Properties

Label 128.2.k.a.5.15
Level $128$
Weight $2$
Character 128.5
Analytic conductor $1.022$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [128,2,Mod(5,128)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(128, base_ring=CyclotomicField(32))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("128.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 128.k (of order \(32\), degree \(16\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.02208514587\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(15\) over \(\Q(\zeta_{32})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label 5.15
Character \(\chi\) \(=\) 128.5
Dual form 128.2.k.a.77.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.37613 - 0.325966i) q^{2} +(-1.74451 - 0.529190i) q^{3} +(1.78749 - 0.897147i) q^{4} +(2.07613 + 0.204481i) q^{5} +(-2.57317 - 0.159587i) q^{6} +(-0.655035 - 0.980329i) q^{7} +(2.16739 - 1.81726i) q^{8} +(0.268850 + 0.179640i) q^{9} +O(q^{10})\) \(q+(1.37613 - 0.325966i) q^{2} +(-1.74451 - 0.529190i) q^{3} +(1.78749 - 0.897147i) q^{4} +(2.07613 + 0.204481i) q^{5} +(-2.57317 - 0.159587i) q^{6} +(-0.655035 - 0.980329i) q^{7} +(2.16739 - 1.81726i) q^{8} +(0.268850 + 0.179640i) q^{9} +(2.92369 - 0.395355i) q^{10} +(-0.641887 + 1.20089i) q^{11} +(-3.59305 + 0.619155i) q^{12} +(0.356345 + 3.61804i) q^{13} +(-1.22097 - 1.13554i) q^{14} +(-3.51361 - 1.45538i) q^{15} +(2.39026 - 3.20729i) q^{16} +(-0.871613 + 0.361034i) q^{17} +(0.428530 + 0.159573i) q^{18} +(-3.46157 + 4.21794i) q^{19} +(3.89451 - 1.49708i) q^{20} +(0.623932 + 2.05683i) q^{21} +(-0.491875 + 1.86182i) q^{22} +(-0.0751658 - 0.377884i) q^{23} +(-4.74270 + 2.02325i) q^{24} +(-0.635429 - 0.126395i) q^{25} +(1.66974 + 4.86275i) q^{26} +(3.09556 + 3.77195i) q^{27} +(-2.05037 - 1.16467i) q^{28} +(-8.81508 + 4.71176i) q^{29} +(-5.30961 - 0.857487i) q^{30} +(-0.693719 - 0.693719i) q^{31} +(2.24385 - 5.19280i) q^{32} +(1.75527 - 1.75527i) q^{33} +(-1.08177 + 0.780948i) q^{34} +(-1.15948 - 2.16923i) q^{35} +(0.641731 + 0.0799069i) q^{36} +(5.99840 - 4.92276i) q^{37} +(-3.38868 + 6.93280i) q^{38} +(1.29298 - 6.50026i) q^{39} +(4.87137 - 3.32967i) q^{40} +(8.66836 - 1.72424i) q^{41} +(1.52907 + 2.62709i) q^{42} +(8.68394 - 2.63425i) q^{43} +(-0.0699970 + 2.72244i) q^{44} +(0.521434 + 0.427930i) q^{45} +(-0.226616 - 0.495517i) q^{46} +(-3.44487 - 8.31666i) q^{47} +(-5.86708 + 4.33023i) q^{48} +(2.14681 - 5.18286i) q^{49} +(-0.915636 + 0.0331923i) q^{50} +(1.71159 - 0.168577i) q^{51} +(3.88287 + 6.14752i) q^{52} +(-9.29271 - 4.96706i) q^{53} +(5.48943 + 4.18166i) q^{54} +(-1.57820 + 2.36194i) q^{55} +(-3.20122 - 0.934388i) q^{56} +(8.27082 - 5.52639i) q^{57} +(-10.5949 + 9.35744i) q^{58} +(-1.18777 + 12.0597i) q^{59} +(-7.58624 + 0.550734i) q^{60} +(-1.32906 + 4.38132i) q^{61} +(-1.18078 - 0.728522i) q^{62} -0.381232i q^{63} +(1.39516 - 7.87741i) q^{64} +7.58437i q^{65} +(1.84333 - 2.98765i) q^{66} +(4.54267 - 14.9752i) q^{67} +(-1.23410 + 1.42731i) q^{68} +(-0.0688453 + 0.698998i) q^{69} +(-2.30269 - 2.60720i) q^{70} +(-5.08045 + 3.39465i) q^{71} +(0.909154 - 0.0992199i) q^{72} +(-1.55710 + 2.33036i) q^{73} +(6.64995 - 8.72965i) q^{74} +(1.04162 + 0.556759i) q^{75} +(-2.40342 + 10.6451i) q^{76} +(1.59772 - 0.157362i) q^{77} +(-0.339548 - 9.36670i) q^{78} +(-2.24899 + 5.42954i) q^{79} +(5.61831 - 6.16998i) q^{80} +(-3.77536 - 9.11451i) q^{81} +(11.3668 - 5.19838i) q^{82} +(2.34298 + 1.92283i) q^{83} +(2.96055 + 3.11680i) q^{84} +(-1.88341 + 0.571325i) q^{85} +(11.0916 - 6.45575i) q^{86} +(17.8714 - 3.55484i) q^{87} +(0.791099 + 3.76926i) q^{88} +(-0.552284 + 2.77652i) q^{89} +(0.857055 + 0.418919i) q^{90} +(3.31344 - 2.71927i) q^{91} +(-0.473375 - 0.608030i) q^{92} +(0.843088 + 1.57731i) q^{93} +(-7.45156 - 10.3219i) q^{94} +(-8.04915 + 8.04915i) q^{95} +(-6.66238 + 7.87145i) q^{96} +(5.35433 + 5.35433i) q^{97} +(1.26486 - 7.83210i) q^{98} +(-0.388299 + 0.207550i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 32 q^{50} - 16 q^{51} + 80 q^{52} - 16 q^{53} + 112 q^{54} - 16 q^{55} + 96 q^{56} - 16 q^{57} + 128 q^{58} - 16 q^{59} + 176 q^{60} - 16 q^{61} + 80 q^{62} + 176 q^{64} + 176 q^{66} - 16 q^{67} + 80 q^{68} - 16 q^{69} + 176 q^{70} - 16 q^{71} + 128 q^{72} - 16 q^{73} + 96 q^{74} - 16 q^{75} + 112 q^{76} - 16 q^{77} + 80 q^{78} - 16 q^{79} + 32 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{32}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.37613 0.325966i 0.973074 0.230493i
\(3\) −1.74451 0.529190i −1.00719 0.305528i −0.256759 0.966476i \(-0.582655\pi\)
−0.750432 + 0.660947i \(0.770155\pi\)
\(4\) 1.78749 0.897147i 0.893746 0.448573i
\(5\) 2.07613 + 0.204481i 0.928473 + 0.0914466i 0.550936 0.834548i \(-0.314271\pi\)
0.377537 + 0.925994i \(0.376771\pi\)
\(6\) −2.57317 0.159587i −1.05049 0.0651510i
\(7\) −0.655035 0.980329i −0.247580 0.370529i 0.686777 0.726868i \(-0.259025\pi\)
−0.934357 + 0.356339i \(0.884025\pi\)
\(8\) 2.16739 1.81726i 0.766288 0.642497i
\(9\) 0.268850 + 0.179640i 0.0896167 + 0.0598799i
\(10\) 2.92369 0.395355i 0.924551 0.125022i
\(11\) −0.641887 + 1.20089i −0.193536 + 0.362081i −0.959907 0.280317i \(-0.909560\pi\)
0.766371 + 0.642398i \(0.222060\pi\)
\(12\) −3.59305 + 0.619155i −1.03722 + 0.178735i
\(13\) 0.356345 + 3.61804i 0.0988324 + 1.00346i 0.908869 + 0.417083i \(0.136947\pi\)
−0.810036 + 0.586380i \(0.800553\pi\)
\(14\) −1.22097 1.13554i −0.326318 0.303487i
\(15\) −3.51361 1.45538i −0.907210 0.375779i
\(16\) 2.39026 3.20729i 0.597564 0.801821i
\(17\) −0.871613 + 0.361034i −0.211397 + 0.0875636i −0.485869 0.874031i \(-0.661497\pi\)
0.274472 + 0.961595i \(0.411497\pi\)
\(18\) 0.428530 + 0.159573i 0.101006 + 0.0376116i
\(19\) −3.46157 + 4.21794i −0.794139 + 0.967661i −0.999940 0.0109329i \(-0.996520\pi\)
0.205801 + 0.978594i \(0.434020\pi\)
\(20\) 3.89451 1.49708i 0.870840 0.334758i
\(21\) 0.623932 + 2.05683i 0.136153 + 0.448836i
\(22\) −0.491875 + 1.86182i −0.104868 + 0.396940i
\(23\) −0.0751658 0.377884i −0.0156731 0.0787942i 0.972157 0.234330i \(-0.0752896\pi\)
−0.987830 + 0.155536i \(0.950290\pi\)
\(24\) −4.74270 + 2.02325i −0.968099 + 0.412995i
\(25\) −0.635429 0.126395i −0.127086 0.0252789i
\(26\) 1.66974 + 4.86275i 0.327462 + 0.953663i
\(27\) 3.09556 + 3.77195i 0.595740 + 0.725912i
\(28\) −2.05037 1.16467i −0.387483 0.220101i
\(29\) −8.81508 + 4.71176i −1.63692 + 0.874952i −0.642876 + 0.765970i \(0.722259\pi\)
−0.994044 + 0.108982i \(0.965241\pi\)
\(30\) −5.30961 0.857487i −0.969397 0.156555i
\(31\) −0.693719 0.693719i −0.124596 0.124596i 0.642059 0.766655i \(-0.278080\pi\)
−0.766655 + 0.642059i \(0.778080\pi\)
\(32\) 2.24385 5.19280i 0.396660 0.917966i
\(33\) 1.75527 1.75527i 0.305554 0.305554i
\(34\) −1.08177 + 0.780948i −0.185522 + 0.133931i
\(35\) −1.15948 2.16923i −0.195987 0.366667i
\(36\) 0.641731 + 0.0799069i 0.106955 + 0.0133178i
\(37\) 5.99840 4.92276i 0.986131 0.809297i 0.00448115 0.999990i \(-0.498574\pi\)
0.981650 + 0.190693i \(0.0610736\pi\)
\(38\) −3.38868 + 6.93280i −0.549717 + 1.12465i
\(39\) 1.29298 6.50026i 0.207043 1.04087i
\(40\) 4.87137 3.32967i 0.770232 0.526467i
\(41\) 8.66836 1.72424i 1.35377 0.269282i 0.535704 0.844406i \(-0.320046\pi\)
0.818066 + 0.575124i \(0.195046\pi\)
\(42\) 1.52907 + 2.62709i 0.235941 + 0.405369i
\(43\) 8.68394 2.63425i 1.32429 0.401719i 0.452572 0.891728i \(-0.350507\pi\)
0.871717 + 0.490009i \(0.163007\pi\)
\(44\) −0.0699970 + 2.72244i −0.0105524 + 0.410424i
\(45\) 0.521434 + 0.427930i 0.0777308 + 0.0637921i
\(46\) −0.226616 0.495517i −0.0334126 0.0730601i
\(47\) −3.44487 8.31666i −0.502486 1.21311i −0.948125 0.317896i \(-0.897024\pi\)
0.445639 0.895213i \(-0.352976\pi\)
\(48\) −5.86708 + 4.33023i −0.846840 + 0.625015i
\(49\) 2.14681 5.18286i 0.306687 0.740408i
\(50\) −0.915636 + 0.0331923i −0.129490 + 0.00469410i
\(51\) 1.71159 0.168577i 0.239670 0.0236055i
\(52\) 3.88287 + 6.14752i 0.538458 + 0.852507i
\(53\) −9.29271 4.96706i −1.27645 0.682278i −0.312896 0.949787i \(-0.601299\pi\)
−0.963555 + 0.267510i \(0.913799\pi\)
\(54\) 5.48943 + 4.18166i 0.747017 + 0.569052i
\(55\) −1.57820 + 2.36194i −0.212804 + 0.318484i
\(56\) −3.20122 0.934388i −0.427782 0.124863i
\(57\) 8.27082 5.52639i 1.09550 0.731988i
\(58\) −10.5949 + 9.35744i −1.39117 + 1.22869i
\(59\) −1.18777 + 12.0597i −0.154635 + 1.57004i 0.534352 + 0.845262i \(0.320556\pi\)
−0.688987 + 0.724773i \(0.741944\pi\)
\(60\) −7.58624 + 0.550734i −0.979380 + 0.0710995i
\(61\) −1.32906 + 4.38132i −0.170169 + 0.560971i 0.829827 + 0.558021i \(0.188439\pi\)
−0.999996 + 0.00294993i \(0.999061\pi\)
\(62\) −1.18078 0.728522i −0.149959 0.0925224i
\(63\) 0.381232i 0.0480307i
\(64\) 1.39516 7.87741i 0.174395 0.984676i
\(65\) 7.58437i 0.940726i
\(66\) 1.84333 2.98765i 0.226899 0.367755i
\(67\) 4.54267 14.9752i 0.554976 1.82951i −0.00350669 0.999994i \(-0.501116\pi\)
0.558483 0.829516i \(-0.311384\pi\)
\(68\) −1.23410 + 1.42731i −0.149657 + 0.173087i
\(69\) −0.0688453 + 0.698998i −0.00828799 + 0.0841494i
\(70\) −2.30269 2.60720i −0.275224 0.311620i
\(71\) −5.08045 + 3.39465i −0.602939 + 0.402871i −0.819236 0.573457i \(-0.805602\pi\)
0.216297 + 0.976328i \(0.430602\pi\)
\(72\) 0.909154 0.0992199i 0.107145 0.0116932i
\(73\) −1.55710 + 2.33036i −0.182245 + 0.272748i −0.911332 0.411672i \(-0.864945\pi\)
0.729087 + 0.684421i \(0.239945\pi\)
\(74\) 6.64995 8.72965i 0.773041 1.01480i
\(75\) 1.04162 + 0.556759i 0.120276 + 0.0642890i
\(76\) −2.40342 + 10.6451i −0.275691 + 1.22107i
\(77\) 1.59772 0.157362i 0.182077 0.0179331i
\(78\) −0.339548 9.36670i −0.0384462 1.06057i
\(79\) −2.24899 + 5.42954i −0.253031 + 0.610871i −0.998446 0.0557298i \(-0.982251\pi\)
0.745415 + 0.666601i \(0.232251\pi\)
\(80\) 5.61831 6.16998i 0.628146 0.689824i
\(81\) −3.77536 9.11451i −0.419484 1.01272i
\(82\) 11.3668 5.19838i 1.25525 0.574065i
\(83\) 2.34298 + 1.92283i 0.257176 + 0.211058i 0.754142 0.656711i \(-0.228053\pi\)
−0.496967 + 0.867770i \(0.665553\pi\)
\(84\) 2.96055 + 3.11680i 0.323022 + 0.340071i
\(85\) −1.88341 + 0.571325i −0.204284 + 0.0619689i
\(86\) 11.0916 6.45575i 1.19604 0.696141i
\(87\) 17.8714 3.55484i 1.91601 0.381119i
\(88\) 0.791099 + 3.76926i 0.0843315 + 0.401805i
\(89\) −0.552284 + 2.77652i −0.0585420 + 0.294310i −0.998954 0.0457268i \(-0.985440\pi\)
0.940412 + 0.340037i \(0.110440\pi\)
\(90\) 0.857055 + 0.418919i 0.0903415 + 0.0441580i
\(91\) 3.31344 2.71927i 0.347343 0.285057i
\(92\) −0.473375 0.608030i −0.0493528 0.0633915i
\(93\) 0.843088 + 1.57731i 0.0874241 + 0.163559i
\(94\) −7.45156 10.3219i −0.768569 1.06463i
\(95\) −8.04915 + 8.04915i −0.825826 + 0.825826i
\(96\) −6.66238 + 7.87145i −0.679976 + 0.803376i
\(97\) 5.35433 + 5.35433i 0.543649 + 0.543649i 0.924597 0.380947i \(-0.124402\pi\)
−0.380947 + 0.924597i \(0.624402\pi\)
\(98\) 1.26486 7.83210i 0.127770 0.791161i
\(99\) −0.388299 + 0.207550i −0.0390255 + 0.0208596i
\(100\) −1.24922 + 0.344143i −0.124922 + 0.0344143i
\(101\) −10.5427 12.8463i −1.04903 1.27825i −0.959331 0.282282i \(-0.908909\pi\)
−0.0897019 0.995969i \(-0.528591\pi\)
\(102\) 2.30043 0.789905i 0.227776 0.0782122i
\(103\) 4.20047 + 0.835525i 0.413885 + 0.0823268i 0.397640 0.917541i \(-0.369829\pi\)
0.0162440 + 0.999868i \(0.494829\pi\)
\(104\) 7.34724 + 7.19412i 0.720456 + 0.705442i
\(105\) 0.874781 + 4.39782i 0.0853698 + 0.429183i
\(106\) −14.4071 3.80623i −1.39934 0.369694i
\(107\) 2.33240 + 7.68890i 0.225482 + 0.743314i 0.994561 + 0.104160i \(0.0332154\pi\)
−0.769079 + 0.639154i \(0.779285\pi\)
\(108\) 8.91727 + 3.96516i 0.858065 + 0.381547i
\(109\) 4.39643 5.35706i 0.421101 0.513114i −0.518643 0.854991i \(-0.673563\pi\)
0.939745 + 0.341877i \(0.111063\pi\)
\(110\) −1.40190 + 3.76479i −0.133666 + 0.358959i
\(111\) −13.0693 + 5.41349i −1.24048 + 0.513826i
\(112\) −4.70989 0.242353i −0.445043 0.0229002i
\(113\) −11.9085 4.93267i −1.12026 0.464027i −0.255800 0.966730i \(-0.582339\pi\)
−0.864459 + 0.502703i \(0.832339\pi\)
\(114\) 9.58035 10.3011i 0.897282 0.964782i
\(115\) −0.0787838 0.799905i −0.00734663 0.0745916i
\(116\) −11.5298 + 16.3307i −1.07051 + 1.51626i
\(117\) −0.554140 + 1.03672i −0.0512302 + 0.0958451i
\(118\) 2.29651 + 16.9829i 0.211411 + 1.56340i
\(119\) 0.924869 + 0.617977i 0.0847826 + 0.0566499i
\(120\) −10.2602 + 3.23074i −0.936621 + 0.294925i
\(121\) 5.08116 + 7.60450i 0.461924 + 0.691318i
\(122\) −0.400801 + 6.46251i −0.0362869 + 0.585088i
\(123\) −16.0345 1.57926i −1.44578 0.142397i
\(124\) −1.86239 0.617650i −0.167247 0.0554666i
\(125\) −11.2751 3.42027i −1.00848 0.305918i
\(126\) −0.124269 0.524626i −0.0110707 0.0467374i
\(127\) 16.2954 1.44598 0.722991 0.690857i \(-0.242767\pi\)
0.722991 + 0.690857i \(0.242767\pi\)
\(128\) −0.647843 11.2951i −0.0572618 0.998359i
\(129\) −16.5432 −1.45655
\(130\) 2.47225 + 10.4371i 0.216831 + 0.915396i
\(131\) 5.06748 + 1.53720i 0.442748 + 0.134306i 0.503785 0.863829i \(-0.331941\pi\)
−0.0610364 + 0.998136i \(0.519441\pi\)
\(132\) 1.56280 4.71228i 0.136024 0.410151i
\(133\) 6.40241 + 0.630582i 0.555159 + 0.0546784i
\(134\) 1.36992 22.0886i 0.118343 1.90817i
\(135\) 5.65548 + 8.46403i 0.486747 + 0.728468i
\(136\) −1.23303 + 2.36645i −0.105732 + 0.202921i
\(137\) −7.53089 5.03198i −0.643407 0.429911i 0.190598 0.981668i \(-0.438957\pi\)
−0.834005 + 0.551757i \(0.813957\pi\)
\(138\) 0.133109 + 0.984356i 0.0113310 + 0.0837939i
\(139\) −1.32082 + 2.47107i −0.112030 + 0.209594i −0.931688 0.363260i \(-0.881664\pi\)
0.819658 + 0.572854i \(0.194164\pi\)
\(140\) −4.01867 2.83726i −0.339640 0.239792i
\(141\) 1.60851 + 16.3314i 0.135461 + 1.37536i
\(142\) −5.88485 + 6.32755i −0.493845 + 0.530996i
\(143\) −4.57359 1.89444i −0.382462 0.158421i
\(144\) 1.21878 0.432894i 0.101565 0.0360745i
\(145\) −19.2647 + 7.97971i −1.59985 + 0.662679i
\(146\) −1.38316 + 3.71445i −0.114471 + 0.307410i
\(147\) −6.48784 + 7.90546i −0.535108 + 0.652031i
\(148\) 6.30565 14.1808i 0.518322 1.16566i
\(149\) 3.26286 + 10.7562i 0.267304 + 0.881183i 0.983131 + 0.182905i \(0.0585501\pi\)
−0.715827 + 0.698278i \(0.753950\pi\)
\(150\) 1.61490 + 0.426641i 0.131856 + 0.0348351i
\(151\) −2.93125 14.7364i −0.238542 1.19923i −0.895416 0.445230i \(-0.853122\pi\)
0.656875 0.754000i \(-0.271878\pi\)
\(152\) 0.162498 + 15.4325i 0.0131803 + 1.25174i
\(153\) −0.299189 0.0595124i −0.0241880 0.00481130i
\(154\) 2.14739 0.737355i 0.173041 0.0594177i
\(155\) −1.29840 1.58210i −0.104290 0.127078i
\(156\) −3.52049 12.7792i −0.281865 1.02315i
\(157\) 4.07689 2.17914i 0.325371 0.173914i −0.300621 0.953744i \(-0.597194\pi\)
0.625992 + 0.779829i \(0.284694\pi\)
\(158\) −1.32507 + 8.20487i −0.105417 + 0.652745i
\(159\) 13.5827 + 13.5827i 1.07718 + 1.07718i
\(160\) 5.72034 10.3221i 0.452233 0.816033i
\(161\) −0.321214 + 0.321214i −0.0253152 + 0.0253152i
\(162\) −8.16642 11.3122i −0.641615 0.888767i
\(163\) 0.183017 + 0.342401i 0.0143350 + 0.0268189i 0.888987 0.457933i \(-0.151410\pi\)
−0.874652 + 0.484752i \(0.838910\pi\)
\(164\) 13.9477 10.8589i 1.08913 0.847935i
\(165\) 4.00309 3.28525i 0.311640 0.255757i
\(166\) 3.85104 + 1.88235i 0.298898 + 0.146098i
\(167\) 0.815829 4.10145i 0.0631307 0.317380i −0.936297 0.351210i \(-0.885770\pi\)
0.999428 + 0.0338299i \(0.0107705\pi\)
\(168\) 5.09008 + 3.32410i 0.392709 + 0.256460i
\(169\) −0.212990 + 0.0423663i −0.0163838 + 0.00325895i
\(170\) −2.40559 + 1.40015i −0.184500 + 0.107386i
\(171\) −1.68835 + 0.512156i −0.129112 + 0.0391656i
\(172\) 13.1592 12.4995i 1.00338 0.953075i
\(173\) −4.13814 3.39608i −0.314617 0.258199i 0.463810 0.885935i \(-0.346482\pi\)
−0.778427 + 0.627735i \(0.783982\pi\)
\(174\) 23.4347 10.7174i 1.77658 0.812484i
\(175\) 0.292319 + 0.705722i 0.0220973 + 0.0533475i
\(176\) 2.31731 + 4.92914i 0.174674 + 0.371548i
\(177\) 8.45394 20.4096i 0.635437 1.53408i
\(178\) 0.145034 + 4.00089i 0.0108708 + 0.299879i
\(179\) 8.41835 0.829135i 0.629217 0.0619725i 0.221618 0.975134i \(-0.428866\pi\)
0.407599 + 0.913161i \(0.366366\pi\)
\(180\) 1.31598 + 0.297119i 0.0980870 + 0.0221459i
\(181\) 4.16051 + 2.22384i 0.309249 + 0.165297i 0.618719 0.785612i \(-0.287652\pi\)
−0.309471 + 0.950909i \(0.600152\pi\)
\(182\) 3.67335 4.82216i 0.272287 0.357442i
\(183\) 4.63710 6.93991i 0.342784 0.513013i
\(184\) −0.849625 0.682426i −0.0626352 0.0503091i
\(185\) 13.4601 8.99372i 0.989603 0.661232i
\(186\) 1.67435 + 1.89577i 0.122769 + 0.139004i
\(187\) 0.125917 1.27845i 0.00920793 0.0934897i
\(188\) −13.6189 11.7754i −0.993263 0.858809i
\(189\) 1.67005 5.50542i 0.121478 0.400460i
\(190\) −8.45296 + 13.7005i −0.613243 + 0.993936i
\(191\) 0.238605i 0.0172649i −0.999963 0.00863244i \(-0.997252\pi\)
0.999963 0.00863244i \(-0.00274783\pi\)
\(192\) −6.60251 + 13.0039i −0.476495 + 0.938474i
\(193\) 3.32647i 0.239444i 0.992807 + 0.119722i \(0.0382004\pi\)
−0.992807 + 0.119722i \(0.961800\pi\)
\(194\) 9.11360 + 5.62294i 0.654318 + 0.403704i
\(195\) 4.01358 13.2310i 0.287418 0.947490i
\(196\) −0.812378 11.1903i −0.0580270 0.799309i
\(197\) −0.0595474 + 0.604595i −0.00424258 + 0.0430756i −0.997073 0.0764564i \(-0.975639\pi\)
0.992830 + 0.119532i \(0.0381394\pi\)
\(198\) −0.466697 + 0.412189i −0.0331667 + 0.0292930i
\(199\) −11.8832 + 7.94010i −0.842377 + 0.562859i −0.900204 0.435468i \(-0.856583\pi\)
0.0578268 + 0.998327i \(0.481583\pi\)
\(200\) −1.60691 + 0.880790i −0.113626 + 0.0622813i
\(201\) −15.8494 + 23.7204i −1.11793 + 1.67311i
\(202\) −18.6956 14.2416i −1.31541 1.00204i
\(203\) 10.3933 + 5.55531i 0.729464 + 0.389907i
\(204\) 2.90821 1.83688i 0.203616 0.128607i
\(205\) 18.3492 1.80724i 1.28156 0.126223i
\(206\) 6.05276 0.219416i 0.421716 0.0152874i
\(207\) 0.0476747 0.115097i 0.00331362 0.00799978i
\(208\) 12.4558 + 7.50513i 0.863656 + 0.520387i
\(209\) −2.84333 6.86440i −0.196677 0.474820i
\(210\) 2.63736 + 5.76684i 0.181995 + 0.397950i
\(211\) −14.6466 12.0202i −1.00832 0.827504i −0.0232592 0.999729i \(-0.507404\pi\)
−0.985058 + 0.172225i \(0.944904\pi\)
\(212\) −21.0668 0.541651i −1.44688 0.0372007i
\(213\) 10.6593 3.23346i 0.730363 0.221553i
\(214\) 5.71602 + 9.82068i 0.390739 + 0.671328i
\(215\) 18.5676 3.69333i 1.26630 0.251883i
\(216\) 13.5639 + 2.54986i 0.922905 + 0.173496i
\(217\) −0.225663 + 1.13448i −0.0153190 + 0.0770137i
\(218\) 4.30386 8.80513i 0.291494 0.596358i
\(219\) 3.94957 3.24133i 0.266887 0.219029i
\(220\) −0.702010 + 5.63783i −0.0473295 + 0.380102i
\(221\) −1.61683 3.02487i −0.108760 0.203475i
\(222\) −16.2205 + 11.7098i −1.08865 + 0.785913i
\(223\) −7.43573 + 7.43573i −0.497933 + 0.497933i −0.910794 0.412861i \(-0.864530\pi\)
0.412861 + 0.910794i \(0.364530\pi\)
\(224\) −6.56045 + 1.20176i −0.438338 + 0.0802957i
\(225\) −0.148129 0.148129i −0.00987530 0.00987530i
\(226\) −17.9956 2.90624i −1.19705 0.193320i
\(227\) −14.5425 + 7.77314i −0.965221 + 0.515921i −0.877162 0.480194i \(-0.840566\pi\)
−0.0880585 + 0.996115i \(0.528066\pi\)
\(228\) 9.82605 17.2985i 0.650746 1.14562i
\(229\) −1.67690 2.04331i −0.110813 0.135026i 0.714650 0.699482i \(-0.246586\pi\)
−0.825463 + 0.564456i \(0.809086\pi\)
\(230\) −0.369159 1.07510i −0.0243416 0.0708898i
\(231\) −2.87051 0.570980i −0.188866 0.0375677i
\(232\) −10.5432 + 26.2315i −0.692198 + 1.72218i
\(233\) 1.22930 + 6.18010i 0.0805340 + 0.404872i 0.999933 + 0.0115464i \(0.00367540\pi\)
−0.919399 + 0.393325i \(0.871325\pi\)
\(234\) −0.424634 + 1.60730i −0.0277592 + 0.105073i
\(235\) −5.45140 17.9709i −0.355610 1.17229i
\(236\) 8.69616 + 22.6222i 0.566072 + 1.47258i
\(237\) 6.79663 8.28172i 0.441489 0.537956i
\(238\) 1.47418 + 0.548944i 0.0955571 + 0.0355828i
\(239\) 13.9153 5.76389i 0.900104 0.372835i 0.115844 0.993267i \(-0.463043\pi\)
0.784260 + 0.620432i \(0.213043\pi\)
\(240\) −13.0663 + 7.79041i −0.843423 + 0.502869i
\(241\) 25.4574 + 10.5448i 1.63985 + 0.679249i 0.996283 0.0861378i \(-0.0274525\pi\)
0.643570 + 0.765387i \(0.277453\pi\)
\(242\) 9.47117 + 8.80852i 0.608830 + 0.566233i
\(243\) 0.327979 + 3.33003i 0.0210399 + 0.213621i
\(244\) 1.55500 + 9.02394i 0.0995490 + 0.577698i
\(245\) 5.51685 10.3213i 0.352459 0.659404i
\(246\) −22.5803 + 3.05342i −1.43967 + 0.194679i
\(247\) −16.4942 11.0210i −1.04950 0.701252i
\(248\) −2.76423 0.242894i −0.175529 0.0154238i
\(249\) −3.06980 4.59428i −0.194541 0.291151i
\(250\) −16.6310 1.03144i −1.05183 0.0652341i
\(251\) −14.4264 1.42088i −0.910587 0.0896850i −0.368135 0.929772i \(-0.620004\pi\)
−0.542451 + 0.840087i \(0.682504\pi\)
\(252\) −0.342021 0.681449i −0.0215453 0.0429272i
\(253\) 0.502044 + 0.152293i 0.0315632 + 0.00957460i
\(254\) 22.4247 5.31175i 1.40705 0.333289i
\(255\) 3.58795 0.224686
\(256\) −4.57336 15.3325i −0.285835 0.958279i
\(257\) 15.7095 0.979934 0.489967 0.871741i \(-0.337009\pi\)
0.489967 + 0.871741i \(0.337009\pi\)
\(258\) −22.7657 + 5.39253i −1.41733 + 0.335724i
\(259\) −8.75508 2.65582i −0.544014 0.165025i
\(260\) 6.80429 + 13.5570i 0.421984 + 0.840770i
\(261\) −3.21636 0.316783i −0.199087 0.0196084i
\(262\) 7.47462 + 0.463571i 0.461783 + 0.0286395i
\(263\) 6.50323 + 9.73277i 0.401006 + 0.600148i 0.975937 0.218054i \(-0.0699709\pi\)
−0.574930 + 0.818202i \(0.694971\pi\)
\(264\) 0.614580 6.99415i 0.0378248 0.430460i
\(265\) −18.2772 12.2124i −1.12276 0.750203i
\(266\) 9.01613 1.21920i 0.552814 0.0747542i
\(267\) 2.43277 4.55139i 0.148883 0.278540i
\(268\) −5.31495 30.8435i −0.324662 1.88406i
\(269\) 0.913425 + 9.27416i 0.0556925 + 0.565455i 0.982025 + 0.188749i \(0.0604433\pi\)
−0.926333 + 0.376706i \(0.877057\pi\)
\(270\) 10.5417 + 9.80415i 0.641547 + 0.596661i
\(271\) −17.0681 7.06983i −1.03681 0.429462i −0.201646 0.979459i \(-0.564629\pi\)
−0.835167 + 0.549997i \(0.814629\pi\)
\(272\) −0.925439 + 3.65847i −0.0561130 + 0.221828i
\(273\) −7.21934 + 2.99035i −0.436934 + 0.180984i
\(274\) −12.0038 4.46986i −0.725174 0.270034i
\(275\) 0.559659 0.681947i 0.0337487 0.0411229i
\(276\) 0.504043 + 1.31122i 0.0303398 + 0.0789260i
\(277\) 7.89250 + 26.0181i 0.474214 + 1.56327i 0.789174 + 0.614170i \(0.210509\pi\)
−0.314960 + 0.949105i \(0.601991\pi\)
\(278\) −1.01213 + 3.83107i −0.0607037 + 0.229772i
\(279\) −0.0618868 0.311126i −0.00370507 0.0186266i
\(280\) −6.45509 2.59450i −0.385765 0.155051i
\(281\) 27.8619 + 5.54208i 1.66210 + 0.330613i 0.934657 0.355551i \(-0.115707\pi\)
0.727447 + 0.686164i \(0.240707\pi\)
\(282\) 7.53702 + 21.9500i 0.448823 + 1.30710i
\(283\) −18.5962 22.6596i −1.10543 1.34697i −0.932139 0.362102i \(-0.882059\pi\)
−0.173293 0.984870i \(-0.555441\pi\)
\(284\) −6.03577 + 10.6258i −0.358157 + 0.630527i
\(285\) 18.3013 9.78226i 1.08408 0.579451i
\(286\) −6.91139 1.11617i −0.408679 0.0660006i
\(287\) −7.36840 7.36840i −0.434943 0.434943i
\(288\) 1.53609 0.993000i 0.0905151 0.0585131i
\(289\) −11.3915 + 11.3915i −0.670085 + 0.670085i
\(290\) −23.9097 + 17.2608i −1.40403 + 1.01359i
\(291\) −6.50720 12.1741i −0.381459 0.713659i
\(292\) −0.692624 + 5.56245i −0.0405328 + 0.325518i
\(293\) 17.8853 14.6781i 1.04487 0.857502i 0.0548585 0.998494i \(-0.482529\pi\)
0.990011 + 0.140992i \(0.0450292\pi\)
\(294\) −6.35123 + 12.9938i −0.370411 + 0.757813i
\(295\) −4.93194 + 24.7945i −0.287149 + 1.44359i
\(296\) 4.05495 21.5702i 0.235689 1.25374i
\(297\) −6.51668 + 1.29625i −0.378136 + 0.0752160i
\(298\) 7.99630 + 13.7384i 0.463213 + 0.795845i
\(299\) 1.34041 0.406610i 0.0775180 0.0235148i
\(300\) 2.36139 + 0.0607138i 0.136335 + 0.00350531i
\(301\) −8.27071 6.78759i −0.476716 0.391230i
\(302\) −8.83736 19.3238i −0.508533 1.11196i
\(303\) 11.5936 + 27.9894i 0.666035 + 1.60795i
\(304\) 5.25408 + 21.1842i 0.301342 + 1.21500i
\(305\) −3.65519 + 8.82442i −0.209296 + 0.505285i
\(306\) −0.431124 + 0.0156285i −0.0246457 + 0.000893420i
\(307\) −0.0743073 + 0.00731863i −0.00424094 + 0.000417696i −0.100137 0.994974i \(-0.531928\pi\)
0.0958964 + 0.995391i \(0.469428\pi\)
\(308\) 2.71474 1.71467i 0.154687 0.0977026i
\(309\) −6.88559 3.68043i −0.391708 0.209372i
\(310\) −2.30248 1.75395i −0.130772 0.0996178i
\(311\) −10.7510 + 16.0900i −0.609632 + 0.912379i −0.999966 0.00829438i \(-0.997360\pi\)
0.390333 + 0.920674i \(0.372360\pi\)
\(312\) −9.01024 16.4383i −0.510104 0.930634i
\(313\) −6.25455 + 4.17916i −0.353528 + 0.236220i −0.719634 0.694353i \(-0.755691\pi\)
0.366106 + 0.930573i \(0.380691\pi\)
\(314\) 4.90002 4.32772i 0.276524 0.244227i
\(315\) 0.0779546 0.791486i 0.00439224 0.0445952i
\(316\) 0.851044 + 11.7229i 0.0478749 + 0.659467i
\(317\) −2.87784 + 9.48696i −0.161636 + 0.532841i −0.999923 0.0123871i \(-0.996057\pi\)
0.838288 + 0.545228i \(0.183557\pi\)
\(318\) 23.1191 + 14.2641i 1.29645 + 0.799890i
\(319\) 13.6103i 0.762033i
\(320\) 4.50731 16.0692i 0.251966 0.898297i
\(321\) 14.6476i 0.817550i
\(322\) −0.337329 + 0.546739i −0.0187986 + 0.0304686i
\(323\) 1.49433 4.92615i 0.0831469 0.274098i
\(324\) −14.9255 12.9051i −0.829193 0.716949i
\(325\) 0.230868 2.34404i 0.0128063 0.130024i
\(326\) 0.363467 + 0.411533i 0.0201306 + 0.0227927i
\(327\) −10.5045 + 7.01888i −0.580900 + 0.388145i
\(328\) 15.6543 19.4897i 0.864365 1.07614i
\(329\) −5.89655 + 8.82480i −0.325087 + 0.486527i
\(330\) 4.43791 5.82583i 0.244299 0.320701i
\(331\) 25.7179 + 13.7465i 1.41358 + 0.755575i 0.988733 0.149690i \(-0.0478274\pi\)
0.424848 + 0.905265i \(0.360327\pi\)
\(332\) 5.91312 + 1.33505i 0.324525 + 0.0732706i
\(333\) 2.49699 0.245932i 0.136834 0.0134770i
\(334\) −0.214244 5.91008i −0.0117229 0.323385i
\(335\) 12.4933 30.1615i 0.682583 1.64790i
\(336\) 8.08819 + 2.91522i 0.441247 + 0.159038i
\(337\) 10.6005 + 25.5919i 0.577446 + 1.39408i 0.895097 + 0.445871i \(0.147106\pi\)
−0.317651 + 0.948208i \(0.602894\pi\)
\(338\) −0.279293 + 0.127729i −0.0151915 + 0.00694756i
\(339\) 18.1642 + 14.9069i 0.986542 + 0.809634i
\(340\) −2.85401 + 2.71093i −0.154780 + 0.147021i
\(341\) 1.27837 0.387789i 0.0692275 0.0209999i
\(342\) −2.15645 + 1.25514i −0.116608 + 0.0678703i
\(343\) −14.5818 + 2.90050i −0.787342 + 0.156612i
\(344\) 14.0344 21.4904i 0.756684 1.15868i
\(345\) −0.285863 + 1.43713i −0.0153904 + 0.0773726i
\(346\) −6.80164 3.32457i −0.365659 0.178730i
\(347\) 8.46328 6.94563i 0.454332 0.372861i −0.379215 0.925308i \(-0.623806\pi\)
0.833548 + 0.552447i \(0.186306\pi\)
\(348\) 28.7557 22.3875i 1.54147 1.20010i
\(349\) −7.17745 13.4281i −0.384200 0.718787i 0.613270 0.789873i \(-0.289854\pi\)
−0.997470 + 0.0710857i \(0.977354\pi\)
\(350\) 0.632312 + 0.875882i 0.0337985 + 0.0468178i
\(351\) −12.5440 + 12.5440i −0.669547 + 0.669547i
\(352\) 4.79567 + 6.02780i 0.255610 + 0.321283i
\(353\) 22.1735 + 22.1735i 1.18018 + 1.18018i 0.979698 + 0.200480i \(0.0642502\pi\)
0.200480 + 0.979698i \(0.435750\pi\)
\(354\) 4.98091 30.8421i 0.264732 1.63924i
\(355\) −11.2418 + 6.00888i −0.596654 + 0.318918i
\(356\) 1.50374 + 5.45848i 0.0796981 + 0.289299i
\(357\) −1.28641 1.56750i −0.0680841 0.0829607i
\(358\) 11.3145 3.88510i 0.597991 0.205334i
\(359\) −10.7095 2.13026i −0.565227 0.112431i −0.0957978 0.995401i \(-0.530540\pi\)
−0.469429 + 0.882970i \(0.655540\pi\)
\(360\) 1.90781 0.0200885i 0.100550 0.00105876i
\(361\) −2.10180 10.5664i −0.110621 0.556129i
\(362\) 6.45032 + 1.70412i 0.339022 + 0.0895664i
\(363\) −4.83989 15.9550i −0.254029 0.837420i
\(364\) 3.48317 7.83333i 0.182568 0.410578i
\(365\) −3.70925 + 4.51973i −0.194151 + 0.236574i
\(366\) 4.11910 11.0618i 0.215309 0.578209i
\(367\) 25.1511 10.4179i 1.31287 0.543810i 0.387152 0.922016i \(-0.373459\pi\)
0.925722 + 0.378205i \(0.123459\pi\)
\(368\) −1.39165 0.662161i −0.0725446 0.0345175i
\(369\) 2.64023 + 1.09362i 0.137445 + 0.0569316i
\(370\) 15.5912 16.7641i 0.810548 0.871524i
\(371\) 1.21770 + 12.3635i 0.0632198 + 0.641881i
\(372\) 2.92209 + 2.06305i 0.151503 + 0.106964i
\(373\) −13.1882 + 24.6733i −0.682858 + 1.27754i 0.266650 + 0.963793i \(0.414083\pi\)
−0.949508 + 0.313743i \(0.898417\pi\)
\(374\) −0.243454 1.80037i −0.0125887 0.0930947i
\(375\) 17.8595 + 11.9334i 0.922262 + 0.616236i
\(376\) −22.5799 11.7652i −1.16447 0.606745i
\(377\) −20.1885 30.2143i −1.03976 1.55611i
\(378\) 0.503634 8.12058i 0.0259041 0.417677i
\(379\) −11.9363 1.17562i −0.613127 0.0603878i −0.213313 0.976984i \(-0.568425\pi\)
−0.399814 + 0.916596i \(0.630925\pi\)
\(380\) −7.16653 + 21.6091i −0.367635 + 1.10852i
\(381\) −28.4274 8.62336i −1.45638 0.441788i
\(382\) −0.0777773 0.328353i −0.00397943 0.0168000i
\(383\) 10.6122 0.542256 0.271128 0.962543i \(-0.412603\pi\)
0.271128 + 0.962543i \(0.412603\pi\)
\(384\) −4.84711 + 20.0473i −0.247353 + 1.02303i
\(385\) 3.34925 0.170694
\(386\) 1.08432 + 4.57767i 0.0551902 + 0.232997i
\(387\) 2.80789 + 0.851765i 0.142733 + 0.0432977i
\(388\) 14.3744 + 4.76720i 0.729751 + 0.242018i
\(389\) −28.0660 2.76426i −1.42300 0.140153i −0.642968 0.765893i \(-0.722297\pi\)
−0.780032 + 0.625739i \(0.784797\pi\)
\(390\) 1.21037 19.5159i 0.0612892 0.988226i
\(391\) 0.201944 + 0.302231i 0.0102128 + 0.0152845i
\(392\) −4.76561 15.1346i −0.240700 0.764412i
\(393\) −8.02678 5.36332i −0.404898 0.270544i
\(394\) 0.115132 + 0.851415i 0.00580028 + 0.0428937i
\(395\) −5.77943 + 10.8126i −0.290795 + 0.544038i
\(396\) −0.507878 + 0.719355i −0.0255218 + 0.0361489i
\(397\) 1.07233 + 10.8876i 0.0538189 + 0.546433i 0.983855 + 0.178965i \(0.0572750\pi\)
−0.930036 + 0.367467i \(0.880225\pi\)
\(398\) −13.7647 + 14.8002i −0.689961 + 0.741865i
\(399\) −10.8353 4.48815i −0.542446 0.224688i
\(400\) −1.92422 + 1.73589i −0.0962110 + 0.0867943i
\(401\) −3.18824 + 1.32061i −0.159213 + 0.0659482i −0.460867 0.887469i \(-0.652461\pi\)
0.301654 + 0.953418i \(0.402461\pi\)
\(402\) −14.0789 + 37.8088i −0.702193 + 1.88573i
\(403\) 2.26270 2.75710i 0.112713 0.137341i
\(404\) −30.3699 13.5043i −1.51096 0.671863i
\(405\) −5.97438 19.6949i −0.296869 0.978647i
\(406\) 16.1134 + 4.25701i 0.799693 + 0.211272i
\(407\) 2.06138 + 10.3633i 0.102179 + 0.513688i
\(408\) 3.40333 3.47577i 0.168490 0.172076i
\(409\) −14.6696 2.91796i −0.725363 0.144284i −0.181420 0.983406i \(-0.558069\pi\)
−0.543943 + 0.839122i \(0.683069\pi\)
\(410\) 24.6619 8.46822i 1.21796 0.418216i
\(411\) 10.4748 + 12.7636i 0.516684 + 0.629581i
\(412\) 8.25789 2.27494i 0.406837 0.112078i
\(413\) 12.6005 6.73509i 0.620029 0.331412i
\(414\) 0.0280891 0.173929i 0.00138050 0.00854815i
\(415\) 4.47115 + 4.47115i 0.219480 + 0.219480i
\(416\) 19.5873 + 6.26789i 0.960347 + 0.307308i
\(417\) 3.61184 3.61184i 0.176872 0.176872i
\(418\) −6.15036 8.51950i −0.300824 0.416703i
\(419\) 14.6707 + 27.4469i 0.716709 + 1.34087i 0.931332 + 0.364172i \(0.118648\pi\)
−0.214623 + 0.976697i \(0.568852\pi\)
\(420\) 5.50915 + 7.07626i 0.268819 + 0.345286i
\(421\) −7.30207 + 5.99265i −0.355881 + 0.292064i −0.795297 0.606220i \(-0.792685\pi\)
0.439416 + 0.898284i \(0.355185\pi\)
\(422\) −24.0739 11.7671i −1.17190 0.572813i
\(423\) 0.567849 2.85477i 0.0276098 0.138804i
\(424\) −29.1673 + 6.12169i −1.41649 + 0.297295i
\(425\) 0.599481 0.119244i 0.0290791 0.00578419i
\(426\) 13.6146 7.92425i 0.659631 0.383931i
\(427\) 5.16571 1.56700i 0.249986 0.0758325i
\(428\) 11.0672 + 11.6513i 0.534954 + 0.563189i
\(429\) 6.97613 + 5.72516i 0.336811 + 0.276413i
\(430\) 24.3477 11.1349i 1.17415 0.536975i
\(431\) −3.95806 9.55561i −0.190653 0.460277i 0.799430 0.600759i \(-0.205135\pi\)
−0.990083 + 0.140482i \(0.955135\pi\)
\(432\) 19.4969 0.912416i 0.938044 0.0438986i
\(433\) 3.12852 7.55292i 0.150347 0.362970i −0.830705 0.556712i \(-0.812063\pi\)
0.981052 + 0.193742i \(0.0620625\pi\)
\(434\) 0.0592609 + 1.63476i 0.00284461 + 0.0784710i
\(435\) 37.8302 3.72595i 1.81382 0.178646i
\(436\) 3.05251 13.5200i 0.146189 0.647488i
\(437\) 1.85408 + 0.991027i 0.0886927 + 0.0474073i
\(438\) 4.37858 5.74793i 0.209217 0.274647i
\(439\) 7.09036 10.6115i 0.338405 0.506458i −0.622768 0.782407i \(-0.713992\pi\)
0.961172 + 0.275948i \(0.0889919\pi\)
\(440\) 0.871681 + 7.98724i 0.0415558 + 0.380777i
\(441\) 1.50822 1.00776i 0.0718199 0.0479885i
\(442\) −3.21098 3.63560i −0.152731 0.172928i
\(443\) −1.19222 + 12.1048i −0.0566441 + 0.575117i 0.924412 + 0.381395i \(0.124556\pi\)
−0.981056 + 0.193722i \(0.937944\pi\)
\(444\) −18.5046 + 21.4017i −0.878190 + 1.01568i
\(445\) −1.71436 + 5.65148i −0.0812683 + 0.267906i
\(446\) −7.80876 + 12.6564i −0.369756 + 0.599296i
\(447\) 20.4909i 0.969188i
\(448\) −8.63632 + 3.79226i −0.408028 + 0.179167i
\(449\) 30.9365i 1.45998i −0.683457 0.729991i \(-0.739524\pi\)
0.683457 0.729991i \(-0.260476\pi\)
\(450\) −0.252131 0.155561i −0.0118856 0.00733321i
\(451\) −3.49349 + 11.5165i −0.164502 + 0.542290i
\(452\) −25.7117 + 1.86658i −1.20938 + 0.0877966i
\(453\) −2.68477 + 27.2589i −0.126141 + 1.28073i
\(454\) −17.4787 + 15.4373i −0.820315 + 0.724506i
\(455\) 7.43518 4.96803i 0.348566 0.232905i
\(456\) 7.88323 27.0080i 0.369166 1.26477i
\(457\) 17.7961 26.6338i 0.832468 1.24588i −0.134484 0.990916i \(-0.542938\pi\)
0.966952 0.254960i \(-0.0820624\pi\)
\(458\) −2.97370 2.26526i −0.138952 0.105849i
\(459\) −4.05993 2.17008i −0.189501 0.101291i
\(460\) −0.858458 1.35914i −0.0400258 0.0633704i
\(461\) −10.3449 + 1.01889i −0.481812 + 0.0474544i −0.336008 0.941859i \(-0.609077\pi\)
−0.145804 + 0.989313i \(0.546577\pi\)
\(462\) −4.13633 + 0.149944i −0.192439 + 0.00697603i
\(463\) 1.84127 4.44522i 0.0855710 0.206587i −0.875302 0.483577i \(-0.839337\pi\)
0.960873 + 0.276991i \(0.0893371\pi\)
\(464\) −5.95835 + 39.5348i −0.276609 + 1.83536i
\(465\) 1.42783 + 3.44709i 0.0662140 + 0.159855i
\(466\) 3.70618 + 8.10394i 0.171686 + 0.375408i
\(467\) −20.9463 17.1901i −0.969277 0.795465i 0.00959173 0.999954i \(-0.496947\pi\)
−0.978869 + 0.204489i \(0.934447\pi\)
\(468\) −0.0604282 + 2.35028i −0.00279330 + 0.108642i
\(469\) −17.6562 + 5.35595i −0.815288 + 0.247315i
\(470\) −13.3598 22.9533i −0.616239 1.05876i
\(471\) −8.26533 + 1.64408i −0.380847 + 0.0757551i
\(472\) 19.3411 + 28.2965i 0.890248 + 1.30245i
\(473\) −2.41068 + 12.1193i −0.110843 + 0.557247i
\(474\) 6.65352 13.6122i 0.305606 0.625231i
\(475\) 2.73271 2.24267i 0.125385 0.102901i
\(476\) 2.20761 + 0.274887i 0.101186 + 0.0125994i
\(477\) −1.60606 3.00473i −0.0735366 0.137577i
\(478\) 17.2704 12.4678i 0.789932 0.570264i
\(479\) 2.42304 2.42304i 0.110712 0.110712i −0.649581 0.760293i \(-0.725056\pi\)
0.760293 + 0.649581i \(0.225056\pi\)
\(480\) −15.4415 + 14.9798i −0.704806 + 0.683731i
\(481\) 19.9482 + 19.9482i 0.909561 + 0.909561i
\(482\) 38.4700 + 6.21280i 1.75226 + 0.282985i
\(483\) 0.730343 0.390377i 0.0332318 0.0177628i
\(484\) 15.9049 + 9.03443i 0.722949 + 0.410656i
\(485\) 10.0214 + 12.2111i 0.455049 + 0.554479i
\(486\) 1.53682 + 4.47565i 0.0697115 + 0.203020i
\(487\) −14.8885 2.96150i −0.674660 0.134198i −0.154142 0.988049i \(-0.549261\pi\)
−0.520519 + 0.853850i \(0.674261\pi\)
\(488\) 5.08139 + 11.9113i 0.230024 + 0.539198i
\(489\) −0.138079 0.694172i −0.00624416 0.0313915i
\(490\) 4.22753 16.0018i 0.190980 0.722888i
\(491\) 0.450665 + 1.48564i 0.0203382 + 0.0670462i 0.966522 0.256583i \(-0.0825968\pi\)
−0.946184 + 0.323630i \(0.895097\pi\)
\(492\) −30.0783 + 11.5624i −1.35603 + 0.521271i
\(493\) 5.98224 7.28938i 0.269426 0.328297i
\(494\) −26.2907 9.78990i −1.18287 0.440468i
\(495\) −0.848598 + 0.351501i −0.0381416 + 0.0157988i
\(496\) −3.88312 + 0.566789i −0.174357 + 0.0254496i
\(497\) 6.65575 + 2.75690i 0.298551 + 0.123664i
\(498\) −5.72203 5.32169i −0.256411 0.238471i
\(499\) 4.05146 + 41.1351i 0.181368 + 1.84146i 0.468371 + 0.883532i \(0.344841\pi\)
−0.287002 + 0.957930i \(0.592659\pi\)
\(500\) −23.2226 + 4.00173i −1.03855 + 0.178963i
\(501\) −3.59366 + 6.72327i −0.160553 + 0.300374i
\(502\) −20.3158 + 2.74720i −0.906740 + 0.122614i
\(503\) −32.7820 21.9042i −1.46168 0.976661i −0.995775 0.0918237i \(-0.970730\pi\)
−0.465901 0.884837i \(-0.654270\pi\)
\(504\) −0.692796 0.826278i −0.0308596 0.0368053i
\(505\) −19.2611 28.8263i −0.857107 1.28275i
\(506\) 0.740522 + 0.0459268i 0.0329202 + 0.00204169i
\(507\) 0.393982 + 0.0388039i 0.0174974 + 0.00172334i
\(508\) 29.1279 14.6194i 1.29234 0.648629i
\(509\) −17.9733 5.45214i −0.796653 0.241662i −0.134385 0.990929i \(-0.542906\pi\)
−0.662268 + 0.749267i \(0.730406\pi\)
\(510\) 4.93750 1.16955i 0.218636 0.0517886i
\(511\) 3.30447 0.146181
\(512\) −11.2914 19.6088i −0.499015 0.866593i
\(513\) −26.6253 −1.17554
\(514\) 21.6184 5.12078i 0.953549 0.225868i
\(515\) 8.54987 + 2.59357i 0.376752 + 0.114286i
\(516\) −29.5708 + 14.8417i −1.30178 + 0.653369i
\(517\) 12.1986 + 1.20146i 0.536493 + 0.0528400i
\(518\) −12.9139 0.800911i −0.567403 0.0351900i
\(519\) 5.42183 + 8.11435i 0.237992 + 0.356180i
\(520\) 13.7828 + 16.4383i 0.604414 + 0.720867i
\(521\) 17.0881 + 11.4179i 0.748645 + 0.500228i 0.870408 0.492331i \(-0.163855\pi\)
−0.121764 + 0.992559i \(0.538855\pi\)
\(522\) −4.52940 + 0.612487i −0.198246 + 0.0268078i
\(523\) 6.16241 11.5291i 0.269463 0.504131i −0.710400 0.703798i \(-0.751486\pi\)
0.979864 + 0.199667i \(0.0639861\pi\)
\(524\) 10.4372 1.79854i 0.455951 0.0785694i
\(525\) −0.136492 1.38583i −0.00595701 0.0604825i
\(526\) 12.1219 + 11.2738i 0.528539 + 0.491560i
\(527\) 0.855111 + 0.354198i 0.0372492 + 0.0154291i
\(528\) −1.43411 9.82522i −0.0624116 0.427588i
\(529\) 21.1121 8.74491i 0.917917 0.380214i
\(530\) −29.1327 10.8482i −1.26544 0.471216i
\(531\) −2.48573 + 3.02887i −0.107872 + 0.131442i
\(532\) 12.0100 4.61674i 0.520699 0.200161i
\(533\) 9.32730 + 30.7480i 0.404010 + 1.33184i
\(534\) 1.86422 7.05632i 0.0806726 0.305357i
\(535\) 3.27013 + 16.4401i 0.141380 + 0.710767i
\(536\) −17.3680 40.7123i −0.750184 1.75850i
\(537\) −15.1246 3.00848i −0.652676 0.129825i
\(538\) 4.28006 + 12.4647i 0.184526 + 0.537393i
\(539\) 4.84602 + 5.90489i 0.208733 + 0.254342i
\(540\) 17.7026 + 10.0556i 0.761799 + 0.432724i
\(541\) 21.8559 11.6822i 0.939657 0.502257i 0.0708936 0.997484i \(-0.477415\pi\)
0.868764 + 0.495227i \(0.164915\pi\)
\(542\) −25.7925 4.16542i −1.10788 0.178920i
\(543\) −6.08121 6.08121i −0.260970 0.260970i
\(544\) −0.0809897 + 5.33622i −0.00347240 + 0.228788i
\(545\) 10.2230 10.2230i 0.437904 0.437904i
\(546\) −8.96003 + 6.46838i −0.383454 + 0.276821i
\(547\) 15.7202 + 29.4105i 0.672148 + 1.25750i 0.954506 + 0.298191i \(0.0963833\pi\)
−0.282358 + 0.959309i \(0.591117\pi\)
\(548\) −17.9758 2.23831i −0.767889 0.0956159i
\(549\) −1.14438 + 0.939166i −0.0488408 + 0.0400826i
\(550\) 0.547875 1.12088i 0.0233615 0.0477945i
\(551\) 10.6401 53.4916i 0.453285 2.27882i
\(552\) 1.12104 + 1.64011i 0.0477148 + 0.0698077i
\(553\) 6.79590 1.35179i 0.288991 0.0574839i
\(554\) 19.3421 + 33.2317i 0.821769 + 1.41188i
\(555\) −28.2405 + 8.56668i −1.19874 + 0.363635i
\(556\) −0.144033 + 5.60199i −0.00610837 + 0.237577i
\(557\) −18.3691 15.0751i −0.778323 0.638753i 0.158975 0.987283i \(-0.449181\pi\)
−0.937298 + 0.348529i \(0.886681\pi\)
\(558\) −0.186581 0.407978i −0.00789861 0.0172711i
\(559\) 12.6253 + 30.4801i 0.533992 + 1.28917i
\(560\) −9.72879 1.46624i −0.411116 0.0619599i
\(561\) −0.896206 + 2.16363i −0.0378379 + 0.0913487i
\(562\) 40.1483 1.45540i 1.69355 0.0613923i
\(563\) −29.5880 + 2.91417i −1.24699 + 0.122818i −0.699889 0.714251i \(-0.746767\pi\)
−0.547098 + 0.837069i \(0.684267\pi\)
\(564\) 17.5269 + 27.7493i 0.738016 + 1.16846i
\(565\) −23.7150 12.6759i −0.997697 0.533280i
\(566\) −32.9772 25.1209i −1.38613 1.05591i
\(567\) −6.46223 + 9.67141i −0.271388 + 0.406161i
\(568\) −4.84237 + 16.5900i −0.203181 + 0.696102i
\(569\) 0.110146 0.0735969i 0.00461754 0.00308534i −0.553259 0.833009i \(-0.686616\pi\)
0.557877 + 0.829924i \(0.311616\pi\)
\(570\) 21.9964 19.4273i 0.921328 0.813721i
\(571\) 0.193840 1.96809i 0.00811197 0.0823622i −0.990276 0.139114i \(-0.955574\pi\)
0.998388 + 0.0567521i \(0.0180745\pi\)
\(572\) −9.87484 + 0.716878i −0.412888 + 0.0299742i
\(573\) −0.126268 + 0.416249i −0.00527491 + 0.0173890i
\(574\) −12.5418 7.73806i −0.523483 0.322980i
\(575\) 0.249619i 0.0104098i
\(576\) 1.79018 1.86721i 0.0745910 0.0778006i
\(577\) 25.9992i 1.08236i −0.840907 0.541180i \(-0.817978\pi\)
0.840907 0.541180i \(-0.182022\pi\)
\(578\) −11.9629 + 19.3894i −0.497593 + 0.806493i
\(579\) 1.76033 5.80304i 0.0731570 0.241166i
\(580\) −27.2766 + 31.5469i −1.13260 + 1.30992i
\(581\) 0.350276 3.55641i 0.0145319 0.147545i
\(582\) −12.9231 14.6321i −0.535681 0.606519i
\(583\) 11.9297 7.97120i 0.494080 0.330133i
\(584\) 0.860027 + 7.88045i 0.0355882 + 0.326095i
\(585\) −1.36246 + 2.03906i −0.0563306 + 0.0843047i
\(586\) 19.8280 26.0290i 0.819087 1.07525i
\(587\) 9.48771 + 5.07129i 0.391600 + 0.209314i 0.655432 0.755254i \(-0.272487\pi\)
−0.263832 + 0.964569i \(0.584987\pi\)
\(588\) −4.50461 + 19.9515i −0.185767 + 0.822785i
\(589\) 5.32742 0.524705i 0.219513 0.0216201i
\(590\) 1.29517 + 35.7283i 0.0533213 + 1.47091i
\(591\) 0.423827 1.02321i 0.0174339 0.0420892i
\(592\) −1.45098 31.0052i −0.0596351 1.27431i
\(593\) −3.52492 8.50992i −0.144751 0.349460i 0.834830 0.550507i \(-0.185566\pi\)
−0.979582 + 0.201047i \(0.935566\pi\)
\(594\) −8.54530 + 3.90803i −0.350618 + 0.160348i
\(595\) 1.79378 + 1.47212i 0.0735379 + 0.0603510i
\(596\) 15.4822 + 16.2994i 0.634177 + 0.667648i
\(597\) 24.9321 7.56308i 1.02040 0.309536i
\(598\) 1.71205 0.996479i 0.0700108 0.0407490i
\(599\) 28.5435 5.67766i 1.16626 0.231983i 0.426264 0.904599i \(-0.359829\pi\)
0.739992 + 0.672616i \(0.234829\pi\)
\(600\) 3.26937 0.686182i 0.133472 0.0280132i
\(601\) −4.44079 + 22.3253i −0.181144 + 0.910670i 0.778111 + 0.628127i \(0.216178\pi\)
−0.959255 + 0.282543i \(0.908822\pi\)
\(602\) −13.5941 6.64467i −0.554055 0.270817i
\(603\) 3.91144 3.21003i 0.159286 0.130723i
\(604\) −18.4603 23.7114i −0.751138 0.964803i
\(605\) 8.99417 + 16.8269i 0.365665 + 0.684111i
\(606\) 25.0780 + 34.7381i 1.01872 + 1.41114i
\(607\) 33.5917 33.5917i 1.36345 1.36345i 0.493961 0.869484i \(-0.335548\pi\)
0.869484 0.493961i \(-0.164452\pi\)
\(608\) 14.1357 + 27.4396i 0.573277 + 1.11282i
\(609\) −15.1913 15.1913i −0.615582 0.615582i
\(610\) −2.15358 + 13.3351i −0.0871957 + 0.539921i
\(611\) 28.8624 15.4273i 1.16765 0.624121i
\(612\) −0.588190 + 0.162039i −0.0237762 + 0.00655002i
\(613\) 3.37561 + 4.11319i 0.136339 + 0.166130i 0.836704 0.547655i \(-0.184479\pi\)
−0.700365 + 0.713785i \(0.746979\pi\)
\(614\) −0.0998712 + 0.0342931i −0.00403047 + 0.00138396i
\(615\) −32.9667 6.55748i −1.32934 0.264423i
\(616\) 3.17692 3.24454i 0.128002 0.130726i
\(617\) 0.223345 + 1.12283i 0.00899152 + 0.0452034i 0.985021 0.172437i \(-0.0551641\pi\)
−0.976029 + 0.217640i \(0.930164\pi\)
\(618\) −10.6752 2.82029i −0.429419 0.113449i
\(619\) −12.0380 39.6841i −0.483850 1.59504i −0.770789 0.637090i \(-0.780138\pi\)
0.286939 0.957949i \(-0.407362\pi\)
\(620\) −3.74025 1.66314i −0.150212 0.0667934i
\(621\) 1.19268 1.45328i 0.0478605 0.0583182i
\(622\) −9.55001 + 25.6464i −0.382920 + 1.02833i
\(623\) 3.08366 1.27730i 0.123544 0.0511738i
\(624\) −17.7576 19.6842i −0.710874 0.788000i
\(625\) −19.7164 8.16680i −0.788656 0.326672i
\(626\) −7.24484 + 7.78985i −0.289562 + 0.311345i
\(627\) 1.32763 + 13.4796i 0.0530204 + 0.538325i
\(628\) 5.33239 7.55276i 0.212786 0.301388i
\(629\) −3.45100 + 6.45637i −0.137600 + 0.257432i
\(630\) −0.150722 1.11460i −0.00600490 0.0444068i
\(631\) −9.92670 6.63281i −0.395176 0.264048i 0.342067 0.939675i \(-0.388873\pi\)
−0.737243 + 0.675627i \(0.763873\pi\)
\(632\) 4.99243 + 15.8549i 0.198588 + 0.630675i
\(633\) 19.1902 + 28.7202i 0.762742 + 1.14152i
\(634\) −0.867864 + 13.9934i −0.0344673 + 0.555750i
\(635\) 33.8313 + 3.33210i 1.34256 + 0.132230i
\(636\) 36.4646 + 12.0933i 1.44591 + 0.479529i
\(637\) 19.5168 + 5.92035i 0.773283 + 0.234573i
\(638\) −4.43651 18.7297i −0.175643 0.741514i
\(639\) −1.97569 −0.0781573
\(640\) 0.964634 23.5826i 0.0381305 0.932186i
\(641\) 23.3499 0.922266 0.461133 0.887331i \(-0.347443\pi\)
0.461133 + 0.887331i \(0.347443\pi\)
\(642\) −4.77463 20.1571i −0.188440 0.795537i
\(643\) 6.27397 + 1.90319i 0.247421 + 0.0750544i 0.411559 0.911383i \(-0.364984\pi\)
−0.164138 + 0.986437i \(0.552484\pi\)
\(644\) −0.285992 + 0.862344i −0.0112696 + 0.0339811i
\(645\) −34.3458 3.38277i −1.35237 0.133196i
\(646\) 0.450642 7.26615i 0.0177303 0.285883i
\(647\) 1.35818 + 2.03267i 0.0533957 + 0.0799124i 0.857207 0.514972i \(-0.172198\pi\)
−0.803811 + 0.594885i \(0.797198\pi\)
\(648\) −24.7461 12.8939i −0.972118 0.506521i
\(649\) −13.7199 9.16733i −0.538553 0.359849i
\(650\) −0.446373 3.30097i −0.0175082 0.129475i
\(651\) 0.994027 1.85969i 0.0389590 0.0728871i
\(652\) 0.634326 + 0.447846i 0.0248421 + 0.0175390i
\(653\) −3.52444 35.7843i −0.137922 1.40035i −0.776174 0.630519i \(-0.782842\pi\)
0.638251 0.769828i \(-0.279658\pi\)
\(654\) −12.1677 + 13.0830i −0.475794 + 0.511587i
\(655\) 10.2064 + 4.22764i 0.398798 + 0.165187i
\(656\) 15.1895 31.9233i 0.593048 1.24639i
\(657\) −0.837252 + 0.346801i −0.0326643 + 0.0135300i
\(658\) −5.23785 + 14.0662i −0.204193 + 0.548357i
\(659\) 18.6662 22.7449i 0.727134 0.886015i −0.269908 0.962886i \(-0.586993\pi\)
0.997041 + 0.0768715i \(0.0244931\pi\)
\(660\) 4.20814 9.46373i 0.163802 0.368375i
\(661\) −12.0772 39.8132i −0.469748 1.54855i −0.797218 0.603691i \(-0.793696\pi\)
0.327470 0.944862i \(-0.393804\pi\)
\(662\) 39.8721 + 10.5339i 1.54967 + 0.409410i
\(663\) 1.21983 + 6.13252i 0.0473744 + 0.238167i
\(664\) 8.57244 0.0902645i 0.332675 0.00350294i
\(665\) 13.1633 + 2.61834i 0.510450 + 0.101535i
\(666\) 3.35603 1.15237i 0.130044 0.0446535i
\(667\) 2.44309 + 2.97691i 0.0945969 + 0.115267i
\(668\) −2.22131 8.06323i −0.0859452 0.311976i
\(669\) 16.9066 9.03676i 0.653646 0.349381i
\(670\) 7.36084 45.5787i 0.284374 1.76086i
\(671\) −4.40836 4.40836i −0.170183 0.170183i
\(672\) 12.0807 + 1.37525i 0.466023 + 0.0530515i
\(673\) −7.67793 + 7.67793i −0.295963 + 0.295963i −0.839430 0.543468i \(-0.817111\pi\)
0.543468 + 0.839430i \(0.317111\pi\)
\(674\) 22.9298 + 31.7625i 0.883223 + 1.22344i
\(675\) −1.49025 2.78807i −0.0573598 0.107313i
\(676\) −0.342709 + 0.266813i −0.0131811 + 0.0102620i
\(677\) −8.10857 + 6.65453i −0.311638 + 0.255755i −0.777190 0.629266i \(-0.783356\pi\)
0.465552 + 0.885020i \(0.345856\pi\)
\(678\) 29.8555 + 14.5931i 1.14659 + 0.560443i
\(679\) 1.74173 8.75627i 0.0668415 0.336035i
\(680\) −3.04383 + 4.66091i −0.116726 + 0.178738i
\(681\) 29.4830 5.86453i 1.12979 0.224729i
\(682\) 1.63280 0.950354i 0.0625232 0.0363909i
\(683\) −26.3643 + 7.99751i −1.00880 + 0.306016i −0.751086 0.660205i \(-0.770470\pi\)
−0.257715 + 0.966221i \(0.582970\pi\)
\(684\) −2.55844 + 2.43018i −0.0978243 + 0.0929201i
\(685\) −14.6061 11.9870i −0.558072 0.457998i
\(686\) −19.1210 + 8.74464i −0.730044 + 0.333872i
\(687\) 1.84407 + 4.45198i 0.0703556 + 0.169853i
\(688\) 12.3081 34.1484i 0.469241 1.30190i
\(689\) 14.6596 35.3913i 0.558485 1.34830i
\(690\) 0.0750701 + 2.07087i 0.00285787 + 0.0788366i
\(691\) 33.0875 3.25883i 1.25871 0.123972i 0.553425 0.832899i \(-0.313320\pi\)
0.705282 + 0.708927i \(0.250820\pi\)
\(692\) −10.4437 2.35795i −0.397009 0.0896359i
\(693\) 0.457816 + 0.244708i 0.0173910 + 0.00929568i
\(694\) 9.38256 12.3169i 0.356157 0.467542i
\(695\) −3.24747 + 4.86018i −0.123184 + 0.184357i
\(696\) 32.2742 40.1816i 1.22335 1.52308i
\(697\) −6.93294 + 4.63244i −0.262604 + 0.175466i
\(698\) −14.2542 16.1392i −0.539530 0.610878i
\(699\) 1.12593 11.4318i 0.0425866 0.432389i
\(700\) 1.15565 + 0.999218i 0.0436796 + 0.0377669i
\(701\) −9.40282 + 30.9969i −0.355140 + 1.17074i 0.579449 + 0.815008i \(0.303268\pi\)
−0.934589 + 0.355730i \(0.884232\pi\)
\(702\) −13.1733 + 21.3511i −0.497193 + 0.805844i
\(703\) 42.3413i 1.59693i
\(704\) 8.56434 + 6.73184i 0.322781 + 0.253716i
\(705\) 34.2351i 1.28937i
\(706\) 37.7416 + 23.2859i 1.42042 + 0.876378i
\(707\) −5.68775 + 18.7500i −0.213910 + 0.705167i
\(708\) −3.19907 44.0664i −0.120228 1.65612i
\(709\) −3.88184 + 39.4130i −0.145786 + 1.48019i 0.592430 + 0.805622i \(0.298169\pi\)
−0.738216 + 0.674564i \(0.764331\pi\)
\(710\) −13.5116 + 11.9335i −0.507080 + 0.447855i
\(711\) −1.58000 + 1.05572i −0.0592547 + 0.0395927i
\(712\) 3.84863 + 7.02144i 0.144234 + 0.263140i
\(713\) −0.210001 + 0.314289i −0.00786461 + 0.0117702i
\(714\) −2.28123 1.73776i −0.0853727 0.0650340i
\(715\) −9.10797 4.86831i −0.340619 0.182065i
\(716\) 14.3039 9.03457i 0.534561 0.337638i
\(717\) −27.3255 + 2.69132i −1.02049 + 0.100509i
\(718\) −15.4321 + 0.559423i −0.575922 + 0.0208775i
\(719\) −14.5874 + 35.2171i −0.544018 + 1.31338i 0.377848 + 0.925868i \(0.376664\pi\)
−0.921866 + 0.387509i \(0.873336\pi\)
\(720\) 2.61886 0.649526i 0.0975990 0.0242064i
\(721\) −1.93236 4.66514i −0.0719650 0.173739i
\(722\) −6.33666 13.8557i −0.235826 0.515657i
\(723\) −38.8303 31.8672i −1.44412 1.18516i
\(724\) 9.43200 + 0.242507i 0.350537 + 0.00901270i
\(725\) 6.19690 1.87981i 0.230147 0.0698143i
\(726\) −11.8611 20.3786i −0.440208 0.756320i
\(727\) −42.5548 + 8.46468i −1.57827 + 0.313938i −0.904985 0.425444i \(-0.860118\pi\)
−0.673287 + 0.739382i \(0.735118\pi\)
\(728\) 2.23991 11.9151i 0.0830165 0.441603i
\(729\) −4.58392 + 23.0449i −0.169775 + 0.853516i
\(730\) −3.63115 + 7.42885i −0.134395 + 0.274954i
\(731\) −6.61799 + 5.43124i −0.244775 + 0.200882i
\(732\) 2.06266 16.5652i 0.0762382 0.612267i
\(733\) 12.4381 + 23.2700i 0.459410 + 0.859496i 0.999836 + 0.0181046i \(0.00576319\pi\)
−0.540426 + 0.841392i \(0.681737\pi\)
\(734\) 31.2153 22.5348i 1.15218 0.831776i
\(735\) −15.0861 + 15.0861i −0.556459 + 0.556459i
\(736\) −2.13093 0.457593i −0.0785473 0.0168671i
\(737\) 15.0676 + 15.0676i 0.555023 + 0.555023i
\(738\) 3.98980 + 0.644341i 0.146866 + 0.0237185i
\(739\) −7.88065 + 4.21230i −0.289894 + 0.154952i −0.609934 0.792452i \(-0.708804\pi\)
0.320039 + 0.947404i \(0.396304\pi\)
\(740\) 15.9911 28.1519i 0.587843 1.03488i
\(741\) 22.9419 + 27.9548i 0.842793 + 1.02695i
\(742\) 5.70580 + 16.6169i 0.209467 + 0.610026i
\(743\) 3.04038 + 0.604770i 0.111541 + 0.0221868i 0.250545 0.968105i \(-0.419390\pi\)
−0.139004 + 0.990292i \(0.544390\pi\)
\(744\) 4.69367 + 1.88653i 0.172078 + 0.0691636i
\(745\) 4.57468 + 22.9985i 0.167603 + 0.842599i
\(746\) −10.1060 + 38.2527i −0.370008 + 1.40053i
\(747\) 0.284493 + 0.937847i 0.0104090 + 0.0343140i
\(748\) −0.921884 2.39819i −0.0337074 0.0876864i
\(749\) 6.00984 7.32302i 0.219595 0.267577i
\(750\) 28.4670 + 10.6003i 1.03947 + 0.387068i
\(751\) −5.50796 + 2.28147i −0.200988 + 0.0832521i −0.480907 0.876772i \(-0.659693\pi\)
0.279919 + 0.960024i \(0.409693\pi\)
\(752\) −34.9080 8.83025i −1.27296 0.322006i
\(753\) 24.4150 + 10.1130i 0.889734 + 0.368540i
\(754\) −37.6310 34.9981i −1.37044 1.27456i
\(755\) −3.07234 31.1940i −0.111814 1.13527i
\(756\) −1.95397 11.3392i −0.0710651 0.412402i
\(757\) −4.47214 + 8.36678i −0.162543 + 0.304096i −0.949987 0.312290i \(-0.898904\pi\)
0.787444 + 0.616386i \(0.211404\pi\)
\(758\) −16.8092 + 2.27302i −0.610537 + 0.0825597i
\(759\) −0.795226 0.531353i −0.0288649 0.0192869i
\(760\) −2.81828 + 32.0730i −0.102230 + 1.16341i
\(761\) 4.57889 + 6.85280i 0.165985 + 0.248414i 0.905132 0.425130i \(-0.139771\pi\)
−0.739148 + 0.673543i \(0.764771\pi\)
\(762\) −41.9309 2.60053i −1.51900 0.0942072i
\(763\) −8.13150 0.800882i −0.294380 0.0289939i
\(764\) −0.214064 0.426505i −0.00774457 0.0154304i
\(765\) −0.608986 0.184734i −0.0220179 0.00667907i
\(766\) 14.6038 3.45921i 0.527655 0.124986i
\(767\) −44.0556 −1.59075
\(768\) −0.135542 + 29.1677i −0.00489096 + 1.05250i
\(769\) −33.4645 −1.20676 −0.603380 0.797454i \(-0.706180\pi\)
−0.603380 + 0.797454i \(0.706180\pi\)
\(770\) 4.60902 1.09174i 0.166098 0.0393437i
\(771\) −27.4054 8.31333i −0.986981 0.299397i
\(772\) 2.98433 + 5.94604i 0.107408 + 0.214002i
\(773\) 8.57623 + 0.844685i 0.308465 + 0.0303812i 0.251066 0.967970i \(-0.419219\pi\)
0.0573999 + 0.998351i \(0.481719\pi\)
\(774\) 4.14169 + 0.256865i 0.148870 + 0.00923282i
\(775\) 0.353127 + 0.528491i 0.0126847 + 0.0189840i
\(776\) 21.3351 + 1.87473i 0.765885 + 0.0672988i
\(777\) 13.8679 + 9.26620i 0.497506 + 0.332423i
\(778\) −39.5236 + 5.34457i −1.41699 + 0.191612i
\(779\) −22.7334 + 42.5312i −0.814508 + 1.52384i
\(780\) −4.69590 27.2510i −0.168140 0.975744i
\(781\) −0.815512 8.28004i −0.0291813 0.296283i
\(782\) 0.376420 + 0.350084i 0.0134607 + 0.0125190i
\(783\) −45.0601 18.6645i −1.61032 0.667015i
\(784\) −11.4915 19.2738i −0.410410 0.688350i
\(785\) 8.90974 3.69053i 0.318002 0.131721i
\(786\) −12.7942 4.76420i −0.456354 0.169933i
\(787\) −28.4120 + 34.6202i −1.01278 + 1.23408i −0.0407616 + 0.999169i \(0.512978\pi\)
−0.972018 + 0.234907i \(0.924522\pi\)
\(788\) 0.435970 + 1.13413i 0.0155308 + 0.0404018i
\(789\) −6.19444 20.4203i −0.220528 0.726983i
\(790\) −4.42874 + 16.7634i −0.157568 + 0.596416i
\(791\) 2.96486 + 14.9053i 0.105418 + 0.529973i
\(792\) −0.464423 + 1.15548i −0.0165026 + 0.0410582i
\(793\) −16.3254 3.24732i −0.579731 0.115316i
\(794\) 5.02466 + 14.6332i 0.178319 + 0.519315i
\(795\) 25.4220 + 30.9768i 0.901624 + 1.09863i
\(796\) −14.1177 + 24.8538i −0.500388 + 0.880921i
\(797\) −33.7948 + 18.0637i −1.19707 + 0.639849i −0.944749 0.327794i \(-0.893695\pi\)
−0.252324 + 0.967643i \(0.581195\pi\)
\(798\) −16.3739 2.64434i −0.579629 0.0936085i
\(799\) 6.00519 + 6.00519i 0.212448 + 0.212448i
\(800\) −2.08215 + 3.01604i −0.0736150 + 0.106633i
\(801\) −0.647255 + 0.647255i −0.0228696 + 0.0228696i
\(802\) −3.95697 + 2.85660i −0.139725 + 0.100870i
\(803\) −1.79902 3.36573i −0.0634860 0.118774i
\(804\) −7.05010 + 56.6192i −0.248638 + 1.99681i
\(805\) −0.732564 + 0.601200i −0.0258195 + 0.0211895i
\(806\) 2.21505 4.53171i 0.0780219 0.159623i
\(807\) 3.31432 16.6622i 0.116669 0.586537i
\(808\) −46.1950 8.68415i −1.62513 0.305507i
\(809\) 15.3470 3.05271i 0.539572 0.107328i 0.0822218 0.996614i \(-0.473798\pi\)
0.457351 + 0.889286i \(0.348798\pi\)
\(810\) −14.6414 25.1554i −0.514447 0.883870i
\(811\) 3.15123 0.955914i 0.110655 0.0335667i −0.234472 0.972123i \(-0.575336\pi\)
0.345126 + 0.938556i \(0.387836\pi\)
\(812\) 23.5618 + 0.605800i 0.826857 + 0.0212594i
\(813\) 26.0341 + 21.3656i 0.913056 + 0.749325i
\(814\) 6.21481 + 13.5893i 0.217829 + 0.476305i
\(815\) 0.309953 + 0.748292i 0.0108572 + 0.0262115i
\(816\) 3.55046 5.89250i 0.124291 0.206279i
\(817\) −18.9490 + 45.7469i −0.662942 + 1.60048i
\(818\) −21.1384 + 0.766280i −0.739088 + 0.0267923i
\(819\) 1.37931 0.135850i 0.0481970 0.00474699i
\(820\) 31.1777 19.6923i 1.08877 0.687687i
\(821\) −15.8735 8.48457i −0.553989 0.296114i 0.170548 0.985349i \(-0.445446\pi\)
−0.724537 + 0.689236i \(0.757946\pi\)
\(822\) 18.5752 + 14.1500i 0.647886 + 0.493537i
\(823\) −15.9328 + 23.8451i −0.555382 + 0.831188i −0.997846 0.0655981i \(-0.979104\pi\)
0.442464 + 0.896786i \(0.354104\pi\)
\(824\) 10.6224 5.82242i 0.370049 0.202834i
\(825\) −1.33721 + 0.893494i −0.0465556 + 0.0311075i
\(826\) 15.1445 13.3757i 0.526946 0.465401i
\(827\) 2.63378 26.7412i 0.0915855 0.929883i −0.834106 0.551604i \(-0.814016\pi\)
0.925692 0.378279i \(-0.123484\pi\)
\(828\) −0.0180406 0.248506i −0.000626956 0.00863618i
\(829\) 9.26047 30.5277i 0.321630 1.06027i −0.635860 0.771804i \(-0.719355\pi\)
0.957490 0.288466i \(-0.0931454\pi\)
\(830\) 7.61034 + 4.69546i 0.264159 + 0.162982i
\(831\) 49.5653i 1.71940i
\(832\) 28.9979 + 2.24065i 1.00532 + 0.0776807i
\(833\) 5.29252i 0.183375i
\(834\) 3.79304 6.14771i 0.131342 0.212878i
\(835\) 2.53243 8.34832i 0.0876385 0.288905i
\(836\) −11.2408 9.71917i −0.388771 0.336145i
\(837\) 0.469225 4.76412i 0.0162188 0.164672i
\(838\) 29.1356 + 32.9885i 1.00647 + 1.13957i
\(839\) 20.7787 13.8839i 0.717362 0.479326i −0.142538 0.989789i \(-0.545526\pi\)
0.859899 + 0.510464i \(0.170526\pi\)
\(840\) 9.88796 + 7.94209i 0.341167 + 0.274028i
\(841\) 39.3935 58.9565i 1.35840 2.03298i
\(842\) −8.09523 + 10.6269i −0.278980 + 0.366228i
\(843\) −45.6725 24.4125i −1.57304 0.840810i
\(844\) −36.9646 8.34581i −1.27238 0.287275i
\(845\) −0.450858 + 0.0444056i −0.0155100 + 0.00152760i
\(846\) −0.149122 4.11365i −0.00512692 0.141430i
\(847\) 4.12657 9.96242i 0.141791 0.342313i
\(848\) −38.1427 + 17.9318i −1.30983 + 0.615782i
\(849\) 20.4500 + 49.3707i 0.701843 + 1.69440i
\(850\) 0.786096 0.359506i 0.0269629 0.0123310i
\(851\) −2.31111 1.89668i −0.0792237 0.0650172i
\(852\) 16.1525 15.3427i 0.553376 0.525634i
\(853\) 48.4007 14.6822i 1.65721 0.502709i 0.683394 0.730050i \(-0.260503\pi\)
0.973815 + 0.227341i \(0.0730034\pi\)
\(854\) 6.59793 3.84025i 0.225776 0.131411i
\(855\) −3.60996 + 0.718066i −0.123458 + 0.0245574i
\(856\) 19.0279 + 12.4263i 0.650361 + 0.424721i
\(857\) −0.452120 + 2.27296i −0.0154441 + 0.0776428i −0.987739 0.156116i \(-0.950103\pi\)
0.972295 + 0.233759i \(0.0751026\pi\)
\(858\) 11.4663 + 5.60461i 0.391453 + 0.191338i
\(859\) 8.04245 6.60027i 0.274405 0.225198i −0.487118 0.873336i \(-0.661952\pi\)
0.761523 + 0.648138i \(0.224452\pi\)
\(860\) 29.8760 23.2597i 1.01876 0.793149i
\(861\) 8.95493 + 16.7535i 0.305183 + 0.570958i
\(862\) −8.56163 11.8596i −0.291610 0.403940i
\(863\) 1.65352 1.65352i 0.0562866 0.0562866i −0.678403 0.734690i \(-0.737328\pi\)
0.734690 + 0.678403i \(0.237328\pi\)
\(864\) 26.5329 7.61093i 0.902668 0.258929i
\(865\) −7.89688 7.89688i −0.268502 0.268502i
\(866\) 1.84327 11.4136i 0.0626369 0.387851i
\(867\) 25.9007 13.8442i 0.879634 0.470174i
\(868\) 0.614427 + 2.23033i 0.0208550 + 0.0757024i
\(869\) −5.07667 6.18594i −0.172214 0.209844i
\(870\) 50.8449 17.4588i 1.72380 0.591908i
\(871\) 55.7995 + 11.0992i 1.89069 + 0.376083i
\(872\) −0.206384 19.6003i −0.00698903 0.663749i
\(873\) 0.477660 + 2.40136i 0.0161664 + 0.0812738i
\(874\) 2.87451 + 0.759419i 0.0972316 + 0.0256877i
\(875\) 4.03260 + 13.2937i 0.136327 + 0.449409i
\(876\) 4.15188 9.33720i 0.140279 0.315475i
\(877\) 4.09874 4.99433i 0.138405 0.168647i −0.699195 0.714931i \(-0.746458\pi\)
0.837600 + 0.546284i \(0.183958\pi\)
\(878\) 6.29831 16.9140i 0.212558 0.570821i
\(879\) −38.9685 + 16.1413i −1.31437 + 0.544431i
\(880\) 3.80312 + 10.7074i 0.128203 + 0.360946i
\(881\) −54.0719 22.3973i −1.82173 0.754584i −0.974873 0.222759i \(-0.928494\pi\)
−0.846854 0.531825i \(-0.821506\pi\)
\(882\) 1.74702 1.87844i 0.0588251 0.0632504i
\(883\) −5.21828 52.9821i −0.175609 1.78299i −0.530104 0.847933i \(-0.677847\pi\)
0.354495 0.935058i \(-0.384653\pi\)
\(884\) −5.60382 3.95641i −0.188477 0.133068i
\(885\) 21.7248 40.6443i 0.730272 1.36624i
\(886\) 2.30511 + 17.0465i 0.0774415 + 0.572688i
\(887\) 13.5149 + 9.03037i 0.453786 + 0.303210i 0.761378 0.648308i \(-0.224523\pi\)
−0.307592 + 0.951518i \(0.599523\pi\)
\(888\) −18.4886 + 35.4834i −0.620437 + 1.19075i
\(889\) −10.6740 15.9748i −0.357996 0.535779i
\(890\) −0.516995 + 8.33601i −0.0173297 + 0.279424i
\(891\) 13.3689 + 1.31672i 0.447873 + 0.0441117i
\(892\) −6.62037 + 19.9622i −0.221666 + 0.668385i
\(893\) 47.0038 + 14.2584i 1.57292 + 0.477141i
\(894\) −6.67936 28.1983i −0.223391 0.943092i
\(895\) 17.6471 0.589878
\(896\) −10.6486 + 8.03381i −0.355745 + 0.268391i
\(897\) −2.55353 −0.0852599
\(898\) −10.0842 42.5727i −0.336516 1.42067i
\(899\) 9.38383 + 2.84655i 0.312968 + 0.0949379i
\(900\) −0.397674 0.131886i −0.0132558 0.00439621i
\(901\) 9.89292 + 0.974368i 0.329581 + 0.0324609i
\(902\) −1.05352 + 16.9870i −0.0350785 + 0.565605i
\(903\) 10.8364 + 16.2178i 0.360612 + 0.539694i
\(904\) −34.7743 + 10.9498i −1.15658 + 0.364186i
\(905\) 8.18303 + 5.46773i 0.272013 + 0.181753i
\(906\) 5.19088 + 38.3870i 0.172455 + 1.27532i
\(907\) −6.86453 + 12.8426i −0.227933 + 0.426432i −0.969726 0.244197i \(-0.921476\pi\)
0.741793 + 0.670629i \(0.233976\pi\)
\(908\) −19.0210 + 26.9412i −0.631234 + 0.894075i
\(909\) −0.526692 5.34760i −0.0174693 0.177369i
\(910\) 8.61239 9.26029i 0.285498 0.306976i
\(911\) 26.9724 + 11.1723i 0.893634 + 0.370155i 0.781769 0.623568i \(-0.214318\pi\)
0.111865 + 0.993723i \(0.464318\pi\)
\(912\) 2.04468 39.7364i 0.0677062 1.31580i
\(913\) −3.81304 + 1.57941i −0.126193 + 0.0522709i
\(914\) 15.8082 42.4526i 0.522887 1.40421i
\(915\) 11.0463 13.4600i 0.365179 0.444972i
\(916\) −4.83061 2.14798i −0.159608 0.0709712i
\(917\) −1.81241 5.97472i −0.0598511 0.197303i
\(918\) −6.29438 1.66292i −0.207746 0.0548845i
\(919\) −1.74253 8.76027i −0.0574806 0.288975i 0.941344 0.337449i \(-0.109564\pi\)
−0.998824 + 0.0484744i \(0.984564\pi\)
\(920\) −1.62439 1.59054i −0.0535545 0.0524384i
\(921\) 0.133502 + 0.0265553i 0.00439906 + 0.000875027i
\(922\) −13.9039 + 4.77423i −0.457901 + 0.157231i
\(923\) −14.0924 17.1716i −0.463856 0.565210i
\(924\) −5.64327 + 1.55465i −0.185650 + 0.0511441i
\(925\) −4.43376 + 2.36990i −0.145781 + 0.0779217i
\(926\) 1.08484 6.71741i 0.0356502 0.220748i
\(927\) 0.979203 + 0.979203i 0.0321612 + 0.0321612i
\(928\) 4.68752 + 56.3474i 0.153876 + 1.84969i
\(929\) −3.78546 + 3.78546i −0.124197 + 0.124197i −0.766473 0.642276i \(-0.777990\pi\)
0.642276 + 0.766473i \(0.277990\pi\)
\(930\) 3.08852 + 4.27823i 0.101277 + 0.140289i
\(931\) 14.4296 + 26.9959i 0.472912 + 0.884756i
\(932\) 7.74182 + 9.94402i 0.253592 + 0.325727i
\(933\) 27.2698 22.3798i 0.892774 0.732680i
\(934\) −34.4283 16.8282i −1.12653 0.550635i
\(935\) 0.522838 2.62848i 0.0170986 0.0859606i
\(936\) 0.682954 + 3.25400i 0.0223230 + 0.106360i
\(937\) −24.0478 + 4.78341i −0.785609 + 0.156267i −0.571565 0.820557i \(-0.693664\pi\)
−0.214044 + 0.976824i \(0.568664\pi\)
\(938\) −22.5515 + 13.1258i −0.736331 + 0.428574i
\(939\) 13.1227 3.98072i 0.428242 0.129906i
\(940\) −25.8668 27.2321i −0.843683 0.888212i
\(941\) −2.18792 1.79558i −0.0713240 0.0585341i 0.598056 0.801454i \(-0.295940\pi\)
−0.669380 + 0.742920i \(0.733440\pi\)
\(942\) −10.8383 + 4.95669i −0.353131 + 0.161498i
\(943\) −1.30313 3.14603i −0.0424357 0.102449i
\(944\) 35.8397 + 32.6352i 1.16648 + 1.06219i
\(945\) 4.59299 11.0885i 0.149410 0.360708i
\(946\) 0.633065 + 17.4636i 0.0205827 + 0.567791i
\(947\) −44.8450 + 4.41685i −1.45727 + 0.143528i −0.795397 0.606089i \(-0.792738\pi\)
−0.661871 + 0.749617i \(0.730238\pi\)
\(948\) 4.71901 20.9011i 0.153266 0.678836i
\(949\) −8.98620 4.80322i −0.291704 0.155919i
\(950\) 3.02953 3.97699i 0.0982911 0.129031i
\(951\) 10.0408 15.0271i 0.325596 0.487288i
\(952\) 3.12757 0.341325i 0.101365 0.0110624i
\(953\) −19.1771 + 12.8137i −0.621208 + 0.415078i −0.825954 0.563737i \(-0.809363\pi\)
0.204746 + 0.978815i \(0.434363\pi\)
\(954\) −3.18960 3.61140i −0.103267 0.116923i
\(955\) 0.0487902 0.495376i 0.00157882 0.0160300i
\(956\) 19.7024 22.7869i 0.637220 0.736983i
\(957\) −7.20246 + 23.7433i −0.232822 + 0.767513i
\(958\) 2.54460 4.12427i 0.0822124 0.133249i
\(959\) 10.6789i 0.344839i
\(960\) −16.3667 + 25.6476i −0.528233 + 0.827774i
\(961\) 30.0375i 0.968952i
\(962\) 33.9539 + 20.9490i 1.09472 + 0.675422i
\(963\) −0.754166 + 2.48615i −0.0243027 + 0.0801152i
\(964\) 54.9651 3.99027i 1.77031 0.128518i
\(965\) −0.680199 + 6.90618i −0.0218964 + 0.222318i
\(966\) 0.877801 0.775278i 0.0282428 0.0249442i
\(967\) −1.70664 + 1.14034i −0.0548818 + 0.0366709i −0.582709 0.812681i \(-0.698007\pi\)
0.527827 + 0.849352i \(0.323007\pi\)
\(968\) 24.8322 + 7.24813i 0.798137 + 0.232964i
\(969\) −5.21374 + 7.80292i −0.167490 + 0.250666i
\(970\) 17.7712 + 13.5375i 0.570600 + 0.434663i
\(971\) 10.4304 + 5.57518i 0.334728 + 0.178916i 0.630195 0.776437i \(-0.282975\pi\)
−0.295467 + 0.955353i \(0.595475\pi\)
\(972\) 3.57378 + 5.65815i 0.114629 + 0.181485i
\(973\) 3.28764 0.323804i 0.105397 0.0103807i
\(974\) −21.4539 + 0.777714i −0.687426 + 0.0249196i
\(975\) −1.64320 + 3.96702i −0.0526244 + 0.127046i
\(976\) 10.8754 + 14.7351i 0.348112 + 0.471661i
\(977\) −5.24366 12.6593i −0.167760 0.405007i 0.817533 0.575881i \(-0.195341\pi\)
−0.985293 + 0.170874i \(0.945341\pi\)
\(978\) −0.416292 0.910264i −0.0133116 0.0291070i
\(979\) −2.97978 2.44544i −0.0952342 0.0781567i
\(980\) 0.601605 23.3987i 0.0192176 0.747443i
\(981\) 2.14432 0.650473i 0.0684629 0.0207680i
\(982\) 1.10445 + 1.89755i 0.0352443 + 0.0605531i
\(983\) 30.4779 6.06243i 0.972093 0.193361i 0.316597 0.948560i \(-0.397460\pi\)
0.655496 + 0.755199i \(0.272460\pi\)
\(984\) −37.6228 + 25.7159i −1.19937 + 0.819791i
\(985\) −0.247256 + 1.24304i −0.00787824 + 0.0396066i
\(986\) 5.85627 11.9812i 0.186502 0.381558i
\(987\) 14.9566 12.2745i 0.476072 0.390703i
\(988\) −39.3707 4.90235i −1.25255 0.155965i
\(989\) −1.64817 3.08352i −0.0524089 0.0980501i
\(990\) −1.05321 + 0.760326i −0.0334731 + 0.0241648i
\(991\) −12.3275 + 12.3275i −0.391596 + 0.391596i −0.875256 0.483660i \(-0.839307\pi\)
0.483660 + 0.875256i \(0.339307\pi\)
\(992\) −5.15894 + 2.04574i −0.163797 + 0.0649524i
\(993\) −37.5905 37.5905i −1.19290 1.19290i
\(994\) 10.0579 + 1.62432i 0.319016 + 0.0515202i
\(995\) −26.2946 + 14.0548i −0.833596 + 0.445566i
\(996\) −9.60898 5.45818i −0.304472 0.172949i
\(997\) −21.2930 25.9456i −0.674356 0.821705i 0.317608 0.948222i \(-0.397120\pi\)
−0.991964 + 0.126517i \(0.959620\pi\)
\(998\) 18.9840 + 55.2868i 0.600929 + 1.75007i
\(999\) 37.1368 + 7.38696i 1.17496 + 0.233713i
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 128.2.k.a.5.15 240
4.3 odd 2 512.2.k.a.113.12 240
128.51 odd 32 512.2.k.a.145.12 240
128.77 even 32 inner 128.2.k.a.77.15 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
128.2.k.a.5.15 240 1.1 even 1 trivial
128.2.k.a.77.15 yes 240 128.77 even 32 inner
512.2.k.a.113.12 240 4.3 odd 2
512.2.k.a.145.12 240 128.51 odd 32