Properties

Label 143.1.d.a.142.2
Level $143$
Weight $1$
Character 143.142
Self dual yes
Analytic conductor $0.071$
Analytic rank $0$
Dimension $2$
Projective image $D_{5}$
CM discriminant -143
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 143.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.0713662968065\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \(x^{2} - x - 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{5}\)
Projective field: Galois closure of 5.1.20449.1
Artin image: $D_5$
Artin field: Galois closure of 5.1.20449.1

Embedding invariants

Embedding label 142.2
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 143.142

$q$-expansion

\(f(q)\) \(=\) \(q+0.618034 q^{2} +0.618034 q^{3} -0.618034 q^{4} +0.381966 q^{6} -1.61803 q^{7} -1.00000 q^{8} -0.618034 q^{9} +O(q^{10})\) \(q+0.618034 q^{2} +0.618034 q^{3} -0.618034 q^{4} +0.381966 q^{6} -1.61803 q^{7} -1.00000 q^{8} -0.618034 q^{9} +1.00000 q^{11} -0.381966 q^{12} +1.00000 q^{13} -1.00000 q^{14} -0.381966 q^{18} +0.618034 q^{19} -1.00000 q^{21} +0.618034 q^{22} -1.61803 q^{23} -0.618034 q^{24} +1.00000 q^{25} +0.618034 q^{26} -1.00000 q^{27} +1.00000 q^{28} +1.00000 q^{32} +0.618034 q^{33} +0.381966 q^{36} +0.381966 q^{38} +0.618034 q^{39} -1.61803 q^{41} -0.618034 q^{42} -0.618034 q^{44} -1.00000 q^{46} +1.61803 q^{49} +0.618034 q^{50} -0.618034 q^{52} +0.618034 q^{53} -0.618034 q^{54} +1.61803 q^{56} +0.381966 q^{57} +1.00000 q^{63} +0.618034 q^{64} +0.381966 q^{66} -1.00000 q^{69} +0.618034 q^{72} +0.618034 q^{73} +0.618034 q^{75} -0.381966 q^{76} -1.61803 q^{77} +0.381966 q^{78} -1.00000 q^{82} -1.61803 q^{83} +0.618034 q^{84} -1.00000 q^{88} -1.61803 q^{91} +1.00000 q^{92} +0.618034 q^{96} +1.00000 q^{98} -0.618034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{3} + q^{4} + 3q^{6} - q^{7} - 2q^{8} + q^{9} + O(q^{10}) \) \( 2q - q^{2} - q^{3} + q^{4} + 3q^{6} - q^{7} - 2q^{8} + q^{9} + 2q^{11} - 3q^{12} + 2q^{13} - 2q^{14} - 3q^{18} - q^{19} - 2q^{21} - q^{22} - q^{23} + q^{24} + 2q^{25} - q^{26} - 2q^{27} + 2q^{28} + 2q^{32} - q^{33} + 3q^{36} + 3q^{38} - q^{39} - q^{41} + q^{42} + q^{44} - 2q^{46} + q^{49} - q^{50} + q^{52} - q^{53} + q^{54} + q^{56} + 3q^{57} + 2q^{63} - q^{64} + 3q^{66} - 2q^{69} - q^{72} - q^{73} - q^{75} - 3q^{76} - q^{77} + 3q^{78} - 2q^{82} - q^{83} - q^{84} - 2q^{88} - q^{91} + 2q^{92} - q^{96} + 2q^{98} + q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(3\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(4\) −0.618034 −0.618034
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0.381966 0.381966
\(7\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(8\) −1.00000 −1.00000
\(9\) −0.618034 −0.618034
\(10\) 0 0
\(11\) 1.00000 1.00000
\(12\) −0.381966 −0.381966
\(13\) 1.00000 1.00000
\(14\) −1.00000 −1.00000
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) −0.381966 −0.381966
\(19\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(20\) 0 0
\(21\) −1.00000 −1.00000
\(22\) 0.618034 0.618034
\(23\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(24\) −0.618034 −0.618034
\(25\) 1.00000 1.00000
\(26\) 0.618034 0.618034
\(27\) −1.00000 −1.00000
\(28\) 1.00000 1.00000
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 1.00000 1.00000
\(33\) 0.618034 0.618034
\(34\) 0 0
\(35\) 0 0
\(36\) 0.381966 0.381966
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0.381966 0.381966
\(39\) 0.618034 0.618034
\(40\) 0 0
\(41\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(42\) −0.618034 −0.618034
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −0.618034 −0.618034
\(45\) 0 0
\(46\) −1.00000 −1.00000
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) 1.61803 1.61803
\(50\) 0.618034 0.618034
\(51\) 0 0
\(52\) −0.618034 −0.618034
\(53\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(54\) −0.618034 −0.618034
\(55\) 0 0
\(56\) 1.61803 1.61803
\(57\) 0.381966 0.381966
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 1.00000 1.00000
\(64\) 0.618034 0.618034
\(65\) 0 0
\(66\) 0.381966 0.381966
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) −1.00000 −1.00000
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0.618034 0.618034
\(73\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(74\) 0 0
\(75\) 0.618034 0.618034
\(76\) −0.381966 −0.381966
\(77\) −1.61803 −1.61803
\(78\) 0.381966 0.381966
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −1.00000 −1.00000
\(83\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(84\) 0.618034 0.618034
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −1.00000 −1.00000
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −1.61803 −1.61803
\(92\) 1.00000 1.00000
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.618034 0.618034
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 1.00000 1.00000
\(99\) −0.618034 −0.618034
\(100\) −0.618034 −0.618034
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(104\) −1.00000 −1.00000
\(105\) 0 0
\(106\) 0.381966 0.381966
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0.618034 0.618034
\(109\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(114\) 0.236068 0.236068
\(115\) 0 0
\(116\) 0 0
\(117\) −0.618034 −0.618034
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) −1.00000 −1.00000
\(124\) 0 0
\(125\) 0 0
\(126\) 0.618034 0.618034
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −0.618034 −0.618034
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) −0.381966 −0.381966
\(133\) −1.00000 −1.00000
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) −0.618034 −0.618034
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.00000 1.00000
\(144\) 0 0
\(145\) 0 0
\(146\) 0.381966 0.381966
\(147\) 1.00000 1.00000
\(148\) 0 0
\(149\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(150\) 0.381966 0.381966
\(151\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(152\) −0.618034 −0.618034
\(153\) 0 0
\(154\) −1.00000 −1.00000
\(155\) 0 0
\(156\) −0.381966 −0.381966
\(157\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(158\) 0 0
\(159\) 0.381966 0.381966
\(160\) 0 0
\(161\) 2.61803 2.61803
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 1.00000 1.00000
\(165\) 0 0
\(166\) −1.00000 −1.00000
\(167\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(168\) 1.00000 1.00000
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) −0.381966 −0.381966
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) −1.61803 −1.61803
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(180\) 0 0
\(181\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(182\) −1.00000 −1.00000
\(183\) 0 0
\(184\) 1.61803 1.61803
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 1.61803 1.61803
\(190\) 0 0
\(191\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(192\) 0.381966 0.381966
\(193\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −1.00000 −1.00000
\(197\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(198\) −0.381966 −0.381966
\(199\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(200\) −1.00000 −1.00000
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −1.00000 −1.00000
\(207\) 1.00000 1.00000
\(208\) 0 0
\(209\) 0.618034 0.618034
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) −0.381966 −0.381966
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 1.00000 1.00000
\(217\) 0 0
\(218\) 0.381966 0.381966
\(219\) 0.381966 0.381966
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) −1.61803 −1.61803
\(225\) −0.618034 −0.618034
\(226\) 0.381966 0.381966
\(227\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(228\) −0.236068 −0.236068
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) −1.00000 −1.00000
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) −0.381966 −0.381966
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(240\) 0 0
\(241\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(242\) 0.618034 0.618034
\(243\) 1.00000 1.00000
\(244\) 0 0
\(245\) 0 0
\(246\) −0.618034 −0.618034
\(247\) 0.618034 0.618034
\(248\) 0 0
\(249\) −1.00000 −1.00000
\(250\) 0 0
\(251\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(252\) −0.618034 −0.618034
\(253\) −1.61803 −1.61803
\(254\) 0 0
\(255\) 0 0
\(256\) −1.00000 −1.00000
\(257\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) −0.618034 −0.618034
\(265\) 0 0
\(266\) −0.618034 −0.618034
\(267\) 0 0
\(268\) 0 0
\(269\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(270\) 0 0
\(271\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(272\) 0 0
\(273\) −1.00000 −1.00000
\(274\) 0 0
\(275\) 1.00000 1.00000
\(276\) 0.618034 0.618034
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0.618034 0.618034
\(287\) 2.61803 2.61803
\(288\) −0.618034 −0.618034
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) −0.381966 −0.381966
\(293\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(294\) 0.618034 0.618034
\(295\) 0 0
\(296\) 0 0
\(297\) −1.00000 −1.00000
\(298\) −1.00000 −1.00000
\(299\) −1.61803 −1.61803
\(300\) −0.381966 −0.381966
\(301\) 0 0
\(302\) 1.23607 1.23607
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(308\) 1.00000 1.00000
\(309\) −1.00000 −1.00000
\(310\) 0 0
\(311\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(312\) −0.618034 −0.618034
\(313\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(314\) −1.00000 −1.00000
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0.236068 0.236068
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 1.61803 1.61803
\(323\) 0 0
\(324\) 0 0
\(325\) 1.00000 1.00000
\(326\) 0 0
\(327\) 0.381966 0.381966
\(328\) 1.61803 1.61803
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 1.00000 1.00000
\(333\) 0 0
\(334\) 0.381966 0.381966
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0.618034 0.618034
\(339\) 0.381966 0.381966
\(340\) 0 0
\(341\) 0 0
\(342\) −0.236068 −0.236068
\(343\) −1.00000 −1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(350\) −1.00000 −1.00000
\(351\) −1.00000 −1.00000
\(352\) 1.00000 1.00000
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 1.23607 1.23607
\(359\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(360\) 0 0
\(361\) −0.618034 −0.618034
\(362\) 0.381966 0.381966
\(363\) 0.618034 0.618034
\(364\) 1.00000 1.00000
\(365\) 0 0
\(366\) 0 0
\(367\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(368\) 0 0
\(369\) 1.00000 1.00000
\(370\) 0 0
\(371\) −1.00000 −1.00000
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 1.00000 1.00000
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0.381966 0.381966
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) −0.381966 −0.381966
\(385\) 0 0
\(386\) −1.00000 −1.00000
\(387\) 0 0
\(388\) 0 0
\(389\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.61803 −1.61803
\(393\) 0 0
\(394\) 0.381966 0.381966
\(395\) 0 0
\(396\) 0.381966 0.381966
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0.381966 0.381966
\(399\) −0.618034 −0.618034
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.00000 1.00000
\(413\) 0 0
\(414\) 0.618034 0.618034
\(415\) 0 0
\(416\) 1.00000 1.00000
\(417\) 0 0
\(418\) 0.381966 0.381966
\(419\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −0.618034 −0.618034
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0.618034 0.618034
\(430\) 0 0
\(431\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(432\) 0 0
\(433\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.381966 −0.381966
\(437\) −1.00000 −1.00000
\(438\) 0.236068 0.236068
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −1.00000 −1.00000
\(442\) 0 0
\(443\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −1.00000 −1.00000
\(448\) −1.00000 −1.00000
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) −0.381966 −0.381966
\(451\) −1.61803 −1.61803
\(452\) −0.381966 −0.381966
\(453\) 1.23607 1.23607
\(454\) 0.381966 0.381966
\(455\) 0 0
\(456\) −0.381966 −0.381966
\(457\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(462\) −0.618034 −0.618034
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(468\) 0.381966 0.381966
\(469\) 0 0
\(470\) 0 0
\(471\) −1.00000 −1.00000
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.618034 0.618034
\(476\) 0 0
\(477\) −0.381966 −0.381966
\(478\) 0.381966 0.381966
\(479\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.00000 −1.00000
\(483\) 1.61803 1.61803
\(484\) −0.618034 −0.618034
\(485\) 0 0
\(486\) 0.618034 0.618034
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0.618034 0.618034
\(493\) 0 0
\(494\) 0.381966 0.381966
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.618034 −0.618034
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0.381966 0.381966
\(502\) −1.00000 −1.00000
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) −1.00000 −1.00000
\(505\) 0 0
\(506\) −1.00000 −1.00000
\(507\) 0.618034 0.618034
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) −1.00000 −1.00000
\(512\) 0 0
\(513\) −0.618034 −0.618034
\(514\) −1.00000 −1.00000
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) −1.00000 −1.00000
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.61803 1.61803
\(530\) 0 0
\(531\) 0 0
\(532\) 0.618034 0.618034
\(533\) −1.61803 −1.61803
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1.23607 1.23607
\(538\) −1.00000 −1.00000
\(539\) 1.61803 1.61803
\(540\) 0 0
\(541\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(542\) 0.381966 0.381966
\(543\) 0.381966 0.381966
\(544\) 0 0
\(545\) 0 0
\(546\) −0.618034 −0.618034
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0.618034 0.618034
\(551\) 0 0
\(552\) 1.00000 1.00000
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0.381966 0.381966
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 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 \(\pi\)
\(572\) −0.618034 −0.618034
\(573\) 0.381966 0.381966
\(574\) 1.61803 1.61803
\(575\) −1.61803 −1.61803
\(576\) −0.381966 −0.381966
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0.618034 0.618034
\(579\) −1.00000 −1.00000
\(580\) 0 0
\(581\) 2.61803 2.61803
\(582\) 0 0
\(583\) 0.618034 0.618034
\(584\) −0.618034 −0.618034
\(585\) 0 0
\(586\) 1.23607 1.23607
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) −0.618034 −0.618034
\(589\) 0 0
\(590\) 0 0
\(591\) 0.381966 0.381966
\(592\) 0 0
\(593\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(594\) −0.618034 −0.618034
\(595\) 0 0
\(596\) 1.00000 1.00000
\(597\) 0.381966 0.381966
\(598\) −1.00000 −1.00000
\(599\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(600\) −0.618034 −0.618034
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1.23607 −1.23607
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0.618034 0.618034
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(614\) 1.23607 1.23607
\(615\) 0 0
\(616\) 1.61803 1.61803
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) −0.618034 −0.618034
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 1.61803 1.61803
\(622\) 0.381966 0.381966
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) −1.00000 −1.00000
\(627\) 0.381966 0.381966
\(628\) 1.00000 1.00000
\(629\) 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
\(636\) −0.236068 −0.236068
\(637\) 1.61803 1.61803
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) −1.61803 −1.61803
\(645\) 0 0
\(646\) 0 0
\(647\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0.618034 0.618034
\(651\) 0 0
\(652\) 0 0
\(653\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(654\) 0.236068 0.236068
\(655\) 0 0
\(656\) 0 0
\(657\) −0.381966 −0.381966
\(658\) 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
\(664\) 1.61803 1.61803
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −0.381966 −0.381966
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −1.00000 −1.00000
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) −1.00000 −1.00000
\(676\) −0.618034 −0.618034
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0.236068 0.236068
\(679\) 0 0
\(680\) 0 0
\(681\) 0.381966 0.381966
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0.236068 0.236068
\(685\) 0 0
\(686\) −0.618034 −0.618034
\(687\) 0 0
\(688\) 0 0
\(689\) 0.618034 0.618034
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 1.00000 1.00000
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −1.00000 −1.00000
\(699\) 0 0
\(700\) 1.00000 1.00000
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) −0.618034 −0.618034
\(703\) 0 0
\(704\) 0.618034 0.618034
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 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
\(716\) −1.23607 −1.23607
\(717\) 0.381966 0.381966
\(718\) −1.00000 −1.00000
\(719\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(720\) 0 0
\(721\) 2.61803 2.61803
\(722\) −0.381966 −0.381966
\(723\) −1.00000 −1.00000
\(724\) −0.381966 −0.381966
\(725\) 0 0
\(726\) 0.381966 0.381966
\(727\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(728\) 1.61803 1.61803
\(729\) 0.618034 0.618034
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(734\) 0.381966 0.381966
\(735\) 0 0
\(736\) −1.61803 −1.61803
\(737\) 0 0
\(738\) 0.618034 0.618034
\(739\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(740\) 0 0
\(741\) 0.381966 0.381966
\(742\) −0.618034 −0.618034
\(743\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.00000 1.00000
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(752\) 0 0
\(753\) −1.00000 −1.00000
\(754\) 0 0
\(755\) 0 0
\(756\) −1.00000 −1.00000
\(757\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(758\) 0 0
\(759\) −1.00000 −1.00000
\(760\) 0 0
\(761\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(762\) 0 0
\(763\) −1.00000 −1.00000
\(764\) −0.381966 −0.381966
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.618034 −0.618034
\(769\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(770\) 0 0
\(771\) −1.00000 −1.00000
\(772\) 1.00000 1.00000
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.381966 0.381966
\(779\) −1.00000 −1.00000
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(788\) −0.381966 −0.381966
\(789\) 0 0
\(790\) 0 0
\(791\) −1.00000 −1.00000
\(792\) 0.618034 0.618034
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −0.381966 −0.381966
\(797\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(798\) −0.381966 −0.381966
\(799\) 0 0
\(800\) 1.00000 1.00000
\(801\) 0 0
\(802\) 0 0
\(803\) 0.618034 0.618034
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −1.00000 −1.00000
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(812\) 0 0
\(813\) 0.381966 0.381966
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 1.23607 1.23607
\(819\) 1.00000 1.00000
\(820\) 0 0
\(821\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(822\) 0 0
\(823\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(824\) 1.61803 1.61803
\(825\) 0.618034 0.618034
\(826\) 0 0
\(827\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(828\) −0.618034 −0.618034
\(829\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0.618034 0.618034
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) −0.381966 −0.381966
\(837\) 0 0
\(838\) −1.00000 −1.00000
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0.381966 0.381966
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −1.61803 −1.61803
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0.381966 0.381966
\(859\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(860\) 0 0
\(861\) 1.61803 1.61803
\(862\) −1.00000 −1.00000
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) −1.00000 −1.00000
\(865\) 0 0
\(866\) 0.381966 0.381966
\(867\) 0.618034 0.618034
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −0.618034 −0.618034
\(873\) 0 0
\(874\) −0.618034 −0.618034
\(875\) 0 0
\(876\) −0.236068 −0.236068
\(877\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(878\) 0 0
\(879\) 1.23607 1.23607
\(880\) 0 0
\(881\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(882\) −0.618034 −0.618034
\(883\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(884\) 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
\(894\) −0.618034 −0.618034
\(895\) 0 0
\(896\) 1.00000 1.00000
\(897\) −1.00000 −1.00000
\(898\) 0 0
\(899\) 0 0
\(900\) 0.381966 0.381966
\(901\) 0 0
\(902\) −1.00000 −1.00000
\(903\) 0 0
\(904\) −0.618034 −0.618034
\(905\) 0 0
\(906\) 0.763932 0.763932
\(907\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(908\) −0.381966 −0.381966
\(909\) 0 0
\(910\) 0 0
\(911\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(912\) 0 0
\(913\) −1.61803 −1.61803
\(914\) 0.381966 0.381966
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 1.23607 1.23607
\(922\) 0.381966 0.381966
\(923\) 0 0
\(924\) 0.618034 0.618034
\(925\) 0 0
\(926\) 0 0
\(927\) 1.00000 1.00000
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 1.00000 1.00000
\(932\) 0 0
\(933\) 0.381966 0.381966
\(934\) 1.23607 1.23607
\(935\) 0 0
\(936\) 0.618034 0.618034
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) −1.00000 −1.00000
\(940\) 0 0
\(941\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(942\) −0.618034 −0.618034
\(943\) 2.61803 2.61803
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 0.618034 0.618034
\(950\) 0.381966 0.381966
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) −0.236068 −0.236068
\(955\) 0 0
\(956\) −0.381966 −0.381966
\(957\) 0 0
\(958\) 1.23607 1.23607
\(959\) 0 0
\(960\) 0 0
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 1.00000 1.00000
\(965\) 0 0
\(966\) 1.00000 1.00000
\(967\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(968\) −1.00000 −1.00000
\(969\) 0 0
\(970\) 0 0
\(971\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(972\) −0.618034 −0.618034
\(973\) 0 0
\(974\) 0 0
\(975\) 0.618034 0.618034
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −0.381966 −0.381966
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 1.00000 1.00000
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −0.381966 −0.381966
\(989\) 0 0
\(990\) 0 0
\(991\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0.618034 0.618034
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 143.1.d.a.142.2 2
3.2 odd 2 1287.1.g.b.1000.1 2
4.3 odd 2 2288.1.m.b.2001.1 2
5.2 odd 4 3575.1.c.d.3574.3 4
5.3 odd 4 3575.1.c.d.3574.2 4
5.4 even 2 3575.1.h.f.2001.1 2
11.2 odd 10 1573.1.l.c.766.1 4
11.3 even 5 1573.1.l.d.233.1 4
11.4 even 5 1573.1.l.d.1546.1 4
11.5 even 5 1573.1.l.b.844.1 4
11.6 odd 10 1573.1.l.c.844.1 4
11.7 odd 10 1573.1.l.a.1546.1 4
11.8 odd 10 1573.1.l.a.233.1 4
11.9 even 5 1573.1.l.b.766.1 4
11.10 odd 2 143.1.d.b.142.1 yes 2
13.2 odd 12 1859.1.k.c.1374.3 8
13.3 even 3 1859.1.i.b.1330.1 4
13.4 even 6 1859.1.i.a.868.2 4
13.5 odd 4 1859.1.c.c.846.2 4
13.6 odd 12 1859.1.k.c.1836.2 8
13.7 odd 12 1859.1.k.c.1836.3 8
13.8 odd 4 1859.1.c.c.846.3 4
13.9 even 3 1859.1.i.b.868.1 4
13.10 even 6 1859.1.i.a.1330.2 4
13.11 odd 12 1859.1.k.c.1374.2 8
13.12 even 2 143.1.d.b.142.1 yes 2
33.32 even 2 1287.1.g.a.1000.2 2
39.38 odd 2 1287.1.g.a.1000.2 2
44.43 even 2 2288.1.m.a.2001.1 2
52.51 odd 2 2288.1.m.a.2001.1 2
55.32 even 4 3575.1.c.c.3574.2 4
55.43 even 4 3575.1.c.c.3574.3 4
55.54 odd 2 3575.1.h.e.2001.2 2
65.12 odd 4 3575.1.c.c.3574.2 4
65.38 odd 4 3575.1.c.c.3574.3 4
65.64 even 2 3575.1.h.e.2001.2 2
143.10 odd 6 1859.1.i.b.1330.1 4
143.21 even 4 1859.1.c.c.846.2 4
143.25 even 10 1573.1.l.a.233.1 4
143.32 even 12 1859.1.k.c.1836.3 8
143.38 even 10 1573.1.l.c.844.1 4
143.43 odd 6 1859.1.i.b.868.1 4
143.51 odd 10 1573.1.l.d.1546.1 4
143.54 even 12 1859.1.k.c.1374.2 8
143.64 even 10 1573.1.l.c.766.1 4
143.76 even 12 1859.1.k.c.1374.3 8
143.87 odd 6 1859.1.i.a.868.2 4
143.90 odd 10 1573.1.l.b.766.1 4
143.98 even 12 1859.1.k.c.1836.2 8
143.103 even 10 1573.1.l.a.1546.1 4
143.109 even 4 1859.1.c.c.846.3 4
143.116 odd 10 1573.1.l.b.844.1 4
143.120 odd 6 1859.1.i.a.1330.2 4
143.129 odd 10 1573.1.l.d.233.1 4
143.142 odd 2 CM 143.1.d.a.142.2 2
429.428 even 2 1287.1.g.b.1000.1 2
572.571 even 2 2288.1.m.b.2001.1 2
715.142 even 4 3575.1.c.d.3574.3 4
715.428 even 4 3575.1.c.d.3574.2 4
715.714 odd 2 3575.1.h.f.2001.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.1.d.a.142.2 2 1.1 even 1 trivial
143.1.d.a.142.2 2 143.142 odd 2 CM
143.1.d.b.142.1 yes 2 11.10 odd 2
143.1.d.b.142.1 yes 2 13.12 even 2
1287.1.g.a.1000.2 2 33.32 even 2
1287.1.g.a.1000.2 2 39.38 odd 2
1287.1.g.b.1000.1 2 3.2 odd 2
1287.1.g.b.1000.1 2 429.428 even 2
1573.1.l.a.233.1 4 11.8 odd 10
1573.1.l.a.233.1 4 143.25 even 10
1573.1.l.a.1546.1 4 11.7 odd 10
1573.1.l.a.1546.1 4 143.103 even 10
1573.1.l.b.766.1 4 11.9 even 5
1573.1.l.b.766.1 4 143.90 odd 10
1573.1.l.b.844.1 4 11.5 even 5
1573.1.l.b.844.1 4 143.116 odd 10
1573.1.l.c.766.1 4 11.2 odd 10
1573.1.l.c.766.1 4 143.64 even 10
1573.1.l.c.844.1 4 11.6 odd 10
1573.1.l.c.844.1 4 143.38 even 10
1573.1.l.d.233.1 4 11.3 even 5
1573.1.l.d.233.1 4 143.129 odd 10
1573.1.l.d.1546.1 4 11.4 even 5
1573.1.l.d.1546.1 4 143.51 odd 10
1859.1.c.c.846.2 4 13.5 odd 4
1859.1.c.c.846.2 4 143.21 even 4
1859.1.c.c.846.3 4 13.8 odd 4
1859.1.c.c.846.3 4 143.109 even 4
1859.1.i.a.868.2 4 13.4 even 6
1859.1.i.a.868.2 4 143.87 odd 6
1859.1.i.a.1330.2 4 13.10 even 6
1859.1.i.a.1330.2 4 143.120 odd 6
1859.1.i.b.868.1 4 13.9 even 3
1859.1.i.b.868.1 4 143.43 odd 6
1859.1.i.b.1330.1 4 13.3 even 3
1859.1.i.b.1330.1 4 143.10 odd 6
1859.1.k.c.1374.2 8 13.11 odd 12
1859.1.k.c.1374.2 8 143.54 even 12
1859.1.k.c.1374.3 8 13.2 odd 12
1859.1.k.c.1374.3 8 143.76 even 12
1859.1.k.c.1836.2 8 13.6 odd 12
1859.1.k.c.1836.2 8 143.98 even 12
1859.1.k.c.1836.3 8 13.7 odd 12
1859.1.k.c.1836.3 8 143.32 even 12
2288.1.m.a.2001.1 2 44.43 even 2
2288.1.m.a.2001.1 2 52.51 odd 2
2288.1.m.b.2001.1 2 4.3 odd 2
2288.1.m.b.2001.1 2 572.571 even 2
3575.1.c.c.3574.2 4 55.32 even 4
3575.1.c.c.3574.2 4 65.12 odd 4
3575.1.c.c.3574.3 4 55.43 even 4
3575.1.c.c.3574.3 4 65.38 odd 4
3575.1.c.d.3574.2 4 5.3 odd 4
3575.1.c.d.3574.2 4 715.428 even 4
3575.1.c.d.3574.3 4 5.2 odd 4
3575.1.c.d.3574.3 4 715.142 even 4
3575.1.h.e.2001.2 2 55.54 odd 2
3575.1.h.e.2001.2 2 65.64 even 2
3575.1.h.f.2001.1 2 5.4 even 2
3575.1.h.f.2001.1 2 715.714 odd 2