Properties

Label 731.2.e.a.307.11
Level 731
Weight 2
Character 731.307
Analytic conductor 5.837
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 307.11
Character \(\chi\) = 731.307
Dual form 731.2.e.a.681.11

$q$-expansion

\(f(q)\) \(=\) \(q-0.966012 q^{2} +(-0.835198 + 1.44661i) q^{3} -1.06682 q^{4} +(-0.811572 + 1.40568i) q^{5} +(0.806812 - 1.39744i) q^{6} +(-1.19805 - 2.07509i) q^{7} +2.96259 q^{8} +(0.104888 + 0.181671i) q^{9} +O(q^{10})\) \(q-0.966012 q^{2} +(-0.835198 + 1.44661i) q^{3} -1.06682 q^{4} +(-0.811572 + 1.40568i) q^{5} +(0.806812 - 1.39744i) q^{6} +(-1.19805 - 2.07509i) q^{7} +2.96259 q^{8} +(0.104888 + 0.181671i) q^{9} +(0.783988 - 1.35791i) q^{10} +5.63250 q^{11} +(0.891006 - 1.54327i) q^{12} +(1.57930 + 2.73543i) q^{13} +(1.15733 + 2.00456i) q^{14} +(-1.35565 - 2.34805i) q^{15} -0.728255 q^{16} +(0.500000 + 0.866025i) q^{17} +(-0.101323 - 0.175497i) q^{18} +(-0.504465 + 0.873759i) q^{19} +(0.865801 - 1.49961i) q^{20} +4.00245 q^{21} -5.44107 q^{22} +(1.36035 - 2.35619i) q^{23} +(-2.47435 + 4.28569i) q^{24} +(1.18270 + 2.04850i) q^{25} +(-1.52563 - 2.64246i) q^{26} -5.36160 q^{27} +(1.27811 + 2.21375i) q^{28} +(1.40740 + 2.43769i) q^{29} +(1.30957 + 2.26824i) q^{30} +(-1.44009 + 2.49432i) q^{31} -5.22167 q^{32} +(-4.70425 + 8.14801i) q^{33} +(-0.483006 - 0.836591i) q^{34} +3.88922 q^{35} +(-0.111897 - 0.193811i) q^{36} +(-1.99180 + 3.44990i) q^{37} +(0.487319 - 0.844062i) q^{38} -5.27612 q^{39} +(-2.40435 + 4.16446i) q^{40} -2.86909 q^{41} -3.86641 q^{42} +(-2.90632 - 5.87821i) q^{43} -6.00886 q^{44} -0.340496 q^{45} +(-1.31411 + 2.27611i) q^{46} -1.65710 q^{47} +(0.608237 - 1.05350i) q^{48} +(0.629337 - 1.09004i) q^{49} +(-1.14251 - 1.97888i) q^{50} -1.67040 q^{51} +(-1.68483 - 2.91821i) q^{52} +(0.0801212 - 0.138774i) q^{53} +5.17937 q^{54} +(-4.57118 + 7.91751i) q^{55} +(-3.54934 - 6.14763i) q^{56} +(-0.842657 - 1.45952i) q^{57} +(-1.35956 - 2.35484i) q^{58} -4.21511 q^{59} +(1.44623 + 2.50494i) q^{60} +(0.614954 + 1.06513i) q^{61} +(1.39115 - 2.40954i) q^{62} +(0.251323 - 0.435304i) q^{63} +6.50071 q^{64} -5.12687 q^{65} +(4.54437 - 7.87108i) q^{66} +(-1.94684 + 3.37202i) q^{67} +(-0.533410 - 0.923893i) q^{68} +(2.27232 + 3.93577i) q^{69} -3.75704 q^{70} +(5.92002 + 10.2538i) q^{71} +(0.310740 + 0.538217i) q^{72} +(3.47752 + 6.02323i) q^{73} +(1.92410 - 3.33264i) q^{74} -3.95117 q^{75} +(0.538173 - 0.932144i) q^{76} +(-6.74803 - 11.6879i) q^{77} +5.09680 q^{78} +(4.80987 + 8.33093i) q^{79} +(0.591031 - 1.02370i) q^{80} +(4.16333 - 7.21110i) q^{81} +2.77158 q^{82} +(1.76086 - 3.04990i) q^{83} -4.26989 q^{84} -1.62314 q^{85} +(2.80754 + 5.67842i) q^{86} -4.70183 q^{87} +16.6868 q^{88} +(-9.13771 + 15.8270i) q^{89} +0.328924 q^{90} +(3.78418 - 6.55438i) q^{91} +(-1.45125 + 2.51363i) q^{92} +(-2.40553 - 4.16650i) q^{93} +1.60078 q^{94} +(-0.818819 - 1.41824i) q^{95} +(4.36113 - 7.55370i) q^{96} -8.05023 q^{97} +(-0.607948 + 1.05300i) q^{98} +(0.590782 + 1.02326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + O(q^{10}) \) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + 4q^{10} + 16q^{11} + 12q^{12} + 2q^{13} - 11q^{14} + 7q^{15} + 30q^{16} + 29q^{17} + 8q^{18} + 8q^{19} - 33q^{20} - 26q^{21} - 22q^{22} - 5q^{23} + 12q^{24} - 36q^{25} - 12q^{27} + 15q^{28} + 2q^{29} + 11q^{30} + 3q^{31} - 40q^{32} + 17q^{33} - 3q^{34} + 38q^{35} - 7q^{36} + 2q^{37} + q^{38} - 54q^{39} + 5q^{40} + 14q^{41} - 112q^{42} + 31q^{43} - 24q^{44} - 46q^{45} - 13q^{46} - 28q^{47} - 28q^{49} - 13q^{50} + 6q^{51} + 85q^{52} - 10q^{53} + 34q^{54} + 36q^{55} - 54q^{56} - 23q^{57} + 3q^{58} + 12q^{59} + 2q^{60} - q^{61} - q^{62} - 14q^{63} + 28q^{64} + 80q^{65} - 74q^{66} + 11q^{67} + 27q^{68} - 11q^{69} + 2q^{70} + 16q^{71} + 21q^{72} + 14q^{73} + 21q^{74} - 54q^{75} + 44q^{76} + 25q^{77} + 88q^{78} - 4q^{79} - 112q^{80} + 11q^{81} - 176q^{82} - 3q^{83} + 100q^{84} - 2q^{85} + 44q^{86} + 8q^{87} - 106q^{88} + 82q^{89} + 54q^{90} - 15q^{91} + 42q^{92} + 88q^{94} + 29q^{95} + 20q^{96} + 20q^{97} + 44q^{98} - 54q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.966012 −0.683074 −0.341537 0.939868i \(-0.610947\pi\)
−0.341537 + 0.939868i \(0.610947\pi\)
\(3\) −0.835198 + 1.44661i −0.482202 + 0.835198i −0.999791 0.0204310i \(-0.993496\pi\)
0.517589 + 0.855629i \(0.326830\pi\)
\(4\) −1.06682 −0.533410
\(5\) −0.811572 + 1.40568i −0.362946 + 0.628641i −0.988444 0.151585i \(-0.951562\pi\)
0.625498 + 0.780225i \(0.284896\pi\)
\(6\) 0.806812 1.39744i 0.329380 0.570502i
\(7\) −1.19805 2.07509i −0.452822 0.784310i 0.545739 0.837956i \(-0.316249\pi\)
−0.998560 + 0.0536456i \(0.982916\pi\)
\(8\) 2.96259 1.04743
\(9\) 0.104888 + 0.181671i 0.0349627 + 0.0605571i
\(10\) 0.783988 1.35791i 0.247919 0.429408i
\(11\) 5.63250 1.69826 0.849131 0.528182i \(-0.177126\pi\)
0.849131 + 0.528182i \(0.177126\pi\)
\(12\) 0.891006 1.54327i 0.257211 0.445503i
\(13\) 1.57930 + 2.73543i 0.438020 + 0.758672i 0.997537 0.0701467i \(-0.0223467\pi\)
−0.559517 + 0.828819i \(0.689013\pi\)
\(14\) 1.15733 + 2.00456i 0.309311 + 0.535742i
\(15\) −1.35565 2.34805i −0.350026 0.606263i
\(16\) −0.728255 −0.182064
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i
\(18\) −0.101323 0.175497i −0.0238821 0.0413650i
\(19\) −0.504465 + 0.873759i −0.115732 + 0.200454i −0.918072 0.396413i \(-0.870255\pi\)
0.802340 + 0.596867i \(0.203588\pi\)
\(20\) 0.865801 1.49961i 0.193599 0.335323i
\(21\) 4.00245 0.873406
\(22\) −5.44107 −1.16004
\(23\) 1.36035 2.35619i 0.283652 0.491300i −0.688629 0.725114i \(-0.741787\pi\)
0.972281 + 0.233814i \(0.0751206\pi\)
\(24\) −2.47435 + 4.28569i −0.505074 + 0.874814i
\(25\) 1.18270 + 2.04850i 0.236541 + 0.409700i
\(26\) −1.52563 2.64246i −0.299200 0.518229i
\(27\) −5.36160 −1.03184
\(28\) 1.27811 + 2.21375i 0.241540 + 0.418359i
\(29\) 1.40740 + 2.43769i 0.261347 + 0.452667i 0.966600 0.256289i \(-0.0824998\pi\)
−0.705253 + 0.708956i \(0.749167\pi\)
\(30\) 1.30957 + 2.26824i 0.239094 + 0.414123i
\(31\) −1.44009 + 2.49432i −0.258649 + 0.447992i −0.965880 0.258990i \(-0.916610\pi\)
0.707232 + 0.706982i \(0.249944\pi\)
\(32\) −5.22167 −0.923069
\(33\) −4.70425 + 8.14801i −0.818905 + 1.41839i
\(34\) −0.483006 0.836591i −0.0828349 0.143474i
\(35\) 3.88922 0.657399
\(36\) −0.111897 0.193811i −0.0186494 0.0323018i
\(37\) −1.99180 + 3.44990i −0.327450 + 0.567160i −0.982005 0.188854i \(-0.939523\pi\)
0.654555 + 0.756014i \(0.272856\pi\)
\(38\) 0.487319 0.844062i 0.0790537 0.136925i
\(39\) −5.27612 −0.844855
\(40\) −2.40435 + 4.16446i −0.380161 + 0.658459i
\(41\) −2.86909 −0.448077 −0.224039 0.974580i \(-0.571924\pi\)
−0.224039 + 0.974580i \(0.571924\pi\)
\(42\) −3.86641 −0.596601
\(43\) −2.90632 5.87821i −0.443210 0.896418i
\(44\) −6.00886 −0.905870
\(45\) −0.340496 −0.0507582
\(46\) −1.31411 + 2.27611i −0.193755 + 0.335594i
\(47\) −1.65710 −0.241713 −0.120857 0.992670i \(-0.538564\pi\)
−0.120857 + 0.992670i \(0.538564\pi\)
\(48\) 0.608237 1.05350i 0.0877915 0.152059i
\(49\) 0.629337 1.09004i 0.0899053 0.155721i
\(50\) −1.14251 1.97888i −0.161575 0.279856i
\(51\) −1.67040 −0.233902
\(52\) −1.68483 2.91821i −0.233644 0.404683i
\(53\) 0.0801212 0.138774i 0.0110055 0.0190621i −0.860470 0.509501i \(-0.829830\pi\)
0.871476 + 0.490439i \(0.163163\pi\)
\(54\) 5.17937 0.704823
\(55\) −4.57118 + 7.91751i −0.616377 + 1.06760i
\(56\) −3.54934 6.14763i −0.474300 0.821512i
\(57\) −0.842657 1.45952i −0.111613 0.193319i
\(58\) −1.35956 2.35484i −0.178520 0.309205i
\(59\) −4.21511 −0.548760 −0.274380 0.961621i \(-0.588473\pi\)
−0.274380 + 0.961621i \(0.588473\pi\)
\(60\) 1.44623 + 2.50494i 0.186708 + 0.323387i
\(61\) 0.614954 + 1.06513i 0.0787368 + 0.136376i 0.902705 0.430260i \(-0.141578\pi\)
−0.823968 + 0.566636i \(0.808245\pi\)
\(62\) 1.39115 2.40954i 0.176676 0.306012i
\(63\) 0.251323 0.435304i 0.0316637 0.0548431i
\(64\) 6.50071 0.812588
\(65\) −5.12687 −0.635909
\(66\) 4.54437 7.87108i 0.559373 0.968862i
\(67\) −1.94684 + 3.37202i −0.237844 + 0.411958i −0.960095 0.279673i \(-0.909774\pi\)
0.722251 + 0.691631i \(0.243107\pi\)
\(68\) −0.533410 0.923893i −0.0646855 0.112039i
\(69\) 2.27232 + 3.93577i 0.273555 + 0.473811i
\(70\) −3.75704 −0.449052
\(71\) 5.92002 + 10.2538i 0.702578 + 1.21690i 0.967559 + 0.252647i \(0.0813010\pi\)
−0.264981 + 0.964254i \(0.585366\pi\)
\(72\) 0.310740 + 0.538217i 0.0366210 + 0.0634295i
\(73\) 3.47752 + 6.02323i 0.407012 + 0.704966i 0.994553 0.104228i \(-0.0332373\pi\)
−0.587541 + 0.809194i \(0.699904\pi\)
\(74\) 1.92410 3.33264i 0.223672 0.387412i
\(75\) −3.95117 −0.456241
\(76\) 0.538173 0.932144i 0.0617327 0.106924i
\(77\) −6.74803 11.6879i −0.769010 1.33196i
\(78\) 5.09680 0.577099
\(79\) 4.80987 + 8.33093i 0.541152 + 0.937303i 0.998838 + 0.0481893i \(0.0153451\pi\)
−0.457686 + 0.889114i \(0.651322\pi\)
\(80\) 0.591031 1.02370i 0.0660793 0.114453i
\(81\) 4.16333 7.21110i 0.462593 0.801234i
\(82\) 2.77158 0.306070
\(83\) 1.76086 3.04990i 0.193279 0.334770i −0.753056 0.657957i \(-0.771421\pi\)
0.946335 + 0.323187i \(0.104754\pi\)
\(84\) −4.26989 −0.465883
\(85\) −1.62314 −0.176055
\(86\) 2.80754 + 5.67842i 0.302745 + 0.612320i
\(87\) −4.70183 −0.504089
\(88\) 16.6868 1.77882
\(89\) −9.13771 + 15.8270i −0.968595 + 1.67766i −0.268966 + 0.963150i \(0.586682\pi\)
−0.699629 + 0.714506i \(0.746651\pi\)
\(90\) 0.328924 0.0346716
\(91\) 3.78418 6.55438i 0.396689 0.687086i
\(92\) −1.45125 + 2.51363i −0.151303 + 0.262064i
\(93\) −2.40553 4.16650i −0.249442 0.432046i
\(94\) 1.60078 0.165108
\(95\) −0.818819 1.41824i −0.0840091 0.145508i
\(96\) 4.36113 7.55370i 0.445106 0.770946i
\(97\) −8.05023 −0.817377 −0.408689 0.912674i \(-0.634014\pi\)
−0.408689 + 0.912674i \(0.634014\pi\)
\(98\) −0.607948 + 1.05300i −0.0614120 + 0.106369i
\(99\) 0.590782 + 1.02326i 0.0593758 + 0.102842i
\(100\) −1.26173 2.18538i −0.126173 0.218538i
\(101\) −1.82223 3.15619i −0.181319 0.314053i 0.761011 0.648739i \(-0.224703\pi\)
−0.942330 + 0.334686i \(0.891370\pi\)
\(102\) 1.61362 0.159773
\(103\) 8.39209 + 14.5355i 0.826897 + 1.43223i 0.900461 + 0.434937i \(0.143229\pi\)
−0.0735636 + 0.997291i \(0.523437\pi\)
\(104\) 4.67882 + 8.10395i 0.458796 + 0.794658i
\(105\) −3.24827 + 5.62617i −0.316999 + 0.549058i
\(106\) −0.0773981 + 0.134057i −0.00751756 + 0.0130208i
\(107\) 0.847248 0.0819065 0.0409533 0.999161i \(-0.486961\pi\)
0.0409533 + 0.999161i \(0.486961\pi\)
\(108\) 5.71986 0.550394
\(109\) −2.05952 + 3.56719i −0.197266 + 0.341675i −0.947641 0.319338i \(-0.896540\pi\)
0.750375 + 0.661012i \(0.229873\pi\)
\(110\) 4.41581 7.64841i 0.421031 0.729248i
\(111\) −3.32709 5.76270i −0.315794 0.546971i
\(112\) 0.872489 + 1.51119i 0.0824424 + 0.142794i
\(113\) −8.31088 −0.781822 −0.390911 0.920429i \(-0.627840\pi\)
−0.390911 + 0.920429i \(0.627840\pi\)
\(114\) 0.814017 + 1.40992i 0.0762396 + 0.132051i
\(115\) 2.20804 + 3.82444i 0.205901 + 0.356631i
\(116\) −1.50144 2.60057i −0.139405 0.241457i
\(117\) −0.331300 + 0.573828i −0.0306287 + 0.0530504i
\(118\) 4.07184 0.374844
\(119\) 1.19805 2.07509i 0.109825 0.190223i
\(120\) −4.01622 6.95630i −0.366629 0.635020i
\(121\) 20.7251 1.88410
\(122\) −0.594053 1.02893i −0.0537830 0.0931550i
\(123\) 2.39626 4.15045i 0.216064 0.374233i
\(124\) 1.53632 2.66099i 0.137966 0.238964i
\(125\) −11.9551 −1.06930
\(126\) −0.242781 + 0.420509i −0.0216286 + 0.0374619i
\(127\) −2.43499 −0.216071 −0.108035 0.994147i \(-0.534456\pi\)
−0.108035 + 0.994147i \(0.534456\pi\)
\(128\) 4.16357 0.368011
\(129\) 10.9308 + 0.705169i 0.962403 + 0.0620867i
\(130\) 4.95262 0.434373
\(131\) −11.0671 −0.966941 −0.483470 0.875361i \(-0.660624\pi\)
−0.483470 + 0.875361i \(0.660624\pi\)
\(132\) 5.01859 8.69246i 0.436812 0.756581i
\(133\) 2.41750 0.209624
\(134\) 1.88067 3.25741i 0.162465 0.281398i
\(135\) 4.35132 7.53671i 0.374502 0.648657i
\(136\) 1.48129 + 2.56567i 0.127020 + 0.220005i
\(137\) 6.83961 0.584347 0.292174 0.956365i \(-0.405622\pi\)
0.292174 + 0.956365i \(0.405622\pi\)
\(138\) −2.19509 3.80201i −0.186858 0.323648i
\(139\) 10.2779 17.8018i 0.871757 1.50993i 0.0115800 0.999933i \(-0.496314\pi\)
0.860177 0.509995i \(-0.170353\pi\)
\(140\) −4.14910 −0.350663
\(141\) 1.38401 2.39717i 0.116555 0.201879i
\(142\) −5.71882 9.90528i −0.479913 0.831233i
\(143\) 8.89542 + 15.4073i 0.743872 + 1.28842i
\(144\) −0.0763852 0.132303i −0.00636544 0.0110253i
\(145\) −4.56882 −0.379420
\(146\) −3.35932 5.81852i −0.278020 0.481544i
\(147\) 1.05124 + 1.82081i 0.0867050 + 0.150178i
\(148\) 2.12489 3.68042i 0.174665 0.302529i
\(149\) −3.52700 + 6.10894i −0.288943 + 0.500464i −0.973558 0.228441i \(-0.926637\pi\)
0.684615 + 0.728905i \(0.259971\pi\)
\(150\) 3.81688 0.311647
\(151\) 8.93045 0.726750 0.363375 0.931643i \(-0.381624\pi\)
0.363375 + 0.931643i \(0.381624\pi\)
\(152\) −1.49452 + 2.58859i −0.121222 + 0.209962i
\(153\) −0.104888 + 0.181671i −0.00847969 + 0.0146873i
\(154\) 6.51869 + 11.2907i 0.525291 + 0.909830i
\(155\) −2.33748 4.04863i −0.187751 0.325194i
\(156\) 5.62867 0.450654
\(157\) 3.08965 + 5.35143i 0.246581 + 0.427091i 0.962575 0.271016i \(-0.0873596\pi\)
−0.715994 + 0.698106i \(0.754026\pi\)
\(158\) −4.64639 8.04779i −0.369647 0.640247i
\(159\) 0.133834 + 0.231808i 0.0106137 + 0.0183835i
\(160\) 4.23776 7.34001i 0.335024 0.580279i
\(161\) −6.51908 −0.513775
\(162\) −4.02183 + 6.96602i −0.315985 + 0.547302i
\(163\) −9.79193 16.9601i −0.766963 1.32842i −0.939203 0.343364i \(-0.888434\pi\)
0.172240 0.985055i \(-0.444900\pi\)
\(164\) 3.06081 0.239009
\(165\) −7.63568 13.2254i −0.594437 1.02959i
\(166\) −1.70101 + 2.94624i −0.132024 + 0.228673i
\(167\) −1.25085 + 2.16653i −0.0967935 + 0.167651i −0.910356 0.413827i \(-0.864192\pi\)
0.813562 + 0.581478i \(0.197525\pi\)
\(168\) 11.8576 0.914833
\(169\) 1.51161 2.61819i 0.116278 0.201399i
\(170\) 1.56798 0.120258
\(171\) −0.211649 −0.0161852
\(172\) 3.10052 + 6.27099i 0.236412 + 0.478158i
\(173\) −10.2228 −0.777227 −0.388614 0.921401i \(-0.627046\pi\)
−0.388614 + 0.921401i \(0.627046\pi\)
\(174\) 4.54202 0.344330
\(175\) 2.83388 4.90843i 0.214221 0.371042i
\(176\) −4.10190 −0.309192
\(177\) 3.52045 6.09760i 0.264613 0.458323i
\(178\) 8.82714 15.2891i 0.661622 1.14596i
\(179\) −3.05215 5.28647i −0.228128 0.395129i 0.729125 0.684380i \(-0.239927\pi\)
−0.957253 + 0.289251i \(0.906594\pi\)
\(180\) 0.363248 0.0270749
\(181\) 5.76750 + 9.98961i 0.428695 + 0.742522i 0.996758 0.0804637i \(-0.0256401\pi\)
−0.568062 + 0.822985i \(0.692307\pi\)
\(182\) −3.65556 + 6.33162i −0.270968 + 0.469331i
\(183\) −2.05443 −0.151868
\(184\) 4.03015 6.98042i 0.297106 0.514603i
\(185\) −3.23298 5.59968i −0.237693 0.411696i
\(186\) 2.32377 + 4.02489i 0.170387 + 0.295119i
\(187\) 2.81625 + 4.87789i 0.205945 + 0.356707i
\(188\) 1.76783 0.128932
\(189\) 6.42348 + 11.1258i 0.467239 + 0.809282i
\(190\) 0.790989 + 1.37003i 0.0573844 + 0.0993927i
\(191\) −8.39356 + 14.5381i −0.607337 + 1.05194i 0.384341 + 0.923191i \(0.374429\pi\)
−0.991677 + 0.128747i \(0.958905\pi\)
\(192\) −5.42938 + 9.40396i −0.391832 + 0.678672i
\(193\) −1.18229 −0.0851030 −0.0425515 0.999094i \(-0.513549\pi\)
−0.0425515 + 0.999094i \(0.513549\pi\)
\(194\) 7.77662 0.558329
\(195\) 4.28195 7.41655i 0.306637 0.531110i
\(196\) −0.671390 + 1.16288i −0.0479564 + 0.0830629i
\(197\) −10.4025 18.0176i −0.741144 1.28370i −0.951975 0.306177i \(-0.900950\pi\)
0.210830 0.977523i \(-0.432383\pi\)
\(198\) −0.570702 0.988485i −0.0405581 0.0702486i
\(199\) −22.1669 −1.57137 −0.785685 0.618626i \(-0.787690\pi\)
−0.785685 + 0.618626i \(0.787690\pi\)
\(200\) 3.50386 + 6.06886i 0.247760 + 0.429133i
\(201\) −3.25199 5.63261i −0.229378 0.397294i
\(202\) 1.76030 + 3.04892i 0.123854 + 0.214521i
\(203\) 3.37228 5.84096i 0.236687 0.409955i
\(204\) 1.78201 0.124766
\(205\) 2.32847 4.03304i 0.162628 0.281679i
\(206\) −8.10686 14.0415i −0.564832 0.978318i
\(207\) 0.570737 0.0396689
\(208\) −1.15013 1.99209i −0.0797475 0.138127i
\(209\) −2.84140 + 4.92145i −0.196544 + 0.340424i
\(210\) 3.13787 5.43495i 0.216534 0.375047i
\(211\) 5.53430 0.380997 0.190499 0.981687i \(-0.438990\pi\)
0.190499 + 0.981687i \(0.438990\pi\)
\(212\) −0.0854749 + 0.148047i −0.00587044 + 0.0101679i
\(213\) −19.7776 −1.35514
\(214\) −0.818452 −0.0559482
\(215\) 10.6216 + 0.685221i 0.724386 + 0.0467317i
\(216\) −15.8842 −1.08078
\(217\) 6.90124 0.468486
\(218\) 1.98952 3.44595i 0.134747 0.233389i
\(219\) −11.6177 −0.785049
\(220\) 4.87662 8.44656i 0.328782 0.569467i
\(221\) −1.57930 + 2.73543i −0.106235 + 0.184005i
\(222\) 3.21401 + 5.56684i 0.215711 + 0.373622i
\(223\) 21.2269 1.42146 0.710728 0.703467i \(-0.248366\pi\)
0.710728 + 0.703467i \(0.248366\pi\)
\(224\) 6.25584 + 10.8354i 0.417986 + 0.723972i
\(225\) −0.248103 + 0.429726i −0.0165402 + 0.0286484i
\(226\) 8.02841 0.534042
\(227\) 10.5173 18.2165i 0.698056 1.20907i −0.271083 0.962556i \(-0.587382\pi\)
0.969139 0.246513i \(-0.0792848\pi\)
\(228\) 0.898963 + 1.55705i 0.0595353 + 0.103118i
\(229\) 11.7257 + 20.3095i 0.774854 + 1.34209i 0.934876 + 0.354973i \(0.115510\pi\)
−0.160022 + 0.987113i \(0.551157\pi\)
\(230\) −2.13299 3.69445i −0.140645 0.243605i
\(231\) 22.5438 1.48327
\(232\) 4.16954 + 7.22186i 0.273744 + 0.474138i
\(233\) −4.16875 7.22049i −0.273104 0.473030i 0.696551 0.717507i \(-0.254717\pi\)
−0.969655 + 0.244477i \(0.921384\pi\)
\(234\) 0.320040 0.554325i 0.0209216 0.0362373i
\(235\) 1.34486 2.32936i 0.0877289 0.151951i
\(236\) 4.49676 0.292714
\(237\) −16.0688 −1.04378
\(238\) −1.15733 + 2.00456i −0.0750188 + 0.129936i
\(239\) 10.7921 18.6925i 0.698084 1.20912i −0.271046 0.962566i \(-0.587369\pi\)
0.969130 0.246551i \(-0.0792972\pi\)
\(240\) 0.987257 + 1.70998i 0.0637271 + 0.110379i
\(241\) −8.52187 14.7603i −0.548942 0.950795i −0.998347 0.0574673i \(-0.981697\pi\)
0.449406 0.893328i \(-0.351636\pi\)
\(242\) −20.0207 −1.28698
\(243\) −1.08798 1.88444i −0.0697940 0.120887i
\(244\) −0.656045 1.13630i −0.0419990 0.0727444i
\(245\) 1.02150 + 1.76930i 0.0652615 + 0.113036i
\(246\) −2.31482 + 4.00938i −0.147587 + 0.255629i
\(247\) −3.18681 −0.202772
\(248\) −4.26640 + 7.38963i −0.270917 + 0.469242i
\(249\) 2.94133 + 5.09454i 0.186399 + 0.322853i
\(250\) 11.5488 0.730409
\(251\) 5.03434 + 8.71972i 0.317764 + 0.550384i 0.980021 0.198893i \(-0.0637346\pi\)
−0.662257 + 0.749277i \(0.730401\pi\)
\(252\) −0.268116 + 0.464391i −0.0168897 + 0.0292539i
\(253\) 7.66216 13.2712i 0.481716 0.834356i
\(254\) 2.35223 0.147592
\(255\) 1.35565 2.34805i 0.0848939 0.147040i
\(256\) −17.0235 −1.06397
\(257\) 4.86599 0.303532 0.151766 0.988416i \(-0.451504\pi\)
0.151766 + 0.988416i \(0.451504\pi\)
\(258\) −10.5593 0.681202i −0.657393 0.0424098i
\(259\) 9.54512 0.593105
\(260\) 5.46944 0.339200
\(261\) −0.295238 + 0.511368i −0.0182748 + 0.0316529i
\(262\) 10.6910 0.660492
\(263\) −0.221067 + 0.382898i −0.0136315 + 0.0236105i −0.872761 0.488148i \(-0.837673\pi\)
0.859129 + 0.511759i \(0.171006\pi\)
\(264\) −13.9368 + 24.1392i −0.857748 + 1.48566i
\(265\) 0.130048 + 0.225250i 0.00798880 + 0.0138370i
\(266\) −2.33534 −0.143189
\(267\) −15.2636 26.4373i −0.934117 1.61794i
\(268\) 2.07692 3.59734i 0.126868 0.219742i
\(269\) −15.7482 −0.960187 −0.480094 0.877217i \(-0.659397\pi\)
−0.480094 + 0.877217i \(0.659397\pi\)
\(270\) −4.20343 + 7.28055i −0.255813 + 0.443080i
\(271\) 15.2225 + 26.3662i 0.924701 + 1.60163i 0.792041 + 0.610468i \(0.209019\pi\)
0.132661 + 0.991162i \(0.457648\pi\)
\(272\) −0.364128 0.630688i −0.0220785 0.0382411i
\(273\) 6.32107 + 10.9484i 0.382569 + 0.662628i
\(274\) −6.60715 −0.399152
\(275\) 6.66157 + 11.5382i 0.401708 + 0.695779i
\(276\) −2.42416 4.19876i −0.145917 0.252736i
\(277\) −3.35046 + 5.80317i −0.201310 + 0.348679i −0.948951 0.315425i \(-0.897853\pi\)
0.747641 + 0.664103i \(0.231186\pi\)
\(278\) −9.92855 + 17.1967i −0.595475 + 1.03139i
\(279\) −0.604194 −0.0361722
\(280\) 11.5222 0.688581
\(281\) −6.33798 + 10.9777i −0.378092 + 0.654875i −0.990785 0.135447i \(-0.956753\pi\)
0.612692 + 0.790321i \(0.290086\pi\)
\(282\) −1.33697 + 2.31570i −0.0796154 + 0.137898i
\(283\) 1.63412 + 2.83038i 0.0971383 + 0.168248i 0.910499 0.413511i \(-0.135698\pi\)
−0.813361 + 0.581760i \(0.802364\pi\)
\(284\) −6.31560 10.9389i −0.374762 0.649107i
\(285\) 2.73550 0.162037
\(286\) −8.59308 14.8837i −0.508120 0.880089i
\(287\) 3.43733 + 5.95362i 0.202899 + 0.351431i
\(288\) −0.547690 0.948627i −0.0322730 0.0558984i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 4.41354 0.259172
\(291\) 6.72354 11.6455i 0.394141 0.682672i
\(292\) −3.70988 6.42571i −0.217104 0.376036i
\(293\) 2.47307 0.144478 0.0722391 0.997387i \(-0.476986\pi\)
0.0722391 + 0.997387i \(0.476986\pi\)
\(294\) −1.01551 1.75892i −0.0592260 0.102582i
\(295\) 3.42086 5.92510i 0.199170 0.344973i
\(296\) −5.90088 + 10.2206i −0.342981 + 0.594061i
\(297\) −30.1992 −1.75234
\(298\) 3.40713 5.90132i 0.197370 0.341854i
\(299\) 8.59360 0.496981
\(300\) 4.21518 0.243364
\(301\) −8.71588 + 13.0733i −0.502375 + 0.753531i
\(302\) −8.62693 −0.496424
\(303\) 6.08769 0.349729
\(304\) 0.367379 0.636320i 0.0210706 0.0364954i
\(305\) −1.99632 −0.114309
\(306\) 0.101323 0.175497i 0.00579226 0.0100325i
\(307\) 1.47371 2.55254i 0.0841092 0.145681i −0.820902 0.571069i \(-0.806529\pi\)
0.905011 + 0.425388i \(0.139862\pi\)
\(308\) 7.19894 + 12.4689i 0.410198 + 0.710483i
\(309\) −28.0362 −1.59493
\(310\) 2.25803 + 3.91103i 0.128248 + 0.222132i
\(311\) 12.8861 22.3194i 0.730703 1.26562i −0.225880 0.974155i \(-0.572526\pi\)
0.956583 0.291460i \(-0.0941410\pi\)
\(312\) −15.6310 −0.884929
\(313\) 3.15636 5.46697i 0.178408 0.309011i −0.762928 0.646484i \(-0.776239\pi\)
0.941335 + 0.337473i \(0.109572\pi\)
\(314\) −2.98464 5.16955i −0.168433 0.291734i
\(315\) 0.407933 + 0.706560i 0.0229844 + 0.0398102i
\(316\) −5.13126 8.88761i −0.288656 0.499967i
\(317\) −7.79584 −0.437858 −0.218929 0.975741i \(-0.570256\pi\)
−0.218929 + 0.975741i \(0.570256\pi\)
\(318\) −0.129285 0.223929i −0.00724997 0.0125573i
\(319\) 7.92717 + 13.7303i 0.443837 + 0.768747i
\(320\) −5.27579 + 9.13794i −0.294926 + 0.510826i
\(321\) −0.707620 + 1.22563i −0.0394955 + 0.0684082i
\(322\) 6.29751 0.350946
\(323\) −1.00893 −0.0561384
\(324\) −4.44153 + 7.69295i −0.246751 + 0.427386i
\(325\) −3.73569 + 6.47041i −0.207219 + 0.358914i
\(326\) 9.45912 + 16.3837i 0.523892 + 0.907408i
\(327\) −3.44021 5.95862i −0.190244 0.329513i
\(328\) −8.49994 −0.469330
\(329\) 1.98530 + 3.43864i 0.109453 + 0.189578i
\(330\) 7.37616 + 12.7759i 0.406044 + 0.703289i
\(331\) 8.78546 + 15.2169i 0.482892 + 0.836394i 0.999807 0.0196428i \(-0.00625289\pi\)
−0.516915 + 0.856037i \(0.672920\pi\)
\(332\) −1.87852 + 3.25369i −0.103097 + 0.178570i
\(333\) −0.835663 −0.0457941
\(334\) 1.20833 2.09290i 0.0661171 0.114518i
\(335\) −3.16000 5.47327i −0.172649 0.299037i
\(336\) −2.91480 −0.159016
\(337\) −2.00377 3.47064i −0.109152 0.189058i 0.806275 0.591541i \(-0.201480\pi\)
−0.915427 + 0.402484i \(0.868147\pi\)
\(338\) −1.46024 + 2.52920i −0.0794263 + 0.137570i
\(339\) 6.94123 12.0226i 0.376996 0.652976i
\(340\) 1.73160 0.0939093
\(341\) −8.11133 + 14.0492i −0.439253 + 0.760809i
\(342\) 0.204456 0.0110557
\(343\) −19.7887 −1.06849
\(344\) −8.61022 17.4147i −0.464232 0.938937i
\(345\) −7.37660 −0.397143
\(346\) 9.87538 0.530904
\(347\) 5.28346 9.15122i 0.283631 0.491263i −0.688645 0.725098i \(-0.741794\pi\)
0.972276 + 0.233835i \(0.0751276\pi\)
\(348\) 5.01600 0.268886
\(349\) 1.12511 1.94875i 0.0602258 0.104314i −0.834340 0.551249i \(-0.814151\pi\)
0.894566 + 0.446935i \(0.147485\pi\)
\(350\) −2.73757 + 4.74160i −0.146329 + 0.253449i
\(351\) −8.46758 14.6663i −0.451966 0.782828i
\(352\) −29.4111 −1.56761
\(353\) −8.58495 14.8696i −0.456931 0.791428i 0.541866 0.840465i \(-0.317718\pi\)
−0.998797 + 0.0490372i \(0.984385\pi\)
\(354\) −3.40080 + 5.89035i −0.180750 + 0.313069i
\(355\) −19.2181 −1.01999
\(356\) 9.74829 16.8845i 0.516658 0.894878i
\(357\) 2.00122 + 3.46622i 0.105916 + 0.183452i
\(358\) 2.94841 + 5.10680i 0.155828 + 0.269903i
\(359\) 17.7554 + 30.7533i 0.937094 + 1.62309i 0.770856 + 0.637009i \(0.219829\pi\)
0.166238 + 0.986086i \(0.446838\pi\)
\(360\) −1.00875 −0.0531658
\(361\) 8.99103 + 15.5729i 0.473212 + 0.819627i
\(362\) −5.57148 9.65009i −0.292830 0.507197i
\(363\) −17.3095 + 29.9810i −0.908515 + 1.57359i
\(364\) −4.03703 + 6.99235i −0.211598 + 0.366499i
\(365\) −11.2890 −0.590894
\(366\) 1.98461 0.103737
\(367\) −12.9865 + 22.4934i −0.677892 + 1.17414i 0.297722 + 0.954653i \(0.403773\pi\)
−0.975614 + 0.219491i \(0.929560\pi\)
\(368\) −0.990680 + 1.71591i −0.0516428 + 0.0894479i
\(369\) −0.300933 0.521232i −0.0156660 0.0271342i
\(370\) 3.12309 + 5.40936i 0.162362 + 0.281219i
\(371\) −0.383958 −0.0199341
\(372\) 2.56627 + 4.44490i 0.133055 + 0.230457i
\(373\) 1.00128 + 1.73427i 0.0518443 + 0.0897969i 0.890783 0.454429i \(-0.150157\pi\)
−0.838939 + 0.544226i \(0.816823\pi\)
\(374\) −2.72053 4.71210i −0.140675 0.243657i
\(375\) 9.98489 17.2943i 0.515617 0.893075i
\(376\) −4.90931 −0.253178
\(377\) −4.44542 + 7.69969i −0.228951 + 0.396554i
\(378\) −6.20516 10.7477i −0.319159 0.552800i
\(379\) 26.9435 1.38400 0.691998 0.721900i \(-0.256731\pi\)
0.691998 + 0.721900i \(0.256731\pi\)
\(380\) 0.873532 + 1.51300i 0.0448113 + 0.0776154i
\(381\) 2.03370 3.52248i 0.104190 0.180462i
\(382\) 8.10828 14.0440i 0.414856 0.718552i
\(383\) −27.4071 −1.40044 −0.700218 0.713930i \(-0.746914\pi\)
−0.700218 + 0.713930i \(0.746914\pi\)
\(384\) −3.47741 + 6.02305i −0.177456 + 0.307362i
\(385\) 21.9061 1.11644
\(386\) 1.14211 0.0581316
\(387\) 0.763063 1.14455i 0.0387887 0.0581806i
\(388\) 8.58815 0.435997
\(389\) −5.58060 −0.282947 −0.141474 0.989942i \(-0.545184\pi\)
−0.141474 + 0.989942i \(0.545184\pi\)
\(390\) −4.13642 + 7.16448i −0.209456 + 0.362788i
\(391\) 2.72070 0.137591
\(392\) 1.86447 3.22935i 0.0941698 0.163107i
\(393\) 9.24326 16.0098i 0.466261 0.807587i
\(394\) 10.0489 + 17.4052i 0.506256 + 0.876862i
\(395\) −15.6142 −0.785636
\(396\) −0.630258 1.09164i −0.0316716 0.0548569i
\(397\) 2.73742 4.74135i 0.137387 0.237961i −0.789120 0.614239i \(-0.789463\pi\)
0.926507 + 0.376278i \(0.122796\pi\)
\(398\) 21.4135 1.07336
\(399\) −2.01909 + 3.49717i −0.101081 + 0.175078i
\(400\) −0.861310 1.49183i −0.0430655 0.0745916i
\(401\) 15.0892 + 26.1352i 0.753516 + 1.30513i 0.946108 + 0.323850i \(0.104977\pi\)
−0.192592 + 0.981279i \(0.561689\pi\)
\(402\) 3.14146 + 5.44117i 0.156682 + 0.271381i
\(403\) −9.09737 −0.453172
\(404\) 1.94399 + 3.36709i 0.0967171 + 0.167519i
\(405\) 6.75769 + 11.7047i 0.335792 + 0.581609i
\(406\) −3.25766 + 5.64244i −0.161675 + 0.280029i
\(407\) −11.2188 + 19.4315i −0.556096 + 0.963186i
\(408\) −4.94869 −0.244997
\(409\) 8.07919 0.399490 0.199745 0.979848i \(-0.435989\pi\)
0.199745 + 0.979848i \(0.435989\pi\)
\(410\) −2.24934 + 3.89596i −0.111087 + 0.192408i
\(411\) −5.71243 + 9.89422i −0.281773 + 0.488046i
\(412\) −8.95285 15.5068i −0.441075 0.763965i
\(413\) 5.04992 + 8.74672i 0.248490 + 0.430398i
\(414\) −0.551339 −0.0270968
\(415\) 2.85813 + 4.95042i 0.140300 + 0.243007i
\(416\) −8.24659 14.2835i −0.404322 0.700307i
\(417\) 17.1681 + 29.7360i 0.840726 + 1.45618i
\(418\) 2.74483 4.75418i 0.134254 0.232535i
\(419\) 30.2812 1.47933 0.739667 0.672973i \(-0.234983\pi\)
0.739667 + 0.672973i \(0.234983\pi\)
\(420\) 3.46532 6.00211i 0.169090 0.292873i
\(421\) 4.05941 + 7.03110i 0.197843 + 0.342675i 0.947829 0.318779i \(-0.103273\pi\)
−0.749985 + 0.661454i \(0.769940\pi\)
\(422\) −5.34621 −0.260249
\(423\) −0.173810 0.301048i −0.00845094 0.0146375i
\(424\) 0.237366 0.411130i 0.0115275 0.0199662i
\(425\) −1.18270 + 2.04850i −0.0573695 + 0.0993669i
\(426\) 19.1054 0.925659
\(427\) 1.47349 2.55217i 0.0713074 0.123508i
\(428\) −0.903861 −0.0436898
\(429\) −29.7177 −1.43479
\(430\) −10.2606 0.661932i −0.494809 0.0319212i
\(431\) 36.7615 1.77074 0.885370 0.464887i \(-0.153905\pi\)
0.885370 + 0.464887i \(0.153905\pi\)
\(432\) 3.90461 0.187861
\(433\) −13.1778 + 22.8247i −0.633286 + 1.09688i 0.353589 + 0.935401i \(0.384961\pi\)
−0.986875 + 0.161483i \(0.948372\pi\)
\(434\) −6.66668 −0.320011
\(435\) 3.81587 6.60928i 0.182957 0.316891i
\(436\) 2.19714 3.80555i 0.105224 0.182253i
\(437\) 1.37250 + 2.37723i 0.0656554 + 0.113718i
\(438\) 11.2228 0.536246
\(439\) 12.5550 + 21.7459i 0.599217 + 1.03787i 0.992937 + 0.118643i \(0.0378545\pi\)
−0.393720 + 0.919230i \(0.628812\pi\)
\(440\) −13.5425 + 23.4563i −0.645614 + 1.11824i
\(441\) 0.264040 0.0125733
\(442\) 1.52563 2.64246i 0.0725666 0.125689i
\(443\) 11.4129 + 19.7677i 0.542244 + 0.939194i 0.998775 + 0.0494864i \(0.0157584\pi\)
−0.456531 + 0.889708i \(0.650908\pi\)
\(444\) 3.54941 + 6.14776i 0.168448 + 0.291760i
\(445\) −14.8318 25.6894i −0.703095 1.21780i
\(446\) −20.5054 −0.970959
\(447\) −5.89149 10.2044i −0.278658 0.482650i
\(448\) −7.78819 13.4895i −0.367958 0.637321i
\(449\) 2.64182 4.57577i 0.124675 0.215944i −0.796931 0.604071i \(-0.793544\pi\)
0.921606 + 0.388127i \(0.126878\pi\)
\(450\) 0.239670 0.415121i 0.0112982 0.0195690i
\(451\) −16.1602 −0.760953
\(452\) 8.86621 0.417031
\(453\) −7.45870 + 12.9188i −0.350440 + 0.606980i
\(454\) −10.1598 + 17.5973i −0.476824 + 0.825884i
\(455\) 6.14226 + 10.6387i 0.287954 + 0.498750i
\(456\) −2.49644 4.32397i −0.116907 0.202488i
\(457\) 3.96331 0.185396 0.0926979 0.995694i \(-0.470451\pi\)
0.0926979 + 0.995694i \(0.470451\pi\)
\(458\) −11.3271 19.6192i −0.529283 0.916744i
\(459\) −2.68080 4.64328i −0.125129 0.216730i
\(460\) −2.35558 4.07998i −0.109829 0.190230i
\(461\) −8.73731 + 15.1335i −0.406937 + 0.704836i −0.994545 0.104310i \(-0.966736\pi\)
0.587608 + 0.809146i \(0.300070\pi\)
\(462\) −21.7776 −1.01318
\(463\) 4.26632 7.38948i 0.198273 0.343418i −0.749696 0.661783i \(-0.769800\pi\)
0.947968 + 0.318364i \(0.103134\pi\)
\(464\) −1.02495 1.77526i −0.0475819 0.0824143i
\(465\) 7.80903 0.362135
\(466\) 4.02706 + 6.97508i 0.186550 + 0.323114i
\(467\) 1.89941 3.28987i 0.0878942 0.152237i −0.818727 0.574184i \(-0.805320\pi\)
0.906621 + 0.421946i \(0.138653\pi\)
\(468\) 0.353437 0.612171i 0.0163376 0.0282976i
\(469\) 9.32966 0.430804
\(470\) −1.29915 + 2.25019i −0.0599253 + 0.103794i
\(471\) −10.3219 −0.475607
\(472\) −12.4876 −0.574789
\(473\) −16.3698 33.1090i −0.752686 1.52235i
\(474\) 15.5226 0.712978
\(475\) −2.38653 −0.109501
\(476\) −1.27811 + 2.21375i −0.0585819 + 0.101467i
\(477\) 0.0336150 0.00153913
\(478\) −10.4253 + 18.0572i −0.476843 + 0.825917i
\(479\) 14.0157 24.2759i 0.640393 1.10919i −0.344953 0.938620i \(-0.612105\pi\)
0.985345 0.170572i \(-0.0545617\pi\)
\(480\) 7.07874 + 12.2607i 0.323099 + 0.559623i
\(481\) −12.5826 −0.573718
\(482\) 8.23223 + 14.2586i 0.374968 + 0.649463i
\(483\) 5.44472 9.43053i 0.247743 0.429104i
\(484\) −22.1099 −1.00500
\(485\) 6.53334 11.3161i 0.296664 0.513837i
\(486\) 1.05100 + 1.82039i 0.0476745 + 0.0825746i
\(487\) −9.32066 16.1439i −0.422359 0.731548i 0.573810 0.818988i \(-0.305465\pi\)
−0.996170 + 0.0874402i \(0.972131\pi\)
\(488\) 1.82185 + 3.15554i 0.0824714 + 0.142845i
\(489\) 32.7128 1.47932
\(490\) −0.986786 1.70916i −0.0445785 0.0772121i
\(491\) −2.48589 4.30568i −0.112187 0.194313i 0.804465 0.594000i \(-0.202452\pi\)
−0.916652 + 0.399687i \(0.869119\pi\)
\(492\) −2.55638 + 4.42778i −0.115250 + 0.199620i
\(493\) −1.40740 + 2.43769i −0.0633861 + 0.109788i
\(494\) 3.07850 0.138508
\(495\) −1.91785 −0.0862008
\(496\) 1.04876 1.81650i 0.0470905 0.0815632i
\(497\) 14.1850 24.5692i 0.636285 1.10208i
\(498\) −2.84136 4.92139i −0.127325 0.220533i
\(499\) −18.9904 32.8923i −0.850126 1.47246i −0.881094 0.472940i \(-0.843193\pi\)
0.0309688 0.999520i \(-0.490141\pi\)
\(500\) 12.7539 0.570374
\(501\) −2.08941 3.61897i −0.0933480 0.161684i
\(502\) −4.86323 8.42336i −0.217057 0.375953i
\(503\) −4.58131 7.93506i −0.204271 0.353807i 0.745630 0.666361i \(-0.232149\pi\)
−0.949900 + 0.312554i \(0.898816\pi\)
\(504\) 0.744565 1.28962i 0.0331656 0.0574445i
\(505\) 5.91548 0.263235
\(506\) −7.40174 + 12.8202i −0.329048 + 0.569927i
\(507\) 2.52499 + 4.37341i 0.112139 + 0.194230i
\(508\) 2.59770 0.115254
\(509\) −16.3223 28.2710i −0.723472 1.25309i −0.959600 0.281369i \(-0.909212\pi\)
0.236127 0.971722i \(-0.424122\pi\)
\(510\) −1.30957 + 2.26824i −0.0579888 + 0.100440i
\(511\) 8.33250 14.4323i 0.368608 0.638448i
\(512\) 8.11775 0.358757
\(513\) 2.70474 4.68474i 0.119417 0.206837i
\(514\) −4.70061 −0.207335
\(515\) −27.2431 −1.20048
\(516\) −11.6612 0.752288i −0.513355 0.0331176i
\(517\) −9.33363 −0.410493
\(518\) −9.22071 −0.405135
\(519\) 8.53809 14.7884i 0.374780 0.649139i
\(520\) −15.1888 −0.666072
\(521\) 17.7285 30.7066i 0.776699 1.34528i −0.157135 0.987577i \(-0.550226\pi\)
0.933834 0.357706i \(-0.116441\pi\)
\(522\) 0.285204 0.493988i 0.0124830 0.0216213i
\(523\) 19.8182 + 34.3261i 0.866588 + 1.50097i 0.865462 + 0.500975i \(0.167025\pi\)
0.00112600 + 0.999999i \(0.499642\pi\)
\(524\) 11.8066 0.515776
\(525\) 4.73371 + 8.19902i 0.206596 + 0.357835i
\(526\) 0.213553 0.369885i 0.00931135 0.0161277i
\(527\) −2.88019 −0.125463
\(528\) 3.42590 5.93383i 0.149093 0.258237i
\(529\) 7.79891 + 13.5081i 0.339083 + 0.587309i
\(530\) −0.125628 0.217594i −0.00545694 0.00945169i
\(531\) −0.442114 0.765764i −0.0191861 0.0332313i
\(532\) −2.57904 −0.111816
\(533\) −4.53116 7.84821i −0.196266 0.339944i
\(534\) 14.7448 + 25.5388i 0.638071 + 1.10517i
\(535\) −0.687602 + 1.19096i −0.0297276 + 0.0514898i
\(536\) −5.76767 + 9.98990i −0.249126 + 0.431498i
\(537\) 10.1966 0.440015
\(538\) 15.2130 0.655879
\(539\) 3.54474 6.13967i 0.152683 0.264454i
\(540\) −4.64208 + 8.04031i −0.199763 + 0.346000i
\(541\) 14.3545 + 24.8627i 0.617149 + 1.06893i 0.990003 + 0.141043i \(0.0450456\pi\)
−0.372855 + 0.927890i \(0.621621\pi\)
\(542\) −14.7051 25.4700i −0.631639 1.09403i
\(543\) −19.2680 −0.826870
\(544\) −2.61083 4.52210i −0.111939 0.193883i
\(545\) −3.34289 5.79006i −0.143194 0.248019i
\(546\) −6.10623 10.5763i −0.261323 0.452624i
\(547\) 4.10831 7.11581i 0.175659 0.304250i −0.764730 0.644351i \(-0.777128\pi\)
0.940389 + 0.340101i \(0.110461\pi\)
\(548\) −7.29663 −0.311697
\(549\) −0.129003 + 0.223439i −0.00550569 + 0.00953614i
\(550\) −6.43516 11.1460i −0.274396 0.475268i
\(551\) −2.83993 −0.120985
\(552\) 6.73194 + 11.6601i 0.286531 + 0.496285i
\(553\) 11.5250 19.9618i 0.490091 0.848862i
\(554\) 3.23659 5.60593i 0.137509 0.238173i
\(555\) 10.8007 0.458464
\(556\) −10.9646 + 18.9913i −0.465004 + 0.805411i
\(557\) 27.0542 1.14632 0.573162 0.819442i \(-0.305717\pi\)
0.573162 + 0.819442i \(0.305717\pi\)
\(558\) 0.583659 0.0247083
\(559\) 11.4895 17.2335i 0.485953 0.728899i
\(560\) −2.83235 −0.119689
\(561\) −9.40851 −0.397228
\(562\) 6.12257 10.6046i 0.258265 0.447328i
\(563\) −29.0459 −1.22414 −0.612070 0.790804i \(-0.709663\pi\)
−0.612070 + 0.790804i \(0.709663\pi\)
\(564\) −1.47649 + 2.55735i −0.0621714 + 0.107684i
\(565\) 6.74487 11.6825i 0.283759 0.491485i
\(566\) −1.57858 2.73418i −0.0663526 0.114926i
\(567\) −19.9516 −0.837887
\(568\) 17.5386 + 30.3777i 0.735903 + 1.27462i
\(569\) 16.7964 29.0922i 0.704142 1.21961i −0.262858 0.964835i \(-0.584665\pi\)
0.967000 0.254776i \(-0.0820017\pi\)
\(570\) −2.64253 −0.110683
\(571\) 15.2367 26.3907i 0.637636 1.10442i −0.348314 0.937378i \(-0.613246\pi\)
0.985950 0.167040i \(-0.0534208\pi\)
\(572\) −9.48981 16.4368i −0.396789 0.687258i
\(573\) −14.0206 24.2843i −0.585718 1.01449i
\(574\) −3.32050 5.75127i −0.138595 0.240054i
\(575\) 6.43555 0.268381
\(576\) 0.681846 + 1.18099i 0.0284103 + 0.0492080i
\(577\) −15.8742 27.4950i −0.660853 1.14463i −0.980392 0.197058i \(-0.936861\pi\)
0.319539 0.947573i \(-0.396472\pi\)
\(578\) 0.483006 0.836591i 0.0200904 0.0347976i
\(579\) 0.987445 1.71030i 0.0410368 0.0710778i
\(580\) 4.87411 0.202386
\(581\) −8.43841 −0.350084
\(582\) −6.49502 + 11.2497i −0.269227 + 0.466315i
\(583\) 0.451283 0.781644i 0.0186902 0.0323724i
\(584\) 10.3024 + 17.8443i 0.426318 + 0.738404i
\(585\) −0.537747 0.931405i −0.0222331 0.0385088i
\(586\) −2.38901 −0.0986893
\(587\) −2.14668 3.71816i −0.0886030 0.153465i 0.818318 0.574766i \(-0.194907\pi\)
−0.906921 + 0.421301i \(0.861574\pi\)
\(588\) −1.12149 1.94247i −0.0462493 0.0801062i
\(589\) −1.45295 2.51659i −0.0598679 0.103694i
\(590\) −3.30459 + 5.72372i −0.136048 + 0.235642i
\(591\) 34.7525 1.42953
\(592\) 1.45054 2.51241i 0.0596168 0.103259i
\(593\) 15.4625 + 26.7818i 0.634967 + 1.09980i 0.986522 + 0.163628i \(0.0523197\pi\)
−0.351555 + 0.936167i \(0.614347\pi\)
\(594\) 29.1728 1.19697
\(595\) 1.94461 + 3.36817i 0.0797213 + 0.138081i
\(596\) 3.76267 6.51714i 0.154125 0.266953i
\(597\) 18.5138 32.0668i 0.757718 1.31241i
\(598\) −8.30152 −0.339475
\(599\) 10.8230 18.7460i 0.442216 0.765940i −0.555638 0.831424i \(-0.687526\pi\)
0.997854 + 0.0654844i \(0.0208592\pi\)
\(600\) −11.7057 −0.477882
\(601\) 18.1882 0.741911 0.370956 0.928651i \(-0.379030\pi\)
0.370956 + 0.928651i \(0.379030\pi\)
\(602\) 8.41964 12.6289i 0.343159 0.514717i
\(603\) −0.816799 −0.0332626
\(604\) −9.52718 −0.387656
\(605\) −16.8199 + 29.1329i −0.683825 + 1.18442i
\(606\) −5.88078 −0.238890
\(607\) −17.9365 + 31.0670i −0.728021 + 1.26097i 0.229698 + 0.973262i \(0.426226\pi\)
−0.957719 + 0.287707i \(0.907107\pi\)
\(608\) 2.63415 4.56248i 0.106829 0.185033i
\(609\) 5.63304 + 9.75671i 0.228262 + 0.395362i
\(610\) 1.92847 0.0780813
\(611\) −2.61707 4.53289i −0.105875 0.183381i
\(612\) 0.111897 0.193811i 0.00452315 0.00783433i
\(613\) 37.7047 1.52288 0.761439 0.648237i \(-0.224493\pi\)
0.761439 + 0.648237i \(0.224493\pi\)
\(614\) −1.42362 + 2.46579i −0.0574528 + 0.0995112i
\(615\) 3.88948 + 6.73677i 0.156839 + 0.271653i
\(616\) −19.9916 34.6265i −0.805486 1.39514i
\(617\) −10.0939 17.4832i −0.406366 0.703847i 0.588113 0.808779i \(-0.299871\pi\)
−0.994479 + 0.104932i \(0.966538\pi\)
\(618\) 27.0833 1.08945
\(619\) −9.66312 16.7370i −0.388394 0.672718i 0.603840 0.797106i \(-0.293637\pi\)
−0.992234 + 0.124388i \(0.960303\pi\)
\(620\) 2.49367 + 4.31916i 0.100148 + 0.173462i
\(621\) −7.29364 + 12.6330i −0.292684 + 0.506943i
\(622\) −12.4481 + 21.5608i −0.499124 + 0.864509i
\(623\) 43.7898 1.75440
\(624\) 3.84236 0.153818
\(625\) 3.78891 6.56259i 0.151556 0.262504i
\(626\) −3.04908 + 5.28116i −0.121866 + 0.211078i
\(627\) −4.74626 8.22077i −0.189547 0.328306i
\(628\) −3.29610 5.70901i −0.131529 0.227814i
\(629\) −3.98360 −0.158836
\(630\) −0.394068 0.682546i −0.0157001 0.0271933i
\(631\) −15.3159 26.5280i −0.609717 1.05606i −0.991287 0.131721i \(-0.957950\pi\)
0.381569 0.924340i \(-0.375384\pi\)
\(632\) 14.2496 + 24.6811i 0.566820 + 0.981762i
\(633\) −4.62224 + 8.00596i −0.183718 + 0.318208i
\(634\) 7.53088 0.299090
\(635\) 1.97617 3.42283i 0.0784220 0.135831i
\(636\) −0.142777 0.247297i −0.00566147 0.00980596i
\(637\) 3.97565 0.157521
\(638\) −7.65775 13.2636i −0.303173 0.525111i
\(639\) −1.24188 + 2.15100i −0.0491280 + 0.0850921i
\(640\) −3.37904 + 5.85267i −0.133568 + 0.231347i
\(641\) −10.9984 −0.434411 −0.217206 0.976126i \(-0.569694\pi\)
−0.217206 + 0.976126i \(0.569694\pi\)
\(642\) 0.683570 1.18398i 0.0269783 0.0467279i
\(643\) 32.7328 1.29086 0.645428 0.763821i \(-0.276679\pi\)
0.645428 + 0.763821i \(0.276679\pi\)
\(644\) 6.95468 0.274053
\(645\) −9.86237 + 14.7929i −0.388330 + 0.582472i
\(646\) 0.974639 0.0383467
\(647\) 1.55886 0.0612852 0.0306426 0.999530i \(-0.490245\pi\)
0.0306426 + 0.999530i \(0.490245\pi\)
\(648\) 12.3342 21.3635i 0.484534 0.839238i
\(649\) −23.7416 −0.931939
\(650\) 3.60872 6.25049i 0.141546 0.245164i
\(651\) −5.76390 + 9.98337i −0.225905 + 0.391279i
\(652\) 10.4462 + 18.0934i 0.409106 + 0.708592i
\(653\) −45.9321 −1.79746 −0.898731 0.438500i \(-0.855510\pi\)
−0.898731 + 0.438500i \(0.855510\pi\)
\(654\) 3.32329 + 5.75610i 0.129951 + 0.225081i
\(655\) 8.98178 15.5569i 0.350947 0.607858i
\(656\) 2.08943 0.0815786
\(657\) −0.729499 + 1.26353i −0.0284605 + 0.0492950i
\(658\) −1.91782 3.32177i −0.0747645 0.129496i
\(659\) −17.4295 30.1889i −0.678959 1.17599i −0.975295 0.220907i \(-0.929098\pi\)
0.296336 0.955084i \(-0.404235\pi\)
\(660\) 8.14589 + 14.1091i 0.317078 + 0.549196i
\(661\) 6.06816 0.236024 0.118012 0.993012i \(-0.462348\pi\)
0.118012 + 0.993012i \(0.462348\pi\)
\(662\) −8.48686 14.6997i −0.329851 0.571319i
\(663\) −2.63806 4.56925i −0.102454 0.177455i
\(664\) 5.21670 9.03559i 0.202447 0.350649i
\(665\) −1.96198 + 3.39824i −0.0760822 + 0.131778i
\(666\) 0.807261 0.0312807
\(667\) 7.65821 0.296527
\(668\) 1.33443 2.31130i 0.0516306 0.0894269i
\(669\) −17.7286 + 30.7069i −0.685429 + 1.18720i
\(670\) 3.05259 + 5.28725i 0.117932 + 0.204264i
\(671\) 3.46373 + 5.99935i 0.133716 + 0.231602i
\(672\) −20.8995 −0.806214
\(673\) 4.15016 + 7.18829i 0.159977 + 0.277088i 0.934860 0.355016i \(-0.115525\pi\)
−0.774883 + 0.632104i \(0.782191\pi\)
\(674\) 1.93567 + 3.35268i 0.0745592 + 0.129140i
\(675\) −6.34118 10.9832i −0.244072 0.422745i
\(676\) −1.61262 + 2.79313i −0.0620237 + 0.107428i
\(677\) 4.29386 0.165027 0.0825133 0.996590i \(-0.473705\pi\)
0.0825133 + 0.996590i \(0.473705\pi\)
\(678\) −6.70531 + 11.6139i −0.257516 + 0.446031i
\(679\) 9.64461 + 16.7049i 0.370126 + 0.641077i
\(680\) −4.80870 −0.184405
\(681\) 17.5680 + 30.4287i 0.673208 + 1.16603i
\(682\) 7.83565 13.5717i 0.300042 0.519689i
\(683\) 6.90684 11.9630i 0.264283 0.457752i −0.703092 0.711098i \(-0.748198\pi\)
0.967376 + 0.253347i \(0.0815313\pi\)
\(684\) 0.225792 0.00863336
\(685\) −5.55083 + 9.61432i −0.212086 + 0.367344i
\(686\) 19.1161 0.729856
\(687\) −39.1730 −1.49454
\(688\) 2.11654 + 4.28083i 0.0806924 + 0.163205i
\(689\) 0.506142 0.0192825
\(690\) 7.12589 0.271278
\(691\) −9.79320 + 16.9623i −0.372551 + 0.645277i −0.989957 0.141368i \(-0.954850\pi\)
0.617406 + 0.786644i \(0.288183\pi\)
\(692\) 10.9059 0.414581
\(693\) 1.41558 2.45185i 0.0537733 0.0931380i
\(694\) −5.10389 + 8.84019i −0.193741 + 0.335569i
\(695\) 16.6825 + 28.8949i 0.632801 + 1.09604i
\(696\) −13.9296 −0.527999
\(697\) −1.43455 2.48471i −0.0543373 0.0941150i
\(698\) −1.08687 + 1.88252i −0.0411387 + 0.0712543i
\(699\) 13.9269 0.526765
\(700\) −3.02324 + 5.23641i −0.114268 + 0.197918i
\(701\) −9.47681 16.4143i −0.357934 0.619960i 0.629681 0.776854i \(-0.283185\pi\)
−0.987616 + 0.156893i \(0.949852\pi\)
\(702\) 8.17979 + 14.1678i 0.308726 + 0.534730i
\(703\) −2.00959 3.48070i −0.0757930 0.131277i
\(704\) 36.6152 1.37999
\(705\) 2.24645 + 3.89096i 0.0846060 + 0.146542i
\(706\) 8.29317 + 14.3642i 0.312118 + 0.540604i
\(707\) −4.36625 + 7.56257i −0.164210 + 0.284420i
\(708\) −3.75568 + 6.50504i −0.141147 + 0.244474i
\(709\) 34.1097 1.28102 0.640508 0.767952i \(-0.278724\pi\)
0.640508 + 0.767952i \(0.278724\pi\)
\(710\) 18.5649 0.696729
\(711\) −1.00899 + 1.74763i −0.0378402 + 0.0655412i
\(712\) −27.0712 + 46.8888i −1.01454 + 1.75723i
\(713\) 3.91806 + 6.78627i 0.146732 + 0.254148i
\(714\) −1.93321 3.34841i −0.0723485 0.125311i
\(715\) −28.8771 −1.07994
\(716\) 3.25609 + 5.63971i 0.121686 + 0.210766i
\(717\) 18.0271 + 31.2239i 0.673235 + 1.16608i
\(718\) −17.1519 29.7080i −0.640105 1.10869i
\(719\) −5.85751 + 10.1455i −0.218448 + 0.378364i −0.954334 0.298742i \(-0.903433\pi\)
0.735885 + 0.677106i \(0.236766\pi\)
\(720\) 0.247968 0.00924123
\(721\) 20.1083 34.8287i 0.748874 1.29709i
\(722\) −8.68545 15.0436i −0.323239 0.559866i
\(723\) 28.4698 1.05880
\(724\) −6.15289 10.6571i −0.228670 0.396068i
\(725\) −3.32907 + 5.76612i −0.123639 + 0.214148i
\(726\) 16.7212 28.9620i 0.620583 1.07488i
\(727\) 28.0986 1.04212 0.521059 0.853521i \(-0.325537\pi\)
0.521059 + 0.853521i \(0.325537\pi\)
\(728\) 11.2109 19.4179i 0.415505 0.719676i
\(729\) 28.6147 1.05980
\(730\) 10.9053 0.403624
\(731\) 3.63752 5.45605i 0.134538 0.201799i
\(732\) 2.19171 0.0810079
\(733\) −5.86421 −0.216600 −0.108300 0.994118i \(-0.534541\pi\)
−0.108300 + 0.994118i \(0.534541\pi\)
\(734\) 12.5452 21.7289i 0.463051 0.802027i
\(735\) −3.41264 −0.125877
\(736\) −7.10329 + 12.3033i −0.261831 + 0.453504i
\(737\) −10.9656 + 18.9929i −0.403922 + 0.699613i
\(738\) 0.290705 + 0.503516i 0.0107010 + 0.0185347i
\(739\) 47.7460 1.75636 0.878182 0.478326i \(-0.158756\pi\)
0.878182 + 0.478326i \(0.158756\pi\)
\(740\) 3.44900 + 5.97385i 0.126788 + 0.219603i
\(741\) 2.66162 4.61006i 0.0977770 0.169355i
\(742\) 0.370908 0.0136165
\(743\) 25.2393 43.7157i 0.925940 1.60378i 0.135898 0.990723i \(-0.456608\pi\)
0.790042 0.613052i \(-0.210059\pi\)
\(744\) −7.12658 12.3436i −0.261273 0.452539i
\(745\) −5.72483 9.91569i −0.209741 0.363283i
\(746\) −0.967248 1.67532i −0.0354135 0.0613380i
\(747\) 0.738772 0.0270303
\(748\) −3.00443 5.20383i −0.109853 0.190271i
\(749\) −1.01505 1.75811i −0.0370890 0.0642401i
\(750\) −9.64552 + 16.7065i −0.352205 + 0.610036i
\(751\) 8.58116 14.8630i 0.313131 0.542359i −0.665907 0.746034i \(-0.731955\pi\)
0.979038 + 0.203675i \(0.0652887\pi\)
\(752\) 1.20679 0.0440073
\(753\) −16.8187 −0.612906
\(754\) 4.29433 7.43799i 0.156390 0.270876i
\(755\) −7.24770 + 12.5534i −0.263771 + 0.456864i
\(756\) −6.85270 11.8692i −0.249230 0.431679i
\(757\) −2.47231 4.28218i −0.0898578 0.155638i 0.817593 0.575796i \(-0.195308\pi\)
−0.907451 + 0.420158i \(0.861975\pi\)
\(758\) −26.0278 −0.945371
\(759\) 12.7988 + 22.1682i 0.464569 + 0.804656i
\(760\) −2.42582 4.20165i −0.0879938 0.152410i
\(761\) −15.4746 26.8027i −0.560952 0.971598i −0.997414 0.0718749i \(-0.977102\pi\)
0.436461 0.899723i \(-0.356232\pi\)
\(762\) −1.96458 + 3.40276i −0.0711693 + 0.123269i
\(763\) 9.86965 0.357305
\(764\) 8.95442 15.5095i 0.323960 0.561114i
\(765\) −0.170248 0.294879i −0.00615534 0.0106614i
\(766\) 26.4756 0.956601
\(767\) −6.65692 11.5301i −0.240368 0.416329i