Properties

Label 403.2.h.b.222.3
Level 403
Weight 2
Character 403.222
Analytic conductor 3.218
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.h (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 222.3
Character \(\chi\) \(=\) 403.222
Dual form 403.2.h.b.118.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.85162 q^{2} +(0.240159 - 0.415967i) q^{3} +1.42848 q^{4} +(0.854909 + 1.48075i) q^{5} +(-0.444682 + 0.770212i) q^{6} +(-0.531962 + 0.921385i) q^{7} +1.05824 q^{8} +(1.38465 + 2.39828i) q^{9} +O(q^{10})\) \(q-1.85162 q^{2} +(0.240159 - 0.415967i) q^{3} +1.42848 q^{4} +(0.854909 + 1.48075i) q^{5} +(-0.444682 + 0.770212i) q^{6} +(-0.531962 + 0.921385i) q^{7} +1.05824 q^{8} +(1.38465 + 2.39828i) q^{9} +(-1.58296 - 2.74177i) q^{10} +(-1.35310 - 2.34363i) q^{11} +(0.343062 - 0.594201i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(0.984989 - 1.70605i) q^{14} +0.821256 q^{15} -4.81641 q^{16} +(-2.30153 + 3.98636i) q^{17} +(-2.56383 - 4.44069i) q^{18} +(-2.35112 + 4.07226i) q^{19} +(1.22122 + 2.11522i) q^{20} +(0.255511 + 0.442558i) q^{21} +(2.50541 + 4.33950i) q^{22} +0.635348 q^{23} +(0.254145 - 0.440192i) q^{24} +(1.03826 - 1.79832i) q^{25} +(0.925808 + 1.60355i) q^{26} +2.77110 q^{27} +(-0.759897 + 1.31618i) q^{28} +8.27995 q^{29} -1.52065 q^{30} +(-3.77960 + 4.08835i) q^{31} +6.80166 q^{32} -1.29983 q^{33} +(4.26154 - 7.38121i) q^{34} -1.81912 q^{35} +(1.97794 + 3.42589i) q^{36} +(-5.38526 + 9.32754i) q^{37} +(4.35337 - 7.54025i) q^{38} -0.480318 q^{39} +(0.904695 + 1.56698i) q^{40} +(2.87333 + 4.97675i) q^{41} +(-0.473108 - 0.819446i) q^{42} +(-3.63911 + 6.30313i) q^{43} +(-1.93287 - 3.34783i) q^{44} +(-2.36750 + 4.10062i) q^{45} -1.17642 q^{46} +1.75655 q^{47} +(-1.15670 + 2.00347i) q^{48} +(2.93403 + 5.08189i) q^{49} +(-1.92246 + 3.32980i) q^{50} +(1.10546 + 1.91472i) q^{51} +(-0.714240 - 1.23710i) q^{52} +(-0.713902 - 1.23651i) q^{53} -5.13100 q^{54} +(2.31355 - 4.00718i) q^{55} +(-0.562941 + 0.975042i) q^{56} +(1.12928 + 1.95598i) q^{57} -15.3313 q^{58} +(-1.20360 + 2.08470i) q^{59} +1.17315 q^{60} +11.0363 q^{61} +(6.99837 - 7.57005i) q^{62} -2.94632 q^{63} -2.96125 q^{64} +(0.854909 - 1.48075i) q^{65} +2.40679 q^{66} +(-2.39741 - 4.15244i) q^{67} +(-3.28768 + 5.69444i) q^{68} +(0.152585 - 0.264284i) q^{69} +3.36830 q^{70} +(-6.06136 - 10.4986i) q^{71} +(1.46528 + 2.53795i) q^{72} +(-3.91127 - 6.77452i) q^{73} +(9.97143 - 17.2710i) q^{74} +(-0.498695 - 0.863766i) q^{75} +(-3.35852 + 5.81713i) q^{76} +2.87918 q^{77} +0.889364 q^{78} +(-3.09572 + 5.36195i) q^{79} +(-4.11759 - 7.13187i) q^{80} +(-3.48844 + 6.04215i) q^{81} +(-5.32029 - 9.21502i) q^{82} +(4.24548 + 7.35339i) q^{83} +(0.364992 + 0.632185i) q^{84} -7.87038 q^{85} +(6.73824 - 11.6710i) q^{86} +(1.98850 - 3.44419i) q^{87} +(-1.43189 - 2.48011i) q^{88} +7.00404 q^{89} +(4.38369 - 7.59277i) q^{90} +1.06392 q^{91} +0.907582 q^{92} +(0.792916 + 2.55405i) q^{93} -3.25245 q^{94} -8.03997 q^{95} +(1.63348 - 2.82927i) q^{96} -9.12762 q^{97} +(-5.43270 - 9.40971i) q^{98} +(3.74712 - 6.49021i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} + O(q^{10}) \) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} - 7q^{10} - 5q^{11} - 28q^{12} - 17q^{13} - 7q^{14} + 8q^{15} + 18q^{16} - 8q^{17} + 6q^{18} + 3q^{19} - 8q^{20} + 13q^{21} + 12q^{22} - 14q^{23} - 6q^{24} - 26q^{25} - 3q^{26} + 28q^{27} - 7q^{28} - 18q^{29} - 60q^{30} - 9q^{31} + 58q^{32} - 14q^{33} - 15q^{34} + 50q^{35} - 49q^{36} - 6q^{37} + 2q^{38} + 4q^{39} - 29q^{40} - 5q^{41} + 8q^{42} - q^{43} - 22q^{44} + 13q^{45} + 34q^{46} + 16q^{47} - 49q^{48} + 3q^{49} - 35q^{51} - 17q^{52} + 30q^{53} - 2q^{54} + 21q^{55} - 7q^{56} + 34q^{58} - 9q^{59} - 38q^{60} - 28q^{61} - 62q^{62} + 88q^{63} + 56q^{64} - 5q^{65} + 140q^{66} - 31q^{67} - 39q^{68} + 5q^{69} + 56q^{70} + q^{71} - 32q^{72} - 10q^{73} - 39q^{74} - 2q^{75} - 16q^{76} + 76q^{77} - 23q^{79} - 22q^{80} - 29q^{81} - 10q^{82} + 3q^{83} + 52q^{84} - 32q^{85} + 4q^{86} + 18q^{87} - 10q^{88} + 26q^{89} + 35q^{90} + 4q^{91} - 94q^{92} - 41q^{93} + 70q^{94} + 28q^{95} - 23q^{96} + 32q^{97} - 38q^{98} - 70q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.85162 −1.30929 −0.654645 0.755937i \(-0.727182\pi\)
−0.654645 + 0.755937i \(0.727182\pi\)
\(3\) 0.240159 0.415967i 0.138656 0.240159i −0.788332 0.615250i \(-0.789055\pi\)
0.926988 + 0.375091i \(0.122388\pi\)
\(4\) 1.42848 0.714240
\(5\) 0.854909 + 1.48075i 0.382327 + 0.662210i 0.991394 0.130909i \(-0.0417895\pi\)
−0.609067 + 0.793118i \(0.708456\pi\)
\(6\) −0.444682 + 0.770212i −0.181541 + 0.314438i
\(7\) −0.531962 + 0.921385i −0.201063 + 0.348251i −0.948871 0.315664i \(-0.897773\pi\)
0.747808 + 0.663915i \(0.231106\pi\)
\(8\) 1.05824 0.374143
\(9\) 1.38465 + 2.39828i 0.461549 + 0.799427i
\(10\) −1.58296 2.74177i −0.500577 0.867024i
\(11\) −1.35310 2.34363i −0.407974 0.706631i 0.586689 0.809813i \(-0.300431\pi\)
−0.994663 + 0.103181i \(0.967098\pi\)
\(12\) 0.343062 0.594201i 0.0990335 0.171531i
\(13\) −0.500000 0.866025i −0.138675 0.240192i
\(14\) 0.984989 1.70605i 0.263249 0.455961i
\(15\) 0.821256 0.212047
\(16\) −4.81641 −1.20410
\(17\) −2.30153 + 3.98636i −0.558202 + 0.966834i 0.439445 + 0.898270i \(0.355175\pi\)
−0.997647 + 0.0685648i \(0.978158\pi\)
\(18\) −2.56383 4.44069i −0.604302 1.04668i
\(19\) −2.35112 + 4.07226i −0.539383 + 0.934239i 0.459554 + 0.888150i \(0.348009\pi\)
−0.998937 + 0.0460895i \(0.985324\pi\)
\(20\) 1.22122 + 2.11522i 0.273073 + 0.472977i
\(21\) 0.255511 + 0.442558i 0.0557570 + 0.0965740i
\(22\) 2.50541 + 4.33950i 0.534156 + 0.925185i
\(23\) 0.635348 0.132479 0.0662396 0.997804i \(-0.478900\pi\)
0.0662396 + 0.997804i \(0.478900\pi\)
\(24\) 0.254145 0.440192i 0.0518771 0.0898537i
\(25\) 1.03826 1.79832i 0.207652 0.359664i
\(26\) 0.925808 + 1.60355i 0.181566 + 0.314481i
\(27\) 2.77110 0.533298
\(28\) −0.759897 + 1.31618i −0.143607 + 0.248735i
\(29\) 8.27995 1.53755 0.768774 0.639520i \(-0.220867\pi\)
0.768774 + 0.639520i \(0.220867\pi\)
\(30\) −1.52065 −0.277632
\(31\) −3.77960 + 4.08835i −0.678836 + 0.734289i
\(32\) 6.80166 1.20237
\(33\) −1.29983 −0.226272
\(34\) 4.26154 7.38121i 0.730848 1.26587i
\(35\) −1.81912 −0.307487
\(36\) 1.97794 + 3.42589i 0.329657 + 0.570982i
\(37\) −5.38526 + 9.32754i −0.885331 + 1.53344i −0.0399978 + 0.999200i \(0.512735\pi\)
−0.845333 + 0.534239i \(0.820598\pi\)
\(38\) 4.35337 7.54025i 0.706209 1.22319i
\(39\) −0.480318 −0.0769124
\(40\) 0.904695 + 1.56698i 0.143045 + 0.247761i
\(41\) 2.87333 + 4.97675i 0.448738 + 0.777237i 0.998304 0.0582131i \(-0.0185403\pi\)
−0.549566 + 0.835450i \(0.685207\pi\)
\(42\) −0.473108 0.819446i −0.0730021 0.126443i
\(43\) −3.63911 + 6.30313i −0.554959 + 0.961218i 0.442947 + 0.896548i \(0.353933\pi\)
−0.997907 + 0.0646703i \(0.979400\pi\)
\(44\) −1.93287 3.34783i −0.291391 0.504704i
\(45\) −2.36750 + 4.10062i −0.352925 + 0.611285i
\(46\) −1.17642 −0.173454
\(47\) 1.75655 0.256219 0.128109 0.991760i \(-0.459109\pi\)
0.128109 + 0.991760i \(0.459109\pi\)
\(48\) −1.15670 + 2.00347i −0.166956 + 0.289176i
\(49\) 2.93403 + 5.08189i 0.419148 + 0.725985i
\(50\) −1.92246 + 3.32980i −0.271877 + 0.470905i
\(51\) 1.10546 + 1.91472i 0.154796 + 0.268114i
\(52\) −0.714240 1.23710i −0.0990472 0.171555i
\(53\) −0.713902 1.23651i −0.0980620 0.169848i 0.812820 0.582514i \(-0.197931\pi\)
−0.910882 + 0.412666i \(0.864598\pi\)
\(54\) −5.13100 −0.698241
\(55\) 2.31355 4.00718i 0.311959 0.540329i
\(56\) −0.562941 + 0.975042i −0.0752262 + 0.130296i
\(57\) 1.12928 + 1.95598i 0.149577 + 0.259075i
\(58\) −15.3313 −2.01310
\(59\) −1.20360 + 2.08470i −0.156695 + 0.271404i −0.933675 0.358121i \(-0.883417\pi\)
0.776980 + 0.629526i \(0.216751\pi\)
\(60\) 1.17315 0.151453
\(61\) 11.0363 1.41305 0.706526 0.707687i \(-0.250261\pi\)
0.706526 + 0.707687i \(0.250261\pi\)
\(62\) 6.99837 7.57005i 0.888794 0.961398i
\(63\) −2.94632 −0.371201
\(64\) −2.96125 −0.370156
\(65\) 0.854909 1.48075i 0.106038 0.183664i
\(66\) 2.40679 0.296255
\(67\) −2.39741 4.15244i −0.292891 0.507302i 0.681601 0.731724i \(-0.261284\pi\)
−0.974492 + 0.224422i \(0.927951\pi\)
\(68\) −3.28768 + 5.69444i −0.398690 + 0.690552i
\(69\) 0.152585 0.264284i 0.0183690 0.0318161i
\(70\) 3.36830 0.402589
\(71\) −6.06136 10.4986i −0.719351 1.24595i −0.961257 0.275653i \(-0.911106\pi\)
0.241906 0.970300i \(-0.422228\pi\)
\(72\) 1.46528 + 2.53795i 0.172685 + 0.299100i
\(73\) −3.91127 6.77452i −0.457780 0.792898i 0.541063 0.840982i \(-0.318022\pi\)
−0.998843 + 0.0480837i \(0.984689\pi\)
\(74\) 9.97143 17.2710i 1.15916 2.00772i
\(75\) −0.498695 0.863766i −0.0575844 0.0997391i
\(76\) −3.35852 + 5.81713i −0.385249 + 0.667271i
\(77\) 2.87918 0.328113
\(78\) 0.889364 0.100701
\(79\) −3.09572 + 5.36195i −0.348296 + 0.603266i −0.985947 0.167059i \(-0.946573\pi\)
0.637651 + 0.770325i \(0.279906\pi\)
\(80\) −4.11759 7.13187i −0.460360 0.797368i
\(81\) −3.48844 + 6.04215i −0.387604 + 0.671350i
\(82\) −5.32029 9.21502i −0.587528 1.01763i
\(83\) 4.24548 + 7.35339i 0.466002 + 0.807139i 0.999246 0.0388224i \(-0.0123607\pi\)
−0.533244 + 0.845961i \(0.679027\pi\)
\(84\) 0.364992 + 0.632185i 0.0398239 + 0.0689770i
\(85\) −7.87038 −0.853663
\(86\) 6.73824 11.6710i 0.726603 1.25851i
\(87\) 1.98850 3.44419i 0.213190 0.369256i
\(88\) −1.43189 2.48011i −0.152641 0.264381i
\(89\) 7.00404 0.742426 0.371213 0.928548i \(-0.378942\pi\)
0.371213 + 0.928548i \(0.378942\pi\)
\(90\) 4.38369 7.59277i 0.462082 0.800349i
\(91\) 1.06392 0.111529
\(92\) 0.907582 0.0946220
\(93\) 0.792916 + 2.55405i 0.0822215 + 0.264842i
\(94\) −3.25245 −0.335464
\(95\) −8.03997 −0.824883
\(96\) 1.63348 2.82927i 0.166716 0.288761i
\(97\) −9.12762 −0.926769 −0.463385 0.886157i \(-0.653365\pi\)
−0.463385 + 0.886157i \(0.653365\pi\)
\(98\) −5.43270 9.40971i −0.548786 0.950525i
\(99\) 3.74712 6.49021i 0.376600 0.652290i
\(100\) 1.48313 2.56886i 0.148313 0.256886i
\(101\) 14.0711 1.40013 0.700064 0.714080i \(-0.253155\pi\)
0.700064 + 0.714080i \(0.253155\pi\)
\(102\) −2.04689 3.54533i −0.202673 0.351040i
\(103\) −5.70879 9.88791i −0.562504 0.974285i −0.997277 0.0737450i \(-0.976505\pi\)
0.434774 0.900540i \(-0.356828\pi\)
\(104\) −0.529118 0.916459i −0.0518843 0.0898662i
\(105\) −0.436877 + 0.756693i −0.0426348 + 0.0738457i
\(106\) 1.32187 + 2.28955i 0.128392 + 0.222381i
\(107\) 9.50665 16.4660i 0.919043 1.59183i 0.118171 0.992993i \(-0.462297\pi\)
0.800872 0.598836i \(-0.204370\pi\)
\(108\) 3.95845 0.380902
\(109\) −12.3913 −1.18687 −0.593436 0.804881i \(-0.702229\pi\)
−0.593436 + 0.804881i \(0.702229\pi\)
\(110\) −4.28380 + 7.41976i −0.408445 + 0.707447i
\(111\) 2.58664 + 4.48019i 0.245513 + 0.425240i
\(112\) 2.56214 4.43776i 0.242100 0.419329i
\(113\) −8.32725 14.4232i −0.783361 1.35682i −0.929973 0.367628i \(-0.880170\pi\)
0.146612 0.989194i \(-0.453163\pi\)
\(114\) −2.09100 3.62172i −0.195840 0.339205i
\(115\) 0.543165 + 0.940789i 0.0506504 + 0.0877291i
\(116\) 11.8277 1.09818
\(117\) 1.38465 2.39828i 0.128011 0.221721i
\(118\) 2.22860 3.86006i 0.205160 0.355347i
\(119\) −2.44865 4.24118i −0.224467 0.388789i
\(120\) 0.869083 0.0793360
\(121\) 1.83826 3.18396i 0.167115 0.289451i
\(122\) −20.4350 −1.85009
\(123\) 2.76022 0.248881
\(124\) −5.39908 + 5.84013i −0.484852 + 0.524459i
\(125\) 12.0996 1.08222
\(126\) 5.45545 0.486010
\(127\) −4.96085 + 8.59244i −0.440204 + 0.762456i −0.997704 0.0677208i \(-0.978427\pi\)
0.557500 + 0.830177i \(0.311761\pi\)
\(128\) −8.12023 −0.717734
\(129\) 1.74793 + 3.02750i 0.153897 + 0.266557i
\(130\) −1.58296 + 2.74177i −0.138835 + 0.240469i
\(131\) 9.78575 16.9494i 0.854985 1.48088i −0.0216736 0.999765i \(-0.506899\pi\)
0.876659 0.481113i \(-0.159767\pi\)
\(132\) −1.85678 −0.161612
\(133\) −2.50141 4.33257i −0.216900 0.375681i
\(134\) 4.43909 + 7.68873i 0.383479 + 0.664205i
\(135\) 2.36903 + 4.10329i 0.203894 + 0.353155i
\(136\) −2.43556 + 4.21851i −0.208847 + 0.361734i
\(137\) 6.48511 + 11.2325i 0.554060 + 0.959660i 0.997976 + 0.0635918i \(0.0202556\pi\)
−0.443916 + 0.896068i \(0.646411\pi\)
\(138\) −0.282528 + 0.489353i −0.0240504 + 0.0416565i
\(139\) 15.0973 1.28054 0.640270 0.768150i \(-0.278823\pi\)
0.640270 + 0.768150i \(0.278823\pi\)
\(140\) −2.59857 −0.219619
\(141\) 0.421850 0.730666i 0.0355262 0.0615332i
\(142\) 11.2233 + 19.4393i 0.941839 + 1.63131i
\(143\) −1.35310 + 2.34363i −0.113152 + 0.195984i
\(144\) −6.66902 11.5511i −0.555752 0.962591i
\(145\) 7.07861 + 12.2605i 0.587846 + 1.01818i
\(146\) 7.24217 + 12.5438i 0.599367 + 1.03813i
\(147\) 2.81854 0.232469
\(148\) −7.69273 + 13.3242i −0.632339 + 1.09524i
\(149\) −6.98591 + 12.1000i −0.572308 + 0.991267i 0.424020 + 0.905653i \(0.360619\pi\)
−0.996328 + 0.0856144i \(0.972715\pi\)
\(150\) 0.923392 + 1.59936i 0.0753946 + 0.130587i
\(151\) 20.0585 1.63233 0.816167 0.577816i \(-0.196095\pi\)
0.816167 + 0.577816i \(0.196095\pi\)
\(152\) −2.48804 + 4.30941i −0.201806 + 0.349539i
\(153\) −12.7472 −1.03055
\(154\) −5.33114 −0.429595
\(155\) −9.28502 2.10146i −0.745791 0.168793i
\(156\) −0.686124 −0.0549339
\(157\) −7.66309 −0.611582 −0.305791 0.952099i \(-0.598921\pi\)
−0.305791 + 0.952099i \(0.598921\pi\)
\(158\) 5.73209 9.92826i 0.456020 0.789850i
\(159\) −0.685800 −0.0543875
\(160\) 5.81480 + 10.0715i 0.459700 + 0.796224i
\(161\) −0.337981 + 0.585400i −0.0266366 + 0.0461360i
\(162\) 6.45925 11.1877i 0.507486 0.878992i
\(163\) −10.1777 −0.797176 −0.398588 0.917130i \(-0.630500\pi\)
−0.398588 + 0.917130i \(0.630500\pi\)
\(164\) 4.10449 + 7.10918i 0.320507 + 0.555134i
\(165\) −1.11124 1.92472i −0.0865098 0.149839i
\(166\) −7.86099 13.6156i −0.610131 1.05678i
\(167\) −1.30887 + 2.26703i −0.101284 + 0.175428i −0.912214 0.409715i \(-0.865628\pi\)
0.810930 + 0.585143i \(0.198962\pi\)
\(168\) 0.270391 + 0.468330i 0.0208611 + 0.0361325i
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) 14.5729 1.11769
\(171\) −13.0219 −0.995808
\(172\) −5.19840 + 9.00389i −0.396374 + 0.686540i
\(173\) −0.582073 1.00818i −0.0442542 0.0766506i 0.843050 0.537835i \(-0.180758\pi\)
−0.887304 + 0.461185i \(0.847424\pi\)
\(174\) −3.68195 + 6.37732i −0.279128 + 0.483463i
\(175\) 1.10463 + 1.91328i 0.0835022 + 0.144630i
\(176\) 6.51706 + 11.2879i 0.491242 + 0.850856i
\(177\) 0.578111 + 1.00132i 0.0434535 + 0.0752636i
\(178\) −12.9688 −0.972051
\(179\) −7.76515 + 13.4496i −0.580394 + 1.00527i 0.415038 + 0.909804i \(0.363768\pi\)
−0.995432 + 0.0954683i \(0.969565\pi\)
\(180\) −3.38192 + 5.85766i −0.252073 + 0.436604i
\(181\) 2.78262 + 4.81964i 0.206830 + 0.358241i 0.950714 0.310068i \(-0.100352\pi\)
−0.743884 + 0.668309i \(0.767018\pi\)
\(182\) −1.96998 −0.146024
\(183\) 2.65046 4.59073i 0.195928 0.339357i
\(184\) 0.672348 0.0495662
\(185\) −18.4156 −1.35394
\(186\) −1.46818 4.72911i −0.107652 0.346755i
\(187\) 12.4567 0.910928
\(188\) 2.50919 0.183002
\(189\) −1.47412 + 2.55325i −0.107226 + 0.185721i
\(190\) 14.8869 1.08001
\(191\) −3.43734 5.95365i −0.248717 0.430791i 0.714453 0.699684i \(-0.246676\pi\)
−0.963170 + 0.268893i \(0.913342\pi\)
\(192\) −0.711170 + 1.23178i −0.0513242 + 0.0888962i
\(193\) 11.7763 20.3971i 0.847675 1.46822i −0.0356036 0.999366i \(-0.511335\pi\)
0.883278 0.468849i \(-0.155331\pi\)
\(194\) 16.9008 1.21341
\(195\) −0.410628 0.711229i −0.0294057 0.0509321i
\(196\) 4.19121 + 7.25938i 0.299372 + 0.518527i
\(197\) 2.73347 + 4.73452i 0.194752 + 0.337320i 0.946819 0.321766i \(-0.104276\pi\)
−0.752067 + 0.659086i \(0.770943\pi\)
\(198\) −6.93823 + 12.0174i −0.493079 + 0.854037i
\(199\) 0.434015 + 0.751736i 0.0307665 + 0.0532891i 0.880999 0.473119i \(-0.156872\pi\)
−0.850232 + 0.526408i \(0.823539\pi\)
\(200\) 1.09872 1.90305i 0.0776916 0.134566i
\(201\) −2.30304 −0.162444
\(202\) −26.0543 −1.83317
\(203\) −4.40462 + 7.62902i −0.309144 + 0.535452i
\(204\) 1.57913 + 2.73514i 0.110561 + 0.191498i
\(205\) −4.91286 + 8.50933i −0.343129 + 0.594317i
\(206\) 10.5705 + 18.3086i 0.736480 + 1.27562i
\(207\) 0.879733 + 1.52374i 0.0611457 + 0.105907i
\(208\) 2.40820 + 4.17113i 0.166979 + 0.289216i
\(209\) 12.7252 0.880217
\(210\) 0.808928 1.40110i 0.0558213 0.0966854i
\(211\) −3.48542 + 6.03692i −0.239946 + 0.415599i −0.960699 0.277594i \(-0.910463\pi\)
0.720753 + 0.693192i \(0.243796\pi\)
\(212\) −1.01979 1.76634i −0.0700398 0.121312i
\(213\) −5.82276 −0.398969
\(214\) −17.6027 + 30.4887i −1.20329 + 2.08417i
\(215\) −12.4444 −0.848704
\(216\) 2.93247 0.199529
\(217\) −1.75634 5.65731i −0.119228 0.384044i
\(218\) 22.9439 1.55396
\(219\) −3.75731 −0.253895
\(220\) 3.30486 5.72418i 0.222813 0.385924i
\(221\) 4.60305 0.309635
\(222\) −4.78946 8.29558i −0.321447 0.556763i
\(223\) 3.62959 6.28663i 0.243055 0.420984i −0.718528 0.695498i \(-0.755184\pi\)
0.961583 + 0.274514i \(0.0885170\pi\)
\(224\) −3.61822 + 6.26695i −0.241753 + 0.418728i
\(225\) 5.75050 0.383367
\(226\) 15.4189 + 26.7062i 1.02565 + 1.77647i
\(227\) 1.56075 + 2.70329i 0.103590 + 0.179424i 0.913161 0.407598i \(-0.133634\pi\)
−0.809571 + 0.587022i \(0.800300\pi\)
\(228\) 1.61316 + 2.79407i 0.106834 + 0.185042i
\(229\) 12.3556 21.4005i 0.816481 1.41419i −0.0917786 0.995779i \(-0.529255\pi\)
0.908260 0.418407i \(-0.137411\pi\)
\(230\) −1.00573 1.74198i −0.0663160 0.114863i
\(231\) 0.691461 1.19765i 0.0454948 0.0787993i
\(232\) 8.76214 0.575263
\(233\) −15.0588 −0.986534 −0.493267 0.869878i \(-0.664197\pi\)
−0.493267 + 0.869878i \(0.664197\pi\)
\(234\) −2.56383 + 4.44069i −0.167603 + 0.290297i
\(235\) 1.50169 + 2.60100i 0.0979593 + 0.169670i
\(236\) −1.71932 + 2.97795i −0.111918 + 0.193848i
\(237\) 1.48693 + 2.57544i 0.0965865 + 0.167293i
\(238\) 4.53395 + 7.85304i 0.293893 + 0.509037i
\(239\) −9.36069 16.2132i −0.605493 1.04874i −0.991973 0.126447i \(-0.959643\pi\)
0.386480 0.922298i \(-0.373691\pi\)
\(240\) −3.95550 −0.255327
\(241\) 3.71497 6.43452i 0.239302 0.414484i −0.721212 0.692714i \(-0.756415\pi\)
0.960514 + 0.278231i \(0.0897480\pi\)
\(242\) −3.40375 + 5.89547i −0.218801 + 0.378975i
\(243\) 5.83220 + 10.1017i 0.374136 + 0.648022i
\(244\) 15.7651 1.00926
\(245\) −5.01666 + 8.68912i −0.320503 + 0.555127i
\(246\) −5.11086 −0.325857
\(247\) 4.70224 0.299196
\(248\) −3.99971 + 4.32644i −0.253982 + 0.274729i
\(249\) 4.07836 0.258455
\(250\) −22.4037 −1.41694
\(251\) 12.3850 21.4514i 0.781732 1.35400i −0.149199 0.988807i \(-0.547670\pi\)
0.930932 0.365193i \(-0.118997\pi\)
\(252\) −4.20876 −0.265127
\(253\) −0.859687 1.48902i −0.0540481 0.0936140i
\(254\) 9.18559 15.9099i 0.576355 0.998276i
\(255\) −1.89014 + 3.27382i −0.118365 + 0.205015i
\(256\) 20.9580 1.30988
\(257\) −7.26926 12.5907i −0.453444 0.785388i 0.545153 0.838337i \(-0.316472\pi\)
−0.998597 + 0.0529481i \(0.983138\pi\)
\(258\) −3.23650 5.60577i −0.201495 0.349000i
\(259\) −5.72951 9.92379i −0.356014 0.616635i
\(260\) 1.22122 2.11522i 0.0757369 0.131180i
\(261\) 11.4648 + 19.8576i 0.709654 + 1.22916i
\(262\) −18.1195 + 31.3838i −1.11942 + 1.93890i
\(263\) 18.1161 1.11708 0.558542 0.829476i \(-0.311361\pi\)
0.558542 + 0.829476i \(0.311361\pi\)
\(264\) −1.37553 −0.0846580
\(265\) 1.22064 2.11422i 0.0749835 0.129875i
\(266\) 4.63165 + 8.02225i 0.283985 + 0.491876i
\(267\) 1.68208 2.91345i 0.102942 0.178300i
\(268\) −3.42466 5.93168i −0.209194 0.362335i
\(269\) 9.37251 + 16.2337i 0.571452 + 0.989783i 0.996417 + 0.0845739i \(0.0269529\pi\)
−0.424965 + 0.905210i \(0.639714\pi\)
\(270\) −4.38654 7.59771i −0.266956 0.462382i
\(271\) 1.64819 0.100121 0.0500603 0.998746i \(-0.484059\pi\)
0.0500603 + 0.998746i \(0.484059\pi\)
\(272\) 11.0851 19.1999i 0.672132 1.16417i
\(273\) 0.255511 0.442558i 0.0154642 0.0267848i
\(274\) −12.0079 20.7983i −0.725425 1.25647i
\(275\) −5.61947 −0.338867
\(276\) 0.217964 0.377525i 0.0131199 0.0227243i
\(277\) −3.48177 −0.209199 −0.104600 0.994514i \(-0.533356\pi\)
−0.104600 + 0.994514i \(0.533356\pi\)
\(278\) −27.9545 −1.67660
\(279\) −15.0384 3.40362i −0.900327 0.203769i
\(280\) −1.92505 −0.115044
\(281\) 14.8454 0.885601 0.442800 0.896620i \(-0.353985\pi\)
0.442800 + 0.896620i \(0.353985\pi\)
\(282\) −0.781104 + 1.35291i −0.0465141 + 0.0805648i
\(283\) 11.2319 0.667664 0.333832 0.942633i \(-0.391658\pi\)
0.333832 + 0.942633i \(0.391658\pi\)
\(284\) −8.65853 14.9970i −0.513789 0.889909i
\(285\) −1.93087 + 3.34436i −0.114375 + 0.198103i
\(286\) 2.50541 4.33950i 0.148148 0.256600i
\(287\) −6.11400 −0.360898
\(288\) 9.41790 + 16.3123i 0.554955 + 0.961210i
\(289\) −2.09405 3.62700i −0.123179 0.213353i
\(290\) −13.1069 22.7017i −0.769661 1.33309i
\(291\) −2.19208 + 3.79679i −0.128502 + 0.222572i
\(292\) −5.58718 9.67727i −0.326965 0.566319i
\(293\) −5.76767 + 9.98989i −0.336951 + 0.583616i −0.983858 0.178953i \(-0.942729\pi\)
0.646907 + 0.762569i \(0.276062\pi\)
\(294\) −5.21885 −0.304369
\(295\) −4.11587 −0.239635
\(296\) −5.69887 + 9.87074i −0.331240 + 0.573725i
\(297\) −3.74956 6.49443i −0.217571 0.376845i
\(298\) 12.9352 22.4045i 0.749318 1.29786i
\(299\) −0.317674 0.550228i −0.0183716 0.0318205i
\(300\) −0.712376 1.23387i −0.0411291 0.0712376i
\(301\) −3.87174 6.70605i −0.223163 0.386530i
\(302\) −37.1405 −2.13720
\(303\) 3.37930 5.85313i 0.194136 0.336253i
\(304\) 11.3239 19.6136i 0.649472 1.12492i
\(305\) 9.43502 + 16.3419i 0.540248 + 0.935736i
\(306\) 23.6029 1.34929
\(307\) 14.2772 24.7288i 0.814842 1.41135i −0.0945991 0.995515i \(-0.530157\pi\)
0.909441 0.415833i \(-0.136510\pi\)
\(308\) 4.11285 0.234352
\(309\) −5.48407 −0.311978
\(310\) 17.1923 + 3.89110i 0.976457 + 0.221000i
\(311\) −9.85332 −0.558730 −0.279365 0.960185i \(-0.590124\pi\)
−0.279365 + 0.960185i \(0.590124\pi\)
\(312\) −0.508290 −0.0287762
\(313\) −0.00983697 + 0.0170381i −0.000556019 + 0.000963053i −0.866303 0.499518i \(-0.833510\pi\)
0.865747 + 0.500481i \(0.166844\pi\)
\(314\) 14.1891 0.800737
\(315\) −2.51883 4.36275i −0.141920 0.245813i
\(316\) −4.42218 + 7.65943i −0.248767 + 0.430877i
\(317\) −2.50984 + 4.34717i −0.140967 + 0.244161i −0.927861 0.372926i \(-0.878354\pi\)
0.786894 + 0.617088i \(0.211688\pi\)
\(318\) 1.26984 0.0712090
\(319\) −11.2036 19.4052i −0.627280 1.08648i
\(320\) −2.53160 4.38485i −0.141520 0.245121i
\(321\) −4.56622 7.90892i −0.254861 0.441433i
\(322\) 0.625811 1.08394i 0.0348751 0.0604054i
\(323\) −10.8223 18.7448i −0.602170 1.04299i
\(324\) −4.98316 + 8.63109i −0.276842 + 0.479505i
\(325\) −2.07652 −0.115185
\(326\) 18.8451 1.04373
\(327\) −2.97588 + 5.15438i −0.164567 + 0.285038i
\(328\) 3.04066 + 5.26657i 0.167892 + 0.290798i
\(329\) −0.934415 + 1.61845i −0.0515160 + 0.0892283i
\(330\) 2.05759 + 3.56384i 0.113266 + 0.196183i
\(331\) 0.399168 + 0.691380i 0.0219403 + 0.0380017i 0.876787 0.480879i \(-0.159682\pi\)
−0.854847 + 0.518880i \(0.826349\pi\)
\(332\) 6.06458 + 10.5042i 0.332837 + 0.576491i
\(333\) −29.8267 −1.63450
\(334\) 2.42353 4.19768i 0.132610 0.229687i
\(335\) 4.09914 7.09992i 0.223960 0.387910i
\(336\) −1.23064 2.13154i −0.0671371 0.116285i
\(337\) 22.3424 1.21707 0.608535 0.793527i \(-0.291758\pi\)
0.608535 + 0.793527i \(0.291758\pi\)
\(338\) 0.925808 1.60355i 0.0503573 0.0872214i
\(339\) −7.99945 −0.434470
\(340\) −11.2427 −0.609720
\(341\) 14.6958 + 3.32606i 0.795820 + 0.180116i
\(342\) 24.1115 1.30380
\(343\) −13.6906 −0.739225
\(344\) −3.85104 + 6.67020i −0.207634 + 0.359633i
\(345\) 0.521784 0.0280919
\(346\) 1.07778 + 1.86676i 0.0579416 + 0.100358i
\(347\) 3.46154 5.99556i 0.185825 0.321858i −0.758029 0.652221i \(-0.773838\pi\)
0.943854 + 0.330362i \(0.107171\pi\)
\(348\) 2.84054 4.91996i 0.152269 0.263737i
\(349\) 1.31962 0.0706374 0.0353187 0.999376i \(-0.488755\pi\)
0.0353187 + 0.999376i \(0.488755\pi\)
\(350\) −2.04535 3.54265i −0.109329 0.189363i
\(351\) −1.38555 2.39984i −0.0739551 0.128094i
\(352\) −9.20330 15.9406i −0.490537 0.849636i
\(353\) 6.18537 10.7134i 0.329214 0.570216i −0.653142 0.757235i \(-0.726550\pi\)
0.982356 + 0.187020i \(0.0598828\pi\)
\(354\) −1.07044 1.85405i −0.0568932 0.0985419i
\(355\) 10.3638 17.9507i 0.550055 0.952723i
\(356\) 10.0051 0.530270
\(357\) −2.35226 −0.124495
\(358\) 14.3781 24.9035i 0.759904 1.31619i
\(359\) 6.59418 + 11.4214i 0.348027 + 0.602801i 0.985899 0.167342i \(-0.0535183\pi\)
−0.637872 + 0.770143i \(0.720185\pi\)
\(360\) −2.50537 + 4.33942i −0.132044 + 0.228708i
\(361\) −1.55551 2.69422i −0.0818688 0.141801i
\(362\) −5.15234 8.92411i −0.270801 0.469041i
\(363\) −0.882949 1.52931i −0.0463428 0.0802681i
\(364\) 1.51979 0.0796588
\(365\) 6.68757 11.5832i 0.350043 0.606293i
\(366\) −4.90764 + 8.50028i −0.256526 + 0.444317i
\(367\) 8.08565 + 14.0048i 0.422067 + 0.731042i 0.996142 0.0877611i \(-0.0279712\pi\)
−0.574074 + 0.818803i \(0.694638\pi\)
\(368\) −3.06009 −0.159518
\(369\) −7.95708 + 13.7821i −0.414229 + 0.717466i
\(370\) 34.0987 1.77271
\(371\) 1.51907 0.0788664
\(372\) 1.13266 + 3.64840i 0.0587259 + 0.189161i
\(373\) −29.8424 −1.54518 −0.772589 0.634906i \(-0.781039\pi\)
−0.772589 + 0.634906i \(0.781039\pi\)
\(374\) −23.0651 −1.19267
\(375\) 2.90582 5.03303i 0.150056 0.259904i
\(376\) 1.85884 0.0958623
\(377\) −4.13998 7.17065i −0.213220 0.369307i
\(378\) 2.72950 4.72763i 0.140390 0.243163i
\(379\) 17.3471 30.0460i 0.891058 1.54336i 0.0524497 0.998624i \(-0.483297\pi\)
0.838609 0.544735i \(-0.183370\pi\)
\(380\) −11.4849 −0.589164
\(381\) 2.38278 + 4.12710i 0.122074 + 0.211438i
\(382\) 6.36463 + 11.0239i 0.325643 + 0.564030i
\(383\) −4.34955 7.53364i −0.222252 0.384951i 0.733240 0.679970i \(-0.238007\pi\)
−0.955491 + 0.295019i \(0.904674\pi\)
\(384\) −1.95015 + 3.37775i −0.0995179 + 0.172370i
\(385\) 2.46144 + 4.26334i 0.125447 + 0.217280i
\(386\) −21.8051 + 37.7676i −1.10985 + 1.92232i
\(387\) −20.1556 −1.02456
\(388\) −13.0386 −0.661936
\(389\) −15.9065 + 27.5509i −0.806491 + 1.39688i 0.108789 + 0.994065i \(0.465303\pi\)
−0.915280 + 0.402819i \(0.868030\pi\)
\(390\) 0.760325 + 1.31692i 0.0385006 + 0.0666849i
\(391\) −1.46227 + 2.53273i −0.0739502 + 0.128086i
\(392\) 3.10490 + 5.37784i 0.156821 + 0.271622i
\(393\) −4.70027 8.14111i −0.237097 0.410665i
\(394\) −5.06134 8.76650i −0.254987 0.441650i
\(395\) −10.5862 −0.532652
\(396\) 5.35269 9.27113i 0.268983 0.465892i
\(397\) −9.46830 + 16.3996i −0.475201 + 0.823072i −0.999597 0.0284030i \(-0.990958\pi\)
0.524396 + 0.851475i \(0.324291\pi\)
\(398\) −0.803628 1.39193i −0.0402823 0.0697709i
\(399\) −2.40294 −0.120298
\(400\) −5.00069 + 8.66144i −0.250034 + 0.433072i
\(401\) −9.39135 −0.468982 −0.234491 0.972118i \(-0.575342\pi\)
−0.234491 + 0.972118i \(0.575342\pi\)
\(402\) 4.26435 0.212686
\(403\) 5.43042 + 1.22906i 0.270508 + 0.0612236i
\(404\) 20.1003 1.00003
\(405\) −11.9292 −0.592766
\(406\) 8.15566 14.1260i 0.404759 0.701063i
\(407\) 29.1471 1.44477
\(408\) 1.16984 + 2.02623i 0.0579158 + 0.100313i
\(409\) 1.42983 2.47653i 0.0707003 0.122457i −0.828508 0.559977i \(-0.810810\pi\)
0.899208 + 0.437521i \(0.144143\pi\)
\(410\) 9.09673 15.7560i 0.449256 0.778134i
\(411\) 6.22983 0.307295
\(412\) −8.15489 14.1247i −0.401762 0.695873i
\(413\) −1.28054 2.21796i −0.0630112 0.109139i
\(414\) −1.62893 2.82139i −0.0800574 0.138664i
\(415\) −7.25900 + 12.5730i −0.356330 + 0.617182i
\(416\) −3.40083 5.89041i −0.166739 0.288801i
\(417\) 3.62576 6.28000i 0.177554 0.307533i
\(418\) −23.5621 −1.15246
\(419\) −14.6691 −0.716635 −0.358317 0.933600i \(-0.616649\pi\)
−0.358317 + 0.933600i \(0.616649\pi\)
\(420\) −0.624070 + 1.08092i −0.0304515 + 0.0527435i
\(421\) 1.66838 + 2.88972i 0.0813118 + 0.140836i 0.903814 0.427926i \(-0.140756\pi\)
−0.822502 + 0.568762i \(0.807422\pi\)
\(422\) 6.45365 11.1781i 0.314159 0.544139i
\(423\) 2.43220 + 4.21269i 0.118257 + 0.204828i
\(424\) −0.755477 1.30852i −0.0366892 0.0635476i
\(425\) 4.77917 + 8.27777i 0.231824 + 0.401531i
\(426\) 10.7815 0.522366
\(427\) −5.87088 + 10.1687i −0.284112 + 0.492096i
\(428\) 13.5801 23.5214i 0.656417 1.13695i
\(429\) 0.649916 + 1.12569i 0.0313783 + 0.0543487i
\(430\) 23.0423 1.11120
\(431\) 9.98926 17.3019i 0.481166 0.833404i −0.518601 0.855017i \(-0.673547\pi\)
0.999766 + 0.0216129i \(0.00688014\pi\)
\(432\) −13.3467 −0.642144
\(433\) 18.1053 0.870087 0.435044 0.900409i \(-0.356733\pi\)
0.435044 + 0.900409i \(0.356733\pi\)
\(434\) 3.25207 + 10.4752i 0.156104 + 0.502824i
\(435\) 6.79996 0.326033
\(436\) −17.7007 −0.847711
\(437\) −1.49378 + 2.58730i −0.0714571 + 0.123767i
\(438\) 6.95709 0.332423
\(439\) 5.34110 + 9.25105i 0.254917 + 0.441528i 0.964873 0.262717i \(-0.0846187\pi\)
−0.709956 + 0.704246i \(0.751285\pi\)
\(440\) 2.44828 4.24055i 0.116717 0.202160i
\(441\) −8.12520 + 14.0733i −0.386914 + 0.670155i
\(442\) −8.52308 −0.405402
\(443\) 8.27714 + 14.3364i 0.393259 + 0.681144i 0.992877 0.119142i \(-0.0380143\pi\)
−0.599619 + 0.800286i \(0.704681\pi\)
\(444\) 3.69496 + 6.39985i 0.175355 + 0.303724i
\(445\) 5.98781 + 10.3712i 0.283850 + 0.491642i
\(446\) −6.72060 + 11.6404i −0.318230 + 0.551190i
\(447\) 3.35546 + 5.81183i 0.158708 + 0.274890i
\(448\) 1.57527 2.72845i 0.0744245 0.128907i
\(449\) 32.4331 1.53061 0.765305 0.643667i \(-0.222588\pi\)
0.765305 + 0.643667i \(0.222588\pi\)
\(450\) −10.6477 −0.501938
\(451\) 7.77577 13.4680i 0.366147 0.634185i
\(452\) −11.8953 20.6033i −0.559508 0.969096i
\(453\) 4.81722 8.34366i 0.226333 0.392019i
\(454\) −2.88990 5.00546i −0.135630 0.234918i
\(455\) 0.909558 + 1.57540i 0.0426407 + 0.0738559i
\(456\) 1.19505 + 2.06988i 0.0559633 + 0.0969312i
\(457\) 5.20588 0.243521 0.121760 0.992560i \(-0.461146\pi\)
0.121760 + 0.992560i \(0.461146\pi\)
\(458\) −22.8778 + 39.6255i −1.06901 + 1.85158i
\(459\) −6.37775 + 11.0466i −0.297688 + 0.515610i
\(460\) 0.775900 + 1.34390i 0.0361765 + 0.0626596i
\(461\) 11.7156 0.545649 0.272824 0.962064i \(-0.412042\pi\)
0.272824 + 0.962064i \(0.412042\pi\)
\(462\) −1.28032 + 2.21758i −0.0595659 + 0.103171i
\(463\) −15.7560 −0.732245 −0.366123 0.930567i \(-0.619315\pi\)
−0.366123 + 0.930567i \(0.619315\pi\)
\(464\) −39.8796 −1.85136
\(465\) −3.10402 + 3.35758i −0.143946 + 0.155704i
\(466\) 27.8831 1.29166
\(467\) −8.65616 −0.400559 −0.200280 0.979739i \(-0.564185\pi\)
−0.200280 + 0.979739i \(0.564185\pi\)
\(468\) 1.97794 3.42589i 0.0914303 0.158362i
\(469\) 5.10133 0.235558
\(470\) −2.78055 4.81605i −0.128257 0.222148i
\(471\) −1.84036 + 3.18760i −0.0847993 + 0.146877i
\(472\) −1.27369 + 2.20610i −0.0586265 + 0.101544i
\(473\) 19.6963 0.905636
\(474\) −2.75322 4.76872i −0.126460 0.219035i
\(475\) 4.88215 + 8.45613i 0.224008 + 0.387994i
\(476\) −3.49784 6.05844i −0.160323 0.277688i
\(477\) 1.97701 3.42427i 0.0905209 0.156787i
\(478\) 17.3324 + 30.0206i 0.792766 + 1.37311i
\(479\) −15.2885 + 26.4804i −0.698549 + 1.20992i 0.270421 + 0.962742i \(0.412837\pi\)
−0.968970 + 0.247180i \(0.920496\pi\)
\(480\) 5.58590 0.254960
\(481\) 10.7705 0.491093
\(482\) −6.87869 + 11.9142i −0.313316 + 0.542679i
\(483\) 0.162338 + 0.281178i 0.00738665 + 0.0127941i
\(484\) 2.62592 4.54822i 0.119360 0.206737i
\(485\) −7.80328 13.5157i −0.354329 0.613716i
\(486\) −10.7990 18.7044i −0.489852 0.848449i
\(487\) −13.0319 22.5720i −0.590534 1.02283i −0.994161 0.107911i \(-0.965584\pi\)
0.403627 0.914924i \(-0.367750\pi\)
\(488\) 11.6790 0.528683
\(489\) −2.44426 + 4.23357i −0.110533 + 0.191449i
\(490\) 9.28893 16.0889i 0.419631 0.726822i
\(491\) 14.5108 + 25.1335i 0.654865 + 1.13426i 0.981928 + 0.189257i \(0.0606081\pi\)
−0.327062 + 0.945003i \(0.606059\pi\)
\(492\) 3.94292 0.177760
\(493\) −19.0565 + 33.0069i −0.858263 + 1.48656i
\(494\) −8.70673 −0.391734
\(495\) 12.8138 0.575937
\(496\) 18.2041 19.6912i 0.817388 0.884159i
\(497\) 12.8977 0.578539
\(498\) −7.55155 −0.338393
\(499\) 9.69877 16.7988i 0.434177 0.752016i −0.563051 0.826422i \(-0.690373\pi\)
0.997228 + 0.0744057i \(0.0237060\pi\)
\(500\) 17.2840 0.772963
\(501\) 0.628675 + 1.08890i 0.0280871 + 0.0486483i
\(502\) −22.9322 + 39.7197i −1.02351 + 1.77278i
\(503\) 3.74310 6.48324i 0.166897 0.289073i −0.770431 0.637524i \(-0.779959\pi\)
0.937327 + 0.348450i \(0.113292\pi\)
\(504\) −3.11790 −0.138882
\(505\) 12.0295 + 20.8357i 0.535307 + 0.927178i
\(506\) 1.59181 + 2.75710i 0.0707646 + 0.122568i
\(507\) 0.240159 + 0.415967i 0.0106658 + 0.0184738i
\(508\) −7.08647 + 12.2741i −0.314411 + 0.544577i
\(509\) −1.25885 2.18038i −0.0557973 0.0966438i 0.836778 0.547543i \(-0.184437\pi\)
−0.892575 + 0.450899i \(0.851103\pi\)
\(510\) 3.49982 6.06186i 0.154975 0.268424i
\(511\) 8.32259 0.368170
\(512\) −22.5658 −0.997275
\(513\) −6.51517 + 11.2846i −0.287652 + 0.498228i
\(514\) 13.4599 + 23.3132i 0.593690 + 1.02830i
\(515\) 9.76099 16.9065i 0.430121 0.744991i
\(516\) 2.49688 + 4.32473i 0.109919 + 0.190386i
\(517\) −2.37678 4.11670i −0.104530 0.181052i
\(518\) 10.6088 + 18.3750i 0.466126 + 0.807353i
\(519\) −0.559160 −0.0245444
\(520\) 0.904695 1.56698i 0.0396735 0.0687165i
\(521\) −16.1216 + 27.9234i −0.706299 + 1.22335i 0.259922 + 0.965630i \(0.416303\pi\)
−0.966221 + 0.257716i \(0.917030\pi\)
\(522\) −21.2284 36.7687i −0.929143 1.60932i
\(523\) −32.9410 −1.44041 −0.720204 0.693763i \(-0.755952\pi\)
−0.720204 + 0.693763i \(0.755952\pi\)
\(524\) 13.9787 24.2119i 0.610664 1.05770i
\(525\) 1.06115 0.0463123
\(526\) −33.5440 −1.46259
\(527\) −7.59879 24.4763i −0.331008 1.06620i
\(528\) 6.26052 0.272454
\(529\) −22.5963 −0.982449
\(530\) −2.26016 + 3.91471i −0.0981751 + 0.170044i
\(531\) −6.66625 −0.289290
\(532\) −3.57321 6.18899i −0.154918 0.268327i
\(533\) 2.87333 4.97675i 0.124458 0.215567i
\(534\) −3.11457 + 5.39459i −0.134781 + 0.233447i
\(535\) 32.5093 1.40550
\(536\) −2.53703 4.39426i −0.109583 0.189803i
\(537\) 3.72974 + 6.46010i 0.160950 + 0.278774i
\(538\) −17.3543 30.0585i −0.748196 1.29591i
\(539\) 7.94006 13.7526i 0.342003 0.592366i
\(540\) 3.38412 + 5.86146i 0.145629 + 0.252237i
\(541\) −5.10494 + 8.84202i −0.219479 + 0.380148i −0.954649 0.297734i \(-0.903769\pi\)
0.735170 + 0.677883i \(0.237102\pi\)
\(542\) −3.05182 −0.131087
\(543\) 2.67308 0.114713
\(544\) −15.6542 + 27.1139i −0.671168 + 1.16250i
\(545\) −10.5934 18.3484i −0.453773 0.785958i
\(546\) −0.473108 + 0.819446i −0.0202471 + 0.0350691i
\(547\) −15.0649 26.0932i −0.644128 1.11566i −0.984502 0.175373i \(-0.943887\pi\)
0.340374 0.940290i \(-0.389446\pi\)
\(548\) 9.26384 + 16.0454i 0.395732 + 0.685428i
\(549\) 15.2814 + 26.4681i 0.652193 + 1.12963i
\(550\) 10.4051 0.443675
\(551\) −19.4671 + 33.7181i −0.829328 + 1.43644i
\(552\) 0.161470 0.279675i 0.00687264 0.0119038i
\(553\) −3.29361 5.70470i −0.140059 0.242589i
\(554\) 6.44690 0.273902
\(555\) −4.42268 + 7.66030i −0.187732 + 0.325162i
\(556\) 21.5662 0.914612
\(557\) 23.4342 0.992938 0.496469 0.868055i \(-0.334630\pi\)
0.496469 + 0.868055i \(0.334630\pi\)
\(558\) 27.8454 + 6.30219i 1.17879 + 0.266793i
\(559\) 7.27823 0.307836
\(560\) 8.76160 0.370245
\(561\) 2.99160 5.18160i 0.126305 0.218767i
\(562\) −27.4879 −1.15951
\(563\) 4.71443 + 8.16564i 0.198690 + 0.344141i 0.948104 0.317961i \(-0.102998\pi\)
−0.749414 + 0.662102i \(0.769665\pi\)
\(564\) 0.602604 1.04374i 0.0253742 0.0439494i
\(565\) 14.2381 24.6611i 0.599000 1.03750i
\(566\) −20.7971 −0.874166
\(567\) −3.71143 6.42839i −0.155866 0.269967i
\(568\) −6.41435 11.1100i −0.269140 0.466164i
\(569\) −20.1124 34.8356i −0.843154 1.46039i −0.887215 0.461357i \(-0.847363\pi\)
0.0440609 0.999029i \(-0.485970\pi\)
\(570\) 3.57523 6.19248i 0.149750 0.259374i
\(571\) 15.8757 + 27.4975i 0.664377 + 1.15073i 0.979454 + 0.201668i \(0.0646362\pi\)
−0.315077 + 0.949066i \(0.602030\pi\)
\(572\) −1.93287 + 3.34783i −0.0808174 + 0.139980i
\(573\) −3.30203 −0.137944
\(574\) 11.3208 0.472520
\(575\) 0.659657 1.14256i 0.0275096 0.0476480i
\(576\) −4.10028 7.10189i −0.170845 0.295912i
\(577\) 1.41944 2.45855i 0.0590922 0.102351i −0.834966 0.550302i \(-0.814513\pi\)
0.894058 + 0.447951i \(0.147846\pi\)
\(578\) 3.87737 + 6.71580i 0.161277 + 0.279341i
\(579\) −5.65635 9.79709i −0.235070 0.407153i
\(580\) 10.1116 + 17.5139i 0.419863 + 0.727225i
\(581\) −9.03373 −0.374782
\(582\) 4.05889 7.03020i 0.168246 0.291411i
\(583\) −1.93196 + 3.34625i −0.0800135 + 0.138587i
\(584\) −4.13905 7.16904i −0.171275 0.296657i
\(585\) 4.73499 0.195768
\(586\) 10.6795 18.4974i 0.441166 0.764122i
\(587\) 38.1659 1.57528 0.787638 0.616139i \(-0.211304\pi\)
0.787638 + 0.616139i \(0.211304\pi\)
\(588\) 4.02622 0.166039
\(589\) −7.76252 25.0037i −0.319849 1.03026i
\(590\) 7.62102 0.313752
\(591\) 2.62587 0.108014
\(592\) 25.9376 44.9252i 1.06603 1.84642i
\(593\) −26.5339 −1.08962 −0.544809 0.838560i \(-0.683398\pi\)
−0.544809 + 0.838560i \(0.683398\pi\)
\(594\) 6.94274 + 12.0252i 0.284864 + 0.493399i
\(595\) 4.18674 7.25165i 0.171640 0.297289i
\(596\) −9.97924 + 17.2845i −0.408765 + 0.708003i
\(597\) 0.416930 0.0170638
\(598\) 0.588210 + 1.01881i 0.0240537 + 0.0416622i
\(599\) 1.75114 + 3.03307i 0.0715497 + 0.123928i 0.899581 0.436755i \(-0.143872\pi\)
−0.828031 + 0.560682i \(0.810539\pi\)
\(600\) −0.527737 0.914068i −0.0215448 0.0373167i
\(601\) 13.8045 23.9101i 0.563097 0.975312i −0.434127 0.900851i \(-0.642943\pi\)
0.997224 0.0744603i \(-0.0237234\pi\)
\(602\) 7.16897 + 12.4170i 0.292185 + 0.506080i
\(603\) 6.63915 11.4993i 0.270367 0.468289i
\(604\) 28.6531 1.16588
\(605\) 6.28618 0.255570
\(606\) −6.25717 + 10.8377i −0.254180 + 0.440253i
\(607\) 21.4814 + 37.2070i 0.871905 + 1.51018i 0.860023 + 0.510254i \(0.170449\pi\)
0.0118816 + 0.999929i \(0.496218\pi\)
\(608\) −15.9915 + 27.6981i −0.648541 + 1.12331i
\(609\) 2.11562 + 3.66436i 0.0857291 + 0.148487i
\(610\) −17.4700 30.2590i −0.707341 1.22515i
\(611\) −0.878273 1.52121i −0.0355311 0.0615417i
\(612\) −18.2091 −0.736060
\(613\) −14.9720 + 25.9323i −0.604715 + 1.04740i 0.387382 + 0.921919i \(0.373380\pi\)
−0.992096 + 0.125477i \(0.959954\pi\)
\(614\) −26.4359 + 45.7883i −1.06686 + 1.84786i
\(615\) 2.35974 + 4.08718i 0.0951537 + 0.164811i
\(616\) 3.04685 0.122761
\(617\) −4.74917 + 8.22581i −0.191194 + 0.331159i −0.945646 0.325197i \(-0.894569\pi\)
0.754452 + 0.656355i \(0.227903\pi\)
\(618\) 10.1544 0.408469
\(619\) −33.9443 −1.36434 −0.682169 0.731195i \(-0.738963\pi\)
−0.682169 + 0.731195i \(0.738963\pi\)
\(620\) −13.2635 3.00190i −0.532674 0.120559i
\(621\) 1.76061 0.0706509
\(622\) 18.2446 0.731540
\(623\) −3.72588 + 6.45341i −0.149274 + 0.258550i
\(624\) 2.31341 0.0926103
\(625\) 5.15272 + 8.92478i 0.206109 + 0.356991i
\(626\) 0.0182143 0.0315481i 0.000727990 0.00126092i
\(627\) 3.05606 5.29325i 0.122047 0.211392i
\(628\) −10.9466 −0.436816
\(629\) −24.7886 42.9352i −0.988388 1.71194i
\(630\) 4.66391 + 8.07813i 0.185815 + 0.321840i
\(631\) −1.72256 2.98356i −0.0685740 0.118774i 0.829700 0.558210i \(-0.188512\pi\)
−0.898274 + 0.439436i \(0.855178\pi\)
\(632\) −3.27600 + 5.67420i −0.130312 + 0.225708i
\(633\) 1.67411 + 2.89964i 0.0665398 + 0.115250i
\(634\) 4.64726 8.04929i 0.184566 0.319678i
\(635\) −16.9643 −0.673208
\(636\) −0.979651 −0.0388457
\(637\) 2.93403 5.08189i 0.116251 0.201352i
\(638\) 20.7447 + 35.9309i 0.821291 + 1.42252i
\(639\) 16.7857 29.0737i 0.664032 1.15014i
\(640\) −6.94206 12.0240i −0.274409 0.475290i
\(641\) 1.30889 + 2.26706i 0.0516980 + 0.0895436i 0.890716 0.454560i \(-0.150203\pi\)
−0.839018 + 0.544103i \(0.816870\pi\)
\(642\) 8.45487 + 14.6443i 0.333687 + 0.577963i
\(643\) −11.1280 −0.438844 −0.219422 0.975630i \(-0.570417\pi\)
−0.219422 + 0.975630i \(0.570417\pi\)
\(644\) −0.482799 + 0.836232i −0.0190249 + 0.0329522i
\(645\) −2.98864 + 5.17648i −0.117678 + 0.203824i
\(646\) 20.0388 + 34.7082i 0.788415 + 1.36557i
\(647\) −23.1745 −0.911085 −0.455543 0.890214i \(-0.650555\pi\)
−0.455543 + 0.890214i \(0.650555\pi\)
\(648\) −3.69159 + 6.39402i −0.145019 + 0.251181i
\(649\) 6.51435 0.255711
\(650\) 3.84492 0.150810
\(651\) −2.77506 0.628074i −0.108763 0.0246162i
\(652\) −14.5386 −0.569375
\(653\) 33.1778 1.29835 0.649173 0.760641i \(-0.275115\pi\)
0.649173 + 0.760641i \(0.275115\pi\)
\(654\) 5.51019 9.54393i 0.215466 0.373197i
\(655\) 33.4637 1.30754
\(656\) −13.8391 23.9700i −0.540326 0.935872i
\(657\) 10.8315 18.7607i 0.422576 0.731923i
\(658\) 1.73018 2.99676i 0.0674494 0.116826i
\(659\) −21.2100 −0.826226 −0.413113 0.910680i \(-0.635559\pi\)
−0.413113 + 0.910680i \(0.635559\pi\)
\(660\) −1.58738 2.74943i −0.0617888 0.107021i
\(661\) −3.39838 5.88617i −0.132182 0.228945i 0.792336 0.610085i \(-0.208865\pi\)
−0.924517 + 0.381140i \(0.875532\pi\)
\(662\) −0.739106 1.28017i −0.0287262 0.0497552i
\(663\) 1.10546 1.91472i 0.0429327 0.0743616i
\(664\) 4.49272 + 7.78162i 0.174351 + 0.301985i
\(665\) 4.27696 7.40790i 0.165853 0.287266i
\(666\) 55.2277 2.14003
\(667\) 5.26065 0.203693
\(668\) −1.86970 + 3.23841i −0.0723408 + 0.125298i
\(669\) −1.74336 3.01958i −0.0674021 0.116744i
\(670\) −7.59003 + 13.1463i −0.293229 + 0.507887i
\(671\) −14.9332 25.8650i −0.576488 0.998507i
\(672\) 1.73790 + 3.01013i 0.0670408 + 0.116118i
\(673\) 11.2521 + 19.4891i 0.433735 + 0.751251i 0.997191 0.0748945i \(-0.0238620\pi\)
−0.563456 + 0.826146i \(0.690529\pi\)
\(674\) −41.3696 −1.59350
\(675\) 2.87712 4.98332i 0.110740 0.191808i
\(676\) −0.714240 + 1.23710i −0.0274708 + 0.0475808i
\(677\) −0.775354 1.34295i −0.0297993 0.0516138i 0.850741 0.525585i \(-0.176153\pi\)
−0.880540 + 0.473971i \(0.842820\pi\)
\(678\) 14.8119 0.568848
\(679\) 4.85555 8.41005i 0.186339 0.322748i
\(680\) −8.32872 −0.319392
\(681\) 1.49931 0.0574537
\(682\) −27.2109 6.15859i −1.04196 0.235824i
\(683\) 2.76304 0.105725 0.0528625 0.998602i \(-0.483166\pi\)
0.0528625 + 0.998602i \(0.483166\pi\)
\(684\) −18.6015 −0.711246
\(685\) −11.0884 + 19.2056i −0.423664 + 0.733808i
\(686\) 25.3498 0.967860
\(687\) −5.93461 10.2791i −0.226420 0.392170i
\(688\) 17.5274 30.3584i 0.668227 1.15740i
\(689\) −0.713902 + 1.23651i −0.0271975 + 0.0471075i
\(690\) −0.966143 −0.0367804
\(691\) 2.06460 + 3.57600i 0.0785412 + 0.136037i 0.902621 0.430437i \(-0.141640\pi\)
−0.824080 + 0.566474i \(0.808307\pi\)
\(692\) −0.831480 1.44017i −0.0316081 0.0547469i
\(693\) 3.98665 + 6.90508i 0.151440 + 0.262302i
\(694\) −6.40944 + 11.1015i −0.243299 + 0.421406i
\(695\) 12.9068 + 22.3553i 0.489585 + 0.847985i
\(696\) 2.10431 3.64477i 0.0797635 0.138155i
\(697\) −26.4521 −1.00195
\(698\) −2.44342 −0.0924848
\(699\) −3.61650 + 6.26397i −0.136789 + 0.236925i
\(700\) 1.57794 + 2.73308i 0.0596406 + 0.103301i
\(701\) −9.18635 + 15.9112i −0.346964 + 0.600959i −0.985709 0.168460i \(-0.946121\pi\)
0.638745 + 0.769419i \(0.279454\pi\)
\(702\) 2.56550 + 4.44358i 0.0968286 + 0.167712i
\(703\) −25.3228 43.8603i −0.955066 1.65422i
\(704\) 4.00685 + 6.94007i 0.151014 + 0.261564i
\(705\) 1.44257 0.0543305
\(706\) −11.4529 + 19.8371i −0.431037 + 0.746578i
\(707\) −7.48529 + 12.9649i −0.281513 + 0.487596i
\(708\) 0.825819 + 1.43036i 0.0310362 + 0.0537563i
\(709\) −28.7385 −1.07930 −0.539649 0.841890i \(-0.681443\pi\)
−0.539649 + 0.841890i \(0.681443\pi\)
\(710\) −19.1898 + 33.2377i −0.720181 + 1.24739i
\(711\) −17.1459 −0.643023
\(712\) 7.41192 0.277773
\(713\) −2.40136 + 2.59753i −0.0899318 + 0.0972781i
\(714\) 4.35548 0.163000
\(715\) −4.62710 −0.173044
\(716\) −11.0924 + 19.2125i −0.414541 + 0.718006i
\(717\) −8.99222 −0.335821
\(718\) −12.2099 21.1481i −0.455669 0.789241i
\(719\) 14.5606 25.2197i 0.543019 0.940537i −0.455709 0.890129i \(-0.650614\pi\)
0.998729 0.0504085i \(-0.0160523\pi\)
\(720\) 11.4028 19.7503i 0.424958 0.736049i
\(721\) 12.1474 0.452394
\(722\) 2.88020 + 4.98866i 0.107190 + 0.185659i
\(723\) −1.78437 3.09061i −0.0663613 0.114941i
\(724\) 3.97491 + 6.88475i 0.147727 + 0.255870i
\(725\) 8.59675 14.8900i 0.319275 0.553001i
\(726\) 1.63488 + 2.83170i 0.0606762 + 0.105094i
\(727\) −11.7725 + 20.3906i −0.436620 + 0.756247i −0.997426 0.0716995i \(-0.977158\pi\)
0.560807 + 0.827947i \(0.310491\pi\)
\(728\) 1.12588 0.0417280
\(729\) −15.3280 −0.567704
\(730\) −12.3828 + 21.4476i −0.458308 + 0.793813i
\(731\) −16.7510 29.0136i −0.619559 1.07311i
\(732\) 3.78613 6.55777i 0.139939 0.242382i
\(733\) 16.1044 + 27.8936i 0.594829 + 1.03027i 0.993571 + 0.113211i \(0.0361136\pi\)
−0.398742 + 0.917063i \(0.630553\pi\)
\(734\) −14.9715 25.9314i −0.552609 0.957146i
\(735\) 2.40959 + 4.17354i 0.0888792 + 0.153943i
\(736\) 4.32142 0.159290
\(737\) −6.48786 + 11.2373i −0.238984 + 0.413932i
\(738\) 14.7335 25.5191i 0.542346 0.939371i
\(739\) 24.6445 + 42.6854i 0.906561 + 1.57021i 0.818808 + 0.574067i \(0.194635\pi\)
0.0877528 + 0.996142i \(0.472031\pi\)
\(740\) −26.3064 −0.967041
\(741\) 1.12928 1.95598i 0.0414853 0.0718546i
\(742\) −2.81274 −0.103259
\(743\) 18.3395 0.672811 0.336406 0.941717i \(-0.390789\pi\)
0.336406 + 0.941717i \(0.390789\pi\)
\(744\) 0.839092 + 2.70278i 0.0307626 + 0.0990888i
\(745\) −23.8893 −0.875236
\(746\) 55.2566 2.02309
\(747\) −11.7570 + 20.3637i −0.430165 + 0.745068i
\(748\) 17.7942 0.650621
\(749\) 10.1144 + 17.5186i 0.369570 + 0.640115i
\(750\) −5.38046 + 9.31923i −0.196467 + 0.340290i
\(751\) −11.2367 + 19.4625i −0.410031 + 0.710195i −0.994893 0.100938i \(-0.967816\pi\)
0.584861 + 0.811133i \(0.301149\pi\)
\(752\) −8.46024 −0.308513
\(753\) −5.94872 10.3035i −0.216783 0.375480i
\(754\) 7.66564 + 13.2773i 0.279166 + 0.483530i
\(755\) 17.1482 + 29.7015i 0.624085 + 1.08095i
\(756\) −2.10575 + 3.64726i −0.0765852 + 0.132650i
\(757\) 13.6772 + 23.6896i 0.497107 + 0.861015i 0.999994 0.00333715i \(-0.00106225\pi\)
−0.502887 + 0.864352i \(0.667729\pi\)
\(758\) −32.1201 + 55.6336i −1.16665 + 2.02070i
\(759\) −0.825846 −0.0299763
\(760\) −8.50818 −0.308624
\(761\) 1.27170 2.20264i 0.0460989 0.0798457i −0.842055 0.539391i \(-0.818654\pi\)
0.888154 + 0.459546i \(0.151988\pi\)
\(762\) −4.41200 7.64181i −0.159830 0.276834i
\(763\) 6.59170 11.4172i 0.238636 0.413329i
\(764\) −4.91017 8.50467i −0.177644 0.307688i
\(765\) −10.8977 18.8754i −0.394007 0.682441i
\(766\) 8.05369 + 13.9494i 0.290992 + 0.504012i
\(767\) 2.40720 0.0869190
\(768\) 5.03326 8.71786i 0.181622 0.314579i
\(769\) 3.84841 6.66565i 0.138777 0.240369i −0.788257 0.615346i \(-0.789016\pi\)
0.927034 + 0.374977i \(0.122349\pi\)
\(770\) −4.55764 7.89406i −0.164246 0.284482i
\(771\) −6.98311 −0.251491