Properties

Label 799.1.h.b.93.2
Level $799$
Weight $1$
Character 799.93
Analytic conductor $0.399$
Analytic rank $0$
Dimension $16$
Projective image $D_{40}$
CM discriminant -47
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 799 = 17 \cdot 47 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 799.h (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.398752945094\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{8})\)
Coefficient field: \(\Q(\zeta_{40})\)
Defining polynomial: \(x^{16} - x^{12} + x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{40}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{40} + \cdots)\)

Embedding invariants

Embedding label 93.2
Root \(-0.987688 + 0.156434i\) of defining polynomial
Character \(\chi\) \(=\) 799.93
Dual form 799.1.h.b.610.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.831254 + 0.831254i) q^{2} +(0.763007 - 1.84206i) q^{3} -0.381966i q^{4} +(0.896969 + 2.16547i) q^{6} +(0.431351 - 0.178671i) q^{7} +(-0.513743 - 0.513743i) q^{8} +(-2.10391 - 2.10391i) q^{9} +O(q^{10})\) \(q+(-0.831254 + 0.831254i) q^{2} +(0.763007 - 1.84206i) q^{3} -0.381966i q^{4} +(0.896969 + 2.16547i) q^{6} +(0.431351 - 0.178671i) q^{7} +(-0.513743 - 0.513743i) q^{8} +(-2.10391 - 2.10391i) q^{9} +(-0.703605 - 0.291443i) q^{12} +(-0.210041 + 0.507083i) q^{14} +1.23607 q^{16} +(-0.309017 - 0.951057i) q^{17} +3.49777 q^{18} -0.930903i q^{21} +(-1.33834 + 0.554357i) q^{24} +(0.707107 + 0.707107i) q^{25} +(-3.63877 + 1.50723i) q^{27} +(-0.0682464 - 0.164761i) q^{28} +(-0.513743 + 0.513743i) q^{32} +(1.04744 + 0.533698i) q^{34} +(-0.803622 + 0.803622i) q^{36} +(-0.0600500 + 0.144974i) q^{37} +(0.773817 + 0.773817i) q^{42} -1.00000i q^{47} +(0.943129 - 2.27692i) q^{48} +(-0.552967 + 0.552967i) q^{49} -1.17557 q^{50} +(-1.98769 - 0.156434i) q^{51} +(1.39680 - 1.39680i) q^{53} +(1.77185 - 4.27763i) q^{54} +(-0.313395 - 0.129812i) q^{56} +(1.14412 + 1.14412i) q^{59} +(0.965451 - 0.399903i) q^{61} +(-1.28343 - 0.531615i) q^{63} +0.381966i q^{64} +(-0.363271 + 0.118034i) q^{68} +(-0.581990 + 1.40505i) q^{71} +2.16174i q^{72} +(-0.0705930 - 0.170427i) q^{74} +(1.84206 - 0.763007i) q^{75} +(-0.581990 - 1.40505i) q^{79} +4.87749i q^{81} +(-1.00000 + 1.00000i) q^{83} -0.355573 q^{84} +1.17557i q^{89} +(0.831254 + 0.831254i) q^{94} +(0.554357 + 1.33834i) q^{96} +(1.57547 + 0.652583i) q^{97} -0.919311i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{3} - 4q^{9} + O(q^{10}) \) \( 16q - 4q^{3} - 4q^{9} - 16q^{16} + 4q^{17} - 20q^{24} - 4q^{27} - 4q^{28} + 4q^{36} - 20q^{42} + 24q^{48} + 4q^{49} - 16q^{51} + 4q^{53} + 20q^{54} + 20q^{56} + 4q^{61} - 4q^{63} - 4q^{71} - 4q^{79} - 16q^{83} + 32q^{84} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/799\mathbb{Z}\right)^\times\).

\(n\) \(52\) \(377\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.831254 + 0.831254i −0.831254 + 0.831254i −0.987688 0.156434i \(-0.950000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(3\) 0.763007 1.84206i 0.763007 1.84206i 0.309017 0.951057i \(-0.400000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(4\) 0.381966i 0.381966i
\(5\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(6\) 0.896969 + 2.16547i 0.896969 + 2.16547i
\(7\) 0.431351 0.178671i 0.431351 0.178671i −0.156434 0.987688i \(-0.550000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(8\) −0.513743 0.513743i −0.513743 0.513743i
\(9\) −2.10391 2.10391i −2.10391 2.10391i
\(10\) 0 0
\(11\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(12\) −0.703605 0.291443i −0.703605 0.291443i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −0.210041 + 0.507083i −0.210041 + 0.507083i
\(15\) 0 0
\(16\) 1.23607 1.23607
\(17\) −0.309017 0.951057i −0.309017 0.951057i
\(18\) 3.49777 3.49777
\(19\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(20\) 0 0
\(21\) 0.930903i 0.930903i
\(22\) 0 0
\(23\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(24\) −1.33834 + 0.554357i −1.33834 + 0.554357i
\(25\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(26\) 0 0
\(27\) −3.63877 + 1.50723i −3.63877 + 1.50723i
\(28\) −0.0682464 0.164761i −0.0682464 0.164761i
\(29\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(30\) 0 0
\(31\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(32\) −0.513743 + 0.513743i −0.513743 + 0.513743i
\(33\) 0 0
\(34\) 1.04744 + 0.533698i 1.04744 + 0.533698i
\(35\) 0 0
\(36\) −0.803622 + 0.803622i −0.803622 + 0.803622i
\(37\) −0.0600500 + 0.144974i −0.0600500 + 0.144974i −0.951057 0.309017i \(-0.900000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(42\) 0.773817 + 0.773817i 0.773817 + 0.773817i
\(43\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.00000i 1.00000i
\(48\) 0.943129 2.27692i 0.943129 2.27692i
\(49\) −0.552967 + 0.552967i −0.552967 + 0.552967i
\(50\) −1.17557 −1.17557
\(51\) −1.98769 0.156434i −1.98769 0.156434i
\(52\) 0 0
\(53\) 1.39680 1.39680i 1.39680 1.39680i 0.587785 0.809017i \(-0.300000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(54\) 1.77185 4.27763i 1.77185 4.27763i
\(55\) 0 0
\(56\) −0.313395 0.129812i −0.313395 0.129812i
\(57\) 0 0
\(58\) 0 0
\(59\) 1.14412 + 1.14412i 1.14412 + 1.14412i 0.987688 + 0.156434i \(0.0500000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(60\) 0 0
\(61\) 0.965451 0.399903i 0.965451 0.399903i 0.156434 0.987688i \(-0.450000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(62\) 0 0
\(63\) −1.28343 0.531615i −1.28343 0.531615i
\(64\) 0.381966i 0.381966i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −0.363271 + 0.118034i −0.363271 + 0.118034i
\(69\) 0 0
\(70\) 0 0
\(71\) −0.581990 + 1.40505i −0.581990 + 1.40505i 0.309017 + 0.951057i \(0.400000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(72\) 2.16174i 2.16174i
\(73\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(74\) −0.0705930 0.170427i −0.0705930 0.170427i
\(75\) 1.84206 0.763007i 1.84206 0.763007i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.581990 1.40505i −0.581990 1.40505i −0.891007 0.453990i \(-0.850000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(80\) 0 0
\(81\) 4.87749i 4.87749i
\(82\) 0 0
\(83\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(84\) −0.355573 −0.355573
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.17557i 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0.831254 + 0.831254i 0.831254 + 0.831254i
\(95\) 0 0
\(96\) 0.554357 + 1.33834i 0.554357 + 1.33834i
\(97\) 1.57547 + 0.652583i 1.57547 + 0.652583i 0.987688 0.156434i \(-0.0500000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(98\) 0.919311i 0.919311i
\(99\) 0 0
\(100\) 0.270091 0.270091i 0.270091 0.270091i
\(101\) 0.907981 0.907981 0.453990 0.891007i \(-0.350000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(102\) 1.78231 1.52224i 1.78231 1.52224i
\(103\) 1.78201 1.78201 0.891007 0.453990i \(-0.150000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 2.32219i 2.32219i
\(107\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(108\) 0.575710 + 1.38989i 0.575710 + 1.38989i
\(109\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(110\) 0 0
\(111\) 0.221232 + 0.221232i 0.221232 + 0.221232i
\(112\) 0.533179 0.220850i 0.533179 0.220850i
\(113\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −1.90211 −1.90211
\(119\) −0.303221 0.355026i −0.303221 0.355026i
\(120\) 0 0
\(121\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(122\) −0.470114 + 1.13496i −0.470114 + 1.13496i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 1.50876 0.624950i 1.50876 0.624950i
\(127\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(128\) −0.831254 0.831254i −0.831254 0.831254i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.57547 0.652583i −1.57547 0.652583i −0.587785 0.809017i \(-0.700000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.329843 + 0.647354i −0.329843 + 0.647354i
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(140\) 0 0
\(141\) −1.84206 0.763007i −1.84206 0.763007i
\(142\) −0.684170 1.65173i −0.684170 1.65173i
\(143\) 0 0
\(144\) −2.60057 2.60057i −2.60057 2.60057i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.596682 + 1.44052i 0.596682 + 1.44052i
\(148\) 0.0553750 + 0.0229371i 0.0553750 + 0.0229371i
\(149\) 1.78201i 1.78201i 0.453990 + 0.891007i \(0.350000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(150\) −0.896969 + 2.16547i −0.896969 + 2.16547i
\(151\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(152\) 0 0
\(153\) −1.35079 + 2.65108i −1.35079 + 2.65108i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.312869i 0.312869i 0.987688 + 0.156434i \(0.0500000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(158\) 1.65173 + 0.684170i 1.65173 + 0.684170i
\(159\) −1.50723 3.63877i −1.50723 3.63877i
\(160\) 0 0
\(161\) 0 0
\(162\) −4.05443 4.05443i −4.05443 4.05443i
\(163\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.66251i 1.66251i
\(167\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(168\) −0.478245 + 0.478245i −0.478245 + 0.478245i
\(169\) −1.00000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −0.744220 + 1.79671i −0.744220 + 1.79671i −0.156434 + 0.987688i \(0.550000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(174\) 0 0
\(175\) 0.431351 + 0.178671i 0.431351 + 0.178671i
\(176\) 0 0
\(177\) 2.98052 1.23457i 2.98052 1.23457i
\(178\) −0.977198 0.977198i −0.977198 0.977198i
\(179\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(180\) 0 0
\(181\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(182\) 0 0
\(183\) 2.08355i 2.08355i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.381966 −0.381966
\(189\) −1.30029 + 1.30029i −1.30029 + 1.30029i
\(190\) 0 0
\(191\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(192\) 0.703605 + 0.291443i 0.703605 + 0.291443i
\(193\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(194\) −1.85208 + 0.767157i −1.85208 + 0.767157i
\(195\) 0 0
\(196\) 0.211214 + 0.211214i 0.211214 + 0.211214i
\(197\) 1.70711 0.707107i 1.70711 0.707107i 0.707107 0.707107i \(-0.250000\pi\)
1.00000 \(0\)
\(198\) 0 0
\(199\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(200\) 0.726543i 0.726543i
\(201\) 0 0
\(202\) −0.754763 + 0.754763i −0.754763 + 0.754763i
\(203\) 0 0
\(204\) −0.0597526 + 0.759229i −0.0597526 + 0.759229i
\(205\) 0 0
\(206\) −1.48131 + 1.48131i −1.48131 + 1.48131i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(212\) −0.533531 0.533531i −0.533531 0.533531i
\(213\) 2.14412 + 2.14412i 2.14412 + 2.14412i
\(214\) 0 0
\(215\) 0 0
\(216\) 2.64372 + 1.09506i 2.64372 + 1.09506i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) −0.367799 −0.367799
\(223\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(224\) −0.129812 + 0.313395i −0.129812 + 0.313395i
\(225\) 2.97538i 2.97538i
\(226\) 0 0
\(227\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(228\) 0 0
\(229\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.437016 0.437016i 0.437016 0.437016i
\(237\) −3.03225 −3.03225
\(238\) 0.547171 + 0.0430633i 0.547171 + 0.0430633i
\(239\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(240\) 0 0
\(241\) 0.0600500 0.144974i 0.0600500 0.144974i −0.891007 0.453990i \(-0.850000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(242\) 1.17557i 1.17557i
\(243\) 5.34588 + 2.21433i 5.34588 + 2.21433i
\(244\) −0.152749 0.368770i −0.152749 0.368770i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 1.07906 + 2.60507i 1.07906 + 2.60507i
\(250\) 0 0
\(251\) 0.907981i 0.907981i 0.891007 + 0.453990i \(0.150000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(252\) −0.203059 + 0.490227i −0.203059 + 0.490227i
\(253\) 0 0
\(254\) 0 0
\(255\) 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
\(259\) 0.0732636i 0.0732636i
\(260\) 0 0
\(261\) 0 0
\(262\) 1.85208 0.767157i 1.85208 0.767157i
\(263\) −1.14412 1.14412i −1.14412 1.14412i −0.987688 0.156434i \(-0.950000\pi\)
−0.156434 0.987688i \(-0.550000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 2.16547 + 0.896969i 2.16547 + 0.896969i
\(268\) 0 0
\(269\) −0.292893 + 0.707107i −0.292893 + 0.707107i 0.707107 + 0.707107i \(0.250000\pi\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −0.907981 −0.907981 −0.453990 0.891007i \(-0.650000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(272\) −0.381966 1.17557i −0.381966 1.17557i
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.40505 0.581990i −1.40505 0.581990i −0.453990 0.891007i \(-0.650000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(282\) 2.16547 0.896969i 2.16547 0.896969i
\(283\) 0.178671 + 0.431351i 0.178671 + 0.431351i 0.987688 0.156434i \(-0.0500000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(284\) 0.536680 + 0.222300i 0.536680 + 0.222300i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 2.16174 2.16174
\(289\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(290\) 0 0
\(291\) 2.40420 2.40420i 2.40420 2.40420i
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) −1.69343 0.701442i −1.69343 0.701442i
\(295\) 0 0
\(296\) 0.105329 0.0436289i 0.105329 0.0436289i
\(297\) 0 0
\(298\) −1.48131 1.48131i −1.48131 1.48131i
\(299\) 0 0
\(300\) −0.291443 0.703605i −0.291443 0.703605i
\(301\) 0 0
\(302\) 0 0
\(303\) 0.692796 1.67256i 0.692796 1.67256i
\(304\) 0 0
\(305\) 0 0
\(306\) −1.08087 3.32657i −1.08087 3.32657i
\(307\) −0.907981 −0.907981 −0.453990 0.891007i \(-0.650000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(308\) 0 0
\(309\) 1.35969 3.28258i 1.35969 3.28258i
\(310\) 0 0
\(311\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(312\) 0 0
\(313\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(314\) −0.260074 0.260074i −0.260074 0.260074i
\(315\) 0 0
\(316\) −0.536680 + 0.222300i −0.536680 + 0.222300i
\(317\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(318\) 4.27763 + 1.77185i 4.27763 + 1.77185i
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.86304 1.86304
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −0.178671 0.431351i −0.178671 0.431351i
\(330\) 0 0
\(331\) −0.831254 0.831254i −0.831254 0.831254i 0.156434 0.987688i \(-0.450000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(332\) 0.381966 + 0.381966i 0.381966 + 0.381966i
\(333\) 0.431351 0.178671i 0.431351 0.178671i
\(334\) 0 0
\(335\) 0 0
\(336\) 1.15066i 1.15066i
\(337\) 0.744220 1.79671i 0.744220 1.79671i 0.156434 0.987688i \(-0.450000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(338\) 0.831254 0.831254i 0.831254 0.831254i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.318395 + 0.768673i −0.318395 + 0.768673i
\(344\) 0 0
\(345\) 0 0
\(346\) −0.874883 2.11215i −0.874883 2.11215i
\(347\) −1.84206 + 0.763007i −1.84206 + 0.763007i −0.891007 + 0.453990i \(0.850000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(350\) −0.507083 + 0.210041i −0.507083 + 0.210041i
\(351\) 0 0
\(352\) 0 0
\(353\) 0.312869i 0.312869i −0.987688 0.156434i \(-0.950000\pi\)
0.987688 0.156434i \(-0.0500000\pi\)
\(354\) −1.45133 + 3.50381i −1.45133 + 3.50381i
\(355\) 0 0
\(356\) 0.449028 0.449028
\(357\) −0.885341 + 0.287665i −0.885341 + 0.287665i
\(358\) 0 0
\(359\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(360\) 0 0
\(361\) 1.00000i 1.00000i
\(362\) 0 0
\(363\) 0.763007 + 1.84206i 0.763007 + 1.84206i
\(364\) 0 0
\(365\) 0 0
\(366\) 1.73196 + 1.73196i 1.73196 + 1.73196i
\(367\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.352943 0.852080i 0.352943 0.852080i
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −0.513743 + 0.513743i −0.513743 + 0.513743i
\(377\) 0 0
\(378\) 2.16174i 2.16174i
\(379\) −1.79671 0.744220i −1.79671 0.744220i −0.987688 0.156434i \(-0.950000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.17557 + 1.17557i 1.17557 + 1.17557i
\(383\) 1.26007 + 1.26007i 1.26007 + 1.26007i 0.951057 + 0.309017i \(0.100000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(384\) −2.16547 + 0.896969i −2.16547 + 0.896969i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0.249264 0.601777i 0.249264 0.601777i
\(389\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.568166 0.568166
\(393\) −2.40420 + 2.40420i −2.40420 + 2.40420i
\(394\) −0.831254 + 2.00682i −0.831254 + 2.00682i
\(395\) 0 0
\(396\) 0 0
\(397\) −0.497066 1.20002i −0.497066 1.20002i −0.951057 0.309017i \(-0.900000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.874032 + 0.874032i 0.874032 + 0.874032i
\(401\) 1.84206 0.763007i 1.84206 0.763007i 0.891007 0.453990i \(-0.150000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.346818i 0.346818i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.940794 + 1.10153i 0.940794 + 1.10153i
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0.680668i 0.680668i
\(413\) 0.697940 + 0.289096i 0.697940 + 0.289096i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) −2.10391 + 2.10391i −2.10391 + 2.10391i
\(424\) −1.43520 −1.43520
\(425\) 0.453990 0.891007i 0.453990 0.891007i
\(426\) −3.56462 −3.56462
\(427\) 0.344997 0.344997i 0.344997 0.344997i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −0.652583 1.57547i −0.652583 1.57547i −0.809017 0.587785i \(-0.800000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(432\) −4.49777 + 1.86304i −4.49777 + 1.86304i
\(433\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0.707107 1.70711i 0.707107 1.70711i 1.00000i \(-0.5\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(440\) 0 0
\(441\) 2.32678 2.32678
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0.0845030 0.0845030i 0.0845030 0.0845030i
\(445\) 0 0
\(446\) 0 0
\(447\) 3.28258 + 1.35969i 3.28258 + 1.35969i
\(448\) 0.0682464 + 0.164761i 0.0682464 + 0.164761i
\(449\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(450\) 2.47329 + 2.47329i 2.47329 + 2.47329i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.642040 0.642040i 0.642040 0.642040i −0.309017 0.951057i \(-0.600000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(458\) 0 0
\(459\) 2.55790 + 2.99492i 2.55790 + 2.99492i
\(460\) 0 0
\(461\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0.576324 + 0.238721i 0.576324 + 0.238721i
\(472\) 1.17557i 1.17557i
\(473\) 0 0
\(474\) 2.52057 2.52057i 2.52057 2.52057i
\(475\) 0 0
\(476\) −0.135608 + 0.115820i −0.135608 + 0.115820i
\(477\) −5.87749 −5.87749
\(478\) −1.58114 + 1.58114i −1.58114 + 1.58114i
\(479\) −0.178671 + 0.431351i −0.178671 + 0.431351i −0.987688 0.156434i \(-0.950000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.0705930 + 0.170427i 0.0705930 + 0.170427i
\(483\) 0 0
\(484\) 0.270091 + 0.270091i 0.270091 + 0.270091i
\(485\) 0 0
\(486\) −6.28445 + 2.60311i −6.28445 + 2.60311i
\(487\) −0.707107 1.70711i −0.707107 1.70711i −0.707107 0.707107i \(-0.750000\pi\)
1.00000i \(-0.5\pi\)
\(488\) −0.701442 0.290547i −0.701442 0.290547i
\(489\) 0 0
\(490\) 0 0
\(491\) −0.221232 + 0.221232i −0.221232 + 0.221232i −0.809017 0.587785i \(-0.800000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.710053i 0.710053i
\(498\) −3.06244 1.26851i −3.06244 1.26851i
\(499\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.754763 0.754763i −0.754763 0.754763i
\(503\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(504\) 0.386241 + 0.932467i 0.386241 + 0.932467i
\(505\) 0 0
\(506\) 0 0
\(507\) −0.763007 + 1.84206i −0.763007 + 1.84206i
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −0.0609007 0.0609007i −0.0609007 0.0609007i
\(519\) 2.74180 + 2.74180i 2.74180 + 2.74180i
\(520\) 0 0
\(521\) −0.744220 1.79671i −0.744220 1.79671i −0.587785 0.809017i \(-0.700000\pi\)
−0.156434 0.987688i \(-0.550000\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) −0.249264 + 0.601777i −0.249264 + 0.601777i
\(525\) 0.658248 0.658248i 0.658248 0.658248i
\(526\) 1.90211 1.90211
\(527\) 0 0
\(528\) 0 0
\(529\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(530\) 0 0
\(531\) 4.81426i 4.81426i
\(532\) 0 0
\(533\) 0 0
\(534\) −2.54567 + 1.05445i −2.54567 + 1.05445i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −0.344317 0.831254i −0.344317 0.831254i
\(539\) 0 0
\(540\) 0 0
\(541\) −0.744220 + 1.79671i −0.744220 + 1.79671i −0.156434 + 0.987688i \(0.550000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(542\) 0.754763 0.754763i 0.754763 0.754763i
\(543\) 0 0
\(544\) 0.647354 + 0.329843i 0.647354 + 0.329843i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(548\) 0 0
\(549\) −2.87258 1.18986i −2.87258 1.18986i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −0.502083 0.502083i −0.502083 0.502083i
\(554\) 1.65173 0.684170i 1.65173 0.684170i
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(564\) −0.291443 + 0.703605i −0.291443 + 0.703605i
\(565\) 0 0
\(566\) −0.507083 0.210041i −0.507083 0.210041i
\(567\) 0.871468 + 2.10391i 0.871468 + 2.10391i
\(568\) 1.02083 0.422840i 1.02083 0.422840i
\(569\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(570\) 0 0
\(571\) −1.20002 + 0.497066i −1.20002 + 0.497066i −0.891007 0.453990i \(-0.850000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(572\) 0 0
\(573\) −2.60507 1.07906i −2.60507 1.07906i
\(574\) 0 0
\(575\) 0 0
\(576\) 0.803622 0.803622i 0.803622 0.803622i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0.183900 1.16110i 0.183900 1.16110i
\(579\) 0 0
\(580\) 0 0
\(581\) −0.252679 + 0.610022i −0.252679 + 0.610022i
\(582\) 3.99700i 3.99700i
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(588\) 0.550229 0.227912i 0.550229 0.227912i
\(589\) 0 0
\(590\) 0 0
\(591\) 3.68413i 3.68413i
\(592\) −0.0742259 + 0.179197i −0.0742259 + 0.179197i
\(593\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.680668 0.680668
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) −1.33834 0.554357i −1.33834 0.554357i
\(601\) 0.399903 + 0.965451i 0.399903 + 0.965451i 0.987688 + 0.156434i \(0.0500000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0.814431 + 1.96621i 0.814431 + 1.96621i
\(607\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 1.01262 + 0.515957i 1.01262 + 0.515957i
\(613\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(614\) 0.754763 0.754763i 0.754763 0.754763i
\(615\) 0 0
\(616\) 0 0
\(617\) 1.20002 + 0.497066i 1.20002 + 0.497066i 0.891007 0.453990i \(-0.150000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(618\) 1.59841 + 3.85890i 1.59841 + 3.85890i
\(619\) −0.707107 + 0.292893i −0.707107 + 0.292893i −0.707107 0.707107i \(-0.750000\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0.210041 + 0.507083i 0.210041 + 0.507083i
\(624\) 0 0
\(625\) 1.00000i 1.00000i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.119505 0.119505
\(629\) 0.156434 + 0.0123117i 0.156434 + 0.0123117i
\(630\) 0 0
\(631\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(632\) −0.422840 + 1.02083i −0.422840 + 1.02083i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −1.38989 + 0.575710i −1.38989 + 0.575710i
\(637\) 0 0
\(638\) 0 0
\(639\) 4.18054 1.73164i 4.18054 1.73164i
\(640\) 0 0
\(641\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(642\) 0 0
\(643\) −0.399903 + 0.965451i −0.399903 + 0.965451i 0.587785 + 0.809017i \(0.300000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.312869 0.312869 0.156434 0.987688i \(-0.450000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(648\) 2.50578 2.50578i 2.50578 2.50578i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0.144974 0.0600500i 0.144974 0.0600500i −0.309017 0.951057i \(-0.600000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0.507083 + 0.210041i 0.507083 + 0.210041i
\(659\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(660\) 0 0
\(661\) −1.34500 + 1.34500i −1.34500 + 1.34500i −0.453990 + 0.891007i \(0.650000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(662\) 1.38197 1.38197
\(663\) 0 0
\(664\) 1.02749 1.02749
\(665\) 0 0
\(666\) −0.210041 + 0.507083i −0.210041 + 0.507083i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0.478245 + 0.478245i 0.478245 + 0.478245i
\(673\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(674\) 0.874883 + 2.11215i 0.874883 + 2.11215i
\(675\) −3.63877 1.50723i −3.63877 1.50723i
\(676\) 0.381966i 0.381966i
\(677\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(678\) 0 0
\(679\) 0.796180 0.796180
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.399903 0.965451i 0.399903 0.965451i −0.587785 0.809017i \(-0.700000\pi\)
0.987688 0.156434i \(-0.0500000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.374295 0.903629i −0.374295 0.903629i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(692\) 0.686280 + 0.284267i 0.686280 + 0.284267i
\(693\) 0 0
\(694\) 0.896969 2.16547i 0.896969 2.16547i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0.0682464 0.164761i 0.0682464 0.164761i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0.260074 + 0.260074i 0.260074 + 0.260074i
\(707\) 0.391658 0.162230i 0.391658 0.162230i
\(708\) −0.471565 1.13846i −0.471565 1.13846i
\(709\) 0.431351 + 0.178671i 0.431351 + 0.178671i 0.587785 0.809017i \(-0.300000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(710\) 0 0
\(711\) −1.73164 + 4.18054i −1.73164 + 4.18054i
\(712\) 0.603941 0.603941i 0.603941 0.603941i
\(713\) 0 0
\(714\) 0.496821 0.975066i 0.496821 0.975066i
\(715\) 0 0
\(716\) 0 0
\(717\) 1.45133 3.50381i 1.45133 3.50381i
\(718\) 0 0
\(719\) −0.965451 0.399903i −0.965451 0.399903i −0.156434 0.987688i \(-0.550000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(720\) 0 0
\(721\) 0.768673 0.318395i 0.768673 0.318395i
\(722\) 0.831254 + 0.831254i 0.831254 + 0.831254i
\(723\) −0.221232 0.221232i −0.221232 0.221232i
\(724\) 0 0
\(725\) 0 0
\(726\) −2.16547 0.896969i −2.16547 0.896969i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 4.70898 4.70898i 4.70898 4.70898i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.795846 −0.795846
\(733\) −1.34500 + 1.34500i −1.34500 + 1.34500i −0.453990 + 0.891007i \(0.650000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.221232 + 0.221232i 0.221232 + 0.221232i 0.809017 0.587785i \(-0.200000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.414910 + 1.00168i 0.414910 + 1.00168i
\(743\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 4.20782 4.20782
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(752\) 1.23607i 1.23607i
\(753\) 1.67256 + 0.692796i 1.67256 + 0.692796i
\(754\) 0 0
\(755\) 0 0
\(756\) 0.496666 + 0.496666i 0.496666 + 0.496666i
\(757\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(758\) 2.11215 0.874883i 2.11215 0.874883i
\(759\) 0 0
\(760\) 0 0
\(761\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −0.540182 −0.540182
\(765\) 0 0
\(766\) −2.09488 −2.09488
\(767\) 0 0
\(768\) 0.763007 1.84206i 0.763007 1.84206i
\(769\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.34500 + 1.34500i 1.34500 + 1.34500i 0.891007 + 0.453990i \(0.150000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −0.474129 1.14465i −0.474129 1.14465i
\(777\) 0.134956 + 0.0559007i 0.134956 + 0.0559007i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.683504 + 0.683504i −0.683504 + 0.683504i
\(785\) 0 0
\(786\) 3.99700i 3.99700i
\(787\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(788\) −0.270091 0.652057i −0.270091 0.652057i
\(789\) −2.98052 + 1.23457i −2.98052 + 1.23457i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 1.41071 + 0.584336i 1.41071 + 0.584336i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(798\) 0 0
\(799\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(800\) −0.726543 −0.726543