Properties

Label 1560.1.cs.e.467.2
Level $1560$
Weight $1$
Character 1560.467
Analytic conductor $0.779$
Analytic rank $0$
Dimension $8$
Projective image $D_{8}$
CM discriminant -39
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1560.cs (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.778541419707\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{16})\)
Defining polynomial: \( x^{8} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{8}\)
Projective field: Galois closure of 8.2.49353408000000.10

Embedding invariants

Embedding label 467.2
Root \(-0.923880 + 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 1560.467
Dual form 1560.1.cs.e.1403.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.382683 + 0.923880i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(-0.382683 - 0.923880i) q^{5} +(0.382683 + 0.923880i) q^{6} +(0.923880 - 0.382683i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-0.382683 + 0.923880i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(-0.382683 - 0.923880i) q^{5} +(0.382683 + 0.923880i) q^{6} +(0.923880 - 0.382683i) q^{8} -1.00000i q^{9} +1.00000 q^{10} -1.84776 q^{11} -1.00000 q^{12} +(-0.707107 - 0.707107i) q^{13} +(-0.923880 - 0.382683i) q^{15} +1.00000i q^{16} +(0.923880 + 0.382683i) q^{18} +(-0.382683 + 0.923880i) q^{20} +(0.707107 - 1.70711i) q^{22} +(0.382683 - 0.923880i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(0.923880 - 0.382683i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.707107 - 0.707107i) q^{30} +(-0.923880 - 0.382683i) q^{32} +(-1.30656 + 1.30656i) q^{33} +(-0.707107 + 0.707107i) q^{36} -1.00000 q^{39} +(-0.707107 - 0.707107i) q^{40} +0.765367 q^{41} +(-1.00000 + 1.00000i) q^{43} +(1.30656 + 1.30656i) q^{44} +(-0.923880 + 0.382683i) q^{45} +(0.541196 - 0.541196i) q^{47} +(0.707107 + 0.707107i) q^{48} -1.00000i q^{49} +(-0.382683 - 0.923880i) q^{50} +1.00000i q^{52} +(0.923880 - 0.382683i) q^{54} +(0.707107 + 1.70711i) q^{55} +0.765367i q^{59} +(0.382683 + 0.923880i) q^{60} -1.41421i q^{61} +(0.707107 - 0.707107i) q^{64} +(-0.382683 + 0.923880i) q^{65} +(-0.707107 - 1.70711i) q^{66} -1.84776i q^{71} +(-0.382683 - 0.923880i) q^{72} +1.00000i q^{75} +(0.382683 - 0.923880i) q^{78} +1.41421 q^{79} +(0.923880 - 0.382683i) q^{80} -1.00000 q^{81} +(-0.292893 + 0.707107i) q^{82} +(1.30656 - 1.30656i) q^{83} +(-0.541196 - 1.30656i) q^{86} +(-1.70711 + 0.707107i) q^{88} -1.84776i q^{89} -1.00000i q^{90} +(0.292893 + 0.707107i) q^{94} +(-0.923880 + 0.382683i) q^{96} +(0.923880 + 0.382683i) q^{98} +1.84776i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{10} - 8 q^{12} - 8 q^{39} - 8 q^{43} - 8 q^{81} - 8 q^{82} - 8 q^{88} + 8 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times\).

\(n\) \(391\) \(521\) \(781\) \(937\) \(1081\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(3\) 0.707107 0.707107i 0.707107 0.707107i
\(4\) −0.707107 0.707107i −0.707107 0.707107i
\(5\) −0.382683 0.923880i −0.382683 0.923880i
\(6\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(7\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(8\) 0.923880 0.382683i 0.923880 0.382683i
\(9\) 1.00000i 1.00000i
\(10\) 1.00000 1.00000
\(11\) −1.84776 −1.84776 −0.923880 0.382683i \(-0.875000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(12\) −1.00000 −1.00000
\(13\) −0.707107 0.707107i −0.707107 0.707107i
\(14\) 0 0
\(15\) −0.923880 0.382683i −0.923880 0.382683i
\(16\) 1.00000i 1.00000i
\(17\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(18\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(21\) 0 0
\(22\) 0.707107 1.70711i 0.707107 1.70711i
\(23\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(24\) 0.382683 0.923880i 0.382683 0.923880i
\(25\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(26\) 0.923880 0.382683i 0.923880 0.382683i
\(27\) −0.707107 0.707107i −0.707107 0.707107i
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0.707107 0.707107i 0.707107 0.707107i
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −0.923880 0.382683i −0.923880 0.382683i
\(33\) −1.30656 + 1.30656i −1.30656 + 1.30656i
\(34\) 0 0
\(35\) 0 0
\(36\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(37\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(38\) 0 0
\(39\) −1.00000 −1.00000
\(40\) −0.707107 0.707107i −0.707107 0.707107i
\(41\) 0.765367 0.765367 0.382683 0.923880i \(-0.375000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(42\) 0 0
\(43\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(44\) 1.30656 + 1.30656i 1.30656 + 1.30656i
\(45\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(46\) 0 0
\(47\) 0.541196 0.541196i 0.541196 0.541196i −0.382683 0.923880i \(-0.625000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(48\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(49\) 1.00000i 1.00000i
\(50\) −0.382683 0.923880i −0.382683 0.923880i
\(51\) 0 0
\(52\) 1.00000i 1.00000i
\(53\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(54\) 0.923880 0.382683i 0.923880 0.382683i
\(55\) 0.707107 + 1.70711i 0.707107 + 1.70711i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.765367i 0.765367i 0.923880 + 0.382683i \(0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(60\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(61\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.707107 0.707107i 0.707107 0.707107i
\(65\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(66\) −0.707107 1.70711i −0.707107 1.70711i
\(67\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.84776i 1.84776i −0.382683 0.923880i \(-0.625000\pi\)
0.382683 0.923880i \(-0.375000\pi\)
\(72\) −0.382683 0.923880i −0.382683 0.923880i
\(73\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(74\) 0 0
\(75\) 1.00000i 1.00000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0.382683 0.923880i 0.382683 0.923880i
\(79\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(80\) 0.923880 0.382683i 0.923880 0.382683i
\(81\) −1.00000 −1.00000
\(82\) −0.292893 + 0.707107i −0.292893 + 0.707107i
\(83\) 1.30656 1.30656i 1.30656 1.30656i 0.382683 0.923880i \(-0.375000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.541196 1.30656i −0.541196 1.30656i
\(87\) 0 0
\(88\) −1.70711 + 0.707107i −1.70711 + 0.707107i
\(89\) 1.84776i 1.84776i −0.382683 0.923880i \(-0.625000\pi\)
0.382683 0.923880i \(-0.375000\pi\)
\(90\) 1.00000i 1.00000i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0.292893 + 0.707107i 0.292893 + 0.707107i
\(95\) 0 0
\(96\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(97\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(98\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(99\) 1.84776i 1.84776i
\(100\) 1.00000 1.00000
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(104\) −0.923880 0.382683i −0.923880 0.382683i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(108\) 1.00000i 1.00000i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) −1.84776 −1.84776
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(118\) −0.707107 0.292893i −0.707107 0.292893i
\(119\) 0 0
\(120\) −1.00000 −1.00000
\(121\) 2.41421 2.41421
\(122\) 1.30656 + 0.541196i 1.30656 + 0.541196i
\(123\) 0.541196 0.541196i 0.541196 0.541196i
\(124\) 0 0
\(125\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(126\) 0 0
\(127\) −1.41421 + 1.41421i −1.41421 + 1.41421i −0.707107 + 0.707107i \(0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(128\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(129\) 1.41421i 1.41421i
\(130\) −0.707107 0.707107i −0.707107 0.707107i
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 1.84776 1.84776
\(133\) 0 0
\(134\) 0 0
\(135\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(136\) 0 0
\(137\) −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i \(-0.375000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0.765367i 0.765367i
\(142\) 1.70711 + 0.707107i 1.70711 + 0.707107i
\(143\) 1.30656 + 1.30656i 1.30656 + 1.30656i
\(144\) 1.00000 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) −0.707107 0.707107i −0.707107 0.707107i
\(148\) 0 0
\(149\) 1.84776 1.84776 0.923880 0.382683i \(-0.125000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(150\) −0.923880 0.382683i −0.923880 0.382683i
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(157\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(158\) −0.541196 + 1.30656i −0.541196 + 1.30656i
\(159\) 0 0
\(160\) 1.00000i 1.00000i
\(161\) 0 0
\(162\) 0.382683 0.923880i 0.382683 0.923880i
\(163\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(164\) −0.541196 0.541196i −0.541196 0.541196i
\(165\) 1.70711 + 0.707107i 1.70711 + 0.707107i
\(166\) 0.707107 + 1.70711i 0.707107 + 1.70711i
\(167\) −1.30656 + 1.30656i −1.30656 + 1.30656i −0.382683 + 0.923880i \(0.625000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(168\) 0 0
\(169\) 1.00000i 1.00000i
\(170\) 0 0
\(171\) 0 0
\(172\) 1.41421 1.41421
\(173\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.84776i 1.84776i
\(177\) 0.541196 + 0.541196i 0.541196 + 0.541196i
\(178\) 1.70711 + 0.707107i 1.70711 + 0.707107i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(181\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(182\) 0 0
\(183\) −1.00000 1.00000i −1.00000 1.00000i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.765367 −0.765367
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 1.00000i 1.00000i
\(193\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(194\) 0 0
\(195\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(196\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(197\) −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i \(-0.875000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(198\) −1.70711 0.707107i −1.70711 0.707107i
\(199\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(200\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −0.292893 0.707107i −0.292893 0.707107i
\(206\) −1.30656 + 0.541196i −1.30656 + 0.541196i
\(207\) 0 0
\(208\) 0.707107 0.707107i 0.707107 0.707107i
\(209\) 0 0
\(210\) 0 0
\(211\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(212\) 0 0
\(213\) −1.30656 1.30656i −1.30656 1.30656i
\(214\) 0 0
\(215\) 1.30656 + 0.541196i 1.30656 + 0.541196i
\(216\) −0.923880 0.382683i −0.923880 0.382683i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0.707107 1.70711i 0.707107 1.70711i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(224\) 0 0
\(225\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(226\) 0 0
\(227\) 0.541196 + 0.541196i 0.541196 + 0.541196i 0.923880 0.382683i \(-0.125000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(234\) −0.382683 0.923880i −0.382683 0.923880i
\(235\) −0.707107 0.292893i −0.707107 0.292893i
\(236\) 0.541196 0.541196i 0.541196 0.541196i
\(237\) 1.00000 1.00000i 1.00000 1.00000i
\(238\) 0 0
\(239\) −1.84776 −1.84776 −0.923880 0.382683i \(-0.875000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(240\) 0.382683 0.923880i 0.382683 0.923880i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −0.923880 + 2.23044i −0.923880 + 2.23044i
\(243\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(244\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(245\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(246\) 0.292893 + 0.707107i 0.292893 + 0.707107i
\(247\) 0 0
\(248\) 0 0
\(249\) 1.84776i 1.84776i
\(250\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −0.765367 1.84776i −0.765367 1.84776i
\(255\) 0 0
\(256\) −1.00000 −1.00000
\(257\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(258\) −1.30656 0.541196i −1.30656 0.541196i
\(259\) 0 0
\(260\) 0.923880 0.382683i 0.923880 0.382683i
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(264\) −0.707107 + 1.70711i −0.707107 + 1.70711i
\(265\) 0 0
\(266\) 0 0
\(267\) −1.30656 1.30656i −1.30656 1.30656i
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) −0.707107 0.707107i −0.707107 0.707107i
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0.707107 0.292893i 0.707107 0.292893i
\(275\) 1.30656 1.30656i 1.30656 1.30656i
\(276\) 0 0
\(277\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.84776 1.84776 0.923880 0.382683i \(-0.125000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(282\) 0.707107 + 0.292893i 0.707107 + 0.292893i
\(283\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(284\) −1.30656 + 1.30656i −1.30656 + 1.30656i
\(285\) 0 0
\(286\) −1.70711 + 0.707107i −1.70711 + 0.707107i
\(287\) 0 0
\(288\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.30656 + 1.30656i 1.30656 + 1.30656i 0.923880 + 0.382683i \(0.125000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(294\) 0.923880 0.382683i 0.923880 0.382683i
\(295\) 0.707107 0.292893i 0.707107 0.292893i
\(296\) 0 0
\(297\) 1.30656 + 1.30656i 1.30656 + 1.30656i
\(298\) −0.707107 + 1.70711i −0.707107 + 1.70711i
\(299\) 0 0
\(300\) 0.707107 0.707107i 0.707107 0.707107i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.30656 + 0.541196i −1.30656 + 0.541196i
\(306\) 0 0
\(307\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(308\) 0 0
\(309\) 1.41421 1.41421
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(313\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(314\) 0.541196 + 1.30656i 0.541196 + 1.30656i
\(315\) 0 0
\(316\) −1.00000 1.00000i −1.00000 1.00000i
\(317\) −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i \(-0.875000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.923880 0.382683i −0.923880 0.382683i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(325\) 1.00000 1.00000
\(326\) 0 0
\(327\) 0 0
\(328\) 0.707107 0.292893i 0.707107 0.292893i
\(329\) 0 0
\(330\) −1.30656 + 1.30656i −1.30656 + 1.30656i
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −1.84776 −1.84776
\(333\) 0 0
\(334\) −0.707107 1.70711i −0.707107 1.70711i
\(335\) 0 0
\(336\) 0 0
\(337\) −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(338\) −0.923880 0.382683i −0.923880 0.382683i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) −0.541196 + 1.30656i −0.541196 + 1.30656i
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 1.00000i 1.00000i
\(352\) 1.70711 + 0.707107i 1.70711 + 0.707107i
\(353\) −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i \(-0.875000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(354\) −0.707107 + 0.292893i −0.707107 + 0.292893i
\(355\) −1.70711 + 0.707107i −1.70711 + 0.707107i
\(356\) −1.30656 + 1.30656i −1.30656 + 1.30656i
\(357\) 0 0
\(358\) 0 0
\(359\) 0.765367 0.765367 0.382683 0.923880i \(-0.375000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(360\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(361\) −1.00000 −1.00000
\(362\) 1.84776 + 0.765367i 1.84776 + 0.765367i
\(363\) 1.70711 1.70711i 1.70711 1.70711i
\(364\) 0 0
\(365\) 0 0
\(366\) 1.30656 0.541196i 1.30656 0.541196i
\(367\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 0.765367i 0.765367i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(374\) 0 0
\(375\) 0.923880 0.382683i 0.923880 0.382683i
\(376\) 0.292893 0.707107i 0.292893 0.707107i
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 2.00000i 2.00000i
\(382\) 0 0
\(383\) 0.541196 + 0.541196i 0.541196 + 0.541196i 0.923880 0.382683i \(-0.125000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(384\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(385\) 0 0
\(386\) 0 0
\(387\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) −1.00000 −1.00000
\(391\) 0 0
\(392\) −0.382683 0.923880i −0.382683 0.923880i
\(393\) 0 0
\(394\) −0.292893 0.707107i −0.292893 0.707107i
\(395\) −0.541196 1.30656i −0.541196 1.30656i
\(396\) 1.30656 1.30656i 1.30656 1.30656i
\(397\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(398\) 0.541196 1.30656i 0.541196 1.30656i
\(399\) 0 0
\(400\) −0.707107 0.707107i −0.707107 0.707107i
\(401\) −0.765367 −0.765367 −0.382683 0.923880i \(-0.625000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0.765367 0.765367
\(411\) −0.765367 −0.765367
\(412\) 1.41421i 1.41421i
\(413\) 0 0
\(414\) 0 0
\(415\) −1.70711 0.707107i −1.70711 0.707107i
\(416\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) −0.541196 + 1.30656i −0.541196 + 1.30656i
\(423\) −0.541196 0.541196i −0.541196 0.541196i
\(424\) 0 0
\(425\) 0 0
\(426\) 1.70711 0.707107i 1.70711 0.707107i
\(427\) 0 0
\(428\) 0 0
\(429\) 1.84776 1.84776
\(430\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(431\) 0.765367i 0.765367i −0.923880 0.382683i \(-0.875000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(432\) 0.707107 0.707107i 0.707107 0.707107i
\(433\) 1.41421 1.41421i 1.41421 1.41421i 0.707107 0.707107i \(-0.250000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(440\) 1.30656 + 1.30656i 1.30656 + 1.30656i
\(441\) −1.00000 −1.00000
\(442\) 0 0
\(443\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(444\) 0 0
\(445\) −1.70711 + 0.707107i −1.70711 + 0.707107i
\(446\) 0 0
\(447\) 1.30656 1.30656i 1.30656 1.30656i
\(448\) 0 0
\(449\) 0.765367i 0.765367i −0.923880 0.382683i \(-0.875000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(450\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(451\) −1.41421 −1.41421
\(452\) 0 0
\(453\) 0 0
\(454\) −0.707107 + 0.292893i −0.707107 + 0.292893i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.765367i 0.765367i 0.923880 + 0.382683i \(0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(462\) 0 0
\(463\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(468\) 1.00000 1.00000
\(469\) 0 0
\(470\) 0.541196 0.541196i 0.541196 0.541196i
\(471\) 1.41421i 1.41421i
\(472\) 0.292893 + 0.707107i 0.292893 + 0.707107i
\(473\) 1.84776 1.84776i 1.84776 1.84776i
\(474\) 0.541196 + 1.30656i 0.541196 + 1.30656i
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0.707107 1.70711i 0.707107 1.70711i
\(479\) 0.765367 0.765367 0.382683 0.923880i \(-0.375000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(480\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −1.70711 1.70711i −1.70711 1.70711i
\(485\) 0 0
\(486\) −0.382683 0.923880i −0.382683 0.923880i
\(487\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(488\) −0.541196 1.30656i −0.541196 1.30656i
\(489\) 0 0
\(490\) 1.00000i 1.00000i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) −0.765367 −0.765367
\(493\) 0 0
\(494\) 0 0
\(495\) 1.70711 0.707107i 1.70711 0.707107i
\(496\) 0 0
\(497\) 0 0
\(498\) 1.70711 + 0.707107i 1.70711 + 0.707107i
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) −0.382683 0.923880i −0.382683 0.923880i
\(501\) 1.84776i 1.84776i
\(502\) 0 0
\(503\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(508\) 2.00000 2.00000
\(509\) −0.765367 −0.765367 −0.382683 0.923880i \(-0.625000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.382683 0.923880i 0.382683 0.923880i
\(513\) 0 0
\(514\) 0 0
\(515\) 0.541196 1.30656i 0.541196 1.30656i
\(516\) 1.00000 1.00000i 1.00000 1.00000i
\(517\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(518\) 0 0
\(519\) 0 0
\(520\) 1.00000i 1.00000i
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −1.30656 1.30656i −1.30656 1.30656i
\(529\) 1.00000i 1.00000i
\(530\) 0 0
\(531\) 0.765367 0.765367
\(532\) 0 0
\(533\) −0.541196 0.541196i −0.541196 0.541196i
\(534\) 1.70711 0.707107i 1.70711 0.707107i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.84776i 1.84776i
\(540\) 0.923880 0.382683i 0.923880 0.382683i
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 0 0
\(543\) −1.41421 1.41421i −1.41421 1.41421i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(548\) 0.765367i 0.765367i
\(549\) −1.41421 −1.41421
\(550\) 0.707107 + 1.70711i 0.707107 + 1.70711i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −0.541196 1.30656i −0.541196 1.30656i
\(555\) 0 0
\(556\) 0 0
\(557\) 1.30656 1.30656i 1.30656 1.30656i 0.382683 0.923880i \(-0.375000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(558\) 0 0
\(559\) 1.41421 1.41421
\(560\) 0 0
\(561\) 0 0
\(562\) −0.707107 + 1.70711i −0.707107 + 1.70711i
\(563\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(564\) −0.541196 + 0.541196i −0.541196 + 0.541196i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) −0.707107 1.70711i −0.707107 1.70711i
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(572\) 1.84776i 1.84776i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.707107 0.707107i −0.707107 0.707107i
\(577\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(578\) −0.923880 0.382683i −0.923880 0.382683i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(586\) −1.70711 + 0.707107i −1.70711 + 0.707107i
\(587\) −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i \(-0.375000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(588\) 1.00000i 1.00000i
\(589\) 0 0
\(590\) 0.765367i 0.765367i
\(591\) 0.765367i 0.765367i
\(592\) 0 0
\(593\) −1.30656 + 1.30656i −1.30656 + 1.30656i −0.382683 + 0.923880i \(0.625000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(594\) −1.70711 + 0.707107i −1.70711 + 0.707107i
\(595\) 0 0
\(596\) −1.30656 1.30656i −1.30656 1.30656i
\(597\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(601\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.923880 2.23044i −0.923880 2.23044i
\(606\) 0 0
\(607\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(608\) 0 0
\(609\) 0 0
\(610\) 1.41421i 1.41421i
\(611\) −0.765367 −0.765367
\(612\) 0 0
\(613\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(614\) 0 0
\(615\) −0.707107 0.292893i −0.707107 0.292893i
\(616\) 0 0
\(617\) 1.30656 + 1.30656i 1.30656 + 1.30656i 0.923880 + 0.382683i \(0.125000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(618\) −0.541196 + 1.30656i −0.541196 + 1.30656i
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 1.00000i 1.00000i
\(625\) 1.00000i 1.00000i
\(626\) 0 0
\(627\) 0 0
\(628\) −1.41421 −1.41421
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 1.30656 0.541196i 1.30656 0.541196i
\(633\) 1.00000 1.00000i 1.00000 1.00000i
\(634\) −0.292893 0.707107i −0.292893 0.707107i
\(635\) 1.84776 + 0.765367i 1.84776 + 0.765367i
\(636\) 0 0
\(637\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(638\) 0 0
\(639\) −1.84776 −1.84776
\(640\) 0.707107 0.707107i 0.707107 0.707107i
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(644\) 0 0
\(645\) 1.30656 0.541196i 1.30656 0.541196i
\(646\) 0 0
\(647\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(648\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(649\) 1.41421i 1.41421i
\(650\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.765367i 0.765367i
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) −0.707107 1.70711i −0.707107 1.70711i
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.707107 1.70711i 0.707107 1.70711i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 1.84776 1.84776
\(669\) 0 0
\(670\) 0 0
\(671\) 2.61313i 2.61313i
\(672\) 0 0
\(673\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(674\) 1.84776 0.765367i 1.84776 0.765367i
\(675\) 1.00000 1.00000
\(676\) 0.707107 0.707107i 0.707107 0.707107i
\(677\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.765367 0.765367
\(682\) 0 0
\(683\) −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i \(-0.875000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(684\) 0 0
\(685\) −0.292893 + 0.707107i −0.292893 + 0.707107i
\(686\) 0 0
\(687\) 0 0
\(688\) −1.00000 1.00000i −1.00000 1.00000i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) −0.923880 0.382683i −0.923880 0.382683i
\(703\) 0 0
\(704\) −1.30656 + 1.30656i −1.30656 + 1.30656i
\(705\) −0.707107 + 0.292893i −0.707107 + 0.292893i
\(706\) −0.292893 0.707107i −0.292893 0.707107i
\(707\) 0 0
\(708\) 0.765367i 0.765367i
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 1.84776i 1.84776i
\(711\) 1.41421i 1.41421i
\(712\) −0.707107 1.70711i −0.707107 1.70711i
\(713\) 0 0
\(714\) 0 0
\(715\) 0.707107 1.70711i 0.707107 1.70711i
\(716\) 0 0
\(717\) −1.30656 + 1.30656i −1.30656 + 1.30656i
\(718\) −0.292893 + 0.707107i −0.292893 + 0.707107i
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) −0.382683 0.923880i −0.382683 0.923880i
\(721\) 0 0
\(722\) 0.382683 0.923880i 0.382683 0.923880i
\(723\) 0 0
\(724\) −1.41421 + 1.41421i −1.41421 + 1.41421i
\(725\) 0 0
\(726\) 0.923880 + 2.23044i 0.923880 + 2.23044i
\(727\) 1.41421 1.41421i 1.41421 1.41421i 0.707107 0.707107i \(-0.250000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(728\) 0 0
\(729\) 1.00000i 1.00000i
\(730\) 0 0
\(731\) 0 0
\(732\) 1.41421i 1.41421i
\(733\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(734\) −0.541196 1.30656i −0.541196 1.30656i
\(735\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(736\) 0 0
\(737\) 0 0
\(738\) 0.707107 + 0.292893i 0.707107 + 0.292893i
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.541196 + 0.541196i 0.541196 + 0.541196i 0.923880 0.382683i \(-0.125000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(744\) 0 0
\(745\) −0.707107 1.70711i −0.707107 1.70711i
\(746\) 0 0
\(747\) −1.30656 1.30656i −1.30656 1.30656i
\(748\) 0 0
\(749\) 0 0
\(750\) 1.00000i 1.00000i
\(751\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(752\) 0.541196 + 0.541196i 0.541196 + 0.541196i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.84776 1.84776 0.923880 0.382683i \(-0.125000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(762\) −1.84776 0.765367i −1.84776 0.765367i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −0.707107 + 0.292893i −0.707107 + 0.292893i
\(767\) 0.541196 0.541196i 0.541196 0.541196i
\(768\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.541196 + 0.541196i 0.541196 + 0.541196i 0.923880 0.382683i \(-0.125000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(774\) −1.30656 + 0.541196i −1.30656 + 0.541196i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0.382683 0.923880i 0.382683 0.923880i
\(781\) 3.41421i 3.41421i
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 1.00000
\(785\) −1.30656 0.541196i −1.30656 0.541196i
\(786\) 0 0
\(787\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(788\) 0.765367 0.765367
\(789\) 0 0
\(790\) 1.41421 1.41421
\(791\) 0 0
\(792\) 0.707107 + 1.70711i 0.707107 + 1.70711i
\(793\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(794\) 0 0
\(795\) 0 0
\(796\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(797\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(798\) 0 0