Properties

Label 3332.1.g.c.883.1
Level $3332$
Weight $1$
Character 3332.883
Self dual yes
Analytic conductor $1.663$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -68
Inner twists $2$

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3332.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(1.66288462209\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 476)
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.3332.1
Artin image: $D_6$
Artin field: Galois closure of 6.2.310862272.1

Embedding invariants

Embedding label 883.1
Character \(\chi\) \(=\) 3332.883

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{22} -2.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{26} +1.00000 q^{27} +2.00000 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -1.00000 q^{39} +1.00000 q^{44} -2.00000 q^{46} -1.00000 q^{48} +1.00000 q^{50} +1.00000 q^{51} +1.00000 q^{52} -1.00000 q^{53} +1.00000 q^{54} +2.00000 q^{62} +1.00000 q^{64} -1.00000 q^{66} -1.00000 q^{68} +2.00000 q^{69} +1.00000 q^{71} -1.00000 q^{75} -1.00000 q^{78} +1.00000 q^{79} -1.00000 q^{81} +1.00000 q^{88} +1.00000 q^{89} -2.00000 q^{92} -2.00000 q^{93} -1.00000 q^{96} +O(q^{100})\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(885\) \(1667\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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
\(3\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(4\) 1.00000 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) −1.00000 −1.00000
\(7\) 0 0
\(8\) 1.00000 1.00000
\(9\) 0 0
\(10\) 0 0
\(11\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(12\) −1.00000 −1.00000
\(13\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) −1.00000 −1.00000
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.00000 1.00000
\(23\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(24\) −1.00000 −1.00000
\(25\) 1.00000 1.00000
\(26\) 1.00000 1.00000
\(27\) 1.00000 1.00000
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(32\) 1.00000 1.00000
\(33\) −1.00000 −1.00000
\(34\) −1.00000 −1.00000
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) −1.00000 −1.00000
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 1.00000 1.00000
\(45\) 0 0
\(46\) −2.00000 −2.00000
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −1.00000 −1.00000
\(49\) 0 0
\(50\) 1.00000 1.00000
\(51\) 1.00000 1.00000
\(52\) 1.00000 1.00000
\(53\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 1.00000 1.00000
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 2.00000 2.00000
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) −1.00000 −1.00000
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −1.00000 −1.00000
\(69\) 2.00000 2.00000
\(70\) 0 0
\(71\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) −1.00000 −1.00000
\(76\) 0 0
\(77\) 0 0
\(78\) −1.00000 −1.00000
\(79\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(80\) 0 0
\(81\) −1.00000 −1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 1.00000 1.00000
\(89\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −2.00000 −2.00000
\(93\) −2.00000 −2.00000
\(94\) 0 0
\(95\) 0 0
\(96\) −1.00000 −1.00000
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000 1.00000
\(101\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(102\) 1.00000 1.00000
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 1.00000 1.00000
\(105\) 0 0
\(106\) −1.00000 −1.00000
\(107\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(108\) 1.00000 1.00000
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) 2.00000 2.00000
\(125\) 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 \(0\)
\(132\) −1.00000 −1.00000
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −1.00000 −1.00000
\(137\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 2.00000 2.00000
\(139\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.00000 1.00000
\(143\) 1.00000 1.00000
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(150\) −1.00000 −1.00000
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −1.00000 −1.00000
\(157\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(158\) 1.00000 1.00000
\(159\) 1.00000 1.00000
\(160\) 0 0
\(161\) 0 0
\(162\) −1.00000 −1.00000
\(163\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.00000 1.00000
\(177\) 0 0
\(178\) 1.00000 1.00000
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −2.00000 −2.00000
\(185\) 0 0
\(186\) −2.00000 −2.00000
\(187\) −1.00000 −1.00000
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −1.00000 −1.00000
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(200\) 1.00000 1.00000
\(201\) 0 0
\(202\) −2.00000 −2.00000
\(203\) 0 0
\(204\) 1.00000 1.00000
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 1.00000 1.00000
\(209\) 0 0
\(210\) 0 0
\(211\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(212\) −1.00000 −1.00000
\(213\) −1.00000 −1.00000
\(214\) 1.00000 1.00000
\(215\) 0 0
\(216\) 1.00000 1.00000
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.00000 −1.00000
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(228\) 0 0
\(229\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1.00000 −1.00000
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 2.00000 2.00000
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) −2.00000 −2.00000
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 2.00000 2.00000
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) −1.00000 −1.00000
\(265\) 0 0
\(266\) 0 0
\(267\) −1.00000 −1.00000
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −1.00000 −1.00000
\(273\) 0 0
\(274\) −1.00000 −1.00000
\(275\) 1.00000 1.00000
\(276\) 2.00000 2.00000
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) −1.00000 −1.00000
\(279\) 0 0
\(280\) 0 0
\(281\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(282\) 0 0
\(283\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(284\) 1.00000 1.00000
\(285\) 0 0
\(286\) 1.00000 1.00000
\(287\) 0 0
\(288\) 0 0
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.00000 1.00000
\(298\) −1.00000 −1.00000
\(299\) −2.00000 −2.00000
\(300\) −1.00000 −1.00000
\(301\) 0 0
\(302\) 0 0
\(303\) 2.00000 2.00000
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) −1.00000 −1.00000
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 1.00000 1.00000
\(315\) 0 0
\(316\) 1.00000 1.00000
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 1.00000 1.00000
\(319\) 0 0
\(320\) 0 0
\(321\) −1.00000 −1.00000
\(322\) 0 0
\(323\) 0 0
\(324\) −1.00000 −1.00000
\(325\) 1.00000 1.00000
\(326\) −2.00000 −2.00000
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −1.00000 −1.00000
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.00000 2.00000
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 1.00000 1.00000
\(352\) 1.00000 1.00000
\(353\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.00000 1.00000
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) −2.00000 −2.00000
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −2.00000 −2.00000
\(373\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) −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 \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) −1.00000 −1.00000
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(390\) 0 0
\(391\) 2.00000 2.00000
\(392\) 0 0
\(393\) −2.00000 −2.00000
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) −1.00000 −1.00000
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 2.00000 2.00000
\(404\) −2.00000 −2.00000
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 1.00000 1.00000
\(409\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(410\) 0 0
\(411\) 1.00000 1.00000
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 1.00000 1.00000
\(417\) 1.00000 1.00000
\(418\) 0 0
\(419\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(420\) 0 0
\(421\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(422\) −2.00000 −2.00000
\(423\) 0 0
\(424\) −1.00000 −1.00000
\(425\) −1.00000 −1.00000
\(426\) −1.00000 −1.00000
\(427\) 0 0
\(428\) 1.00000 1.00000
\(429\) −1.00000 −1.00000
\(430\) 0 0
\(431\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) 1.00000 1.00000
\(433\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −1.00000 −1.00000
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1.00000 1.00000
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −1.00000 −1.00000
\(455\) 0 0
\(456\) 0 0
\(457\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(458\) −2.00000 −2.00000
\(459\) −1.00000 −1.00000
\(460\) 0 0
\(461\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.00000 −1.00000
\(472\) 0 0
\(473\) 0 0
\(474\) −1.00000 −1.00000
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(488\) 0 0
\(489\) 2.00000 2.00000
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 2.00000 2.00000
\(497\) 0 0
\(498\) 0 0
\(499\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(500\) 0 0
\(501\) 1.00000 1.00000
\(502\) 0 0
\(503\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −2.00000 −2.00000
\(507\) 0 0
\(508\) 0 0
\(509\) −2.00000 −2.00000 −1.00000 \(\pi\)
−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
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 2.00000 2.00000
\(525\) 0 0
\(526\) 0 0
\(527\) −2.00000 −2.00000
\(528\) −1.00000 −1.00000
\(529\) 3.00000 3.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −1.00000 −1.00000
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 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 \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(548\) −1.00000 −1.00000
\(549\) 0 0
\(550\) 1.00000 1.00000
\(551\) 0 0
\(552\) 2.00000 2.00000
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −1.00000 −1.00000
\(557\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 1.00000 1.00000
\(562\) −1.00000 −1.00000
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −1.00000 −1.00000
\(567\) 0 0
\(568\) 1.00000 1.00000
\(569\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) 0 0
\(571\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(572\) 1.00000 1.00000
\(573\) 0 0
\(574\) 0 0
\(575\) −2.00000 −2.00000
\(576\) 0 0
\(577\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(578\) 1.00000 1.00000
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −1.00000 −1.00000
\(584\) 0 0
\(585\) 0 0
\(586\) 1.00000 1.00000
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(594\) 1.00000 1.00000
\(595\) 0 0
\(596\) −1.00000 −1.00000
\(597\) 1.00000 1.00000
\(598\) −2.00000 −2.00000
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) −1.00000 −1.00000
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 2.00000 2.00000
\(607\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) −2.00000 −2.00000
\(622\) −1.00000 −1.00000
\(623\) 0 0
\(624\) −1.00000 −1.00000
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 1.00000 1.00000
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 1.00000 1.00000
\(633\) 2.00000 2.00000
\(634\) 0 0
\(635\) 0 0
\(636\) 1.00000 1.00000
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) −1.00000 −1.00000
\(643\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) −1.00000 −1.00000
\(649\) 0 0
\(650\) 1.00000 1.00000
\(651\) 0 0
\(652\) −2.00000 −2.00000
\(653\) 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
\(661\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 1.00000 1.00000
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −1.00000 −1.00000
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 1.00000 1.00000
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.00000 1.00000
\(682\) 2.00000 2.00000
\(683\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 2.00000 2.00000
\(688\) 0 0
\(689\) −1.00000 −1.00000
\(690\) 0 0
\(691\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(692\) 0 0
\(693\) 0 0
\(694\) −2.00000 −2.00000
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −2.00000 −2.00000
\(699\) 0 0
\(700\) 0 0
\(701\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(702\) 1.00000 1.00000
\(703\) 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
\(712\) 1.00000 1.00000
\(713\) −4.00000 −4.00000
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.00000 1.00000
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(734\) −1.00000 −1.00000
\(735\) 0 0
\(736\) −2.00000 −2.00000
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(744\) −2.00000 −2.00000
\(745\) 0 0
\(746\) −1.00000 −1.00000
\(747\) 0 0
\(748\) −1.00000 −1.00000
\(749\) 0 0
\(750\) 0 0
\(751\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(758\) 1.00000 1.00000
\(759\) 2.00000 2.00000
\(760\) 0 0
\(761\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −1.00000 −1.00000
\(769\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(770\) 0 0
\(771\) −1.00000 −1.00000
\(772\) 0 0
\(773\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(774\) 0 0
\(775\) 2.00000 2.00000
\(776\) 0 0
\(777\) 0 0
\(778\) −1.00000 −1.00000
\(779\) 0 0
\(780\) 0 0
\(781\) 1.00000 1.00000
\(782\) 2.00000 2.00000
\(783\) 0 0
\(784\) 0 0
\(785\) 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
\(796\) −1.00000 −1.00000
\(797\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.00000 1.00000
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 2.00000 2.00000
\(807\) 0 0
\(808\) −2.00000 −2.00000
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 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
\(816\) 1.00000 1.00000
\(817\) 0 0
\(818\) 1.00000 1.00000
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 1.00000 1.00000
\(823\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(824\) 0 0
\(825\) −1.00000 −1.00000
\(826\) 0 0
\(827\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(828\) 0 0
\(829\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 1.00000 1.00000
\(833\) 0 0
\(834\) 1.00000 1.00000
\(835\) 0 0
\(836\) 0 0
\(837\) 2.00000 2.00000
\(838\) −1.00000 −1.00000
\(839\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 2.00000 2.00000
\(843\) 1.00000 1.00000
\(844\) −2.00000 −2.00000
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) −1.00000 −1.00000
\(849\) 1.00000 1.00000
\(850\) −1.00000 −1.00000
\(851\) 0 0
\(852\) −1.00000 −1.00000
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 1.00000 1.00000
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) −1.00000 −1.00000
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 1.00000 1.00000
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 1.00000 1.00000
\(865\) 0 0
\(866\) −2.00000 −2.00000
\(867\) −1.00000 −1.00000
\(868\) 0 0
\(869\) 1.00000 1.00000
\(870\) 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 \(\pi\)
\(878\) −1.00000 −1.00000
\(879\) −1.00000 −1.00000
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) −1.00000 −1.00000
\(885\) 0 0
\(886\) 0 0
\(887\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1.00000 −1.00000
\(892\) 0 0
\(893\) 0 0
\(894\) 1.00000 1.00000
\(895\) 0 0
\(896\) 0 0
\(897\) 2.00000 2.00000
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 1.00000 1.00000
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(908\) −1.00000 −1.00000
\(909\) 0 0
\(910\) 0 0
\(911\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 2.00000 2.00000
\(915\) 0 0
\(916\) −2.00000 −2.00000
\(917\) 0 0
\(918\) −1.00000 −1.00000
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 1.00000 1.00000
\(923\) 1.00000 1.00000
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 1.00000 1.00000
\(934\) 0 0
\(935\) 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 \(\pi\)
\(942\) −1.00000 −1.00000
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(948\) −1.00000 −1.00000
\(949\) 0 0
\(950\) 0 0
\(951\) 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
\(958\) 2.00000 2.00000
\(959\) 0 0
\(960\) 0 0
\(961\) 3.00000 3.00000
\(962\) 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 \(\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 1.00000 1.00000
\(975\) −1.00000 −1.00000
\(976\) 0 0
\(977\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(978\) 2.00000 2.00000
\(979\) 1.00000 1.00000
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(992\) 2.00000 2.00000
\(993\) 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 3332.1.g.c.883.1 1
4.3 odd 2 3332.1.g.d.883.1 1
7.2 even 3 3332.1.o.b.67.1 2
7.3 odd 6 476.1.o.a.135.1 yes 2
7.4 even 3 3332.1.o.b.2039.1 2
7.5 odd 6 476.1.o.a.67.1 2
7.6 odd 2 3332.1.g.e.883.1 1
17.16 even 2 3332.1.g.d.883.1 1
28.3 even 6 476.1.o.b.135.1 yes 2
28.11 odd 6 3332.1.o.a.2039.1 2
28.19 even 6 476.1.o.b.67.1 yes 2
28.23 odd 6 3332.1.o.a.67.1 2
28.27 even 2 3332.1.g.b.883.1 1
68.67 odd 2 CM 3332.1.g.c.883.1 1
119.16 even 6 3332.1.o.a.67.1 2
119.33 odd 6 476.1.o.b.67.1 yes 2
119.67 even 6 3332.1.o.a.2039.1 2
119.101 odd 6 476.1.o.b.135.1 yes 2
119.118 odd 2 3332.1.g.b.883.1 1
476.67 odd 6 3332.1.o.b.2039.1 2
476.135 odd 6 3332.1.o.b.67.1 2
476.271 even 6 476.1.o.a.67.1 2
476.339 even 6 476.1.o.a.135.1 yes 2
476.475 even 2 3332.1.g.e.883.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
476.1.o.a.67.1 2 7.5 odd 6
476.1.o.a.67.1 2 476.271 even 6
476.1.o.a.135.1 yes 2 7.3 odd 6
476.1.o.a.135.1 yes 2 476.339 even 6
476.1.o.b.67.1 yes 2 28.19 even 6
476.1.o.b.67.1 yes 2 119.33 odd 6
476.1.o.b.135.1 yes 2 28.3 even 6
476.1.o.b.135.1 yes 2 119.101 odd 6
3332.1.g.b.883.1 1 28.27 even 2
3332.1.g.b.883.1 1 119.118 odd 2
3332.1.g.c.883.1 1 1.1 even 1 trivial
3332.1.g.c.883.1 1 68.67 odd 2 CM
3332.1.g.d.883.1 1 4.3 odd 2
3332.1.g.d.883.1 1 17.16 even 2
3332.1.g.e.883.1 1 7.6 odd 2
3332.1.g.e.883.1 1 476.475 even 2
3332.1.o.a.67.1 2 28.23 odd 6
3332.1.o.a.67.1 2 119.16 even 6
3332.1.o.a.2039.1 2 28.11 odd 6
3332.1.o.a.2039.1 2 119.67 even 6
3332.1.o.b.67.1 2 7.2 even 3
3332.1.o.b.67.1 2 476.135 odd 6
3332.1.o.b.2039.1 2 7.4 even 3
3332.1.o.b.2039.1 2 476.67 odd 6