Properties

Label 731.2.m.c.87.7
Level 731
Weight 2
Character 731.87
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.m (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 87.7
Character \(\chi\) = 731.87
Dual form 731.2.m.c.689.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.14159 - 1.14159i) q^{2} +(-2.60557 + 1.07926i) q^{3} +0.606454i q^{4} +(0.611497 + 1.47629i) q^{5} +(4.20657 + 1.74242i) q^{6} +(-0.771748 + 1.86317i) q^{7} +(-1.59086 + 1.59086i) q^{8} +(3.50287 - 3.50287i) q^{9} +O(q^{10})\) \(q+(-1.14159 - 1.14159i) q^{2} +(-2.60557 + 1.07926i) q^{3} +0.606454i q^{4} +(0.611497 + 1.47629i) q^{5} +(4.20657 + 1.74242i) q^{6} +(-0.771748 + 1.86317i) q^{7} +(-1.59086 + 1.59086i) q^{8} +(3.50287 - 3.50287i) q^{9} +(0.987233 - 2.38339i) q^{10} +(-0.196435 - 0.0813659i) q^{11} +(-0.654523 - 1.58016i) q^{12} +3.95416i q^{13} +(3.00799 - 1.24595i) q^{14} +(-3.18660 - 3.18660i) q^{15} +4.84512 q^{16} +(3.83953 + 1.50267i) q^{17} -7.99767 q^{18} +(1.18065 + 1.18065i) q^{19} +(-0.895300 + 0.370845i) q^{20} -5.68753i q^{21} +(0.131361 + 0.317134i) q^{22} +(-3.83013 - 1.58649i) q^{23} +(2.42814 - 5.86204i) q^{24} +(1.73005 - 1.73005i) q^{25} +(4.51403 - 4.51403i) q^{26} +(-2.10866 + 5.09076i) q^{27} +(-1.12992 - 0.468030i) q^{28} +(-0.633451 - 1.52929i) q^{29} +7.27557i q^{30} +(-3.53886 + 1.46584i) q^{31} +(-2.34943 - 2.34943i) q^{32} +0.599639 q^{33} +(-2.66773 - 6.09860i) q^{34} -3.22248 q^{35} +(2.12433 + 2.12433i) q^{36} +(-8.71079 + 3.60813i) q^{37} -2.69563i q^{38} +(-4.26758 - 10.3028i) q^{39} +(-3.32136 - 1.37575i) q^{40} +(2.83976 - 6.85578i) q^{41} +(-6.49282 + 6.49282i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(0.0493447 - 0.119129i) q^{44} +(7.31322 + 3.02924i) q^{45} +(2.56131 + 6.18356i) q^{46} +9.34141i q^{47} +(-12.6243 + 5.22916i) q^{48} +(2.07396 + 2.07396i) q^{49} -3.95000 q^{50} +(-11.6259 + 0.228540i) q^{51} -2.39802 q^{52} +(-2.72753 - 2.72753i) q^{53} +(8.21879 - 3.40434i) q^{54} -0.339748i q^{55} +(-1.73629 - 4.19177i) q^{56} +(-4.35049 - 1.80203i) q^{57} +(-1.02268 + 2.46896i) q^{58} +(-2.66615 + 2.66615i) q^{59} +(1.93253 - 1.93253i) q^{60} +(-5.30405 + 12.8051i) q^{61} +(5.71331 + 2.36653i) q^{62} +(3.82309 + 9.22975i) q^{63} -4.32608i q^{64} +(-5.83747 + 2.41796i) q^{65} +(-0.684542 - 0.684542i) q^{66} -0.714752 q^{67} +(-0.911302 + 2.32850i) q^{68} +11.6919 q^{69} +(3.67876 + 3.67876i) q^{70} +(-12.4813 + 5.16992i) q^{71} +11.1451i q^{72} +(0.207677 + 0.501377i) q^{73} +(14.0631 + 5.82515i) q^{74} +(-2.64058 + 6.37493i) q^{75} +(-0.716009 + 0.716009i) q^{76} +(0.303196 - 0.303196i) q^{77} +(-6.88980 + 16.6334i) q^{78} +(-2.93176 - 1.21437i) q^{79} +(2.96278 + 7.15278i) q^{80} -0.678738i q^{81} +(-11.0683 + 4.58465i) q^{82} +(-10.8255 - 10.8255i) q^{83} +3.44922 q^{84} +(0.129488 + 6.58712i) q^{85} +1.61445 q^{86} +(3.30100 + 3.30100i) q^{87} +(0.441941 - 0.183058i) q^{88} -16.0725i q^{89} +(-4.89055 - 11.8068i) q^{90} +(-7.36725 - 3.05162i) q^{91} +(0.962134 - 2.32280i) q^{92} +(7.63871 - 7.63871i) q^{93} +(10.6641 - 10.6641i) q^{94} +(-1.02101 + 2.46494i) q^{95} +(8.65724 + 3.58595i) q^{96} +(-2.75322 - 6.64685i) q^{97} -4.73522i q^{98} +(-0.973098 + 0.403070i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q + 4q^{2} + 4q^{3} + 8q^{5} - 12q^{6} + 4q^{7} - 4q^{8} + 8q^{9} + O(q^{10}) \) \( 128q + 4q^{2} + 4q^{3} + 8q^{5} - 12q^{6} + 4q^{7} - 4q^{8} + 8q^{9} - 8q^{10} - 4q^{11} + 12q^{12} + 12q^{14} - 12q^{15} - 144q^{16} - 12q^{17} + 64q^{18} - 28q^{19} - 8q^{20} - 12q^{22} + 16q^{23} - 16q^{24} - 20q^{25} + 16q^{26} - 8q^{27} + 20q^{28} + 12q^{31} - 4q^{32} - 104q^{33} + 20q^{34} + 32q^{35} - 96q^{36} - 12q^{37} + 8q^{39} + 216q^{40} + 24q^{41} - 4q^{42} + 24q^{44} - 28q^{45} - 48q^{46} + 28q^{48} - 80q^{50} - 20q^{51} + 56q^{52} - 36q^{53} - 12q^{54} - 8q^{56} + 72q^{57} - 32q^{58} + 48q^{59} - 40q^{60} - 76q^{61} - 44q^{62} + 36q^{65} - 68q^{66} - 48q^{67} + 32q^{68} + 216q^{69} - 196q^{70} + 4q^{71} + 20q^{73} + 88q^{74} + 80q^{75} + 72q^{76} + 28q^{77} - 120q^{78} + 68q^{79} - 68q^{80} + 28q^{82} - 36q^{83} - 152q^{84} + 28q^{85} - 24q^{86} - 56q^{87} + 20q^{88} - 112q^{90} + 96q^{91} - 28q^{92} + 24q^{93} - 36q^{94} - 108q^{95} + 272q^{96} + 8q^{97} - 20q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(173\) \(562\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.14159 1.14159i −0.807226 0.807226i 0.176987 0.984213i \(-0.443365\pi\)
−0.984213 + 0.176987i \(0.943365\pi\)
\(3\) −2.60557 + 1.07926i −1.50433 + 0.623112i −0.974378 0.224917i \(-0.927789\pi\)
−0.529949 + 0.848030i \(0.677789\pi\)
\(4\) 0.606454i 0.303227i
\(5\) 0.611497 + 1.47629i 0.273470 + 0.660215i 0.999627 0.0273142i \(-0.00869545\pi\)
−0.726157 + 0.687529i \(0.758695\pi\)
\(6\) 4.20657 + 1.74242i 1.71732 + 0.711339i
\(7\) −0.771748 + 1.86317i −0.291693 + 0.704210i −0.999999 0.00169617i \(-0.999460\pi\)
0.708305 + 0.705906i \(0.249460\pi\)
\(8\) −1.59086 + 1.59086i −0.562453 + 0.562453i
\(9\) 3.50287 3.50287i 1.16762 1.16762i
\(10\) 0.987233 2.38339i 0.312190 0.753694i
\(11\) −0.196435 0.0813659i −0.0592273 0.0245327i 0.352873 0.935671i \(-0.385205\pi\)
−0.412100 + 0.911138i \(0.635205\pi\)
\(12\) −0.654523 1.58016i −0.188945 0.456153i
\(13\) 3.95416i 1.09669i 0.836253 + 0.548343i \(0.184741\pi\)
−0.836253 + 0.548343i \(0.815259\pi\)
\(14\) 3.00799 1.24595i 0.803919 0.332994i
\(15\) −3.18660 3.18660i −0.822776 0.822776i
\(16\) 4.84512 1.21128
\(17\) 3.83953 + 1.50267i 0.931222 + 0.364452i
\(18\) −7.99767 −1.88507
\(19\) 1.18065 + 1.18065i 0.270859 + 0.270859i 0.829446 0.558587i \(-0.188656\pi\)
−0.558587 + 0.829446i \(0.688656\pi\)
\(20\) −0.895300 + 0.370845i −0.200195 + 0.0829235i
\(21\) 5.68753i 1.24112i
\(22\) 0.131361 + 0.317134i 0.0280063 + 0.0676132i
\(23\) −3.83013 1.58649i −0.798637 0.330806i −0.0542264 0.998529i \(-0.517269\pi\)
−0.744410 + 0.667723i \(0.767269\pi\)
\(24\) 2.42814 5.86204i 0.495641 1.19658i
\(25\) 1.73005 1.73005i 0.346009 0.346009i
\(26\) 4.51403 4.51403i 0.885274 0.885274i
\(27\) −2.10866 + 5.09076i −0.405812 + 0.979718i
\(28\) −1.12992 0.468030i −0.213536 0.0884494i
\(29\) −0.633451 1.52929i −0.117629 0.283981i 0.854089 0.520127i \(-0.174116\pi\)
−0.971718 + 0.236146i \(0.924116\pi\)
\(30\) 7.27557i 1.32833i
\(31\) −3.53886 + 1.46584i −0.635597 + 0.263273i −0.677129 0.735864i \(-0.736776\pi\)
0.0415319 + 0.999137i \(0.486776\pi\)
\(32\) −2.34943 2.34943i −0.415324 0.415324i
\(33\) 0.599639 0.104384
\(34\) −2.66773 6.09860i −0.457512 1.04590i
\(35\) −3.22248 −0.544699
\(36\) 2.12433 + 2.12433i 0.354055 + 0.354055i
\(37\) −8.71079 + 3.60813i −1.43204 + 0.593172i −0.957855 0.287251i \(-0.907259\pi\)
−0.474189 + 0.880423i \(0.657259\pi\)
\(38\) 2.69563i 0.437289i
\(39\) −4.26758 10.3028i −0.683359 1.64977i
\(40\) −3.32136 1.37575i −0.525154 0.217526i
\(41\) 2.83976 6.85578i 0.443495 1.07069i −0.531218 0.847235i \(-0.678266\pi\)
0.974714 0.223457i \(-0.0717344\pi\)
\(42\) −6.49282 + 6.49282i −1.00186 + 1.00186i
\(43\) −0.707107 + 0.707107i −0.107833 + 0.107833i
\(44\) 0.0493447 0.119129i 0.00743899 0.0179593i
\(45\) 7.31322 + 3.02924i 1.09019 + 0.451572i
\(46\) 2.56131 + 6.18356i 0.377645 + 0.911715i
\(47\) 9.34141i 1.36258i 0.732011 + 0.681292i \(0.238582\pi\)
−0.732011 + 0.681292i \(0.761418\pi\)
\(48\) −12.6243 + 5.22916i −1.82216 + 0.754764i
\(49\) 2.07396 + 2.07396i 0.296280 + 0.296280i
\(50\) −3.95000 −0.558615
\(51\) −11.6259 + 0.228540i −1.62796 + 0.0320019i
\(52\) −2.39802 −0.332545
\(53\) −2.72753 2.72753i −0.374656 0.374656i 0.494514 0.869170i \(-0.335346\pi\)
−0.869170 + 0.494514i \(0.835346\pi\)
\(54\) 8.21879 3.40434i 1.11844 0.463271i
\(55\) 0.339748i 0.0458117i
\(56\) −1.73629 4.19177i −0.232021 0.560149i
\(57\) −4.35049 1.80203i −0.576236 0.238685i
\(58\) −1.02268 + 2.46896i −0.134284 + 0.324190i
\(59\) −2.66615 + 2.66615i −0.347104 + 0.347104i −0.859030 0.511926i \(-0.828932\pi\)
0.511926 + 0.859030i \(0.328932\pi\)
\(60\) 1.93253 1.93253i 0.249488 0.249488i
\(61\) −5.30405 + 12.8051i −0.679114 + 1.63953i 0.0865199 + 0.996250i \(0.472425\pi\)
−0.765634 + 0.643276i \(0.777575\pi\)
\(62\) 5.71331 + 2.36653i 0.725591 + 0.300550i
\(63\) 3.82309 + 9.22975i 0.481664 + 1.16284i
\(64\) 4.32608i 0.540760i
\(65\) −5.83747 + 2.41796i −0.724049 + 0.299911i
\(66\) −0.684542 0.684542i −0.0842613 0.0842613i
\(67\) −0.714752 −0.0873209 −0.0436605 0.999046i \(-0.513902\pi\)
−0.0436605 + 0.999046i \(0.513902\pi\)
\(68\) −0.911302 + 2.32850i −0.110512 + 0.282372i
\(69\) 11.6919 1.40754
\(70\) 3.67876 + 3.67876i 0.439695 + 0.439695i
\(71\) −12.4813 + 5.16992i −1.48126 + 0.613557i −0.969394 0.245509i \(-0.921045\pi\)
−0.511864 + 0.859067i \(0.671045\pi\)
\(72\) 11.1451i 1.31347i
\(73\) 0.207677 + 0.501377i 0.0243068 + 0.0586817i 0.935567 0.353150i \(-0.114889\pi\)
−0.911260 + 0.411831i \(0.864889\pi\)
\(74\) 14.0631 + 5.82515i 1.63481 + 0.677159i
\(75\) −2.64058 + 6.37493i −0.304908 + 0.736113i
\(76\) −0.716009 + 0.716009i −0.0821319 + 0.0821319i
\(77\) 0.303196 0.303196i 0.0345524 0.0345524i
\(78\) −6.88980 + 16.6334i −0.780116 + 1.88337i
\(79\) −2.93176 1.21437i −0.329849 0.136628i 0.211612 0.977354i \(-0.432129\pi\)
−0.541461 + 0.840726i \(0.682129\pi\)
\(80\) 2.96278 + 7.15278i 0.331249 + 0.799705i
\(81\) 0.678738i 0.0754154i
\(82\) −11.0683 + 4.58465i −1.22229 + 0.506290i
\(83\) −10.8255 10.8255i −1.18825 1.18825i −0.977551 0.210697i \(-0.932427\pi\)
−0.210697 0.977551i \(-0.567573\pi\)
\(84\) 3.44922 0.376341
\(85\) 0.129488 + 6.58712i 0.0140449 + 0.714473i
\(86\) 1.61445 0.174091
\(87\) 3.30100 + 3.30100i 0.353904 + 0.353904i
\(88\) 0.441941 0.183058i 0.0471111 0.0195140i
\(89\) 16.0725i 1.70368i −0.523804 0.851839i \(-0.675487\pi\)
0.523804 0.851839i \(-0.324513\pi\)
\(90\) −4.89055 11.8068i −0.515510 1.24455i
\(91\) −7.36725 3.05162i −0.772298 0.319896i
\(92\) 0.962134 2.32280i 0.100309 0.242168i
\(93\) 7.63871 7.63871i 0.792097 0.792097i
\(94\) 10.6641 10.6641i 1.09991 1.09991i
\(95\) −1.02101 + 2.46494i −0.104753 + 0.252897i
\(96\) 8.65724 + 3.58595i 0.883576 + 0.365989i
\(97\) −2.75322 6.64685i −0.279547 0.674885i 0.720277 0.693687i \(-0.244015\pi\)
−0.999823 + 0.0188017i \(0.994015\pi\)
\(98\) 4.73522i 0.478329i
\(99\) −0.973098 + 0.403070i −0.0978000 + 0.0405101i
\(100\) 1.04919 + 1.04919i 0.104919 + 0.104919i
\(101\) −4.02029 −0.400034 −0.200017 0.979792i \(-0.564100\pi\)
−0.200017 + 0.979792i \(0.564100\pi\)
\(102\) 13.5329 + 13.0112i 1.33996 + 1.28830i
\(103\) 13.1156 1.29232 0.646161 0.763201i \(-0.276374\pi\)
0.646161 + 0.763201i \(0.276374\pi\)
\(104\) −6.29051 6.29051i −0.616835 0.616835i
\(105\) 8.39641 3.47791i 0.819406 0.339409i
\(106\) 6.22745i 0.604863i
\(107\) −7.24028 17.4796i −0.699944 1.68981i −0.723716 0.690097i \(-0.757568\pi\)
0.0237723 0.999717i \(-0.492432\pi\)
\(108\) −3.08732 1.27881i −0.297077 0.123053i
\(109\) 1.52347 3.67798i 0.145922 0.352287i −0.833972 0.551807i \(-0.813938\pi\)
0.979894 + 0.199521i \(0.0639385\pi\)
\(110\) −0.387853 + 0.387853i −0.0369804 + 0.0369804i
\(111\) 18.8024 18.8024i 1.78465 1.78465i
\(112\) −3.73921 + 9.02726i −0.353323 + 0.852996i
\(113\) −1.11413 0.461490i −0.104809 0.0434133i 0.329663 0.944099i \(-0.393065\pi\)
−0.434472 + 0.900685i \(0.643065\pi\)
\(114\) 2.90929 + 7.02366i 0.272480 + 0.657826i
\(115\) 6.62449i 0.617737i
\(116\) 0.927442 0.384159i 0.0861108 0.0356683i
\(117\) 13.8509 + 13.8509i 1.28052 + 1.28052i
\(118\) 6.08731 0.560382
\(119\) −5.76288 + 5.99399i −0.528282 + 0.549468i
\(120\) 10.1388 0.925546
\(121\) −7.74621 7.74621i −0.704201 0.704201i
\(122\) 20.6732 8.56313i 1.87167 0.775270i
\(123\) 20.9280i 1.88702i
\(124\) −0.888966 2.14615i −0.0798315 0.192730i
\(125\) 10.9934 + 4.55361i 0.983278 + 0.407287i
\(126\) 6.17219 14.9010i 0.549862 1.32749i
\(127\) 1.82125 1.82125i 0.161610 0.161610i −0.621670 0.783280i \(-0.713545\pi\)
0.783280 + 0.621670i \(0.213545\pi\)
\(128\) −9.63746 + 9.63746i −0.851839 + 0.851839i
\(129\) 1.07926 2.60557i 0.0950237 0.229408i
\(130\) 9.42431 + 3.90368i 0.826567 + 0.342375i
\(131\) −4.28398 10.3424i −0.374293 0.903624i −0.993012 0.118011i \(-0.962348\pi\)
0.618719 0.785612i \(-0.287652\pi\)
\(132\) 0.363654i 0.0316520i
\(133\) −3.11091 + 1.28858i −0.269750 + 0.111734i
\(134\) 0.815954 + 0.815954i 0.0704877 + 0.0704877i
\(135\) −8.80486 −0.757802
\(136\) −8.49868 + 3.71760i −0.728756 + 0.318782i
\(137\) 13.1185 1.12079 0.560396 0.828225i \(-0.310649\pi\)
0.560396 + 0.828225i \(0.310649\pi\)
\(138\) −13.3474 13.3474i −1.13620 1.13620i
\(139\) −3.39690 + 1.40704i −0.288121 + 0.119344i −0.522063 0.852907i \(-0.674837\pi\)
0.233942 + 0.972251i \(0.424837\pi\)
\(140\) 1.95429i 0.165168i
\(141\) −10.0818 24.3397i −0.849043 2.04977i
\(142\) 20.1505 + 8.34659i 1.69099 + 0.700431i
\(143\) 0.321734 0.776734i 0.0269047 0.0649537i
\(144\) 16.9718 16.9718i 1.41432 1.41432i
\(145\) 1.87031 1.87031i 0.155321 0.155321i
\(146\) 0.335284 0.809448i 0.0277483 0.0669904i
\(147\) −7.64219 3.16550i −0.630317 0.261086i
\(148\) −2.18816 5.28270i −0.179866 0.434235i
\(149\) 1.04562i 0.0856602i 0.999082 + 0.0428301i \(0.0136374\pi\)
−0.999082 + 0.0428301i \(0.986363\pi\)
\(150\) 10.2920 4.26309i 0.840339 0.348080i
\(151\) −0.851662 0.851662i −0.0693073 0.0693073i 0.671603 0.740911i \(-0.265606\pi\)
−0.740911 + 0.671603i \(0.765606\pi\)
\(152\) −3.75649 −0.304691
\(153\) 18.7130 8.18569i 1.51286 0.661774i
\(154\) −0.692251 −0.0557832
\(155\) −4.32800 4.32800i −0.347633 0.347633i
\(156\) 6.24820 2.58809i 0.500257 0.207213i
\(157\) 14.0092i 1.11805i 0.829150 + 0.559026i \(0.188825\pi\)
−0.829150 + 0.559026i \(0.811175\pi\)
\(158\) 1.96055 + 4.73318i 0.155973 + 0.376552i
\(159\) 10.0505 + 4.16306i 0.797057 + 0.330152i
\(160\) 2.03176 4.90509i 0.160624 0.387782i
\(161\) 5.91179 5.91179i 0.465914 0.465914i
\(162\) −0.774841 + 0.774841i −0.0608772 + 0.0608772i
\(163\) −7.78356 + 18.7912i −0.609655 + 1.47184i 0.253721 + 0.967277i \(0.418345\pi\)
−0.863376 + 0.504561i \(0.831655\pi\)
\(164\) 4.15772 + 1.72218i 0.324663 + 0.134480i
\(165\) 0.366678 + 0.885238i 0.0285458 + 0.0689157i
\(166\) 24.7165i 1.91837i
\(167\) 0.0919718 0.0380960i 0.00711699 0.00294795i −0.379122 0.925347i \(-0.623774\pi\)
0.386239 + 0.922399i \(0.373774\pi\)
\(168\) 9.04804 + 9.04804i 0.698072 + 0.698072i
\(169\) −2.63539 −0.202722
\(170\) 7.37196 7.66761i 0.565404 0.588079i
\(171\) 8.27130 0.632522
\(172\) −0.428828 0.428828i −0.0326978 0.0326978i
\(173\) −6.42402 + 2.66092i −0.488409 + 0.202306i −0.613277 0.789868i \(-0.710149\pi\)
0.124868 + 0.992173i \(0.460149\pi\)
\(174\) 7.53678i 0.571362i
\(175\) 1.88820 + 4.55852i 0.142735 + 0.344592i
\(176\) −0.951749 0.394228i −0.0717408 0.0297160i
\(177\) 4.06937 9.82433i 0.305873 0.738442i
\(178\) −18.3482 + 18.3482i −1.37525 + 1.37525i
\(179\) 11.3540 11.3540i 0.848637 0.848637i −0.141326 0.989963i \(-0.545137\pi\)
0.989963 + 0.141326i \(0.0451366\pi\)
\(180\) −1.83709 + 4.43514i −0.136929 + 0.330575i
\(181\) 14.2832 + 5.91630i 1.06166 + 0.439755i 0.844042 0.536278i \(-0.180170\pi\)
0.217622 + 0.976033i \(0.430170\pi\)
\(182\) 4.92669 + 11.8941i 0.365190 + 0.881648i
\(183\) 39.0891i 2.88955i
\(184\) 8.61707 3.56931i 0.635259 0.263133i
\(185\) −10.6532 10.6532i −0.783242 0.783242i
\(186\) −17.4405 −1.27880
\(187\) −0.631950 0.607583i −0.0462127 0.0444309i
\(188\) −5.66514 −0.413173
\(189\) −7.85758 7.85758i −0.571555 0.571555i
\(190\) 3.97952 1.64837i 0.288705 0.119585i
\(191\) 6.84137i 0.495024i −0.968885 0.247512i \(-0.920387\pi\)
0.968885 0.247512i \(-0.0796129\pi\)
\(192\) 4.66898 + 11.2719i 0.336954 + 0.813480i
\(193\) 1.90355 + 0.788478i 0.137021 + 0.0567559i 0.450140 0.892958i \(-0.351374\pi\)
−0.313119 + 0.949714i \(0.601374\pi\)
\(194\) −4.44493 + 10.7310i −0.319128 + 0.770442i
\(195\) 12.6003 12.6003i 0.902328 0.902328i
\(196\) −1.25776 + 1.25776i −0.0898401 + 0.0898401i
\(197\) −1.74946 + 4.22357i −0.124644 + 0.300917i −0.973868 0.227116i \(-0.927070\pi\)
0.849224 + 0.528033i \(0.177070\pi\)
\(198\) 1.57102 + 0.650737i 0.111647 + 0.0462459i
\(199\) −0.929618 2.24430i −0.0658989 0.159094i 0.887499 0.460809i \(-0.152441\pi\)
−0.953398 + 0.301715i \(0.902441\pi\)
\(200\) 5.50451i 0.389228i
\(201\) 1.86234 0.771405i 0.131359 0.0544107i
\(202\) 4.58952 + 4.58952i 0.322918 + 0.322918i
\(203\) 3.33818 0.234294
\(204\) −0.138599 7.05060i −0.00970386 0.493641i
\(205\) 11.8576 0.828170
\(206\) −14.9727 14.9727i −1.04320 1.04320i
\(207\) −18.9737 + 7.85916i −1.31876 + 0.546249i
\(208\) 19.1584i 1.32840i
\(209\) −0.135856 0.327985i −0.00939733 0.0226872i
\(210\) −13.5556 5.61491i −0.935425 0.387466i
\(211\) −2.63963 + 6.37262i −0.181719 + 0.438710i −0.988321 0.152386i \(-0.951304\pi\)
0.806602 + 0.591095i \(0.201304\pi\)
\(212\) 1.65413 1.65413i 0.113606 0.113606i
\(213\) 26.9412 26.9412i 1.84598 1.84598i
\(214\) −11.6891 + 28.2199i −0.799049 + 1.92908i
\(215\) −1.47629 0.611497i −0.100682 0.0417038i
\(216\) −4.74410 11.4533i −0.322795 0.779296i
\(217\) 7.72473i 0.524389i
\(218\) −5.93792 + 2.45957i −0.402167 + 0.166583i
\(219\) −1.08223 1.08223i −0.0731306 0.0731306i
\(220\) 0.206042 0.0138913
\(221\) −5.94181 + 15.1821i −0.399689 + 1.02126i
\(222\) −42.9294 −2.88123
\(223\) −11.4929 11.4929i −0.769619 0.769619i 0.208420 0.978039i \(-0.433168\pi\)
−0.978039 + 0.208420i \(0.933168\pi\)
\(224\) 6.19054 2.56420i 0.413623 0.171328i
\(225\) 12.1202i 0.808016i
\(226\) 0.745053 + 1.79872i 0.0495602 + 0.119649i
\(227\) −12.4827 5.17051i −0.828507 0.343179i −0.0721953 0.997391i \(-0.523001\pi\)
−0.756311 + 0.654212i \(0.773001\pi\)
\(228\) 1.09285 2.63837i 0.0723758 0.174731i
\(229\) −14.9022 + 14.9022i −0.984765 + 0.984765i −0.999886 0.0151205i \(-0.995187\pi\)
0.0151205 + 0.999886i \(0.495187\pi\)
\(230\) −7.56245 + 7.56245i −0.498654 + 0.498654i
\(231\) −0.462770 + 1.11723i −0.0304481 + 0.0735081i
\(232\) 3.44061 + 1.42515i 0.225887 + 0.0935654i
\(233\) −3.98404 9.61832i −0.261003 0.630117i 0.737998 0.674803i \(-0.235771\pi\)
−0.999001 + 0.0446856i \(0.985771\pi\)
\(234\) 31.6241i 2.06733i
\(235\) −13.7906 + 5.71225i −0.899599 + 0.372626i
\(236\) −1.61690 1.61690i −0.105251 0.105251i
\(237\) 8.94953 0.581335
\(238\) 13.4215 0.263837i 0.869988 0.0171020i
\(239\) −15.0942 −0.976365 −0.488182 0.872742i \(-0.662340\pi\)
−0.488182 + 0.872742i \(0.662340\pi\)
\(240\) −15.4395 15.4395i −0.996612 0.996612i
\(241\) −8.75492 + 3.62641i −0.563954 + 0.233597i −0.646401 0.762998i \(-0.723727\pi\)
0.0824467 + 0.996595i \(0.473727\pi\)
\(242\) 17.6860i 1.13690i
\(243\) −5.59345 13.5038i −0.358820 0.866269i
\(244\) −7.76572 3.21666i −0.497149 0.205926i
\(245\) −1.79353 + 4.32997i −0.114585 + 0.276632i
\(246\) 23.8912 23.8912i 1.52325 1.52325i
\(247\) −4.66847 + 4.66847i −0.297048 + 0.297048i
\(248\) 3.29787 7.96176i 0.209415 0.505572i
\(249\) 39.8900 + 16.5230i 2.52793 + 1.04710i
\(250\) −7.35158 17.7483i −0.464955 1.12250i
\(251\) 5.21545i 0.329196i 0.986361 + 0.164598i \(0.0526327\pi\)
−0.986361 + 0.164598i \(0.947367\pi\)
\(252\) −5.59742 + 2.31853i −0.352604 + 0.146054i
\(253\) 0.623283 + 0.623283i 0.0391855 + 0.0391855i
\(254\) −4.15825 −0.260912
\(255\) −7.44662 17.0234i −0.466325 1.06605i
\(256\) 13.3519 0.834494
\(257\) 3.01107 + 3.01107i 0.187825 + 0.187825i 0.794755 0.606930i \(-0.207599\pi\)
−0.606930 + 0.794755i \(0.707599\pi\)
\(258\) −4.20657 + 1.74242i −0.261889 + 0.108478i
\(259\) 19.0142i 1.18148i
\(260\) −1.46638 3.54016i −0.0909411 0.219551i
\(261\) −7.57578 3.13799i −0.468929 0.194237i
\(262\) −6.91628 + 16.6974i −0.427289 + 1.03157i
\(263\) −0.267813 + 0.267813i −0.0165141 + 0.0165141i −0.715316 0.698802i \(-0.753717\pi\)
0.698802 + 0.715316i \(0.253717\pi\)
\(264\) −0.953940 + 0.953940i −0.0587110 + 0.0587110i
\(265\) 2.35874 5.69450i 0.144896 0.349810i
\(266\) 5.02241 + 2.08035i 0.307943 + 0.127554i
\(267\) 17.3464 + 41.8779i 1.06158 + 2.56289i
\(268\) 0.433465i 0.0264781i
\(269\) 12.2170 5.06043i 0.744881 0.308540i 0.0222298 0.999753i \(-0.492923\pi\)
0.722651 + 0.691213i \(0.242923\pi\)
\(270\) 10.0515 + 10.0515i 0.611717 + 0.611717i
\(271\) 3.06708 0.186312 0.0931558 0.995652i \(-0.470305\pi\)
0.0931558 + 0.995652i \(0.470305\pi\)
\(272\) 18.6030 + 7.28063i 1.12797 + 0.441453i
\(273\) 22.4894 1.36112
\(274\) −14.9760 14.9760i −0.904732 0.904732i
\(275\) −0.480607 + 0.199074i −0.0289817 + 0.0120046i
\(276\) 7.09061i 0.426804i
\(277\) 0.884252 + 2.13477i 0.0531296 + 0.128266i 0.948216 0.317627i \(-0.102886\pi\)
−0.895086 + 0.445893i \(0.852886\pi\)
\(278\) 5.48412 + 2.27160i 0.328916 + 0.136241i
\(279\) −7.26149 + 17.5308i −0.434734 + 1.04954i
\(280\) 5.12651 5.12651i 0.306368 0.306368i
\(281\) −13.9277 + 13.9277i −0.830855 + 0.830855i −0.987634 0.156779i \(-0.949889\pi\)
0.156779 + 0.987634i \(0.449889\pi\)
\(282\) −16.2766 + 39.2953i −0.969259 + 2.34000i
\(283\) 23.2604 + 9.63475i 1.38268 + 0.572727i 0.945198 0.326498i \(-0.105869\pi\)
0.437487 + 0.899225i \(0.355869\pi\)
\(284\) −3.13532 7.56934i −0.186047 0.449158i
\(285\) 7.52450i 0.445713i
\(286\) −1.25400 + 0.519424i −0.0741505 + 0.0307142i
\(287\) 10.5819 + 10.5819i 0.624628 + 0.624628i
\(288\) −16.4595 −0.969883
\(289\) 12.4840 + 11.5391i 0.734350 + 0.678771i
\(290\) −4.27025 −0.250758
\(291\) 14.3474 + 14.3474i 0.841059 + 0.841059i
\(292\) −0.304062 + 0.125947i −0.0177939 + 0.00737047i
\(293\) 16.1764i 0.945035i −0.881321 0.472517i \(-0.843345\pi\)
0.881321 0.472517i \(-0.156655\pi\)
\(294\) 5.11054 + 12.3379i 0.298053 + 0.719564i
\(295\) −5.56635 2.30566i −0.324085 0.134241i
\(296\) 8.11761 19.5976i 0.471826 1.13909i
\(297\) 0.828429 0.828429i 0.0480703 0.0480703i
\(298\) 1.19366 1.19366i 0.0691471 0.0691471i
\(299\) 6.27324 15.1449i 0.362791 0.875854i
\(300\) −3.86610 1.60139i −0.223209 0.0924564i
\(301\) −0.771748 1.86317i −0.0444828 0.107391i
\(302\) 1.94450i 0.111893i
\(303\) 10.4751 4.33895i 0.601781 0.249266i
\(304\) 5.72038 + 5.72038i 0.328086 + 0.328086i
\(305\) −22.1474 −1.26816
\(306\) −30.7073 12.0179i −1.75542 0.687017i
\(307\) 2.26615 0.129336 0.0646681 0.997907i \(-0.479401\pi\)
0.0646681 + 0.997907i \(0.479401\pi\)
\(308\) 0.183875 + 0.183875i 0.0104772 + 0.0104772i
\(309\) −34.1737 + 14.1552i −1.94407 + 0.805262i
\(310\) 9.88160i 0.561237i
\(311\) 1.45508 + 3.51287i 0.0825099 + 0.199197i 0.959750 0.280855i \(-0.0906180\pi\)
−0.877240 + 0.480051i \(0.840618\pi\)
\(312\) 23.1795 + 9.60125i 1.31228 + 0.543563i
\(313\) 4.60995 11.1294i 0.260570 0.629071i −0.738404 0.674358i \(-0.764420\pi\)
0.998974 + 0.0452872i \(0.0144203\pi\)
\(314\) 15.9927 15.9927i 0.902521 0.902521i
\(315\) −11.2879 + 11.2879i −0.636003 + 0.636003i
\(316\) 0.736463 1.77798i 0.0414293 0.100019i
\(317\) −18.1951 7.53666i −1.02194 0.423301i −0.192142 0.981367i \(-0.561543\pi\)
−0.829796 + 0.558066i \(0.811543\pi\)
\(318\) −6.72105 16.2261i −0.376898 0.909912i
\(319\) 0.351946i 0.0197052i
\(320\) 6.38653 2.64539i 0.357018 0.147882i
\(321\) 37.7301 + 37.7301i 2.10589 + 2.10589i
\(322\) −13.4977 −0.752196
\(323\) 2.75900 + 6.30726i 0.153515 + 0.350945i
\(324\) 0.411624 0.0228680
\(325\) 6.84088 + 6.84088i 0.379464 + 0.379464i
\(326\) 30.3374 12.5662i 1.68024 0.695976i
\(327\) 11.2275i 0.620880i
\(328\) 6.38892 + 15.4242i 0.352769 + 0.851660i
\(329\) −17.4046 7.20922i −0.959546 0.397457i
\(330\) 0.591983 1.42917i 0.0325876 0.0786735i
\(331\) −4.69699 + 4.69699i −0.258170 + 0.258170i −0.824309 0.566139i \(-0.808436\pi\)
0.566139 + 0.824309i \(0.308436\pi\)
\(332\) 6.56515 6.56515i 0.360309 0.360309i
\(333\) −17.8739 + 43.1515i −0.979486 + 2.36469i
\(334\) −0.148484 0.0615041i −0.00812469 0.00336535i
\(335\) −0.437069 1.05518i −0.0238796 0.0576506i
\(336\) 27.5568i 1.50334i
\(337\) 7.91263 3.27752i 0.431028 0.178538i −0.156612 0.987660i \(-0.550057\pi\)
0.587640 + 0.809122i \(0.300057\pi\)
\(338\) 3.00853 + 3.00853i 0.163642 + 0.163642i
\(339\) 3.40102 0.184718
\(340\) −3.99479 + 0.0785285i −0.216648 + 0.00425880i
\(341\) 0.814423 0.0441035
\(342\) −9.44243 9.44243i −0.510588 0.510588i
\(343\) −18.5069 + 7.66579i −0.999276 + 0.413914i
\(344\) 2.24981i 0.121302i
\(345\) 7.14957 + 17.2606i 0.384920 + 0.929278i
\(346\) 10.3713 + 4.29592i 0.557563 + 0.230950i
\(347\) −12.3226 + 29.7493i −0.661511 + 1.59703i 0.133925 + 0.990991i \(0.457242\pi\)
−0.795436 + 0.606037i \(0.792758\pi\)
\(348\) −2.00191 + 2.00191i −0.107313 + 0.107313i
\(349\) −3.80357 + 3.80357i −0.203600 + 0.203600i −0.801541 0.597940i \(-0.795986\pi\)
0.597940 + 0.801541i \(0.295986\pi\)
\(350\) 3.04841 7.35951i 0.162944 0.393382i
\(351\) −20.1297 8.33799i −1.07444 0.445049i
\(352\) 0.270345 + 0.652672i 0.0144095 + 0.0347875i
\(353\) 6.71121i 0.357202i −0.983922 0.178601i \(-0.942843\pi\)
0.983922 0.178601i \(-0.0571571\pi\)
\(354\) −15.8609 + 6.56980i −0.842997 + 0.349181i
\(355\) −15.2646 15.2646i −0.810159 0.810159i
\(356\) 9.74722 0.516602
\(357\) 8.54649 21.8374i 0.452328 1.15576i
\(358\) −25.9232 −1.37008
\(359\) 18.4384 + 18.4384i 0.973139 + 0.973139i 0.999649 0.0265096i \(-0.00843927\pi\)
−0.0265096 + 0.999649i \(0.508439\pi\)
\(360\) −16.4534 + 6.81521i −0.867169 + 0.359193i
\(361\) 16.2121i 0.853271i
\(362\) −9.55159 23.0596i −0.502020 1.21198i
\(363\) 28.5435 + 11.8231i 1.49814 + 0.620552i
\(364\) 1.85067 4.46790i 0.0970013 0.234182i
\(365\) −0.613181 + 0.613181i −0.0320954 + 0.0320954i
\(366\) −44.6237 + 44.6237i −2.33252 + 2.33252i
\(367\) −9.69093 + 23.3960i −0.505862 + 1.22126i 0.440383 + 0.897810i \(0.354843\pi\)
−0.946245 + 0.323450i \(0.895157\pi\)
\(368\) −18.5574 7.68674i −0.967373 0.400699i
\(369\) −14.0676 33.9622i −0.732329 1.76800i
\(370\) 24.3233i 1.26451i
\(371\) 7.18682 2.97688i 0.373121 0.154552i
\(372\) 4.63253 + 4.63253i 0.240185 + 0.240185i
\(373\) 18.3668 0.950997 0.475499 0.879716i \(-0.342268\pi\)
0.475499 + 0.879716i \(0.342268\pi\)
\(374\) 0.0278165 + 1.41504i 0.00143835 + 0.0731699i
\(375\) −33.5586 −1.73296
\(376\) −14.8609 14.8609i −0.766390 0.766390i
\(377\) 6.04704 2.50477i 0.311438 0.129002i
\(378\) 17.9403i 0.922747i
\(379\) 11.7095 + 28.2692i 0.601476 + 1.45209i 0.872062 + 0.489396i \(0.162783\pi\)
−0.270586 + 0.962696i \(0.587217\pi\)
\(380\) −1.49487 0.619196i −0.0766853 0.0317641i
\(381\) −2.77979 + 6.71101i −0.142413 + 0.343815i
\(382\) −7.81003 + 7.81003i −0.399596 + 0.399596i
\(383\) −13.8692 + 13.8692i −0.708683 + 0.708683i −0.966258 0.257575i \(-0.917077\pi\)
0.257575 + 0.966258i \(0.417077\pi\)
\(384\) 14.7097 35.5124i 0.750653 1.81224i
\(385\) 0.633007 + 0.262200i 0.0322610 + 0.0133630i
\(386\) −1.27296 3.07320i −0.0647919 0.156422i
\(387\) 4.95380i 0.251816i
\(388\) 4.03101 1.66970i 0.204644 0.0847662i
\(389\) −3.38037 3.38037i −0.171391 0.171391i 0.616199 0.787590i \(-0.288672\pi\)
−0.787590 + 0.616199i \(0.788672\pi\)
\(390\) −28.7688 −1.45676
\(391\) −12.3219 11.8468i −0.623145 0.599119i
\(392\) −6.59874 −0.333287
\(393\) 22.3244 + 22.3244i 1.12612 + 1.12612i
\(394\) 6.81876 2.82442i 0.343524 0.142292i
\(395\) 5.07070i 0.255135i
\(396\) −0.244444 0.590139i −0.0122838 0.0296556i
\(397\) −12.0134 4.97611i −0.602935 0.249744i 0.0602695 0.998182i \(-0.480804\pi\)
−0.663204 + 0.748438i \(0.730804\pi\)
\(398\) −1.50082 + 3.62331i −0.0752295 + 0.181620i
\(399\) 6.71497 6.71497i 0.336169 0.336169i
\(400\) 8.38228 8.38228i 0.419114 0.419114i
\(401\) −7.57358 + 18.2842i −0.378206 + 0.913071i 0.614096 + 0.789231i \(0.289521\pi\)
−0.992302 + 0.123840i \(0.960479\pi\)
\(402\) −3.00665 1.24540i −0.149958 0.0621147i
\(403\) −5.79617 13.9932i −0.288728 0.697051i
\(404\) 2.43812i 0.121301i
\(405\) 1.00201 0.415047i 0.0497904 0.0206238i
\(406\) −3.81083 3.81083i −0.189128 0.189128i
\(407\) 2.00468 0.0993682
\(408\) 18.1316 18.8588i 0.897650 0.933649i
\(409\) 8.86899 0.438543 0.219272 0.975664i \(-0.429632\pi\)
0.219272 + 0.975664i \(0.429632\pi\)
\(410\) −13.5365 13.5365i −0.668520 0.668520i
\(411\) −34.1812 + 14.1583i −1.68604 + 0.698379i
\(412\) 7.95403i 0.391867i
\(413\) −2.90988 7.02508i −0.143186 0.345682i
\(414\) 30.6321 + 12.6882i 1.50549 + 0.623593i
\(415\) 9.36172 22.6012i 0.459549 1.10945i
\(416\) 9.29001 9.29001i 0.455480 0.455480i
\(417\) 7.33228 7.33228i 0.359063 0.359063i
\(418\) −0.219332 + 0.529515i −0.0107279 + 0.0258994i
\(419\) 31.8479 + 13.1918i 1.55587 + 0.644464i 0.984366 0.176133i \(-0.0563589\pi\)
0.571507 + 0.820597i \(0.306359\pi\)
\(420\) 2.10919 + 5.09204i 0.102918 + 0.248466i
\(421\) 15.8442i 0.772201i 0.922457 + 0.386100i \(0.126178\pi\)
−0.922457 + 0.386100i \(0.873822\pi\)
\(422\) 10.2883 4.26155i 0.500826 0.207449i
\(423\) 32.7217 + 32.7217i 1.59098 + 1.59098i
\(424\) 8.67824 0.421452
\(425\) 9.24225 4.04287i 0.448315 0.196108i
\(426\) −61.5116 −2.98025
\(427\) −19.7646 19.7646i −0.956478 0.956478i
\(428\) 10.6006 4.39090i 0.512398 0.212242i
\(429\) 2.37107i 0.114476i
\(430\) 0.987233 + 2.38339i 0.0476086 + 0.114937i
\(431\) −14.1702 5.86950i −0.682556 0.282724i 0.0143390 0.999897i \(-0.495436\pi\)
−0.696895 + 0.717173i \(0.745436\pi\)
\(432\) −10.2167 + 24.6654i −0.491553 + 1.18671i
\(433\) −16.4718 + 16.4718i −0.791583 + 0.791583i −0.981751 0.190168i \(-0.939097\pi\)
0.190168 + 0.981751i \(0.439097\pi\)
\(434\) −8.81848 + 8.81848i −0.423300 + 0.423300i
\(435\) −2.85466 + 6.89177i −0.136871 + 0.330435i
\(436\) 2.23053 + 0.923915i 0.106823 + 0.0442475i
\(437\) −2.64894 6.39512i −0.126716 0.305920i
\(438\) 2.47093i 0.118066i
\(439\) −31.2963 + 12.9634i −1.49369 + 0.618707i −0.972116 0.234499i \(-0.924655\pi\)
−0.521574 + 0.853206i \(0.674655\pi\)
\(440\) 0.540491 + 0.540491i 0.0257669 + 0.0257669i
\(441\) 14.5296 0.691886
\(442\) 24.1148 10.5486i 1.14703 0.501747i
\(443\) 10.5102 0.499355 0.249678 0.968329i \(-0.419675\pi\)
0.249678 + 0.968329i \(0.419675\pi\)
\(444\) 11.4028 + 11.4028i 0.541154 + 0.541154i
\(445\) 23.7275 9.82827i 1.12479 0.465905i
\(446\) 26.2403i 1.24251i
\(447\) −1.12849 2.72443i −0.0533759 0.128861i
\(448\) 8.06020 + 3.33865i 0.380809 + 0.157736i
\(449\) 11.9390 28.8234i 0.563437 1.36026i −0.343564 0.939129i \(-0.611634\pi\)
0.907001 0.421129i \(-0.138366\pi\)
\(450\) −13.8363 + 13.8363i −0.652251 + 0.652251i
\(451\) −1.11565 + 1.11565i −0.0525340 + 0.0525340i
\(452\) 0.279872 0.675672i 0.0131641 0.0317809i
\(453\) 3.13823 + 1.29990i 0.147447 + 0.0610745i
\(454\) 8.34754 + 20.1527i 0.391769 + 0.945815i
\(455\) 12.7422i 0.597365i
\(456\) 9.78778 4.05423i 0.458355 0.189857i
\(457\) −28.8912 28.8912i −1.35147 1.35147i −0.884017 0.467454i \(-0.845171\pi\)
−0.467454 0.884017i \(-0.654829\pi\)
\(458\) 34.0244 1.58986
\(459\) −15.7460 + 16.3775i −0.734961 + 0.764436i
\(460\) 4.01745 0.187315
\(461\) −3.18214 3.18214i −0.148207 0.148207i 0.629110 0.777317i \(-0.283420\pi\)
−0.777317 + 0.629110i \(0.783420\pi\)
\(462\) 1.80371 0.747120i 0.0839161 0.0347592i
\(463\) 14.1998i 0.659923i 0.943994 + 0.329961i \(0.107036\pi\)
−0.943994 + 0.329961i \(0.892964\pi\)
\(464\) −3.06915 7.40957i −0.142482 0.343981i
\(465\) 15.9480 + 6.60586i 0.739569 + 0.306339i
\(466\) −6.43204 + 15.5283i −0.297959 + 0.719335i
\(467\) 7.90559 7.90559i 0.365827 0.365827i −0.500126 0.865953i \(-0.666713\pi\)
0.865953 + 0.500126i \(0.166713\pi\)
\(468\) −8.39994 + 8.39994i −0.388287 + 0.388287i
\(469\) 0.551609 1.33170i 0.0254709 0.0614923i
\(470\) 22.2642 + 9.22215i 1.02697 + 0.425386i
\(471\) −15.1196 36.5018i −0.696672 1.68192i
\(472\) 8.48294i 0.390459i
\(473\) 0.196435 0.0813659i 0.00903207 0.00374121i
\(474\) −10.2167 10.2167i −0.469268 0.469268i
\(475\) 4.08515 0.187439
\(476\) −3.63508 3.49492i −0.166614 0.160189i
\(477\) −19.1084 −0.874912
\(478\) 17.2314 + 17.2314i 0.788147 + 0.788147i
\(479\) 35.6869 14.7820i 1.63058 0.675407i 0.635279 0.772283i \(-0.280885\pi\)
0.995296 + 0.0968761i \(0.0308851\pi\)
\(480\) 14.9734i 0.683437i
\(481\) −14.2671 34.4439i −0.650524 1.57050i
\(482\) 14.1344 + 5.85466i 0.643804 + 0.266672i
\(483\) −9.02321 + 21.7839i −0.410570 + 0.991204i
\(484\) 4.69772 4.69772i 0.213533 0.213533i
\(485\) 8.12906 8.12906i 0.369122 0.369122i
\(486\) −9.03036 + 21.8012i −0.409625 + 0.988923i
\(487\) 16.8953 + 6.99824i 0.765597 + 0.317121i 0.731087 0.682284i \(-0.239013\pi\)
0.0345095 + 0.999404i \(0.489013\pi\)
\(488\) −11.9331 28.8091i −0.540187 1.30413i
\(489\) 57.3622i 2.59401i
\(490\) 6.99053 2.89557i 0.315800 0.130809i
\(491\) 22.4776 + 22.4776i 1.01440 + 1.01440i 0.999895 + 0.0145030i \(0.00461660\pi\)
0.0145030 + 0.999895i \(0.495383\pi\)
\(492\) −12.6919 −0.572195
\(493\) −0.134137 6.82360i −0.00604121 0.307320i
\(494\) 10.6590 0.479569
\(495\) −1.19009 1.19009i −0.0534907 0.0534907i
\(496\) −17.1462 + 7.10218i −0.769887 + 0.318897i
\(497\) 27.2446i 1.22209i
\(498\) −26.6755 64.4005i −1.19536 2.88585i
\(499\) 7.01373 + 2.90518i 0.313978 + 0.130054i 0.534107 0.845417i \(-0.320648\pi\)
−0.220129 + 0.975471i \(0.570648\pi\)
\(500\) −2.76156 + 6.66699i −0.123501 + 0.298157i
\(501\) −0.198523 + 0.198523i −0.00886937 + 0.00886937i
\(502\) 5.95390 5.95390i 0.265736 0.265736i
\(503\) 4.22782 10.2069i 0.188509 0.455102i −0.801164 0.598445i \(-0.795785\pi\)
0.989673 + 0.143344i \(0.0457854\pi\)
\(504\) −20.7652 8.60123i −0.924956 0.383129i
\(505\) −2.45840 5.93509i −0.109397 0.264108i
\(506\) 1.42307i 0.0632631i
\(507\) 6.86668 2.84427i 0.304960 0.126319i
\(508\) 1.10451 + 1.10451i 0.0490045 + 0.0490045i
\(509\) −39.7947 −1.76387 −0.881935 0.471371i \(-0.843759\pi\)
−0.881935 + 0.471371i \(0.843759\pi\)
\(510\) −10.9328 + 27.9348i −0.484113 + 1.23697i
\(511\) −1.09442 −0.0484144
\(512\) 4.03254 + 4.03254i 0.178215 + 0.178215i
\(513\) −8.49999 + 3.52081i −0.375284 + 0.155448i
\(514\) 6.87480i 0.303235i
\(515\) 8.02017 + 19.3624i 0.353411 + 0.853210i
\(516\) 1.58016 + 0.654523i 0.0695626 + 0.0288138i
\(517\) 0.760072 1.83498i 0.0334279 0.0807022i
\(518\) −21.7064 + 21.7064i −0.953725 + 0.953725i
\(519\) 13.8664 13.8664i 0.608667 0.608667i
\(520\) 5.43995 13.1332i 0.238558 0.575929i
\(521\) 5.62879 + 2.33152i 0.246602 + 0.102146i 0.502561 0.864542i \(-0.332391\pi\)
−0.255959 + 0.966688i \(0.582391\pi\)
\(522\) 5.06613 + 12.2307i 0.221739 + 0.535324i
\(523\) 4.08197i 0.178492i −0.996010 0.0892461i \(-0.971554\pi\)
0.996010 0.0892461i \(-0.0284458\pi\)
\(524\) 6.27222 2.59804i 0.274003 0.113496i
\(525\) −9.83968 9.83968i −0.429439 0.429439i
\(526\) 0.611466 0.0266612
\(527\) −15.7902 + 0.310400i −0.687833 + 0.0135212i
\(528\) 2.90532 0.126438
\(529\) −4.11054 4.11054i −0.178719 0.178719i
\(530\) −9.19349 + 3.80807i −0.399340 + 0.165412i
\(531\) 18.6784i 0.810572i
\(532\) −0.781464 1.88662i −0.0338808 0.0817954i
\(533\) 27.1088 + 11.2289i 1.17421 + 0.486375i
\(534\) 28.0049 67.6099i 1.21189 2.92577i
\(535\) 21.3774 21.3774i 0.924227 0.924227i
\(536\) 1.13707 1.13707i 0.0491139 0.0491139i
\(537\) −17.3297 + 41.8375i −0.747831 + 1.80542i
\(538\) −19.7237 8.16982i −0.850348 0.352226i
\(539\) −0.238648 0.576147i −0.0102793 0.0248164i
\(540\) 5.33975i 0.229786i
\(541\) −5.87812 + 2.43480i −0.252720 + 0.104680i −0.505447 0.862857i \(-0.668673\pi\)
0.252727 + 0.967538i \(0.418673\pi\)
\(542\) −3.50134 3.50134i −0.150396 0.150396i
\(543\) −43.6012 −1.87111
\(544\) −5.49027 12.5511i −0.235393 0.538124i
\(545\) 6.36134 0.272490
\(546\) −25.6737 25.6737i −1.09873 1.09873i
\(547\) 1.78744 0.740382i 0.0764254 0.0316564i −0.344143 0.938917i \(-0.611831\pi\)
0.420569 + 0.907261i \(0.361831\pi\)
\(548\) 7.95579i 0.339854i
\(549\) 26.2752 + 63.4340i 1.12140 + 2.70730i
\(550\) 0.775917 + 0.321395i 0.0330852 + 0.0137043i
\(551\) 1.05767 2.55343i 0.0450581 0.108780i
\(552\) −18.6001 + 18.6001i −0.791675 + 0.791675i
\(553\) 4.52516 4.52516i 0.192429 0.192429i
\(554\) 1.42758 3.44649i 0.0606522 0.146427i
\(555\) 39.2554 + 16.2601i 1.66630 + 0.690204i
\(556\) −0.853306 2.06006i −0.0361882 0.0873661i
\(557\) 9.26384i 0.392522i 0.980552 + 0.196261i \(0.0628799\pi\)
−0.980552 + 0.196261i \(0.937120\pi\)
\(558\) 28.3026 11.7233i 1.19814 0.496288i
\(559\) −2.79601 2.79601i −0.118259 0.118259i
\(560\) −15.6133 −0.659784
\(561\) 2.30233 + 0.901061i 0.0972045 + 0.0380428i
\(562\) 31.7994 1.34138
\(563\) 18.5864 + 18.5864i 0.783324 + 0.783324i 0.980390 0.197066i \(-0.0631415\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(564\) 14.7609 6.11417i 0.621547 0.257453i
\(565\) 1.92698i 0.0810687i
\(566\) −15.5548 37.5527i −0.653819 1.57846i
\(567\) 1.26460 + 0.523815i 0.0531083 + 0.0219982i
\(568\) 11.6314 28.0806i 0.488041 1.17824i
\(569\) −31.8690 + 31.8690i −1.33602 + 1.33602i −0.436138 + 0.899880i \(0.643654\pi\)
−0.899880 + 0.436138i \(0.856346\pi\)
\(570\) −8.58989 + 8.58989i −0.359791 + 0.359791i
\(571\) 13.0004 31.3857i 0.544048 1.31345i −0.377796 0.925889i \(-0.623318\pi\)
0.921845 0.387560i \(-0.126682\pi\)
\(572\) 0.471054 + 0.195117i 0.0196957 + 0.00815824i
\(573\) 7.38363 + 17.8257i 0.308455 + 0.744677i
\(574\) 24.1603i 1.00843i
\(575\) −9.37099 + 3.88159i −0.390797 + 0.161874i
\(576\) −15.1537 15.1537i −0.631403 0.631403i
\(577\) 18.5921 0.773999 0.387000 0.922080i \(-0.373511\pi\)
0.387000 + 0.922080i \(0.373511\pi\)
\(578\) −1.07862 27.4245i −0.0448648 1.14071i
\(579\) −5.81082 −0.241489
\(580\) 1.13426 + 1.13426i 0.0470974 + 0.0470974i
\(581\) 28.5241 11.8151i 1.18338 0.490172i
\(582\) 32.7577i 1.35785i
\(583\) 0.313854 + 0.757710i 0.0129985 + 0.0313812i
\(584\) −1.12800 0.467234i −0.0466771 0.0193343i
\(585\) −11.9781 + 28.9177i −0.495233 + 1.19560i
\(586\) −18.4668 + 18.4668i −0.762856 + 0.762856i
\(587\) −19.8800 + 19.8800i −0.820537 + 0.820537i −0.986185 0.165648i \(-0.947028\pi\)
0.165648 + 0.986185i \(0.447028\pi\)
\(588\) 1.91973 4.63464i 0.0791683 0.191129i
\(589\) −5.90879 2.44750i −0.243467 0.100847i
\(590\) 3.72237 + 8.98660i 0.153248 + 0.369973i
\(591\) 12.8929i 0.530345i
\(592\) −42.2048 + 17.4818i −1.73461 + 0.718498i
\(593\) −0.366821 0.366821i −0.0150636 0.0150636i 0.699535 0.714598i \(-0.253391\pi\)
−0.714598 + 0.699535i \(0.753391\pi\)
\(594\) −1.89145 −0.0776072
\(595\) −12.3728 4.84234i −0.507236 0.198517i
\(596\) −0.634118 −0.0259745
\(597\) 4.84437 + 4.84437i 0.198267 + 0.198267i
\(598\) −24.4508 + 10.1278i −0.999866 + 0.414158i
\(599\) 15.7600i 0.643938i −0.946750 0.321969i \(-0.895655\pi\)
0.946750 0.321969i \(-0.104345\pi\)
\(600\) −5.94081 14.3424i −0.242533 0.585525i
\(601\) 25.3037 + 10.4811i 1.03216 + 0.427534i 0.833491 0.552533i \(-0.186338\pi\)
0.198668 + 0.980067i \(0.436338\pi\)
\(602\) −1.24595 + 3.00799i −0.0507811 + 0.122597i
\(603\) −2.50368 + 2.50368i −0.101958 + 0.101958i
\(604\) 0.516494 0.516494i 0.0210159 0.0210159i
\(605\) 6.69883 16.1724i 0.272346 0.657501i
\(606\) −16.9116 7.00502i −0.686988 0.284560i
\(607\) −5.13490 12.3967i −0.208419 0.503168i 0.784755 0.619806i \(-0.212789\pi\)
−0.993175 + 0.116637i \(0.962789\pi\)
\(608\) 5.54769i 0.224989i
\(609\) −8.69785 + 3.60277i −0.352455 + 0.145992i
\(610\) 25.2833 + 25.2833i 1.02369 + 1.02369i
\(611\) −36.9374 −1.49433
\(612\) 4.96425 + 11.3486i 0.200668 + 0.458740i
\(613\) −37.3138 −1.50709 −0.753545 0.657397i \(-0.771658\pi\)
−0.753545 + 0.657397i \(0.771658\pi\)
\(614\) −2.58702 2.58702i −0.104404 0.104404i
\(615\) −30.8958 + 12.7974i −1.24584 + 0.516043i
\(616\) 0.964683i 0.0388682i
\(617\) 18.3290 + 44.2502i 0.737899 + 1.78145i 0.614236 + 0.789123i \(0.289464\pi\)
0.123664 + 0.992324i \(0.460536\pi\)
\(618\) 55.1718 + 22.8529i 2.21933 + 0.919278i
\(619\) 17.3746 41.9460i 0.698344 1.68595i −0.0289100 0.999582i \(-0.509204\pi\)
0.727254 0.686369i \(-0.240796\pi\)
\(620\) 2.62474 2.62474i 0.105412 0.105412i
\(621\) 16.1529 16.1529i 0.648193 0.648193i
\(622\) 2.34915 5.67136i 0.0941925 0.227401i
\(623\) 29.9457 + 12.4039i 1.19975 + 0.496952i
\(624\) −20.6769 49.9185i −0.827740 1.99834i
\(625\) 6.78062i 0.271225i
\(626\) −17.9679 + 7.44254i −0.718141 + 0.297464i
\(627\) 0.707963 + 0.707963i 0.0282733 + 0.0282733i
\(628\) −8.49592 −0.339024
\(629\) −38.8671 + 0.764040i −1.54973 + 0.0304643i
\(630\) 25.7724 1.02680
\(631\) −10.2301 10.2301i −0.407254 0.407254i 0.473526 0.880780i \(-0.342981\pi\)
−0.880780 + 0.473526i \(0.842981\pi\)
\(632\) 6.59591 2.73212i 0.262371 0.108678i
\(633\) 19.4532i 0.773194i
\(634\) 12.1676 + 29.3751i 0.483236 + 1.16663i
\(635\) 3.80238 + 1.57500i 0.150893 + 0.0625018i
\(636\) −2.52470 + 6.09517i −0.100111 + 0.241689i
\(637\) −8.20077 + 8.20077i −0.324926 + 0.324926i
\(638\) 0.401778 0.401778i 0.0159065 0.0159065i
\(639\) −25.6108 + 61.8299i −1.01315 + 2.44595i
\(640\) −20.1209 8.33436i −0.795349 0.329445i
\(641\) 8.35724 + 20.1762i 0.330091 + 0.796910i 0.998584 + 0.0531922i \(0.0169396\pi\)
−0.668493 + 0.743718i \(0.733060\pi\)
\(642\) 86.1446i 3.39986i
\(643\) −33.7319 + 13.9722i −1.33026 + 0.551011i −0.930729 0.365710i \(-0.880826\pi\)
−0.399529 + 0.916721i \(0.630826\pi\)
\(644\) 3.58523 + 3.58523i 0.141278 + 0.141278i
\(645\) 4.50653 0.177444
\(646\) 4.05065 10.3500i 0.159371 0.407213i
\(647\) 26.2132 1.03055 0.515274 0.857025i \(-0.327690\pi\)
0.515274 + 0.857025i \(0.327690\pi\)
\(648\) 1.07978 + 1.07978i 0.0424176 + 0.0424176i
\(649\) 0.740659 0.306791i 0.0290734 0.0120426i
\(650\) 15.6189i 0.612626i
\(651\) 8.33701 + 20.1273i 0.326753 + 0.788852i
\(652\) −11.3960 4.72037i −0.446301 0.184864i
\(653\) −7.38019 + 17.8174i −0.288809 + 0.697247i −0.999983 0.00576864i \(-0.998164\pi\)
0.711174 + 0.703016i \(0.248164\pi\)
\(654\) 12.8171 12.8171i 0.501190 0.501190i
\(655\) 12.6488 12.6488i 0.494228 0.494228i
\(656\) 13.7590 33.2171i 0.537197 1.29691i
\(657\) 2.48372 + 1.02879i 0.0968991 + 0.0401369i
\(658\) 11.6389 + 28.0989i 0.453733 + 1.09541i
\(659\) 28.4003i 1.10632i 0.833076 + 0.553159i \(0.186578\pi\)
−0.833076 + 0.553159i \(0.813422\pi\)
\(660\) −0.536857 + 0.222373i −0.0208971 + 0.00865587i
\(661\) 12.2287 + 12.2287i 0.475643 + 0.475643i 0.903735 0.428092i \(-0.140814\pi\)
−0.428092 + 0.903735i \(0.640814\pi\)
\(662\) 10.7241 0.416803
\(663\) −0.903682 45.9708i −0.0350961 1.78536i
\(664\) 34.4435 1.33667
\(665\) −3.80462 3.80462i −0.147537 0.147537i
\(666\) 69.6660 28.8566i 2.69950 1.11817i
\(667\) 6.86232i 0.265710i
\(668\) 0.0231035 + 0.0557767i 0.000893900 + 0.00215807i
\(669\) 42.3493 + 17.5416i 1.63732 + 0.678199i
\(670\) −0.705627 + 1.70353i −0.0272608 + 0.0658133i
\(671\) 2.08380 2.08380i 0.0804441 0.0804441i
\(672\) −13.3624 + 13.3624i −0.515467 + 0.515467i
\(673\) 0.501206 1.21002i 0.0193201 0.0466428i −0.913925 0.405883i \(-0.866964\pi\)
0.933245 + 0.359240i \(0.116964\pi\)
\(674\) −12.7746 5.29140i −0.492058 0.203817i
\(675\) 5.15917 + 12.4553i 0.198576 + 0.479406i
\(676\) 1.59824i 0.0614708i
\(677\) −39.1535 + 16.2179i −1.50479 + 0.623305i −0.974475 0.224495i \(-0.927927\pi\)
−0.530316 + 0.847800i \(0.677927\pi\)
\(678\) −3.88257 3.88257i −0.149109 0.149109i
\(679\) 14.5090 0.556803
\(680\) −10.6852 10.2732i −0.409757 0.393958i
\(681\) 38.1049 1.46018
\(682\) −0.929737 0.929737i −0.0356015 0.0356015i
\(683\) 22.8816 9.47789i 0.875542 0.362661i 0.100776 0.994909i \(-0.467868\pi\)
0.774766 + 0.632248i \(0.217868\pi\)
\(684\) 5.01617i 0.191798i
\(685\) 8.02194 + 19.3667i 0.306503 + 0.739963i
\(686\) 29.8784 + 12.3760i 1.14076 + 0.472520i
\(687\) 22.7453 54.9121i 0.867789 2.09503i
\(688\) −3.42602 + 3.42602i −0.130616 + 0.130616i
\(689\) 10.7851 10.7851i 0.410880 0.410880i
\(690\) 11.5426 27.8664i 0.439420 1.06085i
\(691\) −22.8709 9.47343i −0.870049 0.360386i −0.0974197 0.995243i \(-0.531059\pi\)
−0.772629 + 0.634857i \(0.781059\pi\)
\(692\) −1.61372 3.89587i −0.0613446 0.148099i
\(693\) 2.12411i 0.0806883i
\(694\) 48.0289 19.8942i 1.82315 0.755174i
\(695\) −4.15439 4.15439i −0.157585 0.157585i
\(696\) −10.5028 −0.398109
\(697\) 21.2053 22.0557i 0.803208 0.835420i
\(698\) 8.68423 0.328703
\(699\) 20.7614 + 20.7614i 0.785268 + 0.785268i
\(700\) −2.76453 + 1.14511i −0.104490 + 0.0432810i
\(701\) 43.5809i 1.64603i 0.568021 + 0.823014i \(0.307709\pi\)
−0.568021 + 0.823014i \(0.692291\pi\)
\(702\) 13.4613 + 32.4984i 0.508064 + 1.22657i
\(703\) −14.5443 6.02445i −0.548549 0.227216i
\(704\) −0.351995 + 0.849792i −0.0132663 + 0.0320277i
\(705\) 29.7673 29.7673i 1.12110 1.12110i
\(706\) −7.66145 + 7.66145i −0.288342 + 0.288342i
\(707\) 3.10265 7.49047i 0.116687 0.281708i
\(708\) 5.95801 + 2.46789i 0.223916 + 0.0927489i
\(709\) −11.9512 28.8527i −0.448836 1.08359i −0.972759 0.231821i \(-0.925532\pi\)
0.523922 0.851766i \(-0.324468\pi\)
\(710\) 34.8517i 1.30796i
\(711\) −14.5234 + 6.01577i −0.544668 + 0.225609i
\(712\) 25.5690 + 25.5690i 0.958239 + 0.958239i
\(713\) 15.8798 0.594704
\(714\) −34.6860 + 15.1728i −1.29809 + 0.567827i
\(715\) 1.34342 0.0502411
\(716\) 6.88568 + 6.88568i 0.257330 + 0.257330i
\(717\) 39.3291 16.2906i 1.46877 0.608385i
\(718\) 42.0981i 1.57109i
\(719\) 2.70526 + 6.53106i 0.100889 + 0.243568i 0.966262 0.257560i \(-0.0829186\pi\)
−0.865373 + 0.501128i \(0.832919\pi\)
\(720\) 35.4335 + 14.6770i 1.32053 + 0.546980i
\(721\) −10.1220 + 24.4366i −0.376962 + 0.910066i
\(722\) −18.5076 + 18.5076i −0.688782 + 0.688782i
\(723\) 18.8977 18.8977i 0.702814 0.702814i
\(724\) −3.58797 + 8.66212i −0.133346 + 0.321925i
\(725\) −3.74163 1.54983i −0.138961 0.0575594i
\(726\) −19.0878 46.0821i −0.708415 1.71027i
\(727\) 23.3744i 0.866909i −0.901175 0.433455i \(-0.857294\pi\)
0.901175 0.433455i \(-0.142706\pi\)
\(728\) 16.5749 6.86556i 0.614308 0.254455i
\(729\) 30.5881 + 30.5881i 1.13289 + 1.13289i
\(730\) 1.40000 0.0518164
\(731\) −3.77751 + 1.65241i −0.139716 + 0.0611165i
\(732\) 23.7057 0.876189
\(733\) 15.2333 + 15.2333i 0.562655 + 0.562655i 0.930061 0.367406i \(-0.119754\pi\)
−0.367406 + 0.930061i \(0.619754\pi\)
\(734\) 37.7717 15.6455i 1.39418 0.577487i
\(735\) 13.2177i 0.487544i
\(736\) 5.27126 + 12.7259i 0.194301 + 0.469085i
\(737\) 0.140402 + 0.0581564i 0.00517178 + 0.00214222i
\(738\) −22.7114 + 54.8303i −0.836019 + 2.01833i
\(739\) 10.2372 10.2372i 0.376582 0.376582i −0.493285 0.869868i \(-0.664204\pi\)
0.869868 + 0.493285i \(0.164204\pi\)
\(740\) 6.46071 6.46071i 0.237500 0.237500i
\(741\) 7.12552 17.2025i 0.261763 0.631951i
\(742\) −11.6028 4.80602i −0.425951 0.176435i
\(743\) −6.07126 14.6573i −0.222733 0.537725i 0.772526 0.634983i \(-0.218993\pi\)
−0.995259 + 0.0972577i \(0.968993\pi\)
\(744\) 24.3042i 0.891035i
\(745\) −1.54363 + 0.639391i −0.0565541 + 0.0234255i
\(746\) −20.9674 20.9674i −0.767670 0.767670i
\(747\) −75.8402 −2.77485
\(748\) 0.368472 0.383249i 0.0134727 0.0140130i
\(749\) 38.1550 1.39415
\(750\) 38.3101 + 38.3101i 1.39889 + 1.39889i
\(751\) 27.9493 11.5770i 1.01989 0.422450i 0.190834 0.981622i \(-0.438881\pi\)
0.829052 + 0.559172i \(0.188881\pi\)
\(752\) 45.2603i 1.65047i
\(753\) −5.62883 13.5892i −0.205126 0.495218i
\(754\) −9.76266 4.04382i −0.355535 0.147267i
\(755\) 0.736507 1.77809i 0.0268042 0.0647111i
\(756\) 4.76526 4.76526i 0.173311 0.173311i
\(757\) 13.0204 13.0204i 0.473233 0.473233i −0.429726 0.902959i \(-0.641390\pi\)
0.902959 + 0.429726i \(0.141390\pi\)
\(758\) 18.9044 45.6393i 0.686639 1.65769i
\(759\) −2.29669 0.951322i −0.0833647 0.0345308i
\(760\) −2.29708 5.54564i −0.0833239 0.201162i
\(761\) 39.9240i