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Properties

Label 160.3.e.b.79.1
Level $160$
Weight $3$
Character 160.79
Self dual yes
Analytic conductor $4.360$
Analytic rank $0$
Dimension $1$
CM discriminant -40
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] = [160,3,Mod(79,160)] 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("160.79"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(160, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 160.e (of order \(2\), degree \(1\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,0,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(4.35968422976\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 40)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 79.1
Character \(\chi\) \(=\) 160.79

$q$-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)
 
\(f(q)\) \(=\) \(q+5.00000 q^{5} -6.00000 q^{7} +9.00000 q^{9} +18.0000 q^{11} -6.00000 q^{13} +2.00000 q^{19} +26.0000 q^{23} +25.0000 q^{25} -30.0000 q^{35} -54.0000 q^{37} -78.0000 q^{41} +45.0000 q^{45} -86.0000 q^{47} -13.0000 q^{49} +74.0000 q^{53} +90.0000 q^{55} -78.0000 q^{59} -54.0000 q^{63} -30.0000 q^{65} -108.000 q^{77} +81.0000 q^{81} +18.0000 q^{89} +36.0000 q^{91} +10.0000 q^{95} +162.000 q^{99} +O(q^{100})\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(101\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) 0 0
\(5\) 5.00000 1.00000
\(6\) 0 0
\(7\) −6.00000 −0.857143 −0.428571 − 0.903508i \(-0.640983\pi\)
−0.428571 + 0.903508i \(0.640983\pi\)
\(8\) 0 0
\(9\) 9.00000 1.00000
\(10\) 0 0
\(11\) 18.0000 1.63636 0.818182 − 0.574960i \(-0.194982\pi\)
0.818182 + 0.574960i \(0.194982\pi\)
\(12\) 0 0
\(13\) −6.00000 −0.461538 −0.230769 − 0.973009i \(-0.574124\pi\)
−0.230769 + 0.973009i \(0.574124\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 2.00000 0.105263 0.0526316 − 0.998614i \(-0.483239\pi\)
0.0526316 + 0.998614i \(0.483239\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 26.0000 1.13043 0.565217 − 0.824942i \(-0.308792\pi\)
0.565217 + 0.824942i \(0.308792\pi\)
\(24\) 0 0
\(25\) 25.0000 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −30.0000 −0.857143
\(36\) 0 0
\(37\) −54.0000 −1.45946 −0.729730 − 0.683736i \(-0.760354\pi\)
−0.729730 + 0.683736i \(0.760354\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −78.0000 −1.90244 −0.951220 − 0.308515i \(-0.900168\pi\)
−0.951220 + 0.308515i \(0.900168\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 45.0000 1.00000
\(46\) 0 0
\(47\) −86.0000 −1.82979 −0.914894 − 0.403695i \(-0.867726\pi\)
−0.914894 + 0.403695i \(0.867726\pi\)
\(48\) 0 0
\(49\) −13.0000 −0.265306
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 74.0000 1.39623 0.698113 − 0.715987i \(-0.254023\pi\)
0.698113 + 0.715987i \(0.254023\pi\)
\(54\) 0 0
\(55\) 90.0000 1.63636
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −78.0000 −1.32203 −0.661017 − 0.750371i \(-0.729875\pi\)
−0.661017 + 0.750371i \(0.729875\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) −54.0000 −0.857143
\(64\) 0 0
\(65\) −30.0000 −0.461538
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −108.000 −1.40260
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 81.0000 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 18.0000 0.202247 0.101124 − 0.994874i \(-0.467756\pi\)
0.101124 + 0.994874i \(0.467756\pi\)
\(90\) 0 0
\(91\) 36.0000 0.395604
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 10.0000 0.105263
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 162.000 1.63636
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 186.000 1.80583 0.902913 − 0.429824i \(-0.141424\pi\)
0.902913 + 0.429824i \(0.141424\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 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
\(115\) 130.000 1.13043
\(116\) 0 0
\(117\) −54.0000 −0.461538
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 203.000 1.67769
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 1.00000
\(126\) 0 0
\(127\) −246.000 −1.93701 −0.968504 − 0.248998i \(-0.919899\pi\)
−0.968504 + 0.248998i \(0.919899\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −222.000 −1.69466 −0.847328 − 0.531070i \(-0.821790\pi\)
−0.847328 + 0.531070i \(0.821790\pi\)
\(132\) 0 0
\(133\) −12.0000 −0.0902256
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 82.0000 0.589928 0.294964 − 0.955508i \(-0.404692\pi\)
0.294964 + 0.955508i \(0.404692\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −108.000 −0.755245
\(144\) 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
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 186.000 1.18471 0.592357 − 0.805676i \(-0.298198\pi\)
0.592357 + 0.805676i \(0.298198\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −156.000 −0.968944
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 314.000 1.88024 0.940120 − 0.340844i \(-0.110713\pi\)
0.940120 + 0.340844i \(0.110713\pi\)
\(168\) 0 0
\(169\) −133.000 −0.786982
\(170\) 0 0
\(171\) 18.0000 0.105263
\(172\) 0 0
\(173\) −166.000 −0.959538 −0.479769 − 0.877395i \(-0.659279\pi\)
−0.479769 + 0.877395i \(0.659279\pi\)
\(174\) 0 0
\(175\) −150.000 −0.857143
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −318.000 −1.77654 −0.888268 − 0.459325i \(-0.848091\pi\)
−0.888268 + 0.459325i \(0.848091\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −270.000 −1.45946
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 106.000 0.538071 0.269036 − 0.963130i \(-0.413295\pi\)
0.269036 + 0.963130i \(0.413295\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −390.000 −1.90244
\(206\) 0 0
\(207\) 234.000 1.13043
\(208\) 0 0
\(209\) 36.0000 0.172249
\(210\) 0 0
\(211\) −62.0000 −0.293839 −0.146919 − 0.989148i \(-0.546936\pi\)
−0.146919 + 0.989148i \(0.546936\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −54.0000 −0.242152 −0.121076 − 0.992643i \(-0.538635\pi\)
−0.121076 + 0.992643i \(0.538635\pi\)
\(224\) 0 0
\(225\) 225.000 1.00000
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) −430.000 −1.82979
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −158.000 −0.655602 −0.327801 − 0.944747i \(-0.606307\pi\)
−0.327801 + 0.944747i \(0.606307\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −65.0000 −0.265306
\(246\) 0 0
\(247\) −12.0000 −0.0485830
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 498.000 1.98406 0.992032 − 0.125987i \(-0.0402098\pi\)
0.992032 + 0.125987i \(0.0402098\pi\)
\(252\) 0 0
\(253\) 468.000 1.84980
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 324.000 1.25097
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −454.000 −1.72624 −0.863118 − 0.505003i \(-0.831492\pi\)
−0.863118 + 0.505003i \(0.831492\pi\)
\(264\) 0 0
\(265\) 370.000 1.39623
\(266\) 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
\(273\) 0 0
\(274\) 0 0
\(275\) 450.000 1.63636
\(276\) 0 0
\(277\) 426.000 1.53791 0.768953 − 0.639305i \(-0.220778\pi\)
0.768953 + 0.639305i \(0.220778\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −78.0000 −0.277580 −0.138790 − 0.990322i \(-0.544321\pi\)
−0.138790 + 0.990322i \(0.544321\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 468.000 1.63066
\(288\) 0 0
\(289\) 289.000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −566.000 −1.93174 −0.965870 − 0.259026i \(-0.916598\pi\)
−0.965870 + 0.259026i \(0.916598\pi\)
\(294\) 0 0
\(295\) −390.000 −1.32203
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −156.000 −0.521739
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) −270.000 −0.857143
\(316\) 0 0
\(317\) 346.000 1.09148 0.545741 − 0.837954i \(-0.316248\pi\)
0.545741 + 0.837954i \(0.316248\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −150.000 −0.461538
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 516.000 1.56839
\(330\) 0 0
\(331\) 338.000 1.02115 0.510574 − 0.859834i \(-0.329433\pi\)
0.510574 + 0.859834i \(0.329433\pi\)
\(332\) 0 0
\(333\) −486.000 −1.45946
\(334\) 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
\(343\) 372.000 1.08455
\(344\) 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
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) −357.000 −0.988920
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 234.000 0.637602 0.318801 − 0.947822i \(-0.396720\pi\)
0.318801 + 0.947822i \(0.396720\pi\)
\(368\) 0 0
\(369\) −702.000 −1.90244
\(370\) 0 0
\(371\) −444.000 −1.19677
\(372\) 0 0
\(373\) 234.000 0.627346 0.313673 − 0.949531i \(-0.398440\pi\)
0.313673 + 0.949531i \(0.398440\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −398.000 −1.05013 −0.525066 − 0.851062i \(-0.675959\pi\)
−0.525066 + 0.851062i \(0.675959\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 586.000 1.53003 0.765013 − 0.644015i \(-0.222732\pi\)
0.765013 + 0.644015i \(0.222732\pi\)
\(384\) 0 0
\(385\) −540.000 −1.40260
\(386\) 0 0
\(387\) 0 0
\(388\) 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
\(395\) 0 0
\(396\) 0 0
\(397\) −774.000 −1.94962 −0.974811 − 0.223032i \(-0.928404\pi\)
−0.974811 + 0.223032i \(0.928404\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 642.000 1.60100 0.800499 − 0.599334i \(-0.204568\pi\)
0.800499 + 0.599334i \(0.204568\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 405.000 1.00000
\(406\) 0 0
\(407\) −972.000 −2.38821
\(408\) 0 0
\(409\) −622.000 −1.52078 −0.760391 − 0.649465i \(-0.774993\pi\)
−0.760391 + 0.649465i \(0.774993\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 468.000 1.13317
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 162.000 0.386635 0.193317 − 0.981136i \(-0.438075\pi\)
0.193317 + 0.981136i \(0.438075\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) −774.000 −1.82979
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 52.0000 0.118993
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −117.000 −0.265306
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 90.0000 0.202247
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 258.000 0.574610 0.287305 − 0.957839i \(-0.407241\pi\)
0.287305 + 0.957839i \(0.407241\pi\)
\(450\) 0 0
\(451\) −1404.00 −3.11308
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 180.000 0.395604
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 426.000 0.920086 0.460043 − 0.887897i \(-0.347834\pi\)
0.460043 + 0.887897i \(0.347834\pi\)
\(464\) 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
\(473\) 0 0
\(474\) 0 0
\(475\) 50.0000 0.105263
\(476\) 0 0
\(477\) 666.000 1.39623
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 324.000 0.673597
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −6.00000 −0.0123203 −0.00616016 − 0.999981i \(-0.501961\pi\)
−0.00616016 + 0.999981i \(0.501961\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 978.000 1.99185 0.995927 − 0.0901668i \(-0.0287400\pi\)
0.995927 + 0.0901668i \(0.0287400\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 810.000 1.63636
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 962.000 1.92786 0.963928 − 0.266164i \(-0.0857562\pi\)
0.963928 + 0.266164i \(0.0857562\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −614.000 −1.22068 −0.610338 − 0.792141i \(-0.708966\pi\)
−0.610338 + 0.792141i \(0.708966\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 930.000 1.80583
\(516\) 0 0
\(517\) −1548.00 −2.99420
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 402.000 0.771593 0.385797 − 0.922584i \(-0.373927\pi\)
0.385797 + 0.922584i \(0.373927\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 147.000 0.277883
\(530\) 0 0
\(531\) −702.000 −1.32203
\(532\) 0 0
\(533\) 468.000 0.878049
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −234.000 −0.434137
\(540\) 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
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 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
\(557\) −934.000 −1.67684 −0.838420 − 0.545025i \(-0.816520\pi\)
−0.838420 + 0.545025i \(0.816520\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −486.000 −0.857143
\(568\) 0 0
\(569\) 978.000 1.71880 0.859402 − 0.511300i \(-0.170836\pi\)
0.859402 + 0.511300i \(0.170836\pi\)
\(570\) 0 0
\(571\) 818.000 1.43257 0.716287 − 0.697806i \(-0.245840\pi\)
0.716287 + 0.697806i \(0.245840\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 650.000 1.13043
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 1332.00 2.28473
\(584\) 0 0
\(585\) −270.000 −0.461538
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 562.000 0.935108 0.467554 − 0.883964i \(-0.345135\pi\)
0.467554 + 0.883964i \(0.345135\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1015.00 1.67769
\(606\) 0 0
\(607\) −1206.00 −1.98682 −0.993410 − 0.114613i \(-0.963437\pi\)
−0.993410 + 0.114613i \(0.963437\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 516.000 0.844517
\(612\) 0 0
\(613\) 1194.00 1.94780 0.973899 − 0.226982i \(-0.0728860\pi\)
0.973899 + 0.226982i \(0.0728860\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −878.000 −1.41842 −0.709208 − 0.704999i \(-0.750947\pi\)
−0.709208 + 0.704999i \(0.750947\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −108.000 −0.173355
\(624\) 0 0
\(625\) 625.000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1230.00 −1.93701
\(636\) 0 0
\(637\) 78.0000 0.122449
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1278.00 −1.99376 −0.996880 − 0.0789336i \(-0.974848\pi\)
−0.996880 + 0.0789336i \(0.974848\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −326.000 −0.503864 −0.251932 − 0.967745i \(-0.581066\pi\)
−0.251932 + 0.967745i \(0.581066\pi\)
\(648\) 0 0
\(649\) −1404.00 −2.16333
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1286.00 −1.96937 −0.984686 − 0.174337i \(-0.944222\pi\)
−0.984686 + 0.174337i \(0.944222\pi\)
\(654\) 0 0
\(655\) −1110.00 −1.69466
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 642.000 0.974203 0.487102 − 0.873345i \(-0.338054\pi\)
0.487102 + 0.873345i \(0.338054\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −60.0000 −0.0902256
\(666\) 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
\(677\) 1066.00 1.57459 0.787297 − 0.616574i \(-0.211480\pi\)
0.787297 + 0.616574i \(0.211480\pi\)
\(678\) 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
\(689\) −444.000 −0.644412
\(690\) 0 0
\(691\) −382.000 −0.552822 −0.276411 − 0.961040i \(-0.589145\pi\)
−0.276411 + 0.961040i \(0.589145\pi\)
\(692\) 0 0
\(693\) −972.000 −1.40260
\(694\) 0 0
\(695\) 410.000 0.589928
\(696\) 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
\(703\) −108.000 −0.153627
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −540.000 −0.755245
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) −1116.00 −1.54785
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1434.00 1.97249 0.986245 − 0.165291i \(-0.0528563\pi\)
0.986245 + 0.165291i \(0.0528563\pi\)
\(728\) 0 0
\(729\) 729.000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 954.000 1.30150 0.650750 − 0.759292i \(-0.274454\pi\)
0.650750 + 0.759292i \(0.274454\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −1438.00 −1.94587 −0.972936 − 0.231073i \(-0.925776\pi\)
−0.972936 + 0.231073i \(0.925776\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −134.000 −0.180350 −0.0901750 − 0.995926i \(-0.528743\pi\)
−0.0901750 + 0.995926i \(0.528743\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −534.000 −0.705416 −0.352708 − 0.935733i \(-0.614739\pi\)
−0.352708 + 0.935733i \(0.614739\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1038.00 −1.36399 −0.681997 − 0.731355i \(-0.738888\pi\)
−0.681997 + 0.731355i \(0.738888\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 468.000 0.610169
\(768\) 0 0
\(769\) 1378.00 1.79194 0.895969 − 0.444117i \(-0.146483\pi\)
0.895969 + 0.444117i \(0.146483\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1046.00 −1.35317 −0.676585 − 0.736365i \(-0.736541\pi\)
−0.676585 + 0.736365i \(0.736541\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −156.000 −0.200257
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 930.000 1.18471
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 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
\(797\) 26.0000 0.0326223 0.0163112 − 0.999867i \(-0.494808\pi\)
0.0163112 + 0.999867i \(0.494808\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 162.000 0.202247
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −780.000 −0.968944
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −942.000 −1.16440 −0.582200 − 0.813045i \(-0.697808\pi\)
−0.582200 + 0.813045i \(0.697808\pi\)
\(810\) 0 0
\(811\) 1618.00 1.99507 0.997534 − 0.0701862i \(-0.0223593\pi\)
0.997534 + 0.0701862i \(0.0223593\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 324.000 0.395604
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 666.000 0.809235 0.404617 − 0.914486i \(-0.367405\pi\)
0.404617 + 0.914486i \(0.367405\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 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
\(833\) 0 0
\(834\) 0 0
\(835\) 1570.00 1.88024
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 841.000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −665.000 −0.786982
\(846\) 0 0
\(847\) −1218.00 −1.43802
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1404.00 −1.64982
\(852\) 0 0
\(853\) 1674.00 1.96249 0.981243 − 0.192777i \(-0.0617493\pi\)
0.981243 + 0.192777i \(0.0617493\pi\)
\(854\) 0 0
\(855\) 90.0000 0.105263
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 1522.00 1.77183 0.885914 − 0.463850i \(-0.153532\pi\)
0.885914 + 0.463850i \(0.153532\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1654.00 −1.91657 −0.958285 − 0.285814i \(-0.907736\pi\)
−0.958285 + 0.285814i \(0.907736\pi\)
\(864\) 0 0
\(865\) −830.000 −0.959538
\(866\) 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
\(875\) −750.000 −0.857143
\(876\) 0 0
\(877\) 1626.00 1.85405 0.927024 − 0.375002i \(-0.122358\pi\)
0.927024 + 0.375002i \(0.122358\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1602.00 1.81839 0.909194 − 0.416373i \(-0.136699\pi\)
0.909194 + 0.416373i \(0.136699\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1754.00 1.97745 0.988726 − 0.149736i \(-0.0478423\pi\)
0.988726 + 0.149736i \(0.0478423\pi\)
\(888\) 0 0
\(889\) 1476.00 1.66029
\(890\) 0 0
\(891\) 1458.00 1.63636
\(892\) 0 0
\(893\) −172.000 −0.192609
\(894\) 0 0
\(895\) −1590.00 −1.77654
\(896\) 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
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1332.00 1.45256
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −1350.00 −1.45946
\(926\) 0 0
\(927\) 1674.00 1.80583
\(928\) 0 0
\(929\) −702.000 −0.755651 −0.377826 − 0.925877i \(-0.623328\pi\)
−0.377826 + 0.925877i \(0.623328\pi\)
\(930\) 0 0
\(931\) −26.0000 −0.0279270
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) −2028.00 −2.15058
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 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
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 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
\(967\) 954.000 0.986556 0.493278 − 0.869872i \(-0.335798\pi\)
0.493278 + 0.869872i \(0.335798\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1902.00 −1.95881 −0.979403 − 0.201917i \(-0.935283\pi\)
−0.979403 + 0.201917i \(0.935283\pi\)
\(972\) 0 0
\(973\) −492.000 −0.505653
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 324.000 0.330950
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 346.000 0.351984 0.175992 − 0.984392i \(-0.443687\pi\)
0.175992 + 0.984392i \(0.443687\pi\)
\(984\) 0 0
\(985\) 530.000 0.538071
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 426.000 0.427282 0.213641 − 0.976912i \(-0.431468\pi\)
0.213641 + 0.976912i \(0.431468\pi\)
\(998\) 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 160.3.e.b.79.1 1
3.2 odd 2 1440.3.p.a.559.1 1
4.3 odd 2 40.3.e.a.19.1 ✓ 1
5.2 odd 4 800.3.g.c.751.1 2
5.3 odd 4 800.3.g.c.751.2 2
5.4 even 2 160.3.e.a.79.1 1
8.3 odd 2 160.3.e.a.79.1 1
8.5 even 2 40.3.e.b.19.1 yes 1
12.11 even 2 360.3.p.b.19.1 1
15.14 odd 2 1440.3.p.b.559.1 1
16.3 odd 4 1280.3.h.b.1279.1 2
16.5 even 4 1280.3.h.c.1279.2 2
16.11 odd 4 1280.3.h.b.1279.2 2
16.13 even 4 1280.3.h.c.1279.1 2
20.3 even 4 200.3.g.c.51.2 2
20.7 even 4 200.3.g.c.51.1 2
20.19 odd 2 40.3.e.b.19.1 yes 1
24.5 odd 2 360.3.p.a.19.1 1
24.11 even 2 1440.3.p.b.559.1 1
40.3 even 4 800.3.g.c.751.1 2
40.13 odd 4 200.3.g.c.51.1 2
40.19 odd 2 CM 160.3.e.b.79.1 1
40.27 even 4 800.3.g.c.751.2 2
40.29 even 2 40.3.e.a.19.1 ✓ 1
40.37 odd 4 200.3.g.c.51.2 2
60.59 even 2 360.3.p.a.19.1 1
80.19 odd 4 1280.3.h.c.1279.2 2
80.29 even 4 1280.3.h.b.1279.2 2
80.59 odd 4 1280.3.h.c.1279.1 2
80.69 even 4 1280.3.h.b.1279.1 2
120.29 odd 2 360.3.p.b.19.1 1
120.59 even 2 1440.3.p.a.559.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.3.e.a.19.1 ✓ 1 4.3 odd 2
40.3.e.a.19.1 ✓ 1 40.29 even 2
40.3.e.b.19.1 yes 1 8.5 even 2
40.3.e.b.19.1 yes 1 20.19 odd 2
160.3.e.a.79.1 1 5.4 even 2
160.3.e.a.79.1 1 8.3 odd 2
160.3.e.b.79.1 1 1.1 even 1 trivial
160.3.e.b.79.1 1 40.19 odd 2 CM
200.3.g.c.51.1 2 20.7 even 4
200.3.g.c.51.1 2 40.13 odd 4
200.3.g.c.51.2 2 20.3 even 4
200.3.g.c.51.2 2 40.37 odd 4
360.3.p.a.19.1 1 24.5 odd 2
360.3.p.a.19.1 1 60.59 even 2
360.3.p.b.19.1 1 12.11 even 2
360.3.p.b.19.1 1 120.29 odd 2
800.3.g.c.751.1 2 5.2 odd 4
800.3.g.c.751.1 2 40.3 even 4
800.3.g.c.751.2 2 5.3 odd 4
800.3.g.c.751.2 2 40.27 even 4
1280.3.h.b.1279.1 2 16.3 odd 4
1280.3.h.b.1279.1 2 80.69 even 4
1280.3.h.b.1279.2 2 16.11 odd 4
1280.3.h.b.1279.2 2 80.29 even 4
1280.3.h.c.1279.1 2 16.13 even 4
1280.3.h.c.1279.1 2 80.59 odd 4
1280.3.h.c.1279.2 2 16.5 even 4
1280.3.h.c.1279.2 2 80.19 odd 4
1440.3.p.a.559.1 1 3.2 odd 2
1440.3.p.a.559.1 1 120.59 even 2
1440.3.p.b.559.1 1 15.14 odd 2
1440.3.p.b.559.1 1 24.11 even 2