Properties

Label 231.2.y.b.16.5
Level $231$
Weight $2$
Character 231.16
Analytic conductor $1.845$
Analytic rank $0$
Dimension $64$
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] = [231,2,Mod(4,231)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(231, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("231.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.y (of order \(15\), 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: \(1.84454428669\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(8\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 16.5
Character \(\chi\) \(=\) 231.16
Dual form 231.2.y.b.130.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.300702 + 0.0639162i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(-1.74075 - 0.775034i) q^{4} +(-1.51090 - 1.67802i) q^{5} +(-0.0949980 + 0.292374i) q^{6} +(-2.44866 + 1.00203i) q^{7} +(-0.971327 - 0.705711i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\) \(q+(0.300702 + 0.0639162i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(-1.74075 - 0.775034i) q^{4} +(-1.51090 - 1.67802i) q^{5} +(-0.0949980 + 0.292374i) q^{6} +(-2.44866 + 1.00203i) q^{7} +(-0.971327 - 0.705711i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-0.347077 - 0.601155i) q^{10} +(-3.25302 + 0.646421i) q^{11} +(0.952746 - 1.65021i) q^{12} +(-0.617122 - 1.89931i) q^{13} +(-0.800363 + 0.144804i) q^{14} +(1.82676 - 1.32722i) q^{15} +(2.30307 + 2.55782i) q^{16} +(1.60299 - 0.340727i) q^{17} +(-0.280842 - 0.125039i) q^{18} +(-5.17916 + 2.30591i) q^{19} +(1.32958 + 4.09201i) q^{20} +(-0.740587 - 2.53999i) q^{21} +(-1.01951 - 0.0135404i) q^{22} +(3.28422 - 5.68844i) q^{23} +(0.803376 - 0.892240i) q^{24} +(-0.0103017 + 0.0980145i) q^{25} +(-0.0641735 - 0.610570i) q^{26} +(0.309017 - 0.951057i) q^{27} +(5.03912 + 0.153504i) q^{28} +(5.03842 - 3.66062i) q^{29} +(0.634141 - 0.282338i) q^{30} +(-4.40080 + 4.88759i) q^{31} +(1.72968 + 2.99589i) q^{32} +(-0.302847 - 3.30277i) q^{33} +0.503802 q^{34} +(5.38110 + 2.59493i) q^{35} +(1.54158 + 1.12002i) q^{36} +(1.02681 + 9.76946i) q^{37} +(-1.70477 + 0.362360i) q^{38} +(1.95341 - 0.415210i) q^{39} +(0.283378 + 2.69616i) q^{40} +(-5.78824 - 4.20541i) q^{41} +(-0.0603498 - 0.811115i) q^{42} -5.88634 q^{43} +(6.16371 + 1.39594i) q^{44} +(1.12900 + 1.95548i) q^{45} +(1.35116 - 1.50061i) q^{46} +(-7.36751 + 3.28022i) q^{47} +(-2.78455 + 2.02309i) q^{48} +(4.99187 - 4.90727i) q^{49} +(-0.00936247 + 0.0288147i) q^{50} +(0.171302 + 1.62983i) q^{51} +(-0.397769 + 3.78452i) q^{52} +(2.15711 - 2.39572i) q^{53} +(0.153710 - 0.266234i) q^{54} +(5.99968 + 4.48196i) q^{55} +(3.08559 + 0.754745i) q^{56} +(-1.75191 - 5.39182i) q^{57} +(1.74904 - 0.778721i) q^{58} +(-0.350589 - 0.156092i) q^{59} +(-4.20858 + 0.894561i) q^{60} +(6.29866 + 6.99537i) q^{61} +(-1.63573 + 1.18843i) q^{62} +(2.60348 - 0.471029i) q^{63} +(-1.79857 - 5.53544i) q^{64} +(-2.25467 + 3.90520i) q^{65} +(0.120034 - 1.01251i) q^{66} +(-1.85592 - 3.21455i) q^{67} +(-3.05449 - 0.649253i) q^{68} +(5.31398 + 3.86083i) q^{69} +(1.45225 + 1.12424i) q^{70} +(4.60253 - 14.1651i) q^{71} +(0.803376 + 0.892240i) q^{72} +(-13.7812 - 6.13579i) q^{73} +(-0.315662 + 3.00333i) q^{74} +(-0.0964007 - 0.0204906i) q^{75} +10.8028 q^{76} +(7.31780 - 4.84249i) q^{77} +0.613933 q^{78} +(-1.93625 - 0.411564i) q^{79} +(0.812372 - 7.72920i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-1.47174 - 1.63454i) q^{82} +(-1.80359 + 5.55089i) q^{83} +(-0.679395 + 4.99547i) q^{84} +(-2.99370 - 2.17505i) q^{85} +(-1.77003 - 0.376232i) q^{86} +(3.11391 + 5.39346i) q^{87} +(3.61593 + 1.66780i) q^{88} +(4.24164 - 7.34673i) q^{89} +(0.214505 + 0.660179i) q^{90} +(3.41429 + 4.03238i) q^{91} +(-10.1258 + 7.35679i) q^{92} +(-4.40080 - 4.88759i) q^{93} +(-2.42508 + 0.515468i) q^{94} +(11.6945 + 5.20674i) q^{95} +(-3.16028 + 1.40705i) q^{96} +(-2.84952 - 8.76992i) q^{97} +(1.81472 - 1.15656i) q^{98} +(3.31633 + 0.0440453i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.300702 + 0.0639162i 0.212629 + 0.0451956i 0.312994 0.949755i \(-0.398668\pi\)
−0.100366 + 0.994951i \(0.532001\pi\)
\(3\) −0.104528 + 0.994522i −0.0603495 + 0.574187i
\(4\) −1.74075 0.775034i −0.870377 0.387517i
\(5\) −1.51090 1.67802i −0.675693 0.750433i 0.303618 0.952794i \(-0.401805\pi\)
−0.979311 + 0.202361i \(0.935139\pi\)
\(6\) −0.0949980 + 0.292374i −0.0387828 + 0.119361i
\(7\) −2.44866 + 1.00203i −0.925506 + 0.378732i
\(8\) −0.971327 0.705711i −0.343416 0.249506i
\(9\) −0.978148 0.207912i −0.326049 0.0693039i
\(10\) −0.347077 0.601155i −0.109755 0.190102i
\(11\) −3.25302 + 0.646421i −0.980822 + 0.194903i
\(12\) 0.952746 1.65021i 0.275034 0.476373i
\(13\) −0.617122 1.89931i −0.171159 0.526773i 0.828278 0.560317i \(-0.189321\pi\)
−0.999437 + 0.0335439i \(0.989321\pi\)
\(14\) −0.800363 + 0.144804i −0.213906 + 0.0387005i
\(15\) 1.82676 1.32722i 0.471667 0.342686i
\(16\) 2.30307 + 2.55782i 0.575768 + 0.639456i
\(17\) 1.60299 0.340727i 0.388783 0.0826384i −0.00937299 0.999956i \(-0.502984\pi\)
0.398156 + 0.917318i \(0.369650\pi\)
\(18\) −0.280842 0.125039i −0.0661951 0.0294720i
\(19\) −5.17916 + 2.30591i −1.18818 + 0.529012i −0.903074 0.429484i \(-0.858695\pi\)
−0.285106 + 0.958496i \(0.592029\pi\)
\(20\) 1.32958 + 4.09201i 0.297302 + 0.915002i
\(21\) −0.740587 2.53999i −0.161609 0.554270i
\(22\) −1.01951 0.0135404i −0.217360 0.00288682i
\(23\) 3.28422 5.68844i 0.684807 1.18612i −0.288690 0.957423i \(-0.593220\pi\)
0.973497 0.228699i \(-0.0734470\pi\)
\(24\) 0.803376 0.892240i 0.163988 0.182128i
\(25\) −0.0103017 + 0.0980145i −0.00206035 + 0.0196029i
\(26\) −0.0641735 0.610570i −0.0125855 0.119743i
\(27\) 0.309017 0.951057i 0.0594703 0.183031i
\(28\) 5.03912 + 0.153504i 0.952305 + 0.0290095i
\(29\) 5.03842 3.66062i 0.935611 0.679761i −0.0117495 0.999931i \(-0.503740\pi\)
0.947360 + 0.320170i \(0.103740\pi\)
\(30\) 0.634141 0.282338i 0.115778 0.0515476i
\(31\) −4.40080 + 4.88759i −0.790408 + 0.877837i −0.994883 0.101035i \(-0.967785\pi\)
0.204475 + 0.978872i \(0.434451\pi\)
\(32\) 1.72968 + 2.99589i 0.305767 + 0.529604i
\(33\) −0.302847 3.30277i −0.0527189 0.574938i
\(34\) 0.503802 0.0864013
\(35\) 5.38110 + 2.59493i 0.909571 + 0.438624i
\(36\) 1.54158 + 1.12002i 0.256929 + 0.186670i
\(37\) 1.02681 + 9.76946i 0.168807 + 1.60609i 0.671083 + 0.741382i \(0.265829\pi\)
−0.502277 + 0.864707i \(0.667504\pi\)
\(38\) −1.70477 + 0.362360i −0.276550 + 0.0587825i
\(39\) 1.95341 0.415210i 0.312796 0.0664868i
\(40\) 0.283378 + 2.69616i 0.0448060 + 0.426301i
\(41\) −5.78824 4.20541i −0.903972 0.656774i 0.0355112 0.999369i \(-0.488694\pi\)
−0.939483 + 0.342595i \(0.888694\pi\)
\(42\) −0.0603498 0.811115i −0.00931218 0.125158i
\(43\) −5.88634 −0.897658 −0.448829 0.893618i \(-0.648159\pi\)
−0.448829 + 0.893618i \(0.648159\pi\)
\(44\) 6.16371 + 1.39594i 0.929214 + 0.210446i
\(45\) 1.12900 + 1.95548i 0.168301 + 0.291506i
\(46\) 1.35116 1.50061i 0.199217 0.221253i
\(47\) −7.36751 + 3.28022i −1.07466 + 0.478470i −0.866270 0.499576i \(-0.833489\pi\)
−0.208391 + 0.978046i \(0.566823\pi\)
\(48\) −2.78455 + 2.02309i −0.401915 + 0.292008i
\(49\) 4.99187 4.90727i 0.713124 0.701038i
\(50\) −0.00936247 + 0.0288147i −0.00132405 + 0.00407502i
\(51\) 0.171302 + 1.62983i 0.0239871 + 0.228222i
\(52\) −0.397769 + 3.78452i −0.0551606 + 0.524818i
\(53\) 2.15711 2.39572i 0.296302 0.329077i −0.576550 0.817062i \(-0.695601\pi\)
0.872852 + 0.487985i \(0.162268\pi\)
\(54\) 0.153710 0.266234i 0.0209173 0.0362298i
\(55\) 5.99968 + 4.48196i 0.808997 + 0.604347i
\(56\) 3.08559 + 0.754745i 0.412330 + 0.100857i
\(57\) −1.75191 5.39182i −0.232046 0.714164i
\(58\) 1.74904 0.778721i 0.229660 0.102251i
\(59\) −0.350589 0.156092i −0.0456428 0.0203215i 0.383788 0.923421i \(-0.374619\pi\)
−0.429431 + 0.903100i \(0.641286\pi\)
\(60\) −4.20858 + 0.894561i −0.543325 + 0.115487i
\(61\) 6.29866 + 6.99537i 0.806461 + 0.895666i 0.996282 0.0861529i \(-0.0274574\pi\)
−0.189821 + 0.981819i \(0.560791\pi\)
\(62\) −1.63573 + 1.18843i −0.207738 + 0.150930i
\(63\) 2.60348 0.471029i 0.328008 0.0593441i
\(64\) −1.79857 5.53544i −0.224822 0.691929i
\(65\) −2.25467 + 3.90520i −0.279657 + 0.484380i
\(66\) 0.120034 1.01251i 0.0147751 0.124631i
\(67\) −1.85592 3.21455i −0.226737 0.392719i 0.730102 0.683338i \(-0.239472\pi\)
−0.956839 + 0.290618i \(0.906139\pi\)
\(68\) −3.05449 0.649253i −0.370412 0.0787334i
\(69\) 5.31398 + 3.86083i 0.639728 + 0.464790i
\(70\) 1.45225 + 1.12424i 0.173577 + 0.134373i
\(71\) 4.60253 14.1651i 0.546219 1.68109i −0.171854 0.985122i \(-0.554976\pi\)
0.718073 0.695968i \(-0.245024\pi\)
\(72\) 0.803376 + 0.892240i 0.0946788 + 0.105151i
\(73\) −13.7812 6.13579i −1.61297 0.718140i −0.615426 0.788194i \(-0.711016\pi\)
−0.997543 + 0.0700541i \(0.977683\pi\)
\(74\) −0.315662 + 3.00333i −0.0366950 + 0.349130i
\(75\) −0.0964007 0.0204906i −0.0111314 0.00236605i
\(76\) 10.8028 1.23917
\(77\) 7.31780 4.84249i 0.833941 0.551853i
\(78\) 0.613933 0.0695142
\(79\) −1.93625 0.411564i −0.217846 0.0463045i 0.0976958 0.995216i \(-0.468853\pi\)
−0.315541 + 0.948912i \(0.602186\pi\)
\(80\) 0.812372 7.72920i 0.0908260 0.864151i
\(81\) 0.913545 + 0.406737i 0.101505 + 0.0451930i
\(82\) −1.47174 1.63454i −0.162527 0.180504i
\(83\) −1.80359 + 5.55089i −0.197970 + 0.609290i 0.801959 + 0.597379i \(0.203791\pi\)
−0.999929 + 0.0119105i \(0.996209\pi\)
\(84\) −0.679395 + 4.99547i −0.0741281 + 0.545051i
\(85\) −2.99370 2.17505i −0.324713 0.235918i
\(86\) −1.77003 0.376232i −0.190868 0.0405702i
\(87\) 3.11391 + 5.39346i 0.333847 + 0.578239i
\(88\) 3.61593 + 1.66780i 0.385460 + 0.177789i
\(89\) 4.24164 7.34673i 0.449612 0.778752i −0.548748 0.835988i \(-0.684895\pi\)
0.998361 + 0.0572360i \(0.0182288\pi\)
\(90\) 0.214505 + 0.660179i 0.0226108 + 0.0695890i
\(91\) 3.41429 + 4.03238i 0.357914 + 0.422708i
\(92\) −10.1258 + 7.35679i −1.05568 + 0.766998i
\(93\) −4.40080 4.88759i −0.456342 0.506819i
\(94\) −2.42508 + 0.515468i −0.250128 + 0.0531664i
\(95\) 11.6945 + 5.20674i 1.19983 + 0.534200i
\(96\) −3.16028 + 1.40705i −0.322545 + 0.143606i
\(97\) −2.84952 8.76992i −0.289325 0.890450i −0.985069 0.172161i \(-0.944925\pi\)
0.695744 0.718290i \(-0.255075\pi\)
\(98\) 1.81472 1.15656i 0.183314 0.116831i
\(99\) 3.31633 + 0.0440453i 0.333304 + 0.00442672i
\(100\) 0.0938973 0.162635i 0.00938973 0.0162635i
\(101\) −10.0363 + 11.1464i −0.998647 + 1.10911i −0.00461856 + 0.999989i \(0.501470\pi\)
−0.994029 + 0.109121i \(0.965197\pi\)
\(102\) −0.0526616 + 0.501042i −0.00521428 + 0.0496105i
\(103\) −0.831276 7.90906i −0.0819080 0.779303i −0.955965 0.293480i \(-0.905187\pi\)
0.874057 0.485823i \(-0.161480\pi\)
\(104\) −0.740933 + 2.28036i −0.0726545 + 0.223608i
\(105\) −3.14320 + 5.08037i −0.306745 + 0.495794i
\(106\) 0.801774 0.582523i 0.0778751 0.0565796i
\(107\) −2.36805 + 1.05432i −0.228928 + 0.101925i −0.517995 0.855383i \(-0.673322\pi\)
0.289067 + 0.957309i \(0.406655\pi\)
\(108\) −1.27502 + 1.41606i −0.122689 + 0.136260i
\(109\) −2.88773 5.00169i −0.276594 0.479075i 0.693942 0.720031i \(-0.255872\pi\)
−0.970536 + 0.240956i \(0.922539\pi\)
\(110\) 1.51765 + 1.73121i 0.144702 + 0.165064i
\(111\) −9.82327 −0.932383
\(112\) −8.20246 3.95548i −0.775060 0.373758i
\(113\) −0.120685 0.0876829i −0.0113531 0.00824851i 0.582094 0.813121i \(-0.302233\pi\)
−0.593447 + 0.804873i \(0.702233\pi\)
\(114\) −0.182178 1.73331i −0.0170625 0.162339i
\(115\) −14.5074 + 3.08365i −1.35282 + 0.287552i
\(116\) −11.6078 + 2.46730i −1.07775 + 0.229083i
\(117\) 0.208748 + 1.98611i 0.0192988 + 0.183616i
\(118\) −0.0954461 0.0693456i −0.00878652 0.00638378i
\(119\) −3.58377 + 2.44057i −0.328523 + 0.223727i
\(120\) −2.71101 −0.247480
\(121\) 10.1643 4.20564i 0.924025 0.382331i
\(122\) 1.44690 + 2.50611i 0.130997 + 0.226893i
\(123\) 4.78740 5.31695i 0.431666 0.479413i
\(124\) 11.4488 5.09732i 1.02813 0.457753i
\(125\) −8.95376 + 6.50529i −0.800848 + 0.581850i
\(126\) 0.812980 + 0.0247654i 0.0724260 + 0.00220627i
\(127\) −3.88632 + 11.9609i −0.344856 + 1.06136i 0.616806 + 0.787116i \(0.288426\pi\)
−0.961661 + 0.274241i \(0.911574\pi\)
\(128\) −0.910233 8.66029i −0.0804540 0.765469i
\(129\) 0.615290 5.85409i 0.0541733 0.515424i
\(130\) −0.927589 + 1.03019i −0.0813549 + 0.0903538i
\(131\) 3.43525 5.95003i 0.300139 0.519857i −0.676028 0.736876i \(-0.736300\pi\)
0.976167 + 0.217019i \(0.0696335\pi\)
\(132\) −2.03258 + 5.98403i −0.176913 + 0.520843i
\(133\) 10.3714 10.8361i 0.899315 0.939606i
\(134\) −0.352617 1.08524i −0.0304615 0.0937508i
\(135\) −2.06278 + 0.918410i −0.177536 + 0.0790442i
\(136\) −1.79749 0.800293i −0.154133 0.0686245i
\(137\) −11.2296 + 2.38692i −0.959406 + 0.203928i −0.660895 0.750478i \(-0.729823\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(138\) 1.35116 + 1.50061i 0.115018 + 0.127740i
\(139\) 0.0207711 0.0150911i 0.00176178 0.00128001i −0.586904 0.809657i \(-0.699653\pi\)
0.588666 + 0.808377i \(0.299653\pi\)
\(140\) −7.35601 8.68767i −0.621696 0.734243i
\(141\) −2.49214 7.67002i −0.209876 0.645932i
\(142\) 2.28937 3.96531i 0.192120 0.332761i
\(143\) 3.23526 + 5.77956i 0.270546 + 0.483311i
\(144\) −1.72094 2.98076i −0.143412 0.248397i
\(145\) −13.7551 2.92374i −1.14230 0.242803i
\(146\) −3.75187 2.72589i −0.310507 0.225596i
\(147\) 4.35859 + 5.47747i 0.359491 + 0.451774i
\(148\) 5.78423 17.8020i 0.475461 1.46332i
\(149\) 1.19575 + 1.32802i 0.0979599 + 0.108795i 0.790131 0.612938i \(-0.210012\pi\)
−0.692171 + 0.721733i \(0.743346\pi\)
\(150\) −0.0276782 0.0123231i −0.00225992 0.00100618i
\(151\) −0.670138 + 6.37593i −0.0545350 + 0.518866i 0.932820 + 0.360342i \(0.117340\pi\)
−0.987355 + 0.158524i \(0.949327\pi\)
\(152\) 6.65796 + 1.41519i 0.540032 + 0.114787i
\(153\) −1.63881 −0.132490
\(154\) 2.50999 0.988422i 0.202261 0.0796493i
\(155\) 14.8506 1.19283
\(156\) −3.72221 0.791180i −0.298015 0.0633451i
\(157\) −0.260641 + 2.47984i −0.0208014 + 0.197912i −0.999987 0.00505350i \(-0.998391\pi\)
0.979186 + 0.202966i \(0.0650581\pi\)
\(158\) −0.555930 0.247516i −0.0442274 0.0196913i
\(159\) 2.15711 + 2.39572i 0.171070 + 0.189993i
\(160\) 2.41380 7.42892i 0.190828 0.587307i
\(161\) −2.34195 + 17.2199i −0.184571 + 1.35712i
\(162\) 0.248708 + 0.180697i 0.0195403 + 0.0141969i
\(163\) 10.4068 + 2.21204i 0.815124 + 0.173260i 0.596566 0.802564i \(-0.296531\pi\)
0.218558 + 0.975824i \(0.429865\pi\)
\(164\) 6.81658 + 11.8067i 0.532285 + 0.921946i
\(165\) −5.08454 + 5.49832i −0.395831 + 0.428044i
\(166\) −0.897137 + 1.55389i −0.0696313 + 0.120605i
\(167\) 2.64083 + 8.12765i 0.204354 + 0.628936i 0.999739 + 0.0228324i \(0.00726842\pi\)
−0.795386 + 0.606104i \(0.792732\pi\)
\(168\) −1.07314 + 2.98980i −0.0827948 + 0.230668i
\(169\) 7.29069 5.29700i 0.560823 0.407462i
\(170\) −0.761192 0.845389i −0.0583807 0.0648384i
\(171\) 5.54541 1.17871i 0.424068 0.0901384i
\(172\) 10.2467 + 4.56211i 0.781301 + 0.347858i
\(173\) −15.3453 + 6.83217i −1.16668 + 0.519440i −0.896359 0.443330i \(-0.853797\pi\)
−0.270323 + 0.962770i \(0.587130\pi\)
\(174\) 0.591631 + 1.82085i 0.0448514 + 0.138039i
\(175\) −0.0729881 0.250327i −0.00551738 0.0189229i
\(176\) −9.14537 6.83189i −0.689359 0.514973i
\(177\) 0.191884 0.332352i 0.0144229 0.0249811i
\(178\) 1.74504 1.93807i 0.130797 0.145264i
\(179\) 2.43960 23.2112i 0.182344 1.73489i −0.395256 0.918571i \(-0.629344\pi\)
0.577601 0.816319i \(-0.303989\pi\)
\(180\) −0.449744 4.27903i −0.0335219 0.318940i
\(181\) 2.83082 8.71236i 0.210413 0.647585i −0.789035 0.614349i \(-0.789419\pi\)
0.999448 0.0332358i \(-0.0105812\pi\)
\(182\) 0.768949 + 1.43077i 0.0569983 + 0.106056i
\(183\) −7.61544 + 5.53294i −0.562950 + 0.409007i
\(184\) −7.20445 + 3.20763i −0.531119 + 0.236469i
\(185\) 14.8419 16.4836i 1.09120 1.21190i
\(186\) −1.01094 1.75099i −0.0741254 0.128389i
\(187\) −4.99432 + 2.14460i −0.365221 + 0.156829i
\(188\) 15.3673 1.12078
\(189\) 0.196311 + 2.63846i 0.0142795 + 0.191920i
\(190\) 3.18377 + 2.31315i 0.230975 + 0.167813i
\(191\) 0.867433 + 8.25307i 0.0627652 + 0.597171i 0.980024 + 0.198879i \(0.0637302\pi\)
−0.917259 + 0.398292i \(0.869603\pi\)
\(192\) 5.69311 1.21011i 0.410865 0.0873321i
\(193\) 1.38594 0.294591i 0.0997622 0.0212051i −0.157760 0.987477i \(-0.550427\pi\)
0.257522 + 0.966272i \(0.417094\pi\)
\(194\) −0.296317 2.81926i −0.0212743 0.202411i
\(195\) −3.64813 2.65052i −0.261248 0.189808i
\(196\) −12.4929 + 4.67348i −0.892351 + 0.333820i
\(197\) −14.3611 −1.02319 −0.511594 0.859227i \(-0.670945\pi\)
−0.511594 + 0.859227i \(0.670945\pi\)
\(198\) 0.994413 + 0.225212i 0.0706699 + 0.0160051i
\(199\) 3.32092 + 5.75201i 0.235414 + 0.407749i 0.959393 0.282073i \(-0.0910220\pi\)
−0.723979 + 0.689822i \(0.757689\pi\)
\(200\) 0.0791762 0.0879341i 0.00559860 0.00621788i
\(201\) 3.39093 1.50974i 0.239178 0.106489i
\(202\) −3.73037 + 2.71027i −0.262468 + 0.190694i
\(203\) −8.66931 + 14.0123i −0.608466 + 0.983469i
\(204\) 0.964977 2.96990i 0.0675619 0.207934i
\(205\) 1.68868 + 16.0667i 0.117943 + 1.12215i
\(206\) 0.255551 2.43140i 0.0178051 0.169404i
\(207\) −4.39515 + 4.88130i −0.305484 + 0.339274i
\(208\) 3.43681 5.95273i 0.238300 0.412748i
\(209\) 15.3573 10.8491i 1.06229 0.750447i
\(210\) −1.26988 + 1.32678i −0.0876303 + 0.0915564i
\(211\) 6.53482 + 20.1121i 0.449875 + 1.38457i 0.877048 + 0.480403i \(0.159510\pi\)
−0.427172 + 0.904170i \(0.640490\pi\)
\(212\) −5.61176 + 2.49852i −0.385418 + 0.171599i
\(213\) 13.6064 + 6.05797i 0.932297 + 0.415085i
\(214\) −0.779466 + 0.165681i −0.0532832 + 0.0113257i
\(215\) 8.89364 + 9.87739i 0.606541 + 0.673632i
\(216\) −0.971327 + 0.705711i −0.0660905 + 0.0480175i
\(217\) 5.87856 16.3778i 0.399062 1.11180i
\(218\) −0.548657 1.68859i −0.0371597 0.114366i
\(219\) 7.54271 13.0644i 0.509689 0.882807i
\(220\) −6.97030 12.4519i −0.469938 0.839510i
\(221\) −1.63639 2.83431i −0.110075 0.190656i
\(222\) −2.95388 0.627866i −0.198251 0.0421396i
\(223\) 4.08950 + 2.97120i 0.273854 + 0.198966i 0.716232 0.697862i \(-0.245865\pi\)
−0.442379 + 0.896828i \(0.645865\pi\)
\(224\) −7.23737 5.60273i −0.483567 0.374348i
\(225\) 0.0304550 0.0937307i 0.00203033 0.00624872i
\(226\) −0.0306859 0.0340802i −0.00204120 0.00226698i
\(227\) 10.0272 + 4.46438i 0.665525 + 0.296311i 0.711556 0.702629i \(-0.247991\pi\)
−0.0460310 + 0.998940i \(0.514657\pi\)
\(228\) −1.12920 + 10.7436i −0.0747831 + 0.711514i
\(229\) 18.3630 + 3.90318i 1.21346 + 0.257930i 0.769812 0.638270i \(-0.220350\pi\)
0.443651 + 0.896200i \(0.353683\pi\)
\(230\) −4.55951 −0.300645
\(231\) 4.05105 + 7.78390i 0.266539 + 0.512143i
\(232\) −7.47730 −0.490908
\(233\) −5.73002 1.21795i −0.375386 0.0797907i 0.0163552 0.999866i \(-0.494794\pi\)
−0.391741 + 0.920076i \(0.628127\pi\)
\(234\) −0.0641735 + 0.610570i −0.00419515 + 0.0399142i
\(235\) 16.6358 + 7.40674i 1.08520 + 0.483162i
\(236\) 0.489313 + 0.543437i 0.0318515 + 0.0353747i
\(237\) 0.611703 1.88263i 0.0397344 0.122290i
\(238\) −1.23364 + 0.504825i −0.0799649 + 0.0327229i
\(239\) 20.5004 + 14.8944i 1.32606 + 0.963441i 0.999835 + 0.0181490i \(0.00577732\pi\)
0.326227 + 0.945292i \(0.394223\pi\)
\(240\) 7.60195 + 1.61584i 0.490704 + 0.104302i
\(241\) 0.880956 + 1.52586i 0.0567473 + 0.0982893i 0.893004 0.450050i \(-0.148594\pi\)
−0.836256 + 0.548339i \(0.815260\pi\)
\(242\) 3.32523 0.614984i 0.213754 0.0395327i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −5.54277 17.0589i −0.354840 1.09208i
\(245\) −15.7767 0.962085i −1.00793 0.0614654i
\(246\) 1.77942 1.29283i 0.113452 0.0824276i
\(247\) 7.57580 + 8.41378i 0.482037 + 0.535356i
\(248\) 7.72385 1.64175i 0.490465 0.104251i
\(249\) −5.33196 2.37394i −0.337899 0.150442i
\(250\) −3.10821 + 1.38386i −0.196580 + 0.0875232i
\(251\) 0.560761 + 1.72584i 0.0353949 + 0.108934i 0.967193 0.254043i \(-0.0817604\pi\)
−0.931798 + 0.362977i \(0.881760\pi\)
\(252\) −4.89709 1.19784i −0.308488 0.0754570i
\(253\) −7.00651 + 20.6276i −0.440495 + 1.29685i
\(254\) −1.93312 + 3.34826i −0.121295 + 0.210089i
\(255\) 2.47606 2.74995i 0.155057 0.172208i
\(256\) −0.936950 + 8.91449i −0.0585594 + 0.557155i
\(257\) 0.0410324 + 0.390397i 0.00255953 + 0.0243523i 0.995727 0.0923445i \(-0.0294361\pi\)
−0.993168 + 0.116697i \(0.962769\pi\)
\(258\) 0.559190 1.72101i 0.0348137 0.107145i
\(259\) −12.3036 22.8932i −0.764509 1.42251i
\(260\) 6.95148 5.05055i 0.431113 0.313222i
\(261\) −5.68940 + 2.53309i −0.352165 + 0.156794i
\(262\) 1.41329 1.56962i 0.0873134 0.0969714i
\(263\) 0.210710 + 0.364960i 0.0129929 + 0.0225044i 0.872449 0.488706i \(-0.162531\pi\)
−0.859456 + 0.511210i \(0.829197\pi\)
\(264\) −2.03664 + 3.42179i −0.125346 + 0.210597i
\(265\) −7.27923 −0.447160
\(266\) 3.81130 2.59553i 0.233686 0.159142i
\(267\) 6.86311 + 4.98634i 0.420016 + 0.305159i
\(268\) 0.739317 + 7.03414i 0.0451610 + 0.429678i
\(269\) 0.968172 0.205791i 0.0590305 0.0125473i −0.178302 0.983976i \(-0.557060\pi\)
0.237332 + 0.971429i \(0.423727\pi\)
\(270\) −0.678985 + 0.144323i −0.0413217 + 0.00878320i
\(271\) −2.16837 20.6306i −0.131719 1.25322i −0.838150 0.545440i \(-0.816363\pi\)
0.706431 0.707782i \(-0.250304\pi\)
\(272\) 4.56333 + 3.31545i 0.276693 + 0.201029i
\(273\) −4.36718 + 2.97408i −0.264314 + 0.180000i
\(274\) −3.52932 −0.213214
\(275\) −0.0298469 0.325502i −0.00179984 0.0196285i
\(276\) −6.25806 10.8393i −0.376691 0.652448i
\(277\) 16.2369 18.0329i 0.975579 1.08349i −0.0209117 0.999781i \(-0.506657\pi\)
0.996490 0.0837085i \(-0.0266764\pi\)
\(278\) 0.00721048 0.00321031i 0.000432456 0.000192542i
\(279\) 5.32082 3.86580i 0.318549 0.231440i
\(280\) −3.39553 6.31803i −0.202922 0.377574i
\(281\) −4.53606 + 13.9606i −0.270599 + 0.832818i 0.719752 + 0.694232i \(0.244256\pi\)
−0.990350 + 0.138586i \(0.955744\pi\)
\(282\) −0.259153 2.46568i −0.0154324 0.146829i
\(283\) 0.697830 6.63941i 0.0414817 0.394672i −0.954006 0.299786i \(-0.903085\pi\)
0.995488 0.0948858i \(-0.0302486\pi\)
\(284\) −18.9903 + 21.0909i −1.12687 + 1.25151i
\(285\) −6.40063 + 11.0862i −0.379140 + 0.656691i
\(286\) 0.603443 + 1.94471i 0.0356823 + 0.114993i
\(287\) 18.3874 + 4.49761i 1.08537 + 0.265485i
\(288\) −1.06900 3.29005i −0.0629915 0.193868i
\(289\) −13.0768 + 5.82216i −0.769222 + 0.342480i
\(290\) −3.94932 1.75835i −0.231912 0.103254i
\(291\) 9.01973 1.91720i 0.528746 0.112388i
\(292\) 19.2343 + 21.3618i 1.12560 + 1.25011i
\(293\) 18.0644 13.1246i 1.05534 0.766747i 0.0821164 0.996623i \(-0.473832\pi\)
0.973220 + 0.229876i \(0.0738321\pi\)
\(294\) 0.960539 + 1.92567i 0.0560197 + 0.112307i
\(295\) 0.267777 + 0.824134i 0.0155906 + 0.0479830i
\(296\) 5.89704 10.2140i 0.342758 0.593675i
\(297\) −0.390455 + 3.29356i −0.0226565 + 0.191112i
\(298\) 0.274684 + 0.475766i 0.0159120 + 0.0275604i
\(299\) −12.8309 2.72728i −0.742027 0.157723i
\(300\) 0.151929 + 0.110383i 0.00877163 + 0.00637296i
\(301\) 14.4136 5.89829i 0.830788 0.339972i
\(302\) −0.609037 + 1.87442i −0.0350462 + 0.107861i
\(303\) −10.0363 11.1464i −0.576569 0.640345i
\(304\) −17.8261 7.93669i −1.02240 0.455200i
\(305\) 2.22175 21.1386i 0.127217 1.21039i
\(306\) −0.492792 0.104746i −0.0281711 0.00598795i
\(307\) −21.1755 −1.20855 −0.604275 0.796776i \(-0.706537\pi\)
−0.604275 + 0.796776i \(0.706537\pi\)
\(308\) −16.4916 + 2.75805i −0.939696 + 0.157154i
\(309\) 7.95263 0.452409
\(310\) 4.46562 + 0.949196i 0.253630 + 0.0539107i
\(311\) 2.81595 26.7920i 0.159678 1.51923i −0.562078 0.827085i \(-0.689998\pi\)
0.721755 0.692148i \(-0.243336\pi\)
\(312\) −2.19042 0.975237i −0.124008 0.0552119i
\(313\) −1.70023 1.88830i −0.0961027 0.106733i 0.693175 0.720769i \(-0.256211\pi\)
−0.789278 + 0.614037i \(0.789545\pi\)
\(314\) −0.236877 + 0.729033i −0.0133678 + 0.0411417i
\(315\) −4.72399 3.65702i −0.266167 0.206050i
\(316\) 3.05157 + 2.21709i 0.171664 + 0.124721i
\(317\) −25.2405 5.36503i −1.41765 0.301330i −0.565550 0.824714i \(-0.691336\pi\)
−0.852097 + 0.523384i \(0.824669\pi\)
\(318\) 0.495523 + 0.858272i 0.0277876 + 0.0481295i
\(319\) −14.0238 + 15.1650i −0.785180 + 0.849078i
\(320\) −6.57111 + 11.3815i −0.367336 + 0.636245i
\(321\) −0.801019 2.46528i −0.0447085 0.137599i
\(322\) −1.80486 + 5.02838i −0.100581 + 0.280221i
\(323\) −7.51647 + 5.46104i −0.418228 + 0.303860i
\(324\) −1.27502 1.41606i −0.0708346 0.0786698i
\(325\) 0.192517 0.0409207i 0.0106789 0.00226987i
\(326\) 2.98797 + 1.33033i 0.165488 + 0.0736801i
\(327\) 5.27614 2.34909i 0.291771 0.129905i
\(328\) 2.65448 + 8.16965i 0.146569 + 0.451094i
\(329\) 14.7536 15.4146i 0.813394 0.849836i
\(330\) −1.88036 + 1.32837i −0.103511 + 0.0731245i
\(331\) 1.33321 2.30918i 0.0732797 0.126924i −0.827057 0.562118i \(-0.809987\pi\)
0.900337 + 0.435194i \(0.143320\pi\)
\(332\) 7.44175 8.26490i 0.408419 0.453595i
\(333\) 1.02681 9.76946i 0.0562689 0.535363i
\(334\) 0.274616 + 2.61279i 0.0150263 + 0.142966i
\(335\) −2.58997 + 7.97111i −0.141505 + 0.435508i
\(336\) 4.79121 7.74407i 0.261382 0.422473i
\(337\) −20.4033 + 14.8238i −1.11144 + 0.807506i −0.982889 0.184197i \(-0.941031\pi\)
−0.128547 + 0.991703i \(0.541031\pi\)
\(338\) 2.53089 1.12683i 0.137662 0.0612912i
\(339\) 0.0998176 0.110859i 0.00542135 0.00602102i
\(340\) 3.52556 + 6.10645i 0.191200 + 0.331169i
\(341\) 11.1565 18.7442i 0.604156 1.01506i
\(342\) 1.74285 0.0942428
\(343\) −7.30615 + 17.0182i −0.394495 + 0.918898i
\(344\) 5.71756 + 4.15405i 0.308270 + 0.223971i
\(345\) −1.55032 14.7503i −0.0834663 0.794128i
\(346\) −5.05105 + 1.07363i −0.271546 + 0.0577189i
\(347\) −15.1692 + 3.22431i −0.814325 + 0.173090i −0.596205 0.802832i \(-0.703326\pi\)
−0.218119 + 0.975922i \(0.569992\pi\)
\(348\) −1.24045 11.8021i −0.0664950 0.632657i
\(349\) −1.52886 1.11078i −0.0818380 0.0594588i 0.546114 0.837711i \(-0.316107\pi\)
−0.627952 + 0.778252i \(0.716107\pi\)
\(350\) −0.00594774 0.0799389i −0.000317920 0.00427291i
\(351\) −1.99705 −0.106595
\(352\) −7.56329 8.62760i −0.403125 0.459853i
\(353\) −0.150952 0.261456i −0.00803435 0.0139159i 0.861980 0.506942i \(-0.169224\pi\)
−0.870015 + 0.493026i \(0.835891\pi\)
\(354\) 0.0789426 0.0876746i 0.00419575 0.00465985i
\(355\) −30.7233 + 13.6789i −1.63062 + 0.726000i
\(356\) −13.0776 + 9.50144i −0.693112 + 0.503575i
\(357\) −2.05260 3.81924i −0.108635 0.202136i
\(358\) 2.21717 6.82374i 0.117181 0.360646i
\(359\) −3.06004 29.1143i −0.161503 1.53659i −0.712252 0.701924i \(-0.752325\pi\)
0.550750 0.834670i \(-0.314342\pi\)
\(360\) 0.283378 2.69616i 0.0149353 0.142100i
\(361\) 8.79298 9.76559i 0.462788 0.513979i
\(362\) 1.40809 2.43889i 0.0740078 0.128185i
\(363\) 3.12015 + 10.5482i 0.163765 + 0.553637i
\(364\) −2.81820 9.66557i −0.147714 0.506614i
\(365\) 10.5260 + 32.3957i 0.550956 + 1.69567i
\(366\) −2.64362 + 1.17702i −0.138184 + 0.0615237i
\(367\) −7.86134 3.50009i −0.410359 0.182703i 0.191166 0.981558i \(-0.438773\pi\)
−0.601525 + 0.798854i \(0.705440\pi\)
\(368\) 22.1138 4.70044i 1.15276 0.245027i
\(369\) 4.78740 + 5.31695i 0.249222 + 0.276789i
\(370\) 5.51657 4.00803i 0.286793 0.208367i
\(371\) −2.88145 + 8.02779i −0.149598 + 0.416782i
\(372\) 3.87267 + 11.9189i 0.200789 + 0.617964i
\(373\) −16.2298 + 28.1108i −0.840345 + 1.45552i 0.0492588 + 0.998786i \(0.484314\pi\)
−0.889603 + 0.456734i \(0.849019\pi\)
\(374\) −1.63888 + 0.325668i −0.0847443 + 0.0168399i
\(375\) −5.53373 9.58470i −0.285760 0.494952i
\(376\) 9.47115 + 2.01316i 0.488437 + 0.103821i
\(377\) −10.0620 7.31045i −0.518218 0.376507i
\(378\) −0.109609 + 0.805938i −0.00563769 + 0.0414530i
\(379\) −7.13465 + 21.9582i −0.366482 + 1.12792i 0.582565 + 0.812784i \(0.302049\pi\)
−0.949048 + 0.315133i \(0.897951\pi\)
\(380\) −16.3219 18.1273i −0.837296 0.929911i
\(381\) −11.4891 5.11529i −0.588606 0.262064i
\(382\) −0.266666 + 2.53716i −0.0136438 + 0.129812i
\(383\) −1.11473 0.236944i −0.0569602 0.0121073i 0.179343 0.983787i \(-0.442603\pi\)
−0.236304 + 0.971679i \(0.575936\pi\)
\(384\) 8.70800 0.444378
\(385\) −19.1822 4.96292i −0.977617 0.252934i
\(386\) 0.435584 0.0221707
\(387\) 5.75771 + 1.22384i 0.292681 + 0.0622112i
\(388\) −1.83667 + 17.4747i −0.0932428 + 0.887146i
\(389\) 1.09701 + 0.488420i 0.0556206 + 0.0247639i 0.434358 0.900740i \(-0.356975\pi\)
−0.378738 + 0.925504i \(0.623642\pi\)
\(390\) −0.927589 1.03019i −0.0469703 0.0521658i
\(391\) 3.32638 10.2376i 0.168222 0.517735i
\(392\) −8.31185 + 1.24375i −0.419812 + 0.0628187i
\(393\) 5.55836 + 4.03838i 0.280382 + 0.203709i
\(394\) −4.31843 0.917910i −0.217559 0.0462436i
\(395\) 2.23487 + 3.87090i 0.112448 + 0.194766i
\(396\) −5.73878 2.64694i −0.288385 0.133014i
\(397\) −16.1180 + 27.9171i −0.808938 + 1.40112i 0.104663 + 0.994508i \(0.466624\pi\)
−0.913600 + 0.406613i \(0.866710\pi\)
\(398\) 0.630962 + 1.94190i 0.0316273 + 0.0973388i
\(399\) 9.69260 + 11.4473i 0.485237 + 0.573080i
\(400\) −0.274429 + 0.199384i −0.0137215 + 0.00996922i
\(401\) −9.70780 10.7816i −0.484784 0.538408i 0.450279 0.892888i \(-0.351324\pi\)
−0.935063 + 0.354480i \(0.884658\pi\)
\(402\) 1.11616 0.237247i 0.0556689 0.0118328i
\(403\) 11.9989 + 5.34224i 0.597706 + 0.266116i
\(404\) 26.1095 11.6247i 1.29900 0.578351i
\(405\) −0.697760 2.14748i −0.0346720 0.106709i
\(406\) −3.50249 + 3.65941i −0.173826 + 0.181614i
\(407\) −9.65542 31.1165i −0.478602 1.54239i
\(408\) 0.983797 1.70399i 0.0487052 0.0843599i
\(409\) 18.6225 20.6823i 0.920822 1.02268i −0.0788458 0.996887i \(-0.525123\pi\)
0.999667 0.0257892i \(-0.00820986\pi\)
\(410\) −0.519134 + 4.93923i −0.0256382 + 0.243931i
\(411\) −1.20003 11.4175i −0.0591932 0.563186i
\(412\) −4.68274 + 14.4120i −0.230702 + 0.710028i
\(413\) 1.01488 + 0.0309158i 0.0499391 + 0.00152127i
\(414\) −1.63362 + 1.18690i −0.0802883 + 0.0583328i
\(415\) 12.0396 5.36035i 0.590998 0.263129i
\(416\) 4.62270 5.13402i 0.226646 0.251716i
\(417\) 0.0128372 + 0.0222348i 0.000628643 + 0.00108884i
\(418\) 5.31141 2.28076i 0.259790 0.111556i
\(419\) −38.6020 −1.88583 −0.942916 0.333031i \(-0.891929\pi\)
−0.942916 + 0.333031i \(0.891929\pi\)
\(420\) 9.40899 6.40760i 0.459112 0.312659i
\(421\) 21.0498 + 15.2936i 1.02590 + 0.745362i 0.967485 0.252930i \(-0.0813941\pi\)
0.0584188 + 0.998292i \(0.481394\pi\)
\(422\) 0.679544 + 6.46543i 0.0330797 + 0.314732i
\(423\) 7.88851 1.67675i 0.383552 0.0815265i
\(424\) −3.78595 + 0.804727i −0.183862 + 0.0390810i
\(425\) 0.0168825 + 0.160627i 0.000818924 + 0.00779154i
\(426\) 3.70428 + 2.69132i 0.179473 + 0.130395i
\(427\) −22.4329 10.8178i −1.08560 0.523512i
\(428\) 4.93933 0.238752
\(429\) −6.08608 + 2.61341i −0.293839 + 0.126177i
\(430\) 2.04301 + 3.53860i 0.0985228 + 0.170646i
\(431\) 3.19073 3.54366i 0.153692 0.170692i −0.661382 0.750049i \(-0.730030\pi\)
0.815074 + 0.579357i \(0.196696\pi\)
\(432\) 3.14432 1.39994i 0.151281 0.0673548i
\(433\) 13.6207 9.89600i 0.654568 0.475571i −0.210256 0.977646i \(-0.567430\pi\)
0.864824 + 0.502075i \(0.167430\pi\)
\(434\) 2.81450 4.54910i 0.135100 0.218364i
\(435\) 4.34553 13.3742i 0.208352 0.641242i
\(436\) 1.15034 + 10.9448i 0.0550915 + 0.524161i
\(437\) −3.89248 + 37.0344i −0.186202 + 1.77160i
\(438\) 3.10313 3.44638i 0.148273 0.164674i
\(439\) −0.404318 + 0.700299i −0.0192970 + 0.0334235i −0.875513 0.483195i \(-0.839476\pi\)
0.856216 + 0.516619i \(0.172809\pi\)
\(440\) −2.66469 8.58749i −0.127034 0.409392i
\(441\) −5.90306 + 3.76216i −0.281098 + 0.179151i
\(442\) −0.310907 0.956874i −0.0147883 0.0455139i
\(443\) 13.8531 6.16778i 0.658178 0.293040i −0.0503401 0.998732i \(-0.516031\pi\)
0.708518 + 0.705692i \(0.249364\pi\)
\(444\) 17.0999 + 7.61337i 0.811525 + 0.361314i
\(445\) −18.7366 + 3.98259i −0.888201 + 0.188793i
\(446\) 1.03982 + 1.15483i 0.0492367 + 0.0546829i
\(447\) −1.44573 + 1.05039i −0.0683808 + 0.0496816i
\(448\) 9.95077 + 11.7522i 0.470130 + 0.555238i
\(449\) −9.17630 28.2418i −0.433056 1.33281i −0.895065 0.445935i \(-0.852871\pi\)
0.462009 0.886875i \(-0.347129\pi\)
\(450\) 0.0151488 0.0262385i 0.000714121 0.00123689i
\(451\) 21.5477 + 9.93862i 1.01464 + 0.467991i
\(452\) 0.142126 + 0.246170i 0.00668505 + 0.0115788i
\(453\) −6.27096 1.33293i −0.294635 0.0626267i
\(454\) 2.72984 + 1.98334i 0.128118 + 0.0930830i
\(455\) 1.60778 11.8217i 0.0753740 0.554212i
\(456\) −2.10339 + 6.47356i −0.0985002 + 0.303152i
\(457\) −1.85279 2.05773i −0.0866699 0.0962567i 0.698250 0.715854i \(-0.253962\pi\)
−0.784920 + 0.619598i \(0.787296\pi\)
\(458\) 5.27233 + 2.34739i 0.246360 + 0.109686i
\(459\) 0.171302 1.62983i 0.00799569 0.0760739i
\(460\) 27.6438 + 5.87587i 1.28890 + 0.273964i
\(461\) 29.9943 1.39697 0.698487 0.715623i \(-0.253857\pi\)
0.698487 + 0.715623i \(0.253857\pi\)
\(462\) 0.720641 + 2.59956i 0.0335273 + 0.120943i
\(463\) −0.982020 −0.0456383 −0.0228192 0.999740i \(-0.507264\pi\)
−0.0228192 + 0.999740i \(0.507264\pi\)
\(464\) 20.9671 + 4.45669i 0.973372 + 0.206897i
\(465\) −1.55231 + 14.7693i −0.0719868 + 0.684909i
\(466\) −1.64518 0.732482i −0.0762116 0.0339316i
\(467\) 25.9396 + 28.8089i 1.20034 + 1.33312i 0.928751 + 0.370705i \(0.120884\pi\)
0.271593 + 0.962412i \(0.412450\pi\)
\(468\) 1.17592 3.61912i 0.0543570 0.167294i
\(469\) 7.76559 + 6.01164i 0.358582 + 0.277592i
\(470\) 4.52901 + 3.29052i 0.208908 + 0.151780i
\(471\) −2.43901 0.518427i −0.112383 0.0238879i
\(472\) 0.230381 + 0.399031i 0.0106041 + 0.0183669i
\(473\) 19.1484 3.80506i 0.880443 0.174957i
\(474\) 0.304271 0.527012i 0.0139756 0.0242065i
\(475\) −0.172658 0.531387i −0.00792210 0.0243817i
\(476\) 8.12999 1.47090i 0.372637 0.0674185i
\(477\) −2.60807 + 1.89488i −0.119415 + 0.0867604i
\(478\) 5.21253 + 5.78910i 0.238415 + 0.264787i
\(479\) 12.0085 2.55249i 0.548683 0.116626i 0.0747747 0.997200i \(-0.476176\pi\)
0.473908 + 0.880574i \(0.342843\pi\)
\(480\) 7.13591 + 3.17711i 0.325708 + 0.145015i
\(481\) 17.9215 7.97918i 0.817151 0.363819i
\(482\) 0.167378 + 0.515137i 0.00762386 + 0.0234638i
\(483\) −16.8808 4.12909i −0.768103 0.187880i
\(484\) −20.9530 0.556666i −0.952410 0.0253030i
\(485\) −10.4108 + 18.0320i −0.472729 + 0.818790i
\(486\) −0.205704 + 0.228458i −0.00933093 + 0.0103630i
\(487\) 4.20520 40.0098i 0.190556 1.81302i −0.313763 0.949501i \(-0.601590\pi\)
0.504319 0.863518i \(-0.331744\pi\)
\(488\) −1.18135 11.2398i −0.0534774 0.508803i
\(489\) −3.28773 + 10.1186i −0.148676 + 0.457578i
\(490\) −4.68259 1.29769i −0.211538 0.0586235i
\(491\) 4.70152 3.41586i 0.212177 0.154155i −0.476621 0.879109i \(-0.658139\pi\)
0.688798 + 0.724953i \(0.258139\pi\)
\(492\) −12.4545 + 5.54511i −0.561493 + 0.249993i
\(493\) 6.82928 7.58468i 0.307575 0.341597i
\(494\) 1.74028 + 3.01426i 0.0782991 + 0.135618i
\(495\) −4.93672 5.63142i −0.221889 0.253113i
\(496\) −22.6370 −1.01643
\(497\) 2.92387 + 39.2974i 0.131153 + 1.76273i
\(498\) −1.45160 1.05465i −0.0650477 0.0472599i
\(499\) −4.26639 40.5920i −0.190990 1.81715i −0.499929 0.866066i \(-0.666641\pi\)
0.308940 0.951082i \(-0.400026\pi\)
\(500\) 20.6281 4.38464i 0.922517 0.196087i
\(501\) −8.35917 + 1.77680i −0.373460 + 0.0793814i
\(502\) 0.0583125 + 0.554807i 0.00260262 + 0.0247622i
\(503\) −27.8501 20.2343i −1.24178 0.902202i −0.244060 0.969760i \(-0.578479\pi\)
−0.997715 + 0.0675578i \(0.978479\pi\)
\(504\) −2.86125 1.37978i −0.127450 0.0614604i
\(505\) 33.8677 1.50709
\(506\) −3.42531 + 5.75493i −0.152274 + 0.255838i
\(507\) 4.50590 + 7.80444i 0.200114 + 0.346607i
\(508\) 16.0352 17.8089i 0.711448 0.790143i
\(509\) −13.5633 + 6.03876i −0.601182 + 0.267663i −0.684679 0.728845i \(-0.740058\pi\)
0.0834973 + 0.996508i \(0.473391\pi\)
\(510\) 0.920324 0.668655i 0.0407526 0.0296085i
\(511\) 39.8938 + 1.21526i 1.76480 + 0.0537600i
\(512\) −6.23336 + 19.1843i −0.275478 + 0.847835i
\(513\) 0.592603 + 5.63824i 0.0261640 + 0.248934i
\(514\) −0.0126142 + 0.120016i −0.000556388 + 0.00529368i
\(515\) −12.0156 + 13.3447i −0.529470 + 0.588036i
\(516\) −5.60819 + 9.71367i −0.246887 + 0.427620i
\(517\) 21.8462 15.4332i 0.960796 0.678749i
\(518\) −2.23648 7.67043i −0.0982651 0.337019i
\(519\) −5.19072 15.9754i −0.227847 0.701242i
\(520\) 4.94596 2.20208i 0.216895 0.0965677i
\(521\) −26.0336 11.5909i −1.14055 0.507807i −0.252522 0.967591i \(-0.581260\pi\)
−0.888031 + 0.459784i \(0.847927\pi\)
\(522\) −1.87272 + 0.398059i −0.0819668 + 0.0174226i
\(523\) −20.7112 23.0021i −0.905637 1.00581i −0.999947 0.0102690i \(-0.996731\pi\)
0.0943102 0.995543i \(-0.469935\pi\)
\(524\) −10.5914 + 7.69511i −0.462688 + 0.336162i
\(525\) 0.256585 0.0464220i 0.0111983 0.00202602i
\(526\) 0.0400340 + 0.123212i 0.00174557 + 0.00537230i
\(527\) −5.38913 + 9.33425i −0.234754 + 0.406606i
\(528\) 7.75042 8.38115i 0.337294 0.364743i
\(529\) −10.0722 17.4456i −0.437922 0.758504i
\(530\) −2.18888 0.465261i −0.0950789 0.0202096i
\(531\) 0.310474 + 0.225573i 0.0134734 + 0.00978903i
\(532\) −26.4524 + 10.8247i −1.14686 + 0.469312i
\(533\) −4.41530 + 13.5889i −0.191248 + 0.588601i
\(534\) 1.74504 + 1.93807i 0.0755154 + 0.0838684i
\(535\) 5.34705 + 2.38066i 0.231173 + 0.102925i
\(536\) −0.465834 + 4.43212i −0.0201210 + 0.191438i
\(537\) 22.8291 + 4.85247i 0.985148 + 0.209400i
\(538\) 0.304285 0.0131187
\(539\) −13.0665 + 19.1903i −0.562813 + 0.826584i
\(540\) 4.30260 0.185154
\(541\) −27.7142 5.89083i −1.19152 0.253266i −0.430864 0.902417i \(-0.641791\pi\)
−0.760660 + 0.649150i \(0.775125\pi\)
\(542\) 0.666600 6.34227i 0.0286329 0.272424i
\(543\) 8.36873 + 3.72600i 0.359137 + 0.159898i
\(544\) 3.79345 + 4.21305i 0.162643 + 0.180633i
\(545\) −4.02988 + 12.4027i −0.172621 + 0.531273i
\(546\) −1.50331 + 0.615180i −0.0643359 + 0.0263273i
\(547\) −16.0877 11.6884i −0.687859 0.499759i 0.188096 0.982151i \(-0.439768\pi\)
−0.875956 + 0.482391i \(0.839768\pi\)
\(548\) 21.3978 + 4.54825i 0.914071 + 0.194292i
\(549\) −4.70660 8.15207i −0.200873 0.347922i
\(550\) 0.0118298 0.0997869i 0.000504426 0.00425493i
\(551\) −17.6537 + 30.5771i −0.752072 + 1.30263i
\(552\) −2.43698 7.50027i −0.103725 0.319233i
\(553\) 5.15363 0.932408i 0.219154 0.0396500i
\(554\) 6.03505 4.38472i 0.256405 0.186289i
\(555\) 14.8419 + 16.4836i 0.630005 + 0.699691i
\(556\) −0.0478535 + 0.0101716i −0.00202944 + 0.000431371i
\(557\) 33.1248 + 14.7481i 1.40354 + 0.624898i 0.962176 0.272428i \(-0.0878268\pi\)
0.441368 + 0.897326i \(0.354493\pi\)
\(558\) 1.84707 0.822369i 0.0781927 0.0348137i
\(559\) 3.63259 + 11.1800i 0.153642 + 0.472862i
\(560\) 5.75568 + 19.7402i 0.243222 + 0.834176i
\(561\) −1.61080 5.19113i −0.0680082 0.219170i
\(562\) −2.25631 + 3.90805i −0.0951767 + 0.164851i
\(563\) −20.1979 + 22.4320i −0.851240 + 0.945398i −0.999048 0.0436181i \(-0.986112\pi\)
0.147808 + 0.989016i \(0.452778\pi\)
\(564\) −1.60632 + 15.2831i −0.0676383 + 0.643535i
\(565\) 0.0352091 + 0.334992i 0.00148126 + 0.0140932i
\(566\) 0.634205 1.95188i 0.0266576 0.0820437i
\(567\) −2.64452 0.0805587i −0.111060 0.00338315i
\(568\) −14.4670 + 10.5109i −0.607023 + 0.441028i
\(569\) 19.9885 8.89945i 0.837962 0.373085i 0.0575439 0.998343i \(-0.481673\pi\)
0.780418 + 0.625258i \(0.215006\pi\)
\(570\) −2.63327 + 2.92454i −0.110296 + 0.122496i
\(571\) 4.41362 + 7.64461i 0.184704 + 0.319917i 0.943477 0.331439i \(-0.107534\pi\)
−0.758773 + 0.651356i \(0.774201\pi\)
\(572\) −1.15244 12.5682i −0.0481861 0.525504i
\(573\) −8.29853 −0.346676
\(574\) 5.24166 + 2.52769i 0.218783 + 0.105504i
\(575\) 0.523716 + 0.380502i 0.0218405 + 0.0158680i
\(576\) 0.608387 + 5.78842i 0.0253495 + 0.241184i
\(577\) −2.96118 + 0.629418i −0.123276 + 0.0262030i −0.269136 0.963102i \(-0.586738\pi\)
0.145861 + 0.989305i \(0.453405\pi\)
\(578\) −4.30435 + 0.914917i −0.179037 + 0.0380555i
\(579\) 0.148107 + 1.40914i 0.00615511 + 0.0585619i
\(580\) 21.6783 + 15.7502i 0.900142 + 0.653991i
\(581\) −1.14578 15.3995i −0.0475349 0.638879i
\(582\) 2.83479 0.117506
\(583\) −5.46849 + 9.18772i −0.226482 + 0.380516i
\(584\) 9.05598 + 15.6854i 0.374739 + 0.649067i
\(585\) 3.01733 3.35109i 0.124751 0.138550i
\(586\) 6.27089 2.79198i 0.259048 0.115336i
\(587\) 22.4145 16.2851i 0.925144 0.672156i −0.0196553 0.999807i \(-0.506257\pi\)
0.944799 + 0.327651i \(0.106257\pi\)
\(588\) −3.34201 12.9130i −0.137822 0.532523i
\(589\) 11.5221 35.4615i 0.474761 1.46116i
\(590\) 0.0278457 + 0.264934i 0.00114639 + 0.0109072i
\(591\) 1.50115 14.2825i 0.0617490 0.587502i
\(592\) −22.6237 + 25.1262i −0.929829 + 1.03268i
\(593\) 5.12549 8.87762i 0.210479 0.364560i −0.741386 0.671079i \(-0.765831\pi\)
0.951864 + 0.306519i \(0.0991644\pi\)
\(594\) −0.327923 + 0.965425i −0.0134548 + 0.0396119i
\(595\) 9.51003 + 2.32618i 0.389873 + 0.0953641i
\(596\) −1.05225 3.23850i −0.0431020 0.132654i
\(597\) −6.06763 + 2.70148i −0.248332 + 0.110564i
\(598\) −3.68395 1.64020i −0.150648 0.0670727i
\(599\) −14.0315 + 2.98248i −0.573311 + 0.121861i −0.485439 0.874271i \(-0.661340\pi\)
−0.0878723 + 0.996132i \(0.528007\pi\)
\(600\) 0.0791762 + 0.0879341i 0.00323236 + 0.00358989i
\(601\) 13.8216 10.0420i 0.563794 0.409621i −0.269051 0.963126i \(-0.586710\pi\)
0.832846 + 0.553505i \(0.186710\pi\)
\(602\) 4.71121 0.852364i 0.192015 0.0347398i
\(603\) 1.14702 + 3.53017i 0.0467103 + 0.143760i
\(604\) 6.10811 10.5796i 0.248535 0.430476i
\(605\) −22.4143 10.7016i −0.911271 0.435081i
\(606\) −2.30549 3.99323i −0.0936543 0.162214i
\(607\) −7.57314 1.60972i −0.307384 0.0653366i 0.0516369 0.998666i \(-0.483556\pi\)
−0.359021 + 0.933329i \(0.616889\pi\)
\(608\) −15.8665 11.5277i −0.643473 0.467511i
\(609\) −13.0293 10.0865i −0.527975 0.408726i
\(610\) 2.01918 6.21440i 0.0817543 0.251614i
\(611\) 10.7768 + 11.9689i 0.435983 + 0.484208i
\(612\) 2.85276 + 1.27013i 0.115316 + 0.0513420i
\(613\) −0.275524 + 2.62143i −0.0111283 + 0.105879i −0.998676 0.0514409i \(-0.983619\pi\)
0.987548 + 0.157320i \(0.0502853\pi\)
\(614\) −6.36752 1.35346i −0.256972 0.0546212i
\(615\) −16.1552 −0.651441
\(616\) −10.5254 0.460606i −0.424080 0.0185584i
\(617\) 17.4152 0.701110 0.350555 0.936542i \(-0.385993\pi\)
0.350555 + 0.936542i \(0.385993\pi\)
\(618\) 2.39137 + 0.508302i 0.0961951 + 0.0204469i
\(619\) −0.877195 + 8.34595i −0.0352574 + 0.335452i 0.962648 + 0.270757i \(0.0872741\pi\)
−0.997905 + 0.0646949i \(0.979393\pi\)
\(620\) −25.8513 11.5097i −1.03821 0.462242i
\(621\) −4.39515 4.88130i −0.176371 0.195880i
\(622\) 2.55920 7.87642i 0.102615 0.315816i
\(623\) −3.02467 + 22.2399i −0.121181 + 0.891022i
\(624\) 5.56088 + 4.04021i 0.222613 + 0.161738i
\(625\) 24.9262 + 5.29823i 0.997048 + 0.211929i
\(626\) −0.390570 0.676487i −0.0156103 0.0270379i
\(627\) 9.18438 + 16.4072i 0.366789 + 0.655241i
\(628\) 2.37567 4.11478i 0.0947995 0.164198i
\(629\) 4.97469 + 15.3105i 0.198354 + 0.610470i
\(630\) −1.18677 1.40161i −0.0472821 0.0558416i
\(631\) 23.9745 17.4185i 0.954410 0.693419i 0.00256384 0.999997i \(-0.499184\pi\)
0.951846 + 0.306578i \(0.0991839\pi\)
\(632\) 1.59029 + 1.76620i 0.0632584 + 0.0702556i
\(633\) −20.6850 + 4.39673i −0.822155 + 0.174754i
\(634\) −7.24695 3.22655i −0.287813 0.128143i
\(635\) 25.9424 11.5503i 1.02949 0.458360i
\(636\) −1.89824 5.84219i −0.0752702 0.231658i
\(637\) −12.4010 6.45271i −0.491345 0.255666i
\(638\) −5.18627 + 3.66381i −0.205326 + 0.145052i
\(639\) −7.44704 + 12.8987i −0.294600 + 0.510263i
\(640\) −13.1569 + 14.6122i −0.520071 + 0.577597i
\(641\) 2.38372 22.6796i 0.0941514 0.895791i −0.840879 0.541223i \(-0.817961\pi\)
0.935030 0.354568i \(-0.115372\pi\)
\(642\) −0.0832966 0.792514i −0.00328746 0.0312781i
\(643\) 2.46469 7.58553i 0.0971979 0.299144i −0.890622 0.454744i \(-0.849731\pi\)
0.987820 + 0.155599i \(0.0497309\pi\)
\(644\) 17.4228 28.1606i 0.686554 1.10968i
\(645\) −10.7529 + 7.81245i −0.423396 + 0.307615i
\(646\) −2.60927 + 1.16172i −0.102660 + 0.0457073i
\(647\) 13.9561 15.4998i 0.548670 0.609360i −0.403481 0.914988i \(-0.632200\pi\)
0.952151 + 0.305628i \(0.0988665\pi\)
\(648\) −0.600313 1.03977i −0.0235825 0.0408462i
\(649\) 1.24137 + 0.281143i 0.0487282 + 0.0110358i
\(650\) 0.0605058 0.00237323
\(651\) 15.6736 + 7.55830i 0.614296 + 0.296233i
\(652\) −16.4013 11.9162i −0.642324 0.466676i
\(653\) −0.314063 2.98811i −0.0122902 0.116934i 0.986657 0.162815i \(-0.0520572\pi\)
−0.998947 + 0.0458808i \(0.985391\pi\)
\(654\) 1.73669 0.369145i 0.0679100 0.0144347i
\(655\) −15.1746 + 3.22546i −0.592920 + 0.126029i
\(656\) −2.57407 24.4907i −0.100501 0.956199i
\(657\) 12.2044 + 8.86699i 0.476138 + 0.345934i
\(658\) 5.42169 3.69221i 0.211360 0.143938i
\(659\) −49.7577 −1.93828 −0.969142 0.246502i \(-0.920719\pi\)
−0.969142 + 0.246502i \(0.920719\pi\)
\(660\) 13.1123 5.63054i 0.510396 0.219168i
\(661\) 11.8693 + 20.5583i 0.461663 + 0.799624i 0.999044 0.0437156i \(-0.0139195\pi\)
−0.537381 + 0.843340i \(0.680586\pi\)
\(662\) 0.548493 0.609163i 0.0213178 0.0236758i
\(663\) 2.98983 1.33116i 0.116115 0.0516979i
\(664\) 5.66921 4.11892i 0.220008 0.159845i
\(665\) −33.8532 1.03125i −1.31277 0.0399903i
\(666\) 0.933191 2.87207i 0.0361604 0.111290i
\(667\) −4.27596 40.6830i −0.165566 1.57525i
\(668\) 1.70216 16.1950i 0.0658586 0.626602i
\(669\) −3.38239 + 3.75653i −0.130771 + 0.145236i
\(670\) −1.28829 + 2.23139i −0.0497711 + 0.0862061i
\(671\) −25.0116 18.6845i −0.965564 0.721307i
\(672\) 6.32855 6.61208i 0.244129 0.255067i
\(673\) 8.33353 + 25.6480i 0.321234 + 0.988657i 0.973112 + 0.230333i \(0.0739815\pi\)
−0.651878 + 0.758324i \(0.726019\pi\)
\(674\) −7.08279 + 3.15346i −0.272819 + 0.121467i
\(675\) 0.0900339 + 0.0400857i 0.00346541 + 0.00154290i
\(676\) −16.7967 + 3.57024i −0.646025 + 0.137317i
\(677\) −19.9754 22.1849i −0.767716 0.852635i 0.224844 0.974395i \(-0.427813\pi\)
−0.992560 + 0.121760i \(0.961146\pi\)
\(678\) 0.0371010 0.0269555i 0.00142486 0.00103522i
\(679\) 15.7652 + 18.6192i 0.605014 + 0.714541i
\(680\) 1.37291 + 4.22538i 0.0526486 + 0.162036i
\(681\) −5.48804 + 9.50557i −0.210302 + 0.364254i
\(682\) 4.55283 4.92334i 0.174337 0.188525i
\(683\) −8.20575 14.2128i −0.313984 0.543837i 0.665237 0.746633i \(-0.268331\pi\)
−0.979221 + 0.202796i \(0.934997\pi\)
\(684\) −10.5667 2.24603i −0.404029 0.0858790i
\(685\) 20.9720 + 15.2370i 0.801298 + 0.582177i
\(686\) −3.28472 + 4.65044i −0.125411 + 0.177555i
\(687\) −5.80126 + 17.8544i −0.221332 + 0.681189i
\(688\) −13.5567 15.0562i −0.516843 0.574012i
\(689\) −5.88140 2.61857i −0.224064 0.0997595i
\(690\) 0.476598 4.53453i 0.0181438 0.172627i
\(691\) −29.5797 6.28737i −1.12527 0.239183i −0.392559 0.919727i \(-0.628410\pi\)
−0.732707 + 0.680544i \(0.761744\pi\)
\(692\) 32.0076 1.21674
\(693\) −8.16470 + 3.21522i −0.310151 + 0.122136i
\(694\) −4.76749 −0.180972
\(695\) −0.0567061 0.0120533i −0.00215099 0.000457206i
\(696\) 0.781590 7.43633i 0.0296261 0.281873i
\(697\) −10.7114 4.76903i −0.405724 0.180640i
\(698\) −0.388734 0.431733i −0.0147138 0.0163413i
\(699\) 1.81023 5.57132i 0.0684692 0.210727i
\(700\) −0.0669573 + 0.492325i −0.00253075 + 0.0186082i
\(701\) −21.2732 15.4559i −0.803479 0.583762i 0.108453 0.994102i \(-0.465410\pi\)
−0.911933 + 0.410340i \(0.865410\pi\)
\(702\) −0.600517 0.127644i −0.0226651 0.00481761i
\(703\) −27.8455 48.2298i −1.05021 1.81902i
\(704\) 9.42902 + 16.8442i 0.355369 + 0.634841i
\(705\) −9.10508 + 15.7705i −0.342917 + 0.593950i
\(706\) −0.0286802 0.0882686i −0.00107939 0.00332203i
\(707\) 13.4064 37.3504i 0.504199 1.40471i
\(708\) −0.591607 + 0.429827i −0.0222339 + 0.0161539i
\(709\) 21.0300 + 23.3561i 0.789797 + 0.877158i 0.994826 0.101598i \(-0.0323955\pi\)
−0.205029 + 0.978756i \(0.565729\pi\)
\(710\) −10.1129 + 2.14955i −0.379529 + 0.0806713i
\(711\) 1.80837 + 0.805140i 0.0678193 + 0.0301951i
\(712\) −9.30468 + 4.14271i −0.348708 + 0.155255i
\(713\) 13.3495 + 41.0856i 0.499944 + 1.53867i
\(714\) −0.373109 1.27965i −0.0139633 0.0478897i
\(715\) 4.81007 14.1611i 0.179887 0.529597i
\(716\) −22.2362 + 38.5143i −0.831008 + 1.43935i
\(717\) −16.9557 + 18.8312i −0.633223 + 0.703265i
\(718\) 0.940717 8.95032i 0.0351072 0.334023i
\(719\) 3.94615 + 37.5452i 0.147167 + 1.40020i 0.779937 + 0.625858i \(0.215251\pi\)
−0.632770 + 0.774340i \(0.718082\pi\)
\(720\) −2.40161 + 7.39140i −0.0895028 + 0.275461i
\(721\) 9.96064 + 18.5336i 0.370953 + 0.690229i
\(722\) 3.26825 2.37452i 0.121632 0.0883705i
\(723\) −1.60959 + 0.716634i −0.0598612 + 0.0266519i
\(724\) −11.6801 + 12.9721i −0.434089 + 0.482104i
\(725\) 0.306890 + 0.531548i 0.0113976 + 0.0197412i
\(726\) 0.264034 + 3.37130i 0.00979922 + 0.125121i
\(727\) 5.80336 0.215235 0.107617 0.994192i \(-0.465678\pi\)
0.107617 + 0.994192i \(0.465678\pi\)
\(728\) −0.470696 6.32626i −0.0174452 0.234467i
\(729\) −0.809017 0.587785i −0.0299636 0.0217698i
\(730\) 1.09458 + 10.4142i 0.0405122 + 0.385448i
\(731\) −9.43576 + 2.00563i −0.348994 + 0.0741810i
\(732\) 17.5448 3.72927i 0.648476 0.137838i
\(733\) −4.50869 42.8974i −0.166532 1.58445i −0.684476 0.729035i \(-0.739969\pi\)
0.517944 0.855415i \(-0.326698\pi\)
\(734\) −2.14021 1.55495i −0.0789966 0.0573944i
\(735\) 2.60593 15.5897i 0.0961211 0.575034i
\(736\) 22.7226 0.837566
\(737\) 8.11529 + 9.25728i 0.298931 + 0.340996i
\(738\) 1.09974 + 1.90481i 0.0404821 + 0.0701171i
\(739\) 0.708012 0.786327i 0.0260447 0.0289255i −0.729982 0.683467i \(-0.760471\pi\)
0.756026 + 0.654541i \(0.227138\pi\)
\(740\) −38.6115 + 17.1910i −1.41939 + 0.631952i
\(741\) −9.15958 + 6.65482i −0.336485 + 0.244471i
\(742\) −1.37956 + 2.22980i −0.0506454 + 0.0818586i
\(743\) 12.1573 37.4164i 0.446009 1.37267i −0.435365 0.900254i \(-0.643381\pi\)
0.881374 0.472419i \(-0.156619\pi\)
\(744\) 0.825399 + 7.85314i 0.0302606 + 0.287910i
\(745\) 0.421782 4.01299i 0.0154529 0.147025i
\(746\) −6.67705 + 7.41562i −0.244464 + 0.271505i
\(747\) 2.91828 5.05461i 0.106774 0.184938i
\(748\) 10.3560 + 0.137542i 0.378654 + 0.00502902i
\(749\) 4.74208 4.95454i 0.173272 0.181035i
\(750\) −1.05139 3.23583i −0.0383912 0.118156i
\(751\) 3.66926 1.63366i 0.133893 0.0596130i −0.338696 0.940896i \(-0.609986\pi\)
0.472590 + 0.881283i \(0.343319\pi\)
\(752\) −25.3581 11.2902i −0.924716 0.411710i
\(753\) −1.77501 + 0.377289i −0.0646848 + 0.0137492i
\(754\) −2.55840 2.84139i −0.0931714 0.103477i
\(755\) 11.7114 8.50886i 0.426223 0.309669i
\(756\) 1.70317 4.74506i 0.0619435 0.172576i
\(757\) −4.87356 14.9993i −0.177133 0.545158i 0.822592 0.568632i \(-0.192527\pi\)
−0.999724 + 0.0234741i \(0.992527\pi\)
\(758\) −3.54889 + 6.14686i −0.128901 + 0.223264i
\(759\) −19.7822 9.12430i −0.718049 0.331191i
\(760\) −7.68476 13.3104i −0.278756 0.482819i
\(761\) −9.30994 1.97889i −0.337485 0.0717346i 0.0360521 0.999350i \(-0.488522\pi\)
−0.373537 + 0.927615i \(0.621855\pi\)
\(762\) −3.12785 2.27252i −0.113310 0.0823247i
\(763\) 12.0829 + 9.35384i 0.437431 + 0.338632i
\(764\) 4.88642 15.0389i 0.176785 0.544087i
\(765\) 2.47606 + 2.74995i 0.0895223 + 0.0994246i
\(766\) −0.320058 0.142499i −0.0115642 0.00514870i
\(767\) −0.0801109 + 0.762204i −0.00289264 + 0.0275216i
\(768\) −8.76772 1.86364i −0.316378 0.0672481i
\(769\) −37.1116 −1.33828 −0.669139 0.743137i \(-0.733337\pi\)
−0.669139 + 0.743137i \(0.733337\pi\)
\(770\) −5.45093 2.71842i −0.196438 0.0979649i
\(771\) −0.392548 −0.0141373
\(772\) −2.64090 0.561341i −0.0950481 0.0202031i
\(773\) −5.05586 + 48.1033i −0.181847 + 1.73016i 0.399703 + 0.916645i \(0.369113\pi\)
−0.581549 + 0.813511i \(0.697553\pi\)
\(774\) 1.65313 + 0.736022i 0.0594206 + 0.0264558i
\(775\) −0.433718 0.481693i −0.0155796 0.0173029i
\(776\) −3.42121 + 10.5294i −0.122814 + 0.377983i
\(777\) 24.0538 9.84322i 0.862927 0.353124i
\(778\) 0.298655 + 0.216986i 0.0107073 + 0.00777931i
\(779\) 39.6755 + 8.43329i 1.42152 + 0.302154i
\(780\) 4.29625 + 7.44133i 0.153830 + 0.266442i
\(781\) −5.81547 + 49.0546i −0.208094 + 1.75531i
\(782\) 1.65460 2.86584i 0.0591682 0.102482i
\(783\) −1.92450 5.92301i −0.0687762 0.211671i
\(784\) 24.0485 + 1.46652i 0.858877 + 0.0523756i
\(785\) 4.55501 3.30941i 0.162575 0.118118i
\(786\) 1.41329 + 1.56962i 0.0504104 + 0.0559865i
\(787\) 2.72046 0.578252i 0.0969740 0.0206125i −0.159169 0.987251i \(-0.550881\pi\)
0.256143 + 0.966639i \(0.417548\pi\)
\(788\) 24.9992 + 11.1304i 0.890560 + 0.396503i
\(789\) −0.384986 + 0.171407i −0.0137059 + 0.00610224i
\(790\) 0.424616 + 1.30683i 0.0151071 + 0.0464950i
\(791\) 0.383378 + 0.0937753i 0.0136313 + 0.00333427i
\(792\) −3.19016 2.38315i −0.113357 0.0846817i
\(793\) 9.39932 16.2801i 0.333780 0.578123i
\(794\) −6.63107 + 7.36454i −0.235328 + 0.261358i
\(795\) 0.760887 7.23935i 0.0269859 0.256753i
\(796\) −1.32291 12.5867i −0.0468894 0.446122i
\(797\) −5.43248 + 16.7195i −0.192428 + 0.592234i 0.807569 + 0.589774i \(0.200783\pi\)
−0.999997 + 0.00246002i \(0.999217\pi\)
\(798\) 2.18292 + 4.06173i 0.0772745 + 0.143784i
\(799\) −10.6924 + 7.76849i −0.378270 + 0.274829i
\(800\) −0.311460 + 0.138671i −0.0110118 + 0.00490275i
\(801\) −5.67642 + 6.30430i −0.200566 + 0.222751i
\(802\) −2.23004 3.86254i −0.0787453 0.136391i
\(803\) 48.7969 + 11.0514i 1.72200 + 0.389995i
\(804\) −7.07288 −0.249441
\(805\) 32.4338 22.0877i 1.14314 0.778489i
\(806\) 3.26663 + 2.37334i 0.115062 + 0.0835975i
\(807\) 0.103462 + 0.984379i 0.00364205 + 0.0346518i
\(808\) 17.6147 3.74411i 0.619682 0.131717i
\(809\) −34.6577 + 7.36671i −1.21850 + 0.259000i −0.771905 0.635738i \(-0.780696\pi\)
−0.446593 + 0.894737i \(0.647363\pi\)
\(810\) −0.0725588 0.690351i −0.00254946 0.0242565i
\(811\) 3.86508 + 2.80814i 0.135721 + 0.0986072i 0.653574 0.756862i \(-0.273269\pi\)
−0.517853 + 0.855469i \(0.673269\pi\)
\(812\) 25.9511 17.6729i 0.910706 0.620198i
\(813\) 20.7443 0.727534
\(814\) −0.914559 9.97393i −0.0320553 0.349586i
\(815\) −12.0118 20.8050i −0.420754 0.728767i
\(816\) −3.77429 + 4.19177i −0.132127 + 0.146741i
\(817\) 30.4863 13.5734i 1.06658 0.474872i
\(818\) 6.92175 5.02895i 0.242013 0.175833i
\(819\) −2.50130 4.65413i −0.0874024 0.162629i
\(820\) 9.51267 29.2770i 0.332197 1.02240i
\(821\) 0.0296177 + 0.281794i 0.00103367 + 0.00983468i 0.995027 0.0996098i \(-0.0317595\pi\)
−0.993993 + 0.109445i \(0.965093\pi\)
\(822\) 0.368914 3.50998i 0.0128674 0.122425i
\(823\) −24.7562 + 27.4946i −0.862949 + 0.958401i −0.999480 0.0322342i \(-0.989738\pi\)
0.136532 + 0.990636i \(0.456404\pi\)
\(824\) −4.77407 + 8.26893i −0.166313 + 0.288062i
\(825\) 0.326839 + 0.00434085i 0.0113791 + 0.000151129i
\(826\) 0.303201 + 0.0741639i 0.0105497 + 0.00258049i
\(827\) 2.77474 + 8.53976i 0.0964871 + 0.296957i 0.987638 0.156750i \(-0.0501015\pi\)
−0.891151 + 0.453706i \(0.850102\pi\)
\(828\) 11.4340 5.09076i 0.397361 0.176916i
\(829\) 43.3181 + 19.2865i 1.50450 + 0.669847i 0.983034 0.183425i \(-0.0587184\pi\)
0.521467 + 0.853272i \(0.325385\pi\)
\(830\) 3.96293 0.842347i 0.137555 0.0292383i
\(831\) 16.2369 + 18.0329i 0.563251 + 0.625553i
\(832\) −9.40355 + 6.83208i −0.326010 + 0.236860i
\(833\) 6.32990 9.56718i 0.219318 0.331483i
\(834\) 0.00243903 + 0.00750655i 8.44566e−5 + 0.000259931i
\(835\) 9.64833 16.7114i 0.333894 0.578322i
\(836\) −35.1417 + 6.98316i −1.21540 + 0.241518i
\(837\) 3.28845 + 5.69576i 0.113665 + 0.196874i
\(838\) −11.6077 2.46729i −0.400982 0.0852313i
\(839\) 24.5033 + 17.8027i 0.845949 + 0.614618i 0.924026 0.382329i \(-0.124878\pi\)
−0.0780769 + 0.996947i \(0.524878\pi\)
\(840\) 6.63835 2.71652i 0.229045 0.0937288i
\(841\) 3.02398 9.30687i 0.104275 0.320926i
\(842\) 5.35221 + 5.94423i 0.184449 + 0.204852i
\(843\) −13.4099 5.97049i −0.461863 0.205635i
\(844\) 4.21204 40.0749i 0.144985 1.37944i
\(845\) −19.9039 4.23071i −0.684717 0.145541i
\(846\) 2.47926 0.0852388
\(847\) −20.6747 + 20.4831i −0.710390 + 0.703808i
\(848\) 11.0958 0.381031
\(849\) 6.53009 + 1.38801i 0.224112 + 0.0476365i
\(850\) −0.00519003 + 0.0493798i −0.000178017 + 0.00169371i
\(851\) 58.9452 + 26.2441i 2.02062 + 0.899636i
\(852\) −18.9903 21.0909i −0.650597 0.722562i
\(853\) −12.3181 + 37.9113i −0.421764 + 1.29806i 0.484294 + 0.874905i \(0.339076\pi\)
−0.906059 + 0.423152i \(0.860924\pi\)
\(854\) −6.05418 4.68677i −0.207170 0.160378i
\(855\) −10.3564 7.52439i −0.354183 0.257329i
\(856\) 3.04420 + 0.647065i 0.104049 + 0.0221162i
\(857\) −0.101233 0.175341i −0.00345807 0.00598955i 0.864291 0.502992i \(-0.167767\pi\)
−0.867749 + 0.497002i \(0.834434\pi\)
\(858\) −1.99714 + 0.396859i −0.0681811 + 0.0135486i
\(859\) −21.2718 + 36.8438i −0.725783 + 1.25709i 0.232867 + 0.972508i \(0.425189\pi\)
−0.958651 + 0.284585i \(0.908144\pi\)
\(860\) −7.82633 24.0870i −0.266876 0.821359i
\(861\) −6.39497 + 17.8165i −0.217940 + 0.607186i
\(862\) 1.18596 0.861648i 0.0403938 0.0293478i
\(863\) −16.5264 18.3544i −0.562566 0.624792i 0.393012 0.919534i \(-0.371433\pi\)
−0.955577 + 0.294741i \(0.904767\pi\)
\(864\) 3.38376 0.719241i 0.115118 0.0244691i
\(865\) 34.6496 + 15.4270i 1.17812 + 0.524534i
\(866\) 4.72828 2.10517i 0.160674 0.0715365i
\(867\) −4.42337 13.6137i −0.150225 0.462346i
\(868\) −22.9265 + 23.9536i −0.778175 + 0.813039i
\(869\) 6.56472 + 0.0871881i 0.222693 + 0.00295766i
\(870\) 2.16153 3.74389i 0.0732829 0.126930i
\(871\) −4.96008 + 5.50873i −0.168066 + 0.186656i
\(872\) −0.724818 + 6.89618i −0.0245454 + 0.233534i
\(873\) 0.963882 + 9.17072i 0.0326225 + 0.310382i
\(874\) −3.53758 + 10.8875i −0.119660 + 0.368277i
\(875\) 15.4062 24.9012i 0.520825 0.841813i
\(876\) −23.2553 + 16.8960i −0.785725 + 0.570862i
\(877\) 19.3947 8.63509i 0.654913 0.291586i −0.0522526 0.998634i \(-0.516640\pi\)
0.707166 + 0.707048i \(0.249973\pi\)
\(878\) −0.166340 + 0.184739i −0.00561369 + 0.00623464i
\(879\) 11.1644 + 19.3374i 0.376567 + 0.652234i
\(880\) 2.35366 + 25.6684i 0.0793419 + 0.865281i
\(881\) 16.0932 0.542194 0.271097 0.962552i \(-0.412614\pi\)
0.271097 + 0.962552i \(0.412614\pi\)
\(882\) −2.01553 + 0.753989i −0.0678663 + 0.0253881i
\(883\) −42.5791 30.9355i −1.43290 1.04106i −0.989467 0.144757i \(-0.953760\pi\)
−0.443435 0.896307i \(-0.646240\pi\)
\(884\) 0.651866 + 6.20209i 0.0219246 + 0.208599i
\(885\) −0.847610 + 0.180165i −0.0284921 + 0.00605618i
\(886\) 4.55986 0.969229i 0.153192 0.0325619i
\(887\) −2.58177 24.5639i −0.0866875 0.824776i −0.948335 0.317270i \(-0.897234\pi\)
0.861648 0.507507i \(-0.169433\pi\)
\(888\) 9.54161 + 6.93239i 0.320196 + 0.232636i
\(889\) −2.46888 33.1823i −0.0828037 1.11290i
\(890\) −5.88869 −0.197390
\(891\) −3.23470 0.732587i −0.108367 0.0245426i
\(892\) −4.81604 8.34163i −0.161253 0.279299i
\(893\) 30.5936 33.9776i 1.02377 1.13702i
\(894\) −0.501872 + 0.223448i −0.0167851 + 0.00747321i
\(895\) −42.6349 + 30.9761i −1.42513 + 1.03542i
\(896\) 10.9067 + 20.2940i 0.364368 + 0.677976i
\(897\) 4.05353 12.4755i 0.135343 0.416544i
\(898\) −0.954228 9.07887i −0.0318430 0.302966i
\(899\) −4.28146 + 40.7354i −0.142795 + 1.35860i
\(900\) −0.125659 + 0.139559i −0.00418864 + 0.00465195i
\(901\) 2.64155 4.57530i 0.0880029 0.152425i
\(902\) 5.84421 + 4.36582i 0.194591 + 0.145366i
\(903\) 4.35935 + 14.9512i 0.145070 + 0.497545i
\(904\) 0.0553461 + 0.170338i 0.00184078 + 0.00566535i
\(905\) −18.8966 + 8.41330i −0.628144 + 0.279668i
\(906\) −1.80049 0.801632i −0.0598174 0.0266324i
\(907\) 2.55134 0.542304i 0.0847159 0.0180069i −0.165359 0.986233i \(-0.552878\pi\)
0.250075 + 0.968227i \(0.419545\pi\)
\(908\) −13.9948 15.5428i −0.464433 0.515805i
\(909\) 12.1344 8.81618i 0.402474 0.292414i
\(910\) 1.23906 3.45206i 0.0410746 0.114435i
\(911\) 0.435018 + 1.33885i 0.0144128 + 0.0443580i 0.958004 0.286754i \(-0.0925762\pi\)
−0.943591 + 0.331112i \(0.892576\pi\)
\(912\) 9.75654 16.8988i 0.323071 0.559576i
\(913\) 2.27891 19.2231i 0.0754210 0.636190i
\(914\) −0.425616 0.737188i −0.0140781 0.0243840i
\(915\) 20.7905 + 4.41916i 0.687313 + 0.146093i
\(916\) −28.9404 21.0265i −0.956219 0.694734i
\(917\) −2.44965 + 18.0118i −0.0808945 + 0.594803i
\(918\) 0.155683 0.479144i 0.00513831 0.0158141i
\(919\) 23.0403 + 25.5888i 0.760029 + 0.844097i 0.991683 0.128701i \(-0.0410807\pi\)
−0.231655 + 0.972798i \(0.574414\pi\)
\(920\) 16.2676 + 7.24281i 0.536328 + 0.238788i
\(921\) 2.21344 21.0595i 0.0729355 0.693935i
\(922\) 9.01935 + 1.91712i 0.297037 + 0.0631371i
\(923\) −29.7442 −0.979043
\(924\) −1.01910 16.6895i −0.0335258 0.549046i
\(925\) −0.968126 −0.0318318
\(926\) −0.295295 0.0627670i −0.00970401 0.00206265i
\(927\) −0.831276 + 7.90906i −0.0273027 + 0.259768i
\(928\) 19.6817 + 8.76285i 0.646083 + 0.287655i
\(929\) 24.4054 + 27.1049i 0.800715 + 0.889284i 0.995805 0.0915016i \(-0.0291667\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(930\) −1.41078 + 4.34193i −0.0462613 + 0.142378i
\(931\) −14.5380 + 36.9263i −0.476462 + 1.21021i
\(932\) 9.03060 + 6.56111i 0.295807 + 0.214916i
\(933\) 26.3508 + 5.60105i 0.862688 + 0.183370i
\(934\) 5.95875 + 10.3209i 0.194976 + 0.337709i
\(935\) 11.1446 + 5.14029i 0.364467 + 0.168106i
\(936\) 1.19886 2.07648i 0.0391858 0.0678718i
\(937\) 4.89174 + 15.0552i 0.159806 + 0.491833i 0.998616 0.0525914i \(-0.0167481\pi\)
−0.838810 + 0.544424i \(0.816748\pi\)
\(938\) 1.95089 + 2.30406i 0.0636988 + 0.0752302i
\(939\) 2.05567 1.49354i 0.0670844 0.0487397i
\(940\) −23.2184 25.7866i −0.757300 0.841067i
\(941\) 32.7651 6.96444i 1.06811 0.227034i 0.359869 0.933003i \(-0.382821\pi\)
0.708243 + 0.705969i \(0.249488\pi\)
\(942\) −0.700279 0.311784i −0.0228163 0.0101585i
\(943\) −42.9321 + 19.1146i −1.39806 + 0.622457i
\(944\) −0.408176 1.25624i −0.0132850 0.0408870i
\(945\) 4.13078 4.31585i 0.134374 0.140395i
\(946\) 6.00116 + 0.0797034i 0.195115 + 0.00259138i
\(947\) 22.9484 39.7479i 0.745724 1.29163i −0.204132 0.978943i \(-0.565437\pi\)
0.949856 0.312688i \(-0.101230\pi\)
\(948\) −2.52392 + 2.80310i −0.0819732 + 0.0910405i
\(949\) −3.14906 + 29.9613i −0.102223 + 0.972585i
\(950\) −0.0179544 0.170825i −0.000582518 0.00554229i
\(951\) 7.97399 24.5414i 0.258574 0.795810i
\(952\) 5.20335 + 0.158507i 0.168642 + 0.00513724i
\(953\) −23.6880 + 17.2103i −0.767330 + 0.557498i −0.901150 0.433508i \(-0.857276\pi\)
0.133820 + 0.991006i \(0.457276\pi\)
\(954\) −0.905366 + 0.403095i −0.0293123 + 0.0130507i
\(955\) 12.5382 13.9251i 0.405727 0.450606i
\(956\) −24.1425 41.8161i −0.780825 1.35243i
\(957\) −13.6161 15.5321i −0.440145 0.502082i
\(958\) 3.77413 0.121937
\(959\) 25.1056 17.0971i 0.810702 0.552095i
\(960\) −10.6323 7.72481i −0.343156 0.249317i
\(961\) −1.28106 12.1885i −0.0413245 0.393176i
\(962\) 5.89904 1.25388i 0.190193 0.0404267i
\(963\) 2.53551 0.538939i 0.0817056 0.0173671i
\(964\) −0.350934 3.33892i −0.0113028 0.107539i
\(965\) −2.58834 1.88054i −0.0833216 0.0605367i
\(966\) −4.81218 2.32058i −0.154829 0.0746636i
\(967\) 46.5965 1.49844 0.749221 0.662320i \(-0.230428\pi\)
0.749221 + 0.662320i \(0.230428\pi\)
\(968\) −12.8408 3.08798i −0.412719 0.0992515i
\(969\) −4.64544 8.04613i −0.149233 0.258479i
\(970\) −4.28308 + 4.75684i −0.137521 + 0.152733i
\(971\) −14.6474 + 6.52146i −0.470059 + 0.209284i −0.628075 0.778153i \(-0.716157\pi\)
0.158016 + 0.987437i \(0.449490\pi\)
\(972\) 1.54158 1.12002i 0.0494461 0.0359247i
\(973\) −0.0357396 + 0.0577662i −0.00114576 + 0.00185190i
\(974\) 3.82179 11.7623i 0.122458 0.376887i
\(975\) 0.0205731 + 0.195740i 0.000658866 + 0.00626869i
\(976\) −3.38664 + 32.2217i −0.108404 + 1.03139i
\(977\) −18.0314 + 20.0258i −0.576874 + 0.640683i −0.958993 0.283430i \(-0.908528\pi\)
0.382119 + 0.924113i \(0.375194\pi\)
\(978\) −1.63537 + 2.83254i −0.0522933 + 0.0905746i
\(979\) −9.04904 + 26.6409i −0.289209 + 0.851448i
\(980\) 26.7177 + 13.9022i 0.853465 + 0.444090i
\(981\) 1.78471 + 5.49278i 0.0569815 + 0.175371i
\(982\) 1.63209 0.726652i 0.0520820 0.0231884i
\(983\) −16.4814 7.33800i −0.525676 0.234046i 0.126701 0.991941i \(-0.459561\pi\)
−0.652376 + 0.757895i \(0.726228\pi\)
\(984\) −8.40237 + 1.78598i −0.267858 + 0.0569349i
\(985\) 21.6982 + 24.0983i 0.691362 + 0.767835i
\(986\) 2.53836 1.84423i 0.0808380 0.0587322i
\(987\) 13.7880 + 16.2841i 0.438877 + 0.518328i
\(988\) −6.66665 20.5178i −0.212094 0.652759i
\(989\) −19.3320 + 33.4841i −0.614723 + 1.06473i
\(990\) −1.12454 2.00892i −0.0357404 0.0638476i
\(991\) −5.58952 9.68133i −0.177557 0.307537i 0.763486 0.645824i \(-0.223486\pi\)
−0.941043 + 0.338287i \(0.890153\pi\)
\(992\) −22.2547 4.73038i −0.706587 0.150190i
\(993\) 2.15718 + 1.56728i 0.0684559 + 0.0497361i
\(994\) −1.63253 + 12.0037i −0.0517807 + 0.380734i
\(995\) 4.63441 14.2633i 0.146921 0.452176i
\(996\) 7.44175 + 8.26490i 0.235801 + 0.261883i
\(997\) 6.28101 + 2.79648i 0.198921 + 0.0885655i 0.503780 0.863832i \(-0.331942\pi\)
−0.304858 + 0.952398i \(0.598609\pi\)
\(998\) 1.31157 12.4788i 0.0415172 0.395009i
\(999\) 9.60861 + 2.04237i 0.304003 + 0.0646178i
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 231.2.y.b.16.5 64
3.2 odd 2 693.2.by.c.478.4 64
7.4 even 3 inner 231.2.y.b.214.4 yes 64
11.9 even 5 inner 231.2.y.b.163.4 yes 64
21.11 odd 6 693.2.by.c.676.5 64
33.20 odd 10 693.2.by.c.163.5 64
77.53 even 15 inner 231.2.y.b.130.5 yes 64
231.53 odd 30 693.2.by.c.361.4 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.y.b.16.5 64 1.1 even 1 trivial
231.2.y.b.130.5 yes 64 77.53 even 15 inner
231.2.y.b.163.4 yes 64 11.9 even 5 inner
231.2.y.b.214.4 yes 64 7.4 even 3 inner
693.2.by.c.163.5 64 33.20 odd 10
693.2.by.c.361.4 64 231.53 odd 30
693.2.by.c.478.4 64 3.2 odd 2
693.2.by.c.676.5 64 21.11 odd 6