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Properties

Label 560.3.p.a.209.1
Level $560$
Weight $3$
Character 560.209
Self dual yes
Analytic conductor $15.259$
Analytic rank $0$
Dimension $1$
CM discriminant -35
Inner twists $2$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [560,3,Mod(209,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.209"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1, 1])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 560.p (of order \(2\), degree \(1\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,-1,0,-5,0,-7,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(15.2588948042\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 209.1
Character \(\chi\) \(=\) 560.209

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{3} -5.00000 q^{5} -7.00000 q^{7} -8.00000 q^{9} +13.0000 q^{11} -19.0000 q^{13} +5.00000 q^{15} +29.0000 q^{17} +7.00000 q^{21} +25.0000 q^{25} +17.0000 q^{27} +23.0000 q^{29} -13.0000 q^{33} +35.0000 q^{35} +19.0000 q^{39} +40.0000 q^{45} +31.0000 q^{47} +49.0000 q^{49} -29.0000 q^{51} -65.0000 q^{55} +56.0000 q^{63} +95.0000 q^{65} -2.00000 q^{71} -34.0000 q^{73} -25.0000 q^{75} -91.0000 q^{77} +157.000 q^{79} +55.0000 q^{81} -86.0000 q^{83} -145.000 q^{85} -23.0000 q^{87} +133.000 q^{91} +149.000 q^{97} -104.000 q^{99} +O(q^{100})\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(1\)

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
\(3\) −1.00000 −0.333333 −0.166667 − 0.986013i \(-0.553300\pi\)
−0.166667 + 0.986013i \(0.553300\pi\)
\(4\) 0 0
\(5\) −5.00000 −1.00000
\(6\) 0 0
\(7\) −7.00000 −1.00000
\(8\) 0 0
\(9\) −8.00000 −0.888889
\(10\) 0 0
\(11\) 13.0000 1.18182 0.590909 − 0.806738i \(-0.298769\pi\)
0.590909 + 0.806738i \(0.298769\pi\)
\(12\) 0 0
\(13\) −19.0000 −1.46154 −0.730769 − 0.682625i \(-0.760838\pi\)
−0.730769 + 0.682625i \(0.760838\pi\)
\(14\) 0 0
\(15\) 5.00000 0.333333
\(16\) 0 0
\(17\) 29.0000 1.70588 0.852941 − 0.522007i \(-0.174817\pi\)
0.852941 + 0.522007i \(0.174817\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 7.00000 0.333333
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 25.0000 1.00000
\(26\) 0 0
\(27\) 17.0000 0.629630
\(28\) 0 0
\(29\) 23.0000 0.793103 0.396552 − 0.918012i \(-0.370207\pi\)
0.396552 + 0.918012i \(0.370207\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) −13.0000 −0.393939
\(34\) 0 0
\(35\) 35.0000 1.00000
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 19.0000 0.487179
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 40.0000 0.888889
\(46\) 0 0
\(47\) 31.0000 0.659574 0.329787 − 0.944055i \(-0.393023\pi\)
0.329787 + 0.944055i \(0.393023\pi\)
\(48\) 0 0
\(49\) 49.0000 1.00000
\(50\) 0 0
\(51\) −29.0000 −0.568627
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) −65.0000 −1.18182
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 56.0000 0.888889
\(64\) 0 0
\(65\) 95.0000 1.46154
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.00000 −0.0281690 −0.0140845 − 0.999901i \(-0.504483\pi\)
−0.0140845 + 0.999901i \(0.504483\pi\)
\(72\) 0 0
\(73\) −34.0000 −0.465753 −0.232877 − 0.972506i \(-0.574814\pi\)
−0.232877 + 0.972506i \(0.574814\pi\)
\(74\) 0 0
\(75\) −25.0000 −0.333333
\(76\) 0 0
\(77\) −91.0000 −1.18182
\(78\) 0 0
\(79\) 157.000 1.98734 0.993671 − 0.112331i \(-0.0358316\pi\)
0.993671 + 0.112331i \(0.0358316\pi\)
\(80\) 0 0
\(81\) 55.0000 0.679012
\(82\) 0 0
\(83\) −86.0000 −1.03614 −0.518072 − 0.855337i \(-0.673350\pi\)
−0.518072 + 0.855337i \(0.673350\pi\)
\(84\) 0 0
\(85\) −145.000 −1.70588
\(86\) 0 0
\(87\) −23.0000 −0.264368
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 133.000 1.46154
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 149.000 1.53608 0.768041 − 0.640400i \(-0.221232\pi\)
0.768041 + 0.640400i \(0.221232\pi\)
\(98\) 0 0
\(99\) −104.000 −1.05051
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 199.000 1.93204 0.966019 − 0.258470i \(-0.0832182\pi\)
0.966019 + 0.258470i \(0.0832182\pi\)
\(104\) 0 0
\(105\) −35.0000 −0.333333
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) −97.0000 −0.889908 −0.444954 − 0.895553i \(-0.646780\pi\)
−0.444954 + 0.895553i \(0.646780\pi\)
\(110\) 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
\(117\) 152.000 1.29915
\(118\) 0 0
\(119\) −203.000 −1.70588
\(120\) 0 0
\(121\) 48.0000 0.396694
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −1.00000
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 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
\(135\) −85.0000 −0.629630
\(136\) 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
\(141\) −31.0000 −0.219858
\(142\) 0 0
\(143\) −247.000 −1.72727
\(144\) 0 0
\(145\) −115.000 −0.793103
\(146\) 0 0
\(147\) −49.0000 −0.333333
\(148\) 0 0
\(149\) −262.000 −1.75839 −0.879195 − 0.476463i \(-0.841919\pi\)
−0.879195 + 0.476463i \(0.841919\pi\)
\(150\) 0 0
\(151\) 13.0000 0.0860927 0.0430464 − 0.999073i \(-0.486294\pi\)
0.0430464 + 0.999073i \(0.486294\pi\)
\(152\) 0 0
\(153\) −232.000 −1.51634
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 134.000 0.853503 0.426752 − 0.904369i \(-0.359658\pi\)
0.426752 + 0.904369i \(0.359658\pi\)
\(158\) 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
\(165\) 65.0000 0.393939
\(166\) 0 0
\(167\) 271.000 1.62275 0.811377 − 0.584523i \(-0.198718\pi\)
0.811377 + 0.584523i \(0.198718\pi\)
\(168\) 0 0
\(169\) 192.000 1.13609
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 221.000 1.27746 0.638728 − 0.769432i \(-0.279461\pi\)
0.638728 + 0.769432i \(0.279461\pi\)
\(174\) 0 0
\(175\) −175.000 −1.00000
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −218.000 −1.21788 −0.608939 − 0.793217i \(-0.708404\pi\)
−0.608939 + 0.793217i \(0.708404\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 377.000 2.01604
\(188\) 0 0
\(189\) −119.000 −0.629630
\(190\) 0 0
\(191\) −347.000 −1.81675 −0.908377 − 0.418152i \(-0.862678\pi\)
−0.908377 + 0.418152i \(0.862678\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) −95.0000 −0.487179
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −161.000 −0.793103
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −107.000 −0.507109 −0.253555 − 0.967321i \(-0.581600\pi\)
−0.253555 + 0.967321i \(0.581600\pi\)
\(212\) 0 0
\(213\) 2.00000 0.00938967
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 34.0000 0.155251
\(220\) 0 0
\(221\) −551.000 −2.49321
\(222\) 0 0
\(223\) −401.000 −1.79821 −0.899103 − 0.437737i \(-0.855780\pi\)
−0.899103 + 0.437737i \(0.855780\pi\)
\(224\) 0 0
\(225\) −200.000 −0.888889
\(226\) 0 0
\(227\) 391.000 1.72247 0.861233 − 0.508209i \(-0.169692\pi\)
0.861233 + 0.508209i \(0.169692\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 91.0000 0.393939
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) −155.000 −0.659574
\(236\) 0 0
\(237\) −157.000 −0.662447
\(238\) 0 0
\(239\) 397.000 1.66109 0.830544 − 0.556953i \(-0.188030\pi\)
0.830544 + 0.556953i \(0.188030\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) −208.000 −0.855967
\(244\) 0 0
\(245\) −245.000 −1.00000
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 86.0000 0.345382
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 145.000 0.568627
\(256\) 0 0
\(257\) 494.000 1.92218 0.961089 − 0.276237i \(-0.0890875\pi\)
0.961089 + 0.276237i \(0.0890875\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −184.000 −0.704981
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) −133.000 −0.487179
\(274\) 0 0
\(275\) 325.000 1.18182
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 527.000 1.87544 0.937722 − 0.347385i \(-0.112930\pi\)
0.937722 + 0.347385i \(0.112930\pi\)
\(282\) 0 0
\(283\) 559.000 1.97527 0.987633 − 0.156787i \(-0.0501135\pi\)
0.987633 + 0.156787i \(0.0501135\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 552.000 1.91003
\(290\) 0 0
\(291\) −149.000 −0.512027
\(292\) 0 0
\(293\) −19.0000 −0.0648464 −0.0324232 − 0.999474i \(-0.510322\pi\)
−0.0324232 + 0.999474i \(0.510322\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 221.000 0.744108
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −569.000 −1.85342 −0.926710 − 0.375777i \(-0.877376\pi\)
−0.926710 + 0.375777i \(0.877376\pi\)
\(308\) 0 0
\(309\) −199.000 −0.644013
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 221.000 0.706070 0.353035 − 0.935610i \(-0.385150\pi\)
0.353035 + 0.935610i \(0.385150\pi\)
\(314\) 0 0
\(315\) −280.000 −0.888889
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 299.000 0.937304
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −475.000 −1.46154
\(326\) 0 0
\(327\) 97.0000 0.296636
\(328\) 0 0
\(329\) −217.000 −0.659574
\(330\) 0 0
\(331\) 598.000 1.80665 0.903323 − 0.428960i \(-0.141120\pi\)
0.903323 + 0.428960i \(0.141120\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 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
\(343\) −343.000 −1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) −323.000 −0.920228
\(352\) 0 0
\(353\) −139.000 −0.393768 −0.196884 − 0.980427i \(-0.563082\pi\)
−0.196884 + 0.980427i \(0.563082\pi\)
\(354\) 0 0
\(355\) 10.0000 0.0281690
\(356\) 0 0
\(357\) 203.000 0.568627
\(358\) 0 0
\(359\) −578.000 −1.61003 −0.805014 − 0.593256i \(-0.797842\pi\)
−0.805014 + 0.593256i \(0.797842\pi\)
\(360\) 0 0
\(361\) 361.000 1.00000
\(362\) 0 0
\(363\) −48.0000 −0.132231
\(364\) 0 0
\(365\) 170.000 0.465753
\(366\) 0 0
\(367\) 391.000 1.06540 0.532698 − 0.846306i \(-0.321178\pi\)
0.532698 + 0.846306i \(0.321178\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 125.000 0.333333
\(376\) 0 0
\(377\) −437.000 −1.15915
\(378\) 0 0
\(379\) 502.000 1.32454 0.662269 − 0.749266i \(-0.269594\pi\)
0.662269 + 0.749266i \(0.269594\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 514.000 1.34204 0.671018 − 0.741441i \(-0.265857\pi\)
0.671018 + 0.741441i \(0.265857\pi\)
\(384\) 0 0
\(385\) 455.000 1.18182
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 743.000 1.91003 0.955013 − 0.296564i \(-0.0958409\pi\)
0.955013 + 0.296564i \(0.0958409\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −785.000 −1.98734
\(396\) 0 0
\(397\) 389.000 0.979849 0.489924 − 0.871765i \(-0.337024\pi\)
0.489924 + 0.871765i \(0.337024\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −73.0000 −0.182045 −0.0910224 − 0.995849i \(-0.529014\pi\)
−0.0910224 + 0.995849i \(0.529014\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −275.000 −0.679012
\(406\) 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
\(413\) 0 0
\(414\) 0 0
\(415\) 430.000 1.03614
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 527.000 1.25178 0.625891 − 0.779911i \(-0.284736\pi\)
0.625891 + 0.779911i \(0.284736\pi\)
\(422\) 0 0
\(423\) −248.000 −0.586288
\(424\) 0 0
\(425\) 725.000 1.70588
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 247.000 0.575758
\(430\) 0 0
\(431\) 853.000 1.97912 0.989559 − 0.144127i \(-0.0460375\pi\)
0.989559 + 0.144127i \(0.0460375\pi\)
\(432\) 0 0
\(433\) −754.000 −1.74134 −0.870670 − 0.491868i \(-0.836314\pi\)
−0.870670 + 0.491868i \(0.836314\pi\)
\(434\) 0 0
\(435\) 115.000 0.264368
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −392.000 −0.888889
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 262.000 0.586130
\(448\) 0 0
\(449\) −817.000 −1.81960 −0.909800 − 0.415048i \(-0.863765\pi\)
−0.909800 + 0.415048i \(0.863765\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −13.0000 −0.0286976
\(454\) 0 0
\(455\) −665.000 −1.46154
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 493.000 1.07407
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 871.000 1.86510 0.932548 − 0.361046i \(-0.117580\pi\)
0.932548 + 0.361046i \(0.117580\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −134.000 −0.284501
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −745.000 −1.53608
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −107.000 −0.217923 −0.108961 − 0.994046i \(-0.534752\pi\)
−0.108961 + 0.994046i \(0.534752\pi\)
\(492\) 0 0
\(493\) 667.000 1.35294
\(494\) 0 0
\(495\) 520.000 1.05051
\(496\) 0 0
\(497\) 14.0000 0.0281690
\(498\) 0 0
\(499\) −683.000 −1.36874 −0.684369 − 0.729136i \(-0.739922\pi\)
−0.684369 + 0.729136i \(0.739922\pi\)
\(500\) 0 0
\(501\) −271.000 −0.540918
\(502\) 0 0
\(503\) 439.000 0.872763 0.436382 − 0.899762i \(-0.356260\pi\)
0.436382 + 0.899762i \(0.356260\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −192.000 −0.378698
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 238.000 0.465753
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −995.000 −1.93204
\(516\) 0 0
\(517\) 403.000 0.779497
\(518\) 0 0
\(519\) −221.000 −0.425819
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −326.000 −0.623327 −0.311663 − 0.950193i \(-0.600886\pi\)
−0.311663 + 0.950193i \(0.600886\pi\)
\(524\) 0 0
\(525\) 175.000 0.333333
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 529.000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 218.000 0.405959
\(538\) 0 0
\(539\) 637.000 1.18182
\(540\) 0 0
\(541\) 767.000 1.41774 0.708872 − 0.705337i \(-0.249204\pi\)
0.708872 + 0.705337i \(0.249204\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 485.000 0.889908
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −1099.00 −1.98734
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −377.000 −0.672014
\(562\) 0 0
\(563\) 874.000 1.55240 0.776199 − 0.630488i \(-0.217145\pi\)
0.776199 + 0.630488i \(0.217145\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −385.000 −0.679012
\(568\) 0 0
\(569\) −1102.00 −1.93673 −0.968366 − 0.249536i \(-0.919722\pi\)
−0.968366 + 0.249536i \(0.919722\pi\)
\(570\) 0 0
\(571\) 118.000 0.206655 0.103327 − 0.994647i \(-0.467051\pi\)
0.103327 + 0.994647i \(0.467051\pi\)
\(572\) 0 0
\(573\) 347.000 0.605585
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 29.0000 0.0502600 0.0251300 − 0.999684i \(-0.492000\pi\)
0.0251300 + 0.999684i \(0.492000\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 602.000 1.03614
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −760.000 −1.29915
\(586\) 0 0
\(587\) −1094.00 −1.86371 −0.931857 − 0.362826i \(-0.881812\pi\)
−0.931857 + 0.362826i \(0.881812\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −619.000 −1.04384 −0.521922 − 0.852993i \(-0.674785\pi\)
−0.521922 + 0.852993i \(0.674785\pi\)
\(594\) 0 0
\(595\) 1015.00 1.70588
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −323.000 −0.539232 −0.269616 − 0.962968i \(-0.586897\pi\)
−0.269616 + 0.962968i \(0.586897\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −240.000 −0.396694
\(606\) 0 0
\(607\) −809.000 −1.33278 −0.666392 − 0.745601i \(-0.732162\pi\)
−0.666392 + 0.745601i \(0.732162\pi\)
\(608\) 0 0
\(609\) 161.000 0.264368
\(610\) 0 0
\(611\) −589.000 −0.963993
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 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
\(625\) 625.000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −947.000 −1.50079 −0.750396 − 0.660988i \(-0.770137\pi\)
−0.750396 + 0.660988i \(0.770137\pi\)
\(632\) 0 0
\(633\) 107.000 0.169036
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −931.000 −1.46154
\(638\) 0 0
\(639\) 16.0000 0.0250391
\(640\) 0 0
\(641\) −958.000 −1.49454 −0.747270 − 0.664521i \(-0.768636\pi\)
−0.747270 + 0.664521i \(0.768636\pi\)
\(642\) 0 0
\(643\) −1241.00 −1.93002 −0.965008 − 0.262221i \(-0.915545\pi\)
−0.965008 + 0.262221i \(0.915545\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −974.000 −1.50541 −0.752705 − 0.658358i \(-0.771251\pi\)
−0.752705 + 0.658358i \(0.771251\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 272.000 0.414003
\(658\) 0 0
\(659\) −1283.00 −1.94689 −0.973445 − 0.228923i \(-0.926480\pi\)
−0.973445 + 0.228923i \(0.926480\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 551.000 0.831071
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 401.000 0.599402
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 425.000 0.629630
\(676\) 0 0
\(677\) −1291.00 −1.90694 −0.953471 − 0.301484i \(-0.902518\pi\)
−0.953471 + 0.301484i \(0.902518\pi\)
\(678\) 0 0
\(679\) −1043.00 −1.53608
\(680\) 0 0
\(681\) −391.000 −0.574156
\(682\) 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
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 728.000 1.05051
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −313.000 −0.446505 −0.223252 − 0.974761i \(-0.571667\pi\)
−0.223252 + 0.974761i \(0.571667\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 155.000 0.219858
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1417.00 −1.99859 −0.999295 − 0.0375492i \(-0.988045\pi\)
−0.999295 + 0.0375492i \(0.988045\pi\)
\(710\) 0 0
\(711\) −1256.00 −1.76653
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 1235.00 1.72727
\(716\) 0 0
\(717\) −397.000 −0.553696
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) −1393.00 −1.93204
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 575.000 0.793103
\(726\) 0 0
\(727\) 1426.00 1.96149 0.980743 − 0.195304i \(-0.0625693\pi\)
0.980743 + 0.195304i \(0.0625693\pi\)
\(728\) 0 0
\(729\) −287.000 −0.393690
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 1061.00 1.44748 0.723738 − 0.690075i \(-0.242422\pi\)
0.723738 + 0.690075i \(0.242422\pi\)
\(734\) 0 0
\(735\) 245.000 0.333333
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 1357.00 1.83627 0.918133 − 0.396273i \(-0.129697\pi\)
0.918133 + 0.396273i \(0.129697\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 1310.00 1.75839
\(746\) 0 0
\(747\) 688.000 0.921017
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 1333.00 1.77497 0.887483 − 0.460840i \(-0.152452\pi\)
0.887483 + 0.460840i \(0.152452\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −65.0000 −0.0860927
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 679.000 0.889908
\(764\) 0 0
\(765\) 1160.00 1.51634
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) −494.000 −0.640726
\(772\) 0 0
\(773\) 1541.00 1.99353 0.996766 − 0.0803607i \(-0.0256072\pi\)
0.996766 + 0.0803607i \(0.0256072\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −26.0000 −0.0332907
\(782\) 0 0
\(783\) 391.000 0.499361
\(784\) 0 0
\(785\) −670.000 −0.853503
\(786\) 0 0
\(787\) −449.000 −0.570521 −0.285260 − 0.958450i \(-0.592080\pi\)
−0.285260 + 0.958450i \(0.592080\pi\)
\(788\) 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
\(797\) −1531.00 −1.92095 −0.960477 − 0.278360i \(-0.910209\pi\)
−0.960477 + 0.278360i \(0.910209\pi\)
\(798\) 0 0
\(799\) 899.000 1.12516
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −442.000 −0.550436
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −97.0000 −0.119901 −0.0599506 − 0.998201i \(-0.519094\pi\)
−0.0599506 + 0.998201i \(0.519094\pi\)
\(810\) 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
\(819\) −1064.00 −1.29915
\(820\) 0 0
\(821\) 1607.00 1.95737 0.978685 − 0.205369i \(-0.0658396\pi\)
0.978685 + 0.205369i \(0.0658396\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) −325.000 −0.393939
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1421.00 1.70588
\(834\) 0 0
\(835\) −1355.00 −1.62275
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) −312.000 −0.370987
\(842\) 0 0
\(843\) −527.000 −0.625148
\(844\) 0 0
\(845\) −960.000 −1.13609
\(846\) 0 0
\(847\) −336.000 −0.396694
\(848\) 0 0
\(849\) −559.000 −0.658422
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 86.0000 0.100821 0.0504103 − 0.998729i \(-0.483947\pi\)
0.0504103 + 0.998729i \(0.483947\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −706.000 −0.823804 −0.411902 − 0.911228i \(-0.635135\pi\)
−0.411902 + 0.911228i \(0.635135\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) −1105.00 −1.27746
\(866\) 0 0
\(867\) −552.000 −0.636678
\(868\) 0 0
\(869\) 2041.00 2.34868
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −1192.00 −1.36541
\(874\) 0 0
\(875\) 875.000 1.00000
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 19.0000 0.0216155
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −494.000 −0.556933 −0.278467 − 0.960446i \(-0.589826\pi\)
−0.278467 + 0.960446i \(0.589826\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 715.000 0.802469
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 1090.00 1.21788
\(896\) 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
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1678.00 1.84193 0.920966 − 0.389643i \(-0.127402\pi\)
0.920966 + 0.389643i \(0.127402\pi\)
\(912\) 0 0
\(913\) −1118.00 −1.22453
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 997.000 1.08487 0.542437 − 0.840096i \(-0.317502\pi\)
0.542437 + 0.840096i \(0.317502\pi\)
\(920\) 0 0
\(921\) 569.000 0.617807
\(922\) 0 0
\(923\) 38.0000 0.0411701
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −1592.00 −1.71737
\(928\) 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
\(935\) −1885.00 −2.01604
\(936\) 0 0
\(937\) 1829.00 1.95197 0.975987 − 0.217828i \(-0.0698972\pi\)
0.975987 + 0.217828i \(0.0698972\pi\)
\(938\) 0 0
\(939\) −221.000 −0.235357
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 595.000 0.629630
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 646.000 0.680717
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 1735.00 1.81675
\(956\) 0 0
\(957\) −299.000 −0.312435
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 961.000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 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
\(975\) 475.000 0.487179
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 776.000 0.791030
\(982\) 0 0
\(983\) −1121.00 −1.14039 −0.570193 − 0.821511i \(-0.693132\pi\)
−0.570193 + 0.821511i \(0.693132\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 217.000 0.219858
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −722.000 −0.728557 −0.364279 − 0.931290i \(-0.618684\pi\)
−0.364279 + 0.931290i \(0.618684\pi\)
\(992\) 0 0
\(993\) −598.000 −0.602216
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1651.00 −1.65597 −0.827984 − 0.560752i \(-0.810512\pi\)
−0.827984 + 0.560752i \(0.810512\pi\)
\(998\) 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 560.3.p.a.209.1 1
4.3 odd 2 35.3.c.b.34.1 yes 1
5.4 even 2 560.3.p.b.209.1 1
7.6 odd 2 560.3.p.b.209.1 1
12.11 even 2 315.3.e.b.244.1 1
20.3 even 4 175.3.d.e.76.2 2
20.7 even 4 175.3.d.e.76.1 2
20.19 odd 2 35.3.c.a.34.1 ✓ 1
28.3 even 6 245.3.i.b.19.1 2
28.11 odd 6 245.3.i.a.19.1 2
28.19 even 6 245.3.i.b.129.1 2
28.23 odd 6 245.3.i.a.129.1 2
28.27 even 2 35.3.c.a.34.1 ✓ 1
35.34 odd 2 CM 560.3.p.a.209.1 1
60.59 even 2 315.3.e.a.244.1 1
84.83 odd 2 315.3.e.a.244.1 1
140.19 even 6 245.3.i.a.129.1 2
140.27 odd 4 175.3.d.e.76.2 2
140.39 odd 6 245.3.i.b.19.1 2
140.59 even 6 245.3.i.a.19.1 2
140.79 odd 6 245.3.i.b.129.1 2
140.83 odd 4 175.3.d.e.76.1 2
140.139 even 2 35.3.c.b.34.1 yes 1
420.419 odd 2 315.3.e.b.244.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.3.c.a.34.1 ✓ 1 20.19 odd 2
35.3.c.a.34.1 ✓ 1 28.27 even 2
35.3.c.b.34.1 yes 1 4.3 odd 2
35.3.c.b.34.1 yes 1 140.139 even 2
175.3.d.e.76.1 2 20.7 even 4
175.3.d.e.76.1 2 140.83 odd 4
175.3.d.e.76.2 2 20.3 even 4
175.3.d.e.76.2 2 140.27 odd 4
245.3.i.a.19.1 2 28.11 odd 6
245.3.i.a.19.1 2 140.59 even 6
245.3.i.a.129.1 2 28.23 odd 6
245.3.i.a.129.1 2 140.19 even 6
245.3.i.b.19.1 2 28.3 even 6
245.3.i.b.19.1 2 140.39 odd 6
245.3.i.b.129.1 2 28.19 even 6
245.3.i.b.129.1 2 140.79 odd 6
315.3.e.a.244.1 1 60.59 even 2
315.3.e.a.244.1 1 84.83 odd 2
315.3.e.b.244.1 1 12.11 even 2
315.3.e.b.244.1 1 420.419 odd 2
560.3.p.a.209.1 1 1.1 even 1 trivial
560.3.p.a.209.1 1 35.34 odd 2 CM
560.3.p.b.209.1 1 5.4 even 2
560.3.p.b.209.1 1 7.6 odd 2