Properties

Label 6400.2.a.cl.1.2
Level $6400$
Weight $2$
Character 6400.1
Self dual yes
Analytic conductor $51.104$
Analytic rank $0$
Dimension $4$
CM discriminant -40
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 6400 = 2^{8} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6400.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(51.1042572936\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{5})\)
Defining polynomial: \(x^{4} - 6 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 640)
Fricke sign: \(-1\)
Sato-Tate group: $N(\mathrm{U}(1))$

Embedding invariants

Embedding label 1.2
Root \(2.28825\) of defining polynomial
Character \(\chi\) \(=\) 6400.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.82843 q^{7} -3.00000 q^{9} +O(q^{10})\) \(q-2.82843 q^{7} -3.00000 q^{9} +6.32456 q^{11} +4.47214 q^{13} +6.32456 q^{19} -8.48528 q^{23} -4.47214 q^{37} +2.00000 q^{41} +2.82843 q^{47} +1.00000 q^{49} +13.4164 q^{53} -6.32456 q^{59} +8.48528 q^{63} -17.8885 q^{77} +9.00000 q^{81} +14.0000 q^{89} -12.6491 q^{91} -18.9737 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 12q^{9} + O(q^{10}) \) \( 4q - 12q^{9} + 8q^{41} + 4q^{49} + 36q^{81} + 56q^{89} + O(q^{100}) \)

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
\(5\) 0 0
\(6\) 0 0
\(7\) −2.82843 −1.06904 −0.534522 0.845154i \(-0.679509\pi\)
−0.534522 + 0.845154i \(0.679509\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 6.32456 1.90693 0.953463 0.301511i \(-0.0974911\pi\)
0.953463 + 0.301511i \(0.0974911\pi\)
\(12\) 0 0
\(13\) 4.47214 1.24035 0.620174 0.784465i \(-0.287062\pi\)
0.620174 + 0.784465i \(0.287062\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 6.32456 1.45095 0.725476 0.688247i \(-0.241620\pi\)
0.725476 + 0.688247i \(0.241620\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −8.48528 −1.76930 −0.884652 0.466252i \(-0.845604\pi\)
−0.884652 + 0.466252i \(0.845604\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −4.47214 −0.735215 −0.367607 0.929981i \(-0.619823\pi\)
−0.367607 + 0.929981i \(0.619823\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.82843 0.412568 0.206284 0.978492i \(-0.433863\pi\)
0.206284 + 0.978492i \(0.433863\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 13.4164 1.84289 0.921443 0.388514i \(-0.127012\pi\)
0.921443 + 0.388514i \(0.127012\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −6.32456 −0.823387 −0.411693 0.911322i \(-0.635063\pi\)
−0.411693 + 0.911322i \(0.635063\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 8.48528 1.06904
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −17.8885 −2.03859
\(78\) 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
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 14.0000 1.48400 0.741999 0.670402i \(-0.233878\pi\)
0.741999 + 0.670402i \(0.233878\pi\)
\(90\) 0 0
\(91\) −12.6491 −1.32599
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 0 0
\(99\) −18.9737 −1.90693
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) −19.7990 −1.95085 −0.975426 0.220326i \(-0.929288\pi\)
−0.975426 + 0.220326i \(0.929288\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −13.4164 −1.24035
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 29.0000 2.63636
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2.82843 0.250982 0.125491 0.992095i \(-0.459949\pi\)
0.125491 + 0.992095i \(0.459949\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −6.32456 −0.552579 −0.276289 0.961074i \(-0.589105\pi\)
−0.276289 + 0.961074i \(0.589105\pi\)
\(132\) 0 0
\(133\) −17.8885 −1.55113
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 18.9737 1.60933 0.804663 0.593732i \(-0.202346\pi\)
0.804663 + 0.593732i \(0.202346\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 28.2843 2.36525
\(144\) 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
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 22.3607 1.78458 0.892288 0.451466i \(-0.149099\pi\)
0.892288 + 0.451466i \(0.149099\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 24.0000 1.89146
\(162\) 0 0
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −25.4558 −1.96983 −0.984916 0.173032i \(-0.944644\pi\)
−0.984916 + 0.173032i \(0.944644\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) 0 0
\(171\) −18.9737 −1.45095
\(172\) 0 0
\(173\) 13.4164 1.02003 0.510015 0.860165i \(-0.329640\pi\)
0.510015 + 0.860165i \(0.329640\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 6.32456 0.472719 0.236360 0.971666i \(-0.424046\pi\)
0.236360 + 0.971666i \(0.424046\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 22.3607 1.59313 0.796566 0.604551i \(-0.206648\pi\)
0.796566 + 0.604551i \(0.206648\pi\)
\(198\) 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
\(207\) 25.4558 1.76930
\(208\) 0 0
\(209\) 40.0000 2.76686
\(210\) 0 0
\(211\) 18.9737 1.30620 0.653101 0.757271i \(-0.273468\pi\)
0.653101 + 0.757271i \(0.273468\pi\)
\(212\) 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
\(223\) 19.7990 1.32584 0.662919 0.748691i \(-0.269317\pi\)
0.662919 + 0.748691i \(0.269317\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 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
\(241\) 18.0000 1.15948 0.579741 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 28.2843 1.79969
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 31.6228 1.99601 0.998006 0.0631194i \(-0.0201049\pi\)
0.998006 + 0.0631194i \(0.0201049\pi\)
\(252\) 0 0
\(253\) −53.6656 −3.37393
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 12.6491 0.785977
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −8.48528 −0.523225 −0.261612 0.965173i \(-0.584254\pi\)
−0.261612 + 0.965173i \(0.584254\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 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
\(277\) 31.3050 1.88093 0.940466 0.339887i \(-0.110389\pi\)
0.940466 + 0.339887i \(0.110389\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 22.0000 1.31241 0.656205 0.754583i \(-0.272161\pi\)
0.656205 + 0.754583i \(0.272161\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5.65685 −0.333914
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 4.47214 0.261265 0.130632 0.991431i \(-0.458299\pi\)
0.130632 + 0.991431i \(0.458299\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −37.9473 −2.19455
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
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
\(313\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 31.3050 1.75826 0.879131 0.476581i \(-0.158124\pi\)
0.879131 + 0.476581i \(0.158124\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −8.00000 −0.441054
\(330\) 0 0
\(331\) 31.6228 1.73814 0.869072 0.494685i \(-0.164716\pi\)
0.869072 + 0.494685i \(0.164716\pi\)
\(332\) 0 0
\(333\) 13.4164 0.735215
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 16.9706 0.916324
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 21.0000 1.10526
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −31.1127 −1.62407 −0.812035 0.583609i \(-0.801640\pi\)
−0.812035 + 0.583609i \(0.801640\pi\)
\(368\) 0 0
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) −37.9473 −1.97013
\(372\) 0 0
\(373\) −31.3050 −1.62091 −0.810454 0.585802i \(-0.800780\pi\)
−0.810454 + 0.585802i \(0.800780\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 18.9737 0.974612 0.487306 0.873231i \(-0.337980\pi\)
0.487306 + 0.873231i \(0.337980\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −36.7696 −1.87884 −0.939418 0.342773i \(-0.888634\pi\)
−0.939418 + 0.342773i \(0.888634\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −4.47214 −0.224450 −0.112225 0.993683i \(-0.535798\pi\)
−0.112225 + 0.993683i \(0.535798\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 38.0000 1.89763 0.948815 0.315833i \(-0.102284\pi\)
0.948815 + 0.315833i \(0.102284\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −28.2843 −1.40200
\(408\) 0 0
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 17.8885 0.880238
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 31.6228 1.54487 0.772437 0.635092i \(-0.219038\pi\)
0.772437 + 0.635092i \(0.219038\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) −8.48528 −0.412568
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −53.6656 −2.56718
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −34.0000 −1.60456 −0.802280 0.596948i \(-0.796380\pi\)
−0.802280 + 0.596948i \(0.796380\pi\)
\(450\) 0 0
\(451\) 12.6491 0.595623
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) −36.7696 −1.70883 −0.854413 0.519594i \(-0.826083\pi\)
−0.854413 + 0.519594i \(0.826083\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −40.2492 −1.84289
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) −20.0000 −0.911922
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 31.1127 1.40985 0.704925 0.709281i \(-0.250980\pi\)
0.704925 + 0.709281i \(0.250980\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −44.2719 −1.99796 −0.998981 0.0451294i \(-0.985630\pi\)
−0.998981 + 0.0451294i \(0.985630\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −44.2719 −1.98188 −0.990941 0.134298i \(-0.957122\pi\)
−0.990941 + 0.134298i \(0.957122\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −19.7990 −0.882793 −0.441397 0.897312i \(-0.645517\pi\)
−0.441397 + 0.897312i \(0.645517\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 17.8885 0.786737
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 38.0000 1.66481 0.832405 0.554168i \(-0.186963\pi\)
0.832405 + 0.554168i \(0.186963\pi\)
\(522\) 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
\(529\) 49.0000 2.13043
\(530\) 0 0
\(531\) 18.9737 0.823387
\(532\) 0 0
\(533\) 8.94427 0.387419
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 6.32456 0.272418
\(540\) 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
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −13.4164 −0.568471 −0.284236 0.958754i \(-0.591740\pi\)
−0.284236 + 0.958754i \(0.591740\pi\)
\(558\) 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
\(567\) −25.4558 −1.06904
\(568\) 0 0
\(569\) 46.0000 1.92842 0.964210 0.265139i \(-0.0854179\pi\)
0.964210 + 0.265139i \(0.0854179\pi\)
\(570\) 0 0
\(571\) −44.2719 −1.85272 −0.926360 0.376638i \(-0.877080\pi\)
−0.926360 + 0.376638i \(0.877080\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 84.8528 3.51424
\(584\) 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
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −42.0000 −1.71322 −0.856608 0.515968i \(-0.827432\pi\)
−0.856608 + 0.515968i \(0.827432\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 2.82843 0.114802 0.0574012 0.998351i \(-0.481719\pi\)
0.0574012 + 0.998351i \(0.481719\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12.6491 0.511728
\(612\) 0 0
\(613\) 49.1935 1.98691 0.993453 0.114239i \(-0.0364430\pi\)
0.993453 + 0.114239i \(0.0364430\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 18.9737 0.762616 0.381308 0.924448i \(-0.375474\pi\)
0.381308 + 0.924448i \(0.375474\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −39.5980 −1.58646
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 4.47214 0.177192
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.00000 0.0789953 0.0394976 0.999220i \(-0.487424\pi\)
0.0394976 + 0.999220i \(0.487424\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 31.1127 1.22317 0.611583 0.791180i \(-0.290533\pi\)
0.611583 + 0.791180i \(0.290533\pi\)
\(648\) 0 0
\(649\) −40.0000 −1.57014
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.47214 0.175008 0.0875041 0.996164i \(-0.472111\pi\)
0.0875041 + 0.996164i \(0.472111\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −44.2719 −1.72459 −0.862294 0.506408i \(-0.830973\pi\)
−0.862294 + 0.506408i \(0.830973\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 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
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −49.1935 −1.89066 −0.945330 0.326116i \(-0.894260\pi\)
−0.945330 + 0.326116i \(0.894260\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 60.0000 2.28582
\(690\) 0 0
\(691\) −31.6228 −1.20299 −0.601494 0.798878i \(-0.705427\pi\)
−0.601494 + 0.798878i \(0.705427\pi\)
\(692\) 0 0
\(693\) 53.6656 2.03859
\(694\) 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
\(703\) −28.2843 −1.06676
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 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
\(721\) 56.0000 2.08555
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 53.7401 1.99311 0.996555 0.0829312i \(-0.0264282\pi\)
0.996555 + 0.0829312i \(0.0264282\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 49.1935 1.81700 0.908502 0.417881i \(-0.137227\pi\)
0.908502 + 0.417881i \(0.137227\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 6.32456 0.232653 0.116326 0.993211i \(-0.462888\pi\)
0.116326 + 0.993211i \(0.462888\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 36.7696 1.34894 0.674472 0.738300i \(-0.264371\pi\)
0.674472 + 0.738300i \(0.264371\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 31.3050 1.13780 0.568899 0.822407i \(-0.307370\pi\)
0.568899 + 0.822407i \(0.307370\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 22.0000 0.797499 0.398750 0.917060i \(-0.369444\pi\)
0.398750 + 0.917060i \(0.369444\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −28.2843 −1.02129
\(768\) 0 0
\(769\) −54.0000 −1.94729 −0.973645 0.228069i \(-0.926759\pi\)
−0.973645 + 0.228069i \(0.926759\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −22.3607 −0.804258 −0.402129 0.915583i \(-0.631730\pi\)
−0.402129 + 0.915583i \(0.631730\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 12.6491 0.453201
\(780\) 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
\(797\) −40.2492 −1.42570 −0.712850 0.701316i \(-0.752596\pi\)
−0.712850 + 0.701316i \(0.752596\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −42.0000 −1.48400
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 26.0000 0.914111 0.457056 0.889438i \(-0.348904\pi\)
0.457056 + 0.889438i \(0.348904\pi\)
\(810\) 0 0
\(811\) 56.9210 1.99877 0.999383 0.0351147i \(-0.0111797\pi\)
0.999383 + 0.0351147i \(0.0111797\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 37.9473 1.32599
\(820\) 0 0
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) 48.0833 1.67608 0.838039 0.545611i \(-0.183702\pi\)
0.838039 + 0.545611i \(0.183702\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 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
\(845\) 0 0
\(846\) 0 0
\(847\) −82.0244 −2.81839
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 37.9473 1.30082
\(852\) 0 0
\(853\) −58.1378 −1.99060 −0.995300 0.0968435i \(-0.969125\pi\)
−0.995300 + 0.0968435i \(0.969125\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) −56.9210 −1.94212 −0.971060 0.238837i \(-0.923234\pi\)
−0.971060 + 0.238837i \(0.923234\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 8.48528 0.288842 0.144421 0.989516i \(-0.453868\pi\)
0.144421 + 0.989516i \(0.453868\pi\)
\(864\) 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
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 58.1378 1.96317 0.981586 0.191018i \(-0.0611790\pi\)
0.981586 + 0.191018i \(0.0611790\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −58.0000 −1.95407 −0.977035 0.213080i \(-0.931651\pi\)
−0.977035 + 0.213080i \(0.931651\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −59.3970 −1.99436 −0.997178 0.0750798i \(-0.976079\pi\)
−0.997178 + 0.0750798i \(0.976079\pi\)
\(888\) 0 0
\(889\) −8.00000 −0.268311
\(890\) 0 0
\(891\) 56.9210 1.90693
\(892\) 0 0
\(893\) 17.8885 0.598617
\(894\) 0 0
\(895\) 0 0
\(896\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 17.8885 0.590732
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 59.3970 1.95085
\(928\) 0 0
\(929\) −34.0000 −1.11550 −0.557752 0.830008i \(-0.688336\pi\)
−0.557752 + 0.830008i \(0.688336\pi\)
\(930\) 0 0
\(931\) 6.32456 0.207279
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) −16.9706 −0.552638
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 53.7401 1.72817 0.864083 0.503350i \(-0.167899\pi\)
0.864083 + 0.503350i \(0.167899\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 6.32456 0.202965 0.101482 0.994837i \(-0.467641\pi\)
0.101482 + 0.994837i \(0.467641\pi\)
\(972\) 0 0
\(973\) −53.6656 −1.72044
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) 0 0
\(979\) 88.5438 2.82987
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 48.0833 1.53362 0.766809 0.641875i \(-0.221843\pi\)
0.766809 + 0.641875i \(0.221843\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −49.1935 −1.55797 −0.778987 0.627040i \(-0.784266\pi\)
−0.778987 + 0.627040i \(0.784266\pi\)
\(998\) 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 6400.2.a.cl.1.2 4
4.3 odd 2 inner 6400.2.a.cl.1.3 4
5.2 odd 4 1280.2.c.l.769.1 4
5.3 odd 4 1280.2.c.l.769.4 4
5.4 even 2 inner 6400.2.a.cl.1.4 4
8.3 odd 2 inner 6400.2.a.cl.1.4 4
8.5 even 2 inner 6400.2.a.cl.1.1 4
16.3 odd 4 3200.2.d.w.1601.2 4
16.5 even 4 3200.2.d.w.1601.4 4
16.11 odd 4 3200.2.d.w.1601.1 4
16.13 even 4 3200.2.d.w.1601.3 4
20.3 even 4 1280.2.c.l.769.3 4
20.7 even 4 1280.2.c.l.769.2 4
20.19 odd 2 inner 6400.2.a.cl.1.1 4
40.3 even 4 1280.2.c.l.769.1 4
40.13 odd 4 1280.2.c.l.769.2 4
40.19 odd 2 CM 6400.2.a.cl.1.2 4
40.27 even 4 1280.2.c.l.769.4 4
40.29 even 2 inner 6400.2.a.cl.1.3 4
40.37 odd 4 1280.2.c.l.769.3 4
80.3 even 4 640.2.f.d.449.4 yes 4
80.13 odd 4 640.2.f.d.449.3 yes 4
80.19 odd 4 3200.2.d.w.1601.4 4
80.27 even 4 640.2.f.d.449.3 yes 4
80.29 even 4 3200.2.d.w.1601.1 4
80.37 odd 4 640.2.f.d.449.4 yes 4
80.43 even 4 640.2.f.d.449.2 yes 4
80.53 odd 4 640.2.f.d.449.1 4
80.59 odd 4 3200.2.d.w.1601.3 4
80.67 even 4 640.2.f.d.449.1 4
80.69 even 4 3200.2.d.w.1601.2 4
80.77 odd 4 640.2.f.d.449.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
640.2.f.d.449.1 4 80.53 odd 4
640.2.f.d.449.1 4 80.67 even 4
640.2.f.d.449.2 yes 4 80.43 even 4
640.2.f.d.449.2 yes 4 80.77 odd 4
640.2.f.d.449.3 yes 4 80.13 odd 4
640.2.f.d.449.3 yes 4 80.27 even 4
640.2.f.d.449.4 yes 4 80.3 even 4
640.2.f.d.449.4 yes 4 80.37 odd 4
1280.2.c.l.769.1 4 5.2 odd 4
1280.2.c.l.769.1 4 40.3 even 4
1280.2.c.l.769.2 4 20.7 even 4
1280.2.c.l.769.2 4 40.13 odd 4
1280.2.c.l.769.3 4 20.3 even 4
1280.2.c.l.769.3 4 40.37 odd 4
1280.2.c.l.769.4 4 5.3 odd 4
1280.2.c.l.769.4 4 40.27 even 4
3200.2.d.w.1601.1 4 16.11 odd 4
3200.2.d.w.1601.1 4 80.29 even 4
3200.2.d.w.1601.2 4 16.3 odd 4
3200.2.d.w.1601.2 4 80.69 even 4
3200.2.d.w.1601.3 4 16.13 even 4
3200.2.d.w.1601.3 4 80.59 odd 4
3200.2.d.w.1601.4 4 16.5 even 4
3200.2.d.w.1601.4 4 80.19 odd 4
6400.2.a.cl.1.1 4 8.5 even 2 inner
6400.2.a.cl.1.1 4 20.19 odd 2 inner
6400.2.a.cl.1.2 4 1.1 even 1 trivial
6400.2.a.cl.1.2 4 40.19 odd 2 CM
6400.2.a.cl.1.3 4 4.3 odd 2 inner
6400.2.a.cl.1.3 4 40.29 even 2 inner
6400.2.a.cl.1.4 4 5.4 even 2 inner
6400.2.a.cl.1.4 4 8.3 odd 2 inner