Properties

Label 3528.1.co.a.587.3
Level $3528$
Weight $1$
Character 3528.587
Analytic conductor $1.761$
Analytic rank $0$
Dimension $16$
Projective image $D_{24}$
CM discriminant -8
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3528.co (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.76070136457\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{48})\)
Defining polynomial: \(x^{16} - x^{8} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(D_{24}\)
Projective field Galois closure of \(\mathbb{Q}[x]/(x^{24} + \cdots)\)

Embedding invariants

Embedding label 587.3
Root \(-0.608761 + 0.793353i\) of defining polynomial
Character \(\chi\) \(=\) 3528.587
Dual form 3528.1.co.a.2939.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.130526 - 0.991445i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.608761 + 0.793353i) q^{6} -1.00000i q^{8} +(-0.965926 - 0.258819i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.130526 - 0.991445i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.608761 + 0.793353i) q^{6} -1.00000i q^{8} +(-0.965926 - 0.258819i) q^{9} +(-1.67303 - 0.965926i) q^{11} +(0.923880 - 0.382683i) q^{12} +(-0.500000 + 0.866025i) q^{16} -1.21752 q^{17} +(0.707107 + 0.707107i) q^{18} +0.261052i q^{19} +(0.965926 + 1.67303i) q^{22} +(-0.991445 - 0.130526i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.382683 + 0.923880i) q^{27} +(0.866025 - 0.500000i) q^{32} +(-1.17604 + 1.53264i) q^{33} +(1.05441 + 0.608761i) q^{34} +(-0.258819 - 0.965926i) q^{36} +(0.130526 - 0.226078i) q^{38} +(0.793353 + 1.37413i) q^{41} +(0.258819 - 0.448288i) q^{43} -1.93185i q^{44} +(0.793353 + 0.608761i) q^{48} +(0.866025 - 0.500000i) q^{50} +(-0.158919 + 1.20711i) q^{51} +(0.793353 - 0.608761i) q^{54} +(0.258819 + 0.0340742i) q^{57} +(0.991445 + 1.71723i) q^{59} -1.00000 q^{64} +(1.78480 - 0.739288i) q^{66} +(-0.866025 - 1.50000i) q^{67} +(-0.608761 - 1.05441i) q^{68} +(-0.258819 + 0.965926i) q^{72} +1.98289i q^{73} +(0.793353 + 0.608761i) q^{75} +(-0.226078 + 0.130526i) q^{76} +(0.866025 + 0.500000i) q^{81} -1.58671i q^{82} +(-0.382683 + 0.662827i) q^{83} +(-0.448288 + 0.258819i) q^{86} +(-0.965926 + 1.67303i) q^{88} -1.84776 q^{89} +(-0.382683 - 0.923880i) q^{96} +(-1.37413 - 0.793353i) q^{97} +(1.36603 + 1.36603i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{4} + O(q^{10}) \) \( 16q + 8q^{4} - 8q^{16} - 8q^{25} - 16q^{64} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\) \(1765\) \(2647\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.866025 0.500000i
\(3\) 0.130526 0.991445i 0.130526 0.991445i
\(4\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(5\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(6\) −0.608761 + 0.793353i −0.608761 + 0.793353i
\(7\) 0 0
\(8\) 1.00000i 1.00000i
\(9\) −0.965926 0.258819i −0.965926 0.258819i
\(10\) 0 0
\(11\) −1.67303 0.965926i −1.67303 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(12\) 0.923880 0.382683i 0.923880 0.382683i
\(13\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(17\) −1.21752 −1.21752 −0.608761 0.793353i \(-0.708333\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(18\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(19\) 0.261052i 0.261052i 0.991445 + 0.130526i \(0.0416667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.965926 + 1.67303i 0.965926 + 1.67303i
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) −0.991445 0.130526i −0.991445 0.130526i
\(25\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(26\) 0 0
\(27\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(28\) 0 0
\(29\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 0.866025 0.500000i 0.866025 0.500000i
\(33\) −1.17604 + 1.53264i −1.17604 + 1.53264i
\(34\) 1.05441 + 0.608761i 1.05441 + 0.608761i
\(35\) 0 0
\(36\) −0.258819 0.965926i −0.258819 0.965926i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0.130526 0.226078i 0.130526 0.226078i
\(39\) 0 0
\(40\) 0 0
\(41\) 0.793353 + 1.37413i 0.793353 + 1.37413i 0.923880 + 0.382683i \(0.125000\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(42\) 0 0
\(43\) 0.258819 0.448288i 0.258819 0.448288i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(44\) 1.93185i 1.93185i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(48\) 0.793353 + 0.608761i 0.793353 + 0.608761i
\(49\) 0 0
\(50\) 0.866025 0.500000i 0.866025 0.500000i
\(51\) −0.158919 + 1.20711i −0.158919 + 1.20711i
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0.793353 0.608761i 0.793353 0.608761i
\(55\) 0 0
\(56\) 0 0
\(57\) 0.258819 + 0.0340742i 0.258819 + 0.0340742i
\(58\) 0 0
\(59\) 0.991445 + 1.71723i 0.991445 + 1.71723i 0.608761 + 0.793353i \(0.291667\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(60\) 0 0
\(61\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −1.00000 −1.00000
\(65\) 0 0
\(66\) 1.78480 0.739288i 1.78480 0.739288i
\(67\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(68\) −0.608761 1.05441i −0.608761 1.05441i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(73\) 1.98289i 1.98289i 0.130526 + 0.991445i \(0.458333\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(74\) 0 0
\(75\) 0.793353 + 0.608761i 0.793353 + 0.608761i
\(76\) −0.226078 + 0.130526i −0.226078 + 0.130526i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(80\) 0 0
\(81\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(82\) 1.58671i 1.58671i
\(83\) −0.382683 + 0.662827i −0.382683 + 0.662827i −0.991445 0.130526i \(-0.958333\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.448288 + 0.258819i −0.448288 + 0.258819i
\(87\) 0 0
\(88\) −0.965926 + 1.67303i −0.965926 + 1.67303i
\(89\) −1.84776 −1.84776 −0.923880 0.382683i \(-0.875000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.382683 0.923880i −0.382683 0.923880i
\(97\) −1.37413 0.793353i −1.37413 0.793353i −0.382683 0.923880i \(-0.625000\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(98\) 0 0
\(99\) 1.36603 + 1.36603i 1.36603 + 1.36603i
\(100\) −1.00000 −1.00000
\(101\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 0.741181 0.965926i 0.741181 0.965926i
\(103\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(108\) −0.991445 + 0.130526i −0.991445 + 0.130526i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(114\) −0.207107 0.158919i −0.207107 0.158919i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 1.98289i 1.98289i
\(119\) 0 0
\(120\) 0 0
\(121\) 1.36603 + 2.36603i 1.36603 + 2.36603i
\(122\) 0 0
\(123\) 1.46593 0.607206i 1.46593 0.607206i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(129\) −0.410670 0.315118i −0.410670 0.315118i
\(130\) 0 0
\(131\) −0.923880 1.60021i −0.923880 1.60021i −0.793353 0.608761i \(-0.791667\pi\)
−0.130526 0.991445i \(-0.541667\pi\)
\(132\) −1.91532 0.252157i −1.91532 0.252157i
\(133\) 0 0
\(134\) 1.73205i 1.73205i
\(135\) 0 0
\(136\) 1.21752i 1.21752i
\(137\) −0.448288 0.258819i −0.448288 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(138\) 0 0
\(139\) −1.71723 + 0.991445i −1.71723 + 0.991445i −0.793353 + 0.608761i \(0.791667\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.707107 0.707107i 0.707107 0.707107i
\(145\) 0 0
\(146\) 0.991445 1.71723i 0.991445 1.71723i
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(150\) −0.382683 0.923880i −0.382683 0.923880i
\(151\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(152\) 0.261052 0.261052
\(153\) 1.17604 + 0.315118i 1.17604 + 0.315118i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.500000 0.866025i −0.500000 0.866025i
\(163\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(164\) −0.793353 + 1.37413i −0.793353 + 1.37413i
\(165\) 0 0
\(166\) 0.662827 0.382683i 0.662827 0.382683i
\(167\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(168\) 0 0
\(169\) 0.500000 0.866025i 0.500000 0.866025i
\(170\) 0 0
\(171\) 0.0675653 0.252157i 0.0675653 0.252157i
\(172\) 0.517638 0.517638
\(173\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.67303 0.965926i 1.67303 0.965926i
\(177\) 1.83195 0.758819i 1.83195 0.758819i
\(178\) 1.60021 + 0.923880i 1.60021 + 0.923880i
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 2.03696 + 1.17604i 2.03696 + 1.17604i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) −0.130526 + 0.991445i −0.130526 + 0.991445i
\(193\) −0.258819 0.448288i −0.258819 0.448288i 0.707107 0.707107i \(-0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(194\) 0.793353 + 1.37413i 0.793353 + 1.37413i
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) −0.500000 1.86603i −0.500000 1.86603i
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(201\) −1.60021 + 0.662827i −1.60021 + 0.662827i
\(202\) 0 0
\(203\) 0 0
\(204\) −1.12484 + 0.465926i −1.12484 + 0.465926i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.252157 0.436749i 0.252157 0.436749i
\(210\) 0 0
\(211\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(215\) 0 0
\(216\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(217\) 0 0
\(218\) 0 0
\(219\) 1.96593 + 0.258819i 1.96593 + 0.258819i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(224\) 0 0
\(225\) 0.707107 0.707107i 0.707107 0.707107i
\(226\) 1.41421 1.41421
\(227\) 0.793353 1.37413i 0.793353 1.37413i −0.130526 0.991445i \(-0.541667\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(228\) 0.0999004 + 0.241181i 0.0999004 + 0.241181i
\(229\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.517638i 0.517638i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.991445 + 1.71723i −0.991445 + 1.71723i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(240\) 0 0
\(241\) −1.05441 0.608761i −1.05441 0.608761i −0.130526 0.991445i \(-0.541667\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(242\) 2.73205i 2.73205i
\(243\) 0.608761 0.793353i 0.608761 0.793353i
\(244\) 0 0
\(245\) 0 0
\(246\) −1.57313 0.207107i −1.57313 0.207107i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.607206 + 0.465926i 0.607206 + 0.465926i
\(250\) 0 0
\(251\) 0.261052 0.261052 0.130526 0.991445i \(-0.458333\pi\)
0.130526 + 0.991445i \(0.458333\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.500000 0.866025i
\(257\) 0.991445 + 1.71723i 0.991445 + 1.71723i 0.608761 + 0.793353i \(0.291667\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(258\) 0.198092 + 0.478235i 0.198092 + 0.478235i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 1.84776i 1.84776i
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 1.53264 + 1.17604i 1.53264 + 1.17604i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.241181 + 1.83195i −0.241181 + 1.83195i
\(268\) 0.866025 1.50000i 0.866025 1.50000i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0.608761 1.05441i 0.608761 1.05441i
\(273\) 0 0
\(274\) 0.258819 + 0.448288i 0.258819 + 0.448288i
\(275\) 1.67303 0.965926i 1.67303 0.965926i
\(276\) 0 0
\(277\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(278\) 1.98289 1.98289
\(279\) 0 0
\(280\) 0 0
\(281\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(282\) 0 0
\(283\) 1.60021 0.923880i 1.60021 0.923880i 0.608761 0.793353i \(-0.291667\pi\)
0.991445 0.130526i \(-0.0416667\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(289\) 0.482362 0.482362
\(290\) 0 0
\(291\) −0.965926 + 1.25882i −0.965926 + 1.25882i
\(292\) −1.71723 + 0.991445i −1.71723 + 0.991445i
\(293\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.53264 1.17604i 1.53264 1.17604i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.130526 + 0.991445i −0.130526 + 0.991445i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −0.226078 0.130526i −0.226078 0.130526i
\(305\) 0 0
\(306\) −0.860919 0.860919i −0.860919 0.860919i
\(307\) 1.21752i 1.21752i −0.793353 0.608761i \(-0.791667\pi\)
0.793353 0.608761i \(-0.208333\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(312\) 0 0
\(313\) 1.05441 + 0.608761i 1.05441 + 0.608761i 0.923880 0.382683i \(-0.125000\pi\)
0.130526 + 0.991445i \(0.458333\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −1.71723 0.226078i −1.71723 0.226078i
\(322\) 0 0
\(323\) 0.317837i 0.317837i
\(324\) 1.00000i 1.00000i
\(325\) 0 0
\(326\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(327\) 0 0
\(328\) 1.37413 0.793353i 1.37413 0.793353i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(332\) −0.765367 −0.765367
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(338\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(339\) 0.541196 + 1.30656i 0.541196 + 1.30656i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.184592 + 0.184592i −0.184592 + 0.184592i
\(343\) 0 0
\(344\) −0.448288 0.258819i −0.448288 0.258819i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.448288 0.258819i 0.448288 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.93185 −1.93185
\(353\) −0.130526 + 0.226078i −0.130526 + 0.226078i −0.923880 0.382683i \(-0.875000\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(354\) −1.96593 0.258819i −1.96593 0.258819i
\(355\) 0 0
\(356\) −0.923880 1.60021i −0.923880 1.60021i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 0.931852 0.931852
\(362\) 0 0
\(363\) 2.52409 1.04551i 2.52409 1.04551i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(368\) 0 0
\(369\) −0.410670 1.53264i −0.410670 1.53264i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) −1.17604 2.03696i −1.17604 2.03696i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.93185 −1.93185 −0.965926 0.258819i \(-0.916667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(384\) 0.608761 0.793353i 0.608761 0.793353i
\(385\) 0 0
\(386\) 0.517638i 0.517638i
\(387\) −0.366025 + 0.366025i −0.366025 + 0.366025i
\(388\) 1.58671i 1.58671i
\(389\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −1.70711 + 0.707107i −1.70711 + 0.707107i
\(394\) 0 0
\(395\) 0 0
\(396\) −0.500000 + 1.86603i −0.500000 + 1.86603i
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.500000 0.866025i −0.500000 0.866025i
\(401\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(402\) 1.71723 + 0.226078i 1.71723 + 0.226078i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 1.20711 + 0.158919i 1.20711 + 0.158919i
\(409\) −1.37413 + 0.793353i −1.37413 + 0.793353i −0.991445 0.130526i \(-0.958333\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(410\) 0 0
\(411\) −0.315118 + 0.410670i −0.315118 + 0.410670i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.758819 + 1.83195i 0.758819 + 1.83195i
\(418\) −0.436749 + 0.252157i −0.436749 + 0.252157i
\(419\) 0.382683 + 0.662827i 0.382683 + 0.662827i 0.991445 0.130526i \(-0.0416667\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(420\) 0 0
\(421\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.608761 1.05441i 0.608761 1.05441i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.50000 0.866025i 1.50000 0.866025i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) −0.608761 0.793353i −0.608761 0.793353i
\(433\) 0.261052i 0.261052i −0.991445 0.130526i \(-0.958333\pi\)
0.991445 0.130526i \(-0.0416667\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −1.57313 1.20711i −1.57313 1.20711i
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(450\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(451\) 3.06528i 3.06528i
\(452\) −1.22474 0.707107i −1.22474 0.707107i
\(453\) 0 0
\(454\) −1.37413 + 0.793353i −1.37413 + 0.793353i
\(455\) 0 0
\(456\) 0.0340742 0.258819i 0.0340742 0.258819i
\(457\) 0.965926 1.67303i 0.965926 1.67303i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(458\) 0 0
\(459\) 0.465926 1.12484i 0.465926 1.12484i
\(460\) 0 0
\(461\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(462\) 0 0
\(463\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.258819 0.448288i 0.258819 0.448288i
\(467\) −1.21752 −1.21752 −0.608761 0.793353i \(-0.708333\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 1.71723 0.991445i 1.71723 0.991445i
\(473\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(474\) 0 0
\(475\) −0.226078 0.130526i −0.226078 0.130526i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.608761 + 1.05441i 0.608761 + 1.05441i
\(483\) 0 0
\(484\) −1.36603 + 2.36603i −1.36603 + 2.36603i
\(485\) 0 0
\(486\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) −0.184592 + 1.40211i −0.184592 + 1.40211i
\(490\) 0 0
\(491\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(492\) 1.25882 + 0.965926i 1.25882 + 0.965926i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.292893 0.707107i −0.292893 0.707107i
\(499\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.226078 0.130526i −0.226078 0.130526i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.793353 0.608761i −0.793353 0.608761i
\(508\) 0 0
\(509\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 1.00000i
\(513\) −0.241181 0.0999004i −0.241181 0.0999004i
\(514\) 1.98289i 1.98289i
\(515\) 0 0
\(516\) 0.0675653 0.513210i 0.0675653 0.513210i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.98289 −1.98289 −0.991445 0.130526i \(-0.958333\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(522\) 0 0
\(523\) 0.765367i 0.765367i 0.923880 + 0.382683i \(0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(524\) 0.923880 1.60021i 0.923880 1.60021i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.739288 1.78480i −0.739288 1.78480i
\(529\) 0.500000 0.866025i 0.500000 0.866025i
\(530\) 0 0
\(531\) −0.513210 1.91532i −0.513210 1.91532i
\(532\) 0 0
\(533\) 0 0
\(534\) 1.12484 1.46593i 1.12484 1.46593i
\(535\) 0 0
\(536\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.05441 + 0.608761i −1.05441 + 0.608761i
\(545\) 0 0
\(546\) 0 0
\(547\) 0.965926 1.67303i 0.965926 1.67303i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(548\) 0.517638i 0.517638i
\(549\) 0 0
\(550\) −1.93185 −1.93185
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −1.71723 0.991445i −1.71723 0.991445i
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 1.43185 1.86603i 1.43185 1.86603i
\(562\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(563\) −0.130526 0.226078i −0.130526 0.226078i 0.793353 0.608761i \(-0.208333\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −1.84776 −1.84776
\(567\) 0 0
\(568\) 0 0
\(569\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(570\) 0 0
\(571\) 0.965926 + 1.67303i 0.965926 + 1.67303i 0.707107 + 0.707107i \(0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(577\) 0.261052i 0.261052i 0.991445 + 0.130526i \(0.0416667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(578\) −0.417738 0.241181i −0.417738 0.241181i
\(579\) −0.478235 + 0.198092i −0.478235 + 0.198092i
\(580\) 0 0
\(581\) 0 0
\(582\) 1.46593 0.607206i 1.46593 0.607206i
\(583\) 0 0
\(584\) 1.98289 1.98289
\(585\) 0 0
\(586\) 0 0
\(587\) 0.793353 1.37413i 0.793353 1.37413i −0.130526 0.991445i \(-0.541667\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.84776 1.84776 0.923880 0.382683i \(-0.125000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(594\) −1.91532 + 0.252157i −1.91532 + 0.252157i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) 0.608761 0.793353i 0.608761 0.793353i
\(601\) 0.226078 + 0.130526i 0.226078 + 0.130526i 0.608761 0.793353i \(-0.291667\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(602\) 0 0
\(603\) 0.448288 + 1.67303i 0.448288 + 1.67303i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(608\) 0.130526 + 0.226078i 0.130526 + 0.226078i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.315118 + 1.17604i 0.315118 + 1.17604i
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) −0.608761 + 1.05441i −0.608761 + 1.05441i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 1.71723 + 0.991445i 1.71723 + 0.991445i 0.923880 + 0.382683i \(0.125000\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.500000 0.866025i
\(626\) −0.608761 1.05441i −0.608761 1.05441i
\(627\) −0.400100 0.307007i −0.400100 0.307007i
\(628\) 0 0
\(629\) 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 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(642\) 1.37413 + 1.05441i 1.37413 + 1.05441i
\(643\) −1.05441 + 0.608761i −1.05441 + 0.608761i −0.923880 0.382683i \(-0.875000\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.158919 + 0.275255i −0.158919 + 0.275255i
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0.500000 0.866025i 0.500000 0.866025i
\(649\) 3.83065i 3.83065i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.707107 1.22474i −0.707107 1.22474i
\(653\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.58671 −1.58671
\(657\) 0.513210 1.91532i 0.513210 1.91532i
\(658\) 0 0
\(659\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(660\) 0 0
\(661\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(662\) 1.22474 0.707107i 1.22474 0.707107i
\(663\) 0 0
\(664\) 0.662827 + 0.382683i 0.662827 + 0.382683i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(674\) 1.73205i 1.73205i
\(675\) −0.608761 0.793353i −0.608761 0.793353i
\(676\) 1.00000 1.00000
\(677\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(678\) 0.184592 1.40211i 0.184592 1.40211i
\(679\) 0 0
\(680\) 0 0
\(681\) −1.25882 0.965926i −1.25882 0.965926i
\(682\) 0 0
\(683\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(684\) 0.252157 0.0675653i 0.252157 0.0675653i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0.258819 + 0.448288i 0.258819 + 0.448288i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.662827 0.382683i −0.662827 0.382683i 0.130526 0.991445i \(-0.458333\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.517638 −0.517638
\(695\) 0 0
\(696\) 0 0
\(697\) −0.965926 1.67303i −0.965926 1.67303i
\(698\) 0 0
\(699\) 0.513210 + 0.0675653i 0.513210 + 0.0675653i
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.67303 + 0.965926i 1.67303 + 0.965926i
\(705\) 0 0
\(706\) 0.226078 0.130526i 0.226078 0.130526i
\(707\) 0 0
\(708\) 1.57313 + 1.20711i 1.57313 + 1.20711i
\(709\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.84776i 1.84776i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.807007 0.465926i −0.807007 0.465926i
\(723\) −0.741181 + 0.965926i −0.741181 + 0.965926i
\(724\) 0 0
\(725\) 0 0
\(726\) −2.70868 0.356604i −2.70868 0.356604i
\(727\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(728\) 0 0
\(729\) −0.707107 0.707107i −0.707107 0.707107i
\(730\) 0 0
\(731\) −0.315118 + 0.545801i −0.315118 + 0.545801i
\(732\) 0 0
\(733\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.34607i 3.34607i
\(738\) −0.410670 + 1.53264i −0.410670 + 1.53264i
\(739\) −0.517638 −0.517638 −0.258819 0.965926i \(-0.583333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.541196 0.541196i 0.541196 0.541196i
\(748\) 2.35207i 2.35207i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(752\) 0 0
\(753\) 0.0340742 0.258819i 0.0340742 0.258819i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 1.67303 + 0.965926i 1.67303 + 0.965926i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.382683 0.662827i −0.382683 0.662827i 0.608761 0.793353i \(-0.291667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(769\) 0.662827 0.382683i 0.662827 0.382683i −0.130526 0.991445i \(-0.541667\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(770\) 0 0
\(771\) 1.83195 0.758819i 1.83195 0.758819i
\(772\) 0.258819 0.448288i 0.258819 0.448288i
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0.500000 0.133975i 0.500000 0.133975i
\(775\) 0 0
\(776\) −0.793353 + 1.37413i −0.793353 + 1.37413i
\(777\) 0 0
\(778\) 0 0
\(779\) −0.358719 + 0.207107i −0.358719 + 0.207107i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 1.83195 + 0.241181i 1.83195 + 0.241181i
\(787\) −1.60021 + 0.923880i −1.60021 + 0.923880i −0.608761 + 0.793353i \(0.708333\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 1.36603 1.36603i 1.36603 1.36603i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.00000i 1.00000i
\(801\) 1.78480 + 0.478235i 1.78480 + 0.478235i
\(802\) 1.73205 1.73205