Properties

Label 164.2.o.b.75.4
Level $164$
Weight $2$
Character 164.75
Analytic conductor $1.310$
Analytic rank $0$
Dimension $288$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [164,2,Mod(7,164)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(164, base_ring=CyclotomicField(40))
 
chi = DirichletCharacter(H, H._module([20, 39]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("164.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 164 = 2^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 164.o (of order \(40\), degree \(16\), 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: \(1.30954659315\)
Analytic rank: \(0\)
Dimension: \(288\)
Relative dimension: \(18\) over \(\Q(\zeta_{40})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label 75.4
Character \(\chi\) \(=\) 164.75
Dual form 164.2.o.b.35.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.12656 - 0.854909i) q^{2} +(1.15406 - 2.78614i) q^{3} +(0.538261 + 1.92621i) q^{4} +(-0.151868 - 0.958857i) q^{5} +(-3.68200 + 2.15213i) q^{6} +(4.86887 + 0.383188i) q^{7} +(1.04035 - 2.63015i) q^{8} +(-4.30940 - 4.30940i) q^{9} +O(q^{10})\) \(q+(-1.12656 - 0.854909i) q^{2} +(1.15406 - 2.78614i) q^{3} +(0.538261 + 1.92621i) q^{4} +(-0.151868 - 0.958857i) q^{5} +(-3.68200 + 2.15213i) q^{6} +(4.86887 + 0.383188i) q^{7} +(1.04035 - 2.63015i) q^{8} +(-4.30940 - 4.30940i) q^{9} +(-0.648648 + 1.21004i) q^{10} +(-0.728916 + 0.174997i) q^{11} +(5.98786 + 0.723283i) q^{12} +(-3.24854 + 3.80355i) q^{13} +(-5.15747 - 4.59413i) q^{14} +(-2.84677 - 0.683449i) q^{15} +(-3.42055 + 2.07360i) q^{16} +(-1.94650 + 3.17640i) q^{17} +(1.17064 + 8.53892i) q^{18} +(-2.75256 + 2.35091i) q^{19} +(1.76521 - 0.808644i) q^{20} +(6.68657 - 13.1231i) q^{21} +(0.970773 + 0.426013i) q^{22} +(0.323632 - 0.996036i) q^{23} +(-6.12733 - 5.93390i) q^{24} +(3.85894 - 1.25385i) q^{25} +(6.91135 - 1.50771i) q^{26} +(-8.62144 + 3.57112i) q^{27} +(1.88262 + 9.58471i) q^{28} +(0.778565 + 1.27050i) q^{29} +(2.62276 + 3.20368i) q^{30} +(4.75323 - 3.45342i) q^{31} +(5.62619 + 0.588228i) q^{32} +(-0.353644 + 2.23282i) q^{33} +(4.90837 - 1.91431i) q^{34} +(-0.372003 - 4.72675i) q^{35} +(5.98121 - 10.6204i) q^{36} +(-1.06854 - 0.776343i) q^{37} +(5.11072 - 0.295243i) q^{38} +(6.84821 + 13.4404i) q^{39} +(-2.67993 - 0.598113i) q^{40} +(-5.42638 + 3.39918i) q^{41} +(-18.7519 + 9.06754i) q^{42} +(-3.84819 + 1.96075i) q^{43} +(-0.729428 - 1.30985i) q^{44} +(-3.47763 + 4.78655i) q^{45} +(-1.21611 + 0.845416i) q^{46} +(8.53189 - 0.671474i) q^{47} +(1.82984 + 11.9232i) q^{48} +(16.6453 + 2.63635i) q^{49} +(-5.41924 - 1.88651i) q^{50} +(6.60351 + 9.08895i) q^{51} +(-9.07498 - 4.21006i) q^{52} +(-2.36358 + 1.44840i) q^{53} +(12.7655 + 3.34748i) q^{54} +(0.278497 + 0.672350i) q^{55} +(6.07318 - 12.4072i) q^{56} +(3.37334 + 10.3821i) q^{57} +(0.209067 - 2.09690i) q^{58} +(1.03830 + 0.337364i) q^{59} +(-0.215840 - 5.85135i) q^{60} +(-7.37122 - 3.75582i) q^{61} +(-8.30714 - 0.173101i) q^{62} +(-19.3306 - 22.6332i) q^{63} +(-5.83534 - 5.47255i) q^{64} +(4.14041 + 2.53725i) q^{65} +(2.30726 - 2.21306i) q^{66} +(-1.02203 + 4.25705i) q^{67} +(-7.16612 - 2.03963i) q^{68} +(-2.40160 - 2.05116i) q^{69} +(-3.62186 + 5.64298i) q^{70} +(-2.62998 - 10.9546i) q^{71} +(-15.8176 + 6.85106i) q^{72} +(0.557615 - 0.557615i) q^{73} +(0.540073 + 1.78810i) q^{74} +(0.960046 - 12.1985i) q^{75} +(-6.00992 - 4.03659i) q^{76} +(-3.61606 + 0.572727i) q^{77} +(3.77540 - 20.9959i) q^{78} +(1.99818 + 0.827674i) q^{79} +(2.50776 + 2.96491i) q^{80} +9.85856i q^{81} +(9.01911 + 0.809695i) q^{82} -3.72000i q^{83} +(28.8770 + 5.81605i) q^{84} +(3.34132 + 1.38402i) q^{85} +(6.01147 + 1.08096i) q^{86} +(4.43830 - 0.702958i) q^{87} +(-0.298060 + 2.09922i) q^{88} +(-0.600704 + 7.63267i) q^{89} +(8.00982 - 2.41926i) q^{90} +(-17.2742 + 17.2742i) q^{91} +(2.09277 + 0.0872548i) q^{92} +(-4.13622 - 17.2286i) q^{93} +(-10.1857 - 6.53753i) q^{94} +(2.67221 + 2.28228i) q^{95} +(8.13182 - 14.9965i) q^{96} +(-0.788153 + 3.28289i) q^{97} +(-16.4980 - 17.2002i) q^{98} +(3.89532 + 2.38706i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 24 q^{13} - 4 q^{14} - 28 q^{16} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25} + 4 q^{26} - 48 q^{29} - 44 q^{30} + 108 q^{32} - 72 q^{33} + 12 q^{34} - 20 q^{36} - 24 q^{37} + 56 q^{38} + 8 q^{41} - 112 q^{42} - 40 q^{45} - 48 q^{46} - 68 q^{48} - 16 q^{49} - 60 q^{50} - 124 q^{52} - 64 q^{53} + 64 q^{54} - 84 q^{56} - 24 q^{57} + 40 q^{60} - 8 q^{61} - 44 q^{62} - 20 q^{64} + 64 q^{65} + 60 q^{66} - 28 q^{68} - 8 q^{69} + 128 q^{70} + 160 q^{72} - 32 q^{73} + 80 q^{74} + 288 q^{76} - 32 q^{77} + 116 q^{78} + 176 q^{80} + 212 q^{82} + 152 q^{84} - 56 q^{85} + 180 q^{86} + 144 q^{88} - 72 q^{89} + 224 q^{90} + 36 q^{92} - 8 q^{93} + 52 q^{94} + 136 q^{96} - 88 q^{97} + 104 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/164\mathbb{Z}\right)^\times\).

\(n\) \(83\) \(129\)
\(\chi(n)\) \(-1\) \(e\left(\frac{19}{40}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.12656 0.854909i −0.796596 0.604512i
\(3\) 1.15406 2.78614i 0.666294 1.60858i −0.121466 0.992596i \(-0.538760\pi\)
0.787761 0.615982i \(-0.211240\pi\)
\(4\) 0.538261 + 1.92621i 0.269130 + 0.963104i
\(5\) −0.151868 0.958857i −0.0679175 0.428814i −0.998095 0.0617028i \(-0.980347\pi\)
0.930177 0.367111i \(-0.119653\pi\)
\(6\) −3.68200 + 2.15213i −1.50317 + 0.878603i
\(7\) 4.86887 + 0.383188i 1.84026 + 0.144832i 0.950326 0.311257i \(-0.100750\pi\)
0.889935 + 0.456088i \(0.150750\pi\)
\(8\) 1.04035 2.63015i 0.367820 0.929897i
\(9\) −4.30940 4.30940i −1.43647 1.43647i
\(10\) −0.648648 + 1.21004i −0.205120 + 0.382648i
\(11\) −0.728916 + 0.174997i −0.219777 + 0.0527637i −0.341838 0.939759i \(-0.611049\pi\)
0.122062 + 0.992523i \(0.461049\pi\)
\(12\) 5.98786 + 0.723283i 1.72855 + 0.208794i
\(13\) −3.24854 + 3.80355i −0.900982 + 1.05491i 0.0972371 + 0.995261i \(0.468999\pi\)
−0.998219 + 0.0596532i \(0.981001\pi\)
\(14\) −5.15747 4.59413i −1.37839 1.22783i
\(15\) −2.84677 0.683449i −0.735033 0.176466i
\(16\) −3.42055 + 2.07360i −0.855138 + 0.518401i
\(17\) −1.94650 + 3.17640i −0.472095 + 0.770389i −0.996719 0.0809451i \(-0.974206\pi\)
0.524623 + 0.851334i \(0.324206\pi\)
\(18\) 1.17064 + 8.53892i 0.275922 + 2.01264i
\(19\) −2.75256 + 2.35091i −0.631480 + 0.539335i −0.906555 0.422088i \(-0.861297\pi\)
0.275075 + 0.961423i \(0.411297\pi\)
\(20\) 1.76521 0.808644i 0.394714 0.180818i
\(21\) 6.68657 13.1231i 1.45913 2.86370i
\(22\) 0.970773 + 0.426013i 0.206969 + 0.0908262i
\(23\) 0.323632 0.996036i 0.0674819 0.207688i −0.911629 0.411013i \(-0.865175\pi\)
0.979111 + 0.203325i \(0.0651750\pi\)
\(24\) −6.12733 5.93390i −1.25074 1.21125i
\(25\) 3.85894 1.25385i 0.771788 0.250769i
\(26\) 6.91135 1.50771i 1.35543 0.295686i
\(27\) −8.62144 + 3.57112i −1.65920 + 0.687262i
\(28\) 1.88262 + 9.58471i 0.355782 + 1.81134i
\(29\) 0.778565 + 1.27050i 0.144576 + 0.235927i 0.916729 0.399511i \(-0.130820\pi\)
−0.772153 + 0.635437i \(0.780820\pi\)
\(30\) 2.62276 + 3.20368i 0.478849 + 0.584908i
\(31\) 4.75323 3.45342i 0.853705 0.620253i −0.0724604 0.997371i \(-0.523085\pi\)
0.926165 + 0.377119i \(0.123085\pi\)
\(32\) 5.62619 + 0.588228i 0.994579 + 0.103985i
\(33\) −0.353644 + 2.23282i −0.0615614 + 0.388684i
\(34\) 4.90837 1.91431i 0.841779 0.328302i
\(35\) −0.372003 4.72675i −0.0628800 0.798966i
\(36\) 5.98121 10.6204i 0.996869 1.77006i
\(37\) −1.06854 0.776343i −0.175668 0.127630i 0.496477 0.868050i \(-0.334627\pi\)
−0.672145 + 0.740420i \(0.734627\pi\)
\(38\) 5.11072 0.295243i 0.829068 0.0478947i
\(39\) 6.84821 + 13.4404i 1.09659 + 2.15218i
\(40\) −2.67993 0.598113i −0.423734 0.0945700i
\(41\) −5.42638 + 3.39918i −0.847458 + 0.530862i
\(42\) −18.7519 + 9.06754i −2.89348 + 1.39915i
\(43\) −3.84819 + 1.96075i −0.586844 + 0.299012i −0.722089 0.691800i \(-0.756818\pi\)
0.135245 + 0.990812i \(0.456818\pi\)
\(44\) −0.729428 1.30985i −0.109965 0.197467i
\(45\) −3.47763 + 4.78655i −0.518415 + 0.713537i
\(46\) −1.21611 + 0.845416i −0.179306 + 0.124650i
\(47\) 8.53189 0.671474i 1.24450 0.0979445i 0.560953 0.827848i \(-0.310435\pi\)
0.683551 + 0.729903i \(0.260435\pi\)
\(48\) 1.82984 + 11.9232i 0.264114 + 1.72096i
\(49\) 16.6453 + 2.63635i 2.37789 + 0.376621i
\(50\) −5.41924 1.88651i −0.766396 0.266793i
\(51\) 6.60351 + 9.08895i 0.924676 + 1.27271i
\(52\) −9.07498 4.21006i −1.25847 0.583830i
\(53\) −2.36358 + 1.44840i −0.324662 + 0.198953i −0.675273 0.737568i \(-0.735974\pi\)
0.350610 + 0.936521i \(0.385974\pi\)
\(54\) 12.7655 + 3.34748i 1.73717 + 0.455534i
\(55\) 0.278497 + 0.672350i 0.0375525 + 0.0906597i
\(56\) 6.07318 12.4072i 0.811563 1.65798i
\(57\) 3.37334 + 10.3821i 0.446810 + 1.37514i
\(58\) 0.209067 2.09690i 0.0274518 0.275336i
\(59\) 1.03830 + 0.337364i 0.135175 + 0.0439210i 0.375823 0.926691i \(-0.377360\pi\)
−0.240648 + 0.970612i \(0.577360\pi\)
\(60\) −0.215840 5.85135i −0.0278648 0.755406i
\(61\) −7.37122 3.75582i −0.943788 0.480884i −0.0868030 0.996225i \(-0.527665\pi\)
−0.856985 + 0.515342i \(0.827665\pi\)
\(62\) −8.30714 0.173101i −1.05501 0.0219839i
\(63\) −19.3306 22.6332i −2.43542 2.85152i
\(64\) −5.83534 5.47255i −0.729417 0.684069i
\(65\) 4.14041 + 2.53725i 0.513554 + 0.314707i
\(66\) 2.30726 2.21306i 0.284004 0.272409i
\(67\) −1.02203 + 4.25705i −0.124861 + 0.520082i 0.874523 + 0.484983i \(0.161174\pi\)
−0.999384 + 0.0350982i \(0.988826\pi\)
\(68\) −7.16612 2.03963i −0.869020 0.247341i
\(69\) −2.40160 2.05116i −0.289119 0.246931i
\(70\) −3.62186 + 5.64298i −0.432895 + 0.674465i
\(71\) −2.62998 10.9546i −0.312121 1.30008i −0.879215 0.476425i \(-0.841933\pi\)
0.567094 0.823653i \(-0.308067\pi\)
\(72\) −15.8176 + 6.85106i −1.86413 + 0.807405i
\(73\) 0.557615 0.557615i 0.0652639 0.0652639i −0.673721 0.738985i \(-0.735305\pi\)
0.738985 + 0.673721i \(0.235305\pi\)
\(74\) 0.540073 + 1.78810i 0.0627823 + 0.207863i
\(75\) 0.960046 12.1985i 0.110857 1.40857i
\(76\) −6.00992 4.03659i −0.689386 0.463029i
\(77\) −3.61606 + 0.572727i −0.412088 + 0.0652683i
\(78\) 3.77540 20.9959i 0.427480 2.37732i
\(79\) 1.99818 + 0.827674i 0.224813 + 0.0931206i 0.492247 0.870456i \(-0.336176\pi\)
−0.267434 + 0.963576i \(0.586176\pi\)
\(80\) 2.50776 + 2.96491i 0.280376 + 0.331486i
\(81\) 9.85856i 1.09540i
\(82\) 9.01911 + 0.809695i 0.995994 + 0.0894159i
\(83\) 3.72000i 0.408323i −0.978937 0.204162i \(-0.934553\pi\)
0.978937 0.204162i \(-0.0654468\pi\)
\(84\) 28.8770 + 5.81605i 3.15074 + 0.634583i
\(85\) 3.34132 + 1.38402i 0.362417 + 0.150118i
\(86\) 6.01147 + 1.08096i 0.648234 + 0.116562i
\(87\) 4.43830 0.702958i 0.475836 0.0753650i
\(88\) −0.298060 + 2.09922i −0.0317733 + 0.223777i
\(89\) −0.600704 + 7.63267i −0.0636745 + 0.809061i 0.879315 + 0.476240i \(0.158001\pi\)
−0.942990 + 0.332821i \(0.891999\pi\)
\(90\) 8.00982 2.41926i 0.844309 0.255013i
\(91\) −17.2742 + 17.2742i −1.81083 + 1.81083i
\(92\) 2.09277 + 0.0872548i 0.218186 + 0.00909694i
\(93\) −4.13622 17.2286i −0.428906 1.78652i
\(94\) −10.1857 6.53753i −1.05058 0.674295i
\(95\) 2.67221 + 2.28228i 0.274163 + 0.234157i
\(96\) 8.13182 14.9965i 0.829950 1.53057i
\(97\) −0.788153 + 3.28289i −0.0800248 + 0.333327i −0.997993 0.0633271i \(-0.979829\pi\)
0.917968 + 0.396654i \(0.129829\pi\)
\(98\) −16.4980 17.2002i −1.66655 1.73748i
\(99\) 3.89532 + 2.38706i 0.391495 + 0.239908i
\(100\) 4.49228 + 6.75822i 0.449228 + 0.675822i
\(101\) 8.02819 + 9.39981i 0.798835 + 0.935316i 0.999012 0.0444440i \(-0.0141516\pi\)
−0.200177 + 0.979760i \(0.564152\pi\)
\(102\) 0.330999 15.8846i 0.0327737 1.57281i
\(103\) 3.60378 + 1.83622i 0.355091 + 0.180928i 0.622431 0.782674i \(-0.286145\pi\)
−0.267341 + 0.963602i \(0.586145\pi\)
\(104\) 6.62427 + 12.5012i 0.649563 + 1.22584i
\(105\) −13.5987 4.41848i −1.32709 0.431199i
\(106\) 3.90096 + 0.388937i 0.378895 + 0.0377769i
\(107\) 1.77054 + 5.44916i 0.171164 + 0.526790i 0.999438 0.0335347i \(-0.0106764\pi\)
−0.828273 + 0.560324i \(0.810676\pi\)
\(108\) −11.5193 14.6845i −1.10844 1.41302i
\(109\) −4.08462 9.86114i −0.391235 0.944526i −0.989671 0.143355i \(-0.954211\pi\)
0.598436 0.801171i \(-0.295789\pi\)
\(110\) 0.261056 0.995530i 0.0248907 0.0949200i
\(111\) −3.39616 + 2.08117i −0.322349 + 0.197536i
\(112\) −17.4488 + 8.78539i −1.64876 + 0.830142i
\(113\) −7.01751 9.65878i −0.660152 0.908622i 0.339334 0.940666i \(-0.389798\pi\)
−0.999486 + 0.0320443i \(0.989798\pi\)
\(114\) 5.07547 14.5799i 0.475361 1.36553i
\(115\) −1.00421 0.159051i −0.0936427 0.0148315i
\(116\) −2.02818 + 2.18354i −0.188312 + 0.202737i
\(117\) 30.3902 2.39176i 2.80958 0.221119i
\(118\) −0.881287 1.26771i −0.0811291 0.116702i
\(119\) −10.6944 + 14.7196i −0.980355 + 1.34934i
\(120\) −4.75921 + 6.77640i −0.434455 + 0.618598i
\(121\) −9.30038 + 4.73878i −0.845489 + 0.430798i
\(122\) 5.09321 + 10.5329i 0.461118 + 0.953601i
\(123\) 3.20823 + 19.0415i 0.289276 + 1.71691i
\(124\) 9.21048 + 7.29686i 0.827125 + 0.655277i
\(125\) −3.99200 7.83474i −0.357055 0.700760i
\(126\) 2.42767 + 42.0235i 0.216274 + 3.74375i
\(127\) −10.5642 7.67536i −0.937424 0.681078i 0.0103755 0.999946i \(-0.496697\pi\)
−0.947799 + 0.318868i \(0.896697\pi\)
\(128\) 1.89531 + 11.1538i 0.167523 + 0.985868i
\(129\) 1.02189 + 12.9844i 0.0899728 + 1.14321i
\(130\) −2.49529 6.39802i −0.218851 0.561144i
\(131\) 1.46433 9.24543i 0.127939 0.807777i −0.837364 0.546646i \(-0.815904\pi\)
0.965303 0.261131i \(-0.0840956\pi\)
\(132\) −4.49122 + 0.520647i −0.390911 + 0.0453165i
\(133\) −14.3027 + 10.3915i −1.24020 + 0.901058i
\(134\) 4.79076 3.92207i 0.413859 0.338815i
\(135\) 4.73351 + 7.72439i 0.407396 + 0.664810i
\(136\) 6.32935 + 8.42414i 0.542737 + 0.722364i
\(137\) −15.3115 + 6.34224i −1.30815 + 0.541854i −0.924345 0.381559i \(-0.875387\pi\)
−0.383808 + 0.923413i \(0.625387\pi\)
\(138\) 0.951985 + 4.36391i 0.0810384 + 0.371480i
\(139\) 15.1410 4.91961i 1.28424 0.417276i 0.414171 0.910199i \(-0.364072\pi\)
0.870073 + 0.492923i \(0.164072\pi\)
\(140\) 8.90446 3.26078i 0.752564 0.275586i
\(141\) 7.97545 24.5459i 0.671654 2.06714i
\(142\) −6.40241 + 14.5894i −0.537278 + 1.22432i
\(143\) 1.70230 3.34095i 0.142354 0.279385i
\(144\) 23.6765 + 5.80453i 1.97304 + 0.483711i
\(145\) 1.09999 0.939482i 0.0913493 0.0780197i
\(146\) −1.10489 + 0.151475i −0.0914418 + 0.0125361i
\(147\) 26.5548 43.3335i 2.19020 3.57408i
\(148\) 0.920242 2.47611i 0.0756434 0.203535i
\(149\) −2.32059 0.557124i −0.190110 0.0456414i 0.137272 0.990533i \(-0.456166\pi\)
−0.327382 + 0.944892i \(0.606166\pi\)
\(150\) −11.5102 + 12.9216i −0.939803 + 1.05504i
\(151\) 1.11838 1.30946i 0.0910125 0.106562i −0.713031 0.701133i \(-0.752678\pi\)
0.804043 + 0.594571i \(0.202678\pi\)
\(152\) 3.31960 + 9.68539i 0.269255 + 0.785589i
\(153\) 22.0766 5.30012i 1.78479 0.428489i
\(154\) 4.56332 + 2.44619i 0.367723 + 0.197120i
\(155\) −4.03320 4.03320i −0.323954 0.323954i
\(156\) −22.2028 + 20.4255i −1.77765 + 1.63535i
\(157\) 19.0275 + 1.49750i 1.51856 + 0.119513i 0.810124 0.586259i \(-0.199400\pi\)
0.708439 + 0.705772i \(0.249400\pi\)
\(158\) −1.54348 2.64069i −0.122793 0.210082i
\(159\) 1.30775 + 8.25679i 0.103711 + 0.654806i
\(160\) −0.290412 5.48404i −0.0229591 0.433552i
\(161\) 1.95739 4.72556i 0.154264 0.372426i
\(162\) 8.42818 11.1062i 0.662180 0.872588i
\(163\) −7.92854 −0.621011 −0.310505 0.950572i \(-0.600498\pi\)
−0.310505 + 0.950572i \(0.600498\pi\)
\(164\) −9.46833 8.62269i −0.739352 0.673319i
\(165\) 2.19466 0.170854
\(166\) −3.18026 + 4.19079i −0.246836 + 0.325269i
\(167\) −6.92895 + 16.7280i −0.536178 + 1.29445i 0.391194 + 0.920308i \(0.372062\pi\)
−0.927372 + 0.374140i \(0.877938\pi\)
\(168\) −27.5594 31.2393i −2.12625 2.41016i
\(169\) −1.88034 11.8720i −0.144641 0.913230i
\(170\) −2.58098 4.41570i −0.197952 0.338669i
\(171\) 21.9928 + 1.73087i 1.68183 + 0.132363i
\(172\) −5.84814 6.35702i −0.445917 0.484718i
\(173\) 8.35252 + 8.35252i 0.635030 + 0.635030i 0.949325 0.314295i \(-0.101768\pi\)
−0.314295 + 0.949325i \(0.601768\pi\)
\(174\) −5.60097 3.00242i −0.424608 0.227613i
\(175\) 19.2691 4.62611i 1.45661 0.349701i
\(176\) 2.13042 2.11007i 0.160586 0.159053i
\(177\) 2.13820 2.50351i 0.160717 0.188175i
\(178\) 7.20196 8.08509i 0.539810 0.606003i
\(179\) −24.1951 5.80874i −1.80843 0.434165i −0.818355 0.574713i \(-0.805114\pi\)
−0.990074 + 0.140548i \(0.955114\pi\)
\(180\) −11.0918 4.12223i −0.826732 0.307253i
\(181\) 11.8745 19.3774i 0.882625 1.44031i −0.0151627 0.999885i \(-0.504827\pi\)
0.897788 0.440428i \(-0.145173\pi\)
\(182\) 34.2282 4.69249i 2.53716 0.347831i
\(183\) −18.9710 + 16.2028i −1.40238 + 1.19775i
\(184\) −2.28303 1.88743i −0.168307 0.139143i
\(185\) −0.582124 + 1.14248i −0.0427986 + 0.0839970i
\(186\) −10.0692 + 22.9451i −0.738309 + 1.68241i
\(187\) 0.862973 2.65596i 0.0631069 0.194223i
\(188\) 5.88578 + 16.0728i 0.429264 + 1.17223i
\(189\) −43.3451 + 14.0837i −3.15289 + 1.02444i
\(190\) −1.05925 4.85561i −0.0768461 0.352263i
\(191\) 2.61785 1.08435i 0.189421 0.0784607i −0.285957 0.958243i \(-0.592311\pi\)
0.475378 + 0.879782i \(0.342311\pi\)
\(192\) −21.9816 + 9.94243i −1.58638 + 0.717533i
\(193\) −3.21300 5.24315i −0.231277 0.377410i 0.715857 0.698246i \(-0.246036\pi\)
−0.947135 + 0.320836i \(0.896036\pi\)
\(194\) 3.69448 3.02457i 0.265248 0.217151i
\(195\) 11.8474 8.60762i 0.848408 0.616405i
\(196\) 3.88133 + 33.4813i 0.277238 + 2.39152i
\(197\) −3.81390 + 24.0800i −0.271729 + 1.71563i 0.353709 + 0.935355i \(0.384920\pi\)
−0.625438 + 0.780274i \(0.715080\pi\)
\(198\) −2.34759 6.01930i −0.166836 0.427773i
\(199\) 0.211431 + 2.68648i 0.0149879 + 0.190439i 0.999853 + 0.0171194i \(0.00544952\pi\)
−0.984866 + 0.173320i \(0.944550\pi\)
\(200\) 0.716855 11.4540i 0.0506893 0.809921i
\(201\) 10.6813 + 7.76038i 0.753397 + 0.547375i
\(202\) −1.00824 17.4528i −0.0709392 1.22797i
\(203\) 3.30389 + 6.48425i 0.231888 + 0.455105i
\(204\) −13.9528 + 17.6120i −0.976891 + 1.23308i
\(205\) 4.08342 + 4.68690i 0.285198 + 0.327347i
\(206\) −2.49006 5.14950i −0.173491 0.358783i
\(207\) −5.68697 + 2.89766i −0.395272 + 0.201401i
\(208\) 3.22473 19.7464i 0.223595 1.36917i
\(209\) 1.59498 2.19530i 0.110327 0.151852i
\(210\) 11.5423 + 16.6033i 0.796493 + 1.14574i
\(211\) 2.94049 0.231421i 0.202431 0.0159317i 0.0231621 0.999732i \(-0.492627\pi\)
0.179269 + 0.983800i \(0.442627\pi\)
\(212\) −4.06215 3.77312i −0.278989 0.259139i
\(213\) −33.5563 5.31479i −2.29924 0.364164i
\(214\) 2.66392 7.65243i 0.182102 0.523110i
\(215\) 2.46450 + 3.39209i 0.168077 + 0.231339i
\(216\) 0.423236 + 26.3909i 0.0287976 + 1.79567i
\(217\) 24.4662 14.9929i 1.66087 1.01778i
\(218\) −3.82882 + 14.6011i −0.259321 + 0.988912i
\(219\) −0.910073 2.19711i −0.0614970 0.148467i
\(220\) −1.14518 + 0.898342i −0.0772082 + 0.0605662i
\(221\) −5.75831 17.7222i −0.387346 1.19213i
\(222\) 5.60518 + 0.558852i 0.376195 + 0.0375077i
\(223\) −13.9428 4.53029i −0.933678 0.303370i −0.197612 0.980280i \(-0.563319\pi\)
−0.736066 + 0.676910i \(0.763319\pi\)
\(224\) 27.1678 + 5.01990i 1.81522 + 0.335406i
\(225\) −22.0330 11.2264i −1.46887 0.748425i
\(226\) −0.351750 + 16.8805i −0.0233981 + 1.12287i
\(227\) 1.42030 + 1.66296i 0.0942687 + 0.110374i 0.805535 0.592548i \(-0.201878\pi\)
−0.711266 + 0.702923i \(0.751878\pi\)
\(228\) −18.1823 + 12.0860i −1.20415 + 0.800416i
\(229\) −7.56043 4.63304i −0.499607 0.306160i 0.249767 0.968306i \(-0.419646\pi\)
−0.749375 + 0.662146i \(0.769646\pi\)
\(230\) 0.995321 + 1.03768i 0.0656295 + 0.0684229i
\(231\) −2.57744 + 10.7358i −0.169583 + 0.706363i
\(232\) 4.15159 0.725971i 0.272565 0.0476623i
\(233\) 4.23967 + 3.62102i 0.277750 + 0.237221i 0.777400 0.629006i \(-0.216538\pi\)
−0.499650 + 0.866227i \(0.666538\pi\)
\(234\) −36.2811 23.2864i −2.37177 1.52228i
\(235\) −1.93957 8.07888i −0.126523 0.527008i
\(236\) −0.0909571 + 2.18157i −0.00592080 + 0.142008i
\(237\) 4.61203 4.61203i 0.299583 0.299583i
\(238\) 24.6318 7.43971i 1.59664 0.482245i
\(239\) −0.0841237 + 1.06889i −0.00544151 + 0.0691409i −0.999039 0.0438414i \(-0.986040\pi\)
0.993597 + 0.112982i \(0.0360404\pi\)
\(240\) 11.1547 3.56530i 0.720035 0.230139i
\(241\) −3.34241 + 0.529385i −0.215303 + 0.0341007i −0.263154 0.964754i \(-0.584763\pi\)
0.0478508 + 0.998854i \(0.484763\pi\)
\(242\) 14.5286 + 2.61247i 0.933936 + 0.167936i
\(243\) 1.60299 + 0.663982i 0.102832 + 0.0425944i
\(244\) 3.26686 16.2201i 0.209139 1.03839i
\(245\) 16.3608i 1.04525i
\(246\) 12.6645 24.1941i 0.807458 1.54256i
\(247\) 18.1065i 1.15209i
\(248\) −4.13798 16.0944i −0.262762 1.02200i
\(249\) −10.3644 4.29309i −0.656819 0.272064i
\(250\) −2.20078 + 12.2391i −0.139189 + 0.774067i
\(251\) −16.4414 + 2.60406i −1.03777 + 0.164367i −0.651994 0.758224i \(-0.726067\pi\)
−0.385779 + 0.922591i \(0.626067\pi\)
\(252\) 33.1914 49.4173i 2.09086 3.11300i
\(253\) −0.0615968 + 0.782662i −0.00387256 + 0.0492055i
\(254\) 5.33947 + 17.6782i 0.335028 + 1.10923i
\(255\) 7.71214 7.71214i 0.482953 0.482953i
\(256\) 7.40034 14.1857i 0.462521 0.886608i
\(257\) 3.79018 + 15.7872i 0.236425 + 0.984780i 0.956696 + 0.291088i \(0.0940172\pi\)
−0.720271 + 0.693692i \(0.755983\pi\)
\(258\) 9.94926 15.5013i 0.619414 0.965069i
\(259\) −4.90512 4.18937i −0.304789 0.260315i
\(260\) −2.65864 + 9.34098i −0.164882 + 0.579303i
\(261\) 2.11995 8.83025i 0.131222 0.546579i
\(262\) −9.55366 + 9.16363i −0.590227 + 0.566131i
\(263\) −1.26551 0.775508i −0.0780349 0.0478199i 0.482934 0.875657i \(-0.339571\pi\)
−0.560969 + 0.827837i \(0.689571\pi\)
\(264\) 5.50472 + 3.25305i 0.338792 + 0.200211i
\(265\) 1.74776 + 2.04637i 0.107364 + 0.125707i
\(266\) 24.9966 + 0.520871i 1.53264 + 0.0319366i
\(267\) 20.5724 + 10.4822i 1.25901 + 0.641498i
\(268\) −8.75008 + 0.322766i −0.534496 + 0.0197161i
\(269\) 22.5199 + 7.31716i 1.37306 + 0.446135i 0.900383 0.435098i \(-0.143286\pi\)
0.472681 + 0.881234i \(0.343286\pi\)
\(270\) 1.27108 12.7487i 0.0773555 0.775860i
\(271\) 5.45768 + 16.7970i 0.331530 + 1.02035i 0.968406 + 0.249379i \(0.0802265\pi\)
−0.636876 + 0.770967i \(0.719773\pi\)
\(272\) 0.0715091 14.9013i 0.00433588 0.903524i
\(273\) 28.1929 + 68.0636i 1.70631 + 4.11940i
\(274\) 22.6714 + 5.94507i 1.36963 + 0.359155i
\(275\) −2.59342 + 1.58925i −0.156389 + 0.0958355i
\(276\) 2.65828 5.73005i 0.160010 0.344908i
\(277\) 7.99019 + 10.9976i 0.480084 + 0.660779i 0.978521 0.206147i \(-0.0660925\pi\)
−0.498437 + 0.866926i \(0.666092\pi\)
\(278\) −21.2630 7.40197i −1.27527 0.443940i
\(279\) −35.3657 5.60137i −2.11729 0.335346i
\(280\) −12.8190 3.93905i −0.766085 0.235403i
\(281\) −31.2182 + 2.45692i −1.86232 + 0.146568i −0.959183 0.282786i \(-0.908741\pi\)
−0.903137 + 0.429353i \(0.858741\pi\)
\(282\) −29.9693 + 20.8341i −1.78465 + 1.24065i
\(283\) 18.5124 25.4801i 1.10045 1.51464i 0.265657 0.964068i \(-0.414411\pi\)
0.834790 0.550568i \(-0.185589\pi\)
\(284\) 19.6853 10.9623i 1.16811 0.650495i
\(285\) 9.44262 4.81126i 0.559333 0.284994i
\(286\) −4.77395 + 2.30846i −0.282290 + 0.136502i
\(287\) −27.7229 + 14.4708i −1.63643 + 0.854186i
\(288\) −21.7106 26.7804i −1.27931 1.57805i
\(289\) 1.41720 + 2.78141i 0.0833647 + 0.163612i
\(290\) −2.04237 + 0.117987i −0.119932 + 0.00692841i
\(291\) 8.23702 + 5.98455i 0.482863 + 0.350820i
\(292\) 1.37422 + 0.773940i 0.0804204 + 0.0452914i
\(293\) −0.638246 8.10968i −0.0372867 0.473773i −0.987007 0.160674i \(-0.948633\pi\)
0.949721 0.313098i \(-0.101367\pi\)
\(294\) −66.9617 + 26.1157i −3.90528 + 1.52310i
\(295\) 0.165799 1.04681i 0.00965320 0.0609479i
\(296\) −3.15356 + 2.00276i −0.183297 + 0.116408i
\(297\) 5.65937 4.11177i 0.328390 0.238589i
\(298\) 2.13799 + 2.61153i 0.123850 + 0.151282i
\(299\) 2.73714 + 4.46661i 0.158293 + 0.258311i
\(300\) 24.0137 4.71675i 1.38643 0.272322i
\(301\) −19.4877 + 8.07206i −1.12325 + 0.465266i
\(302\) −2.37938 + 0.519062i −0.136918 + 0.0298687i
\(303\) 35.4541 11.5197i 2.03679 0.661792i
\(304\) 4.54041 13.7491i 0.260411 0.788565i
\(305\) −2.48185 + 7.63834i −0.142110 + 0.437370i
\(306\) −29.4016 12.9026i −1.68078 0.737592i
\(307\) −8.45170 + 16.5874i −0.482364 + 0.946692i 0.513693 + 0.857974i \(0.328277\pi\)
−0.996057 + 0.0887181i \(0.971723\pi\)
\(308\) −3.04957 6.65700i −0.173766 0.379318i
\(309\) 9.27491 7.92152i 0.527631 0.450640i
\(310\) 1.09561 + 7.99165i 0.0622264 + 0.453895i
\(311\) 13.5424 22.0991i 0.767918 1.25313i −0.194326 0.980937i \(-0.562252\pi\)
0.962243 0.272191i \(-0.0877481\pi\)
\(312\) 42.4747 4.02909i 2.40466 0.228102i
\(313\) −21.2646 5.10517i −1.20194 0.288561i −0.417452 0.908699i \(-0.637077\pi\)
−0.784493 + 0.620138i \(0.787077\pi\)
\(314\) −20.1554 17.9538i −1.13743 1.01319i
\(315\) −18.7663 + 21.9725i −1.05736 + 1.23801i
\(316\) −0.518729 + 4.29442i −0.0291808 + 0.241580i
\(317\) −2.58544 + 0.620710i −0.145213 + 0.0348625i −0.305400 0.952224i \(-0.598790\pi\)
0.160187 + 0.987087i \(0.448790\pi\)
\(318\) 5.58555 10.4197i 0.313222 0.584311i
\(319\) −0.789844 0.789844i −0.0442228 0.0442228i
\(320\) −4.36119 + 6.42636i −0.243798 + 0.359245i
\(321\) 17.2254 + 1.35567i 0.961428 + 0.0756660i
\(322\) −6.24504 + 3.65022i −0.348022 + 0.203419i
\(323\) −2.10956 13.3192i −0.117379 0.741102i
\(324\) −18.9896 + 5.30648i −1.05498 + 0.294804i
\(325\) −7.76685 + 18.7508i −0.430827 + 1.04011i
\(326\) 8.93195 + 6.77818i 0.494695 + 0.375409i
\(327\) −32.1884 −1.78002
\(328\) 3.29499 + 17.8085i 0.181936 + 0.983310i
\(329\) 41.7980 2.30440
\(330\) −2.47241 1.87624i −0.136102 0.103283i
\(331\) −2.92084 + 7.05154i −0.160544 + 0.387588i −0.983598 0.180376i \(-0.942269\pi\)
0.823054 + 0.567964i \(0.192269\pi\)
\(332\) 7.16550 2.00233i 0.393258 0.109892i
\(333\) 1.25921 + 7.95035i 0.0690044 + 0.435676i
\(334\) 22.1067 12.9214i 1.20963 0.707026i
\(335\) 4.23712 + 0.333468i 0.231498 + 0.0182193i
\(336\) 4.34042 + 58.7536i 0.236789 + 3.20527i
\(337\) −23.4772 23.4772i −1.27889 1.27889i −0.941292 0.337594i \(-0.890387\pi\)
−0.337594 0.941292i \(-0.609613\pi\)
\(338\) −8.03116 + 14.9820i −0.436838 + 0.814912i
\(339\) −35.0093 + 8.40499i −1.90144 + 0.456496i
\(340\) −0.867409 + 7.18104i −0.0470419 + 0.389447i
\(341\) −2.86036 + 3.34906i −0.154897 + 0.181362i
\(342\) −23.2964 20.7518i −1.25973 1.12213i
\(343\) 46.7905 + 11.2334i 2.52645 + 0.606547i
\(344\) 1.15359 + 12.1612i 0.0621976 + 0.655687i
\(345\) −1.60205 + 2.61430i −0.0862513 + 0.140749i
\(346\) −2.26894 16.5502i −0.121979 0.889746i
\(347\) 12.0943 10.3295i 0.649254 0.554515i −0.262664 0.964887i \(-0.584601\pi\)
0.911918 + 0.410372i \(0.134601\pi\)
\(348\) 3.74301 + 8.17072i 0.200646 + 0.437997i
\(349\) 5.84437 11.4702i 0.312842 0.613986i −0.680029 0.733186i \(-0.738033\pi\)
0.992870 + 0.119199i \(0.0380327\pi\)
\(350\) −25.6627 11.2618i −1.37173 0.601968i
\(351\) 14.4241 44.3930i 0.769904 2.36952i
\(352\) −4.20396 + 0.555799i −0.224072 + 0.0296242i
\(353\) 3.17756 1.03245i 0.169124 0.0549518i −0.223231 0.974766i \(-0.571660\pi\)
0.392355 + 0.919814i \(0.371660\pi\)
\(354\) −4.54907 + 0.992378i −0.241780 + 0.0527443i
\(355\) −10.1045 + 4.18543i −0.536293 + 0.222140i
\(356\) −15.0254 + 2.95128i −0.796347 + 0.156418i
\(357\) 28.6689 + 46.7833i 1.51732 + 2.47604i
\(358\) 22.2912 + 27.2285i 1.17813 + 1.43907i
\(359\) 17.3065 12.5739i 0.913401 0.663624i −0.0284719 0.999595i \(-0.509064\pi\)
0.941873 + 0.335970i \(0.109064\pi\)
\(360\) 8.97138 + 14.1264i 0.472833 + 0.744526i
\(361\) −0.922444 + 5.82408i −0.0485497 + 0.306531i
\(362\) −29.9433 + 11.6782i −1.57378 + 0.613790i
\(363\) 2.46973 + 31.3809i 0.129627 + 1.64707i
\(364\) −42.5717 23.9756i −2.23136 1.25667i
\(365\) −0.619357 0.449989i −0.0324186 0.0235535i
\(366\) 35.2239 2.03486i 1.84118 0.106364i
\(367\) −4.59295 9.01418i −0.239750 0.470536i 0.739509 0.673146i \(-0.235058\pi\)
−0.979259 + 0.202610i \(0.935058\pi\)
\(368\) 0.958385 + 4.07808i 0.0499593 + 0.212584i
\(369\) 38.0328 + 8.73602i 1.97991 + 0.454779i
\(370\) 1.63252 0.789409i 0.0848704 0.0410394i
\(371\) −12.0630 + 6.14639i −0.626278 + 0.319105i
\(372\) 30.9595 17.2407i 1.60517 0.893888i
\(373\) 1.57344 2.16565i 0.0814694 0.112133i −0.766337 0.642439i \(-0.777923\pi\)
0.847807 + 0.530306i \(0.177923\pi\)
\(374\) −3.24279 + 2.25433i −0.167681 + 0.116568i
\(375\) −26.4357 + 2.08053i −1.36513 + 0.107438i
\(376\) 7.11008 23.1387i 0.366675 1.19329i
\(377\) −7.36162 1.16597i −0.379143 0.0600503i
\(378\) 60.8710 + 21.1901i 3.13086 + 1.08990i
\(379\) −10.5678 14.5453i −0.542829 0.747140i 0.446188 0.894939i \(-0.352781\pi\)
−0.989017 + 0.147799i \(0.952781\pi\)
\(380\) −2.95780 + 6.37569i −0.151732 + 0.327066i
\(381\) −33.5763 + 20.5756i −1.72017 + 1.05412i
\(382\) −3.87618 1.01644i −0.198322 0.0520058i
\(383\) 2.72072 + 6.56841i 0.139023 + 0.335630i 0.978022 0.208502i \(-0.0668589\pi\)
−0.838999 + 0.544132i \(0.816859\pi\)
\(384\) 33.2634 + 7.59155i 1.69746 + 0.387405i
\(385\) 1.09833 + 3.38030i 0.0559759 + 0.172276i
\(386\) −0.862782 + 8.65353i −0.0439144 + 0.440453i
\(387\) 25.0330 + 8.13373i 1.27250 + 0.413460i
\(388\) −6.74777 + 0.248906i −0.342566 + 0.0126363i
\(389\) 8.62962 + 4.39701i 0.437539 + 0.222937i 0.658863 0.752263i \(-0.271038\pi\)
−0.221324 + 0.975200i \(0.571038\pi\)
\(390\) −20.7055 0.431454i −1.04846 0.0218475i
\(391\) 2.53386 + 2.96677i 0.128143 + 0.150036i
\(392\) 24.2509 41.0367i 1.22486 2.07267i
\(393\) −24.0691 14.7496i −1.21413 0.744018i
\(394\) 24.8828 23.8670i 1.25358 1.20240i
\(395\) 0.490161 2.04167i 0.0246627 0.102728i
\(396\) −2.50127 + 8.78806i −0.125693 + 0.441616i
\(397\) 2.89283 + 2.47071i 0.145187 + 0.124001i 0.719075 0.694932i \(-0.244566\pi\)
−0.573888 + 0.818934i \(0.694566\pi\)
\(398\) 2.05851 3.20723i 0.103184 0.160764i
\(399\) 12.4461 + 51.8416i 0.623083 + 2.59533i
\(400\) −10.5997 + 12.2908i −0.529986 + 0.614538i
\(401\) 19.2638 19.2638i 0.961986 0.961986i −0.0373172 0.999303i \(-0.511881\pi\)
0.999303 + 0.0373172i \(0.0118812\pi\)
\(402\) −5.39862 17.8740i −0.269258 0.891475i
\(403\) −2.30578 + 29.2977i −0.114859 + 1.45942i
\(404\) −13.7847 + 20.5235i −0.685815 + 1.02108i
\(405\) 9.45295 1.49720i 0.469721 0.0743965i
\(406\) 1.82143 10.1294i 0.0903958 0.502714i
\(407\) 0.914737 + 0.378897i 0.0453419 + 0.0187812i
\(408\) 30.7752 7.91249i 1.52360 0.391727i
\(409\) 26.9175i 1.33099i −0.746404 0.665493i \(-0.768222\pi\)
0.746404 0.665493i \(-0.231778\pi\)
\(410\) −0.593333 8.77101i −0.0293026 0.433169i
\(411\) 49.9793i 2.46530i
\(412\) −1.59716 + 7.92999i −0.0786865 + 0.390682i
\(413\) 4.92607 + 2.04044i 0.242396 + 0.100404i
\(414\) 8.88393 + 1.59747i 0.436621 + 0.0785113i
\(415\) −3.56695 + 0.564949i −0.175095 + 0.0277323i
\(416\) −20.5142 + 19.4886i −1.00579 + 0.955507i
\(417\) 3.76686 47.8624i 0.184464 2.34383i
\(418\) −3.67362 + 1.10957i −0.179683 + 0.0542708i
\(419\) 21.6421 21.6421i 1.05729 1.05729i 0.0590310 0.998256i \(-0.481199\pi\)
0.998256 0.0590310i \(-0.0188011\pi\)
\(420\) 1.19127 28.5722i 0.0581281 1.39418i
\(421\) −1.80927 7.53617i −0.0881786 0.367290i 0.910781 0.412889i \(-0.135480\pi\)
−0.998960 + 0.0455989i \(0.985480\pi\)
\(422\) −3.51047 2.25314i −0.170887 0.109681i
\(423\) −39.6609 33.8736i −1.92838 1.64699i
\(424\) 1.35056 + 7.72340i 0.0655890 + 0.375082i
\(425\) −3.52871 + 14.6981i −0.171168 + 0.712964i
\(426\) 33.2594 + 34.6750i 1.61142 + 1.68001i
\(427\) −34.4503 21.1112i −1.66717 1.02164i
\(428\) −9.54319 + 6.34349i −0.461288 + 0.306624i
\(429\) −7.34381 8.59849i −0.354562 0.415139i
\(430\) 0.123532 5.92830i 0.00595724 0.285888i
\(431\) 2.35678 + 1.20084i 0.113522 + 0.0578425i 0.509830 0.860275i \(-0.329708\pi\)
−0.396307 + 0.918118i \(0.629708\pi\)
\(432\) 22.0850 30.0926i 1.06256 1.44783i
\(433\) −5.67072 1.84253i −0.272518 0.0885463i 0.169570 0.985518i \(-0.445762\pi\)
−0.442088 + 0.896972i \(0.645762\pi\)
\(434\) −40.3801 4.02601i −1.93831 0.193255i
\(435\) −1.34807 4.14894i −0.0646352 0.198927i
\(436\) 16.7960 13.1757i 0.804383 0.631001i
\(437\) 1.45077 + 3.50247i 0.0693998 + 0.167546i
\(438\) −0.853081 + 3.25320i −0.0407618 + 0.155444i
\(439\) 8.55027 5.23961i 0.408082 0.250073i −0.303276 0.952903i \(-0.598080\pi\)
0.711358 + 0.702830i \(0.248080\pi\)
\(440\) 2.05811 0.0330064i 0.0981167 0.00157352i
\(441\) −60.3699 83.0921i −2.87476 3.95677i
\(442\) −8.66385 + 24.8879i −0.412097 + 1.18380i
\(443\) 0.676241 + 0.107106i 0.0321292 + 0.00508876i 0.172478 0.985013i \(-0.444823\pi\)
−0.140349 + 0.990102i \(0.544823\pi\)
\(444\) −5.83678 5.42149i −0.277001 0.257293i
\(445\) 7.40986 0.583169i 0.351261 0.0276449i
\(446\) 11.8344 + 17.0234i 0.560373 + 0.806083i
\(447\) −4.23031 + 5.82253i −0.200087 + 0.275396i
\(448\) −26.3145 28.8812i −1.24324 1.36451i
\(449\) −21.3824 + 10.8949i −1.00910 + 0.514162i −0.878738 0.477305i \(-0.841614\pi\)
−0.130362 + 0.991467i \(0.541614\pi\)
\(450\) 15.2239 + 31.4834i 0.717662 + 1.48414i
\(451\) 3.36053 3.42732i 0.158241 0.161386i
\(452\) 14.8276 18.7161i 0.697430 0.880333i
\(453\) −2.35765 4.62715i −0.110772 0.217402i
\(454\) −0.178371 3.08765i −0.00837137 0.144910i
\(455\) 19.1869 + 13.9401i 0.899494 + 0.653521i
\(456\) 30.8158 + 1.92862i 1.44308 + 0.0903161i
\(457\) 1.86349 + 23.6779i 0.0871706 + 1.10761i 0.872528 + 0.488565i \(0.162479\pi\)
−0.785357 + 0.619043i \(0.787521\pi\)
\(458\) 4.55643 + 11.6829i 0.212908 + 0.545904i
\(459\) 5.43833 34.3363i 0.253840 1.60268i
\(460\) −0.234160 2.01992i −0.0109178 0.0941792i
\(461\) −16.6100 + 12.0678i −0.773603 + 0.562056i −0.903052 0.429530i \(-0.858679\pi\)
0.129449 + 0.991586i \(0.458679\pi\)
\(462\) 12.0818 9.89101i 0.562094 0.460171i
\(463\) 8.50704 + 13.8822i 0.395356 + 0.645162i 0.986941 0.161080i \(-0.0514978\pi\)
−0.591585 + 0.806242i \(0.701498\pi\)
\(464\) −5.29764 2.73138i −0.245937 0.126801i
\(465\) −15.8916 + 6.58251i −0.736955 + 0.305257i
\(466\) −1.68059 7.70383i −0.0778517 0.356873i
\(467\) −26.2870 + 8.54115i −1.21642 + 0.395237i −0.845775 0.533539i \(-0.820862\pi\)
−0.370640 + 0.928776i \(0.620862\pi\)
\(468\) 20.9649 + 57.2505i 0.969103 + 2.64640i
\(469\) −6.60737 + 20.3354i −0.305100 + 0.939002i
\(470\) −4.72168 + 10.7595i −0.217795 + 0.496298i
\(471\) 26.1311 51.2851i 1.20406 2.36309i
\(472\) 1.96751 2.37990i 0.0905620 0.109544i
\(473\) 2.46188 2.10265i 0.113198 0.0966798i
\(474\) −9.13858 + 1.25285i −0.419749 + 0.0575452i
\(475\) −7.67428 + 12.5233i −0.352120 + 0.574608i
\(476\) −34.1094 12.6767i −1.56340 0.581034i
\(477\) 16.4273 + 3.94385i 0.752156 + 0.180577i
\(478\) 1.00858 1.13225i 0.0461312 0.0517879i
\(479\) 17.7710 20.8072i 0.811977 0.950703i −0.187525 0.982260i \(-0.560046\pi\)
0.999502 + 0.0315565i \(0.0100464\pi\)
\(480\) −15.6144 5.51976i −0.712699 0.251942i
\(481\) 6.42406 1.54228i 0.292912 0.0703220i
\(482\) 4.21799 + 2.26107i 0.192124 + 0.102989i
\(483\) −10.9071 10.9071i −0.496291 0.496291i
\(484\) −14.1339 15.3638i −0.642450 0.698353i
\(485\) 3.26752 + 0.257159i 0.148370 + 0.0116770i
\(486\) −1.23822 2.11843i −0.0561668 0.0960938i
\(487\) 5.33980 + 33.7142i 0.241969 + 1.52773i 0.747112 + 0.664699i \(0.231440\pi\)
−0.505142 + 0.863036i \(0.668560\pi\)
\(488\) −17.5470 + 15.4800i −0.794316 + 0.700747i
\(489\) −9.14997 + 22.0900i −0.413776 + 0.998944i
\(490\) −13.9870 + 18.4314i −0.631868 + 0.832644i
\(491\) 1.69395 0.0764470 0.0382235 0.999269i \(-0.487830\pi\)
0.0382235 + 0.999269i \(0.487830\pi\)
\(492\) −34.9510 + 16.4290i −1.57571 + 0.740676i
\(493\) −5.55110 −0.250009
\(494\) −15.4794 + 20.3980i −0.696451 + 0.917749i
\(495\) 1.69727 4.09757i 0.0762866 0.184172i
\(496\) −9.09763 + 21.6689i −0.408495 + 0.972963i
\(497\) −8.60733 54.3445i −0.386092 2.43769i
\(498\) 8.00592 + 13.6971i 0.358754 + 0.613780i
\(499\) 13.2898 + 1.04593i 0.594934 + 0.0468223i 0.372352 0.928092i \(-0.378551\pi\)
0.222582 + 0.974914i \(0.428551\pi\)
\(500\) 12.9426 11.9066i 0.578811 0.532477i
\(501\) 38.6100 + 38.6100i 1.72497 + 1.72497i
\(502\) 20.7484 + 11.1223i 0.926047 + 0.496412i
\(503\) 21.0242 5.04746i 0.937422 0.225055i 0.264177 0.964474i \(-0.414900\pi\)
0.673246 + 0.739419i \(0.264900\pi\)
\(504\) −79.6392 + 27.2958i −3.54741 + 1.21585i
\(505\) 7.79385 9.12542i 0.346822 0.406076i
\(506\) 0.738497 0.829053i 0.0328302 0.0368559i
\(507\) −35.2470 8.46205i −1.56537 0.375813i
\(508\) 9.09803 24.4802i 0.403660 1.08613i
\(509\) 0.831786 1.35735i 0.0368683 0.0601635i −0.833675 0.552255i \(-0.813767\pi\)
0.870543 + 0.492092i \(0.163767\pi\)
\(510\) −15.2813 + 2.09499i −0.676669 + 0.0927675i
\(511\) 2.92863 2.50128i 0.129555 0.110650i
\(512\) −20.4644 + 9.65442i −0.904408 + 0.426669i
\(513\) 15.3356 30.0979i 0.677085 1.32885i
\(514\) 9.22679 21.0255i 0.406976 0.927394i
\(515\) 1.21337 3.73437i 0.0534675 0.164556i
\(516\) −24.4606 + 8.95738i −1.07682 + 0.394327i
\(517\) −6.10152 + 1.98251i −0.268345 + 0.0871905i
\(518\) 1.94437 + 8.91299i 0.0854306 + 0.391614i
\(519\) 32.9105 13.6320i 1.44461 0.598378i
\(520\) 10.9808 8.25025i 0.481540 0.361797i
\(521\) −5.95302 9.71444i −0.260806 0.425597i 0.695255 0.718763i \(-0.255291\pi\)
−0.956062 + 0.293165i \(0.905291\pi\)
\(522\) −9.93731 + 8.13541i −0.434944 + 0.356077i
\(523\) 31.4946 22.8822i 1.37716 1.00057i 0.380025 0.924976i \(-0.375915\pi\)
0.997139 0.0755919i \(-0.0240846\pi\)
\(524\) 18.5968 2.15584i 0.812406 0.0941785i
\(525\) 9.34868 59.0253i 0.408010 2.57607i
\(526\) 0.762685 + 1.95555i 0.0332546 + 0.0852662i
\(527\) 1.71729 + 21.8202i 0.0748062 + 0.950503i
\(528\) −3.42032 8.37078i −0.148850 0.364292i
\(529\) 17.7200 + 12.8744i 0.770437 + 0.559755i
\(530\) −0.219496 3.79953i −0.00953430 0.165041i
\(531\) −3.02061 5.92827i −0.131083 0.257265i
\(532\) −27.7148 21.9566i −1.20159 0.951939i
\(533\) 4.69886 31.6818i 0.203530 1.37229i
\(534\) −14.2147 29.3963i −0.615130 1.27210i
\(535\) 4.95607 2.52525i 0.214270 0.109176i
\(536\) 10.1334 + 7.11691i 0.437696 + 0.307404i
\(537\) −44.1065 + 60.7073i −1.90333 + 2.61972i
\(538\) −19.1145 27.4957i −0.824083 1.18542i
\(539\) −12.5944 + 0.991197i −0.542477 + 0.0426939i
\(540\) −12.3309 + 13.2755i −0.530638 + 0.571285i
\(541\) −2.67898 0.424309i −0.115179 0.0182425i 0.0985790 0.995129i \(-0.468570\pi\)
−0.213758 + 0.976887i \(0.568570\pi\)
\(542\) 8.21153 23.5886i 0.352715 1.01322i
\(543\) −40.2843 55.4466i −1.72877 2.37944i
\(544\) −12.8198 + 16.7260i −0.549645 + 0.717122i
\(545\) −8.83510 + 5.41415i −0.378454 + 0.231917i
\(546\) 26.4273 100.780i 1.13099 4.31298i
\(547\) −4.14186 9.99934i −0.177093 0.427541i 0.810261 0.586069i \(-0.199325\pi\)
−0.987354 + 0.158528i \(0.949325\pi\)
\(548\) −20.4581 26.0794i −0.873926 1.11406i
\(549\) 15.5802 + 47.9508i 0.664945 + 2.04649i
\(550\) 4.28031 + 0.426759i 0.182513 + 0.0181971i
\(551\) −5.12988 1.66680i −0.218540 0.0710080i
\(552\) −7.89337 + 4.18264i −0.335964 + 0.178025i
\(553\) 9.41174 + 4.79552i 0.400228 + 0.203926i
\(554\) 0.400506 19.2203i 0.0170158 0.816591i
\(555\) 2.51131 + 2.94037i 0.106599 + 0.124812i
\(556\) 17.6260 + 26.5167i 0.747509 + 1.12456i
\(557\) −34.1364 20.9188i −1.44640 0.886358i −0.446440 0.894814i \(-0.647308\pi\)
−0.999964 + 0.00845575i \(0.997308\pi\)
\(558\) 35.0528 + 36.5447i 1.48390 + 1.54706i
\(559\) 5.04318 21.0064i 0.213304 0.888474i
\(560\) 11.0739 + 15.3967i 0.467956 + 0.650629i
\(561\) −6.40395 5.46949i −0.270375 0.230922i
\(562\) 37.2695 + 23.9208i 1.57212 + 1.00904i
\(563\) −1.05924 4.41205i −0.0446416 0.185946i 0.945594 0.325349i \(-0.105482\pi\)
−0.990236 + 0.139403i \(0.955482\pi\)
\(564\) 51.5734 + 2.15027i 2.17163 + 0.0905429i
\(565\) −8.19565 + 8.19565i −0.344794 + 0.344794i
\(566\) −42.6384 + 12.8784i −1.79223 + 0.541319i
\(567\) −3.77769 + 48.0001i −0.158648 + 2.01581i
\(568\) −31.5484 4.47945i −1.32374 0.187954i
\(569\) 7.49301 1.18678i 0.314123 0.0497522i 0.00261772 0.999997i \(-0.499167\pi\)
0.311506 + 0.950244i \(0.399167\pi\)
\(570\) −14.7508 2.65243i −0.617845 0.111098i
\(571\) 28.0604 + 11.6230i 1.17429 + 0.486408i 0.882610 0.470107i \(-0.155785\pi\)
0.291684 + 0.956515i \(0.405785\pi\)
\(572\) 7.35165 + 1.48068i 0.307388 + 0.0619104i
\(573\) 8.54509i 0.356976i
\(574\) 43.6026 + 7.39832i 1.81994 + 0.308800i
\(575\) 4.24943i 0.177213i
\(576\) 1.56339 + 48.7302i 0.0651414 + 2.03042i
\(577\) 24.9104 + 10.3182i 1.03703 + 0.429553i 0.835246 0.549877i \(-0.185325\pi\)
0.201786 + 0.979430i \(0.435325\pi\)
\(578\) 0.781298 4.34499i 0.0324977 0.180728i
\(579\) −18.3161 + 2.90099i −0.761192 + 0.120561i
\(580\) 2.40172 + 1.61313i 0.0997259 + 0.0669814i
\(581\) 1.42546 18.1122i 0.0591381 0.751421i
\(582\) −4.16323 13.7838i −0.172571 0.571358i
\(583\) 1.46938 1.46938i 0.0608557 0.0608557i
\(584\) −0.886493 2.04672i −0.0366834 0.0846940i
\(585\) −6.90866 28.7766i −0.285638 1.18977i
\(586\) −6.21402 + 9.68166i −0.256699 + 0.399946i
\(587\) 33.8267 + 28.8907i 1.39618 + 1.19245i 0.955577 + 0.294742i \(0.0952338\pi\)
0.440599 + 0.897704i \(0.354766\pi\)
\(588\) 97.7627 + 27.8253i 4.03166 + 1.14750i
\(589\) −4.96486 + 20.6801i −0.204573 + 0.852109i
\(590\) −1.08171 + 1.03755i −0.0445334 + 0.0427154i
\(591\) 62.6887 + 38.4157i 2.57867 + 1.58021i
\(592\) 5.26484 + 0.439783i 0.216384 + 0.0180750i
\(593\) 22.3077 + 26.1189i 0.916066 + 1.07258i 0.997118 + 0.0758657i \(0.0241720\pi\)
−0.0810519 + 0.996710i \(0.525828\pi\)
\(594\) −9.89080 0.206101i −0.405824 0.00845644i
\(595\) 15.7381 + 8.01897i 0.645200 + 0.328746i
\(596\) −0.175945 4.76982i −0.00720700 0.195379i
\(597\) 7.72890 + 2.51127i 0.316323 + 0.102780i
\(598\) 0.734999 7.37190i 0.0300564 0.301459i
\(599\) −9.51168 29.2739i −0.388637 1.19610i −0.933807 0.357776i \(-0.883535\pi\)
0.545171 0.838325i \(-0.316465\pi\)
\(600\) −31.0852 15.2158i −1.26905 0.621184i
\(601\) −9.73186 23.4948i −0.396971 0.958373i −0.988380 0.152001i \(-0.951428\pi\)
0.591409 0.806372i \(-0.298572\pi\)
\(602\) 28.8549 + 7.56656i 1.17604 + 0.308390i
\(603\) 22.7496 13.9410i 0.926437 0.567721i
\(604\) 3.12426 + 1.44940i 0.127124 + 0.0589754i
\(605\) 5.95624 + 8.19806i 0.242156 + 0.333299i
\(606\) −49.7894 17.3324i −2.02256 0.704081i
\(607\) −20.4092 3.23250i −0.828383 0.131203i −0.272177 0.962247i \(-0.587744\pi\)
−0.556206 + 0.831044i \(0.687744\pi\)
\(608\) −16.8693 + 11.6075i −0.684139 + 0.470746i
\(609\) 21.8789 1.72191i 0.886578 0.0697752i
\(610\) 9.32602 6.48327i 0.377600 0.262500i
\(611\) −25.1622 + 34.6327i −1.01795 + 1.40109i
\(612\) 22.0921 + 39.6712i 0.893019 + 1.60361i
\(613\) 5.62915 2.86819i 0.227359 0.115845i −0.336601 0.941647i \(-0.609277\pi\)
0.563960 + 0.825802i \(0.309277\pi\)
\(614\) 23.7020 11.4612i 0.956536 0.462537i
\(615\) 17.7708 5.96802i 0.716589 0.240654i
\(616\) −2.25561 + 10.1066i −0.0908812 + 0.407206i
\(617\) −3.44385 6.75894i −0.138644 0.272105i 0.811236 0.584719i \(-0.198795\pi\)
−0.949880 + 0.312614i \(0.898795\pi\)
\(618\) −17.2209 + 0.994839i −0.692726 + 0.0400183i
\(619\) −26.2843 19.0967i −1.05646 0.767560i −0.0830267 0.996547i \(-0.526459\pi\)
−0.973429 + 0.228987i \(0.926459\pi\)
\(620\) 5.59787 9.93969i 0.224816 0.399188i
\(621\) 0.766790 + 9.74299i 0.0307702 + 0.390973i
\(622\) −34.1490 + 13.3184i −1.36925 + 0.534021i
\(623\) −5.84950 + 36.9323i −0.234355 + 1.47966i
\(624\) −51.2947 31.7730i −2.05343 1.27194i
\(625\) 9.50691 6.90718i 0.380276 0.276287i
\(626\) 19.5913 + 23.9305i 0.783025 + 0.956457i
\(627\) −4.27572 6.97734i −0.170756 0.278648i
\(628\) 7.35728 + 37.4570i 0.293587 + 1.49470i
\(629\) 4.54589 1.88297i 0.181257 0.0750790i
\(630\) 39.9258 8.70981i 1.59068 0.347007i
\(631\) −30.4282 + 9.88672i −1.21133 + 0.393584i −0.843917 0.536474i \(-0.819756\pi\)
−0.367411 + 0.930059i \(0.619756\pi\)
\(632\) 4.25572 4.39444i 0.169283 0.174801i
\(633\) 2.74871 8.45967i 0.109252 0.336242i
\(634\) 3.44330 + 1.51105i 0.136751 + 0.0600116i
\(635\) −5.75520 + 11.2952i −0.228388 + 0.448237i
\(636\) −15.2004 + 6.96330i −0.602734 + 0.276113i
\(637\) −64.1002 + 54.7468i −2.53974 + 2.16915i
\(638\) 0.214559 + 1.56505i 0.00849448 + 0.0619609i
\(639\) −35.8743 + 58.5415i −1.41917 + 2.31587i
\(640\) 10.4071 3.51124i 0.411376 0.138794i
\(641\) 44.7760 + 10.7498i 1.76855 + 0.424591i 0.981368 0.192135i \(-0.0615412\pi\)
0.787178 + 0.616726i \(0.211541\pi\)
\(642\) −18.2464 16.2534i −0.720129 0.641470i
\(643\) −8.13160 + 9.52088i −0.320679 + 0.375467i −0.897207 0.441611i \(-0.854407\pi\)
0.576528 + 0.817078i \(0.304407\pi\)
\(644\) 10.1560 + 1.22676i 0.400202 + 0.0483410i
\(645\) 12.2950 2.95177i 0.484115 0.116226i
\(646\) −9.01020 + 16.8084i −0.354502 + 0.661316i
\(647\) 28.3170 + 28.3170i 1.11326 + 1.11326i 0.992707 + 0.120549i \(0.0384655\pi\)
0.120549 + 0.992707i \(0.461535\pi\)
\(648\) 25.9295 + 10.2564i 1.01861 + 0.402908i
\(649\) −0.815871 0.0642104i −0.0320257 0.00252048i
\(650\) 24.7800 14.4839i 0.971953 0.568106i
\(651\) −13.5369 85.4687i −0.530553 3.34978i
\(652\) −4.26762 15.2720i −0.167133 0.598098i
\(653\) 16.1360 38.9556i 0.631449 1.52445i −0.206354 0.978478i \(-0.566160\pi\)
0.837802 0.545974i \(-0.183840\pi\)
\(654\) 36.2620 + 27.5181i 1.41796 + 1.07604i
\(655\) −9.08743 −0.355075
\(656\) 11.5127 22.8792i 0.449494 0.893283i
\(657\) −4.80597 −0.187499
\(658\) −47.0878 35.7335i −1.83567 1.39304i
\(659\) −1.13582 + 2.74212i −0.0442453 + 0.106818i −0.944457 0.328635i \(-0.893412\pi\)
0.900212 + 0.435452i \(0.143412\pi\)
\(660\) 1.18130 + 4.22737i 0.0459820 + 0.164550i
\(661\) 4.40183 + 27.7921i 0.171211 + 1.08099i 0.912283 + 0.409561i \(0.134318\pi\)
−0.741071 + 0.671426i \(0.765682\pi\)
\(662\) 9.31892 5.44690i 0.362190 0.211700i
\(663\) −56.0220 4.40903i −2.17571 0.171232i
\(664\) −9.78415 3.87011i −0.379699 0.150189i
\(665\) 12.1361 + 12.1361i 0.470617 + 0.470617i
\(666\) 5.37825 10.0330i 0.208403 0.388772i
\(667\) 1.51744 0.364304i 0.0587553 0.0141059i
\(668\) −35.9511 4.34259i −1.39099 0.168020i
\(669\) −28.7128 + 33.6183i −1.11010 + 1.29976i
\(670\) −4.48827 3.99802i −0.173397 0.154457i
\(671\) 6.03026 + 1.44774i 0.232796 + 0.0558893i
\(672\) 45.3393 69.8999i 1.74900 2.69645i
\(673\) −8.56279 + 13.9732i −0.330071 + 0.538627i −0.974026 0.226436i \(-0.927292\pi\)
0.643955 + 0.765064i \(0.277292\pi\)
\(674\) 6.37753 + 46.5193i 0.245653 + 1.79186i
\(675\) −28.7920 + 24.5907i −1.10820 + 0.946496i
\(676\) 21.8558 10.0121i 0.840607 0.385082i
\(677\) 9.33719 18.3253i 0.358858 0.704298i −0.639036 0.769177i \(-0.720666\pi\)
0.997893 + 0.0648796i \(0.0206663\pi\)
\(678\) 46.6255 + 20.4611i 1.79064 + 0.785803i
\(679\) −5.09538 + 15.6820i −0.195543 + 0.601819i
\(680\) 7.11632 7.34830i 0.272899 0.281794i
\(681\) 6.27234 2.03801i 0.240357 0.0780966i
\(682\) 6.08550 1.32755i 0.233026 0.0508346i
\(683\) 5.65966 2.34431i 0.216561 0.0897024i −0.271766 0.962363i \(-0.587608\pi\)
0.488326 + 0.872661i \(0.337608\pi\)
\(684\) 8.50386 + 43.2944i 0.325153 + 1.65540i
\(685\) 8.40664 + 13.7184i 0.321201 + 0.524153i
\(686\) −43.1086 52.6567i −1.64590 2.01044i
\(687\) −21.6334 + 15.7176i −0.825367 + 0.599664i
\(688\) 9.09711 14.6865i 0.346824 0.559917i
\(689\) 2.16910 13.6952i 0.0826362 0.521745i
\(690\) 4.03979 1.57556i 0.153792 0.0599804i
\(691\) 0.690133 + 8.76897i 0.0262539 + 0.333587i 0.995992 + 0.0894405i \(0.0285079\pi\)
−0.969738 + 0.244147i \(0.921492\pi\)
\(692\) −11.5929 + 20.5845i −0.440694 + 0.782506i
\(693\) 18.0511 + 13.1149i 0.685706 + 0.498194i
\(694\) −22.4556 + 1.29725i −0.852404 + 0.0492428i
\(695\) −7.01664 13.7709i −0.266156 0.522361i
\(696\) 2.76851 12.4047i 0.104940 0.470199i
\(697\) −0.234696 23.8528i −0.00888973 0.903490i
\(698\) −16.3900 + 7.92545i −0.620371 + 0.299983i
\(699\) 14.9815 7.63345i 0.566652 0.288724i
\(700\) 19.2827 + 34.6263i 0.728816 + 1.30875i
\(701\) −2.49789 + 3.43805i −0.0943441 + 0.129853i −0.853580 0.520963i \(-0.825573\pi\)
0.759235 + 0.650816i \(0.225573\pi\)
\(702\) −54.2016 + 37.6799i −2.04571 + 1.42213i
\(703\) 4.76634 0.375119i 0.179766 0.0141479i
\(704\) 5.21116 + 2.96786i 0.196403 + 0.111856i
\(705\) −24.7472 3.91958i −0.932035 0.147620i
\(706\) −4.46235 1.55341i −0.167943 0.0584632i
\(707\) 35.4863 + 48.8428i 1.33460 + 1.83692i
\(708\) 5.97318 + 2.77107i 0.224486 + 0.104143i
\(709\) 13.2351 8.11047i 0.497054 0.304595i −0.251283 0.967914i \(-0.580853\pi\)
0.748337 + 0.663319i \(0.230853\pi\)
\(710\) 14.9615 + 3.92333i 0.561495 + 0.147240i
\(711\) −5.04418 12.1777i −0.189172 0.456701i
\(712\) 19.4501 + 9.52059i 0.728923 + 0.356799i
\(713\) −1.90144 5.85202i −0.0712094 0.219160i
\(714\) 7.69839 77.2133i 0.288105 2.88964i
\(715\) −3.46202 1.12488i −0.129472 0.0420681i
\(716\) −1.83445 49.7315i −0.0685568 1.85855i
\(717\) 2.88100 + 1.46794i 0.107593 + 0.0548213i
\(718\) −30.2463 0.630262i −1.12878 0.0235212i
\(719\) 12.7360 + 14.9120i 0.474975 + 0.556124i 0.945229 0.326407i \(-0.105838\pi\)
−0.470255 + 0.882531i \(0.655838\pi\)
\(720\) 1.97001 23.5839i 0.0734180 0.878920i
\(721\) 16.8427 + 10.3212i 0.627255 + 0.384383i
\(722\) 6.01825 5.77255i 0.223976 0.214832i
\(723\) −2.38239 + 9.92335i −0.0886019 + 0.369053i
\(724\) 43.7165 + 12.4427i 1.62471 + 0.462428i
\(725\) 4.59745 + 3.92659i 0.170745 + 0.145830i
\(726\) 24.0456 37.4638i 0.892414 1.39041i
\(727\) 3.33770 + 13.9025i 0.123788 + 0.515615i 0.999465 + 0.0327169i \(0.0104160\pi\)
−0.875676 + 0.482898i \(0.839584\pi\)
\(728\) 27.4624 + 63.4049i 1.01782 + 2.34994i
\(729\) −17.2133 + 17.2133i −0.637529 + 0.637529i
\(730\) 0.313041 + 1.03643i 0.0115862 + 0.0383601i
\(731\) 1.26237 16.0400i 0.0466906 0.593260i
\(732\) −41.4213 27.8208i −1.53098 1.02829i
\(733\) −28.6397 + 4.53608i −1.05783 + 0.167544i −0.661029 0.750360i \(-0.729880\pi\)
−0.396802 + 0.917904i \(0.629880\pi\)
\(734\) −2.53208 + 14.0815i −0.0934608 + 0.519759i
\(735\) −45.5834 18.8813i −1.68137 0.696446i
\(736\) 2.40671 5.41352i 0.0887125 0.199545i
\(737\) 3.28189i 0.120890i
\(738\) −35.3776 42.3562i −1.30227 1.55915i
\(739\) 25.1619i 0.925594i −0.886464 0.462797i \(-0.846846\pi\)
0.886464 0.462797i \(-0.153154\pi\)
\(740\) −2.51399 0.506338i −0.0924163 0.0186134i
\(741\) −50.4471 20.8959i −1.85322 0.767630i
\(742\) 18.8442 + 3.38849i 0.691793 + 0.124395i
\(743\) 19.6521 3.11259i 0.720966 0.114190i 0.214840 0.976649i \(-0.431077\pi\)
0.506126 + 0.862459i \(0.331077\pi\)
\(744\) −49.6168 7.04492i −1.81904 0.258279i
\(745\) −0.181779 + 2.30972i −0.00665987 + 0.0846217i
\(746\) −3.62400 + 1.09458i −0.132684 + 0.0400755i
\(747\) −16.0310 + 16.0310i −0.586542 + 0.586542i
\(748\) 5.58043 + 0.232668i 0.204041 + 0.00850717i
\(749\) 6.53247 + 27.2097i 0.238691 + 0.994220i
\(750\) 31.5599 + 20.2562i 1.15241 + 0.739653i
\(751\) −32.1133 27.4273i −1.17183 1.00084i −0.999876 0.0157318i \(-0.994992\pi\)
−0.171953 0.985105i \(-0.555008\pi\)
\(752\) −27.7914 + 19.9886i −1.01345 + 0.728908i
\(753\) −11.7190 + 48.8133i −0.427065 + 1.77885i
\(754\) 7.29649 + 7.60704i 0.265722 + 0.277032i
\(755\) −1.42543 0.873503i −0.0518766 0.0317900i
\(756\) −50.4590 75.9109i −1.83518 2.76085i
\(757\) 13.3536 + 15.6351i 0.485345 + 0.568266i 0.947999 0.318273i \(-0.103103\pi\)
−0.462654 + 0.886539i \(0.653103\pi\)
\(758\) −0.529705 + 25.4205i −0.0192398 + 0.923316i
\(759\) 2.10952 + 1.07485i 0.0765706 + 0.0390147i
\(760\) 8.78277 4.65392i 0.318584 0.168816i
\(761\) −30.6704 9.96541i −1.11180 0.361246i −0.305167 0.952299i \(-0.598712\pi\)
−0.806633 + 0.591053i \(0.798712\pi\)
\(762\) 55.4159 + 5.52512i 2.00751 + 0.200154i
\(763\) −16.1088 49.5778i −0.583178 1.79484i
\(764\) 3.49777 + 4.45886i 0.126545 + 0.161316i
\(765\) −8.43478 20.3634i −0.304960 0.736239i
\(766\) 2.55034 9.72566i 0.0921477 0.351402i
\(767\) −4.65613 + 2.85328i −0.168123 + 0.103026i
\(768\) −30.9830 36.9895i −1.11800 1.33474i
\(769\) 30.1720 + 41.5283i 1.08803 + 1.49755i 0.850360 + 0.526202i \(0.176384\pi\)
0.237672 + 0.971346i \(0.423616\pi\)
\(770\) 1.65252 4.74707i 0.0595528 0.171073i
\(771\) 48.3595 + 7.65939i 1.74162 + 0.275846i
\(772\) 8.36995 9.01109i 0.301241 0.324316i
\(773\) 45.3447 3.56870i 1.63093 0.128357i 0.770335 0.637640i \(-0.220089\pi\)
0.860599 + 0.509283i \(0.170089\pi\)
\(774\) −21.2475 30.5641i −0.763727 1.09860i
\(775\) 14.0124 19.2864i 0.503339 0.692786i
\(776\) 7.81454 + 5.48832i 0.280525 + 0.197019i
\(777\) −17.3329 + 8.83157i −0.621816 + 0.316831i
\(778\) −5.96271 12.3310i −0.213774 0.442089i
\(779\) 6.94527 22.1133i 0.248840 0.792292i
\(780\) 22.9570 + 18.1874i 0.821994 + 0.651212i
\(781\) 3.83407 + 7.52478i 0.137194 + 0.269258i
\(782\) −0.318219 5.50845i −0.0113795 0.196982i
\(783\) −11.2495 8.17322i −0.402023 0.292087i
\(784\) −62.4027 + 25.4979i −2.22867 + 0.910639i
\(785\) −1.45379 18.4721i −0.0518879 0.659298i
\(786\) 14.5057 + 37.1931i 0.517401 + 1.32664i
\(787\) −1.68634 + 10.6471i −0.0601115 + 0.379529i 0.939231 + 0.343285i \(0.111540\pi\)
−0.999343 + 0.0362447i \(0.988460\pi\)
\(788\) −48.4360 + 5.61496i −1.72546 + 0.200025i
\(789\) −3.62115 + 2.63092i −0.128916 + 0.0936631i
\(790\) −2.29764 + 1.88101i −0.0817462 + 0.0669234i
\(791\) −30.4662 49.7164i −1.08325 1.76771i
\(792\) 10.3308 7.76189i 0.367089 0.275807i
\(793\) 38.2311 15.8359i 1.35763 0.562348i
\(794\) −1.14670 5.25650i −0.0406950 0.186546i
\(795\) 7.71848 2.50789i 0.273746 0.0889455i
\(796\) −5.06091 + 1.85329i −0.179379 + 0.0656880i
\(797\) 5.87042 18.0673i 0.207941 0.639976i −0.791639 0.610989i \(-0.790772\pi\)
0.999580 0.0289870i \(-0.00922814\pi\)
\(798\) 30.2987 69.0428i 1.07256 2.44409i
\(799\) −14.4744 + 28.4077i −0.512069 + 1.00499i
\(800\) 22.4487 4.78443i 0.793680 0.169155i
\(801\) 35.4809 30.3035i 1.25365 1.07072i
\(802\) −38.1705 + 5.23296i −1.34785 + 0.184782i
\(803\) −0.308873 + 0.504036i −0.0108999 + 0.0177870i
\(804\) −9.19881 + 24.7514i −0.324417 + 0.872915i
\(805\) −4.82840 1.15920i −0.170179 0.0408563i
\(806\) 27.6445 31.0343i 0.973734 1.09314i
\(807\) 46.3759 54.2992i 1.63251 1.91142i
\(808\) 33.0750 11.3362i 1.16357 0.398807i
\(809\) −20.9317 + 5.02525i −0.735919 + 0.176678i −0.584045 0.811721i \(-0.698531\pi\)
−0.151874 + 0.988400i \(0.548531\pi\)
\(810\) −11.9293 6.39473i −0.419151 0.224688i
\(811\) −23.3408 23.3408i −0.819605 0.819605i 0.166446 0.986051i \(-0.446771\pi\)
−0.986051 + 0.166446i \(0.946771\pi\)
\(812\) −10.7117 + 9.85420i −0.375906 + 0.345815i
\(813\) 53.0972 + 4.17884i 1.86220 + 0.146558i
\(814\) −0.706582 1.20887i −0.0247657 0.0423707i
\(815\) 1.20409 + 7.60233i 0.0421775 + 0.266298i
\(816\) −41.4345 17.3962i −1.45050 0.608987i
\(817\) 5.98282 14.4438i 0.209312 0.505325i
\(818\) −23.0120 + 30.3241i −0.804597 + 1.06026i
\(819\) 148.883 5.20238
\(820\) −6.82999 + 10.3883i −0.238514 + 0.362775i
\(821\) 18.2757 0.637827 0.318913 0.947784i \(-0.396682\pi\)
0.318913 + 0.947784i \(0.396682\pi\)
\(822\) 42.7278 56.3046i 1.49030 1.96385i
\(823\) −7.73459 + 18.6730i −0.269611 + 0.650899i −0.999465 0.0327044i \(-0.989588\pi\)
0.729854 + 0.683603i \(0.239588\pi\)
\(824\) 8.57871 7.56815i 0.298854 0.263649i
\(825\) 1.43492 + 9.05972i 0.0499575 + 0.315419i
\(826\) −3.80510 6.51002i −0.132396 0.226512i
\(827\) −8.47147 0.666719i −0.294582 0.0231841i −0.0696930 0.997568i \(-0.522202\pi\)
−0.224889 + 0.974384i \(0.572202\pi\)
\(828\) −8.64256 9.39459i −0.300350 0.326485i
\(829\) −20.8920 20.8920i −0.725609 0.725609i 0.244133 0.969742i \(-0.421497\pi\)
−0.969742 + 0.244133i \(0.921497\pi\)
\(830\) 4.50135 + 2.41297i 0.156244 + 0.0837554i
\(831\) 39.8618 9.56998i 1.38279 0.331979i
\(832\) 39.7714 4.41721i 1.37883 0.153139i
\(833\) −40.7741 + 47.7403i −1.41274 + 1.65410i
\(834\) −45.1616 + 50.6994i −1.56382 + 1.75558i
\(835\) 17.0920 + 4.10343i 0.591493 + 0.142005i
\(836\) 5.08713 + 1.89062i 0.175942 + 0.0653884i
\(837\) −28.6471 + 46.7478i −0.990188 + 1.61584i
\(838\) −42.8831 + 5.87903i −1.48137 + 0.203088i
\(839\) 20.8098 17.7733i 0.718436 0.613602i −0.213195 0.977010i \(-0.568387\pi\)
0.931630 + 0.363408i \(0.118387\pi\)
\(840\) −25.7686 + 31.1697i −0.889103 + 1.07546i
\(841\) 12.1577 23.8608i 0.419231 0.822788i
\(842\) −4.40449 + 10.0367i −0.151789 + 0.345887i
\(843\) −29.1822 + 89.8135i −1.00509 + 3.09334i
\(844\) 2.02851 + 5.53942i 0.0698243 + 0.190675i
\(845\) −11.0980 + 3.60595i −0.381782 + 0.124048i
\(846\) 15.7214 + 72.0670i 0.540513 + 2.47772i
\(847\) −47.0982 + 19.5087i −1.61831 + 0.670327i
\(848\) 5.08133 9.85546i 0.174493 0.338438i
\(849\) −49.6268 80.9835i −1.70319 2.77935i
\(850\) 16.5409 13.5416i 0.567347 0.464471i
\(851\) −1.11908 + 0.813060i −0.0383616 + 0.0278713i
\(852\) −7.82464 67.4971i −0.268068 2.31241i
\(853\) −6.05751 + 38.2456i −0.207405 + 1.30951i 0.635775 + 0.771875i \(0.280681\pi\)
−0.843180 + 0.537631i \(0.819319\pi\)
\(854\) 20.7621 + 53.2349i 0.710465 + 1.82166i
\(855\) −1.68035 21.3508i −0.0574667 0.730184i
\(856\) 16.1741 + 1.01226i 0.552818 + 0.0345984i
\(857\) 23.2310 + 16.8783i 0.793555 + 0.576551i 0.909016 0.416761i \(-0.136835\pi\)
−0.115462 + 0.993312i \(0.536835\pi\)
\(858\) 0.922285 + 15.9650i 0.0314863 + 0.545035i
\(859\) −16.1031 31.6040i −0.549430 1.07832i −0.984082 0.177718i \(-0.943129\pi\)
0.434652 0.900598i \(-0.356871\pi\)
\(860\) −5.20733 + 6.57296i −0.177568 + 0.224136i
\(861\) 8.32398 + 93.9399i 0.283680 + 3.20146i
\(862\) −1.62844 3.36765i −0.0554649 0.114703i
\(863\) 17.0853 8.70539i 0.581590 0.296335i −0.138337 0.990385i \(-0.544176\pi\)
0.719926 + 0.694050i \(0.244176\pi\)
\(864\) −50.6065 + 15.0204i −1.72167 + 0.511004i
\(865\) 6.74039 9.27735i 0.229180 0.315439i
\(866\) 4.81320 + 6.92367i 0.163559 + 0.235276i
\(867\) 9.38492 0.738609i 0.318729 0.0250845i
\(868\) 42.0486 + 39.0568i 1.42722 + 1.32567i
\(869\) −1.60135 0.253629i −0.0543220 0.00860377i
\(870\) −2.02829 + 5.82650i −0.0687654 + 0.197537i
\(871\) −12.8718 17.7165i −0.436144 0.600301i
\(872\) −30.1857 + 0.484094i −1.02222 + 0.0163935i
\(873\) 17.5438 10.7508i 0.593766 0.363860i
\(874\) 1.35992 5.18601i 0.0460000 0.175420i
\(875\) −16.4343 39.6760i −0.555582 1.34129i
\(876\) 3.74223 2.93561i 0.126438 0.0991850i
\(877\) −9.02856 27.7870i −0.304873 0.938302i −0.979725 0.200348i \(-0.935793\pi\)
0.674852 0.737953i \(-0.264207\pi\)
\(878\) −14.1118 1.40698i −0.476249 0.0474834i
\(879\) −23.3313 7.58079i −0.786944 0.255694i
\(880\) −2.34680 1.72232i −0.0791106 0.0580593i
\(881\) −41.5729 21.1824i −1.40063 0.713654i −0.419632 0.907694i \(-0.637841\pi\)
−0.980994 + 0.194040i \(0.937841\pi\)
\(882\) −3.02602 + 145.219i −0.101891 + 4.88977i
\(883\) 31.8123 + 37.2474i 1.07057 + 1.25348i 0.965885 + 0.258970i \(0.0833831\pi\)
0.104684 + 0.994506i \(0.466617\pi\)
\(884\) 31.0372 20.6309i 1.04390 0.693891i
\(885\) −2.72523 1.67002i −0.0916075 0.0561372i
\(886\) −0.670258 0.698786i −0.0225178 0.0234762i
\(887\) 4.61576 19.2260i 0.154982 0.645547i −0.839744 0.542982i \(-0.817295\pi\)
0.994726 0.102565i \(-0.0327049\pi\)
\(888\) 1.94058 + 11.0975i 0.0651216 + 0.372409i
\(889\) −48.4948 41.4184i −1.62646 1.38913i
\(890\) −8.84619 5.67779i −0.296525 0.190320i
\(891\) −1.72522 7.18607i −0.0577971 0.240742i
\(892\) 1.22142 29.2952i 0.0408961 0.980875i
\(893\) −21.9059 + 21.9059i −0.733054 + 0.733054i
\(894\) 9.74342 2.94287i 0.325869 0.0984245i
\(895\) −1.89528 + 24.0818i −0.0633523 + 0.804967i
\(896\) 4.95399 + 55.0328i 0.165501 + 1.83852i
\(897\) 15.6034 2.47134i 0.520982 0.0825155i
\(898\) 33.4027 + 6.00632i 1.11466 + 0.200434i
\(899\) 8.08828 + 3.35027i 0.269759 + 0.111738i
\(900\) 9.76483 48.4829i 0.325494 1.61610i
\(901\) 10.3270i 0.344041i
\(902\) −6.71587 + 0.988120i −0.223614 + 0.0329008i
\(903\) 63.6110i 2.11684i
\(904\) −32.7047 + 8.40857i −1.08774 + 0.279665i
\(905\) −20.3835 8.44314i −0.677572 0.280660i
\(906\) −1.29976 + 7.22832i −0.0431818 + 0.240145i
\(907\) 30.9908 4.90846i 1.02903 0.162983i 0.380984 0.924582i \(-0.375585\pi\)
0.648048 + 0.761599i \(0.275585\pi\)
\(908\) −2.43871 + 3.63090i −0.0809315 + 0.120496i
\(909\) 5.91082 75.1042i 0.196050 2.49105i
\(910\) −9.69760 32.1073i −0.321472 1.06435i
\(911\) 8.64845 8.64845i 0.286536 0.286536i −0.549173 0.835709i \(-0.685057\pi\)
0.835709 + 0.549173i \(0.185057\pi\)
\(912\) −33.0670 28.5174i −1.09496 0.944307i
\(913\) 0.650990 + 2.71157i 0.0215446 + 0.0897399i
\(914\) 18.1432 28.2677i 0.600122 0.935011i
\(915\) 18.4173 + 15.7298i 0.608856 + 0.520012i
\(916\) 4.85471 17.0567i 0.160404 0.563571i
\(917\) 10.6724 44.4537i 0.352433 1.46799i
\(918\) −35.4810 + 34.0325i −1.17105 + 1.12324i
\(919\) −13.6902 8.38935i −0.451597 0.276739i 0.278045 0.960568i \(-0.410314\pi\)
−0.729643 + 0.683829i \(0.760314\pi\)
\(920\) −1.46305 + 2.47574i −0.0482354 + 0.0816227i
\(921\) 36.4610 + 42.6904i 1.20143 + 1.40670i
\(922\) 29.0290 + 0.604896i 0.956019 + 0.0199212i
\(923\) 50.2101 + 25.5833i 1.65269 + 0.842085i
\(924\) −22.0667 + 0.813979i −0.725941 + 0.0267779i
\(925\) −5.09686 1.65607i −0.167584 0.0544513i
\(926\) 2.28438 22.9119i 0.0750694 0.752931i
\(927\) −7.61712 23.4431i −0.250179 0.769972i
\(928\) 3.63301 + 7.60606i 0.119259 + 0.249681i
\(929\) −11.4040 27.5317i −0.374153 0.903284i −0.993037 0.117802i \(-0.962415\pi\)
0.618884 0.785482i \(-0.287585\pi\)
\(930\) 23.5302 + 6.17029i 0.771586 + 0.202332i
\(931\) −52.0148 + 31.8747i −1.70472 + 1.04465i
\(932\) −4.69279 + 10.1155i −0.153718 + 0.331346i
\(933\) −45.9426 63.2346i −1.50409 2.07021i
\(934\) 36.9157 + 12.8509i 1.20792 + 0.420493i
\(935\) −2.67774 0.424113i −0.0875716 0.0138700i
\(936\) 25.3258 82.4190i 0.827800 2.69395i
\(937\) 15.8457 1.24708i 0.517656 0.0407404i 0.183060 0.983102i \(-0.441400\pi\)
0.334597 + 0.942361i \(0.391400\pi\)
\(938\) 24.8285 17.2603i 0.810680 0.563568i
\(939\) −38.7642 + 53.3544i −1.26502 + 1.74115i
\(940\) 14.5176 8.08456i 0.473512 0.263689i
\(941\) 27.9609 14.2468i 0.911498 0.464431i 0.0656421 0.997843i \(-0.479090\pi\)
0.845856 + 0.533412i \(0.179090\pi\)
\(942\) −73.2822 + 35.4359i −2.38766 + 1.15456i
\(943\) 1.62955 + 6.50495i 0.0530656 + 0.211830i
\(944\) −4.25111 + 0.999050i −0.138362 + 0.0325163i
\(945\) 20.0870 + 39.4229i 0.653429 + 1.28243i
\(946\) −4.57102 + 0.264065i −0.148617 + 0.00858549i
\(947\) −28.7384 20.8797i −0.933872 0.678498i 0.0130660 0.999915i \(-0.495841\pi\)
−0.946938 + 0.321417i \(0.895841\pi\)
\(948\) 11.3662 + 6.40125i 0.369157 + 0.207903i
\(949\) 0.309482 + 3.93235i 0.0100462 + 0.127649i
\(950\) 19.3518 7.54738i 0.627855 0.244869i
\(951\) −1.25436 + 7.91973i −0.0406755 + 0.256815i
\(952\) 27.5887 + 43.4414i 0.894156 + 1.40794i
\(953\) 44.5577 32.3730i 1.44336 1.04867i 0.456038 0.889960i \(-0.349268\pi\)
0.987326 0.158705i \(-0.0507320\pi\)
\(954\) −15.1347 18.4869i −0.490004 0.598534i
\(955\) −1.43730 2.34547i −0.0465100 0.0758975i
\(956\) −2.10419 + 0.413303i −0.0680544 + 0.0133672i
\(957\) −3.11214 + 1.28909i −0.100601 + 0.0416703i
\(958\) −37.8083 + 8.24786i −1.22153 + 0.266476i
\(959\) −76.9801 + 25.0124i −2.48582 + 0.807691i
\(960\) 12.8717 + 19.5673i 0.415431 + 0.631531i
\(961\) 1.08751 3.34703i 0.0350811 0.107969i
\(962\) −8.55558 3.75452i −0.275843 0.121051i
\(963\) 15.8526 31.1125i 0.510844 1.00259i
\(964\) −2.81879 6.15322i −0.0907872 0.198182i
\(965\) −4.53948 + 3.87708i −0.146131 + 0.124808i
\(966\) 2.96289 + 21.6121i 0.0953296 + 0.695358i
\(967\) −20.5449 + 33.5262i −0.660678 + 1.07813i 0.330270 + 0.943886i \(0.392860\pi\)
−0.990949 + 0.134242i \(0.957140\pi\)
\(968\) 2.78802 + 29.3913i 0.0896105 + 0.944674i
\(969\) −39.5438 9.49362i −1.27033 0.304979i
\(970\) −3.46120 3.08314i −0.111132 0.0989936i
\(971\) −20.9291 + 24.5048i −0.671646 + 0.786396i −0.986678 0.162685i \(-0.947985\pi\)
0.315032 + 0.949081i \(0.397985\pi\)
\(972\) −0.416138 + 3.44509i −0.0133476 + 0.110501i
\(973\) 75.6048 18.1511i 2.42378 0.581898i
\(974\) 22.8070 42.5460i 0.730782 1.36326i
\(975\) 43.2790 + 43.2790i 1.38604 + 1.38604i
\(976\) 33.0017 2.43800i 1.05636 0.0780385i
\(977\) −14.6721 1.15472i −0.469404 0.0369429i −0.158448 0.987367i \(-0.550649\pi\)
−0.310956 + 0.950424i \(0.600649\pi\)
\(978\) 29.1929 17.0632i 0.933486 0.545622i
\(979\) −0.897833 5.66870i −0.0286949 0.181172i
\(980\) 31.5143 8.80638i 1.00669 0.281309i
\(981\) −24.8933 + 60.0978i −0.794782 + 1.91877i
\(982\) −1.90833 1.44817i −0.0608974 0.0462131i
\(983\) −1.16313 −0.0370981 −0.0185490 0.999828i \(-0.505905\pi\)
−0.0185490 + 0.999828i \(0.505905\pi\)
\(984\) 53.4196 + 11.3717i 1.70295 + 0.362517i
\(985\) 23.6685 0.754141
\(986\) 6.25363 + 4.74568i 0.199156 + 0.151133i
\(987\) 48.2372 116.455i 1.53541 3.70680i
\(988\) 34.8768 9.74601i 1.10958 0.310062i
\(989\) 0.707582 + 4.46750i 0.0224998 + 0.142058i
\(990\) −5.41513 + 3.16514i −0.172104 + 0.100595i
\(991\) 17.1259 + 1.34783i 0.544021 + 0.0428154i 0.347493 0.937683i \(-0.387033\pi\)
0.196528 + 0.980498i \(0.437033\pi\)
\(992\) 28.7739 16.6336i 0.913573 0.528118i
\(993\) 16.2757 + 16.2757i 0.516495 + 0.516495i
\(994\) −36.7630 + 68.5807i −1.16605 + 2.17525i
\(995\) 2.54384 0.610722i 0.0806452 0.0193612i
\(996\) 2.69061 22.2749i 0.0852554 0.705806i
\(997\) −21.0729 + 24.6732i −0.667384 + 0.781407i −0.986048 0.166461i \(-0.946766\pi\)
0.318664 + 0.947868i \(0.396766\pi\)
\(998\) −14.0776 12.5399i −0.445617 0.396943i
\(999\) 11.9848 + 2.87730i 0.379182 + 0.0910336i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 164.2.o.b.75.4 yes 288
4.3 odd 2 inner 164.2.o.b.75.10 yes 288
41.35 odd 40 inner 164.2.o.b.35.10 yes 288
164.35 even 40 inner 164.2.o.b.35.4 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
164.2.o.b.35.4 288 164.35 even 40 inner
164.2.o.b.35.10 yes 288 41.35 odd 40 inner
164.2.o.b.75.4 yes 288 1.1 even 1 trivial
164.2.o.b.75.10 yes 288 4.3 odd 2 inner