Properties

Label 168.1.s.b.149.1
Level $168$
Weight $1$
Character 168.149
Analytic conductor $0.084$
Analytic rank $0$
Dimension $2$
Projective image $D_{3}$
CM discriminant -24
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 168.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.0838429221223\)
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 3.1.1176.1
Artin image: $C_6\times S_3$
Artin field: Galois closure of 12.0.458838245376.1

Embedding invariants

Embedding label 149.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 168.149
Dual form 168.1.s.b.53.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} -1.00000 q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{18} +1.00000 q^{20} +(0.500000 - 0.866025i) q^{21} -1.00000 q^{22} +(-0.500000 - 0.866025i) q^{24} -1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +1.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(0.500000 + 0.866025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{33} +1.00000 q^{35} +1.00000 q^{36} +(0.500000 - 0.866025i) q^{40} +(-0.500000 - 0.866025i) q^{42} +(-0.500000 + 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{45} -1.00000 q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{53} +(-0.500000 + 0.866025i) q^{54} +1.00000 q^{55} +(0.500000 + 0.866025i) q^{56} +(0.500000 - 0.866025i) q^{58} +(-0.500000 - 0.866025i) q^{59} +(0.500000 + 0.866025i) q^{60} +1.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{66} +(0.500000 - 0.866025i) q^{70} +(0.500000 - 0.866025i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(-0.500000 + 0.866025i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +1.00000 q^{83} -1.00000 q^{84} +(0.500000 + 0.866025i) q^{87} +(0.500000 + 0.866025i) q^{88} -1.00000 q^{90} +(-0.500000 + 0.866025i) q^{93} +(-0.500000 + 0.866025i) q^{96} -1.00000 q^{97} +(0.500000 + 0.866025i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + q^{3} - q^{4} - q^{5} + 2q^{6} - q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} + q^{3} - q^{4} - q^{5} + 2q^{6} - q^{7} - 2q^{8} - q^{9} + q^{10} - q^{11} + q^{12} - 2q^{14} - 2q^{15} - q^{16} + q^{18} + 2q^{20} + q^{21} - 2q^{22} - q^{24} - 2q^{27} - q^{28} + 2q^{29} - q^{30} + q^{31} + q^{32} + q^{33} + 2q^{35} + 2q^{36} + q^{40} - q^{42} - q^{44} - q^{45} - 2q^{48} - q^{49} - q^{53} - q^{54} + 2q^{55} + q^{56} + q^{58} - q^{59} + q^{60} + 2q^{62} + 2q^{63} + 2q^{64} - q^{66} + q^{70} + q^{72} - 2q^{73} - q^{77} + q^{79} - q^{80} - q^{81} + 2q^{83} - 2q^{84} + q^{87} + q^{88} - 2q^{90} - q^{93} - q^{96} - 2q^{97} + q^{98} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(85\) \(113\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 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 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(6\) 1.00000 1.00000
\(7\) −0.500000 0.866025i −0.500000 0.866025i
\(8\) −1.00000 −1.00000
\(9\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(10\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(11\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(12\) 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 \(0.333333\pi\)
\(18\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(19\) 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
\(22\) −1.00000 −1.00000
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) −0.500000 0.866025i −0.500000 0.866025i
\(25\) 0 0
\(26\) 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 \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(31\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(33\) 0.500000 0.866025i 0.500000 0.866025i
\(34\) 0 0
\(35\) 1.00000 1.00000
\(36\) 1.00000 1.00000
\(37\) 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
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) −0.500000 0.866025i −0.500000 0.866025i
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(45\) −0.500000 0.866025i −0.500000 0.866025i
\(46\) 0 0
\(47\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(48\) −1.00000 −1.00000
\(49\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(54\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(55\) 1.00000 1.00000
\(56\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(57\) 0 0
\(58\) 0.500000 0.866025i 0.500000 0.866025i
\(59\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(60\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(61\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 1.00000 1.00000
\(63\) 1.00000 1.00000
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) −0.500000 0.866025i −0.500000 0.866025i
\(67\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 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
\(73\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(80\) −0.500000 0.866025i −0.500000 0.866025i
\(81\) −0.500000 0.866025i −0.500000 0.866025i
\(82\) 0 0
\(83\) 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 0
\(87\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(88\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(89\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(90\) −1.00000 −1.00000
\(91\) 0 0
\(92\) 0 0
\(93\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(94\) 0 0
\(95\) 0 0
\(96\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(97\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(98\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(99\) 1.00000 1.00000
\(100\) 0 0
\(101\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(102\) 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
\(106\) −1.00000 −1.00000
\(107\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(108\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(109\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 0.500000 0.866025i 0.500000 0.866025i
\(111\) 0 0
\(112\) 1.00000 1.00000
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.500000 0.866025i −0.500000 0.866025i
\(117\) 0 0
\(118\) −1.00000 −1.00000
\(119\) 0 0
\(120\) 1.00000 1.00000
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) 0.500000 0.866025i 0.500000 0.866025i
\(125\) −1.00000 −1.00000
\(126\) 0.500000 0.866025i 0.500000 0.866025i
\(127\) −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
\(129\) 0 0
\(130\) 0 0
\(131\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(132\) −1.00000 −1.00000
\(133\) 0 0
\(134\) 0 0
\(135\) 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 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) −0.500000 0.866025i −0.500000 0.866025i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.500000 0.866025i −0.500000 0.866025i
\(145\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(146\) −2.00000 −2.00000
\(147\) −1.00000 −1.00000
\(148\) 0 0
\(149\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(150\) 0 0
\(151\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(155\) −1.00000 −1.00000
\(156\) 0 0
\(157\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(158\) −0.500000 0.866025i −0.500000 0.866025i
\(159\) 0.500000 0.866025i 0.500000 0.866025i
\(160\) −1.00000 −1.00000
\(161\) 0 0
\(162\) −1.00000 −1.00000
\(163\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(164\) 0 0
\(165\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(166\) 0.500000 0.866025i 0.500000 0.866025i
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(174\) 1.00000 1.00000
\(175\) 0 0
\(176\) 1.00000 1.00000
\(177\) 0.500000 0.866025i 0.500000 0.866025i
\(178\) 0 0
\(179\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(180\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(187\) 0 0
\(188\) 0 0
\(189\) 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
\(193\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(195\) 0 0
\(196\) 1.00000 1.00000
\(197\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(198\) 0.500000 0.866025i 0.500000 0.866025i
\(199\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 2.00000 2.00000
\(203\) −0.500000 0.866025i −0.500000 0.866025i
\(204\) 0 0
\(205\) 0 0
\(206\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 1.00000 1.00000
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(213\) 0 0
\(214\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(215\) 0 0
\(216\) 1.00000 1.00000
\(217\) 0.500000 0.866025i 0.500000 0.866025i
\(218\) 0 0
\(219\) 1.00000 1.73205i 1.00000 1.73205i
\(220\) −0.500000 0.866025i −0.500000 0.866025i
\(221\) 0 0
\(222\) 0 0
\(223\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(224\) 0.500000 0.866025i 0.500000 0.866025i
\(225\) 0 0
\(226\) 0 0
\(227\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) 0 0
\(231\) −1.00000 −1.00000
\(232\) −1.00000 −1.00000
\(233\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(237\) 1.00000 1.00000
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0.500000 0.866025i 0.500000 0.866025i
\(241\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.500000 0.866025i
\(244\) 0 0
\(245\) −0.500000 0.866025i −0.500000 0.866025i
\(246\) 0 0
\(247\) 0 0
\(248\) −0.500000 0.866025i −0.500000 0.866025i
\(249\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(250\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(251\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(252\) −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 \(0.666667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(262\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(263\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(265\) 1.00000 1.00000
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(270\) −0.500000 0.866025i −0.500000 0.866025i
\(271\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(278\) 0 0
\(279\) −1.00000 −1.00000
\(280\) −1.00000 −1.00000
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −1.00000
\(289\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(290\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(291\) −0.500000 0.866025i −0.500000 0.866025i
\(292\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(293\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(294\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(295\) 1.00000 1.00000
\(296\) 0 0
\(297\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(298\) −1.00000 1.73205i −1.00000 1.73205i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 1.00000 1.00000
\(303\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 1.00000 1.00000
\(309\) −2.00000 −2.00000
\(310\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(311\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(312\) 0 0
\(313\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(314\) 0 0
\(315\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(316\) −1.00000 −1.00000
\(317\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(318\) −0.500000 0.866025i −0.500000 0.866025i
\(319\) −0.500000 0.866025i −0.500000 0.866025i
\(320\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(321\) −1.00000 −1.00000
\(322\) 0 0
\(323\) 0 0
\(324\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 1.00000 1.00000
\(331\) 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 0
\(335\) 0 0
\(336\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(337\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(338\) 0.500000 0.866025i 0.500000 0.866025i
\(339\) 0 0
\(340\) 0 0
\(341\) 0.500000 0.866025i 0.500000 0.866025i
\(342\) 0 0
\(343\) 1.00000 1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) −1.00000 1.73205i −1.00000 1.73205i
\(347\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(348\) 0.500000 0.866025i 0.500000 0.866025i
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.500000 0.866025i 0.500000 0.866025i
\(353\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(354\) −0.500000 0.866025i −0.500000 0.866025i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 2.00000 2.00000
\(359\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(360\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(361\) −0.500000 0.866025i −0.500000 0.866025i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.00000 2.00000
\(366\) 0 0
\(367\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(372\) 1.00000 1.00000
\(373\) 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 0
\(377\) 0 0
\(378\) 1.00000 1.00000
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) −0.500000 0.866025i −0.500000 0.866025i
\(382\) 0 0
\(383\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(384\) 1.00000 1.00000
\(385\) −0.500000 0.866025i −0.500000 0.866025i
\(386\) 1.00000 1.00000
\(387\) 0 0
\(388\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(389\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.500000 0.866025i 0.500000 0.866025i
\(393\) −1.00000 −1.00000
\(394\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(395\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(396\) −0.500000 0.866025i −0.500000 0.866025i
\(397\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) −2.00000 −2.00000
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 1.00000 1.73205i 1.00000 1.73205i
\(405\) 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 0
\(411\) 0 0
\(412\) 2.00000 2.00000
\(413\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(414\) 0 0
\(415\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(420\) 0.500000 0.866025i 0.500000 0.866025i
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 1.00000 1.00000
\(429\) 0 0
\(430\) 0 0
\(431\) 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
\(433\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(434\) −0.500000 0.866025i −0.500000 0.866025i
\(435\) −1.00000 −1.00000
\(436\) 0 0
\(437\) 0 0
\(438\) −1.00000 1.73205i −1.00000 1.73205i
\(439\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(440\) −1.00000 −1.00000
\(441\) −0.500000 0.866025i −0.500000 0.866025i
\(442\) 0 0
\(443\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(447\) 2.00000 2.00000
\(448\) −0.500000 0.866025i −0.500000 0.866025i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(454\) −1.00000 −1.00000
\(455\) 0 0
\(456\) 0 0
\(457\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(462\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(463\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(464\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(465\) −0.500000 0.866025i −0.500000 0.866025i
\(466\) 0 0
\(467\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(473\) 0 0
\(474\) 0.500000 0.866025i 0.500000 0.866025i
\(475\) 0 0
\(476\) 0 0
\(477\) 1.00000 1.00000
\(478\) 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
\(482\) 1.00000 1.00000
\(483\) 0 0
\(484\) 0 0
\(485\) 0.500000 0.866025i 0.500000 0.866025i
\(486\) −0.500000 0.866025i −0.500000 0.866025i
\(487\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −1.00000 −1.00000
\(491\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(496\) −1.00000 −1.00000
\(497\) 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 0
\(502\) 0.500000 0.866025i 0.500000 0.866025i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) −1.00000 −1.00000
\(505\) −2.00000 −2.00000
\(506\) 0 0
\(507\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(508\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(509\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(512\) −1.00000 −1.00000
\(513\) 0 0
\(514\) 0 0
\(515\) −1.00000 1.73205i −1.00000 1.73205i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 2.00000 2.00000
\(520\) 0 0
\(521\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(522\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(523\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(524\) 1.00000 1.00000
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(529\) −0.500000 0.866025i −0.500000 0.866025i
\(530\) 0.500000 0.866025i 0.500000 0.866025i
\(531\) 1.00000 1.00000
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −0.500000 0.866025i −0.500000 0.866025i
\(536\) 0 0
\(537\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(538\) −1.00000 −1.00000
\(539\) 1.00000 1.00000
\(540\) −1.00000 −1.00000
\(541\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) −0.500000 0.866025i −0.500000 0.866025i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −1.00000 −1.00000
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(558\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(559\) 0 0
\(560\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(561\) 0 0
\(562\) 0 0
\(563\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(568\) 0 0
\(569\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−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
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(577\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(578\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(579\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(580\) 1.00000 1.00000
\(581\) −0.500000 0.866025i −0.500000 0.866025i
\(582\) −1.00000 −1.00000
\(583\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(584\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(585\) 0 0
\(586\) 0.500000 0.866025i 0.500000 0.866025i
\(587\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(588\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(589\) 0 0
\(590\) 0.500000 0.866025i 0.500000 0.866025i
\(591\) −1.00000 1.73205i −1.00000 1.73205i
\(592\) 0 0
\(593\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(594\) 1.00000 1.00000
\(595\) 0 0
\(596\) −2.00000 −2.00000
\(597\) 1.00000 1.73205i 1.00000 1.73205i
\(598\) 0 0
\(599\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(600\) 0 0
\(601\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.500000 0.866025i 0.500000 0.866025i
\(605\) 0 0
\(606\) 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 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0.500000 0.866025i 0.500000 0.866025i
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(619\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(620\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.500000 0.866025i 0.500000 0.866025i
\(626\) −0.500000 0.866025i −0.500000 0.866025i
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(631\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(632\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(633\) 0 0
\(634\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(635\) 0.500000 0.866025i 0.500000 0.866025i
\(636\) −1.00000 −1.00000
\(637\) 0 0
\(638\) −1.00000 −1.00000
\(639\) 0 0
\(640\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(641\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(642\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(648\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(649\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(650\) 0 0
\(651\) 1.00000 1.00000
\(652\) 0 0
\(653\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) −0.500000 0.866025i −0.500000 0.866025i
\(656\) 0 0
\(657\) 2.00000 2.00000
\(658\) 0 0
\(659\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(660\) 0.500000 0.866025i 0.500000 0.866025i
\(661\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −1.00000 −1.00000
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −0.500000 0.866025i −0.500000 0.866025i
\(670\) 0 0
\(671\) 0 0
\(672\) 1.00000 1.00000
\(673\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(674\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(675\) 0 0
\(676\) −0.500000 0.866025i −0.500000 0.866025i
\(677\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(680\) 0 0
\(681\) 0.500000 0.866025i 0.500000 0.866025i
\(682\) −0.500000 0.866025i −0.500000 0.866025i
\(683\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.500000 0.866025i 0.500000 0.866025i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) −2.00000 −2.00000
\(693\) −0.500000 0.866025i −0.500000 0.866025i
\(694\) 2.00000 2.00000
\(695\) 0 0
\(696\) −0.500000 0.866025i −0.500000 0.866025i
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.500000 0.866025i −0.500000 0.866025i
\(705\) 0 0
\(706\) 0 0
\(707\) 1.00000 1.73205i 1.00000 1.73205i
\(708\) −1.00000 −1.00000
\(709\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) 0 0
\(711\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.00000 1.73205i 1.00000 1.73205i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(720\) 1.00000 1.00000
\(721\) 2.00000 2.00000
\(722\) −1.00000 −1.00000
\(723\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 1.00000 1.73205i 1.00000 1.73205i
\(731\) 0 0
\(732\) 0 0
\(733\) 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
\(736\) 0 0
\(737\) 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
\(742\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0.500000 0.866025i 0.500000 0.866025i
\(745\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(746\) 0 0
\(747\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(748\) 0 0
\(749\) 1.00000 1.00000
\(750\) −1.00000 −1.00000
\(751\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(752\) 0 0
\(753\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(754\) 0 0
\(755\) −1.00000 −1.00000
\(756\) 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
\(761\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(762\) −1.00000 −1.00000
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.500000 0.866025i 0.500000 0.866025i
\(769\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) −1.00000 −1.00000
\(771\) 0 0
\(772\) 0.500000 0.866025i 0.500000 0.866025i
\(773\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 1.00000 1.00000
\(777\) 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
\(786\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(787\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(788\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(789\) 0 0
\(790\) 1.00000 1.00000
\(791\) 0 0
\(792\) −1.00000 −1.00000
\(793\) 0 0
\(794\) 0 0
\(795\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(796\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(797\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(798\) 0 0
\(799\) 0