Properties

Label 171.1.o.a.94.1
Level $171$
Weight $1$
Character 171.94
Analytic conductor $0.085$
Analytic rank $0$
Dimension $4$
Projective image $A_{4}$
CM/RM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 171.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.0853401171602\)
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 4.0.29241.1
Artin image: $\SL(2,3):C_2$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{16} - \cdots)\)

Embedding invariants

Embedding label 94.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 171.94
Dual form 171.1.o.a.151.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +1.00000i q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +1.00000i q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000i q^{8} -1.00000 q^{9} -1.00000i q^{10} +(0.500000 + 0.866025i) q^{11} +(0.866025 + 0.500000i) q^{13} +(0.866025 + 0.500000i) q^{14} +(-0.866025 - 0.500000i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.866025 - 0.500000i) q^{18} +1.00000i q^{19} +(0.866025 - 0.500000i) q^{21} +(-0.866025 - 0.500000i) q^{22} +(0.500000 - 0.866025i) q^{23} +1.00000 q^{24} -1.00000 q^{26} -1.00000i q^{27} +(0.866025 - 0.500000i) q^{29} +1.00000 q^{30} +(-0.866025 - 0.500000i) q^{31} +(-0.866025 + 0.500000i) q^{33} +1.00000 q^{35} +(-0.500000 - 0.866025i) q^{38} +(-0.500000 + 0.866025i) q^{39} +(0.866025 + 0.500000i) q^{40} +(0.866025 + 0.500000i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(0.500000 - 0.866025i) q^{45} +1.00000i q^{46} +(-0.500000 - 0.866025i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(0.500000 + 0.866025i) q^{54} -1.00000 q^{55} +(-0.866025 + 0.500000i) q^{56} -1.00000 q^{57} +(-0.500000 + 0.866025i) q^{58} +(-0.866025 - 0.500000i) q^{59} +(0.500000 + 0.866025i) q^{61} +1.00000 q^{62} +(0.500000 + 0.866025i) q^{63} -1.00000 q^{64} +(-0.866025 + 0.500000i) q^{65} +(0.500000 - 0.866025i) q^{66} +(-0.866025 - 0.500000i) q^{67} +(0.866025 + 0.500000i) q^{69} +(-0.866025 + 0.500000i) q^{70} +1.00000i q^{72} +(0.500000 - 0.866025i) q^{77} -1.00000i q^{78} +(0.866025 - 0.500000i) q^{79} -1.00000 q^{80} +1.00000 q^{81} -1.00000 q^{82} +(0.500000 + 0.866025i) q^{83} +(0.866025 + 0.500000i) q^{86} +(0.500000 + 0.866025i) q^{87} +(0.866025 - 0.500000i) q^{88} +1.00000i q^{90} -1.00000i q^{91} +(0.500000 - 0.866025i) q^{93} +(0.866025 + 0.500000i) q^{94} +(-0.866025 - 0.500000i) q^{95} +(-0.866025 + 0.500000i) q^{97} +(-0.500000 - 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{5} - 2q^{6} - 2q^{7} - 4q^{9} + O(q^{10}) \) \( 4q - 2q^{5} - 2q^{6} - 2q^{7} - 4q^{9} + 2q^{11} + 2q^{16} + 2q^{23} + 4q^{24} - 4q^{26} + 4q^{30} + 4q^{35} - 2q^{38} - 2q^{39} - 2q^{42} - 2q^{43} + 2q^{45} - 2q^{47} + 2q^{54} - 4q^{55} - 4q^{57} - 2q^{58} + 2q^{61} + 4q^{62} + 2q^{63} - 4q^{64} + 2q^{66} + 2q^{77} - 4q^{80} + 4q^{81} - 4q^{82} + 2q^{83} + 2q^{87} + 2q^{93} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(154\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(3\) 1.00000i 1.00000i
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(6\) −0.500000 0.866025i −0.500000 0.866025i
\(7\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(8\) 1.00000i 1.00000i
\(9\) −1.00000 −1.00000
\(10\) 1.00000i 1.00000i
\(11\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) 0 0
\(13\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(14\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(15\) −0.866025 0.500000i −0.866025 0.500000i
\(16\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0.866025 0.500000i 0.866025 0.500000i
\(19\) 1.00000i 1.00000i
\(20\) 0 0
\(21\) 0.866025 0.500000i 0.866025 0.500000i
\(22\) −0.866025 0.500000i −0.866025 0.500000i
\(23\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(24\) 1.00000 1.00000
\(25\) 0 0
\(26\) −1.00000 −1.00000
\(27\) 1.00000i 1.00000i
\(28\) 0 0
\(29\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(30\) 1.00000 1.00000
\(31\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 0 0
\(33\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(34\) 0 0
\(35\) 1.00000 1.00000
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) −0.500000 0.866025i −0.500000 0.866025i
\(39\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(40\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(41\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(42\) −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
\(45\) 0.500000 0.866025i 0.500000 0.866025i
\(46\) 1.00000i 1.00000i
\(47\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(48\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(55\) −1.00000 −1.00000
\(56\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(57\) −1.00000 −1.00000
\(58\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(59\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 1.00000 1.00000
\(63\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(64\) −1.00000 −1.00000
\(65\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(66\) 0.500000 0.866025i 0.500000 0.866025i
\(67\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(68\) 0 0
\(69\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(70\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 1.00000i 1.00000i
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.500000 0.866025i 0.500000 0.866025i
\(78\) 1.00000i 1.00000i
\(79\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(80\) −1.00000 −1.00000
\(81\) 1.00000 1.00000
\(82\) −1.00000 −1.00000
\(83\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(87\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(88\) 0.866025 0.500000i 0.866025 0.500000i
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 1.00000i 1.00000i
\(91\) 1.00000i 1.00000i
\(92\) 0 0
\(93\) 0.500000 0.866025i 0.500000 0.866025i
\(94\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(95\) −0.866025 0.500000i −0.866025 0.500000i
\(96\) 0 0
\(97\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(98\) 0 0
\(99\) −0.500000 0.866025i −0.500000 0.866025i
\(100\) 0 0
\(101\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(104\) 0.500000 0.866025i 0.500000 0.866025i
\(105\) 1.00000i 1.00000i
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(110\) 0.866025 0.500000i 0.866025 0.500000i
\(111\) 0 0
\(112\) 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 \(0.833333\pi\)
\(114\) 0.866025 0.500000i 0.866025 0.500000i
\(115\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(116\) 0 0
\(117\) −0.866025 0.500000i −0.866025 0.500000i
\(118\) 1.00000 1.00000
\(119\) 0 0
\(120\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(121\) 0 0
\(122\) −0.866025 0.500000i −0.866025 0.500000i
\(123\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(124\) 0 0
\(125\) −1.00000 −1.00000
\(126\) −0.866025 0.500000i −0.866025 0.500000i
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0.866025 0.500000i 0.866025 0.500000i
\(129\) 0.866025 0.500000i 0.866025 0.500000i
\(130\) 0.500000 0.866025i 0.500000 0.866025i
\(131\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0.866025 0.500000i 0.866025 0.500000i
\(134\) 1.00000 1.00000
\(135\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(136\) 0 0
\(137\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) −1.00000 −1.00000
\(139\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(140\) 0 0
\(141\) 0.866025 0.500000i 0.866025 0.500000i
\(142\) 0 0
\(143\) 1.00000i 1.00000i
\(144\) −0.500000 0.866025i −0.500000 0.866025i
\(145\) 1.00000i 1.00000i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(152\) 1.00000 1.00000
\(153\) 0 0
\(154\) 1.00000i 1.00000i
\(155\) 0.866025 0.500000i 0.866025 0.500000i
\(156\) 0 0
\(157\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(158\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(159\) 0 0
\(160\) 0 0
\(161\) −1.00000 −1.00000
\(162\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 1.00000i 1.00000i
\(166\) −0.866025 0.500000i −0.866025 0.500000i
\(167\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(168\) −0.500000 0.866025i −0.500000 0.866025i
\(169\) 0 0
\(170\) 0 0
\(171\) 1.00000i 1.00000i
\(172\) 0 0
\(173\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) −0.866025 0.500000i −0.866025 0.500000i
\(175\) 0 0
\(176\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(177\) 0.500000 0.866025i 0.500000 0.866025i
\(178\) 0 0
\(179\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(183\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(184\) −0.866025 0.500000i −0.866025 0.500000i
\(185\) 0 0
\(186\) 1.00000i 1.00000i
\(187\) 0 0
\(188\) 0 0
\(189\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(190\) 1.00000 1.00000
\(191\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(192\) 1.00000i 1.00000i
\(193\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(194\) 0.500000 0.866025i 0.500000 0.866025i
\(195\) −0.500000 0.866025i −0.500000 0.866025i
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 0.500000 0.866025i 0.500000 0.866025i
\(202\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(203\) −0.866025 0.500000i −0.866025 0.500000i
\(204\) 0 0
\(205\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(206\) −1.00000 −1.00000
\(207\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(208\) 1.00000i 1.00000i
\(209\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(210\) −0.500000 0.866025i −0.500000 0.866025i
\(211\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.00000 1.00000
\(216\) −1.00000 −1.00000
\(217\) 1.00000i 1.00000i
\(218\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.00000 1.00000
\(227\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) 0 0
\(229\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(230\) −0.866025 0.500000i −0.866025 0.500000i
\(231\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(232\) −0.500000 0.866025i −0.500000 0.866025i
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 1.00000 1.00000
\(235\) 1.00000 1.00000
\(236\) 0 0
\(237\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(238\) 0 0
\(239\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(240\) 1.00000i 1.00000i
\(241\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(242\) 0 0
\(243\) 1.00000i 1.00000i
\(244\) 0 0
\(245\) 0 0
\(246\) 1.00000i 1.00000i
\(247\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(248\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(249\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(250\) 0.866025 0.500000i 0.866025 0.500000i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 1.00000 1.00000
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(258\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(259\) 0 0
\(260\) 0 0
\(261\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(262\) 1.00000i 1.00000i
\(263\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(264\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(265\) 0 0
\(266\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) −1.00000 −1.00000
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 1.00000 1.00000
\(274\) −0.866025 0.500000i −0.866025 0.500000i
\(275\) 0 0
\(276\) 0 0
\(277\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(278\) 1.00000i 1.00000i
\(279\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(280\) 1.00000i 1.00000i
\(281\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(282\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(283\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 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
\(289\) −1.00000 −1.00000
\(290\) −0.500000 0.866025i −0.500000 0.866025i
\(291\) −0.500000 0.866025i −0.500000 0.866025i
\(292\) 0 0
\(293\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(294\) 0 0
\(295\) 0.866025 0.500000i 0.866025 0.500000i
\(296\) 0 0
\(297\) 0.866025 0.500000i 0.866025 0.500000i
\(298\) 1.00000i 1.00000i
\(299\) 0.866025 0.500000i 0.866025 0.500000i
\(300\) 0 0
\(301\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(302\) 0.500000 0.866025i 0.500000 0.866025i
\(303\) 0.866025 0.500000i 0.866025 0.500000i
\(304\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(305\) −1.00000 −1.00000
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(310\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(311\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(312\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(313\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) 1.00000i 1.00000i
\(315\) −1.00000 −1.00000
\(316\) 0 0
\(317\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(320\) 0.500000 0.866025i 0.500000 0.866025i
\(321\) 0 0
\(322\) 0.866025 0.500000i 0.866025 0.500000i
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 2.00000 2.00000
\(328\) 0.500000 0.866025i 0.500000 0.866025i
\(329\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(330\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(331\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −1.00000 −1.00000
\(335\) 0.866025 0.500000i 0.866025 0.500000i
\(336\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(337\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(338\) 0 0
\(339\) 0.500000 0.866025i 0.500000 0.866025i
\(340\) 0 0
\(341\) 1.00000i 1.00000i
\(342\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(343\) −1.00000 −1.00000
\(344\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(345\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(346\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(347\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(348\) 0 0
\(349\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 0 0
\(351\) 0.500000 0.866025i 0.500000 0.866025i
\(352\) 0 0
\(353\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(354\) 1.00000i 1.00000i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −1.00000 1.73205i −1.00000 1.73205i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) −0.866025 0.500000i −0.866025 0.500000i
\(361\) −1.00000 −1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0.500000 0.866025i 0.500000 0.866025i
\(367\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) 1.00000 1.00000
\(369\) −0.866025 0.500000i −0.866025 0.500000i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(374\) 0 0
\(375\) 1.00000i 1.00000i
\(376\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(377\) 1.00000 1.00000
\(378\) 0.500000 0.866025i 0.500000 0.866025i
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(383\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(385\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(386\) 1.00000 1.00000
\(387\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(388\) 0 0
\(389\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(390\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(391\) 0 0
\(392\) 0 0
\(393\) −0.866025 0.500000i −0.866025 0.500000i
\(394\) 0 0
\(395\) 1.00000i 1.00000i
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(400\) 0 0
\(401\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(402\) 1.00000i 1.00000i
\(403\) −0.500000 0.866025i −0.500000 0.866025i
\(404\) 0 0
\(405\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(406\) 1.00000 1.00000
\(407\) 0 0
\(408\) 0 0
\(409\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(410\) 0.500000 0.866025i 0.500000 0.866025i
\(411\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(412\) 0 0
\(413\) 1.00000i 1.00000i
\(414\) 1.00000i 1.00000i
\(415\) −1.00000 −1.00000
\(416\) 0 0
\(417\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(418\) 0.500000 0.866025i 0.500000 0.866025i
\(419\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(422\) −1.00000 −1.00000
\(423\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.500000 0.866025i 0.500000 0.866025i
\(428\) 0 0
\(429\) −1.00000 −1.00000
\(430\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0.866025 0.500000i 0.866025 0.500000i
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) −0.500000 0.866025i −0.500000 0.866025i
\(435\) −1.00000 −1.00000
\(436\) 0 0
\(437\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(438\) 0 0
\(439\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(440\) 1.00000i 1.00000i
\(441\) 0 0
\(442\) 0 0
\(443\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0.500000 0.866025i 0.500000 0.866025i
\(447\) −0.866025 0.500000i −0.866025 0.500000i
\(448\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(449\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(450\) 0 0
\(451\) 1.00000i 1.00000i
\(452\) 0 0
\(453\) −0.500000 0.866025i −0.500000 0.866025i
\(454\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(455\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(456\) 1.00000i 1.00000i
\(457\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(458\) 1.00000i 1.00000i
\(459\) 0 0
\(460\) 0 0
\(461\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(462\) −1.00000 −1.00000
\(463\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(464\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(465\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(466\) 0 0
\(467\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 1.00000i 1.00000i
\(470\) −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
\(473\) 0.500000 0.866025i 0.500000 0.866025i
\(474\) −0.866025 0.500000i −0.866025 0.500000i
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 1.00000i 1.00000i
\(479\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(483\) 1.00000i 1.00000i
\(484\) 0 0
\(485\) 1.00000i 1.00000i
\(486\) −0.500000 0.866025i −0.500000 0.866025i
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0.866025 0.500000i 0.866025 0.500000i
\(489\) 0 0
\(490\) 0 0
\(491\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 1.00000i 1.00000i
\(495\) 1.00000 1.00000
\(496\) 1.00000i 1.00000i
\(497\) 0 0
\(498\) 0.500000 0.866025i 0.500000 0.866025i
\(499\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(500\) 0 0
\(501\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0.866025 0.500000i 0.866025 0.500000i
\(505\) 1.00000 1.00000
\(506\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(507\) 0 0
\(508\) 0 0
\(509\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 1.00000i
\(513\) 1.00000 1.00000
\(514\) −1.00000 −1.00000
\(515\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(516\) 0 0
\(517\) 0.500000 0.866025i 0.500000 0.866025i
\(518\) 0 0
\(519\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(520\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(521\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(522\) 0.500000 0.866025i 0.500000 0.866025i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(527\) 0 0
\(528\) −0.866025 0.500000i −0.866025 0.500000i
\(529\) 0 0
\(530\) 0 0
\(531\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(532\) 0 0
\(533\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(534\) 0 0
\(535\) 0 0
\(536\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(537\) −2.00000 −2.00000
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(546\) −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 0
\(549\) −0.500000 0.866025i −0.500000 0.866025i
\(550\) 0 0
\(551\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(552\) 0.500000 0.866025i 0.500000 0.866025i
\(553\) −0.866025 0.500000i −0.866025 0.500000i
\(554\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(555\) 0 0
\(556\) 0 0
\(557\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(558\) −1.00000 −1.00000
\(559\) 1.00000i 1.00000i
\(560\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(561\) 0 0
\(562\) 0.500000 0.866025i 0.500000 0.866025i
\(563\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 0.866025 0.500000i 0.866025 0.500000i
\(566\) 1.00000i 1.00000i
\(567\) −0.500000 0.866025i −0.500000 0.866025i
\(568\) 0 0
\(569\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(570\) 1.00000i 1.00000i
\(571\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(572\) 0 0
\(573\) 0.866025 0.500000i 0.866025 0.500000i
\(574\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(575\) 0 0
\(576\) 1.00000 1.00000
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) 0.866025 0.500000i 0.866025 0.500000i
\(579\) 0.500000 0.866025i 0.500000 0.866025i
\(580\) 0 0
\(581\) 0.500000 0.866025i 0.500000 0.866025i
\(582\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(583\) 0 0
\(584\) 0 0
\(585\) 0.866025 0.500000i 0.866025 0.500000i
\(586\) 1.00000 1.00000
\(587\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(588\) 0 0
\(589\) 0.500000 0.866025i 0.500000 0.866025i
\(590\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(599\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) 0 0
\(601\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(602\) 1.00000i 1.00000i
\(603\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(604\) 0 0
\(605\) 0 0
\(606\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(607\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(608\) 0 0
\(609\) 0.500000 0.866025i 0.500000 0.866025i
\(610\) 0.866025 0.500000i 0.866025 0.500000i
\(611\) 1.00000i 1.00000i
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) −0.500000 0.866025i −0.500000 0.866025i
\(616\) −0.866025 0.500000i −0.866025 0.500000i
\(617\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(618\) 1.00000i 1.00000i
\(619\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) −0.866025 0.500000i −0.866025 0.500000i
\(622\) 1.00000i 1.00000i
\(623\) 0 0
\(624\) −1.00000 −1.00000
\(625\) 0.500000 0.866025i 0.500000 0.866025i
\(626\) −0.866025 0.500000i −0.866025 0.500000i
\(627\) −0.500000 0.866025i −0.500000 0.866025i
\(628\) 0 0
\(629\) 0 0
\(630\) 0.866025 0.500000i 0.866025 0.500000i
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) −0.500000 0.866025i −0.500000 0.866025i
\(633\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(634\) 0.500000 0.866025i 0.500000 0.866025i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −1.00000 −1.00000
\(639\) 0 0
\(640\) 1.00000i 1.00000i
\(641\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(644\) 0 0
\(645\) 1.00000i 1.00000i
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 1.00000i 1.00000i
\(649\) 1.00000i 1.00000i
\(650\) 0 0
\(651\) −1.00000 −1.00000
\(652\) 0 0
\(653\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(654\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(655\) −0.500000 0.866025i −0.500000 0.866025i
\(656\) 1.00000i 1.00000i
\(657\) 0 0
\(658\) 1.00000i 1.00000i
\(659\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(662\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(663\) 0 0
\(664\) 0.866025 0.500000i 0.866025 0.500000i
\(665\) 1.00000i 1.00000i
\(666\) 0 0
\(667\) 1.00000i 1.00000i
\(668\) 0 0
\(669\) −0.500000 0.866025i −0.500000 0.866025i
\(670\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(671\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(672\) 0 0
\(673\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(674\) −1.00000 −1.00000
\(675\) 0 0
\(676\) 0 0
\(677\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(678\) 1.00000i 1.00000i
\(679\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(680\) 0 0
\(681\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(682\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) −1.00000 −1.00000
\(686\) 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 0
\(690\) 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
\(693\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(694\) 1.00000i 1.00000i
\(695\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(696\) 0.866025 0.500000i 0.866025 0.500000i
\(697\) 0 0
\(698\) −0.866025 0.500000i −0.866025 0.500000i
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 1.00000i 1.00000i
\(703\) 0 0
\(704\) −0.500000 0.866025i −0.500000 0.866025i
\(705\) 1.00000i 1.00000i
\(706\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(707\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(708\) 0 0
\(709\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(712\) 0 0
\(713\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(714\) 0 0
\(715\) −0.866025 0.500000i −0.866025 0.500000i
\(716\) 0 0
\(717\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 1.00000 1.00000
\(721\) 1.00000i 1.00000i
\(722\) 0.866025 0.500000i 0.866025 0.500000i
\(723\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(728\) −1.00000 −1.00000
\(729\) −1.00000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(734\) −0.866025 0.500000i −0.866025 0.500000i
\(735\) 0 0
\(736\) 0 0
\(737\) 1.00000i 1.00000i
\(738\) 1.00000 1.00000
\(739\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(740\) 0 0
\(741\) −0.866025 0.500000i −0.866025 0.500000i
\(742\) 0 0
\(743\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(744\) −0.866025 0.500000i −0.866025 0.500000i
\(745\) −0.500000 0.866025i −0.500000 0.866025i
\(746\) 1.00000 1.00000
\(747\) −0.500000 0.866025i −0.500000 0.866025i
\(748\) 0 0
\(749\) 0 0
\(750\) 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 \(0.5\pi\)
\(752\) 0.500000 0.866025i 0.500000 0.866025i
\(753\) 0 0
\(754\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(755\) 1.00000i 1.00000i
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 1.00000i 1.00000i
\(760\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(761\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(762\) 0 0
\(763\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(764\) 0 0
\(765\) 0 0
\(766\) 1.00000 1.00000
\(767\) −0.500000 0.866025i −0.500000 0.866025i
\(768\) 0 0
\(769\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(770\) −0.866025 0.500000i −0.866025 0.500000i
\(771\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(772\) 0 0
\(773\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) −0.866025 0.500000i −0.866025 0.500000i
\(775\) 0 0
\(776\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(777\) 0 0
\(778\) −0.866025 0.500000i −0.866025 0.500000i
\(779\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −0.500000 0.866025i −0.500000 0.866025i
\(784\) 0 0
\(785\) −0.500000 0.866025i −0.500000 0.866025i
\(786\) 1.00000 1.00000
\(787\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(788\) 0 0
\(789\) 0.866025 0.500000i 0.866025 0.500000i
\(790\) −0.500000 0.866025i −0.500000 0.866025i
\(791\) 1.00000i 1.00000i
\(792\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(793\) 1.00000i 1.00000i
\(794\) 0