Properties

Label 2520.1.fw.a.2029.4
Level $2520$
Weight $1$
Character 2520.2029
Analytic conductor $1.258$
Analytic rank $0$
Dimension $8$
Projective image $D_{12}$
CM discriminant -56
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2520.fw (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.25764383184\)
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: \(\Z[a_1, a_2, a_3]\)
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 2029.4
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 2520.2029
Dual form 2520.1.fw.a.349.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(-0.965926 - 0.258819i) q^{10} +(-0.258819 - 0.965926i) q^{12} +(-1.22474 - 0.707107i) q^{13} +(-0.500000 + 0.866025i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{18} +0.517638 q^{19} +(-0.965926 + 0.258819i) q^{20} +(-0.258819 + 0.965926i) q^{21} +(1.50000 + 0.866025i) q^{23} +(-0.707107 - 0.707107i) q^{24} +1.00000i q^{25} -1.41421 q^{26} +(-0.707107 - 0.707107i) q^{27} +1.00000i q^{28} +(-0.866025 + 0.500000i) q^{30} +(-0.866025 - 0.500000i) q^{32} +(0.965926 + 0.258819i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(0.448288 - 0.258819i) q^{38} +(-1.36603 + 0.366025i) q^{39} +(-0.707107 + 0.707107i) q^{40} +(0.258819 + 0.965926i) q^{42} +(-0.707107 + 0.707107i) q^{45} +1.73205 q^{46} +(-0.965926 - 0.258819i) q^{48} +(0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-1.22474 + 0.707107i) q^{52} +(-0.965926 - 0.258819i) q^{54} +(0.500000 + 0.866025i) q^{56} +(0.366025 - 0.366025i) q^{57} +(0.707107 - 1.22474i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(-0.258819 - 0.448288i) q^{61} +(0.500000 + 0.866025i) q^{63} -1.00000 q^{64} +(0.366025 + 1.36603i) q^{65} +(1.67303 - 0.448288i) q^{69} +(0.965926 - 0.258819i) q^{70} +1.73205 q^{71} -1.00000 q^{72} +(0.707107 + 0.707107i) q^{75} +(0.258819 - 0.448288i) q^{76} +(-1.00000 + 1.00000i) q^{78} +(-0.866025 - 1.50000i) q^{79} +(-0.258819 + 0.965926i) q^{80} -1.00000 q^{81} +(1.22474 - 0.707107i) q^{83} +(0.707107 + 0.707107i) q^{84} +(-0.258819 + 0.965926i) q^{90} +1.41421 q^{91} +(1.50000 - 0.866025i) q^{92} +(-0.366025 - 0.366025i) q^{95} +(-0.965926 + 0.258819i) q^{96} -1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} + O(q^{10}) \) \( 8q + 4q^{4} - 4q^{14} - 8q^{15} - 4q^{16} - 4q^{18} + 12q^{23} - 4q^{39} + 4q^{49} + 4q^{50} + 4q^{56} - 4q^{57} - 4q^{60} + 4q^{63} - 8q^{64} - 4q^{65} - 8q^{72} - 8q^{78} - 8q^{81} + 12q^{92} + 4q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(1081\) \(1261\) \(2017\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.866025 0.500000i
\(3\) 0.707107 0.707107i 0.707107 0.707107i
\(4\) 0.500000 0.866025i 0.500000 0.866025i
\(5\) −0.707107 0.707107i −0.707107 0.707107i
\(6\) 0.258819 0.965926i 0.258819 0.965926i
\(7\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(8\) 1.00000i 1.00000i
\(9\) 1.00000i 1.00000i
\(10\) −0.965926 0.258819i −0.965926 0.258819i
\(11\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(12\) −0.258819 0.965926i −0.258819 0.965926i
\(13\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(14\) −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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −0.500000 0.866025i −0.500000 0.866025i
\(19\) 0.517638 0.517638 0.258819 0.965926i \(-0.416667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(20\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(21\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(22\) 0 0
\(23\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) −0.707107 0.707107i −0.707107 0.707107i
\(25\) 1.00000i 1.00000i
\(26\) −1.41421 −1.41421
\(27\) −0.707107 0.707107i −0.707107 0.707107i
\(28\) 1.00000i 1.00000i
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(31\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) −0.866025 0.500000i −0.866025 0.500000i
\(33\) 0 0
\(34\) 0 0
\(35\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(36\) −0.866025 0.500000i −0.866025 0.500000i
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0.448288 0.258819i 0.448288 0.258819i
\(39\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(40\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(41\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(43\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(44\) 0 0
\(45\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(46\) 1.73205 1.73205
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) −0.965926 0.258819i −0.965926 0.258819i
\(49\) 0.500000 0.866025i 0.500000 0.866025i
\(50\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(51\) 0 0
\(52\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) −0.965926 0.258819i −0.965926 0.258819i
\(55\) 0 0
\(56\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(57\) 0.366025 0.366025i 0.366025 0.366025i
\(58\) 0 0
\(59\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(60\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(61\) −0.258819 0.448288i −0.258819 0.448288i 0.707107 0.707107i \(-0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(62\) 0 0
\(63\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(64\) −1.00000 −1.00000
\(65\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(66\) 0 0
\(67\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(68\) 0 0
\(69\) 1.67303 0.448288i 1.67303 0.448288i
\(70\) 0.965926 0.258819i 0.965926 0.258819i
\(71\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) −1.00000 −1.00000
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(76\) 0.258819 0.448288i 0.258819 0.448288i
\(77\) 0 0
\(78\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(79\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(80\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(81\) −1.00000 −1.00000
\(82\) 0 0
\(83\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(84\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(91\) 1.41421 1.41421
\(92\) 1.50000 0.866025i 1.50000 0.866025i
\(93\) 0 0
\(94\) 0 0
\(95\) −0.366025 0.366025i −0.366025 0.366025i
\(96\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(97\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(98\) 1.00000i 1.00000i
\(99\) 0 0
\(100\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(101\) 0.965926 + 1.67303i 0.965926 + 1.67303i 0.707107 + 0.707107i \(0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(102\) 0 0
\(103\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(104\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(105\) 0.866025 0.500000i 0.866025 0.500000i
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(113\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(114\) 0.133975 0.500000i 0.133975 0.500000i
\(115\) −0.448288 1.67303i −0.448288 1.67303i
\(116\) 0 0
\(117\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(118\) 1.41421i 1.41421i
\(119\) 0 0
\(120\) 1.00000i 1.00000i
\(121\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(122\) −0.448288 0.258819i −0.448288 0.258819i
\(123\) 0 0
\(124\) 0 0
\(125\) 0.707107 0.707107i 0.707107 0.707107i
\(126\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(127\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(128\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(129\) 0 0
\(130\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(131\) −0.965926 + 1.67303i −0.965926 + 1.67303i −0.258819 + 0.965926i \(0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(132\) 0 0
\(133\) −0.448288 + 0.258819i −0.448288 + 0.258819i
\(134\) 0 0
\(135\) 1.00000i 1.00000i
\(136\) 0 0
\(137\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(138\) 1.22474 1.22474i 1.22474 1.22474i
\(139\) −0.965926 + 1.67303i −0.965926 + 1.67303i −0.258819 + 0.965926i \(0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(140\) 0.707107 0.707107i 0.707107 0.707107i
\(141\) 0 0
\(142\) 1.50000 0.866025i 1.50000 0.866025i
\(143\) 0 0
\(144\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.258819 0.965926i −0.258819 0.965926i
\(148\) 0 0
\(149\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(150\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(151\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(152\) 0.517638i 0.517638i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(157\) 1.67303 + 0.965926i 1.67303 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(158\) −1.50000 0.866025i −1.50000 0.866025i
\(159\) 0 0
\(160\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(161\) −1.73205 −1.73205
\(162\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0.707107 1.22474i 0.707107 1.22474i
\(167\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(168\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(169\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(170\) 0 0
\(171\) 0.517638i 0.517638i
\(172\) 0 0
\(173\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(174\) 0 0
\(175\) −0.500000 0.866025i −0.500000 0.866025i
\(176\) 0 0
\(177\) −0.366025 1.36603i −0.366025 1.36603i
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(181\) 1.93185 1.93185 0.965926 0.258819i \(-0.0833333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(182\) 1.22474 0.707107i 1.22474 0.707107i
\(183\) −0.500000 0.133975i −0.500000 0.133975i
\(184\) 0.866025 1.50000i 0.866025 1.50000i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(190\) −0.500000 0.133975i −0.500000 0.133975i
\(191\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(192\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(193\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(194\) 0 0
\(195\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(196\) −0.500000 0.866025i −0.500000 0.866025i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 1.00000 1.00000
\(201\) 0 0
\(202\) 1.67303 + 0.965926i 1.67303 + 0.965926i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.866025 1.50000i 0.866025 1.50000i
\(208\) 1.41421i 1.41421i
\(209\) 0 0
\(210\) 0.500000 0.866025i 0.500000 0.866025i
\(211\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) 0 0
\(213\) 1.22474 1.22474i 1.22474 1.22474i
\(214\) 0 0
\(215\) 0 0
\(216\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(224\) 1.00000 1.00000
\(225\) 1.00000 1.00000
\(226\) 1.00000 1.00000
\(227\) 1.67303 0.965926i 1.67303 0.965926i 0.707107 0.707107i \(-0.250000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(228\) −0.133975 0.500000i −0.133975 0.500000i
\(229\) −0.965926 + 1.67303i −0.965926 + 1.67303i −0.258819 + 0.965926i \(0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(230\) −1.22474 1.22474i −1.22474 1.22474i
\(231\) 0 0
\(232\) 0 0
\(233\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(234\) 1.41421i 1.41421i
\(235\) 0 0
\(236\) −0.707107 1.22474i −0.707107 1.22474i
\(237\) −1.67303 0.448288i −1.67303 0.448288i
\(238\) 0 0
\(239\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(240\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(241\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(242\) 1.00000i 1.00000i
\(243\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(244\) −0.517638 −0.517638
\(245\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(246\) 0 0
\(247\) −0.633975 0.366025i −0.633975 0.366025i
\(248\) 0 0
\(249\) 0.366025 1.36603i 0.366025 1.36603i
\(250\) 0.258819 0.965926i 0.258819 0.965926i
\(251\) 0.517638 0.517638 0.258819 0.965926i \(-0.416667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(252\) 1.00000 1.00000
\(253\) 0 0
\(254\) −0.866025 1.50000i −0.866025 1.50000i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(257\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(261\) 0 0
\(262\) 1.93185i 1.93185i
\(263\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −0.258819 + 0.448288i −0.258819 + 0.448288i
\(267\) 0 0
\(268\) 0 0
\(269\) −1.93185 −1.93185 −0.965926 0.258819i \(-0.916667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(270\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 1.00000 1.00000i 1.00000 1.00000i
\(274\) 0 0
\(275\) 0 0
\(276\) 0.448288 1.67303i 0.448288 1.67303i
\(277\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(278\) 1.93185i 1.93185i
\(279\) 0 0
\(280\) 0.258819 0.965926i 0.258819 0.965926i
\(281\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 1.67303 + 0.965926i 1.67303 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(284\) 0.866025 1.50000i 0.866025 1.50000i
\(285\) −0.517638 −0.517638
\(286\) 0 0
\(287\) 0 0
\(288\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.448288 + 0.258819i 0.448288 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(294\) −0.707107 0.707107i −0.707107 0.707107i
\(295\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.22474 2.12132i −1.22474 2.12132i
\(300\) 0.965926 0.258819i 0.965926 0.258819i
\(301\) 0 0
\(302\) −0.866025 0.500000i −0.866025 0.500000i
\(303\) 1.86603 + 0.500000i 1.86603 + 0.500000i
\(304\) −0.258819 0.448288i −0.258819 0.448288i
\(305\) −0.133975 + 0.500000i −0.133975 + 0.500000i
\(306\) 0 0
\(307\) 0.517638i 0.517638i −0.965926 0.258819i \(-0.916667\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(313\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(314\) 1.93185 1.93185
\(315\) 0.258819 0.965926i 0.258819 0.965926i
\(316\) −1.73205 −1.73205
\(317\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(321\) 0 0
\(322\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(323\) 0 0
\(324\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(325\) 0.707107 1.22474i 0.707107 1.22474i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) 1.41421i 1.41421i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0.965926 0.258819i 0.965926 0.258819i
\(337\) −1.73205 1.00000i −1.73205 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 0.500000i \(-0.833333\pi\)
\(338\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(339\) 0.965926 0.258819i 0.965926 0.258819i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.258819 0.448288i −0.258819 0.448288i
\(343\) 1.00000i 1.00000i
\(344\) 0 0
\(345\) −1.50000 0.866025i −1.50000 0.866025i
\(346\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(347\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(348\) 0 0
\(349\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(350\) −0.866025 0.500000i −0.866025 0.500000i
\(351\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(352\) 0 0
\(353\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(354\) −1.00000 1.00000i −1.00000 1.00000i
\(355\) −1.22474 1.22474i −1.22474 1.22474i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(360\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(361\) −0.732051 −0.732051
\(362\) 1.67303 0.965926i 1.67303 0.965926i
\(363\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(364\) 0.707107 1.22474i 0.707107 1.22474i
\(365\) 0 0
\(366\) −0.500000 + 0.133975i −0.500000 + 0.133975i
\(367\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(368\) 1.73205i 1.73205i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(374\) 0 0
\(375\) 1.00000i 1.00000i
\(376\) 0 0
\(377\) 0 0
\(378\) 0.965926 0.258819i 0.965926 0.258819i
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) −0.500000 + 0.133975i −0.500000 + 0.133975i
\(381\) −1.22474 1.22474i −1.22474 1.22474i
\(382\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(383\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(385\) 0 0
\(386\) −1.00000 −1.00000
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(390\) 1.41421 1.41421
\(391\) 0 0
\(392\) −0.866025 0.500000i −0.866025 0.500000i
\(393\) 0.500000 + 1.86603i 0.500000 + 1.86603i
\(394\) 0 0
\(395\) −0.448288 + 1.67303i −0.448288 + 1.67303i
\(396\) 0 0
\(397\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(398\) 0 0
\(399\) −0.133975 + 0.500000i −0.133975 + 0.500000i
\(400\) 0.866025 0.500000i 0.866025 0.500000i
\(401\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 1.93185 1.93185
\(405\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.41421i 1.41421i
\(414\) 1.73205i 1.73205i
\(415\) −1.36603 0.366025i −1.36603 0.366025i
\(416\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(417\) 0.500000 + 1.86603i 0.500000 + 1.86603i
\(418\) 0 0
\(419\) −0.258819 + 0.448288i −0.258819 + 0.448288i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(420\) 1.00000i 1.00000i
\(421\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0.448288 1.67303i 0.448288 1.67303i
\(427\) 0.448288 + 0.258819i 0.448288 + 0.258819i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(432\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.776457 + 0.448288i 0.776457 + 0.448288i
\(438\) 0 0
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) −0.866025 0.500000i −0.866025 0.500000i
\(442\) 0 0
\(443\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(444\) 0 0
\(445\) 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 \(0.666667\pi\)
\(450\) 0.866025 0.500000i 0.866025 0.500000i
\(451\) 0 0
\(452\) 0.866025 0.500000i 0.866025 0.500000i
\(453\) −0.965926 0.258819i −0.965926 0.258819i
\(454\) 0.965926 1.67303i 0.965926 1.67303i
\(455\) −1.00000 1.00000i −1.00000 1.00000i
\(456\) −0.366025 0.366025i −0.366025 0.366025i
\(457\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(458\) 1.93185i 1.93185i
\(459\) 0 0
\(460\) −1.67303 0.448288i −1.67303 0.448288i
\(461\) −0.965926 1.67303i −0.965926 1.67303i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 0.965926i \(-0.583333\pi\)
\(462\) 0 0
\(463\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(467\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(468\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(469\) 0 0
\(470\) 0 0
\(471\) 1.86603 0.500000i 1.86603 0.500000i
\(472\) −1.22474 0.707107i −1.22474 0.707107i
\(473\) 0 0
\(474\) −1.67303 + 0.448288i −1.67303 + 0.448288i
\(475\) 0.517638i 0.517638i
\(476\) 0 0
\(477\) 0 0
\(478\) 1.00000i 1.00000i
\(479\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(481\) 0 0
\(482\) 0 0
\(483\) −1.22474 + 1.22474i −1.22474 + 1.22474i
\(484\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(485\) 0 0
\(486\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(487\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) −0.448288 + 0.258819i −0.448288 + 0.258819i
\(489\) 0 0
\(490\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(491\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −0.732051 −0.732051
\(495\) 0 0
\(496\) 0 0
\(497\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(498\) −0.366025 1.36603i −0.366025 1.36603i
\(499\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) −0.258819 0.965926i −0.258819 0.965926i
\(501\) 0 0
\(502\) 0.448288 0.258819i 0.448288 0.258819i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0.866025 0.500000i 0.866025 0.500000i
\(505\) 0.500000 1.86603i 0.500000 1.86603i
\(506\) 0 0
\(507\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(508\) −1.50000 0.866025i −1.50000 0.866025i
\(509\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 1.00000i
\(513\) −0.366025 0.366025i −0.366025 0.366025i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(520\) 1.36603 0.366025i 1.36603 0.366025i
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0.517638i 0.517638i −0.965926 0.258819i \(-0.916667\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(524\) 0.965926 + 1.67303i 0.965926 + 1.67303i
\(525\) −0.965926 0.258819i −0.965926 0.258819i
\(526\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(530\) 0 0
\(531\) −1.22474 0.707107i −1.22474 0.707107i
\(532\) 0.517638i 0.517638i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −1.67303 + 0.965926i −1.67303 + 0.965926i
\(539\) 0 0
\(540\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 1.36603 1.36603i 1.36603 1.36603i
\(544\) 0 0
\(545\) 0 0
\(546\) 0.366025 1.36603i 0.366025 1.36603i
\(547\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(548\) 0 0
\(549\) −0.448288 + 0.258819i −0.448288 + 0.258819i
\(550\) 0 0
\(551\) 0 0
\(552\) −0.448288 1.67303i −0.448288 1.67303i
\(553\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(554\) 0 0
\(555\) 0 0
\(556\) 0.965926 + 1.67303i 0.965926 + 1.67303i
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −0.258819 0.965926i −0.258819 0.965926i
\(561\) 0 0
\(562\) −0.866025 0.500000i −0.866025 0.500000i
\(563\) −1.67303 0.965926i −1.67303 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(564\) 0 0
\(565\) −0.258819 0.965926i −0.258819 0.965926i
\(566\) 1.93185 1.93185
\(567\) 0.866025 0.500000i 0.866025 0.500000i
\(568\) 1.73205i 1.73205i
\(569\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(570\) −0.448288 + 0.258819i −0.448288 + 0.258819i
\(571\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) 1.67303 + 0.448288i 1.67303 + 0.448288i
\(574\) 0 0
\(575\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(576\) 1.00000i 1.00000i
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(579\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(580\) 0 0
\(581\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 1.36603 0.366025i 1.36603 0.366025i
\(586\) 0.517638 0.517638
\(587\) 0.448288 0.258819i 0.448288 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(588\) −0.965926 0.258819i −0.965926 0.258819i
\(589\) 0 0
\(590\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −2.12132 1.22474i −2.12132 1.22474i
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 0.707107 0.707107i 0.707107 0.707107i
\(601\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1.00000 −1.00000
\(605\) 0.965926 0.258819i 0.965926 0.258819i
\(606\) 1.86603 0.500000i 1.86603 0.500000i
\(607\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(608\) −0.448288 0.258819i −0.448288 0.258819i
\(609\) 0 0
\(610\) 0.133975 + 0.500000i 0.133975 + 0.500000i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) −0.258819 0.448288i −0.258819 0.448288i
\(615\) 0 0
\(616\) 0 0
\(617\) 1.73205 + 1.00000i 1.73205 + 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(618\) 0 0
\(619\) 0.258819 + 0.448288i 0.258819 + 0.448288i 0.965926 0.258819i \(-0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(620\) 0 0
\(621\) −0.448288 1.67303i −0.448288 1.67303i
\(622\) 0 0
\(623\) 0 0
\(624\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(625\) −1.00000 −1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 1.67303 0.965926i 1.67303 0.965926i
\(629\) 0 0
\(630\) −0.258819 0.965926i −0.258819 0.965926i
\(631\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(632\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(633\) 0 0
\(634\) 0 0
\(635\) −1.22474 + 1.22474i −1.22474 + 1.22474i
\(636\) 0 0
\(637\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(638\) 0 0
\(639\) 1.73205i 1.73205i
\(640\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(641\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(642\) 0 0
\(643\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(644\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 1.00000i 1.00000i
\(649\) 0 0
\(650\) 1.41421i 1.41421i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(654\) 0 0
\(655\) 1.86603 0.500000i 1.86603 0.500000i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(660\) 0 0
\(661\) −0.965926 + 1.67303i −0.965926 + 1.67303i −0.258819 + 0.965926i \(0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −0.707107 1.22474i −0.707107 1.22474i
\(665\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0.707107 0.707107i 0.707107 0.707107i
\(673\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(674\) −2.00000 −2.00000
\(675\) 0.707107 0.707107i 0.707107 0.707107i
\(676\) 1.00000 1.00000
\(677\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(678\) 0.707107 0.707107i 0.707107 0.707107i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.500000 1.86603i 0.500000 1.86603i
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) −0.448288 0.258819i −0.448288 0.258819i
\(685\) 0 0
\(686\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(687\) 0.500000 + 1.86603i 0.500000 + 1.86603i
\(688\) 0 0
\(689\) 0 0
\(690\) −1.73205 −1.73205
\(691\) −0.965926 1.67303i −0.965926 1.67303i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 0.965926i \(-0.583333\pi\)
\(692\) 1.41421i 1.41421i
\(693\) 0 0
\(694\) 0 0
\(695\) 1.86603 0.500000i 1.86603 0.500000i
\(696\) 0 0
\(697\) 0 0
\(698\) −1.22474 0.707107i −1.22474 0.707107i
\(699\) 1.22474 + 1.22474i 1.22474 + 1.22474i
\(700\) −1.00000 −1.00000
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.67303 0.965926i −1.67303 0.965926i
\(708\) −1.36603 0.366025i −1.36603 0.366025i
\(709\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(710\) −1.67303 0.448288i −1.67303 0.448288i
\(711\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −0.258819 0.965926i −0.258819 0.965926i
\(718\) 0.866025 0.500000i 0.866025 0.500000i
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(721\) 0 0
\(722\) −0.633975 + 0.366025i −0.633975 + 0.366025i
\(723\) 0 0
\(724\) 0.965926 1.67303i 0.965926 1.67303i
\(725\) 0 0
\(726\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(727\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(728\) 1.41421i 1.41421i
\(729\) 1.00000i 1.00000i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.366025 + 0.366025i −0.366025 + 0.366025i
\(733\) −1.67303 0.965926i −1.67303 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(734\) 0 0
\(735\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(736\) −0.866025 1.50000i −0.866025 1.50000i
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) −0.707107 + 0.189469i −0.707107 + 0.189469i
\(742\) 0 0
\(743\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.707107 1.22474i −0.707107 1.22474i
\(748\) 0 0
\(749\) 0 0
\(750\) −0.500000 0.866025i −0.500000 0.866025i
\(751\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0.366025 0.366025i 0.366025 0.366025i
\(754\) 0 0
\(755\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(756\) 0.707107 0.707107i 0.707107 0.707107i
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −0.366025 + 0.366025i −0.366025 + 0.366025i
\(761\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(762\) −1.67303 0.448288i −1.67303 0.448288i
\(763\) 0 0
\(764\) 1.73205 1.73205
\(765\) 0 0
\(766\) 0 0
\(767\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(768\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(769\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(773\) 0.517638i 0.517638i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 1.22474 0.707107i 1.22474 0.707107i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −1.00000 −1.00000
\(785\) −0.500000 1.86603i −0.500000 1.86603i
\(786\) 1.36603 + 1.36603i 1.36603 + 1.36603i
\(787\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(788\) 0 0
\(789\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(790\) 0.448288 + 1.67303i 0.448288 + 1.67303i
\(791\) −1.00000 −1.00000
\(792\) 0 0
\(793\) 0.732051i 0.732051i
\(794\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(795\) 0 0
\(796\) 0