0.965222i \(-0.584195\pi\)
0.261433 0.965222i \(-0.415805\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 21.0541i 0.850368i 0.905107 + 0.425184i \(0.139791\pi\)
−0.905107 + 0.425184i \(0.860209\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −46.4327 −1.86629 −0.933145 0.359501i \(-0.882947\pi\)
−0.933145 + 0.359501i \(0.882947\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) − 11.3620i − 0.455211i
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) − 14.8324i − 0.590468i −0.955425 0.295234i \(-0.904602\pi\)
0.955425 0.295234i \(-0.0953977\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −50.3023 −1.99618
\(636\) 0 0
\(637\) 39.2678i 1.55585i
\(638\) 0 0
\(639\) 44.4972i 1.76028i
\(640\) 0 0
\(641\) −39.7995 −1.57199 −0.785993 0.618236i \(-0.787848\pi\)
−0.785993 + 0.618236i \(0.787848\pi\)
\(642\) 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
\(649\) −13.2665 −0.520756
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −0.785228 −0.0306347
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 29.6648i 1.15383i 0.816805 + 0.576913i \(0.195743\pi\)
−0.816805 + 0.576913i \(0.804257\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −20.1017 −0.774864 −0.387432 0.921898i \(-0.626638\pi\)
−0.387432 + 0.921898i \(0.626638\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 34.7573i 1.33583i 0.744237 + 0.667915i \(0.232813\pi\)
−0.744237 + 0.667915i \(0.767187\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 28.0000 1.06517 0.532585 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) 0 0
\(693\) − 8.52154i − 0.323706i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 4.47214i 0.167955i 0.996468 + 0.0839773i \(0.0267623\pi\)
−0.996468 + 0.0839773i \(0.973238\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 46.4721 1.73796
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 26.8328i 1.00070i 0.865825 + 0.500348i \(0.166794\pi\)
−0.865825 + 0.500348i \(0.833206\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 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
\(731\) 58.6332 2.16863
\(732\) 0 0
\(733\) − 52.9709i − 1.95652i −0.207371 0.978262i \(-0.566491\pi\)
0.207371 0.978262i \(-0.433509\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) − 49.2739i − 1.80769i −0.427865 0.903843i \(-0.640734\pi\)
0.427865 0.903843i \(-0.359266\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −37.0756 −1.35653
\(748\) 0 0
\(749\) − 16.2484i − 0.593703i
\(750\) 0 0
\(751\) − 44.4972i − 1.62373i −0.583848 0.811863i \(-0.698454\pi\)
0.583848 0.811863i \(-0.301546\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) − 46.1193i − 1.66745i
\(766\) 0 0
\(767\) 25.0652i 0.905052i
\(768\) 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
\(775\) 44.7214i 1.60644i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) − 49.1935i − 1.76028i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 11.3116 0.403214 0.201607 0.979467i \(-0.435384\pi\)
0.201607 + 0.979467i \(0.435384\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 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
\(801\) −39.7995 −1.40625
\(802\) 0 0
\(803\) 0.868102 0.0306347
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 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
\(819\) −16.1003 −0.562588
\(820\) 0 0
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −21.7550 −0.756497 −0.378248 0.925704i \(-0.623473\pi\)
−0.378248 + 0.925704i \(0.623473\pi\)
\(828\) 0 0
\(829\) − 22.3607i − 0.776619i −0.921529 0.388309i \(-0.873059\pi\)
0.921529 0.388309i \(-0.126941\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −43.0826 −1.49272
\(834\) 0 0
\(835\) −54.1324 −1.87333
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 14.8324i 0.512071i 0.966667 + 0.256036i \(0.0824164\pi\)
−0.966667 + 0.256036i \(0.917584\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) − 58.7337i − 2.02050i
\(846\) 0 0
\(847\) 9.42091i 0.323706i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 25.6505i 0.878255i 0.898425 + 0.439128i \(0.144712\pi\)
−0.898425 + 0.439128i \(0.855288\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −55.2623 −1.88772 −0.943861 0.330342i \(-0.892836\pi\)
−0.943861 + 0.330342i \(0.892836\pi\)
\(858\) 0 0
\(859\) 46.4327 1.58426 0.792132 0.610349i \(-0.208971\pi\)
0.792132 + 0.610349i \(0.208971\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 21.6722 0.736876
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 9.57536 0.323706
\(876\) 0 0
\(877\) 4.01106i 0.135444i 0.997704 + 0.0677220i \(0.0215731\pi\)
−0.997704 + 0.0677220i \(0.978427\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2.00000 −0.0673817 −0.0336909 0.999432i \(-0.510726\pi\)
−0.0336909 + 0.999432i \(0.510726\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 31.0603i 1.04290i 0.853281 + 0.521452i \(0.174609\pi\)
−0.853281 + 0.521452i \(0.825391\pi\)
\(888\) 0 0
\(889\) −19.2665 −0.646178
\(890\) 0 0
\(891\) −29.8496 −1.00000
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 44.4972i 1.48738i
\(896\) 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
\(905\) 10.0000 0.332411
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) − 8.94427i − 0.296337i −0.988962 0.148168i \(-0.952662\pi\)
0.988962 0.148168i \(-0.0473378\pi\)
\(912\) 0 0
\(913\) 40.9886 1.35653
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −92.9442 −3.05930
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 14.0000 0.459325 0.229663 0.973270i \(-0.426238\pi\)
0.229663 + 0.973270i \(0.426238\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 50.9868i 1.66745i
\(936\) 0 0
\(937\) −49.1724 −1.60639 −0.803196 0.595714i \(-0.796869\pi\)
−0.803196 + 0.595714i \(0.796869\pi\)
\(938\) 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
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) − 1.64016i − 0.0532418i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 12.9649 0.419974 0.209987 0.977704i \(-0.432658\pi\)
0.209987 + 0.977704i \(0.432658\pi\)
\(954\) 0 0
\(955\) −60.0000 −1.94155
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −49.0000 −1.58065
\(962\) 0 0
\(963\) −56.9156 −1.83408
\(964\) 0 0
\(965\) 62.0777i 1.99835i
\(966\) 0 0
\(967\) 37.2837i 1.19896i 0.800389 + 0.599481i \(0.204626\pi\)
−0.800389 + 0.599481i \(0.795374\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 59.6992 1.91584 0.957920 0.287035i \(-0.0926697\pi\)
0.957920 + 0.287035i \(0.0926697\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 44.0000 1.40625
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) −62.3991 −1.98820
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 62.6099i 1.98887i 0.105356 + 0.994435i \(0.466402\pi\)
−0.105356 + 0.994435i \(0.533598\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −33.1662 −1.05144
\(996\) 0 0
\(997\) − 58.6519i − 1.85753i −0.370675 0.928763i \(-0.620874\pi\)
0.370675 0.928763i \(-0.379126\pi\)
\(998\) 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 1760.2.c.b.879.7 8
4.3 odd 2 440.2.c.b.219.4 yes 8
5.4 even 2 inner 1760.2.c.b.879.6 8
8.3 odd 2 inner 1760.2.c.b.879.2 8
8.5 even 2 440.2.c.b.219.3 8
11.10 odd 2 inner 1760.2.c.b.879.6 8
20.19 odd 2 440.2.c.b.219.5 yes 8
40.19 odd 2 inner 1760.2.c.b.879.3 8
40.29 even 2 440.2.c.b.219.6 yes 8
44.43 even 2 440.2.c.b.219.5 yes 8
55.54 odd 2 CM 1760.2.c.b.879.7 8
88.21 odd 2 440.2.c.b.219.6 yes 8
88.43 even 2 inner 1760.2.c.b.879.3 8
220.219 even 2 440.2.c.b.219.4 yes 8
440.109 odd 2 440.2.c.b.219.3 8
440.219 even 2 inner 1760.2.c.b.879.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
440.2.c.b.219.3 8 8.5 even 2
440.2.c.b.219.3 8 440.109 odd 2
440.2.c.b.219.4 yes 8 4.3 odd 2
440.2.c.b.219.4 yes 8 220.219 even 2
440.2.c.b.219.5 yes 8 20.19 odd 2
440.2.c.b.219.5 yes 8 44.43 even 2
440.2.c.b.219.6 yes 8 40.29 even 2
440.2.c.b.219.6 yes 8 88.21 odd 2
1760.2.c.b.879.2 8 8.3 odd 2 inner
1760.2.c.b.879.2 8 440.219 even 2 inner
1760.2.c.b.879.3 8 40.19 odd 2 inner
1760.2.c.b.879.3 8 88.43 even 2 inner
1760.2.c.b.879.6 8 5.4 even 2 inner
1760.2.c.b.879.6 8 11.10 odd 2 inner
1760.2.c.b.879.7 8 1.1 even 1 trivial
1760.2.c.b.879.7 8 55.54 odd 2 CM