Properties

Label 1148.1.o.b.163.1
Level $1148$
Weight $1$
Character 1148.163
Analytic conductor $0.573$
Analytic rank $0$
Dimension $2$
Projective image $D_{3}$
CM discriminant -164
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1148.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.572926634503\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.8036.1
Artin image: $C_3\times S_3$
Artin field: Galois closure of 6.0.216136256.1

Embedding invariants

Embedding label 163.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1148.163
Dual form 1148.1.o.b.655.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.500000 - 0.866025i) q^{14} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{19} -1.00000 q^{20} -1.00000 q^{21} -1.00000 q^{22} +(0.500000 + 0.866025i) q^{24} +1.00000 q^{27} +1.00000 q^{28} +(-0.500000 + 0.866025i) q^{30} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +(0.500000 + 0.866025i) q^{35} +(-1.00000 + 1.73205i) q^{37} +(0.500000 + 0.866025i) q^{38} +(0.500000 - 0.866025i) q^{40} +1.00000 q^{41} +(0.500000 - 0.866025i) q^{42} +(0.500000 - 0.866025i) q^{44} +(-1.00000 + 1.73205i) q^{47} -1.00000 q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{54} +1.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +1.00000 q^{57} +(-0.500000 - 0.866025i) q^{60} +(0.500000 - 0.866025i) q^{61} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{66} +(-1.00000 - 1.73205i) q^{67} -1.00000 q^{70} -1.00000 q^{71} +(-1.00000 - 1.73205i) q^{73} +(-1.00000 - 1.73205i) q^{74} -1.00000 q^{76} -1.00000 q^{77} +(0.500000 - 0.866025i) q^{79} +(0.500000 + 0.866025i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.500000 + 0.866025i) q^{82} +(0.500000 + 0.866025i) q^{84} +(0.500000 + 0.866025i) q^{88} +(-1.00000 - 1.73205i) q^{94} +(-0.500000 - 0.866025i) q^{95} +(0.500000 - 0.866025i) q^{96} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{3} - q^{4} + q^{5} - 2q^{6} - q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} + q^{3} - q^{4} + q^{5} - 2q^{6} - q^{7} + 2q^{8} + q^{10} + q^{11} + q^{12} - q^{14} + 2q^{15} - q^{16} + q^{19} - 2q^{20} - 2q^{21} - 2q^{22} + q^{24} + 2q^{27} + 2q^{28} - q^{30} - q^{32} - q^{33} + q^{35} - 2q^{37} + q^{38} + q^{40} + 2q^{41} + q^{42} + q^{44} - 2q^{47} - 2q^{48} - q^{49} - q^{54} + 2q^{55} - q^{56} + 2q^{57} - q^{60} + q^{61} + 2q^{64} - q^{66} - 2q^{67} - 2q^{70} - 2q^{71} - 2q^{73} - 2q^{74} - 2q^{76} - 2q^{77} + q^{79} + q^{80} + q^{81} - q^{82} + q^{84} + q^{88} - 2q^{94} - q^{95} + q^{96} + 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(3\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(4\) −0.500000 0.866025i −0.500000 0.866025i
\(5\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(6\) −1.00000 −1.00000
\(7\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(8\) 1.00000 1.00000
\(9\) 0 0
\(10\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(11\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) 0.500000 0.866025i 0.500000 0.866025i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −0.500000 0.866025i −0.500000 0.866025i
\(15\) 1.00000 1.00000
\(16\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(17\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) 0 0
\(19\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(20\) −1.00000 −1.00000
\(21\) −1.00000 −1.00000
\(22\) −1.00000 −1.00000
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000 1.00000
\(28\) 1.00000 1.00000
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(31\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(32\) −0.500000 0.866025i −0.500000 0.866025i
\(33\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(34\) 0 0
\(35\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(36\) 0 0
\(37\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(39\) 0 0
\(40\) 0.500000 0.866025i 0.500000 0.866025i
\(41\) 1.00000 1.00000
\(42\) 0.500000 0.866025i 0.500000 0.866025i
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0.500000 0.866025i 0.500000 0.866025i
\(45\) 0 0
\(46\) 0 0
\(47\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(48\) −1.00000 −1.00000
\(49\) −0.500000 0.866025i −0.500000 0.866025i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(55\) 1.00000 1.00000
\(56\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(57\) 1.00000 1.00000
\(58\) 0 0
\(59\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(60\) −0.500000 0.866025i −0.500000 0.866025i
\(61\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) −0.500000 0.866025i −0.500000 0.866025i
\(67\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −1.00000 −1.00000
\(71\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(72\) 0 0
\(73\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(74\) −1.00000 1.73205i −1.00000 1.73205i
\(75\) 0 0
\(76\) −1.00000 −1.00000
\(77\) −1.00000 −1.00000
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(80\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(81\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(82\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(89\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) −1.00000 1.73205i −1.00000 1.73205i
\(95\) −0.500000 0.866025i −0.500000 0.866025i
\(96\) 0.500000 0.866025i 0.500000 0.866025i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 1.00000 1.00000
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(102\) 0 0
\(103\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(104\) 0 0
\(105\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(106\) 0 0
\(107\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) −0.500000 0.866025i −0.500000 0.866025i
\(109\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(111\) −2.00000 −2.00000
\(112\) −0.500000 0.866025i −0.500000 0.866025i
\(113\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(114\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 1.00000 1.00000
\(121\) 0 0
\(122\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(123\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(124\) 0 0
\(125\) 1.00000 1.00000
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(132\) 1.00000 1.00000
\(133\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(134\) 2.00000 2.00000
\(135\) 0.500000 0.866025i 0.500000 0.866025i
\(136\) 0 0
\(137\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0.500000 0.866025i 0.500000 0.866025i
\(141\) −2.00000 −2.00000
\(142\) 0.500000 0.866025i 0.500000 0.866025i
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 2.00000 2.00000
\(147\) 0.500000 0.866025i 0.500000 0.866025i
\(148\) 2.00000 2.00000
\(149\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(150\) 0 0
\(151\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(152\) 0.500000 0.866025i 0.500000 0.866025i
\(153\) 0 0
\(154\) 0.500000 0.866025i 0.500000 0.866025i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(158\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(159\) 0 0
\(160\) −1.00000 −1.00000
\(161\) 0 0
\(162\) −1.00000 −1.00000
\(163\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(164\) −0.500000 0.866025i −0.500000 0.866025i
\(165\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(166\) 0 0
\(167\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(168\) −1.00000 −1.00000
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.00000 −1.00000
\(177\) 0 0
\(178\) 0 0
\(179\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 1.00000 1.00000
\(184\) 0 0
\(185\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(186\) 0 0
\(187\) 0 0
\(188\) 2.00000 2.00000
\(189\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(190\) 1.00000 1.00000
\(191\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(193\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(197\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(198\) 0 0
\(199\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(200\) 0 0
\(201\) 1.00000 1.73205i 1.00000 1.73205i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.500000 0.866025i 0.500000 0.866025i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.00000 1.00000
\(210\) −0.500000 0.866025i −0.500000 0.866025i
\(211\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) 0 0
\(213\) −0.500000 0.866025i −0.500000 0.866025i
\(214\) 0 0
\(215\) 0 0
\(216\) 1.00000 1.00000
\(217\) 0 0
\(218\) 0 0
\(219\) 1.00000 1.73205i 1.00000 1.73205i
\(220\) −0.500000 0.866025i −0.500000 0.866025i
\(221\) 0 0
\(222\) 1.00000 1.73205i 1.00000 1.73205i
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 1.00000 1.00000
\(225\) 0 0
\(226\) 0.500000 0.866025i 0.500000 0.866025i
\(227\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(228\) −0.500000 0.866025i −0.500000 0.866025i
\(229\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) 0 0
\(231\) −0.500000 0.866025i −0.500000 0.866025i
\(232\) 0 0
\(233\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(234\) 0 0
\(235\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(236\) 0 0
\(237\) 1.00000 1.00000
\(238\) 0 0
\(239\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(241\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −1.00000 −1.00000
\(245\) −1.00000 −1.00000
\(246\) −1.00000 −1.00000
\(247\) 0 0
\(248\) 0 0
\(249\) 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 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.500000 0.866025i
\(257\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 0 0
\(259\) −1.00000 1.73205i −1.00000 1.73205i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(264\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(265\) 0 0
\(266\) −1.00000 −1.00000
\(267\) 0 0
\(268\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(269\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(271\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 1.00000 1.73205i 1.00000 1.73205i
\(283\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(284\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(285\) 0.500000 0.866025i 0.500000 0.866025i
\(286\) 0 0
\(287\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(288\) 0 0
\(289\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(290\) 0 0
\(291\) 0 0
\(292\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(295\) 0 0
\(296\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(297\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 2.00000 2.00000
\(303\) 0 0
\(304\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(305\) −0.500000 0.866025i −0.500000 0.866025i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(309\) 0 0
\(310\) 0 0
\(311\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(312\) 0 0
\(313\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −1.00000 −1.00000
\(317\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.500000 0.866025i 0.500000 0.866025i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.500000 0.866025i 0.500000 0.866025i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 1.00000 1.00000
\(329\) −1.00000 1.73205i −1.00000 1.73205i
\(330\) −1.00000 −1.00000
\(331\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(335\) −2.00000 −2.00000
\(336\) 0.500000 0.866025i 0.500000 0.866025i
\(337\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(338\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(339\) −0.500000 0.866025i −0.500000 0.866025i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(347\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(348\) 0 0
\(349\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.500000 0.866025i 0.500000 0.866025i
\(353\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(354\) 0 0
\(355\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(356\) 0 0
\(357\) 0 0
\(358\) −1.00000 −1.00000
\(359\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.00000 −2.00000
\(366\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(367\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −2.00000 −2.00000
\(371\) 0 0
\(372\) 0 0
\(373\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(374\) 0 0
\(375\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(376\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(377\) 0 0
\(378\) −0.500000 0.866025i −0.500000 0.866025i
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(381\) 0 0
\(382\) −1.00000 1.73205i −1.00000 1.73205i
\(383\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(384\) −1.00000 −1.00000
\(385\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.500000 0.866025i −0.500000 0.866025i
\(393\) 0 0
\(394\) 0.500000 0.866025i 0.500000 0.866025i
\(395\) −0.500000 0.866025i −0.500000 0.866025i
\(396\) 0 0
\(397\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) 2.00000 2.00000
\(399\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(400\) 0 0
\(401\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(402\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(403\) 0 0
\(404\) 0 0
\(405\) 1.00000 1.00000
\(406\) 0 0
\(407\) −2.00000 −2.00000
\(408\) 0 0
\(409\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 1.00000 1.00000
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0.500000 0.866025i 0.500000 0.866025i
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 1.00000 1.00000
\(427\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(433\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(439\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(440\) 1.00000 1.00000
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(444\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(449\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(450\) 0 0
\(451\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(452\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(453\) 1.00000 1.73205i 1.00000 1.73205i
\(454\) −1.00000 −1.00000
\(455\) 0 0
\(456\) 1.00000 1.00000
\(457\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(462\) 1.00000 1.00000
\(463\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(468\) 0 0
\(469\) 2.00000 2.00000
\(470\) −2.00000 −2.00000
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0.500000 0.866025i 0.500000 0.866025i
\(479\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(480\) −0.500000 0.866025i −0.500000 0.866025i
\(481\) 0 0
\(482\) 2.00000 2.00000
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(488\) 0.500000 0.866025i 0.500000 0.866025i
\(489\) 0 0
\(490\) 0.500000 0.866025i 0.500000 0.866025i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0.500000 0.866025i 0.500000 0.866025i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.500000 0.866025i 0.500000 0.866025i
\(498\) 0 0
\(499\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) −0.500000 0.866025i −0.500000 0.866025i
\(501\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(502\) 0 0
\(503\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(508\) 0 0
\(509\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(510\) 0 0
\(511\) 2.00000 2.00000
\(512\) 1.00000 1.00000
\(513\) 0.500000 0.866025i 0.500000 0.866025i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −2.00000 −2.00000
\(518\) 2.00000 2.00000
\(519\) 1.00000 1.00000
\(520\) 0 0
\(521\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(522\) 0 0
\(523\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 2.00000 2.00000
\(527\) 0 0
\(528\) −0.500000 0.866025i −0.500000 0.866025i
\(529\) −0.500000 0.866025i −0.500000 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) 0.500000 0.866025i 0.500000 0.866025i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −1.00000 1.73205i −1.00000 1.73205i
\(537\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(538\) −1.00000 −1.00000
\(539\) 0.500000 0.866025i 0.500000 0.866025i
\(540\) −1.00000 −1.00000
\(541\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(554\) −1.00000 −1.00000
\(555\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(556\) 0 0
\(557\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −1.00000 −1.00000
\(561\) 0 0
\(562\) 0 0
\(563\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(564\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(565\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(566\) 0 0
\(567\) −1.00000 −1.00000
\(568\) −1.00000 −1.00000
\(569\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(571\) 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
\(574\) −0.500000 0.866025i −0.500000 0.866025i
\(575\) 0 0
\(576\) 0 0
\(577\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(578\) −0.500000 0.866025i −0.500000 0.866025i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −1.00000 1.73205i −1.00000 1.73205i
\(585\) 0 0
\(586\) 0 0
\(587\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(588\) −1.00000 −1.00000
\(589\) 0 0
\(590\) 0 0
\(591\) −0.500000 0.866025i −0.500000 0.866025i
\(592\) −1.00000 1.73205i −1.00000 1.73205i
\(593\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(594\) −1.00000 −1.00000
\(595\) 0 0
\(596\) 0 0
\(597\) 1.00000 1.73205i 1.00000 1.73205i
\(598\) 0 0
\(599\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) −1.00000 −1.00000
\(609\) 0 0
\(610\) 1.00000 1.00000
\(611\) 0 0
\(612\) 0 0
\(613\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(614\) 0 0
\(615\) 1.00000 1.00000
\(616\) −1.00000 −1.00000
\(617\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(618\) 0 0
\(619\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 2.00000 2.00000
\(623\) 0 0
\(624\) 0 0
\(625\) 0.500000 0.866025i 0.500000 0.866025i
\(626\) 0 0
\(627\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0.500000 0.866025i 0.500000 0.866025i
\(633\) −0.500000 0.866025i −0.500000 0.866025i
\(634\) 0 0
\(635\) 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 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(642\) 0 0
\(643\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(648\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(657\) 0 0
\(658\) 2.00000 2.00000
\(659\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(660\) 0.500000 0.866025i 0.500000 0.866025i
\(661\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) −1.00000 1.73205i −1.00000 1.73205i
\(663\) 0 0
\(664\) 0 0
\(665\) 1.00000 1.00000
\(666\) 0 0
\(667\) 0 0
\(668\) −1.00000 1.73205i −1.00000 1.73205i
\(669\) 0 0
\(670\) 1.00000 1.73205i 1.00000 1.73205i
\(671\) 1.00000 1.00000
\(672\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0.500000 0.866025i 0.500000 0.866025i
\(675\) 0 0
\(676\) −0.500000 0.866025i −0.500000 0.866025i
\(677\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(678\) 1.00000 1.00000
\(679\) 0 0
\(680\) 0 0
\(681\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(682\) 0 0
\(683\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(692\) −1.00000 −1.00000
\(693\) 0 0
\(694\) −1.00000 −1.00000
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(699\) 0 0
\(700\) 0 0
\(701\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(702\) 0 0
\(703\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(704\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(705\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(706\) −1.00000 −1.00000
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) −0.500000 0.866025i −0.500000 0.866025i
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.500000 0.866025i 0.500000 0.866025i
\(717\) −0.500000 0.866025i −0.500000 0.866025i
\(718\) 0 0
\(719\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 1.00000 1.73205i 1.00000 1.73205i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 1.00000 1.73205i 1.00000 1.73205i
\(731\) 0 0
\(732\) −0.500000 0.866025i −0.500000 0.866025i
\(733\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(734\) 0 0
\(735\) −0.500000 0.866025i −0.500000 0.866025i
\(736\) 0 0
\(737\) 1.00000 1.73205i 1.00000 1.73205i
\(738\) 0 0
\(739\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) 1.00000 1.73205i 1.00000 1.73205i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) −1.00000 −1.00000
\(751\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(752\) −1.00000 1.73205i −1.00000 1.73205i
\(753\) 0 0
\(754\) 0 0
\(755\) −2.00000 −2.00000
\(756\) 1.00000 1.00000
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −0.500000 0.866025i −0.500000 0.866025i
\(761\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 2.00000 2.00000
\(765\) 0 0
\(766\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(767\) 0 0
\(768\) 0.500000 0.866025i 0.500000 0.866025i
\(769\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) −0.500000 0.866025i −0.500000 0.866025i
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1.00000 1.73205i 1.00000 1.73205i
\(778\) −1.00000 −1.00000
\(779\) 0.500000 0.866025i 0.500000 0.866025i
\(780\) 0 0
\(781\) −0.500000 0.866025i −0.500000 0.866025i
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 1.00000
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(788\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(789\) 1.00000 1.73205i 1.00000 1.73205i
\(790\) 1.00000 1.00000
\(791\) 0.500000 0.866025i 0.500000 0.866025i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(797\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(798\) −0.500000 0.866025i −0.500000 0.866025i
\(799\) 0 0
\(800\) 0 0
\(801\) 0