Properties

Label 1089.1.h.a.967.2
Level $1089$
Weight $1$
Character 1089.967
Analytic conductor $0.543$
Analytic rank $0$
Dimension $4$
Projective image $S_{4}$
CM/RM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1089.h (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.543481798757\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(S_{4}\)
Projective field: Galois closure of 4.2.107811.1

Embedding invariants

Embedding label 967.2
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1089.967
Dual form 1089.1.h.a.241.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 - 0.707107i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.41421i q^{6} +(-1.22474 + 0.707107i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.22474 - 0.707107i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.41421i q^{6} +(-1.22474 + 0.707107i) q^{7} +(-0.500000 - 0.866025i) q^{9} -1.41421i q^{10} +(-0.500000 - 0.866025i) q^{12} +(-1.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.22474 - 0.707107i) q^{18} +(-0.500000 - 0.866025i) q^{20} +1.41421i q^{21} -1.00000 q^{27} +1.41421i q^{28} +(1.22474 - 0.707107i) q^{29} +(-1.22474 - 0.707107i) q^{30} +(-0.500000 + 0.866025i) q^{31} +(1.22474 + 0.707107i) q^{32} +1.41421i q^{35} -1.00000 q^{36} -1.00000 q^{37} +(1.00000 + 1.73205i) q^{42} -1.00000 q^{45} +(0.500000 + 0.866025i) q^{47} +1.00000 q^{48} +(0.500000 - 0.866025i) q^{49} +1.00000 q^{53} +(-1.22474 + 0.707107i) q^{54} +(1.00000 - 1.73205i) q^{58} +(-0.500000 + 0.866025i) q^{59} -1.00000 q^{60} +(-1.22474 + 0.707107i) q^{61} +1.41421i q^{62} +(1.22474 + 0.707107i) q^{63} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{67} +(1.00000 + 1.73205i) q^{70} -1.00000 q^{71} -1.41421i q^{73} +(-1.22474 + 0.707107i) q^{74} +1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.22474 + 0.707107i) q^{83} +(1.22474 + 0.707107i) q^{84} -1.41421i q^{87} +(-1.22474 + 0.707107i) q^{90} +(0.500000 + 0.866025i) q^{93} +(1.22474 + 0.707107i) q^{94} +(1.22474 - 0.707107i) q^{96} +(-0.500000 - 0.866025i) q^{97} -1.41421i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{9} - 2 q^{12} - 4 q^{14} - 2 q^{15} + 2 q^{16} - 2 q^{20} - 4 q^{27} - 2 q^{31} - 4 q^{36} - 4 q^{37} + 4 q^{42} - 4 q^{45} + 2 q^{47} + 4 q^{48} + 2 q^{49} + 4 q^{53} + 4 q^{58} - 2 q^{59} - 4 q^{60} + 4 q^{64} + 2 q^{67} + 4 q^{70} - 4 q^{71} + 4 q^{80} - 2 q^{81} + 2 q^{93} - 2 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(848\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(3\) 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 \(-0.666667\pi\)
1.00000 \(0\)
\(6\) 1.41421i 1.41421i
\(7\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.500000 0.866025i
\(10\) 1.41421i 1.41421i
\(11\) 0 0
\(12\) −0.500000 0.866025i −0.500000 0.866025i
\(13\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(14\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(15\) −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 \(\pi\)
\(18\) −1.22474 0.707107i −1.22474 0.707107i
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −0.500000 0.866025i −0.500000 0.866025i
\(21\) 1.41421i 1.41421i
\(22\) 0 0
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −1.00000
\(28\) 1.41421i 1.41421i
\(29\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(30\) −1.22474 0.707107i −1.22474 0.707107i
\(31\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(32\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(33\) 0 0
\(34\) 0 0
\(35\) 1.41421i 1.41421i
\(36\) −1.00000 −1.00000
\(37\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(43\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(44\) 0 0
\(45\) −1.00000 −1.00000
\(46\) 0 0
\(47\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(48\) 1.00000 1.00000
\(49\) 0.500000 0.866025i 0.500000 0.866025i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 1.00000 1.73205i 1.00000 1.73205i
\(59\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(60\) −1.00000 −1.00000
\(61\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(62\) 1.41421i 1.41421i
\(63\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(64\) 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 0
\(70\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(71\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(72\) 0 0
\(73\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(74\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(75\) 0 0
\(76\) 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
\(82\) 0 0
\(83\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(84\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(85\) 0 0
\(86\) 0 0
\(87\) 1.41421i 1.41421i
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(91\) 0 0
\(92\) 0 0
\(93\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(94\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(95\) 0 0
\(96\) 1.22474 0.707107i 1.22474 0.707107i
\(97\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(98\) 1.41421i 1.41421i
\(99\) 0 0
\(100\) 0 0
\(101\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(102\) 0 0
\(103\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(104\) 0 0
\(105\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(106\) 1.22474 0.707107i 1.22474 0.707107i
\(107\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(108\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(112\) −1.22474 0.707107i −1.22474 0.707107i
\(113\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(114\) 0 0
\(115\) 0 0
\(116\) 1.41421i 1.41421i
\(117\) 0 0
\(118\) 1.41421i 1.41421i
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(123\) 0 0
\(124\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(125\) 1.00000 1.00000
\(126\) 2.00000 2.00000
\(127\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 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
\(134\) 1.41421i 1.41421i
\(135\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(136\) 0 0
\(137\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 0 0
\(139\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(140\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(141\) 1.00000 1.00000
\(142\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(143\) 0 0
\(144\) 0.500000 0.866025i 0.500000 0.866025i
\(145\) 1.41421i 1.41421i
\(146\) −1.00000 1.73205i −1.00000 1.73205i
\(147\) −0.500000 0.866025i −0.500000 0.866025i
\(148\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(149\) 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 \(0.333333\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(156\) 0 0
\(157\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0.500000 0.866025i 0.500000 0.866025i
\(160\) 1.22474 0.707107i 1.22474 0.707107i
\(161\) 0 0
\(162\) 1.41421i 1.41421i
\(163\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(167\) 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
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) −1.00000 1.73205i −1.00000 1.73205i
\(175\) 0 0
\(176\) 0 0
\(177\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(178\) 0 0
\(179\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(180\) −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
\(183\) 1.41421i 1.41421i
\(184\) 0 0
\(185\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(186\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(187\) 0 0
\(188\) 1.00000 1.00000
\(189\) 1.22474 0.707107i 1.22474 0.707107i
\(190\) 0 0
\(191\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) 0.500000 0.866025i 0.500000 0.866025i
\(193\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) −1.22474 0.707107i −1.22474 0.707107i
\(195\) 0 0
\(196\) −0.500000 0.866025i −0.500000 0.866025i
\(197\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(198\) 0 0
\(199\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(200\) 0 0
\(201\) −0.500000 0.866025i −0.500000 0.866025i
\(202\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(203\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(204\) 0 0
\(205\) 0 0
\(206\) 1.41421i 1.41421i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 2.00000 2.00000
\(211\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(212\) 0.500000 0.866025i 0.500000 0.866025i
\(213\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(214\) −1.00000 1.73205i −1.00000 1.73205i
\(215\) 0 0
\(216\) 0 0
\(217\) 1.41421i 1.41421i
\(218\) 0 0
\(219\) −1.22474 0.707107i −1.22474 0.707107i
\(220\) 0 0
\(221\) 0 0
\(222\) 1.41421i 1.41421i
\(223\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(224\) −2.00000 −2.00000
\(225\) 0 0
\(226\) 1.41421i 1.41421i
\(227\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(228\) 0 0
\(229\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(234\) 0 0
\(235\) 1.00000 1.00000
\(236\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(237\) 0 0
\(238\) 0 0
\(239\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(240\) 0.500000 0.866025i 0.500000 0.866025i
\(241\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(244\) 1.41421i 1.41421i
\(245\) −0.500000 0.866025i −0.500000 0.866025i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 1.41421i 1.41421i
\(250\) 1.22474 0.707107i 1.22474 0.707107i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 1.22474 0.707107i 1.22474 0.707107i
\(253\) 0 0
\(254\) −1.00000 1.73205i −1.00000 1.73205i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(257\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(258\) 0 0
\(259\) 1.22474 0.707107i 1.22474 0.707107i
\(260\) 0 0
\(261\) −1.22474 0.707107i −1.22474 0.707107i
\(262\) 0 0
\(263\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) 0 0
\(265\) 0.500000 0.866025i 0.500000 0.866025i
\(266\) 0 0
\(267\) 0 0
\(268\) −0.500000 0.866025i −0.500000 0.866025i
\(269\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(270\) 1.41421i 1.41421i
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(275\) 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
\(279\) 1.00000 1.00000
\(280\) 0 0
\(281\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(282\) 1.22474 0.707107i 1.22474 0.707107i
\(283\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(284\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 1.41421i 1.41421i
\(289\) 1.00000 1.00000
\(290\) −1.00000 1.73205i −1.00000 1.73205i
\(291\) −1.00000 −1.00000
\(292\) −1.22474 0.707107i −1.22474 0.707107i
\(293\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(294\) −1.22474 0.707107i −1.22474 0.707107i
\(295\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 1.41421i 1.41421i
\(304\) 0 0
\(305\) 1.41421i 1.41421i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) −0.500000 0.866025i −0.500000 0.866025i
\(310\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(311\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(314\) 1.41421i 1.41421i
\(315\) 1.22474 0.707107i 1.22474 0.707107i
\(316\) 0 0
\(317\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(318\) 1.41421i 1.41421i
\(319\) 0 0
\(320\) 0.500000 0.866025i 0.500000 0.866025i
\(321\) −1.22474 0.707107i −1.22474 0.707107i
\(322\) 0 0
\(323\) 0 0
\(324\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(325\) 0 0
\(326\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(327\) 0 0
\(328\) 0 0
\(329\) −1.22474 0.707107i −1.22474 0.707107i
\(330\) 0 0
\(331\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(332\) 1.41421i 1.41421i
\(333\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(334\) 0 0
\(335\) −0.500000 0.866025i −0.500000 0.866025i
\(336\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(337\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(338\) −1.22474 0.707107i −1.22474 0.707107i
\(339\) −0.500000 0.866025i −0.500000 0.866025i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(348\) −1.22474 0.707107i −1.22474 0.707107i
\(349\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(354\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(355\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(356\) 0 0
\(357\) 0 0
\(358\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(359\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(363\) 0 0
\(364\) 0 0
\(365\) −1.22474 0.707107i −1.22474 0.707107i
\(366\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(367\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 1.41421i 1.41421i
\(371\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(372\) 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 1.73205i 1.00000 1.73205i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) −1.22474 0.707107i −1.22474 0.707107i
\(382\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(383\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −1.00000 −1.00000
\(389\) 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
\(394\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(395\) 0 0
\(396\) 0 0
\(397\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(399\) 0 0
\(400\) 0 0
\(401\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(402\) −1.22474 0.707107i −1.22474 0.707107i
\(403\) 0 0
\(404\) 1.41421i 1.41421i
\(405\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(406\) 2.82843i 2.82843i
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) 0 0
\(411\) 1.00000 1.00000
\(412\) −0.500000 0.866025i −0.500000 0.866025i
\(413\) 1.41421i 1.41421i
\(414\) 0 0
\(415\) 1.41421i 1.41421i
\(416\) 0 0
\(417\) 1.22474 0.707107i 1.22474 0.707107i
\(418\) 0 0
\(419\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(420\) 1.22474 0.707107i 1.22474 0.707107i
\(421\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(422\) 2.00000 2.00000
\(423\) 0.500000 0.866025i 0.500000 0.866025i
\(424\) 0 0
\(425\) 0 0
\(426\) 1.41421i 1.41421i
\(427\) 1.00000 1.73205i 1.00000 1.73205i
\(428\) −1.22474 0.707107i −1.22474 0.707107i
\(429\) 0 0
\(430\) 0 0
\(431\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(432\) −0.500000 0.866025i −0.500000 0.866025i
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) −1.00000 1.73205i −1.00000 1.73205i
\(435\) −1.22474 0.707107i −1.22474 0.707107i
\(436\) 0 0
\(437\) 0 0
\(438\) −2.00000 −2.00000
\(439\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(440\) 0 0
\(441\) −1.00000 −1.00000
\(442\) 0 0
\(443\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(444\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(449\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −0.500000 0.866025i −0.500000 0.866025i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(462\) 0 0
\(463\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(464\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(465\) 1.00000 1.00000
\(466\) −1.00000 1.73205i −1.00000 1.73205i
\(467\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(468\) 0 0
\(469\) 1.41421i 1.41421i
\(470\) 1.22474 0.707107i 1.22474 0.707107i
\(471\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.500000 0.866025i −0.500000 0.866025i
\(478\) 2.00000 2.00000
\(479\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(480\) 1.41421i 1.41421i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.00000 −1.00000
\(486\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(487\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 0 0
\(489\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(490\) −1.22474 0.707107i −1.22474 0.707107i
\(491\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −1.00000 −1.00000
\(497\) 1.22474 0.707107i 1.22474 0.707107i
\(498\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(499\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(500\) 0.500000 0.866025i 0.500000 0.866025i
\(501\) 0 0
\(502\) 0 0
\(503\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(504\) 0 0
\(505\) 1.41421i 1.41421i
\(506\) 0 0
\(507\) −1.00000 −1.00000
\(508\) −1.22474 0.707107i −1.22474 0.707107i
\(509\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(510\) 0 0
\(511\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(512\) 1.41421i 1.41421i
\(513\) 0 0
\(514\) 2.82843i 2.82843i
\(515\) −0.500000 0.866025i −0.500000 0.866025i
\(516\) 0 0
\(517\) 0 0
\(518\) 1.00000 1.73205i 1.00000 1.73205i
\(519\) 0 0
\(520\) 0 0
\(521\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) −2.00000 −2.00000
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(530\) 1.41421i 1.41421i
\(531\) 1.00000 1.00000
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −1.22474 0.707107i −1.22474 0.707107i
\(536\) 0 0
\(537\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(538\) 1.22474 0.707107i 1.22474 0.707107i
\(539\) 0 0
\(540\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(541\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(542\) 0 0
\(543\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(548\) 1.00000 1.00000
\(549\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(556\) 1.22474 0.707107i 1.22474 0.707107i
\(557\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(558\) 1.22474 0.707107i 1.22474 0.707107i
\(559\) 0 0
\(560\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(564\) 0.500000 0.866025i 0.500000 0.866025i
\(565\) −0.500000 0.866025i −0.500000 0.866025i
\(566\) −2.00000 −2.00000
\(567\) 1.41421i 1.41421i
\(568\) 0 0
\(569\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(570\) 0 0
\(571\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(572\) 0 0
\(573\) 1.00000 1.00000
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.500000 0.866025i
\(577\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(578\) 1.22474 0.707107i 1.22474 0.707107i
\(579\) 0 0
\(580\) −1.22474 0.707107i −1.22474 0.707107i
\(581\) 1.00000 1.73205i 1.00000 1.73205i
\(582\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) −2.00000 −2.00000
\(587\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(588\) −1.00000 −1.00000
\(589\) 0 0
\(590\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(591\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(592\) −0.500000 0.866025i −0.500000 0.866025i
\(593\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(598\) 0 0
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 0 0
\(601\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(602\) 0 0
\(603\) −1.00000 −1.00000
\(604\) 0 0
\(605\) 0 0
\(606\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(607\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) 0 0
\(609\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(610\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(618\) −1.22474 0.707107i −1.22474 0.707107i
\(619\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(620\) 1.00000 1.00000
\(621\) 0 0
\(622\) 1.41421i 1.41421i
\(623\) 0 0
\(624\) 0 0
\(625\) 0.500000 0.866025i 0.500000 0.866025i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(629\) 0 0
\(630\) 1.00000 1.73205i 1.00000 1.73205i
\(631\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(632\) 0 0
\(633\) 1.22474 0.707107i 1.22474 0.707107i
\(634\) 0 0
\(635\) −1.22474 0.707107i −1.22474 0.707107i
\(636\) −0.500000 0.866025i −0.500000 0.866025i
\(637\) 0 0
\(638\) 0 0
\(639\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(640\) 0 0
\(641\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(642\) −2.00000 −2.00000
\(643\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −1.22474 0.707107i −1.22474 0.707107i
\(652\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(653\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(658\) −2.00000 −2.00000
\(659\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(660\) 0 0
\(661\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(662\) −1.22474 0.707107i −1.22474 0.707107i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) −1.22474 0.707107i −1.22474 0.707107i
\(671\) 0 0
\(672\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(673\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(674\) −2.00000 −2.00000
\(675\) 0 0
\(676\) −1.00000 −1.00000
\(677\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(678\) −1.22474 0.707107i −1.22474 0.707107i
\(679\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(684\) 0 0
\(685\) 1.00000 1.00000
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 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
\(695\) 1.22474 0.707107i 1.22474 0.707107i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −1.22474 0.707107i −1.22474 0.707107i
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 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
\(708\) 1.00000 1.00000
\(709\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(710\) 1.41421i 1.41421i
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(717\) 1.22474 0.707107i 1.22474 0.707107i
\(718\) −1.00000 1.73205i −1.00000 1.73205i
\(719\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(720\) −0.500000 0.866025i −0.500000 0.866025i
\(721\) 1.41421i 1.41421i
\(722\) 1.22474 0.707107i 1.22474 0.707107i
\(723\) 0 0
\(724\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(725\) 0 0
\(726\) 0 0
\(727\) 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
\(730\) −2.00000 −2.00000
\(731\) 0 0
\(732\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(733\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(734\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(735\) −1.00000 −1.00000
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(741\) 0 0
\(742\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(743\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(748\) 0 0
\(749\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(750\) 1.41421i 1.41421i
\(751\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(752\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.41421i 1.41421i
\(757\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(762\) −2.00000 −2.00000
\(763\) 0 0
\(764\) 1.00000 1.00000
\(765\) 0 0
\(766\) 1.41421i 1.41421i
\(767\) 0 0
\(768\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(769\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(770\) 0 0
\(771\) −1.00000 1.73205i −1.00000 1.73205i
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1.41421i 1.41421i
\(778\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(784\) 1.00000 1.00000
\(785\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(786\) 0 0
\(787\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(788\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(789\) 0 0
\(790\) 0 0
\(791\) 1.41421i 1.41421i
\(792\) 0 0
\(793\) 0 0
\(794\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(795\) −0.500000 0.866025i −0.500000 0.866025i
\(796\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(797\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(798\) 0 0