Properties

Label 1444.1.l.a.1111.1
Level $1444$
Weight $1$
Character 1444.1111
Analytic conductor $0.721$
Analytic rank $0$
Dimension $12$
Projective image $D_{5}$
CM discriminant -4
Inner twists $12$

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Newspace parameters

Level: \( N \) \(=\) \( 1444 = 2^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1444.l (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.720649878242\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{18})\)
Coefficient field: 12.0.6053445140625.1
Defining polynomial: \(x^{12} - 4 x^{9} + 17 x^{6} + 4 x^{3} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{5}\)
Projective field: Galois closure of 5.1.2085136.1

Embedding invariants

Embedding label 1111.1
Root \(-1.23949 + 1.04005i\) of defining polynomial
Character \(\chi\) \(=\) 1444.1111
Dual form 1444.1.l.a.967.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.173648 + 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.580762 - 0.211380i) q^{5} +(-0.500000 - 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\) \(q+(0.173648 + 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.580762 - 0.211380i) q^{5} +(-0.500000 - 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +(0.107320 - 0.608645i) q^{10} +(-1.23949 - 1.04005i) q^{13} +(0.766044 - 0.642788i) q^{16} +(-0.280969 - 1.59345i) q^{17} +1.00000 q^{18} +0.618034 q^{20} +(-0.473442 - 0.397265i) q^{25} +(0.809017 - 1.40126i) q^{26} +(-0.280969 + 1.59345i) q^{29} +(0.766044 + 0.642788i) q^{32} +(1.52045 - 0.553400i) q^{34} +(0.173648 + 0.984808i) q^{36} +0.618034 q^{37} +(0.107320 + 0.608645i) q^{40} +(0.473442 - 0.397265i) q^{41} +(-0.309017 + 0.535233i) q^{45} +(-0.500000 - 0.866025i) q^{49} +(0.309017 - 0.535233i) q^{50} +(1.52045 + 0.553400i) q^{52} +(-0.580762 + 0.211380i) q^{53} -1.61803 q^{58} +(1.52045 - 0.553400i) q^{61} +(-0.500000 + 0.866025i) q^{64} +(0.500000 + 0.866025i) q^{65} +(0.809017 + 1.40126i) q^{68} +(-0.939693 + 0.342020i) q^{72} +(0.473442 - 0.397265i) q^{73} +(0.107320 + 0.608645i) q^{74} +(-0.580762 + 0.211380i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(0.473442 + 0.397265i) q^{82} +(-0.173648 + 0.984808i) q^{85} +(0.473442 + 0.397265i) q^{89} +(-0.580762 - 0.211380i) q^{90} +(-0.280969 - 1.59345i) q^{97} +(0.766044 - 0.642788i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 6q^{8} + O(q^{10}) \) \( 12q - 6q^{8} + 12q^{18} - 6q^{20} + 3q^{26} - 6q^{37} + 3q^{45} - 6q^{49} - 3q^{50} - 6q^{58} - 6q^{64} + 6q^{65} + 3q^{68} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1444\mathbb{Z}\right)^\times\).

\(n\) \(723\) \(1085\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(3\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(4\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(5\) −0.580762 0.211380i −0.580762 0.211380i 0.0348995 0.999391i \(-0.488889\pi\)
−0.615661 + 0.788011i \(0.711111\pi\)
\(6\) 0 0
\(7\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) −0.500000 0.866025i −0.500000 0.866025i
\(9\) 0.173648 0.984808i 0.173648 0.984808i
\(10\) 0.107320 0.608645i 0.107320 0.608645i
\(11\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(12\) 0 0
\(13\) −1.23949 1.04005i −1.23949 1.04005i −0.997564 0.0697565i \(-0.977778\pi\)
−0.241922 0.970296i \(-0.577778\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.766044 0.642788i 0.766044 0.642788i
\(17\) −0.280969 1.59345i −0.280969 1.59345i −0.719340 0.694658i \(-0.755556\pi\)
0.438371 0.898794i \(-0.355556\pi\)
\(18\) 1.00000 1.00000
\(19\) 0 0
\(20\) 0.618034 0.618034
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(24\) 0 0
\(25\) −0.473442 0.397265i −0.473442 0.397265i
\(26\) 0.809017 1.40126i 0.809017 1.40126i
\(27\) 0 0
\(28\) 0 0
\(29\) −0.280969 + 1.59345i −0.280969 + 1.59345i 0.438371 + 0.898794i \(0.355556\pi\)
−0.719340 + 0.694658i \(0.755556\pi\)
\(30\) 0 0
\(31\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(33\) 0 0
\(34\) 1.52045 0.553400i 1.52045 0.553400i
\(35\) 0 0
\(36\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(37\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.107320 + 0.608645i 0.107320 + 0.608645i
\(41\) 0.473442 0.397265i 0.473442 0.397265i −0.374607 0.927184i \(-0.622222\pi\)
0.848048 + 0.529919i \(0.177778\pi\)
\(42\) 0 0
\(43\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(44\) 0 0
\(45\) −0.309017 + 0.535233i −0.309017 + 0.535233i
\(46\) 0 0
\(47\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.500000 0.866025i
\(50\) 0.309017 0.535233i 0.309017 0.535233i
\(51\) 0 0
\(52\) 1.52045 + 0.553400i 1.52045 + 0.553400i
\(53\) −0.580762 + 0.211380i −0.580762 + 0.211380i −0.615661 0.788011i \(-0.711111\pi\)
0.0348995 + 0.999391i \(0.488889\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −1.61803 −1.61803
\(59\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(60\) 0 0
\(61\) 1.52045 0.553400i 1.52045 0.553400i 0.559193 0.829038i \(-0.311111\pi\)
0.961262 + 0.275637i \(0.0888889\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(65\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(66\) 0 0
\(67\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(68\) 0.809017 + 1.40126i 0.809017 + 1.40126i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(72\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(73\) 0.473442 0.397265i 0.473442 0.397265i −0.374607 0.927184i \(-0.622222\pi\)
0.848048 + 0.529919i \(0.177778\pi\)
\(74\) 0.107320 + 0.608645i 0.107320 + 0.608645i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(80\) −0.580762 + 0.211380i −0.580762 + 0.211380i
\(81\) −0.939693 0.342020i −0.939693 0.342020i
\(82\) 0.473442 + 0.397265i 0.473442 + 0.397265i
\(83\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(84\) 0 0
\(85\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.473442 + 0.397265i 0.473442 + 0.397265i 0.848048 0.529919i \(-0.177778\pi\)
−0.374607 + 0.927184i \(0.622222\pi\)
\(90\) −0.580762 0.211380i −0.580762 0.211380i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.280969 1.59345i −0.280969 1.59345i −0.719340 0.694658i \(-0.755556\pi\)
0.438371 0.898794i \(-0.355556\pi\)
\(98\) 0.766044 0.642788i 0.766044 0.642788i
\(99\) 0 0
\(100\) 0.580762 + 0.211380i 0.580762 + 0.211380i
\(101\) 0.473442 + 0.397265i 0.473442 + 0.397265i 0.848048 0.529919i \(-0.177778\pi\)
−0.374607 + 0.927184i \(0.622222\pi\)
\(102\) 0 0
\(103\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(104\) −0.280969 + 1.59345i −0.280969 + 1.59345i
\(105\) 0 0
\(106\) −0.309017 0.535233i −0.309017 0.535233i
\(107\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) 0 0
\(109\) −0.580762 0.211380i −0.580762 0.211380i 0.0348995 0.999391i \(-0.488889\pi\)
−0.615661 + 0.788011i \(0.711111\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.280969 1.59345i −0.280969 1.59345i
\(117\) −1.23949 + 1.04005i −1.23949 + 1.04005i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(122\) 0.809017 + 1.40126i 0.809017 + 1.40126i
\(123\) 0 0
\(124\) 0 0
\(125\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(126\) 0 0
\(127\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(128\) −0.939693 0.342020i −0.939693 0.342020i
\(129\) 0 0
\(130\) −0.766044 + 0.642788i −0.766044 + 0.642788i
\(131\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −1.23949 + 1.04005i −1.23949 + 1.04005i
\(137\) −0.580762 + 0.211380i −0.580762 + 0.211380i −0.615661 0.788011i \(-0.711111\pi\)
0.0348995 + 0.999391i \(0.488889\pi\)
\(138\) 0 0
\(139\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.500000 0.866025i −0.500000 0.866025i
\(145\) 0.500000 0.866025i 0.500000 0.866025i
\(146\) 0.473442 + 0.397265i 0.473442 + 0.397265i
\(147\) 0 0
\(148\) −0.580762 + 0.211380i −0.580762 + 0.211380i
\(149\) −1.23949 + 1.04005i −1.23949 + 1.04005i −0.241922 + 0.970296i \(0.577778\pi\)
−0.997564 + 0.0697565i \(0.977778\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) −1.61803 −1.61803
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1.52045 + 0.553400i 1.52045 + 0.553400i 0.961262 0.275637i \(-0.0888889\pi\)
0.559193 + 0.829038i \(0.311111\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −0.309017 0.535233i −0.309017 0.535233i
\(161\) 0 0
\(162\) 0.173648 0.984808i 0.173648 0.984808i
\(163\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(164\) −0.309017 + 0.535233i −0.309017 + 0.535233i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(168\) 0 0
\(169\) 0.280969 + 1.59345i 0.280969 + 1.59345i
\(170\) −1.00000 −1.00000
\(171\) 0 0
\(172\) 0 0
\(173\) 0.107320 + 0.608645i 0.107320 + 0.608645i 0.990268 + 0.139173i \(0.0444444\pi\)
−0.882948 + 0.469472i \(0.844444\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −0.309017 + 0.535233i −0.309017 + 0.535233i
\(179\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(180\) 0.107320 0.608645i 0.107320 0.608645i
\(181\) 0.347296 1.96962i 0.347296 1.96962i 0.173648 0.984808i \(-0.444444\pi\)
0.173648 0.984808i \(-0.444444\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.358931 0.130640i −0.358931 0.130640i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) 1.53209 1.28558i 1.53209 1.28558i 0.766044 0.642788i \(-0.222222\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(194\) 1.52045 0.553400i 1.52045 0.553400i
\(195\) 0 0
\(196\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(197\) 0.809017 1.40126i 0.809017 1.40126i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(198\) 0 0
\(199\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(200\) −0.107320 + 0.608645i −0.107320 + 0.608645i
\(201\) 0 0
\(202\) −0.309017 + 0.535233i −0.309017 + 0.535233i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.358931 + 0.130640i −0.358931 + 0.130640i
\(206\) 0 0
\(207\) 0 0
\(208\) −1.61803 −1.61803
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(212\) 0.473442 0.397265i 0.473442 0.397265i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0.107320 0.608645i 0.107320 0.608645i
\(219\) 0 0
\(220\) 0 0
\(221\) −1.30902 + 2.26728i −1.30902 + 2.26728i
\(222\) 0 0
\(223\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(224\) 0 0
\(225\) −0.473442 + 0.397265i −0.473442 + 0.397265i
\(226\) −0.280969 1.59345i −0.280969 1.59345i
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.52045 0.553400i 1.52045 0.553400i
\(233\) 1.52045 + 0.553400i 1.52045 + 0.553400i 0.961262 0.275637i \(-0.0888889\pi\)
0.559193 + 0.829038i \(0.311111\pi\)
\(234\) −1.23949 1.04005i −1.23949 1.04005i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0 0
\(241\) 1.53209 + 1.28558i 1.53209 + 1.28558i 0.766044 + 0.642788i \(0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(242\) −0.939693 0.342020i −0.939693 0.342020i
\(243\) 0 0
\(244\) −1.23949 + 1.04005i −1.23949 + 1.04005i
\(245\) 0.107320 + 0.608645i 0.107320 + 0.608645i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −0.766044 + 0.642788i −0.766044 + 0.642788i
\(251\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.173648 0.984808i 0.173648 0.984808i
\(257\) 0.107320 0.608645i 0.107320 0.608645i −0.882948 0.469472i \(-0.844444\pi\)
0.990268 0.139173i \(-0.0444444\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.766044 0.642788i −0.766044 0.642788i
\(261\) 1.52045 + 0.553400i 1.52045 + 0.553400i
\(262\) 0 0
\(263\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(264\) 0 0
\(265\) 0.381966 0.381966
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.23949 + 1.04005i −1.23949 + 1.04005i −0.241922 + 0.970296i \(0.577778\pi\)
−0.997564 + 0.0697565i \(0.977778\pi\)
\(270\) 0 0
\(271\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(272\) −1.23949 1.04005i −1.23949 1.04005i
\(273\) 0 0
\(274\) −0.309017 0.535233i −0.309017 0.535233i
\(275\) 0 0
\(276\) 0 0
\(277\) −0.309017 0.535233i −0.309017 0.535233i 0.669131 0.743145i \(-0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.52045 0.553400i 1.52045 0.553400i 0.559193 0.829038i \(-0.311111\pi\)
0.961262 + 0.275637i \(0.0888889\pi\)
\(282\) 0 0
\(283\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.766044 0.642788i 0.766044 0.642788i
\(289\) −1.52045 + 0.553400i −1.52045 + 0.553400i
\(290\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(291\) 0 0
\(292\) −0.309017 + 0.535233i −0.309017 + 0.535233i
\(293\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.309017 0.535233i −0.309017 0.535233i
\(297\) 0 0
\(298\) −1.23949 1.04005i −1.23949 1.04005i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.00000 −1.00000
\(306\) −0.280969 1.59345i −0.280969 1.59345i
\(307\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) 0 0
\(313\) 0.107320 0.608645i 0.107320 0.608645i −0.882948 0.469472i \(-0.844444\pi\)
0.990268 0.139173i \(-0.0444444\pi\)
\(314\) −0.280969 + 1.59345i −0.280969 + 1.59345i
\(315\) 0 0
\(316\) 0 0
\(317\) 0.473442 + 0.397265i 0.473442 + 0.397265i 0.848048 0.529919i \(-0.177778\pi\)
−0.374607 + 0.927184i \(0.622222\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.473442 0.397265i 0.473442 0.397265i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 1.00000
\(325\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(326\) 0 0
\(327\) 0 0
\(328\) −0.580762 0.211380i −0.580762 0.211380i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) 0 0
\(333\) 0.107320 0.608645i 0.107320 0.608645i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.580762 0.211380i −0.580762 0.211380i 0.0348995 0.999391i \(-0.488889\pi\)
−0.615661 + 0.788011i \(0.711111\pi\)
\(338\) −1.52045 + 0.553400i −1.52045 + 0.553400i
\(339\) 0 0
\(340\) −0.173648 0.984808i −0.173648 0.984808i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −0.580762 + 0.211380i −0.580762 + 0.211380i
\(347\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(348\) 0 0
\(349\) 0.809017 1.40126i 0.809017 1.40126i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0.809017 + 1.40126i 0.809017 + 1.40126i 0.913545 + 0.406737i \(0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.580762 0.211380i −0.580762 0.211380i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(360\) 0.618034 0.618034
\(361\) 0 0
\(362\) 2.00000 2.00000
\(363\) 0 0
\(364\) 0 0
\(365\) −0.358931 + 0.130640i −0.358931 + 0.130640i
\(366\) 0 0
\(367\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(368\) 0 0
\(369\) −0.309017 0.535233i −0.309017 0.535233i
\(370\) 0.0663277 0.376163i 0.0663277 0.376163i
\(371\) 0 0
\(372\) 0 0
\(373\) 0.809017 1.40126i 0.809017 1.40126i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.00553 1.68284i 2.00553 1.68284i
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1.53209 + 1.28558i 1.53209 + 1.28558i
\(387\) 0 0
\(388\) 0.809017 + 1.40126i 0.809017 + 1.40126i
\(389\) −0.280969 + 1.59345i −0.280969 + 1.59345i 0.438371 + 0.898794i \(0.355556\pi\)
−0.719340 + 0.694658i \(0.755556\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(393\) 0 0
\(394\) 1.52045 + 0.553400i 1.52045 + 0.553400i
\(395\) 0 0
\(396\) 0 0
\(397\) 0.347296 + 1.96962i 0.347296 + 1.96962i 0.173648 + 0.984808i \(0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.618034 −0.618034
\(401\) 0.347296 + 1.96962i 0.347296 + 1.96962i 0.173648 + 0.984808i \(0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.580762 0.211380i −0.580762 0.211380i
\(405\) 0.473442 + 0.397265i 0.473442 + 0.397265i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0.107320 0.608645i 0.107320 0.608645i −0.882948 0.469472i \(-0.844444\pi\)
0.990268 0.139173i \(-0.0444444\pi\)
\(410\) −0.190983 0.330792i −0.190983 0.330792i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −0.280969 1.59345i −0.280969 1.59345i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0.473442 0.397265i 0.473442 0.397265i −0.374607 0.927184i \(-0.622222\pi\)
0.848048 + 0.529919i \(0.177778\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0.473442 + 0.397265i 0.473442 + 0.397265i
\(425\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(432\) 0 0
\(433\) −0.580762 + 0.211380i −0.580762 + 0.211380i −0.615661 0.788011i \(-0.711111\pi\)
0.0348995 + 0.999391i \(0.488889\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.618034 0.618034
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(440\) 0 0
\(441\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(442\) −2.46015 0.895420i −2.46015 0.895420i
\(443\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(444\) 0 0
\(445\) −0.190983 0.330792i −0.190983 0.330792i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.809017 1.40126i 0.809017 1.40126i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(450\) −0.473442 0.397265i −0.473442 0.397265i
\(451\) 0 0
\(452\) 1.52045 0.553400i 1.52045 0.553400i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(458\) 0.107320 + 0.608645i 0.107320 + 0.608645i
\(459\) 0 0
\(460\) 0 0
\(461\) −1.87939 0.684040i −1.87939 0.684040i −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 0.342020i \(-0.888889\pi\)
\(462\) 0 0
\(463\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(464\) 0.809017 + 1.40126i 0.809017 + 1.40126i
\(465\) 0 0
\(466\) −0.280969 + 1.59345i −0.280969 + 1.59345i
\(467\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(468\) 0.809017 1.40126i 0.809017 1.40126i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.107320 + 0.608645i 0.107320 + 0.608645i
\(478\) 0 0
\(479\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(480\) 0 0
\(481\) −0.766044 0.642788i −0.766044 0.642788i
\(482\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(483\) 0 0
\(484\) 0.173648 0.984808i 0.173648 0.984808i
\(485\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(486\) 0 0
\(487\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) −1.23949 1.04005i −1.23949 1.04005i
\(489\) 0 0
\(490\) −0.580762 + 0.211380i −0.580762 + 0.211380i
\(491\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(492\) 0 0
\(493\) 2.61803 2.61803
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(500\) −0.766044 0.642788i −0.766044 0.642788i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(504\) 0 0
\(505\) −0.190983 0.330792i −0.190983 0.330792i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.52045 0.553400i 1.52045 0.553400i 0.559193 0.829038i \(-0.311111\pi\)
0.961262 + 0.275637i \(0.0888889\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 1.00000
\(513\) 0 0
\(514\) 0.618034 0.618034
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0.500000 0.866025i 0.500000 0.866025i
\(521\) 0.809017 + 1.40126i 0.809017 + 1.40126i 0.913545 + 0.406737i \(0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(522\) −0.280969 + 1.59345i −0.280969 + 1.59345i
\(523\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.766044 0.642788i 0.766044 0.642788i
\(530\) 0.0663277 + 0.376163i 0.0663277 + 0.376163i
\(531\) 0 0
\(532\) 0 0
\(533\) −1.00000 −1.00000
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −1.23949 1.04005i −1.23949 1.04005i
\(539\) 0 0
\(540\) 0 0
\(541\) −0.280969 + 1.59345i −0.280969 + 1.59345i 0.438371 + 0.898794i \(0.355556\pi\)
−0.719340 + 0.694658i \(0.755556\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.809017 1.40126i 0.809017 1.40126i
\(545\) 0.292603 + 0.245523i 0.292603 + 0.245523i
\(546\) 0 0
\(547\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(548\) 0.473442 0.397265i 0.473442 0.397265i
\(549\) −0.280969 1.59345i −0.280969 1.59345i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0.473442 0.397265i 0.473442 0.397265i
\(555\) 0 0
\(556\) 0 0
\(557\) 1.53209 + 1.28558i 1.53209 + 1.28558i 0.766044 + 0.642788i \(0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0.809017 + 1.40126i 0.809017 + 1.40126i
\(563\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(564\) 0 0
\(565\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(577\) 0.809017 1.40126i 0.809017 1.40126i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(578\) −0.809017 1.40126i −0.809017 1.40126i
\(579\) 0 0
\(580\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −0.580762 0.211380i −0.580762 0.211380i
\(585\) 0.939693 0.342020i 0.939693 0.342020i
\(586\) 1.53209 1.28558i 1.53209 1.28558i
\(587\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.473442 0.397265i 0.473442 0.397265i
\(593\) −0.580762 + 0.211380i −0.580762 + 0.211380i −0.615661 0.788011i \(-0.711111\pi\)
0.0348995 + 0.999391i \(0.488889\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.809017 1.40126i 0.809017 1.40126i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(600\) 0 0
\(601\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.473442 0.397265i 0.473442 0.397265i
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −0.173648 0.984808i −0.173648 0.984808i
\(611\) 0 0
\(612\) 1.52045 0.553400i 1.52045 0.553400i
\(613\) −0.580762 0.211380i −0.580762 0.211380i 0.0348995 0.999391i \(-0.488889\pi\)
−0.615661 + 0.788011i \(0.711111\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.347296 1.96962i 0.347296 1.96962i 0.173648 0.984808i \(-0.444444\pi\)
0.173648 0.984808i \(-0.444444\pi\)
\(618\) 0 0
\(619\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0.618034 0.618034
\(627\) 0 0
\(628\) −1.61803 −1.61803
\(629\) −0.173648 0.984808i −0.173648 0.984808i
\(630\) 0 0
\(631\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −0.309017 + 0.535233i −0.309017 + 0.535233i
\(635\) 0 0
\(636\) 0 0
\(637\) −0.280969 + 1.59345i −0.280969 + 1.59345i
\(638\) 0 0
\(639\) 0 0
\(640\) 0.473442 + 0.397265i 0.473442 + 0.397265i
\(641\) 1.52045 + 0.553400i 1.52045 + 0.553400i 0.961262 0.275637i \(-0.0888889\pi\)
0.559193 + 0.829038i \(0.311111\pi\)
\(642\) 0 0
\(643\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(649\) 0 0
\(650\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(651\) 0 0
\(652\) 0 0
\(653\) −0.309017 + 0.535233i −0.309017 + 0.535233i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.107320 0.608645i 0.107320 0.608645i
\(657\) −0.309017 0.535233i −0.309017 0.535233i
\(658\) 0 0
\(659\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(660\) 0 0
\(661\) −1.87939 + 0.684040i −1.87939 + 0.684040i −0.939693 + 0.342020i \(0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0.618034 0.618034
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.309017 0.535233i −0.309017 0.535233i 0.669131 0.743145i \(-0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(674\) 0.107320 0.608645i 0.107320 0.608645i
\(675\) 0 0
\(676\) −0.809017 1.40126i −0.809017 1.40126i
\(677\) 0.809017 1.40126i 0.809017 1.40126i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0.939693 0.342020i 0.939693 0.342020i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0.381966 0.381966
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(690\) 0 0
\(691\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) −0.309017 0.535233i −0.309017 0.535233i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −0.766044 0.642788i −0.766044 0.642788i
\(698\) 1.52045 + 0.553400i 1.52045 + 0.553400i
\(699\) 0 0
\(700\) 0 0
\(701\) 0.107320 + 0.608645i 0.107320 + 0.608645i 0.990268 + 0.139173i \(0.0444444\pi\)
−0.882948 + 0.469472i \(0.844444\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −1.23949 + 1.04005i −1.23949 + 1.04005i
\(707\) 0 0
\(708\) 0 0
\(709\) −1.23949 1.04005i −1.23949 1.04005i −0.997564 0.0697565i \(-0.977778\pi\)
−0.241922 0.970296i \(-0.577778\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.107320 0.608645i 0.107320 0.608645i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(720\) 0.107320 + 0.608645i 0.107320 + 0.608645i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0.347296 + 1.96962i 0.347296 + 1.96962i
\(725\) 0.766044 0.642788i 0.766044 0.642788i
\(726\) 0 0
\(727\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(728\) 0 0
\(729\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(730\) −0.190983 0.330792i −0.190983 0.330792i
\(731\) 0 0
\(732\) 0 0
\(733\) 0.809017 + 1.40126i 0.809017 + 1.40126i 0.913545 + 0.406737i \(0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0.473442 0.397265i 0.473442 0.397265i
\(739\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(740\) 0.381966 0.381966
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(744\) 0 0
\(745\) 0.939693 0.342020i 0.939693 0.342020i
\(746\) 1.52045 + 0.553400i 1.52045 + 0.553400i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 2.00553 + 1.68284i 2.00553 + 1.68284i
\(755\) 0 0
\(756\) 0 0
\(757\) −1.23949 + 1.04005i −1.23949 + 1.04005i −0.241922 + 0.970296i \(0.577778\pi\)
−0.997564 + 0.0697565i \(0.977778\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0.107320 0.608645i 0.107320 0.608645i −0.882948 0.469472i \(-0.844444\pi\)
0.990268 0.139173i \(-0.0444444\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(773\) −1.23949 1.04005i −1.23949 1.04005i −0.997564 0.0697565i \(-0.977778\pi\)
−0.241922 0.970296i \(-0.577778\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −1.23949 + 1.04005i −1.23949 + 1.04005i
\(777\) 0 0
\(778\) −1.61803 −1.61803
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.939693 0.342020i −0.939693 0.342020i
\(785\) −0.766044 0.642788i −0.766044 0.642788i
\(786\) 0 0
\(787\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(788\) −0.280969 + 1.59345i −0.280969 + 1.59345i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −2.46015 0.895420i −2.46015 0.895420i
\(794\) −1.87939 + 0.684040i −1.87939 + 0.684040i
\(795\) 0 0
\(796\) 0 0
\(797\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.107320 0.608645i −0.107320 0.608645i
\(801\) 0.473442 0.397265i 0.473442 0.397265i
\(802\) −1.87939 + 0.684040i −1.87939 + 0.684040i
\(803\)