Properties

Label 675.2.l.f.76.8
Level $675$
Weight $2$
Character 675.76
Analytic conductor $5.390$
Analytic rank $0$
Dimension $66$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [675,2,Mod(76,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.l (of order \(9\), degree \(6\), 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: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(66\)
Relative dimension: \(11\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 76.8
Character \(\chi\) \(=\) 675.76
Dual form 675.2.l.f.151.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.672508 - 0.564301i) q^{2} +(1.45527 - 0.939248i) q^{3} +(-0.213465 + 1.21062i) q^{4} +(0.448662 - 1.45286i) q^{6} +(-0.0883715 - 0.501180i) q^{7} +(1.41750 + 2.45517i) q^{8} +(1.23563 - 2.73372i) q^{9} +O(q^{10})\) \(q+(0.672508 - 0.564301i) q^{2} +(1.45527 - 0.939248i) q^{3} +(-0.213465 + 1.21062i) q^{4} +(0.448662 - 1.45286i) q^{6} +(-0.0883715 - 0.501180i) q^{7} +(1.41750 + 2.45517i) q^{8} +(1.23563 - 2.73372i) q^{9} +(2.28041 + 0.830001i) q^{11} +(0.826424 + 1.96228i) q^{12} +(4.85915 + 4.07731i) q^{13} +(-0.342247 - 0.287179i) q^{14} +(0.0284139 + 0.0103418i) q^{16} +(-2.86909 + 4.96942i) q^{17} +(-0.711675 - 2.53572i) q^{18} +(-1.94493 - 3.36871i) q^{19} +(-0.599337 - 0.646349i) q^{21} +(2.00197 - 0.728656i) q^{22} +(1.12370 - 6.37282i) q^{23} +(4.36886 + 2.24156i) q^{24} +5.56865 q^{26} +(-0.769474 - 5.13886i) q^{27} +0.625603 q^{28} +(-0.324767 + 0.272512i) q^{29} +(1.47718 - 8.37750i) q^{31} +(-5.30309 + 1.93017i) q^{32} +(4.09819 - 0.933994i) q^{33} +(0.874759 + 4.96101i) q^{34} +(3.04574 + 2.07943i) q^{36} +(-1.19190 + 2.06443i) q^{37} +(-3.20895 - 1.16796i) q^{38} +(10.9010 + 1.36964i) q^{39} +(0.938033 + 0.787103i) q^{41} +(-0.767795 - 0.0964687i) q^{42} +(2.34944 + 0.855127i) q^{43} +(-1.49160 + 2.58353i) q^{44} +(-2.84049 - 4.91988i) q^{46} +(0.143949 + 0.816377i) q^{47} +(0.0510634 - 0.0116376i) q^{48} +(6.33448 - 2.30556i) q^{49} +(0.492208 + 9.92664i) q^{51} +(-5.97334 + 5.01222i) q^{52} -8.88536 q^{53} +(-3.41735 - 3.02171i) q^{54} +(1.10522 - 0.927387i) q^{56} +(-5.99445 - 3.07562i) q^{57} +(-0.0646297 + 0.366533i) q^{58} +(-6.58000 + 2.39492i) q^{59} +(0.558258 + 3.16604i) q^{61} +(-3.73402 - 6.46751i) q^{62} +(-1.47928 - 0.377687i) q^{63} +(-2.50742 + 4.34297i) q^{64} +(2.22901 - 2.94073i) q^{66} +(-5.32923 - 4.47176i) q^{67} +(-5.40363 - 4.53418i) q^{68} +(-4.35037 - 10.3296i) q^{69} +(-1.59927 + 2.77002i) q^{71} +(8.46325 - 0.841362i) q^{72} +(5.99262 + 10.3795i) q^{73} +(0.363398 + 2.06093i) q^{74} +(4.49341 - 1.63547i) q^{76} +(0.214457 - 1.21624i) q^{77} +(8.10390 - 5.23035i) q^{78} +(2.06451 - 1.73233i) q^{79} +(-5.94646 - 6.75571i) q^{81} +1.07500 q^{82} +(-6.00558 + 5.03928i) q^{83} +(0.910421 - 0.587596i) q^{84} +(2.06257 - 0.750714i) q^{86} +(-0.216668 + 0.701616i) q^{87} +(1.19467 + 6.77532i) q^{88} +(-9.24733 - 16.0168i) q^{89} +(1.61406 - 2.79563i) q^{91} +(7.47519 + 2.72075i) q^{92} +(-5.71886 - 13.5790i) q^{93} +(0.557490 + 0.467789i) q^{94} +(-5.90453 + 7.78984i) q^{96} +(7.86099 + 2.86117i) q^{97} +(2.95896 - 5.12506i) q^{98} +(5.08672 - 5.20843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27} + 36 q^{28} - 15 q^{29} + 3 q^{31} - 27 q^{32} + 3 q^{33} + 30 q^{36} - 6 q^{37} + 12 q^{38} - 15 q^{39} + 39 q^{41} - 48 q^{42} - 12 q^{43} + 51 q^{44} + 9 q^{46} - 30 q^{47} + 132 q^{48} - 6 q^{49} - 9 q^{52} + 24 q^{53} + 75 q^{54} + 144 q^{56} - 33 q^{57} - 27 q^{58} + 45 q^{59} - 54 q^{61} - 66 q^{62} + 120 q^{63} - 24 q^{64} + 48 q^{66} - 9 q^{67} + 69 q^{68} + 51 q^{69} - 15 q^{71} - 9 q^{72} + 15 q^{73} + 96 q^{74} - 48 q^{76} + 36 q^{77} + 18 q^{78} + 48 q^{79} - 54 q^{81} + 36 q^{82} - 30 q^{83} + 57 q^{84} - 111 q^{86} + 33 q^{87} - 36 q^{88} - 12 q^{89} + 9 q^{91} + 219 q^{92} - 63 q^{93} + 36 q^{94} - 249 q^{96} - 57 q^{97} - 75 q^{98} - 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.672508 0.564301i 0.475535 0.399021i −0.373274 0.927721i \(-0.621765\pi\)
0.848809 + 0.528700i \(0.177320\pi\)
\(3\) 1.45527 0.939248i 0.840201 0.542275i
\(4\) −0.213465 + 1.21062i −0.106733 + 0.605310i
\(5\) 0 0
\(6\) 0.448662 1.45286i 0.183166 0.593129i
\(7\) −0.0883715 0.501180i −0.0334013 0.189428i 0.963542 0.267557i \(-0.0862165\pi\)
−0.996943 + 0.0781292i \(0.975105\pi\)
\(8\) 1.41750 + 2.45517i 0.501160 + 0.868035i
\(9\) 1.23563 2.73372i 0.411875 0.911240i
\(10\) 0 0
\(11\) 2.28041 + 0.830001i 0.687569 + 0.250255i 0.662094 0.749421i \(-0.269668\pi\)
0.0254752 + 0.999675i \(0.491890\pi\)
\(12\) 0.826424 + 1.96228i 0.238568 + 0.566461i
\(13\) 4.85915 + 4.07731i 1.34769 + 1.13084i 0.979579 + 0.201059i \(0.0644383\pi\)
0.368107 + 0.929784i \(0.380006\pi\)
\(14\) −0.342247 0.287179i −0.0914694 0.0767519i
\(15\) 0 0
\(16\) 0.0284139 + 0.0103418i 0.00710347 + 0.00258545i
\(17\) −2.86909 + 4.96942i −0.695857 + 1.20526i 0.274033 + 0.961720i \(0.411642\pi\)
−0.969891 + 0.243540i \(0.921691\pi\)
\(18\) −0.711675 2.53572i −0.167743 0.597674i
\(19\) −1.94493 3.36871i −0.446197 0.772835i 0.551938 0.833885i \(-0.313889\pi\)
−0.998135 + 0.0610497i \(0.980555\pi\)
\(20\) 0 0
\(21\) −0.599337 0.646349i −0.130786 0.141045i
\(22\) 2.00197 0.728656i 0.426820 0.155350i
\(23\) 1.12370 6.37282i 0.234308 1.32882i −0.609760 0.792586i \(-0.708734\pi\)
0.844067 0.536238i \(-0.180155\pi\)
\(24\) 4.36886 + 2.24156i 0.891789 + 0.457557i
\(25\) 0 0
\(26\) 5.56865 1.09210
\(27\) −0.769474 5.13886i −0.148085 0.988975i
\(28\) 0.625603 0.118228
\(29\) −0.324767 + 0.272512i −0.0603078 + 0.0506042i −0.672443 0.740149i \(-0.734755\pi\)
0.612136 + 0.790753i \(0.290311\pi\)
\(30\) 0 0
\(31\) 1.47718 8.37750i 0.265309 1.50464i −0.502844 0.864377i \(-0.667713\pi\)
0.768153 0.640266i \(-0.221176\pi\)
\(32\) −5.30309 + 1.93017i −0.937464 + 0.341209i
\(33\) 4.09819 0.933994i 0.713403 0.162588i
\(34\) 0.874759 + 4.96101i 0.150020 + 0.850806i
\(35\) 0 0
\(36\) 3.04574 + 2.07943i 0.507623 + 0.346571i
\(37\) −1.19190 + 2.06443i −0.195947 + 0.339390i −0.947210 0.320612i \(-0.896111\pi\)
0.751264 + 0.660002i \(0.229445\pi\)
\(38\) −3.20895 1.16796i −0.520560 0.189468i
\(39\) 10.9010 + 1.36964i 1.74555 + 0.219318i
\(40\) 0 0
\(41\) 0.938033 + 0.787103i 0.146496 + 0.122925i 0.713090 0.701072i \(-0.247295\pi\)
−0.566594 + 0.823997i \(0.691739\pi\)
\(42\) −0.767795 0.0964687i −0.118473 0.0148854i
\(43\) 2.34944 + 0.855127i 0.358287 + 0.130406i 0.514891 0.857256i \(-0.327832\pi\)
−0.156604 + 0.987661i \(0.550055\pi\)
\(44\) −1.49160 + 2.58353i −0.224868 + 0.389482i
\(45\) 0 0
\(46\) −2.84049 4.91988i −0.418808 0.725396i
\(47\) 0.143949 + 0.816377i 0.0209972 + 0.119081i 0.993505 0.113790i \(-0.0362991\pi\)
−0.972508 + 0.232871i \(0.925188\pi\)
\(48\) 0.0510634 0.0116376i 0.00737037 0.00167974i
\(49\) 6.33448 2.30556i 0.904925 0.329366i
\(50\) 0 0
\(51\) 0.492208 + 9.92664i 0.0689229 + 1.39001i
\(52\) −5.97334 + 5.01222i −0.828353 + 0.695070i
\(53\) −8.88536 −1.22050 −0.610249 0.792210i \(-0.708931\pi\)
−0.610249 + 0.792210i \(0.708931\pi\)
\(54\) −3.41735 3.02171i −0.465042 0.411203i
\(55\) 0 0
\(56\) 1.10522 0.927387i 0.147691 0.123927i
\(57\) −5.99445 3.07562i −0.793984 0.407376i
\(58\) −0.0646297 + 0.366533i −0.00848630 + 0.0481282i
\(59\) −6.58000 + 2.39492i −0.856643 + 0.311792i −0.732746 0.680503i \(-0.761762\pi\)
−0.123897 + 0.992295i \(0.539539\pi\)
\(60\) 0 0
\(61\) 0.558258 + 3.16604i 0.0714776 + 0.405369i 0.999463 + 0.0327541i \(0.0104278\pi\)
−0.927986 + 0.372615i \(0.878461\pi\)
\(62\) −3.73402 6.46751i −0.474221 0.821375i
\(63\) −1.47928 0.377687i −0.186372 0.0475841i
\(64\) −2.50742 + 4.34297i −0.313427 + 0.542871i
\(65\) 0 0
\(66\) 2.22901 2.94073i 0.274372 0.361979i
\(67\) −5.32923 4.47176i −0.651070 0.546312i 0.256326 0.966590i \(-0.417488\pi\)
−0.907395 + 0.420278i \(0.861932\pi\)
\(68\) −5.40363 4.53418i −0.655286 0.549850i
\(69\) −4.35037 10.3296i −0.523723 1.24354i
\(70\) 0 0
\(71\) −1.59927 + 2.77002i −0.189799 + 0.328741i −0.945183 0.326541i \(-0.894117\pi\)
0.755384 + 0.655282i \(0.227450\pi\)
\(72\) 8.46325 0.841362i 0.997404 0.0991554i
\(73\) 5.99262 + 10.3795i 0.701383 + 1.21483i 0.967981 + 0.251024i \(0.0807672\pi\)
−0.266598 + 0.963808i \(0.585899\pi\)
\(74\) 0.363398 + 2.06093i 0.0422442 + 0.239579i
\(75\) 0 0
\(76\) 4.49341 1.63547i 0.515429 0.187601i
\(77\) 0.214457 1.21624i 0.0244396 0.138604i
\(78\) 8.10390 5.23035i 0.917585 0.592220i
\(79\) 2.06451 1.73233i 0.232276 0.194903i −0.519220 0.854641i \(-0.673777\pi\)
0.751495 + 0.659738i \(0.229333\pi\)
\(80\) 0 0
\(81\) −5.94646 6.75571i −0.660718 0.750634i
\(82\) 1.07500 0.118714
\(83\) −6.00558 + 5.03928i −0.659198 + 0.553133i −0.909846 0.414945i \(-0.863801\pi\)
0.250648 + 0.968078i \(0.419356\pi\)
\(84\) 0.910421 0.587596i 0.0993351 0.0641120i
\(85\) 0 0
\(86\) 2.06257 0.750714i 0.222412 0.0809515i
\(87\) −0.216668 + 0.701616i −0.0232292 + 0.0752211i
\(88\) 1.19467 + 6.77532i 0.127353 + 0.722252i
\(89\) −9.24733 16.0168i −0.980215 1.69778i −0.661525 0.749923i \(-0.730091\pi\)
−0.318690 0.947859i \(-0.603243\pi\)
\(90\) 0 0
\(91\) 1.61406 2.79563i 0.169199 0.293061i
\(92\) 7.47519 + 2.72075i 0.779343 + 0.283658i
\(93\) −5.71886 13.5790i −0.593018 1.40807i
\(94\) 0.557490 + 0.467789i 0.0575007 + 0.0482488i
\(95\) 0 0
\(96\) −5.90453 + 7.78984i −0.602629 + 0.795047i
\(97\) 7.86099 + 2.86117i 0.798163 + 0.290508i 0.708725 0.705485i \(-0.249271\pi\)
0.0894380 + 0.995992i \(0.471493\pi\)
\(98\) 2.95896 5.12506i 0.298900 0.517710i
\(99\) 5.08672 5.20843i 0.511235 0.523467i
\(100\) 0 0
\(101\) 0.772822 + 4.38289i 0.0768986 + 0.436114i 0.998813 + 0.0487190i \(0.0155139\pi\)
−0.921914 + 0.387395i \(0.873375\pi\)
\(102\) 5.93263 + 6.39799i 0.587418 + 0.633496i
\(103\) −10.4849 + 3.81618i −1.03310 + 0.376019i −0.802262 0.596972i \(-0.796370\pi\)
−0.230842 + 0.972991i \(0.574148\pi\)
\(104\) −3.12269 + 17.7096i −0.306204 + 1.73657i
\(105\) 0 0
\(106\) −5.97548 + 5.01402i −0.580390 + 0.487005i
\(107\) −11.5176 −1.11345 −0.556724 0.830698i \(-0.687942\pi\)
−0.556724 + 0.830698i \(0.687942\pi\)
\(108\) 6.38547 + 0.165427i 0.614442 + 0.0159182i
\(109\) −16.8148 −1.61057 −0.805285 0.592888i \(-0.797988\pi\)
−0.805285 + 0.592888i \(0.797988\pi\)
\(110\) 0 0
\(111\) 0.204476 + 4.12379i 0.0194080 + 0.391413i
\(112\) 0.00267213 0.0151544i 0.000252492 0.00143195i
\(113\) −10.0593 + 3.66129i −0.946301 + 0.344425i −0.768651 0.639668i \(-0.779072\pi\)
−0.177650 + 0.984094i \(0.556849\pi\)
\(114\) −5.76689 + 1.31430i −0.540119 + 0.123095i
\(115\) 0 0
\(116\) −0.260582 0.451342i −0.0241945 0.0419060i
\(117\) 17.1503 8.24553i 1.58555 0.762300i
\(118\) −3.07364 + 5.32371i −0.282952 + 0.490087i
\(119\) 2.74412 + 0.998777i 0.251553 + 0.0915577i
\(120\) 0 0
\(121\) −3.91512 3.28518i −0.355920 0.298653i
\(122\) 2.16203 + 1.81416i 0.195741 + 0.164246i
\(123\) 2.10438 + 0.264402i 0.189745 + 0.0238404i
\(124\) 9.82665 + 3.57661i 0.882459 + 0.321189i
\(125\) 0 0
\(126\) −1.20796 + 0.580762i −0.107613 + 0.0517384i
\(127\) 3.89640 + 6.74877i 0.345750 + 0.598857i 0.985490 0.169735i \(-0.0542912\pi\)
−0.639740 + 0.768592i \(0.720958\pi\)
\(128\) −1.19546 6.77978i −0.105664 0.599253i
\(129\) 4.22225 0.962268i 0.371748 0.0847230i
\(130\) 0 0
\(131\) 1.52245 8.63426i 0.133017 0.754378i −0.843203 0.537596i \(-0.819333\pi\)
0.976220 0.216783i \(-0.0695563\pi\)
\(132\) 0.255892 + 5.16073i 0.0222726 + 0.449184i
\(133\) −1.51645 + 1.27246i −0.131493 + 0.110336i
\(134\) −6.10737 −0.527597
\(135\) 0 0
\(136\) −16.2677 −1.39494
\(137\) 12.2406 10.2711i 1.04579 0.877519i 0.0531421 0.998587i \(-0.483076\pi\)
0.992644 + 0.121068i \(0.0386319\pi\)
\(138\) −8.75467 4.49182i −0.745247 0.382369i
\(139\) −0.582428 + 3.30311i −0.0494009 + 0.280167i −0.999494 0.0317992i \(-0.989876\pi\)
0.950093 + 0.311966i \(0.100987\pi\)
\(140\) 0 0
\(141\) 0.976266 + 1.05285i 0.0822164 + 0.0886656i
\(142\) 0.487603 + 2.76534i 0.0409188 + 0.232062i
\(143\) 7.69668 + 13.3310i 0.643629 + 1.11480i
\(144\) 0.0633805 0.0648970i 0.00528171 0.00540808i
\(145\) 0 0
\(146\) 9.88727 + 3.59867i 0.818276 + 0.297828i
\(147\) 7.05288 9.30486i 0.581712 0.767452i
\(148\) −2.24481 1.88362i −0.184522 0.154833i
\(149\) −1.64045 1.37650i −0.134391 0.112767i 0.573114 0.819475i \(-0.305735\pi\)
−0.707505 + 0.706708i \(0.750179\pi\)
\(150\) 0 0
\(151\) −14.8096 5.39026i −1.20519 0.438653i −0.340156 0.940369i \(-0.610480\pi\)
−0.865032 + 0.501716i \(0.832702\pi\)
\(152\) 5.51385 9.55027i 0.447232 0.774629i
\(153\) 10.0399 + 13.9836i 0.811675 + 1.13051i
\(154\) −0.542104 0.938952i −0.0436840 0.0756629i
\(155\) 0 0
\(156\) −3.98510 + 12.9046i −0.319063 + 1.03319i
\(157\) 20.5892 7.49385i 1.64320 0.598074i 0.655602 0.755106i \(-0.272415\pi\)
0.987594 + 0.157032i \(0.0501925\pi\)
\(158\) 0.410845 2.33002i 0.0326851 0.185366i
\(159\) −12.9306 + 8.34556i −1.02546 + 0.661846i
\(160\) 0 0
\(161\) −3.29323 −0.259543
\(162\) −7.81130 1.18767i −0.613714 0.0933125i
\(163\) 19.9707 1.56423 0.782115 0.623134i \(-0.214141\pi\)
0.782115 + 0.623134i \(0.214141\pi\)
\(164\) −1.15312 + 0.967584i −0.0900436 + 0.0755556i
\(165\) 0 0
\(166\) −1.19513 + 6.77791i −0.0927600 + 0.526068i
\(167\) −16.2833 + 5.92664i −1.26004 + 0.458617i −0.883783 0.467897i \(-0.845012\pi\)
−0.376258 + 0.926515i \(0.622789\pi\)
\(168\) 0.737343 2.38767i 0.0568873 0.184213i
\(169\) 4.72945 + 26.8220i 0.363804 + 2.06323i
\(170\) 0 0
\(171\) −11.6123 + 1.15442i −0.888016 + 0.0882808i
\(172\) −1.53676 + 2.66174i −0.117177 + 0.202956i
\(173\) −13.4604 4.89919i −1.02338 0.372478i −0.224821 0.974400i \(-0.572180\pi\)
−0.798555 + 0.601922i \(0.794402\pi\)
\(174\) 0.250212 + 0.594109i 0.0189685 + 0.0450393i
\(175\) 0 0
\(176\) 0.0562116 + 0.0471671i 0.00423711 + 0.00355535i
\(177\) −7.32625 + 9.66551i −0.550675 + 0.726505i
\(178\) −15.2572 5.55318i −1.14358 0.416228i
\(179\) 12.1807 21.0976i 0.910428 1.57691i 0.0969684 0.995287i \(-0.469085\pi\)
0.813460 0.581621i \(-0.197581\pi\)
\(180\) 0 0
\(181\) 2.03955 + 3.53261i 0.151599 + 0.262577i 0.931815 0.362933i \(-0.118225\pi\)
−0.780217 + 0.625509i \(0.784891\pi\)
\(182\) −0.492110 2.79090i −0.0364776 0.206875i
\(183\) 3.78611 + 4.08310i 0.279877 + 0.301831i
\(184\) 17.2392 6.27456i 1.27089 0.462567i
\(185\) 0 0
\(186\) −11.5086 5.90481i −0.843852 0.432962i
\(187\) −10.6673 + 8.95095i −0.780072 + 0.654558i
\(188\) −1.01905 −0.0743219
\(189\) −2.50749 + 0.839774i −0.182393 + 0.0610845i
\(190\) 0 0
\(191\) 5.70298 4.78537i 0.412653 0.346257i −0.412707 0.910864i \(-0.635417\pi\)
0.825360 + 0.564607i \(0.190972\pi\)
\(192\) 0.430160 + 8.67528i 0.0310441 + 0.626085i
\(193\) −1.60633 + 9.10995i −0.115626 + 0.655749i 0.870812 + 0.491616i \(0.163594\pi\)
−0.986438 + 0.164133i \(0.947517\pi\)
\(194\) 6.90115 2.51181i 0.495473 0.180338i
\(195\) 0 0
\(196\) 1.43897 + 8.16081i 0.102784 + 0.582915i
\(197\) 4.51987 + 7.82865i 0.322028 + 0.557768i 0.980906 0.194481i \(-0.0623023\pi\)
−0.658879 + 0.752249i \(0.728969\pi\)
\(198\) 0.481737 6.37316i 0.0342356 0.452921i
\(199\) 3.66921 6.35527i 0.260104 0.450513i −0.706166 0.708047i \(-0.749577\pi\)
0.966269 + 0.257534i \(0.0829099\pi\)
\(200\) 0 0
\(201\) −11.9556 1.50214i −0.843281 0.105953i
\(202\) 2.99300 + 2.51143i 0.210587 + 0.176703i
\(203\) 0.165278 + 0.138684i 0.0116002 + 0.00973374i
\(204\) −12.1225 1.52311i −0.848742 0.106639i
\(205\) 0 0
\(206\) −4.89768 + 8.48303i −0.341238 + 0.591041i
\(207\) −16.0330 10.9463i −1.11437 0.760820i
\(208\) 0.0959005 + 0.166105i 0.00664950 + 0.0115173i
\(209\) −1.63919 9.29633i −0.113385 0.643041i
\(210\) 0 0
\(211\) 15.6493 5.69586i 1.07734 0.392119i 0.258423 0.966032i \(-0.416797\pi\)
0.818917 + 0.573913i \(0.194575\pi\)
\(212\) 1.89671 10.7568i 0.130267 0.738780i
\(213\) 0.274364 + 5.53325i 0.0187991 + 0.379132i
\(214\) −7.74568 + 6.49940i −0.529484 + 0.444290i
\(215\) 0 0
\(216\) 11.5261 9.17350i 0.784250 0.624178i
\(217\) −4.32917 −0.293883
\(218\) −11.3081 + 9.48864i −0.765882 + 0.642652i
\(219\) 18.4698 + 9.47646i 1.24808 + 0.640360i
\(220\) 0 0
\(221\) −34.2032 + 12.4490i −2.30076 + 0.837407i
\(222\) 2.46457 + 2.65790i 0.165411 + 0.178386i
\(223\) −1.47210 8.34872i −0.0985794 0.559072i −0.993592 0.113030i \(-0.963944\pi\)
0.895012 0.446042i \(-0.147167\pi\)
\(224\) 1.43600 + 2.48723i 0.0959470 + 0.166185i
\(225\) 0 0
\(226\) −4.69890 + 8.13874i −0.312566 + 0.541381i
\(227\) 9.11223 + 3.31658i 0.604800 + 0.220129i 0.626227 0.779641i \(-0.284599\pi\)
−0.0214263 + 0.999770i \(0.506821\pi\)
\(228\) 5.00301 6.60047i 0.331333 0.437127i
\(229\) 0.120012 + 0.100702i 0.00793060 + 0.00665457i 0.646744 0.762707i \(-0.276130\pi\)
−0.638814 + 0.769361i \(0.720575\pi\)
\(230\) 0 0
\(231\) −0.830262 1.97139i −0.0546272 0.129708i
\(232\) −1.12942 0.411076i −0.0741501 0.0269884i
\(233\) −8.14148 + 14.1015i −0.533366 + 0.923818i 0.465874 + 0.884851i \(0.345740\pi\)
−0.999241 + 0.0389667i \(0.987593\pi\)
\(234\) 6.88077 15.2231i 0.449810 0.995168i
\(235\) 0 0
\(236\) −1.49474 8.47711i −0.0972995 0.551813i
\(237\) 1.37734 4.46010i 0.0894676 0.289715i
\(238\) 2.40905 0.876823i 0.156156 0.0568360i
\(239\) −3.50159 + 19.8585i −0.226499 + 1.28454i 0.633299 + 0.773907i \(0.281700\pi\)
−0.859798 + 0.510634i \(0.829411\pi\)
\(240\) 0 0
\(241\) 20.2060 16.9549i 1.30158 1.09216i 0.311716 0.950175i \(-0.399096\pi\)
0.989869 0.141984i \(-0.0453481\pi\)
\(242\) −4.48678 −0.288421
\(243\) −14.9990 4.24618i −0.962186 0.272393i
\(244\) −3.95204 −0.253003
\(245\) 0 0
\(246\) 1.56441 1.00969i 0.0997434 0.0643755i
\(247\) 4.28460 24.2991i 0.272622 1.54612i
\(248\) 22.6621 8.24833i 1.43905 0.523770i
\(249\) −4.00661 + 12.9742i −0.253908 + 0.822209i
\(250\) 0 0
\(251\) −10.6490 18.4446i −0.672160 1.16422i −0.977290 0.211905i \(-0.932033\pi\)
0.305130 0.952311i \(-0.401300\pi\)
\(252\) 0.773011 1.71022i 0.0486951 0.107734i
\(253\) 7.85194 13.6000i 0.493647 0.855022i
\(254\) 6.42871 + 2.33986i 0.403373 + 0.146816i
\(255\) 0 0
\(256\) −12.3130 10.3318i −0.769560 0.645737i
\(257\) 8.82228 + 7.40277i 0.550319 + 0.461772i 0.875049 0.484034i \(-0.160829\pi\)
−0.324730 + 0.945807i \(0.605274\pi\)
\(258\) 2.29649 3.02976i 0.142973 0.188624i
\(259\) 1.13998 + 0.414918i 0.0708348 + 0.0257818i
\(260\) 0 0
\(261\) 0.343681 + 1.22455i 0.0212733 + 0.0757975i
\(262\) −3.84846 6.66573i −0.237759 0.411810i
\(263\) 1.87867 + 10.6545i 0.115844 + 0.656983i 0.986329 + 0.164789i \(0.0526942\pi\)
−0.870485 + 0.492195i \(0.836195\pi\)
\(264\) 8.10228 + 8.73784i 0.498661 + 0.537777i
\(265\) 0 0
\(266\) −0.301779 + 1.71147i −0.0185033 + 0.104937i
\(267\) −28.5012 14.6233i −1.74424 0.894932i
\(268\) 6.55121 5.49712i 0.400179 0.335790i
\(269\) −27.5918 −1.68230 −0.841152 0.540798i \(-0.818122\pi\)
−0.841152 + 0.540798i \(0.818122\pi\)
\(270\) 0 0
\(271\) 22.2930 1.35421 0.677103 0.735889i \(-0.263235\pi\)
0.677103 + 0.735889i \(0.263235\pi\)
\(272\) −0.132915 + 0.111529i −0.00805914 + 0.00676242i
\(273\) −0.276899 5.58439i −0.0167587 0.337983i
\(274\) 2.43592 13.8148i 0.147159 0.834582i
\(275\) 0 0
\(276\) 13.4339 3.06164i 0.808625 0.184289i
\(277\) 3.55616 + 20.1680i 0.213669 + 1.21178i 0.883201 + 0.468994i \(0.155383\pi\)
−0.669532 + 0.742783i \(0.733505\pi\)
\(278\) 1.47226 + 2.55004i 0.0883006 + 0.152941i
\(279\) −21.0765 14.3896i −1.26182 0.861486i
\(280\) 0 0
\(281\) 14.8184 + 5.39346i 0.883993 + 0.321747i 0.743820 0.668380i \(-0.233012\pi\)
0.140173 + 0.990127i \(0.455234\pi\)
\(282\) 1.25067 + 0.157139i 0.0744763 + 0.00935749i
\(283\) −8.09200 6.78999i −0.481019 0.403623i 0.369776 0.929121i \(-0.379435\pi\)
−0.850795 + 0.525498i \(0.823879\pi\)
\(284\) −3.01206 2.52742i −0.178733 0.149975i
\(285\) 0 0
\(286\) 12.6988 + 4.62199i 0.750896 + 0.273304i
\(287\) 0.311585 0.539681i 0.0183923 0.0318564i
\(288\) −1.27610 + 16.8821i −0.0751946 + 0.994790i
\(289\) −7.96339 13.7930i −0.468435 0.811353i
\(290\) 0 0
\(291\) 14.1272 3.21965i 0.828152 0.188739i
\(292\) −13.8449 + 5.03913i −0.810211 + 0.294893i
\(293\) 2.86499 16.2482i 0.167375 0.949229i −0.779207 0.626766i \(-0.784378\pi\)
0.946582 0.322463i \(-0.104511\pi\)
\(294\) −0.507624 10.2375i −0.0296052 0.597066i
\(295\) 0 0
\(296\) −6.75804 −0.392803
\(297\) 2.51055 12.3574i 0.145677 0.717048i
\(298\) −1.87998 −0.108904
\(299\) 31.4442 26.3848i 1.81846 1.52587i
\(300\) 0 0
\(301\) 0.220949 1.25306i 0.0127353 0.0722253i
\(302\) −13.0013 + 4.73209i −0.748142 + 0.272301i
\(303\) 5.24129 + 5.65242i 0.301104 + 0.324723i
\(304\) −0.0204243 0.115832i −0.00117142 0.00664343i
\(305\) 0 0
\(306\) 14.6429 + 3.73860i 0.837078 + 0.213721i
\(307\) 7.16633 12.4125i 0.409004 0.708416i −0.585774 0.810474i \(-0.699209\pi\)
0.994778 + 0.102058i \(0.0325428\pi\)
\(308\) 1.42663 + 0.519251i 0.0812898 + 0.0295871i
\(309\) −11.6740 + 15.4015i −0.664109 + 0.876158i
\(310\) 0 0
\(311\) 24.3502 + 20.4322i 1.38077 + 1.15861i 0.968926 + 0.247352i \(0.0795605\pi\)
0.411846 + 0.911253i \(0.364884\pi\)
\(312\) 12.0894 + 28.7053i 0.684427 + 1.62512i
\(313\) −16.0443 5.83964i −0.906876 0.330076i −0.153871 0.988091i \(-0.549174\pi\)
−0.753005 + 0.658015i \(0.771396\pi\)
\(314\) 9.61761 16.6582i 0.542753 0.940076i
\(315\) 0 0
\(316\) 1.65650 + 2.86914i 0.0931852 + 0.161401i
\(317\) 2.37080 + 13.4455i 0.133157 + 0.755173i 0.976125 + 0.217209i \(0.0696952\pi\)
−0.842968 + 0.537964i \(0.819194\pi\)
\(318\) −3.98653 + 12.9092i −0.223553 + 0.723913i
\(319\) −0.966788 + 0.351882i −0.0541297 + 0.0197016i
\(320\) 0 0
\(321\) −16.7612 + 10.8179i −0.935520 + 0.603795i
\(322\) −2.21472 + 1.85837i −0.123422 + 0.103563i
\(323\) 22.3207 1.24196
\(324\) 9.44796 5.75680i 0.524887 0.319822i
\(325\) 0 0
\(326\) 13.4305 11.2695i 0.743846 0.624161i
\(327\) −24.4701 + 15.7933i −1.35320 + 0.873372i
\(328\) −0.602818 + 3.41875i −0.0332851 + 0.188769i
\(329\) 0.396431 0.144289i 0.0218559 0.00795491i
\(330\) 0 0
\(331\) 4.91646 + 27.8827i 0.270233 + 1.53257i 0.753707 + 0.657211i \(0.228264\pi\)
−0.483474 + 0.875359i \(0.660625\pi\)
\(332\) −4.81867 8.34619i −0.264459 0.458057i
\(333\) 4.17083 + 5.80917i 0.228560 + 0.318341i
\(334\) −7.60625 + 13.1744i −0.416196 + 0.720872i
\(335\) 0 0
\(336\) −0.0103451 0.0245635i −0.000564369 0.00134005i
\(337\) 13.2795 + 11.1428i 0.723379 + 0.606987i 0.928318 0.371787i \(-0.121255\pi\)
−0.204938 + 0.978775i \(0.565699\pi\)
\(338\) 18.3163 + 15.3692i 0.996276 + 0.835975i
\(339\) −11.2002 + 14.7764i −0.608310 + 0.802542i
\(340\) 0 0
\(341\) 10.3219 17.8781i 0.558963 0.968152i
\(342\) −7.15794 + 7.32921i −0.387057 + 0.396318i
\(343\) −3.49648 6.05608i −0.188792 0.326997i
\(344\) 1.23084 + 6.98043i 0.0663623 + 0.376359i
\(345\) 0 0
\(346\) −11.8168 + 4.30098i −0.635278 + 0.231222i
\(347\) 0.584994 3.31767i 0.0314041 0.178102i −0.965071 0.261988i \(-0.915622\pi\)
0.996475 + 0.0838860i \(0.0267331\pi\)
\(348\) −0.803140 0.412073i −0.0430528 0.0220894i
\(349\) 5.25034 4.40556i 0.281045 0.235824i −0.491358 0.870958i \(-0.663499\pi\)
0.772402 + 0.635133i \(0.219055\pi\)
\(350\) 0 0
\(351\) 17.2138 28.1079i 0.918802 1.50029i
\(352\) −13.6953 −0.729960
\(353\) 23.3547 19.5969i 1.24304 1.04304i 0.245763 0.969330i \(-0.420961\pi\)
0.997280 0.0737074i \(-0.0234831\pi\)
\(354\) 0.527300 + 10.6344i 0.0280257 + 0.565209i
\(355\) 0 0
\(356\) 21.3643 7.77597i 1.13231 0.412126i
\(357\) 4.93153 1.12392i 0.261004 0.0594840i
\(358\) −3.71378 21.0619i −0.196279 1.11316i
\(359\) 7.50154 + 12.9931i 0.395916 + 0.685747i 0.993218 0.116270i \(-0.0370937\pi\)
−0.597301 + 0.802017i \(0.703760\pi\)
\(360\) 0 0
\(361\) 1.93452 3.35069i 0.101817 0.176352i
\(362\) 3.36507 + 1.22479i 0.176864 + 0.0643733i
\(363\) −8.78316 1.10355i −0.460996 0.0579214i
\(364\) 3.03990 + 2.55078i 0.159334 + 0.133697i
\(365\) 0 0
\(366\) 4.85029 + 0.609409i 0.253529 + 0.0318543i
\(367\) 15.5982 + 5.67728i 0.814219 + 0.296351i 0.715365 0.698751i \(-0.246260\pi\)
0.0988534 + 0.995102i \(0.468483\pi\)
\(368\) 0.0978351 0.169455i 0.00510000 0.00883347i
\(369\) 3.31078 1.59176i 0.172352 0.0828635i
\(370\) 0 0
\(371\) 0.785213 + 4.45316i 0.0407662 + 0.231197i
\(372\) 17.6598 4.02473i 0.915616 0.208673i
\(373\) −6.57037 + 2.39142i −0.340201 + 0.123823i −0.506470 0.862257i \(-0.669050\pi\)
0.166269 + 0.986080i \(0.446828\pi\)
\(374\) −2.12283 + 12.0392i −0.109769 + 0.622531i
\(375\) 0 0
\(376\) −1.80030 + 1.51063i −0.0928434 + 0.0779048i
\(377\) −2.68921 −0.138501
\(378\) −1.21243 + 1.97974i −0.0623604 + 0.101827i
\(379\) −13.7794 −0.707801 −0.353901 0.935283i \(-0.615145\pi\)
−0.353901 + 0.935283i \(0.615145\pi\)
\(380\) 0 0
\(381\) 12.0091 + 6.16160i 0.615245 + 0.315668i
\(382\) 1.13491 6.43640i 0.0580671 0.329315i
\(383\) −9.64267 + 3.50965i −0.492718 + 0.179335i −0.576416 0.817157i \(-0.695549\pi\)
0.0836981 + 0.996491i \(0.473327\pi\)
\(384\) −8.10761 8.74358i −0.413740 0.446194i
\(385\) 0 0
\(386\) 4.06049 + 7.03297i 0.206673 + 0.357969i
\(387\) 5.24071 5.36610i 0.266400 0.272774i
\(388\) −5.14184 + 8.90592i −0.261037 + 0.452130i
\(389\) 36.0005 + 13.1031i 1.82530 + 0.664354i 0.994112 + 0.108358i \(0.0345594\pi\)
0.831185 + 0.555996i \(0.187663\pi\)
\(390\) 0 0
\(391\) 28.4452 + 23.8683i 1.43853 + 1.20707i
\(392\) 14.6396 + 12.2841i 0.739414 + 0.620442i
\(393\) −5.89413 13.9951i −0.297320 0.705961i
\(394\) 7.45737 + 2.71426i 0.375697 + 0.136742i
\(395\) 0 0
\(396\) 5.21960 + 7.26991i 0.262295 + 0.365327i
\(397\) −15.9911 27.6975i −0.802573 1.39010i −0.917917 0.396771i \(-0.870131\pi\)
0.115345 0.993326i \(-0.463203\pi\)
\(398\) −1.11871 6.34451i −0.0560758 0.318022i
\(399\) −1.01170 + 3.27609i −0.0506483 + 0.164010i
\(400\) 0 0
\(401\) −0.893312 + 5.06623i −0.0446099 + 0.252995i −0.998955 0.0457121i \(-0.985444\pi\)
0.954345 + 0.298707i \(0.0965554\pi\)
\(402\) −8.88788 + 5.73634i −0.443287 + 0.286103i
\(403\) 41.3355 34.6846i 2.05907 1.72776i
\(404\) −5.47099 −0.272192
\(405\) 0 0
\(406\) 0.189410 0.00940028
\(407\) −4.43149 + 3.71846i −0.219661 + 0.184317i
\(408\) −23.6739 + 15.2794i −1.17203 + 0.756444i
\(409\) 4.07496 23.1102i 0.201494 1.14273i −0.701369 0.712799i \(-0.747427\pi\)
0.902863 0.429929i \(-0.141462\pi\)
\(410\) 0 0
\(411\) 8.16630 26.4442i 0.402814 1.30440i
\(412\) −2.38179 13.5078i −0.117342 0.665482i
\(413\) 1.78177 + 3.08612i 0.0876752 + 0.151858i
\(414\) −16.9594 + 1.68599i −0.833507 + 0.0828618i
\(415\) 0 0
\(416\) −33.6384 12.2434i −1.64926 0.600281i
\(417\) 2.25485 + 5.35397i 0.110421 + 0.262185i
\(418\) −6.34831 5.32686i −0.310506 0.260545i
\(419\) −7.14090 5.99192i −0.348856 0.292725i 0.451475 0.892284i \(-0.350898\pi\)
−0.800330 + 0.599559i \(0.795343\pi\)
\(420\) 0 0
\(421\) −22.7017 8.26276i −1.10641 0.402702i −0.276738 0.960945i \(-0.589253\pi\)
−0.829677 + 0.558243i \(0.811476\pi\)
\(422\) 7.31007 12.6614i 0.355849 0.616348i
\(423\) 2.40961 + 0.615219i 0.117159 + 0.0299130i
\(424\) −12.5950 21.8151i −0.611665 1.05943i
\(425\) 0 0
\(426\) 3.30693 + 3.56633i 0.160221 + 0.172789i
\(427\) 1.53742 0.559575i 0.0744009 0.0270797i
\(428\) 2.45860 13.9434i 0.118841 0.673982i
\(429\) 23.7219 + 12.1712i 1.14530 + 0.587630i
\(430\) 0 0
\(431\) −10.5453 −0.507950 −0.253975 0.967211i \(-0.581738\pi\)
−0.253975 + 0.967211i \(0.581738\pi\)
\(432\) 0.0312814 0.153973i 0.00150503 0.00740802i
\(433\) −4.12615 −0.198290 −0.0991451 0.995073i \(-0.531611\pi\)
−0.0991451 + 0.995073i \(0.531611\pi\)
\(434\) −2.91141 + 2.44296i −0.139752 + 0.117266i
\(435\) 0 0
\(436\) 3.58938 20.3564i 0.171900 0.974894i
\(437\) −23.6537 + 8.60924i −1.13151 + 0.411836i
\(438\) 17.7687 4.04956i 0.849021 0.193495i
\(439\) −2.08794 11.8413i −0.0996517 0.565153i −0.993222 0.116230i \(-0.962919\pi\)
0.893571 0.448923i \(-0.148192\pi\)
\(440\) 0 0
\(441\) 1.52428 20.1655i 0.0725847 0.960262i
\(442\) −15.9770 + 27.6729i −0.759948 + 1.31627i
\(443\) 31.8626 + 11.5970i 1.51384 + 0.550992i 0.959600 0.281367i \(-0.0907877\pi\)
0.554237 + 0.832359i \(0.313010\pi\)
\(444\) −5.03599 0.632742i −0.238998 0.0300286i
\(445\) 0 0
\(446\) −5.70120 4.78387i −0.269960 0.226523i
\(447\) −3.68018 0.462392i −0.174066 0.0218704i
\(448\) 2.39819 + 0.872871i 0.113304 + 0.0412393i
\(449\) 0.297582 0.515427i 0.0140438 0.0243245i −0.858918 0.512113i \(-0.828863\pi\)
0.872962 + 0.487788i \(0.162196\pi\)
\(450\) 0 0
\(451\) 1.48580 + 2.57349i 0.0699638 + 0.121181i
\(452\) −2.28512 12.9596i −0.107483 0.609567i
\(453\) −26.6148 + 6.06562i −1.25047 + 0.284988i
\(454\) 7.99960 2.91162i 0.375440 0.136649i
\(455\) 0 0
\(456\) −0.945929 19.0771i −0.0442972 0.893367i
\(457\) 6.79746 5.70374i 0.317972 0.266810i −0.469806 0.882770i \(-0.655676\pi\)
0.787778 + 0.615960i \(0.211232\pi\)
\(458\) 0.137535 0.00642659
\(459\) 27.7448 + 10.9200i 1.29502 + 0.509704i
\(460\) 0 0
\(461\) −19.2142 + 16.1226i −0.894895 + 0.750906i −0.969186 0.246331i \(-0.920775\pi\)
0.0742911 + 0.997237i \(0.476331\pi\)
\(462\) −1.67082 0.857259i −0.0777335 0.0398833i
\(463\) −1.99238 + 11.2994i −0.0925939 + 0.525126i 0.902864 + 0.429926i \(0.141460\pi\)
−0.995458 + 0.0952002i \(0.969651\pi\)
\(464\) −0.0120462 + 0.00438444i −0.000559229 + 0.000203543i
\(465\) 0 0
\(466\) 2.48226 + 14.0776i 0.114989 + 0.652132i
\(467\) 0.328021 + 0.568149i 0.0151790 + 0.0262908i 0.873515 0.486797i \(-0.161835\pi\)
−0.858336 + 0.513088i \(0.828502\pi\)
\(468\) 6.32122 + 22.5227i 0.292198 + 1.04111i
\(469\) −1.77020 + 3.06608i −0.0817403 + 0.141578i
\(470\) 0 0
\(471\) 22.9243 30.2439i 1.05629 1.39357i
\(472\) −15.2071 12.7602i −0.699962 0.587338i
\(473\) 4.64793 + 3.90008i 0.213712 + 0.179326i
\(474\) −1.59057 3.77669i −0.0730575 0.173469i
\(475\) 0 0
\(476\) −1.79491 + 3.10888i −0.0822697 + 0.142495i
\(477\) −10.9790 + 24.2901i −0.502693 + 1.11217i
\(478\) 8.85134 + 15.3310i 0.404851 + 0.701223i
\(479\) 3.87971 + 22.0029i 0.177269 + 1.00534i 0.935493 + 0.353346i \(0.114956\pi\)
−0.758224 + 0.651994i \(0.773933\pi\)
\(480\) 0 0
\(481\) −14.2089 + 5.17162i −0.647871 + 0.235806i
\(482\) 4.02106 22.8046i 0.183154 1.03872i
\(483\) −4.79254 + 3.09316i −0.218068 + 0.140744i
\(484\) 4.81285 4.03846i 0.218766 0.183566i
\(485\) 0 0
\(486\) −12.4831 + 5.60836i −0.566244 + 0.254401i
\(487\) −28.3011 −1.28245 −0.641224 0.767354i \(-0.721573\pi\)
−0.641224 + 0.767354i \(0.721573\pi\)
\(488\) −6.98184 + 5.85846i −0.316053 + 0.265200i
\(489\) 29.0628 18.7575i 1.31427 0.848243i
\(490\) 0 0
\(491\) −40.2634 + 14.6547i −1.81706 + 0.661357i −0.821184 + 0.570664i \(0.806686\pi\)
−0.995879 + 0.0906928i \(0.971092\pi\)
\(492\) −0.769302 + 2.49116i −0.0346828 + 0.112310i
\(493\) −0.422438 2.39577i −0.0190257 0.107900i
\(494\) −10.8306 18.7592i −0.487293 0.844015i
\(495\) 0 0
\(496\) 0.128611 0.222761i 0.00577480 0.0100022i
\(497\) 1.52961 + 0.556732i 0.0686124 + 0.0249729i
\(498\) 4.62691 + 10.9862i 0.207337 + 0.492304i
\(499\) −3.09802 2.59955i −0.138686 0.116372i 0.570805 0.821085i \(-0.306631\pi\)
−0.709492 + 0.704714i \(0.751076\pi\)
\(500\) 0 0
\(501\) −18.1300 + 23.9189i −0.809991 + 1.06862i
\(502\) −17.5699 6.39492i −0.784183 0.285419i
\(503\) 11.9697 20.7321i 0.533702 0.924399i −0.465523 0.885036i \(-0.654134\pi\)
0.999225 0.0393633i \(-0.0125330\pi\)
\(504\) −1.16958 4.16726i −0.0520974 0.185624i
\(505\) 0 0
\(506\) −2.39398 13.5769i −0.106425 0.603569i
\(507\) 32.0752 + 34.5912i 1.42451 + 1.53625i
\(508\) −9.00195 + 3.27644i −0.399397 + 0.145369i
\(509\) −4.85069 + 27.5096i −0.215003 + 1.21934i 0.665898 + 0.746043i \(0.268049\pi\)
−0.880901 + 0.473300i \(0.843063\pi\)
\(510\) 0 0
\(511\) 4.67243 3.92064i 0.206696 0.173439i
\(512\) −0.342088 −0.0151183
\(513\) −15.8148 + 12.5868i −0.698239 + 0.555723i
\(514\) 10.1105 0.445953
\(515\) 0 0
\(516\) 0.263639 + 5.31695i 0.0116060 + 0.234066i
\(517\) −0.349331 + 1.98115i −0.0153635 + 0.0871310i
\(518\) 1.00078 0.364256i 0.0439719 0.0160045i
\(519\) −24.1901 + 5.51302i −1.06183 + 0.241995i
\(520\) 0 0
\(521\) −6.07222 10.5174i −0.266029 0.460775i 0.701804 0.712370i \(-0.252378\pi\)
−0.967833 + 0.251595i \(0.919045\pi\)
\(522\) 0.922142 + 0.629577i 0.0403610 + 0.0275559i
\(523\) 11.2405 19.4691i 0.491512 0.851324i −0.508440 0.861097i \(-0.669778\pi\)
0.999952 + 0.00977335i \(0.00311100\pi\)
\(524\) 10.1278 + 3.68622i 0.442436 + 0.161033i
\(525\) 0 0
\(526\) 7.27576 + 6.10509i 0.317238 + 0.266195i
\(527\) 37.3931 + 31.3765i 1.62887 + 1.36678i
\(528\) 0.126105 + 0.0158443i 0.00548800 + 0.000689534i
\(529\) −17.7371 6.45579i −0.771180 0.280687i
\(530\) 0 0
\(531\) −1.58336 + 20.9471i −0.0687119 + 0.909027i
\(532\) −1.21675 2.10748i −0.0527529 0.0913706i
\(533\) 1.34878 + 7.64931i 0.0584221 + 0.331328i
\(534\) −27.4192 + 6.24895i −1.18655 + 0.270419i
\(535\) 0 0
\(536\) 3.42478 19.4229i 0.147928 0.838941i
\(537\) −2.08966 42.1434i −0.0901756 1.81862i
\(538\) −18.5557 + 15.5701i −0.799995 + 0.671276i
\(539\) 16.3588 0.704624
\(540\) 0 0
\(541\) −22.1510 −0.952347 −0.476173 0.879351i \(-0.657977\pi\)
−0.476173 + 0.879351i \(0.657977\pi\)
\(542\) 14.9922 12.5800i 0.643972 0.540357i
\(543\) 6.28609 + 3.22525i 0.269762 + 0.138409i
\(544\) 5.62326 31.8911i 0.241095 1.36732i
\(545\) 0 0
\(546\) −3.33750 3.59929i −0.142832 0.154036i
\(547\) −1.66357 9.43459i −0.0711292 0.403394i −0.999496 0.0317297i \(-0.989898\pi\)
0.928367 0.371664i \(-0.121213\pi\)
\(548\) 9.82146 + 17.0113i 0.419552 + 0.726685i
\(549\) 9.34486 + 2.38591i 0.398829 + 0.101828i
\(550\) 0 0
\(551\) 1.54966 + 0.564031i 0.0660179 + 0.0240285i
\(552\) 19.1943 25.3231i 0.816966 1.07782i
\(553\) −1.05065 0.881604i −0.0446784 0.0374896i
\(554\) 13.7724 + 11.5564i 0.585132 + 0.490984i
\(555\) 0 0
\(556\) −3.87449 1.41020i −0.164315 0.0598058i
\(557\) 0.0452561 0.0783859i 0.00191756 0.00332132i −0.865065 0.501660i \(-0.832723\pi\)
0.866983 + 0.498338i \(0.166056\pi\)
\(558\) −22.2942 + 2.21635i −0.943790 + 0.0938255i
\(559\) 7.92967 + 13.7346i 0.335389 + 0.580911i
\(560\) 0 0
\(561\) −7.11668 + 23.0453i −0.300467 + 0.972975i
\(562\) 13.0090 4.73491i 0.548753 0.199730i
\(563\) 2.55509 14.4906i 0.107684 0.610707i −0.882430 0.470443i \(-0.844094\pi\)
0.990114 0.140263i \(-0.0447949\pi\)
\(564\) −1.48299 + 0.957142i −0.0624453 + 0.0403029i
\(565\) 0 0
\(566\) −9.27354 −0.389796
\(567\) −2.86033 + 3.57726i −0.120122 + 0.150231i
\(568\) −9.06785 −0.380479
\(569\) −5.30885 + 4.45466i −0.222559 + 0.186749i −0.747249 0.664544i \(-0.768626\pi\)
0.524690 + 0.851293i \(0.324181\pi\)
\(570\) 0 0
\(571\) −5.14921 + 29.2026i −0.215488 + 1.22209i 0.664570 + 0.747226i \(0.268615\pi\)
−0.880058 + 0.474866i \(0.842497\pi\)
\(572\) −17.7818 + 6.47205i −0.743495 + 0.270610i
\(573\) 3.80473 12.3205i 0.158945 0.514697i
\(574\) −0.0949993 0.538768i −0.00396519 0.0224877i
\(575\) 0 0
\(576\) 8.77425 + 12.2209i 0.365594 + 0.509202i
\(577\) 2.30175 3.98675i 0.0958231 0.165970i −0.814129 0.580684i \(-0.802785\pi\)
0.909952 + 0.414714i \(0.136118\pi\)
\(578\) −13.1389 4.78215i −0.546505 0.198911i
\(579\) 6.21886 + 14.7662i 0.258447 + 0.613662i
\(580\) 0 0
\(581\) 3.05631 + 2.56455i 0.126797 + 0.106395i
\(582\) 7.68382 10.1373i 0.318505 0.420203i
\(583\) −20.2623 7.37486i −0.839177 0.305435i
\(584\) −16.9890 + 29.4259i −0.703011 + 1.21765i
\(585\) 0 0
\(586\) −7.24214 12.5438i −0.299170 0.518178i
\(587\) 1.69338 + 9.60364i 0.0698933 + 0.396384i 0.999605 + 0.0280969i \(0.00894470\pi\)
−0.929712 + 0.368288i \(0.879944\pi\)
\(588\) 9.75911 + 10.5246i 0.402459 + 0.434028i
\(589\) −31.0944 + 11.3174i −1.28122 + 0.466327i
\(590\) 0 0
\(591\) 13.9307 + 7.14752i 0.573032 + 0.294010i
\(592\) −0.0552163 + 0.0463320i −0.00226938 + 0.00190423i
\(593\) 1.52185 0.0624948 0.0312474 0.999512i \(-0.490052\pi\)
0.0312474 + 0.999512i \(0.490052\pi\)
\(594\) −5.28492 9.72714i −0.216843 0.399110i
\(595\) 0 0
\(596\) 2.01660 1.69213i 0.0826032 0.0693123i
\(597\) −0.629473 12.6949i −0.0257626 0.519569i
\(598\) 6.25749 35.4880i 0.255888 1.45121i
\(599\) 24.2758 8.83566i 0.991881 0.361015i 0.205433 0.978671i \(-0.434140\pi\)
0.786448 + 0.617656i \(0.211918\pi\)
\(600\) 0 0
\(601\) −2.97450 16.8692i −0.121332 0.688109i −0.983419 0.181348i \(-0.941954\pi\)
0.862087 0.506761i \(-0.169157\pi\)
\(602\) −0.558515 0.967376i −0.0227634 0.0394273i
\(603\) −18.8095 + 9.04322i −0.765981 + 0.368268i
\(604\) 9.68689 16.7782i 0.394154 0.682695i
\(605\) 0 0
\(606\) 6.71448 + 0.843633i 0.272757 + 0.0342703i
\(607\) 9.63781 + 8.08708i 0.391187 + 0.328244i 0.817075 0.576531i \(-0.195594\pi\)
−0.425889 + 0.904776i \(0.640038\pi\)
\(608\) 16.8163 + 14.1106i 0.681991 + 0.572259i
\(609\) 0.370783 + 0.0465866i 0.0150249 + 0.00188779i
\(610\) 0 0
\(611\) −2.62915 + 4.55382i −0.106364 + 0.184228i
\(612\) −19.0720 + 9.16946i −0.770942 + 0.370653i
\(613\) −11.7819 20.4069i −0.475867 0.824226i 0.523750 0.851872i \(-0.324532\pi\)
−0.999618 + 0.0276453i \(0.991199\pi\)
\(614\) −2.18495 12.3914i −0.0881773 0.500078i
\(615\) 0 0
\(616\) 3.29008 1.19749i 0.132561 0.0482483i
\(617\) 2.01505 11.4279i 0.0811229 0.460071i −0.917003 0.398880i \(-0.869399\pi\)
0.998126 0.0611910i \(-0.0194899\pi\)
\(618\) 0.840222 + 16.9452i 0.0337987 + 0.681638i
\(619\) −15.1620 + 12.7224i −0.609411 + 0.511357i −0.894455 0.447158i \(-0.852436\pi\)
0.285044 + 0.958514i \(0.407992\pi\)
\(620\) 0 0
\(621\) −33.6137 0.870823i −1.34887 0.0349449i
\(622\) 27.9056 1.11891
\(623\) −7.21012 + 6.05001i −0.288867 + 0.242388i
\(624\) 0.295575 + 0.151653i 0.0118325 + 0.00607097i
\(625\) 0 0
\(626\) −14.0852 + 5.12660i −0.562959 + 0.204900i
\(627\) −11.1170 11.9891i −0.443972 0.478797i
\(628\) 4.67714 + 26.5254i 0.186638 + 1.05848i
\(629\) −6.83933 11.8461i −0.272702 0.472334i
\(630\) 0 0
\(631\) −7.28122 + 12.6114i −0.289861 + 0.502054i −0.973776 0.227508i \(-0.926942\pi\)
0.683916 + 0.729561i \(0.260276\pi\)
\(632\) 7.17962 + 2.61317i 0.285590 + 0.103946i
\(633\) 17.4241 22.9876i 0.692545 0.913673i
\(634\) 9.18168 + 7.70434i 0.364651 + 0.305979i
\(635\) 0 0
\(636\) −7.34307 17.4355i −0.291172 0.691364i
\(637\) 40.1807 + 14.6246i 1.59202 + 0.579446i
\(638\) −0.451605 + 0.782203i −0.0178792 + 0.0309677i
\(639\) 5.59637 + 7.79468i 0.221389 + 0.308353i
\(640\) 0 0
\(641\) 3.38084 + 19.1737i 0.133535 + 0.757315i 0.975869 + 0.218358i \(0.0700702\pi\)
−0.842334 + 0.538957i \(0.818819\pi\)
\(642\) −5.16751 + 16.7335i −0.203945 + 0.660418i
\(643\) 2.97050 1.08118i 0.117145 0.0426374i −0.282782 0.959184i \(-0.591257\pi\)
0.399928 + 0.916547i \(0.369035\pi\)
\(644\) 0.702989 3.98685i 0.0277017 0.157104i
\(645\) 0 0
\(646\) 15.0109 12.5956i 0.590594 0.495567i
\(647\) 18.5045 0.727489 0.363744 0.931499i \(-0.381498\pi\)
0.363744 + 0.931499i \(0.381498\pi\)
\(648\) 8.15736 24.1758i 0.320451 0.949714i
\(649\) −16.9929 −0.667029
\(650\) 0 0
\(651\) −6.30012 + 4.06617i −0.246921 + 0.159366i
\(652\) −4.26306 + 24.1770i −0.166954 + 0.946844i
\(653\) −10.6618 + 3.88059i −0.417230 + 0.151859i −0.542100 0.840314i \(-0.682371\pi\)
0.124870 + 0.992173i \(0.460149\pi\)
\(654\) −7.54418 + 24.4297i −0.295001 + 0.955276i
\(655\) 0 0
\(656\) 0.0185131 + 0.0320656i 0.000722815 + 0.00125195i
\(657\) 35.7794 3.55695i 1.39589 0.138770i
\(658\) 0.185180 0.320742i 0.00721908 0.0125038i
\(659\) −24.1280 8.78187i −0.939893 0.342093i −0.173769 0.984786i \(-0.555595\pi\)
−0.766124 + 0.642693i \(0.777817\pi\)
\(660\) 0 0
\(661\) −6.15873 5.16779i −0.239547 0.201004i 0.515109 0.857125i \(-0.327752\pi\)
−0.754655 + 0.656121i \(0.772196\pi\)
\(662\) 19.0406 + 15.9770i 0.740033 + 0.620962i
\(663\) −38.0823 + 50.2419i −1.47899 + 1.95123i
\(664\) −20.8852 7.60159i −0.810502 0.294999i
\(665\) 0 0
\(666\) 6.08304 + 1.55311i 0.235713 + 0.0601819i
\(667\) 1.37173 + 2.37590i 0.0531135 + 0.0919954i
\(668\) −3.69900 20.9781i −0.143118 0.811665i
\(669\) −9.98383 10.7670i −0.385997 0.416275i
\(670\) 0 0
\(671\) −1.35476 + 7.68321i −0.0522999 + 0.296607i
\(672\) 4.42590 + 2.27083i 0.170733 + 0.0875992i
\(673\) −10.4677 + 8.78341i −0.403499 + 0.338576i −0.821844 0.569712i \(-0.807055\pi\)
0.418346 + 0.908288i \(0.362610\pi\)
\(674\) 15.2185 0.586193
\(675\) 0 0
\(676\) −33.4809 −1.28773
\(677\) −33.6430 + 28.2299i −1.29301 + 1.08496i −0.301698 + 0.953404i \(0.597553\pi\)
−0.991308 + 0.131558i \(0.958002\pi\)
\(678\) 0.806121 + 16.2575i 0.0309589 + 0.624366i
\(679\) 0.739271 4.19262i 0.0283706 0.160898i
\(680\) 0 0
\(681\) 16.3759 3.73213i 0.627524 0.143015i
\(682\) −3.14705 17.8478i −0.120507 0.683428i
\(683\) −2.15285 3.72885i −0.0823767 0.142681i 0.821894 0.569641i \(-0.192918\pi\)
−0.904270 + 0.426960i \(0.859584\pi\)
\(684\) 1.08126 14.3045i 0.0413429 0.546948i
\(685\) 0 0
\(686\) −5.76886 2.09969i −0.220256 0.0801667i
\(687\) 0.269234 + 0.0338276i 0.0102719 + 0.00129060i
\(688\) 0.0579132 + 0.0485949i 0.00220792 + 0.00185266i
\(689\) −43.1753 36.2284i −1.64485 1.38019i
\(690\) 0 0
\(691\) 21.9927 + 8.00468i 0.836641 + 0.304512i 0.724581 0.689189i \(-0.242033\pi\)
0.112059 + 0.993702i \(0.464255\pi\)
\(692\) 8.80438 15.2496i 0.334692 0.579704i
\(693\) −3.05988 2.08909i −0.116235 0.0793578i
\(694\) −1.47875 2.56127i −0.0561326 0.0972245i
\(695\) 0 0
\(696\) −2.02971 + 0.462580i −0.0769361 + 0.0175341i
\(697\) −6.60275 + 2.40320i −0.250097 + 0.0910279i
\(698\) 1.04484 5.92555i 0.0395476 0.224286i
\(699\) 1.39671 + 28.1683i 0.0528286 + 1.06542i
\(700\) 0 0
\(701\) 15.0287 0.567624 0.283812 0.958880i \(-0.408401\pi\)
0.283812 + 0.958880i \(0.408401\pi\)
\(702\) −4.28493 28.6165i −0.161724 1.08006i
\(703\) 9.27261 0.349723
\(704\) −9.32261 + 7.82260i −0.351359 + 0.294825i
\(705\) 0 0
\(706\) 4.64765 26.3581i 0.174917 0.992002i
\(707\) 2.12832 0.774645i 0.0800437 0.0291335i
\(708\) −10.1374 10.9326i −0.380986 0.410871i
\(709\) 4.68507 + 26.5704i 0.175952 + 0.997871i 0.937040 + 0.349223i \(0.113554\pi\)
−0.761088 + 0.648648i \(0.775335\pi\)
\(710\) 0 0
\(711\) −2.18475 7.78432i −0.0819345 0.291935i
\(712\) 26.2161 45.4076i 0.982489 1.70172i
\(713\) −51.7284 18.8276i −1.93724 0.705098i
\(714\) 2.68227 3.53871i 0.100381 0.132433i
\(715\) 0 0
\(716\) 22.9410 + 19.2498i 0.857347 + 0.719399i
\(717\) 13.5563 + 32.1884i 0.506270 + 1.20210i
\(718\) 12.3768 + 4.50480i 0.461900 + 0.168118i
\(719\) −21.0623 + 36.4809i −0.785490 + 1.36051i 0.143216 + 0.989691i \(0.454255\pi\)
−0.928706 + 0.370817i \(0.879078\pi\)
\(720\) 0 0
\(721\) 2.83915 + 4.91756i 0.105736 + 0.183139i
\(722\) −0.589817 3.34502i −0.0219507 0.124489i
\(723\) 13.4804 43.6524i 0.501342 1.62345i
\(724\) −4.71202 + 1.71503i −0.175121 + 0.0637388i
\(725\) 0 0
\(726\) −6.52948 + 4.21420i −0.242332 + 0.156404i
\(727\) 7.96369 6.68233i 0.295357 0.247834i −0.483052 0.875592i \(-0.660472\pi\)
0.778409 + 0.627758i \(0.216027\pi\)
\(728\) 9.15166 0.339183
\(729\) −25.8158 + 7.90844i −0.956142 + 0.292905i
\(730\) 0 0
\(731\) −10.9902 + 9.22191i −0.406489 + 0.341085i
\(732\) −5.75128 + 3.71194i −0.212574 + 0.137197i
\(733\) −7.78456 + 44.1484i −0.287529 + 1.63066i 0.408579 + 0.912723i \(0.366024\pi\)
−0.696108 + 0.717937i \(0.745087\pi\)
\(734\) 13.6936 4.98406i 0.505440 0.183965i
\(735\) 0 0
\(736\) 6.34152 + 35.9646i 0.233752 + 1.32567i
\(737\) −8.44127 14.6207i −0.310938 0.538561i
\(738\) 1.32830 2.93875i 0.0488952 0.108177i
\(739\) 8.15749 14.1292i 0.300078 0.519751i −0.676075 0.736833i \(-0.736321\pi\)
0.976153 + 0.217082i \(0.0696539\pi\)
\(740\) 0 0
\(741\) −16.5877 39.3861i −0.609364 1.44689i
\(742\) 3.04099 + 2.55169i 0.111638 + 0.0936755i
\(743\) 8.85961 + 7.43409i 0.325028 + 0.272730i 0.790670 0.612242i \(-0.209732\pi\)
−0.465643 + 0.884973i \(0.654177\pi\)
\(744\) 25.2323 33.2889i 0.925060 1.22043i
\(745\) 0 0
\(746\) −3.06915 + 5.31592i −0.112369 + 0.194630i
\(747\) 6.35534 + 22.6442i 0.232530 + 0.828509i
\(748\) −8.55910 14.8248i −0.312952 0.542049i
\(749\) 1.01783 + 5.77239i 0.0371906 + 0.210918i
\(750\) 0 0
\(751\) −17.9955 + 6.54983i −0.656666 + 0.239007i −0.648796 0.760962i \(-0.724727\pi\)
−0.00786953 + 0.999969i \(0.502505\pi\)
\(752\) −0.00435265 + 0.0246851i −0.000158725 + 0.000900174i
\(753\) −32.8213 16.8399i −1.19607 0.613679i
\(754\) −1.80852 + 1.51753i −0.0658623 + 0.0552650i
\(755\) 0 0
\(756\) −0.481385 3.21489i −0.0175078 0.116924i
\(757\) −8.63554 −0.313864 −0.156932 0.987609i \(-0.550160\pi\)
−0.156932 + 0.987609i \(0.550160\pi\)
\(758\) −9.26677 + 7.77575i −0.336584 + 0.282428i
\(759\) −1.34704 27.1665i −0.0488945 0.986083i
\(760\) 0 0
\(761\) −1.00649 + 0.366334i −0.0364854 + 0.0132796i −0.360198 0.932876i \(-0.617291\pi\)
0.323713 + 0.946155i \(0.395069\pi\)
\(762\) 11.5532 2.63302i 0.418529 0.0953844i
\(763\) 1.48595 + 8.42726i 0.0537951 + 0.305087i
\(764\) 4.57588 + 7.92566i 0.165550 + 0.286740i
\(765\) 0 0
\(766\) −4.50428 + 7.80164i −0.162746 + 0.281885i
\(767\) −41.7380 15.1914i −1.50707 0.548530i
\(768\) −27.6228 3.47064i −0.996752 0.125236i
\(769\) 7.27290 + 6.10268i 0.262267 + 0.220068i 0.764433 0.644703i \(-0.223019\pi\)
−0.502166 + 0.864771i \(0.667463\pi\)
\(770\) 0 0
\(771\) 19.7918 + 2.48672i 0.712786 + 0.0895572i
\(772\) −10.6858 3.88931i −0.384590 0.139979i
\(773\) −0.387381 + 0.670964i −0.0139331 + 0.0241329i −0.872908 0.487885i \(-0.837769\pi\)
0.858975 + 0.512018i \(0.171102\pi\)
\(774\) 0.496320 6.56609i 0.0178399 0.236013i
\(775\) 0 0
\(776\) 4.11826 +