Properties

Label 192.2.r.a.13.2
Level $192$
Weight $2$
Character 192.13
Analytic conductor $1.533$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [192,2,Mod(13,192)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(192, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([0, 15, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("192.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 192.r (of order \(16\), degree \(8\), 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: \(1.53312771881\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(16\) over \(\Q(\zeta_{16})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 13.2
Character \(\chi\) \(=\) 192.13
Dual form 192.2.r.a.133.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.37379 + 0.335725i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(1.77458 - 0.922428i) q^{4} +(-1.61488 + 0.321219i) q^{5} +(0.955743 - 1.04238i) q^{6} +(0.265757 + 0.641595i) q^{7} +(-2.12821 + 1.86299i) q^{8} +(0.382683 - 0.923880i) q^{9} +O(q^{10})\) \(q+(-1.37379 + 0.335725i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(1.77458 - 0.922428i) q^{4} +(-1.61488 + 0.321219i) q^{5} +(0.955743 - 1.04238i) q^{6} +(0.265757 + 0.641595i) q^{7} +(-2.12821 + 1.86299i) q^{8} +(0.382683 - 0.923880i) q^{9} +(2.11065 - 0.983439i) q^{10} +(-1.87615 + 2.80786i) q^{11} +(-0.963034 + 1.75287i) q^{12} +(-5.98870 - 1.19123i) q^{13} +(-0.580493 - 0.792193i) q^{14} +(1.16426 - 1.16426i) q^{15} +(2.29825 - 3.27384i) q^{16} +(-2.58283 - 2.58283i) q^{17} +(-0.215556 + 1.39769i) q^{18} +(-0.689900 + 3.46836i) q^{19} +(-2.56942 + 2.05963i) q^{20} +(-0.577420 - 0.385820i) q^{21} +(1.63476 - 4.48727i) q^{22} +(-3.97235 - 1.64540i) q^{23} +(0.734520 - 2.73139i) q^{24} +(-2.11476 + 0.875961i) q^{25} +(8.62712 - 0.374064i) q^{26} +(0.195090 + 0.980785i) q^{27} +(1.06343 + 0.893418i) q^{28} +(0.359397 + 0.537876i) q^{29} +(-1.20857 + 1.99032i) q^{30} +5.16071i q^{31} +(-2.05820 + 5.26914i) q^{32} -3.37698i q^{33} +(4.41538 + 2.68114i) q^{34} +(-0.635257 - 0.950729i) q^{35} +(-0.173111 - 1.99249i) q^{36} +(-1.24608 - 6.26446i) q^{37} +(-0.216640 - 4.99641i) q^{38} +(5.64123 - 2.33668i) q^{39} +(2.83836 - 3.69211i) q^{40} +(8.38439 + 3.47293i) q^{41} +(0.922781 + 0.336180i) q^{42} +(7.83860 + 5.23759i) q^{43} +(-0.739328 + 6.71338i) q^{44} +(-0.321219 + 1.61488i) q^{45} +(6.00956 + 0.926814i) q^{46} +(4.59493 + 4.59493i) q^{47} +(-0.0920786 + 3.99894i) q^{48} +(4.60873 - 4.60873i) q^{49} +(2.61114 - 1.91336i) q^{50} +(3.58249 + 0.712601i) q^{51} +(-11.7262 + 3.41022i) q^{52} +(1.12664 - 1.68613i) q^{53} +(-0.597286 - 1.28189i) q^{54} +(2.12781 - 5.13700i) q^{55} +(-1.76087 - 0.870345i) q^{56} +(-1.35329 - 3.26713i) q^{57} +(-0.674314 - 0.618269i) q^{58} +(0.695355 - 0.138315i) q^{59} +(0.992124 - 3.14002i) q^{60} +(-10.3401 + 6.90906i) q^{61} +(-1.73258 - 7.08972i) q^{62} +0.694457 q^{63} +(1.05854 - 7.92966i) q^{64} +10.0536 q^{65} +(1.13374 + 4.63925i) q^{66} +(-6.33942 + 4.23586i) q^{67} +(-6.96591 - 2.20096i) q^{68} +(4.21703 - 0.838819i) q^{69} +(1.19189 + 1.09283i) q^{70} +(-5.26523 - 12.7114i) q^{71} +(0.906747 + 2.67914i) q^{72} +(-2.49830 + 6.03143i) q^{73} +(3.81498 + 8.18769i) q^{74} +(1.27170 - 1.90323i) q^{75} +(1.97503 + 6.79126i) q^{76} +(-2.30011 - 0.457520i) q^{77} +(-6.96537 + 5.10399i) q^{78} +(1.63586 - 1.63586i) q^{79} +(-2.65977 + 6.02509i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(-12.6843 - 1.95621i) q^{82} +(0.236508 - 1.18901i) q^{83} +(-1.38057 - 0.152039i) q^{84} +(5.00060 + 3.34129i) q^{85} +(-12.5269 - 4.56371i) q^{86} +(-0.597656 - 0.247557i) q^{87} +(-1.23817 - 9.47096i) q^{88} +(-5.01170 + 2.07592i) q^{89} +(-0.100868 - 2.32633i) q^{90} +(-0.827256 - 4.15890i) q^{91} +(-8.56701 + 0.744315i) q^{92} +(-2.86714 - 4.29098i) q^{93} +(-7.85509 - 4.76983i) q^{94} -5.82258i q^{95} +(-1.21605 - 5.52460i) q^{96} +10.7336i q^{97} +(-4.78415 + 7.87868i) q^{98} +(1.87615 + 2.80786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(133\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{15}{16}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.37379 + 0.335725i −0.971414 + 0.237393i
\(3\) −0.831470 + 0.555570i −0.480049 + 0.320759i
\(4\) 1.77458 0.922428i 0.887289 0.461214i
\(5\) −1.61488 + 0.321219i −0.722194 + 0.143653i −0.542484 0.840066i \(-0.682516\pi\)
−0.179710 + 0.983720i \(0.557516\pi\)
\(6\) 0.955743 1.04238i 0.390180 0.425550i
\(7\) 0.265757 + 0.641595i 0.100447 + 0.242500i 0.966112 0.258123i \(-0.0831041\pi\)
−0.865665 + 0.500624i \(0.833104\pi\)
\(8\) −2.12821 + 1.86299i −0.752435 + 0.658666i
\(9\) 0.382683 0.923880i 0.127561 0.307960i
\(10\) 2.11065 0.983439i 0.667447 0.310991i
\(11\) −1.87615 + 2.80786i −0.565681 + 0.846601i −0.998493 0.0548830i \(-0.982521\pi\)
0.432812 + 0.901484i \(0.357521\pi\)
\(12\) −0.963034 + 1.75287i −0.278004 + 0.506011i
\(13\) −5.98870 1.19123i −1.66097 0.330387i −0.726698 0.686957i \(-0.758946\pi\)
−0.934269 + 0.356570i \(0.883946\pi\)
\(14\) −0.580493 0.792193i −0.155143 0.211722i
\(15\) 1.16426 1.16426i 0.300611 0.300611i
\(16\) 2.29825 3.27384i 0.574563 0.818460i
\(17\) −2.58283 2.58283i −0.626428 0.626428i 0.320739 0.947168i \(-0.396069\pi\)
−0.947168 + 0.320739i \(0.896069\pi\)
\(18\) −0.215556 + 1.39769i −0.0508070 + 0.329439i
\(19\) −0.689900 + 3.46836i −0.158274 + 0.795697i 0.817332 + 0.576167i \(0.195452\pi\)
−0.975606 + 0.219530i \(0.929548\pi\)
\(20\) −2.56942 + 2.05963i −0.574540 + 0.460548i
\(21\) −0.577420 0.385820i −0.126003 0.0841928i
\(22\) 1.63476 4.48727i 0.348533 0.956689i
\(23\) −3.97235 1.64540i −0.828292 0.343090i −0.0720660 0.997400i \(-0.522959\pi\)
−0.756227 + 0.654310i \(0.772959\pi\)
\(24\) 0.734520 2.73139i 0.149933 0.557542i
\(25\) −2.11476 + 0.875961i −0.422952 + 0.175192i
\(26\) 8.62712 0.374064i 1.69192 0.0733600i
\(27\) 0.195090 + 0.980785i 0.0375451 + 0.188752i
\(28\) 1.06343 + 0.893418i 0.200970 + 0.168840i
\(29\) 0.359397 + 0.537876i 0.0667384 + 0.0998811i 0.863338 0.504627i \(-0.168370\pi\)
−0.796599 + 0.604508i \(0.793370\pi\)
\(30\) −1.20857 + 1.99032i −0.220654 + 0.363380i
\(31\) 5.16071i 0.926892i 0.886125 + 0.463446i \(0.153387\pi\)
−0.886125 + 0.463446i \(0.846613\pi\)
\(32\) −2.05820 + 5.26914i −0.363842 + 0.931461i
\(33\) 3.37698i 0.587857i
\(34\) 4.41538 + 2.68114i 0.757231 + 0.459811i
\(35\) −0.635257 0.950729i −0.107378 0.160703i
\(36\) −0.173111 1.99249i −0.0288518 0.332082i
\(37\) −1.24608 6.26446i −0.204854 1.02987i −0.937161 0.348897i \(-0.886556\pi\)
0.732307 0.680975i \(-0.238444\pi\)
\(38\) −0.216640 4.99641i −0.0351436 0.810524i
\(39\) 5.64123 2.33668i 0.903320 0.374168i
\(40\) 2.83836 3.69211i 0.448785 0.583775i
\(41\) 8.38439 + 3.47293i 1.30942 + 0.542381i 0.924716 0.380658i \(-0.124303\pi\)
0.384707 + 0.923039i \(0.374303\pi\)
\(42\) 0.922781 + 0.336180i 0.142388 + 0.0518737i
\(43\) 7.83860 + 5.23759i 1.19538 + 0.798724i 0.983911 0.178661i \(-0.0571766\pi\)
0.211465 + 0.977386i \(0.432177\pi\)
\(44\) −0.739328 + 6.71338i −0.111458 + 1.01208i
\(45\) −0.321219 + 1.61488i −0.0478844 + 0.240731i
\(46\) 6.00956 + 0.926814i 0.886062 + 0.136651i
\(47\) 4.59493 + 4.59493i 0.670240 + 0.670240i 0.957771 0.287531i \(-0.0928345\pi\)
−0.287531 + 0.957771i \(0.592834\pi\)
\(48\) −0.0920786 + 3.99894i −0.0132904 + 0.577197i
\(49\) 4.60873 4.60873i 0.658390 0.658390i
\(50\) 2.61114 1.91336i 0.369271 0.270590i
\(51\) 3.58249 + 0.712601i 0.501649 + 0.0997841i
\(52\) −11.7262 + 3.41022i −1.62614 + 0.472913i
\(53\) 1.12664 1.68613i 0.154756 0.231608i −0.745988 0.665959i \(-0.768022\pi\)
0.900744 + 0.434351i \(0.143022\pi\)
\(54\) −0.597286 1.28189i −0.0812804 0.174444i
\(55\) 2.12781 5.13700i 0.286914 0.692672i
\(56\) −1.76087 0.870345i −0.235306 0.116305i
\(57\) −1.35329 3.26713i −0.179247 0.432741i
\(58\) −0.674314 0.618269i −0.0885417 0.0811826i
\(59\) 0.695355 0.138315i 0.0905276 0.0180071i −0.149619 0.988744i \(-0.547805\pi\)
0.240146 + 0.970737i \(0.422805\pi\)
\(60\) 0.992124 3.14002i 0.128083 0.405374i
\(61\) −10.3401 + 6.90906i −1.32392 + 0.884615i −0.998148 0.0608339i \(-0.980624\pi\)
−0.325771 + 0.945449i \(0.605624\pi\)
\(62\) −1.73258 7.08972i −0.220038 0.900395i
\(63\) 0.694457 0.0874934
\(64\) 1.05854 7.92966i 0.132318 0.991207i
\(65\) 10.0536 1.24700
\(66\) 1.13374 + 4.63925i 0.139553 + 0.571053i
\(67\) −6.33942 + 4.23586i −0.774483 + 0.517493i −0.878880 0.477043i \(-0.841709\pi\)
0.104397 + 0.994536i \(0.466709\pi\)
\(68\) −6.96591 2.20096i −0.844740 0.266905i
\(69\) 4.21703 0.838819i 0.507670 0.100982i
\(70\) 1.19189 + 1.09283i 0.142458 + 0.130618i
\(71\) −5.26523 12.7114i −0.624868 1.50856i −0.845924 0.533304i \(-0.820950\pi\)
0.221056 0.975261i \(-0.429050\pi\)
\(72\) 0.906747 + 2.67914i 0.106861 + 0.315740i
\(73\) −2.49830 + 6.03143i −0.292404 + 0.705925i −1.00000 0.000692070i \(-0.999780\pi\)
0.707596 + 0.706617i \(0.249780\pi\)
\(74\) 3.81498 + 8.18769i 0.443483 + 0.951800i
\(75\) 1.27170 1.90323i 0.146843 0.219766i
\(76\) 1.97503 + 6.79126i 0.226552 + 0.779011i
\(77\) −2.30011 0.457520i −0.262122 0.0521393i
\(78\) −6.96537 + 5.10399i −0.788673 + 0.577914i
\(79\) 1.63586 1.63586i 0.184049 0.184049i −0.609069 0.793118i \(-0.708457\pi\)
0.793118 + 0.609069i \(0.208457\pi\)
\(80\) −2.65977 + 6.02509i −0.297372 + 0.673625i
\(81\) −0.707107 0.707107i −0.0785674 0.0785674i
\(82\) −12.6843 1.95621i −1.40075 0.216028i
\(83\) 0.236508 1.18901i 0.0259602 0.130511i −0.965632 0.259913i \(-0.916306\pi\)
0.991592 + 0.129403i \(0.0413060\pi\)
\(84\) −1.38057 0.152039i −0.150632 0.0165888i
\(85\) 5.00060 + 3.34129i 0.542391 + 0.362414i
\(86\) −12.5269 4.56371i −1.35082 0.492118i
\(87\) −0.597656 0.247557i −0.0640755 0.0265409i
\(88\) −1.23817 9.47096i −0.131989 1.00961i
\(89\) −5.01170 + 2.07592i −0.531239 + 0.220047i −0.632146 0.774849i \(-0.717826\pi\)
0.100907 + 0.994896i \(0.467826\pi\)
\(90\) −0.100868 2.32633i −0.0106324 0.245217i
\(91\) −0.827256 4.15890i −0.0867200 0.435971i
\(92\) −8.56701 + 0.744315i −0.893173 + 0.0776002i
\(93\) −2.86714 4.29098i −0.297308 0.444954i
\(94\) −7.85509 4.76983i −0.810191 0.491970i
\(95\) 5.82258i 0.597384i
\(96\) −1.21605 5.52460i −0.124112 0.563852i
\(97\) 10.7336i 1.08984i 0.838489 + 0.544918i \(0.183439\pi\)
−0.838489 + 0.544918i \(0.816561\pi\)
\(98\) −4.78415 + 7.87868i −0.483272 + 0.795866i
\(99\) 1.87615 + 2.80786i 0.188560 + 0.282200i
\(100\) −2.94479 + 3.50517i −0.294479 + 0.350517i
\(101\) 0.234855 + 1.18069i 0.0233689 + 0.117483i 0.990709 0.135998i \(-0.0434242\pi\)
−0.967340 + 0.253482i \(0.918424\pi\)
\(102\) −5.16081 + 0.223768i −0.510996 + 0.0221563i
\(103\) −9.87997 + 4.09242i −0.973503 + 0.403238i −0.812015 0.583637i \(-0.801629\pi\)
−0.161488 + 0.986875i \(0.551629\pi\)
\(104\) 14.9645 8.62171i 1.46739 0.845428i
\(105\) 1.05639 + 0.437573i 0.103093 + 0.0427027i
\(106\) −0.981683 + 2.69462i −0.0953494 + 0.261725i
\(107\) 5.99130 + 4.00326i 0.579201 + 0.387010i 0.810383 0.585901i \(-0.199259\pi\)
−0.231182 + 0.972911i \(0.574259\pi\)
\(108\) 1.25091 + 1.56052i 0.120369 + 0.150161i
\(109\) 1.93530 9.72943i 0.185368 0.931910i −0.770349 0.637623i \(-0.779918\pi\)
0.955717 0.294287i \(-0.0950822\pi\)
\(110\) −1.19854 + 7.77149i −0.114277 + 0.740983i
\(111\) 4.51643 + 4.51643i 0.428680 + 0.428680i
\(112\) 2.71126 + 0.604500i 0.256190 + 0.0571199i
\(113\) 13.3228 13.3228i 1.25331 1.25331i 0.299078 0.954229i \(-0.403321\pi\)
0.954229 0.299078i \(-0.0966789\pi\)
\(114\) 2.95598 + 4.03400i 0.276853 + 0.377819i
\(115\) 6.94338 + 1.38113i 0.647474 + 0.128791i
\(116\) 1.13393 + 0.622985i 0.105283 + 0.0578427i
\(117\) −3.39233 + 5.07698i −0.313621 + 0.469367i
\(118\) −0.908834 + 0.423463i −0.0836649 + 0.0389829i
\(119\) 0.970725 2.34354i 0.0889862 0.214832i
\(120\) −0.308785 + 4.64679i −0.0281881 + 0.424192i
\(121\) −0.154609 0.373259i −0.0140554 0.0339327i
\(122\) 11.8856 12.9630i 1.07607 1.17362i
\(123\) −8.90083 + 1.77048i −0.802560 + 0.159639i
\(124\) 4.76039 + 9.15809i 0.427495 + 0.822421i
\(125\) 9.97882 6.66763i 0.892533 0.596371i
\(126\) −0.954036 + 0.233147i −0.0849923 + 0.0207703i
\(127\) −8.02791 −0.712362 −0.356181 0.934417i \(-0.615921\pi\)
−0.356181 + 0.934417i \(0.615921\pi\)
\(128\) 1.20797 + 11.2490i 0.106770 + 0.994284i
\(129\) −9.42741 −0.830037
\(130\) −13.8116 + 3.37526i −1.21135 + 0.296030i
\(131\) −18.3161 + 12.2384i −1.60028 + 1.06928i −0.649077 + 0.760723i \(0.724845\pi\)
−0.951207 + 0.308553i \(0.900155\pi\)
\(132\) −3.11502 5.99272i −0.271128 0.521599i
\(133\) −2.40863 + 0.479106i −0.208855 + 0.0415438i
\(134\) 7.28692 7.94747i 0.629494 0.686557i
\(135\) −0.630093 1.52118i −0.0542298 0.130922i
\(136\) 10.3086 + 0.685018i 0.883954 + 0.0587398i
\(137\) −4.78724 + 11.5574i −0.409001 + 0.987417i 0.576400 + 0.817168i \(0.304457\pi\)
−0.985401 + 0.170249i \(0.945543\pi\)
\(138\) −5.51168 + 2.56812i −0.469185 + 0.218613i
\(139\) 9.66684 14.4674i 0.819931 1.22711i −0.151185 0.988505i \(-0.548309\pi\)
0.971116 0.238608i \(-0.0766910\pi\)
\(140\) −2.00429 1.10116i −0.169394 0.0930654i
\(141\) −6.37336 1.26774i −0.536734 0.106763i
\(142\) 11.5008 + 15.6951i 0.965128 + 1.31710i
\(143\) 14.5805 14.5805i 1.21928 1.21928i
\(144\) −2.14513 3.37615i −0.178761 0.281346i
\(145\) −0.753158 0.753158i −0.0625464 0.0625464i
\(146\) 1.40723 9.12463i 0.116463 0.755160i
\(147\) −1.27155 + 6.39249i −0.104875 + 0.527244i
\(148\) −7.98978 9.96736i −0.656756 0.819312i
\(149\) 13.1041 + 8.75588i 1.07353 + 0.717310i 0.961058 0.276345i \(-0.0891233\pi\)
0.112472 + 0.993655i \(0.464123\pi\)
\(150\) −1.10808 + 3.04157i −0.0904744 + 0.248344i
\(151\) −10.1774 4.21560i −0.828221 0.343061i −0.0720230 0.997403i \(-0.522946\pi\)
−0.756198 + 0.654342i \(0.772946\pi\)
\(152\) −4.99327 8.66667i −0.405008 0.702960i
\(153\) −3.37463 + 1.39782i −0.272823 + 0.113007i
\(154\) 3.31346 0.143669i 0.267006 0.0115771i
\(155\) −1.65772 8.33391i −0.133151 0.669396i
\(156\) 7.85539 9.35025i 0.628935 0.748619i
\(157\) −7.70974 11.5384i −0.615304 0.920868i 0.384694 0.923044i \(-0.374307\pi\)
−0.999998 + 0.00217668i \(0.999307\pi\)
\(158\) −1.69813 + 2.79653i −0.135096 + 0.222480i
\(159\) 2.02789i 0.160822i
\(160\) 1.63119 9.17013i 0.128957 0.724963i
\(161\) 2.98592i 0.235323i
\(162\) 1.20881 + 0.734020i 0.0949728 + 0.0576701i
\(163\) 6.39288 + 9.56762i 0.500729 + 0.749394i 0.992620 0.121263i \(-0.0386943\pi\)
−0.491891 + 0.870657i \(0.663694\pi\)
\(164\) 18.0823 1.57102i 1.41199 0.122676i
\(165\) 1.08475 + 5.45341i 0.0844477 + 0.424547i
\(166\) 0.0742674 + 1.71285i 0.00576427 + 0.132943i
\(167\) −3.84468 + 1.59252i −0.297511 + 0.123233i −0.526446 0.850209i \(-0.676476\pi\)
0.228935 + 0.973442i \(0.426476\pi\)
\(168\) 1.94765 0.254622i 0.150264 0.0196445i
\(169\) 22.4351 + 9.29292i 1.72578 + 0.714840i
\(170\) −7.99151 2.91140i −0.612921 0.223294i
\(171\) 2.94034 + 1.96467i 0.224853 + 0.150242i
\(172\) 18.7415 + 2.06396i 1.42903 + 0.157375i
\(173\) −4.05408 + 20.3813i −0.308226 + 1.54956i 0.447266 + 0.894401i \(0.352398\pi\)
−0.755493 + 0.655157i \(0.772602\pi\)
\(174\) 0.904163 + 0.139443i 0.0685444 + 0.0105711i
\(175\) −1.12402 1.12402i −0.0849683 0.0849683i
\(176\) 4.88061 + 12.5954i 0.367890 + 0.949413i
\(177\) −0.501323 + 0.501323i −0.0376818 + 0.0376818i
\(178\) 6.18807 4.53442i 0.463816 0.339869i
\(179\) −13.4402 2.67342i −1.00457 0.199821i −0.334718 0.942318i \(-0.608641\pi\)
−0.669849 + 0.742497i \(0.733641\pi\)
\(180\) 0.919579 + 3.16202i 0.0685414 + 0.235683i
\(181\) −2.24643 + 3.36202i −0.166976 + 0.249897i −0.905516 0.424313i \(-0.860516\pi\)
0.738540 + 0.674210i \(0.235516\pi\)
\(182\) 2.53272 + 5.43571i 0.187738 + 0.402921i
\(183\) 4.75904 11.4893i 0.351799 0.849317i
\(184\) 11.5194 3.89869i 0.849218 0.287415i
\(185\) 4.02452 + 9.71606i 0.295889 + 0.714339i
\(186\) 5.37942 + 4.93232i 0.394438 + 0.361655i
\(187\) 12.0980 2.40644i 0.884693 0.175976i
\(188\) 12.3926 + 3.91557i 0.903821 + 0.285572i
\(189\) −0.577420 + 0.385820i −0.0420011 + 0.0280643i
\(190\) 1.95478 + 7.99898i 0.141815 + 0.580307i
\(191\) −13.0062 −0.941095 −0.470548 0.882375i \(-0.655944\pi\)
−0.470548 + 0.882375i \(0.655944\pi\)
\(192\) 3.52533 + 7.18137i 0.254419 + 0.518270i
\(193\) 10.3102 0.742143 0.371072 0.928604i \(-0.378990\pi\)
0.371072 + 0.928604i \(0.378990\pi\)
\(194\) −3.60355 14.7457i −0.258720 1.05868i
\(195\) −8.35930 + 5.58551i −0.598622 + 0.399987i
\(196\) 3.92733 12.4298i 0.280523 0.887841i
\(197\) −0.0110939 + 0.00220671i −0.000790407 + 0.000157222i −0.195486 0.980707i \(-0.562628\pi\)
0.194695 + 0.980864i \(0.437628\pi\)
\(198\) −3.52010 3.22753i −0.250162 0.229370i
\(199\) 6.00443 + 14.4960i 0.425643 + 1.02759i 0.980654 + 0.195749i \(0.0627139\pi\)
−0.555011 + 0.831843i \(0.687286\pi\)
\(200\) 2.86874 5.80400i 0.202851 0.410405i
\(201\) 2.91771 7.04398i 0.205800 0.496844i
\(202\) −0.719028 1.54317i −0.0505907 0.108577i
\(203\) −0.249586 + 0.373532i −0.0175175 + 0.0262168i
\(204\) 7.01473 2.04002i 0.491129 0.142830i
\(205\) −14.6553 2.91512i −1.02357 0.203601i
\(206\) 12.1990 8.93906i 0.849948 0.622814i
\(207\) −3.04031 + 3.04031i −0.211316 + 0.211316i
\(208\) −17.6634 + 16.8683i −1.22474 + 1.16961i
\(209\) −8.44431 8.44431i −0.584105 0.584105i
\(210\) −1.59816 0.246474i −0.110284 0.0170083i
\(211\) 3.96580 19.9374i 0.273017 1.37255i −0.564182 0.825651i \(-0.690808\pi\)
0.837199 0.546899i \(-0.184192\pi\)
\(212\) 0.443970 4.03141i 0.0304920 0.276879i
\(213\) 11.4400 + 7.64393i 0.783853 + 0.523754i
\(214\) −9.57476 3.48820i −0.654517 0.238448i
\(215\) −14.3408 5.94014i −0.978032 0.405114i
\(216\) −2.24238 1.72386i −0.152575 0.117294i
\(217\) −3.31109 + 1.37150i −0.224771 + 0.0931033i
\(218\) 0.607716 + 14.0159i 0.0411597 + 0.949276i
\(219\) −1.27362 6.40293i −0.0860634 0.432670i
\(220\) −0.962539 11.0788i −0.0648944 0.746929i
\(221\) 12.3911 + 18.5445i 0.833513 + 1.24744i
\(222\) −7.72088 4.68833i −0.518192 0.314660i
\(223\) 8.77050i 0.587316i 0.955911 + 0.293658i \(0.0948727\pi\)
−0.955911 + 0.293658i \(0.905127\pi\)
\(224\) −3.92763 + 0.0797823i −0.262426 + 0.00533068i
\(225\) 2.28900i 0.152600i
\(226\) −13.8299 + 22.7755i −0.919952 + 1.51501i
\(227\) −12.1072 18.1197i −0.803581 1.20264i −0.976032 0.217626i \(-0.930169\pi\)
0.172451 0.985018i \(-0.444831\pi\)
\(228\) −5.41520 4.54946i −0.358631 0.301295i
\(229\) −4.79701 24.1162i −0.316995 1.59364i −0.730351 0.683072i \(-0.760643\pi\)
0.413356 0.910570i \(-0.364357\pi\)
\(230\) −10.0024 + 0.433695i −0.659539 + 0.0285970i
\(231\) 2.16666 0.897458i 0.142555 0.0590484i
\(232\) −1.76693 0.475160i −0.116005 0.0311958i
\(233\) −11.1411 4.61479i −0.729877 0.302325i −0.0133757 0.999911i \(-0.504258\pi\)
−0.716502 + 0.697586i \(0.754258\pi\)
\(234\) 2.95587 8.11357i 0.193231 0.530401i
\(235\) −8.89622 5.94427i −0.580326 0.387761i
\(236\) 1.10638 0.886866i 0.0720190 0.0577300i
\(237\) −0.451334 + 2.26901i −0.0293173 + 0.147388i
\(238\) −0.546785 + 3.54542i −0.0354428 + 0.229815i
\(239\) 17.4364 + 17.4364i 1.12787 + 1.12787i 0.990523 + 0.137346i \(0.0438573\pi\)
0.137346 + 0.990523i \(0.456143\pi\)
\(240\) −1.13584 6.48737i −0.0733181 0.418758i
\(241\) −14.4104 + 14.4104i −0.928257 + 0.928257i −0.997593 0.0693361i \(-0.977912\pi\)
0.0693361 + 0.997593i \(0.477912\pi\)
\(242\) 0.337712 + 0.460872i 0.0217090 + 0.0296260i
\(243\) 0.980785 + 0.195090i 0.0629174 + 0.0125150i
\(244\) −11.9763 + 21.7987i −0.766702 + 1.39552i
\(245\) −5.96211 + 8.92293i −0.380905 + 0.570065i
\(246\) 11.6334 5.42049i 0.741721 0.345598i
\(247\) 8.26321 19.9492i 0.525776 1.26933i
\(248\) −9.61435 10.9831i −0.610512 0.697426i
\(249\) 0.463928 + 1.12002i 0.0294002 + 0.0709785i
\(250\) −11.4703 + 12.5100i −0.725444 + 0.791204i
\(251\) −13.6787 + 2.72086i −0.863390 + 0.171739i −0.606871 0.794800i \(-0.707576\pi\)
−0.256519 + 0.966539i \(0.582576\pi\)
\(252\) 1.23237 0.640587i 0.0776319 0.0403532i
\(253\) 12.0728 8.06678i 0.759010 0.507154i
\(254\) 11.0286 2.69517i 0.691998 0.169110i
\(255\) −6.01417 −0.376622
\(256\) −5.43607 15.0482i −0.339754 0.940514i
\(257\) −26.7265 −1.66715 −0.833576 0.552405i \(-0.813710\pi\)
−0.833576 + 0.552405i \(0.813710\pi\)
\(258\) 12.9512 3.16501i 0.806309 0.197045i
\(259\) 3.68809 2.46431i 0.229167 0.153124i
\(260\) 17.8410 9.27377i 1.10645 0.575135i
\(261\) 0.634468 0.126204i 0.0392726 0.00781181i
\(262\) 21.0537 22.9621i 1.30070 1.41861i
\(263\) 8.51490 + 20.5568i 0.525051 + 1.26759i 0.934731 + 0.355356i \(0.115640\pi\)
−0.409680 + 0.912229i \(0.634360\pi\)
\(264\) 6.29128 + 7.18692i 0.387202 + 0.442325i
\(265\) −1.27776 + 3.08479i −0.0784923 + 0.189497i
\(266\) 3.14809 1.46683i 0.193022 0.0899369i
\(267\) 3.01376 4.51041i 0.184439 0.276033i
\(268\) −7.34251 + 13.3645i −0.448515 + 0.816368i
\(269\) −9.60906 1.91136i −0.585875 0.116538i −0.106752 0.994286i \(-0.534045\pi\)
−0.479123 + 0.877748i \(0.659045\pi\)
\(270\) 1.37631 + 1.87824i 0.0837596 + 0.114306i
\(271\) −14.7436 + 14.7436i −0.895613 + 0.895613i −0.995044 0.0994315i \(-0.968298\pi\)
0.0994315 + 0.995044i \(0.468298\pi\)
\(272\) −14.3918 + 2.51978i −0.872629 + 0.152784i
\(273\) 2.99840 + 2.99840i 0.181471 + 0.181471i
\(274\) 2.69653 17.4846i 0.162903 1.05628i
\(275\) 1.50803 7.58138i 0.0909376 0.457174i
\(276\) 6.70969 5.37845i 0.403876 0.323745i
\(277\) 25.6474 + 17.1370i 1.54100 + 1.02966i 0.979321 + 0.202311i \(0.0648453\pi\)
0.561681 + 0.827354i \(0.310155\pi\)
\(278\) −8.42309 + 23.1206i −0.505184 + 1.38668i
\(279\) 4.76788 + 1.97492i 0.285445 + 0.118235i
\(280\) 3.12316 + 0.839874i 0.186644 + 0.0501921i
\(281\) −10.0189 + 4.14996i −0.597677 + 0.247566i −0.660949 0.750430i \(-0.729846\pi\)
0.0632727 + 0.997996i \(0.479846\pi\)
\(282\) 9.18124 0.398091i 0.546735 0.0237059i
\(283\) −4.31446 21.6903i −0.256468 1.28935i −0.867377 0.497652i \(-0.834196\pi\)
0.610909 0.791701i \(-0.290804\pi\)
\(284\) −21.0689 17.7006i −1.25021 1.05033i
\(285\) 3.23485 + 4.84130i 0.191616 + 0.286774i
\(286\) −15.1355 + 24.9255i −0.894979 + 1.47388i
\(287\) 6.30234i 0.372015i
\(288\) 4.08041 + 3.91794i 0.240440 + 0.230867i
\(289\) 3.65798i 0.215175i
\(290\) 1.28753 + 0.781824i 0.0756065 + 0.0459103i
\(291\) −5.96330 8.92470i −0.349575 0.523175i
\(292\) 1.13013 + 13.0077i 0.0661360 + 0.761220i
\(293\) −0.368420 1.85217i −0.0215233 0.108205i 0.968530 0.248896i \(-0.0800677\pi\)
−0.990054 + 0.140691i \(0.955068\pi\)
\(294\) −0.399286 9.20881i −0.0232868 0.537069i
\(295\) −1.07848 + 0.446722i −0.0627917 + 0.0260092i
\(296\) 14.3225 + 11.0107i 0.832481 + 0.639981i
\(297\) −3.11993 1.29232i −0.181036 0.0749877i
\(298\) −20.9418 7.62934i −1.21313 0.441956i
\(299\) 21.8292 + 14.5858i 1.26241 + 0.843518i
\(300\) 0.501134 4.55048i 0.0289330 0.262722i
\(301\) −1.27724 + 6.42113i −0.0736191 + 0.370108i
\(302\) 15.3968 + 2.37454i 0.885986 + 0.136640i
\(303\) −0.851233 0.851233i −0.0489021 0.0489021i
\(304\) 9.76930 + 10.2298i 0.560308 + 0.586719i
\(305\) 14.4787 14.4787i 0.829049 0.829049i
\(306\) 4.16674 3.05325i 0.238197 0.174543i
\(307\) −2.30606 0.458704i −0.131614 0.0261796i 0.128844 0.991665i \(-0.458873\pi\)
−0.260458 + 0.965485i \(0.583873\pi\)
\(308\) −4.50375 + 1.30978i −0.256625 + 0.0746316i
\(309\) 5.94127 8.89174i 0.337987 0.505834i
\(310\) 5.07525 + 10.8925i 0.288255 + 0.618651i
\(311\) −4.33635 + 10.4689i −0.245892 + 0.593636i −0.997847 0.0655782i \(-0.979111\pi\)
0.751955 + 0.659214i \(0.229111\pi\)
\(312\) −7.65252 + 15.4825i −0.433239 + 0.876523i
\(313\) −9.46949 22.8614i −0.535247 1.29220i −0.928008 0.372560i \(-0.878480\pi\)
0.392761 0.919641i \(-0.371520\pi\)
\(314\) 14.4653 + 13.2630i 0.816323 + 0.748474i
\(315\) −1.12146 + 0.223073i −0.0631872 + 0.0125687i
\(316\) 1.39400 4.41194i 0.0784187 0.248191i
\(317\) 20.8034 13.9004i 1.16844 0.780724i 0.188900 0.981996i \(-0.439508\pi\)
0.979535 + 0.201273i \(0.0645077\pi\)
\(318\) −0.680814 2.78589i −0.0381782 0.156225i
\(319\) −2.18456 −0.122312
\(320\) 0.837736 + 13.1454i 0.0468309 + 0.734852i
\(321\) −7.20568 −0.402182
\(322\) 1.00245 + 4.10201i 0.0558642 + 0.228596i
\(323\) 10.7401 7.17630i 0.597594 0.399300i
\(324\) −1.90707 0.602561i −0.105948 0.0334756i
\(325\) 13.7081 2.72671i 0.760390 0.151251i
\(326\) −11.9945 10.9976i −0.664316 0.609102i
\(327\) 3.79623 + 9.16492i 0.209932 + 0.506821i
\(328\) −24.3138 + 8.22891i −1.34250 + 0.454366i
\(329\) −1.72695 + 4.16922i −0.0952098 + 0.229857i
\(330\) −3.32106 7.12764i −0.182818 0.392363i
\(331\) −4.46721 + 6.68565i −0.245540 + 0.367476i −0.933684 0.358097i \(-0.883426\pi\)
0.688144 + 0.725574i \(0.258426\pi\)
\(332\) −0.677072 2.32815i −0.0371592 0.127774i
\(333\) −6.26446 1.24608i −0.343290 0.0682847i
\(334\) 4.74713 3.47854i 0.259751 0.190337i
\(335\) 8.87673 8.87673i 0.484987 0.484987i
\(336\) −2.59017 + 1.00367i −0.141305 + 0.0547547i
\(337\) −9.41522 9.41522i −0.512880 0.512880i 0.402528 0.915408i \(-0.368132\pi\)
−0.915408 + 0.402528i \(0.868132\pi\)
\(338\) −33.9409 5.23447i −1.84614 0.284718i
\(339\) −3.67576 + 18.4793i −0.199640 + 1.00366i
\(340\) 11.9561 + 1.31669i 0.648408 + 0.0714077i
\(341\) −14.4906 9.68228i −0.784708 0.524325i
\(342\) −4.69898 1.71189i −0.254092 0.0925685i
\(343\) 8.67291 + 3.59244i 0.468293 + 0.193973i
\(344\) −26.4397 + 3.45655i −1.42554 + 0.186365i
\(345\) −6.54053 + 2.70917i −0.352130 + 0.145857i
\(346\) −1.27305 29.3605i −0.0684394 1.57843i
\(347\) 2.70029 + 13.5753i 0.144959 + 0.728758i 0.983066 + 0.183252i \(0.0586624\pi\)
−0.838107 + 0.545506i \(0.816338\pi\)
\(348\) −1.28894 + 0.111985i −0.0690945 + 0.00600304i
\(349\) −9.07880 13.5874i −0.485977 0.727316i 0.504738 0.863273i \(-0.331589\pi\)
−0.990715 + 0.135957i \(0.956589\pi\)
\(350\) 1.92153 + 1.16681i 0.102710 + 0.0623684i
\(351\) 6.10603i 0.325916i
\(352\) −10.9335 15.6648i −0.582758 0.834938i
\(353\) 9.17429i 0.488298i −0.969738 0.244149i \(-0.921491\pi\)
0.969738 0.244149i \(-0.0785086\pi\)
\(354\) 0.520404 0.857018i 0.0276592 0.0455500i
\(355\) 12.5858 + 18.8360i 0.667986 + 0.999712i
\(356\) −6.97877 + 8.30681i −0.369874 + 0.440260i
\(357\) 0.494871 + 2.48789i 0.0261914 + 0.131673i
\(358\) 19.3615 0.839497i 1.02329 0.0443688i
\(359\) −12.3127 + 5.10007i −0.649837 + 0.269171i −0.683155 0.730273i \(-0.739393\pi\)
0.0333176 + 0.999445i \(0.489393\pi\)
\(360\) −2.32487 4.03522i −0.122532 0.212675i
\(361\) 6.00014 + 2.48534i 0.315797 + 0.130807i
\(362\) 1.95740 5.37289i 0.102879 0.282393i
\(363\) 0.335924 + 0.224458i 0.0176315 + 0.0117810i
\(364\) −5.30432 6.61720i −0.278022 0.346836i
\(365\) 2.09703 10.5425i 0.109764 0.551820i
\(366\) −2.68065 + 17.3816i −0.140120 + 0.908553i
\(367\) 10.4810 + 10.4810i 0.547104 + 0.547104i 0.925602 0.378498i \(-0.123559\pi\)
−0.378498 + 0.925602i \(0.623559\pi\)
\(368\) −14.5163 + 9.22330i −0.756712 + 0.480798i
\(369\) 6.41714 6.41714i 0.334063 0.334063i
\(370\) −8.79076 11.9967i −0.457010 0.623677i
\(371\) 1.38123 + 0.274743i 0.0717097 + 0.0142639i
\(372\) −9.04608 4.96994i −0.469017 0.257680i
\(373\) 0.531377 0.795262i 0.0275137 0.0411771i −0.817458 0.575988i \(-0.804617\pi\)
0.844972 + 0.534811i \(0.179617\pi\)
\(374\) −15.8122 + 7.36754i −0.817628 + 0.380966i
\(375\) −4.59275 + 11.0879i −0.237168 + 0.572575i
\(376\) −18.3393 1.21867i −0.945777 0.0628480i
\(377\) −1.51159 3.64931i −0.0778509 0.187949i
\(378\) 0.663723 0.723888i 0.0341382 0.0372328i
\(379\) 27.1526 5.40100i 1.39474 0.277431i 0.560189 0.828365i \(-0.310728\pi\)
0.834549 + 0.550934i \(0.185728\pi\)
\(380\) −5.37091 10.3326i −0.275522 0.530052i
\(381\) 6.67497 4.46007i 0.341969 0.228496i
\(382\) 17.8677 4.36650i 0.914193 0.223410i
\(383\) 11.9365 0.609928 0.304964 0.952364i \(-0.401356\pi\)
0.304964 + 0.952364i \(0.401356\pi\)
\(384\) −7.25402 8.68212i −0.370180 0.443058i
\(385\) 3.86135 0.196793
\(386\) −14.1640 + 3.46138i −0.720928 + 0.176180i
\(387\) 7.83860 5.23759i 0.398458 0.266241i
\(388\) 9.90102 + 19.0477i 0.502648 + 0.967000i
\(389\) −11.9468 + 2.37636i −0.605724 + 0.120486i −0.488418 0.872610i \(-0.662426\pi\)
−0.117306 + 0.993096i \(0.537426\pi\)
\(390\) 9.60870 10.4797i 0.486556 0.530661i
\(391\) 6.01012 + 14.5097i 0.303945 + 0.733787i
\(392\) −1.22233 + 18.3944i −0.0617368 + 0.929055i
\(393\) 8.42997 20.3517i 0.425236 1.02661i
\(394\) 0.0144998 0.00675605i 0.000730489 0.000340365i
\(395\) −2.11625 + 3.16719i −0.106480 + 0.159358i
\(396\) 5.91942 + 3.25215i 0.297462 + 0.163427i
\(397\) 24.0728 + 4.78837i 1.20818 + 0.240321i 0.757782 0.652508i \(-0.226283\pi\)
0.450396 + 0.892829i \(0.351283\pi\)
\(398\) −13.1155 17.8985i −0.657419 0.897172i
\(399\) 1.73653 1.73653i 0.0869350 0.0869350i
\(400\) −1.99249 + 8.93656i −0.0996245 + 0.446828i
\(401\) −3.83842 3.83842i −0.191681 0.191681i 0.604741 0.796422i \(-0.293277\pi\)
−0.796422 + 0.604741i \(0.793277\pi\)
\(402\) −1.64348 + 10.6565i −0.0819691 + 0.531497i
\(403\) 6.14758 30.9060i 0.306233 1.53954i
\(404\) 1.50587 + 1.87860i 0.0749200 + 0.0934637i
\(405\) 1.36902 + 0.914753i 0.0680274 + 0.0454545i
\(406\) 0.217474 0.596946i 0.0107931 0.0296259i
\(407\) 19.9276 + 8.25427i 0.987773 + 0.409149i
\(408\) −8.95185 + 5.15757i −0.443183 + 0.255338i
\(409\) 10.1062 4.18612i 0.499719 0.206990i −0.118563 0.992947i \(-0.537829\pi\)
0.618282 + 0.785956i \(0.287829\pi\)
\(410\) 21.1120 0.915396i 1.04265 0.0452082i
\(411\) −2.44051 12.2693i −0.120382 0.605199i
\(412\) −13.7578 + 16.3759i −0.677799 + 0.806782i
\(413\) 0.273538 + 0.409378i 0.0134599 + 0.0201442i
\(414\) 3.15602 5.19744i 0.155110 0.255440i
\(415\) 1.99607i 0.0979833i
\(416\) 18.6027 29.1035i 0.912071 1.42692i
\(417\) 17.3999i 0.852074i
\(418\) 14.4356 + 8.76572i 0.706071 + 0.428745i
\(419\) 14.7736 + 22.1103i 0.721738 + 1.08016i 0.993053 + 0.117667i \(0.0375414\pi\)
−0.271315 + 0.962491i \(0.587459\pi\)
\(420\) 2.27828 0.197941i 0.111169 0.00965852i
\(421\) −1.49960 7.53902i −0.0730863 0.367429i 0.926882 0.375352i \(-0.122478\pi\)
−0.999969 + 0.00792250i \(0.997478\pi\)
\(422\) 1.24533 + 28.7212i 0.0606215 + 1.39813i
\(423\) 6.00357 2.48676i 0.291904 0.120910i
\(424\) 0.743525 + 5.68735i 0.0361088 + 0.276202i
\(425\) 7.72452 + 3.19960i 0.374694 + 0.155203i
\(426\) −18.2823 6.66045i −0.885781 0.322700i
\(427\) −7.18079 4.79805i −0.347503 0.232194i
\(428\) 14.3248 + 1.57755i 0.692413 + 0.0762538i
\(429\) −4.02275 + 20.2237i −0.194220 + 0.976412i
\(430\) 21.6954 + 3.34593i 1.04625 + 0.161355i
\(431\) 1.90376 + 1.90376i 0.0917011 + 0.0917011i 0.751469 0.659768i \(-0.229346\pi\)
−0.659768 + 0.751469i \(0.729346\pi\)
\(432\) 3.65930 + 1.61540i 0.176058 + 0.0777209i
\(433\) 6.31254 6.31254i 0.303361 0.303361i −0.538966 0.842327i \(-0.681185\pi\)
0.842327 + 0.538966i \(0.181185\pi\)
\(434\) 4.08828 2.99576i 0.196244 0.143801i
\(435\) 1.04466 + 0.207796i 0.0500876 + 0.00996305i
\(436\) −5.54035 19.0508i −0.265335 0.912368i
\(437\) 8.44737 12.6424i 0.404093 0.604768i
\(438\) 3.89931 + 8.36867i 0.186316 + 0.399871i
\(439\) 5.40640 13.0522i 0.258033 0.622947i −0.740775 0.671753i \(-0.765542\pi\)
0.998808 + 0.0488058i \(0.0155415\pi\)
\(440\) 5.04173 + 14.8967i 0.240355 + 0.710172i
\(441\) −2.49423 6.02160i −0.118773 0.286743i
\(442\) −23.2485 21.3162i −1.10582 1.01391i
\(443\) −10.7828 + 2.14483i −0.512305 + 0.101904i −0.444472 0.895793i \(-0.646609\pi\)
−0.0678331 + 0.997697i \(0.521609\pi\)
\(444\) 12.1808 + 3.84867i 0.578077 + 0.182650i
\(445\) 7.42645 4.96220i 0.352048 0.235231i
\(446\) −2.94447 12.0488i −0.139425 0.570527i
\(447\) −15.7602 −0.745431
\(448\) 5.36894 1.42821i 0.253659 0.0674765i
\(449\) −22.3558 −1.05503 −0.527517 0.849545i \(-0.676877\pi\)
−0.527517 + 0.849545i \(0.676877\pi\)
\(450\) −0.768473 3.14459i −0.0362262 0.148238i
\(451\) −25.4819 + 17.0265i −1.19990 + 0.801744i
\(452\) 11.3530 35.9318i 0.534002 1.69009i
\(453\) 10.8042 2.14909i 0.507627 0.100973i
\(454\) 22.7159 + 20.8279i 1.06611 + 0.977500i
\(455\) 2.67183 + 6.45037i 0.125257 + 0.302398i
\(456\) 8.96670 + 4.43197i 0.419904 + 0.207546i
\(457\) −4.15982 + 10.0427i −0.194588 + 0.469778i −0.990816 0.135220i \(-0.956826\pi\)
0.796227 + 0.604998i \(0.206826\pi\)
\(458\) 14.6865 + 31.5200i 0.686253 + 1.47283i
\(459\) 2.02932 3.03709i 0.0947204 0.141759i
\(460\) 13.5956 3.95386i 0.633896 0.184350i
\(461\) 4.06246 + 0.808074i 0.189208 + 0.0376358i 0.288785 0.957394i \(-0.406749\pi\)
−0.0995768 + 0.995030i \(0.531749\pi\)
\(462\) −2.67522 + 1.96032i −0.124463 + 0.0912021i
\(463\) −10.3561 + 10.3561i −0.481289 + 0.481289i −0.905543 0.424254i \(-0.860536\pi\)
0.424254 + 0.905543i \(0.360536\pi\)
\(464\) 2.58691 + 0.0595655i 0.120094 + 0.00276526i
\(465\) 6.00841 + 6.00841i 0.278633 + 0.278633i
\(466\) 16.8548 + 2.59940i 0.780783 + 0.120415i
\(467\) 6.96096 34.9951i 0.322115 1.61938i −0.392424 0.919784i \(-0.628363\pi\)
0.714539 0.699596i \(-0.246637\pi\)
\(468\) −1.33680 + 12.1387i −0.0617937 + 0.561110i
\(469\) −4.40245 2.94163i −0.203286 0.135832i
\(470\) 14.2171 + 5.17947i 0.655788 + 0.238911i
\(471\) 12.8208 + 5.31056i 0.590752 + 0.244698i
\(472\) −1.22218 + 1.58980i −0.0562555 + 0.0731766i
\(473\) −29.4128 + 12.1832i −1.35240 + 0.560183i
\(474\) −0.141726 3.26866i −0.00650969 0.150134i
\(475\) −1.57918 7.93907i −0.0724577 0.364270i
\(476\) −0.439118 5.05421i −0.0201269 0.231659i
\(477\) −1.12664 1.68613i −0.0515852 0.0772027i
\(478\) −29.8078 18.1001i −1.36338 0.827879i
\(479\) 1.12822i 0.0515496i 0.999668 + 0.0257748i \(0.00820528\pi\)
−0.999668 + 0.0257748i \(0.991795\pi\)
\(480\) 3.73837 + 8.53093i 0.170632 + 0.389382i
\(481\) 39.0004i 1.77826i
\(482\) 14.9589 24.6348i 0.681360 1.12208i
\(483\) 1.65889 + 2.48270i 0.0754820 + 0.112967i
\(484\) −0.618671 0.519762i −0.0281214 0.0236255i
\(485\) −3.44785 17.3335i −0.156559 0.787074i
\(486\) −1.41289 + 0.0612615i −0.0640898 + 0.00277888i
\(487\) −19.5691 + 8.10579i −0.886761 + 0.367308i −0.779115 0.626881i \(-0.784331\pi\)
−0.107646 + 0.994189i \(0.534331\pi\)
\(488\) 9.13447 33.9675i 0.413498 1.53764i
\(489\) −10.6310 4.40349i −0.480749 0.199133i
\(490\) 5.19502 14.2598i 0.234687 0.644194i
\(491\) 21.8135 + 14.5753i 0.984430 + 0.657775i 0.939978 0.341236i \(-0.110846\pi\)
0.0444527 + 0.999011i \(0.485846\pi\)
\(492\) −14.1621 + 11.3522i −0.638475 + 0.511798i
\(493\) 0.460981 2.31751i 0.0207615 0.104375i
\(494\) −4.65446 + 30.1800i −0.209414 + 1.35786i
\(495\) −3.93169 3.93169i −0.176716 0.176716i
\(496\) 16.8954 + 11.8606i 0.758624 + 0.532558i
\(497\) 6.75629 6.75629i 0.303061 0.303061i
\(498\) −1.01336 1.38292i −0.0454096 0.0619700i
\(499\) 13.4099 + 2.66739i 0.600308 + 0.119409i 0.485884 0.874023i \(-0.338498\pi\)
0.114424 + 0.993432i \(0.463498\pi\)
\(500\) 11.5578 21.0370i 0.516880 0.940802i
\(501\) 2.31198 3.46012i 0.103292 0.154587i
\(502\) 17.8781 8.33015i 0.797939 0.371793i
\(503\) 0.633735 1.52997i 0.0282569 0.0682181i −0.909121 0.416532i \(-0.863246\pi\)
0.937378 + 0.348313i \(0.113246\pi\)
\(504\) −1.47795 + 1.29377i −0.0658331 + 0.0576289i
\(505\) −0.758522 1.83123i −0.0337538 0.0814888i
\(506\) −13.8772 + 15.1352i −0.616917 + 0.672840i
\(507\) −23.8170 + 4.73749i −1.05775 + 0.210399i
\(508\) −14.2462 + 7.40517i −0.632071 + 0.328551i
\(509\) 3.47429 2.32145i 0.153995 0.102896i −0.476185 0.879345i \(-0.657981\pi\)
0.630181 + 0.776449i \(0.282981\pi\)
\(510\) 8.26219 2.01911i 0.365856 0.0894075i
\(511\) −4.53367 −0.200558
\(512\) 12.5201 + 18.8480i 0.553314 + 0.832973i
\(513\) −3.53631 −0.156132
\(514\) 36.7165 8.97274i 1.61949 0.395771i
\(515\) 14.6404 9.78238i 0.645131 0.431063i
\(516\) −16.7297 + 8.69610i −0.736482 + 0.382825i
\(517\) −21.5227 + 4.28114i −0.946568 + 0.188284i
\(518\) −4.23932 + 4.62361i −0.186265 + 0.203150i
\(519\) −7.95237 19.1987i −0.349070 0.842730i
\(520\) −21.3963 + 18.7298i −0.938288 + 0.821358i
\(521\) 6.07194 14.6590i 0.266016 0.642220i −0.733272 0.679935i \(-0.762008\pi\)
0.999289 + 0.0377149i \(0.0120079\pi\)
\(522\) −0.829254 + 0.386384i −0.0362955 + 0.0169115i
\(523\) −25.1519 + 37.6425i −1.09982 + 1.64599i −0.431511 + 0.902108i \(0.642019\pi\)
−0.668307 + 0.743886i \(0.732981\pi\)
\(524\) −21.2143 + 38.6133i −0.926749 + 1.68683i
\(525\) 1.55907 + 0.310118i 0.0680433 + 0.0135346i
\(526\) −18.5991 25.3820i −0.810958 1.10671i
\(527\) 13.3292 13.3292i 0.580631 0.580631i
\(528\) −11.0557 7.76116i −0.481138 0.337761i
\(529\) −3.19123 3.19123i −0.138749 0.138749i
\(530\) 0.719731 4.66682i 0.0312631 0.202714i
\(531\) 0.138315 0.695355i 0.00600235 0.0301759i
\(532\) −3.83236 + 3.07200i −0.166154 + 0.133188i
\(533\) −46.0746 30.7861i −1.99571 1.33349i
\(534\) −2.62601 + 7.20814i −0.113638 + 0.311927i
\(535\) −10.9611 4.54025i −0.473891 0.196292i
\(536\) 5.60024 20.8251i 0.241893 0.899506i
\(537\) 12.6604 5.24410i 0.546336 0.226300i
\(538\) 13.8425 0.600198i 0.596792 0.0258764i
\(539\) 4.29399 + 21.5873i 0.184955 + 0.929832i
\(540\) −2.52133 2.11824i −0.108501 0.0911543i
\(541\) 10.4489 + 15.6378i 0.449232 + 0.672323i 0.985101 0.171978i \(-0.0550159\pi\)
−0.535869 + 0.844301i \(0.680016\pi\)
\(542\) 15.3048 25.2044i 0.657398 1.08262i
\(543\) 4.04347i 0.173522i
\(544\) 18.9253 8.29331i 0.811414 0.355573i
\(545\) 16.3335i 0.699649i
\(546\) −5.12580 3.11252i −0.219364 0.133204i
\(547\) 3.28506 + 4.91643i 0.140459 + 0.210211i 0.895029 0.446008i \(-0.147155\pi\)
−0.754570 + 0.656219i \(0.772155\pi\)
\(548\) 2.16556 + 24.9254i 0.0925081 + 1.06476i
\(549\) 2.42614 + 12.1970i 0.103545 + 0.520556i
\(550\) 0.473545 + 10.9215i 0.0201920 + 0.465693i
\(551\) −2.11350 + 0.875440i −0.0900381 + 0.0372950i
\(552\) −7.41200 + 9.64145i −0.315476 + 0.410367i
\(553\) 1.48431 + 0.614819i 0.0631191 + 0.0261448i
\(554\) −40.9874 14.9322i −1.74139 0.634407i
\(555\) −8.74422 5.84270i −0.371172 0.248009i
\(556\) 3.80938 34.5906i 0.161554 1.46697i
\(557\) −3.59757 + 18.0862i −0.152434 + 0.766337i 0.826624 + 0.562755i \(0.190258\pi\)
−0.979058 + 0.203582i \(0.934742\pi\)
\(558\) −7.21308 1.11242i −0.305354 0.0470926i
\(559\) −40.7039 40.7039i −1.72159 1.72159i
\(560\) −4.57252 0.105286i −0.193224 0.00444913i
\(561\) −8.72217 + 8.72217i −0.368250 + 0.368250i
\(562\) 12.3706 9.06475i 0.521821 0.382373i
\(563\) 21.3597 + 4.24871i 0.900204 + 0.179062i 0.623435 0.781875i \(-0.285737\pi\)
0.276768 + 0.960937i \(0.410737\pi\)
\(564\) −12.4794 + 3.62926i −0.525478 + 0.152819i
\(565\) −17.2352 + 25.7942i −0.725089 + 1.08517i
\(566\) 13.2091 + 28.3493i 0.555220 + 1.19161i
\(567\) 0.265757 0.641595i 0.0111608 0.0269445i
\(568\) 34.8867 + 17.2434i 1.46381 + 0.723518i
\(569\) −6.15954 14.8705i −0.258221 0.623402i 0.740600 0.671947i \(-0.234542\pi\)
−0.998821 + 0.0485449i \(0.984542\pi\)
\(570\) −6.06934 5.56489i −0.254217 0.233088i
\(571\) −41.2134 + 8.19785i −1.72473 + 0.343069i −0.955294 0.295659i \(-0.904461\pi\)
−0.769432 + 0.638728i \(0.779461\pi\)
\(572\) 12.4248 39.3237i 0.519506 1.64421i
\(573\) 10.8143 7.22586i 0.451772 0.301864i
\(574\) −2.11585 8.65807i −0.0883140 0.361381i
\(575\) 9.84187 0.410434
\(576\) −6.92096 4.01252i −0.288373 0.167188i
\(577\) −12.7068 −0.528989 −0.264495 0.964387i \(-0.585205\pi\)
−0.264495 + 0.964387i \(0.585205\pi\)
\(578\) 1.22807 + 5.02528i 0.0510811 + 0.209024i
\(579\) −8.57260 + 5.72803i −0.356265 + 0.238049i
\(580\) −2.03127 0.641803i −0.0843440 0.0266494i
\(581\) 0.825716 0.164245i 0.0342565 0.00681403i
\(582\) 11.1885 + 10.2586i 0.463780 + 0.425233i
\(583\) 2.62068 + 6.32688i 0.108537 + 0.262032i
\(584\) −5.91958 17.4904i −0.244954 0.723760i
\(585\) 3.84737 9.28836i 0.159069 0.384026i
\(586\) 1.12795 + 2.42080i 0.0465952 + 0.100002i
\(587\) 4.87220 7.29176i 0.201097 0.300963i −0.717190 0.696877i \(-0.754572\pi\)
0.918288 + 0.395914i \(0.129572\pi\)
\(588\) 3.64016 + 12.5169i 0.150118 + 0.516188i
\(589\) −17.8992 3.56038i −0.737525 0.146703i
\(590\) 1.33163 0.975774i 0.0548223 0.0401720i
\(591\) 0.00799825 0.00799825i 0.000329004 0.000329004i
\(592\) −23.3727 10.3179i −0.960611 0.424061i
\(593\) 16.9884 + 16.9884i 0.697632 + 0.697632i 0.963899 0.266267i \(-0.0857904\pi\)
−0.266267 + 0.963899i \(0.585790\pi\)
\(594\) 4.71997 + 0.727929i 0.193663 + 0.0298673i
\(595\) −0.814811 + 4.09633i −0.0334040 + 0.167933i
\(596\) 31.3309 + 3.45040i 1.28336 + 0.141334i
\(597\) −13.0460 8.71708i −0.533938 0.356766i
\(598\) −34.8854 12.7092i −1.42657 0.519716i
\(599\) −36.9343 15.2987i −1.50909 0.625087i −0.533723 0.845660i \(-0.679207\pi\)
−0.975371 + 0.220573i \(0.929207\pi\)
\(600\) 0.839259 + 6.41963i 0.0342626 + 0.262080i
\(601\) −4.16482 + 1.72513i −0.169887 + 0.0703694i −0.466006 0.884782i \(-0.654307\pi\)
0.296119 + 0.955151i \(0.404307\pi\)
\(602\) −0.401075 9.25007i −0.0163466 0.377005i
\(603\) 1.48744 + 7.47785i 0.0605731 + 0.304522i
\(604\) −21.9491 + 1.90697i −0.893096 + 0.0775936i
\(605\) 0.369572 + 0.553104i 0.0150252 + 0.0224869i
\(606\) 1.45519 + 0.883632i 0.0591131 + 0.0358951i
\(607\) 29.9228i 1.21453i 0.794500 + 0.607264i \(0.207733\pi\)
−0.794500 + 0.607264i \(0.792267\pi\)
\(608\) −16.8553 10.7738i −0.683574 0.436934i
\(609\) 0.449243i 0.0182043i
\(610\) −15.0298 + 24.7515i −0.608539 + 1.00216i
\(611\) −22.0441 32.9913i −0.891808 1.33469i
\(612\) −4.69916 + 5.59339i −0.189952 + 0.226099i
\(613\) 1.29796 + 6.52530i 0.0524242 + 0.263554i 0.998104 0.0615441i \(-0.0196025\pi\)
−0.945680 + 0.325099i \(0.894602\pi\)
\(614\) 3.32204 0.144040i 0.134066 0.00581300i
\(615\) 13.8050 5.71822i 0.556672 0.230581i
\(616\) 5.74747 3.31138i 0.231572 0.133419i
\(617\) −25.4364 10.5361i −1.02403 0.424167i −0.193476 0.981105i \(-0.561976\pi\)
−0.830554 + 0.556938i \(0.811976\pi\)
\(618\) −5.17686 + 14.2100i −0.208244 + 0.571609i
\(619\) −18.7776 12.5468i −0.754733 0.504297i 0.117688 0.993051i \(-0.462452\pi\)
−0.872422 + 0.488754i \(0.837452\pi\)
\(620\) −10.6292 13.2600i −0.426878 0.532536i
\(621\) 0.838819 4.21703i 0.0336606 0.169223i
\(622\) 2.44256 15.8378i 0.0979377 0.635039i
\(623\) −2.66379 2.66379i −0.106723 0.106723i
\(624\) 5.31508 23.8388i 0.212773 0.954315i
\(625\) −5.87995 + 5.87995i −0.235198 + 0.235198i
\(626\) 20.6842 + 28.2275i 0.826706 + 1.12820i
\(627\) 11.7126 + 2.32978i 0.467756 + 0.0930425i
\(628\) −24.3249 13.3642i −0.970670 0.533289i
\(629\) −12.9616 + 19.3985i −0.516814 + 0.773467i
\(630\) 1.46576 0.682957i 0.0583972 0.0272096i
\(631\) 2.27717 5.49757i 0.0906527 0.218855i −0.872050 0.489417i \(-0.837210\pi\)
0.962703 + 0.270562i \(0.0872096\pi\)
\(632\) −0.433864 + 6.52906i −0.0172582 + 0.259712i
\(633\) 7.77920 + 18.7807i 0.309196 + 0.746464i
\(634\) −23.9127 + 26.0804i −0.949696 + 1.03578i
\(635\) 12.9641 2.57872i 0.514464 0.102333i
\(636\) 1.87059 + 3.59865i 0.0741736 + 0.142696i
\(637\) −33.0904 + 22.1103i −1.31109 + 0.876041i
\(638\) 3.00113 0.733412i 0.118816 0.0290361i
\(639\) −13.7587 −0.544286
\(640\) −5.56412 17.7778i −0.219941 0.702728i
\(641\) 49.0818 1.93862 0.969308 0.245851i \(-0.0790674\pi\)
0.969308 + 0.245851i \(0.0790674\pi\)
\(642\) 9.89906 2.41912i 0.390685 0.0954752i
\(643\) 14.3353 9.57854i 0.565329 0.377741i −0.239816 0.970818i \(-0.577087\pi\)
0.805145 + 0.593078i \(0.202087\pi\)
\(644\) −2.75429 5.29874i −0.108534 0.208800i
\(645\) 15.2241 3.02826i 0.599448 0.119238i
\(646\) −12.3453 + 13.4644i −0.485720 + 0.529750i
\(647\) 10.9878 + 26.5269i 0.431975 + 1.04288i 0.978650 + 0.205534i \(0.0658933\pi\)
−0.546675 + 0.837345i \(0.684107\pi\)
\(648\) 2.82220 + 0.187539i 0.110867 + 0.00736722i
\(649\) −0.916223 + 2.21196i −0.0359649 + 0.0868270i
\(650\) −17.9166 + 8.34808i −0.702747 + 0.327439i
\(651\) 1.99111 2.97990i 0.0780376 0.116792i
\(652\) 20.1701 + 11.0815i 0.789922 + 0.433986i
\(653\) 40.3274 + 8.02161i 1.57813 + 0.313910i 0.904934 0.425553i \(-0.139920\pi\)
0.673198 + 0.739463i \(0.264920\pi\)
\(654\) −8.29211 11.3162i −0.324247 0.442497i
\(655\) 25.6470 25.6470i 1.00211 1.00211i
\(656\) 30.6393 19.4675i 1.19626 0.760078i
\(657\) 4.61625 + 4.61625i 0.180097 + 0.180097i
\(658\) 0.972748 6.30740i 0.0379216 0.245888i
\(659\) −4.65724 + 23.4135i −0.181420 + 0.912062i 0.777607 + 0.628750i \(0.216433\pi\)
−0.959028 + 0.283312i \(0.908567\pi\)
\(660\) 6.95535 + 8.67689i 0.270737 + 0.337747i
\(661\) 30.0144 + 20.0550i 1.16743 + 0.780049i 0.979363 0.202109i \(-0.0647794\pi\)
0.188062 + 0.982157i \(0.439779\pi\)
\(662\) 3.89245 10.6844i 0.151284 0.415261i
\(663\) −20.6056 8.53511i −0.800255 0.331476i
\(664\) 1.71177 + 2.97107i 0.0664296 + 0.115300i
\(665\) 3.73574 1.54739i 0.144866 0.0600053i
\(666\) 9.02437 0.391289i 0.349687 0.0151621i
\(667\) −0.542630 2.72799i −0.0210107 0.105628i
\(668\) −5.35370 + 6.37249i −0.207141 + 0.246559i
\(669\) −4.87263 7.29240i −0.188387 0.281941i
\(670\) −9.21459 + 15.1749i −0.355991 + 0.586256i
\(671\) 41.9961i 1.62124i
\(672\) 3.22138 2.24841i 0.124268 0.0867344i
\(673\) 22.0336i 0.849334i 0.905350 + 0.424667i \(0.139609\pi\)
−0.905350 + 0.424667i \(0.860391\pi\)
\(674\) 16.0954 + 9.77358i 0.619973 + 0.376464i
\(675\) −1.27170 1.90323i −0.0489477 0.0732554i
\(676\) 48.3849 4.20375i 1.86096 0.161683i
\(677\) −2.40081 12.0697i −0.0922704 0.463875i −0.999102 0.0423806i \(-0.986506\pi\)
0.906831 0.421494i \(-0.138494\pi\)
\(678\) −1.15425 26.6206i −0.0443286 1.02236i
\(679\) −6.88665 + 2.85255i −0.264286 + 0.109471i
\(680\) −16.8671 + 2.20509i −0.646824 + 0.0845614i
\(681\) 20.1335 + 8.33957i 0.771517 + 0.319573i
\(682\) 23.1575 + 8.43655i 0.886747 + 0.323052i
\(683\) −13.8421 9.24901i −0.529654 0.353904i 0.261810 0.965120i \(-0.415681\pi\)
−0.791464 + 0.611216i \(0.790681\pi\)
\(684\) 7.03012 + 0.774210i 0.268803 + 0.0296027i
\(685\) 4.01834 20.2015i 0.153533 0.771861i
\(686\) −13.1208 2.02353i −0.500954 0.0772587i
\(687\) 17.3868 + 17.3868i 0.663347 + 0.663347i
\(688\) 35.1621 13.6250i 1.34054 0.519450i
\(689\) −8.75566 + 8.75566i −0.333564 + 0.333564i
\(690\) 8.07575 5.91764i 0.307438 0.225281i
\(691\) −3.36771 0.669880i −0.128114 0.0254834i 0.130617 0.991433i \(-0.458304\pi\)
−0.258731 + 0.965949i \(0.583304\pi\)
\(692\) 11.6060 + 39.9077i 0.441192 + 1.51706i
\(693\) −1.30291 + 1.94994i −0.0494933 + 0.0740720i
\(694\) −8.26717 17.7429i −0.313817 0.673513i
\(695\) −10.9635 + 26.4683i −0.415870 + 1.00400i
\(696\) 1.73313 0.586573i 0.0656943 0.0222340i
\(697\) −12.6855 30.6255i −0.480497 1.16002i
\(698\) 17.0340 + 15.6182i 0.644745 + 0.591157i
\(699\) 11.8273 2.35260i 0.447350 0.0889835i
\(700\) −3.03150 0.957837i −0.114580 0.0362028i
\(701\) 13.9444 9.31738i 0.526674 0.351912i −0.263633 0.964623i \(-0.584921\pi\)
0.790307 + 0.612711i \(0.209921\pi\)
\(702\) 2.04994 + 8.38838i 0.0773702 + 0.316599i
\(703\) 22.5871 0.851889
\(704\) 20.2794 + 17.8495i 0.764307 + 0.672728i
\(705\) 10.6994 0.402963
\(706\) 3.08004 + 12.6035i 0.115919 + 0.474339i
\(707\) −0.695113 + 0.464460i −0.0261424 + 0.0174678i
\(708\) −0.427202 + 1.35207i −0.0160553 + 0.0508140i
\(709\) −22.9396 + 4.56297i −0.861514 + 0.171366i −0.606024 0.795446i \(-0.707237\pi\)
−0.255489 + 0.966812i \(0.582237\pi\)
\(710\) −23.6140 21.6513i −0.886216 0.812559i
\(711\) −0.885323 2.13736i −0.0332022 0.0801573i
\(712\) 6.79854 13.7547i 0.254786 0.515480i
\(713\) 8.49145 20.5002i 0.318007 0.767737i
\(714\) −1.51509 3.25168i −0.0567009 0.121691i
\(715\) −18.8622 + 28.2292i −0.705405 + 1.05571i
\(716\) −26.3167 + 7.65342i −0.983502 + 0.286022i
\(717\) −24.1850 4.81070i −0.903207 0.179659i
\(718\) 15.2027 11.1401i 0.567361 0.415744i
\(719\) −7.23308 + 7.23308i −0.269749 + 0.269749i −0.828999 0.559250i \(-0.811089\pi\)
0.559250 + 0.828999i \(0.311089\pi\)
\(720\) 4.54860 + 4.76301i 0.169516 + 0.177507i
\(721\) −5.25135 5.25135i −0.195571 0.195571i
\(722\) −9.07730 1.39993i −0.337822 0.0521000i
\(723\) 3.97583 19.9878i 0.147863 0.743356i
\(724\) −0.885244 + 8.03835i −0.0328998 + 0.298743i
\(725\) −1.23120 0.822660i −0.0457255 0.0305528i
\(726\) −0.536844 0.195579i −0.0199242 0.00725860i
\(727\) 35.0125 + 14.5026i 1.29854 + 0.537873i 0.921520 0.388332i \(-0.126949\pi\)
0.377021 + 0.926205i \(0.376949\pi\)
\(728\) 9.50855 + 7.30983i 0.352410 + 0.270920i
\(729\) −0.923880 + 0.382683i −0.0342178 + 0.0141735i
\(730\) 0.658502 + 15.1872i 0.0243723 + 0.562102i
\(731\) −6.71798 33.7736i −0.248473 1.24916i
\(732\) −2.15280 24.7786i −0.0795700 0.915844i
\(733\) 22.6813 + 33.9450i 0.837754 + 1.25379i 0.965087 + 0.261928i \(0.0843582\pi\)
−0.127333 + 0.991860i \(0.540642\pi\)
\(734\) −17.9174 10.8799i −0.661343 0.401586i
\(735\) 10.7315i 0.395838i
\(736\) 16.8457 17.5443i 0.620942 0.646692i
\(737\) 25.7473i 0.948414i
\(738\) −6.66138 + 10.9702i −0.245209 + 0.403817i
\(739\) 7.02120 + 10.5080i 0.258279 + 0.386542i 0.937835 0.347082i \(-0.112827\pi\)
−0.679556 + 0.733624i \(0.737827\pi\)
\(740\) 16.1042 + 13.5296i 0.592002 + 0.497357i
\(741\) 4.21255 + 21.1779i 0.154752 + 0.777990i
\(742\) −1.98975 + 0.0862736i −0.0730459 + 0.00316720i
\(743\) 35.0632 14.5237i 1.28635 0.532822i 0.368452 0.929647i \(-0.379888\pi\)
0.917894 + 0.396825i \(0.129888\pi\)
\(744\) 14.0959 + 3.79065i 0.516781 + 0.138972i
\(745\) −23.9740 9.93037i −0.878341 0.363821i
\(746\) −0.463010 + 1.27092i −0.0169520 + 0.0465316i
\(747\) −1.00799 0.673519i −0.0368805 0.0246428i
\(748\) 19.2491 15.4300i 0.703816 0.564175i
\(749\) −0.976239 + 4.90789i −0.0356710 + 0.179330i
\(750\) 2.58698 16.7743i 0.0944631 0.612509i
\(751\) −22.3848 22.3848i −0.816834 0.816834i 0.168814 0.985648i \(-0.446006\pi\)
−0.985648 + 0.168814i \(0.946006\pi\)
\(752\) 25.6034 4.48277i 0.933660 0.163470i
\(753\) 9.86177 9.86177i 0.359383 0.359383i
\(754\) 3.30177 + 4.50589i 0.120243 + 0.164095i
\(755\) 17.7893 + 3.53851i 0.647418 + 0.128780i
\(756\) −0.668786 + 1.21730i −0.0243235 + 0.0442726i
\(757\) 2.18439 3.26917i 0.0793929 0.118820i −0.789648 0.613560i \(-0.789737\pi\)
0.869041 + 0.494740i \(0.164737\pi\)
\(758\) −35.4887 + 16.5356i −1.28901 + 0.600601i
\(759\) −5.55649 + 13.4146i −0.201688 + 0.486918i
\(760\) 10.8474 + 12.3917i 0.393477 + 0.449493i
\(761\) 18.2344 + 44.0218i 0.660997 + 1.59579i 0.796244 + 0.604976i \(0.206817\pi\)
−0.135247 + 0.990812i \(0.543183\pi\)
\(762\) −7.67262 + 8.36813i −0.277950 + 0.303146i
\(763\) 6.75667 1.34399i 0.244608 0.0486556i
\(764\) −23.0805 + 11.9973i −0.835023 + 0.434046i
\(765\) 5.00060 3.34129i 0.180797 0.120805i
\(766\) −16.3982 + 4.00739i −0.592492 + 0.144793i
\(767\) −4.32904 −0.156313
\(768\) 12.8803 + 9.49203i 0.464777 + 0.342514i
\(769\) 45.4847 1.64022 0.820109 0.572207i \(-0.193913\pi\)
0.820109 + 0.572207i \(0.193913\pi\)
\(770\) −5.30467 + 1.29635i −0.191167 + 0.0467173i
\(771\) 22.2223 14.8484i 0.800315 0.534753i
\(772\) 18.2962 9.51040i 0.658495 0.342287i
\(773\) −17.7723 + 3.53512i −0.639224 + 0.127150i −0.504053 0.863673i \(-0.668158\pi\)
−0.135171 + 0.990822i \(0.543158\pi\)
\(774\) −9.01018 + 9.82694i −0.323864 + 0.353222i
\(775\) −4.52059 10.9137i −0.162384 0.392030i
\(776\) −19.9967 22.8434i −0.717838 0.820032i
\(777\) −1.69744 + 4.09799i −0.0608954 + 0.147015i
\(778\) 15.6145 7.27543i 0.559806 0.260837i
\(779\) −17.8298 + 26.6841i −0.638818 + 0.956059i
\(780\) −9.68201 + 17.6228i −0.346671 + 0.630997i
\(781\) 45.5702 + 9.06447i 1.63063 + 0.324352i
\(782\) −13.1279 17.9155i −0.469452 0.640656i
\(783\) −0.457426 + 0.457426i −0.0163471 + 0.0163471i
\(784\) −4.49622 25.6803i −0.160579 0.917153i
\(785\) 16.1566 + 16.1566i 0.576655 + 0.576655i
\(786\) −4.74839 + 30.7891i −0.169370 + 1.09821i
\(787\) −2.93945 + 14.7776i −0.104780 + 0.526764i 0.892369 + 0.451306i \(0.149042\pi\)
−0.997149 + 0.0754579i \(0.975958\pi\)
\(788\) −0.0176514 + 0.0141493i −0.000628807 + 0.000504048i
\(789\) −18.5006 12.3617i −0.658639 0.440089i
\(790\) 1.84397 5.06151i 0.0656054 0.180081i
\(791\) 12.0885 + 5.00722i 0.429818 + 0.178036i
\(792\) −9.22385 2.48046i −0.327755 0.0881393i
\(793\) 70.1543 29.0589i 2.49125 1.03191i
\(794\) −34.6784 + 1.50363i −1.23069 + 0.0533617i
\(795\) −0.651397 3.27479i −0.0231027 0.116145i
\(796\) 24.0268 + 20.1856i 0.851608 + 0.715459i
\(797\) 2.57708 + 3.85688i 0.0912849 + 0.136618i 0.874301 0.485383i \(-0.161320\pi\)
−0.783016 + 0.622001i \(0.786320\pi\)
\(798\) −1.80262 + 2.96861i −0.0638121 + 0.105088i
\(799\) 23.7359i 0.839715i
\(800\) −0.262970 12.9459i −0.00929739 0.457705i
\(801\) 5.42463i 0.191670i
\(802\) 6.56182 + 3.98451i 0.231706 + 0.140698i
\(803\) −12.2482 18.3307i −0.432230 0.646878i
\(804\) −1.31986 15.1915i −0.0465478 0.535762i
\(805\) 0.959132 + 4.82188i 0.0338050 + 0.169949i
\(806\) 1.93044 + 44.5221i 0.0679968 + 1.56822i
\(807\) 9.05154 3.74927i 0.318629 0.131981i
\(808\) −2.69944 2.07523i −0.0949660 0.0730064i
\(809\) 49.6648 + 20.5718i 1.74612 + 0.723267i 0.998232 + 0.0594428i \(0.0189324\pi\)
0.747889 + 0.663824i \(0.231068\pi\)
\(810\) −2.18785 0.797060i −0.0768733 0.0280058i
\(811\) −1.65510 1.10590i −0.0581183 0.0388334i 0.526172 0.850378i \(-0.323627\pi\)
−0.584290 + 0.811545i \(0.698627\pi\)
\(812\) −0.0983536 + 0.893087i −0.00345153 + 0.0313412i
\(813\) 4.06776 20.4500i 0.142663 0.717214i
\(814\) −30.1474 4.64942i −1.05666 0.162962i
\(815\) −13.3970 13.3970i −0.469276 0.469276i
\(816\) 10.5664 10.0908i 0.369898 0.353247i
\(817\) −23.5737 + 23.5737i −0.824739 + 0.824739i
\(818\) −12.4784 + 9.14374i −0.436296 + 0.319703i
\(819\) −4.15890 0.827256i −0.145324 0.0289067i
\(820\) −28.6960 + 8.34536i −1.00211 + 0.291433i
\(821\) −7.27440 + 10.8869i −0.253878 + 0.379956i −0.936414 0.350896i \(-0.885877\pi\)
0.682536 + 0.730852i \(0.260877\pi\)
\(822\) 7.47185 + 16.0360i 0.260611 + 0.559321i
\(823\) 12.1106 29.2375i 0.422147 1.01915i −0.559566 0.828786i \(-0.689032\pi\)
0.981713 0.190368i \(-0.0609680\pi\)
\(824\) 13.4025 27.1158i 0.466899 0.944624i
\(825\) 2.95811 + 7.14150i 0.102988 + 0.248635i
\(826\) −0.513221 0.470565i −0.0178572 0.0163730i
\(827\) −4.76381 + 0.947580i −0.165654 + 0.0329506i −0.277220 0.960806i \(-0.589413\pi\)
0.111567 + 0.993757i \(0.464413\pi\)
\(828\) −2.59080 + 8.19972i −0.0900364 + 0.284960i
\(829\) −20.4524 + 13.6659i −0.710341 + 0.474635i −0.857504 0.514478i \(-0.827986\pi\)
0.147163 + 0.989112i \(0.452986\pi\)
\(830\) −0.670130 2.74218i −0.0232606 0.0951823i
\(831\) −30.8459 −1.07003
\(832\) −15.7853 + 46.2274i −0.547258 + 1.60265i
\(833\) −23.8071 −0.824868
\(834\) −5.84156 23.9037i −0.202277 0.827717i
\(835\) 5.69714 3.80670i 0.197158 0.131736i
\(836\) −22.7744 7.19582i −0.787668 0.248873i
\(837\) −5.06155 + 1.00681i −0.174953 + 0.0348003i
\(838\) −27.7187 25.4149i −0.957528 0.877944i
\(839\) −15.0870 36.4233i −0.520863 1.25747i −0.937368 0.348340i \(-0.886745\pi\)
0.416505 0.909133i \(-0.363255\pi\)
\(840\) −3.06342 + 1.03680i −0.105698 + 0.0357731i
\(841\) 10.9377 26.4059i 0.377161 0.910548i
\(842\) 4.59117 + 9.85355i 0.158222 + 0.339576i
\(843\) 6.02481 9.01676i 0.207505 0.310554i
\(844\) −11.3532 39.0387i −0.390794 1.34377i
\(845\) −39.2149 7.80034i −1.34903 0.268340i
\(846\) −7.41276 + 5.43183i −0.254856 + 0.186750i
\(847\) 0.198393 0.198393i 0.00681685 0.00681685i
\(848\) −2.93083 7.56359i −0.100645 0.259735i
\(849\) 15.6378 + 15.6378i 0.536688 + 0.536688i
\(850\) −11.6860 1.80226i −0.400827 0.0618168i
\(851\) −5.35769 + 26.9350i −0.183659 + 0.923318i
\(852\) 27.3521 + 3.01222i 0.937066 + 0.103197i
\(853\) −13.3107 8.89392i −0.455749 0.304522i 0.306424 0.951895i \(-0.400867\pi\)
−0.762173 + 0.647373i \(0.775867\pi\)
\(854\) 11.4757 + 4.18073i 0.392690 + 0.143061i
\(855\) −5.37936 2.22821i −0.183970 0.0762030i
\(856\) −20.2088 + 2.64196i −0.690722 + 0.0903002i
\(857\) 0.233105 0.0965553i 0.00796272 0.00329827i −0.378699 0.925520i \(-0.623628\pi\)
0.386661 + 0.922222i \(0.373628\pi\)
\(858\) −1.26321 29.1336i −0.0431252 0.994606i
\(859\) 6.11286 + 30.7314i 0.208568 + 1.04854i 0.933187 + 0.359392i \(0.117016\pi\)
−0.724619 + 0.689150i \(0.757984\pi\)
\(860\) −30.9282 + 2.68709i −1.05464 + 0.0916289i
\(861\) −3.50139 5.24021i −0.119327 0.178586i
\(862\) −3.25451 1.97622i −0.110849 0.0673105i
\(863\) 25.6911i 0.874534i −0.899332 0.437267i \(-0.855946\pi\)
0.899332 0.437267i \(-0.144054\pi\)
\(864\) −5.56943 0.990693i −0.189476 0.0337041i
\(865\) 34.2154i 1.16336i
\(866\) −6.55280 + 10.7914i −0.222673 + 0.366705i
\(867\) 2.03226 + 3.04150i 0.0690193 + 0.103295i
\(868\) −4.61068 + 5.48807i −0.156497 + 0.186277i
\(869\) 1.52415 + 7.66240i 0.0517031 + 0.259929i
\(870\) −1.50490 + 0.0652512i −0.0510210 + 0.00221222i
\(871\) 43.0107 17.8156i 1.45736 0.603660i
\(872\) 14.0071 + 24.3117i 0.474340 + 0.823298i
\(873\) 9.91660 + 4.10759i 0.335626 + 0.139021i
\(874\) −7.36053 + 20.2039i −0.248973 + 0.683408i
\(875\) 6.92986 + 4.63039i 0.234272 + 0.156536i
\(876\) −8.16638 10.1877i −0.275917 0.344210i
\(877\) 5.65054 28.4072i 0.190805 0.959242i −0.760111 0.649793i \(-0.774856\pi\)
0.950916 0.309449i \(-0.100144\pi\)
\(878\) −3.04529 + 19.7460i −0.102774 + 0.666395i
\(879\) 1.33534 + 1.33534i 0.0450400 + 0.0450400i
\(880\) −11.9275 18.7722i −0.402074 0.632812i
\(881\) −10.6159 + 10.6159i −0.357657 + 0.357657i −0.862949 0.505291i \(-0.831385\pi\)
0.505291 + 0.862949i \(0.331385\pi\)
\(882\) 5.44813 + 7.43501i 0.183448 + 0.250350i
\(883\) −46.6145 9.27219i −1.56870 0.312034i −0.667223 0.744858i \(-0.732517\pi\)
−0.901478 + 0.432824i \(0.857517\pi\)
\(884\) 39.0949 + 21.4789i 1.31490 + 0.722412i
\(885\) 0.648540 0.970609i 0.0218004 0.0326267i
\(886\) 14.0931 6.56657i 0.473469 0.220608i
\(887\) −0.887859 + 2.14348i −0.0298114 + 0.0719711i −0.938084 0.346407i \(-0.887401\pi\)
0.908273 + 0.418379i \(0.137401\pi\)
\(888\) −18.0260 1.19785i −0.604911 0.0401971i
\(889\) −2.13348 5.15067i −0.0715545 0.172748i
\(890\) −8.53642 + 9.31024i −0.286142 + 0.312080i
\(891\) 3.31210 0.658817i 0.110959 0.0220712i
\(892\) 8.09016 + 15.5639i 0.270878 + 0.521119i
\(893\) −19.1069 + 12.7669i −0.639390 + 0.427226i
\(894\) 21.6511 5.29108i 0.724121 0.176960i
\(895\) 22.5630 0.754197
\(896\) −6.89630 + 3.76454i −0.230389 + 0.125764i
\(897\) −26.2537 −0.876587
\(898\) 30.7120 7.50538i 1.02487 0.250458i
\(899\) −2.77583 + 1.85475i −0.0925790 + 0.0618593i
\(900\) 2.11144 + 4.06200i 0.0703812 + 0.135400i
\(901\) −7.26490 + 1.44508i −0.242029 + 0.0481426i
\(902\) 29.2905 31.9456i 0.975266 1.06367i
\(903\) −2.50540 6.04858i −0.0833746 0.201284i
\(904\) −3.53348 + 53.1740i −0.117522 + 1.76854i
\(905\) 2.54776 6.15084i 0.0846905 0.204461i
\(906\) −14.1212 + 6.57964i −0.469145 + 0.218594i
\(907\) 9.23057 13.8145i 0.306496 0.458704i −0.645964 0.763368i \(-0.723544\pi\)
0.952460 + 0.304664i \(0.0985443\pi\)
\(908\) −38.1992 20.9868i −1.26769 0.696470i
\(909\) 1.18069 + 0.234855i 0.0391611 + 0.00778964i
\(910\) −5.83607 7.96443i −0.193464 0.264018i
\(911\) −15.8780 + 15.8780i −0.526061 + 0.526061i −0.919395 0.393335i \(-0.871321\pi\)
0.393335 + 0.919395i \(0.371321\pi\)
\(912\) −13.8062 3.07823i −0.457171 0.101930i
\(913\) 2.89484 + 2.89484i 0.0958053 + 0.0958053i
\(914\) 2.34312 15.1931i 0.0775037 0.502542i
\(915\) −3.99467 + 20.0826i −0.132060 + 0.663909i
\(916\) −30.7581 38.3711i −1.01628 1.26782i
\(917\) −12.7197 8.49906i −0.420043 0.280664i
\(918\) −1.76822 + 4.85360i −0.0583600 + 0.160193i
\(919\) 25.4657 + 10.5482i 0.840036 + 0.347954i 0.760868 0.648907i \(-0.224774\pi\)
0.0791681 + 0.996861i \(0.474774\pi\)
\(920\) −17.3500 + 9.99613i −0.572012 + 0.329563i
\(921\) 2.17226 0.899781i 0.0715785 0.0296488i
\(922\) −5.85225 + 0.253748i −0.192733 + 0.00835675i
\(923\) 16.3897 + 82.3968i 0.539475 + 2.71212i
\(924\) 3.01706 3.59119i 0.0992539 0.118142i
\(925\) 8.12258 + 12.1563i 0.267069 + 0.399697i
\(926\) 10.7503 17.7039i 0.353276 0.581786i
\(927\) 10.6940i 0.351237i
\(928\) −3.57386 + 0.786659i −0.117318 + 0.0258233i
\(929\) 0.420540i 0.0137975i −0.999976 0.00689874i \(-0.997804\pi\)
0.999976 0.00689874i \(-0.00219595\pi\)
\(930\) −10.2714 6.23710i −0.336814 0.204523i
\(931\) 12.8052 + 19.1643i 0.419673 + 0.628085i
\(932\) −24.0275 + 2.08755i −0.787049 + 0.0683800i
\(933\) −2.21065 11.1137i −0.0723735 0.363846i
\(934\) 2.18585 + 50.4128i 0.0715233 + 1.64956i
\(935\) −18.7638 + 7.77221i −0.613641 + 0.254178i
\(936\) −2.23877 17.1247i −0.0731765 0.559739i
\(937\) 8.79787 + 3.64420i 0.287414 + 0.119051i 0.521733 0.853109i \(-0.325286\pi\)
−0.234319 + 0.972160i \(0.575286\pi\)
\(938\) 7.03561 + 2.56315i 0.229721 + 0.0836899i
\(939\) 20.5747 + 13.7476i 0.671429 + 0.448635i
\(940\) −21.2702 2.34244i −0.693757 0.0764019i
\(941\) −1.79951 + 9.04673i −0.0586623 + 0.294915i −0.998968 0.0454152i \(-0.985539\pi\)
0.940306 + 0.340330i \(0.110539\pi\)
\(942\) −19.3960 2.99131i −0.631955 0.0974620i
\(943\) −27.5914 27.5914i −0.898499 0.898499i
\(944\) 1.14528 2.59437i 0.0372757 0.0844394i
\(945\) 0.808529 0.808529i 0.0263014 0.0263014i
\(946\) 36.3167 26.6117i 1.18076 0.865221i
\(947\) −5.83461 1.16058i −0.189599 0.0377136i 0.0993772 0.995050i \(-0.468315\pi\)
−0.288977 + 0.957336i \(0.593315\pi\)
\(948\) 1.29207 + 4.44286i 0.0419645 + 0.144297i
\(949\) 22.1464 33.1444i 0.718901 1.07591i
\(950\) 4.83480 + 10.3764i 0.156862 + 0.336655i
\(951\) −9.57476 + 23.1155i −0.310483 + 0.749572i
\(952\) 2.30008 + 6.79598i 0.0745460 + 0.220259i
\(953\) −1.40708 3.39700i −0.0455799 0.110040i 0.899450 0.437024i \(-0.143968\pi\)
−0.945030 + 0.326984i \(0.893968\pi\)
\(954\) 2.11383 + 1.93814i 0.0684379 + 0.0627497i
\(955\) 21.0034 4.17783i 0.679653 0.135191i
\(956\) 47.0262 + 14.8585i 1.52094 + 0.480557i
\(957\) 1.81640 1.21368i 0.0587158 0.0392327i
\(958\) −0.378771 1.54993i −0.0122375 0.0500760i
\(959\) −8.68742 −0.280532
\(960\) −7.99976 10.4646i −0.258191 0.337744i
\(961\) 4.36703 0.140872
\(962\) −13.0934 53.5782i −0.422148 1.72743i
\(963\) 5.99130 4.00326i 0.193067 0.129003i
\(964\) −12.2798 + 38.8650i −0.395507 + 1.25176i
\(965\) −16.6497 + 3.31182i −0.535971 + 0.106611i
\(966\) −3.11246 2.85377i −0.100142 0.0918185i
\(967\) 14.2117 + 34.3101i 0.457017 + 1.10334i 0.969599 + 0.244699i \(0.0786892\pi\)
−0.512582 + 0.858639i \(0.671311\pi\)
\(968\) 1.02442 + 0.506339i 0.0329260 + 0.0162743i
\(969\) −4.94312 + 11.9337i −0.158796 + 0.383367i
\(970\) 10.5559 + 22.6550i 0.338929 + 0.727408i
\(971\) 14.2494 21.3258i 0.457286 0.684377i −0.529149 0.848529i \(-0.677489\pi\)
0.986435 + 0.164152i \(0.0524888\pi\)
\(972\) 1.92044 0.558501i 0.0615980 0.0179139i
\(973\) 11.8513 + 2.35737i 0.379934 + 0.0755737i
\(974\) 24.1625 17.7055i 0.774215 0.567319i
\(975\) −9.88301 + 9.88301i −0.316509 + 0.316509i
\(976\) −1.14509 + 49.7307i −0.0366534 + 1.59184i
\(977\) 6.15021 + 6.15021i 0.196763 + 0.196763i 0.798611 0.601848i \(-0.205569\pi\)
−0.601848 + 0.798611i \(0.705569\pi\)
\(978\) 16.0830 + 2.48038i 0.514279 + 0.0793137i
\(979\) 3.57383 17.9669i 0.114220 0.574224i
\(980\) −2.34947 + 21.3341i −0.0750510 + 0.681492i
\(981\) −8.24821 5.51128i −0.263345 0.175962i
\(982\) −34.8604 12.7000i −1.11244 0.405275i
\(983\) 23.4412 + 9.70966i 0.747658 + 0.309690i 0.723786 0.690025i \(-0.242400\pi\)
0.0238726 + 0.999715i \(0.492400\pi\)
\(984\) 15.6444 20.3501i 0.498726 0.648737i
\(985\) 0.0172064 0.00712713i 0.000548242 0.000227089i
\(986\) 0.144755 + 3.33852i 0.00460995 + 0.106320i
\(987\) −0.880391 4.42603i −0.0280232 0.140882i
\(988\) −3.73795 43.0236i −0.118920 1.36876i
\(989\) −22.5197 33.7032i −0.716086 1.07170i
\(990\) 6.72126 + 4.08133i 0.213616 + 0.129713i
\(991\) 37.6680i 1.19656i −0.801286 0.598281i \(-0.795850\pi\)
0.801286 0.598281i \(-0.204150\pi\)
\(992\) −27.1925 10.6218i −0.863363 0.337242i
\(993\) 8.04076i 0.255166i
\(994\) −7.01345 + 11.5500i −0.222453 + 0.366342i
\(995\) −14.3528 21.4804i −0.455014 0.680976i
\(996\) 1.85642 + 1.55962i 0.0588228 + 0.0494186i
\(997\) −6.03215 30.3256i −0.191040 0.960423i −0.950702 0.310105i \(-0.899636\pi\)
0.759662 0.650318i \(-0.225364\pi\)
\(998\) −19.3178 + 0.837602i −0.611494 + 0.0265138i
\(999\) 5.90100 2.44427i 0.186699 0.0773334i
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 192.2.r.a.13.2 128
3.2 odd 2 576.2.bd.b.397.15 128
4.3 odd 2 768.2.r.a.145.11 128
64.5 even 16 inner 192.2.r.a.133.2 yes 128
64.59 odd 16 768.2.r.a.625.11 128
192.5 odd 16 576.2.bd.b.325.15 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
192.2.r.a.13.2 128 1.1 even 1 trivial
192.2.r.a.133.2 yes 128 64.5 even 16 inner
576.2.bd.b.325.15 128 192.5 odd 16
576.2.bd.b.397.15 128 3.2 odd 2
768.2.r.a.145.11 128 4.3 odd 2
768.2.r.a.625.11 128 64.59 odd 16