Properties

Label 729.2.e.q.325.1
Level $729$
Weight $2$
Character 729.325
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
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] = [729,2,Mod(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.e (of order \(9\), degree \(6\), not 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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 325.1
Root \(-0.642788 + 0.766044i\) of defining polynomial
Character \(\chi\) \(=\) 729.325
Dual form 729.2.e.q.406.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.50881 + 1.26604i) q^{2} +(0.326352 - 1.85083i) q^{4} +(-3.47843 + 1.26604i) q^{5} +(-0.407604 - 2.31164i) q^{7} +(-0.118782 - 0.205737i) q^{8} +O(q^{10})\) \(q+(-1.50881 + 1.26604i) q^{2} +(0.326352 - 1.85083i) q^{4} +(-3.47843 + 1.26604i) q^{5} +(-0.407604 - 2.31164i) q^{7} +(-0.118782 - 0.205737i) q^{8} +(3.64543 - 6.31407i) q^{10} +(2.04715 + 0.745100i) q^{11} +(-3.61334 - 3.03195i) q^{13} +(3.54163 + 2.97178i) q^{14} +(3.97178 + 1.44561i) q^{16} +(1.46756 - 2.54189i) q^{17} +(3.11334 + 5.39246i) q^{19} +(1.20805 + 6.85117i) q^{20} +(-4.03209 + 1.46756i) q^{22} +(0.0901285 - 0.511144i) q^{23} +(6.66637 - 5.59375i) q^{25} +9.29044 q^{26} -4.41147 q^{28} +(-2.67561 + 2.24510i) q^{29} +(-0.747626 + 4.24000i) q^{31} +(-7.37641 + 2.68479i) q^{32} +(1.00387 + 5.69323i) q^{34} +(4.34445 + 7.52481i) q^{35} +(-1.20574 + 2.08840i) q^{37} +(-11.5245 - 4.19459i) q^{38} +(0.673648 + 0.565258i) q^{40} +(1.91404 + 1.60607i) q^{41} +(-1.00000 - 0.363970i) q^{43} +(2.04715 - 3.54576i) q^{44} +(0.511144 + 0.885328i) q^{46} +(-0.0412527 - 0.233956i) q^{47} +(1.40033 - 0.509678i) q^{49} +(-2.97637 + 16.8799i) q^{50} +(-6.79086 + 5.69821i) q^{52} +4.66717 q^{53} -8.06418 q^{55} +(-0.427173 + 0.358441i) q^{56} +(1.19459 - 6.77487i) q^{58} +(12.5094 - 4.55303i) q^{59} +(-0.638156 - 3.61916i) q^{61} +(-4.24000 - 7.34389i) q^{62} +(3.50387 - 6.06888i) q^{64} +(16.4073 + 5.97178i) q^{65} +(10.9534 + 9.19096i) q^{67} +(-4.22567 - 3.54576i) q^{68} +(-16.0817 - 5.85327i) q^{70} +(-0.601535 + 1.04189i) q^{71} +(2.34002 + 4.05304i) q^{73} +(-0.824773 - 4.67752i) q^{74} +(10.9966 - 4.00243i) q^{76} +(0.887975 - 5.03596i) q^{77} +(-9.80587 + 8.22811i) q^{79} -15.6458 q^{80} -4.92127 q^{82} +(-8.65933 + 7.26604i) q^{83} +(-1.88666 + 10.6998i) q^{85} +(1.96962 - 0.716881i) q^{86} +(-0.0898700 - 0.509678i) q^{88} +(-0.349643 - 0.605600i) q^{89} +(-5.53596 + 9.58856i) q^{91} +(-0.916629 - 0.333626i) q^{92} +(0.358441 + 0.300767i) q^{94} +(-17.6566 - 14.8157i) q^{95} +(6.65910 + 2.42371i) q^{97} +(-1.46756 + 2.54189i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{4} - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{4} - 12 q^{7} + 12 q^{10} - 30 q^{13} + 18 q^{16} + 24 q^{19} - 30 q^{22} + 42 q^{25} - 12 q^{28} + 24 q^{31} - 36 q^{34} + 6 q^{37} + 6 q^{40} - 12 q^{43} - 6 q^{46} - 12 q^{49} - 18 q^{52} - 60 q^{55} + 6 q^{58} + 60 q^{61} - 6 q^{64} + 78 q^{67} - 66 q^{70} - 12 q^{73} + 48 q^{76} + 6 q^{79} - 24 q^{82} - 36 q^{85} - 24 q^{88} - 12 q^{94} + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50881 + 1.26604i −1.06689 + 0.895229i −0.994767 0.102167i \(-0.967422\pi\)
−0.0721247 + 0.997396i \(0.522978\pi\)
\(3\) 0 0
\(4\) 0.326352 1.85083i 0.163176 0.925417i
\(5\) −3.47843 + 1.26604i −1.55560 + 0.566192i −0.969723 0.244207i \(-0.921472\pi\)
−0.585877 + 0.810400i \(0.699250\pi\)
\(6\) 0 0
\(7\) −0.407604 2.31164i −0.154060 0.873716i −0.959640 0.281230i \(-0.909258\pi\)
0.805581 0.592486i \(-0.201854\pi\)
\(8\) −0.118782 0.205737i −0.0419959 0.0727390i
\(9\) 0 0
\(10\) 3.64543 6.31407i 1.15279 1.99668i
\(11\) 2.04715 + 0.745100i 0.617237 + 0.224656i 0.631667 0.775240i \(-0.282371\pi\)
−0.0144295 + 0.999896i \(0.504593\pi\)
\(12\) 0 0
\(13\) −3.61334 3.03195i −1.00216 0.840912i −0.0148781 0.999889i \(-0.504736\pi\)
−0.987282 + 0.158977i \(0.949180\pi\)
\(14\) 3.54163 + 2.97178i 0.946541 + 0.794242i
\(15\) 0 0
\(16\) 3.97178 + 1.44561i 0.992945 + 0.361403i
\(17\) 1.46756 2.54189i 0.355936 0.616499i −0.631342 0.775505i \(-0.717496\pi\)
0.987278 + 0.159006i \(0.0508289\pi\)
\(18\) 0 0
\(19\) 3.11334 + 5.39246i 0.714249 + 1.23712i 0.963248 + 0.268612i \(0.0865651\pi\)
−0.248999 + 0.968504i \(0.580102\pi\)
\(20\) 1.20805 + 6.85117i 0.270127 + 1.53197i
\(21\) 0 0
\(22\) −4.03209 + 1.46756i −0.859644 + 0.312885i
\(23\) 0.0901285 0.511144i 0.0187931 0.106581i −0.973968 0.226684i \(-0.927211\pi\)
0.992761 + 0.120103i \(0.0383226\pi\)
\(24\) 0 0
\(25\) 6.66637 5.59375i 1.33327 1.11875i
\(26\) 9.29044 1.82201
\(27\) 0 0
\(28\) −4.41147 −0.833690
\(29\) −2.67561 + 2.24510i −0.496848 + 0.416905i −0.856473 0.516192i \(-0.827349\pi\)
0.359625 + 0.933097i \(0.382905\pi\)
\(30\) 0 0
\(31\) −0.747626 + 4.24000i −0.134278 + 0.761526i 0.841082 + 0.540907i \(0.181919\pi\)
−0.975360 + 0.220619i \(0.929192\pi\)
\(32\) −7.37641 + 2.68479i −1.30398 + 0.474609i
\(33\) 0 0
\(34\) 1.00387 + 5.69323i 0.172162 + 0.976381i
\(35\) 4.34445 + 7.52481i 0.734347 + 1.27193i
\(36\) 0 0
\(37\) −1.20574 + 2.08840i −0.198222 + 0.343330i −0.947952 0.318413i \(-0.896850\pi\)
0.749730 + 0.661744i \(0.230183\pi\)
\(38\) −11.5245 4.19459i −1.86953 0.680453i
\(39\) 0 0
\(40\) 0.673648 + 0.565258i 0.106513 + 0.0893751i
\(41\) 1.91404 + 1.60607i 0.298922 + 0.250826i 0.779896 0.625910i \(-0.215272\pi\)
−0.480973 + 0.876735i \(0.659717\pi\)
\(42\) 0 0
\(43\) −1.00000 0.363970i −0.152499 0.0555049i 0.264643 0.964346i \(-0.414746\pi\)
−0.417142 + 0.908842i \(0.636968\pi\)
\(44\) 2.04715 3.54576i 0.308619 0.534543i
\(45\) 0 0
\(46\) 0.511144 + 0.885328i 0.0753641 + 0.130534i
\(47\) −0.0412527 0.233956i −0.00601732 0.0341259i 0.981651 0.190685i \(-0.0610709\pi\)
−0.987669 + 0.156559i \(0.949960\pi\)
\(48\) 0 0
\(49\) 1.40033 0.509678i 0.200047 0.0728112i
\(50\) −2.97637 + 16.8799i −0.420923 + 2.38717i
\(51\) 0 0
\(52\) −6.79086 + 5.69821i −0.941723 + 0.790199i
\(53\) 4.66717 0.641085 0.320543 0.947234i \(-0.396135\pi\)
0.320543 + 0.947234i \(0.396135\pi\)
\(54\) 0 0
\(55\) −8.06418 −1.08737
\(56\) −0.427173 + 0.358441i −0.0570834 + 0.0478987i
\(57\) 0 0
\(58\) 1.19459 6.77487i 0.156858 0.889584i
\(59\) 12.5094 4.55303i 1.62858 0.592754i 0.643590 0.765370i \(-0.277444\pi\)
0.984989 + 0.172616i \(0.0552219\pi\)
\(60\) 0 0
\(61\) −0.638156 3.61916i −0.0817075 0.463386i −0.998019 0.0629190i \(-0.979959\pi\)
0.916311 0.400467i \(-0.131152\pi\)
\(62\) −4.24000 7.34389i −0.538480 0.932675i
\(63\) 0 0
\(64\) 3.50387 6.06888i 0.437984 0.758610i
\(65\) 16.4073 + 5.97178i 2.03508 + 0.740708i
\(66\) 0 0
\(67\) 10.9534 + 9.19096i 1.33817 + 1.12285i 0.982093 + 0.188397i \(0.0603291\pi\)
0.356073 + 0.934458i \(0.384115\pi\)
\(68\) −4.22567 3.54576i −0.512438 0.429986i
\(69\) 0 0
\(70\) −16.0817 5.85327i −1.92213 0.699599i
\(71\) −0.601535 + 1.04189i −0.0713891 + 0.123649i −0.899510 0.436900i \(-0.856077\pi\)
0.828121 + 0.560549i \(0.189410\pi\)
\(72\) 0 0
\(73\) 2.34002 + 4.05304i 0.273879 + 0.474372i 0.969852 0.243696i \(-0.0783599\pi\)
−0.695973 + 0.718068i \(0.745027\pi\)
\(74\) −0.824773 4.67752i −0.0958779 0.543750i
\(75\) 0 0
\(76\) 10.9966 4.00243i 1.26140 0.459111i
\(77\) 0.887975 5.03596i 0.101194 0.573901i
\(78\) 0 0
\(79\) −9.80587 + 8.22811i −1.10325 + 0.925734i −0.997639 0.0686737i \(-0.978123\pi\)
−0.105608 + 0.994408i \(0.533679\pi\)
\(80\) −15.6458 −1.74925
\(81\) 0 0
\(82\) −4.92127 −0.543464
\(83\) −8.65933 + 7.26604i −0.950485 + 0.797552i −0.979379 0.202030i \(-0.935246\pi\)
0.0288938 + 0.999582i \(0.490802\pi\)
\(84\) 0 0
\(85\) −1.88666 + 10.6998i −0.204637 + 1.16055i
\(86\) 1.96962 0.716881i 0.212389 0.0773033i
\(87\) 0 0
\(88\) −0.0898700 0.509678i −0.00958018 0.0543319i
\(89\) −0.349643 0.605600i −0.0370621 0.0641935i 0.846899 0.531753i \(-0.178467\pi\)
−0.883961 + 0.467560i \(0.845133\pi\)
\(90\) 0 0
\(91\) −5.53596 + 9.58856i −0.580326 + 1.00515i
\(92\) −0.916629 0.333626i −0.0955652 0.0347829i
\(93\) 0 0
\(94\) 0.358441 + 0.300767i 0.0369703 + 0.0310218i
\(95\) −17.6566 14.8157i −1.81153 1.52006i
\(96\) 0 0
\(97\) 6.65910 + 2.42371i 0.676129 + 0.246091i 0.657185 0.753730i \(-0.271747\pi\)
0.0189446 + 0.999821i \(0.493969\pi\)
\(98\) −1.46756 + 2.54189i −0.148246 + 0.256770i
\(99\) 0 0
\(100\) −8.17752 14.1639i −0.817752 1.41639i
\(101\) 0.812174 + 4.60607i 0.0808143 + 0.458321i 0.998182 + 0.0602789i \(0.0191990\pi\)
−0.917367 + 0.398042i \(0.869690\pi\)
\(102\) 0 0
\(103\) 12.8020 4.65955i 1.26142 0.459119i 0.377174 0.926142i \(-0.376896\pi\)
0.884245 + 0.467023i \(0.154674\pi\)
\(104\) −0.194584 + 1.10354i −0.0190805 + 0.108211i
\(105\) 0 0
\(106\) −7.04189 + 5.90885i −0.683969 + 0.573918i
\(107\) 11.6340 1.12470 0.562350 0.826900i \(-0.309898\pi\)
0.562350 + 0.826900i \(0.309898\pi\)
\(108\) 0 0
\(109\) 14.6040 1.39881 0.699405 0.714725i \(-0.253448\pi\)
0.699405 + 0.714725i \(0.253448\pi\)
\(110\) 12.1673 10.2096i 1.16011 0.973448i
\(111\) 0 0
\(112\) 1.72281 9.77055i 0.162790 0.923230i
\(113\) −4.41263 + 1.60607i −0.415106 + 0.151086i −0.541126 0.840942i \(-0.682002\pi\)
0.126020 + 0.992028i \(0.459780\pi\)
\(114\) 0 0
\(115\) 0.333626 + 1.89209i 0.0311108 + 0.176438i
\(116\) 3.28212 + 5.68479i 0.304737 + 0.527820i
\(117\) 0 0
\(118\) −13.1099 + 22.7071i −1.20687 + 2.09036i
\(119\) −6.47410 2.35638i −0.593480 0.216009i
\(120\) 0 0
\(121\) −4.79086 4.02001i −0.435533 0.365455i
\(122\) 5.54488 + 4.65270i 0.502010 + 0.421236i
\(123\) 0 0
\(124\) 7.60354 + 2.76746i 0.682818 + 0.248525i
\(125\) −6.85240 + 11.8687i −0.612897 + 1.06157i
\(126\) 0 0
\(127\) −3.04576 5.27541i −0.270267 0.468117i 0.698663 0.715451i \(-0.253779\pi\)
−0.968930 + 0.247334i \(0.920445\pi\)
\(128\) −0.329421 1.86824i −0.0291170 0.165131i
\(129\) 0 0
\(130\) −32.3161 + 11.7621i −2.83431 + 1.03161i
\(131\) 1.79698 10.1912i 0.157003 0.890408i −0.799929 0.600095i \(-0.795129\pi\)
0.956932 0.290313i \(-0.0937595\pi\)
\(132\) 0 0
\(133\) 11.1964 9.39490i 0.970851 0.814641i
\(134\) −28.1627 −2.43289
\(135\) 0 0
\(136\) −0.697281 −0.0597914
\(137\) 14.6197 12.2674i 1.24905 1.04807i 0.252285 0.967653i \(-0.418818\pi\)
0.996761 0.0804207i \(-0.0256264\pi\)
\(138\) 0 0
\(139\) −4.04664 + 22.9496i −0.343231 + 1.94656i −0.0213784 + 0.999771i \(0.506805\pi\)
−0.321853 + 0.946790i \(0.604306\pi\)
\(140\) 15.3450 5.58512i 1.29689 0.472029i
\(141\) 0 0
\(142\) −0.411474 2.33359i −0.0345301 0.195830i
\(143\) −5.13793 8.89915i −0.429655 0.744184i
\(144\) 0 0
\(145\) 6.46451 11.1969i 0.536848 0.929848i
\(146\) −8.66198 3.15270i −0.716871 0.260920i
\(147\) 0 0
\(148\) 3.47178 + 2.91317i 0.285379 + 0.239461i
\(149\) 11.8782 + 9.96703i 0.973104 + 0.816531i 0.983035 0.183419i \(-0.0587167\pi\)
−0.00993072 + 0.999951i \(0.503161\pi\)
\(150\) 0 0
\(151\) 5.54576 + 2.01849i 0.451308 + 0.164262i 0.557666 0.830065i \(-0.311697\pi\)
−0.106359 + 0.994328i \(0.533919\pi\)
\(152\) 0.739620 1.28106i 0.0599911 0.103908i
\(153\) 0 0
\(154\) 5.03596 + 8.72254i 0.405809 + 0.702882i
\(155\) −2.76746 15.6951i −0.222288 1.26066i
\(156\) 0 0
\(157\) 1.13903 0.414574i 0.0909047 0.0330866i −0.296167 0.955136i \(-0.595709\pi\)
0.387072 + 0.922049i \(0.373486\pi\)
\(158\) 4.37808 24.8293i 0.348302 1.97532i
\(159\) 0 0
\(160\) 22.2592 18.6777i 1.75975 1.47660i
\(161\) −1.21832 −0.0960168
\(162\) 0 0
\(163\) 2.77332 0.217223 0.108612 0.994084i \(-0.465360\pi\)
0.108612 + 0.994084i \(0.465360\pi\)
\(164\) 3.59721 3.01842i 0.280895 0.235699i
\(165\) 0 0
\(166\) 3.86618 21.9262i 0.300074 1.70180i
\(167\) 3.59721 1.30928i 0.278361 0.101315i −0.199068 0.979986i \(-0.563791\pi\)
0.477428 + 0.878671i \(0.341569\pi\)
\(168\) 0 0
\(169\) 1.60607 + 9.10846i 0.123544 + 0.700651i
\(170\) −10.6998 18.5326i −0.820635 1.42138i
\(171\) 0 0
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) 6.60549 + 2.40420i 0.502206 + 0.182788i 0.580686 0.814128i \(-0.302784\pi\)
−0.0784801 + 0.996916i \(0.525007\pi\)
\(174\) 0 0
\(175\) −15.6480 13.1302i −1.18287 0.992549i
\(176\) 7.05369 + 5.91875i 0.531692 + 0.446142i
\(177\) 0 0
\(178\) 1.29426 + 0.471073i 0.0970091 + 0.0353084i
\(179\) 7.19269 12.4581i 0.537607 0.931163i −0.461425 0.887179i \(-0.652662\pi\)
0.999032 0.0439838i \(-0.0140050\pi\)
\(180\) 0 0
\(181\) −6.60014 11.4318i −0.490584 0.849717i 0.509357 0.860555i \(-0.329883\pi\)
−0.999941 + 0.0108384i \(0.996550\pi\)
\(182\) −3.78682 21.4761i −0.280698 1.59192i
\(183\) 0 0
\(184\) −0.115867 + 0.0421721i −0.00854183 + 0.00310897i
\(185\) 1.55007 8.79086i 0.113963 0.646317i
\(186\) 0 0
\(187\) 4.89827 4.11014i 0.358197 0.300563i
\(188\) −0.446476 −0.0325626
\(189\) 0 0
\(190\) 45.3979 3.29351
\(191\) 10.2829 8.62836i 0.744043 0.624326i −0.189877 0.981808i \(-0.560809\pi\)
0.933920 + 0.357482i \(0.116365\pi\)
\(192\) 0 0
\(193\) 2.60560 14.7771i 0.187555 1.06368i −0.735073 0.677988i \(-0.762852\pi\)
0.922628 0.385690i \(-0.126037\pi\)
\(194\) −13.1159 + 4.77379i −0.941664 + 0.342738i
\(195\) 0 0
\(196\) −0.486329 2.75811i −0.0347378 0.197008i
\(197\) 11.1606 + 19.3307i 0.795158 + 1.37725i 0.922739 + 0.385426i \(0.125946\pi\)
−0.127580 + 0.991828i \(0.540721\pi\)
\(198\) 0 0
\(199\) 4.55051 7.88171i 0.322577 0.558720i −0.658442 0.752631i \(-0.728784\pi\)
0.981019 + 0.193912i \(0.0621176\pi\)
\(200\) −1.94269 0.707081i −0.137369 0.0499982i
\(201\) 0 0
\(202\) −7.05690 5.92145i −0.496522 0.416631i
\(203\) 6.28044 + 5.26991i 0.440800 + 0.369876i
\(204\) 0 0
\(205\) −8.69119 3.16333i −0.607019 0.220937i
\(206\) −13.4166 + 23.2383i −0.934781 + 1.61909i
\(207\) 0 0
\(208\) −9.96838 17.2657i −0.691183 1.19716i
\(209\) 2.35554 + 13.3589i 0.162936 + 0.924055i
\(210\) 0 0
\(211\) 5.61721 2.04450i 0.386705 0.140749i −0.141349 0.989960i \(-0.545144\pi\)
0.528054 + 0.849211i \(0.322922\pi\)
\(212\) 1.52314 8.63816i 0.104610 0.593271i
\(213\) 0 0
\(214\) −17.5535 + 14.7291i −1.19993 + 1.00686i
\(215\) 3.93923 0.268653
\(216\) 0 0
\(217\) 10.1061 0.686045
\(218\) −22.0347 + 18.4893i −1.49238 + 1.25225i
\(219\) 0 0
\(220\) −2.63176 + 14.9254i −0.177433 + 1.00627i
\(221\) −13.0097 + 4.73514i −0.875126 + 0.318520i
\(222\) 0 0
\(223\) −1.54576 8.76644i −0.103512 0.587044i −0.991804 0.127766i \(-0.959219\pi\)
0.888293 0.459278i \(-0.151892\pi\)
\(224\) 9.21291 + 15.9572i 0.615564 + 1.06619i
\(225\) 0 0
\(226\) 4.62449 8.00984i 0.307616 0.532807i
\(227\) 10.0251 + 3.64883i 0.665388 + 0.242182i 0.652561 0.757736i \(-0.273695\pi\)
0.0128273 + 0.999918i \(0.495917\pi\)
\(228\) 0 0
\(229\) −6.33615 5.31666i −0.418705 0.351335i 0.408965 0.912550i \(-0.365890\pi\)
−0.827670 + 0.561215i \(0.810334\pi\)
\(230\) −2.89884 2.43242i −0.191144 0.160389i
\(231\) 0 0
\(232\) 0.779715 + 0.283793i 0.0511908 + 0.0186319i
\(233\) −6.36965 + 11.0326i −0.417290 + 0.722767i −0.995666 0.0930034i \(-0.970353\pi\)
0.578376 + 0.815770i \(0.303687\pi\)
\(234\) 0 0
\(235\) 0.439693 + 0.761570i 0.0286824 + 0.0496793i
\(236\) −4.34445 24.6386i −0.282800 1.60384i
\(237\) 0 0
\(238\) 12.7515 4.64117i 0.826557 0.300842i
\(239\) 2.60743 14.7875i 0.168660 0.956521i −0.776549 0.630057i \(-0.783032\pi\)
0.945210 0.326464i \(-0.105857\pi\)
\(240\) 0 0
\(241\) 0.609470 0.511406i 0.0392594 0.0329426i −0.622947 0.782264i \(-0.714065\pi\)
0.662206 + 0.749322i \(0.269620\pi\)
\(242\) 12.3180 0.791832
\(243\) 0 0
\(244\) −6.90673 −0.442158
\(245\) −4.22567 + 3.54576i −0.269968 + 0.226530i
\(246\) 0 0
\(247\) 5.10014 28.9243i 0.324514 1.84041i
\(248\) 0.961130 0.349823i 0.0610318 0.0222138i
\(249\) 0 0
\(250\) −4.68732 26.5831i −0.296452 1.68126i
\(251\) −4.15749 7.20099i −0.262419 0.454522i 0.704465 0.709738i \(-0.251187\pi\)
−0.966884 + 0.255216i \(0.917853\pi\)
\(252\) 0 0
\(253\) 0.565360 0.979232i 0.0355439 0.0615638i
\(254\) 11.2744 + 4.10354i 0.707418 + 0.257479i
\(255\) 0 0
\(256\) 13.5988 + 11.4107i 0.849925 + 0.713171i
\(257\) −19.6262 16.4684i −1.22425 1.02727i −0.998591 0.0530632i \(-0.983102\pi\)
−0.225661 0.974206i \(-0.572454\pi\)
\(258\) 0 0
\(259\) 5.31908 + 1.93599i 0.330511 + 0.120296i
\(260\) 16.4073 28.4183i 1.01754 1.76243i
\(261\) 0 0
\(262\) 10.1912 + 17.6517i 0.629614 + 1.09052i
\(263\) 4.87343 + 27.6386i 0.300509 + 1.70427i 0.643926 + 0.765088i \(0.277304\pi\)
−0.343417 + 0.939183i \(0.611585\pi\)
\(264\) 0 0
\(265\) −16.2344 + 5.90885i −0.997273 + 0.362978i
\(266\) −4.99892 + 28.3503i −0.306504 + 1.73827i
\(267\) 0 0
\(268\) 20.5856 17.2734i 1.25746 1.05514i
\(269\) −30.1710 −1.83956 −0.919778 0.392439i \(-0.871631\pi\)
−0.919778 + 0.392439i \(0.871631\pi\)
\(270\) 0 0
\(271\) −19.0000 −1.15417 −0.577084 0.816685i \(-0.695809\pi\)
−0.577084 + 0.816685i \(0.695809\pi\)
\(272\) 9.50341 7.97431i 0.576229 0.483513i
\(273\) 0 0
\(274\) −6.52734 + 37.0184i −0.394331 + 2.23636i
\(275\) 17.8149 6.48411i 1.07428 0.391006i
\(276\) 0 0
\(277\) 3.66772 + 20.8007i 0.220372 + 1.24979i 0.871338 + 0.490684i \(0.163253\pi\)
−0.650966 + 0.759107i \(0.725636\pi\)
\(278\) −22.9496 39.7499i −1.37643 2.38404i
\(279\) 0 0
\(280\) 1.03209 1.78763i 0.0616791 0.106831i
\(281\) 1.64192 + 0.597611i 0.0979489 + 0.0356505i 0.390530 0.920590i \(-0.372292\pi\)
−0.292581 + 0.956241i \(0.594514\pi\)
\(282\) 0 0
\(283\) −5.58306 4.68475i −0.331879 0.278479i 0.461586 0.887095i \(-0.347281\pi\)
−0.793465 + 0.608616i \(0.791725\pi\)
\(284\) 1.73205 + 1.45336i 0.102778 + 0.0862412i
\(285\) 0 0
\(286\) 19.0189 + 6.92231i 1.12461 + 0.409325i
\(287\) 2.93247 5.07919i 0.173098 0.299815i
\(288\) 0 0
\(289\) 4.19253 + 7.26168i 0.246620 + 0.427158i
\(290\) 4.42198 + 25.0783i 0.259668 + 1.47265i
\(291\) 0 0
\(292\) 8.26517 3.00827i 0.483682 0.176046i
\(293\) −2.66565 + 15.1177i −0.155729 + 0.883184i 0.802387 + 0.596804i \(0.203563\pi\)
−0.958116 + 0.286380i \(0.907548\pi\)
\(294\) 0 0
\(295\) −37.7486 + 31.6748i −2.19781 + 1.84418i
\(296\) 0.572881 0.0332980
\(297\) 0 0
\(298\) −30.5408 −1.76918
\(299\) −1.87543 + 1.57367i −0.108459 + 0.0910079i
\(300\) 0 0
\(301\) −0.433763 + 2.45999i −0.0250017 + 0.141792i
\(302\) −10.9230 + 3.97565i −0.628549 + 0.228773i
\(303\) 0 0
\(304\) 4.57011 + 25.9184i 0.262114 + 1.48652i
\(305\) 6.80180 + 11.7811i 0.389470 + 0.674581i
\(306\) 0 0
\(307\) −8.38191 + 14.5179i −0.478381 + 0.828580i −0.999693 0.0247861i \(-0.992110\pi\)
0.521312 + 0.853366i \(0.325443\pi\)
\(308\) −9.03093 3.28699i −0.514585 0.187294i
\(309\) 0 0
\(310\) 24.0462 + 20.1772i 1.36573 + 1.14599i
\(311\) 12.2744 + 10.2995i 0.696020 + 0.584030i 0.920638 0.390417i \(-0.127669\pi\)
−0.224619 + 0.974447i \(0.572114\pi\)
\(312\) 0 0
\(313\) −32.3307 11.7674i −1.82744 0.665133i −0.993577 0.113160i \(-0.963903\pi\)
−0.833862 0.551973i \(-0.813875\pi\)
\(314\) −1.19372 + 2.06758i −0.0673654 + 0.116680i
\(315\) 0 0
\(316\) 12.0287 + 20.8343i 0.676666 + 1.17202i
\(317\) 2.83239 + 16.0633i 0.159083 + 0.902205i 0.954957 + 0.296743i \(0.0959005\pi\)
−0.795874 + 0.605462i \(0.792988\pi\)
\(318\) 0 0
\(319\) −7.15018 + 2.60245i −0.400333 + 0.145709i
\(320\) −4.50449 + 25.5462i −0.251809 + 1.42808i
\(321\) 0 0
\(322\) 1.83821 1.54244i 0.102440 0.0859570i
\(323\) 18.2761 1.01691
\(324\) 0 0
\(325\) −41.0479 −2.27693
\(326\) −4.18442 + 3.51114i −0.231754 + 0.194464i
\(327\) 0 0
\(328\) 0.103074 0.584561i 0.00569130 0.0322770i
\(329\) −0.524005 + 0.190722i −0.0288893 + 0.0105149i
\(330\) 0 0
\(331\) −5.48380 31.1002i −0.301417 1.70942i −0.639908 0.768452i \(-0.721028\pi\)
0.338491 0.940970i \(-0.390084\pi\)
\(332\) 10.6222 + 18.3983i 0.582972 + 1.00974i
\(333\) 0 0
\(334\) −3.76991 + 6.52968i −0.206281 + 0.357288i
\(335\) −49.7367 18.1027i −2.71740 0.989054i
\(336\) 0 0
\(337\) 4.60014 + 3.85997i 0.250585 + 0.210266i 0.759424 0.650596i \(-0.225481\pi\)
−0.508839 + 0.860862i \(0.669925\pi\)
\(338\) −13.9550 11.7096i −0.759050 0.636919i
\(339\) 0 0
\(340\) 19.1878 + 6.98378i 1.04060 + 0.378749i
\(341\) −4.68972 + 8.12284i −0.253963 + 0.439876i
\(342\) 0 0
\(343\) −9.96451 17.2590i −0.538033 0.931900i
\(344\) 0.0439002 + 0.248970i 0.00236694 + 0.0134236i
\(345\) 0 0
\(346\) −13.0103 + 4.73535i −0.699436 + 0.254574i
\(347\) −3.99919 + 22.6805i −0.214688 + 1.21755i 0.666760 + 0.745272i \(0.267680\pi\)
−0.881448 + 0.472281i \(0.843431\pi\)
\(348\) 0 0
\(349\) −8.86025 + 7.43463i −0.474278 + 0.397967i −0.848352 0.529432i \(-0.822405\pi\)
0.374074 + 0.927399i \(0.377961\pi\)
\(350\) 40.2332 2.15056
\(351\) 0 0
\(352\) −17.1010 −0.911487
\(353\) 1.63522 1.37211i 0.0870339 0.0730301i −0.598233 0.801322i \(-0.704130\pi\)
0.685267 + 0.728292i \(0.259686\pi\)
\(354\) 0 0
\(355\) 0.773318 4.38571i 0.0410435 0.232769i
\(356\) −1.23497 + 0.449493i −0.0654533 + 0.0238231i
\(357\) 0 0
\(358\) 4.92009 + 27.9032i 0.260035 + 1.47473i
\(359\) 12.1118 + 20.9782i 0.639234 + 1.10719i 0.985601 + 0.169087i \(0.0540818\pi\)
−0.346367 + 0.938099i \(0.612585\pi\)
\(360\) 0 0
\(361\) −9.88578 + 17.1227i −0.520304 + 0.901193i
\(362\) 24.4315 + 8.89234i 1.28409 + 0.467371i
\(363\) 0 0
\(364\) 15.9402 + 13.3754i 0.835491 + 0.701061i
\(365\) −13.2709 11.1356i −0.694632 0.582865i
\(366\) 0 0
\(367\) 2.66385 + 0.969561i 0.139052 + 0.0506107i 0.410609 0.911812i \(-0.365316\pi\)
−0.271557 + 0.962422i \(0.587538\pi\)
\(368\) 1.09689 1.89986i 0.0571792 0.0990372i
\(369\) 0 0
\(370\) 8.79086 + 15.2262i 0.457015 + 0.791573i
\(371\) −1.90236 10.7888i −0.0987654 0.560127i
\(372\) 0 0
\(373\) 27.0945 9.86160i 1.40290 0.510614i 0.473863 0.880599i \(-0.342859\pi\)
0.929038 + 0.369985i \(0.120637\pi\)
\(374\) −2.18696 + 12.4029i −0.113085 + 0.641336i
\(375\) 0 0
\(376\) −0.0432332 + 0.0362770i −0.00222958 + 0.00187084i
\(377\) 16.4749 0.848501
\(378\) 0 0
\(379\) 32.1985 1.65393 0.826963 0.562256i \(-0.190066\pi\)
0.826963 + 0.562256i \(0.190066\pi\)
\(380\) −33.1836 + 27.8444i −1.70228 + 1.42839i
\(381\) 0 0
\(382\) −4.59105 + 26.0372i −0.234899 + 1.33218i
\(383\) 0.631708 0.229923i 0.0322788 0.0117485i −0.325830 0.945428i \(-0.605644\pi\)
0.358109 + 0.933680i \(0.383422\pi\)
\(384\) 0 0
\(385\) 3.28699 + 18.6414i 0.167520 + 0.950056i
\(386\) 14.7771 + 25.5947i 0.752134 + 1.30273i
\(387\) 0 0
\(388\) 6.65910 11.5339i 0.338065 0.585545i
\(389\) −4.00243 1.45677i −0.202931 0.0738610i 0.238555 0.971129i \(-0.423326\pi\)
−0.441486 + 0.897268i \(0.645549\pi\)
\(390\) 0 0
\(391\) −1.16700 0.979232i −0.0590179 0.0495219i
\(392\) −0.271194 0.227559i −0.0136974 0.0114935i
\(393\) 0 0
\(394\) −41.3127 15.0366i −2.08131 0.757533i
\(395\) 23.6919 41.0355i 1.19207 2.06472i
\(396\) 0 0
\(397\) 4.43242 + 7.67717i 0.222457 + 0.385306i 0.955553 0.294818i \(-0.0952591\pi\)
−0.733097 + 0.680124i \(0.761926\pi\)
\(398\) 3.11273 + 17.6532i 0.156027 + 0.884873i
\(399\) 0 0
\(400\) 34.5638 12.5802i 1.72819 0.629009i
\(401\) −6.43956 + 36.5205i −0.321576 + 1.82375i 0.211142 + 0.977455i \(0.432282\pi\)
−0.532718 + 0.846293i \(0.678829\pi\)
\(402\) 0 0
\(403\) 15.5569 13.0538i 0.774945 0.650256i
\(404\) 8.79012 0.437325
\(405\) 0 0
\(406\) −16.1480 −0.801410
\(407\) −4.02438 + 3.37686i −0.199481 + 0.167385i
\(408\) 0 0
\(409\) −0.588526 + 3.33770i −0.0291007 + 0.165038i −0.995895 0.0905183i \(-0.971148\pi\)
0.966794 + 0.255557i \(0.0822588\pi\)
\(410\) 17.1183 6.23055i 0.845413 0.307705i
\(411\) 0 0
\(412\) −4.44609 25.2150i −0.219043 1.24226i
\(413\) −15.6238 27.0612i −0.768798 1.33160i
\(414\) 0 0
\(415\) 20.9217 36.2375i 1.02701 1.77883i
\(416\) 34.7936 + 12.6638i 1.70590 + 0.620896i
\(417\) 0 0
\(418\) −20.4670 17.1739i −1.00108 0.840002i
\(419\) 15.8237 + 13.2777i 0.773038 + 0.648656i 0.941485 0.337055i \(-0.109431\pi\)
−0.168447 + 0.985711i \(0.553875\pi\)
\(420\) 0 0
\(421\) −25.8726 9.41685i −1.26095 0.458949i −0.376864 0.926269i \(-0.622998\pi\)
−0.884088 + 0.467320i \(0.845220\pi\)
\(422\) −5.88690 + 10.1964i −0.286570 + 0.496353i
\(423\) 0 0
\(424\) −0.554378 0.960210i −0.0269230 0.0466319i
\(425\) −4.43539 25.1544i −0.215148 1.22017i
\(426\) 0 0
\(427\) −8.10607 + 2.95037i −0.392280 + 0.142778i
\(428\) 3.79677 21.5326i 0.183524 1.04082i
\(429\) 0 0
\(430\) −5.94356 + 4.98724i −0.286624 + 0.240506i
\(431\) 2.58110 0.124327 0.0621636 0.998066i \(-0.480200\pi\)
0.0621636 + 0.998066i \(0.480200\pi\)
\(432\) 0 0
\(433\) −27.0137 −1.29820 −0.649098 0.760704i \(-0.724854\pi\)
−0.649098 + 0.760704i \(0.724854\pi\)
\(434\) −15.2482 + 12.7947i −0.731935 + 0.614167i
\(435\) 0 0
\(436\) 4.76604 27.0296i 0.228252 1.29448i
\(437\) 3.03693 1.10535i 0.145276 0.0528761i
\(438\) 0 0
\(439\) 2.03343 + 11.5322i 0.0970505 + 0.550401i 0.994100 + 0.108470i \(0.0345951\pi\)
−0.897049 + 0.441931i \(0.854294\pi\)
\(440\) 0.957882 + 1.65910i 0.0456652 + 0.0790945i
\(441\) 0 0
\(442\) 13.6343 23.6153i 0.648517 1.12326i
\(443\) 1.95529 + 0.711667i 0.0928986 + 0.0338123i 0.388051 0.921638i \(-0.373148\pi\)
−0.295153 + 0.955450i \(0.595371\pi\)
\(444\) 0 0
\(445\) 1.98293 + 1.66387i 0.0939997 + 0.0788751i
\(446\) 13.4310 + 11.2699i 0.635974 + 0.533646i
\(447\) 0 0
\(448\) −15.4572 5.62597i −0.730286 0.265802i
\(449\) 5.27541 9.13728i 0.248962 0.431215i −0.714276 0.699864i \(-0.753244\pi\)
0.963238 + 0.268649i \(0.0865772\pi\)
\(450\) 0 0
\(451\) 2.72163 + 4.71400i 0.128157 + 0.221974i
\(452\) 1.53249 + 8.69119i 0.0720823 + 0.408799i
\(453\) 0 0
\(454\) −19.7456 + 7.18680i −0.926705 + 0.337293i
\(455\) 7.11689 40.3619i 0.333645 1.89220i
\(456\) 0 0
\(457\) −6.05896 + 5.08407i −0.283426 + 0.237823i −0.773406 0.633911i \(-0.781449\pi\)
0.489980 + 0.871734i \(0.337004\pi\)
\(458\) 16.2912 0.761238
\(459\) 0 0
\(460\) 3.61081 0.168355
\(461\) 29.9468 25.1284i 1.39476 1.17034i 0.431393 0.902164i \(-0.358022\pi\)
0.963369 0.268180i \(-0.0864222\pi\)
\(462\) 0 0
\(463\) 4.11422 23.3329i 0.191204 1.08437i −0.726518 0.687148i \(-0.758863\pi\)
0.917722 0.397224i \(-0.130026\pi\)
\(464\) −13.8725 + 5.04916i −0.644013 + 0.234402i
\(465\) 0 0
\(466\) −4.35710 24.7103i −0.201839 1.14468i
\(467\) −17.3576 30.0642i −0.803214 1.39121i −0.917490 0.397758i \(-0.869788\pi\)
0.114277 0.993449i \(-0.463545\pi\)
\(468\) 0 0
\(469\) 16.7815 29.0665i 0.774899 1.34216i
\(470\) −1.62760 0.592396i −0.0750754 0.0273252i
\(471\) 0 0
\(472\) −2.42262 2.03282i −0.111510 0.0935680i
\(473\) −1.77595 1.49020i −0.0816583 0.0685195i
\(474\) 0 0
\(475\) 50.9188 + 18.5329i 2.33631 + 0.850349i
\(476\) −6.47410 + 11.2135i −0.296740 + 0.513969i
\(477\) 0 0
\(478\) 14.7875 + 25.6126i 0.676362 + 1.17149i
\(479\) 1.12554 + 6.38326i 0.0514272 + 0.291658i 0.999664 0.0259046i \(-0.00824661\pi\)
−0.948237 + 0.317563i \(0.897136\pi\)
\(480\) 0 0
\(481\) 10.6887 3.89036i 0.487361 0.177385i
\(482\) −0.272114 + 1.54323i −0.0123944 + 0.0702923i
\(483\) 0 0
\(484\) −9.00387 + 7.55514i −0.409267 + 0.343416i
\(485\) −26.2317 −1.19112
\(486\) 0 0
\(487\) 19.9828 0.905505 0.452753 0.891636i \(-0.350442\pi\)
0.452753 + 0.891636i \(0.350442\pi\)
\(488\) −0.668794 + 0.561185i −0.0302749 + 0.0254036i
\(489\) 0 0
\(490\) 1.88666 10.6998i 0.0852306 0.483367i
\(491\) −24.6454 + 8.97019i −1.11223 + 0.404819i −0.831811 0.555059i \(-0.812696\pi\)
−0.280420 + 0.959877i \(0.590474\pi\)
\(492\) 0 0
\(493\) 1.78018 + 10.0959i 0.0801754 + 0.454697i
\(494\) 28.9243 + 50.0984i 1.30137 + 2.25403i
\(495\) 0 0
\(496\) −9.09879 + 15.7596i −0.408548 + 0.707626i
\(497\) 2.65366 + 0.965852i 0.119033 + 0.0433244i
\(498\) 0 0
\(499\) 4.83931 + 4.06066i 0.216637 + 0.181780i 0.744648 0.667458i \(-0.232617\pi\)
−0.528011 + 0.849238i \(0.677062\pi\)
\(500\) 19.7307 + 16.5560i 0.882384 + 0.740408i
\(501\) 0 0
\(502\) 15.3897 + 5.60138i 0.686874 + 0.250002i
\(503\) −10.9131 + 18.9020i −0.486589 + 0.842798i −0.999881 0.0154166i \(-0.995093\pi\)
0.513292 + 0.858214i \(0.328426\pi\)
\(504\) 0 0
\(505\) −8.65657 14.9936i −0.385212 0.667208i
\(506\) 0.386729 + 2.19325i 0.0171922 + 0.0975018i
\(507\) 0 0
\(508\) −10.7579 + 3.91555i −0.477304 + 0.173725i
\(509\) −5.05196 + 28.6511i −0.223924 + 1.26994i 0.640806 + 0.767703i \(0.278600\pi\)
−0.864731 + 0.502236i \(0.832511\pi\)
\(510\) 0 0
\(511\) 8.41534 7.06131i 0.372273 0.312374i
\(512\) −31.1704 −1.37755
\(513\) 0 0
\(514\) 50.4620 2.22579
\(515\) −38.6317 + 32.4158i −1.70231 + 1.42841i
\(516\) 0 0
\(517\) 0.0898700 0.509678i 0.00395248 0.0224156i
\(518\) −10.4765 + 3.81315i −0.460313 + 0.167540i
\(519\) 0 0
\(520\) −0.720285 4.08494i −0.0315866 0.179136i
\(521\) −6.84743 11.8601i −0.299991 0.519600i 0.676142 0.736771i \(-0.263650\pi\)
−0.976134 + 0.217171i \(0.930317\pi\)
\(522\) 0 0
\(523\) −6.57532 + 11.3888i −0.287519 + 0.497997i −0.973217 0.229889i \(-0.926164\pi\)
0.685698 + 0.727886i \(0.259497\pi\)
\(524\) −18.2757 6.65183i −0.798380 0.290586i
\(525\) 0 0
\(526\) −42.3448 35.5315i −1.84632 1.54925i
\(527\) 9.68042 + 8.12284i 0.421686 + 0.353836i
\(528\) 0 0
\(529\) 21.3598 + 7.77433i 0.928686 + 0.338014i
\(530\) 17.0138 29.4688i 0.739034 1.28004i
\(531\) 0 0
\(532\) −13.7344 23.7887i −0.595463 1.03137i
\(533\) −2.04655 11.6065i −0.0886457 0.502735i
\(534\) 0 0
\(535\) −40.4680 + 14.7291i −1.74958 + 0.636796i
\(536\) 0.589856 3.34524i 0.0254779 0.144492i
\(537\) 0 0
\(538\) 45.5223 38.1978i 1.96261 1.64682i
\(539\) 3.24644 0.139834
\(540\) 0 0
\(541\) 6.26083 0.269174 0.134587 0.990902i \(-0.457029\pi\)
0.134587 + 0.990902i \(0.457029\pi\)
\(542\) 28.6674 24.0548i 1.23137 1.03324i
\(543\) 0 0
\(544\) −4.00088 + 22.6901i −0.171536 + 0.972830i
\(545\) −50.7990 + 18.4893i −2.17599 + 0.791996i
\(546\) 0 0
\(547\) −5.44878 30.9016i −0.232973 1.32126i −0.846841 0.531846i \(-0.821498\pi\)
0.613868 0.789409i \(-0.289613\pi\)
\(548\) −17.9337 31.0621i −0.766091 1.32691i
\(549\) 0 0
\(550\) −18.6702 + 32.3378i −0.796102 + 1.37889i
\(551\) −20.4367 7.43835i −0.870632 0.316884i
\(552\) 0 0
\(553\) 23.0173 + 19.3138i 0.978795 + 0.821306i
\(554\) −31.8685 26.7408i −1.35396 1.13611i
\(555\) 0 0
\(556\) 41.1553 + 14.9793i 1.74537 + 0.635264i
\(557\) −21.7196 + 37.6195i −0.920290 + 1.59399i −0.121324 + 0.992613i \(0.538714\pi\)
−0.798966 + 0.601376i \(0.794619\pi\)
\(558\) 0 0
\(559\) 2.50980 + 4.34710i 0.106153 + 0.183863i
\(560\) 6.37727 + 36.1673i 0.269489 + 1.52835i
\(561\) 0 0
\(562\) −3.23396 + 1.17706i −0.136416 + 0.0496514i
\(563\) 5.55980 31.5312i 0.234318 1.32888i −0.609728 0.792611i \(-0.708721\pi\)
0.844046 0.536271i \(-0.180168\pi\)
\(564\) 0 0
\(565\) 13.3157 11.1732i 0.560195 0.470059i
\(566\) 14.3549 0.603381
\(567\) 0 0
\(568\) 0.285807 0.0119922
\(569\) 5.18761 4.35292i 0.217476 0.182484i −0.527541 0.849530i \(-0.676886\pi\)
0.745017 + 0.667046i \(0.232441\pi\)
\(570\) 0 0
\(571\) −3.67318 + 20.8316i −0.153718 + 0.871777i 0.806231 + 0.591601i \(0.201504\pi\)
−0.959949 + 0.280176i \(0.909607\pi\)
\(572\) −18.1476 + 6.60519i −0.758790 + 0.276177i
\(573\) 0 0
\(574\) 2.00593 + 11.3762i 0.0837259 + 0.474833i
\(575\) −2.25838 3.91164i −0.0941811 0.163127i
\(576\) 0 0
\(577\) −5.95811 + 10.3198i −0.248039 + 0.429617i −0.962982 0.269567i \(-0.913120\pi\)
0.714942 + 0.699183i \(0.246453\pi\)
\(578\) −15.5194 5.64858i −0.645520 0.234950i
\(579\) 0 0
\(580\) −18.6138 15.6188i −0.772896 0.648537i
\(581\) 20.3260 + 17.0556i 0.843266 + 0.707584i
\(582\) 0 0
\(583\) 9.55438 + 3.47751i 0.395702 + 0.144024i
\(584\) 0.555907 0.962859i 0.0230036 0.0398434i
\(585\) 0 0
\(586\) −15.1177 26.1846i −0.624506 1.08168i
\(587\) 0.0225502 + 0.127889i 0.000930748 + 0.00527853i 0.985270 0.171008i \(-0.0547025\pi\)
−0.984339 + 0.176287i \(0.943591\pi\)
\(588\) 0 0
\(589\) −25.1917 + 9.16901i −1.03800 + 0.377803i
\(590\) 16.8538 95.5827i 0.693860 3.93508i
\(591\) 0 0
\(592\) −7.80793 + 6.55163i −0.320904 + 0.269271i
\(593\) −26.2622 −1.07846 −0.539230 0.842158i \(-0.681285\pi\)
−0.539230 + 0.842158i \(0.681285\pi\)
\(594\) 0 0
\(595\) 25.5030 1.04552
\(596\) 22.3238 18.7319i 0.914419 0.767288i
\(597\) 0 0
\(598\) 0.837334 4.74876i 0.0342411 0.194191i
\(599\) 25.9310 9.43810i 1.05951 0.385630i 0.247266 0.968948i \(-0.420468\pi\)
0.812244 + 0.583317i \(0.198246\pi\)
\(600\) 0 0
\(601\) 0.231429 + 1.31250i 0.00944020 + 0.0535380i 0.989164 0.146815i \(-0.0469022\pi\)
−0.979724 + 0.200353i \(0.935791\pi\)
\(602\) −2.45999 4.26083i −0.100262 0.173658i
\(603\) 0 0
\(604\) 5.54576 9.60554i 0.225654 0.390844i
\(605\) 21.7542 + 7.91787i 0.884433 + 0.321907i
\(606\) 0 0
\(607\) −9.62495 8.07629i −0.390665 0.327807i 0.426207 0.904626i \(-0.359849\pi\)
−0.816872 + 0.576819i \(0.804294\pi\)
\(608\) −37.4429 31.4183i −1.51851 1.27418i
\(609\) 0 0
\(610\) −25.1780 9.16404i −1.01943 0.371041i
\(611\) −0.560282 + 0.970437i −0.0226666 + 0.0392597i
\(612\) 0 0
\(613\) 6.99912 + 12.1228i 0.282692 + 0.489637i 0.972047 0.234787i \(-0.0754393\pi\)
−0.689355 + 0.724424i \(0.742106\pi\)
\(614\) −5.73357 32.5167i −0.231388 1.31227i
\(615\) 0 0
\(616\) −1.14156 + 0.415494i −0.0459947 + 0.0167407i
\(617\) −4.17567 + 23.6814i −0.168106 + 0.953377i 0.777698 + 0.628638i \(0.216387\pi\)
−0.945804 + 0.324738i \(0.894724\pi\)
\(618\) 0 0
\(619\) 5.26399 4.41701i 0.211577 0.177535i −0.530840 0.847472i \(-0.678124\pi\)
0.742418 + 0.669937i \(0.233679\pi\)
\(620\) −29.9521 −1.20291
\(621\) 0 0
\(622\) −31.5594 −1.26542
\(623\) −1.25741 + 1.05509i −0.0503771 + 0.0422714i
\(624\) 0 0
\(625\) 1.25356 7.10927i 0.0501422 0.284371i
\(626\) 63.6790 23.1773i 2.54513 0.926350i
\(627\) 0 0
\(628\) −0.395582 2.24346i −0.0157854 0.0895237i
\(629\) 3.53898 + 6.12970i 0.141109 + 0.244407i
\(630\) 0 0
\(631\) 17.6887 30.6377i 0.704175 1.21967i −0.262814 0.964847i \(-0.584651\pi\)
0.966989 0.254820i \(-0.0820161\pi\)
\(632\) 2.85759 + 1.04008i 0.113669 + 0.0413721i
\(633\) 0 0
\(634\) −24.6104 20.6506i −0.977404 0.820139i
\(635\) 17.2734 + 14.4941i 0.685472 + 0.575180i
\(636\) 0 0
\(637\) −6.60519 2.40409i −0.261707 0.0952536i
\(638\) 7.49346 12.9791i 0.296669 0.513846i
\(639\) 0 0
\(640\) 3.51114 + 6.08148i 0.138790 + 0.240392i
\(641\) 3.32947 + 18.8824i 0.131506 + 0.745809i 0.977229 + 0.212187i \(0.0680585\pi\)
−0.845723 + 0.533622i \(0.820830\pi\)
\(642\) 0 0
\(643\) −18.2079 + 6.62712i −0.718048 + 0.261348i −0.675097 0.737729i \(-0.735898\pi\)
−0.0429509 + 0.999077i \(0.513676\pi\)
\(644\) −0.397600 + 2.25490i −0.0156676 + 0.0888555i
\(645\) 0 0
\(646\) −27.5752 + 23.1383i −1.08493 + 0.910364i
\(647\) −8.77141 −0.344840 −0.172420 0.985024i \(-0.555159\pi\)
−0.172420 + 0.985024i \(0.555159\pi\)
\(648\) 0 0
\(649\) 29.0009 1.13839
\(650\) 61.9336 51.9684i 2.42923 2.03837i
\(651\) 0 0
\(652\) 0.905078 5.13295i 0.0354456 0.201022i
\(653\) 30.8307 11.2215i 1.20650 0.439130i 0.341011 0.940059i \(-0.389231\pi\)
0.865488 + 0.500929i \(0.167008\pi\)
\(654\) 0 0
\(655\) 6.65183 + 37.7244i 0.259908 + 1.47401i
\(656\) 5.28039 + 9.14590i 0.206164 + 0.357087i
\(657\) 0 0
\(658\) 0.549163 0.951178i 0.0214086 0.0370808i
\(659\) 17.5268 + 6.37922i 0.682746 + 0.248499i 0.660026 0.751243i \(-0.270545\pi\)
0.0227199 + 0.999742i \(0.492767\pi\)
\(660\) 0 0
\(661\) 27.8897 + 23.4022i 1.08478 + 0.910240i 0.996309 0.0858386i \(-0.0273570\pi\)
0.0884727 + 0.996079i \(0.471801\pi\)
\(662\) 47.6483 + 39.9816i 1.85190 + 1.55393i
\(663\) 0 0
\(664\) 2.52347 + 0.918468i 0.0979297 + 0.0356435i
\(665\) −27.0515 + 46.8546i −1.04901 + 1.81694i
\(666\) 0 0
\(667\) 0.906422 + 1.56997i 0.0350968 + 0.0607894i
\(668\) −1.24930 7.08512i −0.0483368 0.274132i
\(669\) 0 0
\(670\) 97.9621 35.6553i 3.78461 1.37748i
\(671\) 1.39024 7.88444i 0.0536696 0.304375i
\(672\) 0 0
\(673\) 30.1746 25.3195i 1.16314 0.975994i 0.163201 0.986593i \(-0.447818\pi\)
0.999944 + 0.0105986i \(0.00337371\pi\)
\(674\) −11.8276 −0.455584
\(675\) 0 0
\(676\) 17.3824 0.668553
\(677\) −24.2648 + 20.3606i −0.932571 + 0.782520i −0.976277 0.216525i \(-0.930528\pi\)
0.0437064 + 0.999044i \(0.486083\pi\)
\(678\) 0 0
\(679\) 2.88847 16.3813i 0.110849 0.628658i
\(680\) 2.42544 0.882789i 0.0930115 0.0338534i
\(681\) 0 0
\(682\) −3.20796 18.1932i −0.122839 0.696655i
\(683\) −14.5328 25.1716i −0.556083 0.963164i −0.997818 0.0660187i \(-0.978970\pi\)
0.441735 0.897145i \(-0.354363\pi\)
\(684\) 0 0
\(685\) −35.3225 + 61.1804i −1.34960 + 2.33758i
\(686\) 36.8853 + 13.4251i 1.40829 + 0.512574i
\(687\) 0 0
\(688\) −3.44562 2.89122i −0.131363 0.110227i
\(689\) −16.8641 14.1506i −0.642470 0.539097i
\(690\) 0 0
\(691\) −5.03431 1.83234i −0.191514 0.0697055i 0.244483 0.969654i \(-0.421382\pi\)
−0.435997 + 0.899948i \(0.643604\pi\)
\(692\) 6.60549 11.4410i 0.251103 0.434923i
\(693\) 0 0
\(694\) −22.6805 39.2838i −0.860940 1.49119i
\(695\) −14.9793 84.9518i −0.568197 3.22241i
\(696\) 0 0
\(697\) 6.89141 2.50827i 0.261031 0.0950074i
\(698\) 3.95589 22.4349i 0.149732 0.849175i
\(699\) 0 0
\(700\) −29.4085 + 24.6767i −1.11154 + 0.932691i
\(701\) 25.6536 0.968922 0.484461 0.874813i \(-0.339016\pi\)
0.484461 + 0.874813i \(0.339016\pi\)
\(702\) 0 0
\(703\) −15.0155 −0.566320
\(704\) 11.6949 9.81315i 0.440766 0.369847i
\(705\) 0 0
\(706\) −0.730085 + 4.14052i −0.0274771 + 0.155830i
\(707\) 10.3165 3.75490i 0.387992 0.141218i
\(708\) 0 0
\(709\) −0.814492 4.61922i −0.0305889 0.173478i 0.965686 0.259712i \(-0.0836278\pi\)
−0.996275 + 0.0862342i \(0.972517\pi\)
\(710\) 4.38571 + 7.59627i 0.164593 + 0.285083i
\(711\) 0 0
\(712\) −0.0830629 + 0.143869i −0.00311291 + 0.00539173i
\(713\) 2.09987 + 0.764290i 0.0786407 + 0.0286229i
\(714\) 0 0
\(715\) 29.1386 + 24.4502i 1.08972 + 0.914386i
\(716\) −20.7105 17.3782i −0.773989 0.649454i
\(717\) 0 0
\(718\) −44.8337 16.3181i −1.67318 0.608987i
\(719\) 19.5335 33.8330i 0.728476 1.26176i −0.229052 0.973414i \(-0.573562\pi\)
0.957527 0.288343i \(-0.0931042\pi\)
\(720\) 0 0
\(721\) −15.9893 27.6943i −0.595473 1.03139i
\(722\) −6.76227 38.3508i −0.251666 1.42727i
\(723\) 0 0
\(724\) −23.3123 + 8.48497i −0.866394 + 0.315342i
\(725\) −5.27806 + 29.9334i −0.196022 + 1.11170i
\(726\) 0 0
\(727\) −8.29267 + 6.95838i −0.307558 + 0.258072i −0.783482 0.621415i \(-0.786558\pi\)
0.475924 + 0.879487i \(0.342114\pi\)
\(728\) 2.63030 0.0974853
\(729\) 0 0
\(730\) 34.1215 1.26290
\(731\) −2.39273 + 2.00774i −0.0884984 + 0.0742590i
\(732\) 0 0
\(733\) −0.592558 + 3.36057i −0.0218866 + 0.124125i −0.993794 0.111240i \(-0.964518\pi\)
0.971907 + 0.235366i \(0.0756288\pi\)
\(734\) −5.24676 + 1.90966i −0.193661 + 0.0704870i
\(735\) 0 0
\(736\) 0.707492 + 4.01239i 0.0260785 + 0.147898i
\(737\) 15.5749 + 26.9766i 0.573710 + 0.993695i
\(738\) 0 0
\(739\) −13.1505 + 22.7773i −0.483748 + 0.837877i −0.999826 0.0186653i \(-0.994058\pi\)
0.516077 + 0.856542i \(0.327392\pi\)
\(740\) −15.7645 5.73783i −0.579516 0.210927i
\(741\) 0 0
\(742\) 16.5294 + 13.8698i 0.606813 + 0.509177i
\(743\) −22.1723 18.6048i −0.813423 0.682543i 0.137999 0.990432i \(-0.455933\pi\)
−0.951422 + 0.307889i \(0.900377\pi\)
\(744\) 0 0
\(745\) −53.9363 19.6312i −1.97607 0.719232i
\(746\) −28.3953 + 49.1822i −1.03963 + 1.80069i
\(747\) 0 0
\(748\) −6.00862 10.4072i −0.219697 0.380526i
\(749\) −4.74205 26.8935i −0.173271 0.982668i
\(750\) 0 0
\(751\) 18.2754 6.65171i 0.666880 0.242724i 0.0136761 0.999906i \(-0.495647\pi\)
0.653204 + 0.757182i \(0.273424\pi\)
\(752\) 0.174362 0.988856i 0.00635833 0.0360599i
\(753\) 0 0
\(754\) −24.8576 + 20.8580i −0.905259 + 0.759603i
\(755\) −21.8460 −0.795058
\(756\) 0 0
\(757\) 6.59627 0.239745 0.119873 0.992789i \(-0.461751\pi\)
0.119873 + 0.992789i \(0.461751\pi\)
\(758\) −48.5815 + 40.7648i −1.76456 + 1.48064i
\(759\) 0 0
\(760\) −0.950837 + 5.39246i −0.0344905 + 0.195605i
\(761\) 9.70674 3.53297i 0.351869 0.128070i −0.160038 0.987111i \(-0.551162\pi\)
0.511907 + 0.859041i \(0.328939\pi\)
\(762\) 0 0
\(763\) −5.95265 33.7591i −0.215500 1.22216i
\(764\) −12.6138 21.8478i −0.456352 0.790424i
\(765\) 0 0
\(766\) −0.662037 + 1.14668i −0.0239204 + 0.0414313i
\(767\) −59.0052 21.4761i −2.13055 0.775458i
\(768\) 0 0
\(769\) 34.3640 + 28.8348i 1.23920 + 1.03981i 0.997586 + 0.0694355i \(0.0221198\pi\)
0.241610 + 0.970374i \(0.422325\pi\)
\(770\) −28.5603 23.9650i −1.02924 0.863638i
\(771\) 0 0
\(772\) −26.4996 9.64506i −0.953741 0.347133i
\(773\) 21.4677 37.1832i 0.772141 1.33739i −0.164247 0.986419i \(-0.552519\pi\)
0.936388 0.350968i \(-0.114147\pi\)
\(774\) 0 0
\(775\) 18.7335 + 32.4475i 0.672929 + 1.16555i
\(776\) −0.292336 1.65792i −0.0104942 0.0595158i
\(777\) 0 0
\(778\) 7.88326 2.86927i 0.282628 0.102868i
\(779\) −2.70161 + 15.3216i −0.0967953 + 0.548953i
\(780\) 0 0