Properties

Label 799.1.h.b.281.2
Level $799$
Weight $1$
Character 799.281
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 281.2
Root \(0.156434 - 0.987688i\) of defining polynomial
Character \(\chi\) \(=\) 799.281
Dual form 799.1.h.b.563.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.831254 + 0.831254i) q^{2} +(1.20002 + 0.497066i) q^{3} -0.381966i q^{4} +(-1.41071 + 0.584336i) q^{6} +(0.399903 + 0.965451i) q^{7} +(-0.513743 - 0.513743i) q^{8} +(0.485875 + 0.485875i) q^{9} +O(q^{10})\) \(q+(-0.831254 + 0.831254i) q^{2} +(1.20002 + 0.497066i) q^{3} -0.381966i q^{4} +(-1.41071 + 0.584336i) q^{6} +(0.399903 + 0.965451i) q^{7} +(-0.513743 - 0.513743i) q^{8} +(0.485875 + 0.485875i) q^{9} +(0.189862 - 0.458368i) q^{12} +(-1.13496 - 0.470114i) q^{14} +1.23607 q^{16} +(-0.309017 + 0.951057i) q^{17} -0.807771 q^{18} +1.35734i q^{21} +(-0.361140 - 0.871868i) q^{24} +(-0.707107 - 0.707107i) q^{25} +(-0.155517 - 0.375450i) q^{27} +(0.368770 - 0.152749i) q^{28} +(-0.513743 + 0.513743i) q^{32} +(-0.533698 - 1.04744i) q^{34} +(0.185588 - 0.185588i) q^{36} +(1.40505 + 0.581990i) q^{37} +(-1.12830 - 1.12830i) q^{42} -1.00000i q^{47} +(1.48331 + 0.614407i) q^{48} +(-0.0650673 + 0.0650673i) q^{49} +1.17557 q^{50} +(-0.843566 + 0.987688i) q^{51} +(0.221232 - 0.221232i) q^{53} +(0.441368 + 0.182821i) q^{54} +(0.290547 - 0.701442i) q^{56} +(-1.14412 - 1.14412i) q^{59} +(-0.178671 - 0.431351i) q^{61} +(-0.274786 + 0.663392i) q^{63} +0.381966i q^{64} +(0.363271 + 0.118034i) q^{68} +(-0.144974 - 0.0600500i) q^{71} -0.499230i q^{72} +(-1.65173 + 0.684170i) q^{74} +(-0.497066 - 1.20002i) q^{75} +(-0.144974 + 0.0600500i) q^{79} -1.21498i q^{81} +(-1.00000 + 1.00000i) q^{83} +0.518459 q^{84} -1.17557i q^{89} +(0.831254 + 0.831254i) q^{94} +(-0.871868 + 0.361140i) q^{96} +(-0.744220 + 1.79671i) q^{97} -0.108175i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{3} - 4 q^{9} + O(q^{10}) \) \( 16 q - 4 q^{3} - 4 q^{9} - 16 q^{16} + 4 q^{17} - 20 q^{24} - 4 q^{27} - 4 q^{28} + 4 q^{36} - 20 q^{42} + 24 q^{48} + 4 q^{49} - 16 q^{51} + 4 q^{53} + 20 q^{54} + 20 q^{56} + 4 q^{61} - 4 q^{63} - 4 q^{71} - 4 q^{79} - 16 q^{83} + 32 q^{84} + O(q^{100}) \)

Character values

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

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

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 \(0.450000\pi\)
\(3\) 1.20002 + 0.497066i 1.20002 + 0.497066i 0.891007 0.453990i \(-0.150000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(4\) 0.381966i 0.381966i
\(5\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(6\) −1.41071 + 0.584336i −1.41071 + 0.584336i
\(7\) 0.399903 + 0.965451i 0.399903 + 0.965451i 0.987688 + 0.156434i \(0.0500000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(8\) −0.513743 0.513743i −0.513743 0.513743i
\(9\) 0.485875 + 0.485875i 0.485875 + 0.485875i
\(10\) 0 0
\(11\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(12\) 0.189862 0.458368i 0.189862 0.458368i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −1.13496 0.470114i −1.13496 0.470114i
\(15\) 0 0
\(16\) 1.23607 1.23607
\(17\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(18\) −0.807771 −0.807771
\(19\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(20\) 0 0
\(21\) 1.35734i 1.35734i
\(22\) 0 0
\(23\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(24\) −0.361140 0.871868i −0.361140 0.871868i
\(25\) −0.707107 0.707107i −0.707107 0.707107i
\(26\) 0 0
\(27\) −0.155517 0.375450i −0.155517 0.375450i
\(28\) 0.368770 0.152749i 0.368770 0.152749i
\(29\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(30\) 0 0
\(31\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(32\) −0.513743 + 0.513743i −0.513743 + 0.513743i
\(33\) 0 0
\(34\) −0.533698 1.04744i −0.533698 1.04744i
\(35\) 0 0
\(36\) 0.185588 0.185588i 0.185588 0.185588i
\(37\) 1.40505 + 0.581990i 1.40505 + 0.581990i 0.951057 0.309017i \(-0.100000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(42\) −1.12830 1.12830i −1.12830 1.12830i
\(43\) 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
\(48\) 1.48331 + 0.614407i 1.48331 + 0.614407i
\(49\) −0.0650673 + 0.0650673i −0.0650673 + 0.0650673i
\(50\) 1.17557 1.17557
\(51\) −0.843566 + 0.987688i −0.843566 + 0.987688i
\(52\) 0 0
\(53\) 0.221232 0.221232i 0.221232 0.221232i −0.587785 0.809017i \(-0.700000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(54\) 0.441368 + 0.182821i 0.441368 + 0.182821i
\(55\) 0 0
\(56\) 0.290547 0.701442i 0.290547 0.701442i
\(57\) 0 0
\(58\) 0 0
\(59\) −1.14412 1.14412i −1.14412 1.14412i −0.987688 0.156434i \(-0.950000\pi\)
−0.156434 0.987688i \(-0.550000\pi\)
\(60\) 0 0
\(61\) −0.178671 0.431351i −0.178671 0.431351i 0.809017 0.587785i \(-0.200000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(62\) 0 0
\(63\) −0.274786 + 0.663392i −0.274786 + 0.663392i
\(64\) 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
\(71\) −0.144974 0.0600500i −0.144974 0.0600500i 0.309017 0.951057i \(-0.400000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(72\) 0.499230i 0.499230i
\(73\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(74\) −1.65173 + 0.684170i −1.65173 + 0.684170i
\(75\) −0.497066 1.20002i −0.497066 1.20002i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.144974 + 0.0600500i −0.144974 + 0.0600500i −0.453990 0.891007i \(-0.650000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(80\) 0 0
\(81\) 1.21498i 1.21498i
\(82\) 0 0
\(83\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(84\) 0.518459 0.518459
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0.831254 + 0.831254i 0.831254 + 0.831254i
\(95\) 0 0
\(96\) −0.871868 + 0.361140i −0.871868 + 0.361140i
\(97\) −0.744220 + 1.79671i −0.744220 + 1.79671i −0.156434 + 0.987688i \(0.550000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(98\) 0.108175i 0.108175i
\(99\) 0 0
\(100\) −0.270091 + 0.270091i −0.270091 + 0.270091i
\(101\) 1.78201 1.78201 0.891007 0.453990i \(-0.150000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(102\) −0.119803 1.52224i −0.119803 1.52224i
\(103\) 0.907981 0.907981 0.453990 0.891007i \(-0.350000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0.367799i 0.367799i
\(107\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(108\) −0.143409 + 0.0594020i −0.143409 + 0.0594020i
\(109\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(110\) 0 0
\(111\) 1.39680 + 1.39680i 1.39680 + 1.39680i
\(112\) 0.494307 + 1.19336i 0.494307 + 1.19336i
\(113\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 1.90211 1.90211
\(119\) −1.04178 + 0.0819895i −1.04178 + 0.0819895i
\(120\) 0 0
\(121\) 0.707107 0.707107i 0.707107 0.707107i
\(122\) 0.507083 + 0.210041i 0.507083 + 0.210041i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −0.323030 0.779864i −0.323030 0.779864i
\(127\) 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
\(131\) 0.744220 1.79671i 0.744220 1.79671i 0.156434 0.987688i \(-0.450000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0.647354 0.329843i 0.647354 0.329843i
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(140\) 0 0
\(141\) 0.497066 1.20002i 0.497066 1.20002i
\(142\) 0.170427 0.0705930i 0.170427 0.0705930i
\(143\) 0 0
\(144\) 0.600575 + 0.600575i 0.600575 + 0.600575i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.110425 + 0.0457395i −0.110425 + 0.0457395i
\(148\) 0.222300 0.536680i 0.222300 0.536680i
\(149\) 0.907981i 0.907981i 0.891007 + 0.453990i \(0.150000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(150\) 1.41071 + 0.584336i 1.41071 + 0.584336i
\(151\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(152\) 0 0
\(153\) −0.612238 + 0.311951i −0.612238 + 0.311951i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1.97538i 1.97538i −0.156434 0.987688i \(-0.550000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(158\) 0.0705930 0.170427i 0.0705930 0.170427i
\(159\) 0.375450 0.155517i 0.375450 0.155517i
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00996 + 1.00996i 1.00996 + 1.00996i
\(163\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.66251i 1.66251i
\(167\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(168\) 0.697326 0.697326i 0.697326 0.697326i
\(169\) −1.00000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.57547 + 0.652583i 1.57547 + 0.652583i 0.987688 0.156434i \(-0.0500000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(174\) 0 0
\(175\) 0.399903 0.965451i 0.399903 0.965451i
\(176\) 0 0
\(177\) −0.804270 1.94168i −0.804270 1.94168i
\(178\) 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 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(182\) 0 0
\(183\) 0.606443i 0.606443i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.381966 −0.381966
\(189\) 0.300287 0.300287i 0.300287 0.300287i
\(190\) 0 0
\(191\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) −0.189862 + 0.458368i −0.189862 + 0.458368i
\(193\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(194\) −0.874883 2.11215i −0.874883 2.11215i
\(195\) 0 0
\(196\) 0.0248535 + 0.0248535i 0.0248535 + 0.0248535i
\(197\) 0.292893 + 0.707107i 0.292893 + 0.707107i 1.00000 \(0\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(198\) 0 0
\(199\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(200\) 0.726543i 0.726543i
\(201\) 0 0
\(202\) −1.48131 + 1.48131i −1.48131 + 1.48131i
\(203\) 0 0
\(204\) 0.377263 + 0.322213i 0.377263 + 0.322213i
\(205\) 0 0
\(206\) −0.754763 + 0.754763i −0.754763 + 0.754763i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(212\) −0.0845030 0.0845030i −0.0845030 0.0845030i
\(213\) −0.144123 0.144123i −0.144123 0.144123i
\(214\) 0 0
\(215\) 0 0
\(216\) −0.112989 + 0.272780i −0.112989 + 0.272780i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) −2.32219 −2.32219
\(223\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(224\) −0.701442 0.290547i −0.701442 0.290547i
\(225\) 0.687131i 0.687131i
\(226\) 0 0
\(227\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(228\) 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 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.437016 + 0.437016i −0.437016 + 0.437016i
\(237\) −0.203820 −0.203820
\(238\) 0.797826 0.934134i 0.797826 0.934134i
\(239\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(240\) 0 0
\(241\) −1.40505 0.581990i −1.40505 0.581990i −0.453990 0.891007i \(-0.650000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(242\) 1.17557i 1.17557i
\(243\) 0.448410 1.08256i 0.448410 1.08256i
\(244\) −0.164761 + 0.0682464i −0.164761 + 0.0682464i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −1.69709 + 0.702958i −1.69709 + 0.702958i
\(250\) 0 0
\(251\) 1.78201i 1.78201i 0.453990 + 0.891007i \(0.350000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(252\) 0.253393 + 0.104959i 0.253393 + 0.104959i
\(253\) 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
\(259\) 1.58924i 1.58924i
\(260\) 0 0
\(261\) 0 0
\(262\) 0.874883 + 2.11215i 0.874883 + 2.11215i
\(263\) 1.14412 + 1.14412i 1.14412 + 1.14412i 0.987688 + 0.156434i \(0.0500000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0.584336 1.41071i 0.584336 1.41071i
\(268\) 0 0
\(269\) −1.70711 0.707107i −1.70711 0.707107i −0.707107 0.707107i \(-0.750000\pi\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −1.78201 −1.78201 −0.891007 0.453990i \(-0.850000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(272\) −0.381966 + 1.17557i −0.381966 + 1.17557i
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0.0600500 0.144974i 0.0600500 0.144974i −0.891007 0.453990i \(-0.850000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(282\) 0.584336 + 1.41071i 0.584336 + 1.41071i
\(283\) −0.965451 + 0.399903i −0.965451 + 0.399903i −0.809017 0.587785i \(-0.800000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(284\) −0.0229371 + 0.0553750i −0.0229371 + 0.0553750i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.499230 −0.499230
\(289\) −0.809017 0.587785i −0.809017 0.587785i
\(290\) 0 0
\(291\) −1.78616 + 1.78616i −1.78616 + 1.78616i
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0.0537700 0.129812i 0.0537700 0.129812i
\(295\) 0 0
\(296\) −0.422840 1.02083i −0.422840 1.02083i
\(297\) 0 0
\(298\) −0.754763 0.754763i −0.754763 0.754763i
\(299\) 0 0
\(300\) −0.458368 + 0.189862i −0.458368 + 0.189862i
\(301\) 0 0
\(302\) 0 0
\(303\) 2.13846 + 0.885778i 2.13846 + 0.885778i
\(304\) 0 0
\(305\) 0 0
\(306\) 0.249615 0.768236i 0.249615 0.768236i
\(307\) −1.78201 −1.78201 −0.891007 0.453990i \(-0.850000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(308\) 0 0
\(309\) 1.08960 + 0.451326i 1.08960 + 0.451326i
\(310\) 0 0
\(311\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(312\) 0 0
\(313\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(314\) 1.64204 + 1.64204i 1.64204 + 1.64204i
\(315\) 0 0
\(316\) 0.0229371 + 0.0553750i 0.0229371 + 0.0553750i
\(317\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(318\) −0.182821 + 0.441368i −0.182821 + 0.441368i
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.464082 −0.464082
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0.965451 0.399903i 0.965451 0.399903i
\(330\) 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
\(333\) 0.399903 + 0.965451i 0.399903 + 0.965451i
\(334\) 0 0
\(335\) 0 0
\(336\) 1.67777i 1.67777i
\(337\) −1.57547 0.652583i −1.57547 0.652583i −0.587785 0.809017i \(-0.700000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(338\) 0.831254 0.831254i 0.831254 0.831254i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.876612 + 0.363104i 0.876612 + 0.363104i
\(344\) 0 0
\(345\) 0 0
\(346\) −1.85208 + 0.767157i −1.85208 + 0.767157i
\(347\) 0.497066 + 1.20002i 0.497066 + 1.20002i 0.951057 + 0.309017i \(0.100000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(350\) 0.470114 + 1.13496i 0.470114 + 1.13496i
\(351\) 0 0
\(352\) 0 0
\(353\) 1.97538i 1.97538i 0.156434 + 0.987688i \(0.450000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(354\) 2.28258 + 0.945476i 2.28258 + 0.945476i
\(355\) 0 0
\(356\) −0.449028 −0.449028
\(357\) −1.29091 0.419442i −1.29091 0.419442i
\(358\) 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
\(363\) 1.20002 0.497066i 1.20002 0.497066i
\(364\) 0 0
\(365\) 0 0
\(366\) 0.504108 + 0.504108i 0.504108 + 0.504108i
\(367\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.302060 + 0.125117i 0.302060 + 0.125117i
\(372\) 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
\(378\) 0.499230i 0.499230i
\(379\) −0.652583 + 1.57547i −0.652583 + 1.57547i 0.156434 + 0.987688i \(0.450000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −1.17557 1.17557i −1.17557 1.17557i
\(383\) −0.642040 0.642040i −0.642040 0.642040i 0.309017 0.951057i \(-0.400000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(384\) −0.584336 1.41071i −0.584336 1.41071i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0.686280 + 0.284267i 0.686280 + 0.284267i
\(389\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.0668557 0.0668557
\(393\) 1.78616 1.78616i 1.78616 1.78616i
\(394\) −0.831254 0.344317i −0.831254 0.344317i
\(395\) 0 0
\(396\) 0 0
\(397\) 1.84206 0.763007i 1.84206 0.763007i 0.891007 0.453990i \(-0.150000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.874032 0.874032i −0.874032 0.874032i
\(401\) −0.497066 1.20002i −0.497066 1.20002i −0.951057 0.309017i \(-0.900000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.680668i 0.680668i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.940794 0.0740421i 0.940794 0.0740421i
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0.346818i 0.346818i
\(413\) 0.647057 1.56213i 0.647057 1.56213i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) 0.485875 0.485875i 0.485875 0.485875i
\(424\) −0.227313 −0.227313
\(425\) 0.891007 0.453990i 0.891007 0.453990i
\(426\) 0.239605 0.239605
\(427\) 0.344997 0.344997i 0.344997 0.344997i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.79671 + 0.744220i −1.79671 + 0.744220i −0.809017 + 0.587785i \(0.800000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(432\) −0.192229 0.464082i −0.192229 0.464082i
\(433\) 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 0.292893i −0.707107 0.292893i 1.00000i \(-0.5\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(440\) 0 0
\(441\) −0.0632291 −0.0632291
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0.533531 0.533531i 0.533531 0.533531i
\(445\) 0 0
\(446\) 0 0
\(447\) −0.451326 + 1.08960i −0.451326 + 1.08960i
\(448\) −0.368770 + 0.152749i −0.368770 + 0.152749i
\(449\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(450\) 0.571180 + 0.571180i 0.571180 + 0.571180i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.26007 + 1.26007i −1.26007 + 1.26007i −0.309017 + 0.951057i \(0.600000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(458\) 0 0
\(459\) 0.405131 0.0318845i 0.405131 0.0318845i
\(460\) 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
\(471\) 0.981893 2.37050i 0.981893 2.37050i
\(472\) 1.17557i 1.17557i
\(473\) 0 0
\(474\) 0.169427 0.169427i 0.169427 0.169427i
\(475\) 0 0
\(476\) 0.0313172 + 0.397923i 0.0313172 + 0.397923i
\(477\) 0.214982 0.214982
\(478\) 1.58114 1.58114i 1.58114 1.58114i
\(479\) 0.965451 + 0.399903i 0.965451 + 0.399903i 0.809017 0.587785i \(-0.200000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1.65173 0.684170i 1.65173 0.684170i
\(483\) 0 0
\(484\) −0.270091 0.270091i −0.270091 0.270091i
\(485\) 0 0
\(486\) 0.527137 + 1.27262i 0.527137 + 1.27262i
\(487\) 0.707107 0.292893i 0.707107 0.292893i 1.00000i \(-0.5\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(488\) −0.129812 + 0.313395i −0.129812 + 0.313395i
\(489\) 0 0
\(490\) 0 0
\(491\) −1.39680 + 1.39680i −1.39680 + 1.39680i −0.587785 + 0.809017i \(0.700000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.163979i 0.163979i
\(498\) 0.826376 1.99505i 0.826376 1.99505i
\(499\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −1.48131 1.48131i −1.48131 1.48131i
\(503\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(504\) 0.481982 0.199644i 0.481982 0.199644i
\(505\) 0 0
\(506\) 0 0
\(507\) −1.20002 0.497066i −1.20002 0.497066i
\(508\) 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
\(518\) −1.32107 1.32107i −1.32107 1.32107i
\(519\) 1.56623 + 1.56623i 1.56623 + 1.56623i
\(520\) 0 0
\(521\) 1.57547 0.652583i 1.57547 0.652583i 0.587785 0.809017i \(-0.300000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) −0.686280 0.284267i −0.686280 0.284267i
\(525\) 0.959786 0.959786i 0.959786 0.959786i
\(526\) −1.90211 −1.90211
\(527\) 0 0
\(528\) 0 0
\(529\) 0.707107 0.707107i 0.707107 0.707107i
\(530\) 0 0
\(531\) 1.11180i 1.11180i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.686928 + 1.65839i 0.686928 + 1.65839i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 2.00682 0.831254i 2.00682 0.831254i
\(539\) 0 0
\(540\) 0 0
\(541\) 1.57547 + 0.652583i 1.57547 + 0.652583i 0.987688 0.156434i \(-0.0500000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(542\) 1.48131 1.48131i 1.48131 1.48131i
\(543\) 0 0
\(544\) −0.329843 0.647354i −0.329843 0.647354i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(548\) 0 0
\(549\) 0.122771 0.296395i 0.122771 0.296395i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −0.115951 0.115951i −0.115951 0.115951i
\(554\) 0.0705930 + 0.170427i 0.0705930 + 0.170427i
\(555\) 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 \(0.750000\pi\)
\(564\) −0.458368 0.189862i −0.458368 0.189862i
\(565\) 0 0
\(566\) 0.470114 1.13496i 0.470114 1.13496i
\(567\) 1.17301 0.485875i 1.17301 0.485875i
\(568\) 0.0436289 + 0.105329i 0.0436289 + 0.105329i
\(569\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(570\) 0 0
\(571\) −0.763007 1.84206i −0.763007 1.84206i −0.453990 0.891007i \(-0.650000\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(572\) 0 0
\(573\) −0.702958 + 1.69709i −0.702958 + 1.69709i
\(574\) 0 0
\(575\) 0 0
\(576\) −0.185588 + 0.185588i −0.185588 + 0.185588i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 1.16110 0.183900i 1.16110 0.183900i
\(579\) 0 0
\(580\) 0 0
\(581\) −1.36535 0.565548i −1.36535 0.565548i
\(582\) 2.96951i 2.96951i
\(583\) 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 \(0.250000\pi\)
\(588\) 0.0174709 + 0.0421786i 0.0174709 + 0.0421786i
\(589\) 0 0
\(590\) 0 0
\(591\) 0.994132i 0.994132i
\(592\) 1.73673 + 0.719379i 1.73673 + 0.719379i
\(593\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.346818 0.346818
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) −0.361140 + 0.871868i −0.361140 + 0.871868i
\(601\) 0.431351 0.178671i 0.431351 0.178671i −0.156434 0.987688i \(-0.550000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) −2.51391 + 1.04129i −2.51391 + 1.04129i
\(607\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.119155 + 0.233854i 0.119155 + 0.233854i
\(613\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(614\) 1.48131 1.48131i 1.48131 1.48131i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.763007 1.84206i 0.763007 1.84206i 0.309017 0.951057i \(-0.400000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(618\) −1.28090 + 0.530566i −1.28090 + 0.530566i
\(619\) 0.707107 + 1.70711i 0.707107 + 1.70711i 0.707107 + 0.707107i \(0.250000\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.13496 0.470114i 1.13496 0.470114i
\(624\) 0 0
\(625\) 1.00000i 1.00000i
\(626\) 0 0
\(627\) 0 0
\(628\) −0.754527 −0.754527
\(629\) −0.987688 + 1.15643i −0.987688 + 1.15643i
\(630\) 0 0
\(631\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(632\) 0.105329 + 0.0436289i 0.105329 + 0.0436289i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −0.0594020 0.143409i −0.0594020 0.143409i
\(637\) 0 0
\(638\) 0 0
\(639\) −0.0412622 0.0996158i −0.0412622 0.0996158i
\(640\) 0 0
\(641\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(642\) 0 0
\(643\) −0.431351 0.178671i −0.431351 0.178671i 0.156434 0.987688i \(-0.450000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.97538 −1.97538 −0.987688 0.156434i \(-0.950000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(648\) −0.624189 + 0.624189i −0.624189 + 0.624189i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0.581990 + 1.40505i 0.581990 + 1.40505i 0.891007 + 0.453990i \(0.150000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) −0.470114 + 1.13496i −0.470114 + 1.13496i
\(659\) 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
\(666\) −1.13496 0.470114i −1.13496 0.470114i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −0.697326 0.697326i −0.697326 0.697326i
\(673\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(674\) 1.85208 0.767157i 1.85208 0.767157i
\(675\) −0.155517 + 0.375450i −0.155517 + 0.375450i
\(676\) 0.381966i 0.381966i
\(677\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(678\) 0 0
\(679\) −2.03225 −2.03225
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.431351 + 0.178671i 0.431351 + 0.178671i 0.587785 0.809017i \(-0.300000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.03052 + 0.426855i −1.03052 + 0.426855i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(692\) 0.249264 0.601777i 0.249264 0.601777i
\(693\) 0 0
\(694\) −1.41071 0.584336i −1.41071 0.584336i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −0.368770 0.152749i −0.368770 0.152749i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −1.64204 1.64204i −1.64204 1.64204i
\(707\) 0.712633 + 1.72045i 0.712633 + 1.72045i
\(708\) −0.741655 + 0.307204i −0.741655 + 0.307204i
\(709\) 0.399903 0.965451i 0.399903 0.965451i −0.587785 0.809017i \(-0.700000\pi\)
0.987688 0.156434i \(-0.0500000\pi\)
\(710\) 0 0
\(711\) −0.0996158 0.0412622i −0.0996158 0.0412622i
\(712\) −0.603941 + 0.603941i −0.603941 + 0.603941i
\(713\) 0 0
\(714\) 1.42174 0.724411i 1.42174 0.724411i
\(715\) 0 0
\(716\) 0 0
\(717\) −2.28258 0.945476i −2.28258 0.945476i
\(718\) 0 0
\(719\) 0.178671 0.431351i 0.178671 0.431351i −0.809017 0.587785i \(-0.800000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(720\) 0 0
\(721\) 0.363104 + 0.876612i 0.363104 + 0.876612i
\(722\) 0.831254 + 0.831254i 0.831254 + 0.831254i
\(723\) −1.39680 1.39680i −1.39680 1.39680i
\(724\) 0 0
\(725\) 0 0
\(726\) −0.584336 + 1.41071i −0.584336 + 1.41071i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 0.217082 0.217082i 0.217082 0.217082i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.231640 −0.231640
\(733\) −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
\(739\) 1.39680 + 1.39680i 1.39680 + 1.39680i 0.809017 + 0.587785i \(0.200000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.355093 + 0.147084i −0.355093 + 0.147084i
\(743\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.971750 −0.971750
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(752\) 1.23607i 1.23607i
\(753\) −0.885778 + 2.13846i −0.885778 + 2.13846i
\(754\) 0 0
\(755\) 0 0
\(756\) −0.114700 0.114700i −0.114700 0.114700i
\(757\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(758\) −0.767157 1.85208i −0.767157 1.85208i
\(759\) 0 0
\(760\) 0 0
\(761\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0.540182 0.540182
\(765\) 0 0
\(766\) 1.06740 1.06740
\(767\) 0 0
\(768\) 1.20002 + 0.497066i 1.20002 + 0.497066i
\(769\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(770\) 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
\(776\) 1.30538 0.540707i 1.30538 0.540707i
\(777\) −0.789959 + 1.90713i −0.789959 + 1.90713i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.0804276 + 0.0804276i −0.0804276 + 0.0804276i
\(785\) 0 0
\(786\) 2.96951i 2.96951i
\(787\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(788\) 0.270091 0.111875i 0.270091 0.111875i
\(789\) 0.804270 + 1.94168i 0.804270 + 1.94168i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) −0.896969 + 2.16547i −0.896969 + 2.16547i
\(795\) 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