Properties

Label 731.2.e.a.307.12
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 307.12
Character \(\chi\) = 731.307
Dual form 731.2.e.a.681.12

$q$-expansion

\(f(q)\) \(=\) \(q-0.884748 q^{2} +(-1.14431 + 1.98200i) q^{3} -1.21722 q^{4} +(-1.47938 + 2.56236i) q^{5} +(1.01242 - 1.75357i) q^{6} +(-0.890904 - 1.54309i) q^{7} +2.84643 q^{8} +(-1.11888 - 1.93795i) q^{9} +O(q^{10})\) \(q-0.884748 q^{2} +(-1.14431 + 1.98200i) q^{3} -1.21722 q^{4} +(-1.47938 + 2.56236i) q^{5} +(1.01242 - 1.75357i) q^{6} +(-0.890904 - 1.54309i) q^{7} +2.84643 q^{8} +(-1.11888 - 1.93795i) q^{9} +(1.30888 - 2.26704i) q^{10} -5.91864 q^{11} +(1.39288 - 2.41253i) q^{12} +(-1.61336 - 2.79442i) q^{13} +(0.788225 + 1.36525i) q^{14} +(-3.38573 - 5.86425i) q^{15} -0.0839291 q^{16} +(0.500000 + 0.866025i) q^{17} +(0.989925 + 1.71460i) q^{18} +(1.92061 - 3.32660i) q^{19} +(1.80073 - 3.11896i) q^{20} +4.07787 q^{21} +5.23650 q^{22} +(-2.29863 + 3.98134i) q^{23} +(-3.25719 + 5.64162i) q^{24} +(-1.87712 - 3.25127i) q^{25} +(1.42741 + 2.47235i) q^{26} -1.74448 q^{27} +(1.08443 + 1.87828i) q^{28} +(3.37037 + 5.83765i) q^{29} +(2.99552 + 5.18839i) q^{30} +(-2.41125 + 4.17641i) q^{31} -5.61860 q^{32} +(6.77274 - 11.7307i) q^{33} +(-0.442374 - 0.766214i) q^{34} +5.27194 q^{35} +(1.36192 + 2.35892i) q^{36} +(3.72972 - 6.46006i) q^{37} +(-1.69926 + 2.94320i) q^{38} +7.38470 q^{39} +(-4.21095 + 7.29358i) q^{40} -5.27679 q^{41} -3.60789 q^{42} +(5.26744 + 3.90564i) q^{43} +7.20429 q^{44} +6.62098 q^{45} +(2.03371 - 3.52248i) q^{46} +3.01158 q^{47} +(0.0960407 - 0.166347i) q^{48} +(1.91258 - 3.31269i) q^{49} +(1.66078 + 2.87656i) q^{50} -2.28861 q^{51} +(1.96381 + 3.40142i) q^{52} +(2.64573 - 4.58255i) q^{53} +1.54342 q^{54} +(8.75591 - 15.1657i) q^{55} +(-2.53590 - 4.39230i) q^{56} +(4.39554 + 7.61330i) q^{57} +(-2.98193 - 5.16485i) q^{58} +4.48808 q^{59} +(4.12118 + 7.13810i) q^{60} +(7.30851 + 12.6587i) q^{61} +(2.13335 - 3.69507i) q^{62} +(-1.99363 + 3.45306i) q^{63} +5.13890 q^{64} +9.54706 q^{65} +(-5.99217 + 10.3787i) q^{66} +(-2.53867 + 4.39710i) q^{67} +(-0.608611 - 1.05414i) q^{68} +(-5.26067 - 9.11176i) q^{69} -4.66434 q^{70} +(-3.08476 - 5.34297i) q^{71} +(-3.18481 - 5.51625i) q^{72} +(-4.01874 - 6.96066i) q^{73} +(-3.29986 + 5.71553i) q^{74} +8.59203 q^{75} +(-2.33781 + 4.04920i) q^{76} +(5.27294 + 9.13300i) q^{77} -6.53360 q^{78} +(-8.45272 - 14.6405i) q^{79} +(0.124163 - 0.215056i) q^{80} +(5.35286 - 9.27142i) q^{81} +4.66863 q^{82} +(-7.37425 + 12.7726i) q^{83} -4.96367 q^{84} -2.95876 q^{85} +(-4.66036 - 3.45551i) q^{86} -15.4270 q^{87} -16.8470 q^{88} +(7.06642 - 12.2394i) q^{89} -5.85790 q^{90} +(-2.87469 + 4.97911i) q^{91} +(2.79794 - 4.84617i) q^{92} +(-5.51843 - 9.55819i) q^{93} -2.66449 q^{94} +(5.68262 + 9.84259i) q^{95} +(6.42941 - 11.1361i) q^{96} +3.75573 q^{97} +(-1.69215 + 2.93089i) q^{98} +(6.62224 + 11.4701i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.884748 −0.625611 −0.312806 0.949817i \(-0.601269\pi\)
−0.312806 + 0.949817i \(0.601269\pi\)
\(3\) −1.14431 + 1.98200i −0.660666 + 1.14431i 0.319775 + 0.947494i \(0.396393\pi\)
−0.980441 + 0.196814i \(0.936941\pi\)
\(4\) −1.21722 −0.608611
\(5\) −1.47938 + 2.56236i −0.661598 + 1.14592i 0.318597 + 0.947890i \(0.396788\pi\)
−0.980196 + 0.198032i \(0.936545\pi\)
\(6\) 1.01242 1.75357i 0.413320 0.715891i
\(7\) −0.890904 1.54309i −0.336730 0.583234i 0.647086 0.762417i \(-0.275988\pi\)
−0.983816 + 0.179184i \(0.942654\pi\)
\(8\) 2.84643 1.00636
\(9\) −1.11888 1.93795i −0.372960 0.645985i
\(10\) 1.30888 2.26704i 0.413903 0.716902i
\(11\) −5.91864 −1.78454 −0.892268 0.451506i \(-0.850887\pi\)
−0.892268 + 0.451506i \(0.850887\pi\)
\(12\) 1.39288 2.41253i 0.402089 0.696438i
\(13\) −1.61336 2.79442i −0.447465 0.775031i 0.550756 0.834666i \(-0.314340\pi\)
−0.998220 + 0.0596352i \(0.981006\pi\)
\(14\) 0.788225 + 1.36525i 0.210662 + 0.364877i
\(15\) −3.38573 5.86425i −0.874191 1.51414i
\(16\) −0.0839291 −0.0209823
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i
\(18\) 0.989925 + 1.71460i 0.233328 + 0.404135i
\(19\) 1.92061 3.32660i 0.440618 0.763174i −0.557117 0.830434i \(-0.688093\pi\)
0.997735 + 0.0672605i \(0.0214259\pi\)
\(20\) 1.80073 3.11896i 0.402656 0.697420i
\(21\) 4.07787 0.889865
\(22\) 5.23650 1.11643
\(23\) −2.29863 + 3.98134i −0.479297 + 0.830167i −0.999718 0.0237428i \(-0.992442\pi\)
0.520421 + 0.853910i \(0.325775\pi\)
\(24\) −3.25719 + 5.64162i −0.664871 + 1.15159i
\(25\) −1.87712 3.25127i −0.375425 0.650255i
\(26\) 1.42741 + 2.47235i 0.279939 + 0.484868i
\(27\) −1.74448 −0.335725
\(28\) 1.08443 + 1.87828i 0.204938 + 0.354962i
\(29\) 3.37037 + 5.83765i 0.625862 + 1.08403i 0.988373 + 0.152046i \(0.0485861\pi\)
−0.362511 + 0.931979i \(0.618081\pi\)
\(30\) 2.99552 + 5.18839i 0.546904 + 0.947265i
\(31\) −2.41125 + 4.17641i −0.433074 + 0.750105i −0.997136 0.0756266i \(-0.975904\pi\)
0.564063 + 0.825732i \(0.309238\pi\)
\(32\) −5.61860 −0.993238
\(33\) 6.77274 11.7307i 1.17898 2.04206i
\(34\) −0.442374 0.766214i −0.0758665 0.131405i
\(35\) 5.27194 0.891120
\(36\) 1.36192 + 2.35892i 0.226987 + 0.393153i
\(37\) 3.72972 6.46006i 0.613162 1.06203i −0.377542 0.925993i \(-0.623231\pi\)
0.990704 0.136035i \(-0.0434361\pi\)
\(38\) −1.69926 + 2.94320i −0.275656 + 0.477450i
\(39\) 7.38470 1.18250
\(40\) −4.21095 + 7.29358i −0.665809 + 1.15322i
\(41\) −5.27679 −0.824096 −0.412048 0.911162i \(-0.635186\pi\)
−0.412048 + 0.911162i \(0.635186\pi\)
\(42\) −3.60789 −0.556709
\(43\) 5.26744 + 3.90564i 0.803278 + 0.595605i
\(44\) 7.20429 1.08609
\(45\) 6.62098 0.986998
\(46\) 2.03371 3.52248i 0.299854 0.519362i
\(47\) 3.01158 0.439284 0.219642 0.975581i \(-0.429511\pi\)
0.219642 + 0.975581i \(0.429511\pi\)
\(48\) 0.0960407 0.166347i 0.0138623 0.0240102i
\(49\) 1.91258 3.31269i 0.273226 0.473241i
\(50\) 1.66078 + 2.87656i 0.234870 + 0.406807i
\(51\) −2.28861 −0.320470
\(52\) 1.96381 + 3.40142i 0.272332 + 0.471692i
\(53\) 2.64573 4.58255i 0.363420 0.629461i −0.625102 0.780543i \(-0.714942\pi\)
0.988521 + 0.151082i \(0.0482758\pi\)
\(54\) 1.54342 0.210033
\(55\) 8.75591 15.1657i 1.18065 2.04494i
\(56\) −2.53590 4.39230i −0.338873 0.586946i
\(57\) 4.39554 + 7.61330i 0.582203 + 1.00841i
\(58\) −2.98193 5.16485i −0.391546 0.678178i
\(59\) 4.48808 0.584299 0.292149 0.956373i \(-0.405630\pi\)
0.292149 + 0.956373i \(0.405630\pi\)
\(60\) 4.12118 + 7.13810i 0.532042 + 0.921524i
\(61\) 7.30851 + 12.6587i 0.935759 + 1.62078i 0.773275 + 0.634071i \(0.218617\pi\)
0.162484 + 0.986711i \(0.448049\pi\)
\(62\) 2.13335 3.69507i 0.270936 0.469274i
\(63\) −1.99363 + 3.45306i −0.251173 + 0.435045i
\(64\) 5.13890 0.642363
\(65\) 9.54706 1.18417
\(66\) −5.99217 + 10.3787i −0.737585 + 1.27753i
\(67\) −2.53867 + 4.39710i −0.310148 + 0.537191i −0.978394 0.206749i \(-0.933712\pi\)
0.668247 + 0.743940i \(0.267045\pi\)
\(68\) −0.608611 1.05414i −0.0738049 0.127834i
\(69\) −5.26067 9.11176i −0.633311 1.09693i
\(70\) −4.66434 −0.557495
\(71\) −3.08476 5.34297i −0.366094 0.634094i 0.622857 0.782336i \(-0.285972\pi\)
−0.988951 + 0.148242i \(0.952638\pi\)
\(72\) −3.18481 5.51625i −0.375333 0.650096i
\(73\) −4.01874 6.96066i −0.470358 0.814684i 0.529067 0.848580i \(-0.322542\pi\)
−0.999425 + 0.0338958i \(0.989209\pi\)
\(74\) −3.29986 + 5.71553i −0.383601 + 0.664417i
\(75\) 8.59203 0.992122
\(76\) −2.33781 + 4.04920i −0.268165 + 0.464476i
\(77\) 5.27294 + 9.13300i 0.600907 + 1.04080i
\(78\) −6.53360 −0.739784
\(79\) −8.45272 14.6405i −0.951005 1.64719i −0.743255 0.669008i \(-0.766719\pi\)
−0.207750 0.978182i \(-0.566614\pi\)
\(80\) 0.124163 0.215056i 0.0138818 0.0240440i
\(81\) 5.35286 9.27142i 0.594762 1.03016i
\(82\) 4.66863 0.515564
\(83\) −7.37425 + 12.7726i −0.809429 + 1.40197i 0.103830 + 0.994595i \(0.466890\pi\)
−0.913260 + 0.407378i \(0.866443\pi\)
\(84\) −4.96367 −0.541581
\(85\) −2.95876 −0.320922
\(86\) −4.66036 3.45551i −0.502540 0.372617i
\(87\) −15.4270 −1.65394
\(88\) −16.8470 −1.79589
\(89\) 7.06642 12.2394i 0.749039 1.29737i −0.199245 0.979950i \(-0.563849\pi\)
0.948284 0.317423i \(-0.102818\pi\)
\(90\) −5.85790 −0.617477
\(91\) −2.87469 + 4.97911i −0.301350 + 0.521953i
\(92\) 2.79794 4.84617i 0.291705 0.505249i
\(93\) −5.51843 9.55819i −0.572234 0.991139i
\(94\) −2.66449 −0.274821
\(95\) 5.68262 + 9.84259i 0.583025 + 1.00983i
\(96\) 6.42941 11.1361i 0.656199 1.13657i
\(97\) 3.75573 0.381336 0.190668 0.981655i \(-0.438935\pi\)
0.190668 + 0.981655i \(0.438935\pi\)
\(98\) −1.69215 + 2.93089i −0.170933 + 0.296065i
\(99\) 6.62224 + 11.4701i 0.665560 + 1.15278i
\(100\) 2.28488 + 3.95752i 0.228488 + 0.395752i
\(101\) −1.81875 3.15016i −0.180972 0.313453i 0.761240 0.648471i \(-0.224591\pi\)
−0.942212 + 0.335018i \(0.891258\pi\)
\(102\) 2.02485 0.200490
\(103\) 1.96481 + 3.40315i 0.193598 + 0.335322i 0.946440 0.322879i \(-0.104651\pi\)
−0.752842 + 0.658202i \(0.771317\pi\)
\(104\) −4.59230 7.95411i −0.450313 0.779964i
\(105\) −6.03272 + 10.4490i −0.588733 + 1.01972i
\(106\) −2.34081 + 4.05440i −0.227359 + 0.393798i
\(107\) 7.69252 0.743664 0.371832 0.928300i \(-0.378730\pi\)
0.371832 + 0.928300i \(0.378730\pi\)
\(108\) 2.12342 0.204326
\(109\) 0.506907 0.877989i 0.0485529 0.0840961i −0.840728 0.541458i \(-0.817872\pi\)
0.889280 + 0.457362i \(0.151206\pi\)
\(110\) −7.74677 + 13.4178i −0.738625 + 1.27934i
\(111\) 8.53589 + 14.7846i 0.810191 + 1.40329i
\(112\) 0.0747727 + 0.129510i 0.00706536 + 0.0122376i
\(113\) −5.07172 −0.477107 −0.238554 0.971129i \(-0.576673\pi\)
−0.238554 + 0.971129i \(0.576673\pi\)
\(114\) −3.88894 6.73585i −0.364233 0.630870i
\(115\) −6.80108 11.7798i −0.634204 1.09847i
\(116\) −4.10249 7.10572i −0.380906 0.659749i
\(117\) −3.61030 + 6.25322i −0.333772 + 0.578111i
\(118\) −3.97082 −0.365544
\(119\) 0.890904 1.54309i 0.0816690 0.141455i
\(120\) −9.63724 16.6922i −0.879755 1.52378i
\(121\) 24.0303 2.18457
\(122\) −6.46619 11.1998i −0.585421 1.01398i
\(123\) 6.03827 10.4586i 0.544452 0.943019i
\(124\) 2.93503 5.08362i 0.263573 0.456522i
\(125\) −3.68588 −0.329675
\(126\) 1.76386 3.05509i 0.157137 0.272169i
\(127\) 1.16768 0.103615 0.0518075 0.998657i \(-0.483502\pi\)
0.0518075 + 0.998657i \(0.483502\pi\)
\(128\) 6.69057 0.591369
\(129\) −13.7685 + 5.97081i −1.21225 + 0.525701i
\(130\) −8.44674 −0.740828
\(131\) −1.64480 −0.143707 −0.0718536 0.997415i \(-0.522891\pi\)
−0.0718536 + 0.997415i \(0.522891\pi\)
\(132\) −8.24392 + 14.2789i −0.717542 + 1.24282i
\(133\) −6.84432 −0.593478
\(134\) 2.24608 3.89032i 0.194032 0.336073i
\(135\) 2.58075 4.46998i 0.222115 0.384715i
\(136\) 1.42321 + 2.46508i 0.122040 + 0.211379i
\(137\) −6.00933 −0.513411 −0.256706 0.966490i \(-0.582637\pi\)
−0.256706 + 0.966490i \(0.582637\pi\)
\(138\) 4.65437 + 8.06161i 0.396206 + 0.686249i
\(139\) 7.81601 13.5377i 0.662945 1.14826i −0.316893 0.948461i \(-0.602639\pi\)
0.979838 0.199794i \(-0.0640272\pi\)
\(140\) −6.41712 −0.542345
\(141\) −3.44617 + 5.96894i −0.290220 + 0.502676i
\(142\) 2.72924 + 4.72718i 0.229033 + 0.396696i
\(143\) 9.54887 + 16.5391i 0.798517 + 1.38307i
\(144\) 0.0939064 + 0.162651i 0.00782554 + 0.0135542i
\(145\) −19.9442 −1.65628
\(146\) 3.55557 + 6.15843i 0.294261 + 0.509675i
\(147\) 4.37716 + 7.58146i 0.361022 + 0.625308i
\(148\) −4.53990 + 7.86333i −0.373177 + 0.646362i
\(149\) −1.44652 + 2.50545i −0.118504 + 0.205254i −0.919175 0.393850i \(-0.871143\pi\)
0.800671 + 0.599104i \(0.204476\pi\)
\(150\) −7.60178 −0.620682
\(151\) −23.2299 −1.89042 −0.945212 0.326457i \(-0.894145\pi\)
−0.945212 + 0.326457i \(0.894145\pi\)
\(152\) 5.46688 9.46892i 0.443423 0.768031i
\(153\) 1.11888 1.93795i 0.0904560 0.156674i
\(154\) −4.66522 8.08040i −0.375934 0.651137i
\(155\) −7.13431 12.3570i −0.573042 0.992537i
\(156\) −8.98882 −0.719681
\(157\) 6.81926 + 11.8113i 0.544236 + 0.942645i 0.998655 + 0.0518566i \(0.0165139\pi\)
−0.454418 + 0.890789i \(0.650153\pi\)
\(158\) 7.47853 + 12.9532i 0.594960 + 1.03050i
\(159\) 6.05507 + 10.4877i 0.480198 + 0.831727i
\(160\) 8.31204 14.3969i 0.657125 1.13817i
\(161\) 8.19143 0.645575
\(162\) −4.73593 + 8.20287i −0.372090 + 0.644478i
\(163\) −9.64261 16.7015i −0.755267 1.30816i −0.945241 0.326372i \(-0.894174\pi\)
0.189974 0.981789i \(-0.439160\pi\)
\(164\) 6.42302 0.501554
\(165\) 20.0389 + 34.7084i 1.56003 + 2.70204i
\(166\) 6.52435 11.3005i 0.506388 0.877090i
\(167\) 7.61294 13.1860i 0.589107 1.02036i −0.405243 0.914209i \(-0.632813\pi\)
0.994350 0.106154i \(-0.0338537\pi\)
\(168\) 11.6074 0.895528
\(169\) 1.29416 2.24156i 0.0995510 0.172427i
\(170\) 2.61775 0.200773
\(171\) −8.59572 −0.657331
\(172\) −6.41165 4.75403i −0.488883 0.362491i
\(173\) 1.66919 0.126906 0.0634531 0.997985i \(-0.479789\pi\)
0.0634531 + 0.997985i \(0.479789\pi\)
\(174\) 13.6490 1.03473
\(175\) −3.34467 + 5.79315i −0.252834 + 0.437921i
\(176\) 0.496746 0.0374436
\(177\) −5.13575 + 8.89538i −0.386026 + 0.668617i
\(178\) −6.25200 + 10.8288i −0.468607 + 0.811651i
\(179\) −3.20258 5.54703i −0.239372 0.414604i 0.721162 0.692766i \(-0.243608\pi\)
−0.960534 + 0.278162i \(0.910275\pi\)
\(180\) −8.05920 −0.600697
\(181\) −7.48635 12.9667i −0.556456 0.963810i −0.997789 0.0664662i \(-0.978828\pi\)
0.441333 0.897343i \(-0.354506\pi\)
\(182\) 2.54338 4.40526i 0.188528 0.326539i
\(183\) −33.4527 −2.47290
\(184\) −6.54288 + 11.3326i −0.482348 + 0.835451i
\(185\) 11.0353 + 19.1138i 0.811334 + 1.40527i
\(186\) 4.88241 + 8.45659i 0.357996 + 0.620067i
\(187\) −2.95932 5.12569i −0.216407 0.374828i
\(188\) −3.66576 −0.267353
\(189\) 1.55416 + 2.69189i 0.113049 + 0.195806i
\(190\) −5.02769 8.70821i −0.364747 0.631760i
\(191\) 9.95930 17.2500i 0.720630 1.24817i −0.240118 0.970744i \(-0.577186\pi\)
0.960748 0.277423i \(-0.0894805\pi\)
\(192\) −5.88049 + 10.1853i −0.424388 + 0.735061i
\(193\) −6.90060 −0.496716 −0.248358 0.968668i \(-0.579891\pi\)
−0.248358 + 0.968668i \(0.579891\pi\)
\(194\) −3.32287 −0.238568
\(195\) −10.9248 + 18.9223i −0.782339 + 1.35505i
\(196\) −2.32803 + 4.03227i −0.166288 + 0.288019i
\(197\) 3.21595 + 5.57019i 0.229127 + 0.396860i 0.957550 0.288268i \(-0.0930795\pi\)
−0.728422 + 0.685128i \(0.759746\pi\)
\(198\) −5.85901 10.1481i −0.416382 0.721194i
\(199\) 12.6847 0.899194 0.449597 0.893231i \(-0.351568\pi\)
0.449597 + 0.893231i \(0.351568\pi\)
\(200\) −5.34310 9.25452i −0.377814 0.654394i
\(201\) −5.81003 10.0633i −0.409808 0.709808i
\(202\) 1.60913 + 2.78710i 0.113218 + 0.196100i
\(203\) 6.00535 10.4016i 0.421493 0.730048i
\(204\) 2.78575 0.195042
\(205\) 7.80637 13.5210i 0.545221 0.944350i
\(206\) −1.73836 3.01093i −0.121117 0.209781i
\(207\) 10.2875 0.715034
\(208\) 0.135408 + 0.234533i 0.00938882 + 0.0162619i
\(209\) −11.3674 + 19.6889i −0.786300 + 1.36191i
\(210\) 5.33743 9.24471i 0.368318 0.637945i
\(211\) −10.5626 −0.727160 −0.363580 0.931563i \(-0.618446\pi\)
−0.363580 + 0.931563i \(0.618446\pi\)
\(212\) −3.22044 + 5.57797i −0.221181 + 0.383097i
\(213\) 14.1197 0.967464
\(214\) −6.80594 −0.465244
\(215\) −17.8002 + 7.71917i −1.21396 + 0.526443i
\(216\) −4.96554 −0.337862
\(217\) 8.59277 0.583316
\(218\) −0.448485 + 0.776799i −0.0303752 + 0.0526115i
\(219\) 18.3947 1.24300
\(220\) −10.6579 + 18.4600i −0.718554 + 1.24457i
\(221\) 1.61336 2.79442i 0.108526 0.187973i
\(222\) −7.55211 13.0806i −0.506864 0.877915i
\(223\) −27.8701 −1.86632 −0.933162 0.359457i \(-0.882962\pi\)
−0.933162 + 0.359457i \(0.882962\pi\)
\(224\) 5.00564 + 8.67001i 0.334453 + 0.579290i
\(225\) −4.20055 + 7.27556i −0.280037 + 0.485037i
\(226\) 4.48719 0.298484
\(227\) 3.99015 6.91114i 0.264836 0.458709i −0.702685 0.711501i \(-0.748016\pi\)
0.967521 + 0.252792i \(0.0813490\pi\)
\(228\) −5.35034 9.26707i −0.354335 0.613727i
\(229\) 2.01000 + 3.48142i 0.132824 + 0.230059i 0.924764 0.380540i \(-0.124262\pi\)
−0.791940 + 0.610599i \(0.790929\pi\)
\(230\) 6.01724 + 10.4222i 0.396765 + 0.687218i
\(231\) −24.1354 −1.58800
\(232\) 9.59352 + 16.6165i 0.629846 + 1.09092i
\(233\) 4.12138 + 7.13843i 0.270000 + 0.467654i 0.968862 0.247603i \(-0.0796428\pi\)
−0.698861 + 0.715257i \(0.746310\pi\)
\(234\) 3.19420 5.53252i 0.208812 0.361672i
\(235\) −4.45526 + 7.71674i −0.290629 + 0.503385i
\(236\) −5.46299 −0.355610
\(237\) 38.6900 2.51319
\(238\) −0.788225 + 1.36525i −0.0510931 + 0.0884958i
\(239\) 8.01667 13.8853i 0.518556 0.898164i −0.481212 0.876604i \(-0.659803\pi\)
0.999768 0.0215603i \(-0.00686338\pi\)
\(240\) 0.284161 + 0.492181i 0.0183425 + 0.0317702i
\(241\) −3.83986 6.65083i −0.247347 0.428418i 0.715442 0.698672i \(-0.246225\pi\)
−0.962789 + 0.270255i \(0.912892\pi\)
\(242\) −21.2607 −1.36669
\(243\) 9.63391 + 16.6864i 0.618015 + 1.07043i
\(244\) −8.89608 15.4085i −0.569513 0.986425i
\(245\) 5.65886 + 9.80144i 0.361531 + 0.626191i
\(246\) −5.34235 + 9.25321i −0.340615 + 0.589963i
\(247\) −12.3945 −0.788644
\(248\) −6.86346 + 11.8879i −0.435830 + 0.754880i
\(249\) −16.8768 29.2315i −1.06953 1.85247i
\(250\) 3.26107 0.206248
\(251\) 5.21413 + 9.03113i 0.329113 + 0.570040i 0.982336 0.187125i \(-0.0599171\pi\)
−0.653223 + 0.757165i \(0.726584\pi\)
\(252\) 2.42669 4.20314i 0.152867 0.264773i
\(253\) 13.6047 23.5641i 0.855323 1.48146i
\(254\) −1.03310 −0.0648228
\(255\) 3.38573 5.86425i 0.212023 0.367234i
\(256\) −16.1973 −1.01233
\(257\) 20.8134 1.29831 0.649153 0.760658i \(-0.275124\pi\)
0.649153 + 0.760658i \(0.275124\pi\)
\(258\) 12.1817 5.28266i 0.758399 0.328884i
\(259\) −13.2913 −0.825881
\(260\) −11.6209 −0.720697
\(261\) 7.54207 13.0633i 0.466843 0.808595i
\(262\) 1.45524 0.0899049
\(263\) 15.1872 26.3050i 0.936483 1.62204i 0.164515 0.986375i \(-0.447394\pi\)
0.771968 0.635662i \(-0.219273\pi\)
\(264\) 19.2781 33.3907i 1.18649 2.05506i
\(265\) 7.82809 + 13.5586i 0.480876 + 0.832901i
\(266\) 6.05550 0.371286
\(267\) 16.1723 + 28.0113i 0.989729 + 1.71426i
\(268\) 3.09012 5.35225i 0.188759 0.326940i
\(269\) −4.36699 −0.266260 −0.133130 0.991099i \(-0.542503\pi\)
−0.133130 + 0.991099i \(0.542503\pi\)
\(270\) −2.28331 + 3.95481i −0.138958 + 0.240682i
\(271\) 0.804729 + 1.39383i 0.0488838 + 0.0846692i 0.889432 0.457068i \(-0.151100\pi\)
−0.840548 + 0.541737i \(0.817767\pi\)
\(272\) −0.0419645 0.0726847i −0.00254447 0.00440716i
\(273\) −6.57906 11.3953i −0.398183 0.689673i
\(274\) 5.31674 0.321196
\(275\) 11.1100 + 19.2431i 0.669959 + 1.16040i
\(276\) 6.40341 + 11.0910i 0.385440 + 0.667601i
\(277\) −0.204446 + 0.354112i −0.0122840 + 0.0212765i −0.872102 0.489324i \(-0.837244\pi\)
0.859818 + 0.510601i \(0.170577\pi\)
\(278\) −6.91520 + 11.9775i −0.414746 + 0.718361i
\(279\) 10.7916 0.646076
\(280\) 15.0062 0.896792
\(281\) −5.49996 + 9.52621i −0.328100 + 0.568286i −0.982135 0.188178i \(-0.939742\pi\)
0.654035 + 0.756465i \(0.273075\pi\)
\(282\) 3.04899 5.28101i 0.181565 0.314479i
\(283\) 6.94125 + 12.0226i 0.412614 + 0.714669i 0.995175 0.0981184i \(-0.0312824\pi\)
−0.582560 + 0.812787i \(0.697949\pi\)
\(284\) 3.75484 + 6.50357i 0.222809 + 0.385916i
\(285\) −26.0107 −1.54074
\(286\) −8.44834 14.6330i −0.499561 0.865265i
\(287\) 4.70111 + 8.14257i 0.277498 + 0.480641i
\(288\) 6.28653 + 10.8886i 0.370438 + 0.641617i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 17.6456 1.03619
\(291\) −4.29771 + 7.44385i −0.251936 + 0.436366i
\(292\) 4.89170 + 8.47267i 0.286265 + 0.495825i
\(293\) 24.4827 1.43029 0.715146 0.698975i \(-0.246360\pi\)
0.715146 + 0.698975i \(0.246360\pi\)
\(294\) −3.87268 6.70768i −0.225859 0.391200i
\(295\) −6.63958 + 11.5001i −0.386571 + 0.669561i
\(296\) 10.6164 18.3881i 0.617065 1.06879i
\(297\) 10.3249 0.599114
\(298\) 1.27981 2.21669i 0.0741372 0.128409i
\(299\) 14.8340 0.857874
\(300\) −10.4584 −0.603816
\(301\) 1.33397 11.6077i 0.0768888 0.669057i
\(302\) 20.5526 1.18267
\(303\) 8.32483 0.478249
\(304\) −0.161195 + 0.279198i −0.00924517 + 0.0160131i
\(305\) −43.2482 −2.47639
\(306\) −0.989925 + 1.71460i −0.0565903 + 0.0980172i
\(307\) −16.5499 + 28.6653i −0.944554 + 1.63602i −0.187912 + 0.982186i \(0.560172\pi\)
−0.756642 + 0.653829i \(0.773161\pi\)
\(308\) −6.41833 11.1169i −0.365718 0.633443i
\(309\) −8.99338 −0.511615
\(310\) 6.31206 + 10.9328i 0.358501 + 0.620942i
\(311\) 1.55444 2.69236i 0.0881441 0.152670i −0.818583 0.574389i \(-0.805240\pi\)
0.906727 + 0.421719i \(0.138573\pi\)
\(312\) 21.0200 1.19003
\(313\) 13.9714 24.1992i 0.789711 1.36782i −0.136433 0.990649i \(-0.543564\pi\)
0.926144 0.377171i \(-0.123103\pi\)
\(314\) −6.03333 10.4500i −0.340480 0.589729i
\(315\) −5.89866 10.2168i −0.332352 0.575650i
\(316\) 10.2888 + 17.8208i 0.578792 + 1.00250i
\(317\) 3.61564 0.203074 0.101537 0.994832i \(-0.467624\pi\)
0.101537 + 0.994832i \(0.467624\pi\)
\(318\) −5.35721 9.27895i −0.300417 0.520338i
\(319\) −19.9480 34.5510i −1.11687 1.93448i
\(320\) −7.60239 + 13.1677i −0.424986 + 0.736098i
\(321\) −8.80260 + 15.2466i −0.491313 + 0.850980i
\(322\) −7.24735 −0.403879
\(323\) 3.84122 0.213731
\(324\) −6.51561 + 11.2854i −0.361978 + 0.626965i
\(325\) −6.05694 + 10.4909i −0.335979 + 0.581932i
\(326\) 8.53128 + 14.7766i 0.472504 + 0.818400i
\(327\) 1.16012 + 2.00938i 0.0641545 + 0.111119i
\(328\) −15.0200 −0.829341
\(329\) −2.68303 4.64714i −0.147920 0.256205i
\(330\) −17.7294 30.7082i −0.975970 1.69043i
\(331\) −10.0168 17.3495i −0.550571 0.953616i −0.998233 0.0594137i \(-0.981077\pi\)
0.447663 0.894202i \(-0.352256\pi\)
\(332\) 8.97610 15.5471i 0.492627 0.853256i
\(333\) −16.6924 −0.914739
\(334\) −6.73553 + 11.6663i −0.368552 + 0.638351i
\(335\) −7.51130 13.0100i −0.410386 0.710810i
\(336\) −0.342252 −0.0186714
\(337\) −4.35288 7.53940i −0.237116 0.410697i 0.722769 0.691089i \(-0.242869\pi\)
−0.959886 + 0.280392i \(0.909536\pi\)
\(338\) −1.14501 + 1.98321i −0.0622802 + 0.107872i
\(339\) 5.80361 10.0521i 0.315209 0.545957i
\(340\) 3.60146 0.195317
\(341\) 14.2713 24.7187i 0.772836 1.33859i
\(342\) 7.60505 0.411234
\(343\) −19.2884 −1.04147
\(344\) 14.9934 + 11.1171i 0.808390 + 0.599395i
\(345\) 31.1301 1.67599
\(346\) −1.47681 −0.0793940
\(347\) −16.2399 + 28.1284i −0.871806 + 1.51001i −0.0116784 + 0.999932i \(0.503717\pi\)
−0.860127 + 0.510080i \(0.829616\pi\)
\(348\) 18.7780 1.00661
\(349\) 15.3539 26.5938i 0.821877 1.42353i −0.0824052 0.996599i \(-0.526260\pi\)
0.904283 0.426934i \(-0.140406\pi\)
\(350\) 2.95919 5.12547i 0.158176 0.273968i
\(351\) 2.81447 + 4.87480i 0.150225 + 0.260198i
\(352\) 33.2545 1.77247
\(353\) 0.525182 + 0.909642i 0.0279526 + 0.0484154i 0.879663 0.475597i \(-0.157768\pi\)
−0.851711 + 0.524012i \(0.824435\pi\)
\(354\) 4.54384 7.87016i 0.241502 0.418294i
\(355\) 18.2541 0.968829
\(356\) −8.60139 + 14.8980i −0.455873 + 0.789595i
\(357\) 2.03894 + 3.53154i 0.107912 + 0.186909i
\(358\) 2.83347 + 4.90772i 0.149754 + 0.259381i
\(359\) −10.5878 18.3386i −0.558802 0.967873i −0.997597 0.0692857i \(-0.977928\pi\)
0.438795 0.898587i \(-0.355405\pi\)
\(360\) 18.8462 0.993280
\(361\) 2.12251 + 3.67629i 0.111711 + 0.193489i
\(362\) 6.62353 + 11.4723i 0.348125 + 0.602970i
\(363\) −27.4980 + 47.6280i −1.44327 + 2.49982i
\(364\) 3.49914 6.06068i 0.183405 0.317666i
\(365\) 23.7810 1.24475
\(366\) 29.5972 1.54707
\(367\) 12.0588 20.8865i 0.629465 1.09026i −0.358195 0.933647i \(-0.616608\pi\)
0.987659 0.156618i \(-0.0500591\pi\)
\(368\) 0.192922 0.334150i 0.0100567 0.0174188i
\(369\) 5.90409 + 10.2262i 0.307355 + 0.532354i
\(370\) −9.76349 16.9109i −0.507580 0.879154i
\(371\) −9.42838 −0.489497
\(372\) 6.71715 + 11.6344i 0.348268 + 0.603218i
\(373\) 12.6331 + 21.8812i 0.654117 + 1.13296i 0.982114 + 0.188286i \(0.0602931\pi\)
−0.327997 + 0.944679i \(0.606374\pi\)
\(374\) 2.61825 + 4.53494i 0.135387 + 0.234496i
\(375\) 4.21778 7.30541i 0.217805 0.377250i
\(376\) 8.57224 0.442080
\(377\) 10.8752 18.8364i 0.560102 0.970126i
\(378\) −1.37504 2.38164i −0.0707246 0.122499i
\(379\) 11.2354 0.577124 0.288562 0.957461i \(-0.406823\pi\)
0.288562 + 0.957461i \(0.406823\pi\)
\(380\) −6.91701 11.9806i −0.354835 0.614593i
\(381\) −1.33619 + 2.31435i −0.0684550 + 0.118568i
\(382\) −8.81147 + 15.2619i −0.450834 + 0.780867i
\(383\) −17.7309 −0.906005 −0.453003 0.891509i \(-0.649647\pi\)
−0.453003 + 0.891509i \(0.649647\pi\)
\(384\) −7.65607 + 13.2607i −0.390697 + 0.676707i
\(385\) −31.2027 −1.59024
\(386\) 6.10529 0.310751
\(387\) 1.67532 14.5780i 0.0851614 0.741042i
\(388\) −4.57155 −0.232085
\(389\) −4.69744 −0.238170 −0.119085 0.992884i \(-0.537996\pi\)
−0.119085 + 0.992884i \(0.537996\pi\)
\(390\) 9.66567 16.7414i 0.489440 0.847735i
\(391\) −4.59726 −0.232493
\(392\) 5.44402 9.42933i 0.274965 0.476253i
\(393\) 1.88216 3.26000i 0.0949425 0.164445i
\(394\) −2.84531 4.92822i −0.143345 0.248280i
\(395\) 50.0191 2.51673
\(396\) −8.06073 13.9616i −0.405067 0.701596i
\(397\) 4.83915 8.38165i 0.242870 0.420663i −0.718661 0.695361i \(-0.755245\pi\)
0.961531 + 0.274698i \(0.0885779\pi\)
\(398\) −11.2228 −0.562546
\(399\) 7.83201 13.5654i 0.392091 0.679121i
\(400\) 0.157545 + 0.272876i 0.00787726 + 0.0136438i
\(401\) −5.91103 10.2382i −0.295183 0.511272i 0.679845 0.733356i \(-0.262047\pi\)
−0.975027 + 0.222084i \(0.928714\pi\)
\(402\) 5.14041 + 8.90345i 0.256380 + 0.444064i
\(403\) 15.5608 0.775140
\(404\) 2.21382 + 3.83445i 0.110142 + 0.190771i
\(405\) 15.8378 + 27.4319i 0.786987 + 1.36310i
\(406\) −5.31322 + 9.20277i −0.263691 + 0.456726i
\(407\) −22.0749 + 38.2348i −1.09421 + 1.89523i
\(408\) −6.51438 −0.322510
\(409\) −19.5934 −0.968829 −0.484415 0.874839i \(-0.660967\pi\)
−0.484415 + 0.874839i \(0.660967\pi\)
\(410\) −6.90667 + 11.9627i −0.341096 + 0.590796i
\(411\) 6.87652 11.9105i 0.339194 0.587500i
\(412\) −2.39161 4.14238i −0.117826 0.204081i
\(413\) −3.99845 6.92552i −0.196751 0.340783i
\(414\) −9.10188 −0.447333
\(415\) −21.8186 37.7910i −1.07103 1.85509i
\(416\) 9.06481 + 15.7007i 0.444439 + 0.769791i
\(417\) 17.8878 + 30.9826i 0.875971 + 1.51723i
\(418\) 10.0573 17.4197i 0.491918 0.852027i
\(419\) −32.5125 −1.58834 −0.794169 0.607697i \(-0.792093\pi\)
−0.794169 + 0.607697i \(0.792093\pi\)
\(420\) 7.34315 12.7187i 0.358309 0.620610i
\(421\) 0.299567 + 0.518866i 0.0146000 + 0.0252880i 0.873233 0.487303i \(-0.162019\pi\)
−0.858633 + 0.512591i \(0.828686\pi\)
\(422\) 9.34525 0.454920
\(423\) −3.36959 5.83630i −0.163835 0.283771i
\(424\) 7.53090 13.0439i 0.365733 0.633468i
\(425\) 1.87712 3.25127i 0.0910539 0.157710i
\(426\) −12.4923 −0.605256
\(427\) 13.0224 22.5554i 0.630196 1.09153i
\(428\) −9.36350 −0.452602
\(429\) −43.7074 −2.11021
\(430\) 15.7487 6.82951i 0.759469 0.329348i
\(431\) −7.08237 −0.341146 −0.170573 0.985345i \(-0.554562\pi\)
−0.170573 + 0.985345i \(0.554562\pi\)
\(432\) 0.146413 0.00704428
\(433\) 14.9415 25.8795i 0.718045 1.24369i −0.243729 0.969843i \(-0.578371\pi\)
0.961773 0.273846i \(-0.0882960\pi\)
\(434\) −7.60244 −0.364929
\(435\) 22.8223 39.5294i 1.09425 1.89529i
\(436\) −0.617018 + 1.06871i −0.0295498 + 0.0511818i
\(437\) 8.82954 + 15.2932i 0.422374 + 0.731574i
\(438\) −16.2747 −0.777634
\(439\) −13.2687 22.9821i −0.633283 1.09688i −0.986876 0.161479i \(-0.948374\pi\)
0.353594 0.935399i \(-0.384960\pi\)
\(440\) 24.9231 43.1680i 1.18816 2.05795i
\(441\) −8.55978 −0.407609
\(442\) −1.42741 + 2.47235i −0.0678951 + 0.117598i
\(443\) 0.0865349 + 0.149883i 0.00411140 + 0.00712115i 0.868074 0.496435i \(-0.165358\pi\)
−0.863962 + 0.503556i \(0.832025\pi\)
\(444\) −10.3901 17.9961i −0.493091 0.854059i
\(445\) 20.9078 + 36.2134i 0.991125 + 1.71668i
\(446\) 24.6580 1.16759
\(447\) −3.31053 5.73401i −0.156583 0.271209i
\(448\) −4.57827 7.92980i −0.216303 0.374648i
\(449\) −6.12943 + 10.6165i −0.289266 + 0.501023i −0.973635 0.228113i \(-0.926744\pi\)
0.684369 + 0.729136i \(0.260078\pi\)
\(450\) 3.71643 6.43704i 0.175194 0.303445i
\(451\) 31.2314 1.47063
\(452\) 6.17341 0.290373
\(453\) 26.5822 46.0417i 1.24894 2.16323i
\(454\) −3.53028 + 6.11462i −0.165684 + 0.286973i
\(455\) −8.50551 14.7320i −0.398745 0.690646i
\(456\) 12.5116 + 21.6707i 0.585909 + 1.01482i
\(457\) −23.0440 −1.07795 −0.538977 0.842320i \(-0.681189\pi\)
−0.538977 + 0.842320i \(0.681189\pi\)
\(458\) −1.77834 3.08018i −0.0830965 0.143927i
\(459\) −0.872240 1.51076i −0.0407127 0.0705164i
\(460\) 8.27843 + 14.3387i 0.385984 + 0.668543i
\(461\) 13.8615 24.0089i 0.645596 1.11821i −0.338567 0.940942i \(-0.609942\pi\)
0.984163 0.177263i \(-0.0567244\pi\)
\(462\) 21.3538 0.993468
\(463\) −18.6633 + 32.3257i −0.867355 + 1.50230i −0.00266633 + 0.999996i \(0.500849\pi\)
−0.864689 + 0.502307i \(0.832485\pi\)
\(464\) −0.282872 0.489949i −0.0131320 0.0227453i
\(465\) 32.6554 1.51436
\(466\) −3.64638 6.31571i −0.168915 0.292570i
\(467\) −11.0720 + 19.1773i −0.512351 + 0.887418i 0.487546 + 0.873097i \(0.337892\pi\)
−0.999897 + 0.0143211i \(0.995441\pi\)
\(468\) 4.39453 7.61156i 0.203137 0.351844i
\(469\) 9.04683 0.417744
\(470\) 3.94179 6.82737i 0.181821 0.314923i
\(471\) −31.2133 −1.43823
\(472\) 12.7750 0.588018
\(473\) −31.1761 23.1161i −1.43348 1.06288i
\(474\) −34.2309 −1.57228
\(475\) −14.4209 −0.661676
\(476\) −1.08443 + 1.87828i −0.0497046 + 0.0860910i
\(477\) −11.8410 −0.542163
\(478\) −7.09273 + 12.2850i −0.324414 + 0.561902i
\(479\) 3.29848 5.71314i 0.150712 0.261040i −0.780778 0.624809i \(-0.785177\pi\)
0.931489 + 0.363769i \(0.118510\pi\)
\(480\) 19.0231 + 32.9489i 0.868280 + 1.50391i
\(481\) −24.0695 −1.09747
\(482\) 3.39731 + 5.88431i 0.154743 + 0.268023i
\(483\) −9.37351 + 16.2354i −0.426510 + 0.738736i
\(484\) −29.2502 −1.32955
\(485\) −5.55614 + 9.62352i −0.252292 + 0.436982i
\(486\) −8.52358 14.7633i −0.386637 0.669676i
\(487\) 19.0839 + 33.0543i 0.864775 + 1.49783i 0.867270 + 0.497838i \(0.165873\pi\)
−0.00249455 + 0.999997i \(0.500794\pi\)
\(488\) 20.8032 + 36.0321i 0.941715 + 1.63110i
\(489\) 44.1364 1.99592
\(490\) −5.00667 8.67180i −0.226178 0.391752i
\(491\) −14.7992 25.6329i −0.667877 1.15680i −0.978497 0.206262i \(-0.933870\pi\)
0.310620 0.950534i \(-0.399463\pi\)
\(492\) −7.34991 + 12.7304i −0.331360 + 0.573932i
\(493\) −3.37037 + 5.83765i −0.151794 + 0.262915i
\(494\) 10.9660 0.493385
\(495\) −39.1872 −1.76133
\(496\) 0.202374 0.350522i 0.00908687 0.0157389i
\(497\) −5.49646 + 9.52014i −0.246550 + 0.427037i
\(498\) 14.9317 + 25.8625i 0.669107 + 1.15893i
\(499\) 4.01808 + 6.95952i 0.179874 + 0.311551i 0.941837 0.336069i \(-0.109098\pi\)
−0.761963 + 0.647620i \(0.775764\pi\)
\(500\) 4.48653 0.200644
\(501\) 17.4231 + 30.1777i 0.778406 + 1.34824i
\(502\) −4.61319 7.99027i −0.205897 0.356623i
\(503\) −1.14464 1.98258i −0.0510370 0.0883987i 0.839378 0.543548i \(-0.182919\pi\)
−0.890415 + 0.455149i \(0.849586\pi\)
\(504\) −5.67472 + 9.82890i −0.252772 + 0.437814i
\(505\) 10.7625 0.478924
\(506\) −12.0368 + 20.8483i −0.535100 + 0.926820i
\(507\) 2.96184 + 5.13006i 0.131540 + 0.227834i
\(508\) −1.42133 −0.0630613
\(509\) −8.25621 14.3002i −0.365950 0.633844i 0.622978 0.782239i \(-0.285923\pi\)
−0.988928 + 0.148395i \(0.952589\pi\)
\(510\) −2.99552 + 5.18839i −0.132644 + 0.229746i
\(511\) −7.16062 + 12.4026i −0.316767 + 0.548657i
\(512\) 0.949361 0.0419562
\(513\) −3.35047 + 5.80318i −0.147927 + 0.256217i
\(514\) −18.4146 −0.812234
\(515\) −11.6268 −0.512337
\(516\) 16.7594 7.26780i 0.737790 0.319947i
\(517\) −17.8244 −0.783918
\(518\) 11.7594 0.516680
\(519\) −1.91007 + 3.30834i −0.0838427 + 0.145220i
\(520\) 27.1750 1.19170
\(521\) 5.15304 8.92532i 0.225759 0.391025i −0.730788 0.682604i \(-0.760847\pi\)
0.956547 + 0.291579i \(0.0941806\pi\)
\(522\) −6.67283 + 11.5577i −0.292062 + 0.505866i
\(523\) 16.1741 + 28.0144i 0.707245 + 1.22498i 0.965875 + 0.259008i \(0.0833957\pi\)
−0.258630 + 0.965977i \(0.583271\pi\)
\(524\) 2.00209 0.0874618
\(525\) −7.65467 13.2583i −0.334077 0.578639i
\(526\) −13.4368 + 23.2733i −0.585874 + 1.01476i
\(527\) −4.82250 −0.210072
\(528\) −0.568430 + 0.984549i −0.0247377 + 0.0428470i
\(529\) 0.932616 + 1.61534i 0.0405485 + 0.0702321i
\(530\) −6.92588 11.9960i −0.300841 0.521072i
\(531\) −5.02162 8.69770i −0.217920 0.377448i
\(532\) 8.33105 0.361197
\(533\) 8.51334 + 14.7455i 0.368754 + 0.638700i
\(534\) −14.3084 24.7829i −0.619185 1.07246i
\(535\) −11.3801 + 19.7110i −0.492007 + 0.852181i
\(536\) −7.22614 + 12.5160i −0.312122 + 0.540610i
\(537\) 14.6589 0.632580
\(538\) 3.86369 0.166575
\(539\) −11.3199 + 19.6066i −0.487581 + 0.844516i
\(540\) −3.14134 + 5.44096i −0.135182 + 0.234142i
\(541\) 13.3471 + 23.1179i 0.573838 + 0.993917i 0.996167 + 0.0874741i \(0.0278795\pi\)
−0.422329 + 0.906443i \(0.638787\pi\)
\(542\) −0.711982 1.23319i −0.0305822 0.0529700i
\(543\) 34.2667 1.47053
\(544\) −2.80930 4.86585i −0.120448 0.208622i
\(545\) 1.49982 + 2.59776i 0.0642450 + 0.111276i
\(546\) 5.82081 + 10.0819i 0.249108 + 0.431467i
\(547\) −11.1370 + 19.2899i −0.476185 + 0.824776i −0.999628 0.0272848i \(-0.991314\pi\)
0.523443 + 0.852061i \(0.324647\pi\)
\(548\) 7.31468 0.312468
\(549\) 16.3547 28.3271i 0.698000 1.20897i
\(550\) −9.82956 17.0253i −0.419134 0.725961i
\(551\) 25.8927 1.10307
\(552\) −14.9741 25.9360i −0.637342 1.10391i
\(553\) −15.0611 + 26.0866i −0.640464 + 1.10932i
\(554\) 0.180884 0.313299i 0.00768500 0.0133108i
\(555\) −50.5113 −2.14408
\(556\) −9.51382 + 16.4784i −0.403476 + 0.698840i
\(557\) −10.3391 −0.438082 −0.219041 0.975716i \(-0.570293\pi\)
−0.219041 + 0.975716i \(0.570293\pi\)
\(558\) −9.54784 −0.404192
\(559\) 2.41571 21.0206i 0.102174 0.889077i
\(560\) −0.442469 −0.0186977
\(561\) 13.5455 0.571891
\(562\) 4.86608 8.42830i 0.205263 0.355526i
\(563\) −25.7885 −1.08686 −0.543429 0.839455i \(-0.682874\pi\)
−0.543429 + 0.839455i \(0.682874\pi\)
\(564\) 4.19475 7.26552i 0.176631 0.305934i
\(565\) 7.50300 12.9956i 0.315653 0.546728i
\(566\) −6.14125 10.6370i −0.258136 0.447105i
\(567\) −19.0755 −0.801097
\(568\) −8.78056 15.2084i −0.368424 0.638129i
\(569\) −18.8913 + 32.7207i −0.791965 + 1.37172i 0.132784 + 0.991145i \(0.457608\pi\)
−0.924749 + 0.380578i \(0.875725\pi\)
\(570\) 23.0129 0.963904
\(571\) 19.1637 33.1924i 0.801974 1.38906i −0.116341 0.993209i \(-0.537117\pi\)
0.918315 0.395851i \(-0.129550\pi\)
\(572\) −11.6231 20.1318i −0.485986 0.841752i
\(573\) 22.7930 + 39.4786i 0.952191 + 1.64924i
\(574\) −4.15930 7.20412i −0.173606 0.300694i
\(575\) 17.2592 0.719760
\(576\) −5.74981 9.95896i −0.239575 0.414957i
\(577\) 5.36843 + 9.29839i 0.223491 + 0.387097i 0.955866 0.293805i \(-0.0949215\pi\)
−0.732375 + 0.680902i \(0.761588\pi\)
\(578\) 0.442374 0.766214i 0.0184003 0.0318703i
\(579\) 7.89640 13.6770i 0.328163 0.568395i
\(580\) 24.2765 1.00803
\(581\) 26.2790 1.09024
\(582\) 3.80239 6.58593i 0.157614 0.272995i
\(583\) −15.6591 + 27.1224i −0.648535 + 1.12330i
\(584\) −11.4391 19.8130i −0.473352 0.819869i
\(585\) −10.6820 18.5018i −0.441646 0.764954i
\(586\) −21.6610 −0.894807
\(587\) 16.8698 + 29.2194i 0.696292 + 1.20601i 0.969743 + 0.244127i \(0.0785015\pi\)
−0.273451 + 0.961886i \(0.588165\pi\)
\(588\) −5.32797 9.22832i −0.219722 0.380569i
\(589\) 9.26215 + 16.0425i 0.381640 + 0.661021i
\(590\) 5.87435 10.1747i 0.241843 0.418885i
\(591\) −14.7202 −0.605506
\(592\) −0.313032 + 0.542187i −0.0128655 + 0.0222838i
\(593\) −1.03037 1.78465i −0.0423122 0.0732868i 0.844094 0.536196i \(-0.180139\pi\)
−0.886406 + 0.462909i \(0.846806\pi\)
\(594\) −9.13497 −0.374812
\(595\) 2.63597 + 4.56563i 0.108064 + 0.187173i
\(596\) 1.76074 3.04969i 0.0721226 0.124920i
\(597\) −14.5152 + 25.1411i −0.594067 + 1.02895i
\(598\) −13.1244 −0.536695
\(599\) −12.3540 + 21.3978i −0.504771 + 0.874290i 0.495213 + 0.868771i \(0.335090\pi\)
−0.999985 + 0.00551824i \(0.998243\pi\)
\(600\) 24.4566 0.998436
\(601\) 7.70294 0.314210 0.157105 0.987582i \(-0.449784\pi\)
0.157105 + 0.987582i \(0.449784\pi\)
\(602\) −1.18023 + 10.2699i −0.0481025 + 0.418569i
\(603\) 11.3618 0.462690
\(604\) 28.2760 1.15053
\(605\) −35.5499 + 61.5742i −1.44531 + 2.50335i
\(606\) −7.36537 −0.299198
\(607\) 9.65038 16.7150i 0.391697 0.678439i −0.600977 0.799267i \(-0.705222\pi\)
0.992674 + 0.120828i \(0.0385548\pi\)
\(608\) −10.7912 + 18.6908i −0.437639 + 0.758013i
\(609\) 13.7439 + 23.8052i 0.556933 + 0.964636i
\(610\) 38.2638 1.54925
\(611\) −4.85875 8.41560i −0.196564 0.340459i
\(612\) −1.36192 + 2.35892i −0.0550525 + 0.0953537i
\(613\) 4.94444 0.199704 0.0998520 0.995002i \(-0.468163\pi\)
0.0998520 + 0.995002i \(0.468163\pi\)
\(614\) 14.6425 25.3616i 0.590923 1.02351i
\(615\) 17.8658 + 30.9444i 0.720418 + 1.24780i
\(616\) 15.0090 + 25.9964i 0.604732 + 1.04743i
\(617\) 12.0895 + 20.9397i 0.486707 + 0.843000i 0.999883 0.0152825i \(-0.00486477\pi\)
−0.513177 + 0.858283i \(0.671531\pi\)
\(618\) 7.95687 0.320072
\(619\) 12.3448 + 21.3819i 0.496181 + 0.859410i 0.999990 0.00440460i \(-0.00140203\pi\)
−0.503810 + 0.863815i \(0.668069\pi\)
\(620\) 8.68403 + 15.0412i 0.348759 + 0.604069i
\(621\) 4.00991 6.94537i 0.160912 0.278708i
\(622\) −1.37528 + 2.38206i −0.0551439 + 0.0955120i
\(623\) −25.1820 −1.00890
\(624\) −0.619791 −0.0248115
\(625\) 14.8384 25.7009i 0.593537 1.02804i
\(626\) −12.3612 + 21.4102i −0.494052 + 0.855723i
\(627\) −26.0156 45.0603i −1.03896 1.79954i
\(628\) −8.30055 14.3770i −0.331228 0.573704i
\(629\) 7.45944 0.297427
\(630\) 5.21883 + 9.03927i 0.207923 + 0.360133i
\(631\) 0.911709 + 1.57913i 0.0362946 + 0.0628641i 0.883602 0.468239i \(-0.155111\pi\)
−0.847308 + 0.531103i \(0.821778\pi\)
\(632\) −24.0601 41.6733i −0.957058 1.65767i
\(633\) 12.0869 20.9351i 0.480410 0.832095i
\(634\) −3.19892 −0.127046
\(635\) −1.72745 + 2.99202i −0.0685516 + 0.118735i
\(636\) −7.37036 12.7658i −0.292254 0.506198i
\(637\) −12.3427 −0.489035
\(638\) 17.6490 + 30.5689i 0.698729 + 1.21023i
\(639\) −6.90295 + 11.9563i −0.273077 + 0.472982i
\(640\) −9.89789 + 17.1436i −0.391248 + 0.677662i
\(641\) −31.6504 −1.25012 −0.625058 0.780578i \(-0.714925\pi\)
−0.625058 + 0.780578i \(0.714925\pi\)
\(642\) 7.78808 13.4894i 0.307371 0.532383i
\(643\) 36.1224 1.42453 0.712264 0.701912i \(-0.247670\pi\)
0.712264 + 0.701912i \(0.247670\pi\)
\(644\) −9.97078 −0.392904
\(645\) 5.06953 44.1131i 0.199612 1.73695i
\(646\) −3.39851 −0.133713
\(647\) −40.2037 −1.58057 −0.790284 0.612740i \(-0.790067\pi\)
−0.790284 + 0.612740i \(0.790067\pi\)
\(648\) 15.2365 26.3904i 0.598547 1.03671i
\(649\) −26.5633 −1.04270
\(650\) 5.35886 9.28182i 0.210192 0.364063i
\(651\) −9.83278 + 17.0309i −0.385377 + 0.667492i
\(652\) 11.7372 + 20.3294i 0.459664 + 0.796161i
\(653\) −34.8497 −1.36378 −0.681888 0.731457i \(-0.738841\pi\)
−0.681888 + 0.731457i \(0.738841\pi\)
\(654\) −1.02641 1.77779i −0.0401358 0.0695172i
\(655\) 2.43329 4.21458i 0.0950765 0.164677i
\(656\) 0.442876 0.0172914
\(657\) −8.99297 + 15.5763i −0.350849 + 0.607688i
\(658\) 2.37380 + 4.11154i 0.0925404 + 0.160285i
\(659\) −8.35401 14.4696i −0.325426 0.563655i 0.656172 0.754611i \(-0.272174\pi\)
−0.981599 + 0.190956i \(0.938841\pi\)
\(660\) −24.3918 42.2478i −0.949449 1.64449i
\(661\) −23.3107 −0.906683 −0.453341 0.891337i \(-0.649768\pi\)
−0.453341 + 0.891337i \(0.649768\pi\)
\(662\) 8.86230 + 15.3500i 0.344443 + 0.596593i
\(663\) 3.69235 + 6.39534i 0.143399 + 0.248374i
\(664\) −20.9903 + 36.3562i −0.814581 + 1.41090i
\(665\) 10.1253 17.5376i 0.392644 0.680079i
\(666\) 14.7686 0.572271
\(667\) −30.9889 −1.19990
\(668\) −9.26663 + 16.0503i −0.358537 + 0.621004i
\(669\) 31.8920 55.2386i 1.23302 2.13565i
\(670\) 6.64561 + 11.5105i 0.256742 + 0.444691i
\(671\) −43.2564 74.9223i −1.66990 2.89234i
\(672\) −22.9119 −0.883847
\(673\) 2.17009 + 3.75870i 0.0836507 + 0.144887i 0.904815 0.425804i \(-0.140009\pi\)
−0.821165 + 0.570691i \(0.806675\pi\)
\(674\) 3.85120 + 6.67047i 0.148343 + 0.256937i
\(675\) 3.27461 + 5.67178i 0.126040 + 0.218307i
\(676\) −1.57528 + 2.72847i −0.0605878 + 0.104941i
\(677\) 35.9756 1.38266 0.691328 0.722541i \(-0.257026\pi\)
0.691328 + 0.722541i \(0.257026\pi\)
\(678\) −5.13473 + 8.89361i −0.197198 + 0.341557i
\(679\) −3.34599 5.79543i −0.128407 0.222408i
\(680\) −8.42190 −0.322965
\(681\) 9.13192 + 15.8169i 0.349936 + 0.606107i
\(682\) −12.6265 + 21.8698i −0.483494 + 0.837437i
\(683\) −8.97636 + 15.5475i −0.343471 + 0.594909i −0.985075 0.172127i \(-0.944936\pi\)
0.641604 + 0.767036i \(0.278269\pi\)
\(684\) 10.4629 0.400059
\(685\) 8.89007 15.3981i 0.339672 0.588329i
\(686\) 17.0653 0.651557
\(687\) −9.20023 −0.351010
\(688\) −0.442092 0.327797i −0.0168546 0.0124971i
\(689\) −17.0741 −0.650470
\(690\) −27.5423 −1.04852
\(691\) 9.68869 16.7813i 0.368575 0.638391i −0.620768 0.783994i \(-0.713179\pi\)
0.989343 + 0.145603i \(0.0465124\pi\)
\(692\) −2.03178 −0.0772365
\(693\) 11.7996 20.4374i 0.448228 0.776354i
\(694\) 14.3682 24.8865i 0.545411 0.944680i
\(695\) 23.1257 + 40.0549i 0.877207 + 1.51937i
\(696\) −43.9118 −1.66447
\(697\) −2.63840 4.56983i −0.0999363 0.173095i
\(698\) −13.5844 + 23.5288i −0.514176 + 0.890578i
\(699\) −18.8645 −0.713520
\(700\) 4.07121 7.05154i 0.153877 0.266523i
\(701\) −8.54187 14.7949i −0.322622 0.558797i 0.658406 0.752663i \(-0.271231\pi\)
−0.981028 + 0.193865i \(0.937898\pi\)
\(702\) −2.49009 4.31297i −0.0939825 0.162783i
\(703\) −14.3267 24.8145i −0.540341 0.935898i
\(704\) −30.4153 −1.14632
\(705\) −10.1964 17.6607i −0.384018 0.665139i
\(706\) −0.464654 0.804804i −0.0174875 0.0302892i
\(707\) −3.24066 + 5.61299i −0.121878 + 0.211098i
\(708\) 6.25134 10.8276i 0.234940 0.406928i
\(709\) −2.03338 −0.0763653 −0.0381827 0.999271i \(-0.512157\pi\)
−0.0381827 + 0.999271i \(0.512157\pi\)
\(710\) −16.1503 −0.606110
\(711\) −18.9151 + 32.7620i −0.709373 + 1.22867i
\(712\) 20.1141 34.8386i 0.753806 1.30563i
\(713\) −11.0851 19.2000i −0.415142 0.719047i
\(714\) −1.80394 3.12452i −0.0675109 0.116932i
\(715\) −56.5056 −2.11319
\(716\) 3.89825 + 6.75196i 0.145684 + 0.252333i
\(717\) 18.3471 + 31.7781i 0.685184 + 1.18677i
\(718\) 9.36751 + 16.2250i 0.349593 + 0.605512i
\(719\) 5.00777 8.67370i 0.186758 0.323475i −0.757409 0.652940i \(-0.773535\pi\)
0.944168 + 0.329466i \(0.106869\pi\)
\(720\) −0.555693 −0.0207095
\(721\) 3.50091 6.06376i 0.130381 0.225826i
\(722\) −1.87788 3.25259i −0.0698875 0.121049i
\(723\) 17.5759 0.653655
\(724\) 9.11254 + 15.7834i 0.338665 + 0.586585i
\(725\) 12.6532 21.9160i 0.469928 0.813940i
\(726\) 24.3288 42.1387i 0.902927 1.56391i
\(727\) 12.8775 0.477598 0.238799 0.971069i \(-0.423246\pi\)
0.238799 + 0.971069i \(0.423246\pi\)
\(728\) −8.18261 + 14.1727i −0.303268 + 0.525275i
\(729\) −11.9795 −0.443684
\(730\) −21.0402 −0.778731
\(731\) −0.748661 + 6.51456i −0.0276902 + 0.240950i
\(732\) 40.7194 1.50503
\(733\) −36.4849 −1.34760 −0.673801 0.738913i \(-0.735339\pi\)
−0.673801 + 0.738913i \(0.735339\pi\)
\(734\) −10.6690 + 18.4793i −0.393800 + 0.682082i
\(735\) −25.9019 −0.955406
\(736\) 12.9151 22.3696i 0.476056 0.824553i
\(737\) 15.0255 26.0248i 0.553470 0.958637i
\(738\) −5.22363 9.04759i −0.192284 0.333046i
\(739\) −29.7323 −1.09372 −0.546861 0.837223i \(-0.684177\pi\)
−0.546861 + 0.837223i \(0.684177\pi\)
\(740\) −13.4325 23.2657i −0.493787 0.855264i
\(741\) 14.1831 24.5659i 0.521031 0.902452i
\(742\) 8.34174 0.306235
\(743\) 10.2325 17.7232i 0.375395 0.650203i −0.614991 0.788534i \(-0.710841\pi\)
0.990386 + 0.138331i \(0.0441738\pi\)
\(744\) −15.7078 27.2067i −0.575876 0.997447i
\(745\) −4.27991 7.41302i −0.156804 0.271592i
\(746\) −11.1771 19.3593i −0.409223 0.708795i
\(747\) 33.0036 1.20754
\(748\) 3.60215 + 6.23910i 0.131708 + 0.228124i
\(749\) −6.85329 11.8703i −0.250414 0.433730i
\(750\) −3.73167 + 6.46344i −0.136261 + 0.236011i
\(751\) −5.34838 + 9.26367i −0.195165 + 0.338036i −0.946955 0.321367i \(-0.895858\pi\)
0.751789 + 0.659403i \(0.229191\pi\)
\(752\) −0.252759 −0.00921717
\(753\) −23.8663 −0.869735
\(754\) −9.62183 + 16.6655i −0.350406 + 0.606921i
\(755\) 34.3659 59.5234i 1.25070 2.16628i
\(756\) −1.89176 3.27663i −0.0688027 0.119170i
\(757\) −14.3441 24.8447i −0.521344 0.902995i −0.999692 0.0248240i \(-0.992097\pi\)
0.478348 0.878171i \(-0.341236\pi\)
\(758\) −9.94050 −0.361055
\(759\) 31.1360 + 53.9292i 1.13017 + 1.95751i
\(760\) 16.1752 + 28.0162i 0.586736 + 1.01626i
\(761\) −15.1393 26.2220i −0.548798 0.950547i −0.998357 0.0572959i \(-0.981752\pi\)
0.449559 0.893251i \(-0.351581\pi\)
\(762\) 1.18219 2.04761i 0.0428262 0.0741772i
\(763\) −1.80642 −0.0653969
\(764\) −12.1227 + 20.9971i −0.438583 + 0.759648i
\(765\) 3.31049 + 5.73394i 0.119691 + 0.207311i
\(766\) 15.6874 0.566807
\(767\) −7.24088 12.5416i −0.261453 0.452850i