Properties

Label 1045.1.w.f.284.1
Level $1045$
Weight $1$
Character 1045.284
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 284.1
Root \(-0.453990 + 0.891007i\) of defining polynomial
Character \(\chi\) \(=\) 1045.284
Dual form 1045.1.w.f.379.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.610425 + 1.87869i) q^{2} +(-0.734572 + 0.533698i) q^{3} +(-2.34786 - 1.70582i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.554254 - 1.70582i) q^{6} +(3.03979 - 2.20854i) q^{8} +(-0.0542543 + 0.166977i) q^{9} +O(q^{10})\) \(q+(-0.610425 + 1.87869i) q^{2} +(-0.734572 + 0.533698i) q^{3} +(-2.34786 - 1.70582i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.554254 - 1.70582i) q^{6} +(3.03979 - 2.20854i) q^{8} +(-0.0542543 + 0.166977i) q^{9} +1.97538 q^{10} +(0.951057 + 0.309017i) q^{11} +2.63506 q^{12} +(-0.0966818 + 0.297556i) q^{13} +(0.734572 + 0.533698i) q^{15} +(1.39680 + 4.29892i) q^{16} +(-0.280582 - 0.203854i) q^{18} +(0.809017 - 0.587785i) q^{19} +(-0.896802 + 2.76007i) q^{20} +(-1.16110 + 1.59811i) q^{22} +(-1.05425 + 3.24466i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-0.500000 - 0.363271i) q^{26} +(-0.329843 - 1.01515i) q^{27} +(-1.45106 + 1.05425i) q^{30} -5.17160 q^{32} +(-0.863541 + 0.280582i) q^{33} +(0.412215 - 0.299492i) q^{36} +(1.44168 + 1.04744i) q^{37} +(0.610425 + 1.87869i) q^{38} +(-0.0877853 - 0.270175i) q^{39} +(-3.03979 - 2.20854i) q^{40} +(-1.70582 - 2.34786i) q^{44} +0.175571 q^{45} +(-3.32037 - 2.41239i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.610425 - 1.87869i) q^{50} +(0.734572 - 0.533698i) q^{52} +(-0.437016 + 1.34500i) q^{53} +2.10851 q^{54} -1.00000i q^{55} +(-0.280582 + 0.863541i) q^{57} +(-0.814279 - 2.50609i) q^{60} +(0.587785 + 1.80902i) q^{61} +(1.76007 - 5.41695i) q^{64} +0.312869 q^{65} -1.79360i q^{66} +1.78201 q^{67} +(0.203854 + 0.627399i) q^{72} +(-2.84786 + 2.06909i) q^{74} +(0.280582 - 0.863541i) q^{75} -2.90211 q^{76} +0.561163 q^{78} +(3.65688 - 2.65688i) q^{80} +(0.642040 + 0.466469i) q^{81} +(3.57349 - 1.16110i) q^{88} +(-0.107173 + 0.329843i) q^{90} +(-0.809017 - 0.587785i) q^{95} +(3.79892 - 2.76007i) q^{96} +(0.610425 - 1.87869i) q^{97} -1.97538 q^{98} +(-0.103198 + 0.142040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{4} + 4 q^{5} - 12 q^{6} - 4 q^{9} + O(q^{10}) \) \( 16 q - 4 q^{4} + 4 q^{5} - 12 q^{6} - 4 q^{9} + 4 q^{16} + 4 q^{19} + 4 q^{20} - 20 q^{24} - 4 q^{25} - 8 q^{26} - 8 q^{30} + 16 q^{36} + 8 q^{39} - 16 q^{45} - 4 q^{49} + 40 q^{54} + 4 q^{64} - 12 q^{74} - 16 q^{76} + 16 q^{80} + 4 q^{81} - 4 q^{95} + 12 q^{96} - 20 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(496\) \(761\) \(837\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.610425 + 1.87869i −0.610425 + 1.87869i −0.156434 + 0.987688i \(0.550000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(3\) −0.734572 + 0.533698i −0.734572 + 0.533698i −0.891007 0.453990i \(-0.850000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(4\) −2.34786 1.70582i −2.34786 1.70582i
\(5\) −0.309017 0.951057i −0.309017 0.951057i
\(6\) −0.554254 1.70582i −0.554254 1.70582i
\(7\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(8\) 3.03979 2.20854i 3.03979 2.20854i
\(9\) −0.0542543 + 0.166977i −0.0542543 + 0.166977i
\(10\) 1.97538 1.97538
\(11\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(12\) 2.63506 2.63506
\(13\) −0.0966818 + 0.297556i −0.0966818 + 0.297556i −0.987688 0.156434i \(-0.950000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(14\) 0 0
\(15\) 0.734572 + 0.533698i 0.734572 + 0.533698i
\(16\) 1.39680 + 4.29892i 1.39680 + 4.29892i
\(17\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(18\) −0.280582 0.203854i −0.280582 0.203854i
\(19\) 0.809017 0.587785i 0.809017 0.587785i
\(20\) −0.896802 + 2.76007i −0.896802 + 2.76007i
\(21\) 0 0
\(22\) −1.16110 + 1.59811i −1.16110 + 1.59811i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) −1.05425 + 3.24466i −1.05425 + 3.24466i
\(25\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(26\) −0.500000 0.363271i −0.500000 0.363271i
\(27\) −0.329843 1.01515i −0.329843 1.01515i
\(28\) 0 0
\(29\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(30\) −1.45106 + 1.05425i −1.45106 + 1.05425i
\(31\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(32\) −5.17160 −5.17160
\(33\) −0.863541 + 0.280582i −0.863541 + 0.280582i
\(34\) 0 0
\(35\) 0 0
\(36\) 0.412215 0.299492i 0.412215 0.299492i
\(37\) 1.44168 + 1.04744i 1.44168 + 1.04744i 0.987688 + 0.156434i \(0.0500000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(38\) 0.610425 + 1.87869i 0.610425 + 1.87869i
\(39\) −0.0877853 0.270175i −0.0877853 0.270175i
\(40\) −3.03979 2.20854i −3.03979 2.20854i
\(41\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −1.70582 2.34786i −1.70582 2.34786i
\(45\) 0.175571 0.175571
\(46\) 0 0
\(47\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(48\) −3.32037 2.41239i −3.32037 2.41239i
\(49\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(50\) −0.610425 1.87869i −0.610425 1.87869i
\(51\) 0 0
\(52\) 0.734572 0.533698i 0.734572 0.533698i
\(53\) −0.437016 + 1.34500i −0.437016 + 1.34500i 0.453990 + 0.891007i \(0.350000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(54\) 2.10851 2.10851
\(55\) 1.00000i 1.00000i
\(56\) 0 0
\(57\) −0.280582 + 0.863541i −0.280582 + 0.863541i
\(58\) 0 0
\(59\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(60\) −0.814279 2.50609i −0.814279 2.50609i
\(61\) 0.587785 + 1.80902i 0.587785 + 1.80902i 0.587785 + 0.809017i \(0.300000\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.76007 5.41695i 1.76007 5.41695i
\(65\) 0.312869 0.312869
\(66\) 1.79360i 1.79360i
\(67\) 1.78201 1.78201 0.891007 0.453990i \(-0.150000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(72\) 0.203854 + 0.627399i 0.203854 + 0.627399i
\(73\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(74\) −2.84786 + 2.06909i −2.84786 + 2.06909i
\(75\) 0.280582 0.863541i 0.280582 0.863541i
\(76\) −2.90211 −2.90211
\(77\) 0 0
\(78\) 0.561163 0.561163
\(79\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(80\) 3.65688 2.65688i 3.65688 2.65688i
\(81\) 0.642040 + 0.466469i 0.642040 + 0.466469i
\(82\) 0 0
\(83\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 3.57349 1.16110i 3.57349 1.16110i
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) −0.107173 + 0.329843i −0.107173 + 0.329843i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.809017 0.587785i −0.809017 0.587785i
\(96\) 3.79892 2.76007i 3.79892 2.76007i
\(97\) 0.610425 1.87869i 0.610425 1.87869i 0.156434 0.987688i \(-0.450000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(98\) −1.97538 −1.97538
\(99\) −0.103198 + 0.142040i −0.103198 + 0.142040i
\(100\) 2.90211 2.90211
\(101\) 0.363271 1.11803i 0.363271 1.11803i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(102\) 0 0
\(103\) 0.253116 + 0.183900i 0.253116 + 0.183900i 0.707107 0.707107i \(-0.250000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(104\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(105\) 0 0
\(106\) −2.26007 1.64204i −2.26007 1.64204i
\(107\) −1.44168 + 1.04744i −1.44168 + 1.04744i −0.453990 + 0.891007i \(0.650000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(108\) −0.957243 + 2.94609i −0.957243 + 2.94609i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 1.87869 + 0.610425i 1.87869 + 0.610425i
\(111\) −1.61803 −1.61803
\(112\) 0 0
\(113\) 0.253116 0.183900i 0.253116 0.183900i −0.453990 0.891007i \(-0.650000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(114\) −1.45106 1.05425i −1.45106 1.05425i
\(115\) 0 0
\(116\) 0 0
\(117\) −0.0444398 0.0322874i −0.0444398 0.0322874i
\(118\) 0 0
\(119\) 0 0
\(120\) 3.41164 3.41164
\(121\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(122\) −3.75739 −3.75739
\(123\) 0 0
\(124\) 0 0
\(125\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(126\) 0 0
\(127\) −0.437016 1.34500i −0.437016 1.34500i −0.891007 0.453990i \(-0.850000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(128\) 4.91849 + 3.57349i 4.91849 + 3.57349i
\(129\) 0 0
\(130\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(131\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(132\) 2.50609 + 0.814279i 2.50609 + 0.814279i
\(133\) 0 0
\(134\) −1.08779 + 3.34786i −1.08779 + 3.34786i
\(135\) −0.863541 + 0.627399i −0.863541 + 0.627399i
\(136\) 0 0
\(137\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(138\) 0 0
\(139\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.183900 + 0.253116i −0.183900 + 0.253116i
\(144\) −0.793604 −0.793604
\(145\) 0 0
\(146\) 0 0
\(147\) −0.734572 0.533698i −0.734572 0.533698i
\(148\) −1.59811 4.91849i −1.59811 4.91849i
\(149\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(150\) 1.45106 + 1.05425i 1.45106 + 1.05425i
\(151\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(152\) 1.16110 3.57349i 1.16110 3.57349i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.254763 + 0.784079i −0.254763 + 0.784079i
\(157\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(158\) 0 0
\(159\) −0.396802 1.22123i −0.396802 1.22123i
\(160\) 1.59811 + 4.91849i 1.59811 + 4.91849i
\(161\) 0 0
\(162\) −1.26827 + 0.921452i −1.26827 + 0.921452i
\(163\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(164\) 0 0
\(165\) 0.533698 + 0.734572i 0.533698 + 0.734572i
\(166\) 0 0
\(167\) 0.280582 0.863541i 0.280582 0.863541i −0.707107 0.707107i \(-0.750000\pi\)
0.987688 0.156434i \(-0.0500000\pi\)
\(168\) 0 0
\(169\) 0.729825 + 0.530249i 0.729825 + 0.530249i
\(170\) 0 0
\(171\) 0.0542543 + 0.166977i 0.0542543 + 0.166977i
\(172\) 0 0
\(173\) −1.14412 + 0.831254i −1.14412 + 0.831254i −0.987688 0.156434i \(-0.950000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 4.52015i 4.52015i
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(180\) −0.412215 0.299492i −0.412215 0.299492i
\(181\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(182\) 0 0
\(183\) −1.39724 1.01515i −1.39724 1.01515i
\(184\) 0 0
\(185\) 0.550672 1.69480i 0.550672 1.69480i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 1.59811 1.16110i 1.59811 1.16110i
\(191\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(192\) 1.59811 + 4.91849i 1.59811 + 4.91849i
\(193\) 0.280582 + 0.863541i 0.280582 + 0.863541i 0.987688 + 0.156434i \(0.0500000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(194\) 3.15688 + 2.29360i 3.15688 + 2.29360i
\(195\) −0.229825 + 0.166977i −0.229825 + 0.166977i
\(196\) 0.896802 2.76007i 0.896802 2.76007i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −0.203854 0.280582i −0.203854 0.280582i
\(199\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(200\) −1.16110 + 3.57349i −1.16110 + 3.57349i
\(201\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(202\) 1.87869 + 1.36495i 1.87869 + 1.36495i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(207\) 0 0
\(208\) −1.41421 −1.41421
\(209\) 0.951057 0.309017i 0.951057 0.309017i
\(210\) 0 0
\(211\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(212\) 3.32037 2.41239i 3.32037 2.41239i
\(213\) 0 0
\(214\) −1.08779 3.34786i −1.08779 3.34786i
\(215\) 0 0
\(216\) −3.24466 2.35738i −3.24466 2.35738i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −1.70582 + 2.34786i −1.70582 + 2.34786i
\(221\) 0 0
\(222\) 0.987688 3.03979i 0.987688 3.03979i
\(223\) 1.14412 0.831254i 1.14412 0.831254i 0.156434 0.987688i \(-0.450000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(224\) 0 0
\(225\) −0.0542543 0.166977i −0.0542543 0.166977i
\(226\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(227\) 0.734572 + 0.533698i 0.734572 + 0.533698i 0.891007 0.453990i \(-0.150000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(228\) 2.13181 1.54885i 2.13181 1.54885i
\(229\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(234\) 0.0877853 0.0637797i 0.0877853 0.0637797i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(240\) −1.26827 + 3.90333i −1.26827 + 3.90333i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −1.59811 + 1.16110i −1.59811 + 1.16110i
\(243\) 0.346818 0.346818
\(244\) 1.70582 5.24997i 1.70582 5.24997i
\(245\) 0.809017 0.587785i 0.809017 0.587785i
\(246\) 0 0
\(247\) 0.0966818 + 0.297556i 0.0966818 + 0.297556i
\(248\) 0 0
\(249\) 0 0
\(250\) −1.59811 + 1.16110i −1.59811 + 1.16110i
\(251\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 2.79360 2.79360
\(255\) 0 0
\(256\) −5.10793 + 3.71113i −5.10793 + 3.71113i
\(257\) −0.253116 0.183900i −0.253116 0.183900i 0.453990 0.891007i \(-0.350000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.734572 0.533698i −0.734572 0.533698i
\(261\) 0 0
\(262\) −0.377263 + 1.16110i −0.377263 + 1.16110i
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) −2.00531 + 2.76007i −2.00531 + 2.76007i
\(265\) 1.41421 1.41421
\(266\) 0 0
\(267\) 0 0
\(268\) −4.18391 3.03979i −4.18391 3.03979i
\(269\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(270\) −0.651565 2.00531i −0.651565 2.00531i
\(271\) −0.951057 0.690983i −0.951057 0.690983i 1.00000i \(-0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(276\) 0 0
\(277\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(282\) 0 0
\(283\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(284\) 0 0
\(285\) 0.907981 0.907981
\(286\) −0.363271 0.500000i −0.363271 0.500000i
\(287\) 0 0
\(288\) 0.280582 0.863541i 0.280582 0.863541i
\(289\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(290\) 0 0
\(291\) 0.554254 + 1.70582i 0.554254 + 1.70582i
\(292\) 0 0
\(293\) −1.59811 1.16110i −1.59811 1.16110i −0.891007 0.453990i \(-0.850000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(294\) 1.45106 1.05425i 1.45106 1.05425i
\(295\) 0 0
\(296\) 6.69572 6.69572
\(297\) 1.06740i 1.06740i
\(298\) 0 0
\(299\) 0 0
\(300\) −2.13181 + 1.54885i −2.13181 + 1.54885i
\(301\) 0 0
\(302\) 0 0
\(303\) 0.329843 + 1.01515i 0.329843 + 1.01515i
\(304\) 3.65688 + 2.65688i 3.65688 + 2.65688i
\(305\) 1.53884 1.11803i 1.53884 1.11803i
\(306\) 0 0
\(307\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(308\) 0 0
\(309\) −0.284079 −0.284079
\(310\) 0 0
\(311\) −0.951057 + 0.690983i −0.951057 + 0.690983i −0.951057 0.309017i \(-0.900000\pi\)
1.00000i \(0.5\pi\)
\(312\) −0.863541 0.627399i −0.863541 0.627399i
\(313\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.437016 1.34500i 0.437016 1.34500i −0.453990 0.891007i \(-0.650000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(318\) 2.53654 2.53654
\(319\) 0 0
\(320\) −5.69572 −5.69572
\(321\) 0.500000 1.53884i 0.500000 1.53884i
\(322\) 0 0
\(323\) 0 0
\(324\) −0.711706 2.19041i −0.711706 2.19041i
\(325\) −0.0966818 0.297556i −0.0966818 0.297556i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) −1.70582 + 0.554254i −1.70582 + 0.554254i
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) −0.253116 + 0.183900i −0.253116 + 0.183900i
\(334\) 1.45106 + 1.05425i 1.45106 + 1.05425i
\(335\) −0.550672 1.69480i −0.550672 1.69480i
\(336\) 0 0
\(337\) −1.14412 0.831254i −1.14412 0.831254i −0.156434 0.987688i \(-0.550000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(338\) −1.44168 + 1.04744i −1.44168 + 1.04744i
\(339\) −0.0877853 + 0.270175i −0.0877853 + 0.270175i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.346818 −0.346818
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −0.863271 2.65688i −0.863271 2.65688i
\(347\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(348\) 0 0
\(349\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0.333955 0.333955
\(352\) −4.91849 1.59811i −4.91849 1.59811i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.53884 1.11803i −1.53884 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
−0.587785 0.809017i \(-0.700000\pi\)
\(360\) 0.533698 0.387754i 0.533698 0.387754i
\(361\) 0.309017 0.951057i 0.309017 0.951057i
\(362\) 0 0
\(363\) −0.907981 −0.907981
\(364\) 0 0
\(365\) 0 0
\(366\) 2.76007 2.00531i 2.76007 2.00531i
\(367\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 2.84786 + 2.06909i 2.84786 + 2.06909i
\(371\) 0 0
\(372\) 0 0
\(373\) −1.78201 −1.78201 −0.891007 0.453990i \(-0.850000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(374\) 0 0
\(375\) −0.907981 −0.907981
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(380\) 0.896802 + 2.76007i 0.896802 + 2.76007i
\(381\) 1.03884 + 0.754763i 1.03884 + 0.754763i
\(382\) 2.58580 1.87869i 2.58580 1.87869i
\(383\) 0.437016 1.34500i 0.437016 1.34500i −0.453990 0.891007i \(-0.650000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(384\) −5.52015 −5.52015
\(385\) 0 0
\(386\) −1.79360 −1.79360
\(387\) 0 0
\(388\) −4.63791 + 3.36964i −4.63791 + 3.36964i
\(389\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(390\) −0.173409 0.533698i −0.173409 0.533698i
\(391\) 0 0
\(392\) 3.03979 + 2.20854i 3.03979 + 2.20854i
\(393\) −0.453990 + 0.329843i −0.453990 + 0.329843i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.484587 0.157452i 0.484587 0.157452i
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0.377263 1.16110i 0.377263 1.16110i
\(399\) 0 0
\(400\) −3.65688 2.65688i −3.65688 2.65688i
\(401\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(402\) −0.987688 3.03979i −0.987688 3.03979i
\(403\) 0 0
\(404\) −2.76007 + 2.00531i −2.76007 + 2.00531i
\(405\) 0.245237 0.754763i 0.245237 0.754763i
\(406\) 0 0
\(407\) 1.04744 + 1.44168i 1.04744 + 1.44168i
\(408\) 0 0
\(409\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.280582 0.863541i −0.280582 0.863541i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0.500000 1.53884i 0.500000 1.53884i
\(417\) 0 0
\(418\) 1.97538i 1.97538i
\(419\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(420\) 0 0
\(421\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 1.64204 + 5.05368i 1.64204 + 5.05368i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 5.17160 5.17160
\(429\) 0.284079i 0.284079i
\(430\) 0 0
\(431\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(432\) 3.90333 2.83594i 3.90333 2.83594i
\(433\) 1.59811 + 1.16110i 1.59811 + 1.16110i 0.891007 + 0.453990i \(0.150000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) −2.20854 3.03979i −2.20854 3.03979i
\(441\) −0.175571 −0.175571
\(442\) 0 0
\(443\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(444\) 3.79892 + 2.76007i 3.79892 + 2.76007i
\(445\) 0 0
\(446\) 0.863271 + 2.65688i 0.863271 + 2.65688i
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(450\) 0.346818 0.346818
\(451\) 0 0
\(452\) −0.907981 −0.907981
\(453\) 0 0
\(454\) −1.45106 + 1.05425i −1.45106 + 1.05425i
\(455\) 0 0
\(456\) 1.05425 + 3.24466i 1.05425 + 3.24466i
\(457\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(468\) 0.0492618 + 0.151612i 0.0492618 + 0.151612i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(476\) 0 0
\(477\) −0.200874 0.145944i −0.200874 0.145944i
\(478\) 0.987688 + 3.03979i 0.987688 + 3.03979i
\(479\) −0.363271 1.11803i −0.363271 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(480\) −3.79892 2.76007i −3.79892 2.76007i
\(481\) −0.451057 + 0.327712i −0.451057 + 0.327712i
\(482\) 0 0
\(483\) 0 0
\(484\) −0.896802 2.76007i −0.896802 2.76007i
\(485\) −1.97538 −1.97538
\(486\) −0.211706 + 0.651565i −0.211706 + 0.651565i
\(487\) −1.14412 + 0.831254i −1.14412 + 0.831254i −0.987688 0.156434i \(-0.950000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(488\) 5.78203 + 4.20089i 5.78203 + 4.20089i
\(489\) 0 0
\(490\) 0.610425 + 1.87869i 0.610425 + 1.87869i
\(491\) 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i \(-0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −0.618034 −0.618034
\(495\) 0.166977 + 0.0542543i 0.166977 + 0.0542543i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(500\) −0.896802 2.76007i −0.896802 2.76007i
\(501\) 0.254763 + 0.784079i 0.254763 + 0.784079i
\(502\) −0.987688 0.717598i −0.987688 0.717598i
\(503\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(504\) 0 0
\(505\) −1.17557 −1.17557
\(506\) 0 0
\(507\) −0.819101 −0.819101
\(508\) −1.26827 + 3.90333i −1.26827 + 3.90333i
\(509\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.97538 6.07958i −1.97538 6.07958i
\(513\) −0.863541 0.627399i −0.863541 0.627399i
\(514\) 0.500000 0.363271i 0.500000 0.363271i
\(515\) 0.0966818 0.297556i 0.0966818 0.297556i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0.396802 1.22123i 0.396802 1.22123i
\(520\) 0.951057 0.690983i 0.951057 0.690983i
\(521\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(522\) 0 0
\(523\) 0.0966818 + 0.297556i 0.0966818 + 0.297556i 0.987688 0.156434i \(-0.0500000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(524\) −1.45106 1.05425i −1.45106 1.05425i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −2.41239 3.32037i −2.41239 3.32037i
\(529\) 1.00000 1.00000
\(530\) −0.863271 + 2.65688i −0.863271 + 2.65688i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 1.44168 + 1.04744i 1.44168 + 1.04744i
\(536\) 5.41695 3.93564i 5.41695 3.93564i
\(537\) 0 0
\(538\) 0 0
\(539\) 1.00000i 1.00000i
\(540\) 3.09770 3.09770
\(541\) −0.587785 + 1.80902i −0.587785 + 1.80902i 1.00000i \(0.5\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(542\) 1.87869 1.36495i 1.87869 1.36495i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.734572 + 0.533698i −0.734572 + 0.533698i −0.891007 0.453990i \(-0.850000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(548\) 0 0
\(549\) −0.333955 −0.333955
\(550\) 1.97538i 1.97538i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(556\) 0 0
\(557\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0.610425 1.87869i 0.610425 1.87869i 0.156434 0.987688i \(-0.450000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(564\) 0 0
\(565\) −0.253116 0.183900i −0.253116 0.183900i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(570\) −0.554254 + 1.70582i −0.554254 + 1.70582i
\(571\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(572\) 0.863541 0.280582i 0.863541 0.280582i
\(573\) 1.46914 1.46914
\(574\) 0 0
\(575\) 0 0
\(576\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(577\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(578\) −0.610425 1.87869i −0.610425 1.87869i
\(579\) −0.666977 0.484587i −0.666977 0.484587i
\(580\) 0 0
\(581\) 0 0
\(582\) −3.54304 −3.54304
\(583\) −0.831254 + 1.14412i −0.831254 + 1.14412i
\(584\) 0 0
\(585\) −0.0169745 + 0.0522421i −0.0169745 + 0.0522421i
\(586\) 3.15688 2.29360i 3.15688 2.29360i
\(587\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(588\) 0.814279 + 2.50609i 0.814279 + 2.50609i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −2.48912 + 7.66072i −2.48912 + 7.66072i
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 2.00531 + 0.651565i 2.00531 + 0.651565i
\(595\) 0 0
\(596\) 0 0
\(597\) 0.453990 0.329843i 0.453990 0.329843i
\(598\) 0 0
\(599\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(600\) −1.05425 3.24466i −1.05425 3.24466i
\(601\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(602\) 0 0
\(603\) −0.0966818 + 0.297556i −0.0966818 + 0.297556i
\(604\) 0 0
\(605\) 0.309017 0.951057i 0.309017 0.951057i
\(606\) −2.10851 −2.10851
\(607\) −0.280582 + 0.863541i −0.280582 + 0.863541i 0.707107 + 0.707107i \(0.250000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(608\) −4.18391 + 3.03979i −4.18391 + 3.03979i
\(609\) 0 0
\(610\) 1.16110 + 3.57349i 1.16110 + 3.57349i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(614\) −0.863271 + 2.65688i −0.863271 + 2.65688i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0.173409 0.533698i 0.173409 0.533698i
\(619\) 1.53884 1.11803i 1.53884 1.11803i 0.587785 0.809017i \(-0.300000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −0.717598 2.20854i −0.717598 2.20854i
\(623\) 0 0
\(624\) 1.03884 0.754763i 1.03884 0.754763i
\(625\) 0.309017 0.951057i 0.309017 0.951057i
\(626\) 0 0
\(627\) −0.533698 + 0.734572i −0.533698 + 0.734572i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −0.951057 0.690983i −0.951057 0.690983i 1.00000i \(-0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 2.26007 + 1.64204i 2.26007 + 1.64204i
\(635\) −1.14412 + 0.831254i −1.14412 + 0.831254i
\(636\) −1.15156 + 3.54415i −1.15156 + 3.54415i
\(637\) −0.312869 −0.312869
\(638\) 0 0
\(639\) 0 0
\(640\) 1.87869 5.78203i 1.87869 5.78203i
\(641\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(642\) 2.58580 + 1.87869i 2.58580 + 1.87869i
\(643\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(648\) 2.98188 2.98188
\(649\) 0 0
\(650\) 0.618034 0.618034
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(654\) 0 0
\(655\) −0.190983 0.587785i −0.190983 0.587785i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 2.63506i 2.63506i
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −0.190983 0.587785i −0.190983 0.587785i
\(667\) 0 0
\(668\) −2.13181 + 1.54885i −2.13181 + 1.54885i
\(669\) −0.396802 + 1.22123i −0.396802 + 1.22123i
\(670\) 3.52015 3.52015
\(671\) 1.90211i 1.90211i
\(672\) 0 0
\(673\) 0.550672 1.69480i 0.550672 1.69480i −0.156434 0.987688i \(-0.550000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(674\) 2.26007 1.64204i 2.26007 1.64204i
\(675\) 0.863541 + 0.627399i 0.863541 + 0.627399i
\(676\) −0.809017 2.48990i −0.809017 2.48990i
\(677\) 0.280582 + 0.863541i 0.280582 + 0.863541i 0.987688 + 0.156434i \(0.0500000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(678\) −0.453990 0.329843i −0.453990 0.329843i
\(679\) 0 0
\(680\) 0 0
\(681\) −0.824429 −0.824429
\(682\) 0 0
\(683\) 1.97538 1.97538 0.987688 0.156434i \(-0.0500000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(684\) 0.157452 0.484587i 0.157452 0.484587i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −0.357960 0.260074i −0.357960 0.260074i
\(690\) 0 0
\(691\) 0.363271 1.11803i 0.363271 1.11803i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(692\) 4.10421 4.10421
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −0.987688 3.03979i −0.987688 3.03979i
\(699\) 0 0
\(700\) 0 0
\(701\) 0.951057 0.690983i 0.951057 0.690983i 1.00000i \(-0.5\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(702\) −0.203854 + 0.627399i −0.203854 + 0.627399i
\(703\) 1.78201 1.78201
\(704\) 3.34786 4.60793i 3.34786 4.60793i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0.297556 + 0.0966818i 0.297556 + 0.0966818i
\(716\) 0 0
\(717\) −0.453990 + 1.39724i −0.453990 + 1.39724i
\(718\) 3.03979 2.20854i 3.03979 2.20854i
\(719\) −1.53884 1.11803i −1.53884 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
−0.587785 0.809017i \(-0.700000\pi\)
\(720\) 0.245237 + 0.754763i 0.245237 + 0.754763i
\(721\) 0 0
\(722\) 1.59811 + 1.16110i 1.59811 + 1.16110i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0.554254 1.70582i 0.554254 1.70582i
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −0.896802 + 0.651565i −0.896802 + 0.651565i
\(730\) 0 0
\(731\) 0 0
\(732\) 1.54885 + 4.76687i 1.54885 + 4.76687i
\(733\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(734\) 0 0
\(735\) −0.280582 + 0.863541i −0.280582 + 0.863541i
\(736\) 0 0
\(737\) 1.69480 + 0.550672i 1.69480 + 0.550672i
\(738\) 0 0
\(739\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(740\) −4.18391 + 3.03979i −4.18391 + 3.03979i
\(741\) −0.229825 0.166977i −0.229825 0.166977i
\(742\) 0 0
\(743\) 0.610425 + 1.87869i 0.610425 + 1.87869i 0.453990 + 0.891007i \(0.350000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 1.08779 3.34786i 1.08779 3.34786i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0.554254 1.70582i 0.554254 1.70582i
\(751\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(752\) 0 0
\(753\) −0.173409 0.533698i −0.173409 0.533698i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −3.75739 −3.75739
\(761\) 0.587785 1.80902i 0.587785 1.80902i 1.00000i \(-0.5\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(762\) −2.05210 + 1.49094i −2.05210 + 1.49094i
\(763\) 0 0
\(764\) 1.45106 + 4.46589i 1.45106 + 4.46589i
\(765\) 0 0
\(766\) 2.26007 + 1.64204i 2.26007 + 1.64204i
\(767\) 0 0
\(768\) 1.77152 5.45218i 1.77152 5.45218i
\(769\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(770\) 0 0
\(771\) 0.284079 0.284079
\(772\) 0.814279 2.50609i 0.814279 2.50609i
\(773\) 0.734572 0.533698i 0.734572 0.533698i −0.156434 0.987688i \(-0.550000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −2.29360 7.05899i −2.29360 7.05899i
\(777\) 0 0
\(778\) −2.58580 + 1.87869i −2.58580 + 1.87869i
\(779\) 0 0
\(780\) 0.824429 0.824429
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −3.65688 + 2.65688i −3.65688 + 2.65688i
\(785\) 0 0
\(786\) −0.342548 1.05425i −0.342548 1.05425i
\(787\) −0.550672 1.69480i −0.550672 1.69480i −0.707107 0.707107i \(-0.750000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.659687i 0.659687i
\(793\) −0.595112 −0.595112
\(794\) 0 0
\(795\) −1.03884 + 0.754763i −1.03884 + 0.754763i
\(796\) 1.45106 + 1.05425i 1.45106 + 1.05425i
\(797\) 0.610425 + 1.87869i 0.610425 + 1.87869i 0.453990 + 0.891007i \(0.350000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)