Properties

Label 1148.1.o.d.163.4
Level $1148$
Weight $1$
Character 1148.163
Analytic conductor $0.573$
Analytic rank $0$
Dimension $8$
Projective image $D_{12}$
CM discriminant -164
Inner twists $8$

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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: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{12}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{12} - \cdots)\)

Embedding invariants

Embedding label 163.4
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1148.163
Dual form 1148.1.o.d.655.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.965926 + 1.67303i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 1.50000i) q^{5} +1.93185 q^{6} +(-0.258819 - 0.965926i) q^{7} -1.00000 q^{8} +(-1.36603 + 2.36603i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.965926 + 1.67303i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 1.50000i) q^{5} +1.93185 q^{6} +(-0.258819 - 0.965926i) q^{7} -1.00000 q^{8} +(-1.36603 + 2.36603i) q^{9} +(-0.866025 - 1.50000i) q^{10} +(0.258819 + 0.448288i) q^{11} +(0.965926 - 1.67303i) q^{12} +(-0.965926 - 0.258819i) q^{14} +3.34607 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.36603 + 2.36603i) q^{18} +(-0.258819 + 0.448288i) q^{19} -1.73205 q^{20} +(1.36603 - 1.36603i) q^{21} +0.517638 q^{22} +(-0.965926 - 1.67303i) q^{24} +(-1.00000 - 1.73205i) q^{25} -3.34607 q^{27} +(-0.707107 + 0.707107i) q^{28} +(1.67303 - 2.89778i) q^{30} +(0.500000 + 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +(-1.67303 - 0.448288i) q^{35} +2.73205 q^{36} +(0.258819 + 0.448288i) q^{38} +(-0.866025 + 1.50000i) q^{40} +1.00000 q^{41} +(-0.500000 - 1.86603i) q^{42} +(0.258819 - 0.448288i) q^{44} +(2.36603 + 4.09808i) q^{45} +(-0.707107 + 1.22474i) q^{47} -1.93185 q^{48} +(-0.866025 + 0.500000i) q^{49} -2.00000 q^{50} +(-1.67303 + 2.89778i) q^{54} +0.896575 q^{55} +(0.258819 + 0.965926i) q^{56} -1.00000 q^{57} +(-1.67303 - 2.89778i) q^{60} +(-0.500000 + 0.866025i) q^{61} +(2.63896 + 0.707107i) q^{63} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} +(0.707107 + 1.22474i) q^{67} +(-1.22474 + 1.22474i) q^{70} -1.93185 q^{71} +(1.36603 - 2.36603i) q^{72} +(1.93185 - 3.34607i) q^{75} +0.517638 q^{76} +(0.366025 - 0.366025i) q^{77} +(0.965926 - 1.67303i) q^{79} +(0.866025 + 1.50000i) q^{80} +(-1.86603 - 3.23205i) q^{81} +(0.500000 - 0.866025i) q^{82} +(-1.86603 - 0.500000i) q^{84} +(-0.258819 - 0.448288i) q^{88} +4.73205 q^{90} +(0.707107 + 1.22474i) q^{94} +(0.448288 + 0.776457i) q^{95} +(-0.965926 + 1.67303i) q^{96} +1.00000i q^{98} -1.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{2} - 4q^{4} - 8q^{8} - 4q^{9} + O(q^{10}) \) \( 8q + 4q^{2} - 4q^{4} - 8q^{8} - 4q^{9} - 4q^{16} + 4q^{18} + 4q^{21} - 8q^{25} + 4q^{32} - 4q^{33} + 8q^{36} + 8q^{41} - 4q^{42} + 12q^{45} - 16q^{50} - 8q^{57} - 4q^{61} + 8q^{64} + 4q^{66} + 4q^{72} - 4q^{77} - 8q^{81} + 4q^{82} - 8q^{84} + 24q^{90} + O(q^{100}) \)

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
\(3\) 0.965926 + 1.67303i 0.965926 + 1.67303i 0.707107 + 0.707107i \(0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(4\) −0.500000 0.866025i −0.500000 0.866025i
\(5\) 0.866025 1.50000i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(6\) 1.93185 1.93185
\(7\) −0.258819 0.965926i −0.258819 0.965926i
\(8\) −1.00000 −1.00000
\(9\) −1.36603 + 2.36603i −1.36603 + 2.36603i
\(10\) −0.866025 1.50000i −0.866025 1.50000i
\(11\) 0.258819 + 0.448288i 0.258819 + 0.448288i 0.965926 0.258819i \(-0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(12\) 0.965926 1.67303i 0.965926 1.67303i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −0.965926 0.258819i −0.965926 0.258819i
\(15\) 3.34607 3.34607
\(16\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(17\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) 1.36603 + 2.36603i 1.36603 + 2.36603i
\(19\) −0.258819 + 0.448288i −0.258819 + 0.448288i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(20\) −1.73205 −1.73205
\(21\) 1.36603 1.36603i 1.36603 1.36603i
\(22\) 0.517638 0.517638
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) −0.965926 1.67303i −0.965926 1.67303i
\(25\) −1.00000 1.73205i −1.00000 1.73205i
\(26\) 0 0
\(27\) −3.34607 −3.34607
\(28\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 1.67303 2.89778i 1.67303 2.89778i
\(31\) 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
\(35\) −1.67303 0.448288i −1.67303 0.448288i
\(36\) 2.73205 2.73205
\(37\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(38\) 0.258819 + 0.448288i 0.258819 + 0.448288i
\(39\) 0 0
\(40\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(41\) 1.00000 1.00000
\(42\) −0.500000 1.86603i −0.500000 1.86603i
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0.258819 0.448288i 0.258819 0.448288i
\(45\) 2.36603 + 4.09808i 2.36603 + 4.09808i
\(46\) 0 0
\(47\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(48\) −1.93185 −1.93185
\(49\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(50\) −2.00000 −2.00000
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) −1.67303 + 2.89778i −1.67303 + 2.89778i
\(55\) 0.896575 0.896575
\(56\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(57\) −1.00000 −1.00000
\(58\) 0 0
\(59\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(60\) −1.67303 2.89778i −1.67303 2.89778i
\(61\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 2.63896 + 0.707107i 2.63896 + 0.707107i
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(67\) 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −1.22474 + 1.22474i −1.22474 + 1.22474i
\(71\) −1.93185 −1.93185 −0.965926 0.258819i \(-0.916667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(72\) 1.36603 2.36603i 1.36603 2.36603i
\(73\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(74\) 0 0
\(75\) 1.93185 3.34607i 1.93185 3.34607i
\(76\) 0.517638 0.517638
\(77\) 0.366025 0.366025i 0.366025 0.366025i
\(78\) 0 0
\(79\) 0.965926 1.67303i 0.965926 1.67303i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(80\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(81\) −1.86603 3.23205i −1.86603 3.23205i
\(82\) 0.500000 0.866025i 0.500000 0.866025i
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −1.86603 0.500000i −1.86603 0.500000i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −0.258819 0.448288i −0.258819 0.448288i
\(89\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(90\) 4.73205 4.73205
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(95\) 0.448288 + 0.776457i 0.448288 + 0.776457i
\(96\) −0.965926 + 1.67303i −0.965926 + 1.67303i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 1.00000i 1.00000i
\(99\) −1.41421 −1.41421
\(100\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(101\) 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
\(105\) −0.866025 3.23205i −0.866025 3.23205i
\(106\) 0 0
\(107\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) 1.67303 + 2.89778i 1.67303 + 2.89778i
\(109\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 0.448288 0.776457i 0.448288 0.776457i
\(111\) 0 0
\(112\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(113\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(114\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −3.34607 −3.34607
\(121\) 0.366025 0.633975i 0.366025 0.633975i
\(122\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(123\) 0.965926 + 1.67303i 0.965926 + 1.67303i
\(124\) 0 0
\(125\) −1.73205 −1.73205
\(126\) 1.93185 1.93185i 1.93185 1.93185i
\(127\) 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 + 0.133975i 0.500000 + 0.133975i
\(134\) 1.41421 1.41421
\(135\) −2.89778 + 5.01910i −2.89778 + 5.01910i
\(136\) 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 \(\pi\)
\(140\) 0.448288 + 1.67303i 0.448288 + 1.67303i
\(141\) −2.73205 −2.73205
\(142\) −0.965926 + 1.67303i −0.965926 + 1.67303i
\(143\) 0 0
\(144\) −1.36603 2.36603i −1.36603 2.36603i
\(145\) 0 0
\(146\) 0 0
\(147\) −1.67303 0.965926i −1.67303 0.965926i
\(148\) 0 0
\(149\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(150\) −1.93185 3.34607i −1.93185 3.34607i
\(151\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(152\) 0.258819 0.448288i 0.258819 0.448288i
\(153\) 0 0
\(154\) −0.133975 0.500000i −0.133975 0.500000i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(158\) −0.965926 1.67303i −0.965926 1.67303i
\(159\) 0 0
\(160\) 1.73205 1.73205
\(161\) 0 0
\(162\) −3.73205 −3.73205
\(163\) 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
\(165\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(166\) 0 0
\(167\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(168\) −1.36603 + 1.36603i −1.36603 + 1.36603i
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) −0.707107 1.22474i −0.707107 1.22474i
\(172\) 0 0
\(173\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(174\) 0 0
\(175\) −1.41421 + 1.41421i −1.41421 + 1.41421i
\(176\) −0.517638 −0.517638
\(177\) 0 0
\(178\) 0 0
\(179\) −0.965926 1.67303i −0.965926 1.67303i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 0.965926i \(-0.583333\pi\)
\(180\) 2.36603 4.09808i 2.36603 4.09808i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) −1.93185 −1.93185
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 1.41421 1.41421
\(189\) 0.866025 + 3.23205i 0.866025 + 3.23205i
\(190\) 0.896575 0.896575
\(191\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(192\) 0.965926 + 1.67303i 0.965926 + 1.67303i
\(193\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(197\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(198\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(199\) 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(200\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(201\) −1.36603 + 2.36603i −1.36603 + 2.36603i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.866025 1.50000i 0.866025 1.50000i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.267949 −0.267949
\(210\) −3.23205 0.866025i −3.23205 0.866025i
\(211\) 1.93185 1.93185 0.965926 0.258819i \(-0.0833333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(212\) 0 0
\(213\) −1.86603 3.23205i −1.86603 3.23205i
\(214\) 0 0
\(215\) 0 0
\(216\) 3.34607 3.34607
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −0.448288 0.776457i −0.448288 0.776457i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0.707107 0.707107i 0.707107 0.707107i
\(225\) 5.46410 5.46410
\(226\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(227\) −0.258819 0.448288i −0.258819 0.448288i 0.707107 0.707107i \(-0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(228\) 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
\(231\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(232\) 0 0
\(233\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(234\) 0 0
\(235\) 1.22474 + 2.12132i 1.22474 + 2.12132i
\(236\) 0 0
\(237\) 3.73205 3.73205
\(238\) 0 0
\(239\) 0.517638 0.517638 0.258819 0.965926i \(-0.416667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(240\) −1.67303 + 2.89778i −1.67303 + 2.89778i
\(241\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(242\) −0.366025 0.633975i −0.366025 0.633975i
\(243\) 1.93185 3.34607i 1.93185 3.34607i
\(244\) 1.00000 1.00000
\(245\) 1.73205i 1.73205i
\(246\) 1.93185 1.93185
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −0.707107 2.63896i −0.707107 2.63896i
\(253\) 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
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(264\) 0.500000 0.866025i 0.500000 0.866025i
\(265\) 0 0
\(266\) 0.366025 0.366025i 0.366025 0.366025i
\(267\) 0 0
\(268\) 0.707107 1.22474i 0.707107 1.22474i
\(269\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(270\) 2.89778 + 5.01910i 2.89778 + 5.01910i
\(271\) 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
\(275\) 0.517638 0.896575i 0.517638 0.896575i
\(276\) 0 0
\(277\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 1.67303 + 0.448288i 1.67303 + 0.448288i
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) −1.36603 + 2.36603i −1.36603 + 2.36603i
\(283\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(284\) 0.965926 + 1.67303i 0.965926 + 1.67303i
\(285\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(286\) 0 0
\(287\) −0.258819 0.965926i −0.258819 0.965926i
\(288\) −2.73205 −2.73205
\(289\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) −1.67303 + 0.965926i −1.67303 + 0.965926i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.866025 1.50000i −0.866025 1.50000i
\(298\) 0 0
\(299\) 0 0
\(300\) −3.86370 −3.86370
\(301\) 0 0
\(302\) −1.41421 −1.41421
\(303\) 0 0
\(304\) −0.258819 0.448288i −0.258819 0.448288i
\(305\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) −0.500000 0.133975i −0.500000 0.133975i
\(309\) 0 0
\(310\) 0 0
\(311\) 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(312\) 0 0
\(313\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) 0 0
\(315\) 3.34607 3.34607i 3.34607 3.34607i
\(316\) −1.93185 −1.93185
\(317\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.866025 1.50000i 0.866025 1.50000i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −1.86603 + 3.23205i −1.86603 + 3.23205i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) −1.00000 −1.00000
\(329\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(330\) 1.73205 1.73205
\(331\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(335\) 2.44949 2.44949
\(336\) 0.500000 + 1.86603i 0.500000 + 1.86603i
\(337\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(338\) 0.500000 0.866025i 0.500000 0.866025i
\(339\) −1.67303 2.89778i −1.67303 2.89778i
\(340\) 0 0
\(341\) 0 0
\(342\) −1.41421 −1.41421
\(343\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(344\) 0 0
\(345\) 0 0
\(346\) −0.500000 0.866025i −0.500000 0.866025i
\(347\) −0.258819 0.448288i −0.258819 0.448288i 0.707107 0.707107i \(-0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0.517638 + 1.93185i 0.517638 + 1.93185i
\(351\) 0 0
\(352\) −0.258819 + 0.448288i −0.258819 + 0.448288i
\(353\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(354\) 0 0
\(355\) −1.67303 + 2.89778i −1.67303 + 2.89778i
\(356\) 0 0
\(357\) 0 0
\(358\) −1.93185 −1.93185
\(359\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(360\) −2.36603 4.09808i −2.36603 4.09808i
\(361\) 0.366025 + 0.633975i 0.366025 + 0.633975i
\(362\) 0 0
\(363\) 1.41421 1.41421
\(364\) 0 0
\(365\) 0 0
\(366\) −0.965926 + 1.67303i −0.965926 + 1.67303i
\(367\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(368\) 0 0
\(369\) −1.36603 + 2.36603i −1.36603 + 2.36603i
\(370\) 0 0
\(371\) 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
\(375\) −1.67303 2.89778i −1.67303 2.89778i
\(376\) 0.707107 1.22474i 0.707107 1.22474i
\(377\) 0 0
\(378\) 3.23205 + 0.866025i 3.23205 + 0.866025i
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0.448288 0.776457i 0.448288 0.776457i
\(381\) 0 0
\(382\) −0.707107 1.22474i −0.707107 1.22474i
\(383\) −0.965926 + 1.67303i −0.965926 + 1.67303i −0.258819 + 0.965926i \(0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(384\) 1.93185 1.93185
\(385\) −0.232051 0.866025i −0.232051 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
\(392\) 0.866025 0.500000i 0.866025 0.500000i
\(393\) 0 0
\(394\) 0.500000 0.866025i 0.500000 0.866025i
\(395\) −1.67303 2.89778i −1.67303 2.89778i
\(396\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(397\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) 1.41421 1.41421
\(399\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(400\) 2.00000 2.00000
\(401\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(402\) 1.36603 + 2.36603i 1.36603 + 2.36603i
\(403\) 0 0
\(404\) 0 0
\(405\) −6.46410 −6.46410
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(410\) −0.866025 1.50000i −0.866025 1.50000i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) −0.133975 + 0.232051i −0.133975 + 0.232051i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) −2.36603 + 2.36603i −2.36603 + 2.36603i
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0.965926 1.67303i 0.965926 1.67303i
\(423\) −1.93185 3.34607i −1.93185 3.34607i
\(424\) 0 0
\(425\) 0 0
\(426\) −3.73205 −3.73205
\(427\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) 1.67303 2.89778i 1.67303 2.89778i
\(433\) −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
\(438\) 0 0
\(439\) −0.965926 + 1.67303i −0.965926 + 1.67303i −0.258819 + 0.965926i \(0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(440\) −0.896575 −0.896575
\(441\) 2.73205i 2.73205i
\(442\) 0 0
\(443\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.258819 0.965926i −0.258819 0.965926i
\(449\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(450\) 2.73205 4.73205i 2.73205 4.73205i
\(451\) 0.258819 + 0.448288i 0.258819 + 0.448288i
\(452\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(453\) 1.36603 2.36603i 1.36603 2.36603i
\(454\) −0.517638 −0.517638
\(455\) 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
\(461\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(462\) 0.707107 0.707107i 0.707107 0.707107i
\(463\) −1.93185 −1.93185 −0.965926 0.258819i \(-0.916667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(464\) 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
\(469\) 1.00000 1.00000i 1.00000 1.00000i
\(470\) 2.44949 2.44949
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 1.86603 3.23205i 1.86603 3.23205i
\(475\) 1.03528 1.03528
\(476\) 0 0
\(477\) 0 0
\(478\) 0.258819 0.448288i 0.258819 0.448288i
\(479\) 0.258819 + 0.448288i 0.258819 + 0.448288i 0.965926 0.258819i \(-0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(480\) 1.67303 + 2.89778i 1.67303 + 2.89778i
\(481\) 0 0
\(482\) 2.00000 2.00000
\(483\) 0 0
\(484\) −0.732051 −0.732051
\(485\) 0 0
\(486\) −1.93185 3.34607i −1.93185 3.34607i
\(487\) 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
\(490\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0.965926 1.67303i 0.965926 1.67303i
\(493\) 0 0
\(494\) 0 0
\(495\) −1.22474 + 2.12132i −1.22474 + 2.12132i
\(496\) 0 0
\(497\) 0.500000 + 1.86603i 0.500000 + 1.86603i
\(498\) 0 0
\(499\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(500\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(501\) −1.36603 2.36603i −1.36603 2.36603i
\(502\) 0 0
\(503\) 0.517638 0.517638 0.258819 0.965926i \(-0.416667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(504\) −2.63896 0.707107i −2.63896 0.707107i
\(505\) 0 0
\(506\) 0 0
\(507\) 0.965926 + 1.67303i 0.965926 + 1.67303i
\(508\) 0 0
\(509\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 0.866025 1.50000i 0.866025 1.50000i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −0.732051 −0.732051
\(518\) 0 0
\(519\) 1.93185 1.93185
\(520\) 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
\(525\) −3.73205 1.00000i −3.73205 1.00000i
\(526\) −1.41421 −1.41421
\(527\) 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
\(532\) −0.133975 0.500000i −0.133975 0.500000i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −0.707107 1.22474i −0.707107 1.22474i
\(537\) 1.86603 3.23205i 1.86603 3.23205i
\(538\) −1.00000 −1.00000
\(539\) −0.448288 0.258819i −0.448288 0.258819i
\(540\) 5.79555 5.79555
\(541\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(548\) 0 0
\(549\) −1.36603 2.36603i −1.36603 2.36603i
\(550\) −0.517638 0.896575i −0.517638 0.896575i
\(551\) 0 0
\(552\) 0 0
\(553\) −1.86603 0.500000i −1.86603 0.500000i
\(554\) −1.73205 −1.73205
\(555\) 0 0
\(556\) 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
\(560\) 1.22474 1.22474i 1.22474 1.22474i
\(561\) 0 0
\(562\) 0 0
\(563\) −0.965926 1.67303i −0.965926 1.67303i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 0.965926i \(-0.583333\pi\)
\(564\) 1.36603 + 2.36603i 1.36603 + 2.36603i
\(565\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(566\) 0 0
\(567\) −2.63896 + 2.63896i −2.63896 + 2.63896i
\(568\) 1.93185 1.93185
\(569\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(570\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(571\) −0.965926 1.67303i −0.965926 1.67303i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 0.965926i \(-0.583333\pi\)
\(572\) 0 0
\(573\) 2.73205 2.73205
\(574\) −0.965926 0.258819i −0.965926 0.258819i
\(575\) 0 0
\(576\) −1.36603 + 2.36603i −1.36603 + 2.36603i
\(577\) 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
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −0.517638 −0.517638 −0.258819 0.965926i \(-0.583333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(588\) 1.93185i 1.93185i
\(589\) 0 0
\(590\) 0 0
\(591\) 0.965926 + 1.67303i 0.965926 + 1.67303i
\(592\) 0 0
\(593\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(594\) −1.73205 −1.73205
\(595\) 0 0
\(596\) 0 0
\(597\) −1.36603 + 2.36603i −1.36603 + 2.36603i
\(598\) 0 0
\(599\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(600\) −1.93185 + 3.34607i −1.93185 + 3.34607i
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) −3.86370 −3.86370
\(604\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(605\) −0.633975 1.09808i −0.633975 1.09808i
\(606\) 0 0
\(607\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) −0.517638 −0.517638
\(609\) 0 0
\(610\) 1.73205 1.73205
\(611\) 0 0
\(612\) 0 0
\(613\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) 3.34607 3.34607
\(616\) −0.366025 + 0.366025i −0.366025 + 0.366025i
\(617\) −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
\(622\) 1.41421 1.41421
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(626\) 0 0
\(627\) −0.258819 0.448288i −0.258819 0.448288i
\(628\) 0 0
\(629\) 0 0
\(630\) −1.22474 4.57081i −1.22474 4.57081i
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) −0.965926 + 1.67303i −0.965926 + 1.67303i
\(633\) 1.86603 + 3.23205i 1.86603 + 3.23205i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 2.63896 4.57081i 2.63896 4.57081i
\(640\) −0.866025 1.50000i −0.866025 1.50000i
\(641\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(642\) 0 0
\(643\) 1.93185 1.93185 0.965926 0.258819i \(-0.0833333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(648\) 1.86603 + 3.23205i 1.86603 + 3.23205i
\(649\) 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
\(658\) 1.00000 1.00000i 1.00000 1.00000i
\(659\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(660\) 0.866025 1.50000i 0.866025 1.50000i
\(661\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(662\) −0.707107 1.22474i −0.707107 1.22474i
\(663\) 0 0
\(664\) 0 0
\(665\) 0.633975 0.633975i 0.633975 0.633975i
\(666\) 0 0
\(667\) 0 0
\(668\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(669\) 0 0
\(670\) 1.22474 2.12132i 1.22474 2.12132i
\(671\) −0.517638 −0.517638
\(672\) 1.86603 + 0.500000i 1.86603 + 0.500000i
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0.866025 1.50000i 0.866025 1.50000i
\(675\) 3.34607 + 5.79555i 3.34607 + 5.79555i
\(676\) −0.500000 0.866025i −0.500000 0.866025i
\(677\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(678\) −3.34607 −3.34607
\(679\) 0 0
\(680\) 0 0
\(681\) 0.500000 0.866025i 0.500000 0.866025i
\(682\) 0 0
\(683\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(684\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(685\) 0 0
\(686\) 0.965926 0.258819i 0.965926 0.258819i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.965926 1.67303i 0.965926 1.67303i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(692\) −1.00000 −1.00000
\(693\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(694\) −0.517638 −0.517638
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 1.93185 + 0.517638i 1.93185 + 0.517638i
\(701\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.258819 + 0.448288i 0.258819 + 0.448288i
\(705\) −2.36603 + 4.09808i −2.36603 + 4.09808i
\(706\) −1.73205 −1.73205
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) 1.67303 + 2.89778i 1.67303 + 2.89778i
\(711\) 2.63896 + 4.57081i 2.63896 + 4.57081i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.965926 + 1.67303i −0.965926 + 1.67303i
\(717\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(718\) 0 0
\(719\) −0.258819 + 0.448288i −0.258819 + 0.448288i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(720\) −4.73205 −4.73205
\(721\) 0 0
\(722\) 0.732051 0.732051
\(723\) −1.93185 + 3.34607i −1.93185 + 3.34607i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.707107 1.22474i 0.707107 1.22474i
\(727\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(728\) 0 0
\(729\) 3.73205 3.73205
\(730\) 0 0
\(731\) 0 0
\(732\) 0.965926 + 1.67303i 0.965926 + 1.67303i
\(733\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(734\) 0 0
\(735\) −2.89778 + 1.67303i −2.89778 + 1.67303i
\(736\) 0 0
\(737\) −0.366025 + 0.633975i −0.366025 + 0.633975i
\(738\) 1.36603 + 2.36603i 1.36603 + 2.36603i
\(739\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) 0 0
\(741\) 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
\(750\) −3.34607 −3.34607
\(751\) 0.258819 0.448288i 0.258819 0.448288i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(752\) −0.707107 1.22474i −0.707107 1.22474i
\(753\) 0 0
\(754\) 0 0
\(755\) −2.44949 −2.44949
\(756\) 2.36603 2.36603i 2.36603 2.36603i
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −0.448288 0.776457i −0.448288 0.776457i
\(761\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1.41421 −1.41421
\(765\) 0 0
\(766\) 0.965926 + 1.67303i 0.965926 + 1.67303i
\(767\) 0 0
\(768\) 0.965926 1.67303i 0.965926 1.67303i
\(769\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) −0.866025 0.232051i −0.866025 0.232051i
\(771\) 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
\(777\) 0 0
\(778\) 1.00000 1.00000
\(779\) −0.258819 + 0.448288i −0.258819 + 0.448288i
\(780\) 0 0
\(781\) −0.500000 0.866025i −0.500000 0.866025i
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000i 1.00000i
\(785\) 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
\(789\) 1.36603 2.36603i 1.36603 2.36603i
\(790\) −3.34607 −3.34607
\(791\) 0.448288 + 1.67303i 0.448288 + 1.67303i
\(792\) 1.41421 1.41421
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0.707107 1.22474i 0.707107 1.22474i
\(797\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(798\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(799\)