Properties

Label 1800.1.bk.c.1651.1
Level 1800
Weight 1
Character 1800.1651
Analytic conductor 0.898
Analytic rank 0
Dimension 2
Projective image \(D_{3}\)
CM disc. -8
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 1800.bk (of order \(6\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.898317022739\)
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 3.1.16200.2

Embedding invariants

Embedding label 1651.1
Root \(0.500000 - 0.866025i\)
Character \(\chi\) = 1800.1651
Dual form 1800.1.bk.c.1051.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -1.00000 q^{8} +1.00000 q^{9} +(-1.00000 - 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.500000 - 0.866025i) q^{16} -2.00000 q^{17} +(0.500000 + 0.866025i) q^{18} -1.00000 q^{19} +(1.00000 - 1.73205i) q^{22} +1.00000 q^{24} -1.00000 q^{27} +(0.500000 - 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{33} +(-1.00000 - 1.73205i) q^{34} +(-0.500000 + 0.866025i) q^{36} +(-0.500000 - 0.866025i) q^{38} +(0.500000 - 0.866025i) q^{41} +(-0.500000 - 0.866025i) q^{43} +2.00000 q^{44} +(0.500000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +2.00000 q^{51} +(-0.500000 - 0.866025i) q^{54} +1.00000 q^{57} +(0.500000 - 0.866025i) q^{59} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{66} +(-0.500000 + 0.866025i) q^{67} +(1.00000 - 1.73205i) q^{68} -1.00000 q^{72} +1.00000 q^{73} +(0.500000 - 0.866025i) q^{76} +1.00000 q^{81} +1.00000 q^{82} +(-0.500000 - 0.866025i) q^{83} +(0.500000 - 0.866025i) q^{86} +(1.00000 + 1.73205i) q^{88} -1.00000 q^{89} +(-0.500000 + 0.866025i) q^{96} +(-0.500000 - 0.866025i) q^{97} -1.00000 q^{98} +(-1.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - 2q^{3} - q^{4} - q^{6} - 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q + q^{2} - 2q^{3} - q^{4} - q^{6} - 2q^{8} + 2q^{9} - 2q^{11} + q^{12} - q^{16} - 4q^{17} + q^{18} - 2q^{19} + 2q^{22} + 2q^{24} - 2q^{27} + q^{32} + 2q^{33} - 2q^{34} - q^{36} - q^{38} + q^{41} - q^{43} + 4q^{44} + q^{48} - q^{49} + 4q^{51} - q^{54} + 2q^{57} + q^{59} + 2q^{64} - 2q^{66} - q^{67} + 2q^{68} - 2q^{72} + 2q^{73} + q^{76} + 2q^{81} + 2q^{82} - q^{83} + q^{86} + 2q^{88} - 2q^{89} - q^{96} - q^{97} - 2q^{98} - 2q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1001\) \(1351\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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
\(3\) −1.00000 −1.00000
\(4\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(5\) 0 0
\(6\) −0.500000 0.866025i −0.500000 0.866025i
\(7\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(8\) −1.00000 −1.00000
\(9\) 1.00000 1.00000
\(10\) 0 0
\(11\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(12\) 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 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.500000 0.866025i
\(17\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(18\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(19\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.00000 1.73205i 1.00000 1.73205i
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 1.00000 1.00000
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −1.00000
\(28\) 0 0
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) 0 0
\(31\) 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
\(33\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(34\) −1.00000 1.73205i −1.00000 1.73205i
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) −0.500000 0.866025i −0.500000 0.866025i
\(39\) 0 0
\(40\) 0 0
\(41\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(42\) 0 0
\(43\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(44\) 2.00000 2.00000
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(48\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(49\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(50\) 0 0
\(51\) 2.00000 2.00000
\(52\) 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 0
\(57\) 1.00000 1.00000
\(58\) 0 0
\(59\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(60\) 0 0
\(61\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(67\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(68\) 1.00000 1.73205i 1.00000 1.73205i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −1.00000 −1.00000
\(73\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0.500000 0.866025i 0.500000 0.866025i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(80\) 0 0
\(81\) 1.00000 1.00000
\(82\) 1.00000 1.00000
\(83\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.500000 0.866025i 0.500000 0.866025i
\(87\) 0 0
\(88\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(89\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(97\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(98\) −1.00000 −1.00000
\(99\) −1.00000 1.73205i −1.00000 1.73205i
\(100\) 0 0
\(101\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(102\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(103\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(108\) 0.500000 0.866025i 0.500000 0.866025i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(114\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 1.00000 1.00000
\(119\) 0 0
\(120\) 0 0
\(121\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(122\) 0 0
\(123\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(129\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(130\) 0 0
\(131\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(132\) −2.00000 −2.00000
\(133\) 0 0
\(134\) −1.00000 −1.00000
\(135\) 0 0
\(136\) 2.00000 2.00000
\(137\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(138\) 0 0
\(139\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.500000 0.866025i −0.500000 0.866025i
\(145\) 0 0
\(146\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(147\) 0.500000 0.866025i 0.500000 0.866025i
\(148\) 0 0
\(149\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(150\) 0 0
\(151\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(152\) 1.00000 1.00000
\(153\) −2.00000 −2.00000
\(154\) 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 0
\(161\) 0 0
\(162\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(163\) 1.00000 1.00000 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
\(167\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(168\) 0 0
\(169\) −0.500000 0.866025i −0.500000 0.866025i
\(170\) 0 0
\(171\) −1.00000 −1.00000
\(172\) 1.00000 1.00000
\(173\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(177\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(178\) −0.500000 0.866025i −0.500000 0.866025i
\(179\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 2.00000 + 3.46410i 2.00000 + 3.46410i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) −1.00000 −1.00000
\(193\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(194\) 0.500000 0.866025i 0.500000 0.866025i
\(195\) 0 0
\(196\) −0.500000 0.866025i −0.500000 0.866025i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 1.00000 1.73205i 1.00000 1.73205i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0.500000 0.866025i 0.500000 0.866025i
\(202\) 0 0
\(203\) 0 0
\(204\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(210\) 0 0
\(211\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(215\) 0 0
\(216\) 1.00000 1.00000
\(217\) 0 0
\(218\) 0 0
\(219\) −1.00000 −1.00000
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −1.00000 −1.00000
\(227\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(228\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(229\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) −3.00000 −3.00000
\(243\) −1.00000 −1.00000
\(244\) 0 0
\(245\) 0 0
\(246\) −1.00000 −1.00000
\(247\) 0 0
\(248\) 0 0
\(249\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(250\) 0 0
\(251\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(257\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(258\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −2.00000 −2.00000
\(263\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) −1.00000 1.73205i −1.00000 1.73205i
\(265\) 0 0
\(266\) 0 0
\(267\) 1.00000 1.00000
\(268\) −0.500000 0.866025i −0.500000 0.866025i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(273\) 0 0
\(274\) 0.500000 0.866025i 0.500000 0.866025i
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(278\) −2.00000 −2.00000
\(279\) 0 0
\(280\) 0 0
\(281\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(282\) 0 0
\(283\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.500000 0.866025i 0.500000 0.866025i
\(289\) 3.00000 3.00000
\(290\) 0 0
\(291\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(292\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(293\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(294\) 1.00000 1.00000
\(295\) 0 0
\(296\) 0 0
\(297\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(305\) 0 0
\(306\) −1.00000 1.73205i −1.00000 1.73205i
\(307\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) 0 0
\(313\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 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 0
\(321\) −1.00000 −1.00000
\(322\) 0 0
\(323\) 2.00000 2.00000
\(324\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(325\) 0 0
\(326\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(327\) 0 0
\(328\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(329\) 0 0
\(330\) 0 0
\(331\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 1.00000 1.00000
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(338\) 0.500000 0.866025i 0.500000 0.866025i
\(339\) 0.500000 0.866025i 0.500000 0.866025i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.500000 0.866025i −0.500000 0.866025i
\(343\) 0 0
\(344\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(345\) 0 0
\(346\) 0 0
\(347\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(348\) 0 0
\(349\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.00000 −2.00000
\(353\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(354\) −1.00000 −1.00000
\(355\) 0 0
\(356\) 0.500000 0.866025i 0.500000 0.866025i
\(357\) 0 0
\(358\) −0.500000 0.866025i −0.500000 0.866025i
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) 1.50000 2.59808i 1.50000 2.59808i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(368\) 0 0
\(369\) 0.500000 0.866025i 0.500000 0.866025i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) −2.00000 + 3.46410i −2.00000 + 3.46410i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(384\) −0.500000 0.866025i −0.500000 0.866025i
\(385\) 0 0
\(386\) 2.00000 2.00000
\(387\) −0.500000 0.866025i −0.500000 0.866025i
\(388\) 1.00000 1.00000
\(389\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
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 1.73205i 1.00000 1.73205i
\(394\) 0 0
\(395\) 0 0
\(396\) 2.00000 2.00000
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 1.00000 1.00000
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −2.00000 −2.00000
\(409\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(410\) 0 0
\(411\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.00000 1.73205i 1.00000 1.73205i
\(418\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(419\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(420\) 0 0
\(421\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(422\) 1.00000 1.00000
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(433\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.500000 0.866025i −0.500000 0.866025i
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(442\) 0 0
\(443\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(450\) 0 0
\(451\) −2.00000 −2.00000
\(452\) −0.500000 0.866025i −0.500000 0.866025i
\(453\) 0 0
\(454\) 0.500000 0.866025i 0.500000 0.866025i
\(455\) 0 0
\(456\) −1.00000 −1.00000
\(457\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(458\) 0 0
\(459\) 2.00000 2.00000
\(460\) 0 0
\(461\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(462\) 0 0
\(463\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(467\) 1.00000 1.00000 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
\(473\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(474\) 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 0
\(481\) 0 0
\(482\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(483\) 0 0
\(484\) −1.50000 2.59808i −1.50000 2.59808i
\(485\) 0 0
\(486\) −0.500000 0.866025i −0.500000 0.866025i
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) −1.00000 −1.00000
\(490\) 0 0
\(491\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(492\) −0.500000 0.866025i −0.500000 0.866025i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(499\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.500000 0.866025i −0.500000 0.866025i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(508\) 0 0
\(509\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 1.00000 1.00000
\(514\) −1.00000 −1.00000
\(515\) 0 0
\(516\) −1.00000 −1.00000
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(522\) 0 0
\(523\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(524\) −1.00000 1.73205i −1.00000 1.73205i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 1.00000 1.73205i 1.00000 1.73205i
\(529\) −0.500000 0.866025i −0.500000 0.866025i
\(530\) 0 0
\(531\) 0.500000 0.866025i 0.500000 0.866025i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(535\) 0 0
\(536\) 0.500000 0.866025i 0.500000 0.866025i
\(537\) 1.00000 1.00000
\(538\) 0 0
\(539\) 2.00000 2.00000
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(545\) 0 0
\(546\) 0 0
\(547\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(548\) 1.00000 1.00000
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −1.00000 1.73205i −1.00000 1.73205i
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −2.00000 3.46410i −2.00000 3.46410i
\(562\) 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 \(1.00000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −1.00000 −1.00000
\(567\) 0 0
\(568\) 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
\(571\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 1.00000
\(577\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(578\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(579\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(580\) 0 0
\(581\) 0 0
\(582\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(583\) 0 0
\(584\) −1.00000 −1.00000
\(585\) 0 0
\(586\) 0 0
\(587\) 1.00000 + 1.73205i 1.00000 + 1.73205i 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 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(594\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0 0
\(601\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(602\) 0 0
\(603\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 1.00000 1.73205i 1.00000 1.73205i
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) −1.00000 1.73205i −1.00000 1.73205i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(618\) 0 0
\(619\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0.500000 0.866025i 0.500000 0.866025i
\(627\) −1.00000 1.73205i −1.00000 1.73205i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 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
\(643\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) −1.00000 −1.00000
\(649\) −2.00000 −2.00000
\(650\) 0 0
\(651\) 0 0
\(652\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(653\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.00000 −1.00000
\(657\) 1.00000 1.00000
\(658\) 0 0
\(659\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(660\) 0 0
\(661\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(663\) 0 0
\(664\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(674\) 2.00000 2.00000
\(675\) 0 0
\(676\) 1.00000 1.00000
\(677\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(678\) 1.00000 1.00000
\(679\) 0 0
\(680\) 0 0
\(681\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(682\) 0 0
\(683\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(684\) 0.500000 0.866025i 0.500000 0.866025i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(689\) 0 0
\(690\) 0 0
\(691\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 2.00000 2.00000
\(695\) 0 0
\(696\) 0 0
\(697\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(698\) 0 0
\(699\) −1.00000 −1.00000
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.00000 1.73205i −1.00000 1.73205i
\(705\) 0 0
\(706\) 0.500000 0.866025i 0.500000 0.866025i
\(707\) 0 0
\(708\) −0.500000 0.866025i −0.500000 0.866025i
\(709\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.00000 1.00000
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.500000 0.866025i 0.500000 0.866025i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −0.500000 0.866025i −0.500000 0.866025i
\(724\) 0 0
\(725\) 0 0
\(726\) 3.00000 3.00000
\(727\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(732\) 0 0
\(733\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.00000 2.00000
\(738\) 1.00000 1.00000
\(739\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.500000 0.866025i −0.500000 0.866025i
\(748\) −4.00000 −4.00000
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 0 0
\(753\) 1.00000 1.00000
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(759\) 0 0
\(760\) 0 0
\(761\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.500000 0.866025i 0.500000 0.866025i
\(769\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(770\) 0 0
\(771\) 0.500000 0.866025i 0.500000 0.866025i
\(772\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0.500000 0.866025i 0.500000 0.866025i
\(775\) 0 0
\(776\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(777\) 0 0
\(778\) 0 0
\(779\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 1.00000
\(785\) 0 0
\(786\) 2.00000 2.00000
\(787\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(793\) 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
\(799\) 0 0
\(800\) 0 0
\(801\) −1.00000 −1.00000
\(802\) −2.00000 −2.00000
\(803\) −1.00000 1.73205i −1.00000 1.73205i
\(804\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(810\) 0 0
\(811\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) −1.00000 1.73205i −1.00000 1.73205i
\(817\) 0.500000 + 0.866025i 0.500000 + 0.866025i