Properties

Label 133.1.m.a.125.2
Level 133
Weight 1
Character 133.125
Analytic conductor 0.066
Analytic rank 0
Dimension 4
Projective image \(A_{4}\)
CM/RM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 133 = 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 133.m (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.0663756466802\)
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 4.0.17689.1
Artin image $\SL(2,3):C_2$
Artin field Galois closure of \(\mathbb{Q}[x]/(x^{16} - \cdots)\)

Embedding invariants

Embedding label 125.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 133.125
Dual form 133.1.m.a.83.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(-0.866025 + 0.500000i) q^{6} -1.00000i q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(-0.866025 + 0.500000i) q^{6} -1.00000i q^{7} -1.00000 q^{8} +(0.866025 - 0.500000i) q^{10} +(-0.866025 + 0.500000i) q^{13} +(0.866025 + 0.500000i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.866025 + 0.500000i) q^{17} +1.00000i q^{19} +(0.500000 - 0.866025i) q^{21} +(-0.500000 - 0.866025i) q^{23} +(-0.866025 - 0.500000i) q^{24} -1.00000i q^{26} -1.00000i q^{27} +(0.500000 + 0.866025i) q^{29} +1.00000 q^{30} +(-0.866025 + 0.500000i) q^{34} +(-0.500000 + 0.866025i) q^{35} +(-0.866025 - 0.500000i) q^{38} -1.00000 q^{39} +(0.866025 + 0.500000i) q^{40} +(0.866025 + 0.500000i) q^{41} +(0.500000 + 0.866025i) q^{42} +(-0.500000 + 0.866025i) q^{43} +1.00000 q^{46} +(-0.866025 + 0.500000i) q^{47} +(0.866025 - 0.500000i) q^{48} -1.00000 q^{49} +(0.500000 + 0.866025i) q^{51} +(0.500000 + 0.866025i) q^{53} +(0.866025 + 0.500000i) q^{54} +1.00000i q^{56} +(-0.500000 + 0.866025i) q^{57} -1.00000 q^{58} +(-0.866025 - 0.500000i) q^{59} +(0.866025 - 0.500000i) q^{61} +1.00000 q^{64} +1.00000 q^{65} +(-0.500000 - 0.866025i) q^{67} -1.00000i q^{69} +(-0.500000 - 0.866025i) q^{70} +(0.500000 - 0.866025i) q^{71} +(-0.866025 - 0.500000i) q^{73} +(0.500000 - 0.866025i) q^{78} +(-0.500000 + 0.866025i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-0.866025 + 0.500000i) q^{82} +(-0.500000 - 0.866025i) q^{85} +(-0.500000 - 0.866025i) q^{86} +1.00000i q^{87} +(0.866025 - 0.500000i) q^{89} +(0.500000 + 0.866025i) q^{91} -1.00000i q^{94} +(0.500000 - 0.866025i) q^{95} +(0.866025 + 0.500000i) q^{97} +(0.500000 - 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 4q^{8} + O(q^{10}) \) \( 4q - 2q^{2} - 4q^{8} - 2q^{15} + 2q^{16} + 2q^{21} - 2q^{23} + 2q^{29} + 4q^{30} - 2q^{35} - 4q^{39} + 2q^{42} - 2q^{43} + 4q^{46} - 4q^{49} + 2q^{51} + 2q^{53} - 2q^{57} - 4q^{58} + 4q^{64} + 4q^{65} - 2q^{67} - 2q^{70} + 2q^{71} + 2q^{78} - 2q^{79} + 2q^{81} - 2q^{85} - 2q^{86} + 2q^{91} + 2q^{95} + 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/133\mathbb{Z}\right)^\times\).

\(n\) \(78\) \(115\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(3\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.500000\pi\)
\(4\) 0 0
\(5\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(7\) 1.00000i 1.00000i
\(8\) −1.00000 −1.00000
\(9\) 0 0
\(10\) 0.866025 0.500000i 0.866025 0.500000i
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(14\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(15\) −0.500000 0.866025i −0.500000 0.866025i
\(16\) 0.500000 0.866025i 0.500000 0.866025i
\(17\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.500000\pi\)
\(18\) 0 0
\(19\) 1.00000i 1.00000i
\(20\) 0 0
\(21\) 0.500000 0.866025i 0.500000 0.866025i
\(22\) 0 0
\(23\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(24\) −0.866025 0.500000i −0.866025 0.500000i
\(25\) 0 0
\(26\) 1.00000i 1.00000i
\(27\) 1.00000i 1.00000i
\(28\) 0 0
\(29\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 1.00000 1.00000
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(35\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) −0.866025 0.500000i −0.866025 0.500000i
\(39\) −1.00000 −1.00000
\(40\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(41\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.500000\pi\)
\(42\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(43\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 1.00000 1.00000
\(47\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(48\) 0.866025 0.500000i 0.866025 0.500000i
\(49\) −1.00000 −1.00000
\(50\) 0 0
\(51\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(52\) 0 0
\(53\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(55\) 0 0
\(56\) 1.00000i 1.00000i
\(57\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(58\) −1.00000 −1.00000
\(59\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 1.00000 1.00000
\(66\) 0 0
\(67\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(68\) 0 0
\(69\) 1.00000i 1.00000i
\(70\) −0.500000 0.866025i −0.500000 0.866025i
\(71\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(72\) 0 0
\(73\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0.500000 0.866025i 0.500000 0.866025i
\(79\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(80\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(81\) 0.500000 0.866025i 0.500000 0.866025i
\(82\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) −0.500000 0.866025i −0.500000 0.866025i
\(86\) −0.500000 0.866025i −0.500000 0.866025i
\(87\) 1.00000i 1.00000i
\(88\) 0 0
\(89\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 0 0
\(91\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(92\) 0 0
\(93\) 0 0
\(94\) 1.00000i 1.00000i
\(95\) 0.500000 0.866025i 0.500000 0.866025i
\(96\) 0 0
\(97\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.500000\pi\)
\(98\) 0.500000 0.866025i 0.500000 0.866025i
\(99\) 0 0
\(100\) 0 0
\(101\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) −1.00000 −1.00000
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0.866025 0.500000i 0.866025 0.500000i
\(105\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(106\) −1.00000 −1.00000
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.866025 0.500000i −0.866025 0.500000i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) −0.500000 0.866025i −0.500000 0.866025i
\(115\) 1.00000i 1.00000i
\(116\) 0 0
\(117\) 0 0
\(118\) 0.866025 0.500000i 0.866025 0.500000i
\(119\) 0.500000 0.866025i 0.500000 0.866025i
\(120\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(121\) −1.00000 −1.00000
\(122\) 1.00000i 1.00000i
\(123\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(124\) 0 0
\(125\) 1.00000i 1.00000i
\(126\) 0 0
\(127\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(128\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(129\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(130\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(131\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) 1.00000 1.00000
\(134\) 1.00000 1.00000
\(135\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(136\) −0.866025 0.500000i −0.866025 0.500000i
\(137\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(139\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(140\) 0 0
\(141\) −1.00000 −1.00000
\(142\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(143\) 0 0
\(144\) 0 0
\(145\) 1.00000i 1.00000i
\(146\) 0.866025 0.500000i 0.866025 0.500000i
\(147\) −0.866025 0.500000i −0.866025 0.500000i
\(148\) 0 0
\(149\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 1.00000i 1.00000i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.500000\pi\)
\(158\) −0.500000 0.866025i −0.500000 0.866025i
\(159\) 1.00000i 1.00000i
\(160\) 0 0
\(161\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(162\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(163\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(168\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(169\) 0 0
\(170\) 1.00000 1.00000
\(171\) 0 0
\(172\) 0 0
\(173\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(174\) −0.866025 0.500000i −0.866025 0.500000i
\(175\) 0 0
\(176\) 0 0
\(177\) −0.500000 0.866025i −0.500000 0.866025i
\(178\) 1.00000i 1.00000i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(182\) −1.00000 −1.00000
\(183\) 1.00000 1.00000
\(184\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −1.00000 −1.00000
\(190\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(193\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(194\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(195\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) 0 0
\(201\) 1.00000i 1.00000i
\(202\) 1.00000i 1.00000i
\(203\) 0.866025 0.500000i 0.866025 0.500000i
\(204\) 0 0
\(205\) −0.500000 0.866025i −0.500000 0.866025i
\(206\) 0 0
\(207\) 0 0
\(208\) 1.00000i 1.00000i
\(209\) 0 0
\(210\) 1.00000i 1.00000i
\(211\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(212\) 0 0
\(213\) 0.866025 0.500000i 0.866025 0.500000i
\(214\) 0 0
\(215\) 0.866025 0.500000i 0.866025 0.500000i
\(216\) 1.00000i 1.00000i
\(217\) 0 0
\(218\) −0.500000 0.866025i −0.500000 0.866025i
\(219\) −0.500000 0.866025i −0.500000 0.866025i
\(220\) 0 0
\(221\) −1.00000 −1.00000
\(222\) 0 0
\(223\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) −0.866025 0.500000i −0.866025 0.500000i
\(231\) 0 0
\(232\) −0.500000 0.866025i −0.500000 0.866025i
\(233\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(234\) 0 0
\(235\) 1.00000 1.00000
\(236\) 0 0
\(237\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(238\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) −1.00000 −1.00000
\(241\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(242\) 0.500000 0.866025i 0.500000 0.866025i
\(243\) 0 0
\(244\) 0 0
\(245\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(246\) −1.00000 −1.00000
\(247\) −0.500000 0.866025i −0.500000 0.866025i
\(248\) 0 0
\(249\) 0 0
\(250\) −0.866025 0.500000i −0.866025 0.500000i
\(251\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 1.00000 1.00000
\(255\) 1.00000i 1.00000i
\(256\) 0 0
\(257\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(258\) 1.00000i 1.00000i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0.866025 0.500000i 0.866025 0.500000i
\(263\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(264\) 0 0
\(265\) 1.00000i 1.00000i
\(266\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(267\) 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 \(-0.166667\pi\)
1.00000i \(0.500000\pi\)
\(272\) 0.866025 0.500000i 0.866025 0.500000i
\(273\) 1.00000i 1.00000i
\(274\) −1.00000 −1.00000
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 1.00000i 1.00000i
\(279\) 0 0
\(280\) 0.500000 0.866025i 0.500000 0.866025i
\(281\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(282\) 0.500000 0.866025i 0.500000 0.866025i
\(283\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(284\) 0 0
\(285\) 0.866025 0.500000i 0.866025 0.500000i
\(286\) 0 0
\(287\) 0.500000 0.866025i 0.500000 0.866025i
\(288\) 0 0
\(289\) 0 0
\(290\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(291\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(292\) 0 0
\(293\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0.866025 0.500000i 0.866025 0.500000i
\(295\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(296\) 0 0
\(297\) 0 0
\(298\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(299\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(300\) 0 0
\(301\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(302\) 0 0
\(303\) 1.00000 1.00000
\(304\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(305\) −1.00000 −1.00000
\(306\) 0 0
\(307\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 1.00000 1.00000
\(313\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(314\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(315\) 0 0
\(316\) 0 0
\(317\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(318\) −0.866025 0.500000i −0.866025 0.500000i
\(319\) 0 0
\(320\) −0.866025 0.500000i −0.866025 0.500000i
\(321\) 0 0
\(322\) 1.00000i 1.00000i
\(323\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(324\) 0 0
\(325\) 0 0
\(326\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(327\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(328\) −0.866025 0.500000i −0.866025 0.500000i
\(329\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 1.00000i 1.00000i
\(335\) 1.00000i 1.00000i
\(336\) −0.500000 0.866025i −0.500000 0.866025i
\(337\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000i 1.00000i
\(344\) 0.500000 0.866025i 0.500000 0.866025i
\(345\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(346\) 0.866025 0.500000i 0.866025 0.500000i
\(347\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(352\) 0 0
\(353\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(354\) 1.00000 1.00000
\(355\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(356\) 0 0
\(357\) 0.866025 0.500000i 0.866025 0.500000i
\(358\) 0 0
\(359\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(360\) 0 0
\(361\) −1.00000 −1.00000
\(362\) 1.00000i 1.00000i
\(363\) −0.866025 0.500000i −0.866025 0.500000i
\(364\) 0 0
\(365\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(366\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(367\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(368\) −1.00000 −1.00000
\(369\) 0 0
\(370\) 0 0
\(371\) 0.866025 0.500000i 0.866025 0.500000i
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) −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
\(378\) 0.500000 0.866025i 0.500000 0.866025i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 1.00000i 1.00000i
\(382\) 0 0
\(383\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.500000\pi\)
\(384\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(385\) 0 0
\(386\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(387\) 0 0
\(388\) 0 0
\(389\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(390\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(391\) 1.00000i 1.00000i
\(392\) 1.00000 1.00000
\(393\) −0.500000 0.866025i −0.500000 0.866025i
\(394\) 0 0
\(395\) 0.866025 0.500000i 0.866025 0.500000i
\(396\) 0 0
\(397\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.500000\pi\)
\(398\) 1.00000i 1.00000i
\(399\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(400\) 0 0
\(401\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(402\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(403\) 0 0
\(404\) 0 0
\(405\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(406\) 1.00000i 1.00000i
\(407\) 0 0
\(408\) −0.500000 0.866025i −0.500000 0.866025i
\(409\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(410\) 1.00000 1.00000
\(411\) 1.00000i 1.00000i
\(412\) 0 0
\(413\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.00000 1.00000
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(422\) −0.500000 0.866025i −0.500000 0.866025i
\(423\) 0 0
\(424\) −0.500000 0.866025i −0.500000 0.866025i
\(425\) 0 0
\(426\) 1.00000i 1.00000i
\(427\) −0.500000 0.866025i −0.500000 0.866025i
\(428\) 0 0
\(429\) 0 0
\(430\) 1.00000i 1.00000i
\(431\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(432\) −0.866025 0.500000i −0.866025 0.500000i
\(433\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(434\) 0 0
\(435\) 0.500000 0.866025i 0.500000 0.866025i
\(436\) 0 0
\(437\) 0.866025 0.500000i 0.866025 0.500000i
\(438\) 1.00000 1.00000
\(439\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 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 \(-1.00000\pi\)
\(444\) 0 0
\(445\) −1.00000 −1.00000
\(446\) 0.866025 0.500000i 0.866025 0.500000i
\(447\) 0.866025 0.500000i 0.866025 0.500000i
\(448\) 1.00000i 1.00000i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.00000i 1.00000i
\(456\) 0.500000 0.866025i 0.500000 0.866025i
\(457\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0 0
\(459\) 0.500000 0.866025i 0.500000 0.866025i
\(460\) 0 0
\(461\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 1.00000 1.00000
\(465\) 0 0
\(466\) −0.500000 0.866025i −0.500000 0.866025i
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(470\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(471\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(472\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(473\) 0 0
\(474\) 1.00000i 1.00000i
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1.00000i 1.00000i
\(483\) −1.00000 −1.00000
\(484\) 0 0
\(485\) −0.500000 0.866025i −0.500000 0.866025i
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(489\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(490\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(491\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(492\) 0 0
\(493\) 1.00000i 1.00000i
\(494\) 1.00000 1.00000
\(495\) 0 0
\(496\) 0 0
\(497\) −0.866025 0.500000i −0.866025 0.500000i
\(498\) 0 0
\(499\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(500\) 0 0
\(501\) 1.00000 1.00000
\(502\) 1.00000i 1.00000i
\(503\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(504\) 0 0
\(505\) −1.00000 −1.00000
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(510\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(511\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(512\) −1.00000 −1.00000
\(513\) 1.00000 1.00000
\(514\) 1.00000i 1.00000i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −0.500000 0.866025i −0.500000 0.866025i
\(520\) −1.00000 −1.00000
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 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
\(526\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(531\) 0 0
\(532\) 0 0
\(533\) −1.00000 −1.00000
\(534\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(535\) 0 0
\(536\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(537\) 0 0
\(538\) 0.866025 0.500000i 0.866025 0.500000i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(543\) −1.00000 −1.00000
\(544\) 0 0
\(545\) 0.866025 0.500000i 0.866025 0.500000i
\(546\) −0.866025 0.500000i −0.866025 0.500000i
\(547\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(552\) 1.00000i 1.00000i
\(553\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) 0 0
\(559\) 1.00000i 1.00000i
\(560\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(561\) 0 0
\(562\) 1.00000 1.00000
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.866025 0.500000i 0.866025 0.500000i
\(567\) −0.866025 0.500000i −0.866025 0.500000i
\(568\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 1.00000i 1.00000i
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(575\) 0 0
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0.866025 0.500000i 0.866025 0.500000i
\(580\) 0 0
\(581\) 0 0
\(582\) −1.00000 −1.00000
\(583\) 0 0
\(584\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(585\) 0 0
\(586\) −1.73205 1.00000i −1.73205 1.00000i
\(587\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.500000\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −1.00000 −1.00000
\(591\) 0 0
\(592\) 0 0
\(593\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(594\) 0 0
\(595\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(596\) 0 0
\(597\) 1.00000 1.00000
\(598\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(599\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(603\) 0 0
\(604\) 0 0
\(605\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(606\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 1.00000 1.00000
\(610\) 0.500000 0.866025i 0.500000 0.866025i
\(611\) 0.500000 0.866025i 0.500000 0.866025i
\(612\) 0 0
\(613\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(614\) 0.866025 0.500000i 0.866025 0.500000i
\(615\) 1.00000i 1.00000i
\(616\) 0 0
\(617\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(622\) 0 0
\(623\) −0.500000 0.866025i −0.500000 0.866025i
\(624\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(625\) 0.500000 0.866025i 0.500000 0.866025i
\(626\) 1.00000i 1.00000i
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(632\) 0.500000 0.866025i 0.500000 0.866025i
\(633\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(634\) −1.00000 −1.00000
\(635\) 1.00000i 1.00000i
\(636\) 0 0
\(637\) 0.866025 0.500000i 0.866025 0.500000i
\(638\) 0 0
\(639\) 0 0
\(640\) 0.866025 0.500000i 0.866025 0.500000i
\(641\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(642\) 0 0
\(643\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.500000\pi\)
\(644\) 0 0
\(645\) 1.00000 1.00000
\(646\) −0.500000 0.866025i −0.500000 0.866025i
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 1.00000i 1.00000i
\(655\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(656\) 0.866025 0.500000i 0.866025 0.500000i
\(657\) 0 0
\(658\) −1.00000 −1.00000
\(659\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(660\) 0 0
\(661\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(662\) 0 0
\(663\) −0.866025 0.500000i −0.866025 0.500000i
\(664\) 0 0
\(665\) −0.866025 0.500000i −0.866025 0.500000i
\(666\) 0 0
\(667\) 0.500000 0.866025i 0.500000 0.866025i
\(668\) 0 0
\(669\) −0.500000 0.866025i −0.500000 0.866025i
\(670\) −0.866025 0.500000i −0.866025 0.500000i
\(671\) 0 0
\(672\) 0 0
\(673\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(674\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0.500000 0.866025i 0.500000 0.866025i
\(680\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(681\) 0 0
\(682\) 0 0
\(683\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 1.00000i 1.00000i
\(686\) −0.866025 0.500000i −0.866025 0.500000i
\(687\) 0 0
\(688\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(689\) −0.866025 0.500000i −0.866025 0.500000i
\(690\) −0.500000 0.866025i −0.500000 0.866025i
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.500000 0.866025i −0.500000 0.866025i
\(695\) −1.00000 −1.00000
\(696\) 1.00000i 1.00000i
\(697\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(698\) 0 0
\(699\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(700\) 0 0
\(701\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(702\) −1.00000 −1.00000
\(703\) 0 0
\(704\) 0 0
\(705\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(706\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(707\) −0.500000 0.866025i −0.500000 0.866025i
\(708\) 0 0
\(709\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) 1.00000i 1.00000i
\(711\) 0 0
\(712\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(713\) 0 0
\(714\) 1.00000i 1.00000i
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) −0.500000 0.866025i −0.500000 0.866025i
\(719\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.500000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.500000 0.866025i 0.500000 0.866025i
\(723\) −1.00000 −1.00000
\(724\) 0 0
\(725\) 0 0
\(726\) 0.866025 0.500000i 0.866025 0.500000i
\(727\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.500000\pi\)
\(728\) −0.500000 0.866025i −0.500000 0.866025i
\(729\) −1.00000 −1.00000
\(730\) −1.00000 −1.00000
\(731\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 1.00000i 1.00000i
\(735\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(740\) 0 0
\(741\) 1.00000i 1.00000i
\(742\) 1.00000i 1.00000i
\(743\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(744\) 0 0
\(745\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) −0.500000 0.866025i −0.500000 0.866025i
\(751\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 1.00000i 1.00000i
\(753\) −1.00000 −1.00000
\(754\) 0.866025 0.500000i 0.866025 0.500000i
\(755\) 0 0
\(756\) 0 0
\(757\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(761\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(763\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(764\) 0 0
\(765\) 0 0
\(766\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(767\) 1.00000 1.00000
\(768\) 0 0
\(769\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(770\) 0 0
\(771\) −1.00000 −1.00000
\(772\) 0 0
\(773\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −0.866025 0.500000i −0.866025 0.500000i
\(777\) 0 0
\(778\) 1.00000 1.00000
\(779\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(780\) 0 0
\(781\) 0 0
\(782\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(783\) 0.866025 0.500000i 0.866025 0.500000i
\(784\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(785\) −0.500000 0.866025i −0.500000 0.866025i
\(786\) 1.00000 1.00000
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 0.866025 0.500000i 0.866025 0.500000i
\(790\) 1.00000i 1.00000i
\(791\) 0 0
\(792\) 0 0
\(793\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(794\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(795\) 0.500000 0.866025i 0.500000 0.866025i
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(799\) −1.00000 −1.00000
\(800\) 0 0
\(801\) 0 0
\(802\) −0.500000 0.866025i −0.500000 0.866025i
\(803\) 0 0