Properties

Label 140.1.p.b.79.1
Level 140
Weight 1
Character 140.79
Analytic conductor 0.070
Analytic rank 0
Dimension 2
Projective image \(D_{3}\)
CM disc. -20
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 140.p (of order \(6\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.0698691017686\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Projective image \(D_{3}\)
Projective field Galois closure of 3.1.980.1

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\)
Character \(\chi\) = 140.79
Dual form 140.1.p.b.39.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{12} +1.00000 q^{14} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +1.00000 q^{20} +(0.500000 - 0.866025i) q^{21} +(-0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} -1.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(0.500000 + 0.866025i) q^{32} -1.00000 q^{35} +(0.500000 - 0.866025i) q^{40} -1.00000 q^{41} +(-0.500000 - 0.866025i) q^{42} +1.00000 q^{43} +(0.500000 + 0.866025i) q^{46} +(1.00000 - 1.73205i) q^{47} +1.00000 q^{48} +(-0.500000 + 0.866025i) q^{49} -1.00000 q^{50} +(-0.500000 + 0.866025i) q^{54} +(-0.500000 - 0.866025i) q^{56} +(-0.500000 + 0.866025i) q^{58} +(-0.500000 - 0.866025i) q^{60} +(0.500000 - 0.866025i) q^{61} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{67} +1.00000 q^{69} +(-0.500000 + 0.866025i) q^{70} +(-0.500000 + 0.866025i) q^{75} +(-0.500000 - 0.866025i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.500000 + 0.866025i) q^{82} +1.00000 q^{83} -1.00000 q^{84} +(0.500000 - 0.866025i) q^{86} +(0.500000 + 0.866025i) q^{87} +(0.500000 - 0.866025i) q^{89} +1.00000 q^{92} +(-1.00000 - 1.73205i) q^{94} +(0.500000 - 0.866025i) q^{96} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{3} - q^{4} - q^{5} - 2q^{6} + q^{7} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{3} - q^{4} - q^{5} - 2q^{6} + q^{7} - 2q^{8} + q^{10} - q^{12} + 2q^{14} + 2q^{15} - q^{16} + 2q^{20} + q^{21} - q^{23} + q^{24} - q^{25} - 2q^{27} + q^{28} - 2q^{29} + q^{30} + q^{32} - 2q^{35} + q^{40} - 2q^{41} - q^{42} + 2q^{43} + q^{46} + 2q^{47} + 2q^{48} - q^{49} - 2q^{50} - q^{54} - q^{56} - q^{58} - q^{60} + q^{61} + 2q^{64} - q^{67} + 2q^{69} - q^{70} - q^{75} - q^{80} + q^{81} - q^{82} + 2q^{83} - 2q^{84} + q^{86} + q^{87} + q^{89} + 2q^{92} - 2q^{94} + q^{96} + q^{98} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(101\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.500000 0.866025i
\(3\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(4\) −0.500000 0.866025i −0.500000 0.866025i
\(5\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(6\) −1.00000 −1.00000
\(7\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(8\) −1.00000 −1.00000
\(9\) 0 0
\(10\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(11\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(12\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 1.00000 1.00000
\(15\) 1.00000 1.00000
\(16\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(17\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) 0 0
\(19\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(20\) 1.00000 1.00000
\(21\) 0.500000 0.866025i 0.500000 0.866025i
\(22\) 0 0
\(23\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(24\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(25\) −0.500000 0.866025i −0.500000 0.866025i
\(26\) 0 0
\(27\) −1.00000 −1.00000
\(28\) 0.500000 0.866025i 0.500000 0.866025i
\(29\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 0.500000 0.866025i 0.500000 0.866025i
\(31\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(32\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(33\) 0 0
\(34\) 0 0
\(35\) −1.00000 −1.00000
\(36\) 0 0
\(37\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.500000 0.866025i 0.500000 0.866025i
\(41\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) −0.500000 0.866025i −0.500000 0.866025i
\(43\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(47\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(48\) 1.00000 1.00000
\(49\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(50\) −1.00000 −1.00000
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(55\) 0 0
\(56\) −0.500000 0.866025i −0.500000 0.866025i
\(57\) 0 0
\(58\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(59\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(60\) −0.500000 0.866025i −0.500000 0.866025i
\(61\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(68\) 0 0
\(69\) 1.00000 1.00000
\(70\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(74\) 0 0
\(75\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(80\) −0.500000 0.866025i −0.500000 0.866025i
\(81\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(82\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(83\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(84\) −1.00000 −1.00000
\(85\) 0 0
\(86\) 0.500000 0.866025i 0.500000 0.866025i
\(87\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(88\) 0 0
\(89\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.00000 1.00000
\(93\) 0 0
\(94\) −1.00000 1.73205i −1.00000 1.73205i
\(95\) 0 0
\(96\) 0.500000 0.866025i 0.500000 0.866025i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(99\) 0 0
\(100\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(101\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 0 0
\(103\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(104\) 0 0
\(105\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(106\) 0 0
\(107\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(108\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(109\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.00000 −1.00000
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) −0.500000 0.866025i −0.500000 0.866025i
\(116\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −1.00000 −1.00000
\(121\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(122\) −0.500000 0.866025i −0.500000 0.866025i
\(123\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(124\) 0 0
\(125\) 1.00000 1.00000
\(126\) 0 0
\(127\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(128\) 0.500000 0.866025i 0.500000 0.866025i
\(129\) −0.500000 0.866025i −0.500000 0.866025i
\(130\) 0 0
\(131\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.00000 −1.00000
\(135\) 0.500000 0.866025i 0.500000 0.866025i
\(136\) 0 0
\(137\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(138\) 0.500000 0.866025i 0.500000 0.866025i
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(141\) −2.00000 −2.00000
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0.500000 0.866025i 0.500000 0.866025i
\(146\) 0 0
\(147\) 1.00000 1.00000
\(148\) 0 0
\(149\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(150\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(151\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −1.00000 −1.00000
\(161\) −1.00000 −1.00000
\(162\) 1.00000 1.00000
\(163\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(164\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(165\) 0 0
\(166\) 0.500000 0.866025i 0.500000 0.866025i
\(167\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(168\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) −0.500000 0.866025i −0.500000 0.866025i
\(173\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(174\) 1.00000 1.00000
\(175\) 0.500000 0.866025i 0.500000 0.866025i
\(176\) 0 0
\(177\) 0 0
\(178\) −0.500000 0.866025i −0.500000 0.866025i
\(179\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(180\) 0 0
\(181\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(182\) 0 0
\(183\) −1.00000 −1.00000
\(184\) 0.500000 0.866025i 0.500000 0.866025i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −2.00000 −2.00000
\(189\) −0.500000 0.866025i −0.500000 0.866025i
\(190\) 0 0
\(191\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) −0.500000 0.866025i −0.500000 0.866025i
\(193\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.00000 1.00000
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(200\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(201\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(202\) 1.00000 1.00000
\(203\) −0.500000 0.866025i −0.500000 0.866025i
\(204\) 0 0
\(205\) 0.500000 0.866025i 0.500000 0.866025i
\(206\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 1.00000 1.00000
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(215\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(216\) 1.00000 1.00000
\(217\) 0 0
\(218\) 1.00000 1.00000
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(224\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(225\) 0 0
\(226\) 0 0
\(227\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(228\) 0 0
\(229\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) −1.00000 −1.00000
\(231\) 0 0
\(232\) 1.00000 1.00000
\(233\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(234\) 0 0
\(235\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(241\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(242\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(243\) 0 0
\(244\) −1.00000 −1.00000
\(245\) −0.500000 0.866025i −0.500000 0.866025i
\(246\) 1.00000 1.00000
\(247\) 0 0
\(248\) 0 0
\(249\) −0.500000 0.866025i −0.500000 0.866025i
\(250\) 0.500000 0.866025i 0.500000 0.866025i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.500000 0.866025i
\(257\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) −1.00000 −1.00000
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −1.00000 −1.00000
\(268\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(269\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) −0.500000 0.866025i −0.500000 0.866025i
\(271\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −0.500000 0.866025i −0.500000 0.866025i
\(277\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 1.00000 1.00000
\(281\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(282\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(283\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.500000 0.866025i −0.500000 0.866025i
\(288\) 0 0
\(289\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(290\) −0.500000 0.866025i −0.500000 0.866025i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0.500000 0.866025i 0.500000 0.866025i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −0.500000 0.866025i −0.500000 0.866025i
\(299\) 0 0
\(300\) 1.00000 1.00000
\(301\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(302\) 0 0
\(303\) 0.500000 0.866025i 0.500000 0.866025i
\(304\) 0 0
\(305\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(306\) 0 0
\(307\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(308\) 0 0
\(309\) 1.00000 1.00000
\(310\) 0 0
\(311\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(312\) 0 0
\(313\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(321\) 1.00000 1.00000
\(322\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(323\) 0 0
\(324\) 0.500000 0.866025i 0.500000 0.866025i
\(325\) 0 0
\(326\) −1.00000 1.73205i −1.00000 1.73205i
\(327\) 0.500000 0.866025i 0.500000 0.866025i
\(328\) 1.00000 1.00000
\(329\) 2.00000 2.00000
\(330\) 0 0
\(331\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) −0.500000 0.866025i −0.500000 0.866025i
\(333\) 0 0
\(334\) 0.500000 0.866025i 0.500000 0.866025i
\(335\) 1.00000 1.00000
\(336\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0.500000 0.866025i 0.500000 0.866025i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −1.00000
\(344\) −1.00000 −1.00000
\(345\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(346\) 0 0
\(347\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(348\) 0.500000 0.866025i 0.500000 0.866025i
\(349\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) −0.500000 0.866025i −0.500000 0.866025i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1.00000 −1.00000
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(360\) 0 0
\(361\) −0.500000 0.866025i −0.500000 0.866025i
\(362\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(363\) 1.00000 1.00000
\(364\) 0 0
\(365\) 0 0
\(366\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(367\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(368\) −0.500000 0.866025i −0.500000 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
\(375\) −0.500000 0.866025i −0.500000 0.866025i
\(376\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(377\) 0 0
\(378\) −1.00000 −1.00000
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(382\) 0 0
\(383\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(384\) −1.00000 −1.00000
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.500000 0.866025i 0.500000 0.866025i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(402\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(403\) 0 0
\(404\) 0.500000 0.866025i 0.500000 0.866025i
\(405\) −1.00000 −1.00000
\(406\) −1.00000 −1.00000
\(407\) 0 0
\(408\) 0 0
\(409\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) −0.500000 0.866025i −0.500000 0.866025i
\(411\) 0 0
\(412\) 1.00000 1.00000
\(413\) 0 0
\(414\) 0 0
\(415\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0.500000 0.866025i 0.500000 0.866025i
\(421\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.00000 1.00000
\(428\) 1.00000 1.00000
\(429\) 0 0
\(430\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) 0.500000 0.866025i 0.500000 0.866025i
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) −1.00000 −1.00000
\(436\) 0.500000 0.866025i 0.500000 0.866025i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(444\) 0 0
\(445\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(446\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(447\) −1.00000 −1.00000
\(448\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(449\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 2.00000 2.00000
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(459\) 0 0
\(460\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(461\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(462\) 0 0
\(463\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(464\) 0.500000 0.866025i 0.500000 0.866025i
\(465\) 0 0
\(466\) 0 0
\(467\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(468\) 0 0
\(469\) 0.500000 0.866025i 0.500000 0.866025i
\(470\) 2.00000 2.00000
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(481\) 0 0
\(482\) −2.00000 −2.00000
\(483\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(484\) 1.00000 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(488\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(489\) −2.00000 −2.00000
\(490\) −1.00000 −1.00000
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0.500000 0.866025i 0.500000 0.866025i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −1.00000 −1.00000
\(499\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) −0.500000 0.866025i −0.500000 0.866025i
\(501\) −0.500000 0.866025i −0.500000 0.866025i
\(502\) 0 0
\(503\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(504\) 0 0
\(505\) −1.00000 −1.00000
\(506\) 0 0
\(507\) −0.500000 0.866025i −0.500000 0.866025i
\(508\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(509\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 0 0
\(514\) 0 0
\(515\) −0.500000 0.866025i −0.500000 0.866025i
\(516\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(522\) 0 0
\(523\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(524\) 0 0
\(525\) −1.00000 −1.00000
\(526\) −1.00000 −1.00000
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(535\) −0.500000 0.866025i −0.500000 0.866025i
\(536\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(537\) 0 0
\(538\) 1.00000 1.00000
\(539\) 0 0
\(540\) −1.00000 −1.00000
\(541\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(542\) 0 0
\(543\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(544\) 0 0
\(545\) −1.00000 −1.00000
\(546\) 0 0
\(547\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) −1.00000 −1.00000
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.500000 0.866025i 0.500000 0.866025i
\(561\) 0 0
\(562\) 1.00000 1.73205i 1.00000 1.73205i
\(563\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(564\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(565\) 0 0
\(566\) 2.00000 2.00000
\(567\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(568\) 0 0
\(569\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) 0 0
\(571\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −1.00000 −1.00000
\(575\) 1.00000 1.00000
\(576\) 0 0
\(577\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(578\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(579\) 0 0
\(580\) −1.00000 −1.00000
\(581\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(588\) −0.500000 0.866025i −0.500000 0.866025i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.00000 −1.00000
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(600\) 0.500000 0.866025i 0.500000 0.866025i
\(601\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(602\) 1.00000 1.00000
\(603\) 0 0
\(604\) 0 0
\(605\) −0.500000 0.866025i −0.500000 0.866025i
\(606\) −0.500000 0.866025i −0.500000 0.866025i
\(607\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(608\) 0 0
\(609\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(610\) 1.00000 1.00000
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(614\) 0.500000 0.866025i 0.500000 0.866025i
\(615\) −1.00000 −1.00000
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0.500000 0.866025i 0.500000 0.866025i
\(619\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(620\) 0 0
\(621\) 0.500000 0.866025i 0.500000 0.866025i
\(622\) 0 0
\(623\) 1.00000 1.00000
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(626\) 0 0
\(627\) 0 0
\(628\) 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
\(635\) 1.00000 1.73205i 1.00000 1.73205i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(641\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 0.500000 0.866025i 0.500000 0.866025i
\(643\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(644\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(645\) 1.00000 1.00000
\(646\) 0 0
\(647\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(648\) −0.500000 0.866025i −0.500000 0.866025i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −2.00000 −2.00000
\(653\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(654\) −0.500000 0.866025i −0.500000 0.866025i
\(655\) 0 0
\(656\) 0.500000 0.866025i 0.500000 0.866025i
\(657\) 0 0
\(658\) 1.00000 1.73205i 1.00000 1.73205i
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −1.00000 −1.00000
\(665\) 0 0
\(666\) 0 0
\(667\) 0.500000 0.866025i 0.500000 0.866025i
\(668\) −0.500000 0.866025i −0.500000 0.866025i
\(669\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(670\) 0.500000 0.866025i 0.500000 0.866025i
\(671\) 0 0
\(672\) 1.00000 1.00000
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(676\) −0.500000 0.866025i −0.500000 0.866025i
\(677\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.00000 1.73205i 1.00000 1.73205i
\(682\) 0 0
\(683\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(687\) 2.00000 2.00000
\(688\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(689\) 0 0
\(690\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(691\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −1.00000 −1.00000
\(695\) 0 0
\(696\) −0.500000 0.866025i −0.500000 0.866025i
\(697\) 0 0
\(698\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(699\) 0 0
\(700\) −1.00000 −1.00000
\(701\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 1.00000 1.73205i 1.00000 1.73205i
\(706\) 0 0
\(707\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(708\) 0 0
\(709\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(720\) 0 0
\(721\) −1.00000 −1.00000
\(722\) −1.00000 −1.00000
\(723\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(724\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(725\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(726\) 0.500000 0.866025i 0.500000 0.866025i
\(727\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(733\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(734\) −1.00000 −1.00000
\(735\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(736\) −1.00000 −1.00000
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(744\) 0 0
\(745\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.00000 −1.00000
\(750\) −1.00000 −1.00000
\(751\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(762\) 2.00000 2.00000
\(763\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(764\) 0 0
\(765\) 0 0
\(766\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(767\) 0 0
\(768\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(769\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −2.00000 −2.00000
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 1.00000 1.00000
\(784\) −0.500000 0.866025i −0.500000 0.866025i
\(785\) 0 0
\(786\) 0 0
\(787\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(788\) 0 0
\(789\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.500000 0.866025i 0.500000 0.866025i
\(801\) 0 0
\(802\) −0.500000 0.866025i −0.500000 0.866025i
\(803\) 0 0
\(804\) 1.00000 1.00000
\(805\) 0.500000 0.866025i 0.500000 0.866025i
\(806\) 0 0
\(807\) 0.500000 0.866025i 0.500000 0.866025i
\(808\) −0.500000 0.866025i −0.500000 0.866025i
\(809\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(810\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(813\) 0 0
\(814\) 0 0