Properties

Label 1045.1.w.f.949.2
Level $1045$
Weight $1$
Character 1045.949
Analytic conductor $0.522$
Analytic rank $0$
Dimension $16$
Projective image $D_{20}$
CM discriminant -95
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1045.w (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.521522938201\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{40})\)
Defining polynomial: \(x^{16} - x^{12} + x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{20}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{20} + \cdots)\)

Embedding invariants

Embedding label 949.2
Root \(0.156434 + 0.987688i\) of defining polynomial
Character \(\chi\) \(=\) 1045.949
Dual form 1045.1.w.f.664.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.734572 + 0.533698i) q^{2} +(-0.0966818 - 0.297556i) q^{3} +(-0.0542543 + 0.166977i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.229825 + 0.166977i) q^{6} +(-0.329843 - 1.01515i) q^{8} +(0.729825 - 0.530249i) q^{9} +O(q^{10})\) \(q+(-0.734572 + 0.533698i) q^{2} +(-0.0966818 - 0.297556i) q^{3} +(-0.0542543 + 0.166977i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.229825 + 0.166977i) q^{6} +(-0.329843 - 1.01515i) q^{8} +(0.729825 - 0.530249i) q^{9} -0.907981 q^{10} +(-0.587785 - 0.809017i) q^{11} +0.0549306 q^{12} +(1.44168 - 1.04744i) q^{13} +(0.0966818 - 0.297556i) q^{15} +(0.642040 + 0.466469i) q^{16} +(-0.253116 + 0.779012i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(-0.142040 + 0.103198i) q^{20} +(0.863541 + 0.280582i) q^{22} +(-0.270175 + 0.196294i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.500000 + 1.53884i) q^{26} +(-0.481456 - 0.349798i) q^{27} +(0.0877853 + 0.270175i) q^{30} +0.346818 q^{32} +(-0.183900 + 0.253116i) q^{33} +(0.0489435 + 0.150633i) q^{36} +(-0.610425 + 1.87869i) q^{37} +(0.734572 + 0.533698i) q^{38} +(-0.451057 - 0.327712i) q^{39} +(0.329843 - 1.01515i) q^{40} +(0.166977 - 0.0542543i) q^{44} +0.902113 q^{45} +(0.0767271 - 0.236142i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.734572 - 0.533698i) q^{50} +(0.0966818 + 0.297556i) q^{52} +(-1.14412 + 0.831254i) q^{53} +0.540350 q^{54} -1.00000i q^{55} +(-0.253116 + 0.183900i) q^{57} +(0.0444398 + 0.0322874i) q^{60} +(0.951057 + 0.690983i) q^{61} +(-0.896802 + 0.651565i) q^{64} +1.78201 q^{65} -0.284079i q^{66} +1.97538 q^{67} +(-0.779012 - 0.565985i) q^{72} +(-0.554254 - 1.70582i) q^{74} +(0.253116 - 0.183900i) q^{75} +0.175571 q^{76} +0.506233 q^{78} +(0.245237 + 0.754763i) q^{80} +(0.221232 - 0.680881i) q^{81} +(-0.627399 + 0.863541i) q^{88} +(-0.662667 + 0.481456i) q^{90} +(0.309017 - 0.951057i) q^{95} +(-0.0335310 - 0.103198i) q^{96} +(0.734572 - 0.533698i) q^{97} +0.907981 q^{98} +(-0.857960 - 0.278768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{4} + 4q^{5} - 12q^{6} - 4q^{9} + O(q^{10}) \) \( 16q - 4q^{4} + 4q^{5} - 12q^{6} - 4q^{9} + 4q^{16} + 4q^{19} + 4q^{20} - 20q^{24} - 4q^{25} - 8q^{26} - 8q^{30} + 16q^{36} + 8q^{39} - 16q^{45} - 4q^{49} + 40q^{54} + 4q^{64} - 12q^{74} - 16q^{76} + 16q^{80} + 4q^{81} - 4q^{95} + 12q^{96} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).

\(n\) \(496\) \(761\) \(837\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.734572 + 0.533698i −0.734572 + 0.533698i −0.891007 0.453990i \(-0.850000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(3\) −0.0966818 0.297556i −0.0966818 0.297556i 0.891007 0.453990i \(-0.150000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(4\) −0.0542543 + 0.166977i −0.0542543 + 0.166977i
\(5\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(6\) 0.229825 + 0.166977i 0.229825 + 0.166977i
\(7\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(8\) −0.329843 1.01515i −0.329843 1.01515i
\(9\) 0.729825 0.530249i 0.729825 0.530249i
\(10\) −0.907981 −0.907981
\(11\) −0.587785 0.809017i −0.587785 0.809017i
\(12\) 0.0549306 0.0549306
\(13\) 1.44168 1.04744i 1.44168 1.04744i 0.453990 0.891007i \(-0.350000\pi\)
0.987688 0.156434i \(-0.0500000\pi\)
\(14\) 0 0
\(15\) 0.0966818 0.297556i 0.0966818 0.297556i
\(16\) 0.642040 + 0.466469i 0.642040 + 0.466469i
\(17\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(18\) −0.253116 + 0.779012i −0.253116 + 0.779012i
\(19\) −0.309017 0.951057i −0.309017 0.951057i
\(20\) −0.142040 + 0.103198i −0.142040 + 0.103198i
\(21\) 0 0
\(22\) 0.863541 + 0.280582i 0.863541 + 0.280582i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) −0.270175 + 0.196294i −0.270175 + 0.196294i
\(25\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(26\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(27\) −0.481456 0.349798i −0.481456 0.349798i
\(28\) 0 0
\(29\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(30\) 0.0877853 + 0.270175i 0.0877853 + 0.270175i
\(31\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(32\) 0.346818 0.346818
\(33\) −0.183900 + 0.253116i −0.183900 + 0.253116i
\(34\) 0 0
\(35\) 0 0
\(36\) 0.0489435 + 0.150633i 0.0489435 + 0.150633i
\(37\) −0.610425 + 1.87869i −0.610425 + 1.87869i −0.156434 + 0.987688i \(0.550000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(38\) 0.734572 + 0.533698i 0.734572 + 0.533698i
\(39\) −0.451057 0.327712i −0.451057 0.327712i
\(40\) 0.329843 1.01515i 0.329843 1.01515i
\(41\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0.166977 0.0542543i 0.166977 0.0542543i
\(45\) 0.902113 0.902113
\(46\) 0 0
\(47\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(48\) 0.0767271 0.236142i 0.0767271 0.236142i
\(49\) −0.809017 0.587785i −0.809017 0.587785i
\(50\) −0.734572 0.533698i −0.734572 0.533698i
\(51\) 0 0
\(52\) 0.0966818 + 0.297556i 0.0966818 + 0.297556i
\(53\) −1.14412 + 0.831254i −1.14412 + 0.831254i −0.987688 0.156434i \(-0.950000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(54\) 0.540350 0.540350
\(55\) 1.00000i 1.00000i
\(56\) 0 0
\(57\) −0.253116 + 0.183900i −0.253116 + 0.183900i
\(58\) 0 0
\(59\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(60\) 0.0444398 + 0.0322874i 0.0444398 + 0.0322874i
\(61\) 0.951057 + 0.690983i 0.951057 + 0.690983i 0.951057 0.309017i \(-0.100000\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.896802 + 0.651565i −0.896802 + 0.651565i
\(65\) 1.78201 1.78201
\(66\) 0.284079i 0.284079i
\(67\) 1.97538 1.97538 0.987688 0.156434i \(-0.0500000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(72\) −0.779012 0.565985i −0.779012 0.565985i
\(73\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(74\) −0.554254 1.70582i −0.554254 1.70582i
\(75\) 0.253116 0.183900i 0.253116 0.183900i
\(76\) 0.175571 0.175571
\(77\) 0 0
\(78\) 0.506233 0.506233
\(79\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(80\) 0.245237 + 0.754763i 0.245237 + 0.754763i
\(81\) 0.221232 0.680881i 0.221232 0.680881i
\(82\) 0 0
\(83\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −0.627399 + 0.863541i −0.627399 + 0.863541i
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) −0.662667 + 0.481456i −0.662667 + 0.481456i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.309017 0.951057i 0.309017 0.951057i
\(96\) −0.0335310 0.103198i −0.0335310 0.103198i
\(97\) 0.734572 0.533698i 0.734572 0.533698i −0.156434 0.987688i \(-0.550000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(98\) 0.907981 0.907981
\(99\) −0.857960 0.278768i −0.857960 0.278768i
\(100\) −0.175571 −0.175571
\(101\) −1.53884 + 1.11803i −1.53884 + 1.11803i −0.587785 + 0.809017i \(0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(102\) 0 0
\(103\) −0.550672 + 1.69480i −0.550672 + 1.69480i 0.156434 + 0.987688i \(0.450000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(104\) −1.53884 1.11803i −1.53884 1.11803i
\(105\) 0 0
\(106\) 0.396802 1.22123i 0.396802 1.22123i
\(107\) 0.610425 + 1.87869i 0.610425 + 1.87869i 0.453990 + 0.891007i \(0.350000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(108\) 0.0845294 0.0614142i 0.0845294 0.0614142i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0.533698 + 0.734572i 0.533698 + 0.734572i
\(111\) 0.618034 0.618034
\(112\) 0 0
\(113\) −0.550672 1.69480i −0.550672 1.69480i −0.707107 0.707107i \(-0.750000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(114\) 0.0877853 0.270175i 0.0877853 0.270175i
\(115\) 0 0
\(116\) 0 0
\(117\) 0.496769 1.52890i 0.496769 1.52890i
\(118\) 0 0
\(119\) 0 0
\(120\) −0.333955 −0.333955
\(121\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(122\) −1.06740 −1.06740
\(123\) 0 0
\(124\) 0 0
\(125\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(126\) 0 0
\(127\) −1.14412 0.831254i −1.14412 0.831254i −0.156434 0.987688i \(-0.550000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(128\) 0.203854 0.627399i 0.203854 0.627399i
\(129\) 0 0
\(130\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(131\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(132\) −0.0322874 0.0444398i −0.0322874 0.0444398i
\(133\) 0 0
\(134\) −1.45106 + 1.05425i −1.45106 + 1.05425i
\(135\) −0.183900 0.565985i −0.183900 0.565985i
\(136\) 0 0
\(137\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(138\) 0 0
\(139\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.69480 0.550672i −1.69480 0.550672i
\(144\) 0.715921 0.715921
\(145\) 0 0
\(146\) 0 0
\(147\) −0.0966818 + 0.297556i −0.0966818 + 0.297556i
\(148\) −0.280582 0.203854i −0.280582 0.203854i
\(149\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(150\) −0.0877853 + 0.270175i −0.0877853 + 0.270175i
\(151\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(152\) −0.863541 + 0.627399i −0.863541 + 0.627399i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0.0791922 0.0575365i 0.0791922 0.0575365i
\(157\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(158\) 0 0
\(159\) 0.357960 + 0.260074i 0.357960 + 0.260074i
\(160\) 0.280582 + 0.203854i 0.280582 + 0.203854i
\(161\) 0 0
\(162\) 0.200874 + 0.618227i 0.200874 + 0.618227i
\(163\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(164\) 0 0
\(165\) −0.297556 + 0.0966818i −0.297556 + 0.0966818i
\(166\) 0 0
\(167\) 0.253116 0.183900i 0.253116 0.183900i −0.453990 0.891007i \(-0.650000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(168\) 0 0
\(169\) 0.672288 2.06909i 0.672288 2.06909i
\(170\) 0 0
\(171\) −0.729825 0.530249i −0.729825 0.530249i
\(172\) 0 0
\(173\) −0.437016 1.34500i −0.437016 1.34500i −0.891007 0.453990i \(-0.850000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.793604i 0.793604i
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(180\) −0.0489435 + 0.150633i −0.0489435 + 0.150633i
\(181\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(182\) 0 0
\(183\) 0.113656 0.349798i 0.113656 0.349798i
\(184\) 0 0
\(185\) −1.59811 + 1.16110i −1.59811 + 1.16110i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0.280582 + 0.863541i 0.280582 + 0.863541i
\(191\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(192\) 0.280582 + 0.203854i 0.280582 + 0.203854i
\(193\) 0.253116 + 0.183900i 0.253116 + 0.183900i 0.707107 0.707107i \(-0.250000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(194\) −0.254763 + 0.784079i −0.254763 + 0.784079i
\(195\) −0.172288 0.530249i −0.172288 0.530249i
\(196\) 0.142040 0.103198i 0.142040 0.103198i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0.779012 0.253116i 0.779012 0.253116i
\(199\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(200\) 0.863541 0.627399i 0.863541 0.627399i
\(201\) −0.190983 0.587785i −0.190983 0.587785i
\(202\) 0.533698 1.64255i 0.533698 1.64255i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −0.500000 1.53884i −0.500000 1.53884i
\(207\) 0 0
\(208\) 1.41421 1.41421
\(209\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(210\) 0 0
\(211\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(212\) −0.0767271 0.236142i −0.0767271 0.236142i
\(213\) 0 0
\(214\) −1.45106 1.05425i −1.45106 1.05425i
\(215\) 0 0
\(216\) −0.196294 + 0.604130i −0.196294 + 0.604130i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0.166977 + 0.0542543i 0.166977 + 0.0542543i
\(221\) 0 0
\(222\) −0.453990 + 0.329843i −0.453990 + 0.329843i
\(223\) 0.437016 + 1.34500i 0.437016 + 1.34500i 0.891007 + 0.453990i \(0.150000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(224\) 0 0
\(225\) 0.729825 + 0.530249i 0.729825 + 0.530249i
\(226\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(227\) 0.0966818 0.297556i 0.0966818 0.297556i −0.891007 0.453990i \(-0.850000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(228\) −0.0169745 0.0522421i −0.0169745 0.0522421i
\(229\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(234\) 0.451057 + 1.38821i 0.451057 + 1.38821i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(240\) 0.200874 0.145944i 0.200874 0.145944i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −0.280582 0.863541i −0.280582 0.863541i
\(243\) −0.819101 −0.819101
\(244\) −0.166977 + 0.121316i −0.166977 + 0.121316i
\(245\) −0.309017 0.951057i −0.309017 0.951057i
\(246\) 0 0
\(247\) −1.44168 1.04744i −1.44168 1.04744i
\(248\) 0 0
\(249\) 0 0
\(250\) −0.280582 0.863541i −0.280582 0.863541i
\(251\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 1.28408 1.28408
\(255\) 0 0
\(256\) −0.157452 0.484587i −0.157452 0.484587i
\(257\) 0.550672 1.69480i 0.550672 1.69480i −0.156434 0.987688i \(-0.550000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.0966818 + 0.297556i −0.0966818 + 0.297556i
\(261\) 0 0
\(262\) 1.18856 0.863541i 1.18856 0.863541i
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0.317610 + 0.103198i 0.317610 + 0.103198i
\(265\) −1.41421 −1.41421
\(266\) 0 0
\(267\) 0 0
\(268\) −0.107173 + 0.329843i −0.107173 + 0.329843i
\(269\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(270\) 0.437153 + 0.317610i 0.437153 + 0.317610i
\(271\) 0.587785 1.80902i 0.587785 1.80902i 1.00000i \(-0.5\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.587785 0.809017i 0.587785 0.809017i
\(276\) 0 0
\(277\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(282\) 0 0
\(283\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(284\) 0 0
\(285\) −0.312869 −0.312869
\(286\) 1.53884 0.500000i 1.53884 0.500000i
\(287\) 0 0
\(288\) 0.253116 0.183900i 0.253116 0.183900i
\(289\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(290\) 0 0
\(291\) −0.229825 0.166977i −0.229825 0.166977i
\(292\) 0 0
\(293\) −0.280582 + 0.863541i −0.280582 + 0.863541i 0.707107 + 0.707107i \(0.250000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(294\) −0.0877853 0.270175i −0.0877853 0.270175i
\(295\) 0 0
\(296\) 2.10851 2.10851
\(297\) 0.595112i 0.595112i
\(298\) 0 0
\(299\) 0 0
\(300\) 0.0169745 + 0.0522421i 0.0169745 + 0.0522421i
\(301\) 0 0
\(302\) 0 0
\(303\) 0.481456 + 0.349798i 0.481456 + 0.349798i
\(304\) 0.245237 0.754763i 0.245237 0.754763i
\(305\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(306\) 0 0
\(307\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(308\) 0 0
\(309\) 0.557537 0.557537
\(310\) 0 0
\(311\) 0.587785 + 1.80902i 0.587785 + 1.80902i 0.587785 + 0.809017i \(0.300000\pi\)
1.00000i \(0.5\pi\)
\(312\) −0.183900 + 0.565985i −0.183900 + 0.565985i
\(313\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.14412 0.831254i 1.14412 0.831254i 0.156434 0.987688i \(-0.450000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(318\) −0.401748 −0.401748
\(319\) 0 0
\(320\) −1.10851 −1.10851
\(321\) 0.500000 0.363271i 0.500000 0.363271i
\(322\) 0 0
\(323\) 0 0
\(324\) 0.101689 + 0.0738814i 0.101689 + 0.0738814i
\(325\) 1.44168 + 1.04744i 1.44168 + 1.04744i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0.166977 0.229825i 0.166977 0.229825i
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0.550672 + 1.69480i 0.550672 + 1.69480i
\(334\) −0.0877853 + 0.270175i −0.0877853 + 0.270175i
\(335\) 1.59811 + 1.16110i 1.59811 + 1.16110i
\(336\) 0 0
\(337\) −0.437016 + 1.34500i −0.437016 + 1.34500i 0.453990 + 0.891007i \(0.350000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(338\) 0.610425 + 1.87869i 0.610425 + 1.87869i
\(339\) −0.451057 + 0.327712i −0.451057 + 0.327712i
\(340\) 0 0
\(341\) 0 0
\(342\) 0.819101 0.819101
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 1.03884 + 0.754763i 1.03884 + 0.754763i
\(347\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(348\) 0 0
\(349\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) −1.06050 −1.06050
\(352\) −0.203854 0.280582i −0.203854 0.280582i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −0.363271 + 1.11803i −0.363271 + 1.11803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(360\) −0.297556 0.915783i −0.297556 0.915783i
\(361\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(362\) 0 0
\(363\) 0.312869 0.312869
\(364\) 0 0
\(365\) 0 0
\(366\) 0.103198 + 0.317610i 0.103198 + 0.317610i
\(367\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0.554254 1.70582i 0.554254 1.70582i
\(371\) 0 0
\(372\) 0 0
\(373\) −1.97538 −1.97538 −0.987688 0.156434i \(-0.950000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(374\) 0 0
\(375\) 0.312869 0.312869
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(380\) 0.142040 + 0.103198i 0.142040 + 0.103198i
\(381\) −0.136729 + 0.420808i −0.136729 + 0.420808i
\(382\) −0.173409 0.533698i −0.173409 0.533698i
\(383\) 1.14412 0.831254i 1.14412 0.831254i 0.156434 0.987688i \(-0.450000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(384\) −0.206396 −0.206396
\(385\) 0 0
\(386\) −0.284079 −0.284079
\(387\) 0 0
\(388\) 0.0492618 + 0.151612i 0.0492618 + 0.151612i
\(389\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(390\) 0.409551 + 0.297556i 0.409551 + 0.297556i
\(391\) 0 0
\(392\) −0.329843 + 1.01515i −0.329843 + 1.01515i
\(393\) 0.156434 + 0.481456i 0.156434 + 0.481456i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.0930960 0.128136i 0.0930960 0.128136i
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) −1.18856 + 0.863541i −1.18856 + 0.863541i
\(399\) 0 0
\(400\) −0.245237 + 0.754763i −0.245237 + 0.754763i
\(401\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(402\) 0.453990 + 0.329843i 0.453990 + 0.329843i
\(403\) 0 0
\(404\) −0.103198 0.317610i −0.103198 0.317610i
\(405\) 0.579192 0.420808i 0.579192 0.420808i
\(406\) 0 0
\(407\) 1.87869 0.610425i 1.87869 0.610425i
\(408\) 0 0
\(409\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.253116 0.183900i −0.253116 0.183900i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0.500000 0.363271i 0.500000 0.363271i
\(417\) 0 0
\(418\) 0.907981i 0.907981i
\(419\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(420\) 0 0
\(421\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 1.22123 + 0.887277i 1.22123 + 0.887277i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −0.346818 −0.346818
\(429\) 0.557537i 0.557537i
\(430\) 0 0
\(431\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(432\) −0.145944 0.449168i −0.145944 0.449168i
\(433\) 0.280582 0.863541i 0.280582 0.863541i −0.707107 0.707107i \(-0.750000\pi\)
0.987688 0.156434i \(-0.0500000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) −1.01515 + 0.329843i −1.01515 + 0.329843i
\(441\) −0.902113 −0.902113
\(442\) 0 0
\(443\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(444\) −0.0335310 + 0.103198i −0.0335310 + 0.103198i
\(445\) 0 0
\(446\) −1.03884 0.754763i −1.03884 0.754763i
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(450\) −0.819101 −0.819101
\(451\) 0 0
\(452\) 0.312869 0.312869
\(453\) 0 0
\(454\) 0.0877853 + 0.270175i 0.0877853 + 0.270175i
\(455\) 0 0
\(456\) 0.270175 + 0.196294i 0.270175 + 0.196294i
\(457\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(468\) 0.228339 + 0.165898i 0.228339 + 0.165898i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.809017 0.587785i 0.809017 0.587785i
\(476\) 0 0
\(477\) −0.394238 + 1.21334i −0.394238 + 1.21334i
\(478\) −0.453990 0.329843i −0.453990 0.329843i
\(479\) 1.53884 + 1.11803i 1.53884 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(480\) 0.0335310 0.103198i 0.0335310 0.103198i
\(481\) 1.08779 + 3.34786i 1.08779 + 3.34786i
\(482\) 0 0
\(483\) 0 0
\(484\) −0.142040 0.103198i −0.142040 0.103198i
\(485\) 0.907981 0.907981
\(486\) 0.601689 0.437153i 0.601689 0.437153i
\(487\) −0.437016 1.34500i −0.437016 1.34500i −0.891007 0.453990i \(-0.850000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(488\) 0.387754 1.19338i 0.387754 1.19338i
\(489\) 0 0
\(490\) 0.734572 + 0.533698i 0.734572 + 0.533698i
\(491\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 1.61803 1.61803
\(495\) −0.530249 0.729825i −0.530249 0.729825i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(500\) −0.142040 0.103198i −0.142040 0.103198i
\(501\) −0.0791922 0.0575365i −0.0791922 0.0575365i
\(502\) 0.453990 1.39724i 0.453990 1.39724i
\(503\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(504\) 0 0
\(505\) −1.90211 −1.90211
\(506\) 0 0
\(507\) −0.680668 −0.680668
\(508\) 0.200874 0.145944i 0.200874 0.145944i
\(509\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.907981 + 0.659687i 0.907981 + 0.659687i
\(513\) −0.183900 + 0.565985i −0.183900 + 0.565985i
\(514\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(515\) −1.44168 + 1.04744i −1.44168 + 1.04744i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −0.357960 + 0.260074i −0.357960 + 0.260074i
\(520\) −0.587785 1.80902i −0.587785 1.80902i
\(521\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(522\) 0 0
\(523\) −1.44168 1.04744i −1.44168 1.04744i −0.987688 0.156434i \(-0.950000\pi\)
−0.453990 0.891007i \(-0.650000\pi\)
\(524\) 0.0877853 0.270175i 0.0877853 0.270175i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.236142 + 0.0767271i −0.236142 + 0.0767271i
\(529\) 1.00000 1.00000
\(530\) 1.03884 0.754763i 1.03884 0.754763i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −0.610425 + 1.87869i −0.610425 + 1.87869i
\(536\) −0.651565 2.00531i −0.651565 2.00531i
\(537\) 0 0
\(538\) 0 0
\(539\) 1.00000i 1.00000i
\(540\) 0.104484 0.104484
\(541\) −0.951057 + 0.690983i −0.951057 + 0.690983i −0.951057 0.309017i \(-0.900000\pi\)
1.00000i \(0.5\pi\)
\(542\) 0.533698 + 1.64255i 0.533698 + 1.64255i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.0966818 0.297556i −0.0966818 0.297556i 0.891007 0.453990i \(-0.150000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(548\) 0 0
\(549\) 1.06050 1.06050
\(550\) 0.907981i 0.907981i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(556\) 0 0
\(557\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0.734572 0.533698i 0.734572 0.533698i −0.156434 0.987688i \(-0.550000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(564\) 0 0
\(565\) 0.550672 1.69480i 0.550672 1.69480i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(570\) 0.229825 0.166977i 0.229825 0.166977i
\(571\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(572\) 0.183900 0.253116i 0.183900 0.253116i
\(573\) 0.193364 0.193364
\(574\) 0 0
\(575\) 0 0
\(576\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(577\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(578\) −0.734572 0.533698i −0.734572 0.533698i
\(579\) 0.0302487 0.0930960i 0.0302487 0.0930960i
\(580\) 0 0
\(581\) 0 0
\(582\) 0.257938 0.257938
\(583\) 1.34500 + 0.437016i 1.34500 + 0.437016i
\(584\) 0 0
\(585\) 1.30056 0.944910i 1.30056 0.944910i
\(586\) −0.254763 0.784079i −0.254763 0.784079i
\(587\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(588\) −0.0444398 0.0322874i −0.0444398 0.0322874i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −1.26827 + 0.921452i −1.26827 + 0.921452i
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) −0.317610 0.437153i −0.317610 0.437153i
\(595\) 0 0
\(596\) 0 0
\(597\) −0.156434 0.481456i −0.156434 0.481456i
\(598\) 0 0
\(599\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(600\) −0.270175 0.196294i −0.270175 0.196294i
\(601\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(602\) 0 0
\(603\) 1.44168 1.04744i 1.44168 1.04744i
\(604\) 0 0
\(605\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(606\) −0.540350 −0.540350
\(607\) −0.253116 + 0.183900i −0.253116 + 0.183900i −0.707107 0.707107i \(-0.750000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(608\) −0.107173 0.329843i −0.107173 0.329843i
\(609\) 0 0
\(610\) −0.863541 0.627399i −0.863541 0.627399i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(614\) 1.03884 0.754763i 1.03884 0.754763i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) −0.409551 + 0.297556i −0.409551 + 0.297556i
\(619\) 0.363271 + 1.11803i 0.363271 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −1.39724 1.01515i −1.39724 1.01515i
\(623\) 0 0
\(624\) −0.136729 0.420808i −0.136729 0.420808i
\(625\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(626\) 0 0
\(627\) 0.297556 + 0.0966818i 0.297556 + 0.0966818i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0.587785 1.80902i 0.587785 1.80902i 1.00000i \(-0.5\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −0.396802 + 1.22123i −0.396802 + 1.22123i
\(635\) −0.437016 1.34500i −0.437016 1.34500i
\(636\) −0.0628473 + 0.0456612i −0.0628473 + 0.0456612i
\(637\) −1.78201 −1.78201
\(638\) 0 0
\(639\) 0 0
\(640\) 0.533698 0.387754i 0.533698 0.387754i
\(641\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(642\) −0.173409 + 0.533698i −0.173409 + 0.533698i
\(643\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(648\) −0.764171 −0.764171
\(649\) 0 0
\(650\) −1.61803 −1.61803
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(654\) 0 0
\(655\) −1.30902 0.951057i −1.30902 0.951057i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0.0549306i 0.0549306i
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −1.30902 0.951057i −1.30902 0.951057i
\(667\) 0 0
\(668\) 0.0169745 + 0.0522421i 0.0169745 + 0.0522421i
\(669\) 0.357960 0.260074i 0.357960 0.260074i
\(670\) −1.79360 −1.79360
\(671\) 1.17557i 1.17557i
\(672\) 0 0
\(673\) −1.59811 + 1.16110i −1.59811 + 1.16110i −0.707107 + 0.707107i \(0.750000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(674\) −0.396802 1.22123i −0.396802 1.22123i
\(675\) 0.183900 0.565985i 0.183900 0.565985i
\(676\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(677\) 0.253116 + 0.183900i 0.253116 + 0.183900i 0.707107 0.707107i \(-0.250000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(678\) 0.156434 0.481456i 0.156434 0.481456i
\(679\) 0 0
\(680\) 0 0
\(681\) −0.0978870 −0.0978870
\(682\) 0 0
\(683\) −0.907981 −0.907981 −0.453990 0.891007i \(-0.650000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(684\) 0.128136 0.0930960i 0.128136 0.0930960i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −0.778768 + 2.39680i −0.778768 + 2.39680i
\(690\) 0 0
\(691\) −1.53884 + 1.11803i −1.53884 + 1.11803i −0.587785 + 0.809017i \(0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(692\) 0.248294 0.248294
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0.453990 + 0.329843i 0.453990 + 0.329843i
\(699\) 0 0
\(700\) 0 0
\(701\) −0.587785 1.80902i −0.587785 1.80902i −0.587785 0.809017i \(-0.700000\pi\)
1.00000i \(-0.5\pi\)
\(702\) 0.779012 0.565985i 0.779012 0.565985i
\(703\) 1.97538 1.97538
\(704\) 1.05425 + 0.342548i 1.05425 + 0.342548i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −1.04744 1.44168i −1.04744 1.44168i
\(716\) 0 0
\(717\) 0.156434 0.113656i 0.156434 0.113656i
\(718\) −0.329843 1.01515i −0.329843 1.01515i
\(719\) −0.363271 + 1.11803i −0.363271 + 1.11803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(720\) 0.579192 + 0.420808i 0.579192 + 0.420808i
\(721\) 0 0
\(722\) 0.280582 0.863541i 0.280582 0.863541i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) −0.229825 + 0.166977i −0.229825 + 0.166977i
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −0.142040 0.437153i −0.142040 0.437153i
\(730\) 0 0
\(731\) 0 0
\(732\) 0.0522421 + 0.0379561i 0.0522421 + 0.0379561i
\(733\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(734\) 0 0
\(735\) −0.253116 + 0.183900i −0.253116 + 0.183900i
\(736\) 0 0
\(737\) −1.16110 1.59811i −1.16110 1.59811i
\(738\) 0 0
\(739\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(740\) −0.107173 0.329843i −0.107173 0.329843i
\(741\) −0.172288 + 0.530249i −0.172288 + 0.530249i
\(742\) 0 0
\(743\) 0.734572 + 0.533698i 0.734572 + 0.533698i 0.891007 0.453990i \(-0.150000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 1.45106 1.05425i 1.45106 1.05425i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) −0.229825 + 0.166977i −0.229825 + 0.166977i
\(751\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(752\) 0 0
\(753\) 0.409551 + 0.297556i 0.409551 + 0.297556i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −1.06740 −1.06740
\(761\) 0.951057 0.690983i 0.951057 0.690983i 1.00000i \(-0.5\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(762\) −0.124147 0.382085i −0.124147 0.382085i
\(763\) 0 0
\(764\) −0.0877853 0.0637797i −0.0877853 0.0637797i
\(765\) 0 0
\(766\) −0.396802 + 1.22123i −0.396802 + 1.22123i
\(767\) 0 0
\(768\) −0.128969 + 0.0937016i −0.128969 + 0.0937016i
\(769\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(770\) 0 0
\(771\) −0.557537 −0.557537
\(772\) −0.0444398 + 0.0322874i −0.0444398 + 0.0322874i
\(773\) 0.0966818 + 0.297556i 0.0966818 + 0.297556i 0.987688 0.156434i \(-0.0500000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −0.784079 0.569667i −0.784079 0.569667i
\(777\) 0 0
\(778\) 0.173409 + 0.533698i 0.173409 + 0.533698i
\(779\) 0 0
\(780\) 0.0978870 0.0978870
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.245237 0.754763i −0.245237 0.754763i
\(785\) 0 0
\(786\) −0.371864 0.270175i −0.371864 0.270175i
\(787\) 1.59811 + 1.16110i 1.59811 + 1.16110i 0.891007 + 0.453990i \(0.150000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.962912i 0.962912i
\(793\) 2.09488 2.09488
\(794\) 0 0
\(795\) 0.136729 + 0.420808i 0.136729 + 0.420808i
\(796\) −0.0877853 + 0.270175i −0.0877853 + 0.270175i
\(797\) 0.734572 + 0.533698i 0.734572 + 0.533698i 0.891007 0.453990i \(-0.150000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)