Properties

Label 1760.2.c.b.879.8
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 879.8
Root \(-1.35246 + 0.413333i\) of defining polynomial
Character \(\chi\) \(=\) 1760.879
Dual form 1760.2.c.b.879.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.23607i q^{5} +5.22173i q^{7} +3.00000 q^{9} +3.31662 q^{11} +3.56840i q^{13} +4.55341 q^{17} -5.00000 q^{25} -8.94427i q^{31} -11.6762 q^{35} +9.96326 q^{43} +6.70820i q^{45} -20.2665 q^{49} +7.41620i q^{55} +4.00000 q^{59} +15.6652i q^{63} -7.97919 q^{65} -14.8324i q^{71} -17.0860 q^{73} +17.3185i q^{77} +9.00000 q^{81} -13.3890 q^{83} +10.1817i q^{85} +13.2665 q^{89} -18.6332 q^{91} +9.94987 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 24 q^{9} - 40 q^{25} - 56 q^{49} + 32 q^{59} + 72 q^{81} - 96 q^{91}+O(q^{100}) \) 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
\(7\) 5.22173i 1.97363i 0.161853 + 0.986815i \(0.448253\pi\)
−0.161853 + 0.986815i \(0.551747\pi\)
\(8\) 0 0
\(9\) 3.00000 1.00000
\(10\) 0 0
\(11\) 3.31662 1.00000
\(12\) 0 0
\(13\) 3.56840i 0.989697i 0.868979 + 0.494848i \(0.164776\pi\)
−0.868979 + 0.494848i \(0.835224\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.55341 1.10436 0.552182 0.833724i \(-0.313796\pi\)
0.552182 + 0.833724i \(0.313796\pi\)
\(18\) 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
\(35\) −11.6762 −1.97363
\(36\) 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
\(43\) 9.96326 1.51938 0.759691 0.650284i \(-0.225350\pi\)
0.759691 + 0.650284i \(0.225350\pi\)
\(44\) 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
\(49\) −20.2665 −2.89521
\(50\) 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
\(63\) 15.6652i 1.97363i
\(64\) 0 0
\(65\) −7.97919 −0.989697
\(66\) 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 \(-0.657448\pi\)
0.474713 0.880141i \(-0.342552\pi\)
\(72\) 0 0
\(73\) −17.0860 −1.99977 −0.999883 0.0153173i \(-0.995124\pi\)
−0.999883 + 0.0153173i \(0.995124\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 17.3185i 1.97363i
\(78\) 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
\(83\) −13.3890 −1.46964 −0.734819 0.678263i \(-0.762733\pi\)
−0.734819 + 0.678263i \(0.762733\pi\)
\(84\) 0 0
\(85\) 10.1817i 1.10436i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 13.2665 1.40625 0.703123 0.711068i \(-0.251788\pi\)
0.703123 + 0.711068i \(0.251788\pi\)
\(90\) 0 0
\(91\) −18.6332 −1.95330
\(92\) 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
\(107\) 8.25036 0.797593 0.398796 0.917039i \(-0.369428\pi\)
0.398796 + 0.917039i \(0.369428\pi\)
\(108\) 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
\(117\) 10.7052i 0.989697i
\(118\) 0 0
\(119\) 23.7767i 2.17960i
\(120\) 0 0
\(121\) 11.0000 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 11.1803i − 1.00000i
\(126\) 0 0
\(127\) − 1.39159i − 0.123483i −0.998092 0.0617417i \(-0.980334\pi\)
0.998092 0.0617417i \(-0.0196655\pi\)
\(128\) 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
\(143\) 11.8351i 0.989697i
\(144\) 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
\(153\) 13.6602 1.10436
\(154\) 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
\(167\) 9.05188i 0.700455i 0.936665 + 0.350228i \(0.113896\pi\)
−0.936665 + 0.350228i \(0.886104\pi\)
\(168\) 0 0
\(169\) 0.266499 0.0204999
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 24.4553i − 1.85930i −0.368438 0.929652i \(-0.620107\pi\)
0.368438 0.929652i \(-0.379893\pi\)
\(174\) 0 0
\(175\) − 26.1087i − 1.97363i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −19.8997 −1.48738 −0.743689 0.668526i \(-0.766925\pi\)
−0.743689 + 0.668526i \(0.766925\pi\)
\(180\) 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
\(187\) 15.1019 1.10436
\(188\) 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
\(193\) −1.12762 −0.0811678 −0.0405839 0.999176i \(-0.512922\pi\)
−0.0405839 + 0.999176i \(0.512922\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 3.04492i − 0.216941i −0.994100 0.108471i \(-0.965405\pi\)
0.994100 0.108471i \(-0.0345954\pi\)
\(198\) 0 0
\(199\) − 14.8324i − 1.05144i −0.850657 0.525720i \(-0.823796\pi\)
0.850657 0.525720i \(-0.176204\pi\)
\(200\) 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
\(215\) 22.2785i 1.51938i
\(216\) 0 0
\(217\) 46.7046 3.17052
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 16.2484i 1.09298i
\(222\) 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
\(227\) −6.53747 −0.433907 −0.216954 0.976182i \(-0.569612\pi\)
−0.216954 + 0.976182i \(0.569612\pi\)
\(228\) 0 0
\(229\) − 29.6648i − 1.96030i −0.198246 0.980152i \(-0.563524\pi\)
0.198246 0.980152i \(-0.436476\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −29.6186 −1.94038 −0.970190 0.242348i \(-0.922083\pi\)
−0.970190 + 0.242348i \(0.922083\pi\)
\(234\) 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
\(245\) − 45.3173i − 2.89521i
\(246\) 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
\(263\) − 19.4953i − 1.20213i −0.799198 0.601067i \(-0.794742\pi\)
0.799198 0.601067i \(-0.205258\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 29.6648i 1.80869i 0.426798 + 0.904347i \(0.359642\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 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
\(277\) − 31.0687i − 1.86673i −0.358923 0.933367i \(-0.616856\pi\)
0.358923 0.933367i \(-0.383144\pi\)
\(278\) 0 0
\(279\) − 26.8328i − 1.60644i
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −33.3156 −1.98040 −0.990202 0.139641i \(-0.955405\pi\)
−0.990202 + 0.139641i \(0.955405\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 3.73350 0.219618
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 23.9319i 1.39811i 0.715066 + 0.699057i \(0.246397\pi\)
−0.715066 + 0.699057i \(0.753603\pi\)
\(294\) 0 0
\(295\) 8.94427i 0.520756i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 52.0255i 2.99870i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 31.6027 1.80366 0.901830 0.432092i \(-0.142224\pi\)
0.901830 + 0.432092i \(0.142224\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 14.8324i 0.841068i 0.907277 + 0.420534i \(0.138157\pi\)
−0.907277 + 0.420534i \(0.861843\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) −35.0285 −1.97363
\(316\) 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
\(325\) − 17.8420i − 0.989697i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 6.63325 0.364596 0.182298 0.983243i \(-0.441646\pi\)
0.182298 + 0.983243i \(0.441646\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 11.4050 0.621269 0.310634 0.950529i \(-0.399459\pi\)
0.310634 + 0.950529i \(0.399459\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) − 29.6648i − 1.60644i
\(342\) 0 0
\(343\) − 69.2741i − 3.74045i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 16.8148 0.902667 0.451334 0.892355i \(-0.350948\pi\)
0.451334 + 0.892355i \(0.350948\pi\)
\(348\) 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
\(365\) − 38.2055i − 1.99977i
\(366\) 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
\(373\) − 31.5921i − 1.63578i −0.575375 0.817890i \(-0.695144\pi\)
0.575375 0.817890i \(-0.304856\pi\)
\(374\) 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
\(385\) −38.7254 −1.97363
\(386\) 0 0
\(387\) 29.8898 1.51938
\(388\) 0 0
\(389\) − 29.6648i − 1.50406i −0.659126 0.752032i \(-0.729074\pi\)
0.659126 0.752032i \(-0.270926\pi\)
\(390\) 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 \(-0.0356180\pi\)
0.993746 + 0.111664i \(0.0356180\pi\)
\(402\) 0 0
\(403\) 31.9168 1.58989
\(404\) 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
\(413\) 20.8869i 1.02778i
\(414\) 0 0
\(415\) − 29.9388i − 1.46964i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 19.8997 0.972166 0.486083 0.873913i \(-0.338425\pi\)
0.486083 + 0.873913i \(0.338425\pi\)
\(420\) 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
\(425\) −22.7670 −1.10436
\(426\) 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
\(441\) −60.7995 −2.89521
\(442\) 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 \(-0.601348\pi\)
−0.313042 + 0.949739i \(0.601348\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) − 41.6652i − 1.95330i
\(456\) 0 0
\(457\) −10.2344 −0.478746 −0.239373 0.970928i \(-0.576942\pi\)
−0.239373 + 0.970928i \(0.576942\pi\)
\(458\) 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
\(473\) 33.0444 1.51938
\(474\) 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
\(497\) 77.4508 3.47414
\(498\) 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
\(503\) − 8.00491i − 0.356921i −0.983947 0.178461i \(-0.942888\pi\)
0.983947 0.178461i \(-0.0571117\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 29.6648i 1.31487i 0.753512 + 0.657434i \(0.228358\pi\)
−0.753512 + 0.657434i \(0.771642\pi\)
\(510\) 0 0
\(511\) − 89.2186i − 3.94680i
\(512\) 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 \(-0.837063\pi\)
−0.871824 + 0.489820i \(0.837063\pi\)
\(522\) 0 0
\(523\) −28.1769 −1.23209 −0.616044 0.787711i \(-0.711266\pi\)
−0.616044 + 0.787711i \(0.711266\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) − 40.7269i − 1.77409i
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 18.4484i 0.797593i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −67.2164 −2.89521
\(540\) 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
\(547\) 38.4542 1.64418 0.822092 0.569354i \(-0.192807\pi\)
0.822092 + 0.569354i \(0.192807\pi\)
\(548\) 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
\(557\) 45.3423i 1.92121i 0.277911 + 0.960607i \(0.410358\pi\)
−0.277911 + 0.960607i \(0.589642\pi\)
\(558\) 0 0
\(559\) 35.5529i 1.50373i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −18.5277 −0.780850 −0.390425 0.920635i \(-0.627672\pi\)
−0.390425 + 0.920635i \(0.627672\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 46.9956i 1.97363i
\(568\) 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
\(581\) − 69.9140i − 2.90052i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −23.9376 −0.989697
\(586\) 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
\(593\) −2.29817 −0.0943744 −0.0471872 0.998886i \(-0.515026\pi\)
−0.0471872 + 0.998886i \(0.515026\pi\)
\(594\) 0 0
\(595\) −53.1662 −2.17960
\(596\) 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
\(607\) − 12.8820i − 0.522865i −0.965222 0.261433i \(-0.915805\pi\)
0.965222 0.261433i \(-0.0841949\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) − 44.8188i − 1.81021i −0.425184 0.905107i \(-0.639791\pi\)
0.425184 0.905107i \(-0.360209\pi\)
\(614\) 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 \(-0.117053\pi\)
0.933145 + 0.359501i \(0.117053\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 69.2741i 2.77541i
\(624\) 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 \(0.0953977\pi\)
−0.955425 + 0.295234i \(0.904602\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3.11168 0.123483
\(636\) 0 0
\(637\) − 72.3190i − 2.86538i
\(638\) 0 0
\(639\) − 44.4972i − 1.76028i
\(640\) 0 0
\(641\) 39.7995 1.57199 0.785993 0.618236i \(-0.212152\pi\)
0.785993 + 0.618236i \(0.212152\pi\)
\(642\) 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
\(657\) −51.2580 −1.99977
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) − 29.6648i − 1.15383i −0.816805 0.576913i \(-0.804257\pi\)
0.816805 0.576913i \(-0.195743\pi\)
\(662\) 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
\(673\) 47.8322 1.84380 0.921898 0.387432i \(-0.126638\pi\)
0.921898 + 0.387432i \(0.126638\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 38.7289i 1.48847i 0.667915 + 0.744237i \(0.267187\pi\)
−0.667915 + 0.744237i \(0.732813\pi\)
\(678\) 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
\(693\) 51.9556i 1.97363i
\(694\) 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
\(715\) −26.4640 −0.989697
\(716\) 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
\(731\) 45.3668 1.67795
\(732\) 0 0
\(733\) − 11.2287i − 0.414741i −0.978262 0.207371i \(-0.933509\pi\)
0.978262 0.207371i \(-0.0664906\pi\)
\(734\) 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
\(743\) − 23.3255i − 0.855729i −0.903843 0.427865i \(-0.859266\pi\)
0.903843 0.427865i \(-0.140734\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −40.1671 −1.46964
\(748\) 0 0
\(749\) 43.0812i 1.57415i
\(750\) 0 0
\(751\) 44.4972i 1.62373i 0.583848 + 0.811863i \(0.301546\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) 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
\(765\) 30.5452i 1.10436i
\(766\) 0 0
\(767\) 14.2736i 0.515390i
\(768\) 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
\(787\) −54.9550 −1.95893 −0.979467 0.201607i \(-0.935384\pi\)
−0.979467 + 0.201607i \(0.935384\pi\)
\(788\) 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
\(803\) −56.6679 −1.99977
\(804\) 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
\(819\) −55.8997 −1.95330
\(820\) 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
\(827\) 53.2421 1.85141 0.925704 0.378248i \(-0.123473\pi\)
0.925704 + 0.378248i \(0.123473\pi\)
\(828\) 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
\(833\) −92.2816 −3.19737
\(834\) 0 0
\(835\) −20.2406 −0.700455
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) − 14.8324i − 0.512071i −0.966667 0.256036i \(-0.917584\pi\)
0.966667 0.256036i \(-0.0824164\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0.595910i 0.0204999i
\(846\) 0 0
\(847\) 57.4391i 1.97363i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 52.4791i 1.79685i 0.439128 + 0.898425i \(0.355288\pi\)
−0.439128 + 0.898425i \(0.644712\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 19.3412 0.660684 0.330342 0.943861i \(-0.392836\pi\)
0.330342 + 0.943861i \(0.392836\pi\)
\(858\) 0 0
\(859\) −46.4327 −1.58426 −0.792132 0.610349i \(-0.791029\pi\)
−0.792132 + 0.610349i \(0.791029\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 54.6838 1.85930
\(866\) 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
\(875\) 58.3808 1.97363
\(876\) 0 0
\(877\) 59.0924i 1.99541i 0.0677220 + 0.997704i \(0.478427\pi\)
−0.0677220 + 0.997704i \(0.521573\pi\)
\(878\) 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
\(887\) 50.8257i 1.70656i 0.521452 + 0.853281i \(0.325391\pi\)
−0.521452 + 0.853281i \(0.674609\pi\)
\(888\) 0 0
\(889\) 7.26650 0.243711
\(890\) 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
\(913\) −44.4064 −1.46964
\(914\) 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
\(923\) 52.9280 1.74215
\(924\) 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
\(935\) 33.7690i 1.10436i
\(936\) 0 0
\(937\) −36.4702 −1.19143 −0.595714 0.803196i \(-0.703131\pi\)
−0.595714 + 0.803196i \(0.703131\pi\)
\(938\) 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
\(949\) − 60.9697i − 1.97916i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −60.3648 −1.95541 −0.977704 0.209987i \(-0.932658\pi\)
−0.977704 + 0.209987i \(0.932658\pi\)
\(954\) 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
\(963\) 24.7511 0.797593
\(964\) 0 0
\(965\) − 2.52143i − 0.0811678i
\(966\) 0 0
\(967\) − 49.7788i − 1.60078i −0.599481 0.800389i \(-0.704626\pi\)
0.599481 0.800389i \(-0.295374\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −59.6992 −1.91584 −0.957920 0.287035i \(-0.907330\pi\)
−0.957920 + 0.287035i \(0.907330\pi\)
\(972\) 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
\(985\) 6.80864 0.216941
\(986\) 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
\(997\) 23.4084i 0.741350i 0.928763 + 0.370675i \(0.120874\pi\)
−0.928763 + 0.370675i \(0.879126\pi\)
\(998\) 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.879.8 8
4.3 odd 2 440.2.c.b.219.7 yes 8
5.4 even 2 inner 1760.2.c.b.879.5 8
8.3 odd 2 inner 1760.2.c.b.879.1 8
8.5 even 2 440.2.c.b.219.8 yes 8
11.10 odd 2 inner 1760.2.c.b.879.5 8
20.19 odd 2 440.2.c.b.219.2 yes 8
40.19 odd 2 inner 1760.2.c.b.879.4 8
40.29 even 2 440.2.c.b.219.1 8
44.43 even 2 440.2.c.b.219.2 yes 8
55.54 odd 2 CM 1760.2.c.b.879.8 8
88.21 odd 2 440.2.c.b.219.1 8
88.43 even 2 inner 1760.2.c.b.879.4 8
220.219 even 2 440.2.c.b.219.7 yes 8
440.109 odd 2 440.2.c.b.219.8 yes 8
440.219 even 2 inner 1760.2.c.b.879.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
440.2.c.b.219.1 8 40.29 even 2
440.2.c.b.219.1 8 88.21 odd 2
440.2.c.b.219.2 yes 8 20.19 odd 2
440.2.c.b.219.2 yes 8 44.43 even 2
440.2.c.b.219.7 yes 8 4.3 odd 2
440.2.c.b.219.7 yes 8 220.219 even 2
440.2.c.b.219.8 yes 8 8.5 even 2
440.2.c.b.219.8 yes 8 440.109 odd 2
1760.2.c.b.879.1 8 8.3 odd 2 inner
1760.2.c.b.879.1 8 440.219 even 2 inner
1760.2.c.b.879.4 8 40.19 odd 2 inner
1760.2.c.b.879.4 8 88.43 even 2 inner
1760.2.c.b.879.5 8 5.4 even 2 inner
1760.2.c.b.879.5 8 11.10 odd 2 inner
1760.2.c.b.879.8 8 1.1 even 1 trivial
1760.2.c.b.879.8 8 55.54 odd 2 CM