Properties

Label 47.1.b.a.46.2
Level 47
Weight 1
Character 47.46
Self dual Yes
Analytic conductor 0.023
Analytic rank 0
Dimension 2
Projective image \(D_{5}\)
CM disc. -47
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 47 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 47.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(0.0234560555938\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Projective image \(D_{5}\)
Projective field Galois closure of 5.1.2209.1
Artin image size \(10\)
Artin image $D_5$
Artin field Galois closure of 5.1.2209.1

Embedding invariants

Embedding label 46.2
Root \(1.61803\)
Character \(\chi\) = 47.46

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.618034 q^{2}\) \(-1.61803 q^{3}\) \(-0.618034 q^{4}\) \(-1.00000 q^{6}\) \(+0.618034 q^{7}\) \(-1.00000 q^{8}\) \(+1.61803 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.618034 q^{2}\) \(-1.61803 q^{3}\) \(-0.618034 q^{4}\) \(-1.00000 q^{6}\) \(+0.618034 q^{7}\) \(-1.00000 q^{8}\) \(+1.61803 q^{9}\) \(+1.00000 q^{12}\) \(+0.381966 q^{14}\) \(-1.61803 q^{17}\) \(+1.00000 q^{18}\) \(-1.00000 q^{21}\) \(+1.61803 q^{24}\) \(+1.00000 q^{25}\) \(-1.00000 q^{27}\) \(-0.381966 q^{28}\) \(+1.00000 q^{32}\) \(-1.00000 q^{34}\) \(-1.00000 q^{36}\) \(-1.61803 q^{37}\) \(-0.618034 q^{42}\) \(+1.00000 q^{47}\) \(-0.618034 q^{49}\) \(+0.618034 q^{50}\) \(+2.61803 q^{51}\) \(+0.618034 q^{53}\) \(-0.618034 q^{54}\) \(-0.618034 q^{56}\) \(+0.618034 q^{59}\) \(+0.618034 q^{61}\) \(+1.00000 q^{63}\) \(+0.618034 q^{64}\) \(+1.00000 q^{68}\) \(-1.61803 q^{71}\) \(-1.61803 q^{72}\) \(-1.00000 q^{74}\) \(-1.61803 q^{75}\) \(-1.61803 q^{79}\) \(+2.00000 q^{83}\) \(+0.618034 q^{84}\) \(+0.618034 q^{89}\) \(+0.618034 q^{94}\) \(-1.61803 q^{96}\) \(+0.618034 q^{97}\) \(-0.381966 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut q^{17} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 2q^{21} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut 3q^{28} \) \(\mathstrut +\mathstrut 2q^{32} \) \(\mathstrut -\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut +\mathstrut q^{42} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut -\mathstrut q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut +\mathstrut q^{56} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut q^{61} \) \(\mathstrut +\mathstrut 2q^{63} \) \(\mathstrut -\mathstrut q^{64} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut -\mathstrut q^{72} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut -\mathstrut q^{79} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut q^{84} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut q^{94} \) \(\mathstrut -\mathstrut q^{96} \) \(\mathstrut -\mathstrut q^{97} \) \(\mathstrut -\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/47\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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 \(0.400000\pi\)
\(3\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(4\) −0.618034 −0.618034
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) −1.00000 −1.00000
\(7\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(8\) −1.00000 −1.00000
\(9\) 1.61803 1.61803
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 1.00000 1.00000
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0.381966 0.381966
\(15\) 0 0
\(16\) 0 0
\(17\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(18\) 1.00000 1.00000
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) −1.00000 −1.00000
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 1.61803 1.61803
\(25\) 1.00000 1.00000
\(26\) 0 0
\(27\) −1.00000 −1.00000
\(28\) −0.381966 −0.381966
\(29\) 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
\(36\) −1.00000 −1.00000
\(37\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) −0.618034 −0.618034
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.00000 1.00000
\(48\) 0 0
\(49\) −0.618034 −0.618034
\(50\) 0.618034 0.618034
\(51\) 2.61803 2.61803
\(52\) 0 0
\(53\) 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
\(56\) −0.618034 −0.618034
\(57\) 0 0
\(58\) 0 0
\(59\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(60\) 0 0
\(61\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(62\) 0 0
\(63\) 1.00000 1.00000
\(64\) 0.618034 0.618034
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 1.00000 1.00000
\(69\) 0 0
\(70\) 0 0
\(71\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(72\) −1.61803 −1.61803
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) −1.00000 −1.00000
\(75\) −1.61803 −1.61803
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(84\) 0.618034 0.618034
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0.618034 0.618034
\(95\) 0 0
\(96\) −1.61803 −1.61803
\(97\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(98\) −0.381966 −0.381966
\(99\) 0 0
\(100\) −0.618034 −0.618034
\(101\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(102\) 1.61803 1.61803
\(103\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0.381966 0.381966
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0.618034 0.618034
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 2.61803 2.61803
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0.381966 0.381966
\(119\) −1.00000 −1.00000
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 0.381966 0.381966
\(123\) 0 0
\(124\) 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
\(131\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 1.61803 1.61803
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) −1.61803 −1.61803
\(142\) −1.00000 −1.00000
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 1.00000 1.00000
\(148\) 1.00000 1.00000
\(149\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(150\) −1.00000 −1.00000
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) −2.61803 −2.61803
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(158\) −1.00000 −1.00000
\(159\) −1.00000 −1.00000
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.23607 1.23607
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 1.00000 1.00000
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(174\) 0 0
\(175\) 0.618034 0.618034
\(176\) 0 0
\(177\) −1.00000 −1.00000
\(178\) 0.381966 0.381966
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) −1.00000 −1.00000
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.618034 −0.618034
\(189\) −0.618034 −0.618034
\(190\) 0 0
\(191\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(192\) −1.00000 −1.00000
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0.381966 0.381966
\(195\) 0 0
\(196\) 0.381966 0.381966
\(197\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −1.00000 −1.00000
\(201\) 0 0
\(202\) −1.00000 −1.00000
\(203\) 0 0
\(204\) −1.61803 −1.61803
\(205\) 0 0
\(206\) −1.00000 −1.00000
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) −0.381966 −0.381966
\(213\) 2.61803 2.61803
\(214\) 0 0
\(215\) 0 0
\(216\) 1.00000 1.00000
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 1.61803 1.61803
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0.618034 0.618034
\(225\) 1.61803 1.61803
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−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
\(236\) −0.381966 −0.381966
\(237\) 2.61803 2.61803
\(238\) −0.618034 −0.618034
\(239\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(240\) 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
\(244\) −0.381966 −0.381966
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −3.23607 −3.23607
\(250\) 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
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −1.00000 −1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −1.00000 −1.00000
\(260\) 0 0
\(261\) 0 0
\(262\) 0.381966 0.381966
\(263\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −1.00000 −1.00000
\(268\) 0 0
\(269\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(270\) 0 0
\(271\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) −1.00000 −1.00000
\(283\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(284\) 1.00000 1.00000
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 1.61803 1.61803
\(289\) 1.61803 1.61803
\(290\) 0 0
\(291\) −1.00000 −1.00000
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0.618034 0.618034
\(295\) 0 0
\(296\) 1.61803 1.61803
\(297\) 0 0
\(298\) −1.00000 −1.00000
\(299\) 0 0
\(300\) 1.00000 1.00000
\(301\) 0 0
\(302\) 0 0
\(303\) 2.61803 2.61803
\(304\) 0 0
\(305\) 0 0
\(306\) −1.61803 −1.61803
\(307\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(308\) 0 0
\(309\) 2.61803 2.61803
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0.381966 0.381966
\(315\) 0 0
\(316\) 1.00000 1.00000
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) −0.618034 −0.618034
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0.618034 0.618034
\(330\) 0 0
\(331\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(332\) −1.23607 −1.23607
\(333\) −2.61803 −2.61803
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(338\) 0.618034 0.618034
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) 0.381966 0.381966
\(347\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0.381966 0.381966
\(351\) 0 0
\(352\) 0 0
\(353\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(354\) −0.618034 −0.618034
\(355\) 0 0
\(356\) −0.381966 −0.381966
\(357\) 1.61803 1.61803
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) −1.61803 −1.61803
\(364\) 0 0
\(365\) 0 0
\(366\) −0.618034 −0.618034
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.381966 0.381966
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −1.00000 −1.00000
\(377\) 0 0
\(378\) −0.381966 −0.381966
\(379\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.23607 1.23607
\(383\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(384\) 1.00000 1.00000
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −0.381966 −0.381966
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.618034 0.618034
\(393\) −1.00000 −1.00000
\(394\) 1.23607 1.23607
\(395\) 0 0
\(396\) 0 0
\(397\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 1.00000 1.00000
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −2.61803 −2.61803
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.00000 1.00000
\(413\) 0.381966 0.381966
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 1.61803 1.61803
\(424\) −0.618034 −0.618034
\(425\) −1.61803 −1.61803
\(426\) 1.61803 1.61803
\(427\) 0.381966 0.381966
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(440\) 0 0
\(441\) −1.00000 −1.00000
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) −1.61803 −1.61803
\(445\) 0 0
\(446\) 0 0
\(447\) 2.61803 2.61803
\(448\) 0.381966 0.381966
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 1.00000 1.00000
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(458\) 0 0
\(459\) 1.61803 1.61803
\(460\) 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
\(466\) 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
\(472\) −0.618034 −0.618034
\(473\) 0 0
\(474\) 1.61803 1.61803
\(475\) 0 0
\(476\) 0.618034 0.618034
\(477\) 1.00000 1.00000
\(478\) −1.00000 −1.00000
\(479\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.00000 −1.00000
\(483\) 0 0
\(484\) −0.618034 −0.618034
\(485\) 0 0
\(486\) 0.618034 0.618034
\(487\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(488\) −0.618034 −0.618034
\(489\) 0 0
\(490\) 0 0
\(491\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.00000 −1.00000
\(498\) −2.00000 −2.00000
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −1.00000 −1.00000
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) −1.00000 −1.00000
\(505\) 0 0
\(506\) 0 0
\(507\) −1.61803 −1.61803
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −0.618034 −0.618034
\(519\) −1.00000 −1.00000
\(520\) 0 0
\(521\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(522\) 0 0
\(523\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(524\) −0.381966 −0.381966
\(525\) −1.00000 −1.00000
\(526\) 0.381966 0.381966
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 1.00000 1.00000
\(532\) 0 0
\(533\) 0 0
\(534\) −0.618034 −0.618034
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 1.23607 1.23607
\(539\) 0 0
\(540\) 0 0
\(541\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(542\) −1.00000 −1.00000
\(543\) 0 0
\(544\) −1.61803 −1.61803
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 1.00000 1.00000
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −1.00000 −1.00000
\(554\) −1.00000 −1.00000
\(555\) 0 0
\(556\) 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 \(\pi\)
\(564\) 1.00000 1.00000
\(565\) 0 0
\(566\) 0.381966 0.381966
\(567\) 0 0
\(568\) 1.61803 1.61803
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(572\) 0 0
\(573\) −3.23607 −3.23607
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 1.00000
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 1.00000 1.00000
\(579\) 0 0
\(580\) 0 0
\(581\) 1.23607 1.23607
\(582\) −0.618034 −0.618034
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) −0.618034 −0.618034
\(589\) 0 0
\(590\) 0 0
\(591\) −3.23607 −3.23607
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.00000 1.00000
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 1.61803 1.61803
\(601\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 1.61803 1.61803
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 1.61803 1.61803
\(613\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(614\) −1.00000 −1.00000
\(615\) 0 0
\(616\) 0 0
\(617\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(618\) 1.61803 1.61803
\(619\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0.381966 0.381966
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) −0.381966 −0.381966
\(629\) 2.61803 2.61803
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 1.61803 1.61803
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0.618034 0.618034
\(637\) 0 0
\(638\) 0 0
\(639\) −2.61803 −2.61803
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(644\) 0 0
\(645\) 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 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0.381966 0.381966
\(659\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(660\) 0 0
\(661\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(662\) 0.381966 0.381966
\(663\) 0 0
\(664\) −2.00000 −2.00000
\(665\) 0 0
\(666\) −1.61803 −1.61803
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −1.00000 −1.00000
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0.381966 0.381966
\(675\) −1.00000 −1.00000
\(676\) −0.618034 −0.618034
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0.381966 0.381966
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.618034 −0.618034
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) −0.381966 −0.381966
\(693\) 0 0
\(694\) −1.00000 −1.00000
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −0.381966 −0.381966
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0.381966 0.381966
\(707\) −1.00000 −1.00000
\(708\) 0.618034 0.618034
\(709\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(710\) 0 0
\(711\) −2.61803 −2.61803
\(712\) −0.618034 −0.618034
\(713\) 0 0
\(714\) 1.00000 1.00000
\(715\) 0 0
\(716\) 0 0
\(717\) 2.61803 2.61803
\(718\) 0 0
\(719\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(720\) 0 0
\(721\) −1.00000 −1.00000
\(722\) 0.618034 0.618034
\(723\) 2.61803 2.61803
\(724\) 0 0
\(725\) 0 0
\(726\) −1.00000 −1.00000
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −1.61803 −1.61803
\(730\) 0 0
\(731\) 0 0
\(732\) 0.618034 0.618034
\(733\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.236068 0.236068
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 3.23607 3.23607
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 2.61803 2.61803
\(754\) 0 0
\(755\) 0 0
\(756\) 0.381966 0.381966
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0.381966 0.381966
\(759\) 0 0
\(760\) 0 0
\(761\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1.23607 −1.23607
\(765\) 0 0
\(766\) −1.00000 −1.00000
\(767\) 0 0
\(768\) 1.61803 1.61803
\(769\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −0.618034 −0.618034
\(777\) 1.61803 1.61803
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) −0.618034 −0.618034
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) −1.23607 −1.23607
\(789\) −1.00000 −1.00000
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) −1.00000 −1.00000
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) −1.61803 −1.61803
\(800\) 1.00000 1.00000
\(801\) 1.00000 1.00000
\(802\) −1.00000 −1.00000
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −3.23607 −3.23607
\(808\) 1.61803 1.61803
\(809\) 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
\(813\) 2.61803 2.61803
\(814\) 0 0
\(815\) 0 0
\(816\) 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
\(823\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(824\) 1.61803 1.61803
\(825\) 0 0
\(826\) 0.236068 0.236068
\(827\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 2.61803 2.61803
\(832\) 0 0
\(833\) 1.00000 1.00000
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 1.00000 1.00000
\(847\) 0.618034 0.618034
\(848\) 0 0
\(849\) −1.00000 −1.00000
\(850\) −1.00000 −1.00000
\(851\) 0 0
\(852\) −1.61803 −1.61803
\(853\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(854\) 0.236068 0.236068
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0.381966 0.381966
\(863\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(864\) −1.00000 −1.00000
\(865\) 0 0
\(866\) 0 0
\(867\) −2.61803 −2.61803
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 1.00000 1.00000
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 1.23607 1.23607
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −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
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) −2.61803 −2.61803
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 1.61803 1.61803
\(895\) 0 0
\(896\) −0.381966 −0.381966
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −1.00000 −1.00000
\(901\) −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 \(0\)
1.00000 \(0\)
\(908\) 0 0
\(909\) −2.61803 −2.61803
\(910\) 0 0
\(911\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −1.00000 −1.00000
\(915\) 0 0
\(916\) 0 0
\(917\) 0.381966 0.381966
\(918\) 1.00000 1.00000
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 2.61803 2.61803
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −1.61803 −1.61803
\(926\) 0 0
\(927\) −2.61803 −2.61803
\(928\) 0 0
\(929\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 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
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(948\) −1.61803 −1.61803
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 1.00000 1.00000
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0.618034 0.618034
\(955\) 0 0
\(956\) 1.00000 1.00000
\(957\) 0 0
\(958\) 0.381966 0.381966
\(959\) 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
\(967\) 0.618034 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 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) −0.618034 −0.618034
\(973\) 0 0
\(974\) 1.23607 1.23607
\(975\) 0 0
\(976\) 0 0
\(977\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0.381966 0.381966
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −1.00000 −1.00000
\(988\) 0 0
\(989\) 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
\(993\) −1.00000 −1.00000
\(994\) −0.618034 −0.618034
\(995\) 0 0
\(996\) 2.00000 2.00000
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0 0
\(999\) 1.61803 1.61803
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 \(a_p\))