Properties

Label 1400.1.m.b.1301.1
Level $1400$
Weight $1$
Character 1400.1301
Self dual yes
Analytic conductor $0.699$
Analytic rank $0$
Dimension $2$
Projective image $D_{4}$
CM discriminant -56
Inner twists $4$

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1400.m (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.698691017686\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Defining polynomial: \(x^{2} - 2\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 280)
Projective image: \(D_{4}\)
Projective field: Galois closure of 4.2.11200.2
Artin image: $D_8$
Artin field: Galois closure of 8.0.19208000000.2

Embedding invariants

Embedding label 1301.1
Root \(1.41421\) of defining polynomial
Character \(\chi\) \(=\) 1400.1301

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.41421 q^{3} +1.00000 q^{4} +1.41421 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.41421 q^{3} +1.00000 q^{4} +1.41421 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.41421 q^{12} +1.41421 q^{13} -1.00000 q^{14} +1.00000 q^{16} -1.00000 q^{18} -1.41421 q^{19} -1.41421 q^{21} +1.41421 q^{24} -1.41421 q^{26} +1.00000 q^{28} -1.00000 q^{32} +1.00000 q^{36} +1.41421 q^{38} -2.00000 q^{39} +1.41421 q^{42} -1.41421 q^{48} +1.00000 q^{49} +1.41421 q^{52} -1.00000 q^{56} +2.00000 q^{57} +1.41421 q^{59} +1.41421 q^{61} +1.00000 q^{63} +1.00000 q^{64} -1.00000 q^{72} -1.41421 q^{76} +2.00000 q^{78} -1.00000 q^{81} +1.41421 q^{83} -1.41421 q^{84} +1.41421 q^{91} +1.41421 q^{96} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} + 2q^{4} + 2q^{7} - 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q - 2q^{2} + 2q^{4} + 2q^{7} - 2q^{8} + 2q^{9} - 2q^{14} + 2q^{16} - 2q^{18} + 2q^{28} - 2q^{32} + 2q^{36} - 4q^{39} + 2q^{49} - 2q^{56} + 4q^{57} + 2q^{63} + 2q^{64} - 2q^{72} + 4q^{78} - 2q^{81} - 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −1.00000
\(3\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(4\) 1.00000 1.00000
\(5\) 0 0
\(6\) 1.41421 1.41421
\(7\) 1.00000 1.00000
\(8\) −1.00000 −1.00000
\(9\) 1.00000 1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) −1.41421 −1.41421
\(13\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(14\) −1.00000 −1.00000
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) −1.00000 −1.00000
\(19\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(20\) 0 0
\(21\) −1.41421 −1.41421
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 1.41421 1.41421
\(25\) 0 0
\(26\) −1.41421 −1.41421
\(27\) 0 0
\(28\) 1.00000 1.00000
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) −1.00000 −1.00000
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 1.00000
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 1.41421 1.41421
\(39\) −2.00000 −2.00000
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 1.41421 1.41421
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −1.41421 −1.41421
\(49\) 1.00000 1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 1.41421 1.41421
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.00000 −1.00000
\(57\) 2.00000 2.00000
\(58\) 0 0
\(59\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(60\) 0 0
\(61\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(62\) 0 0
\(63\) 1.00000 1.00000
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −1.00000 −1.00000
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −1.41421 −1.41421
\(77\) 0 0
\(78\) 2.00000 2.00000
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) −1.00000 −1.00000
\(82\) 0 0
\(83\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(84\) −1.41421 −1.41421
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 1.41421 1.41421
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 1.41421 1.41421
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −1.00000 −1.00000
\(99\) 0 0
\(100\) 0 0
\(101\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) −1.41421 −1.41421
\(105\) 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
\(112\) 1.00000 1.00000
\(113\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(114\) −2.00000 −2.00000
\(115\) 0 0
\(116\) 0 0
\(117\) 1.41421 1.41421
\(118\) −1.41421 −1.41421
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) −1.41421 −1.41421
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −1.00000 −1.00000
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) −1.00000 −1.00000
\(129\) 0 0
\(130\) 0 0
\(131\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(132\) 0 0
\(133\) −1.41421 −1.41421
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) −1.41421 −1.41421
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(152\) 1.41421 1.41421
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −2.00000 −2.00000
\(157\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000 1.00000
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −1.41421 −1.41421
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 1.41421 1.41421
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) −1.41421 −1.41421
\(172\) 0 0
\(173\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −2.00000 −2.00000
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(182\) −1.41421 −1.41421
\(183\) −2.00000 −2.00000
\(184\) 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 \(0.5\pi\)
\(192\) −1.41421 −1.41421
\(193\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.00000 1.00000
\(197\) 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
\(202\) −1.41421 −1.41421
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 1.41421 1.41421
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) −1.00000 −1.00000
\(225\) 0 0
\(226\) −2.00000 −2.00000
\(227\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(228\) 2.00000 2.00000
\(229\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) −1.41421 −1.41421
\(235\) 0 0
\(236\) 1.41421 1.41421
\(237\) 0 0
\(238\) 0 0
\(239\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −1.00000 −1.00000
\(243\) 1.41421 1.41421
\(244\) 1.41421 1.41421
\(245\) 0 0
\(246\) 0 0
\(247\) −2.00000 −2.00000
\(248\) 0 0
\(249\) −2.00000 −2.00000
\(250\) 0 0
\(251\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(252\) 1.00000 1.00000
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 1.41421 1.41421
\(263\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(264\) 0 0
\(265\) 0 0
\(266\) 1.41421 1.41421
\(267\) 0 0
\(268\) 0 0
\(269\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) −2.00000 −2.00000
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) −1.41421 −1.41421
\(279\) 0 0
\(280\) 0 0
\(281\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −1.00000
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(294\) 1.41421 1.41421
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 2.00000 2.00000
\(303\) −2.00000 −2.00000
\(304\) −1.41421 −1.41421
\(305\) 0 0
\(306\) 0 0
\(307\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 2.00000 2.00000
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 1.41421 1.41421
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −1.00000 −1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 1.41421 1.41421
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −1.41421 −1.41421
\(337\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(338\) −1.00000 −1.00000
\(339\) −2.82843 −2.82843
\(340\) 0 0
\(341\) 0 0
\(342\) 1.41421 1.41421
\(343\) 1.00000 1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) 1.41421 1.41421
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 2.00000 2.00000
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) 1.41421 1.41421
\(363\) −1.41421 −1.41421
\(364\) 1.41421 1.41421
\(365\) 0 0
\(366\) 2.00000 2.00000
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 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
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 1.41421 1.41421
\(385\) 0 0
\(386\) 2.00000 2.00000
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.00000 −1.00000
\(393\) 2.00000 2.00000
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(398\) 0 0
\(399\) 2.00000 2.00000
\(400\) 0 0
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 1.41421 1.41421
\(405\) 0 0
\(406\) 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
\(413\) 1.41421 1.41421
\(414\) 0 0
\(415\) 0 0
\(416\) −1.41421 −1.41421
\(417\) −2.00000 −2.00000
\(418\) 0 0
\(419\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.41421 1.41421
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 1.00000 1.00000
\(449\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 2.00000 2.00000
\(453\) 2.82843 2.82843
\(454\) −1.41421 −1.41421
\(455\) 0 0
\(456\) −2.00000 −2.00000
\(457\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(458\) −1.41421 −1.41421
\(459\) 0 0
\(460\) 0 0
\(461\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(462\) 0 0
\(463\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(468\) 1.41421 1.41421
\(469\) 0 0
\(470\) 0 0
\(471\) 2.00000 2.00000
\(472\) −1.41421 −1.41421
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 2.00000 2.00000
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1.00000 1.00000
\(485\) 0 0
\(486\) −1.41421 −1.41421
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) −1.41421 −1.41421
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 2.00000 2.00000
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 2.00000 2.00000
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −1.41421 −1.41421
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) −1.00000 −1.00000
\(505\) 0 0
\(506\) 0 0
\(507\) −1.41421 −1.41421
\(508\) 0 0
\(509\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 2.00000 2.00000
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(524\) −1.41421 −1.41421
\(525\) 0 0
\(526\) −2.00000 −2.00000
\(527\) 0 0
\(528\) 0 0
\(529\) −1.00000 −1.00000
\(530\) 0 0
\(531\) 1.41421 1.41421
\(532\) −1.41421 −1.41421
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 1.41421 1.41421
\(539\) 0 0
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 2.00000 2.00000
\(544\) 0 0
\(545\) 0 0
\(546\) 2.00000 2.00000
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 1.41421 1.41421
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 1.41421 1.41421
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 2.00000 2.00000
\(563\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −1.41421 −1.41421
\(567\) −1.00000 −1.00000
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 1.00000
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −1.00000 −1.00000
\(579\) 2.82843 2.82843
\(580\) 0 0
\(581\) 1.41421 1.41421
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 1.41421 1.41421
\(587\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(588\) −1.41421 −1.41421
\(589\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −2.00000 −2.00000
\(605\) 0 0
\(606\) 2.00000 2.00000
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 1.41421 1.41421
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) −1.41421 −1.41421
\(615\) 0 0
\(616\) 0 0
\(617\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(618\) 0 0
\(619\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −2.00000 −2.00000
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) −1.41421 −1.41421
\(629\) 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
\(637\) 1.41421 1.41421
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 1.00000 1.00000
\(649\) 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
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −1.41421 −1.41421
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 1.41421 1.41421
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 2.00000 2.00000
\(675\) 0 0
\(676\) 1.00000 1.00000
\(677\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(678\) 2.82843 2.82843
\(679\) 0 0
\(680\) 0 0
\(681\) −2.00000 −2.00000
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −1.41421 −1.41421
\(685\) 0 0
\(686\) −1.00000 −1.00000
\(687\) −2.00000 −2.00000
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(692\) −1.41421 −1.41421
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 1.41421 1.41421
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.41421 1.41421
\(708\) −2.00000 −2.00000
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 2.82843 2.82843
\(718\) −2.00000 −2.00000
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.00000 −1.00000
\(723\) 0 0
\(724\) −1.41421 −1.41421
\(725\) 0 0
\(726\) 1.41421 1.41421
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) −1.41421 −1.41421
\(729\) −1.00000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) −2.00000 −2.00000
\(733\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 2.82843 2.82843
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.41421 1.41421
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) −2.00000 −2.00000
\(754\) 0 0
\(755\) 0 0
\(756\) 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
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.00000 2.00000
\(768\) −1.41421 −1.41421
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.00000 −2.00000
\(773\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(774\) 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
\(784\) 1.00000 1.00000
\(785\) 0 0
\(786\) −2.00000 −2.00000
\(787\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(788\) 0 0
\(789\) −2.82843 −2.82843
\(790\) 0 0
\(791\) 2.00000 2.00000
\(792\) 0 0
\(793\) 2.00000 2.00000
\(794\) 1.41421 1.41421
\(795\) 0 0
\(796\) 0 0
\(797\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(798\) −2.00000 −2.00000
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 2.00000 2.00000
\(808\) −1.41421 −1.41421
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) 0 0
\(811\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 1.41421 1.41421
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) −1.41421 −1.41421
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 1.41421 1.41421
\(833\) 0 0
\(834\) 2.00000 2.00000
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 1.41421 1.41421
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 2.82843 2.82843
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 1.00000 1.00000
\(848\) 0 0
\(849\) −2.00000 −2.00000
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(854\) −1.41421 −1.41421
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −2.00000 −2.00000
\(863\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −1.41421 −1.41421
\(868\) 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
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 2.00000 2.00000
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −1.00000 −1.00000
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) −1.00000 −1.00000
\(897\) 0 0
\(898\) 2.00000 2.00000
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) −2.00000 −2.00000
\(905\) 0 0
\(906\) −2.82843 −2.82843
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 1.41421 1.41421
\(909\) 1.41421 1.41421
\(910\) 0 0
\(911\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(912\) 2.00000 2.00000
\(913\) 0 0
\(914\) −2.00000 −2.00000
\(915\) 0 0
\(916\) 1.41421 1.41421
\(917\) −1.41421 −1.41421
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) −2.00000 −2.00000
\(922\) 1.41421 1.41421
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 2.00000 2.00000
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) −1.41421 −1.41421
\(932\) 0 0
\(933\) 0 0
\(934\) 1.41421 1.41421
\(935\) 0 0
\(936\) −1.41421 −1.41421
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(942\) −2.00000 −2.00000
\(943\) 0 0
\(944\) 1.41421 1.41421
\(945\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −2.00000 −2.00000
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) −1.00000 −1.00000
\(969\) 0 0
\(970\) 0 0
\(971\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(972\) 1.41421 1.41421
\(973\) 1.41421 1.41421
\(974\) 0 0
\(975\) 0 0
\(976\) 1.41421 1.41421
\(977\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −2.00000 −2.00000
\(989\) 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
\(996\) −2.00000 −2.00000
\(997\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(998\) 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 1400.1.m.b.1301.1 2
5.2 odd 4 280.1.c.a.69.2 yes 4
5.3 odd 4 280.1.c.a.69.3 yes 4
5.4 even 2 1400.1.m.e.1301.2 2
7.6 odd 2 inner 1400.1.m.b.1301.2 2
8.5 even 2 inner 1400.1.m.b.1301.2 2
15.2 even 4 2520.1.h.e.1189.4 4
15.8 even 4 2520.1.h.e.1189.2 4
20.3 even 4 1120.1.c.a.209.3 4
20.7 even 4 1120.1.c.a.209.1 4
35.2 odd 12 1960.1.bk.a.1109.1 8
35.3 even 12 1960.1.bk.a.509.2 8
35.12 even 12 1960.1.bk.a.1109.2 8
35.13 even 4 280.1.c.a.69.4 yes 4
35.17 even 12 1960.1.bk.a.509.3 8
35.18 odd 12 1960.1.bk.a.509.1 8
35.23 odd 12 1960.1.bk.a.1109.4 8
35.27 even 4 280.1.c.a.69.1 4
35.32 odd 12 1960.1.bk.a.509.4 8
35.33 even 12 1960.1.bk.a.1109.3 8
35.34 odd 2 1400.1.m.e.1301.1 2
40.3 even 4 1120.1.c.a.209.2 4
40.13 odd 4 280.1.c.a.69.4 yes 4
40.27 even 4 1120.1.c.a.209.4 4
40.29 even 2 1400.1.m.e.1301.1 2
40.37 odd 4 280.1.c.a.69.1 4
56.13 odd 2 CM 1400.1.m.b.1301.1 2
105.62 odd 4 2520.1.h.e.1189.3 4
105.83 odd 4 2520.1.h.e.1189.1 4
120.53 even 4 2520.1.h.e.1189.1 4
120.77 even 4 2520.1.h.e.1189.3 4
140.27 odd 4 1120.1.c.a.209.4 4
140.83 odd 4 1120.1.c.a.209.2 4
280.13 even 4 280.1.c.a.69.3 yes 4
280.27 odd 4 1120.1.c.a.209.1 4
280.37 odd 12 1960.1.bk.a.1109.2 8
280.53 odd 12 1960.1.bk.a.509.2 8
280.69 odd 2 1400.1.m.e.1301.2 2
280.83 odd 4 1120.1.c.a.209.3 4
280.93 odd 12 1960.1.bk.a.1109.3 8
280.117 even 12 1960.1.bk.a.1109.1 8
280.157 even 12 1960.1.bk.a.509.4 8
280.173 even 12 1960.1.bk.a.1109.4 8
280.213 even 12 1960.1.bk.a.509.1 8
280.237 even 4 280.1.c.a.69.2 yes 4
280.277 odd 12 1960.1.bk.a.509.3 8
840.293 odd 4 2520.1.h.e.1189.2 4
840.797 odd 4 2520.1.h.e.1189.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.1.c.a.69.1 4 35.27 even 4
280.1.c.a.69.1 4 40.37 odd 4
280.1.c.a.69.2 yes 4 5.2 odd 4
280.1.c.a.69.2 yes 4 280.237 even 4
280.1.c.a.69.3 yes 4 5.3 odd 4
280.1.c.a.69.3 yes 4 280.13 even 4
280.1.c.a.69.4 yes 4 35.13 even 4
280.1.c.a.69.4 yes 4 40.13 odd 4
1120.1.c.a.209.1 4 20.7 even 4
1120.1.c.a.209.1 4 280.27 odd 4
1120.1.c.a.209.2 4 40.3 even 4
1120.1.c.a.209.2 4 140.83 odd 4
1120.1.c.a.209.3 4 20.3 even 4
1120.1.c.a.209.3 4 280.83 odd 4
1120.1.c.a.209.4 4 40.27 even 4
1120.1.c.a.209.4 4 140.27 odd 4
1400.1.m.b.1301.1 2 1.1 even 1 trivial
1400.1.m.b.1301.1 2 56.13 odd 2 CM
1400.1.m.b.1301.2 2 7.6 odd 2 inner
1400.1.m.b.1301.2 2 8.5 even 2 inner
1400.1.m.e.1301.1 2 35.34 odd 2
1400.1.m.e.1301.1 2 40.29 even 2
1400.1.m.e.1301.2 2 5.4 even 2
1400.1.m.e.1301.2 2 280.69 odd 2
1960.1.bk.a.509.1 8 35.18 odd 12
1960.1.bk.a.509.1 8 280.213 even 12
1960.1.bk.a.509.2 8 35.3 even 12
1960.1.bk.a.509.2 8 280.53 odd 12
1960.1.bk.a.509.3 8 35.17 even 12
1960.1.bk.a.509.3 8 280.277 odd 12
1960.1.bk.a.509.4 8 35.32 odd 12
1960.1.bk.a.509.4 8 280.157 even 12
1960.1.bk.a.1109.1 8 35.2 odd 12
1960.1.bk.a.1109.1 8 280.117 even 12
1960.1.bk.a.1109.2 8 35.12 even 12
1960.1.bk.a.1109.2 8 280.37 odd 12
1960.1.bk.a.1109.3 8 35.33 even 12
1960.1.bk.a.1109.3 8 280.93 odd 12
1960.1.bk.a.1109.4 8 35.23 odd 12
1960.1.bk.a.1109.4 8 280.173 even 12
2520.1.h.e.1189.1 4 105.83 odd 4
2520.1.h.e.1189.1 4 120.53 even 4
2520.1.h.e.1189.2 4 15.8 even 4
2520.1.h.e.1189.2 4 840.293 odd 4
2520.1.h.e.1189.3 4 105.62 odd 4
2520.1.h.e.1189.3 4 120.77 even 4
2520.1.h.e.1189.4 4 15.2 even 4
2520.1.h.e.1189.4 4 840.797 odd 4