Properties

Label 1148.1.o.c.163.1
Level $1148$
Weight $1$
Character 1148.163
Analytic conductor $0.573$
Analytic rank $0$
Dimension $4$
Projective image $D_{6}$
CM discriminant -164
Inner twists $8$

Related objects

Downloads

Learn more

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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{6}\)
Projective field: Galois closure of 6.0.258309184.1

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.73205 q^{6} +(-0.866025 - 0.500000i) q^{7} +1.00000 q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.73205 q^{6} +(-0.866025 - 0.500000i) q^{7} +1.00000 q^{8} +(-1.00000 + 1.73205i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.866025 + 1.50000i) q^{11} +(-0.866025 + 1.50000i) q^{12} +(0.866025 - 0.500000i) q^{14} +1.73205 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{18} +(0.866025 - 1.50000i) q^{19} +1.00000 q^{20} +1.73205i q^{21} -1.73205 q^{22} +(-0.866025 - 1.50000i) q^{24} +1.73205 q^{27} +1.00000i q^{28} +(-0.866025 + 1.50000i) q^{30} +(-0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +(0.866025 - 0.500000i) q^{35} +2.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(0.866025 + 1.50000i) q^{38} +(-0.500000 + 0.866025i) q^{40} +1.00000 q^{41} +(-1.50000 - 0.866025i) q^{42} +(0.866025 - 1.50000i) q^{44} +(-1.00000 - 1.73205i) q^{45} +1.73205 q^{48} +(0.500000 + 0.866025i) q^{49} +(-0.866025 + 1.50000i) q^{54} -1.73205 q^{55} +(-0.866025 - 0.500000i) q^{56} -3.00000 q^{57} +(-0.866025 - 1.50000i) q^{60} +(0.500000 - 0.866025i) q^{61} +(1.73205 - 1.00000i) q^{63} +1.00000 q^{64} +(1.50000 + 2.59808i) q^{66} +1.00000i q^{70} +1.73205 q^{71} +(-1.00000 + 1.73205i) q^{72} +(1.00000 + 1.73205i) q^{73} +(1.00000 + 1.73205i) q^{74} -1.73205 q^{76} -1.73205i q^{77} +(-0.866025 + 1.50000i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.500000 + 0.866025i) q^{82} +(1.50000 - 0.866025i) q^{84} +(0.866025 + 1.50000i) q^{88} +2.00000 q^{90} +(0.866025 + 1.50000i) q^{95} +(-0.866025 + 1.50000i) q^{96} -1.00000 q^{98} -3.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{4} - 2q^{5} + 4q^{8} - 4q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{4} - 2q^{5} + 4q^{8} - 4q^{9} - 2q^{10} - 2q^{16} - 4q^{18} + 4q^{20} - 2q^{32} + 6q^{33} + 8q^{36} + 4q^{37} - 2q^{40} + 4q^{41} - 6q^{42} - 4q^{45} + 2q^{49} - 12q^{57} + 2q^{61} + 4q^{64} + 6q^{66} - 4q^{72} + 4q^{73} + 4q^{74} - 2q^{80} - 2q^{81} - 2q^{82} + 6q^{84} + 8q^{90} - 4q^{98} + O(q^{100}) \)

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
\(3\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(4\) −0.500000 0.866025i −0.500000 0.866025i
\(5\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(6\) 1.73205 1.73205
\(7\) −0.866025 0.500000i −0.866025 0.500000i
\(8\) 1.00000 1.00000
\(9\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(10\) −0.500000 0.866025i −0.500000 0.866025i
\(11\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(12\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0.866025 0.500000i 0.866025 0.500000i
\(15\) 1.73205 1.73205
\(16\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(17\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) −1.00000 1.73205i −1.00000 1.73205i
\(19\) 0.866025 1.50000i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(20\) 1.00000 1.00000
\(21\) 1.73205i 1.73205i
\(22\) −1.73205 −1.73205
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) −0.866025 1.50000i −0.866025 1.50000i
\(25\) 0 0
\(26\) 0 0
\(27\) 1.73205 1.73205
\(28\) 1.00000i 1.00000i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(31\) 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
\(33\) 1.50000 2.59808i 1.50000 2.59808i
\(34\) 0 0
\(35\) 0.866025 0.500000i 0.866025 0.500000i
\(36\) 2.00000 2.00000
\(37\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(38\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(39\) 0 0
\(40\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(41\) 1.00000 1.00000
\(42\) −1.50000 0.866025i −1.50000 0.866025i
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0.866025 1.50000i 0.866025 1.50000i
\(45\) −1.00000 1.73205i −1.00000 1.73205i
\(46\) 0 0
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 1.73205 1.73205
\(49\) 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 \(0.333333\pi\)
\(54\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(55\) −1.73205 −1.73205
\(56\) −0.866025 0.500000i −0.866025 0.500000i
\(57\) −3.00000 −3.00000
\(58\) 0 0
\(59\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(60\) −0.866025 1.50000i −0.866025 1.50000i
\(61\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(62\) 0 0
\(63\) 1.73205 1.00000i 1.73205 1.00000i
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(67\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 1.00000i 1.00000i
\(71\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(73\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(74\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(75\) 0 0
\(76\) −1.73205 −1.73205
\(77\) 1.73205i 1.73205i
\(78\) 0 0
\(79\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) −0.500000 0.866025i −0.500000 0.866025i
\(81\) −0.500000 0.866025i −0.500000 0.866025i
\(82\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 1.50000 0.866025i 1.50000 0.866025i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(89\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(90\) 2.00000 2.00000
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(96\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −1.00000 −1.00000
\(99\) −3.46410 −3.46410
\(100\) 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
\(105\) −1.50000 0.866025i −1.50000 0.866025i
\(106\) 0 0
\(107\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) −0.866025 1.50000i −0.866025 1.50000i
\(109\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 0.866025 1.50000i 0.866025 1.50000i
\(111\) −3.46410 −3.46410
\(112\) 0.866025 0.500000i 0.866025 0.500000i
\(113\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(114\) 1.50000 2.59808i 1.50000 2.59808i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 1.73205 1.73205
\(121\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(122\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(123\) −0.866025 1.50000i −0.866025 1.50000i
\(124\) 0 0
\(125\) −1.00000 −1.00000
\(126\) 2.00000i 2.00000i
\(127\) 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 \(0.666667\pi\)
\(132\) −3.00000 −3.00000
\(133\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(134\) 0 0
\(135\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(136\) 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 \(\pi\)
\(140\) −0.866025 0.500000i −0.866025 0.500000i
\(141\) 0 0
\(142\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(143\) 0 0
\(144\) −1.00000 1.73205i −1.00000 1.73205i
\(145\) 0 0
\(146\) −2.00000 −2.00000
\(147\) 0.866025 1.50000i 0.866025 1.50000i
\(148\) −2.00000 −2.00000
\(149\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(150\) 0 0
\(151\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(152\) 0.866025 1.50000i 0.866025 1.50000i
\(153\) 0 0
\(154\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(158\) −0.866025 1.50000i −0.866025 1.50000i
\(159\) 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
\(165\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 1.73205i 1.73205i
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 1.73205 + 3.00000i 1.73205 + 3.00000i
\(172\) 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
\(176\) −1.73205 −1.73205
\(177\) 0 0
\(178\) 0 0
\(179\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(180\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) −1.73205 −1.73205
\(184\) 0 0
\(185\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −1.50000 0.866025i −1.50000 0.866025i
\(190\) −1.73205 −1.73205
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) −0.866025 1.50000i −0.866025 1.50000i
\(193\) 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 \(0.666667\pi\)
\(198\) 1.73205 3.00000i 1.73205 3.00000i
\(199\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 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
\(209\) 3.00000 3.00000
\(210\) 1.50000 0.866025i 1.50000 0.866025i
\(211\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(212\) 0 0
\(213\) −1.50000 2.59808i −1.50000 2.59808i
\(214\) 0 0
\(215\) 0 0
\(216\) 1.73205 1.73205
\(217\) 0 0
\(218\) 0 0
\(219\) 1.73205 3.00000i 1.73205 3.00000i
\(220\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(221\) 0 0
\(222\) 1.73205 3.00000i 1.73205 3.00000i
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 1.00000i 1.00000i
\(225\) 0 0
\(226\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(227\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(228\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(229\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) 0 0
\(231\) −2.59808 + 1.50000i −2.59808 + 1.50000i
\(232\) 0 0
\(233\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 3.00000 3.00000
\(238\) 0 0
\(239\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(240\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(241\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(242\) −1.00000 1.73205i −1.00000 1.73205i
\(243\) 0 0
\(244\) −1.00000 −1.00000
\(245\) −1.00000 −1.00000
\(246\) 1.73205 1.73205
\(247\) 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 \(\pi\)
\(252\) −1.73205 1.00000i −1.73205 1.00000i
\(253\) 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
\(259\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 1.50000 2.59808i 1.50000 2.59808i
\(265\) 0 0
\(266\) 1.73205i 1.73205i
\(267\) 0 0
\(268\) 0 0
\(269\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) −0.866025 1.50000i −0.866025 1.50000i
\(271\) 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 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0.866025 0.500000i 0.866025 0.500000i
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(284\) −0.866025 1.50000i −0.866025 1.50000i
\(285\) 1.50000 2.59808i 1.50000 2.59808i
\(286\) 0 0
\(287\) −0.866025 0.500000i −0.866025 0.500000i
\(288\) 2.00000 2.00000
\(289\) −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 \(\pi\)
\(294\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(295\) 0 0
\(296\) 1.00000 1.73205i 1.00000 1.73205i
\(297\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(305\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(312\) 0 0
\(313\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) 0 0
\(315\) 2.00000i 2.00000i
\(316\) 1.73205 1.73205
\(317\) 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
\(329\) 0 0
\(330\) −3.00000 −3.00000
\(331\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(332\) 0 0
\(333\) 2.00000 + 3.46410i 2.00000 + 3.46410i
\(334\) 0 0
\(335\) 0 0
\(336\) −1.50000 0.866025i −1.50000 0.866025i
\(337\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(338\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(339\) −0.866025 1.50000i −0.866025 1.50000i
\(340\) 0 0
\(341\) 0 0
\(342\) −3.46410 −3.46410
\(343\) 1.00000i 1.00000i
\(344\) 0 0
\(345\) 0 0
\(346\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(347\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.866025 1.50000i 0.866025 1.50000i
\(353\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(356\) 0 0
\(357\) 0 0
\(358\) 1.73205 1.73205
\(359\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(360\) −1.00000 1.73205i −1.00000 1.73205i
\(361\) −1.00000 1.73205i −1.00000 1.73205i
\(362\) 0 0
\(363\) 3.46410 3.46410
\(364\) 0 0
\(365\) −2.00000 −2.00000
\(366\) 0.866025 1.50000i 0.866025 1.50000i
\(367\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(368\) 0 0
\(369\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(370\) −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
\(375\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(376\) 0 0
\(377\) 0 0
\(378\) 1.50000 0.866025i 1.50000 0.866025i
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0.866025 1.50000i 0.866025 1.50000i
\(381\) 0 0
\(382\) 0 0
\(383\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) 1.73205 1.73205
\(385\) 1.50000 + 0.866025i 1.50000 + 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
\(395\) −0.866025 1.50000i −0.866025 1.50000i
\(396\) 1.73205 + 3.00000i 1.73205 + 3.00000i
\(397\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) 0 0
\(399\) 2.59808 + 1.50000i 2.59808 + 1.50000i
\(400\) 0 0
\(401\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 1.00000 1.00000
\(406\) 0 0
\(407\) 3.46410 3.46410
\(408\) 0 0
\(409\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(410\) −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
\(418\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 1.73205i 1.73205i
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 3.00000 3.00000
\(427\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(433\) −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
\(438\) 1.73205 + 3.00000i 1.73205 + 3.00000i
\(439\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) −1.73205 −1.73205
\(441\) −2.00000 −2.00000
\(442\) 0 0
\(443\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(444\) 1.73205 + 3.00000i 1.73205 + 3.00000i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.866025 0.500000i −0.866025 0.500000i
\(449\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(450\) 0 0
\(451\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(452\) −0.500000 0.866025i −0.500000 0.866025i
\(453\) 0 0
\(454\) −1.73205 −1.73205
\(455\) 0 0
\(456\) −3.00000 −3.00000
\(457\) 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 \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(462\) 3.00000i 3.00000i
\(463\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(464\) 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
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0.866025 1.50000i 0.866025 1.50000i
\(479\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(480\) −0.866025 1.50000i −0.866025 1.50000i
\(481\) 0 0
\(482\) 2.00000 2.00000
\(483\) 0 0
\(484\) 2.00000 2.00000
\(485\) 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 \(\pi\)
\(492\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(493\) 0 0
\(494\) 0 0
\(495\) 1.73205 3.00000i 1.73205 3.00000i
\(496\) 0 0
\(497\) −1.50000 0.866025i −1.50000 0.866025i
\(498\) 0 0
\(499\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(500\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(501\) 0 0
\(502\) 0 0
\(503\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(504\) 1.73205 1.00000i 1.73205 1.00000i
\(505\) 0 0
\(506\) 0 0
\(507\) −0.866025 1.50000i −0.866025 1.50000i
\(508\) 0 0
\(509\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(510\) 0 0
\(511\) 2.00000i 2.00000i
\(512\) 1.00000 1.00000
\(513\) 1.50000 2.59808i 1.50000 2.59808i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 2.00000i 2.00000i
\(519\) −1.73205 −1.73205
\(520\) 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
\(526\) 0 0
\(527\) 0 0
\(528\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(529\) −0.500000 0.866025i −0.500000 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(538\) −1.00000 −1.00000
\(539\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(540\) 1.73205 1.73205
\(541\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 1.50000 0.866025i 1.50000 0.866025i
\(554\) 1.00000 1.00000
\(555\) 1.73205 3.00000i 1.73205 3.00000i
\(556\) 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
\(560\) 1.00000i 1.00000i
\(561\) 0 0
\(562\) 0 0
\(563\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(564\) 0 0
\(565\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(566\) 0 0
\(567\) 1.00000i 1.00000i
\(568\) 1.73205 1.73205
\(569\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(570\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(571\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0.866025 0.500000i 0.866025 0.500000i
\(575\) 0 0
\(576\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(577\) 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
\(587\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(588\) −1.73205 −1.73205
\(589\) 0 0
\(590\) 0 0
\(591\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(592\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(593\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(594\) −3.00000 −3.00000
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 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
\(604\) 0 0
\(605\) −1.00000 1.73205i −1.00000 1.73205i
\(606\) 0 0
\(607\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) −1.73205 −1.73205
\(609\) 0 0
\(610\) −1.00000 −1.00000
\(611\) 0 0
\(612\) 0 0
\(613\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 1.73205 1.73205
\(616\) 1.73205i 1.73205i
\(617\) −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
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.500000 0.866025i 0.500000 0.866025i
\(626\) 0 0
\(627\) −2.59808 4.50000i −2.59808 4.50000i
\(628\) 0 0
\(629\) 0 0
\(630\) −1.73205 1.00000i −1.73205 1.00000i
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(633\) −1.50000 2.59808i −1.50000 2.59808i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −1.73205 + 3.00000i −1.73205 + 3.00000i
\(640\) −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
\(643\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(644\) 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
\(657\) −4.00000 −4.00000
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 1.50000 2.59808i 1.50000 2.59808i
\(661\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.73205i 1.73205i
\(666\) −4.00000 −4.00000
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.73205 1.73205
\(672\) 1.50000 0.866025i 1.50000 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 \(0.333333\pi\)
−1.00000 \(\pi\)
\(678\) 1.73205 1.73205
\(679\) 0 0
\(680\) 0 0
\(681\) 1.50000 2.59808i 1.50000 2.59808i
\(682\) 0 0
\(683\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(684\) 1.73205 3.00000i 1.73205 3.00000i
\(685\) 0 0
\(686\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(692\) −1.00000 −1.00000
\(693\) 3.00000 + 1.73205i 3.00000 + 1.73205i
\(694\) −1.73205 −1.73205
\(695\) 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 \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(702\) 0 0
\(703\) −1.73205 3.00000i −1.73205 3.00000i
\(704\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(705\) 0 0
\(706\) 1.00000 1.00000
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) −0.866025 1.50000i −0.866025 1.50000i
\(711\) −1.73205 3.00000i −1.73205 3.00000i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(717\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(718\) 0 0
\(719\) 0.866025 1.50000i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(720\) 2.00000 2.00000
\(721\) 0 0
\(722\) 2.00000 2.00000
\(723\) −1.73205 + 3.00000i −1.73205 + 3.00000i
\(724\) 0 0
\(725\) 0 0
\(726\) −1.73205 + 3.00000i −1.73205 + 3.00000i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) −1.00000 −1.00000
\(730\) 1.00000 1.73205i 1.00000 1.73205i
\(731\) 0 0
\(732\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(733\) −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
\(735\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(736\) 0 0
\(737\) 0 0
\(738\) −1.00000 1.73205i −1.00000 1.73205i
\(739\) 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
\(750\) −1.73205 −1.73205
\(751\) 0.866025 1.50000i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.73205i 1.73205i
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(761\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −0.866025 1.50000i −0.866025 1.50000i
\(767\) 0 0
\(768\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(769\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) −1.50000 + 0.866025i −1.50000 + 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
\(777\) 3.00000 + 1.73205i 3.00000 + 1.73205i
\(778\) −1.00000 −1.00000
\(779\) 0.866025 1.50000i 0.866025 1.50000i
\(780\) 0 0
\(781\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(782\) 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
\(789\) 0 0
\(790\) 1.73205 1.73205
\(791\) −0.866025 0.500000i −0.866025 0.500000i
\(792\) −3.46410 −3.46410
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(798\) −2.59808 + 1.50000i −2.59808 + 1.50000i
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0