Properties

Label 567.2.u.a.100.19
Level $567$
Weight $2$
Character 567.100
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(100,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.100");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.u (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 100.19
Character \(\chi\) \(=\) 567.100
Dual form 567.2.u.a.550.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.324131 - 1.83824i) q^{2} +(-1.39467 - 0.507617i) q^{4} +(-1.37479 - 0.500384i) q^{5} +(-2.42382 - 1.06071i) q^{7} +(0.481419 - 0.833843i) q^{8} +O(q^{10})\) \(q+(0.324131 - 1.83824i) q^{2} +(-1.39467 - 0.507617i) q^{4} +(-1.37479 - 0.500384i) q^{5} +(-2.42382 - 1.06071i) q^{7} +(0.481419 - 0.833843i) q^{8} +(-1.36544 + 2.36501i) q^{10} +(-4.29056 + 1.56163i) q^{11} +(0.925783 + 0.336957i) q^{13} +(-2.73547 + 4.11174i) q^{14} +(-3.65064 - 3.06325i) q^{16} +(-0.620234 + 1.07428i) q^{17} +(-0.718027 - 1.24366i) q^{19} +(1.66338 + 1.39574i) q^{20} +(1.47995 + 8.39323i) q^{22} +(-0.165636 - 0.939366i) q^{23} +(-2.19055 - 1.83809i) q^{25} +(0.919482 - 1.59259i) q^{26} +(2.84199 + 2.70971i) q^{28} +(-5.18835 + 1.88840i) q^{29} +(6.28413 + 2.28724i) q^{31} +(-5.33911 + 4.48005i) q^{32} +(1.77374 + 1.48834i) q^{34} +(2.80149 + 2.67110i) q^{35} -2.88764 q^{37} +(-2.51887 + 0.916795i) q^{38} +(-1.07909 + 0.905468i) q^{40} +(-11.1576 - 4.06104i) q^{41} +(0.559660 - 3.17399i) q^{43} +6.77661 q^{44} -1.78046 q^{46} +(10.6381 - 3.87197i) q^{47} +(4.74979 + 5.14193i) q^{49} +(-4.08886 + 3.43096i) q^{50} +(-1.12011 - 0.939887i) q^{52} +(-2.32509 - 4.02717i) q^{53} +6.68005 q^{55} +(-2.05134 + 1.51044i) q^{56} +(1.78963 + 10.1495i) q^{58} +(4.83431 - 4.05647i) q^{59} +(-4.93482 + 1.79613i) q^{61} +(6.24136 - 10.8104i) q^{62} +(1.73924 + 3.01245i) q^{64} +(-1.10415 - 0.926495i) q^{65} +(-2.28146 - 12.9388i) q^{67} +(1.41034 - 1.18342i) q^{68} +(5.81816 - 4.28402i) q^{70} +(5.80593 + 10.0562i) q^{71} +9.93018 q^{73} +(-0.935973 + 5.30816i) q^{74} +(0.370105 + 2.09897i) q^{76} +(12.0560 + 0.765911i) q^{77} +(2.45710 - 13.9349i) q^{79} +(3.48608 + 6.03807i) q^{80} +(-11.0817 + 19.1940i) q^{82} +(7.82112 - 2.84665i) q^{83} +(1.39025 - 1.16656i) q^{85} +(-5.65314 - 2.05757i) q^{86} +(-0.763399 + 4.32945i) q^{88} +(-0.307487 - 0.532584i) q^{89} +(-1.88652 - 1.79871i) q^{91} +(-0.245832 + 1.39418i) q^{92} +(-3.66944 - 20.8104i) q^{94} +(0.364832 + 2.06907i) q^{95} +(-0.991251 + 5.62167i) q^{97} +(10.9916 - 7.06459i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} + 3 q^{10} + 15 q^{11} - 12 q^{13} + 30 q^{14} + 9 q^{16} - 27 q^{17} + 3 q^{19} + 18 q^{20} - 12 q^{22} + 36 q^{23} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} + 75 q^{32} - 18 q^{34} - 15 q^{35} - 6 q^{37} - 69 q^{38} + 51 q^{40} - 12 q^{43} + 6 q^{44} - 6 q^{46} + 21 q^{47} - 42 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 111 q^{56} - 3 q^{58} - 27 q^{59} - 21 q^{61} - 75 q^{62} - 30 q^{64} + 90 q^{65} - 3 q^{67} + 30 q^{68} + 39 q^{70} + 18 q^{71} - 42 q^{73} - 51 q^{74} - 24 q^{76} - 15 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} + 93 q^{86} - 51 q^{88} - 75 q^{89} - 21 q^{91} + 66 q^{92} + 33 q^{94} - 15 q^{95} - 12 q^{97} + 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.324131 1.83824i 0.229195 1.29983i −0.625306 0.780380i \(-0.715026\pi\)
0.854501 0.519450i \(-0.173863\pi\)
\(3\) 0 0
\(4\) −1.39467 0.507617i −0.697333 0.253809i
\(5\) −1.37479 0.500384i −0.614827 0.223779i 0.0157870 0.999875i \(-0.494975\pi\)
−0.630614 + 0.776097i \(0.717197\pi\)
\(6\) 0 0
\(7\) −2.42382 1.06071i −0.916117 0.400910i
\(8\) 0.481419 0.833843i 0.170207 0.294808i
\(9\) 0 0
\(10\) −1.36544 + 2.36501i −0.431789 + 0.747881i
\(11\) −4.29056 + 1.56163i −1.29365 + 0.470851i −0.894924 0.446219i \(-0.852770\pi\)
−0.398727 + 0.917069i \(0.630548\pi\)
\(12\) 0 0
\(13\) 0.925783 + 0.336957i 0.256766 + 0.0934552i 0.467196 0.884154i \(-0.345264\pi\)
−0.210430 + 0.977609i \(0.567486\pi\)
\(14\) −2.73547 + 4.11174i −0.731084 + 1.09891i
\(15\) 0 0
\(16\) −3.65064 3.06325i −0.912661 0.765813i
\(17\) −0.620234 + 1.07428i −0.150429 + 0.260550i −0.931385 0.364035i \(-0.881399\pi\)
0.780956 + 0.624586i \(0.214732\pi\)
\(18\) 0 0
\(19\) −0.718027 1.24366i −0.164727 0.285315i 0.771832 0.635827i \(-0.219341\pi\)
−0.936558 + 0.350512i \(0.886008\pi\)
\(20\) 1.66338 + 1.39574i 0.371942 + 0.312097i
\(21\) 0 0
\(22\) 1.47995 + 8.39323i 0.315527 + 1.78944i
\(23\) −0.165636 0.939366i −0.0345374 0.195871i 0.962657 0.270723i \(-0.0872628\pi\)
−0.997195 + 0.0748517i \(0.976152\pi\)
\(24\) 0 0
\(25\) −2.19055 1.83809i −0.438109 0.367617i
\(26\) 0.919482 1.59259i 0.180325 0.312333i
\(27\) 0 0
\(28\) 2.84199 + 2.70971i 0.537085 + 0.512087i
\(29\) −5.18835 + 1.88840i −0.963452 + 0.350668i −0.775385 0.631488i \(-0.782444\pi\)
−0.188067 + 0.982156i \(0.560222\pi\)
\(30\) 0 0
\(31\) 6.28413 + 2.28724i 1.12866 + 0.410800i 0.837807 0.545967i \(-0.183837\pi\)
0.290857 + 0.956767i \(0.406060\pi\)
\(32\) −5.33911 + 4.48005i −0.943831 + 0.791968i
\(33\) 0 0
\(34\) 1.77374 + 1.48834i 0.304194 + 0.255249i
\(35\) 2.80149 + 2.67110i 0.473538 + 0.451498i
\(36\) 0 0
\(37\) −2.88764 −0.474725 −0.237363 0.971421i \(-0.576283\pi\)
−0.237363 + 0.971421i \(0.576283\pi\)
\(38\) −2.51887 + 0.916795i −0.408615 + 0.148724i
\(39\) 0 0
\(40\) −1.07909 + 0.905468i −0.170620 + 0.143167i
\(41\) −11.1576 4.06104i −1.74253 0.634227i −0.743135 0.669141i \(-0.766662\pi\)
−0.999390 + 0.0349137i \(0.988884\pi\)
\(42\) 0 0
\(43\) 0.559660 3.17399i 0.0853473 0.484029i −0.911934 0.410337i \(-0.865411\pi\)
0.997281 0.0736913i \(-0.0234780\pi\)
\(44\) 6.77661 1.02161
\(45\) 0 0
\(46\) −1.78046 −0.262515
\(47\) 10.6381 3.87197i 1.55173 0.564785i 0.582909 0.812537i \(-0.301914\pi\)
0.968823 + 0.247753i \(0.0796920\pi\)
\(48\) 0 0
\(49\) 4.74979 + 5.14193i 0.678542 + 0.734562i
\(50\) −4.08886 + 3.43096i −0.578252 + 0.485211i
\(51\) 0 0
\(52\) −1.12011 0.939887i −0.155332 0.130339i
\(53\) −2.32509 4.02717i −0.319376 0.553175i 0.660982 0.750402i \(-0.270140\pi\)
−0.980358 + 0.197227i \(0.936806\pi\)
\(54\) 0 0
\(55\) 6.68005 0.900738
\(56\) −2.05134 + 1.51044i −0.274122 + 0.201841i
\(57\) 0 0
\(58\) 1.78963 + 10.1495i 0.234990 + 1.33269i
\(59\) 4.83431 4.05647i 0.629374 0.528108i −0.271360 0.962478i \(-0.587473\pi\)
0.900734 + 0.434370i \(0.143029\pi\)
\(60\) 0 0
\(61\) −4.93482 + 1.79613i −0.631839 + 0.229970i −0.638031 0.770010i \(-0.720251\pi\)
0.00619278 + 0.999981i \(0.498029\pi\)
\(62\) 6.24136 10.8104i 0.792654 1.37292i
\(63\) 0 0
\(64\) 1.73924 + 3.01245i 0.217405 + 0.376557i
\(65\) −1.10415 0.926495i −0.136953 0.114918i
\(66\) 0 0
\(67\) −2.28146 12.9388i −0.278725 1.58073i −0.726875 0.686770i \(-0.759028\pi\)
0.448150 0.893958i \(-0.352083\pi\)
\(68\) 1.41034 1.18342i 0.171029 0.143510i
\(69\) 0 0
\(70\) 5.81816 4.28402i 0.695403 0.512038i
\(71\) 5.80593 + 10.0562i 0.689037 + 1.19345i 0.972150 + 0.234360i \(0.0752995\pi\)
−0.283113 + 0.959087i \(0.591367\pi\)
\(72\) 0 0
\(73\) 9.93018 1.16224 0.581120 0.813818i \(-0.302615\pi\)
0.581120 + 0.813818i \(0.302615\pi\)
\(74\) −0.935973 + 5.30816i −0.108805 + 0.617062i
\(75\) 0 0
\(76\) 0.370105 + 2.09897i 0.0424540 + 0.240769i
\(77\) 12.0560 + 0.765911i 1.37391 + 0.0872837i
\(78\) 0 0
\(79\) 2.45710 13.9349i 0.276445 1.56780i −0.457887 0.889010i \(-0.651394\pi\)
0.734333 0.678790i \(-0.237495\pi\)
\(80\) 3.48608 + 6.03807i 0.389756 + 0.675077i
\(81\) 0 0
\(82\) −11.0817 + 19.1940i −1.22377 + 2.11962i
\(83\) 7.82112 2.84665i 0.858479 0.312461i 0.124987 0.992158i \(-0.460111\pi\)
0.733493 + 0.679697i \(0.237889\pi\)
\(84\) 0 0
\(85\) 1.39025 1.16656i 0.150793 0.126531i
\(86\) −5.65314 2.05757i −0.609594 0.221874i
\(87\) 0 0
\(88\) −0.763399 + 4.32945i −0.0813786 + 0.461521i
\(89\) −0.307487 0.532584i −0.0325936 0.0564538i 0.849268 0.527961i \(-0.177043\pi\)
−0.881862 + 0.471507i \(0.843710\pi\)
\(90\) 0 0
\(91\) −1.88652 1.79871i −0.197761 0.188556i
\(92\) −0.245832 + 1.39418i −0.0256298 + 0.145354i
\(93\) 0 0
\(94\) −3.66944 20.8104i −0.378474 2.14643i
\(95\) 0.364832 + 2.06907i 0.0374310 + 0.212282i
\(96\) 0 0
\(97\) −0.991251 + 5.62167i −0.100646 + 0.570794i 0.892224 + 0.451593i \(0.149144\pi\)
−0.992870 + 0.119200i \(0.961967\pi\)
\(98\) 10.9916 7.06459i 1.11032 0.713631i
\(99\) 0 0
\(100\) 2.12204 + 3.67548i 0.212204 + 0.367548i
\(101\) 2.05653 11.6632i 0.204632 1.16053i −0.693385 0.720567i \(-0.743881\pi\)
0.898017 0.439960i \(-0.145007\pi\)
\(102\) 0 0
\(103\) −12.0593 4.38923i −1.18824 0.432484i −0.329134 0.944283i \(-0.606757\pi\)
−0.859105 + 0.511800i \(0.828979\pi\)
\(104\) 0.726659 0.609740i 0.0712548 0.0597899i
\(105\) 0 0
\(106\) −8.15653 + 2.96873i −0.792232 + 0.288349i
\(107\) −5.52411 + 9.56804i −0.534036 + 0.924977i 0.465173 + 0.885220i \(0.345992\pi\)
−0.999209 + 0.0397577i \(0.987341\pi\)
\(108\) 0 0
\(109\) −9.52408 16.4962i −0.912242 1.58005i −0.810890 0.585198i \(-0.801017\pi\)
−0.101352 0.994851i \(-0.532317\pi\)
\(110\) 2.16521 12.2795i 0.206445 1.17081i
\(111\) 0 0
\(112\) 5.59928 + 11.2970i 0.529082 + 1.06747i
\(113\) −1.36095 7.71833i −0.128027 0.726080i −0.979464 0.201621i \(-0.935379\pi\)
0.851436 0.524458i \(-0.175732\pi\)
\(114\) 0 0
\(115\) −0.242329 + 1.37432i −0.0225973 + 0.128156i
\(116\) 8.19460 0.760850
\(117\) 0 0
\(118\) −5.88980 10.2014i −0.542200 0.939119i
\(119\) 2.64283 1.94596i 0.242268 0.178386i
\(120\) 0 0
\(121\) 7.54368 6.32990i 0.685789 0.575445i
\(122\) 1.70218 + 9.65354i 0.154108 + 0.873990i
\(123\) 0 0
\(124\) −7.60323 6.37987i −0.682790 0.572929i
\(125\) 5.74937 + 9.95820i 0.514239 + 0.890688i
\(126\) 0 0
\(127\) −6.35187 + 11.0018i −0.563637 + 0.976249i 0.433538 + 0.901136i \(0.357265\pi\)
−0.997175 + 0.0751132i \(0.976068\pi\)
\(128\) −6.99744 + 2.54686i −0.618492 + 0.225113i
\(129\) 0 0
\(130\) −2.06101 + 1.72939i −0.180762 + 0.151677i
\(131\) 1.45783 + 8.26775i 0.127371 + 0.722357i 0.979871 + 0.199630i \(0.0639741\pi\)
−0.852500 + 0.522727i \(0.824915\pi\)
\(132\) 0 0
\(133\) 0.421207 + 3.77602i 0.0365233 + 0.327423i
\(134\) −24.5241 −2.11856
\(135\) 0 0
\(136\) 0.597185 + 1.03436i 0.0512082 + 0.0886953i
\(137\) 1.77965 + 1.49330i 0.152046 + 0.127581i 0.715637 0.698472i \(-0.246136\pi\)
−0.563592 + 0.826054i \(0.690581\pi\)
\(138\) 0 0
\(139\) 16.4618 13.8131i 1.39627 1.17161i 0.433546 0.901131i \(-0.357262\pi\)
0.962726 0.270480i \(-0.0871824\pi\)
\(140\) −2.55125 5.14738i −0.215620 0.435033i
\(141\) 0 0
\(142\) 20.3675 7.41316i 1.70920 0.622098i
\(143\) −4.49833 −0.376169
\(144\) 0 0
\(145\) 8.07784 0.670828
\(146\) 3.21868 18.2540i 0.266380 1.51071i
\(147\) 0 0
\(148\) 4.02730 + 1.46582i 0.331042 + 0.120489i
\(149\) −3.36481 + 2.82341i −0.275656 + 0.231303i −0.770126 0.637892i \(-0.779807\pi\)
0.494470 + 0.869195i \(0.335362\pi\)
\(150\) 0 0
\(151\) −13.9287 + 5.06965i −1.13351 + 0.412562i −0.839564 0.543261i \(-0.817189\pi\)
−0.293942 + 0.955823i \(0.594967\pi\)
\(152\) −1.38269 −0.112151
\(153\) 0 0
\(154\) 5.31564 21.9135i 0.428346 1.76584i
\(155\) −7.49490 6.28896i −0.602005 0.505142i
\(156\) 0 0
\(157\) 0.289738 0.243119i 0.0231236 0.0194030i −0.631153 0.775659i \(-0.717418\pi\)
0.654276 + 0.756256i \(0.272973\pi\)
\(158\) −24.8192 9.03346i −1.97451 0.718664i
\(159\) 0 0
\(160\) 9.58193 3.48754i 0.757518 0.275714i
\(161\) −0.594923 + 2.45254i −0.0468865 + 0.193288i
\(162\) 0 0
\(163\) −2.58086 + 4.47018i −0.202148 + 0.350131i −0.949220 0.314612i \(-0.898126\pi\)
0.747072 + 0.664743i \(0.231459\pi\)
\(164\) 13.4997 + 11.3276i 1.05415 + 0.884536i
\(165\) 0 0
\(166\) −2.69776 15.2998i −0.209387 1.18749i
\(167\) 1.88838 + 10.7095i 0.146127 + 0.828727i 0.966455 + 0.256834i \(0.0826795\pi\)
−0.820329 + 0.571893i \(0.806209\pi\)
\(168\) 0 0
\(169\) −9.21504 7.73234i −0.708850 0.594795i
\(170\) −1.69378 2.93372i −0.129907 0.225006i
\(171\) 0 0
\(172\) −2.39171 + 4.14256i −0.182366 + 0.315868i
\(173\) −9.27634 7.78377i −0.705267 0.591789i 0.218000 0.975949i \(-0.430047\pi\)
−0.923267 + 0.384160i \(0.874491\pi\)
\(174\) 0 0
\(175\) 3.35981 + 6.77872i 0.253978 + 0.512423i
\(176\) 20.4470 + 7.44209i 1.54125 + 0.560969i
\(177\) 0 0
\(178\) −1.07868 + 0.392608i −0.0808505 + 0.0294272i
\(179\) 6.18889 10.7195i 0.462579 0.801211i −0.536510 0.843894i \(-0.680257\pi\)
0.999089 + 0.0426837i \(0.0135908\pi\)
\(180\) 0 0
\(181\) −7.93495 + 13.7437i −0.589800 + 1.02156i 0.404458 + 0.914557i \(0.367460\pi\)
−0.994258 + 0.107007i \(0.965873\pi\)
\(182\) −3.91793 + 2.88485i −0.290416 + 0.213839i
\(183\) 0 0
\(184\) −0.863024 0.314115i −0.0636230 0.0231569i
\(185\) 3.96991 + 1.44493i 0.291874 + 0.106233i
\(186\) 0 0
\(187\) 0.983521 5.57783i 0.0719222 0.407891i
\(188\) −16.8021 −1.22542
\(189\) 0 0
\(190\) 3.92168 0.284509
\(191\) 2.63991 14.9717i 0.191017 1.08331i −0.726960 0.686680i \(-0.759068\pi\)
0.917977 0.396633i \(-0.129821\pi\)
\(192\) 0 0
\(193\) 17.6672 + 6.43032i 1.27171 + 0.462865i 0.887682 0.460456i \(-0.152314\pi\)
0.384028 + 0.923321i \(0.374536\pi\)
\(194\) 10.0127 + 3.64431i 0.718867 + 0.261646i
\(195\) 0 0
\(196\) −4.01425 9.58236i −0.286732 0.684454i
\(197\) −0.130567 + 0.226149i −0.00930255 + 0.0161125i −0.870639 0.491922i \(-0.836294\pi\)
0.861337 + 0.508035i \(0.169628\pi\)
\(198\) 0 0
\(199\) 0.818784 1.41818i 0.0580421 0.100532i −0.835544 0.549423i \(-0.814848\pi\)
0.893586 + 0.448891i \(0.148181\pi\)
\(200\) −2.58725 + 0.941681i −0.182946 + 0.0665869i
\(201\) 0 0
\(202\) −20.7731 7.56077i −1.46159 0.531974i
\(203\) 14.5787 + 0.926177i 1.02322 + 0.0650049i
\(204\) 0 0
\(205\) 13.3073 + 11.1662i 0.929425 + 0.779880i
\(206\) −11.9772 + 20.7452i −0.834493 + 1.44538i
\(207\) 0 0
\(208\) −2.34752 4.06602i −0.162771 0.281928i
\(209\) 5.02288 + 4.21469i 0.347440 + 0.291536i
\(210\) 0 0
\(211\) 1.10692 + 6.27765i 0.0762034 + 0.432171i 0.998910 + 0.0466690i \(0.0148606\pi\)
−0.922707 + 0.385502i \(0.874028\pi\)
\(212\) 1.19846 + 6.79682i 0.0823108 + 0.466808i
\(213\) 0 0
\(214\) 15.7978 + 13.2559i 1.07991 + 0.906156i
\(215\) −2.35763 + 4.08354i −0.160789 + 0.278495i
\(216\) 0 0
\(217\) −12.8055 12.2095i −0.869294 0.828834i
\(218\) −33.4110 + 12.1606i −2.26288 + 0.823619i
\(219\) 0 0
\(220\) −9.31645 3.39091i −0.628115 0.228615i
\(221\) −0.936188 + 0.785555i −0.0629748 + 0.0528421i
\(222\) 0 0
\(223\) 4.42813 + 3.71564i 0.296529 + 0.248818i 0.778898 0.627151i \(-0.215779\pi\)
−0.482369 + 0.875968i \(0.660223\pi\)
\(224\) 17.6931 5.19558i 1.18217 0.347144i
\(225\) 0 0
\(226\) −14.6292 −0.973123
\(227\) 12.0490 4.38547i 0.799718 0.291074i 0.0903484 0.995910i \(-0.471202\pi\)
0.709370 + 0.704837i \(0.248980\pi\)
\(228\) 0 0
\(229\) −4.48966 + 3.76727i −0.296685 + 0.248948i −0.778963 0.627070i \(-0.784254\pi\)
0.482278 + 0.876018i \(0.339810\pi\)
\(230\) 2.44777 + 0.890917i 0.161401 + 0.0587453i
\(231\) 0 0
\(232\) −0.923139 + 5.23538i −0.0606070 + 0.343720i
\(233\) −0.971513 −0.0636459 −0.0318230 0.999494i \(-0.510131\pi\)
−0.0318230 + 0.999494i \(0.510131\pi\)
\(234\) 0 0
\(235\) −16.5627 −1.08043
\(236\) −8.80139 + 3.20345i −0.572922 + 0.208527i
\(237\) 0 0
\(238\) −2.72052 5.48889i −0.176345 0.355792i
\(239\) 18.1999 15.2715i 1.17726 0.987834i 0.177262 0.984164i \(-0.443276\pi\)
0.999993 0.00367051i \(-0.00116836\pi\)
\(240\) 0 0
\(241\) −0.219263 0.183983i −0.0141239 0.0118514i 0.635698 0.771938i \(-0.280712\pi\)
−0.649822 + 0.760086i \(0.725157\pi\)
\(242\) −9.19071 15.9188i −0.590801 1.02330i
\(243\) 0 0
\(244\) 7.79417 0.498971
\(245\) −3.95705 9.44582i −0.252807 0.603472i
\(246\) 0 0
\(247\) −0.245677 1.39330i −0.0156320 0.0886537i
\(248\) 4.93250 4.13886i 0.313214 0.262818i
\(249\) 0 0
\(250\) 20.1691 7.34094i 1.27560 0.464282i
\(251\) −3.91719 + 6.78477i −0.247251 + 0.428251i −0.962762 0.270350i \(-0.912861\pi\)
0.715511 + 0.698601i \(0.246194\pi\)
\(252\) 0 0
\(253\) 2.17762 + 3.77174i 0.136906 + 0.237127i
\(254\) 18.1650 + 15.2423i 1.13977 + 0.956384i
\(255\) 0 0
\(256\) 3.62171 + 20.5397i 0.226357 + 1.28373i
\(257\) 7.40124 6.21038i 0.461677 0.387393i −0.382071 0.924133i \(-0.624789\pi\)
0.843748 + 0.536740i \(0.180344\pi\)
\(258\) 0 0
\(259\) 6.99912 + 3.06295i 0.434904 + 0.190322i
\(260\) 1.06962 + 1.85264i 0.0663351 + 0.114896i
\(261\) 0 0
\(262\) 15.6706 0.968134
\(263\) −3.18277 + 18.0504i −0.196258 + 1.11304i 0.714358 + 0.699781i \(0.246719\pi\)
−0.910616 + 0.413254i \(0.864392\pi\)
\(264\) 0 0
\(265\) 1.18139 + 6.69998i 0.0725720 + 0.411576i
\(266\) 7.07774 + 0.449647i 0.433964 + 0.0275696i
\(267\) 0 0
\(268\) −3.38609 + 19.2035i −0.206838 + 1.17304i
\(269\) −2.28434 3.95659i −0.139279 0.241238i 0.787945 0.615745i \(-0.211145\pi\)
−0.927224 + 0.374508i \(0.877812\pi\)
\(270\) 0 0
\(271\) −6.60709 + 11.4438i −0.401352 + 0.695162i −0.993889 0.110381i \(-0.964793\pi\)
0.592537 + 0.805543i \(0.298126\pi\)
\(272\) 5.55504 2.02187i 0.336824 0.122594i
\(273\) 0 0
\(274\) 3.32188 2.78739i 0.200682 0.168392i
\(275\) 12.2691 + 4.46558i 0.739853 + 0.269285i
\(276\) 0 0
\(277\) −5.27455 + 29.9135i −0.316917 + 1.79733i 0.244345 + 0.969688i \(0.421427\pi\)
−0.561262 + 0.827638i \(0.689684\pi\)
\(278\) −20.0560 34.7379i −1.20288 2.08344i
\(279\) 0 0
\(280\) 3.57597 1.05009i 0.213705 0.0627546i
\(281\) −3.38213 + 19.1810i −0.201761 + 1.14424i 0.700695 + 0.713461i \(0.252873\pi\)
−0.902456 + 0.430782i \(0.858238\pi\)
\(282\) 0 0
\(283\) 1.33894 + 7.59351i 0.0795917 + 0.451387i 0.998393 + 0.0566670i \(0.0180473\pi\)
−0.918801 + 0.394720i \(0.870842\pi\)
\(284\) −2.99265 16.9722i −0.177581 1.00711i
\(285\) 0 0
\(286\) −1.45805 + 8.26899i −0.0862161 + 0.488956i
\(287\) 22.7364 + 21.6782i 1.34209 + 1.27962i
\(288\) 0 0
\(289\) 7.73062 + 13.3898i 0.454742 + 0.787637i
\(290\) 2.61828 14.8490i 0.153750 0.871962i
\(291\) 0 0
\(292\) −13.8493 5.04073i −0.810469 0.294987i
\(293\) −10.4784 + 8.79240i −0.612153 + 0.513657i −0.895326 0.445411i \(-0.853057\pi\)
0.283173 + 0.959069i \(0.408613\pi\)
\(294\) 0 0
\(295\) −8.67599 + 3.15780i −0.505135 + 0.183854i
\(296\) −1.39017 + 2.40784i −0.0808017 + 0.139953i
\(297\) 0 0
\(298\) 4.09946 + 7.10047i 0.237475 + 0.411319i
\(299\) 0.163184 0.925461i 0.00943716 0.0535208i
\(300\) 0 0
\(301\) −4.72319 + 7.09954i −0.272240 + 0.409211i
\(302\) 4.80448 + 27.2476i 0.276467 + 1.56792i
\(303\) 0 0
\(304\) −1.18838 + 6.73965i −0.0681584 + 0.386546i
\(305\) 7.68311 0.439934
\(306\) 0 0
\(307\) 8.70668 + 15.0804i 0.496916 + 0.860684i 0.999994 0.00355714i \(-0.00113228\pi\)
−0.503077 + 0.864241i \(0.667799\pi\)
\(308\) −16.4253 7.18801i −0.935917 0.409575i
\(309\) 0 0
\(310\) −13.9899 + 11.7389i −0.794575 + 0.666727i
\(311\) −5.19029 29.4356i −0.294315 1.66914i −0.669975 0.742383i \(-0.733695\pi\)
0.375661 0.926757i \(-0.377416\pi\)
\(312\) 0 0
\(313\) 2.42961 + 2.03869i 0.137330 + 0.115233i 0.708865 0.705344i \(-0.249208\pi\)
−0.571535 + 0.820578i \(0.693652\pi\)
\(314\) −0.352998 0.611410i −0.0199208 0.0345039i
\(315\) 0 0
\(316\) −10.5004 + 18.1873i −0.590696 + 1.02311i
\(317\) −6.27590 + 2.28424i −0.352489 + 0.128296i −0.512195 0.858869i \(-0.671168\pi\)
0.159706 + 0.987165i \(0.448945\pi\)
\(318\) 0 0
\(319\) 19.3119 16.2046i 1.08126 0.907284i
\(320\) −0.883715 5.01180i −0.0494012 0.280168i
\(321\) 0 0
\(322\) 4.31552 + 1.88855i 0.240495 + 0.105245i
\(323\) 1.78138 0.0991186
\(324\) 0 0
\(325\) −1.40861 2.43979i −0.0781358 0.135335i
\(326\) 7.38070 + 6.19315i 0.408779 + 0.343007i
\(327\) 0 0
\(328\) −8.75776 + 7.34863i −0.483566 + 0.405760i
\(329\) −29.8920 1.89903i −1.64800 0.104697i
\(330\) 0 0
\(331\) −4.68844 + 1.70645i −0.257700 + 0.0937951i −0.467640 0.883919i \(-0.654895\pi\)
0.209940 + 0.977714i \(0.432673\pi\)
\(332\) −12.3529 −0.677952
\(333\) 0 0
\(334\) 20.2987 1.11070
\(335\) −3.33784 + 18.9298i −0.182366 + 1.03425i
\(336\) 0 0
\(337\) 13.6802 + 4.97920i 0.745209 + 0.271234i 0.686588 0.727046i \(-0.259107\pi\)
0.0586210 + 0.998280i \(0.481330\pi\)
\(338\) −17.2007 + 14.4331i −0.935597 + 0.785059i
\(339\) 0 0
\(340\) −2.53109 + 0.921243i −0.137268 + 0.0499614i
\(341\) −30.5343 −1.65352
\(342\) 0 0
\(343\) −6.05855 17.5013i −0.327131 0.944979i
\(344\) −2.37718 1.99469i −0.128169 0.107546i
\(345\) 0 0
\(346\) −17.3152 + 14.5291i −0.930868 + 0.781091i
\(347\) −8.17009 2.97367i −0.438593 0.159635i 0.113280 0.993563i \(-0.463864\pi\)
−0.551873 + 0.833928i \(0.686087\pi\)
\(348\) 0 0
\(349\) −10.4169 + 3.79143i −0.557602 + 0.202950i −0.605421 0.795906i \(-0.706995\pi\)
0.0478190 + 0.998856i \(0.484773\pi\)
\(350\) 13.5499 3.97894i 0.724273 0.212683i
\(351\) 0 0
\(352\) 15.9116 27.5596i 0.848090 1.46893i
\(353\) 17.7388 + 14.8846i 0.944140 + 0.792228i 0.978301 0.207189i \(-0.0664314\pi\)
−0.0341608 + 0.999416i \(0.510876\pi\)
\(354\) 0 0
\(355\) −2.95001 16.7304i −0.156570 0.887955i
\(356\) 0.158494 + 0.898863i 0.00840015 + 0.0476396i
\(357\) 0 0
\(358\) −17.6989 14.8511i −0.935416 0.784907i
\(359\) −1.03966 1.80074i −0.0548710 0.0950394i 0.837285 0.546766i \(-0.184141\pi\)
−0.892156 + 0.451727i \(0.850808\pi\)
\(360\) 0 0
\(361\) 8.46888 14.6685i 0.445730 0.772027i
\(362\) 22.6923 + 19.0411i 1.19268 + 1.00078i
\(363\) 0 0
\(364\) 1.71801 + 3.46623i 0.0900480 + 0.181680i
\(365\) −13.6520 4.96891i −0.714576 0.260085i
\(366\) 0 0
\(367\) 14.3862 5.23615i 0.750954 0.273325i 0.0619470 0.998079i \(-0.480269\pi\)
0.689007 + 0.724754i \(0.258047\pi\)
\(368\) −2.27284 + 3.93668i −0.118480 + 0.205213i
\(369\) 0 0
\(370\) 3.94289 6.82929i 0.204981 0.355038i
\(371\) 1.36394 + 12.2274i 0.0708121 + 0.634814i
\(372\) 0 0
\(373\) −28.8193 10.4894i −1.49221 0.543119i −0.538177 0.842832i \(-0.680887\pi\)
−0.954029 + 0.299713i \(0.903109\pi\)
\(374\) −9.93457 3.61589i −0.513704 0.186973i
\(375\) 0 0
\(376\) 1.89280 10.7346i 0.0976135 0.553594i
\(377\) −5.43960 −0.280153
\(378\) 0 0
\(379\) 33.1265 1.70159 0.850797 0.525495i \(-0.176120\pi\)
0.850797 + 0.525495i \(0.176120\pi\)
\(380\) 0.541474 3.07085i 0.0277770 0.157531i
\(381\) 0 0
\(382\) −26.6658 9.70556i −1.36434 0.496580i
\(383\) −11.1640 4.06336i −0.570453 0.207628i 0.0406578 0.999173i \(-0.487055\pi\)
−0.611110 + 0.791545i \(0.709277\pi\)
\(384\) 0 0
\(385\) −16.1912 7.08559i −0.825182 0.361115i
\(386\) 17.5469 30.3922i 0.893115 1.54692i
\(387\) 0 0
\(388\) 4.23612 7.33718i 0.215056 0.372489i
\(389\) 21.4924 7.82259i 1.08971 0.396621i 0.266195 0.963919i \(-0.414234\pi\)
0.823512 + 0.567298i \(0.192011\pi\)
\(390\) 0 0
\(391\) 1.11187 + 0.404689i 0.0562298 + 0.0204660i
\(392\) 6.57421 1.48516i 0.332048 0.0750117i
\(393\) 0 0
\(394\) 0.373395 + 0.313316i 0.0188114 + 0.0157846i
\(395\) −10.3508 + 17.9281i −0.520806 + 0.902063i
\(396\) 0 0
\(397\) −11.1473 19.3077i −0.559466 0.969023i −0.997541 0.0700851i \(-0.977673\pi\)
0.438075 0.898938i \(-0.355660\pi\)
\(398\) −2.34155 1.96479i −0.117371 0.0984862i
\(399\) 0 0
\(400\) 2.36638 + 13.4204i 0.118319 + 0.671020i
\(401\) −0.878529 4.98238i −0.0438716 0.248808i 0.954983 0.296661i \(-0.0958732\pi\)
−0.998854 + 0.0478529i \(0.984762\pi\)
\(402\) 0 0
\(403\) 5.04704 + 4.23497i 0.251411 + 0.210959i
\(404\) −8.78859 + 15.2223i −0.437249 + 0.757337i
\(405\) 0 0
\(406\) 6.42792 26.4988i 0.319013 1.31511i
\(407\) 12.3896 4.50944i 0.614129 0.223525i
\(408\) 0 0
\(409\) −21.3726 7.77898i −1.05681 0.384646i −0.245578 0.969377i \(-0.578978\pi\)
−0.811227 + 0.584731i \(0.801200\pi\)
\(410\) 24.8394 20.8427i 1.22673 1.02935i
\(411\) 0 0
\(412\) 14.5907 + 12.2430i 0.718831 + 0.603171i
\(413\) −16.0202 + 4.70435i −0.788304 + 0.231486i
\(414\) 0 0
\(415\) −12.1769 −0.597738
\(416\) −6.45245 + 2.34850i −0.316357 + 0.115145i
\(417\) 0 0
\(418\) 9.37567 7.86712i 0.458579 0.384793i
\(419\) −28.5404 10.3878i −1.39429 0.507480i −0.467811 0.883829i \(-0.654957\pi\)
−0.926478 + 0.376349i \(0.877179\pi\)
\(420\) 0 0
\(421\) 5.43779 30.8393i 0.265022 1.50301i −0.503951 0.863732i \(-0.668121\pi\)
0.768973 0.639281i \(-0.220768\pi\)
\(422\) 11.8986 0.579214
\(423\) 0 0
\(424\) −4.47737 −0.217440
\(425\) 3.33327 1.21321i 0.161687 0.0588493i
\(426\) 0 0
\(427\) 13.8663 + 0.880919i 0.671036 + 0.0426307i
\(428\) 12.5612 10.5401i 0.607168 0.509475i
\(429\) 0 0
\(430\) 6.74233 + 5.65748i 0.325144 + 0.272828i
\(431\) 5.25777 + 9.10673i 0.253258 + 0.438656i 0.964421 0.264372i \(-0.0851645\pi\)
−0.711163 + 0.703027i \(0.751831\pi\)
\(432\) 0 0
\(433\) −6.33812 −0.304591 −0.152295 0.988335i \(-0.548667\pi\)
−0.152295 + 0.988335i \(0.548667\pi\)
\(434\) −26.5946 + 19.5821i −1.27658 + 0.939970i
\(435\) 0 0
\(436\) 4.90917 + 27.8413i 0.235107 + 1.33336i
\(437\) −1.04932 + 0.880484i −0.0501958 + 0.0421193i
\(438\) 0 0
\(439\) −19.0176 + 6.92183i −0.907659 + 0.330361i −0.753318 0.657657i \(-0.771548\pi\)
−0.154341 + 0.988018i \(0.549326\pi\)
\(440\) 3.21591 5.57011i 0.153312 0.265545i
\(441\) 0 0
\(442\) 1.14059 + 1.97556i 0.0542523 + 0.0939677i
\(443\) −6.80079 5.70654i −0.323115 0.271126i 0.466772 0.884377i \(-0.345417\pi\)
−0.789888 + 0.613252i \(0.789861\pi\)
\(444\) 0 0
\(445\) 0.156235 + 0.886055i 0.00740627 + 0.0420030i
\(446\) 8.26552 6.93559i 0.391384 0.328410i
\(447\) 0 0
\(448\) −1.02027 9.14647i −0.0482032 0.432130i
\(449\) −6.01834 10.4241i −0.284023 0.491943i 0.688349 0.725380i \(-0.258336\pi\)
−0.972372 + 0.233437i \(0.925003\pi\)
\(450\) 0 0
\(451\) 54.2142 2.55285
\(452\) −2.01989 + 11.4553i −0.0950075 + 0.538814i
\(453\) 0 0
\(454\) −4.15608 23.5703i −0.195055 1.10621i
\(455\) 1.69353 + 3.41684i 0.0793937 + 0.160184i
\(456\) 0 0
\(457\) −0.558880 + 3.16957i −0.0261433 + 0.148266i −0.995085 0.0990224i \(-0.968428\pi\)
0.968942 + 0.247289i \(0.0795396\pi\)
\(458\) 5.46990 + 9.47414i 0.255591 + 0.442697i
\(459\) 0 0
\(460\) 1.03560 1.79370i 0.0482849 0.0836319i
\(461\) −32.0957 + 11.6819i −1.49485 + 0.544080i −0.954720 0.297505i \(-0.903846\pi\)
−0.540126 + 0.841584i \(0.681623\pi\)
\(462\) 0 0
\(463\) 8.38189 7.03324i 0.389539 0.326862i −0.426894 0.904302i \(-0.640392\pi\)
0.816434 + 0.577439i \(0.195948\pi\)
\(464\) 24.7255 + 8.99933i 1.14785 + 0.417784i
\(465\) 0 0
\(466\) −0.314897 + 1.78587i −0.0145873 + 0.0827288i
\(467\) −20.7032 35.8590i −0.958031 1.65936i −0.727275 0.686346i \(-0.759214\pi\)
−0.230755 0.973012i \(-0.574120\pi\)
\(468\) 0 0
\(469\) −8.19447 + 33.7813i −0.378385 + 1.55988i
\(470\) −5.36849 + 30.4462i −0.247630 + 1.40438i
\(471\) 0 0
\(472\) −1.05513 5.98392i −0.0485662 0.275432i
\(473\) 2.55536 + 14.4922i 0.117496 + 0.666350i
\(474\) 0 0
\(475\) −0.713082 + 4.04409i −0.0327184 + 0.185555i
\(476\) −4.67367 + 1.37243i −0.214217 + 0.0629051i
\(477\) 0 0
\(478\) −22.1736 38.4057i −1.01420 1.75664i
\(479\) −1.44178 + 8.17673i −0.0658765 + 0.373604i 0.933990 + 0.357298i \(0.116302\pi\)
−0.999867 + 0.0163066i \(0.994809\pi\)
\(480\) 0 0
\(481\) −2.67333 0.973012i −0.121893 0.0443655i
\(482\) −0.409274 + 0.343422i −0.0186419 + 0.0156424i
\(483\) 0 0
\(484\) −13.7341 + 4.99880i −0.624277 + 0.227218i
\(485\) 4.17576 7.23263i 0.189612 0.328417i
\(486\) 0 0
\(487\) 11.9736 + 20.7388i 0.542574 + 0.939766i 0.998755 + 0.0498789i \(0.0158835\pi\)
−0.456181 + 0.889887i \(0.650783\pi\)
\(488\) −0.878029 + 4.97955i −0.0397465 + 0.225414i
\(489\) 0 0
\(490\) −18.6463 + 4.21231i −0.842352 + 0.190293i
\(491\) −6.82562 38.7100i −0.308036 1.74696i −0.608859 0.793278i \(-0.708373\pi\)
0.300823 0.953680i \(-0.402739\pi\)
\(492\) 0 0
\(493\) 1.18932 6.74498i 0.0535643 0.303778i
\(494\) −2.64085 −0.118817
\(495\) 0 0
\(496\) −15.9347 27.5998i −0.715491 1.23927i
\(497\) −3.40586 30.5327i −0.152774 1.36958i
\(498\) 0 0
\(499\) −4.79773 + 4.02577i −0.214776 + 0.180218i −0.743828 0.668371i \(-0.766992\pi\)
0.529052 + 0.848589i \(0.322548\pi\)
\(500\) −2.96350 16.8068i −0.132532 0.751625i
\(501\) 0 0
\(502\) 11.2023 + 9.39988i 0.499985 + 0.419537i
\(503\) 1.54894 + 2.68284i 0.0690637 + 0.119622i 0.898489 0.438995i \(-0.144665\pi\)
−0.829426 + 0.558617i \(0.811332\pi\)
\(504\) 0 0
\(505\) −8.66337 + 15.0054i −0.385515 + 0.667731i
\(506\) 7.63918 2.78044i 0.339603 0.123605i
\(507\) 0 0
\(508\) 14.4434 12.1195i 0.640824 0.537715i
\(509\) 0.840121 + 4.76457i 0.0372377 + 0.211186i 0.997749 0.0670543i \(-0.0213601\pi\)
−0.960512 + 0.278240i \(0.910249\pi\)
\(510\) 0 0
\(511\) −24.0690 10.5330i −1.06475 0.465954i
\(512\) 24.0378 1.06233
\(513\) 0 0
\(514\) −9.01718 15.6182i −0.397731 0.688890i
\(515\) 14.3828 + 12.0686i 0.633781 + 0.531805i
\(516\) 0 0
\(517\) −39.5970 + 33.2258i −1.74147 + 1.46127i
\(518\) 7.89904 11.8732i 0.347064 0.521680i
\(519\) 0 0
\(520\) −1.30411 + 0.474658i −0.0571891 + 0.0208151i
\(521\) 30.4398 1.33359 0.666796 0.745240i \(-0.267665\pi\)
0.666796 + 0.745240i \(0.267665\pi\)
\(522\) 0 0
\(523\) 33.7422 1.47545 0.737723 0.675104i \(-0.235901\pi\)
0.737723 + 0.675104i \(0.235901\pi\)
\(524\) 2.16367 12.2708i 0.0945203 0.536051i
\(525\) 0 0
\(526\) 32.1493 + 11.7014i 1.40177 + 0.510204i
\(527\) −6.35476 + 5.33228i −0.276818 + 0.232278i
\(528\) 0 0
\(529\) 20.7580 7.55528i 0.902520 0.328490i
\(530\) 12.6991 0.551612
\(531\) 0 0
\(532\) 1.32933 5.48010i 0.0576338 0.237593i
\(533\) −8.96113 7.51928i −0.388149 0.325696i
\(534\) 0 0
\(535\) 12.3822 10.3899i 0.535330 0.449195i
\(536\) −11.8873 4.32662i −0.513452 0.186881i
\(537\) 0 0
\(538\) −8.01357 + 2.91670i −0.345490 + 0.125748i
\(539\) −28.4091 14.6443i −1.22367 0.630775i
\(540\) 0 0
\(541\) 7.87553 13.6408i 0.338596 0.586465i −0.645573 0.763698i \(-0.723382\pi\)
0.984169 + 0.177234i \(0.0567148\pi\)
\(542\) 18.8949 + 15.8547i 0.811604 + 0.681017i
\(543\) 0 0
\(544\) −1.50131 8.51437i −0.0643683 0.365050i
\(545\) 4.83922 + 27.4446i 0.207289 + 1.17560i
\(546\) 0 0
\(547\) −16.6514 13.9722i −0.711963 0.597408i 0.213186 0.977012i \(-0.431616\pi\)
−0.925149 + 0.379603i \(0.876060\pi\)
\(548\) −1.72399 2.98604i −0.0736452 0.127557i
\(549\) 0 0
\(550\) 12.1856 21.1060i 0.519595 0.899964i
\(551\) 6.07390 + 5.09661i 0.258757 + 0.217123i
\(552\) 0 0
\(553\) −20.7364 + 31.1694i −0.881803 + 1.32546i
\(554\) 53.2784 + 19.3918i 2.26358 + 0.823877i
\(555\) 0 0
\(556\) −29.9705 + 10.9084i −1.27103 + 0.462618i
\(557\) 12.3971 21.4723i 0.525280 0.909811i −0.474287 0.880370i \(-0.657294\pi\)
0.999567 0.0294409i \(-0.00937270\pi\)
\(558\) 0 0
\(559\) 1.58762 2.74984i 0.0671493 0.116306i
\(560\) −2.04499 18.3329i −0.0864168 0.774707i
\(561\) 0 0
\(562\) 34.1630 + 12.4343i 1.44108 + 0.524509i
\(563\) 17.9677 + 6.53971i 0.757248 + 0.275616i 0.691652 0.722230i \(-0.256883\pi\)
0.0655957 + 0.997846i \(0.479105\pi\)
\(564\) 0 0
\(565\) −1.99111 + 11.2921i −0.0837665 + 0.475063i
\(566\) 14.3927 0.604968
\(567\) 0 0
\(568\) 11.1803 0.469117
\(569\) 3.50374 19.8707i 0.146884 0.833022i −0.818951 0.573864i \(-0.805444\pi\)
0.965835 0.259158i \(-0.0834451\pi\)
\(570\) 0 0
\(571\) −1.27023 0.462325i −0.0531574 0.0193477i 0.315305 0.948991i \(-0.397893\pi\)
−0.368462 + 0.929643i \(0.620116\pi\)
\(572\) 6.27367 + 2.28343i 0.262315 + 0.0954750i
\(573\) 0 0
\(574\) 47.2192 34.7684i 1.97089 1.45120i
\(575\) −1.36380 + 2.36218i −0.0568746 + 0.0985096i
\(576\) 0 0
\(577\) −6.07544 + 10.5230i −0.252924 + 0.438077i −0.964330 0.264705i \(-0.914726\pi\)
0.711406 + 0.702782i \(0.248059\pi\)
\(578\) 27.1194 9.87065i 1.12802 0.410565i
\(579\) 0 0
\(580\) −11.2659 4.10045i −0.467791 0.170262i
\(581\) −21.9764 1.39616i −0.911737 0.0579223i
\(582\) 0 0
\(583\) 16.2649 + 13.6479i 0.673623 + 0.565237i
\(584\) 4.78058 8.28021i 0.197822 0.342638i
\(585\) 0 0
\(586\) 12.7661 + 22.1116i 0.527365 + 0.913422i
\(587\) 36.1996 + 30.3750i 1.49412 + 1.25371i 0.889282 + 0.457360i \(0.151205\pi\)
0.604834 + 0.796352i \(0.293239\pi\)
\(588\) 0 0
\(589\) −1.66763 9.45762i −0.0687136 0.389694i
\(590\) 2.99263 + 16.9721i 0.123205 + 0.698728i
\(591\) 0 0
\(592\) 10.5417 + 8.84557i 0.433263 + 0.363551i
\(593\) −5.30960 + 9.19649i −0.218039 + 0.377655i −0.954208 0.299143i \(-0.903299\pi\)
0.736169 + 0.676797i \(0.236633\pi\)
\(594\) 0 0
\(595\) −4.60708 + 1.35287i −0.188872 + 0.0554623i
\(596\) 6.12600 2.22968i 0.250931 0.0913314i
\(597\) 0 0
\(598\) −1.64832 0.599941i −0.0674050 0.0245334i
\(599\) −7.85627 + 6.59219i −0.320999 + 0.269350i −0.789020 0.614367i \(-0.789411\pi\)
0.468022 + 0.883717i \(0.344967\pi\)
\(600\) 0 0
\(601\) −19.1642 16.0807i −0.781724 0.655945i 0.161958 0.986798i \(-0.448219\pi\)
−0.943682 + 0.330853i \(0.892664\pi\)
\(602\) 11.5197 + 10.9835i 0.469508 + 0.447655i
\(603\) 0 0
\(604\) 21.9994 0.895143
\(605\) −13.5384 + 4.92757i −0.550414 + 0.200334i
\(606\) 0 0
\(607\) 0.503454 0.422448i 0.0204346 0.0171466i −0.632513 0.774550i \(-0.717977\pi\)
0.652948 + 0.757403i \(0.273532\pi\)
\(608\) 9.40528 + 3.42324i 0.381434 + 0.138831i
\(609\) 0 0
\(610\) 2.49033 14.1234i 0.100831 0.571839i
\(611\) 11.1533 0.451214
\(612\) 0 0
\(613\) −27.7448 −1.12060 −0.560301 0.828289i \(-0.689314\pi\)
−0.560301 + 0.828289i \(0.689314\pi\)
\(614\) 30.5435 11.1169i 1.23263 0.448642i
\(615\) 0 0
\(616\) 6.44263 9.68406i 0.259581 0.390182i
\(617\) −12.7820 + 10.7253i −0.514582 + 0.431786i −0.862738 0.505651i \(-0.831252\pi\)
0.348156 + 0.937437i \(0.386808\pi\)
\(618\) 0 0
\(619\) −7.28444 6.11237i −0.292787 0.245677i 0.484548 0.874765i \(-0.338984\pi\)
−0.777334 + 0.629088i \(0.783429\pi\)
\(620\) 7.26050 + 12.5755i 0.291589 + 0.505046i
\(621\) 0 0
\(622\) −55.7920 −2.23705
\(623\) 0.180377 + 1.61704i 0.00722667 + 0.0647854i
\(624\) 0 0
\(625\) −0.438492 2.48681i −0.0175397 0.0994725i
\(626\) 4.53510 3.80540i 0.181259 0.152094i
\(627\) 0 0
\(628\) −0.527500 + 0.191994i −0.0210495 + 0.00766141i
\(629\) 1.79101 3.10213i 0.0714124 0.123690i
\(630\) 0 0
\(631\) −22.9465 39.7445i −0.913486 1.58220i −0.809103 0.587667i \(-0.800047\pi\)
−0.104383 0.994537i \(-0.533287\pi\)
\(632\) −10.4366 8.75737i −0.415147 0.348349i
\(633\) 0 0
\(634\) 2.16476 + 12.2770i 0.0859737 + 0.487581i
\(635\) 14.2376 11.9468i 0.565003 0.474094i
\(636\) 0 0
\(637\) 2.66467 + 6.36079i 0.105578 + 0.252024i
\(638\) −23.5283 40.7523i −0.931495 1.61340i
\(639\) 0 0
\(640\) 10.8945 0.430641
\(641\) 4.98155 28.2518i 0.196759 1.11588i −0.713132 0.701030i \(-0.752724\pi\)
0.909891 0.414847i \(-0.136165\pi\)
\(642\) 0 0
\(643\) 0.172431 + 0.977906i 0.00680002 + 0.0385648i 0.988019 0.154332i \(-0.0493227\pi\)
−0.981219 + 0.192897i \(0.938212\pi\)
\(644\) 2.07467 3.11849i 0.0817536 0.122886i
\(645\) 0 0
\(646\) 0.577400 3.27460i 0.0227175 0.128837i
\(647\) −8.87356 15.3695i −0.348856 0.604236i 0.637191 0.770706i \(-0.280096\pi\)
−0.986046 + 0.166470i \(0.946763\pi\)
\(648\) 0 0
\(649\) −14.4072 + 24.9540i −0.565531 + 0.979528i
\(650\) −4.94148 + 1.79855i −0.193821 + 0.0705451i
\(651\) 0 0
\(652\) 5.86857 4.92432i 0.229831 0.192851i
\(653\) −17.1213 6.23165i −0.670008 0.243863i −0.0154569 0.999881i \(-0.504920\pi\)
−0.654552 + 0.756017i \(0.727143\pi\)
\(654\) 0 0
\(655\) 2.13284 12.0959i 0.0833370 0.472627i
\(656\) 28.2925 + 49.0040i 1.10463 + 1.91328i
\(657\) 0 0
\(658\) −13.1798 + 54.3330i −0.513800 + 2.11812i
\(659\) 0.516836 2.93112i 0.0201331 0.114180i −0.973085 0.230446i \(-0.925981\pi\)
0.993218 + 0.116266i \(0.0370925\pi\)
\(660\) 0 0
\(661\) 4.25035 + 24.1049i 0.165320 + 0.937574i 0.948734 + 0.316075i \(0.102365\pi\)
−0.783415 + 0.621499i \(0.786524\pi\)
\(662\) 1.61720 + 9.17158i 0.0628541 + 0.356463i
\(663\) 0 0
\(664\) 1.39158 7.89202i 0.0540036 0.306270i
\(665\) 1.31039 5.40202i 0.0508147 0.209481i
\(666\) 0 0
\(667\) 2.63328 + 4.56097i 0.101961 + 0.176602i
\(668\) 2.80268 15.8948i 0.108439 0.614987i
\(669\) 0 0
\(670\) 33.7156 + 12.2715i 1.30255 + 0.474089i
\(671\) 18.3682 15.4128i 0.709097 0.595003i
\(672\) 0 0
\(673\) 23.3965 8.51562i 0.901868 0.328253i 0.150867 0.988554i \(-0.451794\pi\)
0.751001 + 0.660301i \(0.229571\pi\)
\(674\) 13.5871 23.5336i 0.523356 0.906480i
\(675\) 0 0
\(676\) 8.92685 + 15.4618i 0.343340 + 0.594683i
\(677\) −1.53657 + 8.71430i −0.0590550 + 0.334918i −0.999993 0.00366049i \(-0.998835\pi\)
0.940938 + 0.338578i \(0.109946\pi\)
\(678\) 0 0
\(679\) 8.36556 12.5745i 0.321041 0.482564i
\(680\) −0.303432 1.72085i −0.0116361 0.0659916i
\(681\) 0 0
\(682\) −9.89709 + 56.1292i −0.378979 + 2.14930i
\(683\) −6.28032 −0.240310 −0.120155 0.992755i \(-0.538339\pi\)
−0.120155 + 0.992755i \(0.538339\pi\)
\(684\) 0 0
\(685\) −1.69943 2.94349i −0.0649317 0.112465i
\(686\) −34.1352 + 5.46435i −1.30329 + 0.208630i
\(687\) 0 0
\(688\) −11.7658 + 9.87272i −0.448569 + 0.376394i
\(689\) −0.795542 4.51174i −0.0303077 0.171884i
\(690\) 0 0
\(691\) −8.61563 7.22938i −0.327754 0.275018i 0.464030 0.885820i \(-0.346403\pi\)
−0.791784 + 0.610801i \(0.790847\pi\)
\(692\) 8.98622 + 15.5646i 0.341605 + 0.591677i
\(693\) 0 0
\(694\) −8.11448 + 14.0547i −0.308022 + 0.533509i
\(695\) −29.5435 + 10.7529i −1.12065 + 0.407882i
\(696\) 0 0
\(697\) 11.2830 9.46757i 0.427374 0.358610i
\(698\) 3.59312 + 20.3776i 0.136001 + 0.771302i
\(699\) 0 0
\(700\) −1.24482 11.1596i −0.0470499 0.421791i
\(701\) −11.0400 −0.416976 −0.208488 0.978025i \(-0.566854\pi\)
−0.208488 + 0.978025i \(0.566854\pi\)
\(702\) 0 0
\(703\) 2.07340 + 3.59124i 0.0781999 + 0.135446i
\(704\) −12.1667 10.2090i −0.458549 0.384768i
\(705\) 0 0
\(706\) 33.1111 27.7835i 1.24615 1.04565i
\(707\) −17.3559 + 26.0880i −0.652735 + 0.981140i
\(708\) 0 0
\(709\) 17.8195 6.48575i 0.669224 0.243577i 0.0150100 0.999887i \(-0.495222\pi\)
0.654214 + 0.756310i \(0.273000\pi\)
\(710\) −31.7105 −1.19008
\(711\) 0 0
\(712\) −0.592121 −0.0221907
\(713\) 1.10768 6.28195i 0.0414828 0.235261i
\(714\) 0 0
\(715\) 6.18428 + 2.25089i 0.231279 + 0.0841786i
\(716\) −14.0728 + 11.8085i −0.525926 + 0.441304i
\(717\) 0 0
\(718\) −3.64717 + 1.32746i −0.136111 + 0.0495404i
\(719\) −3.54116 −0.132063 −0.0660316 0.997818i \(-0.521034\pi\)
−0.0660316 + 0.997818i \(0.521034\pi\)
\(720\) 0 0
\(721\) 24.5739 + 23.4301i 0.915179 + 0.872583i
\(722\) −24.2192 20.3223i −0.901345 0.756318i
\(723\) 0 0
\(724\) 18.0432 15.1400i 0.670569 0.562674i
\(725\) 14.8364 + 5.40000i 0.551009 + 0.200551i
\(726\) 0 0
\(727\) 34.1662 12.4355i 1.26715 0.461206i 0.380990 0.924579i \(-0.375583\pi\)
0.886163 + 0.463373i \(0.153361\pi\)
\(728\) −2.40805 + 0.707124i −0.0892481 + 0.0262078i
\(729\) 0 0
\(730\) −13.5590 + 23.4850i −0.501843 + 0.869217i
\(731\) 3.06262 + 2.56985i 0.113275 + 0.0950492i
\(732\) 0 0
\(733\) −3.73447 21.1792i −0.137936 0.782272i −0.972770 0.231771i \(-0.925548\pi\)
0.834835 0.550501i \(-0.185563\pi\)
\(734\) −4.96227 28.1425i −0.183161 1.03876i
\(735\) 0 0
\(736\) 5.09275 + 4.27333i 0.187721 + 0.157517i
\(737\) 29.9945 + 51.9519i 1.10486 + 1.91367i
\(738\) 0 0
\(739\) −3.59765 + 6.23131i −0.132342 + 0.229223i −0.924579 0.380991i \(-0.875583\pi\)
0.792237 + 0.610213i \(0.208916\pi\)
\(740\) −4.80323 4.03039i −0.176570 0.148160i
\(741\) 0 0
\(742\) 22.9189 + 1.45603i 0.841380 + 0.0534525i
\(743\) 5.28136 + 1.92226i 0.193754 + 0.0705207i 0.437075 0.899425i \(-0.356015\pi\)
−0.243321 + 0.969946i \(0.578237\pi\)
\(744\) 0 0
\(745\) 6.03872 2.19791i 0.221242 0.0805253i
\(746\) −28.6232 + 49.5768i −1.04797 + 1.81513i
\(747\) 0 0
\(748\) −4.20308 + 7.27996i −0.153680 + 0.266182i
\(749\) 23.5383 17.3317i 0.860072 0.633287i
\(750\) 0 0
\(751\) −40.3558 14.6883i −1.47260 0.535984i −0.523797 0.851843i \(-0.675485\pi\)
−0.948806 + 0.315860i \(0.897707\pi\)
\(752\) −50.6969 18.4522i −1.84873 0.672881i
\(753\) 0 0
\(754\) −1.76314 + 9.99926i −0.0642098 + 0.364152i
\(755\) 21.6859 0.789232
\(756\) 0 0
\(757\) −18.7190 −0.680354 −0.340177 0.940361i \(-0.610487\pi\)
−0.340177 + 0.940361i \(0.610487\pi\)
\(758\) 10.7373 60.8943i 0.389997 2.21178i
\(759\) 0 0
\(760\) 1.90091 + 0.691876i 0.0689533 + 0.0250970i
\(761\) −11.7685 4.28340i −0.426609 0.155273i 0.119787 0.992800i \(-0.461779\pi\)
−0.546397 + 0.837526i \(0.684001\pi\)
\(762\) 0 0
\(763\) 5.58699 + 50.0861i 0.202263 + 1.81324i
\(764\) −11.2817 + 19.5404i −0.408157 + 0.706948i
\(765\) 0 0
\(766\) −11.0880 + 19.2050i −0.400626 + 0.693904i
\(767\) 5.84238 2.12645i 0.210956 0.0767818i
\(768\) 0 0
\(769\) 18.4388 + 6.71117i 0.664920 + 0.242011i 0.652359 0.757910i \(-0.273779\pi\)
0.0125608 + 0.999921i \(0.496002\pi\)
\(770\) −18.2731 + 27.4667i −0.658516 + 0.989830i
\(771\) 0 0
\(772\) −21.3757 17.9363i −0.769327 0.645542i
\(773\) 5.39853 9.35052i 0.194171 0.336315i −0.752457 0.658641i \(-0.771132\pi\)
0.946629 + 0.322326i \(0.104465\pi\)
\(774\) 0 0
\(775\) −9.56154 16.5611i −0.343461 0.594891i
\(776\) 4.21038 + 3.53293i 0.151144 + 0.126825i
\(777\) 0 0
\(778\) −7.41343 42.0436i −0.265784 1.50734i
\(779\) 2.96092 + 16.7922i 0.106086 + 0.601643i
\(780\) 0 0
\(781\) −40.6147 34.0798i −1.45331 1.21947i
\(782\) 1.10431 1.91271i 0.0394899 0.0683985i
\(783\) 0