Properties

Label 124.1.i.a.67.2
Level 124
Weight 1
Character 124.67
Analytic conductor 0.062
Analytic rank 0
Dimension 4
Projective image \(A_{4}\)
CM/RM No
Inner twists 4

Related objects

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Newspace parameters

Level: \( N \) = \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 124.i (of order \(6\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.0618840615665\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Projective image \(A_{4}\)
Projective field Galois closure of 4.0.15376.1

Embedding invariants

Embedding label 67.2
Root \(-0.866025 - 0.500000i\)
Character \(\chi\) = 124.67
Dual form 124.1.i.a.87.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(0.866025 - 0.500000i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(0.500000 + 0.866025i) q^{13} +(0.500000 - 0.866025i) q^{14} -1.00000i q^{15} +1.00000 q^{16} +(-0.500000 + 0.866025i) q^{17} +(0.866025 + 0.500000i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-0.500000 - 0.866025i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(0.500000 - 0.866025i) q^{24} +(-0.866025 + 0.500000i) q^{26} -1.00000i q^{27} +(0.866025 + 0.500000i) q^{28} +1.00000 q^{30} -1.00000i q^{31} +1.00000i q^{32} -1.00000 q^{33} +(-0.866025 - 0.500000i) q^{34} +1.00000i q^{35} +(-0.500000 + 0.866025i) q^{37} +(-0.500000 + 0.866025i) q^{38} +1.00000i q^{39} +(-0.866025 + 0.500000i) q^{40} +(-0.500000 - 0.866025i) q^{41} +(0.866025 - 0.500000i) q^{42} +(0.866025 + 0.500000i) q^{43} +(0.866025 - 0.500000i) q^{44} +(0.866025 + 0.500000i) q^{48} +(-0.866025 + 0.500000i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(0.500000 + 0.866025i) q^{53} +1.00000 q^{54} +(0.866025 + 0.500000i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(0.500000 + 0.866025i) q^{57} +(-0.866025 - 0.500000i) q^{59} +1.00000i q^{60} +1.00000 q^{62} -1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} -1.00000i q^{66} +(-0.866025 + 0.500000i) q^{67} +(0.500000 - 0.866025i) q^{68} -1.00000 q^{70} +(0.866025 - 0.500000i) q^{71} +(-0.500000 - 0.866025i) q^{73} +(-0.866025 - 0.500000i) q^{74} +(-0.866025 - 0.500000i) q^{76} +1.00000 q^{77} -1.00000 q^{78} +(-0.866025 - 0.500000i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.866025 - 0.500000i) q^{82} +(0.866025 - 0.500000i) q^{83} +(0.500000 + 0.866025i) q^{84} +1.00000 q^{85} +(-0.500000 + 0.866025i) q^{86} +(0.500000 + 0.866025i) q^{88} -1.00000i q^{91} +(0.500000 - 0.866025i) q^{93} -1.00000i q^{95} +(-0.500000 + 0.866025i) q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{4} - 2q^{5} - 2q^{6} + O(q^{10}) \) \( 4q - 4q^{4} - 2q^{5} - 2q^{6} + 2q^{13} + 2q^{14} + 4q^{16} - 2q^{17} + 2q^{20} - 2q^{21} - 2q^{22} + 2q^{24} + 4q^{30} - 4q^{33} - 2q^{37} - 2q^{38} - 2q^{41} - 2q^{52} + 2q^{53} + 4q^{54} - 2q^{56} + 2q^{57} + 4q^{62} - 4q^{64} + 2q^{65} + 2q^{68} - 4q^{70} - 2q^{73} + 4q^{77} - 4q^{78} - 2q^{80} + 2q^{81} + 2q^{84} + 4q^{85} - 2q^{86} + 2q^{88} + 2q^{93} - 2q^{96} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).

\(n\) \(63\) \(65\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 1.00000i
\(3\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(4\) −1.00000 −1.00000
\(5\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(6\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(7\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(8\) 1.00000i 1.00000i
\(9\) 0 0
\(10\) 0.866025 0.500000i 0.866025 0.500000i
\(11\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(12\) −0.866025 0.500000i −0.866025 0.500000i
\(13\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(14\) 0.500000 0.866025i 0.500000 0.866025i
\(15\) 1.00000i 1.00000i
\(16\) 1.00000 1.00000
\(17\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(18\) 0 0
\(19\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(20\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(21\) −0.500000 0.866025i −0.500000 0.866025i
\(22\) −0.500000 0.866025i −0.500000 0.866025i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0.500000 0.866025i 0.500000 0.866025i
\(25\) 0 0
\(26\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(27\) 1.00000i 1.00000i
\(28\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 1.00000 1.00000
\(31\) 1.00000i 1.00000i
\(32\) 1.00000i 1.00000i
\(33\) −1.00000 −1.00000
\(34\) −0.866025 0.500000i −0.866025 0.500000i
\(35\) 1.00000i 1.00000i
\(36\) 0 0
\(37\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(38\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(39\) 1.00000i 1.00000i
\(40\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(41\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(42\) 0.866025 0.500000i 0.866025 0.500000i
\(43\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(44\) 0.866025 0.500000i 0.866025 0.500000i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(49\) 0 0
\(50\) 0 0
\(51\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(52\) −0.500000 0.866025i −0.500000 0.866025i
\(53\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 1.00000 1.00000
\(55\) 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
\(58\) 0 0
\(59\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 1.00000i 1.00000i
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 1.00000 1.00000
\(63\) 0 0
\(64\) −1.00000 −1.00000
\(65\) 0.500000 0.866025i 0.500000 0.866025i
\(66\) 1.00000i 1.00000i
\(67\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(68\) 0.500000 0.866025i 0.500000 0.866025i
\(69\) 0 0
\(70\) −1.00000 −1.00000
\(71\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) 0 0
\(73\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(74\) −0.866025 0.500000i −0.866025 0.500000i
\(75\) 0 0
\(76\) −0.866025 0.500000i −0.866025 0.500000i
\(77\) 1.00000 1.00000
\(78\) −1.00000 −1.00000
\(79\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) −0.500000 0.866025i −0.500000 0.866025i
\(81\) 0.500000 0.866025i 0.500000 0.866025i
\(82\) 0.866025 0.500000i 0.866025 0.500000i
\(83\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(84\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(85\) 1.00000 1.00000
\(86\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(87\) 0 0
\(88\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 1.00000i 1.00000i
\(92\) 0 0
\(93\) 0.500000 0.866025i 0.500000 0.866025i
\(94\) 0 0
\(95\) 1.00000i 1.00000i
\(96\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) −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 \(0.500000\pi\)
\(104\) 0.866025 0.500000i 0.866025 0.500000i
\(105\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(106\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(107\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(108\) 1.00000i 1.00000i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(111\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(112\) −0.866025 0.500000i −0.866025 0.500000i
\(113\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(114\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0.500000 0.866025i 0.500000 0.866025i
\(119\) 0.866025 0.500000i 0.866025 0.500000i
\(120\) −1.00000 −1.00000
\(121\) 0 0
\(122\) 0 0
\(123\) 1.00000i 1.00000i
\(124\) 1.00000i 1.00000i
\(125\) −1.00000 −1.00000
\(126\) 0 0
\(127\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(128\) 1.00000i 1.00000i
\(129\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(130\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(131\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(132\) 1.00000 1.00000
\(133\) −0.500000 0.866025i −0.500000 0.866025i
\(134\) −0.500000 0.866025i −0.500000 0.866025i
\(135\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(136\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(137\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 1.00000i 1.00000i
\(141\) 0 0
\(142\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(143\) −0.866025 0.500000i −0.866025 0.500000i
\(144\) 0 0
\(145\) 0 0
\(146\) 0.866025 0.500000i 0.866025 0.500000i
\(147\) 0 0
\(148\) 0.500000 0.866025i 0.500000 0.866025i
\(149\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(150\) 0 0
\(151\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0.500000 0.866025i 0.500000 0.866025i
\(153\) 0 0
\(154\) 1.00000i 1.00000i
\(155\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(156\) 1.00000i 1.00000i
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0.500000 0.866025i 0.500000 0.866025i
\(159\) 1.00000i 1.00000i
\(160\) 0.866025 0.500000i 0.866025 0.500000i
\(161\) 0 0
\(162\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(165\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(166\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(167\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(168\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(169\) 0 0
\(170\) 1.00000i 1.00000i
\(171\) 0 0
\(172\) −0.866025 0.500000i −0.866025 0.500000i
\(173\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(177\) −0.500000 0.866025i −0.500000 0.866025i
\(178\) 0 0
\(179\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) 0 0
\(181\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(182\) 1.00000 1.00000
\(183\) 0 0
\(184\) 0 0
\(185\) 1.00000 1.00000
\(186\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(187\) 1.00000i 1.00000i
\(188\) 0 0
\(189\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(190\) 1.00000 1.00000
\(191\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) −0.866025 0.500000i −0.866025 0.500000i
\(193\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(194\) 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 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
\(201\) −1.00000 −1.00000
\(202\) 0 0
\(203\) 0 0
\(204\) 0.866025 0.500000i 0.866025 0.500000i
\(205\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(206\) −0.500000 0.866025i −0.500000 0.866025i
\(207\) 0 0
\(208\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(209\) −1.00000 −1.00000
\(210\) −0.866025 0.500000i −0.866025 0.500000i
\(211\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(212\) −0.500000 0.866025i −0.500000 0.866025i
\(213\) 1.00000 1.00000
\(214\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(215\) 1.00000i 1.00000i
\(216\) −1.00000 −1.00000
\(217\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(218\) 0 0
\(219\) 1.00000i 1.00000i
\(220\) −0.866025 0.500000i −0.866025 0.500000i
\(221\) −1.00000 −1.00000
\(222\) −0.500000 0.866025i −0.500000 0.866025i
\(223\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(224\) 0.500000 0.866025i 0.500000 0.866025i
\(225\) 0 0
\(226\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(227\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(228\) −0.500000 0.866025i −0.500000 0.866025i
\(229\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(230\) 0 0
\(231\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(237\) −0.500000 0.866025i −0.500000 0.866025i
\(238\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(239\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(240\) 1.00000i 1.00000i
\(241\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 1.00000 1.00000
\(247\) 1.00000i 1.00000i
\(248\) −1.00000 −1.00000
\(249\) 1.00000 1.00000
\(250\) 1.00000i 1.00000i
\(251\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(255\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(256\) 1.00000 1.00000
\(257\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(259\) 0.866025 0.500000i 0.866025 0.500000i
\(260\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(261\) 0 0
\(262\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 1.00000i 1.00000i
\(265\) 0.500000 0.866025i 0.500000 0.866025i
\(266\) 0.866025 0.500000i 0.866025 0.500000i
\(267\) 0 0
\(268\) 0.866025 0.500000i 0.866025 0.500000i
\(269\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) −0.500000 0.866025i −0.500000 0.866025i
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(273\) 0.500000 0.866025i 0.500000 0.866025i
\(274\) 0.866025 0.500000i 0.866025 0.500000i
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 1.00000 1.00000
\(281\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(285\) 0.500000 0.866025i 0.500000 0.866025i
\(286\) 0.500000 0.866025i 0.500000 0.866025i
\(287\) 1.00000i 1.00000i
\(288\) 0 0
\(289\) 0 0
\(290\) 0 0
\(291\) 0 0
\(292\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(293\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(294\) 0 0
\(295\) 1.00000i 1.00000i
\(296\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(297\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(298\) −0.866025 0.500000i −0.866025 0.500000i
\(299\) 0 0
\(300\) 0 0
\(301\) −0.500000 0.866025i −0.500000 0.866025i
\(302\) −2.00000 −2.00000
\(303\) 0 0
\(304\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(305\) 0 0
\(306\) 0 0
\(307\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(308\) −1.00000 −1.00000
\(309\) −1.00000 −1.00000
\(310\) −0.500000 0.866025i −0.500000 0.866025i
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 1.00000 1.00000
\(313\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(317\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(318\) −1.00000 −1.00000
\(319\) 0 0
\(320\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(321\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(322\) 0 0
\(323\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(324\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(329\) 0 0
\(330\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(331\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(332\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(333\) 0 0
\(334\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(335\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(336\) −0.500000 0.866025i −0.500000 0.866025i
\(337\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 1.00000i 1.00000i
\(340\) −1.00000 −1.00000
\(341\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(342\) 0 0
\(343\) 1.00000i 1.00000i
\(344\) 0.500000 0.866025i 0.500000 0.866025i
\(345\) 0 0
\(346\) 0.866025 0.500000i 0.866025 0.500000i
\(347\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0.866025 0.500000i 0.866025 0.500000i
\(352\) −0.500000 0.866025i −0.500000 0.866025i
\(353\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(354\) 0.866025 0.500000i 0.866025 0.500000i
\(355\) −0.866025 0.500000i −0.866025 0.500000i
\(356\) 0 0
\(357\) 1.00000 1.00000
\(358\) 0.500000 0.866025i 0.500000 0.866025i
\(359\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0.866025 0.500000i 0.866025 0.500000i
\(363\) 0 0
\(364\) 1.00000i 1.00000i
\(365\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(366\) 0 0
\(367\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 1.00000i 1.00000i
\(371\) 1.00000i 1.00000i
\(372\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(373\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(374\) 1.00000 1.00000
\(375\) −0.866025 0.500000i −0.866025 0.500000i
\(376\) 0 0
\(377\) 0 0
\(378\) −0.866025 0.500000i −0.866025 0.500000i
\(379\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(380\) 1.00000i 1.00000i
\(381\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(382\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(383\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(384\) 0.500000 0.866025i 0.500000 0.866025i
\(385\) −0.500000 0.866025i −0.500000 0.866025i
\(386\) −0.866025 0.500000i −0.866025 0.500000i
\(387\) 0 0
\(388\) 0 0
\(389\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(390\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(391\) 0 0
\(392\) 0 0
\(393\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(394\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(395\) 1.00000i 1.00000i
\(396\) 0 0
\(397\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(398\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(399\) 1.00000i 1.00000i
\(400\) 0 0
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 1.00000i 1.00000i
\(403\) 0.866025 0.500000i 0.866025 0.500000i
\(404\) 0 0
\(405\) −1.00000 −1.00000
\(406\) 0 0
\(407\) 1.00000i 1.00000i
\(408\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(409\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(410\) −0.866025 0.500000i −0.866025 0.500000i
\(411\) 1.00000i 1.00000i
\(412\) 0.866025 0.500000i 0.866025 0.500000i
\(413\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(414\) 0 0
\(415\) −0.866025 0.500000i −0.866025 0.500000i
\(416\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(417\) 0 0
\(418\) 1.00000i 1.00000i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0.500000 0.866025i 0.500000 0.866025i
\(421\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) 0.500000 0.866025i 0.500000 0.866025i
\(423\) 0 0
\(424\) 0.866025 0.500000i 0.866025 0.500000i
\(425\) 0 0
\(426\) 1.00000i 1.00000i
\(427\) 0 0
\(428\) −0.866025 0.500000i −0.866025 0.500000i
\(429\) −0.500000 0.866025i −0.500000 0.866025i
\(430\) 1.00000 1.00000
\(431\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(432\) 1.00000i 1.00000i
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) −0.866025 0.500000i −0.866025 0.500000i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 1.00000 1.00000
\(439\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(440\) 0.500000 0.866025i 0.500000 0.866025i
\(441\) 0 0
\(442\) 1.00000i 1.00000i
\(443\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(444\) 0.866025 0.500000i 0.866025 0.500000i
\(445\) 0 0
\(446\) 0.500000 0.866025i 0.500000 0.866025i
\(447\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(448\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(449\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(452\) −0.500000 0.866025i −0.500000 0.866025i
\(453\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(454\) −0.500000 0.866025i −0.500000 0.866025i
\(455\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(456\) 0.866025 0.500000i 0.866025 0.500000i
\(457\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(459\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) −1.00000 −1.00000
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 1.00000 1.00000
\(470\) 0 0
\(471\) 0 0
\(472\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(473\) −1.00000 −1.00000
\(474\) 0.866025 0.500000i 0.866025 0.500000i
\(475\) 0 0
\(476\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(477\) 0 0
\(478\) −0.500000 0.866025i −0.500000 0.866025i
\(479\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 1.00000 1.00000
\(481\) −1.00000 −1.00000
\(482\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(492\) 1.00000i 1.00000i
\(493\) 0 0
\(494\) −1.00000 −1.00000
\(495\) 0 0
\(496\) 1.00000i 1.00000i
\(497\) −1.00000 −1.00000
\(498\) 1.00000i 1.00000i
\(499\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(500\) 1.00000 1.00000
\(501\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(502\) 0.500000 0.866025i 0.500000 0.866025i
\(503\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) −0.866025 0.500000i −0.866025 0.500000i
\(509\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(510\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(511\) 1.00000i 1.00000i
\(512\) 1.00000i 1.00000i
\(513\) 0.500000 0.866025i 0.500000 0.866025i
\(514\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(515\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(516\) −0.500000 0.866025i −0.500000 0.866025i
\(517\) 0 0
\(518\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(519\) 1.00000i 1.00000i
\(520\) −0.866025 0.500000i −0.866025 0.500000i
\(521\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) −0.866025 0.500000i −0.866025 0.500000i
\(525\) 0 0
\(526\) 0 0
\(527\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(528\) −1.00000 −1.00000
\(529\) 1.00000 1.00000
\(530\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(531\) 0 0
\(532\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(533\) 0.500000 0.866025i 0.500000 0.866025i
\(534\) 0 0
\(535\) 1.00000i 1.00000i
\(536\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(537\) −0.500000 0.866025i −0.500000 0.866025i
\(538\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(539\) 0 0
\(540\) 0.866025 0.500000i 0.866025 0.500000i
\(541\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(542\) 0 0
\(543\) 1.00000i 1.00000i
\(544\) −0.866025 0.500000i −0.866025 0.500000i
\(545\) 0 0
\(546\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(547\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(548\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(554\) 0 0
\(555\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(556\) 0 0
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 1.00000i 1.00000i
\(560\) 1.00000i 1.00000i
\(561\) 0.500000 0.866025i 0.500000 0.866025i
\(562\) 2.00000i 2.00000i
\(563\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 0 0
\(565\) 0.500000 0.866025i 0.500000 0.866025i
\(566\) 0 0
\(567\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(568\) −0.500000 0.866025i −0.500000 0.866025i
\(569\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(570\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(571\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(572\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(573\) 1.00000 1.00000
\(574\) −1.00000 −1.00000
\(575\) 0 0
\(576\) 0 0
\(577\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(578\) 0 0
\(579\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(580\) 0 0
\(581\) −1.00000 −1.00000
\(582\) 0 0
\(583\) −0.866025 0.500000i −0.866025 0.500000i
\(584\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(585\) 0 0
\(586\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(587\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) 0.500000 0.866025i 0.500000 0.866025i
\(590\) −1.00000 −1.00000
\(591\) 1.00000i 1.00000i
\(592\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(593\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(594\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(595\) −0.866025 0.500000i −0.866025 0.500000i
\(596\) 0.500000 0.866025i 0.500000 0.866025i
\(597\) 1.00000 1.00000
\(598\) 0 0
\(599\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 0 0
\(601\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(602\) 0.866025 0.500000i 0.866025 0.500000i
\(603\) 0 0
\(604\) 2.00000i 2.00000i
\(605\) 0 0
\(606\) 0 0
\(607\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(608\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(614\) 0.500000 0.866025i 0.500000 0.866025i
\(615\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(616\) 1.00000i 1.00000i
\(617\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(618\) 1.00000i 1.00000i
\(619\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0.866025 0.500000i 0.866025 0.500000i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 1.00000i 1.00000i
\(625\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(626\) −0.866025 0.500000i −0.866025 0.500000i
\(627\) −0.866025 0.500000i −0.866025 0.500000i
\(628\) 0 0
\(629\) −0.500000 0.866025i −0.500000 0.866025i
\(630\) 0 0
\(631\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(632\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(633\) −0.500000 0.866025i −0.500000 0.866025i
\(634\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(635\) 1.00000i 1.00000i
\(636\) 1.00000i 1.00000i
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(641\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0.500000 0.866025i 0.500000 0.866025i
\(646\) −0.500000 0.866025i −0.500000 0.866025i
\(647\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(648\) −0.866025 0.500000i −0.866025 0.500000i
\(649\) 1.00000 1.00000
\(650\) 0 0
\(651\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 1.00000i 1.00000i
\(656\) −0.500000 0.866025i −0.500000 0.866025i
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) −0.500000 0.866025i −0.500000 0.866025i
\(661\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(663\) −0.866025 0.500000i −0.866025 0.500000i
\(664\) −0.500000 0.866025i −0.500000 0.866025i
\(665\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(666\) 0 0
\(667\) 0 0
\(668\) −0.866025 0.500000i −0.866025 0.500000i
\(669\) −0.500000 0.866025i −0.500000 0.866025i
\(670\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(671\) 0 0
\(672\) 0.866025 0.500000i 0.866025 0.500000i
\(673\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(674\) 2.00000i 2.00000i
\(675\) 0 0
\(676\) 0 0
\(677\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(678\) −1.00000 −1.00000
\(679\) 0 0
\(680\) 1.00000i 1.00000i
\(681\) −1.00000 −1.00000
\(682\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(686\) −1.00000 −1.00000
\(687\) 0.866025 0.500000i 0.866025 0.500000i
\(688\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(689\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(690\) 0 0
\(691\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(692\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(693\) 0 0
\(694\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(695\) 0 0
\(696\) 0 0
\(697\) 1.00000 1.00000
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(702\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(703\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(704\) 0.866025 0.500000i 0.866025 0.500000i
\(705\) 0 0
\(706\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(707\) 0 0
\(708\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(709\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(710\) 0.500000 0.866025i 0.500000 0.866025i
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 1.00000i 1.00000i
\(715\) 1.00000i 1.00000i
\(716\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(717\) −1.00000 −1.00000
\(718\) 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 \(0.5\pi\)
\(720\) 0 0
\(721\) 1.00000 1.00000
\(722\) 0 0
\(723\) 0.866025 0.500000i 0.866025 0.500000i
\(724\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(725\) 0 0
\(726\) 0 0
\(727\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(728\) −1.00000 −1.00000
\(729\) −1.00000 −1.00000
\(730\) −0.866025 0.500000i −0.866025 0.500000i
\(731\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(732\) 0 0
\(733\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(734\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(735\) 0 0
\(736\) 0 0
\(737\) 0.500000 0.866025i 0.500000 0.866025i
\(738\) 0 0
\(739\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(740\) −1.00000 −1.00000
\(741\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(742\) 1.00000 1.00000
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) −0.866025 0.500000i −0.866025 0.500000i
\(745\) 1.00000 1.00000
\(746\) 2.00000i 2.00000i
\(747\) 0 0
\(748\) 1.00000i 1.00000i
\(749\) −0.500000 0.866025i −0.500000 0.866025i
\(750\) 0.500000 0.866025i 0.500000 0.866025i
\(751\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) −0.500000 0.866025i −0.500000 0.866025i
\(754\) 0 0
\(755\) 1.73205 1.00000i 1.73205 1.00000i
\(756\) 0.500000 0.866025i 0.500000 0.866025i
\(757\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(758\) 0.500000 0.866025i 0.500000 0.866025i
\(759\) 0 0
\(760\) −1.00000 −1.00000
\(761\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(762\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(763\) 0 0
\(764\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(765\) 0 0
\(766\) −0.500000 0.866025i −0.500000 0.866025i
\(767\) 1.00000i 1.00000i
\(768\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(769\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(770\) 0.866025 0.500000i 0.866025 0.500000i
\(771\) 1.00000i 1.00000i
\(772\) 0.500000 0.866025i 0.500000 0.866025i
\(773\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1.00000 1.00000
\(778\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(779\) 1.00000i 1.00000i
\(780\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(781\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(787\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(788\) −0.500000 0.866025i −0.500000 0.866025i
\(789\) 0 0
\(790\) −1.00000 −1.00000
\(791\) 1.00000i 1.00000i
\(792\) 0 0
\(793\) 0 0
\(794\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(795\) 0.866025 0.500000i 0.866025 0.500000i
\(796\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(797\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(798\) 1.00000 1.00000
\(799\)