Properties

Label 3528.1.bi.a.2909.2
Level $3528$
Weight $1$
Character 3528.2909
Analytic conductor $1.761$
Analytic rank $0$
Dimension $8$
Projective image $D_{12}$
CM discriminant -56
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.bi (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.76070136457\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(D_{12}\)
Projective field Galois closure of \(\mathbb{Q}[x]/(x^{12} + \cdots)\)

Embedding invariants

Embedding label 2909.2
Root \(0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 3528.2909
Dual form 3528.1.bi.a.1157.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(0.965926 - 0.258819i) q^{3} -1.00000 q^{4} +(-0.258819 + 0.448288i) q^{5} +(-0.258819 - 0.965926i) q^{6} +1.00000i q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(0.965926 - 0.258819i) q^{3} -1.00000 q^{4} +(-0.258819 + 0.448288i) q^{5} +(-0.258819 - 0.965926i) q^{6} +1.00000i q^{8} +(0.866025 - 0.500000i) q^{9} +(0.448288 + 0.258819i) q^{10} +(-0.965926 + 0.258819i) q^{12} +(-1.22474 + 0.707107i) q^{13} +(-0.133975 + 0.500000i) q^{15} +1.00000 q^{16} +(-0.500000 - 0.866025i) q^{18} +(1.67303 - 0.965926i) q^{19} +(0.258819 - 0.448288i) q^{20} +(1.50000 + 0.866025i) q^{23} +(0.258819 + 0.965926i) q^{24} +(0.366025 + 0.633975i) q^{25} +(0.707107 + 1.22474i) q^{26} +(0.707107 - 0.707107i) q^{27} +(0.500000 + 0.133975i) q^{30} -1.00000i q^{32} +(-0.866025 + 0.500000i) q^{36} +(-0.965926 - 1.67303i) q^{38} +(-1.00000 + 1.00000i) q^{39} +(-0.448288 - 0.258819i) q^{40} +0.517638i q^{45} +(0.866025 - 1.50000i) q^{46} +(0.965926 - 0.258819i) q^{48} +(0.633975 - 0.366025i) q^{50} +(1.22474 - 0.707107i) q^{52} +(-0.707107 - 0.707107i) q^{54} +(1.36603 - 1.36603i) q^{57} -1.41421 q^{59} +(0.133975 - 0.500000i) q^{60} -1.93185i q^{61} -1.00000 q^{64} -0.732051i q^{65} +(1.67303 + 0.448288i) q^{69} -1.00000i q^{71} +(0.500000 + 0.866025i) q^{72} +(0.517638 + 0.517638i) q^{75} +(-1.67303 + 0.965926i) q^{76} +(1.00000 + 1.00000i) q^{78} +1.73205 q^{79} +(-0.258819 + 0.448288i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-0.707107 + 1.22474i) q^{83} +0.517638 q^{90} +(-1.50000 - 0.866025i) q^{92} +1.00000i q^{95} +(-0.258819 - 0.965926i) q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{4} + O(q^{10}) \) \( 8q - 8q^{4} - 8q^{15} + 8q^{16} - 4q^{18} + 12q^{23} - 4q^{25} + 4q^{30} - 8q^{39} + 12q^{50} + 4q^{57} + 8q^{60} - 8q^{64} + 4q^{72} + 8q^{78} + 4q^{81} - 12q^{92} + O(q^{100}) \)

Character values

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

\(n\) \(785\) \(1081\) \(1765\) \(2647\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 1.00000i
\(3\) 0.965926 0.258819i 0.965926 0.258819i
\(4\) −1.00000 −1.00000
\(5\) −0.258819 + 0.448288i −0.258819 + 0.448288i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(6\) −0.258819 0.965926i −0.258819 0.965926i
\(7\) 0 0
\(8\) 1.00000i 1.00000i
\(9\) 0.866025 0.500000i 0.866025 0.500000i
\(10\) 0.448288 + 0.258819i 0.448288 + 0.258819i
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(13\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(14\) 0 0
\(15\) −0.133975 + 0.500000i −0.133975 + 0.500000i
\(16\) 1.00000 1.00000
\(17\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) −0.500000 0.866025i −0.500000 0.866025i
\(19\) 1.67303 0.965926i 1.67303 0.965926i 0.707107 0.707107i \(-0.250000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(20\) 0.258819 0.448288i 0.258819 0.448288i
\(21\) 0 0
\(22\) 0 0
\(23\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(25\) 0.366025 + 0.633975i 0.366025 + 0.633975i
\(26\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(27\) 0.707107 0.707107i 0.707107 0.707107i
\(28\) 0 0
\(29\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(30\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 1.00000i 1.00000i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) −0.965926 1.67303i −0.965926 1.67303i
\(39\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(40\) −0.448288 0.258819i −0.448288 0.258819i
\(41\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(42\) 0 0
\(43\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(44\) 0 0
\(45\) 0.517638i 0.517638i
\(46\) 0.866025 1.50000i 0.866025 1.50000i
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0.965926 0.258819i 0.965926 0.258819i
\(49\) 0 0
\(50\) 0.633975 0.366025i 0.633975 0.366025i
\(51\) 0 0
\(52\) 1.22474 0.707107i 1.22474 0.707107i
\(53\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(54\) −0.707107 0.707107i −0.707107 0.707107i
\(55\) 0 0
\(56\) 0 0
\(57\) 1.36603 1.36603i 1.36603 1.36603i
\(58\) 0 0
\(59\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(60\) 0.133975 0.500000i 0.133975 0.500000i
\(61\) 1.93185i 1.93185i −0.258819 0.965926i \(-0.583333\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −1.00000 −1.00000
\(65\) 0.732051i 0.732051i
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 1.67303 + 0.448288i 1.67303 + 0.448288i
\(70\) 0 0
\(71\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(72\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(73\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(74\) 0 0
\(75\) 0.517638 + 0.517638i 0.517638 + 0.517638i
\(76\) −1.67303 + 0.965926i −1.67303 + 0.965926i
\(77\) 0 0
\(78\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(79\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(80\) −0.258819 + 0.448288i −0.258819 + 0.448288i
\(81\) 0.500000 0.866025i 0.500000 0.866025i
\(82\) 0 0
\(83\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(90\) 0.517638 0.517638
\(91\) 0 0
\(92\) −1.50000 0.866025i −1.50000 0.866025i
\(93\) 0 0
\(94\) 0 0
\(95\) 1.00000i 1.00000i
\(96\) −0.258819 0.965926i −0.258819 0.965926i
\(97\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.366025 0.633975i −0.366025 0.633975i
\(101\) 0.965926 + 1.67303i 0.965926 + 1.67303i 0.707107 + 0.707107i \(0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(102\) 0 0
\(103\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(104\) −0.707107 1.22474i −0.707107 1.22474i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(108\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(109\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(114\) −1.36603 1.36603i −1.36603 1.36603i
\(115\) −0.776457 + 0.448288i −0.776457 + 0.448288i
\(116\) 0 0
\(117\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(118\) 1.41421i 1.41421i
\(119\) 0 0
\(120\) −0.500000 0.133975i −0.500000 0.133975i
\(121\) 0.500000 0.866025i 0.500000 0.866025i
\(122\) −1.93185 −1.93185
\(123\) 0 0
\(124\) 0 0
\(125\) −0.896575 −0.896575
\(126\) 0 0
\(127\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(128\) 1.00000i 1.00000i
\(129\) 0 0
\(130\) −0.732051 −0.732051
\(131\) −0.965926 + 1.67303i −0.965926 + 1.67303i −0.258819 + 0.965926i \(0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0.133975 + 0.500000i 0.133975 + 0.500000i
\(136\) 0 0
\(137\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(138\) 0.448288 1.67303i 0.448288 1.67303i
\(139\) 0.448288 0.258819i 0.448288 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.00000 −1.00000
\(143\) 0 0
\(144\) 0.866025 0.500000i 0.866025 0.500000i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(150\) 0.517638 0.517638i 0.517638 0.517638i
\(151\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(152\) 0.965926 + 1.67303i 0.965926 + 1.67303i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 1.00000 1.00000i 1.00000 1.00000i
\(157\) 1.93185i 1.93185i −0.258819 0.965926i \(-0.583333\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(158\) 1.73205i 1.73205i
\(159\) 0 0
\(160\) 0.448288 + 0.258819i 0.448288 + 0.258819i
\(161\) 0 0
\(162\) −0.866025 0.500000i −0.866025 0.500000i
\(163\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(167\) 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
\(171\) 0.965926 1.67303i 0.965926 1.67303i
\(172\) 0 0
\(173\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(178\) 0 0
\(179\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(180\) 0.517638i 0.517638i
\(181\) 0.517638i 0.517638i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(182\) 0 0
\(183\) −0.500000 1.86603i −0.500000 1.86603i
\(184\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 1.00000 1.00000
\(191\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(192\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(193\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(194\) 0 0
\(195\) −0.189469 0.707107i −0.189469 0.707107i
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) −0.633975 + 0.366025i −0.633975 + 0.366025i
\(201\) 0 0
\(202\) 1.67303 0.965926i 1.67303 0.965926i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.73205 1.73205
\(208\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) 0 0
\(213\) −0.258819 0.965926i −0.258819 0.965926i
\(214\) 0 0
\(215\) 0 0
\(216\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 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
\(225\) 0.633975 + 0.366025i 0.633975 + 0.366025i
\(226\) −0.500000 0.866025i −0.500000 0.866025i
\(227\) −0.258819 0.448288i −0.258819 0.448288i 0.707107 0.707107i \(-0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(228\) −1.36603 + 1.36603i −1.36603 + 1.36603i
\(229\) 0.448288 + 0.258819i 0.448288 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(230\) 0.448288 + 0.776457i 0.448288 + 0.776457i
\(231\) 0 0
\(232\) 0 0
\(233\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(234\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(235\) 0 0
\(236\) 1.41421 1.41421
\(237\) 1.67303 0.448288i 1.67303 0.448288i
\(238\) 0 0
\(239\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(240\) −0.133975 + 0.500000i −0.133975 + 0.500000i
\(241\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(242\) −0.866025 0.500000i −0.866025 0.500000i
\(243\) 0.258819 0.965926i 0.258819 0.965926i
\(244\) 1.93185i 1.93185i
\(245\) 0 0
\(246\) 0 0
\(247\) −1.36603 + 2.36603i −1.36603 + 2.36603i
\(248\) 0 0
\(249\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(250\) 0.896575i 0.896575i
\(251\) −0.517638 −0.517638 −0.258819 0.965926i \(-0.583333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 1.00000i 1.00000i
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0.732051i 0.732051i
\(261\) 0 0
\(262\) 1.67303 + 0.965926i 1.67303 + 0.965926i
\(263\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.965926 + 1.67303i −0.965926 + 1.67303i −0.258819 + 0.965926i \(0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(270\) 0.500000 0.133975i 0.500000 0.133975i
\(271\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −1.67303 0.448288i −1.67303 0.448288i
\(277\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(278\) −0.258819 0.448288i −0.258819 0.448288i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(282\) 0 0
\(283\) 1.93185i 1.93185i 0.258819 + 0.965926i \(0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(284\) 1.00000i 1.00000i
\(285\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(286\) 0 0
\(287\) 0 0
\(288\) −0.500000 0.866025i −0.500000 0.866025i
\(289\) −0.500000 0.866025i −0.500000 0.866025i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −0.965926 1.67303i −0.965926 1.67303i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 0.965926i \(-0.583333\pi\)
\(294\) 0 0
\(295\) 0.366025 0.633975i 0.366025 0.633975i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.44949 −2.44949
\(300\) −0.517638 0.517638i −0.517638 0.517638i
\(301\) 0 0
\(302\) 0.866025 0.500000i 0.866025 0.500000i
\(303\) 1.36603 + 1.36603i 1.36603 + 1.36603i
\(304\) 1.67303 0.965926i 1.67303 0.965926i
\(305\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(306\) 0 0
\(307\) 0.517638i 0.517638i −0.965926 0.258819i \(-0.916667\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) −1.00000 1.00000i −1.00000 1.00000i
\(313\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(314\) −1.93185 −1.93185
\(315\) 0 0
\(316\) −1.73205 −1.73205
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.258819 0.448288i 0.258819 0.448288i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(325\) −0.896575 0.517638i −0.896575 0.517638i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0.707107 1.22474i 0.707107 1.22474i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(338\) −0.866025 0.500000i −0.866025 0.500000i
\(339\) 0.707107 0.707107i 0.707107 0.707107i
\(340\) 0 0
\(341\) 0 0
\(342\) −1.67303 0.965926i −1.67303 0.965926i
\(343\) 0 0
\(344\) 0 0
\(345\) −0.633975 + 0.633975i −0.633975 + 0.633975i
\(346\) 1.41421i 1.41421i
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(350\) 0 0
\(351\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(352\) 0 0
\(353\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(354\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(355\) 0.448288 + 0.258819i 0.448288 + 0.258819i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(360\) −0.517638 −0.517638
\(361\) 1.36603 2.36603i 1.36603 2.36603i
\(362\) 0.517638 0.517638
\(363\) 0.258819 0.965926i 0.258819 0.965926i
\(364\) 0 0
\(365\) 0 0
\(366\) −1.86603 + 0.500000i −1.86603 + 0.500000i
\(367\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(368\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) 0 0
\(375\) −0.866025 + 0.232051i −0.866025 + 0.232051i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 1.00000i 1.00000i
\(381\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(382\) −1.00000 −1.00000
\(383\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(384\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(385\) 0 0
\(386\) 1.73205i 1.73205i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(390\) −0.707107 + 0.189469i −0.707107 + 0.189469i
\(391\) 0 0
\(392\) 0 0
\(393\) −0.500000 + 1.86603i −0.500000 + 1.86603i
\(394\) 0 0
\(395\) −0.448288 + 0.776457i −0.448288 + 0.776457i
\(396\) 0 0
\(397\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.366025 + 0.633975i 0.366025 + 0.633975i
\(401\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.965926 1.67303i −0.965926 1.67303i
\(405\) 0.258819 + 0.448288i 0.258819 + 0.448288i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 1.73205i 1.73205i
\(415\) −0.366025 0.633975i −0.366025 0.633975i
\(416\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(417\) 0.366025 0.366025i 0.366025 0.366025i
\(418\) 0 0
\(419\) 0.258819 + 0.448288i 0.258819 + 0.448288i 0.965926 0.258819i \(-0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(420\) 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 0
\(426\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) 0.707107 0.707107i 0.707107 0.707107i
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.34607 3.34607
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(450\) 0.366025 0.633975i 0.366025 0.633975i
\(451\) 0 0
\(452\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(453\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(454\) −0.448288 + 0.258819i −0.448288 + 0.258819i
\(455\) 0 0
\(456\) 1.36603 + 1.36603i 1.36603 + 1.36603i
\(457\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(458\) 0.258819 0.448288i 0.258819 0.448288i
\(459\) 0 0
\(460\) 0.776457 0.448288i 0.776457 0.448288i
\(461\) 0.965926 1.67303i 0.965926 1.67303i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(462\) 0 0
\(463\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(467\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(468\) 0.707107 1.22474i 0.707107 1.22474i
\(469\) 0 0
\(470\) 0 0
\(471\) −0.500000 1.86603i −0.500000 1.86603i
\(472\) 1.41421i 1.41421i
\(473\) 0 0
\(474\) −0.448288 1.67303i −0.448288 1.67303i
\(475\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(476\) 0 0
\(477\) 0 0
\(478\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(479\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(485\) 0 0
\(486\) −0.965926 0.258819i −0.965926 0.258819i
\(487\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(488\) 1.93185 1.93185
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 2.36603 + 1.36603i 2.36603 + 1.36603i
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(499\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0.896575 0.896575
\(501\) 0 0
\(502\) 0.517638i 0.517638i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) −1.00000 −1.00000
\(506\) 0 0
\(507\) 0.258819 0.965926i 0.258819 0.965926i
\(508\) 1.00000 1.00000
\(509\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 1.00000i
\(513\) 0.500000 1.86603i 0.500000 1.86603i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(520\) 0.732051 0.732051
\(521\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0 0
\(523\) 0.448288 0.258819i 0.448288 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(524\) 0.965926 1.67303i 0.965926 1.67303i
\(525\) 0 0
\(526\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(530\) 0 0
\(531\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 1.67303 + 0.965926i 1.67303 + 0.965926i
\(539\) 0 0
\(540\) −0.133975 0.500000i −0.133975 0.500000i
\(541\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(542\) 0 0
\(543\) 0.133975 + 0.500000i 0.133975 + 0.500000i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) 0 0
\(549\) −0.965926 1.67303i −0.965926 1.67303i
\(550\) 0 0
\(551\) 0 0
\(552\) −0.448288 + 1.67303i −0.448288 + 1.67303i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.448288 + 0.258819i −0.448288 + 0.258819i
\(557\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0.866025 1.50000i 0.866025 1.50000i
\(563\) 0.517638 0.517638 0.258819 0.965926i \(-0.416667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(564\) 0 0
\(565\) 0.517638i 0.517638i
\(566\) 1.93185 1.93185
\(567\) 0 0
\(568\) 1.00000 1.00000
\(569\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(570\) 0.965926 0.258819i 0.965926 0.258819i
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) −0.258819 0.965926i −0.258819 0.965926i
\(574\) 0 0
\(575\) 1.26795i 1.26795i
\(576\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(577\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(578\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(579\) −1.67303 + 0.448288i −1.67303 + 0.448288i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −0.366025 0.633975i −0.366025 0.633975i
\(586\) −1.67303 + 0.965926i −1.67303 + 0.965926i
\(587\) −0.965926 + 1.67303i −0.965926 + 1.67303i −0.258819 + 0.965926i \(0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −0.633975 0.366025i −0.633975 0.366025i
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 2.44949i 2.44949i
\(599\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(600\) −0.517638 + 0.517638i −0.517638 + 0.517638i
\(601\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −0.500000 0.866025i −0.500000 0.866025i
\(605\) 0.258819 + 0.448288i 0.258819 + 0.448288i
\(606\) 1.36603 1.36603i 1.36603 1.36603i
\(607\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(608\) −0.965926 1.67303i −0.965926 1.67303i
\(609\) 0 0
\(610\) 0.500000 0.866025i 0.500000 0.866025i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(614\) −0.517638 −0.517638
\(615\) 0 0
\(616\) 0 0
\(617\) −1.73205 + 1.00000i −1.73205 + 1.00000i −0.866025 + 0.500000i \(0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(618\) 0 0
\(619\) −1.67303 + 0.965926i −1.67303 + 0.965926i −0.707107 + 0.707107i \(0.750000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(620\) 0 0
\(621\) 1.67303 0.448288i 1.67303 0.448288i
\(622\) 0 0
\(623\) 0 0
\(624\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(625\) −0.133975 + 0.232051i −0.133975 + 0.232051i
\(626\) 0 0
\(627\) 0 0
\(628\) 1.93185i 1.93185i
\(629\) 0 0
\(630\) 0 0
\(631\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(632\) 1.73205i 1.73205i
\(633\) 0 0
\(634\) 0 0
\(635\) 0.258819 0.448288i 0.258819 0.448288i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −0.500000 0.866025i −0.500000 0.866025i
\(640\) −0.448288 0.258819i −0.448288 0.258819i
\(641\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(642\) 0 0
\(643\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(648\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(649\) 0 0
\(650\) −0.517638 + 0.896575i −0.517638 + 0.896575i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(654\) 0 0
\(655\) −0.500000 0.866025i −0.500000 0.866025i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(660\) 0 0
\(661\) 0.517638i 0.517638i −0.965926 0.258819i \(-0.916667\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −1.22474 0.707107i −1.22474 0.707107i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0.707107 + 0.189469i 0.707107 + 0.189469i
\(676\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(677\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(678\) −0.707107 0.707107i −0.707107 0.707107i
\(679\) 0 0
\(680\) 0 0
\(681\) −0.366025 0.366025i −0.366025 0.366025i
\(682\) 0 0
\(683\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(684\) −0.965926 + 1.67303i −0.965926 + 1.67303i
\(685\) 0 0
\(686\) 0 0
\(687\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(688\) 0 0
\(689\) 0 0
\(690\) 0.633975 + 0.633975i 0.633975 + 0.633975i
\(691\) 0.517638i 0.517638i −0.965926 0.258819i \(-0.916667\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(692\) 1.41421 1.41421
\(693\) 0 0
\(694\) 0 0
\(695\) 0.267949i 0.267949i
\(696\) 0 0
\(697\) 0 0
\(698\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(699\) −1.22474 + 1.22474i −1.22474 + 1.22474i
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 1.36603 0.366025i 1.36603 0.366025i
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0.258819 0.448288i 0.258819 0.448288i
\(711\) 1.50000 0.866025i 1.50000 0.866025i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −1.22474 + 1.22474i −1.22474 + 1.22474i
\(718\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(719\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(720\) 0.517638i 0.517638i
\(721\) 0 0
\(722\) −2.36603 1.36603i −2.36603 1.36603i
\(723\) 0 0
\(724\) 0.517638i 0.517638i
\(725\) 0 0
\(726\) −0.965926 0.258819i −0.965926 0.258819i
\(727\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(728\) 0 0
\(729\) 1.00000i 1.00000i
\(730\) 0 0
\(731\) 0 0
\(732\) 0.500000 + 1.86603i 0.500000 + 1.86603i
\(733\) −1.67303 0.965926i −1.67303 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.866025 1.50000i 0.866025 1.50000i
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) 0 0
\(741\) −0.707107 + 2.63896i −0.707107 + 2.63896i
\(742\) 0 0
\(743\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.41421i 1.41421i
\(748\) 0 0
\(749\) 0 0
\(750\) 0.232051 + 0.866025i 0.232051 + 0.866025i
\(751\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(752\) 0 0
\(753\) −0.500000 + 0.133975i −0.500000 + 0.133975i
\(754\) 0 0
\(755\) −0.517638 −0.517638
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −1.00000 −1.00000
\(761\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(762\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(763\) 0 0
\(764\) 1.00000i 1.00000i
\(765\) 0 0
\(766\) 0 0
\(767\) 1.73205 1.00000i 1.73205 1.00000i
\(768\) 0.965926 0.258819i 0.965926 0.258819i
\(769\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.73205 1.73205
\(773\) 0.965926 1.67303i 0.965926 1.67303i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0.189469 + 0.707107i 0.189469 + 0.707107i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(786\) 1.86603 + 0.500000i 1.86603 + 0.500000i
\(787\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(788\) 0 0
\(789\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(790\) 0.776457 + 0.448288i 0.776457 + 0.448288i
\(791\) 0 0
\(792\) 0 0
\(793\) 1.36603 + 2.36603i 1.36603 + 2.36603i
\(794\) −0.707107 1.22474i −0.707107 1.22474i
\(795\) 0 0
\(796\) 0 0
\(797\) 0.965926 + 1.67303i 0.965926 + 1.67303i 0.707107 + 0.707107i \(0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.633975 0.366025i 0.633975 0.366025i