Properties

Label 475.2.bc.a.386.32
Level $475$
Weight $2$
Character 475.386
Analytic conductor $3.793$
Analytic rank $0$
Dimension $1152$
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] = [475,2,Mod(6,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(90))
 
chi = DirichletCharacter(H, H._module([36, 70]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.6");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.bc (of order \(45\), degree \(24\), 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: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(1152\)
Relative dimension: \(48\) over \(\Q(\zeta_{45})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label 386.32
Character \(\chi\) \(=\) 475.386
Dual form 475.2.bc.a.16.32

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.235316 - 0.943803i) q^{2} +(-0.767384 + 0.982207i) q^{3} +(0.930506 + 0.494759i) q^{4} +(1.56582 + 1.59631i) q^{5} +(0.746431 + 0.955388i) q^{6} +(1.73336 - 3.00227i) q^{7} +(1.98764 - 2.20750i) q^{8} +(0.349914 + 1.40343i) q^{9} +O(q^{10})\) \(q+(0.235316 - 0.943803i) q^{2} +(-0.767384 + 0.982207i) q^{3} +(0.930506 + 0.494759i) q^{4} +(1.56582 + 1.59631i) q^{5} +(0.746431 + 0.955388i) q^{6} +(1.73336 - 3.00227i) q^{7} +(1.98764 - 2.20750i) q^{8} +(0.349914 + 1.40343i) q^{9} +(1.87506 - 1.10219i) q^{10} +(-4.69845 - 2.09189i) q^{11} +(-1.20001 + 0.534279i) q^{12} +(2.54941 + 0.731032i) q^{13} +(-2.42567 - 2.34244i) q^{14} +(-2.76949 + 0.312978i) q^{15} +(-0.437092 - 0.648015i) q^{16} +(0.933471 + 0.583297i) q^{17} +1.40690 q^{18} +(2.56785 + 3.52224i) q^{19} +(0.667218 + 2.26008i) q^{20} +(1.61870 + 4.00642i) q^{21} +(-3.07995 + 3.94216i) q^{22} +(0.515454 + 1.05684i) q^{23} +(0.642936 + 3.64627i) q^{24} +(-0.0964071 + 4.99907i) q^{25} +(1.28987 - 2.23412i) q^{26} +(-5.06301 - 2.25420i) q^{27} +(3.09831 - 1.93604i) q^{28} +(6.59530 - 4.12120i) q^{29} +(-0.356318 + 2.68750i) q^{30} +(-7.87467 - 1.67381i) q^{31} +(4.86822 - 1.77189i) q^{32} +(5.66018 - 3.00957i) q^{33} +(0.770178 - 0.743753i) q^{34} +(7.50670 - 1.93404i) q^{35} +(-0.368761 + 1.47902i) q^{36} +(4.56145 + 3.31409i) q^{37} +(3.92855 - 1.59470i) q^{38} +(-2.67440 + 1.94307i) q^{39} +(6.63613 - 0.283659i) q^{40} +(-5.26675 - 7.80827i) q^{41} +(4.16217 - 0.584956i) q^{42} +(1.13747 + 6.45089i) q^{43} +(-3.33696 - 4.27111i) q^{44} +(-1.69240 + 2.75609i) q^{45} +(1.11874 - 0.237796i) q^{46} +(-5.50976 + 3.44288i) q^{47} +(0.971902 + 0.0679620i) q^{48} +(-2.50910 - 4.34589i) q^{49} +(4.69545 + 1.26735i) q^{50} +(-1.28925 + 0.469248i) q^{51} +(2.01056 + 1.94157i) q^{52} +(0.935362 + 0.497341i) q^{53} +(-3.31893 + 4.24803i) q^{54} +(-4.01764 - 10.7757i) q^{55} +(-3.18221 - 9.79383i) q^{56} +(-5.43009 - 0.180751i) q^{57} +(-2.33762 - 7.19445i) q^{58} +(-6.78986 + 0.474793i) q^{59} +(-2.73188 - 1.07900i) q^{60} +(-2.13863 - 4.38485i) q^{61} +(-3.43279 + 7.03826i) q^{62} +(4.82000 + 1.38211i) q^{63} +(-0.690149 - 6.56633i) q^{64} +(2.82497 + 5.21432i) q^{65} +(-1.50851 - 6.05030i) q^{66} +(1.95407 - 4.83648i) q^{67} +(0.580008 + 1.00460i) q^{68} +(-1.43358 - 0.304718i) q^{69} +(-0.0589032 - 7.53995i) q^{70} +(-2.28218 - 0.320740i) q^{71} +(3.79356 + 2.01707i) q^{72} +(6.64413 - 1.90517i) q^{73} +(4.20123 - 3.52525i) q^{74} +(-4.83614 - 3.93090i) q^{75} +(0.646740 + 4.54793i) q^{76} +(-14.4245 + 10.4800i) q^{77} +(1.20454 + 2.98134i) q^{78} +(-2.59825 + 3.32561i) q^{79} +(0.350025 - 1.71241i) q^{80} +(2.26809 - 1.20597i) q^{81} +(-8.60882 + 3.13335i) q^{82} +(-6.16926 - 1.31132i) q^{83} +(-0.476002 + 4.52886i) q^{84} +(0.530525 + 2.40345i) q^{85} +(6.35603 + 0.444457i) q^{86} +(-1.01326 + 9.64049i) q^{87} +(-13.9567 + 6.21391i) q^{88} +(-2.49167 + 3.69405i) q^{89} +(2.20295 + 2.24585i) q^{90} +(6.61382 - 6.38689i) q^{91} +(-0.0432465 + 1.23842i) q^{92} +(7.68693 - 6.45010i) q^{93} +(1.95286 + 6.01029i) q^{94} +(-1.60179 + 9.61427i) q^{95} +(-1.99544 + 6.14132i) q^{96} +(-4.88431 - 12.0891i) q^{97} +(-4.69209 + 1.34544i) q^{98} +(1.29176 - 7.32592i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1152 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 24 q^{5} - 18 q^{6} - 30 q^{7} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1152 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 24 q^{5} - 18 q^{6} - 30 q^{7} - 9 q^{8} - 18 q^{9} - 33 q^{10} - 9 q^{12} - 18 q^{13} - 18 q^{14} + 27 q^{15} - 30 q^{16} - 36 q^{17} - 144 q^{18} - 18 q^{19} - 54 q^{20} + 9 q^{21} + 6 q^{22} - 24 q^{23} - 120 q^{24} - 90 q^{25} - 24 q^{26} - 9 q^{27} + 54 q^{28} + 9 q^{30} - 45 q^{31} - 138 q^{32} + 54 q^{33} - 18 q^{34} + 45 q^{35} - 72 q^{36} - 36 q^{37} + 93 q^{38} - 36 q^{39} + 57 q^{40} - 18 q^{41} + 36 q^{42} - 252 q^{43} - 42 q^{44} - 90 q^{45} - 69 q^{46} - 18 q^{47} + 6 q^{48} - 486 q^{49} + 21 q^{50} + 12 q^{51} - 36 q^{53} - 120 q^{54} - 3 q^{55} + 234 q^{56} + 90 q^{57} + 180 q^{58} + 18 q^{59} + 69 q^{60} - 90 q^{61} - 144 q^{62} - 27 q^{63} + 93 q^{64} - 72 q^{65} + 42 q^{66} + 54 q^{67} - 48 q^{68} - 57 q^{69} + 12 q^{70} - 60 q^{71} - 318 q^{72} - 36 q^{73} - 66 q^{74} - 132 q^{75} - 48 q^{76} + 222 q^{77} - 39 q^{78} + 6 q^{79} + 129 q^{80} - 84 q^{81} + 120 q^{82} + 45 q^{83} - 63 q^{84} - 18 q^{85} + 72 q^{86} - 33 q^{87} - 45 q^{88} + 18 q^{89} + 57 q^{90} + 45 q^{91} + 324 q^{92} - 78 q^{93} - 24 q^{94} + 81 q^{95} - 132 q^{96} - 96 q^{97} - 153 q^{98} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.235316 0.943803i 0.166394 0.667369i −0.827917 0.560851i \(-0.810474\pi\)
0.994311 0.106518i \(-0.0339703\pi\)
\(3\) −0.767384 + 0.982207i −0.443049 + 0.567077i −0.956757 0.290888i \(-0.906049\pi\)
0.513708 + 0.857965i \(0.328272\pi\)
\(4\) 0.930506 + 0.494759i 0.465253 + 0.247379i
\(5\) 1.56582 + 1.59631i 0.700257 + 0.713891i
\(6\) 0.746431 + 0.955388i 0.304729 + 0.390036i
\(7\) 1.73336 3.00227i 0.655150 1.13475i −0.326706 0.945126i \(-0.605939\pi\)
0.981856 0.189627i \(-0.0607279\pi\)
\(8\) 1.98764 2.20750i 0.702736 0.780468i
\(9\) 0.349914 + 1.40343i 0.116638 + 0.467809i
\(10\) 1.87506 1.10219i 0.592947 0.348543i
\(11\) −4.69845 2.09189i −1.41664 0.630728i −0.451452 0.892295i \(-0.649094\pi\)
−0.965185 + 0.261568i \(0.915761\pi\)
\(12\) −1.20001 + 0.534279i −0.346413 + 0.154233i
\(13\) 2.54941 + 0.731032i 0.707080 + 0.202752i 0.609858 0.792511i \(-0.291227\pi\)
0.0972219 + 0.995263i \(0.469004\pi\)
\(14\) −2.42567 2.34244i −0.648286 0.626043i
\(15\) −2.76949 + 0.312978i −0.715080 + 0.0808106i
\(16\) −0.437092 0.648015i −0.109273 0.162004i
\(17\) 0.933471 + 0.583297i 0.226400 + 0.141470i 0.638377 0.769724i \(-0.279606\pi\)
−0.411977 + 0.911194i \(0.635162\pi\)
\(18\) 1.40690 0.331609
\(19\) 2.56785 + 3.52224i 0.589105 + 0.808057i
\(20\) 0.667218 + 2.26008i 0.149194 + 0.505369i
\(21\) 1.61870 + 4.00642i 0.353229 + 0.874272i
\(22\) −3.07995 + 3.94216i −0.656648 + 0.840471i
\(23\) 0.515454 + 1.05684i 0.107480 + 0.220366i 0.945755 0.324882i \(-0.105324\pi\)
−0.838275 + 0.545248i \(0.816436\pi\)
\(24\) 0.642936 + 3.64627i 0.131239 + 0.744292i
\(25\) −0.0964071 + 4.99907i −0.0192814 + 0.999814i
\(26\) 1.28987 2.23412i 0.252964 0.438147i
\(27\) −5.06301 2.25420i −0.974376 0.433820i
\(28\) 3.09831 1.93604i 0.585525 0.365876i
\(29\) 6.59530 4.12120i 1.22472 0.765288i 0.245754 0.969332i \(-0.420964\pi\)
0.978962 + 0.204045i \(0.0654088\pi\)
\(30\) −0.356318 + 2.68750i −0.0650544 + 0.490669i
\(31\) −7.87467 1.67381i −1.41433 0.300626i −0.563523 0.826100i \(-0.690554\pi\)
−0.850809 + 0.525475i \(0.823888\pi\)
\(32\) 4.86822 1.77189i 0.860588 0.313228i
\(33\) 5.66018 3.00957i 0.985311 0.523899i
\(34\) 0.770178 0.743753i 0.132084 0.127553i
\(35\) 7.50670 1.93404i 1.26886 0.326912i
\(36\) −0.368761 + 1.47902i −0.0614602 + 0.246503i
\(37\) 4.56145 + 3.31409i 0.749898 + 0.544833i 0.895795 0.444467i \(-0.146607\pi\)
−0.145897 + 0.989300i \(0.546607\pi\)
\(38\) 3.92855 1.59470i 0.637296 0.258695i
\(39\) −2.67440 + 1.94307i −0.428247 + 0.311140i
\(40\) 6.63613 0.283659i 1.04927 0.0448504i
\(41\) −5.26675 7.80827i −0.822528 1.21945i −0.972994 0.230832i \(-0.925855\pi\)
0.150466 0.988615i \(-0.451923\pi\)
\(42\) 4.16217 0.584956i 0.642238 0.0902606i
\(43\) 1.13747 + 6.45089i 0.173462 + 0.983752i 0.939904 + 0.341438i \(0.110914\pi\)
−0.766442 + 0.642313i \(0.777975\pi\)
\(44\) −3.33696 4.27111i −0.503066 0.643894i
\(45\) −1.69240 + 2.75609i −0.252288 + 0.410853i
\(46\) 1.11874 0.237796i 0.164949 0.0350611i
\(47\) −5.50976 + 3.44288i −0.803681 + 0.502195i −0.868493 0.495702i \(-0.834911\pi\)
0.0648120 + 0.997897i \(0.479355\pi\)
\(48\) 0.971902 + 0.0679620i 0.140282 + 0.00980948i
\(49\) −2.50910 4.34589i −0.358443 0.620841i
\(50\) 4.69545 + 1.26735i 0.664037 + 0.179231i
\(51\) −1.28925 + 0.469248i −0.180531 + 0.0657079i
\(52\) 2.01056 + 1.94157i 0.278814 + 0.269248i
\(53\) 0.935362 + 0.497341i 0.128482 + 0.0683150i 0.532468 0.846450i \(-0.321265\pi\)
−0.403986 + 0.914765i \(0.632376\pi\)
\(54\) −3.31893 + 4.24803i −0.451649 + 0.578084i
\(55\) −4.01764 10.7757i −0.541739 1.45300i
\(56\) −3.18221 9.79383i −0.425241 1.30876i
\(57\) −5.43009 0.180751i −0.719233 0.0239410i
\(58\) −2.33762 7.19445i −0.306944 0.944677i
\(59\) −6.78986 + 0.474793i −0.883964 + 0.0618128i −0.504518 0.863401i \(-0.668330\pi\)
−0.379446 + 0.925214i \(0.623885\pi\)
\(60\) −2.73188 1.07900i −0.352684 0.139299i
\(61\) −2.13863 4.38485i −0.273824 0.561422i 0.716922 0.697154i \(-0.245550\pi\)
−0.990746 + 0.135731i \(0.956662\pi\)
\(62\) −3.43279 + 7.03826i −0.435965 + 0.893860i
\(63\) 4.82000 + 1.38211i 0.607263 + 0.174130i
\(64\) −0.690149 6.56633i −0.0862686 0.820791i
\(65\) 2.82497 + 5.21432i 0.350394 + 0.646756i
\(66\) −1.50851 6.05030i −0.185685 0.744740i
\(67\) 1.95407 4.83648i 0.238727 0.590871i −0.759492 0.650516i \(-0.774553\pi\)
0.998220 + 0.0596456i \(0.0189971\pi\)
\(68\) 0.580008 + 1.00460i 0.0703363 + 0.121826i
\(69\) −1.43358 0.304718i −0.172583 0.0366837i
\(70\) −0.0589032 7.53995i −0.00704027 0.901197i
\(71\) −2.28218 0.320740i −0.270845 0.0380648i 0.00244298 0.999997i \(-0.499222\pi\)
−0.273288 + 0.961932i \(0.588111\pi\)
\(72\) 3.79356 + 2.01707i 0.447076 + 0.237714i
\(73\) 6.64413 1.90517i 0.777637 0.222984i 0.136736 0.990608i \(-0.456339\pi\)
0.640901 + 0.767624i \(0.278561\pi\)
\(74\) 4.20123 3.52525i 0.488383 0.409802i
\(75\) −4.83614 3.93090i −0.558429 0.453901i
\(76\) 0.646740 + 4.54793i 0.0741861 + 0.521683i
\(77\) −14.4245 + 10.4800i −1.64383 + 1.19431i
\(78\) 1.20454 + 2.98134i 0.136387 + 0.337571i
\(79\) −2.59825 + 3.32561i −0.292326 + 0.374160i −0.911645 0.410980i \(-0.865187\pi\)
0.619318 + 0.785140i \(0.287409\pi\)
\(80\) 0.350025 1.71241i 0.0391340 0.191453i
\(81\) 2.26809 1.20597i 0.252010 0.133996i
\(82\) −8.60882 + 3.13335i −0.950685 + 0.346021i
\(83\) −6.16926 1.31132i −0.677164 0.143936i −0.143523 0.989647i \(-0.545843\pi\)
−0.533641 + 0.845711i \(0.679177\pi\)
\(84\) −0.476002 + 4.52886i −0.0519361 + 0.494139i
\(85\) 0.530525 + 2.40345i 0.0575436 + 0.260690i
\(86\) 6.35603 + 0.444457i 0.685389 + 0.0479271i
\(87\) −1.01326 + 9.64049i −0.108632 + 1.03357i
\(88\) −13.9567 + 6.21391i −1.48779 + 0.662405i
\(89\) −2.49167 + 3.69405i −0.264116 + 0.391569i −0.937646 0.347591i \(-0.887000\pi\)
0.673530 + 0.739160i \(0.264777\pi\)
\(90\) 2.20295 + 2.24585i 0.232212 + 0.236733i
\(91\) 6.61382 6.38689i 0.693316 0.669528i
\(92\) −0.0432465 + 1.23842i −0.00450876 + 0.129114i
\(93\) 7.68693 6.45010i 0.797097 0.668844i
\(94\) 1.95286 + 6.01029i 0.201422 + 0.619914i
\(95\) −1.60179 + 9.61427i −0.164340 + 0.986404i
\(96\) −1.99544 + 6.14132i −0.203658 + 0.626796i
\(97\) −4.88431 12.0891i −0.495927 1.22746i −0.942949 0.332938i \(-0.891960\pi\)
0.447022 0.894523i \(-0.352485\pi\)
\(98\) −4.69209 + 1.34544i −0.473973 + 0.135910i
\(99\) 1.29176 7.32592i 0.129827 0.736283i
\(100\) −2.56304 + 4.60396i −0.256304 + 0.460396i
\(101\) −2.40242 + 0.874411i −0.239050 + 0.0870071i −0.458767 0.888557i \(-0.651709\pi\)
0.219717 + 0.975564i \(0.429487\pi\)
\(102\) 0.139496 + 1.32722i 0.0138122 + 0.131414i
\(103\) −3.49366 + 0.742600i −0.344240 + 0.0731706i −0.376788 0.926300i \(-0.622971\pi\)
0.0325473 + 0.999470i \(0.489638\pi\)
\(104\) 6.68106 4.17479i 0.655132 0.409372i
\(105\) −3.86089 + 8.85728i −0.376784 + 0.864382i
\(106\) 0.689498 0.765765i 0.0669700 0.0743777i
\(107\) 7.56451 13.1021i 0.731289 1.26663i −0.225044 0.974349i \(-0.572253\pi\)
0.956333 0.292281i \(-0.0944141\pi\)
\(108\) −3.59587 4.60251i −0.346013 0.442877i
\(109\) −3.78907 + 7.76875i −0.362927 + 0.744111i −0.999636 0.0269935i \(-0.991407\pi\)
0.636708 + 0.771105i \(0.280296\pi\)
\(110\) −11.1156 + 1.25616i −1.05983 + 0.119770i
\(111\) −6.75551 + 1.93711i −0.641204 + 0.183862i
\(112\) −2.70316 + 0.189023i −0.255425 + 0.0178610i
\(113\) −8.80767 6.39914i −0.828555 0.601981i 0.0905948 0.995888i \(-0.471123\pi\)
−0.919150 + 0.393907i \(0.871123\pi\)
\(114\) −1.44838 + 5.08240i −0.135653 + 0.476010i
\(115\) −0.879931 + 2.47764i −0.0820540 + 0.231041i
\(116\) 8.17596 0.571719i 0.759119 0.0530828i
\(117\) −0.133876 + 3.83371i −0.0123769 + 0.354427i
\(118\) −1.14965 + 6.52001i −0.105834 + 0.600216i
\(119\) 3.36926 1.79147i 0.308860 0.164224i
\(120\) −4.81385 + 6.73573i −0.439443 + 0.614885i
\(121\) 10.3390 + 11.4827i 0.939913 + 1.04388i
\(122\) −4.64169 + 0.986621i −0.420239 + 0.0893245i
\(123\) 11.7110 + 0.818910i 1.05594 + 0.0738386i
\(124\) −6.49929 5.45355i −0.583654 0.489743i
\(125\) −8.13102 + 7.67376i −0.727260 + 0.686362i
\(126\) 2.43867 4.22390i 0.217254 0.376295i
\(127\) 6.08133 9.01594i 0.539631 0.800036i −0.456331 0.889810i \(-0.650837\pi\)
0.995962 + 0.0897743i \(0.0286146\pi\)
\(128\) 3.90075 + 0.548215i 0.344781 + 0.0484558i
\(129\) −7.20898 3.83308i −0.634716 0.337484i
\(130\) 5.58605 1.43920i 0.489929 0.126226i
\(131\) −8.29098 5.18078i −0.724386 0.452647i 0.116965 0.993136i \(-0.462684\pi\)
−0.841351 + 0.540489i \(0.818239\pi\)
\(132\) 6.75584 0.588021
\(133\) 15.0257 1.60407i 1.30290 0.139090i
\(134\) −4.10486 2.98236i −0.354606 0.257636i
\(135\) −4.32937 11.6118i −0.372613 0.999384i
\(136\) 3.14303 0.901249i 0.269512 0.0772815i
\(137\) −7.71467 + 7.44997i −0.659109 + 0.636494i −0.947024 0.321162i \(-0.895927\pi\)
0.287916 + 0.957656i \(0.407038\pi\)
\(138\) −0.624940 + 1.28132i −0.0531984 + 0.109073i
\(139\) −10.0987 + 14.9719i −0.856558 + 1.26990i 0.104771 + 0.994496i \(0.466589\pi\)
−0.961329 + 0.275403i \(0.911189\pi\)
\(140\) 7.94191 + 1.91437i 0.671214 + 0.161794i
\(141\) 0.846481 8.05373i 0.0712866 0.678246i
\(142\) −0.839750 + 2.07845i −0.0704703 + 0.174420i
\(143\) −10.4491 8.76780i −0.873794 0.733200i
\(144\) 0.756498 0.840177i 0.0630415 0.0700147i
\(145\) 16.9058 + 4.07507i 1.40395 + 0.338416i
\(146\) −0.234635 6.71907i −0.0194185 0.556074i
\(147\) 6.19401 + 0.870511i 0.510873 + 0.0717985i
\(148\) 2.60478 + 5.34060i 0.214112 + 0.438994i
\(149\) −22.5293 8.19998i −1.84567 0.671769i −0.987328 0.158690i \(-0.949273\pi\)
−0.858341 0.513079i \(-0.828505\pi\)
\(150\) −4.84802 + 3.63936i −0.395839 + 0.297152i
\(151\) −3.87523 −0.315361 −0.157681 0.987490i \(-0.550402\pi\)
−0.157681 + 0.987490i \(0.550402\pi\)
\(152\) 12.8793 + 1.33242i 1.04465 + 0.108074i
\(153\) −0.491981 + 1.51416i −0.0397743 + 0.122413i
\(154\) 6.49676 + 16.0801i 0.523524 + 1.29577i
\(155\) −9.65840 15.1913i −0.775782 1.22019i
\(156\) −3.44990 + 0.484851i −0.276213 + 0.0388192i
\(157\) 1.05167 + 5.96430i 0.0839322 + 0.476003i 0.997582 + 0.0695007i \(0.0221406\pi\)
−0.913650 + 0.406502i \(0.866748\pi\)
\(158\) 2.52731 + 3.23481i 0.201062 + 0.257347i
\(159\) −1.20627 + 0.537068i −0.0956637 + 0.0425922i
\(160\) 10.4512 + 4.99673i 0.826244 + 0.395026i
\(161\) 4.06639 + 0.284349i 0.320476 + 0.0224099i
\(162\) −0.604475 2.42442i −0.0474920 0.190480i
\(163\) 2.28889 21.7773i 0.179280 1.70573i −0.421919 0.906633i \(-0.638643\pi\)
0.601199 0.799099i \(-0.294690\pi\)
\(164\) −1.03753 9.87141i −0.0810173 0.770828i
\(165\) 13.6670 + 4.32295i 1.06398 + 0.336541i
\(166\) −2.68935 + 5.51399i −0.208734 + 0.427968i
\(167\) −13.6203 + 1.91420i −1.05397 + 0.148125i −0.644813 0.764340i \(-0.723065\pi\)
−0.409154 + 0.912466i \(0.634176\pi\)
\(168\) 12.0615 + 4.39004i 0.930568 + 0.338699i
\(169\) −5.05953 3.16155i −0.389195 0.243196i
\(170\) 2.39322 + 0.0648592i 0.183552 + 0.00497448i
\(171\) −4.04468 + 4.83627i −0.309304 + 0.369839i
\(172\) −2.13322 + 6.56536i −0.162656 + 0.500604i
\(173\) 4.95323 19.8663i 0.376587 1.51041i −0.420919 0.907098i \(-0.638292\pi\)
0.797506 0.603311i \(-0.206152\pi\)
\(174\) 8.86028 + 3.22488i 0.671696 + 0.244477i
\(175\) 14.8415 + 8.95465i 1.12191 + 0.676908i
\(176\) 0.698082 + 3.95902i 0.0526199 + 0.298422i
\(177\) 4.74408 7.03339i 0.356587 0.528662i
\(178\) 2.90013 + 3.22092i 0.217374 + 0.241418i
\(179\) 9.22882 1.96165i 0.689795 0.146620i 0.150339 0.988634i \(-0.451963\pi\)
0.539456 + 0.842014i \(0.318630\pi\)
\(180\) −2.93839 + 1.72722i −0.219015 + 0.128740i
\(181\) 0.496277 1.22833i 0.0368880 0.0913009i −0.907615 0.419803i \(-0.862099\pi\)
0.944503 + 0.328502i \(0.106544\pi\)
\(182\) −4.47162 7.74508i −0.331459 0.574103i
\(183\) 5.94798 + 1.26428i 0.439687 + 0.0934585i
\(184\) 3.35750 + 0.962749i 0.247518 + 0.0709748i
\(185\) 1.85211 + 12.4708i 0.136170 + 0.916869i
\(186\) −4.27876 8.77275i −0.313734 0.643250i
\(187\) −3.16568 4.69331i −0.231497 0.343209i
\(188\) −6.83025 + 0.477618i −0.498147 + 0.0348339i
\(189\) −15.5438 + 11.2932i −1.13064 + 0.821459i
\(190\) 8.69705 + 3.77417i 0.630950 + 0.273807i
\(191\) 15.9587 + 11.5947i 1.15473 + 0.838960i 0.989102 0.147229i \(-0.0470355\pi\)
0.165626 + 0.986189i \(0.447035\pi\)
\(192\) 6.97910 + 4.36103i 0.503673 + 0.314730i
\(193\) 2.58406 + 0.940521i 0.186005 + 0.0677002i 0.433343 0.901229i \(-0.357334\pi\)
−0.247339 + 0.968929i \(0.579556\pi\)
\(194\) −12.5591 + 1.76506i −0.901689 + 0.126724i
\(195\) −7.28937 1.22668i −0.522003 0.0878442i
\(196\) −0.184566 5.28527i −0.0131833 0.377520i
\(197\) 7.65039 + 8.49662i 0.545068 + 0.605359i 0.951245 0.308435i \(-0.0998053\pi\)
−0.406178 + 0.913794i \(0.633139\pi\)
\(198\) −6.61025 2.94307i −0.469770 0.209155i
\(199\) 9.11252 + 7.64631i 0.645969 + 0.542032i 0.905845 0.423610i \(-0.139237\pi\)
−0.259876 + 0.965642i \(0.583682\pi\)
\(200\) 10.8438 + 10.1492i 0.766773 + 0.717654i
\(201\) 3.25091 + 5.63074i 0.229301 + 0.397162i
\(202\) 0.259941 + 2.47318i 0.0182894 + 0.174012i
\(203\) −0.940920 26.9444i −0.0660397 1.89113i
\(204\) −1.43182 0.201229i −0.100247 0.0140888i
\(205\) 4.21764 20.6337i 0.294572 1.44112i
\(206\) −0.121247 + 3.47207i −0.00844771 + 0.241911i
\(207\) −1.30283 + 1.09321i −0.0905530 + 0.0759830i
\(208\) −0.640607 1.97159i −0.0444181 0.136705i
\(209\) −4.69680 21.9207i −0.324884 1.51629i
\(210\) 7.45099 + 5.72818i 0.514167 + 0.395282i
\(211\) 0.905493 3.63174i 0.0623367 0.250019i −0.931041 0.364915i \(-0.881098\pi\)
0.993378 + 0.114896i \(0.0366535\pi\)
\(212\) 0.624296 + 0.925557i 0.0428768 + 0.0635675i
\(213\) 2.06634 1.99544i 0.141583 0.136726i
\(214\) −10.5858 10.2225i −0.723627 0.698799i
\(215\) −8.51655 + 11.9167i −0.580824 + 0.812712i
\(216\) −15.0396 + 6.69605i −1.02331 + 0.455608i
\(217\) −18.6749 + 20.7406i −1.26774 + 1.40796i
\(218\) 6.44054 + 5.40425i 0.436208 + 0.366022i
\(219\) −3.22733 + 7.98791i −0.218082 + 0.539773i
\(220\) 1.59294 12.0146i 0.107396 0.810025i
\(221\) 1.95339 + 2.16946i 0.131399 + 0.145934i
\(222\) 0.238568 + 6.83170i 0.0160117 + 0.458514i
\(223\) 3.95062 + 3.81507i 0.264553 + 0.255476i 0.815089 0.579335i \(-0.196688\pi\)
−0.550536 + 0.834811i \(0.685577\pi\)
\(224\) 3.11871 17.6871i 0.208377 1.18177i
\(225\) −7.04957 + 1.61394i −0.469971 + 0.107596i
\(226\) −8.11212 + 6.80687i −0.539610 + 0.452787i
\(227\) 12.8307 9.32205i 0.851604 0.618726i −0.0739839 0.997259i \(-0.523571\pi\)
0.925588 + 0.378533i \(0.123571\pi\)
\(228\) −4.96330 2.85477i −0.328703 0.189062i
\(229\) −5.94364 + 18.2926i −0.392767 + 1.20881i 0.537921 + 0.842995i \(0.319210\pi\)
−0.930687 + 0.365816i \(0.880790\pi\)
\(230\) 2.13134 + 1.41351i 0.140537 + 0.0932042i
\(231\) 0.775594 22.2101i 0.0510303 1.46132i
\(232\) 4.01154 22.7506i 0.263370 1.49365i
\(233\) −17.4156 + 9.26003i −1.14093 + 0.606645i −0.928795 0.370595i \(-0.879154\pi\)
−0.212138 + 0.977240i \(0.568043\pi\)
\(234\) 3.58677 + 1.02849i 0.234474 + 0.0672344i
\(235\) −14.1232 3.40434i −0.921296 0.222075i
\(236\) −6.55291 2.91754i −0.426558 0.189916i
\(237\) −1.27258 5.10404i −0.0826630 0.331543i
\(238\) −0.897950 3.60148i −0.0582054 0.233449i
\(239\) 24.9509 + 11.1089i 1.61394 + 0.718572i 0.997622 0.0689262i \(-0.0219573\pi\)
0.616317 + 0.787498i \(0.288624\pi\)
\(240\) 1.41334 + 1.65787i 0.0912305 + 0.107015i
\(241\) 11.1324 + 3.19215i 0.717098 + 0.205625i 0.614294 0.789077i \(-0.289441\pi\)
0.102804 + 0.994702i \(0.467219\pi\)
\(242\) 13.2703 7.05596i 0.853049 0.453574i
\(243\) 2.33116 13.2207i 0.149544 0.848108i
\(244\) 0.179431 5.13823i 0.0114869 0.328942i
\(245\) 3.00858 10.8102i 0.192211 0.690638i
\(246\) 3.52867 10.8601i 0.224980 0.692417i
\(247\) 3.97163 + 10.8568i 0.252709 + 0.690802i
\(248\) −19.3469 + 14.0564i −1.22853 + 0.892580i
\(249\) 6.02217 5.05320i 0.381640 0.320234i
\(250\) 5.32915 + 9.47984i 0.337045 + 0.599558i
\(251\) 3.74128 21.2179i 0.236148 1.33926i −0.604035 0.796958i \(-0.706441\pi\)
0.840183 0.542303i \(-0.182447\pi\)
\(252\) 3.80123 + 3.67080i 0.239455 + 0.231239i
\(253\) −0.211053 6.04378i −0.0132688 0.379969i
\(254\) −7.07824 7.86118i −0.444128 0.493254i
\(255\) −2.76780 1.32328i −0.173326 0.0828671i
\(256\) 6.38199 15.7960i 0.398875 0.987249i
\(257\) 10.5281 + 8.83415i 0.656727 + 0.551059i 0.909104 0.416570i \(-0.136768\pi\)
−0.252377 + 0.967629i \(0.581212\pi\)
\(258\) −5.31407 + 5.90187i −0.330839 + 0.367434i
\(259\) 17.8565 7.95021i 1.10955 0.494002i
\(260\) 0.0488230 + 6.24963i 0.00302787 + 0.387585i
\(261\) 8.09159 + 7.81396i 0.500857 + 0.483672i
\(262\) −6.84063 + 6.60592i −0.422616 + 0.408115i
\(263\) −5.16206 7.65307i −0.318306 0.471909i 0.635598 0.772021i \(-0.280754\pi\)
−0.953904 + 0.300112i \(0.902976\pi\)
\(264\) 4.60678 18.4768i 0.283528 1.13717i
\(265\) 0.670700 + 2.27187i 0.0412008 + 0.139560i
\(266\) 2.02188 14.5588i 0.123970 0.892657i
\(267\) −1.71626 5.28209i −0.105033 0.323259i
\(268\) 4.21116 3.53358i 0.257238 0.215848i
\(269\) −0.606079 + 17.3558i −0.0369533 + 1.05820i 0.829363 + 0.558709i \(0.188703\pi\)
−0.866317 + 0.499495i \(0.833519\pi\)
\(270\) −11.9780 + 1.35363i −0.728959 + 0.0823790i
\(271\) 8.77195 + 1.23282i 0.532858 + 0.0748883i 0.400470 0.916310i \(-0.368847\pi\)
0.132388 + 0.991198i \(0.457736\pi\)
\(272\) −0.0300269 0.859858i −0.00182065 0.0521365i
\(273\) 1.19791 + 11.3973i 0.0725007 + 0.689798i
\(274\) 5.21591 + 9.03423i 0.315105 + 0.545778i
\(275\) 10.9105 23.2862i 0.657925 1.40421i
\(276\) −1.18320 0.992820i −0.0712201 0.0597607i
\(277\) −2.81581 1.25368i −0.169186 0.0753263i 0.320396 0.947284i \(-0.396184\pi\)
−0.489582 + 0.871957i \(0.662851\pi\)
\(278\) 11.7541 + 13.0543i 0.704966 + 0.782944i
\(279\) −0.406381 11.6372i −0.0243294 0.696702i
\(280\) 10.6512 20.4152i 0.636532 1.22004i
\(281\) −2.74880 + 0.386319i −0.163980 + 0.0230458i −0.220685 0.975345i \(-0.570829\pi\)
0.0567055 + 0.998391i \(0.481940\pi\)
\(282\) −7.40194 2.69409i −0.440779 0.160430i
\(283\) 22.5679 + 14.1020i 1.34152 + 0.838277i 0.995011 0.0997685i \(-0.0318102\pi\)
0.346513 + 0.938045i \(0.387366\pi\)
\(284\) −1.96489 1.42758i −0.116595 0.0847113i
\(285\) −8.21402 8.95113i −0.486556 0.530219i
\(286\) −10.7339 + 7.79864i −0.634709 + 0.461143i
\(287\) −32.5718 + 2.27764i −1.92265 + 0.134445i
\(288\) 4.19018 + 6.21219i 0.246908 + 0.366057i
\(289\) −6.92118 14.1905i −0.407128 0.834736i
\(290\) 7.82427 14.9968i 0.459457 0.880641i
\(291\) 15.6221 + 4.47957i 0.915785 + 0.262597i
\(292\) 7.12500 + 1.51447i 0.416959 + 0.0886274i
\(293\) −0.0696395 0.120619i −0.00406838 0.00704665i 0.863984 0.503519i \(-0.167962\pi\)
−0.868052 + 0.496473i \(0.834628\pi\)
\(294\) 2.27914 5.64107i 0.132922 0.328994i
\(295\) −11.3896 10.0953i −0.663129 0.587770i
\(296\) 16.3824 3.48218i 0.952206 0.202398i
\(297\) 19.0728 + 21.1825i 1.10672 + 1.22913i
\(298\) −13.0407 + 19.3336i −0.755426 + 1.11997i
\(299\) 0.541523 + 3.07113i 0.0313171 + 0.177608i
\(300\) −2.55521 6.05044i −0.147525 0.349323i
\(301\) 21.3390 + 7.76676i 1.22996 + 0.447668i
\(302\) −0.911904 + 3.65745i −0.0524742 + 0.210463i
\(303\) 0.984729 3.03069i 0.0565712 0.174108i
\(304\) 1.16008 3.20355i 0.0665351 0.183736i
\(305\) 3.65086 10.2798i 0.209047 0.588620i
\(306\) 1.31330 + 0.820640i 0.0750763 + 0.0469129i
\(307\) 23.0553 + 8.39145i 1.31584 + 0.478925i 0.902122 0.431481i \(-0.142009\pi\)
0.413715 + 0.910407i \(0.364231\pi\)
\(308\) −18.6072 + 2.61507i −1.06024 + 0.149008i
\(309\) 1.95159 4.00135i 0.111022 0.227629i
\(310\) −16.6104 + 5.54086i −0.943406 + 0.314700i
\(311\) 3.38417 + 32.1982i 0.191899 + 1.82579i 0.490529 + 0.871425i \(0.336804\pi\)
−0.298630 + 0.954369i \(0.596530\pi\)
\(312\) −1.02643 + 9.76585i −0.0581103 + 0.552882i
\(313\) 7.95470 + 31.9046i 0.449626 + 1.80335i 0.583218 + 0.812316i \(0.301793\pi\)
−0.133592 + 0.991036i \(0.542651\pi\)
\(314\) 5.87660 + 0.410932i 0.331636 + 0.0231902i
\(315\) 5.34098 + 9.85836i 0.300930 + 0.555456i
\(316\) −4.06306 + 1.80899i −0.228565 + 0.101764i
\(317\) −4.32140 5.53113i −0.242714 0.310659i 0.651193 0.758912i \(-0.274269\pi\)
−0.893907 + 0.448253i \(0.852047\pi\)
\(318\) 0.223030 + 1.26487i 0.0125069 + 0.0709301i
\(319\) −39.6088 + 5.56665i −2.21767 + 0.311673i
\(320\) 9.40124 11.3834i 0.525545 0.636351i
\(321\) 7.06410 + 17.4843i 0.394280 + 0.975876i
\(322\) 1.22526 3.77095i 0.0682809 0.210147i
\(323\) 0.342500 + 4.78572i 0.0190572 + 0.266285i
\(324\) 2.70714 0.150396
\(325\) −3.90026 + 12.6742i −0.216348 + 0.703039i
\(326\) −20.0149 7.28483i −1.10852 0.403469i
\(327\) −4.72284 9.68327i −0.261174 0.535486i
\(328\) −27.7051 3.89370i −1.52976 0.214994i
\(329\) 0.786051 + 22.5096i 0.0433364 + 1.24099i
\(330\) 7.29609 11.8817i 0.401637 0.654068i
\(331\) −18.7787 + 20.8559i −1.03217 + 1.14634i −0.0430761 + 0.999072i \(0.513716\pi\)
−0.989096 + 0.147272i \(0.952951\pi\)
\(332\) −5.09174 4.27248i −0.279446 0.234483i
\(333\) −3.05497 + 7.56132i −0.167411 + 0.414358i
\(334\) −1.39844 + 13.3053i −0.0765193 + 0.728032i
\(335\) 10.7802 4.45378i 0.588988 0.243336i
\(336\) 1.88870 2.80011i 0.103037 0.152759i
\(337\) 6.35789 13.0356i 0.346337 0.710095i −0.652527 0.757766i \(-0.726291\pi\)
0.998863 + 0.0476707i \(0.0151798\pi\)
\(338\) −4.17447 + 4.03124i −0.227061 + 0.219270i
\(339\) 13.0441 3.74035i 0.708461 0.203148i
\(340\) −0.695469 + 2.49890i −0.0377171 + 0.135522i
\(341\) 33.4973 + 24.3372i 1.81398 + 1.31794i
\(342\) 3.61270 + 4.95543i 0.195353 + 0.267959i
\(343\) 6.87036 0.370964
\(344\) 16.5012 + 10.3111i 0.889685 + 0.555937i
\(345\) −1.75831 2.76558i −0.0946644 0.148894i
\(346\) −17.5843 9.34975i −0.945339 0.502645i
\(347\) 24.7999 + 3.48540i 1.33133 + 0.187106i 0.768703 0.639606i \(-0.220903\pi\)
0.562625 + 0.826712i \(0.309791\pi\)
\(348\) −5.71255 + 8.46921i −0.306225 + 0.453997i
\(349\) 15.2284 26.3764i 0.815158 1.41189i −0.0940566 0.995567i \(-0.529983\pi\)
0.909214 0.416328i \(-0.136683\pi\)
\(350\) 11.9439 11.9002i 0.638426 0.636095i
\(351\) −11.2598 9.44810i −0.601004 0.504302i
\(352\) −26.5797 1.85863i −1.41670 0.0990655i
\(353\) 0.509052 0.108202i 0.0270941 0.00575903i −0.194345 0.980933i \(-0.562258\pi\)
0.221439 + 0.975174i \(0.428925\pi\)
\(354\) −5.52177 6.13255i −0.293479 0.325941i
\(355\) −3.06149 4.14529i −0.162487 0.220009i
\(356\) −4.14618 + 2.20456i −0.219747 + 0.116842i
\(357\) −0.825925 + 4.68406i −0.0437126 + 0.247907i
\(358\) 0.320286 9.17180i 0.0169277 0.484744i
\(359\) −14.5259 + 1.01575i −0.766646 + 0.0536091i −0.447724 0.894172i \(-0.647765\pi\)
−0.318922 + 0.947781i \(0.603321\pi\)
\(360\) 2.72017 + 9.21408i 0.143366 + 0.485625i
\(361\) −5.81231 + 18.0891i −0.305911 + 0.952060i
\(362\) −1.04252 0.757433i −0.0547935 0.0398098i
\(363\) −19.2124 + 1.34346i −1.00839 + 0.0705134i
\(364\) 9.31416 2.67079i 0.488195 0.139988i
\(365\) 13.4448 + 7.62293i 0.703731 + 0.399002i
\(366\) 2.59289 5.31621i 0.135533 0.277883i
\(367\) 2.74130 + 3.50870i 0.143094 + 0.183153i 0.854219 0.519914i \(-0.174036\pi\)
−0.711124 + 0.703066i \(0.751814\pi\)
\(368\) 0.459546 0.795958i 0.0239555 0.0414922i
\(369\) 9.11544 10.1237i 0.474531 0.527020i
\(370\) 12.2058 + 1.18655i 0.634548 + 0.0616858i
\(371\) 3.11448 1.94614i 0.161696 0.101039i
\(372\) 10.3440 2.19868i 0.536310 0.113996i
\(373\) 1.51512 + 14.4154i 0.0784498 + 0.746400i 0.961068 + 0.276310i \(0.0891118\pi\)
−0.882619 + 0.470090i \(0.844222\pi\)
\(374\) −5.17449 + 1.88336i −0.267567 + 0.0973863i
\(375\) −1.29760 13.8751i −0.0670078 0.716505i
\(376\) −3.35127 + 19.0060i −0.172828 + 0.980158i
\(377\) 19.8269 5.68526i 1.02114 0.292806i
\(378\) 7.00085 + 17.3277i 0.360085 + 0.891241i
\(379\) 3.96395 12.1998i 0.203614 0.626661i −0.796153 0.605095i \(-0.793135\pi\)
0.999767 0.0215655i \(-0.00686503\pi\)
\(380\) −6.24722 + 8.15364i −0.320476 + 0.418273i
\(381\) 4.18880 + 12.8918i 0.214599 + 0.660468i
\(382\) 14.6984 12.3334i 0.752036 0.631033i
\(383\) −0.779746 + 22.3290i −0.0398431 + 1.14096i 0.800649 + 0.599134i \(0.204488\pi\)
−0.840492 + 0.541824i \(0.817734\pi\)
\(384\) −3.53183 + 3.41065i −0.180233 + 0.174049i
\(385\) −39.3157 6.61616i −2.00371 0.337191i
\(386\) 1.49574 2.21752i 0.0761310 0.112869i
\(387\) −8.65535 + 3.85361i −0.439976 + 0.195890i
\(388\) 1.43630 13.6655i 0.0729173 0.693762i
\(389\) 22.0049 + 1.53874i 1.11569 + 0.0780170i 0.615677 0.787998i \(-0.288882\pi\)
0.500017 + 0.866015i \(0.333327\pi\)
\(390\) −2.87305 + 6.59107i −0.145483 + 0.333752i
\(391\) −0.135289 + 1.28719i −0.00684187 + 0.0650960i
\(392\) −14.5807 3.09923i −0.736438 0.156535i
\(393\) 11.4510 4.16781i 0.577624 0.210238i
\(394\) 9.81939 5.22106i 0.494694 0.263033i
\(395\) −9.37710 + 1.05970i −0.471813 + 0.0533192i
\(396\) 4.82655 6.17770i 0.242543 0.310441i
\(397\) −1.47900 3.66066i −0.0742291 0.183724i 0.885507 0.464625i \(-0.153811\pi\)
−0.959737 + 0.280902i \(0.909367\pi\)
\(398\) 9.36093 6.80111i 0.469221 0.340909i
\(399\) −9.95499 + 15.9893i −0.498373 + 0.800467i
\(400\) 3.28161 2.12258i 0.164081 0.106129i
\(401\) −15.5637 + 13.0595i −0.777217 + 0.652162i −0.942546 0.334076i \(-0.891576\pi\)
0.165329 + 0.986238i \(0.447131\pi\)
\(402\) 6.07930 1.74321i 0.303208 0.0869434i
\(403\) −18.8522 10.0239i −0.939093 0.499325i
\(404\) −2.66809 0.374976i −0.132742 0.0186557i
\(405\) 5.47653 + 1.73225i 0.272131 + 0.0860762i
\(406\) −25.6516 5.45242i −1.27307 0.270599i
\(407\) −14.4991 25.1131i −0.718693 1.24481i
\(408\) −1.52670 + 3.77871i −0.0755828 + 0.187074i
\(409\) −7.85775 31.5157i −0.388541 1.55835i −0.772508 0.635005i \(-0.780998\pi\)
0.383967 0.923347i \(-0.374558\pi\)
\(410\) −18.4817 8.83607i −0.912745 0.436382i
\(411\) −1.39730 13.2944i −0.0689236 0.655764i
\(412\) −3.61828 1.03752i −0.178260 0.0511151i
\(413\) −10.3438 + 21.2080i −0.508987 + 1.04358i
\(414\) 0.725192 + 1.48686i 0.0356413 + 0.0730754i
\(415\) −7.56669 11.9013i −0.371434 0.584213i
\(416\) 13.7064 0.958446i 0.672012 0.0469917i
\(417\) −6.95593 21.4082i −0.340634 1.04836i
\(418\) −21.7941 0.725457i −1.06598 0.0354832i
\(419\) −3.21043 9.88068i −0.156840 0.482703i 0.841503 0.540252i \(-0.181671\pi\)
−0.998343 + 0.0575497i \(0.981671\pi\)
\(420\) −7.97480 + 6.33154i −0.389130 + 0.308947i
\(421\) 6.20274 7.93914i 0.302303 0.386930i −0.612741 0.790284i \(-0.709933\pi\)
0.915044 + 0.403353i \(0.132155\pi\)
\(422\) −3.21456 1.70921i −0.156483 0.0832033i
\(423\) −6.75977 6.52784i −0.328671 0.317394i
\(424\) 2.95704 1.07627i 0.143607 0.0522685i
\(425\) −3.00594 + 4.61025i −0.145809 + 0.223630i
\(426\) −1.39706 2.41978i −0.0676878 0.117239i
\(427\) −16.8716 1.17977i −0.816472 0.0570933i
\(428\) 13.5212 8.44898i 0.653572 0.408397i
\(429\) 16.6302 3.53487i 0.802915 0.170665i
\(430\) 9.24292 + 10.8421i 0.445733 + 0.522854i
\(431\) −17.1467 21.9468i −0.825929 1.05714i −0.997408 0.0719535i \(-0.977077\pi\)
0.171479 0.985188i \(-0.445146\pi\)
\(432\) 0.752246 + 4.26620i 0.0361924 + 0.205258i
\(433\) 0.383095 0.0538405i 0.0184104 0.00258741i −0.129962 0.991519i \(-0.541486\pi\)
0.148372 + 0.988932i \(0.452597\pi\)
\(434\) 15.1805 + 22.5060i 0.728688 + 1.08032i
\(435\) −16.9758 + 13.4778i −0.813926 + 0.646212i
\(436\) −7.36941 + 5.35419i −0.352931 + 0.256419i
\(437\) −2.39883 + 4.52935i −0.114751 + 0.216668i
\(438\) 6.77957 + 4.92564i 0.323940 + 0.235356i
\(439\) −5.25411 + 21.0731i −0.250765 + 1.00576i 0.704427 + 0.709776i \(0.251204\pi\)
−0.955192 + 0.295987i \(0.904352\pi\)
\(440\) −31.7730 12.5493i −1.51472 0.598264i
\(441\) 5.22117 5.04203i 0.248627 0.240097i
\(442\) 2.50721 1.33311i 0.119256 0.0634094i
\(443\) 6.00921 2.18718i 0.285506 0.103916i −0.195297 0.980744i \(-0.562567\pi\)
0.480804 + 0.876828i \(0.340345\pi\)
\(444\) −7.24444 1.53985i −0.343806 0.0730782i
\(445\) −9.79836 + 1.80675i −0.464487 + 0.0856482i
\(446\) 4.53032 2.83086i 0.214517 0.134045i
\(447\) 25.3427 15.8359i 1.19867 0.749011i
\(448\) −20.9102 9.30982i −0.987914 0.439848i
\(449\) −14.3302 + 24.8206i −0.676282 + 1.17136i 0.299810 + 0.953999i \(0.403077\pi\)
−0.976092 + 0.217356i \(0.930257\pi\)
\(450\) −0.135635 + 7.03319i −0.00639390 + 0.331548i
\(451\) 8.41155 + 47.7043i 0.396084 + 2.24631i
\(452\) −5.02955 10.3121i −0.236570 0.485041i
\(453\) 2.97379 3.80627i 0.139721 0.178834i
\(454\) −5.77890 14.3033i −0.271217 0.671287i
\(455\) 20.5515 + 0.556971i 0.963469 + 0.0261112i
\(456\) −11.1921 + 11.6276i −0.524117 + 0.544514i
\(457\) −13.6106 −0.636676 −0.318338 0.947977i \(-0.603125\pi\)
−0.318338 + 0.947977i \(0.603125\pi\)
\(458\) 15.8660 + 9.91418i 0.741369 + 0.463259i
\(459\) −3.41130 5.05746i −0.159226 0.236062i
\(460\) −2.04462 + 1.87011i −0.0953307 + 0.0871942i
\(461\) −24.4166 23.5788i −1.13719 1.09817i −0.994100 0.108464i \(-0.965407\pi\)
−0.143092 0.989709i \(-0.545704\pi\)
\(462\) −20.7794 5.95841i −0.966747 0.277210i
\(463\) 9.02971 4.02029i 0.419646 0.186839i −0.186040 0.982542i \(-0.559565\pi\)
0.605686 + 0.795704i \(0.292899\pi\)
\(464\) −5.55335 2.47251i −0.257808 0.114783i
\(465\) 22.3327 + 2.17101i 1.03565 + 0.100678i
\(466\) 4.64147 + 18.6159i 0.215012 + 0.862365i
\(467\) −4.71796 + 5.23982i −0.218321 + 0.242470i −0.842350 0.538931i \(-0.818828\pi\)
0.624029 + 0.781402i \(0.285495\pi\)
\(468\) −2.02134 + 3.50106i −0.0934363 + 0.161836i
\(469\) −11.1333 14.2500i −0.514090 0.658005i
\(470\) −6.53645 + 12.5284i −0.301504 + 0.577892i
\(471\) −6.66521 3.54395i −0.307117 0.163297i
\(472\) −12.4477 + 15.9323i −0.572951 + 0.733344i
\(473\) 8.15020 32.6887i 0.374747 1.50303i
\(474\) −5.11667 −0.235016
\(475\) −17.8555 + 12.4973i −0.819265 + 0.573415i
\(476\) 4.02146 0.184323
\(477\) −0.370686 + 1.48674i −0.0169725 + 0.0680731i
\(478\) 16.3559 20.9346i 0.748102 0.957527i
\(479\) 13.1186 + 6.97531i 0.599406 + 0.318710i 0.741302 0.671172i \(-0.234209\pi\)
−0.141896 + 0.989882i \(0.545320\pi\)
\(480\) −12.9279 + 6.43088i −0.590077 + 0.293528i
\(481\) 9.20632 + 11.7835i 0.419772 + 0.537284i
\(482\) 5.63239 9.75558i 0.256548 0.444355i
\(483\) −3.39977 + 3.77583i −0.154695 + 0.171806i
\(484\) 3.93939 + 15.8000i 0.179063 + 0.718183i
\(485\) 11.6500 26.7262i 0.528998 1.21358i
\(486\) −11.9292 5.31120i −0.541118 0.240921i
\(487\) −22.2856 + 9.92219i −1.00986 + 0.449618i −0.843891 0.536514i \(-0.819741\pi\)
−0.165966 + 0.986131i \(0.553074\pi\)
\(488\) −13.9304 3.99447i −0.630598 0.180821i
\(489\) 19.6334 + 18.9597i 0.887853 + 0.857389i
\(490\) −9.49472 5.38332i −0.428928 0.243194i
\(491\) 0.0529271 + 0.0784677i 0.00238857 + 0.00354120i 0.830230 0.557421i \(-0.188209\pi\)
−0.827841 + 0.560962i \(0.810431\pi\)
\(492\) 10.4919 + 6.55610i 0.473014 + 0.295572i
\(493\) 8.56040 0.385541
\(494\) 11.1813 1.19365i 0.503070 0.0537050i
\(495\) 13.7171 9.40904i 0.616538 0.422905i
\(496\) 2.35730 + 5.83452i 0.105846 + 0.261978i
\(497\) −4.91880 + 6.29578i −0.220638 + 0.282404i
\(498\) −3.35211 6.87284i −0.150212 0.307979i
\(499\) 4.90413 + 27.8127i 0.219539 + 1.24507i 0.872854 + 0.487981i \(0.162266\pi\)
−0.653316 + 0.757086i \(0.726622\pi\)
\(500\) −11.3626 + 3.11758i −0.508152 + 0.139422i
\(501\) 8.57182 14.8468i 0.382961 0.663307i
\(502\) −19.1451 8.52395i −0.854488 0.380442i
\(503\) −23.1930 + 14.4926i −1.03412 + 0.646192i −0.937090 0.349089i \(-0.886491\pi\)
−0.0970342 + 0.995281i \(0.530936\pi\)
\(504\) 12.6314 7.89300i 0.562649 0.351582i
\(505\) −5.15760 2.46584i −0.229510 0.109728i
\(506\) −5.75380 1.22301i −0.255787 0.0543693i
\(507\) 6.98790 2.54339i 0.310343 0.112956i
\(508\) 10.1194 5.38060i 0.448977 0.238725i
\(509\) −6.47219 + 6.25012i −0.286875 + 0.277032i −0.824146 0.566378i \(-0.808344\pi\)
0.537271 + 0.843410i \(0.319455\pi\)
\(510\) −1.90022 + 2.30087i −0.0841434 + 0.101884i
\(511\) 5.79684 23.2499i 0.256437 1.02851i
\(512\) −7.03293 5.10973i −0.310815 0.225820i
\(513\) −5.06122 23.6216i −0.223458 1.04292i
\(514\) 10.8151 7.85766i 0.477035 0.346586i
\(515\) −6.65587 4.41418i −0.293292 0.194512i
\(516\) −4.81155 7.13341i −0.211817 0.314031i
\(517\) 33.0895 4.65042i 1.45527 0.204525i
\(518\) −3.30151 18.7238i −0.145060 0.822676i
\(519\) 15.7118 + 20.1102i 0.689672 + 0.882740i
\(520\) 17.1256 + 4.12806i 0.751007 + 0.181028i
\(521\) −12.7433 + 2.70868i −0.558296 + 0.118669i −0.478413 0.878135i \(-0.658788\pi\)
−0.0798827 + 0.996804i \(0.525455\pi\)
\(522\) 9.27892 5.79811i 0.406127 0.253777i
\(523\) −11.2461 0.786403i −0.491757 0.0343870i −0.178274 0.983981i \(-0.557051\pi\)
−0.313483 + 0.949594i \(0.601496\pi\)
\(524\) −5.15157 8.92277i −0.225047 0.389793i
\(525\) −20.1844 + 7.70574i −0.880920 + 0.336306i
\(526\) −8.43771 + 3.07107i −0.367902 + 0.133905i
\(527\) −6.37444 6.15573i −0.277675 0.268148i
\(528\) −4.42427 2.35243i −0.192542 0.102376i
\(529\) 13.3090 17.0347i 0.578652 0.740641i
\(530\) 2.30203 0.0983992i 0.0999937 0.00427419i
\(531\) −3.04220 9.36294i −0.132020 0.406317i
\(532\) 14.7752 + 5.94152i 0.640584 + 0.257598i
\(533\) −7.71901 23.7567i −0.334347 1.02902i
\(534\) −5.38911 + 0.376844i −0.233210 + 0.0163076i
\(535\) 32.7597 8.44027i 1.41633 0.364905i
\(536\) −6.79254 13.9268i −0.293393 0.601545i
\(537\) −5.15531 + 10.5699i −0.222468 + 0.456127i
\(538\) 16.2379 + 4.65613i 0.700064 + 0.200740i
\(539\) 2.69779 + 25.6677i 0.116202 + 1.10559i
\(540\) 1.71653 12.9468i 0.0738678 0.557143i
\(541\) −5.23207 20.9847i −0.224944 0.902202i −0.971531 0.236914i \(-0.923864\pi\)
0.746586 0.665288i \(-0.231691\pi\)
\(542\) 3.22772 7.98889i 0.138642 0.343152i
\(543\) 0.825638 + 1.43005i 0.0354315 + 0.0613692i
\(544\) 5.57788 + 1.18561i 0.239150 + 0.0508328i
\(545\) −18.3343 + 6.11594i −0.785357 + 0.261978i
\(546\) 11.0387 + 1.55139i 0.472414 + 0.0663934i
\(547\) 30.2238 + 16.0703i 1.29228 + 0.687115i 0.966094 0.258192i \(-0.0831266\pi\)
0.326182 + 0.945307i \(0.394238\pi\)
\(548\) −10.8645 + 3.11534i −0.464108 + 0.133081i
\(549\) 5.40548 4.53574i 0.230700 0.193581i
\(550\) −19.4102 15.7769i −0.827654 0.672731i
\(551\) 31.4516 + 12.6476i 1.33988 + 0.538805i
\(552\) −3.52211 + 2.55896i −0.149911 + 0.108917i
\(553\) 5.48068 + 13.5652i 0.233062 + 0.576849i
\(554\) −1.84583 + 2.36256i −0.0784220 + 0.100376i
\(555\) −13.6701 7.75071i −0.580265 0.328999i
\(556\) −16.8043 + 8.93502i −0.712663 + 0.378929i
\(557\) −1.61339 + 0.587227i −0.0683617 + 0.0248816i −0.375975 0.926630i \(-0.622692\pi\)
0.307613 + 0.951512i \(0.400470\pi\)
\(558\) −11.0789 2.35489i −0.469006 0.0996903i
\(559\) −1.81594 + 17.2775i −0.0768060 + 0.730761i
\(560\) −4.53440 4.01910i −0.191614 0.169838i
\(561\) 7.03909 + 0.492221i 0.297191 + 0.0207816i
\(562\) −0.282229 + 2.68523i −0.0119051 + 0.113270i
\(563\) 4.37065 1.94594i 0.184201 0.0820114i −0.312564 0.949897i \(-0.601188\pi\)
0.496765 + 0.867885i \(0.334521\pi\)
\(564\) 4.77231 7.07524i 0.200950 0.297921i
\(565\) −3.57622 24.0797i −0.150453 1.01304i
\(566\) 18.6201 17.9812i 0.782661 0.755807i
\(567\) 0.310789 8.89982i 0.0130519 0.373757i
\(568\) −5.24419 + 4.40039i −0.220041 + 0.184636i
\(569\) 3.68570 + 11.3434i 0.154513 + 0.475541i 0.998111 0.0614336i \(-0.0195672\pi\)
−0.843599 + 0.536974i \(0.819567\pi\)
\(570\) −10.3810 + 5.64606i −0.434812 + 0.236488i
\(571\) −9.93584 + 30.5794i −0.415802 + 1.27971i 0.495730 + 0.868477i \(0.334901\pi\)
−0.911532 + 0.411230i \(0.865099\pi\)
\(572\) −5.38496 13.3282i −0.225157 0.557282i
\(573\) −23.6348 + 6.77716i −0.987357 + 0.283120i
\(574\) −5.51503 + 31.2773i −0.230193 + 1.30549i
\(575\) −5.33290 + 2.47491i −0.222397 + 0.103211i
\(576\) 8.97387 3.26622i 0.373911 0.136093i
\(577\) −3.56825 33.9496i −0.148548 1.41334i −0.774053 0.633121i \(-0.781774\pi\)
0.625505 0.780220i \(-0.284893\pi\)
\(578\) −15.0217 + 3.19296i −0.624821 + 0.132810i
\(579\) −2.90675 + 1.81634i −0.120800 + 0.0754845i
\(580\) 13.7147 + 12.1562i 0.569473 + 0.504757i
\(581\) −14.6305 + 16.2488i −0.606975 + 0.674114i
\(582\) 7.90398 13.6901i 0.327630 0.567472i
\(583\) −3.35438 4.29341i −0.138924 0.177815i
\(584\) 9.00047 18.4537i 0.372442 0.763619i
\(585\) −6.32942 + 5.78920i −0.261689 + 0.239354i
\(586\) −0.130228 + 0.0373423i −0.00537967 + 0.00154260i
\(587\) −17.1286 + 1.19775i −0.706975 + 0.0494365i −0.418718 0.908116i \(-0.637520\pi\)
−0.288257 + 0.957553i \(0.593076\pi\)
\(588\) 5.33286 + 3.87455i 0.219924 + 0.159784i
\(589\) −14.3254 32.0346i −0.590267 1.31996i
\(590\) −12.2081 + 8.37397i −0.502600 + 0.344751i
\(591\) −14.2162 + 0.994095i −0.584777 + 0.0408916i
\(592\) 0.153807 4.40445i 0.00632143 0.181022i
\(593\) −5.65771 + 32.0865i −0.232334 + 1.31763i 0.615821 + 0.787886i \(0.288825\pi\)
−0.848155 + 0.529748i \(0.822286\pi\)
\(594\) 24.4802 13.0164i 1.00444 0.534068i
\(595\) 8.13540 + 2.57327i 0.333519 + 0.105494i
\(596\) −16.9066 18.7767i −0.692521 0.769123i
\(597\) −14.5031 + 3.08272i −0.593571 + 0.126167i
\(598\) 3.02597 + 0.211596i 0.123741 + 0.00865282i
\(599\) 29.0442 + 24.3709i 1.18671 + 0.995769i 0.999911 + 0.0133717i \(0.00425647\pi\)
0.186801 + 0.982398i \(0.440188\pi\)
\(600\) −18.2899 + 2.86255i −0.746684 + 0.116863i
\(601\) −23.9049 + 41.4046i −0.975103 + 1.68893i −0.295506 + 0.955341i \(0.595488\pi\)
−0.679596 + 0.733586i \(0.737845\pi\)
\(602\) 12.3517 18.3122i 0.503418 0.746348i
\(603\) 7.47141 + 1.05004i 0.304259 + 0.0427609i
\(604\) −3.60592 1.91730i −0.146723 0.0780139i
\(605\) −2.14080 + 34.4841i −0.0870359 + 1.40198i
\(606\) −2.62865 1.64256i −0.106781 0.0667244i
\(607\) −46.5402 −1.88901 −0.944505 0.328498i \(-0.893458\pi\)
−0.944505 + 0.328498i \(0.893458\pi\)
\(608\) 18.7419 + 12.5971i 0.760083 + 0.510880i
\(609\) 27.1870 + 19.7525i 1.10167 + 0.800414i
\(610\) −8.84301 5.86470i −0.358043 0.237455i
\(611\) −16.5635 + 4.74951i −0.670087 + 0.192144i
\(612\) −1.20694 + 1.16552i −0.0487875 + 0.0471135i
\(613\) 20.4187 41.8645i 0.824702 1.69089i 0.107305 0.994226i \(-0.465778\pi\)
0.717397 0.696664i \(-0.245333\pi\)
\(614\) 13.3452 19.7850i 0.538567 0.798459i
\(615\) 17.0300 + 19.9766i 0.686717 + 0.805533i
\(616\) −5.53612 + 52.6727i −0.223057 + 2.12224i
\(617\) 15.5826 38.5683i 0.627331 1.55270i −0.193237 0.981152i \(-0.561899\pi\)
0.820569 0.571548i \(-0.193657\pi\)
\(618\) −3.31725 2.78350i −0.133439 0.111969i
\(619\) 13.2993 14.7703i 0.534542 0.593669i −0.414017 0.910269i \(-0.635875\pi\)
0.948559 + 0.316600i \(0.102541\pi\)
\(620\) −1.47117 18.9142i −0.0590837 0.759611i
\(621\) −0.227429 6.51271i −0.00912641 0.261346i
\(622\) 31.1851 + 4.38278i 1.25041 + 0.175734i
\(623\) 6.77159 + 13.8838i 0.271298 + 0.556243i
\(624\) 2.42810 + 0.883755i 0.0972017 + 0.0353785i
\(625\) −24.9814 0.963892i −0.999256 0.0385557i
\(626\) 31.9835 1.27832
\(627\) 25.1349 + 12.2084i 1.00379 + 0.487556i
\(628\) −1.97231 + 6.07014i −0.0787036 + 0.242225i
\(629\) 2.32488 + 5.75429i 0.0926992 + 0.229438i
\(630\) 10.5612 2.72100i 0.420767 0.108407i
\(631\) 38.6166 5.42721i 1.53730 0.216054i 0.680906 0.732371i \(-0.261586\pi\)
0.856397 + 0.516317i \(0.172697\pi\)
\(632\) 2.17689 + 12.3457i 0.0865919 + 0.491087i
\(633\) 2.87225 + 3.67632i 0.114162 + 0.146121i
\(634\) −6.23719 + 2.77698i −0.247711 + 0.110288i
\(635\) 23.9145 4.40967i 0.949019 0.174993i
\(636\) −1.38816 0.0970698i −0.0550443 0.00384907i
\(637\) −3.21975 12.9137i −0.127571 0.511659i
\(638\) −4.06678 + 38.6928i −0.161005 + 1.53186i
\(639\) −0.348432 3.31511i −0.0137838 0.131144i
\(640\) 5.23276 + 7.08521i 0.206843 + 0.280068i
\(641\) 14.7091 30.1582i 0.580976 1.19118i −0.382643 0.923896i \(-0.624986\pi\)
0.963619 0.267281i \(-0.0861251\pi\)
\(642\) 18.1640 2.55278i 0.716876 0.100750i
\(643\) −15.3315 5.58022i −0.604617 0.220063i 0.0215293 0.999768i \(-0.493146\pi\)
−0.626146 + 0.779706i \(0.715369\pi\)
\(644\) 3.64311 + 2.27647i 0.143559 + 0.0897054i
\(645\) −5.16919 17.5097i −0.203537 0.689443i
\(646\) 4.59737 + 0.802907i 0.180881 + 0.0315900i
\(647\) −10.2385 + 31.5109i −0.402517 + 1.23882i 0.520433 + 0.853902i \(0.325771\pi\)
−0.922950 + 0.384919i \(0.874229\pi\)
\(648\) 1.84598 7.40384i 0.0725171 0.290850i
\(649\) 32.8951 + 11.9728i 1.29124 + 0.469974i
\(650\) 11.0442 + 6.66353i 0.433188 + 0.261365i
\(651\) −6.04072 34.2586i −0.236754 1.34270i
\(652\) 12.9043 19.1315i 0.505373 0.749247i
\(653\) 17.9974 + 19.9881i 0.704293 + 0.782197i 0.984053 0.177873i \(-0.0569217\pi\)
−0.279760 + 0.960070i \(0.590255\pi\)
\(654\) −10.2505 + 2.17880i −0.400825 + 0.0851979i
\(655\) −4.71206 21.3471i −0.184116 0.834101i
\(656\) −2.75783 + 6.82587i −0.107675 + 0.266505i
\(657\) 4.99865 + 8.65791i 0.195016 + 0.337777i
\(658\) 21.4296 + 4.55499i 0.835411 + 0.177572i
\(659\) 20.0680 + 5.75439i 0.781736 + 0.224159i 0.642690 0.766127i \(-0.277818\pi\)
0.139047 + 0.990286i \(0.455596\pi\)
\(660\) 10.5784 + 10.7844i 0.411765 + 0.419783i
\(661\) 5.79974 + 11.8912i 0.225584 + 0.462515i 0.981325 0.192355i \(-0.0616124\pi\)
−0.755742 + 0.654870i \(0.772723\pi\)
\(662\) 15.2649 + 22.6311i 0.593287 + 0.879584i
\(663\) −3.62986 + 0.253825i −0.140972 + 0.00985773i
\(664\) −15.1570 + 11.0122i −0.588205 + 0.427356i
\(665\) 26.0882 + 21.4740i 1.01166 + 0.832728i
\(666\) 6.41751 + 4.66259i 0.248673 + 0.180672i
\(667\) 7.75501 + 4.84587i 0.300275 + 0.187633i
\(668\) −13.6208 4.95756i −0.527004 0.191814i
\(669\) −6.77883 + 0.952702i −0.262085 + 0.0368336i
\(670\) −1.66672 11.2225i −0.0643909 0.433562i
\(671\) 0.875666 + 25.0758i 0.0338047 + 0.968040i
\(672\) 14.9791 + 16.6360i 0.577832 + 0.641747i
\(673\) 35.9314 + 15.9977i 1.38505 + 0.616666i 0.957792 0.287461i \(-0.0928113\pi\)
0.427263 + 0.904128i \(0.359478\pi\)
\(674\) −10.8069 9.06809i −0.416267 0.349290i
\(675\) 11.7570 25.0930i 0.452527 0.965831i
\(676\) −3.14372 5.44508i −0.120912 0.209426i
\(677\) −1.35048 12.8490i −0.0519033 0.493827i −0.989335 0.145658i \(-0.953470\pi\)
0.937432 0.348169i \(-0.113196\pi\)
\(678\) −0.460649 13.1913i −0.0176911 0.506607i
\(679\) −44.7611 6.29076i −1.71777 0.241417i
\(680\) 6.36009 + 3.60605i 0.243898 + 0.138286i
\(681\) −0.689895 + 19.7560i −0.0264368 + 0.757052i
\(682\) 30.8520 25.8879i 1.18139 0.991300i
\(683\) 9.76055 + 30.0399i 0.373477 + 1.14944i 0.944500 + 0.328510i \(0.106547\pi\)
−0.571023 + 0.820934i \(0.693453\pi\)
\(684\) −6.15638 + 2.49904i −0.235395 + 0.0955530i
\(685\) −23.9723 0.649678i −0.915933 0.0248229i
\(686\) 1.61671 6.48426i 0.0617262 0.247570i
\(687\) −13.4061 19.8754i −0.511474 0.758292i
\(688\) 3.68310 3.55673i 0.140417 0.135599i
\(689\) 2.02105 + 1.95171i 0.0769959 + 0.0743541i
\(690\) −3.02392 + 1.00871i −0.115119 + 0.0384011i
\(691\) 2.68948 1.19743i 0.102313 0.0455525i −0.354942 0.934888i \(-0.615499\pi\)
0.457255 + 0.889336i \(0.348833\pi\)
\(692\) 14.4380 16.0351i 0.548852 0.609562i
\(693\) −19.7553 16.5767i −0.750443 0.629697i
\(694\) 9.12535 22.5860i 0.346393 0.857354i
\(695\) −39.7125 + 7.32271i −1.50638 + 0.277766i
\(696\) 19.2674 + 21.3986i 0.730327 + 0.811111i
\(697\) −0.361810 10.3609i −0.0137045 0.392446i
\(698\) −21.3106 20.5794i −0.806618 0.778942i
\(699\) 4.26918 24.2117i 0.161475 0.915771i
\(700\) 9.37968 + 15.6753i 0.354519 + 0.592471i
\(701\) 24.8144 20.8217i 0.937226 0.786426i −0.0398747 0.999205i \(-0.512696\pi\)
0.977100 + 0.212779i \(0.0682514\pi\)
\(702\) −11.5668 + 8.40374i −0.436559 + 0.317179i
\(703\) 0.0401086 + 24.5766i 0.00151273 + 0.926924i
\(704\) −10.4934 + 32.2953i −0.395484 + 1.21717i
\(705\) 14.1817 11.2595i 0.534113 0.424056i
\(706\) 0.0176666 0.505907i 0.000664893 0.0190400i
\(707\) −1.53905 + 8.72841i −0.0578821 + 0.328266i
\(708\) 7.89423 4.19744i 0.296683 0.157749i
\(709\) −0.979517 0.280872i −0.0367865 0.0105484i 0.257194 0.966360i \(-0.417202\pi\)
−0.293980 + 0.955812i \(0.594980\pi\)
\(710\) −4.63275 + 1.91399i −0.173864 + 0.0718307i
\(711\) −5.57642 2.48278i −0.209132 0.0931116i
\(712\) 3.20207 + 12.8428i 0.120003 + 0.481304i
\(713\) −2.29008 9.18502i −0.0857643 0.343982i
\(714\) 4.22647 + 1.88175i 0.158172 + 0.0704226i
\(715\) −2.36524 30.4087i −0.0884548 1.13722i
\(716\) 9.55801 + 2.74072i 0.357200 + 0.102425i
\(717\) −30.0581 + 15.9822i −1.12254 + 0.596865i
\(718\) −2.45951 + 13.9486i −0.0917881 + 0.520556i
\(719\) 0.00452713 0.129640i 0.000168833 0.00483476i −0.999303 0.0373168i \(-0.988119\pi\)
0.999472 + 0.0324820i \(0.0103412\pi\)
\(720\) 2.52572 0.107961i 0.0941281 0.00402347i
\(721\) −3.82629 + 11.7761i −0.142499 + 0.438566i
\(722\) 15.7048 + 9.74235i 0.584474 + 0.362573i
\(723\) −11.6781 + 8.48467i −0.434315 + 0.315548i
\(724\) 1.06951 0.897429i 0.0397482 0.0333527i
\(725\) 19.9663 + 33.3677i 0.741531 + 1.23924i
\(726\) −3.25303 + 18.4488i −0.120731 + 0.684700i
\(727\) −28.8969 27.9054i −1.07173 1.03495i −0.999294 0.0375800i \(-0.988035\pi\)
−0.0724319 0.997373i \(-0.523076\pi\)
\(728\) −0.953156 27.2948i −0.0353263 1.01161i
\(729\) 16.3531 + 18.1619i 0.605670 + 0.672665i
\(730\) 10.3583 10.8954i 0.383378 0.403257i
\(731\) −2.70100 + 6.68520i −0.0998999 + 0.247261i
\(732\) 4.90912 + 4.11924i 0.181446 + 0.152251i
\(733\) 5.33494 5.92505i 0.197050 0.218847i −0.636519 0.771261i \(-0.719627\pi\)
0.833570 + 0.552414i \(0.186293\pi\)
\(734\) 3.95659 1.76159i 0.146040 0.0650214i
\(735\) 8.30910 + 11.2506i 0.306486 + 0.414985i
\(736\) 4.38194 + 4.23159i 0.161521 + 0.155979i
\(737\) −19.2985 + 18.6363i −0.710868 + 0.686477i
\(738\) −7.40978 10.9855i −0.272758 0.404380i
\(739\) −4.00320 + 16.0560i −0.147260 + 0.590628i 0.850634 + 0.525759i \(0.176219\pi\)
−0.997894 + 0.0648693i \(0.979337\pi\)
\(740\) −4.44662 + 12.5205i −0.163461 + 0.460261i
\(741\) −13.7114 4.43038i −0.503701 0.162754i
\(742\) −1.10389 3.39741i −0.0405249 0.124723i
\(743\) 23.3459 19.5895i 0.856477 0.718670i −0.104729 0.994501i \(-0.533397\pi\)
0.961206 + 0.275831i \(0.0889530\pi\)
\(744\) 1.04027 29.7893i 0.0381380 1.09213i
\(745\) −22.1871 48.8034i −0.812873 1.78802i
\(746\) 13.9618 + 1.96220i 0.511178 + 0.0718414i
\(747\) −0.318371 9.11695i −0.0116486 0.333572i
\(748\) −0.623625 5.93340i −0.0228020 0.216946i
\(749\) −26.2241 45.4215i −0.958208 1.65966i
\(750\) −13.4007 2.04035i −0.489323 0.0745031i
\(751\) 11.2893 + 9.47286i 0.411953 + 0.345669i 0.825092 0.564998i \(-0.191123\pi\)
−0.413139 + 0.910668i \(0.635568\pi\)
\(752\) 4.63931 + 2.06555i 0.169178 + 0.0753230i
\(753\) 17.9693 + 19.9570i 0.654839 + 0.727272i
\(754\) −0.700178 20.0505i −0.0254990 0.730195i
\(755\) −6.06791 6.18606i −0.220834 0.225134i
\(756\) −20.0510 + 2.81798i −0.729246 + 0.102489i
\(757\) 21.4164 + 7.79494i 0.778393 + 0.283312i 0.700502 0.713650i \(-0.252959\pi\)
0.0778907 + 0.996962i \(0.475181\pi\)
\(758\) −10.5814 6.61200i −0.384334 0.240159i
\(759\) 6.09820 + 4.43060i 0.221351 + 0.160821i
\(760\) 18.0397 + 22.6456i 0.654369 + 0.821444i
\(761\) 39.2499 28.5167i 1.42281 1.03373i 0.431509 0.902109i \(-0.357981\pi\)
0.991300 0.131623i \(-0.0420187\pi\)
\(762\) 13.1530 0.919749i 0.476484 0.0333190i
\(763\) 16.7561 + 24.8419i 0.606611 + 0.899337i
\(764\) 9.11308 + 18.6846i 0.329700 + 0.675984i
\(765\) −3.18743 + 1.58555i −0.115242 + 0.0573258i
\(766\) 20.8907 + 5.99031i 0.754811 + 0.216439i
\(767\) −17.6572 3.75316i −0.637566 0.135519i
\(768\) 10.6175 + 18.3900i 0.383126 + 0.663593i
\(769\) −13.7252 + 33.9711i −0.494944 + 1.22503i 0.448586 + 0.893740i \(0.351928\pi\)
−0.943529 + 0.331289i \(0.892517\pi\)
\(770\) −15.4960 + 35.5493i −0.558436 + 1.28111i
\(771\) −16.7561 + 3.56161i −0.603455 + 0.128268i
\(772\) 1.93915 + 2.15365i 0.0697916 + 0.0775114i
\(773\) 4.16102 6.16897i 0.149662 0.221882i −0.746750 0.665105i \(-0.768387\pi\)
0.896412 + 0.443222i \(0.146165\pi\)
\(774\) 1.60030 + 9.07576i 0.0575216 + 0.326221i
\(775\) 9.12668 39.2047i 0.327840 1.40827i
\(776\) −36.3949 13.2467i −1.30650 0.475527i
\(777\) −5.89402 + 23.6396i −0.211447 + 0.848066i
\(778\) 6.63039 20.4062i 0.237711 0.731599i
\(779\) 13.9784 38.6012i 0.500828 1.38303i
\(780\) −6.17589 4.74791i −0.221132 0.170002i
\(781\) 10.0518 + 6.28105i 0.359681 + 0.224754i
\(782\) 1.18302 + 0.430583i 0.0423046 + 0.0153976i
\(783\) −42.6820 + 5.99857i −1.52533 + 0.214371i
\(784\) −1.71950 + 3.52549i −0.0614106 + 0.125910i
\(785\) −7.87415 + 11.0178i −0.281040 + 0.393243i
\(786\) −1.23899 11.7882i −0.0441933 0.420471i
\(787\) 3.45177 32.8414i 0.123042 1.17067i −0.742504 0.669842i \(-0.766362\pi\)
0.865546 0.500829i \(-0.166971\pi\)
\(788\) 2.91496 + 11.6912i 0.103841 + 0.416483i
\(789\) 11.4782 + 0.802633i 0.408634 + 0.0285745i
\(790\) −1.20644 + 9.09950i −0.0429232 + 0.323746i
\(791\) −34.4789 + 15.3510i −1.22593 + 0.545818i
\(792\) −13.6044 17.4128i −0.483411 0.618738i
\(793\) −2.24679 12.7422i −0.0797860 0.452489i
\(794\) −3.80298 + 0.534474i −0.134963 + 0.0189678i
\(795\) −2.74614 1.08463i −0.0973954 0.0384680i
\(796\) 4.69617 + 11.6234i 0.166451 + 0.411982i
\(797\) −1.18629 + 3.65103i −0.0420206 + 0.129326i −0.969866 0.243639i \(-0.921659\pi\)
0.927845 + 0.372965i \(0.121659\pi\)
\(798\) 12.7482 + 13.1581i 0.451281 + 0.465791i
\(799\) −7.15142 −0.252999
\(800\) 8.38846 + 24.5074i 0.296577 + 0.866468i
\(801\) −6.05621 2.20428i −0.213985 0.0778843i
\(802\) 8.66322 + 17.7622i 0.305909 + 0.627206i
\(803\) −35.2026 4.94740i −1.24227 0.174590i
\(804\) 0.239132 + 6.84785i 0.00843354 + 0.241505i
\(805\) 5.91333 + 6.93645i 0.208417 + 0.244478i
\(806\) −13.8968 + 15.4339i −0.489493 + 0.543637i
\(807\) −16.5819 13.9139i −0.583712 0.489792i
\(808\) −2.84489 + 7.04135i −0.100083 + 0.247714i
\(809\) 0.983435 9.35676i 0.0345757 0.328966i −0.963538 0.267572i \(-0.913779\pi\)
0.998114 0.0613941i \(-0.0195547\pi\)
\(810\) 2.92362 4.76113i 0.102726 0.167289i
\(811\) 9.88741 14.6587i 0.347194 0.514736i −0.614480 0.788933i \(-0.710634\pi\)
0.961674 + 0.274196i \(0.0884118\pi\)
\(812\) 12.4555 25.5375i 0.437101 0.896190i
\(813\) −7.94234 + 7.66982i −0.278550 + 0.268993i
\(814\) −27.1137 + 7.77474i −0.950336 + 0.272504i
\(815\) 38.3474 30.4456i 1.34325 1.06646i
\(816\) 0.867600 + 0.630348i 0.0303721 + 0.0220666i
\(817\) −19.8007 + 20.5713i −0.692740 + 0.719700i
\(818\) −31.5937 −1.10465
\(819\) 11.2778 + 7.04715i 0.394078 + 0.246247i
\(820\) 14.1332 17.1131i 0.493554 0.597615i
\(821\) 46.7776 + 24.8721i 1.63255 + 0.868042i 0.995242 + 0.0974327i \(0.0310631\pi\)
0.637308 + 0.770609i \(0.280048\pi\)
\(822\) −12.8761 1.80962i −0.449105 0.0631176i
\(823\) 30.4382 45.1265i 1.06101 1.57301i 0.268376 0.963314i \(-0.413513\pi\)
0.792634 0.609698i \(-0.208709\pi\)
\(824\) −5.30485 + 9.18826i −0.184803 + 0.320088i
\(825\) 14.4994 + 28.5858i 0.504804 + 0.995230i
\(826\) 17.5821 + 14.7531i 0.611759 + 0.513327i
\(827\) 14.2431 + 0.995973i 0.495280 + 0.0346334i 0.315213 0.949021i \(-0.397924\pi\)
0.180067 + 0.983654i \(0.442368\pi\)
\(828\) −1.75316 + 0.372647i −0.0609267 + 0.0129504i
\(829\) −13.1325 14.5851i −0.456109 0.506560i 0.470597 0.882348i \(-0.344039\pi\)
−0.926706 + 0.375788i \(0.877372\pi\)
\(830\) −13.0131 + 4.34088i −0.451690 + 0.150674i
\(831\) 3.39218 1.80366i 0.117673 0.0625681i
\(832\) 3.04072 17.2448i 0.105418 0.597856i
\(833\) 0.192774 5.52031i 0.00667921 0.191267i
\(834\) −21.8419 + 1.52734i −0.756324 + 0.0528873i
\(835\) −24.3825 18.7448i −0.843793 0.648692i
\(836\) 6.47507 22.7211i 0.223945 0.785827i
\(837\) 36.0964 + 26.2256i 1.24767 + 0.906489i
\(838\) −10.0809 + 0.704924i −0.348238 + 0.0243512i
\(839\) 31.6978 9.08920i 1.09433 0.313794i 0.320539 0.947235i \(-0.396136\pi\)
0.773791 + 0.633441i \(0.218358\pi\)
\(840\) 11.8784 + 26.1280i 0.409842 + 0.901501i
\(841\) 13.8009 28.2960i 0.475893 0.975726i
\(842\) −6.03338 7.72237i −0.207924 0.266131i
\(843\) 1.72994 2.99634i 0.0595823 0.103200i
\(844\) 2.63940 2.93135i 0.0908519 0.100901i
\(845\) −2.87552 13.0270i −0.0989208 0.448142i
\(846\) −7.75167 + 4.84378i −0.266508 + 0.166533i
\(847\) 52.3955 11.1370i 1.80033 0.382672i
\(848\) −0.0865547 0.823513i −0.00297230 0.0282796i
\(849\) −31.1693 + 11.3447i −1.06973 + 0.389349i
\(850\) 3.64382 + 3.92188i 0.124982 + 0.134519i
\(851\) −1.15124 + 6.52898i −0.0394638 + 0.223811i
\(852\) 2.91001 0.834431i 0.0996952 0.0285871i
\(853\) −4.72895 11.7046i −0.161916 0.400757i 0.824314 0.566132i \(-0.191561\pi\)
−0.986231 + 0.165375i \(0.947116\pi\)
\(854\) −5.08363 + 15.6458i −0.173958 + 0.535388i
\(855\) −14.0534 + 1.11617i −0.480617 + 0.0381723i
\(856\) −13.8874 42.7409i −0.474660 1.46085i
\(857\) 3.30450 2.77280i 0.112879 0.0947171i −0.584601 0.811321i \(-0.698749\pi\)
0.697480 + 0.716604i \(0.254304\pi\)
\(858\) 0.577152 16.5275i 0.0197036 0.564239i
\(859\) −5.36438 + 5.18032i −0.183030 + 0.176750i −0.780529 0.625120i \(-0.785050\pi\)
0.597499 + 0.801870i \(0.296161\pi\)
\(860\) −13.8206 + 6.87491i −0.471278 + 0.234433i
\(861\) 22.7579 33.7400i 0.775589 1.14986i
\(862\) −24.7484 + 11.0187i −0.842933 + 0.375298i
\(863\) 2.78439 26.4917i 0.0947818 0.901789i −0.839045 0.544063i \(-0.816885\pi\)
0.933826 0.357726i \(-0.116448\pi\)
\(864\) −28.6420 2.00285i −0.974422 0.0681382i
\(865\) 39.4687 23.2002i 1.34198 0.788831i
\(866\) 0.0393338 0.374236i 0.00133662 0.0127171i
\(867\) 19.2492 + 4.09155i 0.653738 + 0.138956i
\(868\) −27.6387 + 10.0597i −0.938118 + 0.341447i
\(869\) 19.1646 10.1900i 0.650113 0.345671i
\(870\) 8.72571 + 19.1933i 0.295829 + 0.650715i
\(871\) 8.51734 10.9017i 0.288599 0.369390i
\(872\) 9.61818 + 23.8058i 0.325713 + 0.806167i
\(873\) 15.2571 11.0849i 0.516374 0.375168i
\(874\) 3.71033 + 3.32985i 0.125504 + 0.112634i
\(875\) 8.94470 + 37.7130i 0.302386 + 1.27493i
\(876\) −6.95513 + 5.83605i −0.234992 + 0.197182i
\(877\) −29.6959 + 8.51516i −1.00276 + 0.287537i −0.736553 0.676380i \(-0.763548\pi\)
−0.266206 + 0.963916i \(0.585770\pi\)
\(878\) 18.6524 + 9.91768i 0.629489 + 0.334705i
\(879\) 0.171913 + 0.0241608i 0.00579849 + 0.000814925i
\(880\) −5.22675 + 7.31347i −0.176194 + 0.246537i
\(881\) −9.66406 2.05416i −0.325590 0.0692064i 0.0422167 0.999108i \(-0.486558\pi\)
−0.367807 + 0.929902i \(0.619891\pi\)
\(882\) −3.53005 6.11423i −0.118863 0.205877i
\(883\) 8.77622 21.7219i 0.295343 0.731000i −0.704431 0.709772i \(-0.748798\pi\)
0.999775 0.0212282i \(-0.00675765\pi\)
\(884\) 0.744282 + 2.98515i 0.0250329 + 0.100402i
\(885\) 18.6559 3.44001i 0.627110 0.115635i
\(886\) −0.650195 6.18619i −0.0218437 0.207829i
\(887\) 40.1597 + 11.5156i 1.34843 + 0.386657i 0.870685 0.491841i \(-0.163676\pi\)
0.477747 + 0.878498i \(0.341454\pi\)
\(888\) −9.15134 + 18.7630i −0.307099 + 0.629646i
\(889\) −16.5272 33.8857i −0.554304 1.13649i
\(890\) −0.600499 + 9.67288i −0.0201288 + 0.324236i
\(891\) −13.1793 + 0.921585i −0.441523 + 0.0308743i
\(892\) 1.78853 + 5.50454i 0.0598846 + 0.184306i
\(893\) −26.2749 10.5659i −0.879254 0.353574i
\(894\) −8.98238 27.6449i −0.300416 0.924585i
\(895\) 17.5821 + 11.6605i 0.587704 + 0.389766i
\(896\) 8.40731 10.7609i 0.280869 0.359495i
\(897\) −3.43204 1.82485i −0.114592 0.0609299i
\(898\) 20.0536 + 19.3655i 0.669197 + 0.646236i
\(899\) −58.8339 + 21.4138i −1.96222 + 0.714190i
\(900\) −7.35818 1.98605i −0.245273 0.0662017i
\(901\) 0.583036 + 1.00985i 0.0194237 + 0.0336429i
\(902\) 47.0028 + 3.28675i 1.56502 + 0.109437i
\(903\) −24.0038 + 14.9992i −0.798795 + 0.499143i
\(904\) −31.6325 + 6.72371i −1.05208 + 0.223627i
\(905\) 2.73787 1.13113i 0.0910100 0.0376001i
\(906\) −2.89259 3.70235i −0.0960999 0.123002i
\(907\) −2.33641 13.2504i −0.0775792 0.439973i −0.998713 0.0507263i \(-0.983846\pi\)
0.921133 0.389247i \(-0.127265\pi\)
\(908\) 16.5512 2.32612i 0.549271 0.0771950i
\(909\) −2.06781 3.06566i −0.0685851 0.101682i
\(910\) 5.36178 19.2655i 0.177741 0.638645i
\(911\) −23.8385 + 17.3197i −0.789804 + 0.573826i −0.907905 0.419175i \(-0.862319\pi\)
0.118101 + 0.993002i \(0.462319\pi\)
\(912\) 2.25632 + 3.59779i 0.0747142 + 0.119135i
\(913\) 26.2428 + 19.0665i 0.868511 + 0.631011i
\(914\) −3.20279 + 12.8457i −0.105939 + 0.424898i
\(915\) 7.29529 + 11.4745i 0.241175 + 0.379334i
\(916\) −14.5810 + 14.0807i −0.481771 + 0.465240i
\(917\) −29.9254 + 15.9116i −0.988223 + 0.525448i
\(918\) −5.57598 + 2.02949i −0.184035 + 0.0669832i
\(919\) −40.2126 8.54744i −1.32649 0.281954i −0.510429 0.859920i \(-0.670513\pi\)
−0.816061 + 0.577966i \(0.803847\pi\)
\(920\) 3.72041 + 6.86711i 0.122658 + 0.226402i
\(921\) −25.9344 + 16.2056i −0.854568 + 0.533993i
\(922\) −27.9993 + 17.4959i −0.922109 + 0.576198i
\(923\) −5.58375 2.48605i −0.183791 0.0818292i
\(924\) 11.7103 20.2829i 0.385242 0.667258i
\(925\) −17.0071 + 22.4835i −0.559191 + 0.739254i
\(926\) −1.66952 9.46830i −0.0548637 0.311148i
\(927\) −2.26467 4.64325i −0.0743814 0.152504i
\(928\) 24.8051 31.7490i 0.814266 1.04221i
\(929\) 15.7105 + 38.8848i 0.515445 + 1.27577i 0.930606 + 0.366022i \(0.119281\pi\)
−0.415161 + 0.909748i \(0.636275\pi\)
\(930\) 7.30426 20.5668i 0.239516 0.674411i
\(931\) 8.86427 19.9972i 0.290515 0.655383i
\(932\) −20.7868 −0.680894
\(933\) −34.2223 21.3845i −1.12039 0.700096i
\(934\) 3.83515 + 5.68584i 0.125490 + 0.186046i
\(935\) 2.53509 12.4023i 0.0829063 0.405598i
\(936\) 8.19681 + 7.91557i 0.267921 + 0.258728i
\(937\) −34.5680 9.91221i −1.12929 0.323818i −0.341570 0.939856i \(-0.610959\pi\)
−0.787716 + 0.616039i \(0.788737\pi\)
\(938\) −16.0691 + 7.15441i −0.524674 + 0.233600i
\(939\) −37.4412 16.6699i −1.22185 0.544001i
\(940\) −11.4574 10.1553i −0.373699 0.331230i
\(941\) −11.9924 48.0988i −0.390940 1.56798i −0.767166 0.641448i \(-0.778334\pi\)
0.376226 0.926528i \(-0.377222\pi\)
\(942\) −4.91323 + 5.45669i −0.160082 + 0.177789i
\(943\) 5.53731 9.59091i 0.180320 0.312323i
\(944\) 3.27547 + 4.19240i 0.106607 + 0.136451i
\(945\) −42.3662 7.12951i −1.37817 0.231923i
\(946\) −28.9338 15.3844i −0.940718 0.500189i
\(947\) 2.69321 3.44715i 0.0875175 0.112017i −0.742259 0.670113i \(-0.766246\pi\)
0.829777 + 0.558096i \(0.188468\pi\)
\(948\) 1.34112 5.37896i 0.0435577 0.174700i
\(949\) 18.3314 0.595061
\(950\) 7.59329 + 19.7929i 0.246359 + 0.642165i
\(951\) 8.74889 0.283702
\(952\) 2.74222 10.9984i 0.0888757 0.356461i
\(953\) −9.48512 + 12.1404i −0.307253 + 0.393266i −0.916710 0.399553i \(-0.869165\pi\)
0.609457 + 0.792819i \(0.291388\pi\)
\(954\) 1.31596 + 0.699709i 0.0426058 + 0.0226539i
\(955\) 6.47977 + 43.6301i 0.209681 + 1.41184i
\(956\) 17.7207 + 22.6815i 0.573130 + 0.733573i
\(957\) 24.9275 43.1758i 0.805793 1.39567i
\(958\) 9.67034 10.7400i 0.312435 0.346994i
\(959\) 8.99452 + 36.0751i 0.290448 + 1.16492i
\(960\) 3.96648 + 17.9694i 0.128018 + 0.579960i
\(961\) 30.8889 + 13.7526i 0.996415 + 0.443632i
\(962\) 13.2877 5.91608i 0.428414 0.190742i
\(963\) 21.0348 + 6.03163i 0.677837 + 0.194367i
\(964\) 8.77938 + 8.47815i 0.282765 + 0.273063i
\(965\) 2.54481 + 5.59764i 0.0819204 + 0.180195i
\(966\) 2.76361 + 4.09723i 0.0889178 + 0.131826i
\(967\) −34.0753 21.2926i −1.09579 0.684724i −0.143416 0.989663i \(-0.545809\pi\)
−0.952372 + 0.304938i \(0.901364\pi\)
\(968\) 45.8983 1.47523
\(969\) −4.96340 3.33608i −0.159447 0.107170i
\(970\) −22.4829 17.2844i −0.721881 0.554969i
\(971\) −2.32129 5.74538i −0.0744936 0.184378i 0.885343 0.464939i \(-0.153924\pi\)
−0.959836 + 0.280561i \(0.909479\pi\)
\(972\) 8.71021 11.1486i 0.279380 0.357590i
\(973\) 27.4451 + 56.2707i 0.879848 + 1.80396i
\(974\) 4.12042 + 23.3681i 0.132027 + 0.748761i
\(975\) −9.45570 13.5569i −0.302825 0.434167i
\(976\) −1.90667 + 3.30245i −0.0610310 + 0.105709i
\(977\) 13.7922 + 6.14070i 0.441253 + 0.196458i 0.615323 0.788275i \(-0.289025\pi\)
−0.174071 + 0.984733i \(0.555692\pi\)
\(978\) 22.5143 14.0685i 0.719928 0.449861i
\(979\) 19.4345 12.1440i 0.621130 0.388125i
\(980\) 8.14793 8.57042i 0.260276 0.273772i
\(981\) −12.2287 2.59930i −0.390433 0.0829892i
\(982\) 0.0865126 0.0314880i 0.00276073 0.00100482i
\(983\) −26.4500 + 14.0637i −0.843623 + 0.448563i −0.834245 0.551393i \(-0.814096\pi\)
−0.00937815 + 0.999956i \(0.502985\pi\)
\(984\) 25.0849 24.2242i 0.799677 0.772239i
\(985\) −1.58409 + 25.5166i −0.0504733 + 0.813026i
\(986\) 2.01440 8.07933i 0.0641517 0.257298i
\(987\) −22.7122 16.5014i −0.722939 0.525246i
\(988\) −1.67587 + 12.0673i −0.0533166 + 0.383913i
\(989\) −6.23124 + 4.52726i −0.198142 + 0.143958i
\(990\) −5.65242 15.1603i −0.179646 0.481827i
\(991\) −2.06380 3.05971i −0.0655588 0.0971949i 0.794833 0.606829i \(-0.207559\pi\)
−0.860391 + 0.509634i \(0.829781\pi\)
\(992\) −41.3014 + 5.80454i −1.31132 + 0.184294i
\(993\) −6.07430 34.4491i −0.192762 1.09321i
\(994\) 4.78450 + 6.12388i 0.151755 + 0.194238i
\(995\) 2.06270 + 26.5191i 0.0653919 + 0.840714i
\(996\) 8.10378 1.72251i 0.256778 0.0545799i
\(997\) −17.8511 + 11.1546i −0.565351 + 0.353271i −0.782290 0.622915i \(-0.785948\pi\)
0.216939 + 0.976185i \(0.430393\pi\)
\(998\) 27.4037 + 1.91625i 0.867449 + 0.0606579i
\(999\) −15.6241 27.0617i −0.494324 0.856194i
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 475.2.bc.a.386.32 yes 1152
19.16 even 9 inner 475.2.bc.a.111.32 yes 1152
25.16 even 5 inner 475.2.bc.a.291.32 yes 1152
475.16 even 45 inner 475.2.bc.a.16.32 1152
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
475.2.bc.a.16.32 1152 475.16 even 45 inner
475.2.bc.a.111.32 yes 1152 19.16 even 9 inner
475.2.bc.a.291.32 yes 1152 25.16 even 5 inner
475.2.bc.a.386.32 yes 1152 1.1 even 1 trivial