Properties

Label 1183.1.z.a.268.2
Level $1183$
Weight $1$
Character 1183.268
Analytic conductor $0.590$
Analytic rank $0$
Dimension $8$
Projective image $A_{4}$
CM/RM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1183.z (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.590393909945\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(A_{4}\)
Projective field: Galois closure of 4.0.8281.1
Artin image: $C_8.A_4$
Artin field: Galois closure of 32.0.515207889456069254383620937908064472169867121.1

Embedding invariants

Embedding label 268.2
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1183.268
Dual form 1183.1.z.a.746.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.965926 + 0.258819i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.965926 + 0.258819i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{10} +(-0.965926 - 0.258819i) q^{11} +(-0.500000 + 0.866025i) q^{14} +(0.707107 + 0.707107i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.866025 + 0.500000i) q^{17} +(-0.965926 + 0.258819i) q^{19} +(0.965926 + 0.258819i) q^{21} -1.00000 q^{22} +(0.866025 + 0.500000i) q^{23} +(0.965926 + 0.258819i) q^{24} -1.00000 q^{27} +(0.866025 + 0.500000i) q^{30} +(0.258819 - 0.965926i) q^{31} +(0.258819 + 0.965926i) q^{33} +(-0.707107 + 0.707107i) q^{34} +(0.500000 - 0.866025i) q^{35} +(0.258819 + 0.965926i) q^{37} +(-0.866025 + 0.500000i) q^{38} +(0.500000 - 0.866025i) q^{40} +1.00000 q^{42} +(0.965926 + 0.258819i) q^{46} +(-0.258819 - 0.965926i) q^{47} +1.00000 q^{48} -1.00000i q^{49} +(0.866025 + 0.500000i) q^{51} +(-0.500000 - 0.866025i) q^{53} +(-0.965926 + 0.258819i) q^{54} +1.00000 q^{55} -1.00000i q^{56} +(0.707107 + 0.707107i) q^{57} +(-0.965926 - 0.258819i) q^{59} +(-0.500000 + 0.866025i) q^{61} -1.00000i q^{62} -1.00000i q^{64} +(0.500000 + 0.866025i) q^{66} +(-0.258819 + 0.965926i) q^{67} -1.00000i q^{69} +(0.258819 - 0.965926i) q^{70} +(0.965926 + 0.258819i) q^{73} +(0.500000 + 0.866025i) q^{74} +(0.866025 - 0.500000i) q^{77} +(0.500000 - 0.866025i) q^{79} +(0.258819 - 0.965926i) q^{80} +(0.500000 + 0.866025i) q^{81} +(0.707107 - 0.707107i) q^{85} +(0.866025 - 0.500000i) q^{88} +(-0.258819 - 0.965926i) q^{89} +(-0.965926 + 0.258819i) q^{93} +(-0.500000 - 0.866025i) q^{94} +(0.866025 - 0.500000i) q^{95} +(1.41421 + 1.41421i) q^{97} +(-0.258819 - 0.965926i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{3} + O(q^{10}) \) \( 8q - 4q^{3} - 4q^{14} - 4q^{16} - 8q^{22} - 8q^{27} + 4q^{35} + 4q^{40} + 8q^{42} + 8q^{48} - 4q^{53} + 8q^{55} - 4q^{61} + 4q^{66} + 4q^{74} + 4q^{79} + 4q^{81} - 4q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(4\) 0 0
\(5\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(6\) −0.707107 0.707107i −0.707107 0.707107i
\(7\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(8\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(9\) 0 0
\(10\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(11\) −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(15\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(16\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(17\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(20\) 0 0
\(21\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(22\) −1.00000 −1.00000
\(23\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(24\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −1.00000
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(31\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(32\) 0 0
\(33\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(34\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(35\) 0.500000 0.866025i 0.500000 0.866025i
\(36\) 0 0
\(37\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(38\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(39\) 0 0
\(40\) 0.500000 0.866025i 0.500000 0.866025i
\(41\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(42\) 1.00000 1.00000
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(47\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(48\) 1.00000 1.00000
\(49\) 1.00000i 1.00000i
\(50\) 0 0
\(51\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(52\) 0 0
\(53\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(54\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(55\) 1.00000 1.00000
\(56\) 1.00000i 1.00000i
\(57\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(58\) 0 0
\(59\) −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(60\) 0 0
\(61\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(62\) 1.00000i 1.00000i
\(63\) 0 0
\(64\) 1.00000i 1.00000i
\(65\) 0 0
\(66\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(67\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(68\) 0 0
\(69\) 1.00000i 1.00000i
\(70\) 0.258819 0.965926i 0.258819 0.965926i
\(71\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(72\) 0 0
\(73\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(74\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(75\) 0 0
\(76\) 0 0
\(77\) 0.866025 0.500000i 0.866025 0.500000i
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(80\) 0.258819 0.965926i 0.258819 0.965926i
\(81\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(82\) 0 0
\(83\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(84\) 0 0
\(85\) 0.707107 0.707107i 0.707107 0.707107i
\(86\) 0 0
\(87\) 0 0
\(88\) 0.866025 0.500000i 0.866025 0.500000i
\(89\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(94\) −0.500000 0.866025i −0.500000 0.866025i
\(95\) 0.866025 0.500000i 0.866025 0.500000i
\(96\) 0 0
\(97\) 1.41421 + 1.41421i 1.41421 + 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(98\) −0.258819 0.965926i −0.258819 0.965926i
\(99\) 0 0
\(100\) 0 0
\(101\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(102\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(103\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(104\) 0 0
\(105\) −1.00000 −1.00000
\(106\) −0.707107 0.707107i −0.707107 0.707107i
\(107\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(110\) 0.965926 0.258819i 0.965926 0.258819i
\(111\) 0.707107 0.707107i 0.707107 0.707107i
\(112\) −0.258819 0.965926i −0.258819 0.965926i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(115\) −0.965926 0.258819i −0.965926 0.258819i
\(116\) 0 0
\(117\) 0 0
\(118\) −1.00000 −1.00000
\(119\) 0.258819 0.965926i 0.258819 0.965926i
\(120\) −1.00000 −1.00000
\(121\) 0 0
\(122\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(123\) 0 0
\(124\) 0 0
\(125\) 0.707107 0.707107i 0.707107 0.707107i
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −0.258819 0.965926i −0.258819 0.965926i
\(129\) 0 0
\(130\) 0 0
\(131\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0.500000 0.866025i 0.500000 0.866025i
\(134\) 1.00000i 1.00000i
\(135\) 0.965926 0.258819i 0.965926 0.258819i
\(136\) 0.258819 0.965926i 0.258819 0.965926i
\(137\) −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(138\) −0.258819 0.965926i −0.258819 0.965926i
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 1.00000 1.00000
\(147\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(148\) 0 0
\(149\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(150\) 0 0
\(151\) −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(152\) 0.500000 0.866025i 0.500000 0.866025i
\(153\) 0 0
\(154\) 0.707107 0.707107i 0.707107 0.707107i
\(155\) 1.00000i 1.00000i
\(156\) 0 0
\(157\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) 0.258819 0.965926i 0.258819 0.965926i
\(159\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(160\) 0 0
\(161\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(162\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(163\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(164\) 0 0
\(165\) −0.500000 0.866025i −0.500000 0.866025i
\(166\) 0 0
\(167\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(168\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(169\) 0 0
\(170\) 0.500000 0.866025i 0.500000 0.866025i
\(171\) 0 0
\(172\) 0 0
\(173\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.707107 0.707107i 0.707107 0.707107i
\(177\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(178\) −0.500000 0.866025i −0.500000 0.866025i
\(179\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 1.00000 1.00000
\(184\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(185\) −0.500000 0.866025i −0.500000 0.866025i
\(186\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(187\) 0.965926 0.258819i 0.965926 0.258819i
\(188\) 0 0
\(189\) 0.707107 0.707107i 0.707107 0.707107i
\(190\) 0.707107 0.707107i 0.707107 0.707107i
\(191\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(192\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(193\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(194\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(198\) 0 0
\(199\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 0.965926 0.258819i 0.965926 0.258819i
\(202\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −0.965926 0.258819i −0.965926 0.258819i
\(207\) 0 0
\(208\) 0 0
\(209\) 1.00000 1.00000
\(210\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(215\) 0 0
\(216\) 0.707107 0.707107i 0.707107 0.707107i
\(217\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(218\) 1.00000i 1.00000i
\(219\) −0.258819 0.965926i −0.258819 0.965926i
\(220\) 0 0
\(221\) 0 0
\(222\) 0.500000 0.866025i 0.500000 0.866025i
\(223\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(228\) 0 0
\(229\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(230\) −1.00000 −1.00000
\(231\) −0.866025 0.500000i −0.866025 0.500000i
\(232\) 0 0
\(233\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(234\) 0 0
\(235\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(236\) 0 0
\(237\) −1.00000 −1.00000
\(238\) 1.00000i 1.00000i
\(239\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(240\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(241\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(246\) 0 0
\(247\) 0 0
\(248\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(249\) 0 0
\(250\) 0.500000 0.866025i 0.500000 0.866025i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) −0.707107 0.707107i −0.707107 0.707107i
\(254\) 0 0
\(255\) −0.965926 0.258819i −0.965926 0.258819i
\(256\) 0 0
\(257\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) −0.866025 0.500000i −0.866025 0.500000i
\(260\) 0 0
\(261\) 0 0
\(262\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(263\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(264\) −0.866025 0.500000i −0.866025 0.500000i
\(265\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(266\) 0.258819 0.965926i 0.258819 0.965926i
\(267\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(268\) 0 0
\(269\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(270\) 0.866025 0.500000i 0.866025 0.500000i
\(271\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(272\) 1.00000i 1.00000i
\(273\) 0 0
\(274\) −1.00000 −1.00000
\(275\) 0 0
\(276\) 0 0
\(277\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(281\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(282\) −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 \(0.166667\pi\)
\(284\) 0 0
\(285\) −0.866025 0.500000i −0.866025 0.500000i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0 0
\(290\) 0 0
\(291\) 0.517638 1.93185i 0.517638 1.93185i
\(292\) 0 0
\(293\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(294\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(295\) 1.00000 1.00000
\(296\) −0.866025 0.500000i −0.866025 0.500000i
\(297\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(298\) 0.866025 0.500000i 0.866025 0.500000i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) −1.00000 −1.00000
\(303\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(304\) 0.258819 0.965926i 0.258819 0.965926i
\(305\) 0.258819 0.965926i 0.258819 0.965926i
\(306\) 0 0
\(307\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(308\) 0 0
\(309\) 1.00000i 1.00000i
\(310\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(311\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0 0
\(313\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(314\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(315\) 0 0
\(316\) 0 0
\(317\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(318\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(319\) 0 0
\(320\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(321\) 1.00000 1.00000
\(322\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(323\) 0.707107 0.707107i 0.707107 0.707107i
\(324\) 0 0
\(325\) 0 0
\(326\) −0.500000 0.866025i −0.500000 0.866025i
\(327\) 0.965926 0.258819i 0.965926 0.258819i
\(328\) 0 0
\(329\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(330\) −0.707107 0.707107i −0.707107 0.707107i
\(331\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.00000i 1.00000i
\(336\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(337\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(342\) 0 0
\(343\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(344\) 0 0
\(345\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(346\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(347\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(348\) 0 0
\(349\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(354\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(355\) 0 0
\(356\) 0 0
\(357\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(358\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(359\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.00000 −1.00000
\(366\) 0.965926 0.258819i 0.965926 0.258819i
\(367\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(369\) 0 0
\(370\) −0.707107 0.707107i −0.707107 0.707107i
\(371\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(372\) 0 0
\(373\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(374\) 0.866025 0.500000i 0.866025 0.500000i
\(375\) −0.965926 0.258819i −0.965926 0.258819i
\(376\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(377\) 0 0
\(378\) 0.500000 0.866025i 0.500000 0.866025i
\(379\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(383\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(384\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(385\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(386\) 1.00000 1.00000
\(387\) 0 0
\(388\) 0 0
\(389\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) −1.00000 −1.00000
\(392\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(393\) 1.00000 1.00000
\(394\) 0 0
\(395\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(396\) 0 0
\(397\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(398\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(399\) −1.00000 −1.00000
\(400\) 0 0
\(401\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(402\) 0.866025 0.500000i 0.866025 0.500000i
\(403\) 0 0
\(404\) 0 0
\(405\) −0.707107 0.707107i −0.707107 0.707107i
\(406\) 0 0
\(407\) 1.00000i 1.00000i
\(408\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(409\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(410\) 0 0
\(411\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(412\) 0 0
\(413\) 0.866025 0.500000i 0.866025 0.500000i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0.965926 0.258819i 0.965926 0.258819i
\(419\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(420\) 0 0
\(421\) −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(425\) 0 0
\(426\) 0 0
\(427\) −0.258819 0.965926i −0.258819 0.965926i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(432\) 0.500000 0.866025i 0.500000 0.866025i
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(435\) 0 0
\(436\) 0 0
\(437\) −0.965926 0.258819i −0.965926 0.258819i
\(438\) −0.500000 0.866025i −0.500000 0.866025i
\(439\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(441\) 0 0
\(442\) 0 0
\(443\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(444\) 0 0
\(445\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(446\) 0 0
\(447\) −0.707107 0.707107i −0.707107 0.707107i
\(448\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(449\) −1.41421 + 1.41421i −1.41421 + 1.41421i −0.707107 + 0.707107i \(0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(454\) 1.00000i 1.00000i
\(455\) 0 0
\(456\) −1.00000 −1.00000
\(457\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(458\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(459\) 0.866025 0.500000i 0.866025 0.500000i
\(460\) 0 0
\(461\) −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(462\) −0.965926 0.258819i −0.965926 0.258819i
\(463\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(464\) 0 0
\(465\) 0.866025 0.500000i 0.866025 0.500000i
\(466\) −0.965926 0.258819i −0.965926 0.258819i
\(467\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(468\) 0 0
\(469\) −0.500000 0.866025i −0.500000 0.866025i
\(470\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(471\) 0.500000 0.866025i 0.500000 0.866025i
\(472\) 0.866025 0.500000i 0.866025 0.500000i
\(473\) 0 0
\(474\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1.00000 1.00000
\(483\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(484\) 0 0
\(485\) −1.73205 1.00000i −1.73205 1.00000i
\(486\) 0 0
\(487\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(488\) −0.258819 0.965926i −0.258819 0.965926i
\(489\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(490\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(497\) 0 0
\(498\) 0 0
\(499\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0.707107 0.707107i 0.707107 0.707107i
\(506\) −0.866025 0.500000i −0.866025 0.500000i
\(507\) 0 0
\(508\) 0 0
\(509\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(510\) −1.00000 −1.00000
\(511\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(512\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(513\) 0.965926 0.258819i 0.965926 0.258819i
\(514\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(515\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(516\) 0 0
\(517\) 1.00000i 1.00000i
\(518\) −0.965926 0.258819i −0.965926 0.258819i
\(519\) 1.00000i 1.00000i
\(520\) 0 0
\(521\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −0.707107 0.707107i −0.707107 0.707107i
\(527\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(528\) −0.965926 0.258819i −0.965926 0.258819i
\(529\) 0 0
\(530\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(535\) 0.258819 0.965926i 0.258819 0.965926i
\(536\) −0.500000 0.866025i −0.500000 0.866025i
\(537\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(538\) −0.707107 0.707107i −0.707107 0.707107i
\(539\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(540\) 0 0
\(541\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(542\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(543\) 0 0
\(544\) 0 0
\(545\) 1.00000i 1.00000i
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(553\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(554\) 0.707107 0.707107i 0.707107 0.707107i
\(555\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(556\) 0 0
\(557\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(561\) −0.707107 0.707107i −0.707107 0.707107i
\(562\) 0 0
\(563\) 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 0
\(566\) 0.707107 0.707107i 0.707107 0.707107i
\(567\) −0.965926 0.258819i −0.965926 0.258819i
\(568\) 0 0
\(569\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(570\) −0.965926 0.258819i −0.965926 0.258819i
\(571\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(572\) 0 0
\(573\) 1.00000 1.00000
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(578\) 0 0
\(579\) −0.258819 0.965926i −0.258819 0.965926i
\(580\) 0 0
\(581\) 0 0
\(582\) 2.00000i 2.00000i
\(583\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(584\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(585\) 0 0
\(586\) 0 0
\(587\) −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(588\) 0 0
\(589\) 1.00000i 1.00000i
\(590\) 0.965926 0.258819i 0.965926 0.258819i
\(591\) 0 0
\(592\) −0.965926 0.258819i −0.965926 0.258819i
\(593\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(594\) 1.00000 1.00000
\(595\) 1.00000i 1.00000i
\(596\) 0 0
\(597\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(598\) 0 0
\(599\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0 0
\(601\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(607\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(608\) 0 0
\(609\) 0 0
\(610\) 1.00000i 1.00000i
\(611\) 0 0
\(612\) 0 0
\(613\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(617\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(618\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(619\) −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(620\) 0 0
\(621\) −0.866025 0.500000i −0.866025 0.500000i
\(622\) 0.707107 0.707107i 0.707107 0.707107i
\(623\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(626\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(627\) −0.500000 0.866025i −0.500000 0.866025i
\(628\) 0 0
\(629\) −0.707107 0.707107i −0.707107 0.707107i
\(630\) 0 0
\(631\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(632\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(633\) 0 0
\(634\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(641\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(642\) 0.965926 0.258819i 0.965926 0.258819i
\(643\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.500000 0.866025i 0.500000 0.866025i
\(647\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(648\) −0.965926 0.258819i −0.965926 0.258819i
\(649\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(650\) 0 0
\(651\) 0.500000 0.866025i 0.500000 0.866025i
\(652\) 0 0
\(653\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(654\) 0.866025 0.500000i 0.866025 0.500000i
\(655\) 0.258819 0.965926i 0.258819 0.965926i
\(656\) 0 0
\(657\) 0 0
\(658\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(662\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(663\) 0 0
\(664\) 0 0
\(665\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) −0.258819 0.965926i −0.258819 0.965926i
\(671\) 0.707107 0.707107i 0.707107 0.707107i
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0.517638 + 1.93185i 0.517638 + 1.93185i
\(675\) 0 0
\(676\) 0 0
\(677\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) −2.00000 −2.00000
\(680\) 1.00000i 1.00000i
\(681\) 0.965926 0.258819i 0.965926 0.258819i
\(682\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(683\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(684\) 0 0
\(685\) 1.00000 1.00000
\(686\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(687\) 0.707107 0.707107i 0.707107 0.707107i
\(688\) 0 0
\(689\) 0 0
\(690\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(691\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 1.00000i 1.00000i
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) −0.500000 0.866025i −0.500000 0.866025i
\(704\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(705\) 0.500000 0.866025i 0.500000 0.866025i
\(706\) 1.00000i 1.00000i
\(707\) 0.258819 0.965926i 0.258819 0.965926i
\(708\) 0 0
\(709\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(713\) 0.707107 0.707107i 0.707107 0.707107i
\(714\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(715\) 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 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) 0 0
\(721\) 0.965926 0.258819i 0.965926 0.258819i
\(722\) 0 0
\(723\) −0.258819 0.965926i −0.258819 0.965926i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(731\) 0 0
\(732\) 0 0
\(733\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(734\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(735\) 0.707107 0.707107i 0.707107 0.707107i
\(736\) 0 0
\(737\) 0.500000 0.866025i 0.500000 0.866025i
\(738\) 0 0
\(739\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 1.00000 1.00000
\(743\) −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(744\) 0.500000 0.866025i 0.500000 0.866025i
\(745\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(746\) 0.258819 0.965926i 0.258819 0.965926i
\(747\) 0 0
\(748\) 0 0
\(749\) −0.258819 0.965926i −0.258819 0.965926i
\(750\) −1.00000 −1.00000
\(751\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(752\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(753\) 0 0
\(754\) 0 0
\(755\) 1.00000 1.00000
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(760\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(761\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(762\) 0 0
\(763\) −0.500000 0.866025i −0.500000 0.866025i
\(764\) 0 0
\(765\) 0 0
\(766\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(770\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(771\) 1.00000i 1.00000i
\(772\) 0 0
\(773\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −2.00000 −2.00000
\(777\) 1.00000i 1.00000i
\(778\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(783\) 0 0
\(784\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(785\) −0.707107 0.707107i −0.707107 0.707107i
\(786\) 0.965926 0.258819i 0.965926 0.258819i
\(787\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(788\) 0 0
\(789\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(790\) 1.00000i 1.00000i
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) −0.500000 0.866025i