Properties

Label 840.1.bp.c.797.1
Level $840$
Weight $1$
Character 840.797
Analytic conductor $0.419$
Analytic rank $0$
Dimension $8$
Projective image $D_{8}$
CM discriminant -56
Inner twists $8$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 840.bp (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.419214610612\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{16})\)
Defining polynomial: \(x^{8} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{8}\)
Projective field: Galois closure of 8.2.1778112000000.2

Embedding invariants

Embedding label 797.1
Root \(0.923880 - 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 840.797
Dual form 840.1.bp.c.293.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.382683 - 0.923880i) q^{3} -1.00000i q^{4} +(0.382683 + 0.923880i) q^{5} +(0.923880 + 0.382683i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.382683 - 0.923880i) q^{3} -1.00000i q^{4} +(0.382683 + 0.923880i) q^{5} +(0.923880 + 0.382683i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(-0.923880 - 0.382683i) q^{10} +(-0.923880 + 0.382683i) q^{12} +(-1.30656 + 1.30656i) q^{13} -1.00000 q^{14} +(0.707107 - 0.707107i) q^{15} -1.00000 q^{16} -1.00000i q^{18} -0.765367i q^{19} +(0.923880 - 0.382683i) q^{20} +(0.382683 - 0.923880i) q^{21} +(1.00000 + 1.00000i) q^{23} +(0.382683 - 0.923880i) q^{24} +(-0.707107 + 0.707107i) q^{25} -1.84776i q^{26} +(0.923880 + 0.382683i) q^{27} +(0.707107 - 0.707107i) q^{28} +1.00000i q^{30} +(0.707107 - 0.707107i) q^{32} +(-0.382683 + 0.923880i) q^{35} +(0.707107 + 0.707107i) q^{36} +(0.541196 + 0.541196i) q^{38} +(1.70711 + 0.707107i) q^{39} +(-0.382683 + 0.923880i) q^{40} +(0.382683 + 0.923880i) q^{42} +(-0.923880 - 0.382683i) q^{45} -1.41421 q^{46} +(0.382683 + 0.923880i) q^{48} +1.00000i q^{49} -1.00000i q^{50} +(1.30656 + 1.30656i) q^{52} +(-0.923880 + 0.382683i) q^{54} +1.00000i q^{56} +(-0.707107 + 0.292893i) q^{57} +0.765367 q^{59} +(-0.707107 - 0.707107i) q^{60} +1.84776 q^{61} -1.00000 q^{63} +1.00000i q^{64} +(-1.70711 - 0.707107i) q^{65} +(0.541196 - 1.30656i) q^{69} +(-0.382683 - 0.923880i) q^{70} -1.41421i q^{71} -1.00000 q^{72} +(0.923880 + 0.382683i) q^{75} -0.765367 q^{76} +(-1.70711 + 0.707107i) q^{78} -1.41421i q^{79} +(-0.382683 - 0.923880i) q^{80} -1.00000i q^{81} +(-0.541196 - 0.541196i) q^{83} +(-0.923880 - 0.382683i) q^{84} +(0.923880 - 0.382683i) q^{90} -1.84776 q^{91} +(1.00000 - 1.00000i) q^{92} +(0.707107 - 0.292893i) q^{95} +(-0.923880 - 0.382683i) q^{96} +(-0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q - 8q^{14} - 8q^{16} + 8q^{23} + 8q^{39} - 8q^{63} - 8q^{65} - 8q^{72} - 8q^{78} + 8q^{92} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/840\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(281\) \(337\) \(421\) \(631\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(3\) −0.382683 0.923880i −0.382683 0.923880i
\(4\) 1.00000i 1.00000i
\(5\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(6\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(7\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(8\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(9\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(10\) −0.923880 0.382683i −0.923880 0.382683i
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(13\) −1.30656 + 1.30656i −1.30656 + 1.30656i −0.382683 + 0.923880i \(0.625000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(14\) −1.00000 −1.00000
\(15\) 0.707107 0.707107i 0.707107 0.707107i
\(16\) −1.00000 −1.00000
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) 1.00000i 1.00000i
\(19\) 0.765367i 0.765367i −0.923880 0.382683i \(-0.875000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(20\) 0.923880 0.382683i 0.923880 0.382683i
\(21\) 0.382683 0.923880i 0.382683 0.923880i
\(22\) 0 0
\(23\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(24\) 0.382683 0.923880i 0.382683 0.923880i
\(25\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(26\) 1.84776i 1.84776i
\(27\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(28\) 0.707107 0.707107i 0.707107 0.707107i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 1.00000i 1.00000i
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0.707107 0.707107i 0.707107 0.707107i
\(33\) 0 0
\(34\) 0 0
\(35\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(36\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(37\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(38\) 0.541196 + 0.541196i 0.541196 + 0.541196i
\(39\) 1.70711 + 0.707107i 1.70711 + 0.707107i
\(40\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(43\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(44\) 0 0
\(45\) −0.923880 0.382683i −0.923880 0.382683i
\(46\) −1.41421 −1.41421
\(47\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(48\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(49\) 1.00000i 1.00000i
\(50\) 1.00000i 1.00000i
\(51\) 0 0
\(52\) 1.30656 + 1.30656i 1.30656 + 1.30656i
\(53\) 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 0
\(56\) 1.00000i 1.00000i
\(57\) −0.707107 + 0.292893i −0.707107 + 0.292893i
\(58\) 0 0
\(59\) 0.765367 0.765367 0.382683 0.923880i \(-0.375000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(60\) −0.707107 0.707107i −0.707107 0.707107i
\(61\) 1.84776 1.84776 0.923880 0.382683i \(-0.125000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(62\) 0 0
\(63\) −1.00000 −1.00000
\(64\) 1.00000i 1.00000i
\(65\) −1.70711 0.707107i −1.70711 0.707107i
\(66\) 0 0
\(67\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(68\) 0 0
\(69\) 0.541196 1.30656i 0.541196 1.30656i
\(70\) −0.382683 0.923880i −0.382683 0.923880i
\(71\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(72\) −1.00000 −1.00000
\(73\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(74\) 0 0
\(75\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(76\) −0.765367 −0.765367
\(77\) 0 0
\(78\) −1.70711 + 0.707107i −1.70711 + 0.707107i
\(79\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(80\) −0.382683 0.923880i −0.382683 0.923880i
\(81\) 1.00000i 1.00000i
\(82\) 0 0
\(83\) −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i \(-0.375000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(84\) −0.923880 0.382683i −0.923880 0.382683i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0.923880 0.382683i 0.923880 0.382683i
\(91\) −1.84776 −1.84776
\(92\) 1.00000 1.00000i 1.00000 1.00000i
\(93\) 0 0
\(94\) 0 0
\(95\) 0.707107 0.292893i 0.707107 0.292893i
\(96\) −0.923880 0.382683i −0.923880 0.382683i
\(97\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(98\) −0.707107 0.707107i −0.707107 0.707107i
\(99\) 0 0
\(100\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(101\) 0.765367i 0.765367i 0.923880 + 0.382683i \(0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(102\) 0 0
\(103\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(104\) −1.84776 −1.84776
\(105\) 1.00000 1.00000
\(106\) 0 0
\(107\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(108\) 0.382683 0.923880i 0.382683 0.923880i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.707107 0.707107i −0.707107 0.707107i
\(113\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(114\) 0.292893 0.707107i 0.292893 0.707107i
\(115\) −0.541196 + 1.30656i −0.541196 + 1.30656i
\(116\) 0 0
\(117\) 1.84776i 1.84776i
\(118\) −0.541196 + 0.541196i −0.541196 + 0.541196i
\(119\) 0 0
\(120\) 1.00000 1.00000
\(121\) −1.00000 −1.00000
\(122\) −1.30656 + 1.30656i −1.30656 + 1.30656i
\(123\) 0 0
\(124\) 0 0
\(125\) −0.923880 0.382683i −0.923880 0.382683i
\(126\) 0.707107 0.707107i 0.707107 0.707107i
\(127\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(128\) −0.707107 0.707107i −0.707107 0.707107i
\(129\) 0 0
\(130\) 1.70711 0.707107i 1.70711 0.707107i
\(131\) 1.84776i 1.84776i 0.382683 + 0.923880i \(0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(132\) 0 0
\(133\) 0.541196 0.541196i 0.541196 0.541196i
\(134\) 0 0
\(135\) 1.00000i 1.00000i
\(136\) 0 0
\(137\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(138\) 0.541196 + 1.30656i 0.541196 + 1.30656i
\(139\) 1.84776i 1.84776i −0.382683 0.923880i \(-0.625000\pi\)
0.382683 0.923880i \(-0.375000\pi\)
\(140\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(141\) 0 0
\(142\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(143\) 0 0
\(144\) 0.707107 0.707107i 0.707107 0.707107i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.923880 0.382683i 0.923880 0.382683i
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0.541196 0.541196i 0.541196 0.541196i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0.707107 1.70711i 0.707107 1.70711i
\(157\) 0.541196 + 0.541196i 0.541196 + 0.541196i 0.923880 0.382683i \(-0.125000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(158\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(159\) 0 0
\(160\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(161\) 1.41421i 1.41421i
\(162\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(163\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0.765367 0.765367
\(167\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(168\) 0.923880 0.382683i 0.923880 0.382683i
\(169\) 2.41421i 2.41421i
\(170\) 0 0
\(171\) 0.541196 + 0.541196i 0.541196 + 0.541196i
\(172\) 0 0
\(173\) −1.30656 1.30656i −1.30656 1.30656i −0.923880 0.382683i \(-0.875000\pi\)
−0.382683 0.923880i \(-0.625000\pi\)
\(174\) 0 0
\(175\) −1.00000 −1.00000
\(176\) 0 0
\(177\) −0.292893 0.707107i −0.292893 0.707107i
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(181\) 0.765367 0.765367 0.382683 0.923880i \(-0.375000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(182\) 1.30656 1.30656i 1.30656 1.30656i
\(183\) −0.707107 1.70711i −0.707107 1.70711i
\(184\) 1.41421i 1.41421i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(190\) −0.292893 + 0.707107i −0.292893 + 0.707107i
\(191\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) 0.923880 0.382683i 0.923880 0.382683i
\(193\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(194\) 0 0
\(195\) 1.84776i 1.84776i
\(196\) 1.00000 1.00000
\(197\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) −1.00000 −1.00000
\(201\) 0 0
\(202\) −0.541196 0.541196i −0.541196 0.541196i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.41421 −1.41421
\(208\) 1.30656 1.30656i 1.30656 1.30656i
\(209\) 0 0
\(210\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) −1.30656 + 0.541196i −1.30656 + 0.541196i
\(214\) 0 0
\(215\) 0 0
\(216\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(224\) 1.00000 1.00000
\(225\) 1.00000i 1.00000i
\(226\) 0 0
\(227\) 0.541196 0.541196i 0.541196 0.541196i −0.382683 0.923880i \(-0.625000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(228\) 0.292893 + 0.707107i 0.292893 + 0.707107i
\(229\) 1.84776i 1.84776i 0.382683 + 0.923880i \(0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(230\) −0.541196 1.30656i −0.541196 1.30656i
\(231\) 0 0
\(232\) 0 0
\(233\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(234\) 1.30656 + 1.30656i 1.30656 + 1.30656i
\(235\) 0 0
\(236\) 0.765367i 0.765367i
\(237\) −1.30656 + 0.541196i −1.30656 + 0.541196i
\(238\) 0 0
\(239\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(240\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0.707107 0.707107i 0.707107 0.707107i
\(243\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(244\) 1.84776i 1.84776i
\(245\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(246\) 0 0
\(247\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(248\) 0 0
\(249\) −0.292893 + 0.707107i −0.292893 + 0.707107i
\(250\) 0.923880 0.382683i 0.923880 0.382683i
\(251\) 0.765367i 0.765367i −0.923880 0.382683i \(-0.875000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(252\) 1.00000i 1.00000i
\(253\) 0 0
\(254\) 1.41421 1.41421
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.707107 + 1.70711i −0.707107 + 1.70711i
\(261\) 0 0
\(262\) −1.30656 1.30656i −1.30656 1.30656i
\(263\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0.765367i 0.765367i
\(267\) 0 0
\(268\) 0 0
\(269\) 1.84776 1.84776 0.923880 0.382683i \(-0.125000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(270\) −0.707107 0.707107i −0.707107 0.707107i
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0.707107 + 1.70711i 0.707107 + 1.70711i
\(274\) 1.41421i 1.41421i
\(275\) 0 0
\(276\) −1.30656 0.541196i −1.30656 0.541196i
\(277\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(278\) 1.30656 + 1.30656i 1.30656 + 1.30656i
\(279\) 0 0
\(280\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(281\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 1.30656 1.30656i 1.30656 1.30656i 0.382683 0.923880i \(-0.375000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(284\) −1.41421 −1.41421
\(285\) −0.541196 0.541196i −0.541196 0.541196i
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000i 1.00000i
\(289\) 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 \(0.375000\pi\)
\(294\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(295\) 0.292893 + 0.707107i 0.292893 + 0.707107i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.61313 −2.61313
\(300\) 0.382683 0.923880i 0.382683 0.923880i
\(301\) 0 0
\(302\) 0 0
\(303\) 0.707107 0.292893i 0.707107 0.292893i
\(304\) 0.765367i 0.765367i
\(305\) 0.707107 + 1.70711i 0.707107 + 1.70711i
\(306\) 0 0
\(307\) −1.30656 1.30656i −1.30656 1.30656i −0.923880 0.382683i \(-0.875000\pi\)
−0.382683 0.923880i \(-0.625000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0.707107 + 1.70711i 0.707107 + 1.70711i
\(313\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(314\) −0.765367 −0.765367
\(315\) −0.382683 0.923880i −0.382683 0.923880i
\(316\) −1.41421 −1.41421
\(317\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(321\) 0 0
\(322\) −1.00000 1.00000i −1.00000 1.00000i
\(323\) 0 0
\(324\) −1.00000 −1.00000
\(325\) 1.84776i 1.84776i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −0.541196 + 0.541196i −0.541196 + 0.541196i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(337\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(338\) 1.70711 + 1.70711i 1.70711 + 1.70711i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) −0.765367 −0.765367
\(343\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(344\) 0 0
\(345\) 1.41421 1.41421
\(346\) 1.84776 1.84776
\(347\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(348\) 0 0
\(349\) 0.765367i 0.765367i 0.923880 + 0.382683i \(0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(350\) 0.707107 0.707107i 0.707107 0.707107i
\(351\) −1.70711 + 0.707107i −1.70711 + 0.707107i
\(352\) 0 0
\(353\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(354\) 0.707107 + 0.292893i 0.707107 + 0.292893i
\(355\) 1.30656 0.541196i 1.30656 0.541196i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) −0.382683 0.923880i −0.382683 0.923880i
\(361\) 0.414214 0.414214
\(362\) −0.541196 + 0.541196i −0.541196 + 0.541196i
\(363\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(364\) 1.84776i 1.84776i
\(365\) 0 0
\(366\) 1.70711 + 0.707107i 1.70711 + 0.707107i
\(367\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(368\) −1.00000 1.00000i −1.00000 1.00000i
\(369\) 0 0
\(370\) 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
\(375\) 1.00000i 1.00000i
\(376\) 0 0
\(377\) 0 0
\(378\) −0.923880 0.382683i −0.923880 0.382683i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) −0.292893 0.707107i −0.292893 0.707107i
\(381\) −0.541196 + 1.30656i −0.541196 + 1.30656i
\(382\) −1.00000 1.00000i −1.00000 1.00000i
\(383\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(384\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) −1.30656 1.30656i −1.30656 1.30656i
\(391\) 0 0
\(392\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(393\) 1.70711 0.707107i 1.70711 0.707107i
\(394\) 0 0
\(395\) 1.30656 0.541196i 1.30656 0.541196i
\(396\) 0 0
\(397\) −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i \(-0.375000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(398\) 0 0
\(399\) −0.707107 0.292893i −0.707107 0.292893i
\(400\) 0.707107 0.707107i 0.707107 0.707107i
\(401\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.765367 0.765367
\(405\) 0.923880 0.382683i 0.923880 0.382683i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) −1.30656 0.541196i −1.30656 0.541196i
\(412\) 0 0
\(413\) 0.541196 + 0.541196i 0.541196 + 0.541196i
\(414\) 1.00000 1.00000i 1.00000 1.00000i
\(415\) 0.292893 0.707107i 0.292893 0.707107i
\(416\) 1.84776i 1.84776i
\(417\) −1.70711 + 0.707107i −1.70711 + 0.707107i
\(418\) 0 0
\(419\) 1.84776 1.84776 0.923880 0.382683i \(-0.125000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(420\) 1.00000i 1.00000i
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0.541196 1.30656i 0.541196 1.30656i
\(427\) 1.30656 + 1.30656i 1.30656 + 1.30656i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −0.923880 0.382683i −0.923880 0.382683i
\(433\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.765367 0.765367i 0.765367 0.765367i
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −0.707107 0.707107i −0.707107 0.707107i
\(442\) 0 0
\(443\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(449\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(450\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0.765367i 0.765367i
\(455\) −0.707107 1.70711i −0.707107 1.70711i
\(456\) −0.707107 0.292893i −0.707107 0.292893i
\(457\) 1.41421 + 1.41421i 1.41421 + 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(458\) −1.30656 1.30656i −1.30656 1.30656i
\(459\) 0 0
\(460\) 1.30656 + 0.541196i 1.30656 + 0.541196i
\(461\) 1.84776i 1.84776i −0.382683 0.923880i \(-0.625000\pi\)
0.382683 0.923880i \(-0.375000\pi\)
\(462\) 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
\(466\) 1.41421 1.41421
\(467\) 1.30656 1.30656i 1.30656 1.30656i 0.382683 0.923880i \(-0.375000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(468\) −1.84776 −1.84776
\(469\) 0 0
\(470\) 0 0
\(471\) 0.292893 0.707107i 0.292893 0.707107i
\(472\) 0.541196 + 0.541196i 0.541196 + 0.541196i
\(473\) 0 0
\(474\) 0.541196 1.30656i 0.541196 1.30656i
\(475\) 0.541196 + 0.541196i 0.541196 + 0.541196i
\(476\) 0 0
\(477\) 0 0
\(478\) 1.41421 1.41421i 1.41421 1.41421i
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 1.00000i 1.00000i
\(481\) 0 0
\(482\) 0 0
\(483\) 1.30656 0.541196i 1.30656 0.541196i
\(484\) 1.00000i 1.00000i
\(485\) 0 0
\(486\) 0.382683 0.923880i 0.382683 0.923880i
\(487\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(488\) 1.30656 + 1.30656i 1.30656 + 1.30656i
\(489\) 0 0
\(490\) 0.382683 0.923880i 0.382683 0.923880i
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −1.41421 −1.41421
\(495\) 0 0
\(496\) 0 0
\(497\) 1.00000 1.00000i 1.00000 1.00000i
\(498\) −0.292893 0.707107i −0.292893 0.707107i
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(501\) 0 0
\(502\) 0.541196 + 0.541196i 0.541196 + 0.541196i
\(503\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(504\) −0.707107 0.707107i −0.707107 0.707107i
\(505\) −0.707107 + 0.292893i −0.707107 + 0.292893i
\(506\) 0 0
\(507\) −2.23044 + 0.923880i −2.23044 + 0.923880i
\(508\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(509\) −0.765367 −0.765367 −0.382683 0.923880i \(-0.625000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(513\) 0.292893 0.707107i 0.292893 0.707107i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −0.707107 + 1.70711i −0.707107 + 1.70711i
\(520\) −0.707107 1.70711i −0.707107 1.70711i
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i \(-0.875000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(524\) 1.84776 1.84776
\(525\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000i 1.00000i
\(530\) 0 0
\(531\) −0.541196 + 0.541196i −0.541196 + 0.541196i
\(532\) −0.541196 0.541196i −0.541196 0.541196i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −1.30656 + 1.30656i −1.30656 + 1.30656i
\(539\) 0 0
\(540\) 1.00000 1.00000
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −0.292893 0.707107i −0.292893 0.707107i
\(544\) 0 0
\(545\) 0 0
\(546\) −1.70711 0.707107i −1.70711 0.707107i
\(547\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(548\) −1.00000 1.00000i −1.00000 1.00000i
\(549\) −1.30656 + 1.30656i −1.30656 + 1.30656i
\(550\) 0 0
\(551\) 0 0
\(552\) 1.30656 0.541196i 1.30656 0.541196i
\(553\) 1.00000 1.00000i 1.00000 1.00000i
\(554\) 0 0
\(555\) 0 0
\(556\) −1.84776 −1.84776
\(557\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.382683 0.923880i 0.382683 0.923880i
\(561\) 0 0
\(562\) −1.41421 1.41421i −1.41421 1.41421i
\(563\) −1.30656 1.30656i −1.30656 1.30656i −0.923880 0.382683i \(-0.875000\pi\)
−0.382683 0.923880i \(-0.625000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 1.84776i 1.84776i
\(567\) 0.707107 0.707107i 0.707107 0.707107i
\(568\) 1.00000 1.00000i 1.00000 1.00000i
\(569\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(570\) 0.765367 0.765367
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 1.30656 0.541196i 1.30656 0.541196i
\(574\) 0 0
\(575\) −1.41421 −1.41421
\(576\) −0.707107 0.707107i −0.707107 0.707107i
\(577\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(578\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(579\) 0 0
\(580\) 0 0
\(581\) 0.765367i 0.765367i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 1.70711 0.707107i 1.70711 0.707107i
\(586\) −1.84776 −1.84776
\(587\) −1.30656 + 1.30656i −1.30656 + 1.30656i −0.382683 + 0.923880i \(0.625000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(588\) −0.382683 0.923880i −0.382683 0.923880i
\(589\) 0 0
\(590\) −0.707107 0.292893i −0.707107 0.292893i
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 1.84776 1.84776i 1.84776 1.84776i
\(599\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(600\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.382683 0.923880i −0.382683 0.923880i
\(606\) −0.292893 + 0.707107i −0.292893 + 0.707107i
\(607\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(608\) −0.541196 0.541196i −0.541196 0.541196i
\(609\) 0 0
\(610\) −1.70711 0.707107i −1.70711 0.707107i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(614\) 1.84776 1.84776
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(618\) 0 0
\(619\) 1.84776i 1.84776i 0.382683 + 0.923880i \(0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(620\) 0 0
\(621\) 0.541196 + 1.30656i 0.541196 + 1.30656i
\(622\) 0 0
\(623\) 0 0
\(624\) −1.70711 0.707107i −1.70711 0.707107i
\(625\) 1.00000i 1.00000i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.541196 0.541196i 0.541196 0.541196i
\(629\) 0 0
\(630\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(631\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(632\) 1.00000 1.00000i 1.00000 1.00000i
\(633\) 0 0
\(634\) 0 0
\(635\) 0.541196 1.30656i 0.541196 1.30656i
\(636\) 0 0
\(637\) −1.30656 1.30656i −1.30656 1.30656i
\(638\) 0 0
\(639\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(640\) 0.382683 0.923880i 0.382683 0.923880i
\(641\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(642\) 0 0
\(643\) 0.541196 0.541196i 0.541196 0.541196i −0.382683 0.923880i \(-0.625000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(644\) 1.41421 1.41421
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(648\) 0.707107 0.707107i 0.707107 0.707107i
\(649\) 0 0
\(650\) 1.30656 + 1.30656i 1.30656 + 1.30656i
\(651\) 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
\(655\) −1.70711 + 0.707107i −1.70711 + 0.707107i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −0.765367 −0.765367 −0.382683 0.923880i \(-0.625000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.765367i 0.765367i
\(665\) 0.707107 + 0.292893i 0.707107 + 0.292893i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −0.382683 0.923880i −0.382683 0.923880i
\(673\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(676\) −2.41421 −2.41421
\(677\) −1.30656 + 1.30656i −1.30656 + 1.30656i −0.382683 + 0.923880i \(0.625000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −0.707107 0.292893i −0.707107 0.292893i
\(682\) 0 0
\(683\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(684\) 0.541196 0.541196i 0.541196 0.541196i
\(685\) 1.30656 + 0.541196i 1.30656 + 0.541196i
\(686\) 1.00000i 1.00000i
\(687\) 1.70711 0.707107i 1.70711 0.707107i
\(688\) 0 0
\(689\) 0 0
\(690\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(691\) −0.765367 −0.765367 −0.382683 0.923880i \(-0.625000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(692\) −1.30656 + 1.30656i −1.30656 + 1.30656i
\(693\) 0 0
\(694\) 0 0
\(695\) 1.70711 0.707107i 1.70711 0.707107i
\(696\) 0 0
\(697\) 0 0
\(698\) −0.541196 0.541196i −0.541196 0.541196i
\(699\) −0.541196 + 1.30656i −0.541196 + 1.30656i
\(700\) 1.00000i 1.00000i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0.707107 1.70711i 0.707107 1.70711i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −0.541196 + 0.541196i −0.541196 + 0.541196i
\(708\) −0.707107 + 0.292893i −0.707107 + 0.292893i
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) −0.541196 + 1.30656i −0.541196 + 1.30656i
\(711\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0.765367 + 1.84776i 0.765367 + 1.84776i
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(721\) 0 0
\(722\) −0.292893 + 0.292893i −0.292893 + 0.292893i
\(723\) 0 0
\(724\) 0.765367i 0.765367i
\(725\) 0 0
\(726\) −0.923880 0.382683i −0.923880 0.382683i
\(727\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(728\) −1.30656 1.30656i −1.30656 1.30656i
\(729\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(730\) 0 0
\(731\) 0 0
\(732\) −1.70711 + 0.707107i −1.70711 + 0.707107i
\(733\) −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i \(-0.875000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(734\) 0 0
\(735\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(736\) 1.41421 1.41421
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 0 0
\(741\) 0.541196 1.30656i 0.541196 1.30656i
\(742\) 0 0
\(743\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.765367 0.765367
\(748\) 0 0
\(749\) 0 0
\(750\) −0.707107 0.707107i −0.707107 0.707107i
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) −0.707107 + 0.292893i −0.707107 + 0.292893i
\(754\) 0 0
\(755\) 0 0
\(756\) 0.923880 0.382683i 0.923880 0.382683i
\(757\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0.707107 + 0.292893i 0.707107 + 0.292893i
\(761\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) −0.541196 1.30656i −0.541196 1.30656i
\(763\) 0 0
\(764\) 1.41421 1.41421
\(765\) 0 0
\(766\) 0 0
\(767\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(768\) −0.382683 0.923880i −0.382683 0.923880i
\(769\) 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 0.382683 0.923880i \(-0.375000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 1.84776 1.84776
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000i 1.00000i
\(785\) −0.292893 + 0.707107i −0.292893 + 0.707107i
\(786\) −0.707107 + 1.70711i −0.707107 + 1.70711i
\(787\) −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i \(-0.375000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) −0.541196 + 1.30656i −0.541196 + 1.30656i
\(791\) 0 0
\(792\) 0 0
\(793\) −2.41421 + 2.41421i −2.41421 + 2.41421i
\(794\) 0.765367 0.765367
\(795\) 0 0
\(796\) 0 0
\(797\) 0.541196 0.541196i 0.541196 0.541196i −0.382683 0.923880i \(-0.625000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(798\) 0.707107 0.292893i 0.707107 0.292893i
\(799\) 0