Properties

Label 180.1.p.a.139.1
Level $180$
Weight $1$
Character 180.139
Analytic conductor $0.090$
Analytic rank $0$
Dimension $2$
Projective image $D_{3}$
CM discriminant -20
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 180.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.0898317022739\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.1620.1
Artin image: $C_3\times S_3$
Artin field: Galois closure of 6.0.648000.1

Embedding invariants

Embedding label 139.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 180.139
Dual form 180.1.p.a.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +(-0.500000 - 0.866025i) q^{12} +(0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{20} -1.00000 q^{21} +(0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} -1.00000 q^{28} +(0.500000 + 0.866025i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(-0.500000 + 0.866025i) q^{32} -1.00000 q^{35} +1.00000 q^{36} +(-0.500000 + 0.866025i) q^{40} +(0.500000 - 0.866025i) q^{41} +(0.500000 + 0.866025i) q^{42} +(-1.00000 - 1.73205i) q^{43} +1.00000 q^{45} -1.00000 q^{46} +(0.500000 + 0.866025i) q^{47} +1.00000 q^{48} +(-0.500000 + 0.866025i) q^{50} +(-0.500000 - 0.866025i) q^{54} +(0.500000 + 0.866025i) q^{56} +(0.500000 - 0.866025i) q^{58} +1.00000 q^{60} +(0.500000 + 0.866025i) q^{61} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{67} +(0.500000 + 0.866025i) q^{69} +(0.500000 + 0.866025i) q^{70} +(-0.500000 - 0.866025i) q^{72} +1.00000 q^{75} +1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} -1.00000 q^{82} +(0.500000 + 0.866025i) q^{83} +(0.500000 - 0.866025i) q^{84} +(-1.00000 + 1.73205i) q^{86} -1.00000 q^{87} -1.00000 q^{89} +(-0.500000 - 0.866025i) q^{90} +(0.500000 + 0.866025i) q^{92} +(0.500000 - 0.866025i) q^{94} +(-0.500000 - 0.866025i) q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{3} - q^{4} - q^{5} + 2 q^{6} + q^{7} + 2 q^{8} - q^{9} + O(q^{10}) \) \( 2 q - q^{2} - q^{3} - q^{4} - q^{5} + 2 q^{6} + q^{7} + 2 q^{8} - q^{9} + 2 q^{10} - q^{12} + q^{14} - q^{15} - q^{16} - q^{18} - q^{20} - 2 q^{21} + q^{23} - q^{24} - q^{25} + 2 q^{27} - 2 q^{28} + q^{29} - q^{30} - q^{32} - 2 q^{35} + 2 q^{36} - q^{40} + q^{41} + q^{42} - 2 q^{43} + 2 q^{45} - 2 q^{46} + q^{47} + 2 q^{48} - q^{50} - q^{54} + q^{56} + q^{58} + 2 q^{60} + q^{61} + q^{63} + 2 q^{64} + q^{67} + q^{69} + q^{70} - q^{72} + 2 q^{75} + 2 q^{80} - q^{81} - 2 q^{82} + q^{83} + q^{84} - 2 q^{86} - 2 q^{87} - 2 q^{89} - q^{90} + q^{92} + q^{94} - q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/180\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(91\) \(101\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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
\(4\) −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 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) 1.00000 1.00000
\(9\) −0.500000 0.866025i −0.500000 0.866025i
\(10\) 1.00000 1.00000
\(11\) 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 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(14\) 0.500000 0.866025i 0.500000 0.866025i
\(15\) −0.500000 0.866025i −0.500000 0.866025i
\(16\) −0.500000 0.866025i −0.500000 0.866025i
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −0.500000 0.866025i −0.500000 0.866025i
\(21\) −1.00000 −1.00000
\(22\) 0 0
\(23\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(24\) −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
\(28\) −1.00000 −1.00000
\(29\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(31\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(33\) 0 0
\(34\) 0 0
\(35\) −1.00000 −1.00000
\(36\) 1.00000 1.00000
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(41\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(42\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(43\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(44\) 0 0
\(45\) 1.00000 1.00000
\(46\) −1.00000 −1.00000
\(47\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(48\) 1.00000 1.00000
\(49\) 0 0
\(50\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) −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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 1.00000 1.00000
\(61\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 0 0
\(63\) 0.500000 0.866025i 0.500000 0.866025i
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(68\) 0 0
\(69\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(70\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −0.500000 0.866025i −0.500000 0.866025i
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 1.00000 1.00000
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(80\) 1.00000 1.00000
\(81\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(82\) −1.00000 −1.00000
\(83\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(84\) 0.500000 0.866025i 0.500000 0.866025i
\(85\) 0 0
\(86\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(87\) −1.00000 −1.00000
\(88\) 0 0
\(89\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(90\) −0.500000 0.866025i −0.500000 0.866025i
\(91\) 0 0
\(92\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(93\) 0 0
\(94\) 0.500000 0.866025i 0.500000 0.866025i
\(95\) 0 0
\(96\) −0.500000 0.866025i −0.500000 0.866025i
\(97\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000 1.00000
\(101\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(102\) 0 0
\(103\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(104\) 0 0
\(105\) 0.500000 0.866025i 0.500000 0.866025i
\(106\) 0 0
\(107\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(109\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.500000 0.866025i 0.500000 0.866025i
\(113\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(114\) 0 0
\(115\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(116\) −1.00000 −1.00000
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −0.500000 0.866025i −0.500000 0.866025i
\(121\) −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
\(126\) −1.00000 −1.00000
\(127\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(128\) −0.500000 0.866025i −0.500000 0.866025i
\(129\) 2.00000 2.00000
\(130\) 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 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 0.500000 0.866025i 0.500000 0.866025i
\(141\) −1.00000 −1.00000
\(142\) 0 0
\(143\) 0 0
\(144\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(145\) −1.00000 −1.00000
\(146\) 0 0
\(147\) 0 0
\(148\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −0.500000 0.866025i −0.500000 0.866025i
\(161\) 1.00000 1.00000
\(162\) 1.00000 1.00000
\(163\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(164\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(165\) 0 0
\(166\) 0.500000 0.866025i 0.500000 0.866025i
\(167\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(168\) −1.00000 −1.00000
\(169\) −0.500000 0.866025i −0.500000 0.866025i
\(170\) 0 0
\(171\) 0 0
\(172\) 2.00000 2.00000
\(173\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(175\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(181\) −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
\(188\) −1.00000 −1.00000
\(189\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(190\) 0 0
\(191\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(193\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −0.500000 0.866025i −0.500000 0.866025i
\(201\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(202\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(203\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(204\) 0 0
\(205\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(206\) 2.00000 2.00000
\(207\) −1.00000 −1.00000
\(208\) 0 0
\(209\) 0 0
\(210\) −1.00000 −1.00000
\(211\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(215\) 2.00000 2.00000
\(216\) 1.00000 1.00000
\(217\) 0 0
\(218\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(224\) −1.00000 −1.00000
\(225\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(226\) 0 0
\(227\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(228\) 0 0
\(229\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(230\) 0.500000 0.866025i 0.500000 0.866025i
\(231\) 0 0
\(232\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) −1.00000 −1.00000
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(241\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) 1.00000 1.00000
\(243\) −0.500000 0.866025i −0.500000 0.866025i
\(244\) −1.00000 −1.00000
\(245\) 0 0
\(246\) 0.500000 0.866025i 0.500000 0.866025i
\(247\) 0 0
\(248\) 0 0
\(249\) −1.00000 −1.00000
\(250\) −0.500000 0.866025i −0.500000 0.866025i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(253\) 0 0
\(254\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(255\) 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 1.73205i −1.00000 1.73205i
\(259\) 0 0
\(260\) 0 0
\(261\) 0.500000 0.866025i 0.500000 0.866025i
\(262\) 0 0
\(263\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0.500000 0.866025i 0.500000 0.866025i
\(268\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(269\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 1.00000 1.00000
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −1.00000 −1.00000
\(277\) 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
\(281\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(282\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(283\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.00000 1.00000
\(288\) 1.00000 1.00000
\(289\) 1.00000 1.00000
\(290\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −1.00000 −1.00000
\(299\) 0 0
\(300\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(301\) 1.00000 1.73205i 1.00000 1.73205i
\(302\) 0 0
\(303\) 2.00000 2.00000
\(304\) 0 0
\(305\) −1.00000 −1.00000
\(306\) 0 0
\(307\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(308\) 0 0
\(309\) −1.00000 1.73205i −1.00000 1.73205i
\(310\) 0 0
\(311\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) 0 0
\(313\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(314\) 0 0
\(315\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(316\) 0 0
\(317\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(321\) 0.500000 0.866025i 0.500000 0.866025i
\(322\) −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
\(328\) 0.500000 0.866025i 0.500000 0.866025i
\(329\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(330\) 0 0
\(331\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) −1.00000 −1.00000
\(333\) 0 0
\(334\) −1.00000 −1.00000
\(335\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(336\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(337\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(338\) −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 1.73205i −1.00000 1.73205i
\(345\) −1.00000 −1.00000
\(346\) 0 0
\(347\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(348\) 0.500000 0.866025i 0.500000 0.866025i
\(349\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) −1.00000 −1.00000
\(351\) 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
\(356\) 0.500000 0.866025i 0.500000 0.866025i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 1.00000 1.00000
\(361\) 1.00000 1.00000
\(362\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(363\) −0.500000 0.866025i −0.500000 0.866025i
\(364\) 0 0
\(365\) 0 0
\(366\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(367\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(368\) −1.00000 −1.00000
\(369\) −1.00000 −1.00000
\(370\) 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
\(376\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(377\) 0 0
\(378\) 0.500000 0.866025i 0.500000 0.866025i
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0.500000 0.866025i 0.500000 0.866025i
\(382\) 0 0
\(383\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(384\) 1.00000 1.00000
\(385\) 0 0
\(386\) 0 0
\(387\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(388\) 0 0
\(389\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(401\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 0.500000 0.866025i 0.500000 0.866025i
\(403\) 0 0
\(404\) 2.00000 2.00000
\(405\) −0.500000 0.866025i −0.500000 0.866025i
\(406\) 1.00000 1.00000
\(407\) 0 0
\(408\) 0 0
\(409\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) 0.500000 0.866025i 0.500000 0.866025i
\(411\) 0 0
\(412\) −1.00000 1.73205i −1.00000 1.73205i
\(413\) 0 0
\(414\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(415\) −1.00000 −1.00000
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(420\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(421\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(422\) 0 0
\(423\) 0.500000 0.866025i 0.500000 0.866025i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(428\) 0.500000 0.866025i 0.500000 0.866025i
\(429\) 0 0
\(430\) −1.00000 1.73205i −1.00000 1.73205i
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −0.500000 0.866025i −0.500000 0.866025i
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0.500000 0.866025i 0.500000 0.866025i
\(436\) 0.500000 0.866025i 0.500000 0.866025i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(444\) 0 0
\(445\) 0.500000 0.866025i 0.500000 0.866025i
\(446\) 0.500000 0.866025i 0.500000 0.866025i
\(447\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(448\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(449\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(450\) 1.00000 1.00000
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(458\) −1.00000 −1.00000
\(459\) 0 0
\(460\) −1.00000 −1.00000
\(461\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(462\) 0 0
\(463\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(464\) 0.500000 0.866025i 0.500000 0.866025i
\(465\) 0 0
\(466\) 0 0
\(467\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(468\) 0 0
\(469\) 1.00000 1.00000
\(470\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(471\) 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 \(0.333333\pi\)
\(480\) 1.00000 1.00000
\(481\) 0 0
\(482\) 0.500000 0.866025i 0.500000 0.866025i
\(483\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(484\) −0.500000 0.866025i −0.500000 0.866025i
\(485\) 0 0
\(486\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(487\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(488\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(489\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(490\) 0 0
\(491\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(492\) −1.00000 −1.00000
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(499\) 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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(504\) 0.500000 0.866025i 0.500000 0.866025i
\(505\) 2.00000 2.00000
\(506\) 0 0
\(507\) 1.00000 1.00000
\(508\) 0.500000 0.866025i 0.500000 0.866025i
\(509\) 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
\(515\) −1.00000 1.73205i −1.00000 1.73205i
\(516\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) −1.00000 −1.00000
\(523\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(524\) 0 0
\(525\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(526\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −1.00000 −1.00000
\(535\) 0.500000 0.866025i 0.500000 0.866025i
\(536\) 0.500000 0.866025i 0.500000 0.866025i
\(537\) 0 0
\(538\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(539\) 0 0
\(540\) −0.500000 0.866025i −0.500000 0.866025i
\(541\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) 0 0
\(543\) 0.500000 0.866025i 0.500000 0.866025i
\(544\) 0 0
\(545\) 0.500000 0.866025i 0.500000 0.866025i
\(546\) 0 0
\(547\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) 0 0
\(549\) 0.500000 0.866025i 0.500000 0.866025i
\(550\) 0 0
\(551\) 0 0
\(552\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(561\) 0 0
\(562\) 0.500000 0.866025i 0.500000 0.866025i
\(563\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(564\) 0.500000 0.866025i 0.500000 0.866025i
\(565\) 0 0
\(566\) −1.00000 −1.00000
\(567\) −1.00000 −1.00000
\(568\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −0.500000 0.866025i −0.500000 0.866025i
\(575\) −1.00000 −1.00000
\(576\) −0.500000 0.866025i −0.500000 0.866025i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −0.500000 0.866025i −0.500000 0.866025i
\(579\) 0 0
\(580\) 0.500000 0.866025i 0.500000 0.866025i
\(581\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 1.00000 1.00000
\(601\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(602\) −2.00000 −2.00000
\(603\) −1.00000 −1.00000
\(604\) 0 0
\(605\) −0.500000 0.866025i −0.500000 0.866025i
\(606\) −1.00000 1.73205i −1.00000 1.73205i
\(607\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(608\) 0 0
\(609\) −0.500000 0.866025i −0.500000 0.866025i
\(610\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(615\) −1.00000 −1.00000
\(616\) 0 0
\(617\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(618\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(619\) 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
\(623\) −0.500000 0.866025i −0.500000 0.866025i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0.500000 0.866025i 0.500000 0.866025i
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.500000 0.866025i 0.500000 0.866025i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 1.00000 1.00000
\(641\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) −1.00000 −1.00000
\(643\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(644\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(645\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(646\) 0 0
\(647\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(648\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(653\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(654\) −1.00000 −1.00000
\(655\) 0 0
\(656\) −1.00000 −1.00000
\(657\) 0 0
\(658\) 1.00000 1.00000
\(659\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(660\) 0 0
\(661\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(665\) 0 0
\(666\) 0 0
\(667\) 1.00000 1.00000
\(668\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(669\) −1.00000 −1.00000
\(670\) 0.500000 0.866025i 0.500000 0.866025i
\(671\) 0 0
\(672\) 0.500000 0.866025i 0.500000 0.866025i
\(673\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(674\) 0 0
\(675\) −0.500000 0.866025i −0.500000 0.866025i
\(676\) 1.00000 1.00000
\(677\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 2.00000 2.00000
\(682\) 0 0
\(683\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.500000 0.866025i −0.500000 0.866025i
\(687\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(688\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(689\) 0 0
\(690\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(691\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 2.00000 2.00000
\(695\) 0 0
\(696\) −1.00000 −1.00000
\(697\) 0 0
\(698\) 0.500000 0.866025i 0.500000 0.866025i
\(699\) 0 0
\(700\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(701\) −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
\(705\) 0.500000 0.866025i 0.500000 0.866025i
\(706\) 0 0
\(707\) 1.00000 1.73205i 1.00000 1.73205i
\(708\) 0 0
\(709\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.00000 −1.00000
\(713\) 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 \(\pi\)
\(720\) −0.500000 0.866025i −0.500000 0.866025i
\(721\) −2.00000 −2.00000
\(722\) −0.500000 0.866025i −0.500000 0.866025i
\(723\) −1.00000 −1.00000
\(724\) 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
\(727\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(728\) 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 + 1.73205i −1.00000 + 1.73205i
\(735\) 0 0
\(736\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(737\) 0 0
\(738\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(744\) 0 0
\(745\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(746\) 0 0
\(747\) 0.500000 0.866025i 0.500000 0.866025i
\(748\) 0 0
\(749\) −0.500000 0.866025i −0.500000 0.866025i
\(750\) 1.00000 1.00000
\(751\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 0.500000 0.866025i 0.500000 0.866025i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −1.00000 −1.00000
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(762\) −1.00000 −1.00000
\(763\) −0.500000 0.866025i −0.500000 0.866025i
\(764\) 0 0
\(765\) 0 0
\(766\) 2.00000 2.00000
\(767\) 0 0
\(768\) −0.500000 0.866025i −0.500000 0.866025i
\(769\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 2.00000 2.00000
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.500000 0.866025i 0.500000 0.866025i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(788\) 0 0
\(789\) 2.00000 2.00000
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(798\) 0 0
\(799\)