Properties

Label 273.1.bm.b.191.2
Level $273$
Weight $1$
Character 273.191
Analytic conductor $0.136$
Analytic rank $0$
Dimension $4$
Projective image $A_{4}$
CM/RM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 273.bm (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.136244748449\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(A_{4}\)
Projective field: Galois closure of 4.0.74529.1
Artin image: $\SL(2,3):C_2$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{16} - \cdots)\)

Embedding invariants

Embedding label 191.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 273.191
Dual form 273.1.bm.b.263.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} -1.00000i q^{3} +(-0.866025 - 0.500000i) q^{5} +(-0.500000 - 0.866025i) q^{6} +1.00000 q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} -1.00000i q^{3} +(-0.866025 - 0.500000i) q^{5} +(-0.500000 - 0.866025i) q^{6} +1.00000 q^{7} +1.00000i q^{8} -1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{13} +(0.866025 - 0.500000i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.866025 + 0.500000i) q^{17} +(-0.866025 + 0.500000i) q^{18} -1.00000i q^{21} +(-0.866025 + 0.500000i) q^{23} +1.00000 q^{24} +(-0.866025 + 0.500000i) q^{26} +1.00000i q^{27} +(0.866025 + 0.500000i) q^{29} +1.00000i q^{30} +(0.500000 + 0.866025i) q^{31} +1.00000 q^{34} +(-0.866025 - 0.500000i) q^{35} +(-0.500000 - 0.866025i) q^{37} +1.00000i q^{39} +(0.500000 - 0.866025i) q^{40} +(-0.866025 - 0.500000i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(0.866025 + 0.500000i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(-0.866025 - 0.500000i) q^{47} +(0.866025 - 0.500000i) q^{48} +1.00000 q^{49} +(0.500000 - 0.866025i) q^{51} +(0.866025 - 0.500000i) q^{53} +(0.500000 + 0.866025i) q^{54} +1.00000i q^{56} +1.00000 q^{58} +(-0.866025 - 0.500000i) q^{59} +(0.866025 + 0.500000i) q^{62} -1.00000 q^{63} -1.00000 q^{64} +(0.866025 + 0.500000i) q^{65} +(0.500000 + 0.866025i) q^{69} -1.00000 q^{70} +(-0.866025 + 0.500000i) q^{71} -1.00000i q^{72} +(-0.500000 - 0.866025i) q^{73} +(-0.866025 - 0.500000i) q^{74} +(0.500000 + 0.866025i) q^{78} +(-0.500000 + 0.866025i) q^{79} -1.00000i q^{80} +1.00000 q^{81} -1.00000 q^{82} +(-0.500000 - 0.866025i) q^{85} +(-0.866025 - 0.500000i) q^{86} +(0.500000 - 0.866025i) q^{87} +(0.866025 - 0.500000i) q^{89} +1.00000 q^{90} -1.00000 q^{91} +(0.866025 - 0.500000i) q^{93} -1.00000 q^{94} +(0.500000 + 0.866025i) q^{97} +(0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{6} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 4q - 2q^{6} + 4q^{7} - 4q^{9} - 4q^{10} - 4q^{13} - 2q^{15} + 2q^{16} + 4q^{24} + 2q^{31} + 4q^{34} - 2q^{37} + 2q^{40} - 2q^{42} - 2q^{43} - 2q^{46} + 4q^{49} + 2q^{51} + 2q^{54} + 4q^{58} - 4q^{63} - 4q^{64} + 2q^{69} - 4q^{70} - 2q^{73} + 2q^{78} - 2q^{79} + 4q^{81} - 4q^{82} - 2q^{85} + 2q^{87} + 4q^{90} - 4q^{91} - 4q^{94} + 2q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(3\) 1.00000i 1.00000i
\(4\) 0 0
\(5\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) −0.500000 0.866025i −0.500000 0.866025i
\(7\) 1.00000 1.00000
\(8\) 1.00000i 1.00000i
\(9\) −1.00000 −1.00000
\(10\) −1.00000 −1.00000
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) −1.00000 −1.00000
\(14\) 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 \(0.5\pi\)
\(18\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 1.00000i 1.00000i
\(22\) 0 0
\(23\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(24\) 1.00000 1.00000
\(25\) 0 0
\(26\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(27\) 1.00000i 1.00000i
\(28\) 0 0
\(29\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(30\) 1.00000i 1.00000i
\(31\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 1.00000 1.00000
\(35\) −0.866025 0.500000i −0.866025 0.500000i
\(36\) 0 0
\(37\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 1.00000i 1.00000i
\(40\) 0.500000 0.866025i 0.500000 0.866025i
\(41\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) −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 \(\pi\)
\(44\) 0 0
\(45\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(46\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(47\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 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
\(53\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(54\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(55\) 0 0
\(56\) 1.00000i 1.00000i
\(57\) 0 0
\(58\) 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 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(63\) −1.00000 −1.00000
\(64\) −1.00000 −1.00000
\(65\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(70\) −1.00000 −1.00000
\(71\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(72\) 1.00000i 1.00000i
\(73\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(74\) −0.866025 0.500000i −0.866025 0.500000i
\(75\) 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 \(\pi\)
\(80\) 1.00000i 1.00000i
\(81\) 1.00000 1.00000
\(82\) −1.00000 −1.00000
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) −0.500000 0.866025i −0.500000 0.866025i
\(86\) −0.866025 0.500000i −0.866025 0.500000i
\(87\) 0.500000 0.866025i 0.500000 0.866025i
\(88\) 0 0
\(89\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 1.00000 1.00000
\(91\) −1.00000 −1.00000
\(92\) 0 0
\(93\) 0.866025 0.500000i 0.866025 0.500000i
\(94\) −1.00000 −1.00000
\(95\) 0 0
\(96\) 0 0
\(97\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(98\) 0.866025 0.500000i 0.866025 0.500000i
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 1.00000i 1.00000i
\(103\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(104\) 1.00000i 1.00000i
\(105\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(106\) 0.500000 0.866025i 0.500000 0.866025i
\(107\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(108\) 0 0
\(109\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(112\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(113\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(114\) 0 0
\(115\) 1.00000 1.00000
\(116\) 0 0
\(117\) 1.00000 1.00000
\(118\) −1.00000 −1.00000
\(119\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(120\) −0.866025 0.500000i −0.866025 0.500000i
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(124\) 0 0
\(125\) 1.00000i 1.00000i
\(126\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(127\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(128\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(129\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(130\) 1.00000 1.00000
\(131\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0.500000 0.866025i 0.500000 0.866025i
\(136\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(137\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(138\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(139\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 0 0
\(141\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(142\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(143\) 0 0
\(144\) −0.500000 0.866025i −0.500000 0.866025i
\(145\) −0.500000 0.866025i −0.500000 0.866025i
\(146\) −0.866025 0.500000i −0.866025 0.500000i
\(147\) 1.00000i 1.00000i
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) −0.866025 0.500000i −0.866025 0.500000i
\(154\) 0 0
\(155\) 1.00000i 1.00000i
\(156\) 0 0
\(157\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(158\) 1.00000i 1.00000i
\(159\) −0.500000 0.866025i −0.500000 0.866025i
\(160\) 0 0
\(161\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(162\) 0.866025 0.500000i 0.866025 0.500000i
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(168\) 1.00000 1.00000
\(169\) 1.00000 1.00000
\(170\) −0.866025 0.500000i −0.866025 0.500000i
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 1.00000i 1.00000i
\(175\) 0 0
\(176\) 0 0
\(177\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(178\) 0.500000 0.866025i 0.500000 0.866025i
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(183\) 0 0
\(184\) −0.500000 0.866025i −0.500000 0.866025i
\(185\) 1.00000i 1.00000i
\(186\) 0.500000 0.866025i 0.500000 0.866025i
\(187\) 0 0
\(188\) 0 0
\(189\) 1.00000i 1.00000i
\(190\) 0 0
\(191\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 1.00000i 1.00000i
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(195\) 0.500000 0.866025i 0.500000 0.866025i
\(196\) 0 0
\(197\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(198\) 0 0
\(199\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(204\) 0 0
\(205\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(206\) 1.00000i 1.00000i
\(207\) 0.866025 0.500000i 0.866025 0.500000i
\(208\) −0.500000 0.866025i −0.500000 0.866025i
\(209\) 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 \(\pi\)
\(212\) 0 0
\(213\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(214\) 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
\(218\) −0.866025 0.500000i −0.866025 0.500000i
\(219\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(220\) 0 0
\(221\) −0.866025 0.500000i −0.866025 0.500000i
\(222\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(223\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0.500000 0.866025i 0.500000 0.866025i
\(227\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(228\) 0 0
\(229\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(230\) 0.866025 0.500000i 0.866025 0.500000i
\(231\) 0 0
\(232\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(233\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(234\) 0.866025 0.500000i 0.866025 0.500000i
\(235\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(236\) 0 0
\(237\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(238\) 1.00000 1.00000
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) −1.00000 −1.00000
\(241\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(242\) 0.866025 0.500000i 0.866025 0.500000i
\(243\) 1.00000i 1.00000i
\(244\) 0 0
\(245\) −0.866025 0.500000i −0.866025 0.500000i
\(246\) 1.00000i 1.00000i
\(247\) 0 0
\(248\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(249\) 0 0
\(250\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(251\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 1.00000i 1.00000i
\(255\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(256\) 0 0
\(257\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(259\) −0.500000 0.866025i −0.500000 0.866025i
\(260\) 0 0
\(261\) −0.866025 0.500000i −0.866025 0.500000i
\(262\) 1.00000 1.00000
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) −1.00000 −1.00000
\(266\) 0 0
\(267\) −0.500000 0.866025i −0.500000 0.866025i
\(268\) 0 0
\(269\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(270\) 1.00000i 1.00000i
\(271\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) 1.00000i 1.00000i
\(273\) 1.00000i 1.00000i
\(274\) 1.00000 1.00000
\(275\) 0 0
\(276\) 0 0
\(277\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(278\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(279\) −0.500000 0.866025i −0.500000 0.866025i
\(280\) 0.500000 0.866025i 0.500000 0.866025i
\(281\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(282\) 1.00000i 1.00000i
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.866025 0.500000i −0.866025 0.500000i
\(288\) 0 0
\(289\) 0 0
\(290\) −0.866025 0.500000i −0.866025 0.500000i
\(291\) 0.866025 0.500000i 0.866025 0.500000i
\(292\) 0 0
\(293\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(294\) −0.500000 0.866025i −0.500000 0.866025i
\(295\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(296\) 0.866025 0.500000i 0.866025 0.500000i
\(297\) 0 0
\(298\) 0 0
\(299\) 0.866025 0.500000i 0.866025 0.500000i
\(300\) 0 0
\(301\) −0.500000 0.866025i −0.500000 0.866025i
\(302\) −0.866025 0.500000i −0.866025 0.500000i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) −1.00000 −1.00000
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(310\) −0.500000 0.866025i −0.500000 0.866025i
\(311\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) −1.00000 −1.00000
\(313\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(314\) −0.866025 0.500000i −0.866025 0.500000i
\(315\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(316\) 0 0
\(317\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(318\) −0.866025 0.500000i −0.866025 0.500000i
\(319\) 0 0
\(320\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(321\) −0.500000 0.866025i −0.500000 0.866025i
\(322\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(328\) 0.500000 0.866025i 0.500000 0.866025i
\(329\) −0.866025 0.500000i −0.866025 0.500000i
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 0 0
\(333\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(334\) 1.00000 1.00000
\(335\) 0 0
\(336\) 0.866025 0.500000i 0.866025 0.500000i
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0.866025 0.500000i 0.866025 0.500000i
\(339\) −0.500000 0.866025i −0.500000 0.866025i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 1.00000
\(344\) 0.866025 0.500000i 0.866025 0.500000i
\(345\) 1.00000i 1.00000i
\(346\) 0 0
\(347\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 0 0
\(349\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(350\) 0 0
\(351\) 1.00000i 1.00000i
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 1.00000i 1.00000i
\(355\) 1.00000 1.00000
\(356\) 0 0
\(357\) 0.500000 0.866025i 0.500000 0.866025i
\(358\) 0 0
\(359\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(360\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(361\) −1.00000 −1.00000
\(362\) 0 0
\(363\) 1.00000i 1.00000i
\(364\) 0 0
\(365\) 1.00000i 1.00000i
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) −0.866025 0.500000i −0.866025 0.500000i
\(369\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(370\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(371\) 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
\(375\) 1.00000 1.00000
\(376\) 0.500000 0.866025i 0.500000 0.866025i
\(377\) −0.866025 0.500000i −0.866025 0.500000i
\(378\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(379\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) −0.866025 0.500000i −0.866025 0.500000i
\(382\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(385\) 0 0
\(386\) 0 0
\(387\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(388\) 0 0
\(389\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(390\) 1.00000i 1.00000i
\(391\) −1.00000 −1.00000
\(392\) 1.00000i 1.00000i
\(393\) 0.500000 0.866025i 0.500000 0.866025i
\(394\) −1.00000 −1.00000
\(395\) 0.866025 0.500000i 0.866025 0.500000i
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 1.00000i 1.00000i
\(399\) 0 0
\(400\) 0 0
\(401\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(402\) 0 0
\(403\) −0.500000 0.866025i −0.500000 0.866025i
\(404\) 0 0
\(405\) −0.866025 0.500000i −0.866025 0.500000i
\(406\) 1.00000 1.00000
\(407\) 0 0
\(408\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(409\) 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
\(411\) 0.500000 0.866025i 0.500000 0.866025i
\(412\) 0 0
\(413\) −0.866025 0.500000i −0.866025 0.500000i
\(414\) 0.500000 0.866025i 0.500000 0.866025i
\(415\) 0 0
\(416\) 0 0
\(417\) 0.866025 0.500000i 0.866025 0.500000i
\(418\) 0 0
\(419\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 1.00000i 1.00000i
\(423\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(424\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(425\) 0 0
\(426\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(431\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(433\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(434\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(435\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(436\) 0 0
\(437\) 0 0
\(438\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(439\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −1.00000 −1.00000
\(442\) −1.00000 −1.00000
\(443\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(444\) 0 0
\(445\) −1.00000 −1.00000
\(446\) 1.00000i 1.00000i
\(447\) 0 0
\(448\) −1.00000 −1.00000
\(449\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(454\) −1.00000 −1.00000
\(455\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(456\) 0 0
\(457\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 1.00000i 1.00000i
\(459\) −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 \(0.166667\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 1.00000i 1.00000i
\(465\) −1.00000 −1.00000
\(466\) −1.00000 −1.00000
\(467\) −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 0
\(470\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(471\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(472\) 0.500000 0.866025i 0.500000 0.866025i
\(473\) 0 0
\(474\) 1.00000 1.00000
\(475\) 0 0
\(476\) 0 0
\(477\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(482\) 1.00000i 1.00000i
\(483\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(484\) 0 0
\(485\) 1.00000i 1.00000i
\(486\) −0.500000 0.866025i −0.500000 0.866025i
\(487\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(488\) 0 0
\(489\) 0 0
\(490\) −1.00000 −1.00000
\(491\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(494\) 0 0
\(495\) 0 0
\(496\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(497\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(498\) 0 0
\(499\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 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 \(0.166667\pi\)
\(504\) 1.00000i 1.00000i
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000i 1.00000i
\(508\) 0 0
\(509\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(510\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(511\) −0.500000 0.866025i −0.500000 0.866025i
\(512\) 1.00000i 1.00000i
\(513\) 0 0
\(514\) 0.500000 0.866025i 0.500000 0.866025i
\(515\) 0.866025 0.500000i 0.866025 0.500000i
\(516\) 0 0
\(517\) 0 0
\(518\) −0.866025 0.500000i −0.866025 0.500000i
\(519\) 0 0
\(520\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(521\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(522\) −1.00000 −1.00000
\(523\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.00000i 1.00000i
\(528\) 0 0
\(529\) 0 0
\(530\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(531\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(532\) 0 0
\(533\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(534\) −0.866025 0.500000i −0.866025 0.500000i
\(535\) −1.00000 −1.00000
\(536\) 0 0
\(537\) 0 0
\(538\) 1.00000 1.00000
\(539\) 0 0
\(540\) 0 0
\(541\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(542\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(543\) 0 0
\(544\) 0 0
\(545\) 1.00000i 1.00000i
\(546\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(553\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(554\) 1.00000i 1.00000i
\(555\) 1.00000 1.00000
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) −0.866025 0.500000i −0.866025 0.500000i
\(559\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(560\) 1.00000i 1.00000i
\(561\) 0 0
\(562\) −1.00000 1.73205i −1.00000 1.73205i
\(563\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) −1.00000 −1.00000
\(566\) 0 0
\(567\) 1.00000 1.00000
\(568\) −0.500000 0.866025i −0.500000 0.866025i
\(569\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) 2.00000 2.00000
\(574\) −1.00000 −1.00000
\(575\) 0 0
\(576\) 1.00000 1.00000
\(577\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0.500000 0.866025i 0.500000 0.866025i
\(583\) 0 0
\(584\) 0.866025 0.500000i 0.866025 0.500000i
\(585\) −0.866025 0.500000i −0.866025 0.500000i
\(586\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(587\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(591\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(592\) 0.500000 0.866025i 0.500000 0.866025i
\(593\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) −0.500000 0.866025i −0.500000 0.866025i
\(596\) 0 0
\(597\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(598\) 0.500000 0.866025i 0.500000 0.866025i
\(599\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(602\) −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 0
\(607\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0.500000 0.866025i 0.500000 0.866025i
\(610\) 0 0
\(611\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(612\) 0 0
\(613\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(614\) 0 0
\(615\) 0.866025 0.500000i 0.866025 0.500000i
\(616\) 0 0
\(617\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(618\) 1.00000 1.00000
\(619\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) −0.500000 0.866025i −0.500000 0.866025i
\(622\) 0.500000 0.866025i 0.500000 0.866025i
\(623\) 0.866025 0.500000i 0.866025 0.500000i
\(624\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(625\) 0.500000 0.866025i 0.500000 0.866025i
\(626\) 1.00000i 1.00000i
\(627\) 0 0
\(628\) 0 0
\(629\) 1.00000i 1.00000i
\(630\) 1.00000 1.00000
\(631\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(632\) −0.866025 0.500000i −0.866025 0.500000i
\(633\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(634\) 1.00000 1.00000
\(635\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(636\) 0 0
\(637\) −1.00000 −1.00000
\(638\) 0 0
\(639\) 0.866025 0.500000i 0.866025 0.500000i
\(640\) 1.00000 1.00000
\(641\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(642\) −0.866025 0.500000i −0.866025 0.500000i
\(643\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(644\) 0 0
\(645\) 1.00000 1.00000
\(646\) 0 0
\(647\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(648\) 1.00000i 1.00000i
\(649\) 0 0
\(650\) 0 0
\(651\) 0.866025 0.500000i 0.866025 0.500000i
\(652\) 0 0
\(653\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(654\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(655\) −0.500000 0.866025i −0.500000 0.866025i
\(656\) 1.00000i 1.00000i
\(657\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(658\) −1.00000 −1.00000
\(659\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 0 0
\(663\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(664\) 0 0
\(665\) 0 0
\(666\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(667\) −1.00000 −1.00000
\(668\) 0 0
\(669\) −0.866025 0.500000i −0.866025 0.500000i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(678\) −0.866025 0.500000i −0.866025 0.500000i
\(679\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(680\) 0.866025 0.500000i 0.866025 0.500000i
\(681\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(682\) 0 0
\(683\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(684\) 0 0
\(685\) −0.500000 0.866025i −0.500000 0.866025i
\(686\) 0.866025 0.500000i 0.866025 0.500000i
\(687\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(688\) 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
\(691\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −1.00000 −1.00000
\(695\) 1.00000i 1.00000i
\(696\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(697\) −0.500000 0.866025i −0.500000 0.866025i
\(698\) 1.00000i 1.00000i
\(699\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(700\) 0 0
\(701\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) −0.500000 0.866025i −0.500000 0.866025i
\(703\) 0 0
\(704\) 0 0
\(705\) 0.866025 0.500000i 0.866025 0.500000i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 0.866025 0.500000i 0.866025 0.500000i
\(711\) 0.500000 0.866025i 0.500000 0.866025i
\(712\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(713\) −0.866025 0.500000i −0.866025 0.500000i
\(714\) 1.00000i 1.00000i
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) −1.00000 −1.00000
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 1.00000i 1.00000i
\(721\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(722\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(723\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(724\) 0 0
\(725\) 0 0
\(726\) −0.500000 0.866025i −0.500000 0.866025i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 1.00000i 1.00000i
\(729\) −1.00000 −1.00000
\(730\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(731\) 1.00000i 1.00000i
\(732\) 0 0
\(733\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(736\) 0 0
\(737\) 0 0
\(738\) 1.00000 1.00000
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.500000 0.866025i 0.500000 0.866025i
\(743\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(744\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0.866025 0.500000i 0.866025 0.500000i
\(750\) 0.866025 0.500000i 0.866025 0.500000i
\(751\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(752\) 1.00000i 1.00000i
\(753\) −0.500000 0.866025i −0.500000 0.866025i
\(754\) −1.00000 −1.00000
\(755\) 1.00000i 1.00000i
\(756\) 0 0
\(757\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(758\) 1.00000i 1.00000i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) −1.00000 −1.00000
\(763\) −0.500000 0.866025i −0.500000 0.866025i
\(764\) 0 0
\(765\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(766\) 0 0
\(767\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(768\) 0 0
\(769\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) −0.500000 0.866025i −0.500000 0.866025i
\(772\) 0 0
\(773\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(774\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(775\) 0 0
\(776\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(777\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(778\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(783\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(784\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(785\) 1.00000i 1.00000i
\(786\) 1.00000i 1.00000i
\(787\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0.500000 0.866025i 0.500000 0.866025i
\(791\) 0.866025 0.500000i 0.866025 0.500000i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0