Properties

Label 1859.1.c.a.846.3
Level $1859$
Weight $1$
Character 1859.846
Self dual yes
Analytic conductor $0.928$
Analytic rank $0$
Dimension $3$
Projective image $D_{7}$
CM discriminant -11
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1859.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.927761858485\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
Defining polynomial: \( x^{3} - x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{7}\)
Projective field: Galois closure of 7.1.6424482779.1
Artin image: $D_7$
Artin field: Galois closure of 7.1.6424482779.1

Embedding invariants

Embedding label 846.3
Root \(0.445042\) of defining polynomial
Character \(\chi\) \(=\) 1859.846

$q$-expansion

\(f(q)\) \(=\) \(q+1.24698 q^{3} +1.00000 q^{4} -0.445042 q^{5} +0.554958 q^{9} +O(q^{10})\) \(q+1.24698 q^{3} +1.00000 q^{4} -0.445042 q^{5} +0.554958 q^{9} +1.00000 q^{11} +1.24698 q^{12} -0.554958 q^{15} +1.00000 q^{16} -0.445042 q^{20} -1.80194 q^{23} -0.801938 q^{25} -0.554958 q^{27} -1.80194 q^{31} +1.24698 q^{33} +0.554958 q^{36} +1.24698 q^{37} +1.00000 q^{44} -0.246980 q^{45} -1.80194 q^{47} +1.24698 q^{48} +1.00000 q^{49} -0.445042 q^{53} -0.445042 q^{55} +1.24698 q^{59} -0.554958 q^{60} +1.00000 q^{64} +2.00000 q^{67} -2.24698 q^{69} +1.24698 q^{71} -1.00000 q^{75} -0.445042 q^{80} -1.24698 q^{81} -1.80194 q^{89} -1.80194 q^{92} -2.24698 q^{93} -0.445042 q^{97} +0.554958 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{3} + 3 q^{4} - q^{5} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - q^{3} + 3 q^{4} - q^{5} + 2 q^{9} + 3 q^{11} - q^{12} - 2 q^{15} + 3 q^{16} - q^{20} - q^{23} + 2 q^{25} - 2 q^{27} - q^{31} - q^{33} + 2 q^{36} - q^{37} + 3 q^{44} + 4 q^{45} - q^{47} - q^{48} + 3 q^{49} - q^{53} - q^{55} - q^{59} - 2 q^{60} + 3 q^{64} + 6 q^{67} - 2 q^{69} - q^{71} - 3 q^{75} - q^{80} + q^{81} - q^{89} - q^{92} - 2 q^{93} - q^{97} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1859\mathbb{Z}\right)^\times\).

\(n\) \(508\) \(1354\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(4\) 1.00000 1.00000
\(5\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 0 0
\(9\) 0.554958 0.554958
\(10\) 0 0
\(11\) 1.00000 1.00000
\(12\) 1.24698 1.24698
\(13\) 0 0
\(14\) 0 0
\(15\) −0.554958 −0.554958
\(16\) 1.00000 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −0.445042 −0.445042
\(21\) 0 0
\(22\) 0 0
\(23\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(24\) 0 0
\(25\) −0.801938 −0.801938
\(26\) 0 0
\(27\) −0.554958 −0.554958
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(32\) 0 0
\(33\) 1.24698 1.24698
\(34\) 0 0
\(35\) 0 0
\(36\) 0.554958 0.554958
\(37\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(38\) 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 \(\pi\)
\(44\) 1.00000 1.00000
\(45\) −0.246980 −0.246980
\(46\) 0 0
\(47\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(48\) 1.24698 1.24698
\(49\) 1.00000 1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(54\) 0 0
\(55\) −0.445042 −0.445042
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(60\) −0.554958 −0.554958
\(61\) 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
\(67\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(68\) 0 0
\(69\) −2.24698 −2.24698
\(70\) 0 0
\(71\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(72\) 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
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −0.445042 −0.445042
\(81\) −1.24698 −1.24698
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1.80194 −1.80194
\(93\) −2.24698 −2.24698
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(98\) 0 0
\(99\) 0.554958 0.554958
\(100\) −0.801938 −0.801938
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −0.554958 −0.554958
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 1.55496 1.55496
\(112\) 0 0
\(113\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(114\) 0 0
\(115\) 0.801938 0.801938
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) −1.80194 −1.80194
\(125\) 0.801938 0.801938
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 1.24698 1.24698
\(133\) 0 0
\(134\) 0 0
\(135\) 0.246980 0.246980
\(136\) 0 0
\(137\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) −2.24698 −2.24698
\(142\) 0 0
\(143\) 0 0
\(144\) 0.554958 0.554958
\(145\) 0 0
\(146\) 0 0
\(147\) 1.24698 1.24698
\(148\) 1.24698 1.24698
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.801938 0.801938
\(156\) 0 0
\(157\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(158\) 0 0
\(159\) −0.554958 −0.554958
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(164\) 0 0
\(165\) −0.554958 −0.554958
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 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
\(177\) 1.55496 1.55496
\(178\) 0 0
\(179\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(180\) −0.246980 −0.246980
\(181\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.554958 −0.554958
\(186\) 0 0
\(187\) 0 0
\(188\) −1.80194 −1.80194
\(189\) 0 0
\(190\) 0 0
\(191\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(192\) 1.24698 1.24698
\(193\) 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
\(199\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(200\) 0 0
\(201\) 2.49396 2.49396
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.00000 −1.00000
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) −0.445042 −0.445042
\(213\) 1.55496 1.55496
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −0.445042 −0.445042
\(221\) 0 0
\(222\) 0 0
\(223\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(224\) 0 0
\(225\) −0.445042 −0.445042
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0.801938 0.801938
\(236\) 1.24698 1.24698
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) −0.554958 −0.554958
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) −1.00000 −1.00000
\(244\) 0 0
\(245\) −0.445042 −0.445042
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(252\) 0 0
\(253\) −1.80194 −1.80194
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0.198062 0.198062
\(266\) 0 0
\(267\) −2.24698 −2.24698
\(268\) 2.00000 2.00000
\(269\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.801938 −0.801938
\(276\) −2.24698 −2.24698
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) −1.00000 −1.00000
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 1.24698 1.24698
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) −0.554958 −0.554958
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) −0.554958 −0.554958
\(296\) 0 0
\(297\) −0.554958 −0.554958
\(298\) 0 0
\(299\) 0 0
\(300\) −1.00000 −1.00000
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) −0.554958 −0.554958
\(310\) 0 0
\(311\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(312\) 0 0
\(313\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.445042 −0.445042
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −1.24698 −1.24698
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(332\) 0 0
\(333\) 0.692021 0.692021
\(334\) 0 0
\(335\) −0.890084 −0.890084
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) −0.554958 −0.554958
\(340\) 0 0
\(341\) −1.80194 −1.80194
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 1.00000 1.00000
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(354\) 0 0
\(355\) −0.554958 −0.554958
\(356\) −1.80194 −1.80194
\(357\) 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
\(363\) 1.24698 1.24698
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(368\) −1.80194 −1.80194
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −2.24698 −2.24698
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 1.00000 1.00000
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −0.445042 −0.445042
\(389\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0.554958 0.554958
\(397\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.801938 −0.801938
\(401\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0.554958 0.554958
\(406\) 0 0
\(407\) 1.24698 1.24698
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) −2.24698 −2.24698
\(412\) −0.445042 −0.445042
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(420\) 0 0
\(421\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(422\) 0 0
\(423\) −1.00000 −1.00000
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −0.554958 −0.554958
\(433\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(434\) 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
\(441\) 0.554958 0.554958
\(442\) 0 0
\(443\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(444\) 1.55496 1.55496
\(445\) 0.801938 0.801938
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(450\) 0 0
\(451\) 0 0
\(452\) −0.445042 −0.445042
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0.801938 0.801938
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(464\) 0 0
\(465\) 1.00000 1.00000
\(466\) 0 0
\(467\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 1.55496 1.55496
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.246980 −0.246980
\(478\) 0 0
\(479\) 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
\(485\) 0.198062 0.198062
\(486\) 0 0
\(487\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(488\) 0 0
\(489\) −2.24698 −2.24698
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −0.246980 −0.246980
\(496\) −1.80194 −1.80194
\(497\) 0 0
\(498\) 0 0
\(499\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(500\) 0.801938 0.801938
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.198062 0.198062
\(516\) 0 0
\(517\) −1.80194 −1.80194
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 1.24698 1.24698
\(529\) 2.24698 2.24698
\(530\) 0 0
\(531\) 0.692021 0.692021
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1.55496 1.55496
\(538\) 0 0
\(539\) 1.00000 1.00000
\(540\) 0.246980 0.246980
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −2.24698 −2.24698
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) −1.80194 −1.80194
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −0.692021 −0.692021
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) −2.24698 −2.24698
\(565\) 0.198062 0.198062
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) −2.24698 −2.24698
\(574\) 0 0
\(575\) 1.44504 1.44504
\(576\) 0.554958 0.554958
\(577\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −0.445042 −0.445042
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(588\) 1.24698 1.24698
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1.24698 1.24698
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.55496 1.55496
\(598\) 0 0
\(599\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 1.10992 1.10992
\(604\) 0 0
\(605\) −0.445042 −0.445042
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(618\) 0 0
\(619\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(620\) 0.801938 0.801938
\(621\) 1.00000 1.00000
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.445042 0.445042
\(626\) 0 0
\(627\) 0 0
\(628\) 1.24698 1.24698
\(629\) 0 0
\(630\) 0 0
\(631\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −0.554958 −0.554958
\(637\) 0 0
\(638\) 0 0
\(639\) 0.692021 0.692021
\(640\) 0 0
\(641\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(642\) 0 0
\(643\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(648\) 0 0
\(649\) 1.24698 1.24698
\(650\) 0 0
\(651\) 0 0
\(652\) −1.80194 −1.80194
\(653\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) −0.554958 −0.554958
\(661\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −0.554958 −0.554958
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0.445042 0.445042
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(684\) 0 0
\(685\) 0.801938 0.801938
\(686\) 0 0
\(687\) 1.55496 1.55496
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.00000 1.00000
\(705\) 1.00000 1.00000
\(706\) 0 0
\(707\) 0 0
\(708\) 1.55496 1.55496
\(709\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.24698 3.24698
\(714\) 0 0
\(715\) 0 0
\(716\) 1.24698 1.24698
\(717\) 0 0
\(718\) 0 0
\(719\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(720\) −0.246980 −0.246980
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) −1.80194 −1.80194
\(725\) 0 0
\(726\) 0 0
\(727\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) −0.554958 −0.554958
\(736\) 0 0
\(737\) 2.00000 2.00000
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) −0.554958 −0.554958
\(741\) 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
\(751\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(752\) −1.80194 −1.80194
\(753\) −0.554958 −0.554958
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(758\) 0 0
\(759\) −2.24698 −2.24698
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1.80194 −1.80194
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.24698 1.24698
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 1.55496 1.55496
\(772\) 0 0
\(773\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(774\) 0 0
\(775\) 1.44504 1.44504
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 1.24698 1.24698
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 1.00000
\(785\) −0.554958 −0.554958
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0.246980 0.246980
\(796\) 1.24698 1.24698
\(797\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −1.00000 −1.00000
\(802\) 0 0
\(803\) 0 0
\(804\) 2.49396 2.49396
\(805\) 0 0
\(806\) 0 0
\(807\) 1.55496 1.55496
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0.801938 0.801938
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(824\) 0 0
\(825\) −1.00000 −1.00000
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) −1.00000 −1.00000
\(829\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1.00000 1.00000
\(838\) 0 0
\(839\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) −0.445042 −0.445042
\(849\) 0 0
\(850\) 0 0
\(851\) −2.24698 −2.24698
\(852\) 1.55496 1.55496
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 1.24698 1.24698
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −0.246980 −0.246980
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) −0.445042 −0.445042
\(881\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(882\) 0 0
\(883\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(884\) 0 0
\(885\) −0.692021 −0.692021
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1.24698 −1.24698
\(892\) −0.445042 −0.445042
\(893\) 0 0
\(894\) 0 0
\(895\) −0.554958 −0.554958
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −0.445042 −0.445042
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0.801938 0.801938
\(906\) 0 0
\(907\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 1.24698 1.24698
\(917\) 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
\(925\) −1.00000 −1.00000
\(926\) 0 0
\(927\) −0.246980 −0.246980
\(928\) 0 0
\(929\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −2.24698 −2.24698
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) −0.554958 −0.554958
\(940\) 0.801938 0.801938
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 1.24698 1.24698
\(945\) 0 0
\(946\) 0 0
\(947\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 1.55496 1.55496
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0.801938 0.801938
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −0.554958 −0.554958
\(961\) 2.24698 2.24698
\(962\) 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
\(971\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(972\) −1.00000 −1.00000
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(978\) 0 0
\(979\) −1.80194 −1.80194
\(980\) −0.445042 −0.445042
\(981\) 0 0
\(982\) 0 0
\(983\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(992\) 0 0
\(993\) −0.554958 −0.554958
\(994\) 0 0
\(995\) −0.554958 −0.554958
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0 0
\(999\) −0.692021 −0.692021
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 1859.1.c.a.846.3 3
11.10 odd 2 CM 1859.1.c.a.846.3 3
13.2 odd 12 1859.1.i.c.1330.2 12
13.3 even 3 1859.1.k.a.1374.1 6
13.4 even 6 1859.1.k.b.1836.1 6
13.5 odd 4 1859.1.d.a.1858.6 6
13.6 odd 12 1859.1.i.c.868.2 12
13.7 odd 12 1859.1.i.c.868.1 12
13.8 odd 4 1859.1.d.a.1858.5 6
13.9 even 3 1859.1.k.a.1836.1 6
13.10 even 6 1859.1.k.b.1374.1 6
13.11 odd 12 1859.1.i.c.1330.1 12
13.12 even 2 1859.1.c.b.846.3 yes 3
143.10 odd 6 1859.1.k.b.1374.1 6
143.21 even 4 1859.1.d.a.1858.5 6
143.32 even 12 1859.1.i.c.868.2 12
143.43 odd 6 1859.1.k.b.1836.1 6
143.54 even 12 1859.1.i.c.1330.2 12
143.76 even 12 1859.1.i.c.1330.1 12
143.87 odd 6 1859.1.k.a.1836.1 6
143.98 even 12 1859.1.i.c.868.1 12
143.109 even 4 1859.1.d.a.1858.6 6
143.120 odd 6 1859.1.k.a.1374.1 6
143.142 odd 2 1859.1.c.b.846.3 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.1.c.a.846.3 3 1.1 even 1 trivial
1859.1.c.a.846.3 3 11.10 odd 2 CM
1859.1.c.b.846.3 yes 3 13.12 even 2
1859.1.c.b.846.3 yes 3 143.142 odd 2
1859.1.d.a.1858.5 6 13.8 odd 4
1859.1.d.a.1858.5 6 143.21 even 4
1859.1.d.a.1858.6 6 13.5 odd 4
1859.1.d.a.1858.6 6 143.109 even 4
1859.1.i.c.868.1 12 13.7 odd 12
1859.1.i.c.868.1 12 143.98 even 12
1859.1.i.c.868.2 12 13.6 odd 12
1859.1.i.c.868.2 12 143.32 even 12
1859.1.i.c.1330.1 12 13.11 odd 12
1859.1.i.c.1330.1 12 143.76 even 12
1859.1.i.c.1330.2 12 13.2 odd 12
1859.1.i.c.1330.2 12 143.54 even 12
1859.1.k.a.1374.1 6 13.3 even 3
1859.1.k.a.1374.1 6 143.120 odd 6
1859.1.k.a.1836.1 6 13.9 even 3
1859.1.k.a.1836.1 6 143.87 odd 6
1859.1.k.b.1374.1 6 13.10 even 6
1859.1.k.b.1374.1 6 143.10 odd 6
1859.1.k.b.1836.1 6 13.4 even 6
1859.1.k.b.1836.1 6 143.43 odd 6