Properties

Label 648.1.b.b.163.1
Level $648$
Weight $1$
Character 648.163
Self dual yes
Analytic conductor $0.323$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -8
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 648.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.323394128186\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 72)
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.648.1
Artin image: $S_3$
Artin field: Galois closure of 3.1.648.1

Embedding invariants

Embedding label 163.1
Character \(\chi\) \(=\) 648.163

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{8} -1.00000 q^{11} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{19} -1.00000 q^{22} +1.00000 q^{25} +1.00000 q^{32} -1.00000 q^{34} -1.00000 q^{38} -1.00000 q^{41} -1.00000 q^{43} -1.00000 q^{44} +1.00000 q^{49} +1.00000 q^{50} -1.00000 q^{59} +1.00000 q^{64} -1.00000 q^{67} -1.00000 q^{68} -1.00000 q^{73} -1.00000 q^{76} -1.00000 q^{82} +2.00000 q^{83} -1.00000 q^{86} -1.00000 q^{88} +2.00000 q^{89} -1.00000 q^{97} +1.00000 q^{98} +O(q^{100})\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000
\(3\) 0 0
\(4\) 1.00000 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 1.00000 1.00000
\(9\) 0 0
\(10\) 0 0
\(11\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) 0 0
\(19\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.00000 −1.00000
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 1.00000 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 \(\pi\)
\(32\) 1.00000 1.00000
\(33\) 0 0
\(34\) −1.00000 −1.00000
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) −1.00000 −1.00000
\(39\) 0 0
\(40\) 0 0
\(41\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 0 0
\(43\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(44\) −1.00000 −1.00000
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) 1.00000 1.00000
\(50\) 1.00000 1.00000
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 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
\(67\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) −1.00000 −1.00000
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −1.00000 −1.00000
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −1.00000 −1.00000
\(83\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.00000 −1.00000
\(87\) 0 0
\(88\) −1.00000 −1.00000
\(89\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(98\) 1.00000 1.00000
\(99\) 0 0
\(100\) 1.00000 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −1.00000 −1.00000
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 1.00000 1.00000
\(129\) 0 0
\(130\) 0 0
\(131\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.00000 −1.00000
\(135\) 0 0
\(136\) −1.00000 −1.00000
\(137\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 0 0
\(139\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) −1.00000 −1.00000
\(147\) 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 \(\pi\)
\(152\) −1.00000 −1.00000
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(164\) −1.00000 −1.00000
\(165\) 0 0
\(166\) 2.00000 2.00000
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) −1.00000 −1.00000
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.00000 −1.00000
\(177\) 0 0
\(178\) 2.00000 2.00000
\(179\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1.00000 1.00000
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) −1.00000 −1.00000
\(195\) 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 \(\pi\)
\(200\) 1.00000 1.00000
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.00000 1.00000
\(210\) 0 0
\(211\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.00000 −1.00000
\(215\) 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 \(\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 2.00000 2.00000
\(227\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.00000 −1.00000
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 2.00000 2.00000
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −1.00000 −1.00000
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −1.00000 −1.00000
\(273\) 0 0
\(274\) −1.00000 −1.00000
\(275\) −1.00000 −1.00000
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) −1.00000 −1.00000
\(279\) 0 0
\(280\) 0 0
\(281\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(282\) 0 0
\(283\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0 0
\(290\) 0 0
\(291\) 0 0
\(292\) −1.00000 −1.00000
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −1.00000 −1.00000
\(305\) 0 0
\(306\) 0 0
\(307\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.00000 1.00000
\(324\) 0 0
\(325\) 0 0
\(326\) 2.00000 2.00000
\(327\) 0 0
\(328\) −1.00000 −1.00000
\(329\) 0 0
\(330\) 0 0
\(331\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(332\) 2.00000 2.00000
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(338\) 1.00000 1.00000
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) −1.00000 −1.00000
\(345\) 0 0
\(346\) 0 0
\(347\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.00000 −1.00000
\(353\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 2.00000 2.00000
\(357\) 0 0
\(358\) 2.00000 2.00000
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 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 \(\pi\)
\(374\) 1.00000 1.00000
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −1.00000 −1.00000
\(387\) 0 0
\(388\) −1.00000 −1.00000
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.00000 1.00000
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 1.00000 1.00000
\(419\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 2.00000 2.00000
\(423\) 0 0
\(424\) 0 0
\(425\) −1.00000 −1.00000
\(426\) 0 0
\(427\) 0 0
\(428\) −1.00000 −1.00000
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(434\) 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
\(441\) 0 0
\(442\) 0 0
\(443\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(450\) 0 0
\(451\) 1.00000 1.00000
\(452\) 2.00000 2.00000
\(453\) 0 0
\(454\) −1.00000 −1.00000
\(455\) 0 0
\(456\) 0 0
\(457\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −1.00000 −1.00000
\(467\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.00000 −1.00000
\(473\) 1.00000 1.00000
\(474\) 0 0
\(475\) −1.00000 −1.00000
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.00000 −1.00000
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −1.00000 −1.00000
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 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
\(512\) 1.00000 1.00000
\(513\) 0 0
\(514\) −1.00000 −1.00000
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0 0
\(523\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(524\) 2.00000 2.00000
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −1.00000 −1.00000
\(537\) 0 0
\(538\) 0 0
\(539\) −1.00000 −1.00000
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.00000 −1.00000
\(545\) 0 0
\(546\) 0 0
\(547\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) −1.00000 −1.00000
\(549\) 0 0
\(550\) −1.00000 −1.00000
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −1.00000 −1.00000
\(557\) 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
\(563\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 2.00000 2.00000
\(567\) 0 0
\(568\) 0 0
\(569\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) 0 0
\(571\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −1.00000 −1.00000
\(585\) 0 0
\(586\) 0 0
\(587\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(594\) 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
\(601\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) −1.00000 −1.00000
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) −1.00000 −1.00000
\(615\) 0 0
\(616\) 0 0
\(617\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(618\) 0 0
\(619\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) −1.00000 −1.00000
\(627\) 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
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 0 0
\(643\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1.00000 1.00000
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) 1.00000 1.00000
\(650\) 0 0
\(651\) 0 0
\(652\) 2.00000 2.00000
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.00000 −1.00000
\(657\) 0 0
\(658\) 0 0
\(659\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 2.00000 2.00000
\(663\) 0 0
\(664\) 2.00000 2.00000
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(674\) −1.00000 −1.00000
\(675\) 0 0
\(676\) 1.00000 1.00000
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −1.00000 −1.00000
\(689\) 0 0
\(690\) 0 0
\(691\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(692\) 0 0
\(693\) 0 0
\(694\) −1.00000 −1.00000
\(695\) 0 0
\(696\) 0 0
\(697\) 1.00000 1.00000
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.00000 −1.00000
\(705\) 0 0
\(706\) −1.00000 −1.00000
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 2.00000 2.00000
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 2.00000 2.00000
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.00000 1.00000
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.00000 1.00000
\(738\) 0 0
\(739\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) 0 0
\(741\) 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
\(748\) 1.00000 1.00000
\(749\) 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
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) −1.00000 −1.00000
\(759\) 0 0
\(760\) 0 0
\(761\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.00000 −1.00000
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −1.00000 −1.00000
\(777\) 0 0
\(778\) 0 0
\(779\) 1.00000 1.00000
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 1.00000
\(785\) 0 0
\(786\) 0 0
\(787\) 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
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.00000 1.00000
\(801\) 0 0
\(802\) −1.00000 −1.00000
\(803\) 1.00000 1.00000
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(810\) 0 0
\(811\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 1.00000 1.00000
\(818\) −1.00000 −1.00000
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.00000 −1.00000
\(834\) 0 0
\(835\) 0 0
\(836\) 1.00000 1.00000
\(837\) 0 0
\(838\) 2.00000 2.00000
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 2.00000 2.00000
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) −1.00000 −1.00000
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −1.00000 −1.00000
\(857\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(858\) 0 0
\(859\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −1.00000 −1.00000
\(867\) 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
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(882\) 0 0
\(883\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −1.00000 −1.00000
\(887\) 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
\(896\) 0 0
\(897\) 0 0
\(898\) −1.00000 −1.00000
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 1.00000 1.00000
\(903\) 0 0
\(904\) 2.00000 2.00000
\(905\) 0 0
\(906\) 0 0
\(907\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(908\) −1.00000 −1.00000
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) −2.00000 −2.00000
\(914\) −1.00000 −1.00000
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 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
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(930\) 0 0
\(931\) −1.00000 −1.00000
\(932\) −1.00000 −1.00000
\(933\) 0 0
\(934\) −1.00000 −1.00000
\(935\) 0 0
\(936\) 0 0
\(937\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −1.00000 −1.00000
\(945\) 0 0
\(946\) 1.00000 1.00000
\(947\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −1.00000 −1.00000
\(951\) 0 0
\(952\) 0 0
\(953\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) −1.00000 −1.00000
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(978\) 0 0
\(979\) −2.00000 −2.00000
\(980\) 0 0
\(981\) 0 0
\(982\) −1.00000 −1.00000
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−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 \(\pi\)
\(998\) −1.00000 −1.00000
\(999\) 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 648.1.b.b.163.1 1
3.2 odd 2 648.1.b.a.163.1 1
4.3 odd 2 2592.1.b.b.1135.1 1
8.3 odd 2 CM 648.1.b.b.163.1 1
8.5 even 2 2592.1.b.b.1135.1 1
9.2 odd 6 216.1.p.a.91.1 2
9.4 even 3 72.1.p.a.43.1 2
9.5 odd 6 216.1.p.a.19.1 2
9.7 even 3 72.1.p.a.67.1 yes 2
12.11 even 2 2592.1.b.a.1135.1 1
24.5 odd 2 2592.1.b.a.1135.1 1
24.11 even 2 648.1.b.a.163.1 1
36.7 odd 6 288.1.t.a.175.1 2
36.11 even 6 864.1.t.a.847.1 2
36.23 even 6 864.1.t.a.559.1 2
36.31 odd 6 288.1.t.a.79.1 2
45.4 even 6 1800.1.bk.d.1051.1 2
45.7 odd 12 1800.1.ba.b.499.2 4
45.13 odd 12 1800.1.ba.b.1699.2 4
45.22 odd 12 1800.1.ba.b.1699.1 4
45.34 even 6 1800.1.bk.d.1651.1 2
45.43 odd 12 1800.1.ba.b.499.1 4
63.4 even 3 3528.1.ba.b.1843.1 2
63.13 odd 6 3528.1.cg.a.2059.1 2
63.16 even 3 3528.1.ba.b.67.1 2
63.25 even 3 3528.1.ce.a.3019.1 2
63.31 odd 6 3528.1.ba.a.1843.1 2
63.34 odd 6 3528.1.cg.a.3235.1 2
63.40 odd 6 3528.1.ce.b.2419.1 2
63.52 odd 6 3528.1.ce.b.3019.1 2
63.58 even 3 3528.1.ce.a.2419.1 2
63.61 odd 6 3528.1.ba.a.67.1 2
72.5 odd 6 864.1.t.a.559.1 2
72.11 even 6 216.1.p.a.91.1 2
72.13 even 6 288.1.t.a.79.1 2
72.29 odd 6 864.1.t.a.847.1 2
72.43 odd 6 72.1.p.a.67.1 yes 2
72.59 even 6 216.1.p.a.19.1 2
72.61 even 6 288.1.t.a.175.1 2
72.67 odd 6 72.1.p.a.43.1 2
144.13 even 12 2304.1.o.c.511.1 4
144.43 odd 12 2304.1.o.c.2047.2 4
144.61 even 12 2304.1.o.c.2047.2 4
144.67 odd 12 2304.1.o.c.511.2 4
144.85 even 12 2304.1.o.c.511.2 4
144.115 odd 12 2304.1.o.c.2047.1 4
144.133 even 12 2304.1.o.c.2047.1 4
144.139 odd 12 2304.1.o.c.511.1 4
360.43 even 12 1800.1.ba.b.499.1 4
360.67 even 12 1800.1.ba.b.1699.1 4
360.139 odd 6 1800.1.bk.d.1051.1 2
360.187 even 12 1800.1.ba.b.499.2 4
360.259 odd 6 1800.1.bk.d.1651.1 2
360.283 even 12 1800.1.ba.b.1699.2 4
504.67 odd 6 3528.1.ba.b.1843.1 2
504.115 even 6 3528.1.ce.b.3019.1 2
504.139 even 6 3528.1.cg.a.2059.1 2
504.187 even 6 3528.1.ba.a.67.1 2
504.283 even 6 3528.1.ba.a.1843.1 2
504.331 odd 6 3528.1.ba.b.67.1 2
504.355 even 6 3528.1.ce.b.2419.1 2
504.403 odd 6 3528.1.ce.a.3019.1 2
504.475 even 6 3528.1.cg.a.3235.1 2
504.499 odd 6 3528.1.ce.a.2419.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.1.p.a.43.1 2 9.4 even 3
72.1.p.a.43.1 2 72.67 odd 6
72.1.p.a.67.1 yes 2 9.7 even 3
72.1.p.a.67.1 yes 2 72.43 odd 6
216.1.p.a.19.1 2 9.5 odd 6
216.1.p.a.19.1 2 72.59 even 6
216.1.p.a.91.1 2 9.2 odd 6
216.1.p.a.91.1 2 72.11 even 6
288.1.t.a.79.1 2 36.31 odd 6
288.1.t.a.79.1 2 72.13 even 6
288.1.t.a.175.1 2 36.7 odd 6
288.1.t.a.175.1 2 72.61 even 6
648.1.b.a.163.1 1 3.2 odd 2
648.1.b.a.163.1 1 24.11 even 2
648.1.b.b.163.1 1 1.1 even 1 trivial
648.1.b.b.163.1 1 8.3 odd 2 CM
864.1.t.a.559.1 2 36.23 even 6
864.1.t.a.559.1 2 72.5 odd 6
864.1.t.a.847.1 2 36.11 even 6
864.1.t.a.847.1 2 72.29 odd 6
1800.1.ba.b.499.1 4 45.43 odd 12
1800.1.ba.b.499.1 4 360.43 even 12
1800.1.ba.b.499.2 4 45.7 odd 12
1800.1.ba.b.499.2 4 360.187 even 12
1800.1.ba.b.1699.1 4 45.22 odd 12
1800.1.ba.b.1699.1 4 360.67 even 12
1800.1.ba.b.1699.2 4 45.13 odd 12
1800.1.ba.b.1699.2 4 360.283 even 12
1800.1.bk.d.1051.1 2 45.4 even 6
1800.1.bk.d.1051.1 2 360.139 odd 6
1800.1.bk.d.1651.1 2 45.34 even 6
1800.1.bk.d.1651.1 2 360.259 odd 6
2304.1.o.c.511.1 4 144.13 even 12
2304.1.o.c.511.1 4 144.139 odd 12
2304.1.o.c.511.2 4 144.67 odd 12
2304.1.o.c.511.2 4 144.85 even 12
2304.1.o.c.2047.1 4 144.115 odd 12
2304.1.o.c.2047.1 4 144.133 even 12
2304.1.o.c.2047.2 4 144.43 odd 12
2304.1.o.c.2047.2 4 144.61 even 12
2592.1.b.a.1135.1 1 12.11 even 2
2592.1.b.a.1135.1 1 24.5 odd 2
2592.1.b.b.1135.1 1 4.3 odd 2
2592.1.b.b.1135.1 1 8.5 even 2
3528.1.ba.a.67.1 2 63.61 odd 6
3528.1.ba.a.67.1 2 504.187 even 6
3528.1.ba.a.1843.1 2 63.31 odd 6
3528.1.ba.a.1843.1 2 504.283 even 6
3528.1.ba.b.67.1 2 63.16 even 3
3528.1.ba.b.67.1 2 504.331 odd 6
3528.1.ba.b.1843.1 2 63.4 even 3
3528.1.ba.b.1843.1 2 504.67 odd 6
3528.1.ce.a.2419.1 2 63.58 even 3
3528.1.ce.a.2419.1 2 504.499 odd 6
3528.1.ce.a.3019.1 2 63.25 even 3
3528.1.ce.a.3019.1 2 504.403 odd 6
3528.1.ce.b.2419.1 2 63.40 odd 6
3528.1.ce.b.2419.1 2 504.355 even 6
3528.1.ce.b.3019.1 2 63.52 odd 6
3528.1.ce.b.3019.1 2 504.115 even 6
3528.1.cg.a.2059.1 2 63.13 odd 6
3528.1.cg.a.2059.1 2 504.139 even 6
3528.1.cg.a.3235.1 2 63.34 odd 6
3528.1.cg.a.3235.1 2 504.475 even 6