Properties

Label 731.2.e.a.307.20
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 307.20
Character \(\chi\) = 731.307
Dual form 731.2.e.a.681.20

$q$-expansion

\(f(q)\) \(=\) \(q+0.875460 q^{2} +(-0.791784 + 1.37141i) q^{3} -1.23357 q^{4} +(-1.30803 + 2.26557i) q^{5} +(-0.693175 + 1.20061i) q^{6} +(1.95679 + 3.38927i) q^{7} -2.83086 q^{8} +(0.246156 + 0.426354i) q^{9} +O(q^{10})\) \(q+0.875460 q^{2} +(-0.791784 + 1.37141i) q^{3} -1.23357 q^{4} +(-1.30803 + 2.26557i) q^{5} +(-0.693175 + 1.20061i) q^{6} +(1.95679 + 3.38927i) q^{7} -2.83086 q^{8} +(0.246156 + 0.426354i) q^{9} +(-1.14512 + 1.98341i) q^{10} -0.537434 q^{11} +(0.976721 - 1.69173i) q^{12} +(-3.29996 - 5.71570i) q^{13} +(1.71309 + 2.96717i) q^{14} +(-2.07135 - 3.58768i) q^{15} -0.0111645 q^{16} +(0.500000 + 0.866025i) q^{17} +(0.215500 + 0.373256i) q^{18} +(0.210982 - 0.365431i) q^{19} +(1.61354 - 2.79474i) q^{20} -6.19743 q^{21} -0.470502 q^{22} +(2.04118 - 3.53542i) q^{23} +(2.24143 - 3.88227i) q^{24} +(-0.921869 - 1.59672i) q^{25} +(-2.88898 - 5.00387i) q^{26} -5.53031 q^{27} +(-2.41384 - 4.18090i) q^{28} +(-0.523622 - 0.906939i) q^{29} +(-1.81338 - 3.14087i) q^{30} +(-3.88892 + 6.73581i) q^{31} +5.65195 q^{32} +(0.425532 - 0.737042i) q^{33} +(0.437730 + 0.758170i) q^{34} -10.2382 q^{35} +(-0.303650 - 0.525938i) q^{36} +(0.963247 - 1.66839i) q^{37} +(0.184706 - 0.319920i) q^{38} +10.4514 q^{39} +(3.70284 - 6.41351i) q^{40} +6.80451 q^{41} -5.42560 q^{42} +(-6.53444 + 0.548721i) q^{43} +0.662962 q^{44} -1.28791 q^{45} +(1.78697 - 3.09512i) q^{46} -7.39617 q^{47} +(0.00883986 - 0.0153111i) q^{48} +(-4.15808 + 7.20201i) q^{49} +(-0.807059 - 1.39787i) q^{50} -1.58357 q^{51} +(4.07073 + 7.05072i) q^{52} +(-2.03019 + 3.51640i) q^{53} -4.84157 q^{54} +(0.702978 - 1.21759i) q^{55} +(-5.53941 - 9.59454i) q^{56} +(0.334104 + 0.578685i) q^{57} +(-0.458410 - 0.793989i) q^{58} -7.30342 q^{59} +(2.55516 + 4.42566i) q^{60} +(-1.31763 - 2.28220i) q^{61} +(-3.40459 + 5.89693i) q^{62} +(-0.963352 + 1.66858i) q^{63} +4.97038 q^{64} +17.2658 q^{65} +(0.372536 - 0.645251i) q^{66} +(-5.67123 + 9.82286i) q^{67} +(-0.616785 - 1.06830i) q^{68} +(3.23234 + 5.59858i) q^{69} -8.96309 q^{70} +(-1.56580 - 2.71205i) q^{71} +(-0.696833 - 1.20695i) q^{72} +(2.84738 + 4.93180i) q^{73} +(0.843284 - 1.46061i) q^{74} +2.91968 q^{75} +(-0.260261 + 0.450785i) q^{76} +(-1.05165 - 1.82151i) q^{77} +9.14981 q^{78} +(7.54020 + 13.0600i) q^{79} +(0.0146034 - 0.0252939i) q^{80} +(3.64035 - 6.30527i) q^{81} +5.95708 q^{82} +(6.60094 - 11.4332i) q^{83} +7.64497 q^{84} -2.61605 q^{85} +(-5.72064 + 0.480383i) q^{86} +1.65838 q^{87} +1.52140 q^{88} +(3.59425 - 6.22543i) q^{89} -1.12752 q^{90} +(12.9147 - 22.3689i) q^{91} +(-2.51793 + 4.36119i) q^{92} +(-6.15837 - 10.6666i) q^{93} -6.47505 q^{94} +(0.551939 + 0.955987i) q^{95} +(-4.47512 + 7.75114i) q^{96} -1.23173 q^{97} +(-3.64023 + 6.30507i) q^{98} +(-0.132292 - 0.229137i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.875460 0.619044 0.309522 0.950892i \(-0.399831\pi\)
0.309522 + 0.950892i \(0.399831\pi\)
\(3\) −0.791784 + 1.37141i −0.457137 + 0.791784i −0.998808 0.0488061i \(-0.984458\pi\)
0.541671 + 0.840590i \(0.317792\pi\)
\(4\) −1.23357 −0.616785
\(5\) −1.30803 + 2.26557i −0.584967 + 1.01319i 0.409912 + 0.912125i \(0.365559\pi\)
−0.994879 + 0.101068i \(0.967774\pi\)
\(6\) −0.693175 + 1.20061i −0.282988 + 0.490149i
\(7\) 1.95679 + 3.38927i 0.739598 + 1.28102i 0.952676 + 0.303987i \(0.0983179\pi\)
−0.213078 + 0.977035i \(0.568349\pi\)
\(8\) −2.83086 −1.00086
\(9\) 0.246156 + 0.426354i 0.0820519 + 0.142118i
\(10\) −1.14512 + 1.98341i −0.362120 + 0.627211i
\(11\) −0.537434 −0.162042 −0.0810212 0.996712i \(-0.525818\pi\)
−0.0810212 + 0.996712i \(0.525818\pi\)
\(12\) 0.976721 1.69173i 0.281955 0.488361i
\(13\) −3.29996 5.71570i −0.915245 1.58525i −0.806543 0.591176i \(-0.798664\pi\)
−0.108702 0.994074i \(-0.534669\pi\)
\(14\) 1.71309 + 2.96717i 0.457844 + 0.793008i
\(15\) −2.07135 3.58768i −0.534820 0.926336i
\(16\) −0.0111645 −0.00279112
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i
\(18\) 0.215500 + 0.373256i 0.0507937 + 0.0879773i
\(19\) 0.210982 0.365431i 0.0484025 0.0838356i −0.840809 0.541332i \(-0.817920\pi\)
0.889212 + 0.457496i \(0.151254\pi\)
\(20\) 1.61354 2.79474i 0.360799 0.624922i
\(21\) −6.19743 −1.35239
\(22\) −0.470502 −0.100311
\(23\) 2.04118 3.53542i 0.425615 0.737186i −0.570863 0.821045i \(-0.693391\pi\)
0.996478 + 0.0838591i \(0.0267246\pi\)
\(24\) 2.24143 3.88227i 0.457530 0.792465i
\(25\) −0.921869 1.59672i −0.184374 0.319345i
\(26\) −2.88898 5.00387i −0.566576 0.981339i
\(27\) −5.53031 −1.06431
\(28\) −2.41384 4.18090i −0.456173 0.790115i
\(29\) −0.523622 0.906939i −0.0972341 0.168414i 0.813305 0.581838i \(-0.197666\pi\)
−0.910539 + 0.413424i \(0.864333\pi\)
\(30\) −1.81338 3.14087i −0.331077 0.573442i
\(31\) −3.88892 + 6.73581i −0.698471 + 1.20979i 0.270526 + 0.962713i \(0.412803\pi\)
−0.968997 + 0.247074i \(0.920531\pi\)
\(32\) 5.65195 0.999133
\(33\) 0.425532 0.737042i 0.0740755 0.128303i
\(34\) 0.437730 + 0.758170i 0.0750701 + 0.130025i
\(35\) −10.2382 −1.73056
\(36\) −0.303650 0.525938i −0.0506084 0.0876563i
\(37\) 0.963247 1.66839i 0.158357 0.274282i −0.775919 0.630832i \(-0.782714\pi\)
0.934276 + 0.356550i \(0.116047\pi\)
\(38\) 0.184706 0.319920i 0.0299633 0.0518979i
\(39\) 10.4514 1.67357
\(40\) 3.70284 6.41351i 0.585471 1.01407i
\(41\) 6.80451 1.06269 0.531343 0.847157i \(-0.321687\pi\)
0.531343 + 0.847157i \(0.321687\pi\)
\(42\) −5.42560 −0.837189
\(43\) −6.53444 + 0.548721i −0.996493 + 0.0836791i
\(44\) 0.662962 0.0999453
\(45\) −1.28791 −0.191991
\(46\) 1.78697 3.09512i 0.263474 0.456350i
\(47\) −7.39617 −1.07884 −0.539421 0.842036i \(-0.681357\pi\)
−0.539421 + 0.842036i \(0.681357\pi\)
\(48\) 0.00883986 0.0153111i 0.00127592 0.00220996i
\(49\) −4.15808 + 7.20201i −0.594012 + 1.02886i
\(50\) −0.807059 1.39787i −0.114135 0.197688i
\(51\) −1.58357 −0.221744
\(52\) 4.07073 + 7.05072i 0.564509 + 0.977759i
\(53\) −2.03019 + 3.51640i −0.278868 + 0.483014i −0.971104 0.238658i \(-0.923293\pi\)
0.692235 + 0.721672i \(0.256626\pi\)
\(54\) −4.84157 −0.658854
\(55\) 0.702978 1.21759i 0.0947895 0.164180i
\(56\) −5.53941 9.59454i −0.740235 1.28212i
\(57\) 0.334104 + 0.578685i 0.0442531 + 0.0766487i
\(58\) −0.458410 0.793989i −0.0601922 0.104256i
\(59\) −7.30342 −0.950824 −0.475412 0.879763i \(-0.657701\pi\)
−0.475412 + 0.879763i \(0.657701\pi\)
\(60\) 2.55516 + 4.42566i 0.329869 + 0.571350i
\(61\) −1.31763 2.28220i −0.168705 0.292205i 0.769260 0.638936i \(-0.220625\pi\)
−0.937965 + 0.346731i \(0.887292\pi\)
\(62\) −3.40459 + 5.89693i −0.432384 + 0.748911i
\(63\) −0.963352 + 1.66858i −0.121371 + 0.210221i
\(64\) 4.97038 0.621298
\(65\) 17.2658 2.14155
\(66\) 0.372536 0.645251i 0.0458560 0.0794249i
\(67\) −5.67123 + 9.82286i −0.692851 + 1.20005i 0.278049 + 0.960567i \(0.410312\pi\)
−0.970900 + 0.239486i \(0.923021\pi\)
\(68\) −0.616785 1.06830i −0.0747962 0.129551i
\(69\) 3.23234 + 5.59858i 0.389128 + 0.673990i
\(70\) −8.96309 −1.07129
\(71\) −1.56580 2.71205i −0.185827 0.321861i 0.758028 0.652222i \(-0.226163\pi\)
−0.943855 + 0.330361i \(0.892830\pi\)
\(72\) −0.696833 1.20695i −0.0821225 0.142240i
\(73\) 2.84738 + 4.93180i 0.333260 + 0.577224i 0.983149 0.182806i \(-0.0585179\pi\)
−0.649889 + 0.760029i \(0.725185\pi\)
\(74\) 0.843284 1.46061i 0.0980298 0.169793i
\(75\) 2.91968 0.337136
\(76\) −0.260261 + 0.450785i −0.0298540 + 0.0517086i
\(77\) −1.05165 1.82151i −0.119846 0.207580i
\(78\) 9.14981 1.03601
\(79\) 7.54020 + 13.0600i 0.848339 + 1.46937i 0.882689 + 0.469957i \(0.155731\pi\)
−0.0343502 + 0.999410i \(0.510936\pi\)
\(80\) 0.0146034 0.0252939i 0.00163271 0.00282794i
\(81\) 3.64035 6.30527i 0.404483 0.700585i
\(82\) 5.95708 0.657849
\(83\) 6.60094 11.4332i 0.724547 1.25495i −0.234613 0.972089i \(-0.575382\pi\)
0.959160 0.282863i \(-0.0912843\pi\)
\(84\) 7.64497 0.834134
\(85\) −2.61605 −0.283751
\(86\) −5.72064 + 0.480383i −0.616872 + 0.0518010i
\(87\) 1.65838 0.177797
\(88\) 1.52140 0.162182
\(89\) 3.59425 6.22543i 0.380990 0.659894i −0.610214 0.792237i \(-0.708917\pi\)
0.991204 + 0.132342i \(0.0422498\pi\)
\(90\) −1.12752 −0.118851
\(91\) 12.9147 22.3689i 1.35383 2.34490i
\(92\) −2.51793 + 4.36119i −0.262513 + 0.454685i
\(93\) −6.15837 10.6666i −0.638593 1.10608i
\(94\) −6.47505 −0.667850
\(95\) 0.551939 + 0.955987i 0.0566278 + 0.0980822i
\(96\) −4.47512 + 7.75114i −0.456740 + 0.791097i
\(97\) −1.23173 −0.125064 −0.0625319 0.998043i \(-0.519918\pi\)
−0.0625319 + 0.998043i \(0.519918\pi\)
\(98\) −3.64023 + 6.30507i −0.367719 + 0.636908i
\(99\) −0.132292 0.229137i −0.0132959 0.0230292i
\(100\) 1.13719 + 1.96967i 0.113719 + 0.196967i
\(101\) 3.47676 + 6.02192i 0.345950 + 0.599204i 0.985526 0.169525i \(-0.0542232\pi\)
−0.639576 + 0.768728i \(0.720890\pi\)
\(102\) −1.38635 −0.137269
\(103\) 4.30243 + 7.45203i 0.423931 + 0.734270i 0.996320 0.0857120i \(-0.0273165\pi\)
−0.572389 + 0.819982i \(0.693983\pi\)
\(104\) 9.34173 + 16.1804i 0.916032 + 1.58661i
\(105\) 8.10641 14.0407i 0.791104 1.37023i
\(106\) −1.77735 + 3.07846i −0.172632 + 0.299007i
\(107\) 18.7614 1.81374 0.906868 0.421415i \(-0.138467\pi\)
0.906868 + 0.421415i \(0.138467\pi\)
\(108\) 6.82203 0.656450
\(109\) −6.00967 + 10.4091i −0.575622 + 0.997007i 0.420352 + 0.907361i \(0.361907\pi\)
−0.995974 + 0.0896453i \(0.971427\pi\)
\(110\) 0.615429 1.06595i 0.0586788 0.101635i
\(111\) 1.52537 + 2.64201i 0.144782 + 0.250769i
\(112\) −0.0218466 0.0378394i −0.00206431 0.00357549i
\(113\) −10.2607 −0.965248 −0.482624 0.875828i \(-0.660316\pi\)
−0.482624 + 0.875828i \(0.660316\pi\)
\(114\) 0.292495 + 0.506615i 0.0273946 + 0.0474489i
\(115\) 5.33983 + 9.24885i 0.497941 + 0.862460i
\(116\) 0.645924 + 1.11877i 0.0599726 + 0.103876i
\(117\) 1.62461 2.81391i 0.150195 0.260146i
\(118\) −6.39385 −0.588602
\(119\) −1.95679 + 3.38927i −0.179379 + 0.310693i
\(120\) 5.86370 + 10.1562i 0.535280 + 0.927133i
\(121\) −10.7112 −0.973742
\(122\) −1.15353 1.99797i −0.104436 0.180888i
\(123\) −5.38771 + 9.33178i −0.485793 + 0.841418i
\(124\) 4.79726 8.30909i 0.430806 0.746179i
\(125\) −8.25695 −0.738524
\(126\) −0.843376 + 1.46077i −0.0751339 + 0.130136i
\(127\) 17.9591 1.59361 0.796806 0.604235i \(-0.206521\pi\)
0.796806 + 0.604235i \(0.206521\pi\)
\(128\) −6.95253 −0.614522
\(129\) 4.42134 9.39587i 0.389278 0.827260i
\(130\) 15.1155 1.32571
\(131\) −11.1845 −0.977197 −0.488599 0.872509i \(-0.662492\pi\)
−0.488599 + 0.872509i \(0.662492\pi\)
\(132\) −0.524923 + 0.909193i −0.0456887 + 0.0791351i
\(133\) 1.65139 0.143194
\(134\) −4.96493 + 8.59952i −0.428905 + 0.742885i
\(135\) 7.23380 12.5293i 0.622586 1.07835i
\(136\) −1.41543 2.45160i −0.121372 0.210223i
\(137\) −1.82986 −0.156335 −0.0781677 0.996940i \(-0.524907\pi\)
−0.0781677 + 0.996940i \(0.524907\pi\)
\(138\) 2.82979 + 4.90133i 0.240887 + 0.417229i
\(139\) −3.88102 + 6.72213i −0.329184 + 0.570163i −0.982350 0.187051i \(-0.940107\pi\)
0.653166 + 0.757215i \(0.273440\pi\)
\(140\) 12.6295 1.06739
\(141\) 5.85617 10.1432i 0.493178 0.854210i
\(142\) −1.37080 2.37429i −0.115035 0.199246i
\(143\) 1.77351 + 3.07181i 0.148308 + 0.256878i
\(144\) −0.00274820 0.00476002i −0.000229017 0.000396669i
\(145\) 2.73965 0.227515
\(146\) 2.49276 + 4.31759i 0.206303 + 0.357327i
\(147\) −6.58461 11.4049i −0.543089 0.940658i
\(148\) −1.18823 + 2.05808i −0.0976722 + 0.169173i
\(149\) −4.35260 + 7.53893i −0.356579 + 0.617613i −0.987387 0.158326i \(-0.949390\pi\)
0.630808 + 0.775939i \(0.282724\pi\)
\(150\) 2.55607 0.208702
\(151\) −2.98204 −0.242675 −0.121338 0.992611i \(-0.538718\pi\)
−0.121338 + 0.992611i \(0.538718\pi\)
\(152\) −0.597260 + 1.03448i −0.0484442 + 0.0839078i
\(153\) −0.246156 + 0.426354i −0.0199005 + 0.0344687i
\(154\) −0.920675 1.59466i −0.0741901 0.128501i
\(155\) −10.1736 17.6212i −0.817165 1.41537i
\(156\) −12.8926 −1.03223
\(157\) −5.15773 8.93346i −0.411632 0.712967i 0.583436 0.812159i \(-0.301708\pi\)
−0.995068 + 0.0991914i \(0.968374\pi\)
\(158\) 6.60115 + 11.4335i 0.525159 + 0.909602i
\(159\) −3.21495 5.56845i −0.254962 0.441607i
\(160\) −7.39290 + 12.8049i −0.584460 + 1.01231i
\(161\) 15.9766 1.25914
\(162\) 3.18698 5.52001i 0.250393 0.433693i
\(163\) 4.96681 + 8.60277i 0.389031 + 0.673821i 0.992319 0.123702i \(-0.0394766\pi\)
−0.603289 + 0.797523i \(0.706143\pi\)
\(164\) −8.39384 −0.655449
\(165\) 1.11321 + 1.92814i 0.0866636 + 0.150106i
\(166\) 5.77886 10.0093i 0.448526 0.776870i
\(167\) −7.28153 + 12.6120i −0.563462 + 0.975944i 0.433729 + 0.901043i \(0.357197\pi\)
−0.997191 + 0.0749009i \(0.976136\pi\)
\(168\) 17.5441 1.35355
\(169\) −15.2795 + 26.4649i −1.17535 + 2.03576i
\(170\) −2.29025 −0.175654
\(171\) 0.207738 0.0158861
\(172\) 8.06069 0.676885i 0.614622 0.0516120i
\(173\) −3.28029 −0.249396 −0.124698 0.992195i \(-0.539796\pi\)
−0.124698 + 0.992195i \(0.539796\pi\)
\(174\) 1.45185 0.110064
\(175\) 3.60781 6.24892i 0.272725 0.472374i
\(176\) 0.00600017 0.000452280
\(177\) 5.78273 10.0160i 0.434657 0.752848i
\(178\) 3.14662 5.45011i 0.235850 0.408503i
\(179\) 5.88823 + 10.1987i 0.440107 + 0.762288i 0.997697 0.0678289i \(-0.0216072\pi\)
−0.557590 + 0.830116i \(0.688274\pi\)
\(180\) 1.58873 0.118417
\(181\) −11.9584 20.7126i −0.888863 1.53956i −0.841221 0.540691i \(-0.818163\pi\)
−0.0476416 0.998864i \(-0.515171\pi\)
\(182\) 11.3063 19.5831i 0.838078 1.45159i
\(183\) 4.17310 0.308485
\(184\) −5.77829 + 10.0083i −0.425981 + 0.737820i
\(185\) 2.51991 + 4.36461i 0.185267 + 0.320892i
\(186\) −5.39141 9.33819i −0.395317 0.684709i
\(187\) −0.268717 0.465431i −0.0196505 0.0340357i
\(188\) 9.12369 0.665414
\(189\) −10.8217 18.7437i −0.787162 1.36340i
\(190\) 0.483201 + 0.836928i 0.0350551 + 0.0607172i
\(191\) −10.5217 + 18.2241i −0.761323 + 1.31865i 0.180847 + 0.983511i \(0.442116\pi\)
−0.942169 + 0.335138i \(0.891217\pi\)
\(192\) −3.93547 + 6.81643i −0.284018 + 0.491934i
\(193\) −2.19986 −0.158349 −0.0791745 0.996861i \(-0.525228\pi\)
−0.0791745 + 0.996861i \(0.525228\pi\)
\(194\) −1.07833 −0.0774199
\(195\) −13.6708 + 23.6784i −0.978983 + 1.69565i
\(196\) 5.12929 8.88418i 0.366378 0.634584i
\(197\) 3.34009 + 5.78520i 0.237971 + 0.412179i 0.960132 0.279547i \(-0.0901842\pi\)
−0.722161 + 0.691725i \(0.756851\pi\)
\(198\) −0.115817 0.200601i −0.00823074 0.0142561i
\(199\) −21.0271 −1.49057 −0.745285 0.666746i \(-0.767687\pi\)
−0.745285 + 0.666746i \(0.767687\pi\)
\(200\) 2.60968 + 4.52010i 0.184532 + 0.319619i
\(201\) −8.98078 15.5552i −0.633455 1.09718i
\(202\) 3.04376 + 5.27195i 0.214158 + 0.370933i
\(203\) 2.04924 3.54939i 0.143828 0.249118i
\(204\) 1.95344 0.136768
\(205\) −8.90049 + 15.4161i −0.621637 + 1.07671i
\(206\) 3.76661 + 6.52395i 0.262432 + 0.454545i
\(207\) 2.00979 0.139690
\(208\) 0.0368424 + 0.0638128i 0.00255456 + 0.00442462i
\(209\) −0.113389 + 0.196395i −0.00784326 + 0.0135849i
\(210\) 7.09683 12.2921i 0.489728 0.848234i
\(211\) 13.5050 0.929721 0.464861 0.885384i \(-0.346104\pi\)
0.464861 + 0.885384i \(0.346104\pi\)
\(212\) 2.50438 4.33772i 0.172002 0.297916i
\(213\) 4.95911 0.339793
\(214\) 16.4249 1.12278
\(215\) 7.30406 15.5220i 0.498133 1.05859i
\(216\) 15.6555 1.06523
\(217\) −30.4393 −2.06635
\(218\) −5.26122 + 9.11271i −0.356335 + 0.617190i
\(219\) −9.01803 −0.609382
\(220\) −0.867173 + 1.50199i −0.0584648 + 0.101264i
\(221\) 3.29996 5.71570i 0.221979 0.384480i
\(222\) 1.33540 + 2.31298i 0.0896261 + 0.155237i
\(223\) 2.25488 0.150998 0.0754989 0.997146i \(-0.475945\pi\)
0.0754989 + 0.997146i \(0.475945\pi\)
\(224\) 11.0597 + 19.1560i 0.738957 + 1.27991i
\(225\) 0.453847 0.786085i 0.0302564 0.0524057i
\(226\) −8.98285 −0.597530
\(227\) 12.1463 21.0380i 0.806177 1.39634i −0.109317 0.994007i \(-0.534866\pi\)
0.915494 0.402332i \(-0.131800\pi\)
\(228\) −0.412141 0.713849i −0.0272947 0.0472758i
\(229\) 7.62451 + 13.2060i 0.503842 + 0.872680i 0.999990 + 0.00444197i \(0.00141393\pi\)
−0.496148 + 0.868238i \(0.665253\pi\)
\(230\) 4.67480 + 8.09700i 0.308247 + 0.533900i
\(231\) 3.33071 0.219145
\(232\) 1.48230 + 2.56742i 0.0973178 + 0.168559i
\(233\) −3.45177 5.97864i −0.226133 0.391674i 0.730526 0.682885i \(-0.239275\pi\)
−0.956659 + 0.291211i \(0.905942\pi\)
\(234\) 1.42228 2.46346i 0.0929774 0.161042i
\(235\) 9.67439 16.7565i 0.631087 1.09308i
\(236\) 9.00928 0.586454
\(237\) −23.8809 −1.55123
\(238\) −1.71309 + 2.96717i −0.111043 + 0.192333i
\(239\) −6.86769 + 11.8952i −0.444234 + 0.769436i −0.997999 0.0632376i \(-0.979857\pi\)
0.553765 + 0.832673i \(0.313191\pi\)
\(240\) 0.0231255 + 0.0400546i 0.00149275 + 0.00258551i
\(241\) 0.477803 + 0.827579i 0.0307780 + 0.0533090i 0.881004 0.473109i \(-0.156868\pi\)
−0.850226 + 0.526418i \(0.823535\pi\)
\(242\) −9.37719 −0.602789
\(243\) −2.53073 4.38336i −0.162347 0.281193i
\(244\) 1.62538 + 2.81525i 0.104055 + 0.180228i
\(245\) −10.8778 18.8408i −0.694955 1.20370i
\(246\) −4.71672 + 8.16960i −0.300727 + 0.520875i
\(247\) −2.78493 −0.177201
\(248\) 11.0090 19.0681i 0.699072 1.21083i
\(249\) 10.4530 + 18.1052i 0.662434 + 1.14737i
\(250\) −7.22863 −0.457179
\(251\) 10.5866 + 18.3366i 0.668221 + 1.15739i 0.978401 + 0.206715i \(0.0662773\pi\)
−0.310180 + 0.950678i \(0.600389\pi\)
\(252\) 1.18836 2.05830i 0.0748598 0.129661i
\(253\) −1.09700 + 1.90006i −0.0689676 + 0.119455i
\(254\) 15.7225 0.986515
\(255\) 2.07135 3.58768i 0.129713 0.224669i
\(256\) −16.0274 −1.00171
\(257\) −8.86379 −0.552908 −0.276454 0.961027i \(-0.589159\pi\)
−0.276454 + 0.961027i \(0.589159\pi\)
\(258\) 3.87071 8.22570i 0.240980 0.512110i
\(259\) 7.53950 0.468482
\(260\) −21.2985 −1.32088
\(261\) 0.257785 0.446497i 0.0159565 0.0276375i
\(262\) −9.79161 −0.604928
\(263\) 15.0575 26.0804i 0.928488 1.60819i 0.142635 0.989775i \(-0.454443\pi\)
0.785853 0.618413i \(-0.212224\pi\)
\(264\) −1.20462 + 2.08646i −0.0741393 + 0.128413i
\(265\) −5.31109 9.19908i −0.326258 0.565095i
\(266\) 1.44573 0.0886432
\(267\) 5.69175 + 9.85839i 0.348329 + 0.603324i
\(268\) 6.99586 12.1172i 0.427340 0.740175i
\(269\) −9.62669 −0.586950 −0.293475 0.955967i \(-0.594812\pi\)
−0.293475 + 0.955967i \(0.594812\pi\)
\(270\) 6.33290 10.9689i 0.385408 0.667546i
\(271\) −6.22577 10.7833i −0.378188 0.655042i 0.612610 0.790385i \(-0.290120\pi\)
−0.990799 + 0.135344i \(0.956786\pi\)
\(272\) −0.00558224 0.00966872i −0.000338473 0.000586252i
\(273\) 20.4513 + 35.4227i 1.23777 + 2.14388i
\(274\) −1.60197 −0.0967785
\(275\) 0.495443 + 0.858133i 0.0298764 + 0.0517474i
\(276\) −3.98732 6.90624i −0.240008 0.415707i
\(277\) 10.3487 17.9245i 0.621794 1.07698i −0.367358 0.930080i \(-0.619738\pi\)
0.989152 0.146899i \(-0.0469291\pi\)
\(278\) −3.39768 + 5.88495i −0.203779 + 0.352956i
\(279\) −3.82912 −0.229244
\(280\) 28.9828 1.73205
\(281\) 15.7738 27.3210i 0.940984 1.62983i 0.177386 0.984141i \(-0.443236\pi\)
0.763598 0.645691i \(-0.223431\pi\)
\(282\) 5.12684 8.87995i 0.305299 0.528793i
\(283\) 16.1243 + 27.9281i 0.958491 + 1.66016i 0.726168 + 0.687517i \(0.241299\pi\)
0.232323 + 0.972639i \(0.425367\pi\)
\(284\) 1.93153 + 3.34550i 0.114615 + 0.198519i
\(285\) −1.74807 −0.103547
\(286\) 1.55264 + 2.68925i 0.0918094 + 0.159019i
\(287\) 13.3150 + 23.0623i 0.785961 + 1.36132i
\(288\) 1.39126 + 2.40973i 0.0819808 + 0.141995i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 2.39845 0.140842
\(291\) 0.975268 1.68921i 0.0571712 0.0990235i
\(292\) −3.51244 6.08372i −0.205550 0.356023i
\(293\) 2.81702 0.164572 0.0822859 0.996609i \(-0.473778\pi\)
0.0822859 + 0.996609i \(0.473778\pi\)
\(294\) −5.76456 9.98451i −0.336196 0.582308i
\(295\) 9.55307 16.5464i 0.556201 0.963369i
\(296\) −2.72682 + 4.72299i −0.158493 + 0.274518i
\(297\) 2.97218 0.172463
\(298\) −3.81053 + 6.60003i −0.220738 + 0.382329i
\(299\) −26.9432 −1.55817
\(300\) −3.60163 −0.207940
\(301\) −14.6463 21.0732i −0.844199 1.21464i
\(302\) −2.61066 −0.150227
\(303\) −11.0114 −0.632587
\(304\) −0.00235550 + 0.00407985i −0.000135097 + 0.000233995i
\(305\) 6.89396 0.394747
\(306\) −0.215500 + 0.373256i −0.0123193 + 0.0213376i
\(307\) −5.32273 + 9.21923i −0.303784 + 0.526169i −0.976990 0.213286i \(-0.931583\pi\)
0.673206 + 0.739455i \(0.264917\pi\)
\(308\) 1.29728 + 2.24696i 0.0739194 + 0.128032i
\(309\) −13.6264 −0.775178
\(310\) −8.90660 15.4267i −0.505861 0.876177i
\(311\) −0.460133 + 0.796973i −0.0260917 + 0.0451922i −0.878776 0.477234i \(-0.841640\pi\)
0.852685 + 0.522426i \(0.174973\pi\)
\(312\) −29.5865 −1.67501
\(313\) −4.83693 + 8.37780i −0.273399 + 0.473541i −0.969730 0.244180i \(-0.921481\pi\)
0.696331 + 0.717721i \(0.254815\pi\)
\(314\) −4.51539 7.82088i −0.254818 0.441358i
\(315\) −2.52018 4.36508i −0.141996 0.245945i
\(316\) −9.30137 16.1104i −0.523243 0.906283i
\(317\) 6.24375 0.350684 0.175342 0.984508i \(-0.443897\pi\)
0.175342 + 0.984508i \(0.443897\pi\)
\(318\) −2.81456 4.87496i −0.157833 0.273374i
\(319\) 0.281412 + 0.487420i 0.0157561 + 0.0272903i
\(320\) −6.50139 + 11.2607i −0.363439 + 0.629495i
\(321\) −14.8550 + 25.7296i −0.829125 + 1.43609i
\(322\) 13.9869 0.779460
\(323\) 0.421963 0.0234787
\(324\) −4.49062 + 7.77799i −0.249479 + 0.432110i
\(325\) −6.08426 + 10.5383i −0.337494 + 0.584557i
\(326\) 4.34825 + 7.53138i 0.240827 + 0.417125i
\(327\) −9.51672 16.4834i −0.526276 0.911537i
\(328\) −19.2626 −1.06360
\(329\) −14.4728 25.0676i −0.797910 1.38202i
\(330\) 0.974574 + 1.68801i 0.0536485 + 0.0929220i
\(331\) 13.9820 + 24.2175i 0.768518 + 1.33111i 0.938366 + 0.345642i \(0.112339\pi\)
−0.169848 + 0.985470i \(0.554328\pi\)
\(332\) −8.14272 + 14.1036i −0.446890 + 0.774036i
\(333\) 0.948436 0.0519740
\(334\) −6.37469 + 11.0413i −0.348807 + 0.604152i
\(335\) −14.8362 25.6971i −0.810591 1.40398i
\(336\) 0.0691911 0.00377468
\(337\) 10.3743 + 17.9688i 0.565123 + 0.978822i 0.997038 + 0.0769078i \(0.0245047\pi\)
−0.431915 + 0.901914i \(0.642162\pi\)
\(338\) −13.3766 + 23.1689i −0.727590 + 1.26022i
\(339\) 8.12428 14.0717i 0.441250 0.764268i
\(340\) 3.22709 0.175013
\(341\) 2.09004 3.62005i 0.113182 0.196037i
\(342\) 0.181866 0.00983418
\(343\) −5.15092 −0.278124
\(344\) 18.4981 1.55335i 0.997350 0.0837511i
\(345\) −16.9120 −0.910509
\(346\) −2.87176 −0.154387
\(347\) 8.82640 15.2878i 0.473826 0.820691i −0.525725 0.850655i \(-0.676206\pi\)
0.999551 + 0.0299638i \(0.00953921\pi\)
\(348\) −2.04573 −0.109663
\(349\) 7.87572 13.6411i 0.421578 0.730194i −0.574516 0.818493i \(-0.694810\pi\)
0.996094 + 0.0882991i \(0.0281431\pi\)
\(350\) 3.15850 5.47067i 0.168829 0.292420i
\(351\) 18.2498 + 31.6096i 0.974104 + 1.68720i
\(352\) −3.03755 −0.161902
\(353\) 8.92597 + 15.4602i 0.475082 + 0.822865i 0.999593 0.0285382i \(-0.00908523\pi\)
−0.524511 + 0.851404i \(0.675752\pi\)
\(354\) 5.06255 8.76859i 0.269072 0.466046i
\(355\) 8.19244 0.434810
\(356\) −4.43376 + 7.67951i −0.234989 + 0.407013i
\(357\) −3.09872 5.36713i −0.164001 0.284059i
\(358\) 5.15491 + 8.92856i 0.272445 + 0.471889i
\(359\) −12.2382 21.1973i −0.645910 1.11875i −0.984091 0.177667i \(-0.943145\pi\)
0.338181 0.941081i \(-0.390188\pi\)
\(360\) 3.64590 0.192156
\(361\) 9.41097 + 16.3003i 0.495314 + 0.857910i
\(362\) −10.4691 18.1331i −0.550245 0.953052i
\(363\) 8.48093 14.6894i 0.445133 0.770994i
\(364\) −15.9312 + 27.5936i −0.835020 + 1.44630i
\(365\) −14.8978 −0.779785
\(366\) 3.65338 0.190965
\(367\) −1.91704 + 3.32041i −0.100069 + 0.173324i −0.911713 0.410828i \(-0.865240\pi\)
0.811644 + 0.584152i \(0.198573\pi\)
\(368\) −0.0227887 + 0.0394711i −0.00118794 + 0.00205757i
\(369\) 1.67497 + 2.90113i 0.0871955 + 0.151027i
\(370\) 2.20608 + 3.82104i 0.114688 + 0.198646i
\(371\) −15.8907 −0.825002
\(372\) 7.59678 + 13.1580i 0.393875 + 0.682211i
\(373\) 11.7409 + 20.3359i 0.607922 + 1.05295i 0.991582 + 0.129478i \(0.0413301\pi\)
−0.383660 + 0.923474i \(0.625337\pi\)
\(374\) −0.235251 0.407466i −0.0121645 0.0210696i
\(375\) 6.53772 11.3237i 0.337607 0.584752i
\(376\) 20.9375 1.07977
\(377\) −3.45586 + 5.98573i −0.177986 + 0.308281i
\(378\) −9.47395 16.4094i −0.487287 0.844006i
\(379\) 9.85963 0.506455 0.253227 0.967407i \(-0.418508\pi\)
0.253227 + 0.967407i \(0.418508\pi\)
\(380\) −0.680856 1.17928i −0.0349272 0.0604956i
\(381\) −14.2197 + 24.6293i −0.728499 + 1.26180i
\(382\) −9.21131 + 15.9545i −0.471292 + 0.816301i
\(383\) 21.7284 1.11027 0.555135 0.831760i \(-0.312667\pi\)
0.555135 + 0.831760i \(0.312667\pi\)
\(384\) 5.50490 9.53476i 0.280921 0.486569i
\(385\) 5.50233 0.280425
\(386\) −1.92589 −0.0980250
\(387\) −1.84244 2.65092i −0.0936565 0.134754i
\(388\) 1.51943 0.0771374
\(389\) 9.04604 0.458652 0.229326 0.973350i \(-0.426348\pi\)
0.229326 + 0.973350i \(0.426348\pi\)
\(390\) −11.9682 + 20.7295i −0.606033 + 1.04968i
\(391\) 4.08235 0.206453
\(392\) 11.7710 20.3879i 0.594523 1.02974i
\(393\) 8.85573 15.3386i 0.446713 0.773729i
\(394\) 2.92411 + 5.06471i 0.147315 + 0.255157i
\(395\) −39.4512 −1.98500
\(396\) 0.163192 + 0.282657i 0.00820071 + 0.0142040i
\(397\) −11.2959 + 19.5650i −0.566924 + 0.981941i 0.429944 + 0.902856i \(0.358533\pi\)
−0.996868 + 0.0790853i \(0.974800\pi\)
\(398\) −18.4084 −0.922728
\(399\) −1.30754 + 2.26473i −0.0654591 + 0.113379i
\(400\) 0.0102922 + 0.0178266i 0.000514609 + 0.000891329i
\(401\) −7.99395 13.8459i −0.399199 0.691433i 0.594428 0.804149i \(-0.297378\pi\)
−0.993627 + 0.112716i \(0.964045\pi\)
\(402\) −7.86231 13.6179i −0.392136 0.679200i
\(403\) 51.3332 2.55709
\(404\) −4.28883 7.42846i −0.213377 0.369580i
\(405\) 9.52334 + 16.4949i 0.473219 + 0.819639i
\(406\) 1.79403 3.10735i 0.0890360 0.154215i
\(407\) −0.517682 + 0.896651i −0.0256605 + 0.0444453i
\(408\) 4.48286 0.221935
\(409\) −23.1473 −1.14456 −0.572281 0.820058i \(-0.693941\pi\)
−0.572281 + 0.820058i \(0.693941\pi\)
\(410\) −7.79202 + 13.4962i −0.384820 + 0.666528i
\(411\) 1.44885 2.50949i 0.0714667 0.123784i
\(412\) −5.30735 9.19260i −0.261474 0.452887i
\(413\) −14.2913 24.7532i −0.703228 1.21803i
\(414\) 1.75949 0.0864742
\(415\) 17.2684 + 29.9098i 0.847673 + 1.46821i
\(416\) −18.6512 32.3048i −0.914451 1.58388i
\(417\) −6.14586 10.6449i −0.300964 0.521285i
\(418\) −0.0992673 + 0.171936i −0.00485532 + 0.00840966i
\(419\) −14.3872 −0.702861 −0.351430 0.936214i \(-0.614305\pi\)
−0.351430 + 0.936214i \(0.614305\pi\)
\(420\) −9.99982 + 17.3202i −0.487941 + 0.845139i
\(421\) −12.6295 21.8749i −0.615523 1.06612i −0.990293 0.138999i \(-0.955612\pi\)
0.374770 0.927118i \(-0.377722\pi\)
\(422\) 11.8231 0.575538
\(423\) −1.82061 3.15339i −0.0885211 0.153323i
\(424\) 5.74719 9.95443i 0.279108 0.483430i
\(425\) 0.921869 1.59672i 0.0447172 0.0774525i
\(426\) 4.34150 0.210346
\(427\) 5.15665 8.93157i 0.249548 0.432229i
\(428\) −23.1435 −1.11868
\(429\) −5.61695 −0.271189
\(430\) 6.39441 13.5889i 0.308366 0.655313i
\(431\) −13.8495 −0.667107 −0.333553 0.942731i \(-0.608248\pi\)
−0.333553 + 0.942731i \(0.608248\pi\)
\(432\) 0.0617431 0.00297061
\(433\) 11.3713 19.6957i 0.546470 0.946514i −0.452043 0.891996i \(-0.649304\pi\)
0.998513 0.0545179i \(-0.0173622\pi\)
\(434\) −26.6484 −1.27916
\(435\) −2.16921 + 3.75718i −0.104006 + 0.180143i
\(436\) 7.41335 12.8403i 0.355035 0.614939i
\(437\) −0.861302 1.49182i −0.0412016 0.0713633i
\(438\) −7.89492 −0.377234
\(439\) 13.9182 + 24.1070i 0.664280 + 1.15057i 0.979480 + 0.201541i \(0.0645950\pi\)
−0.315200 + 0.949025i \(0.602072\pi\)
\(440\) −1.99003 + 3.44684i −0.0948711 + 0.164322i
\(441\) −4.09414 −0.194959
\(442\) 2.88898 5.00387i 0.137415 0.238010i
\(443\) −0.918462 1.59082i −0.0436375 0.0755823i 0.843382 0.537315i \(-0.180561\pi\)
−0.887019 + 0.461733i \(0.847228\pi\)
\(444\) −1.88165 3.25911i −0.0892991 0.154671i
\(445\) 9.40276 + 16.2861i 0.445734 + 0.772033i
\(446\) 1.97405 0.0934742
\(447\) −6.89264 11.9384i −0.326011 0.564667i
\(448\) 9.72601 + 16.8459i 0.459511 + 0.795896i
\(449\) 3.06636 5.31110i 0.144711 0.250646i −0.784554 0.620060i \(-0.787108\pi\)
0.929265 + 0.369414i \(0.120442\pi\)
\(450\) 0.397325 0.688186i 0.0187301 0.0324414i
\(451\) −3.65698 −0.172200
\(452\) 12.6573 0.595350
\(453\) 2.36114 4.08961i 0.110936 0.192146i
\(454\) 10.6336 18.4179i 0.499058 0.864395i
\(455\) 33.7855 + 58.5182i 1.58389 + 2.74338i
\(456\) −0.945802 1.63818i −0.0442912 0.0767146i
\(457\) 15.8784 0.742761 0.371381 0.928481i \(-0.378884\pi\)
0.371381 + 0.928481i \(0.378884\pi\)
\(458\) 6.67495 + 11.5614i 0.311900 + 0.540227i
\(459\) −2.76516 4.78939i −0.129066 0.223550i
\(460\) −6.58705 11.4091i −0.307123 0.531952i
\(461\) 7.38758 12.7957i 0.344074 0.595953i −0.641111 0.767448i \(-0.721526\pi\)
0.985185 + 0.171495i \(0.0548597\pi\)
\(462\) 2.91590 0.135660
\(463\) −1.38268 + 2.39488i −0.0642588 + 0.111299i −0.896365 0.443317i \(-0.853802\pi\)
0.832106 + 0.554616i \(0.187135\pi\)
\(464\) 0.00584596 + 0.0101255i 0.000271392 + 0.000470065i
\(465\) 32.2213 1.49423
\(466\) −3.02188 5.23406i −0.139986 0.242463i
\(467\) −13.5496 + 23.4686i −0.627001 + 1.08600i 0.361149 + 0.932508i \(0.382385\pi\)
−0.988150 + 0.153490i \(0.950949\pi\)
\(468\) −2.00407 + 3.47115i −0.0926382 + 0.160454i
\(469\) −44.3897 −2.04973
\(470\) 8.46954 14.6697i 0.390671 0.676661i
\(471\) 16.3352 0.752688
\(472\) 20.6750 0.951643
\(473\) 3.51183 0.294901i 0.161474 0.0135596i
\(474\) −20.9067 −0.960278
\(475\) −0.777990 −0.0356966
\(476\) 2.41384 4.18090i 0.110638 0.191631i
\(477\) −1.99897 −0.0915268
\(478\) −6.01239 + 10.4138i −0.275000 + 0.476314i
\(479\) 8.69131 15.0538i 0.397116 0.687825i −0.596253 0.802797i \(-0.703344\pi\)
0.993369 + 0.114971i \(0.0366777\pi\)
\(480\) −11.7072 20.2774i −0.534356 0.925532i
\(481\) −12.7147 −0.579741
\(482\) 0.418297 + 0.724512i 0.0190529 + 0.0330006i
\(483\) −12.6501 + 21.9105i −0.575597 + 0.996964i
\(484\) 13.2130 0.600590
\(485\) 1.61114 2.79058i 0.0731582 0.126714i
\(486\) −2.21555 3.83745i −0.100500 0.174070i
\(487\) 12.6660 + 21.9382i 0.573952 + 0.994114i 0.996155 + 0.0876124i \(0.0279237\pi\)
−0.422203 + 0.906501i \(0.638743\pi\)
\(488\) 3.73002 + 6.46058i 0.168850 + 0.292457i
\(489\) −15.7306 −0.711361
\(490\) −9.52305 16.4944i −0.430207 0.745141i
\(491\) −2.56685 4.44592i −0.115841 0.200642i 0.802275 0.596955i \(-0.203623\pi\)
−0.918115 + 0.396313i \(0.870289\pi\)
\(492\) 6.64611 11.5114i 0.299630 0.518974i
\(493\) 0.523622 0.906939i 0.0235827 0.0408465i
\(494\) −2.43809 −0.109695
\(495\) 0.692169 0.0311107
\(496\) 0.0434178 0.0752018i 0.00194952 0.00337666i
\(497\) 6.12790 10.6138i 0.274874 0.476096i
\(498\) 9.15121 + 15.8504i 0.410076 + 0.710272i
\(499\) 13.9263 + 24.1211i 0.623429 + 1.07981i 0.988842 + 0.148965i \(0.0475942\pi\)
−0.365414 + 0.930845i \(0.619073\pi\)
\(500\) 10.1855 0.455511
\(501\) −11.5308 19.9719i −0.515158 0.892280i
\(502\) 9.26815 + 16.0529i 0.413658 + 0.716477i
\(503\) 6.58243 + 11.4011i 0.293496 + 0.508350i 0.974634 0.223805i \(-0.0718480\pi\)
−0.681138 + 0.732155i \(0.738515\pi\)
\(504\) 2.72712 4.72350i 0.121475 0.210402i
\(505\) −18.1908 −0.809479
\(506\) −0.960377 + 1.66342i −0.0426940 + 0.0739481i
\(507\) −24.1961 41.9089i −1.07459 1.86124i
\(508\) −22.1538 −0.982916
\(509\) −15.2029 26.3321i −0.673855 1.16715i −0.976802 0.214144i \(-0.931304\pi\)
0.302947 0.953007i \(-0.402029\pi\)
\(510\) 1.81338 3.14087i 0.0802980 0.139080i
\(511\) −11.1435 + 19.3010i −0.492957 + 0.853827i
\(512\) −0.126311 −0.00558222
\(513\) −1.16680 + 2.02095i −0.0515153 + 0.0892270i
\(514\) −7.75990 −0.342274
\(515\) −22.5108 −0.991944
\(516\) −5.45404 + 11.5905i −0.240101 + 0.510242i
\(517\) 3.97495 0.174818
\(518\) 6.60053 0.290011
\(519\) 2.59728 4.49862i 0.114008 0.197467i
\(520\) −48.8769 −2.14340
\(521\) 8.47568 14.6803i 0.371326 0.643156i −0.618444 0.785829i \(-0.712236\pi\)
0.989770 + 0.142673i \(0.0455698\pi\)
\(522\) 0.225680 0.390890i 0.00987777 0.0171088i
\(523\) −5.68232 9.84206i −0.248470 0.430363i 0.714631 0.699501i \(-0.246595\pi\)
−0.963102 + 0.269138i \(0.913261\pi\)
\(524\) 13.7969 0.602721
\(525\) 5.71322 + 9.89558i 0.249345 + 0.431879i
\(526\) 13.1823 22.8324i 0.574775 0.995539i
\(527\) −7.77784 −0.338808
\(528\) −0.00475084 + 0.00822869i −0.000206754 + 0.000358108i
\(529\) 3.16720 + 5.48575i 0.137704 + 0.238511i
\(530\) −4.64965 8.05343i −0.201968 0.349819i
\(531\) −1.79778 3.11385i −0.0780170 0.135129i
\(532\) −2.03711 −0.0883197
\(533\) −22.4546 38.8926i −0.972618 1.68462i
\(534\) 4.98290 + 8.63063i 0.215631 + 0.373484i
\(535\) −24.5404 + 42.5053i −1.06098 + 1.83766i
\(536\) 16.0545 27.8071i 0.693447 1.20109i
\(537\) −18.6488 −0.804756
\(538\) −8.42778 −0.363348
\(539\) 2.23469 3.87060i 0.0962551 0.166719i
\(540\) −8.92340 + 15.4558i −0.384002 + 0.665111i
\(541\) 14.4620 + 25.0490i 0.621771 + 1.07694i 0.989156 + 0.146870i \(0.0469199\pi\)
−0.367385 + 0.930069i \(0.619747\pi\)
\(542\) −5.45041 9.44038i −0.234115 0.405499i
\(543\) 37.8740 1.62533
\(544\) 2.82597 + 4.89473i 0.121163 + 0.209860i
\(545\) −15.7216 27.2306i −0.673440 1.16643i
\(546\) 17.9043 + 31.0111i 0.766233 + 1.32715i
\(547\) 11.2979 19.5685i 0.483062 0.836687i −0.516749 0.856137i \(-0.672858\pi\)
0.999811 + 0.0194495i \(0.00619134\pi\)
\(548\) 2.25726 0.0964254
\(549\) 0.648683 1.12355i 0.0276851 0.0479520i
\(550\) 0.433741 + 0.751261i 0.0184948 + 0.0320339i
\(551\) −0.441898 −0.0188255
\(552\) −9.15031 15.8488i −0.389463 0.674570i
\(553\) −29.5092 + 51.1115i −1.25486 + 2.17348i
\(554\) 9.05988 15.6922i 0.384917 0.666696i
\(555\) −7.98089 −0.338770
\(556\) 4.78751 8.29222i 0.203036 0.351668i
\(557\) −38.6913 −1.63940 −0.819702 0.572791i \(-0.805861\pi\)
−0.819702 + 0.572791i \(0.805861\pi\)
\(558\) −3.35224 −0.141912
\(559\) 24.6997 + 35.5382i 1.04469 + 1.50310i
\(560\) 0.114304 0.00483021
\(561\) 0.851063 0.0359319
\(562\) 13.8093 23.9184i 0.582510 1.00894i
\(563\) 12.6692 0.533944 0.266972 0.963704i \(-0.413977\pi\)
0.266972 + 0.963704i \(0.413977\pi\)
\(564\) −7.22399 + 12.5123i −0.304185 + 0.526864i
\(565\) 13.4213 23.2464i 0.564638 0.977982i
\(566\) 14.1162 + 24.4500i 0.593348 + 1.02771i
\(567\) 28.4936 1.19662
\(568\) 4.43257 + 7.67743i 0.185986 + 0.322138i
\(569\) −21.6328 + 37.4691i −0.906894 + 1.57079i −0.0885384 + 0.996073i \(0.528220\pi\)
−0.818355 + 0.574713i \(0.805114\pi\)
\(570\) −1.53036 −0.0640999
\(571\) 11.1439 19.3018i 0.466357 0.807754i −0.532905 0.846175i \(-0.678900\pi\)
0.999262 + 0.0384214i \(0.0122329\pi\)
\(572\) −2.18775 3.78930i −0.0914744 0.158438i
\(573\) −16.6618 28.8591i −0.696057 1.20561i
\(574\) 11.6568 + 20.1901i 0.486544 + 0.842719i
\(575\) −7.52679 −0.313889
\(576\) 1.22349 + 2.11914i 0.0509787 + 0.0882977i
\(577\) −5.01994 8.69479i −0.208983 0.361969i 0.742412 0.669944i \(-0.233682\pi\)
−0.951394 + 0.307975i \(0.900349\pi\)
\(578\) −0.437730 + 0.758170i −0.0182072 + 0.0315357i
\(579\) 1.74181 3.01691i 0.0723872 0.125378i
\(580\) −3.37954 −0.140328
\(581\) 51.6667 2.14350
\(582\) 0.853808 1.47884i 0.0353915 0.0612998i
\(583\) 1.09109 1.88983i 0.0451885 0.0782688i
\(584\) −8.06053 13.9612i −0.333547 0.577720i
\(585\) 4.25007 + 7.36133i 0.175719 + 0.304354i
\(586\) 2.46619 0.101877
\(587\) 1.87725 + 3.25150i 0.0774826 + 0.134204i 0.902163 0.431395i \(-0.141978\pi\)
−0.824681 + 0.565599i \(0.808645\pi\)
\(588\) 8.12257 + 14.0687i 0.334969 + 0.580184i
\(589\) 1.64098 + 2.84227i 0.0676155 + 0.117114i
\(590\) 8.36333 14.4857i 0.344313 0.596367i
\(591\) −10.5785 −0.435142
\(592\) −0.0107542 + 0.0186267i −0.000441993 + 0.000765554i
\(593\) −18.0751 31.3070i −0.742256 1.28563i −0.951466 0.307754i \(-0.900422\pi\)
0.209210 0.977871i \(-0.432911\pi\)
\(594\) 2.60202 0.106762
\(595\) −5.11908 8.86650i −0.209862 0.363491i
\(596\) 5.36924 9.29980i 0.219933 0.380935i
\(597\) 16.6489 28.8367i 0.681394 1.18021i
\(598\) −23.5877 −0.964573
\(599\) 13.0864 22.6663i 0.534695 0.926120i −0.464483 0.885582i \(-0.653760\pi\)
0.999178 0.0405374i \(-0.0129070\pi\)
\(600\) −8.26522 −0.337426
\(601\) −16.7308 −0.682466 −0.341233 0.939979i \(-0.610844\pi\)
−0.341233 + 0.939979i \(0.610844\pi\)
\(602\) −12.8223 18.4488i −0.522596 0.751915i
\(603\) −5.58403 −0.227399
\(604\) 3.67856 0.149679
\(605\) 14.0105 24.2669i 0.569607 0.986589i
\(606\) −9.64001 −0.391599
\(607\) 16.9239 29.3130i 0.686919 1.18978i −0.285911 0.958256i \(-0.592296\pi\)
0.972830 0.231522i \(-0.0743704\pi\)
\(608\) 1.19246 2.06540i 0.0483605 0.0837629i
\(609\) 3.24511 + 5.62070i 0.131499 + 0.227762i
\(610\) 6.03539 0.244366
\(611\) 24.4071 + 42.2743i 0.987405 + 1.71023i
\(612\) 0.303650 0.525938i 0.0122743 0.0212598i
\(613\) 18.0687 0.729789 0.364895 0.931049i \(-0.381105\pi\)
0.364895 + 0.931049i \(0.381105\pi\)
\(614\) −4.65983 + 8.07107i −0.188056 + 0.325722i
\(615\) −14.0945 24.4124i −0.568346 0.984404i
\(616\) 2.97707 + 5.15643i 0.119949 + 0.207759i
\(617\) −0.634114 1.09832i −0.0255285 0.0442166i 0.852979 0.521945i \(-0.174794\pi\)
−0.878507 + 0.477729i \(0.841460\pi\)
\(618\) −11.9294 −0.479869
\(619\) 20.4208 + 35.3699i 0.820781 + 1.42163i 0.905101 + 0.425196i \(0.139795\pi\)
−0.0843199 + 0.996439i \(0.526872\pi\)
\(620\) 12.5499 + 21.7370i 0.504015 + 0.872980i
\(621\) −11.2883 + 19.5520i −0.452986 + 0.784594i
\(622\) −0.402828 + 0.697718i −0.0161519 + 0.0279759i
\(623\) 28.1329 1.12712
\(624\) −0.116685 −0.00467113
\(625\) 15.4097 26.6903i 0.616386 1.06761i
\(626\) −4.23454 + 7.33443i −0.169246 + 0.293143i
\(627\) −0.179559 0.311005i −0.00717089 0.0124203i
\(628\) 6.36242 + 11.0200i 0.253888 + 0.439748i
\(629\) 1.92649 0.0768144
\(630\) −2.20632 3.82145i −0.0879018 0.152250i
\(631\) 11.5883 + 20.0715i 0.461322 + 0.799033i 0.999027 0.0441001i \(-0.0140421\pi\)
−0.537705 + 0.843133i \(0.680709\pi\)
\(632\) −21.3453 36.9711i −0.849069 1.47063i
\(633\) −10.6930 + 18.5209i −0.425010 + 0.736138i
\(634\) 5.46615 0.217089
\(635\) −23.4910 + 40.6876i −0.932211 + 1.61464i
\(636\) 3.96586 + 6.86908i 0.157257 + 0.272377i
\(637\) 54.8860 2.17466
\(638\) 0.246365 + 0.426717i 0.00975368 + 0.0168939i
\(639\) 0.770863 1.33517i 0.0304949 0.0528186i
\(640\) 9.09409 15.7514i 0.359475 0.622630i
\(641\) 28.9498 1.14345 0.571724 0.820446i \(-0.306275\pi\)
0.571724 + 0.820446i \(0.306275\pi\)
\(642\) −13.0050 + 22.5252i −0.513265 + 0.889000i
\(643\) −21.8632 −0.862202 −0.431101 0.902304i \(-0.641875\pi\)
−0.431101 + 0.902304i \(0.641875\pi\)
\(644\) −19.7083 −0.776616
\(645\) 15.5037 + 22.3069i 0.610459 + 0.878334i
\(646\) 0.369412 0.0145343
\(647\) 26.8876 1.05706 0.528531 0.848914i \(-0.322743\pi\)
0.528531 + 0.848914i \(0.322743\pi\)
\(648\) −10.3053 + 17.8493i −0.404831 + 0.701188i
\(649\) 3.92511 0.154074
\(650\) −5.32653 + 9.22582i −0.208924 + 0.361866i
\(651\) 24.1013 41.7447i 0.944605 1.63610i
\(652\) −6.12691 10.6121i −0.239948 0.415603i
\(653\) 31.7157 1.24113 0.620566 0.784154i \(-0.286903\pi\)
0.620566 + 0.784154i \(0.286903\pi\)
\(654\) −8.33151 14.4306i −0.325788 0.564281i
\(655\) 14.6297 25.3393i 0.571628 0.990089i
\(656\) −0.0759688 −0.00296608
\(657\) −1.40180 + 2.42798i −0.0546893 + 0.0947246i
\(658\) −12.6703 21.9457i −0.493941 0.855531i
\(659\) 20.3332 + 35.2182i 0.792069 + 1.37190i 0.924683 + 0.380737i \(0.124330\pi\)
−0.132614 + 0.991168i \(0.542337\pi\)
\(660\) −1.37323 2.37850i −0.0534528 0.0925829i
\(661\) −7.84995 −0.305328 −0.152664 0.988278i \(-0.548785\pi\)
−0.152664 + 0.988278i \(0.548785\pi\)
\(662\) 12.2406 + 21.2014i 0.475746 + 0.824016i
\(663\) 5.22571 + 9.05120i 0.202950 + 0.351520i
\(664\) −18.6863 + 32.3657i −0.725170 + 1.25603i
\(665\) −2.16006 + 3.74134i −0.0837637 + 0.145083i
\(666\) 0.830317 0.0321741
\(667\) −4.27522 −0.165537
\(668\) 8.98228 15.5578i 0.347535 0.601948i
\(669\) −1.78538 + 3.09236i −0.0690266 + 0.119558i
\(670\) −12.9885 22.4968i −0.501791 0.869127i
\(671\) 0.708137 + 1.22653i 0.0273373 + 0.0473497i
\(672\) −35.0276 −1.35122
\(673\) 8.39393 + 14.5387i 0.323562 + 0.560427i 0.981220 0.192890i \(-0.0617861\pi\)
−0.657658 + 0.753317i \(0.728453\pi\)
\(674\) 9.08227 + 15.7309i 0.349836 + 0.605934i
\(675\) 5.09822 + 8.83038i 0.196231 + 0.339882i
\(676\) 18.8483 32.6463i 0.724936 1.25563i
\(677\) 33.7004 1.29521 0.647607 0.761975i \(-0.275770\pi\)
0.647607 + 0.761975i \(0.275770\pi\)
\(678\) 7.11248 12.3192i 0.273153 0.473115i
\(679\) −2.41025 4.17468i −0.0924969 0.160209i
\(680\) 7.40568 0.283995
\(681\) 19.2345 + 33.3151i 0.737066 + 1.27664i
\(682\) 1.82974 3.16921i 0.0700645 0.121355i
\(683\) 19.9884 34.6209i 0.764835 1.32473i −0.175499 0.984480i \(-0.556154\pi\)
0.940334 0.340253i \(-0.110513\pi\)
\(684\) −0.256259 −0.00979830
\(685\) 2.39351 4.14567i 0.0914512 0.158398i
\(686\) −4.50942 −0.172171
\(687\) −24.1479 −0.921299
\(688\) 0.0729536 0.00612618i 0.00278133 0.000233558i
\(689\) 26.7982 1.02093
\(690\) −14.8057 −0.563645
\(691\) −10.6771 + 18.4933i −0.406177 + 0.703519i −0.994458 0.105138i \(-0.966472\pi\)
0.588281 + 0.808657i \(0.299805\pi\)
\(692\) 4.04646 0.153823
\(693\) 0.517738 0.896749i 0.0196672 0.0340647i
\(694\) 7.72716 13.3838i 0.293319 0.508043i
\(695\) −10.1530 17.5854i −0.385124 0.667054i
\(696\) −4.69465 −0.177950
\(697\) 3.40226 + 5.89288i 0.128870 + 0.223209i
\(698\) 6.89488 11.9423i 0.260975 0.452022i
\(699\) 10.9322 0.413495
\(700\) −4.45049 + 7.70848i −0.168213 + 0.291353i
\(701\) 2.66625 + 4.61809i 0.100703 + 0.174423i 0.911975 0.410247i \(-0.134557\pi\)
−0.811271 + 0.584670i \(0.801224\pi\)
\(702\) 15.9770 + 27.6730i 0.603013 + 1.04445i
\(703\) −0.406455 0.704001i −0.0153297 0.0265519i
\(704\) −2.67125 −0.100677
\(705\) 15.3201 + 26.5351i 0.576987 + 0.999370i
\(706\) 7.81433 + 13.5348i 0.294096 + 0.509389i
\(707\) −13.6066 + 23.5673i −0.511729 + 0.886340i
\(708\) −7.13341 + 12.3554i −0.268090 + 0.464345i
\(709\) −25.7338 −0.966454 −0.483227 0.875495i \(-0.660535\pi\)
−0.483227 + 0.875495i \(0.660535\pi\)
\(710\) 7.17216 0.269166
\(711\) −3.71213 + 6.42960i −0.139216 + 0.241129i
\(712\) −10.1748 + 17.6233i −0.381318 + 0.660462i
\(713\) 15.8759 + 27.4979i 0.594559 + 1.02981i
\(714\) −2.71280 4.69871i −0.101524 0.175845i
\(715\) −9.27920 −0.347022
\(716\) −7.26354 12.5808i −0.271451 0.470168i
\(717\) −10.8755 18.8368i −0.406151 0.703475i
\(718\) −10.7141 18.5573i −0.399846 0.692554i
\(719\) −2.99804 + 5.19276i −0.111808 + 0.193657i −0.916499 0.400036i \(-0.868998\pi\)
0.804691 + 0.593694i \(0.202331\pi\)
\(720\) 0.0143789 0.000535869
\(721\) −16.8379 + 29.1642i −0.627078 + 1.08613i
\(722\) 8.23893 + 14.2702i 0.306621 + 0.531083i
\(723\) −1.51327 −0.0562790
\(724\) 14.7516 + 25.5504i 0.548237 + 0.949575i
\(725\) −0.965421 + 1.67216i −0.0358548 + 0.0621024i
\(726\) 7.42471 12.8600i 0.275557 0.477279i
\(727\) −33.1210 −1.22839 −0.614195 0.789154i \(-0.710519\pi\)
−0.614195 + 0.789154i \(0.710519\pi\)
\(728\) −36.5597 + 63.3232i −1.35499 + 2.34691i
\(729\) 29.8573 1.10582
\(730\) −13.0424 −0.482721
\(731\) −3.74243 5.38463i −0.138419 0.199158i
\(732\) −5.14782 −0.190269
\(733\) −17.6481 −0.651848 −0.325924 0.945396i \(-0.605675\pi\)
−0.325924 + 0.945396i \(0.605675\pi\)
\(734\) −1.67829 + 2.90688i −0.0619468 + 0.107295i
\(735\) 34.4514 1.27076
\(736\) 11.5366 19.9820i 0.425245 0.736547i
\(737\) 3.04791 5.27914i 0.112271 0.194460i
\(738\) 1.46637 + 2.53983i 0.0539778 + 0.0934923i
\(739\) −0.363048 −0.0133549 −0.00667747 0.999978i \(-0.502126\pi\)
−0.00667747 + 0.999978i \(0.502126\pi\)
\(740\) −3.10848 5.38405i −0.114270 0.197922i
\(741\) 2.20506 3.81928i 0.0810049 0.140305i
\(742\) −13.9116 −0.510712
\(743\) 16.1025 27.8903i 0.590743 1.02320i −0.403389 0.915028i \(-0.632168\pi\)
0.994133 0.108169i \(-0.0344987\pi\)
\(744\) 17.4335 + 30.1957i 0.639143 + 1.10703i
\(745\) −11.3866 19.7222i −0.417174 0.722567i
\(746\) 10.2787 + 17.8033i 0.376330 + 0.651823i
\(747\) 6.49944 0.237802
\(748\) 0.331481 + 0.574142i 0.0121202 + 0.0209927i
\(749\) 36.7122 + 63.5875i 1.34144 + 2.32344i
\(750\) 5.72351 9.91342i 0.208993 0.361987i
\(751\) −25.3916 + 43.9795i −0.926552 + 1.60484i −0.137506 + 0.990501i \(0.543909\pi\)
−0.789046 + 0.614335i \(0.789425\pi\)
\(752\) 0.0825744 0.00301118
\(753\) −33.5292 −1.22187
\(754\) −3.02547 + 5.24027i −0.110181 + 0.190839i
\(755\) 3.90059 6.75603i 0.141957 0.245877i
\(756\) 13.3493 + 23.1217i 0.485509 + 0.840927i
\(757\) −18.6944 32.3797i −0.679460 1.17686i −0.975144 0.221574i \(-0.928881\pi\)
0.295684 0.955286i \(-0.404453\pi\)
\(758\) 8.63171 0.313518
\(759\) −1.73717 3.00887i −0.0630553 0.109215i
\(760\) −1.56246 2.70627i −0.0566765 0.0981666i
\(761\) 18.6909 + 32.3736i 0.677546 + 1.17354i 0.975718 + 0.219031i \(0.0702897\pi\)
−0.298172 + 0.954512i \(0.596377\pi\)
\(762\) −12.4488 + 21.5620i −0.450972 + 0.781107i
\(763\) −47.0387 −1.70292
\(764\) 12.9792 22.4807i 0.469572 0.813323i
\(765\) −0.643957 1.11537i −0.0232823 0.0403261i
\(766\) 19.0224 0.687305
\(767\) 24.1010 + 41.7442i 0.870237 + 1.50729i