Properties

Label 2240.2.n.d.1119.3
Level $2240$
Weight $2$
Character 2240.1119
Analytic conductor $17.886$
Analytic rank $0$
Dimension $8$
CM discriminant -280
Inner twists $16$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2240,2,Mod(1119,2240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2240, 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("2240.1119");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2240.n (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: no
Analytic conductor: \(17.8864900528\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.384160000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 9x^{6} + 37x^{4} - 36x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 1119.3
Root \(0.817582 - 0.309017i\) of defining polynomial
Character \(\chi\) \(=\) 2240.1119
Dual form 2240.2.n.d.1119.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.23607 q^{5} +2.64575i q^{7} -3.00000 q^{9} +O(q^{10})\) \(q-2.23607 q^{5} +2.64575i q^{7} -3.00000 q^{9} -5.29150 q^{17} -4.47214i q^{19} +5.00000 q^{25} -5.91608i q^{35} +11.8322 q^{37} -11.8322i q^{43} +6.70820 q^{45} +5.29150i q^{47} -7.00000 q^{49} +11.8322 q^{53} +13.4164i q^{59} -4.47214 q^{61} -7.93725i q^{63} -11.8322i q^{67} +2.00000i q^{71} +15.8745 q^{73} -6.00000i q^{79} +9.00000 q^{81} +11.8322 q^{85} +10.0000i q^{95} -5.29150 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 24 q^{9} + 40 q^{25} - 56 q^{49} + 72 q^{81}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).

\(n\) \(897\) \(1471\) \(1541\) \(1921\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(-1\)

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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) −2.23607 −1.00000
\(6\) 0 0
\(7\) 2.64575i 1.00000i
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −5.29150 −1.28338 −0.641689 0.766965i \(-0.721766\pi\)
−0.641689 + 0.766965i \(0.721766\pi\)
\(18\) 0 0
\(19\) − 4.47214i − 1.02598i −0.858395 0.512989i \(-0.828538\pi\)
0.858395 0.512989i \(-0.171462\pi\)
\(20\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 5.91608i − 1.00000i
\(36\) 0 0
\(37\) 11.8322 1.94520 0.972598 0.232495i \(-0.0746890\pi\)
0.972598 + 0.232495i \(0.0746890\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) − 11.8322i − 1.80439i −0.431331 0.902194i \(-0.641956\pi\)
0.431331 0.902194i \(-0.358044\pi\)
\(44\) 0 0
\(45\) 6.70820 1.00000
\(46\) 0 0
\(47\) 5.29150i 0.771845i 0.922531 + 0.385922i \(0.126117\pi\)
−0.922531 + 0.385922i \(0.873883\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 11.8322 1.62527 0.812636 0.582772i \(-0.198032\pi\)
0.812636 + 0.582772i \(0.198032\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 13.4164i 1.74667i 0.487122 + 0.873334i \(0.338047\pi\)
−0.487122 + 0.873334i \(0.661953\pi\)
\(60\) 0 0
\(61\) −4.47214 −0.572598 −0.286299 0.958140i \(-0.592425\pi\)
−0.286299 + 0.958140i \(0.592425\pi\)
\(62\) 0 0
\(63\) − 7.93725i − 1.00000i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) − 11.8322i − 1.44553i −0.691095 0.722764i \(-0.742871\pi\)
0.691095 0.722764i \(-0.257129\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.00000i 0.237356i 0.992933 + 0.118678i \(0.0378657\pi\)
−0.992933 + 0.118678i \(0.962134\pi\)
\(72\) 0 0
\(73\) 15.8745 1.85797 0.928985 0.370117i \(-0.120682\pi\)
0.928985 + 0.370117i \(0.120682\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) − 6.00000i − 0.675053i −0.941316 0.337526i \(-0.890410\pi\)
0.941316 0.337526i \(-0.109590\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 11.8322 1.28338
\(86\) 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
\(95\) 10.0000i 1.02598i
\(96\) 0 0
\(97\) −5.29150 −0.537271 −0.268635 0.963242i \(-0.586573\pi\)
−0.268635 + 0.963242i \(0.586573\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 13.4164 1.33498 0.667491 0.744618i \(-0.267368\pi\)
0.667491 + 0.744618i \(0.267368\pi\)
\(102\) 0 0
\(103\) − 15.8745i − 1.56416i −0.623177 0.782081i \(-0.714158\pi\)
0.623177 0.782081i \(-0.285842\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 11.8322i − 1.14386i −0.820303 0.571929i \(-0.806195\pi\)
0.820303 0.571929i \(-0.193805\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 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
\(117\) 0 0
\(118\) 0 0
\(119\) − 14.0000i − 1.28338i
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −11.1803 −1.00000
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) − 4.47214i − 0.390732i −0.980730 0.195366i \(-0.937410\pi\)
0.980730 0.195366i \(-0.0625895\pi\)
\(132\) 0 0
\(133\) 11.8322 1.02598
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) − 22.3607i − 1.89661i −0.317363 0.948304i \(-0.602797\pi\)
0.317363 0.948304i \(-0.397203\pi\)
\(140\) 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
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 18.0000i 1.46482i 0.680864 + 0.732410i \(0.261604\pi\)
−0.680864 + 0.732410i \(0.738396\pi\)
\(152\) 0 0
\(153\) 15.8745 1.28338
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) − 11.8322i − 0.926766i −0.886158 0.463383i \(-0.846635\pi\)
0.886158 0.463383i \(-0.153365\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.29150i 0.409469i 0.978818 + 0.204734i \(0.0656331\pi\)
−0.978818 + 0.204734i \(0.934367\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) 13.4164i 1.02598i
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 13.2288i 1.00000i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) −22.3607 −1.66206 −0.831028 0.556230i \(-0.812247\pi\)
−0.831028 + 0.556230i \(0.812247\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −26.4575 −1.94520
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) − 22.0000i − 1.59186i −0.605386 0.795932i \(-0.706981\pi\)
0.605386 0.795932i \(-0.293019\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 11.8322 0.843006 0.421503 0.906827i \(-0.361503\pi\)
0.421503 + 0.906827i \(0.361503\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 26.4575i 1.80439i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) − 15.8745i − 1.06304i −0.847047 0.531518i \(-0.821622\pi\)
0.847047 0.531518i \(-0.178378\pi\)
\(224\) 0 0
\(225\) −15.0000 −1.00000
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) −4.47214 −0.295527 −0.147764 0.989023i \(-0.547207\pi\)
−0.147764 + 0.989023i \(0.547207\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) − 11.8322i − 0.771845i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 26.0000i 1.68180i 0.541190 + 0.840900i \(0.317974\pi\)
−0.541190 + 0.840900i \(0.682026\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 15.6525 1.00000
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 22.3607i − 1.41139i −0.708514 0.705697i \(-0.750634\pi\)
0.708514 0.705697i \(-0.249366\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5.29150 −0.330075 −0.165037 0.986287i \(-0.552774\pi\)
−0.165037 + 0.986287i \(0.552774\pi\)
\(258\) 0 0
\(259\) 31.3050i 1.94520i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −26.4575 −1.62527
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 13.4164 0.818013 0.409006 0.912532i \(-0.365875\pi\)
0.409006 + 0.912532i \(0.365875\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 11.8322 0.710926 0.355463 0.934690i \(-0.384323\pi\)
0.355463 + 0.934690i \(0.384323\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2.00000 0.119310 0.0596550 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 11.0000 0.647059
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) − 30.0000i − 1.74667i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 31.3050 1.80439
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 10.0000 0.572598
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 15.8745 0.897280 0.448640 0.893713i \(-0.351909\pi\)
0.448640 + 0.893713i \(0.351909\pi\)
\(314\) 0 0
\(315\) 17.7482i 1.00000i
\(316\) 0 0
\(317\) −35.4965 −1.99368 −0.996840 0.0794301i \(-0.974690\pi\)
−0.996840 + 0.0794301i \(0.974690\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 23.6643i 1.31672i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −14.0000 −0.771845
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 0 0
\(333\) −35.4965 −1.94520
\(334\) 0 0
\(335\) 26.4575i 1.44553i
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 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
\(347\) 35.4965i 1.90555i 0.303676 + 0.952775i \(0.401786\pi\)
−0.303676 + 0.952775i \(0.598214\pi\)
\(348\) 0 0
\(349\) −22.3607 −1.19694 −0.598470 0.801145i \(-0.704224\pi\)
−0.598470 + 0.801145i \(0.704224\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 37.0405 1.97147 0.985734 0.168311i \(-0.0538313\pi\)
0.985734 + 0.168311i \(0.0538313\pi\)
\(354\) 0 0
\(355\) − 4.47214i − 0.237356i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 34.0000i 1.79445i 0.441572 + 0.897226i \(0.354421\pi\)
−0.441572 + 0.897226i \(0.645579\pi\)
\(360\) 0 0
\(361\) −1.00000 −0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −35.4965 −1.85797
\(366\) 0 0
\(367\) 5.29150i 0.276214i 0.990417 + 0.138107i \(0.0441018\pi\)
−0.990417 + 0.138107i \(0.955898\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 31.3050i 1.62527i
\(372\) 0 0
\(373\) 11.8322 0.612646 0.306323 0.951928i \(-0.400901\pi\)
0.306323 + 0.951928i \(0.400901\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) − 37.0405i − 1.89268i −0.323170 0.946341i \(-0.604748\pi\)
0.323170 0.946341i \(-0.395252\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 35.4965i 1.80439i
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 13.4164i 0.675053i
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −22.0000 −1.09863 −0.549314 0.835616i \(-0.685111\pi\)
−0.549314 + 0.835616i \(0.685111\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −20.1246 −1.00000
\(406\) 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
\(413\) −35.4965 −1.74667
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 40.2492i − 1.96630i −0.182792 0.983152i \(-0.558513\pi\)
0.182792 0.983152i \(-0.441487\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) − 15.8745i − 0.771845i
\(424\) 0 0
\(425\) −26.4575 −1.28338
\(426\) 0 0
\(427\) − 11.8322i − 0.572598i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) − 38.0000i − 1.83040i −0.403005 0.915198i \(-0.632034\pi\)
0.403005 0.915198i \(-0.367966\pi\)
\(432\) 0 0
\(433\) 37.0405 1.78005 0.890027 0.455908i \(-0.150685\pi\)
0.890027 + 0.455908i \(0.150685\pi\)
\(434\) 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
\(443\) 35.4965i 1.68649i 0.537531 + 0.843244i \(0.319357\pi\)
−0.537531 + 0.843244i \(0.680643\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 26.0000 1.22702 0.613508 0.789689i \(-0.289758\pi\)
0.613508 + 0.789689i \(0.289758\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −40.2492 −1.87459 −0.937297 0.348533i \(-0.886680\pi\)
−0.937297 + 0.348533i \(0.886680\pi\)
\(462\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 31.3050 1.44553
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) − 22.3607i − 1.02598i
\(476\) 0 0
\(477\) −35.4965 −1.62527
\(478\) 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
\(485\) 11.8322 0.537271
\(486\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.29150 −0.237356
\(498\) 0 0
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) − 37.0405i − 1.65156i −0.563996 0.825778i \(-0.690737\pi\)
0.563996 0.825778i \(-0.309263\pi\)
\(504\) 0 0
\(505\) −30.0000 −1.33498
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4.47214 −0.198224 −0.0991120 0.995076i \(-0.531600\pi\)
−0.0991120 + 0.995076i \(0.531600\pi\)
\(510\) 0 0
\(511\) 42.0000i 1.85797i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 35.4965i 1.56416i
\(516\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) − 40.2492i − 1.74667i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 26.4575i 1.14386i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) − 11.8322i − 0.505907i −0.967478 0.252953i \(-0.918598\pi\)
0.967478 0.252953i \(-0.0814019\pi\)
\(548\) 0 0
\(549\) 13.4164 0.572598
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 15.8745 0.675053
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −35.4965 −1.50403 −0.752017 0.659144i \(-0.770919\pi\)
−0.752017 + 0.659144i \(0.770919\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 23.8118i 1.00000i
\(568\) 0 0
\(569\) 34.0000 1.42535 0.712677 0.701492i \(-0.247483\pi\)
0.712677 + 0.701492i \(0.247483\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −47.6235 −1.98259 −0.991297 0.131647i \(-0.957973\pi\)
−0.991297 + 0.131647i \(0.957973\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 37.0405 1.52107 0.760536 0.649296i \(-0.224936\pi\)
0.760536 + 0.649296i \(0.224936\pi\)
\(594\) 0 0
\(595\) 31.3050i 1.28338i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) − 46.0000i − 1.87951i −0.341850 0.939755i \(-0.611053\pi\)
0.341850 0.939755i \(-0.388947\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 35.4965i 1.44553i
\(604\) 0 0
\(605\) 24.5967 1.00000
\(606\) 0 0
\(607\) 47.6235i 1.93298i 0.256706 + 0.966490i \(0.417363\pi\)
−0.256706 + 0.966490i \(0.582637\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 11.8322 0.477896 0.238948 0.971032i \(-0.423197\pi\)
0.238948 + 0.971032i \(0.423197\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 49.1935i 1.97725i 0.150390 + 0.988627i \(0.451947\pi\)
−0.150390 + 0.988627i \(0.548053\pi\)
\(620\) 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
\(629\) −62.6099 −2.49642
\(630\) 0 0
\(631\) 2.00000i 0.0796187i 0.999207 + 0.0398094i \(0.0126751\pi\)
−0.999207 + 0.0398094i \(0.987325\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) − 6.00000i − 0.237356i
\(640\) 0 0
\(641\) −38.0000 −1.50091 −0.750455 0.660922i \(-0.770166\pi\)
−0.750455 + 0.660922i \(0.770166\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.29150i 0.208030i 0.994576 + 0.104015i \(0.0331691\pi\)
−0.994576 + 0.104015i \(0.966831\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −35.4965 −1.38908 −0.694542 0.719452i \(-0.744393\pi\)
−0.694542 + 0.719452i \(0.744393\pi\)
\(654\) 0 0
\(655\) 10.0000i 0.390732i
\(656\) 0 0
\(657\) −47.6235 −1.85797
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 49.1935 1.91341 0.956703 0.291067i \(-0.0940103\pi\)
0.956703 + 0.291067i \(0.0940103\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −26.4575 −1.02598
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 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
\(679\) − 14.0000i − 0.537271i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 11.8322i − 0.452745i −0.974041 0.226373i \(-0.927313\pi\)
0.974041 0.226373i \(-0.0726867\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) − 4.47214i − 0.170128i −0.996375 0.0850640i \(-0.972891\pi\)
0.996375 0.0850640i \(-0.0271095\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 50.0000i 1.89661i
\(696\) 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
\(703\) − 52.9150i − 1.99573i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 35.4965i 1.33498i
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 18.0000i 0.675053i
\(712\) 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
\(721\) 42.0000 1.56416
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 47.6235i 1.76626i 0.469130 + 0.883129i \(0.344568\pi\)
−0.469130 + 0.883129i \(0.655432\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 62.6099i 2.31571i
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 31.3050 1.14386
\(750\) 0 0
\(751\) − 22.0000i − 0.802791i −0.915905 0.401396i \(-0.868525\pi\)
0.915905 0.401396i \(-0.131475\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) − 40.2492i − 1.46482i
\(756\) 0 0
\(757\) 11.8322 0.430047 0.215024 0.976609i \(-0.431017\pi\)
0.215024 + 0.976609i \(0.431017\pi\)
\(758\) 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
\(765\) −35.4965 −1.28338
\(766\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) − 28.0000i − 0.990569i
\(800\) 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
\(809\) −46.0000 −1.61727 −0.808637 0.588308i \(-0.799794\pi\)
−0.808637 + 0.588308i \(0.799794\pi\)
\(810\) 0 0
\(811\) − 22.3607i − 0.785190i −0.919712 0.392595i \(-0.871577\pi\)
0.919712 0.392595i \(-0.128423\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 26.4575i 0.926766i
\(816\) 0 0
\(817\) −52.9150 −1.85126
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 35.4965i 1.23433i 0.786832 + 0.617167i \(0.211720\pi\)
−0.786832 + 0.617167i \(0.788280\pi\)
\(828\) 0 0
\(829\) 49.1935 1.70856 0.854280 0.519813i \(-0.173998\pi\)
0.854280 + 0.519813i \(0.173998\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 37.0405 1.28338
\(834\) 0 0
\(835\) − 11.8322i − 0.409469i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 29.0000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −29.0689 −1.00000
\(846\) 0 0
\(847\) − 29.1033i − 1.00000i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) − 30.0000i − 1.02598i
\(856\) 0 0
\(857\) 58.2065 1.98830 0.994149 0.108021i \(-0.0344515\pi\)
0.994149 + 0.108021i \(0.0344515\pi\)
\(858\) 0 0
\(859\) − 58.1378i − 1.98364i −0.127664 0.991818i \(-0.540748\pi\)
0.127664 0.991818i \(-0.459252\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 15.8745 0.537271
\(874\) 0 0
\(875\) − 29.5804i − 1.00000i
\(876\) 0 0
\(877\) 59.1608 1.99772 0.998859 0.0477546i \(-0.0152065\pi\)
0.998859 + 0.0477546i \(0.0152065\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) − 59.1608i − 1.99092i −0.0951842 0.995460i \(-0.530344\pi\)
0.0951842 0.995460i \(-0.469656\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) − 58.2065i − 1.95438i −0.212358 0.977192i \(-0.568114\pi\)
0.212358 0.977192i \(-0.431886\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 23.6643 0.791896
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) −62.6099 −2.08584
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 50.0000 1.66206
\(906\) 0 0
\(907\) − 59.1608i − 1.96440i −0.187833 0.982201i \(-0.560146\pi\)
0.187833 0.982201i \(-0.439854\pi\)
\(908\) 0 0
\(909\) −40.2492 −1.33498
\(910\) 0 0
\(911\) 58.0000i 1.92163i 0.277198 + 0.960813i \(0.410594\pi\)
−0.277198 + 0.960813i \(0.589406\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 11.8322 0.390732
\(918\) 0 0
\(919\) 34.0000i 1.12156i 0.827966 + 0.560778i \(0.189498\pi\)
−0.827966 + 0.560778i \(0.810502\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 59.1608 1.94520
\(926\) 0 0
\(927\) 47.6235i 1.56416i
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 31.3050i 1.02598i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 58.2065 1.90152 0.950762 0.309921i \(-0.100303\pi\)
0.950762 + 0.309921i \(0.100303\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 13.4164 0.437362 0.218681 0.975796i \(-0.429825\pi\)
0.218681 + 0.975796i \(0.429825\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 59.1608i − 1.92247i −0.275735 0.961234i \(-0.588921\pi\)
0.275735 0.961234i \(-0.411079\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 49.1935i 1.59186i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 35.4965i 1.14386i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) − 58.1378i − 1.86573i −0.360226 0.932865i \(-0.617301\pi\)
0.360226 0.932865i \(-0.382699\pi\)
\(972\) 0 0
\(973\) 59.1608 1.89661
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) − 37.0405i − 1.18141i −0.806888 0.590705i \(-0.798850\pi\)
0.806888 0.590705i \(-0.201150\pi\)
\(984\) 0 0
\(985\) −26.4575 −0.843006
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) − 38.0000i − 1.20711i −0.797321 0.603555i \(-0.793750\pi\)
0.797321 0.603555i \(-0.206250\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 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 2240.2.n.d.1119.3 yes 8
4.3 odd 2 inner 2240.2.n.d.1119.1 8
5.4 even 2 inner 2240.2.n.d.1119.2 yes 8
7.6 odd 2 inner 2240.2.n.d.1119.6 yes 8
8.3 odd 2 inner 2240.2.n.d.1119.5 yes 8
8.5 even 2 inner 2240.2.n.d.1119.7 yes 8
20.19 odd 2 inner 2240.2.n.d.1119.4 yes 8
28.27 even 2 inner 2240.2.n.d.1119.8 yes 8
35.34 odd 2 inner 2240.2.n.d.1119.7 yes 8
40.19 odd 2 inner 2240.2.n.d.1119.8 yes 8
40.29 even 2 inner 2240.2.n.d.1119.6 yes 8
56.13 odd 2 inner 2240.2.n.d.1119.2 yes 8
56.27 even 2 inner 2240.2.n.d.1119.4 yes 8
140.139 even 2 inner 2240.2.n.d.1119.5 yes 8
280.69 odd 2 CM 2240.2.n.d.1119.3 yes 8
280.139 even 2 inner 2240.2.n.d.1119.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2240.2.n.d.1119.1 8 4.3 odd 2 inner
2240.2.n.d.1119.1 8 280.139 even 2 inner
2240.2.n.d.1119.2 yes 8 5.4 even 2 inner
2240.2.n.d.1119.2 yes 8 56.13 odd 2 inner
2240.2.n.d.1119.3 yes 8 1.1 even 1 trivial
2240.2.n.d.1119.3 yes 8 280.69 odd 2 CM
2240.2.n.d.1119.4 yes 8 20.19 odd 2 inner
2240.2.n.d.1119.4 yes 8 56.27 even 2 inner
2240.2.n.d.1119.5 yes 8 8.3 odd 2 inner
2240.2.n.d.1119.5 yes 8 140.139 even 2 inner
2240.2.n.d.1119.6 yes 8 7.6 odd 2 inner
2240.2.n.d.1119.6 yes 8 40.29 even 2 inner
2240.2.n.d.1119.7 yes 8 8.5 even 2 inner
2240.2.n.d.1119.7 yes 8 35.34 odd 2 inner
2240.2.n.d.1119.8 yes 8 28.27 even 2 inner
2240.2.n.d.1119.8 yes 8 40.19 odd 2 inner