Properties

Label 819.1.ek.a.601.1
Level $819$
Weight $1$
Character 819.601
Analytic conductor $0.409$
Analytic rank $0$
Dimension $4$
Projective image $A_{4}$
CM/RM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 819.ek (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.408734245346\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(A_{4}\)
Projective field: Galois closure of 4.0.670761.1

Embedding invariants

Embedding label 601.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 819.601
Dual form 819.1.ek.a.139.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.866025 + 0.500000i) q^{10} -1.00000 q^{11} +(-0.866025 - 0.500000i) q^{13} +(-0.500000 - 0.866025i) q^{14} +1.00000 q^{15} -1.00000 q^{16} +(-0.866025 - 0.500000i) q^{17} +(0.500000 + 0.866025i) q^{18} +(0.866025 + 0.500000i) q^{19} +1.00000i q^{21} -1.00000 q^{22} +(0.866025 + 0.500000i) q^{24} +(-0.866025 - 0.500000i) q^{26} -1.00000i q^{27} -1.00000 q^{29} +1.00000 q^{30} +(0.866025 - 0.500000i) q^{31} +(0.866025 + 0.500000i) q^{33} +(-0.866025 - 0.500000i) q^{34} +(0.866025 + 0.500000i) q^{35} +(-0.500000 - 0.866025i) q^{37} +(0.866025 + 0.500000i) q^{38} +(0.500000 + 0.866025i) q^{39} +(0.866025 - 0.500000i) q^{40} +1.00000i q^{42} +(-0.866025 - 0.500000i) q^{45} +(0.866025 + 0.500000i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{51} -1.00000i q^{54} +(0.866025 - 0.500000i) q^{55} +(0.500000 + 0.866025i) q^{56} +(-0.500000 - 0.866025i) q^{57} -1.00000 q^{58} -1.00000i q^{59} +(-1.73205 + 1.00000i) q^{61} +(0.866025 - 0.500000i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +1.00000 q^{65} +(0.866025 + 0.500000i) q^{66} +(1.00000 - 1.73205i) q^{67} +(0.866025 + 0.500000i) q^{70} +(-0.500000 + 0.866025i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-0.500000 - 0.866025i) q^{74} +(0.500000 + 0.866025i) q^{77} +(0.500000 + 0.866025i) q^{78} +(0.500000 - 0.866025i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.866025 - 0.500000i) q^{83} +1.00000 q^{85} +(0.866025 + 0.500000i) q^{87} +1.00000 q^{88} +(0.866025 - 0.500000i) q^{89} +(-0.866025 - 0.500000i) q^{90} +1.00000i q^{91} -1.00000 q^{93} +(0.866025 + 0.500000i) q^{94} -1.00000 q^{95} +(-0.500000 + 0.866025i) q^{98} +(-0.500000 - 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} - 2q^{7} - 4q^{8} + 2q^{9} + O(q^{10}) \) \( 4q + 4q^{2} - 2q^{7} - 4q^{8} + 2q^{9} - 4q^{11} - 2q^{14} + 4q^{15} - 4q^{16} + 2q^{18} - 4q^{22} - 4q^{29} + 4q^{30} - 2q^{37} + 2q^{39} - 2q^{49} + 2q^{51} + 2q^{56} - 2q^{57} - 4q^{58} + 2q^{63} + 4q^{64} + 4q^{65} + 4q^{67} - 2q^{71} - 2q^{72} - 2q^{74} + 2q^{77} + 2q^{78} + 2q^{79} - 2q^{81} + 4q^{85} + 4q^{88} - 4q^{93} - 4q^{95} - 2q^{98} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(3\) −0.866025 0.500000i −0.866025 0.500000i
\(4\) 0 0
\(5\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(6\) −0.866025 0.500000i −0.866025 0.500000i
\(7\) −0.500000 0.866025i −0.500000 0.866025i
\(8\) −1.00000 −1.00000
\(9\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(10\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(11\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) 0 0
\(13\) −0.866025 0.500000i −0.866025 0.500000i
\(14\) −0.500000 0.866025i −0.500000 0.866025i
\(15\) 1.00000 1.00000
\(16\) −1.00000 −1.00000
\(17\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(19\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 1.00000i 1.00000i
\(22\) −1.00000 −1.00000
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(25\) 0 0
\(26\) −0.866025 0.500000i −0.866025 0.500000i
\(27\) 1.00000i 1.00000i
\(28\) 0 0
\(29\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 1.00000 1.00000
\(31\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 0 0
\(33\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(34\) −0.866025 0.500000i −0.866025 0.500000i
\(35\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(36\) 0 0
\(37\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(38\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(39\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(40\) 0.866025 0.500000i 0.866025 0.500000i
\(41\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 1.00000i 1.00000i
\(43\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(44\) 0 0
\(45\) −0.866025 0.500000i −0.866025 0.500000i
\(46\) 0 0
\(47\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(48\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(49\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(50\) 0 0
\(51\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 1.00000i 1.00000i
\(55\) 0.866025 0.500000i 0.866025 0.500000i
\(56\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(57\) −0.500000 0.866025i −0.500000 0.866025i
\(58\) −1.00000 −1.00000
\(59\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(60\) 0 0
\(61\) −1.73205 + 1.00000i −1.73205 + 1.00000i −0.866025 + 0.500000i \(0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(62\) 0.866025 0.500000i 0.866025 0.500000i
\(63\) 0.500000 0.866025i 0.500000 0.866025i
\(64\) 1.00000 1.00000
\(65\) 1.00000 1.00000
\(66\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(67\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(71\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(72\) −0.500000 0.866025i −0.500000 0.866025i
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) −0.500000 0.866025i −0.500000 0.866025i
\(75\) 0 0
\(76\) 0 0
\(77\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(78\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(79\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(80\) 0.866025 0.500000i 0.866025 0.500000i
\(81\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(84\) 0 0
\(85\) 1.00000 1.00000
\(86\) 0 0
\(87\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(88\) 1.00000 1.00000
\(89\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) −0.866025 0.500000i −0.866025 0.500000i
\(91\) 1.00000i 1.00000i
\(92\) 0 0
\(93\) −1.00000 −1.00000
\(94\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(95\) −1.00000 −1.00000
\(96\) 0 0
\(97\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(98\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(99\) −0.500000 0.866025i −0.500000 0.866025i
\(100\) 0 0
\(101\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(103\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(104\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(105\) −0.500000 0.866025i −0.500000 0.866025i
\(106\) 0 0
\(107\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0.866025 0.500000i 0.866025 0.500000i
\(111\) 1.00000i 1.00000i
\(112\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(113\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(114\) −0.500000 0.866025i −0.500000 0.866025i
\(115\) 0 0
\(116\) 0 0
\(117\) 1.00000i 1.00000i
\(118\) 1.00000i 1.00000i
\(119\) 1.00000i 1.00000i
\(120\) −1.00000 −1.00000
\(121\) 0 0
\(122\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000i 1.00000i
\(126\) 0.500000 0.866025i 0.500000 0.866025i
\(127\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(128\) 1.00000 1.00000
\(129\) 0 0
\(130\) 1.00000 1.00000
\(131\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 1.00000i 1.00000i
\(134\) 1.00000 1.73205i 1.00000 1.73205i
\(135\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(136\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(137\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(138\) 0 0
\(139\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(140\) 0 0
\(141\) −0.500000 0.866025i −0.500000 0.866025i
\(142\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(143\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(144\) −0.500000 0.866025i −0.500000 0.866025i
\(145\) 0.866025 0.500000i 0.866025 0.500000i
\(146\) 0 0
\(147\) 0.866025 0.500000i 0.866025 0.500000i
\(148\) 0 0
\(149\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(150\) 0 0
\(151\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(152\) −0.866025 0.500000i −0.866025 0.500000i
\(153\) 1.00000i 1.00000i
\(154\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(155\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(156\) 0 0
\(157\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(158\) 0.500000 0.866025i 0.500000 0.866025i
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(163\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) −1.00000 −1.00000
\(166\) −0.866025 0.500000i −0.866025 0.500000i
\(167\) −1.73205 1.00000i −1.73205 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 0.500000i \(-0.833333\pi\)
\(168\) 1.00000i 1.00000i
\(169\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(170\) 1.00000 1.00000
\(171\) 1.00000i 1.00000i
\(172\) 0 0
\(173\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(175\) 0 0
\(176\) 1.00000 1.00000
\(177\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(178\) 0.866025 0.500000i 0.866025 0.500000i
\(179\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 1.00000i 1.00000i
\(183\) 2.00000 2.00000
\(184\) 0 0
\(185\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(186\) −1.00000 −1.00000
\(187\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(188\) 0 0
\(189\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(190\) −1.00000 −1.00000
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) −0.866025 0.500000i −0.866025 0.500000i
\(193\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(194\) 0 0
\(195\) −0.866025 0.500000i −0.866025 0.500000i
\(196\) 0 0
\(197\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(198\) −0.500000 0.866025i −0.500000 0.866025i
\(199\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(200\) 0 0
\(201\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(202\) 1.00000i 1.00000i
\(203\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(204\) 0 0
\(205\) 0 0
\(206\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(207\) 0 0
\(208\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(209\) −0.866025 0.500000i −0.866025 0.500000i
\(210\) −0.500000 0.866025i −0.500000 0.866025i
\(211\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(212\) 0 0
\(213\) 0.866025 0.500000i 0.866025 0.500000i
\(214\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(215\) 0 0
\(216\) 1.00000i 1.00000i
\(217\) −0.866025 0.500000i −0.866025 0.500000i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(222\) 1.00000i 1.00000i
\(223\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −1.00000 −1.00000
\(227\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(228\) 0 0
\(229\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(230\) 0 0
\(231\) 1.00000i 1.00000i
\(232\) 1.00000 1.00000
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 1.00000i 1.00000i
\(235\) −1.00000 −1.00000
\(236\) 0 0
\(237\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(238\) 1.00000i 1.00000i
\(239\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) −1.00000 −1.00000
\(241\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(242\) 0 0
\(243\) 0.866025 0.500000i 0.866025 0.500000i
\(244\) 0 0
\(245\) 1.00000i 1.00000i
\(246\) 0 0
\(247\) −0.500000 0.866025i −0.500000 0.866025i
\(248\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(249\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(250\) 1.00000i 1.00000i
\(251\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −0.500000 0.866025i −0.500000 0.866025i
\(255\) −0.866025 0.500000i −0.866025 0.500000i
\(256\) 0 0
\(257\) 1.73205 + 1.00000i 1.73205 + 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) 0 0
\(259\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(260\) 0 0
\(261\) −0.500000 0.866025i −0.500000 0.866025i
\(262\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(263\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) −0.866025 0.500000i −0.866025 0.500000i
\(265\) 0 0
\(266\) 1.00000i 1.00000i
\(267\) −1.00000 −1.00000
\(268\) 0 0
\(269\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(271\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(272\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(273\) 0.500000 0.866025i 0.500000 0.866025i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(278\) 1.00000i 1.00000i
\(279\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(280\) −0.866025 0.500000i −0.866025 0.500000i
\(281\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(282\) −0.500000 0.866025i −0.500000 0.866025i
\(283\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(284\) 0 0
\(285\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(286\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(287\) 0 0
\(288\) 0 0
\(289\) 0 0
\(290\) 0.866025 0.500000i 0.866025 0.500000i
\(291\) 0 0
\(292\) 0 0
\(293\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(294\) 0.866025 0.500000i 0.866025 0.500000i
\(295\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(296\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(297\) 1.00000i 1.00000i
\(298\) −1.00000 −1.00000
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0.500000 0.866025i 0.500000 0.866025i
\(303\) 0.500000 0.866025i 0.500000 0.866025i
\(304\) −0.866025 0.500000i −0.866025 0.500000i
\(305\) 1.00000 1.73205i 1.00000 1.73205i
\(306\) 1.00000i 1.00000i
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 1.00000 1.00000
\(310\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(311\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) −0.500000 0.866025i −0.500000 0.866025i
\(313\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(314\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(315\) 1.00000i 1.00000i
\(316\) 0 0
\(317\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(318\) 0 0
\(319\) 1.00000 1.00000
\(320\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(321\) 1.00000i 1.00000i
\(322\) 0 0
\(323\) −0.500000 0.866025i −0.500000 0.866025i
\(324\) 0 0
\(325\) 0 0
\(326\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(327\) 0 0
\(328\) 0 0
\(329\) 1.00000i 1.00000i
\(330\) −1.00000 −1.00000
\(331\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(332\) 0 0
\(333\) 0.500000 0.866025i 0.500000 0.866025i
\(334\) −1.73205 1.00000i −1.73205 1.00000i
\(335\) 2.00000i 2.00000i
\(336\) 1.00000i 1.00000i
\(337\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(338\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(339\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(340\) 0 0
\(341\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(342\) 1.00000i 1.00000i
\(343\) 1.00000 1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(348\) 0 0
\(349\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(350\) 0 0
\(351\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(352\) 0 0
\(353\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(354\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(355\) 1.00000i 1.00000i
\(356\) 0 0
\(357\) 0.500000 0.866025i 0.500000 0.866025i
\(358\) −0.500000 0.866025i −0.500000 0.866025i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(361\) 0 0
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 2.00000 2.00000
\(367\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(371\) 0 0
\(372\) 0 0
\(373\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(375\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(376\) −0.866025 0.500000i −0.866025 0.500000i
\(377\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(378\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(379\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(380\) 0 0
\(381\) 1.00000i 1.00000i
\(382\) 0 0
\(383\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(384\) −0.866025 0.500000i −0.866025 0.500000i
\(385\) −0.866025 0.500000i −0.866025 0.500000i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(390\) −0.866025 0.500000i −0.866025 0.500000i
\(391\) 0 0
\(392\) 0.500000 0.866025i 0.500000 0.866025i
\(393\) 1.00000 1.00000
\(394\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(395\) 1.00000i 1.00000i
\(396\) 0 0
\(397\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(398\) −0.866025 0.500000i −0.866025 0.500000i
\(399\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(400\) 0 0
\(401\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(402\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(403\) −1.00000 −1.00000
\(404\) 0 0
\(405\) 1.00000i 1.00000i
\(406\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(407\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(408\) −0.500000 0.866025i −0.500000 0.866025i
\(409\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(414\) 0 0
\(415\) 1.00000 1.00000
\(416\) 0 0
\(417\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(418\) −0.866025 0.500000i −0.866025 0.500000i
\(419\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(420\) 0 0
\(421\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 1.00000i 1.00000i
\(424\) 0 0
\(425\) 0 0
\(426\) 0.866025 0.500000i 0.866025 0.500000i
\(427\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(428\) 0 0
\(429\) −0.500000 0.866025i −0.500000 0.866025i
\(430\) 0 0
\(431\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(432\) 1.00000i 1.00000i
\(433\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(434\) −0.866025 0.500000i −0.866025 0.500000i
\(435\) −1.00000 −1.00000
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(440\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(441\) −1.00000 −1.00000
\(442\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(443\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(446\) 1.00000i 1.00000i
\(447\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(448\) −0.500000 0.866025i −0.500000 0.866025i
\(449\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(454\) 0 0
\(455\) −0.500000 0.866025i −0.500000 0.866025i
\(456\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(457\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 0.866025 0.500000i 0.866025 0.500000i
\(459\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(460\) 0 0
\(461\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(462\) 1.00000i 1.00000i
\(463\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(464\) 1.00000 1.00000
\(465\) 0.866025 0.500000i 0.866025 0.500000i
\(466\) 0 0
\(467\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(468\) 0 0
\(469\) −2.00000 −2.00000
\(470\) −1.00000 −1.00000
\(471\) 1.00000 1.00000
\(472\) 1.00000i 1.00000i
\(473\) 0 0
\(474\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(479\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(480\) 0 0
\(481\) 1.00000i 1.00000i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0.866025 0.500000i 0.866025 0.500000i
\(487\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(488\) 1.73205 1.00000i 1.73205 1.00000i
\(489\) 0.866025 0.500000i 0.866025 0.500000i
\(490\) 1.00000i 1.00000i
\(491\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(492\) 0 0
\(493\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(494\) −0.500000 0.866025i −0.500000 0.866025i
\(495\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(496\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(497\) 1.00000 1.00000
\(498\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(499\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0 0
\(501\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(502\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(503\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(504\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(505\) −0.500000 0.866025i −0.500000 0.866025i
\(506\) 0 0
\(507\) 1.00000i 1.00000i
\(508\) 0 0
\(509\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(510\) −0.866025 0.500000i −0.866025 0.500000i
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 0.500000 0.866025i 0.500000 0.866025i
\(514\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(515\) 0.500000 0.866025i 0.500000 0.866025i
\(516\) 0 0
\(517\) −0.866025 0.500000i −0.866025 0.500000i
\(518\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(519\) 0 0
\(520\) −1.00000 −1.00000
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −0.500000 0.866025i −0.500000 0.866025i
\(523\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −1.00000 −1.00000
\(527\) −1.00000 −1.00000
\(528\) −0.866025 0.500000i −0.866025 0.500000i
\(529\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) 0.866025 0.500000i 0.866025 0.500000i
\(532\) 0 0
\(533\) 0 0
\(534\) −1.00000 −1.00000
\(535\) −0.866025 0.500000i −0.866025 0.500000i
\(536\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(537\) 1.00000i 1.00000i
\(538\) −0.866025 0.500000i −0.866025 0.500000i
\(539\) 0.500000 0.866025i 0.500000 0.866025i
\(540\) 0 0
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0.500000 0.866025i 0.500000 0.866025i
\(547\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) −1.73205 1.00000i −1.73205 1.00000i
\(550\) 0 0
\(551\) −0.866025 0.500000i −0.866025 0.500000i
\(552\) 0 0
\(553\) −1.00000 −1.00000
\(554\) 0 0
\(555\) −0.500000 0.866025i −0.500000 0.866025i
\(556\) 0 0
\(557\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(559\) 0 0
\(560\) −0.866025 0.500000i −0.866025 0.500000i
\(561\) −0.500000 0.866025i −0.500000 0.866025i
\(562\) 0.500000 0.866025i 0.500000 0.866025i
\(563\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) 0 0
\(565\) 0.866025 0.500000i 0.866025 0.500000i
\(566\) 0 0
\(567\) 1.00000 1.00000
\(568\) 0.500000 0.866025i 0.500000 0.866025i
\(569\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(571\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(577\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.00000i 1.00000i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(586\) 1.00000i 1.00000i
\(587\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(588\) 0 0
\(589\) 1.00000 1.00000
\(590\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(591\) 1.00000i 1.00000i
\(592\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(593\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 1.00000i 1.00000i
\(595\) −0.500000 0.866025i −0.500000 0.866025i
\(596\) 0 0
\(597\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(598\) 0 0
\(599\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(602\) 0 0
\(603\) 2.00000 2.00000
\(604\) 0 0
\(605\) 0 0
\(606\) 0.500000 0.866025i 0.500000 0.866025i
\(607\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(608\) 0 0
\(609\) 1.00000i 1.00000i
\(610\) 1.00000 1.73205i 1.00000 1.73205i
\(611\) −0.500000 0.866025i −0.500000 0.866025i
\(612\) 0 0
\(613\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −0.500000 0.866025i −0.500000 0.866025i
\(617\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(618\) 1.00000 1.00000
\(619\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0.866025 0.500000i 0.866025 0.500000i
\(623\) −0.866025 0.500000i −0.866025 0.500000i
\(624\) −0.500000 0.866025i −0.500000 0.866025i
\(625\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(626\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(627\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(628\) 0 0
\(629\) 1.00000i 1.00000i
\(630\) 1.00000i 1.00000i
\(631\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(632\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(633\) 0 0
\(634\) 0.500000 0.866025i 0.500000 0.866025i
\(635\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(636\) 0 0
\(637\) 0.866025 0.500000i 0.866025 0.500000i
\(638\) 1.00000 1.00000
\(639\) −1.00000 −1.00000
\(640\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(641\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(642\) 1.00000i 1.00000i
\(643\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.500000 0.866025i −0.500000 0.866025i
\(647\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(648\) 0.500000 0.866025i 0.500000 0.866025i
\(649\) 1.00000i 1.00000i
\(650\) 0 0
\(651\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(652\) 0 0
\(653\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(654\) 0 0
\(655\) 0.500000 0.866025i 0.500000 0.866025i
\(656\) 0 0
\(657\) 0 0
\(658\) 1.00000i 1.00000i
\(659\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(660\) 0 0
\(661\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) 0 0
\(663\) 1.00000i 1.00000i
\(664\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(665\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(666\) 0.500000 0.866025i 0.500000 0.866025i
\(667\) 0 0
\(668\) 0 0
\(669\) 0.500000 0.866025i 0.500000 0.866025i
\(670\) 2.00000i 2.00000i
\(671\) 1.73205 1.00000i 1.73205 1.00000i
\(672\) 0 0
\(673\) −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 0
\(677\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(678\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(679\) 0 0
\(680\) −1.00000 −1.00000
\(681\) 0 0
\(682\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(683\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000 1.00000
\(687\) −1.00000 −1.00000
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(692\) 0 0
\(693\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(694\) 1.00000 1.00000
\(695\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(696\) −0.866025 0.500000i −0.866025 0.500000i
\(697\) 0 0
\(698\) 1.00000i 1.00000i
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(703\) 1.00000i 1.00000i
\(704\) −1.00000 −1.00000
\(705\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(706\) 1.00000i 1.00000i
\(707\) 0.866025 0.500000i 0.866025 0.500000i
\(708\) 0 0
\(709\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(710\) 1.00000i 1.00000i
\(711\) 1.00000 1.00000
\(712\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(713\) 0 0
\(714\) 0.500000 0.866025i 0.500000 0.866025i
\(715\) −1.00000 −1.00000
\(716\) 0 0
\(717\) 1.00000i 1.00000i
\(718\) 0 0
\(719\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(720\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(721\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(728\) 1.00000i 1.00000i
\(729\) −1.00000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(734\) 1.00000i 1.00000i
\(735\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(736\) 0 0
\(737\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(738\) 0 0
\(739\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) 0 0
\(741\) 1.00000i 1.00000i
\(742\) 0 0
\(743\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(744\) 1.00000 1.00000
\(745\) 0.866025 0.500000i 0.866025 0.500000i
\(746\) −1.00000 −1.00000
\(747\) 1.00000i 1.00000i
\(748\) 0 0
\(749\) 0.500000 0.866025i 0.500000 0.866025i
\(750\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(751\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(752\) −0.866025 0.500000i −0.866025 0.500000i
\(753\) −0.500000 0.866025i −0.500000 0.866025i
\(754\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(755\) 1.00000i 1.00000i
\(756\) 0 0
\(757\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(758\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(759\) 0 0
\(760\) 1.00000 1.00000
\(761\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(762\) 1.00000i 1.00000i
\(763\) 0 0
\(764\) 0 0
\(765\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(766\) 1.00000i 1.00000i
\(767\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(768\) 0 0
\(769\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) −0.866025 0.500000i −0.866025 0.500000i
\(771\) −1.00000 1.73205i −1.00000 1.73205i
\(772\) 0 0
\(773\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0.866025 0.500000i 0.866025 0.500000i
\(778\) 0.500000 0.866025i 0.500000 0.866025i
\(779\) 0 0
\(780\) 0 0
\(781\) 0.500000 0.866025i 0.500000 0.866025i
\(782\) 0 0
\(783\) 1.00000i 1.00000i
\(784\) 0.500000 0.866025i 0.500000 0.866025i
\(785\) 0.500000 0.866025i 0.500000 0.866025i
\(786\) 1.00000 1.00000
\(787\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(788\) 0 0
\(789\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(790\) 1.00000i 1.00000i
\(791\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(792\) 0.500000 + 0.866025i 0.500000 + 0.866025i