Properties

Label 799.1.h.b.610.1
Level $799$
Weight $1$
Character 799.610
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 610.1
Root \(-0.453990 + 0.891007i\) of defining polynomial
Character \(\chi\) \(=\) 799.610
Dual form 799.1.h.b.93.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.34500 - 1.34500i) q^{2} +(-0.652583 - 1.57547i) q^{3} +2.61803i q^{4} +(-1.24129 + 2.99673i) q^{6} +(1.84206 + 0.763007i) q^{7} +(2.17625 - 2.17625i) q^{8} +(-1.34915 + 1.34915i) q^{9} +O(q^{10})\) \(q+(-1.34500 - 1.34500i) q^{2} +(-0.652583 - 1.57547i) q^{3} +2.61803i q^{4} +(-1.24129 + 2.99673i) q^{6} +(1.84206 + 0.763007i) q^{7} +(2.17625 - 2.17625i) q^{8} +(-1.34915 + 1.34915i) q^{9} +(4.12464 - 1.70848i) q^{12} +(-1.45133 - 3.50381i) q^{14} -3.23607 q^{16} +(0.809017 - 0.587785i) q^{17} +3.62920 q^{18} -3.40005i q^{21} +(-4.84881 - 2.00844i) q^{24} +(0.707107 - 0.707107i) q^{25} +(1.43050 + 0.592533i) q^{27} +(-1.99758 + 4.82258i) q^{28} +(2.17625 + 2.17625i) q^{32} +(-1.87869 - 0.297556i) q^{34} +(-3.53211 - 3.53211i) q^{36} +(-0.399903 - 0.965451i) q^{37} +(-4.57305 + 4.57305i) q^{42} +1.00000i q^{47} +(2.11180 + 5.09834i) q^{48} +(2.10391 + 2.10391i) q^{49} -1.90211 q^{50} +(-1.45399 - 0.891007i) q^{51} +(0.642040 + 0.642040i) q^{53} +(-1.12706 - 2.72097i) q^{54} +(5.66929 - 2.34830i) q^{56} +(-0.437016 + 0.437016i) q^{59} +(-1.20002 - 0.497066i) q^{61} +(-3.51462 + 1.45580i) q^{63} -2.61803i q^{64} +(1.53884 + 2.11803i) q^{68} +(0.178671 + 0.431351i) q^{71} +5.87216i q^{72} +(-0.760661 + 1.83640i) q^{74} +(-1.57547 - 0.652583i) q^{75} +(0.178671 - 0.431351i) q^{79} -0.732410i q^{81} +(-1.00000 - 1.00000i) q^{83} +8.90144 q^{84} -1.90211i q^{89} +(1.34500 - 1.34500i) q^{94} +(2.00844 - 4.84881i) q^{96} +(1.40505 - 0.581990i) q^{97} -5.65950i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{3} - 4q^{9} + O(q^{10}) \) \( 16q - 4q^{3} - 4q^{9} - 16q^{16} + 4q^{17} - 20q^{24} - 4q^{27} - 4q^{28} + 4q^{36} - 20q^{42} + 24q^{48} + 4q^{49} - 16q^{51} + 4q^{53} + 20q^{54} + 20q^{56} + 4q^{61} - 4q^{63} - 4q^{71} - 4q^{79} - 16q^{83} + 32q^{84} + O(q^{100}) \)

Character values

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

\(n\) \(52\) \(377\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34500 1.34500i −1.34500 1.34500i −0.891007 0.453990i \(-0.850000\pi\)
−0.453990 0.891007i \(-0.650000\pi\)
\(3\) −0.652583 1.57547i −0.652583 1.57547i −0.809017 0.587785i \(-0.800000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(4\) 2.61803i 2.61803i
\(5\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(6\) −1.24129 + 2.99673i −1.24129 + 2.99673i
\(7\) 1.84206 + 0.763007i 1.84206 + 0.763007i 0.951057 + 0.309017i \(0.100000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(8\) 2.17625 2.17625i 2.17625 2.17625i
\(9\) −1.34915 + 1.34915i −1.34915 + 1.34915i
\(10\) 0 0
\(11\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(12\) 4.12464 1.70848i 4.12464 1.70848i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −1.45133 3.50381i −1.45133 3.50381i
\(15\) 0 0
\(16\) −3.23607 −3.23607
\(17\) 0.809017 0.587785i 0.809017 0.587785i
\(18\) 3.62920 3.62920
\(19\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(20\) 0 0
\(21\) 3.40005i 3.40005i
\(22\) 0 0
\(23\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(24\) −4.84881 2.00844i −4.84881 2.00844i
\(25\) 0.707107 0.707107i 0.707107 0.707107i
\(26\) 0 0
\(27\) 1.43050 + 0.592533i 1.43050 + 0.592533i
\(28\) −1.99758 + 4.82258i −1.99758 + 4.82258i
\(29\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(30\) 0 0
\(31\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(32\) 2.17625 + 2.17625i 2.17625 + 2.17625i
\(33\) 0 0
\(34\) −1.87869 0.297556i −1.87869 0.297556i
\(35\) 0 0
\(36\) −3.53211 3.53211i −3.53211 3.53211i
\(37\) −0.399903 0.965451i −0.399903 0.965451i −0.987688 0.156434i \(-0.950000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(42\) −4.57305 + 4.57305i −4.57305 + 4.57305i
\(43\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.00000i 1.00000i
\(48\) 2.11180 + 5.09834i 2.11180 + 5.09834i
\(49\) 2.10391 + 2.10391i 2.10391 + 2.10391i
\(50\) −1.90211 −1.90211
\(51\) −1.45399 0.891007i −1.45399 0.891007i
\(52\) 0 0
\(53\) 0.642040 + 0.642040i 0.642040 + 0.642040i 0.951057 0.309017i \(-0.100000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(54\) −1.12706 2.72097i −1.12706 2.72097i
\(55\) 0 0
\(56\) 5.66929 2.34830i 5.66929 2.34830i
\(57\) 0 0
\(58\) 0 0
\(59\) −0.437016 + 0.437016i −0.437016 + 0.437016i −0.891007 0.453990i \(-0.850000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(60\) 0 0
\(61\) −1.20002 0.497066i −1.20002 0.497066i −0.309017 0.951057i \(-0.600000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(62\) 0 0
\(63\) −3.51462 + 1.45580i −3.51462 + 1.45580i
\(64\) 2.61803i 2.61803i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 1.53884 + 2.11803i 1.53884 + 2.11803i
\(69\) 0 0
\(70\) 0 0
\(71\) 0.178671 + 0.431351i 0.178671 + 0.431351i 0.987688 0.156434i \(-0.0500000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(72\) 5.87216i 5.87216i
\(73\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(74\) −0.760661 + 1.83640i −0.760661 + 1.83640i
\(75\) −1.57547 0.652583i −1.57547 0.652583i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0.178671 0.431351i 0.178671 0.431351i −0.809017 0.587785i \(-0.800000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(80\) 0 0
\(81\) 0.732410i 0.732410i
\(82\) 0 0
\(83\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(84\) 8.90144 8.90144
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 1.34500 1.34500i 1.34500 1.34500i
\(95\) 0 0
\(96\) 2.00844 4.84881i 2.00844 4.84881i
\(97\) 1.40505 0.581990i 1.40505 0.581990i 0.453990 0.891007i \(-0.350000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(98\) 5.65950i 5.65950i
\(99\) 0 0
\(100\) 1.85123 + 1.85123i 1.85123 + 1.85123i
\(101\) 0.312869 0.312869 0.156434 0.987688i \(-0.450000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(102\) 0.757212 + 3.15401i 0.757212 + 3.15401i
\(103\) −1.97538 −1.97538 −0.987688 0.156434i \(-0.950000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 1.72708i 1.72708i
\(107\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(108\) −1.55127 + 3.74510i −1.55127 + 3.74510i
\(109\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(110\) 0 0
\(111\) −1.26007 + 1.26007i −1.26007 + 1.26007i
\(112\) −5.96104 2.46914i −5.96104 2.46914i
\(113\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 1.17557 1.17557
\(119\) 1.93874 0.465451i 1.93874 0.465451i
\(120\) 0 0
\(121\) −0.707107 0.707107i −0.707107 0.707107i
\(122\) 0.945476 + 2.28258i 0.945476 + 2.28258i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 6.68521 + 2.76910i 6.68521 + 2.76910i
\(127\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(128\) −1.34500 + 1.34500i −1.34500 + 1.34500i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.40505 + 0.581990i −1.40505 + 0.581990i −0.951057 0.309017i \(-0.900000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0.481456 3.03979i 0.481456 3.03979i
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(140\) 0 0
\(141\) 1.57547 0.652583i 1.57547 0.652583i
\(142\) 0.339853 0.820478i 0.339853 0.820478i
\(143\) 0 0
\(144\) 4.36593 4.36593i 4.36593 4.36593i
\(145\) 0 0
\(146\) 0 0
\(147\) 1.94168 4.68763i 1.94168 4.68763i
\(148\) 2.52758 1.04696i 2.52758 1.04696i
\(149\) 1.97538i 1.97538i 0.156434 + 0.987688i \(0.450000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(150\) 1.24129 + 2.99673i 1.24129 + 2.99673i
\(151\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(152\) 0 0
\(153\) −0.298474 + 1.88449i −0.298474 + 1.88449i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1.78201i 1.78201i 0.453990 + 0.891007i \(0.350000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(158\) −0.820478 + 0.339853i −0.820478 + 0.339853i
\(159\) 0.592533 1.43050i 0.592533 1.43050i
\(160\) 0 0
\(161\) 0 0
\(162\) −0.985090 + 0.985090i −0.985090 + 0.985090i
\(163\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 2.68999i 2.68999i
\(167\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(168\) −7.39936 7.39936i −7.39936 7.39936i
\(169\) −1.00000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −0.0600500 0.144974i −0.0600500 0.144974i 0.891007 0.453990i \(-0.150000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(174\) 0 0
\(175\) 1.84206 0.763007i 1.84206 0.763007i
\(176\) 0 0
\(177\) 0.973696 + 0.403318i 0.973696 + 0.403318i
\(178\) −2.55834 + 2.55834i −2.55834 + 2.55834i
\(179\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(180\) 0 0
\(181\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(182\) 0 0
\(183\) 2.21498i 2.21498i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −2.61803 −2.61803
\(189\) 2.18296 + 2.18296i 2.18296 + 2.18296i
\(190\) 0 0
\(191\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) −4.12464 + 1.70848i −4.12464 + 1.70848i
\(193\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(194\) −2.67256 1.10701i −2.67256 1.10701i
\(195\) 0 0
\(196\) −5.50811 + 5.50811i −5.50811 + 5.50811i
\(197\) 1.70711 + 0.707107i 1.70711 + 0.707107i 1.00000 \(0\)
0.707107 + 0.707107i \(0.250000\pi\)
\(198\) 0 0
\(199\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(200\) 3.07768i 3.07768i
\(201\) 0 0
\(202\) −0.420808 0.420808i −0.420808 0.420808i
\(203\) 0 0
\(204\) 2.33269 3.80660i 2.33269 3.80660i
\(205\) 0 0
\(206\) 2.65688 + 2.65688i 2.65688 + 2.65688i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(212\) −1.68088 + 1.68088i −1.68088 + 1.68088i
\(213\) 0.562984 0.562984i 0.562984 0.562984i
\(214\) 0 0
\(215\) 0 0
\(216\) 4.40263 1.82363i 4.40263 1.82363i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 3.38959 3.38959
\(223\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(224\) 2.34830 + 5.66929i 2.34830 + 5.66929i
\(225\) 1.90798i 1.90798i
\(226\) 0 0
\(227\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(228\) 0 0
\(229\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.14412 1.14412i −1.14412 1.14412i
\(237\) −0.796180 −0.796180
\(238\) −3.23364 1.98158i −3.23364 1.98158i
\(239\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(240\) 0 0
\(241\) 0.399903 + 0.965451i 0.399903 + 0.965451i 0.987688 + 0.156434i \(0.0500000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(242\) 1.90211i 1.90211i
\(243\) 0.276607 0.114574i 0.276607 0.114574i
\(244\) 1.30134 3.14170i 1.30134 3.14170i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −0.922891 + 2.22806i −0.922891 + 2.22806i
\(250\) 0 0
\(251\) 0.312869i 0.312869i −0.987688 0.156434i \(-0.950000\pi\)
0.987688 0.156434i \(-0.0500000\pi\)
\(252\) −3.81134 9.20140i −3.81134 9.20140i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(258\) 0 0
\(259\) 2.08355i 2.08355i
\(260\) 0 0
\(261\) 0 0
\(262\) 2.67256 + 1.10701i 2.67256 + 1.10701i
\(263\) 0.437016 0.437016i 0.437016 0.437016i −0.453990 0.891007i \(-0.650000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −2.99673 + 1.24129i −2.99673 + 1.24129i
\(268\) 0 0
\(269\) −0.292893 0.707107i −0.292893 0.707107i 0.707107 0.707107i \(-0.250000\pi\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −0.312869 −0.312869 −0.156434 0.987688i \(-0.550000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(272\) −2.61803 + 1.90211i −2.61803 + 1.90211i
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0.431351 0.178671i 0.431351 0.178671i −0.156434 0.987688i \(-0.550000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(282\) −2.99673 1.24129i −2.99673 1.24129i
\(283\) 0.763007 1.84206i 0.763007 1.84206i 0.309017 0.951057i \(-0.400000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(284\) −1.12929 + 0.467768i −1.12929 + 0.467768i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −5.87216 −5.87216
\(289\) 0.309017 0.951057i 0.309017 0.951057i
\(290\) 0 0
\(291\) −1.83382 1.83382i −1.83382 1.83382i
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) −8.91640 + 3.69329i −8.91640 + 3.69329i
\(295\) 0 0
\(296\) −2.97135 1.23078i −2.97135 1.23078i
\(297\) 0 0
\(298\) 2.65688 2.65688i 2.65688 2.65688i
\(299\) 0 0
\(300\) 1.70848 4.12464i 1.70848 4.12464i
\(301\) 0 0
\(302\) 0 0
\(303\) −0.204173 0.492917i −0.204173 0.492917i
\(304\) 0 0
\(305\) 0 0
\(306\) 2.93608 2.13319i 2.93608 2.13319i
\(307\) −0.312869 −0.312869 −0.156434 0.987688i \(-0.550000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(308\) 0 0
\(309\) 1.28910 + 3.11215i 1.28910 + 3.11215i
\(310\) 0 0
\(311\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(312\) 0 0
\(313\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(314\) 2.39680 2.39680i 2.39680 2.39680i
\(315\) 0 0
\(316\) 1.12929 + 0.467768i 1.12929 + 0.467768i
\(317\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(318\) −2.72097 + 1.12706i −2.72097 + 1.12706i
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.91748 1.91748
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −0.763007 + 1.84206i −0.763007 + 1.84206i
\(330\) 0 0
\(331\) −1.34500 + 1.34500i −1.34500 + 1.34500i −0.453990 + 0.891007i \(0.650000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(332\) 2.61803 2.61803i 2.61803 2.61803i
\(333\) 1.84206 + 0.763007i 1.84206 + 0.763007i
\(334\) 0 0
\(335\) 0 0
\(336\) 11.0028i 11.0028i
\(337\) 0.0600500 + 0.144974i 0.0600500 + 0.144974i 0.951057 0.309017i \(-0.100000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(338\) 1.34500 + 1.34500i 1.34500 + 1.34500i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.50723 + 3.63877i 1.50723 + 3.63877i
\(344\) 0 0
\(345\) 0 0
\(346\) −0.114222 + 0.275756i −0.114222 + 0.275756i
\(347\) 1.57547 + 0.652583i 1.57547 + 0.652583i 0.987688 0.156434i \(-0.0500000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(348\) 0 0
\(349\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(350\) −3.50381 1.45133i −3.50381 1.45133i
\(351\) 0 0
\(352\) 0 0
\(353\) 1.78201i 1.78201i −0.453990 0.891007i \(-0.650000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(354\) −0.767157 1.85208i −0.767157 1.85208i
\(355\) 0 0
\(356\) 4.97980 4.97980
\(357\) −1.99850 2.75070i −1.99850 2.75070i
\(358\) 0 0
\(359\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(360\) 0 0
\(361\) 1.00000i 1.00000i
\(362\) 0 0
\(363\) −0.652583 + 1.57547i −0.652583 + 1.57547i
\(364\) 0 0
\(365\) 0 0
\(366\) 2.97914 2.97914i 2.97914 2.97914i
\(367\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.692796 + 1.67256i 0.692796 + 1.67256i
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 2.17625 + 2.17625i 2.17625 + 2.17625i
\(377\) 0 0
\(378\) 5.87216i 5.87216i
\(379\) −0.144974 + 0.0600500i −0.144974 + 0.0600500i −0.453990 0.891007i \(-0.650000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.90211 1.90211i 1.90211 1.90211i
\(383\) −1.39680 + 1.39680i −1.39680 + 1.39680i −0.587785 + 0.809017i \(0.700000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(384\) 2.99673 + 1.24129i 2.99673 + 1.24129i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 1.52367 + 3.67846i 1.52367 + 3.67846i
\(389\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 9.15727 9.15727
\(393\) 1.83382 + 1.83382i 1.83382 + 1.83382i
\(394\) −1.34500 3.24711i −1.34500 3.24711i
\(395\) 0 0
\(396\) 0 0
\(397\) 0.744220 1.79671i 0.744220 1.79671i 0.156434 0.987688i \(-0.450000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −2.28825 + 2.28825i −2.28825 + 2.28825i
\(401\) −1.57547 0.652583i −1.57547 0.652583i −0.587785 0.809017i \(-0.700000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.819101i 0.819101i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −5.10330 + 1.22519i −5.10330 + 1.22519i
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 5.17160i 5.17160i
\(413\) −1.13846 + 0.471565i −1.13846 + 0.471565i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) −1.34915 1.34915i −1.34915 1.34915i
\(424\) 2.79448 2.79448
\(425\) 0.156434 0.987688i 0.156434 0.987688i
\(426\) −1.51442 −1.51442
\(427\) −1.83125 1.83125i −1.83125 1.83125i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −0.581990 + 1.40505i −0.581990 + 1.40505i 0.309017 + 0.951057i \(0.400000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(432\) −4.62920 1.91748i −4.62920 1.91748i
\(433\) 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 0
\(438\) 0 0
\(439\) 0.707107 + 1.70711i 0.707107 + 1.70711i 0.707107 + 0.707107i \(0.250000\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −5.67696 −5.67696
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) −3.29892 3.29892i −3.29892 3.29892i
\(445\) 0 0
\(446\) 0 0
\(447\) 3.11215 1.28910i 3.11215 1.28910i
\(448\) 1.99758 4.82258i 1.99758 4.82258i
\(449\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(450\) 2.56623 2.56623i 2.56623 2.56623i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.221232 + 0.221232i 0.221232 + 0.221232i 0.809017 0.587785i \(-0.200000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(458\) 0 0
\(459\) 1.50558 0.361458i 1.50558 0.361458i
\(460\) 0 0
\(461\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(462\) 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 \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 2.80751 1.16291i 2.80751 1.16291i
\(472\) 1.90211i 1.90211i
\(473\) 0 0
\(474\) 1.07086 + 1.07086i 1.07086 + 1.07086i
\(475\) 0 0
\(476\) 1.21857 + 5.07570i 1.21857 + 5.07570i
\(477\) −1.73241 −1.73241
\(478\) 1.58114 + 1.58114i 1.58114 + 1.58114i
\(479\) −0.763007 1.84206i −0.763007 1.84206i −0.453990 0.891007i \(-0.650000\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.760661 1.83640i 0.760661 1.83640i
\(483\) 0 0
\(484\) 1.85123 1.85123i 1.85123 1.85123i
\(485\) 0 0
\(486\) −0.526137 0.217933i −0.526137 0.217933i
\(487\) −0.707107 + 1.70711i −0.707107 + 1.70711i 1.00000i \(0.5\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(488\) −3.69329 + 1.52981i −3.69329 + 1.52981i
\(489\) 0 0
\(490\) 0 0
\(491\) 1.26007 + 1.26007i 1.26007 + 1.26007i 0.951057 + 0.309017i \(0.100000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.930903i 0.930903i
\(498\) 4.23801 1.75544i 4.23801 1.75544i
\(499\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.420808 + 0.420808i −0.420808 + 0.420808i
\(503\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(504\) −4.48050 + 10.8169i −4.48050 + 10.8169i
\(505\) 0 0
\(506\) 0 0
\(507\) 0.652583 + 1.57547i 0.652583 + 1.57547i
\(508\) 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
\(518\) −2.80237 + 2.80237i −2.80237 + 2.80237i
\(519\) −0.189214 + 0.189214i −0.189214 + 0.189214i
\(520\) 0 0
\(521\) −0.0600500 + 0.144974i −0.0600500 + 0.144974i −0.951057 0.309017i \(-0.900000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) −1.52367 3.67846i −1.52367 3.67846i
\(525\) −2.40420 2.40420i −2.40420 2.40420i
\(526\) −1.17557 −1.17557
\(527\) 0 0
\(528\) 0 0
\(529\) −0.707107 0.707107i −0.707107 0.707107i
\(530\) 0 0
\(531\) 1.17920i 1.17920i
\(532\) 0 0
\(533\) 0 0
\(534\) 5.70012 + 2.36107i 5.70012 + 2.36107i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −0.557116 + 1.34500i −0.557116 + 1.34500i
\(539\) 0 0
\(540\) 0 0
\(541\) −0.0600500 0.144974i −0.0600500 0.144974i 0.891007 0.453990i \(-0.150000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(542\) 0.420808 + 0.420808i 0.420808 + 0.420808i
\(543\) 0 0
\(544\) 3.03979 + 0.481456i 3.03979 + 0.481456i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(548\) 0 0
\(549\) 2.28962 0.948393i 2.28962 0.948393i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0.658248 0.658248i 0.658248 0.658248i
\(554\) −0.820478 0.339853i −0.820478 0.339853i
\(555\) 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 \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(564\) 1.70848 + 4.12464i 1.70848 + 4.12464i
\(565\) 0 0
\(566\) −3.50381 + 1.45133i −3.50381 + 1.45133i
\(567\) 0.558835 1.34915i 0.558835 1.34915i
\(568\) 1.32756 + 0.549894i 1.32756 + 0.549894i
\(569\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(570\) 0 0
\(571\) 1.79671 + 0.744220i 1.79671 + 0.744220i 0.987688 + 0.156434i \(0.0500000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(572\) 0 0
\(573\) 2.22806 0.922891i 2.22806 0.922891i
\(574\) 0 0
\(575\) 0 0
\(576\) 3.53211 + 3.53211i 3.53211 + 3.53211i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −1.69480 + 0.863541i −1.69480 + 0.863541i
\(579\) 0 0
\(580\) 0 0
\(581\) −1.07906 2.60507i −1.07906 2.60507i
\(582\) 4.93296i 4.93296i
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(588\) 12.2724 + 5.08338i 12.2724 + 5.08338i
\(589\) 0 0
\(590\) 0 0
\(591\) 3.15095i 3.15095i
\(592\) 1.29411 + 3.12427i 1.29411 + 3.12427i
\(593\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −5.17160 −5.17160
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) −4.84881 + 2.00844i −4.84881 + 2.00844i
\(601\) −0.497066 + 1.20002i −0.497066 + 1.20002i 0.453990 + 0.891007i \(0.350000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) −0.388360 + 0.937583i −0.388360 + 0.937583i
\(607\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −4.93366 0.781415i −4.93366 0.781415i
\(613\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(614\) 0.420808 + 0.420808i 0.420808 + 0.420808i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.79671 + 0.744220i −1.79671 + 0.744220i −0.809017 + 0.587785i \(0.800000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(618\) 2.45201 5.91967i 2.45201 5.91967i
\(619\) −0.707107 0.292893i −0.707107 0.292893i 1.00000i \(-0.5\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.45133 3.50381i 1.45133 3.50381i
\(624\) 0 0
\(625\) 1.00000i 1.00000i
\(626\) 0 0
\(627\) 0 0
\(628\) −4.66537 −4.66537
\(629\) −0.891007 0.546010i −0.891007 0.546010i
\(630\) 0 0
\(631\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(632\) −0.549894 1.32756i −0.549894 1.32756i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 3.74510 + 1.55127i 3.74510 + 1.55127i
\(637\) 0 0
\(638\) 0 0
\(639\) −0.823009 0.340902i −0.823009 0.340902i
\(640\) 0 0
\(641\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(642\) 0 0
\(643\) 0.497066 + 1.20002i 0.497066 + 1.20002i 0.951057 + 0.309017i \(0.100000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.78201 −1.78201 −0.891007 0.453990i \(-0.850000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(648\) −1.59391 1.59391i −1.59391 1.59391i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0.965451 + 0.399903i 0.965451 + 0.399903i 0.809017 0.587785i \(-0.200000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 3.50381 1.45133i 3.50381 1.45133i
\(659\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(660\) 0 0
\(661\) 0.831254 + 0.831254i 0.831254 + 0.831254i 0.987688 0.156434i \(-0.0500000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(662\) 3.61803 3.61803
\(663\) 0 0
\(664\) −4.35250 −4.35250
\(665\) 0 0
\(666\) −1.45133 3.50381i −1.45133 3.50381i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 7.39936 7.39936i 7.39936 7.39936i
\(673\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(674\) 0.114222 0.275756i 0.114222 0.275756i
\(675\) 1.43050 0.592533i 1.43050 0.592533i
\(676\) 2.61803i 2.61803i
\(677\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(678\) 0 0
\(679\) 3.03225 3.03225
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.497066 1.20002i −0.497066 1.20002i −0.951057 0.309017i \(-0.900000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 2.86692 6.92135i 2.86692 6.92135i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(692\) 0.379546 0.157213i 0.379546 0.157213i
\(693\) 0 0
\(694\) −1.24129 2.99673i −1.24129 2.99673i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 1.99758 + 4.82258i 1.99758 + 4.82258i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −2.39680 + 2.39680i −2.39680 + 2.39680i
\(707\) 0.576324 + 0.238721i 0.576324 + 0.238721i
\(708\) −1.05590 + 2.54917i −1.05590 + 2.54917i
\(709\) 1.84206 0.763007i 1.84206 0.763007i 0.891007 0.453990i \(-0.150000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(710\) 0 0
\(711\) 0.340902 + 0.823009i 0.340902 + 0.823009i
\(712\) −4.13948 4.13948i −4.13948 4.13948i
\(713\) 0 0
\(714\) −1.01170 + 6.38765i −1.01170 + 6.38765i
\(715\) 0 0
\(716\) 0 0
\(717\) 0.767157 + 1.85208i 0.767157 + 1.85208i
\(718\) 0 0
\(719\) 1.20002 0.497066i 1.20002 0.497066i 0.309017 0.951057i \(-0.400000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(720\) 0 0
\(721\) −3.63877 1.50723i −3.63877 1.50723i
\(722\) 1.34500 1.34500i 1.34500 1.34500i
\(723\) 1.26007 1.26007i 1.26007 1.26007i
\(724\) 0 0
\(725\) 0 0
\(726\) 2.99673 1.24129i 2.99673 1.24129i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) −0.878910 0.878910i −0.878910 0.878910i
\(730\) 0 0
\(731\) 0 0
\(732\) −5.79890 −5.79890
\(733\) 0.831254 + 0.831254i 0.831254 + 0.831254i 0.987688 0.156434i \(-0.0500000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −1.26007 + 1.26007i −1.26007 + 1.26007i −0.309017 + 0.951057i \(0.600000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 1.31778 3.18139i 1.31778 3.18139i
\(743\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 2.69829 2.69829
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(752\) 3.23607i 3.23607i
\(753\) −0.492917 + 0.204173i −0.492917 + 0.204173i
\(754\) 0 0
\(755\) 0 0
\(756\) −5.71508 + 5.71508i −5.71508 + 5.71508i
\(757\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(758\) 0.275756 + 0.114222i 0.275756 + 0.114222i
\(759\) 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
\(764\) −3.70246 −3.70246
\(765\) 0 0
\(766\) 3.75739 3.75739
\(767\) 0 0
\(768\) −0.652583 1.57547i −0.652583 1.57547i
\(769\) 1.17557i 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.831254 + 0.831254i −0.831254 + 0.831254i −0.987688 0.156434i \(-0.950000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 1.79118 4.32429i 1.79118 4.32429i
\(777\) −3.28258 + 1.35969i −3.28258 + 1.35969i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −6.80839 6.80839i −6.80839 6.80839i
\(785\) 0 0
\(786\) 4.93296i 4.93296i
\(787\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(788\) −1.85123 + 4.46926i −1.85123 + 4.46926i
\(789\) −0.973696 0.403318i −0.973696 0.403318i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) −3.41754 + 1.41559i −3.41754 + 1.41559i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(798\) 0 0
\(799\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(800\) 3.07768 3.07768