Properties

Label 111.1.d.b.110.2
Level 111
Weight 1
Character 111.110
Self dual yes
Analytic conductor 0.055
Analytic rank 0
Dimension 2
Projective image \(D_{4}\)
CM discriminant -111
Inner twists 4

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 111 = 3 \cdot 37 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 111.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.0553962164023\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Defining polynomial: \(x^{2} - 2\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(D_{4}\)
Projective field Galois closure of 4.2.4107.1
Artin image $D_8$
Artin field Galois closure of 8.0.4102893.1

Embedding invariants

Embedding label 110.2
Root \(-1.41421\) of defining polynomial
Character \(\chi\) \(=\) 111.110

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.41421 q^{5} -1.41421 q^{6} +1.00000 q^{9} +O(q^{10})\) \(q+1.41421 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.41421 q^{5} -1.41421 q^{6} +1.00000 q^{9} -2.00000 q^{10} -1.00000 q^{12} +1.41421 q^{15} -1.00000 q^{16} +1.41421 q^{17} +1.41421 q^{18} -1.41421 q^{20} -1.41421 q^{23} +1.00000 q^{25} -1.00000 q^{27} +1.41421 q^{29} +2.00000 q^{30} -1.41421 q^{32} +2.00000 q^{34} +1.00000 q^{36} -1.00000 q^{37} -1.41421 q^{45} -2.00000 q^{46} +1.00000 q^{48} -1.00000 q^{49} +1.41421 q^{50} -1.41421 q^{51} -1.41421 q^{54} +2.00000 q^{58} +1.41421 q^{59} +1.41421 q^{60} -1.00000 q^{64} +1.41421 q^{68} +1.41421 q^{69} -1.41421 q^{74} -1.00000 q^{75} +1.41421 q^{80} +1.00000 q^{81} -2.00000 q^{85} -1.41421 q^{87} -1.41421 q^{89} -2.00000 q^{90} -1.41421 q^{92} +1.41421 q^{96} -1.41421 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{3} + 2q^{4} + 2q^{9} + O(q^{10}) \) \( 2q - 2q^{3} + 2q^{4} + 2q^{9} - 4q^{10} - 2q^{12} - 2q^{16} + 2q^{25} - 2q^{27} + 4q^{30} + 4q^{34} + 2q^{36} - 2q^{37} - 4q^{46} + 2q^{48} - 2q^{49} + 4q^{58} - 2q^{64} - 2q^{75} + 2q^{81} - 4q^{85} - 4q^{90} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/111\mathbb{Z}\right)^\times\).

\(n\) \(38\) \(76\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) −1.00000 −1.00000
\(4\) 1.00000 1.00000
\(5\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(6\) −1.41421 −1.41421
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 1.00000 1.00000
\(10\) −2.00000 −2.00000
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) −1.00000 −1.00000
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 1.41421 1.41421
\(16\) −1.00000 −1.00000
\(17\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(18\) 1.41421 1.41421
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −1.41421 −1.41421
\(21\) 0 0
\(22\) 0 0
\(23\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(24\) 0 0
\(25\) 1.00000 1.00000
\(26\) 0 0
\(27\) −1.00000 −1.00000
\(28\) 0 0
\(29\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(30\) 2.00000 2.00000
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) −1.41421 −1.41421
\(33\) 0 0
\(34\) 2.00000 2.00000
\(35\) 0 0
\(36\) 1.00000 1.00000
\(37\) −1.00000 −1.00000
\(38\) 0 0
\(39\) 0 0
\(40\) 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
\(45\) −1.41421 −1.41421
\(46\) −2.00000 −2.00000
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 1.00000 1.00000
\(49\) −1.00000 −1.00000
\(50\) 1.41421 1.41421
\(51\) −1.41421 −1.41421
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) −1.41421 −1.41421
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 2.00000 2.00000
\(59\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(60\) 1.41421 1.41421
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −1.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 1.41421 1.41421
\(69\) 1.41421 1.41421
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) −1.41421 −1.41421
\(75\) −1.00000 −1.00000
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 1.41421 1.41421
\(81\) 1.00000 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) −2.00000 −2.00000
\(86\) 0 0
\(87\) −1.41421 −1.41421
\(88\) 0 0
\(89\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(90\) −2.00000 −2.00000
\(91\) 0 0
\(92\) −1.41421 −1.41421
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 1.41421 1.41421
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −1.41421 −1.41421
\(99\) 0 0
\(100\) 1.00000 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) −2.00000 −2.00000
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −1.00000 −1.00000
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 1.00000 1.00000
\(112\) 0 0
\(113\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(114\) 0 0
\(115\) 2.00000 2.00000
\(116\) 1.41421 1.41421
\(117\) 0 0
\(118\) 2.00000 2.00000
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.41421 1.41421
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 2.00000 2.00000
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −1.00000 −1.00000
\(145\) −2.00000 −2.00000
\(146\) 0 0
\(147\) 1.00000 1.00000
\(148\) −1.00000 −1.00000
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) −1.41421 −1.41421
\(151\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 1.41421 1.41421
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 2.00000 2.00000
\(161\) 0 0
\(162\) 1.41421 1.41421
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(168\) 0 0
\(169\) 1.00000 1.00000
\(170\) −2.82843 −2.82843
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) −2.00000 −2.00000
\(175\) 0 0
\(176\) 0 0
\(177\) −1.41421 −1.41421
\(178\) −2.00000 −2.00000
\(179\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(180\) −1.41421 −1.41421
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.41421 1.41421
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(192\) 1.00000 1.00000
\(193\) 0 0 1.00000 \(0\)
−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
\(202\) 0 0
\(203\) 0 0
\(204\) −1.41421 −1.41421
\(205\) 0 0
\(206\) 0 0
\(207\) −1.41421 −1.41421
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(212\) 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
\(222\) 1.41421 1.41421
\(223\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 1.00000 1.00000
\(226\) −2.00000 −2.00000
\(227\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(228\) 0 0
\(229\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(230\) 2.82843 2.82843
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.41421 1.41421
\(237\) 0 0
\(238\) 0 0
\(239\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(240\) −1.41421 −1.41421
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 1.41421 1.41421
\(243\) −1.00000 −1.00000
\(244\) 0 0
\(245\) 1.41421 1.41421
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 2.82843 2.82843
\(255\) 2.00000 2.00000
\(256\) 1.00000 1.00000
\(257\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1.41421 1.41421
\(262\) 2.00000 2.00000
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 1.41421 1.41421
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 2.00000 2.00000
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) −1.41421 −1.41421
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 1.41421 1.41421
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.41421 −1.41421
\(289\) 1.00000 1.00000
\(290\) −2.82843 −2.82843
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 1.41421 1.41421
\(295\) −2.00000 −2.00000
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −1.00000 −1.00000
\(301\) 0 0
\(302\) −2.82843 −2.82843
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 2.00000 2.00000
\(307\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.41421 1.41421
\(321\) 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 \(\pi\)
\(332\) 0 0
\(333\) −1.00000 −1.00000
\(334\) 2.00000 2.00000
\(335\) 0 0
\(336\) 0 0
\(337\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(338\) 1.41421 1.41421
\(339\) 1.41421 1.41421
\(340\) −2.00000 −2.00000
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −2.00000 −2.00000
\(346\) 0 0
\(347\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(348\) −1.41421 −1.41421
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(354\) −2.00000 −2.00000
\(355\) 0 0
\(356\) −1.41421 −1.41421
\(357\) 0 0
\(358\) −2.00000 −2.00000
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) −1.00000 −1.00000
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(368\) 1.41421 1.41421
\(369\) 0 0
\(370\) 2.00000 2.00000
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) −2.00000 −2.00000
\(382\) 2.00000 2.00000
\(383\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(390\) 0 0
\(391\) −2.00000 −2.00000
\(392\) 0 0
\(393\) −1.41421 −1.41421
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −1.00000 −1.00000
\(401\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −1.41421 −1.41421
\(406\) 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
\(414\) −2.00000 −2.00000
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 2.82843 2.82843
\(423\) 0 0
\(424\) 0 0
\(425\) 1.41421 1.41421
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(432\) 1.00000 1.00000
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 2.00000 2.00000
\(436\) 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 \(\pi\)
\(444\) 1.00000 1.00000
\(445\) 2.00000 2.00000
\(446\) −2.82843 −2.82843
\(447\) 0 0
\(448\) 0 0
\(449\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(450\) 1.41421 1.41421
\(451\) 0 0
\(452\) −1.41421 −1.41421
\(453\) 2.00000 2.00000
\(454\) −2.00000 −2.00000
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) −2.82843 −2.82843
\(459\) −1.41421 −1.41421
\(460\) 2.00000 2.00000
\(461\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) −1.41421 −1.41421
\(465\) 0 0
\(466\) 0 0
\(467\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(468\) 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
\(477\) 0 0
\(478\) −2.00000 −2.00000
\(479\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(480\) −2.00000 −2.00000
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1.00000 1.00000
\(485\) 0 0
\(486\) −1.41421 −1.41421
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 2.00000 2.00000
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 2.00000 2.00000
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) −1.41421 −1.41421
\(502\) −2.00000 −2.00000
\(503\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −1.00000
\(508\) 2.00000 2.00000
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 2.82843 2.82843
\(511\) 0 0
\(512\) 1.41421 1.41421
\(513\) 0 0
\(514\) −2.00000 −2.00000
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 2.00000 2.00000
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 1.41421 1.41421
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 1.41421 1.41421
\(532\) 0 0
\(533\) 0 0
\(534\) 2.00000 2.00000
\(535\) 0 0
\(536\) 0 0
\(537\) 1.41421 1.41421
\(538\) 0 0
\(539\) 0 0
\(540\) 1.41421 1.41421
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −2.00000 −2.00000
\(545\) 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
\(555\) −1.41421 −1.41421
\(556\) 0 0
\(557\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(558\) 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
\(565\) 2.00000 2.00000
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) −1.41421 −1.41421
\(574\) 0 0
\(575\) −1.41421 −1.41421
\(576\) −1.00000 −1.00000
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 1.41421 1.41421
\(579\) 0 0
\(580\) −2.00000 −2.00000
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(588\) 1.00000 1.00000
\(589\) 0 0
\(590\) −2.82843 −2.82843
\(591\) 0 0
\(592\) 1.00000 1.00000
\(593\) 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
\(601\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −2.00000 −2.00000
\(605\) −1.41421 −1.41421
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 1.41421 1.41421
\(613\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(614\) 2.82843 2.82843
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 1.41421 1.41421
\(622\) −2.00000 −2.00000
\(623\) 0 0
\(624\) 0 0
\(625\) −1.00000 −1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.41421 −1.41421
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) −2.00000 −2.00000
\(634\) 0 0
\(635\) −2.82843 −2.82843
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(654\) 0 0
\(655\) −2.00000 −2.00000
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −1.41421 −1.41421
\(667\) −2.00000 −2.00000
\(668\) 1.41421 1.41421
\(669\) 2.00000 2.00000
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) −2.82843 −2.82843
\(675\) −1.00000 −1.00000
\(676\) 1.00000 1.00000
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 2.00000 2.00000
\(679\) 0 0
\(680\) 0 0
\(681\) 1.41421 1.41421
\(682\) 0 0
\(683\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 2.00000 2.00000
\(688\) 0 0
\(689\) 0 0
\(690\) −2.82843 −2.82843
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 2.00000 2.00000
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 2.00000 2.00000
\(707\) 0 0
\(708\) −1.41421 −1.41421
\(709\) 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
\(716\) −1.41421 −1.41421
\(717\) 1.41421 1.41421
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 1.41421 1.41421
\(721\) 0 0
\(722\) 1.41421 1.41421
\(723\) 0 0
\(724\) 0 0
\(725\) 1.41421 1.41421
\(726\) −1.41421 −1.41421
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(734\) 2.82843 2.82843
\(735\) −1.41421 −1.41421
\(736\) 2.00000 2.00000
\(737\) 0 0
\(738\) 0 0
\(739\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(740\) 1.41421 1.41421
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 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
\(753\) 1.41421 1.41421
\(754\) 0 0
\(755\) 2.82843 2.82843
\(756\) 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 \(\pi\)
\(762\) −2.82843 −2.82843
\(763\) 0 0
\(764\) 1.41421 1.41421
\(765\) −2.00000 −2.00000
\(766\) 2.00000 2.00000
\(767\) 0 0
\(768\) −1.00000 −1.00000
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 1.41421 1.41421
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −2.00000 −2.00000
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) −2.82843 −2.82843
\(783\) −1.41421 −1.41421
\(784\) 1.00000 1.00000
\(785\) 0 0
\(786\) −2.00000 −2.00000
\(787\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(788\) 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
\(797\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −1.41421 −1.41421
\(801\) −1.41421 −1.41421
\(802\) 2.00000 2.00000
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(810\) −2.00000 −2.00000
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 1.41421 1.41421
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 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
\(826\) 0 0
\(827\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(828\) −1.41421 −1.41421
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.41421 −1.41421
\(834\) 0 0
\(835\) −2.00000 −2.00000
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 1.41421 1.41421
\(844\) 2.00000 2.00000
\(845\) −1.41421 −1.41421
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 2.00000 2.00000
\(851\) 1.41421 1.41421
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −2.00000 −2.00000
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 1.41421 1.41421
\(865\) 0 0
\(866\) 0 0
\(867\) −1.00000 −1.00000
\(868\) 0 0
\(869\) 0 0
\(870\) 2.82843 2.82843
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −1.41421 −1.41421
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 2.00000 2.00000
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 2.82843 2.82843
\(891\) 0 0
\(892\) −2.00000 −2.00000
\(893\) 0 0
\(894\) 0 0
\(895\) 2.00000 2.00000
\(896\) 0 0
\(897\) 0 0
\(898\) 2.00000 2.00000
\(899\) 0 0
\(900\) 1.00000 1.00000
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 2.82843 2.82843
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) −1.41421 −1.41421
\(909\) 0 0
\(910\) 0 0
\(911\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −2.00000 −2.00000
\(917\) 0 0
\(918\) −2.00000 −2.00000
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) −2.00000 −2.00000
\(922\) −2.00000 −2.00000
\(923\) 0 0
\(924\) 0 0
\(925\) −1.00000 −1.00000
\(926\) 0 0
\(927\) 0 0
\(928\) −2.00000 −2.00000
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 1.41421 1.41421
\(934\) 2.00000 2.00000
\(935\) 0 0
\(936\) 0 0
\(937\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −1.41421 −1.41421
\(945\) 0 0
\(946\) 0 0
\(947\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(948\) 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
\(955\) −2.00000 −2.00000
\(956\) −1.41421 −1.41421
\(957\) 0 0
\(958\) 2.00000 2.00000
\(959\) 0 0
\(960\) −1.41421 −1.41421
\(961\) 1.00000 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 \(\pi\)
\(972\) −1.00000 −1.00000
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 1.41421 1.41421
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 2.82843 2.82843
\(987\) 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
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0 0
\(999\) 1.00000 1.00000
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 111.1.d.b.110.2 yes 2
3.2 odd 2 inner 111.1.d.b.110.1 2
4.3 odd 2 1776.1.n.c.1553.1 2
5.2 odd 4 2775.1.b.b.2774.4 4
5.3 odd 4 2775.1.b.b.2774.1 4
5.4 even 2 2775.1.h.b.776.1 2
9.2 odd 6 2997.1.n.d.1997.2 4
9.4 even 3 2997.1.n.d.998.1 4
9.5 odd 6 2997.1.n.d.998.2 4
9.7 even 3 2997.1.n.d.1997.1 4
12.11 even 2 1776.1.n.c.1553.2 2
15.2 even 4 2775.1.b.b.2774.2 4
15.8 even 4 2775.1.b.b.2774.3 4
15.14 odd 2 2775.1.h.b.776.2 2
37.36 even 2 inner 111.1.d.b.110.1 2
111.110 odd 2 CM 111.1.d.b.110.2 yes 2
148.147 odd 2 1776.1.n.c.1553.2 2
185.73 odd 4 2775.1.b.b.2774.3 4
185.147 odd 4 2775.1.b.b.2774.2 4
185.184 even 2 2775.1.h.b.776.2 2
333.110 odd 6 2997.1.n.d.1997.1 4
333.184 even 6 2997.1.n.d.998.2 4
333.221 odd 6 2997.1.n.d.998.1 4
333.295 even 6 2997.1.n.d.1997.2 4
444.443 even 2 1776.1.n.c.1553.1 2
555.332 even 4 2775.1.b.b.2774.4 4
555.443 even 4 2775.1.b.b.2774.1 4
555.554 odd 2 2775.1.h.b.776.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
111.1.d.b.110.1 2 3.2 odd 2 inner
111.1.d.b.110.1 2 37.36 even 2 inner
111.1.d.b.110.2 yes 2 1.1 even 1 trivial
111.1.d.b.110.2 yes 2 111.110 odd 2 CM
1776.1.n.c.1553.1 2 4.3 odd 2
1776.1.n.c.1553.1 2 444.443 even 2
1776.1.n.c.1553.2 2 12.11 even 2
1776.1.n.c.1553.2 2 148.147 odd 2
2775.1.b.b.2774.1 4 5.3 odd 4
2775.1.b.b.2774.1 4 555.443 even 4
2775.1.b.b.2774.2 4 15.2 even 4
2775.1.b.b.2774.2 4 185.147 odd 4
2775.1.b.b.2774.3 4 15.8 even 4
2775.1.b.b.2774.3 4 185.73 odd 4
2775.1.b.b.2774.4 4 5.2 odd 4
2775.1.b.b.2774.4 4 555.332 even 4
2775.1.h.b.776.1 2 5.4 even 2
2775.1.h.b.776.1 2 555.554 odd 2
2775.1.h.b.776.2 2 15.14 odd 2
2775.1.h.b.776.2 2 185.184 even 2
2997.1.n.d.998.1 4 9.4 even 3
2997.1.n.d.998.1 4 333.221 odd 6
2997.1.n.d.998.2 4 9.5 odd 6
2997.1.n.d.998.2 4 333.184 even 6
2997.1.n.d.1997.1 4 9.7 even 3
2997.1.n.d.1997.1 4 333.110 odd 6
2997.1.n.d.1997.2 4 9.2 odd 6
2997.1.n.d.1997.2 4 333.295 even 6