Properties

Label 804.2.e.a.535.5
Level 804
Weight 2
Character 804.535
Analytic conductor 6.420
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(34\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 535.5
Character \(\chi\) = 804.535
Dual form 804.2.e.a.535.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.31376 - 0.523490i) q^{2} -1.00000 q^{3} +(1.45192 + 1.37548i) q^{4} +1.71706i q^{5} +(1.31376 + 0.523490i) q^{6} -3.43662 q^{7} +(-1.18741 - 2.56711i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-1.31376 - 0.523490i) q^{2} -1.00000 q^{3} +(1.45192 + 1.37548i) q^{4} +1.71706i q^{5} +(1.31376 + 0.523490i) q^{6} -3.43662 q^{7} +(-1.18741 - 2.56711i) q^{8} +1.00000 q^{9} +(0.898862 - 2.25579i) q^{10} +1.17026 q^{11} +(-1.45192 - 1.37548i) q^{12} +1.11142i q^{13} +(4.51489 + 1.79904i) q^{14} -1.71706i q^{15} +(0.216118 + 3.99416i) q^{16} -6.00763 q^{17} +(-1.31376 - 0.523490i) q^{18} +1.61491i q^{19} +(-2.36177 + 2.49302i) q^{20} +3.43662 q^{21} +(-1.53743 - 0.612619i) q^{22} -5.58871i q^{23} +(1.18741 + 2.56711i) q^{24} +2.05172 q^{25} +(0.581818 - 1.46014i) q^{26} -1.00000 q^{27} +(-4.98969 - 4.72700i) q^{28} -2.67857 q^{29} +(-0.898862 + 2.25579i) q^{30} +3.52610 q^{31} +(1.80698 - 5.36049i) q^{32} -1.17026 q^{33} +(7.89257 + 3.14494i) q^{34} -5.90087i q^{35} +(1.45192 + 1.37548i) q^{36} +4.31616 q^{37} +(0.845389 - 2.12160i) q^{38} -1.11142i q^{39} +(4.40787 - 2.03886i) q^{40} -8.77192i q^{41} +(-4.51489 - 1.79904i) q^{42} +1.55663 q^{43} +(1.69912 + 1.60966i) q^{44} +1.71706i q^{45} +(-2.92563 + 7.34220i) q^{46} -3.12725i q^{47} +(-0.216118 - 3.99416i) q^{48} +4.81038 q^{49} +(-2.69546 - 1.07406i) q^{50} +6.00763 q^{51} +(-1.52873 + 1.61369i) q^{52} -9.63385i q^{53} +(1.31376 + 0.523490i) q^{54} +2.00940i q^{55} +(4.08070 + 8.82218i) q^{56} -1.61491i q^{57} +(3.51899 + 1.40220i) q^{58} +5.48116i q^{59} +(2.36177 - 2.49302i) q^{60} -3.17038i q^{61} +(-4.63244 - 1.84588i) q^{62} -3.43662 q^{63} +(-5.18009 + 6.09644i) q^{64} -1.90837 q^{65} +(1.53743 + 0.612619i) q^{66} +(-3.55266 - 7.37419i) q^{67} +(-8.72257 - 8.26336i) q^{68} +5.58871i q^{69} +(-3.08905 + 7.75231i) q^{70} -14.4279i q^{71} +(-1.18741 - 2.56711i) q^{72} -7.90152 q^{73} +(-5.67038 - 2.25947i) q^{74} -2.05172 q^{75} +(-2.22127 + 2.34471i) q^{76} -4.02173 q^{77} +(-0.581818 + 1.46014i) q^{78} +7.48688 q^{79} +(-6.85819 + 0.371086i) q^{80} +1.00000 q^{81} +(-4.59201 + 11.5242i) q^{82} +3.57916i q^{83} +(4.98969 + 4.72700i) q^{84} -10.3154i q^{85} +(-2.04503 - 0.814881i) q^{86} +2.67857 q^{87} +(-1.38958 - 3.00418i) q^{88} -13.9566 q^{89} +(0.898862 - 2.25579i) q^{90} -3.81953i q^{91} +(7.68715 - 8.11433i) q^{92} -3.52610 q^{93} +(-1.63709 + 4.10845i) q^{94} -2.77289 q^{95} +(-1.80698 + 5.36049i) q^{96} -7.37562i q^{97} +(-6.31967 - 2.51819i) q^{98} +1.17026 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 34q^{3} + 2q^{4} - 4q^{7} + 6q^{8} + 34q^{9} + O(q^{10}) \) \( 34q - 34q^{3} + 2q^{4} - 4q^{7} + 6q^{8} + 34q^{9} - 6q^{10} - 2q^{12} - 4q^{14} + 2q^{16} + 12q^{20} + 4q^{21} - 8q^{22} - 6q^{24} - 34q^{25} + 10q^{26} - 34q^{27} + 8q^{28} - 16q^{29} + 6q^{30} + 4q^{31} + 2q^{36} + 12q^{37} - 26q^{38} - 18q^{40} + 4q^{42} + 4q^{43} - 26q^{44} + 4q^{46} - 2q^{48} + 46q^{49} + 18q^{50} - 32q^{52} + 14q^{56} - 4q^{58} - 12q^{60} - 2q^{62} - 4q^{63} + 26q^{64} + 8q^{66} + 18q^{67} - 34q^{68} - 56q^{70} + 6q^{72} + 12q^{73} - 22q^{74} + 34q^{75} - 32q^{76} - 8q^{77} - 10q^{78} + 12q^{79} + 2q^{80} + 34q^{81} + 26q^{82} - 8q^{84} + 6q^{86} + 16q^{87} - 28q^{88} - 6q^{90} - 46q^{92} - 4q^{93} - 32q^{94} + 40q^{95} + 40q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31376 0.523490i −0.928967 0.370164i
\(3\) −1.00000 −0.577350
\(4\) 1.45192 + 1.37548i 0.725958 + 0.687739i
\(5\) 1.71706i 0.767891i 0.923356 + 0.383945i \(0.125435\pi\)
−0.923356 + 0.383945i \(0.874565\pi\)
\(6\) 1.31376 + 0.523490i 0.536339 + 0.213714i
\(7\) −3.43662 −1.29892 −0.649461 0.760395i \(-0.725005\pi\)
−0.649461 + 0.760395i \(0.725005\pi\)
\(8\) −1.18741 2.56711i −0.419814 0.907610i
\(9\) 1.00000 0.333333
\(10\) 0.898862 2.25579i 0.284245 0.713345i
\(11\) 1.17026 0.352846 0.176423 0.984314i \(-0.443547\pi\)
0.176423 + 0.984314i \(0.443547\pi\)
\(12\) −1.45192 1.37548i −0.419132 0.397066i
\(13\) 1.11142i 0.308252i 0.988051 + 0.154126i \(0.0492562\pi\)
−0.988051 + 0.154126i \(0.950744\pi\)
\(14\) 4.51489 + 1.79904i 1.20665 + 0.480813i
\(15\) 1.71706i 0.443342i
\(16\) 0.216118 + 3.99416i 0.0540294 + 0.998539i
\(17\) −6.00763 −1.45706 −0.728532 0.685012i \(-0.759797\pi\)
−0.728532 + 0.685012i \(0.759797\pi\)
\(18\) −1.31376 0.523490i −0.309656 0.123388i
\(19\) 1.61491i 0.370485i 0.982693 + 0.185243i \(0.0593071\pi\)
−0.982693 + 0.185243i \(0.940693\pi\)
\(20\) −2.36177 + 2.49302i −0.528109 + 0.557456i
\(21\) 3.43662 0.749933
\(22\) −1.53743 0.612619i −0.327782 0.130611i
\(23\) 5.58871i 1.16533i −0.812714 0.582663i \(-0.802011\pi\)
0.812714 0.582663i \(-0.197989\pi\)
\(24\) 1.18741 + 2.56711i 0.242380 + 0.524009i
\(25\) 2.05172 0.410344
\(26\) 0.581818 1.46014i 0.114104 0.286356i
\(27\) −1.00000 −0.192450
\(28\) −4.98969 4.72700i −0.942962 0.893319i
\(29\) −2.67857 −0.497397 −0.248699 0.968581i \(-0.580003\pi\)
−0.248699 + 0.968581i \(0.580003\pi\)
\(30\) −0.898862 + 2.25579i −0.164109 + 0.411850i
\(31\) 3.52610 0.633307 0.316653 0.948541i \(-0.397441\pi\)
0.316653 + 0.948541i \(0.397441\pi\)
\(32\) 1.80698 5.36049i 0.319431 0.947609i
\(33\) −1.17026 −0.203716
\(34\) 7.89257 + 3.14494i 1.35356 + 0.539352i
\(35\) 5.90087i 0.997430i
\(36\) 1.45192 + 1.37548i 0.241986 + 0.229246i
\(37\) 4.31616 0.709572 0.354786 0.934948i \(-0.384554\pi\)
0.354786 + 0.934948i \(0.384554\pi\)
\(38\) 0.845389 2.12160i 0.137140 0.344168i
\(39\) 1.11142i 0.177970i
\(40\) 4.40787 2.03886i 0.696945 0.322372i
\(41\) 8.77192i 1.36994i −0.728570 0.684972i \(-0.759815\pi\)
0.728570 0.684972i \(-0.240185\pi\)
\(42\) −4.51489 1.79904i −0.696662 0.277598i
\(43\) 1.55663 0.237384 0.118692 0.992931i \(-0.462130\pi\)
0.118692 + 0.992931i \(0.462130\pi\)
\(44\) 1.69912 + 1.60966i 0.256151 + 0.242666i
\(45\) 1.71706i 0.255964i
\(46\) −2.92563 + 7.34220i −0.431361 + 1.08255i
\(47\) 3.12725i 0.456157i −0.973643 0.228078i \(-0.926756\pi\)
0.973643 0.228078i \(-0.0732442\pi\)
\(48\) −0.216118 3.99416i −0.0311939 0.576507i
\(49\) 4.81038 0.687197
\(50\) −2.69546 1.07406i −0.381196 0.151894i
\(51\) 6.00763 0.841236
\(52\) −1.52873 + 1.61369i −0.211997 + 0.223778i
\(53\) 9.63385i 1.32331i −0.749808 0.661655i \(-0.769854\pi\)
0.749808 0.661655i \(-0.230146\pi\)
\(54\) 1.31376 + 0.523490i 0.178780 + 0.0712380i
\(55\) 2.00940i 0.270947i
\(56\) 4.08070 + 8.82218i 0.545306 + 1.17891i
\(57\) 1.61491i 0.213900i
\(58\) 3.51899 + 1.40220i 0.462065 + 0.184118i
\(59\) 5.48116i 0.713586i 0.934183 + 0.356793i \(0.116130\pi\)
−0.934183 + 0.356793i \(0.883870\pi\)
\(60\) 2.36177 2.49302i 0.304904 0.321847i
\(61\) 3.17038i 0.405926i −0.979186 0.202963i \(-0.934943\pi\)
0.979186 0.202963i \(-0.0650571\pi\)
\(62\) −4.63244 1.84588i −0.588321 0.234427i
\(63\) −3.43662 −0.432974
\(64\) −5.18009 + 6.09644i −0.647512 + 0.762056i
\(65\) −1.90837 −0.236704
\(66\) 1.53743 + 0.612619i 0.189245 + 0.0754081i
\(67\) −3.55266 7.37419i −0.434026 0.900900i
\(68\) −8.72257 8.26336i −1.05777 1.00208i
\(69\) 5.58871i 0.672801i
\(70\) −3.08905 + 7.75231i −0.369212 + 0.926579i
\(71\) 14.4279i 1.71228i −0.516748 0.856138i \(-0.672857\pi\)
0.516748 0.856138i \(-0.327143\pi\)
\(72\) −1.18741 2.56711i −0.139938 0.302537i
\(73\) −7.90152 −0.924803 −0.462402 0.886671i \(-0.653012\pi\)
−0.462402 + 0.886671i \(0.653012\pi\)
\(74\) −5.67038 2.25947i −0.659169 0.262658i
\(75\) −2.05172 −0.236912
\(76\) −2.22127 + 2.34471i −0.254797 + 0.268957i
\(77\) −4.02173 −0.458319
\(78\) −0.581818 + 1.46014i −0.0658779 + 0.165328i
\(79\) 7.48688 0.842340 0.421170 0.906982i \(-0.361620\pi\)
0.421170 + 0.906982i \(0.361620\pi\)
\(80\) −6.85819 + 0.371086i −0.766769 + 0.0414887i
\(81\) 1.00000 0.111111
\(82\) −4.59201 + 11.5242i −0.507103 + 1.27263i
\(83\) 3.57916i 0.392863i 0.980518 + 0.196432i \(0.0629354\pi\)
−0.980518 + 0.196432i \(0.937065\pi\)
\(84\) 4.98969 + 4.72700i 0.544419 + 0.515758i
\(85\) 10.3154i 1.11887i
\(86\) −2.04503 0.814881i −0.220522 0.0878709i
\(87\) 2.67857 0.287172
\(88\) −1.38958 3.00418i −0.148130 0.320247i
\(89\) −13.9566 −1.47939 −0.739696 0.672941i \(-0.765031\pi\)
−0.739696 + 0.672941i \(0.765031\pi\)
\(90\) 0.898862 2.25579i 0.0947484 0.237782i
\(91\) 3.81953i 0.400396i
\(92\) 7.68715 8.11433i 0.801440 0.845977i
\(93\) −3.52610 −0.365640
\(94\) −1.63709 + 4.10845i −0.168853 + 0.423754i
\(95\) −2.77289 −0.284492
\(96\) −1.80698 + 5.36049i −0.184424 + 0.547103i
\(97\) 7.37562i 0.748880i −0.927251 0.374440i \(-0.877835\pi\)
0.927251 0.374440i \(-0.122165\pi\)
\(98\) −6.31967 2.51819i −0.638383 0.254375i
\(99\) 1.17026 0.117615
\(100\) 2.97892 + 2.82210i 0.297892 + 0.282210i
\(101\) 11.4184i 1.13617i −0.822968 0.568087i \(-0.807684\pi\)
0.822968 0.568087i \(-0.192316\pi\)
\(102\) −7.89257 3.14494i −0.781480 0.311395i
\(103\) 12.6926i 1.25064i −0.780368 0.625320i \(-0.784968\pi\)
0.780368 0.625320i \(-0.215032\pi\)
\(104\) 2.85314 1.31972i 0.279773 0.129409i
\(105\) 5.90087i 0.575866i
\(106\) −5.04323 + 12.6565i −0.489841 + 1.22931i
\(107\) 15.0145i 1.45151i −0.687955 0.725753i \(-0.741491\pi\)
0.687955 0.725753i \(-0.258509\pi\)
\(108\) −1.45192 1.37548i −0.139711 0.132355i
\(109\) 0.414438i 0.0396959i 0.999803 + 0.0198480i \(0.00631822\pi\)
−0.999803 + 0.0198480i \(0.993682\pi\)
\(110\) 1.05190 2.63986i 0.100295 0.251701i
\(111\) −4.31616 −0.409672
\(112\) −0.742714 13.7264i −0.0701799 1.29702i
\(113\) 8.28821i 0.779689i 0.920881 + 0.389844i \(0.127471\pi\)
−0.920881 + 0.389844i \(0.872529\pi\)
\(114\) −0.845389 + 2.12160i −0.0791779 + 0.198706i
\(115\) 9.59612 0.894843
\(116\) −3.88905 3.68431i −0.361089 0.342080i
\(117\) 1.11142i 0.102751i
\(118\) 2.86933 7.20091i 0.264144 0.662898i
\(119\) 20.6460 1.89261
\(120\) −4.40787 + 2.03886i −0.402382 + 0.186121i
\(121\) −9.63050 −0.875500
\(122\) −1.65967 + 4.16511i −0.150259 + 0.377092i
\(123\) 8.77192i 0.790937i
\(124\) 5.11960 + 4.85008i 0.459754 + 0.435550i
\(125\) 12.1082i 1.08299i
\(126\) 4.51489 + 1.79904i 0.402218 + 0.160271i
\(127\) 10.2190i 0.906792i 0.891309 + 0.453396i \(0.149788\pi\)
−0.891309 + 0.453396i \(0.850212\pi\)
\(128\) 9.99681 5.29752i 0.883602 0.468239i
\(129\) −1.55663 −0.137054
\(130\) 2.50713 + 0.999013i 0.219890 + 0.0876193i
\(131\) 5.16804i 0.451534i 0.974181 + 0.225767i \(0.0724888\pi\)
−0.974181 + 0.225767i \(0.927511\pi\)
\(132\) −1.69912 1.60966i −0.147889 0.140103i
\(133\) 5.54983i 0.481231i
\(134\) 0.807016 + 11.5477i 0.0697156 + 0.997567i
\(135\) 1.71706i 0.147781i
\(136\) 7.13355 + 15.4222i 0.611697 + 1.32245i
\(137\) 21.9540i 1.87566i 0.347097 + 0.937829i \(0.387167\pi\)
−0.347097 + 0.937829i \(0.612833\pi\)
\(138\) 2.92563 7.34220i 0.249047 0.625010i
\(139\) −9.91101 −0.840641 −0.420320 0.907376i \(-0.638082\pi\)
−0.420320 + 0.907376i \(0.638082\pi\)
\(140\) 8.11652 8.56757i 0.685972 0.724092i
\(141\) 3.12725i 0.263362i
\(142\) −7.55286 + 18.9547i −0.633822 + 1.59065i
\(143\) 1.30065i 0.108766i
\(144\) 0.216118 + 3.99416i 0.0180098 + 0.332846i
\(145\) 4.59925i 0.381947i
\(146\) 10.3807 + 4.13637i 0.859111 + 0.342329i
\(147\) −4.81038 −0.396753
\(148\) 6.26670 + 5.93678i 0.515119 + 0.488001i
\(149\) 17.2963 1.41697 0.708483 0.705728i \(-0.249380\pi\)
0.708483 + 0.705728i \(0.249380\pi\)
\(150\) 2.69546 + 1.07406i 0.220083 + 0.0876963i
\(151\) 1.72171i 0.140111i −0.997543 0.0700553i \(-0.977682\pi\)
0.997543 0.0700553i \(-0.0223176\pi\)
\(152\) 4.14564 1.91756i 0.336256 0.155535i
\(153\) −6.00763 −0.485688
\(154\) 5.28358 + 2.10534i 0.425763 + 0.169653i
\(155\) 6.05452i 0.486310i
\(156\) 1.52873 1.61369i 0.122397 0.129198i
\(157\) 20.4651 1.63329 0.816645 0.577141i \(-0.195832\pi\)
0.816645 + 0.577141i \(0.195832\pi\)
\(158\) −9.83595 3.91931i −0.782506 0.311804i
\(159\) 9.63385i 0.764014i
\(160\) 9.20426 + 3.10268i 0.727660 + 0.245288i
\(161\) 19.2063i 1.51367i
\(162\) −1.31376 0.523490i −0.103219 0.0411293i
\(163\) 4.88761i 0.382827i −0.981509 0.191414i \(-0.938693\pi\)
0.981509 0.191414i \(-0.0613072\pi\)
\(164\) 12.0656 12.7361i 0.942164 0.994521i
\(165\) 2.00940i 0.156431i
\(166\) 1.87365 4.70214i 0.145424 0.364957i
\(167\) 2.32807i 0.180151i 0.995935 + 0.0900756i \(0.0287109\pi\)
−0.995935 + 0.0900756i \(0.971289\pi\)
\(168\) −4.08070 8.82218i −0.314833 0.680646i
\(169\) 11.7647 0.904980
\(170\) −5.40003 + 13.5520i −0.414163 + 1.03939i
\(171\) 1.61491i 0.123495i
\(172\) 2.26010 + 2.14111i 0.172331 + 0.163258i
\(173\) −5.54784 −0.421794 −0.210897 0.977508i \(-0.567639\pi\)
−0.210897 + 0.977508i \(0.567639\pi\)
\(174\) −3.51899 1.40220i −0.266774 0.106301i
\(175\) −7.05099 −0.533004
\(176\) 0.252913 + 4.67419i 0.0190641 + 0.352331i
\(177\) 5.48116i 0.411989i
\(178\) 18.3355 + 7.30612i 1.37431 + 0.547617i
\(179\) −7.50648 −0.561061 −0.280530 0.959845i \(-0.590510\pi\)
−0.280530 + 0.959845i \(0.590510\pi\)
\(180\) −2.36177 + 2.49302i −0.176036 + 0.185819i
\(181\) −6.75725 −0.502263 −0.251131 0.967953i \(-0.580803\pi\)
−0.251131 + 0.967953i \(0.580803\pi\)
\(182\) −1.99949 + 5.01794i −0.148212 + 0.371954i
\(183\) 3.17038i 0.234362i
\(184\) −14.3468 + 6.63611i −1.05766 + 0.489221i
\(185\) 7.41109i 0.544874i
\(186\) 4.63244 + 1.84588i 0.339667 + 0.135347i
\(187\) −7.03047 −0.514119
\(188\) 4.30147 4.54051i 0.313717 0.331150i
\(189\) 3.43662 0.249978
\(190\) 3.64290 + 1.45158i 0.264284 + 0.105309i
\(191\) 14.3393 1.03755 0.518776 0.854910i \(-0.326388\pi\)
0.518776 + 0.854910i \(0.326388\pi\)
\(192\) 5.18009 6.09644i 0.373841 0.439973i
\(193\) −6.63609 −0.477677 −0.238838 0.971059i \(-0.576767\pi\)
−0.238838 + 0.971059i \(0.576767\pi\)
\(194\) −3.86106 + 9.68977i −0.277208 + 0.695685i
\(195\) 1.90837 0.136661
\(196\) 6.98426 + 6.61657i 0.498876 + 0.472612i
\(197\) 10.9332i 0.778955i −0.921036 0.389478i \(-0.872656\pi\)
0.921036 0.389478i \(-0.127344\pi\)
\(198\) −1.53743 0.612619i −0.109261 0.0435369i
\(199\) 21.7663i 1.54297i 0.636247 + 0.771485i \(0.280486\pi\)
−0.636247 + 0.771485i \(0.719514\pi\)
\(200\) −2.43624 5.26699i −0.172268 0.372432i
\(201\) 3.55266 + 7.37419i 0.250585 + 0.520135i
\(202\) −5.97743 + 15.0010i −0.420570 + 1.05547i
\(203\) 9.20522 0.646080
\(204\) 8.72257 + 8.26336i 0.610702 + 0.578551i
\(205\) 15.0619 1.05197
\(206\) −6.64446 + 16.6750i −0.462942 + 1.16180i
\(207\) 5.58871i 0.388442i
\(208\) −4.43919 + 0.240197i −0.307802 + 0.0166547i
\(209\) 1.88986i 0.130724i
\(210\) 3.08905 7.75231i 0.213165 0.534961i
\(211\) 24.8456i 1.71044i −0.518263 0.855221i \(-0.673421\pi\)
0.518263 0.855221i \(-0.326579\pi\)
\(212\) 13.2511 13.9875i 0.910093 0.960668i
\(213\) 14.4279i 0.988583i
\(214\) −7.85995 + 19.7254i −0.537295 + 1.34840i
\(215\) 2.67282i 0.182285i
\(216\) 1.18741 + 2.56711i 0.0807933 + 0.174670i
\(217\) −12.1179 −0.822616
\(218\) 0.216954 0.544470i 0.0146940 0.0368762i
\(219\) 7.90152 0.533936
\(220\) −2.76388 + 2.91748i −0.186341 + 0.196696i
\(221\) 6.67700i 0.449144i
\(222\) 5.67038 + 2.25947i 0.380571 + 0.151646i
\(223\) 10.3441i 0.692695i 0.938106 + 0.346348i \(0.112578\pi\)
−0.938106 + 0.346348i \(0.887422\pi\)
\(224\) −6.20990 + 18.4220i −0.414916 + 1.23087i
\(225\) 2.05172 0.136781
\(226\) 4.33880 10.8887i 0.288612 0.724305i
\(227\) 6.48668i 0.430536i 0.976555 + 0.215268i \(0.0690625\pi\)
−0.976555 + 0.215268i \(0.930937\pi\)
\(228\) 2.22127 2.34471i 0.147107 0.155282i
\(229\) 17.8420i 1.17903i −0.807756 0.589516i \(-0.799318\pi\)
0.807756 0.589516i \(-0.200682\pi\)
\(230\) −12.6070 5.02348i −0.831279 0.331238i
\(231\) 4.02173 0.264611
\(232\) 3.18057 + 6.87617i 0.208815 + 0.451443i
\(233\) 0.250483i 0.0164097i −0.999966 0.00820483i \(-0.997388\pi\)
0.999966 0.00820483i \(-0.00261171\pi\)
\(234\) 0.581818 1.46014i 0.0380346 0.0954521i
\(235\) 5.36967 0.350278
\(236\) −7.53922 + 7.95818i −0.490761 + 0.518033i
\(237\) −7.48688 −0.486325
\(238\) −27.1238 10.8080i −1.75817 0.700576i
\(239\) −18.6682 −1.20754 −0.603772 0.797157i \(-0.706336\pi\)
−0.603772 + 0.797157i \(0.706336\pi\)
\(240\) 6.85819 0.371086i 0.442694 0.0239535i
\(241\) 0.761920 0.0490796 0.0245398 0.999699i \(-0.492188\pi\)
0.0245398 + 0.999699i \(0.492188\pi\)
\(242\) 12.6521 + 5.04147i 0.813310 + 0.324078i
\(243\) −1.00000 −0.0641500
\(244\) 4.36079 4.60313i 0.279171 0.294685i
\(245\) 8.25969i 0.527692i
\(246\) 4.59201 11.5242i 0.292776 0.734754i
\(247\) −1.79484 −0.114203
\(248\) −4.18695 9.05189i −0.265871 0.574796i
\(249\) 3.57916i 0.226820i
\(250\) 6.33852 15.9072i 0.400883 1.00606i
\(251\) 16.0512 1.01314 0.506570 0.862199i \(-0.330913\pi\)
0.506570 + 0.862199i \(0.330913\pi\)
\(252\) −4.98969 4.72700i −0.314321 0.297773i
\(253\) 6.54023i 0.411181i
\(254\) 5.34956 13.4253i 0.335662 0.842380i
\(255\) 10.3154i 0.645978i
\(256\) −15.9066 + 1.72641i −0.994162 + 0.107901i
\(257\) −21.7232 −1.35506 −0.677528 0.735497i \(-0.736949\pi\)
−0.677528 + 0.735497i \(0.736949\pi\)
\(258\) 2.04503 + 0.814881i 0.127318 + 0.0507323i
\(259\) −14.8330 −0.921678
\(260\) −2.77079 2.62492i −0.171837 0.162791i
\(261\) −2.67857 −0.165799
\(262\) 2.70542 6.78955i 0.167142 0.419460i
\(263\) 2.29514i 0.141524i 0.997493 + 0.0707621i \(0.0225431\pi\)
−0.997493 + 0.0707621i \(0.977457\pi\)
\(264\) 1.38958 + 3.00418i 0.0855228 + 0.184894i
\(265\) 16.5419 1.01616
\(266\) −2.90528 + 7.29113i −0.178134 + 0.447048i
\(267\) 13.9566 0.854127
\(268\) 4.98487 15.5933i 0.304500 0.952512i
\(269\) 2.80644 0.171112 0.0855559 0.996333i \(-0.472733\pi\)
0.0855559 + 0.996333i \(0.472733\pi\)
\(270\) −0.898862 + 2.25579i −0.0547030 + 0.137283i
\(271\) −25.8915 −1.57279 −0.786397 0.617722i \(-0.788056\pi\)
−0.786397 + 0.617722i \(0.788056\pi\)
\(272\) −1.29835 23.9954i −0.0787243 1.45494i
\(273\) 3.81953i 0.231169i
\(274\) 11.4927 28.8422i 0.694300 1.74242i
\(275\) 2.40104 0.144788
\(276\) −7.68715 + 8.11433i −0.462712 + 0.488425i
\(277\) −19.8880 −1.19495 −0.597477 0.801886i \(-0.703830\pi\)
−0.597477 + 0.801886i \(0.703830\pi\)
\(278\) 13.0207 + 5.18832i 0.780927 + 0.311175i
\(279\) 3.52610 0.211102
\(280\) −15.1482 + 7.00678i −0.905277 + 0.418735i
\(281\) 5.26843i 0.314288i −0.987576 0.157144i \(-0.949771\pi\)
0.987576 0.157144i \(-0.0502287\pi\)
\(282\) 1.63709 4.10845i 0.0974871 0.244655i
\(283\) 4.08352i 0.242740i 0.992607 + 0.121370i \(0.0387288\pi\)
−0.992607 + 0.121370i \(0.961271\pi\)
\(284\) 19.8453 20.9481i 1.17760 1.24304i
\(285\) 2.77289 0.164252
\(286\) 0.680877 1.70874i 0.0402611 0.101040i
\(287\) 30.1458i 1.77945i
\(288\) 1.80698 5.36049i 0.106477 0.315870i
\(289\) 19.0916 1.12304
\(290\) −2.40766 + 6.04229i −0.141383 + 0.354816i
\(291\) 7.37562i 0.432366i
\(292\) −11.4723 10.8684i −0.671368 0.636024i
\(293\) 9.95443 0.581544 0.290772 0.956792i \(-0.406088\pi\)
0.290772 + 0.956792i \(0.406088\pi\)
\(294\) 6.31967 + 2.51819i 0.368571 + 0.146864i
\(295\) −9.41145 −0.547956
\(296\) −5.12507 11.0800i −0.297889 0.644015i
\(297\) −1.17026 −0.0679052
\(298\) −22.7231 9.05443i −1.31631 0.524509i
\(299\) 6.21140 0.359215
\(300\) −2.97892 2.82210i −0.171988 0.162934i
\(301\) −5.34955 −0.308343
\(302\) −0.901298 + 2.26191i −0.0518639 + 0.130158i
\(303\) 11.4184i 0.655971i
\(304\) −6.45019 + 0.349010i −0.369944 + 0.0200171i
\(305\) 5.44373 0.311707
\(306\) 7.89257 + 3.14494i 0.451188 + 0.179784i
\(307\) 9.48993i 0.541619i 0.962633 + 0.270809i \(0.0872913\pi\)
−0.962633 + 0.270809i \(0.912709\pi\)
\(308\) −5.83922 5.53181i −0.332720 0.315204i
\(309\) 12.6926i 0.722058i
\(310\) 3.16948 7.95416i 0.180014 0.451766i
\(311\) −10.6476 −0.603770 −0.301885 0.953344i \(-0.597616\pi\)
−0.301885 + 0.953344i \(0.597616\pi\)
\(312\) −2.85314 + 1.31972i −0.161527 + 0.0747142i
\(313\) 5.82795i 0.329415i 0.986342 + 0.164707i \(0.0526680\pi\)
−0.986342 + 0.164707i \(0.947332\pi\)
\(314\) −26.8861 10.7133i −1.51727 0.604584i
\(315\) 5.90087i 0.332477i
\(316\) 10.8703 + 10.2980i 0.611503 + 0.579310i
\(317\) 15.2367 0.855779 0.427890 0.903831i \(-0.359257\pi\)
0.427890 + 0.903831i \(0.359257\pi\)
\(318\) 5.04323 12.6565i 0.282810 0.709743i
\(319\) −3.13461 −0.175505
\(320\) −10.4679 8.89451i −0.585175 0.497218i
\(321\) 15.0145i 0.838028i
\(322\) 10.0543 25.2324i 0.560304 1.40615i
\(323\) 9.70176i 0.539821i
\(324\) 1.45192 + 1.37548i 0.0806620 + 0.0764155i
\(325\) 2.28032i 0.126490i
\(326\) −2.55862 + 6.42113i −0.141709 + 0.355634i
\(327\) 0.414438i 0.0229184i
\(328\) −22.5185 + 10.4159i −1.24337 + 0.575122i
\(329\) 10.7472i 0.592512i
\(330\) −1.05190 + 2.63986i −0.0579052 + 0.145320i
\(331\) −8.30227 −0.456334 −0.228167 0.973622i \(-0.573273\pi\)
−0.228167 + 0.973622i \(0.573273\pi\)
\(332\) −4.92305 + 5.19663i −0.270188 + 0.285202i
\(333\) 4.31616 0.236524
\(334\) 1.21872 3.05851i 0.0666854 0.167354i
\(335\) 12.6619 6.10011i 0.691793 0.333285i
\(336\) 0.742714 + 13.7264i 0.0405184 + 0.748837i
\(337\) 22.6621i 1.23448i 0.786774 + 0.617241i \(0.211750\pi\)
−0.786774 + 0.617241i \(0.788250\pi\)
\(338\) −15.4560 6.15873i −0.840697 0.334991i
\(339\) 8.28821i 0.450154i
\(340\) 14.1887 14.9771i 0.769488 0.812249i
\(341\) 4.12645 0.223460
\(342\) 0.845389 2.12160i 0.0457134 0.114723i
\(343\) 7.52491 0.406307
\(344\) −1.84837 3.99604i −0.0996572 0.215452i
\(345\) −9.59612 −0.516638
\(346\) 7.28851 + 2.90424i 0.391833 + 0.156133i
\(347\) −0.960707 −0.0515734 −0.0257867 0.999667i \(-0.508209\pi\)
−0.0257867 + 0.999667i \(0.508209\pi\)
\(348\) 3.88905 + 3.68431i 0.208475 + 0.197500i
\(349\) 12.3546 0.661327 0.330663 0.943749i \(-0.392727\pi\)
0.330663 + 0.943749i \(0.392727\pi\)
\(350\) 9.26328 + 3.69112i 0.495143 + 0.197299i
\(351\) 1.11142i 0.0593232i
\(352\) 2.11463 6.27315i 0.112710 0.334360i
\(353\) 12.0578i 0.641771i 0.947118 + 0.320885i \(0.103980\pi\)
−0.947118 + 0.320885i \(0.896020\pi\)
\(354\) −2.86933 + 7.20091i −0.152503 + 0.382724i
\(355\) 24.7735 1.31484
\(356\) −20.2637 19.1969i −1.07398 1.01744i
\(357\) −20.6460 −1.09270
\(358\) 9.86169 + 3.92957i 0.521206 + 0.207684i
\(359\) 23.1026i 1.21931i −0.792667 0.609654i \(-0.791308\pi\)
0.792667 0.609654i \(-0.208692\pi\)
\(360\) 4.40787 2.03886i 0.232315 0.107457i
\(361\) 16.3921 0.862741
\(362\) 8.87739 + 3.53736i 0.466585 + 0.185919i
\(363\) 9.63050 0.505470
\(364\) 5.25368 5.54564i 0.275368 0.290670i
\(365\) 13.5674i 0.710148i
\(366\) 1.65967 4.16511i 0.0867521 0.217714i
\(367\) −9.00548 −0.470082 −0.235041 0.971985i \(-0.575522\pi\)
−0.235041 + 0.971985i \(0.575522\pi\)
\(368\) 22.3222 1.20782i 1.16362 0.0629618i
\(369\) 8.77192i 0.456648i
\(370\) 3.87963 9.73637i 0.201692 0.506170i
\(371\) 33.1079i 1.71888i
\(372\) −5.11960 4.85008i −0.265439 0.251465i
\(373\) 11.5801i 0.599597i −0.954003 0.299798i \(-0.903081\pi\)
0.954003 0.299798i \(-0.0969194\pi\)
\(374\) 9.23634 + 3.68039i 0.477600 + 0.190308i
\(375\) 12.1082i 0.625265i
\(376\) −8.02800 + 3.71335i −0.414012 + 0.191501i
\(377\) 2.97701i 0.153324i
\(378\) −4.51489 1.79904i −0.232221 0.0925326i
\(379\) −36.2809 −1.86362 −0.931812 0.362941i \(-0.881773\pi\)
−0.931812 + 0.362941i \(0.881773\pi\)
\(380\) −4.02600 3.81405i −0.206529 0.195656i
\(381\) 10.2190i 0.523537i
\(382\) −18.8383 7.50646i −0.963851 0.384064i
\(383\) −32.8451 −1.67831 −0.839153 0.543895i \(-0.816949\pi\)
−0.839153 + 0.543895i \(0.816949\pi\)
\(384\) −9.99681 + 5.29752i −0.510148 + 0.270338i
\(385\) 6.90554i 0.351939i
\(386\) 8.71822 + 3.47393i 0.443746 + 0.176818i
\(387\) 1.55663 0.0791280
\(388\) 10.1450 10.7088i 0.515034 0.543655i
\(389\) −31.1926 −1.58153 −0.790764 0.612122i \(-0.790316\pi\)
−0.790764 + 0.612122i \(0.790316\pi\)
\(390\) −2.50713 0.999013i −0.126954 0.0505870i
\(391\) 33.5749i 1.69795i
\(392\) −5.71191 12.3488i −0.288495 0.623707i
\(393\) 5.16804i 0.260693i
\(394\) −5.72340 + 14.3635i −0.288341 + 0.723623i
\(395\) 12.8554i 0.646825i
\(396\) 1.69912 + 1.60966i 0.0853838 + 0.0808887i
\(397\) 10.3801 0.520962 0.260481 0.965479i \(-0.416119\pi\)
0.260481 + 0.965479i \(0.416119\pi\)
\(398\) 11.3944 28.5956i 0.571151 1.43337i
\(399\) 5.54983i 0.277839i
\(400\) 0.443413 + 8.19489i 0.0221706 + 0.409745i
\(401\) 3.19079i 0.159340i 0.996821 + 0.0796702i \(0.0253867\pi\)
−0.996821 + 0.0796702i \(0.974613\pi\)
\(402\) −0.807016 11.5477i −0.0402503 0.575946i
\(403\) 3.91898i 0.195218i
\(404\) 15.7058 16.5786i 0.781392 0.824815i
\(405\) 1.71706i 0.0853212i
\(406\) −12.0934 4.81885i −0.600187 0.239155i
\(407\) 5.05102 0.250370
\(408\) −7.13355 15.4222i −0.353163 0.763514i
\(409\) 23.3932i 1.15672i −0.815782 0.578359i \(-0.803693\pi\)
0.815782 0.578359i \(-0.196307\pi\)
\(410\) −19.7876 7.88474i −0.977242 0.389400i
\(411\) 21.9540i 1.08291i
\(412\) 17.4584 18.4286i 0.860115 0.907912i
\(413\) 18.8367i 0.926892i
\(414\) −2.92563 + 7.34220i −0.143787 + 0.360850i
\(415\) −6.14561 −0.301676
\(416\) 5.95775 + 2.00831i 0.292103 + 0.0984655i
\(417\) 9.91101 0.485344
\(418\) 0.989323 2.48281i 0.0483893 0.121438i
\(419\) 5.86519i 0.286534i −0.989684 0.143267i \(-0.954239\pi\)
0.989684 0.143267i \(-0.0457607\pi\)
\(420\) −8.11652 + 8.56757i −0.396046 + 0.418055i
\(421\) 0.631708 0.0307876 0.0153938 0.999882i \(-0.495100\pi\)
0.0153938 + 0.999882i \(0.495100\pi\)
\(422\) −13.0064 + 32.6411i −0.633144 + 1.58894i
\(423\) 3.12725i 0.152052i
\(424\) −24.7311 + 11.4394i −1.20105 + 0.555545i
\(425\) −12.3260 −0.597897
\(426\) 7.55286 18.9547i 0.365937 0.918360i
\(427\) 10.8954i 0.527266i
\(428\) 20.6521 21.7998i 0.998258 1.05373i
\(429\) 1.30065i 0.0627959i
\(430\) 1.39920 3.51144i 0.0674752 0.169337i
\(431\) 15.9423i 0.767911i 0.923351 + 0.383956i \(0.125438\pi\)
−0.923351 + 0.383956i \(0.874562\pi\)
\(432\) −0.216118 3.99416i −0.0103980 0.192169i
\(433\) 36.7027i 1.76382i −0.471420 0.881909i \(-0.656259\pi\)
0.471420 0.881909i \(-0.343741\pi\)
\(434\) 15.9200 + 6.34360i 0.764183 + 0.304502i
\(435\) 4.59925i 0.220517i
\(436\) −0.570050 + 0.601728i −0.0273004 + 0.0288176i
\(437\) 9.02524 0.431736
\(438\) −10.3807 4.13637i −0.496008 0.197644i
\(439\) 16.3559i 0.780624i −0.920683 0.390312i \(-0.872367\pi\)
0.920683 0.390312i \(-0.127633\pi\)
\(440\) 5.15834 2.38599i 0.245914 0.113748i
\(441\) 4.81038 0.229066
\(442\) −3.49534 + 8.77195i −0.166257 + 0.417239i
\(443\) −39.5681 −1.87993 −0.939967 0.341264i \(-0.889145\pi\)
−0.939967 + 0.341264i \(0.889145\pi\)
\(444\) −6.26670 5.93678i −0.297404 0.281747i
\(445\) 23.9642i 1.13601i
\(446\) 5.41506 13.5897i 0.256411 0.643491i
\(447\) −17.2963 −0.818085
\(448\) 17.8020 20.9512i 0.841067 0.989850i
\(449\) 16.4326 0.775502 0.387751 0.921764i \(-0.373252\pi\)
0.387751 + 0.921764i \(0.373252\pi\)
\(450\) −2.69546 1.07406i −0.127065 0.0506315i
\(451\) 10.2654i 0.483379i
\(452\) −11.4003 + 12.0338i −0.536223 + 0.566021i
\(453\) 1.72171i 0.0808929i
\(454\) 3.39572 8.52192i 0.159369 0.399954i
\(455\) 6.55835 0.307460
\(456\) −4.14564 + 1.91756i −0.194138 + 0.0897982i
\(457\) −25.4258 −1.18937 −0.594685 0.803959i \(-0.702723\pi\)
−0.594685 + 0.803959i \(0.702723\pi\)
\(458\) −9.34012 + 23.4401i −0.436435 + 1.09528i
\(459\) 6.00763 0.280412
\(460\) 13.9328 + 13.1993i 0.649618 + 0.615419i
\(461\) −15.3459 −0.714730 −0.357365 0.933965i \(-0.616325\pi\)
−0.357365 + 0.933965i \(0.616325\pi\)
\(462\) −5.28358 2.10534i −0.245814 0.0979493i
\(463\) 7.90078 0.367181 0.183590 0.983003i \(-0.441228\pi\)
0.183590 + 0.983003i \(0.441228\pi\)
\(464\) −0.578885 10.6986i −0.0268741 0.496671i
\(465\) 6.05452i 0.280771i
\(466\) −0.131125 + 0.329073i −0.00607426 + 0.0152440i
\(467\) 8.56126i 0.396168i −0.980185 0.198084i \(-0.936528\pi\)
0.980185 0.198084i \(-0.0634718\pi\)
\(468\) −1.52873 + 1.61369i −0.0706658 + 0.0745928i
\(469\) 12.2092 + 25.3423i 0.563766 + 1.17020i
\(470\) −7.05444 2.81097i −0.325397 0.129660i
\(471\) −20.4651 −0.942980
\(472\) 14.0707 6.50841i 0.647658 0.299574i
\(473\) 1.82166 0.0837599
\(474\) 9.83595 + 3.91931i 0.451780 + 0.180020i
\(475\) 3.31334i 0.152026i
\(476\) 29.9762 + 28.3981i 1.37396 + 1.30162i
\(477\) 9.63385i 0.441104i
\(478\) 24.5255 + 9.77261i 1.12177 + 0.446989i
\(479\) 29.1248i 1.33075i 0.746510 + 0.665374i \(0.231728\pi\)
−0.746510 + 0.665374i \(0.768272\pi\)
\(480\) −9.20426 3.10268i −0.420115 0.141617i
\(481\) 4.79707i 0.218727i
\(482\) −1.00098 0.398858i −0.0455933 0.0181675i
\(483\) 19.2063i 0.873916i
\(484\) −13.9827 13.2465i −0.635576 0.602116i
\(485\) 12.6643 0.575058
\(486\) 1.31376 + 0.523490i 0.0595932 + 0.0237460i
\(487\) 2.54391 0.115276 0.0576378 0.998338i \(-0.481643\pi\)
0.0576378 + 0.998338i \(0.481643\pi\)
\(488\) −8.13872 + 3.76456i −0.368423 + 0.170414i
\(489\) 4.88761i 0.221025i
\(490\) 4.32387 10.8512i 0.195332 0.490208i
\(491\) 16.6449i 0.751172i 0.926788 + 0.375586i \(0.122559\pi\)
−0.926788 + 0.375586i \(0.877441\pi\)
\(492\) −12.0656 + 12.7361i −0.543959 + 0.574187i
\(493\) 16.0918 0.724740
\(494\) 2.35798 + 0.939582i 0.106091 + 0.0422738i
\(495\) 2.00940i 0.0903157i
\(496\) 0.762053 + 14.0838i 0.0342172 + 0.632382i
\(497\) 49.5832i 2.22411i
\(498\) −1.87365 + 4.70214i −0.0839605 + 0.210708i
\(499\) 4.08382 0.182817 0.0914085 0.995813i \(-0.470863\pi\)
0.0914085 + 0.995813i \(0.470863\pi\)
\(500\) −16.6546 + 17.5801i −0.744815 + 0.786205i
\(501\) 2.32807i 0.104010i
\(502\) −21.0873 8.40263i −0.941174 0.375028i
\(503\) −35.4800 −1.58197 −0.790987 0.611833i \(-0.790432\pi\)
−0.790987 + 0.611833i \(0.790432\pi\)
\(504\) 4.08070 + 8.82218i 0.181769 + 0.392971i
\(505\) 19.6061 0.872458
\(506\) −3.42375 + 8.59227i −0.152204 + 0.381973i
\(507\) −11.7647 −0.522491
\(508\) −14.0561 + 14.8372i −0.623637 + 0.658293i
\(509\) 28.8834 1.28023 0.640117 0.768277i \(-0.278886\pi\)
0.640117 + 0.768277i \(0.278886\pi\)
\(510\) 5.40003 13.5520i 0.239117 0.600092i
\(511\) 27.1546 1.20125
\(512\) 21.8012 + 6.05886i 0.963484 + 0.267766i
\(513\) 1.61491i 0.0712999i
\(514\) 28.5390 + 11.3719i 1.25880 + 0.501593i
\(515\) 21.7939 0.960355
\(516\) −2.26010 2.14111i −0.0994952 0.0942572i
\(517\) 3.65969i 0.160953i
\(518\) 19.4870 + 7.76494i 0.856208 + 0.341172i
\(519\) 5.54784 0.243523
\(520\) 2.26603 + 4.89899i 0.0993718 + 0.214835i
\(521\) 28.2902i 1.23942i −0.784832 0.619709i \(-0.787251\pi\)
0.784832 0.619709i \(-0.212749\pi\)
\(522\) 3.51899 + 1.40220i 0.154022 + 0.0613728i
\(523\) 31.8548i 1.39292i −0.717598 0.696458i \(-0.754758\pi\)
0.717598 0.696458i \(-0.245242\pi\)
\(524\) −7.10853 + 7.50356i −0.310538 + 0.327795i
\(525\) 7.05099 0.307730
\(526\) 1.20148 3.01525i 0.0523871 0.131471i
\(527\) −21.1835 −0.922769
\(528\) −0.252913 4.67419i −0.0110066 0.203418i
\(529\) −8.23364 −0.357984
\(530\) −21.7320 8.65950i −0.943977 0.376145i
\(531\) 5.48116i 0.237862i
\(532\) 7.63367 8.05788i 0.330962 0.349353i
\(533\) 9.74928 0.422288
\(534\) −18.3355 7.30612i −0.793455 0.316167i
\(535\) 25.7807 1.11460
\(536\) −14.7119 + 17.8763i −0.635455 + 0.772138i
\(537\) 7.50648 0.323928
\(538\) −3.68698 1.46915i −0.158957 0.0633393i
\(539\) 5.62938 0.242475
\(540\) 2.36177 2.49302i 0.101635 0.107282i
\(541\) 27.5286i 1.18355i −0.806104 0.591774i \(-0.798428\pi\)
0.806104 0.591774i \(-0.201572\pi\)
\(542\) 34.0151 + 13.5539i 1.46107 + 0.582191i
\(543\) 6.75725 0.289982
\(544\) −10.8556 + 32.2038i −0.465432 + 1.38073i
\(545\) −0.711612 −0.0304821
\(546\) 1.99949 5.01794i 0.0855702 0.214748i
\(547\) −8.24041 −0.352334 −0.176167 0.984360i \(-0.556370\pi\)
−0.176167 + 0.984360i \(0.556370\pi\)
\(548\) −30.1973 + 31.8754i −1.28996 + 1.36165i
\(549\) 3.17038i 0.135309i
\(550\) −3.15438 1.25692i −0.134503 0.0535953i
\(551\) 4.32564i 0.184278i
\(552\) 14.3468 6.63611i 0.610641 0.282452i
\(553\) −25.7296 −1.09413
\(554\) 26.1280 + 10.4112i 1.11007 + 0.442328i
\(555\) 7.41109i 0.314583i
\(556\) −14.3899 13.6324i −0.610270 0.578142i
\(557\) 16.4605 0.697453 0.348726 0.937225i \(-0.386614\pi\)
0.348726 + 0.937225i \(0.386614\pi\)
\(558\) −4.63244 1.84588i −0.196107 0.0781424i
\(559\) 1.73007i 0.0731742i
\(560\) 23.5690 1.27528i 0.995973 0.0538905i
\(561\) 7.03047 0.296827
\(562\) −2.75797 + 6.92144i −0.116338 + 0.291963i
\(563\) −39.4200 −1.66136 −0.830678 0.556753i \(-0.812047\pi\)
−0.830678 + 0.556753i \(0.812047\pi\)
\(564\) −4.30147 + 4.54051i −0.181125 + 0.191190i
\(565\) −14.2313 −0.598716
\(566\) 2.13769 5.36476i 0.0898537 0.225498i
\(567\) −3.43662 −0.144325
\(568\) −37.0380 + 17.1319i −1.55408 + 0.718838i
\(569\) 17.5843 0.737173 0.368586 0.929593i \(-0.379842\pi\)
0.368586 + 0.929593i \(0.379842\pi\)
\(570\) −3.64290 1.45158i −0.152584 0.0608000i
\(571\) 29.6052i 1.23894i −0.785020 0.619470i \(-0.787348\pi\)
0.785020 0.619470i \(-0.212652\pi\)
\(572\) −1.78901 + 1.88843i −0.0748024 + 0.0789593i
\(573\) −14.3393 −0.599031
\(574\) 15.7810 39.6042i 0.658687 1.65305i
\(575\) 11.4665i 0.478184i
\(576\) −5.18009 + 6.09644i −0.215837 + 0.254019i
\(577\) 24.8946i 1.03638i 0.855267 + 0.518188i \(0.173393\pi\)
−0.855267 + 0.518188i \(0.826607\pi\)
\(578\) −25.0817 9.99427i −1.04326 0.415707i
\(579\) 6.63609 0.275787
\(580\) 6.32617 6.67772i 0.262680 0.277277i
\(581\) 12.3002i 0.510299i
\(582\) 3.86106 9.68977i 0.160046 0.401654i
\(583\) 11.2741i 0.466925i
\(584\) 9.38238 + 20.2841i 0.388246 + 0.839361i
\(585\) −1.90837 −0.0789014
\(586\) −13.0777 5.21105i −0.540235 0.215266i
\(587\) −8.76986 −0.361971 −0.180985 0.983486i \(-0.557929\pi\)
−0.180985 + 0.983486i \(0.557929\pi\)
\(588\) −6.98426 6.61657i −0.288026 0.272863i
\(589\) 5.69433i 0.234631i
\(590\) 12.3644 + 4.92681i 0.509033 + 0.202833i
\(591\) 10.9332i 0.449730i
\(592\) 0.932798 + 17.2394i 0.0383377 + 0.708536i
\(593\) 13.1468i 0.539875i 0.962878 + 0.269938i \(0.0870031\pi\)
−0.962878 + 0.269938i \(0.912997\pi\)
\(594\) 1.53743 + 0.612619i 0.0630817 + 0.0251360i
\(595\) 35.4503i 1.45332i
\(596\) 25.1127 + 23.7906i 1.02866 + 0.974503i
\(597\) 21.7663i 0.890834i
\(598\) −8.16027 3.25161i −0.333698 0.132968i
\(599\) −1.49884 −0.0612408 −0.0306204 0.999531i \(-0.509748\pi\)
−0.0306204 + 0.999531i \(0.509748\pi\)
\(600\) 2.43624 + 5.26699i 0.0994591 + 0.215024i
\(601\) −35.0733 −1.43067 −0.715336 0.698781i \(-0.753726\pi\)
−0.715336 + 0.698781i \(0.753726\pi\)
\(602\) 7.02801 + 2.80044i 0.286440 + 0.114137i
\(603\) −3.55266 7.37419i −0.144675 0.300300i
\(604\) 2.36817 2.49977i 0.0963596 0.101714i
\(605\) 16.5361i 0.672288i
\(606\) 5.97743 15.0010i 0.242816 0.609375i
\(607\) 27.4233i 1.11308i −0.830822 0.556538i \(-0.812129\pi\)
0.830822 0.556538i \(-0.187871\pi\)
\(608\) 8.65669 + 2.91810i 0.351075 + 0.118345i
\(609\) −9.20522 −0.373014
\(610\) −7.15173 2.84974i −0.289565 0.115383i
\(611\) 3.47569 0.140611
\(612\) −8.72257 8.26336i −0.352589 0.334027i
\(613\) 8.13038 0.328383 0.164192 0.986428i \(-0.447498\pi\)
0.164192 + 0.986428i \(0.447498\pi\)
\(614\) 4.96788 12.4675i 0.200488 0.503146i
\(615\) −15.0619 −0.607353
\(616\) 4.77547 + 10.3242i 0.192409 + 0.415975i
\(617\) 34.0281 1.36992 0.684961 0.728580i \(-0.259819\pi\)
0.684961 + 0.728580i \(0.259819\pi\)
\(618\) 6.64446 16.6750i 0.267280 0.670768i
\(619\) 14.2214i 0.571608i 0.958288 + 0.285804i \(0.0922607\pi\)
−0.958288 + 0.285804i \(0.907739\pi\)
\(620\) −8.32786 + 8.79065i −0.334455 + 0.353041i
\(621\) 5.58871i 0.224267i
\(622\) 13.9884 + 5.57392i 0.560882 + 0.223494i
\(623\) 47.9634 1.92161
\(624\) 4.43919 0.240197i 0.177710 0.00961559i
\(625\) −10.5318 −0.421274
\(626\) 3.05087 7.65650i 0.121937 0.306015i
\(627\) 1.88986i 0.0754737i
\(628\) 29.7135 + 28.1492i 1.18570 + 1.12328i
\(629\) −25.9299 −1.03389
\(630\) −3.08905 + 7.75231i −0.123071 + 0.308860i
\(631\) 23.8524 0.949549 0.474775 0.880107i \(-0.342530\pi\)
0.474775 + 0.880107i \(0.342530\pi\)
\(632\) −8.89003 19.2196i −0.353627 0.764516i
\(633\) 24.8456i 0.987525i
\(634\) −20.0173 7.97627i −0.794990 0.316778i
\(635\) −17.5466 −0.696317
\(636\) −13.2511 + 13.9875i −0.525442 + 0.554642i
\(637\) 5.34635i 0.211830i
\(638\) 4.11812 + 1.64094i 0.163038 + 0.0649654i
\(639\) 14.4279i 0.570759i
\(640\) 9.09613 + 17.1651i 0.359556 + 0.678510i
\(641\) 45.5542i 1.79928i 0.436628 + 0.899642i \(0.356172\pi\)
−0.436628 + 0.899642i \(0.643828\pi\)
\(642\) 7.85995 19.7254i 0.310207 0.778500i
\(643\) 25.3323i 0.999007i −0.866312 0.499504i \(-0.833516\pi\)
0.866312 0.499504i \(-0.166484\pi\)
\(644\) −26.4178 + 27.8859i −1.04101 + 1.09886i
\(645\) 2.67282i 0.105242i
\(646\) −5.07878 + 12.7458i −0.199822 + 0.501475i
\(647\) 21.7790 0.856219 0.428110 0.903727i \(-0.359180\pi\)
0.428110 + 0.903727i \(0.359180\pi\)
\(648\) −1.18741 2.56711i −0.0466460 0.100846i
\(649\) 6.41437i 0.251786i
\(650\) 1.19373 2.99579i 0.0468218 0.117505i
\(651\) 12.1179 0.474937
\(652\) 6.72280 7.09640i 0.263285 0.277916i
\(653\) 35.5811i 1.39240i −0.717850 0.696198i \(-0.754874\pi\)
0.717850 0.696198i \(-0.245126\pi\)
\(654\) −0.216954 + 0.544470i −0.00848358 + 0.0212905i
\(655\) −8.87382 −0.346729
\(656\) 35.0364 1.89577i 1.36794 0.0740172i
\(657\) −7.90152 −0.308268
\(658\) 5.62605 14.1192i 0.219326 0.550424i
\(659\) 16.1633i 0.629633i 0.949153 + 0.314816i \(0.101943\pi\)
−0.949153 + 0.314816i \(0.898057\pi\)
\(660\) 2.76388 2.91748i 0.107584 0.113563i
\(661\) 44.1823i 1.71849i 0.511562 + 0.859247i \(0.329067\pi\)
−0.511562 + 0.859247i \(0.670933\pi\)
\(662\) 10.9072 + 4.34616i 0.423919 + 0.168918i
\(663\) 6.67700i 0.259313i
\(664\) 9.18808 4.24994i 0.356567 0.164930i
\(665\) 9.52936 0.369533
\(666\) −5.67038 2.25947i −0.219723 0.0875526i
\(667\) 14.9697i 0.579630i
\(668\) −3.20220 + 3.38016i −0.123897 + 0.130782i
\(669\) 10.3441i 0.399928i
\(670\) −19.8280 + 1.38569i −0.766022 + 0.0535339i
\(671\) 3.71017i 0.143229i
\(672\) 6.20990 18.4220i 0.239552 0.710643i
\(673\) 14.9441i 0.576054i 0.957622 + 0.288027i \(0.0929994\pi\)
−0.957622 + 0.288027i \(0.907001\pi\)
\(674\) 11.8634 29.7725i 0.456960 1.14679i
\(675\) −2.05172 −0.0789707
\(676\) 17.0814 + 16.1822i 0.656978 + 0.622391i
\(677\) 6.35008i 0.244054i 0.992527 + 0.122027i \(0.0389394\pi\)
−0.992527 + 0.122027i \(0.961061\pi\)
\(678\) −4.33880 + 10.8887i −0.166630 + 0.418178i
\(679\) 25.3472i 0.972737i
\(680\) −26.4808 + 12.2487i −1.01549 + 0.469716i
\(681\) 6.48668i 0.248570i
\(682\) −5.42115 2.16016i −0.207587 0.0827167i
\(683\) 44.9065 1.71830 0.859150 0.511724i \(-0.170993\pi\)
0.859150 + 0.511724i \(0.170993\pi\)
\(684\) −2.22127 + 2.34471i −0.0849324 + 0.0896522i
\(685\) −37.6963 −1.44030
\(686\) −9.88590 3.93922i −0.377445 0.150400i
\(687\) 17.8420i 0.680715i
\(688\) 0.336415 + 6.21743i 0.0128257 + 0.237037i
\(689\) 10.7072 0.407914
\(690\) 12.6070 + 5.02348i 0.479939 + 0.191241i
\(691\) 20.5238i 0.780764i −0.920653 0.390382i \(-0.872343\pi\)
0.920653 0.390382i \(-0.127657\pi\)
\(692\) −8.05500 7.63094i −0.306205 0.290085i
\(693\) −4.02173 −0.152773
\(694\) 1.26214 + 0.502921i 0.0479100 + 0.0190906i
\(695\) 17.0178i 0.645520i
\(696\) −3.18057 6.87617i −0.120559 0.260641i
\(697\) 52.6984i 1.99610i
\(698\) −16.2310 6.46752i −0.614351 0.244799i
\(699\) 0.250483i 0.00947412i
\(700\) −10.2374 9.69848i −0.386939 0.366568i
\(701\) 38.5142i 1.45466i −0.686287 0.727331i \(-0.740760\pi\)
0.686287 0.727331i \(-0.259240\pi\)
\(702\) −0.581818 + 1.46014i −0.0219593 + 0.0551093i
\(703\) 6.97020i 0.262886i
\(704\) −6.06204 + 7.13441i −0.228472 + 0.268888i
\(705\) −5.36967 −0.202233
\(706\) 6.31213 15.8410i 0.237560 0.596184i
\(707\) 39.2408i 1.47580i
\(708\) 7.53922 7.95818i 0.283341 0.299087i
\(709\) 8.41092 0.315879 0.157939 0.987449i \(-0.449515\pi\)
0.157939 + 0.987449i \(0.449515\pi\)
\(710\) −32.5464 12.9687i −1.22144 0.486706i
\(711\) 7.48688 0.280780
\(712\) 16.5722 + 35.8280i 0.621070 + 1.34271i
\(713\) 19.7064i 0.738009i
\(714\) 27.1238 + 10.8080i 1.01508 + 0.404478i
\(715\) −2.23328 −0.0835201
\(716\) −10.8988 10.3250i −0.407306 0.385863i
\(717\) 18.6682 0.697176
\(718\) −12.0940 + 30.3512i −0.451344 + 1.13270i
\(719\) 26.0757i 0.972461i −0.873831 0.486230i \(-0.838372\pi\)
0.873831 0.486230i \(-0.161628\pi\)
\(720\) −6.85819 + 0.371086i −0.255590 + 0.0138296i
\(721\) 43.6197i 1.62448i
\(722\) −21.5352 8.58109i −0.801457 0.319355i
\(723\) −0.761920 −0.0283361
\(724\) −9.81096 9.29446i −0.364622 0.345426i
\(725\) −5.49567 −0.204104
\(726\) −12.6521 5.04147i −0.469565 0.187107i
\(727\) 47.8363 1.77415 0.887074 0.461627i \(-0.152734\pi\)
0.887074 + 0.461627i \(0.152734\pi\)
\(728\) −9.80515 + 4.53537i −0.363403 + 0.168092i
\(729\) 1.00000 0.0370370
\(730\) −7.10238 + 17.8242i −0.262871 + 0.659704i
\(731\) −9.35166 −0.345884
\(732\) −4.36079 + 4.60313i −0.161180 + 0.170137i
\(733\) 44.2327i 1.63377i −0.576798 0.816887i \(-0.695698\pi\)
0.576798 0.816887i \(-0.304302\pi\)
\(734\) 11.8310 + 4.71428i 0.436691 + 0.174007i
\(735\) 8.25969i 0.304663i
\(736\) −29.9582 10.0987i −1.10427 0.372242i
\(737\) −4.15753 8.62970i −0.153144 0.317879i
\(738\) −4.59201 + 11.5242i −0.169034 + 0.424211i
\(739\) 21.7388 0.799673 0.399837 0.916586i \(-0.369067\pi\)
0.399837 + 0.916586i \(0.369067\pi\)
\(740\) −10.1938 + 10.7603i −0.374731 + 0.395555i
\(741\) 1.79484 0.0659351
\(742\) 17.3317 43.4957i 0.636266 1.59678i
\(743\) 5.66794i 0.207937i −0.994581 0.103968i \(-0.966846\pi\)
0.994581 0.103968i \(-0.0331541\pi\)
\(744\) 4.18695 + 9.05189i 0.153501 + 0.331858i
\(745\) 29.6987i 1.08807i
\(746\) −6.06209 + 15.2135i −0.221949 + 0.557005i
\(747\) 3.57916i 0.130954i
\(748\) −10.2077 9.67027i −0.373229 0.353580i
\(749\) 51.5992i 1.88539i
\(750\) −6.33852 + 15.9072i −0.231450 + 0.580850i
\(751\) 29.4760i 1.07560i −0.843074 0.537798i \(-0.819256\pi\)
0.843074 0.537798i \(-0.180744\pi\)
\(752\) 12.4907 0.675854i 0.455490 0.0246459i
\(753\) −16.0512 −0.584937
\(754\) −1.55844 + 3.91107i −0.0567549 + 0.142433i
\(755\) 2.95627 0.107590
\(756\) 4.98969 + 4.72700i 0.181473 + 0.171919i
\(757\) 35.9361i 1.30612i −0.757307 0.653060i \(-0.773485\pi\)
0.757307 0.653060i \(-0.226515\pi\)
\(758\) 47.6643 + 18.9927i 1.73124 + 0.689846i
\(759\) 6.54023i 0.237395i
\(760\) 3.29257 + 7.11830i 0.119434 + 0.258208i
\(761\) −46.8165 −1.69710 −0.848548 0.529119i \(-0.822523\pi\)
−0.848548 + 0.529119i \(0.822523\pi\)
\(762\) −5.34956 + 13.4253i −0.193794 + 0.486348i
\(763\) 1.42427i 0.0515619i
\(764\) 20.8194 + 19.7233i 0.753219 + 0.713565i
\(765\) 10.3154i 0.372955i
\(766\) 43.1505 + 17.1941i 1.55909 + 0.621248i
\(767\) −6.09187 −0.219965
\(768\) 15.9066 1.72641i 0.573979 0.0622966i
\(769\) 50.4895i 1.82070i 0.413840 + 0.910350i \(0.364187\pi\)
−0.413840 + 0.910350i \(0.635813\pi\)
\(770\) −3.61499 + 9.07221i −0.130275 + 0.326940i
\(771\) 21.7232 0.782342
\(772\)