LMFDB - Embedded newform 92.2.h.a.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,2,Mod(7,92)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 19]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("92.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$92 = 2^{2} \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	92.h (of order $22$ , degree $10$ , 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:	$0.734623698596$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.8
Character	$\chi$	$=$	92.19
Dual form			92.2.h.a.63.8

$q$ -expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.908675 + 1.08366i) q^{2} +(-0.814220 - 2.77298i) q^{3} +(-0.348619 + 1.96938i) q^{4} +(1.74032 - 2.70799i) q^{5} +(2.26509 - 3.40207i) q^{6} +(0.439673 + 3.05800i) q^{7} +(-2.45091 + 1.41175i) q^{8} +(-4.50270 + 2.89371i) q^{9} +(4.51592 - 0.574777i) q^{10} +(0.0147862 - 0.0323773i) q^{11} +(5.74491 - 0.636797i) q^{12} +(-0.214704 + 1.49330i) q^{13} +(-2.91429 + 3.25518i) q^{14} +(-8.92621 - 2.62097i) q^{15} +(-3.75693 - 1.37313i) q^{16} +(-2.81816 + 2.44195i) q^{17} +(-7.22727 - 2.24993i) q^{18} +(-0.225545 + 0.260293i) q^{19} +(4.72636 + 4.37142i) q^{20} +(8.12177 - 3.70909i) q^{21} +(0.0485217 - 0.0133973i) q^{22} +(4.15401 - 2.39670i) q^{23} +(5.91032 + 5.64686i) q^{24} +(-2.22743 - 4.87740i) q^{25} +(-1.81332 + 1.12426i) q^{26} +(5.13792 + 4.45203i) q^{27} +(-6.17564 - 0.200191i) q^{28} +(-0.217665 - 0.251198i) q^{29} +(-5.27080 - 12.0546i) q^{30} +(-1.06260 + 3.61888i) q^{31} +(-1.92583 - 5.31895i) q^{32} +(-0.101821 - 0.0146396i) q^{33} +(-5.20703 - 0.834977i) q^{34} +(9.04621 + 4.13126i) q^{35} +(-4.12909 - 9.87633i) q^{36} +(-4.10489 - 6.38734i) q^{37} +(-0.487015 - 0.00789152i) q^{38} +(4.31571 - 0.620505i) q^{39} +(-0.442381 + 9.09395i) q^{40} +(7.08463 + 4.55301i) q^{41} +(11.3994 + 5.43084i) q^{42} +(-7.63873 + 2.24293i) q^{43} +(0.0586085 + 0.0404070i) q^{44} +17.2293i q^{45} +(6.37185 + 2.32369i) q^{46} -12.4933i q^{47} +(-0.748689 + 11.5359i) q^{48} +(-2.44157 + 0.716911i) q^{49} +(3.26141 - 6.84575i) q^{50} +(9.06608 + 5.82642i) q^{51} +(-2.86603 - 0.943427i) q^{52} +(-4.98512 + 0.716752i) q^{53} +(-0.155771 + 9.61319i) q^{54} +(-0.0619447 - 0.0963878i) q^{55} +(-5.39471 - 6.87418i) q^{56} +(0.905430 + 0.413496i) q^{57} +(0.0744261 - 0.464131i) q^{58} +(11.5305 + 1.65784i) q^{59} +(8.27354 - 16.6654i) q^{60} +(1.07769 - 3.67028i) q^{61} +(-4.88718 + 2.13690i) q^{62} +(-10.8287 - 12.4969i) q^{63} +(4.01395 - 6.92013i) q^{64} +(3.67019 + 3.18024i) q^{65} +(-0.0766576 - 0.123641i) q^{66} +(-2.05467 - 4.49910i) q^{67} +(-3.82667 - 6.40135i) q^{68} +(-10.0283 - 9.56754i) q^{69} +(3.74319 + 13.5569i) q^{70} +(-4.38573 + 2.00290i) q^{71} +(6.95054 - 13.4489i) q^{72} +(4.95391 - 5.71712i) q^{73} +(3.19166 - 10.2523i) q^{74} +(-11.7113 + 10.1479i) q^{75} +(-0.433987 - 0.534927i) q^{76} +(0.105511 + 0.0309807i) q^{77} +(4.59399 + 4.11290i) q^{78} +(-0.475186 + 3.30499i) q^{79} +(-10.2567 + 7.78406i) q^{80} +(1.49164 - 3.26623i) q^{81} +(1.50373 + 11.8145i) q^{82} +(-4.11011 + 2.64141i) q^{83} +(4.47320 + 17.2879i) q^{84} +(1.70828 + 11.8813i) q^{85} +(-9.37170 - 6.23966i) q^{86} +(-0.519341 + 0.808110i) q^{87} +(0.00946875 + 0.100228i) q^{88} +(-3.09200 - 10.5304i) q^{89} +(-18.6706 + 15.6558i) q^{90} -4.66091 q^{91} +(3.27186 + 9.01637i) q^{92} +10.9003 q^{93} +(13.5385 - 11.3524i) q^{94} +(0.312350 + 1.06377i) q^{95} +(-13.1813 + 9.67108i) q^{96} +(-5.11806 + 7.96386i) q^{97} +(-2.99548 - 1.99439i) q^{98} +(0.0271126 + 0.188572i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$100 q - 7 q^{2} - 11 q^{4} - 22 q^{5} - 12 q^{6} - 10 q^{8} - 12 q^{9} - 11 q^{10} - 18 q^{12} - 18 q^{13} - 11 q^{14} + 5 q^{16} - 22 q^{17} - 24 q^{18} - 11 q^{20} - 22 q^{21} - 30 q^{24} - 16 q^{25}+ \cdots - 71 q^{98}+O(q^{100})$ 100 * q - 7 * q^2 - 11 * q^4 - 22 * q^5 - 12 * q^6 - 10 * q^8 - 12 * q^9 - 11 * q^10 - 18 * q^12 - 18 * q^13 - 11 * q^14 + 5 * q^16 - 22 * q^17 - 24 * q^18 - 11 * q^20 - 22 * q^21 - 30 * q^24 - 16 * q^25 + 12 * q^26 - 11 * q^28 - 42 * q^29 - 11 * q^30 - 27 * q^32 - 22 * q^33 + 11 * q^34 + 77 * q^36 - 22 * q^37 + 44 * q^38 + 77 * q^40 - 10 * q^41 + 99 * q^42 + 66 * q^44 + 65 * q^46 + 38 * q^48 - 8 * q^49 + 30 * q^50 + 96 * q^52 - 22 * q^53 + 48 * q^54 + 44 * q^56 - 22 * q^57 + 79 * q^58 + 11 * q^60 - 22 * q^61 - 36 * q^62 + 10 * q^64 - 22 * q^65 - 44 * q^66 - 10 * q^69 + 34 * q^70 - 21 * q^72 - 18 * q^73 - 22 * q^74 - 66 * q^76 + 122 * q^77 - 66 * q^78 - 110 * q^80 + 8 * q^81 - 122 * q^82 - 165 * q^84 + 54 * q^85 - 121 * q^86 - 99 * q^88 + 22 * q^89 - 198 * q^90 - 86 * q^92 + 212 * q^93 - 61 * q^94 - 147 * q^96 + 22 * q^97 - 71 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$ .

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{15}{22}\right)$	$-1$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	0.908675	+	1.08366i	0.642530	+	0.766260i
$2$	0.908675	+	1.08366i	0.642530	+	0.766260i
$3$	−0.814220	−	2.77298i	−0.470090	−	1.60098i	−0.764047	−	0.645161i	$-0.776790\pi$
$3$	−0.814220	−	2.77298i	−0.470090	−	1.60098i	0.293956	−	0.955819i	$-0.405028\pi$
$4$	−0.348619	+	1.96938i	−0.174310	+	0.984691i
$5$	1.74032	−	2.70799i	0.778296	−	1.21105i	−0.194844	−	0.980834i	$-0.562420\pi$
$5$	1.74032	−	2.70799i	0.778296	−	1.21105i	0.973139	−	0.230217i	$-0.0739437\pi$
$6$	2.26509	−	3.40207i	0.924720	−	1.38889i
$7$	0.439673	+	3.05800i	0.166181	+	1.15581i	0.886689	+	0.462367i	$0.153000\pi$
$7$	0.439673	+	3.05800i	0.166181	+	1.15581i	−0.720508	+	0.693447i	$0.756091\pi$
$8$	−2.45091	+	1.41175i	−0.866529	+	0.499127i
$9$	−4.50270	+	2.89371i	−1.50090	+	0.964569i
$10$	4.51592	−	0.574777i	1.42806	−	0.181760i
$11$	0.0147862	−	0.0323773i	0.00445821	−	0.00976211i	−0.907390	−	0.420290i	$-0.861928\pi$
$11$	0.0147862	−	0.0323773i	0.00445821	−	0.00976211i	0.911848	+	0.410528i	$0.134656\pi$
$12$	5.74491	−	0.636797i	1.65841	−	0.183827i
$13$	−0.214704	+	1.49330i	−0.0595482	+	0.414167i	0.938143	+	0.346249i	$0.112545\pi$
$13$	−0.214704	+	1.49330i	−0.0595482	+	0.414167i	−0.997691	+	0.0679180i	$0.978364\pi$
$14$	−2.91429	+	3.25518i	−0.778878	+	0.869983i
$15$	−8.92621	−	2.62097i	−2.30474	−	0.676732i
$16$	−3.75693	−	1.37313i	−0.939232	−	0.343282i
$17$	−2.81816	+	2.44195i	−0.683505	+	0.592260i	−0.925832	−	0.377934i	$-0.876635\pi$
$17$	−2.81816	+	2.44195i	−0.683505	+	0.592260i	0.242328	+	0.970194i	$0.422089\pi$
$18$	−7.22727	−	2.24993i	−1.70348	−	0.530314i
$19$	−0.225545	+	0.260293i	−0.0517436	+	0.0597153i	−0.781031	−	0.624492i	$-0.785306\pi$
$19$	−0.225545	+	0.260293i	−0.0517436	+	0.0597153i	0.729288	+	0.684207i	$0.239852\pi$
$20$	4.72636	+	4.37142i	1.05685	+	0.977478i
$21$	8.12177	−	3.70909i	1.77231	−	0.809389i
$22$	0.0485217	−	0.0133973i	0.0103449	−	0.00285631i
$23$	4.15401	−	2.39670i	0.866171	−	0.499747i
$23$	4.15401	−	2.39670i	0.866171	−	0.499747i
$24$	5.91032	+	5.64686i	1.20644	+	1.15266i
$25$	−2.22743	−	4.87740i	−0.445487	−	0.975480i
$26$	−1.81332	+	1.12426i	−0.355621	+	0.220485i
$27$	5.13792	+	4.45203i	0.988793	+	0.856794i
$28$	−6.17564	−	0.200191i	−1.16709	−	0.0378325i
$29$	−0.217665	−	0.251198i	−0.0404193	−	0.0466464i	0.735180	−	0.677872i	$-0.237098\pi$
$29$	−0.217665	−	0.251198i	−0.0404193	−	0.0466464i	−0.775599	+	0.631226i	$0.782552\pi$
$30$	−5.27080	−	12.0546i	−0.962311	−	2.20085i
$31$	−1.06260	+	3.61888i	−0.190849	+	0.649970i	0.807356	+	0.590065i	$0.200898\pi$
$31$	−1.06260	+	3.61888i	−0.190849	+	0.649970i	−0.998204	+	0.0599052i	$0.980920\pi$
$32$	−1.92583	−	5.31895i	−0.340442	−	0.940266i
$33$	−0.101821	−	0.0146396i	−0.0177247	−	0.00254843i
$34$	−5.20703	−	0.834977i	−0.892998	−	0.143197i
$35$	9.04621	+	4.13126i	1.52909	+	0.698311i
$36$	−4.12909	−	9.87633i	−0.688181	−	1.64605i
$37$	−4.10489	−	6.38734i	−0.674840	−	1.05007i	−0.994721	−	0.102614i	$-0.967279\pi$
$37$	−4.10489	−	6.38734i	−0.674840	−	1.05007i	0.319881	−	0.947458i	$-0.396357\pi$
$38$	−0.487015	−	0.00789152i	−0.0790043	−	0.00128017i
$39$	4.31571	−	0.620505i	0.691066	−	0.0993603i
$40$	−0.442381	+	9.09395i	−0.0699466	+	1.43788i
$41$	7.08463	+	4.55301i	1.10643	+	0.711061i	0.960513	−	0.278235i	$-0.0897495\pi$
$41$	7.08463	+	4.55301i	1.10643	+	0.711061i	0.145920	+	0.989296i	$0.453386\pi$
$42$	11.3994	+	5.43084i	1.75897	+	0.837997i
$43$	−7.63873	+	2.24293i	−1.16490	+	0.342044i	−0.806333	−	0.591461i	$-0.798551\pi$
$43$	−7.63873	+	2.24293i	−1.16490	+	0.342044i	−0.358563	+	0.933506i	$0.616733\pi$
$44$	0.0586085	+	0.0404070i	0.00883556	+	0.00609159i
$45$			17.2293i			2.56839i
$46$	6.37185	+	2.32369i	0.939478	+	0.342610i
$47$		−	12.4933i		−	1.82234i	−0.412031	−	0.911170i	$-0.635180\pi$
$47$		−	12.4933i		−	1.82234i	0.412031	−	0.911170i	$-0.364820\pi$
$48$	−0.748689	+	11.5359i	−0.108064	+	1.66507i
$49$	−2.44157	+	0.716911i	−0.348796	+	0.102416i
$50$	3.26141	−	6.84575i	0.461233	−	0.968135i
$51$	9.06608	+	5.82642i	1.26951	+	0.815861i
$52$	−2.86603	−	0.943427i	−0.397447	−	0.130830i
$53$	−4.98512	+	0.716752i	−0.684759	+	0.0984534i	−0.475909	−	0.879494i	$-0.657881\pi$
$53$	−4.98512	+	0.716752i	−0.684759	+	0.0984534i	−0.208849	+	0.977948i	$0.566972\pi$
$54$	−0.155771	+	9.61319i	−0.0211977	+	1.30819i
$55$	−0.0619447	−	0.0963878i	−0.00835262	−	0.0129969i
$56$	−5.39471	−	6.87418i	−0.720899	−	0.918600i
$57$	0.905430	+	0.413496i	0.119927	+	0.0547689i
$58$	0.0744261	−	0.464131i	0.00977263	−	0.0609434i
$59$	11.5305	+	1.65784i	1.50114	+	0.215832i	0.843349	−	0.537366i	$-0.180581\pi$
$59$	11.5305	+	1.65784i	1.50114	+	0.215832i	0.657794	+	0.753198i	$0.271490\pi$
$60$	8.27354	−	16.6654i	1.06811	−	2.15149i
$61$	1.07769	−	3.67028i	0.137984	−	0.469931i	−0.861286	−	0.508120i	$-0.830341\pi$
$61$	1.07769	−	3.67028i	0.137984	−	0.469931i	0.999271	+	0.0381888i	$0.0121588\pi$
$62$	−4.88718	+	2.13690i	−0.620673	+	0.271386i
$63$	−10.8287	−	12.4969i	−1.36428	−	1.57447i
$64$	4.01395	−	6.92013i	0.501744	−	0.865016i
$65$	3.67019	+	3.18024i	0.455231	+	0.394460i
$66$	−0.0766576	−	0.123641i	−0.00943590	−	0.0152192i
$67$	−2.05467	−	4.49910i	−0.251018	−	0.549653i	0.741613	−	0.670828i	$-0.234061\pi$
$67$	−2.05467	−	4.49910i	−0.251018	−	0.549653i	−0.992631	+	0.121175i	$0.961334\pi$
$68$	−3.82667	−	6.40135i	−0.464052	−	0.776277i
$69$	−10.0283	−	9.56754i	−1.20726	−	1.15180i
$70$	3.74319	+	13.5569i	0.447397	+	1.62037i
$71$	−4.38573	+	2.00290i	−0.520490	+	0.237700i	−0.658296	−	0.752759i	$-0.728722\pi$
$71$	−4.38573	+	2.00290i	−0.520490	+	0.237700i	0.137805	+	0.990459i	$0.455995\pi$
$72$	6.95054	−	13.4489i	0.819129	−	1.58497i
$73$	4.95391	−	5.71712i	0.579812	−	0.669138i	−0.387753	−	0.921763i	$-0.626749\pi$
$73$	4.95391	−	5.71712i	0.579812	−	0.669138i	0.967564	+	0.252625i	$0.0812940\pi$
$74$	3.19166	−	10.2523i	0.371023	−	1.19181i
$75$	−11.7113	+	10.1479i	−1.35231	+	1.17178i
$76$	−0.433987	−	0.534927i	−0.0497817	−	0.0613604i
$77$	0.105511	+	0.0309807i	0.0120241	+	0.00353058i
$78$	4.59399	+	4.11290i	0.520167	+	0.465694i
$79$	−0.475186	+	3.30499i	−0.0534626	+	0.371840i	0.945472	+	0.325702i	$0.105601\pi$
$79$	−0.475186	+	3.30499i	−0.0534626	+	0.371840i	−0.998935	+	0.0461383i	$0.985308\pi$
$80$	−10.2567	+	7.78406i	−1.14673	+	0.870284i
$81$	1.49164	−	3.26623i	0.165737	−	0.362914i
$82$	1.50373	+	11.8145i	0.166059	+	1.30469i
$83$	−4.11011	+	2.64141i	−0.451143	+	0.289932i	−0.746415	−	0.665481i	$-0.768226\pi$
$83$	−4.11011	+	2.64141i	−0.451143	+	0.289932i	0.295271	+	0.955413i	$0.404590\pi$
$84$	4.47320	+	17.2879i	0.488067	+	1.88627i
$85$	1.70828	+	11.8813i	0.185289	+	1.28871i
$86$	−9.37170	−	6.23966i	−1.01058	−	0.672840i
$87$	−0.519341	+	0.808110i	−0.0556792	+	0.0866385i
$88$	0.00946875	+	0.100228i	0.00100937	+	0.0106844i
$89$	−3.09200	−	10.5304i	−0.327752	−	1.11622i	−0.944350	−	0.328942i	$-0.893308\pi$
$89$	−3.09200	−	10.5304i	−0.327752	−	1.11622i	0.616598	−	0.787278i	$-0.288510\pi$
$90$	−18.6706	+	15.6558i	−1.96805	+	1.65027i
$91$	−4.66091			−0.488596
$92$	3.27186	+	9.01637i	0.341115	+	0.940022i
$93$	10.9003			1.13031
$94$	13.5385	−	11.3524i	1.39639	−	1.17091i
$95$	0.312350	+	1.06377i	0.0320465	+	0.109140i
$96$	−13.1813	+	9.67108i	−1.34531	+	0.987050i
$97$	−5.11806	+	7.96386i	−0.519660	+	0.808607i	−0.997561	−	0.0698070i	$-0.977762\pi$
$97$	−5.11806	+	7.96386i	−0.519660	+	0.808607i	0.477900	+	0.878414i	$0.341398\pi$
$98$	−2.99548	−	1.99439i	−0.302589	−	0.201464i
$99$	0.0271126	+	0.188572i	0.00272491	+	0.0189522i
$100$	10.3820	−	2.68631i	1.03820	−	0.268631i
$101$	2.95662	−	1.90011i	0.294195	−	0.189068i	−0.385214	−	0.922827i	$-0.625873\pi$
$101$	2.95662	−	1.90011i	0.294195	−	0.189068i	0.679409	+	0.733760i	$0.262236\pi$
$102$	1.92429	+	15.1188i	0.190533	+	1.49699i
$103$	1.93240	−	4.23136i	0.190405	−	0.416928i	−0.790220	−	0.612823i	$-0.790034\pi$
$103$	1.93240	−	4.23136i	0.190405	−	0.416928i	0.980625	+	0.195895i	$0.0627612\pi$
$104$	−1.58194	−	3.96306i	−0.155122	−	0.388610i
$105$	4.09030	−	28.4487i	0.399173	−	2.77631i
$106$	−5.30657	−	4.75086i	−0.515419	−	0.461444i
$107$	2.37791	+	0.698218i	0.229881	+	0.0674992i	0.394644	−	0.918834i	$-0.370868\pi$
$107$	2.37791	+	0.698218i	0.229881	+	0.0674992i	−0.164763	+	0.986333i	$0.552686\pi$
$108$	−10.5589	+	8.56646i	−1.01603	+	0.824308i
$109$	−5.19693	+	4.50317i	−0.497776	+	0.431325i	−0.867218	−	0.497928i	$-0.834094\pi$
$109$	−5.19693	+	4.50317i	−0.497776	+	0.431325i	0.369442	+	0.929254i	$0.379549\pi$
$110$	0.0481636	−	0.154712i	0.00459222	−	0.0147512i
$111$	−14.3697	+	16.5835i	−1.36391	+	1.57403i
$112$	2.54720	−	12.0924i	0.240688	−	1.14262i
$113$	−7.83329	+	3.57734i	−0.736894	+	0.336528i	−0.748259	−	0.663407i	$-0.769110\pi$
$113$	−7.83329	+	3.57734i	−0.736894	+	0.336528i	0.0113644	+	0.999935i	$0.496383\pi$
$114$	0.374654	+	1.35691i	0.0350896	+	0.127086i
$115$	0.739056	−	15.4201i	0.0689173	−	1.43793i
$116$	0.570587	−	0.341092i	0.0529777	−	0.0316696i
$117$	−3.35443	−	7.34517i	−0.310117	−	0.679061i
$118$	8.68096	+	14.0015i	0.799147	+	1.28894i
$119$	−8.70655	−	7.54427i	−0.798128	−	0.691582i
$120$	25.5775	−	6.17776i	2.33490	−	0.563950i
$121$	7.20264	+	8.31229i	0.654785	+	0.755663i
$122$	4.95659	−	2.16725i	0.448749	−	0.196213i
$123$	6.85696	−	23.3527i	0.618272	−	2.10564i
$124$	−6.75652	−	3.35428i	−0.606753	−	0.301223i
$125$	−1.15326	−	0.165813i	−0.103151	−	0.0148308i
$126$	3.70265	−	23.0902i	0.329858	−	2.05704i
$127$	−2.50526	−	1.14412i	−0.222306	−	0.101524i	0.301149	−	0.953577i	$-0.402630\pi$
$127$	−2.50526	−	1.14412i	−0.222306	−	0.101524i	−0.523455	+	0.852053i	$0.675357\pi$
$128$	11.1464	−	1.93841i	0.985213	−	0.171333i
$129$	12.4392	+	19.3558i	1.09521	+	1.70418i
$130$	−0.111272	+	6.86703i	−0.00975924	+	0.602278i
$131$	5.99257	−	0.861601i	0.523573	−	0.0752784i	0.124539	−	0.992215i	$-0.460255\pi$
$131$	5.99257	−	0.861601i	0.523573	−	0.0752784i	0.399034	+	0.916936i	$0.369346\pi$
$132$	0.0643276	−	0.195420i	0.00559900	−	0.0170091i
$133$	−0.895141	−	0.575272i	−0.0776185	−	0.0498824i
$134$	3.00845	−	6.31478i	0.259891	−	0.545514i
$135$	20.9977	−	6.16548i	1.80719	−	0.530640i
$136$	3.45966	−	9.96354i	0.296663	−	0.854366i
$137$			13.9104i			1.18844i	0.804302	+	0.594221i	$0.202539\pi$
$137$			13.9104i			1.18844i	−0.804302	+	0.594221i	$0.797461\pi$
$138$	1.25546	−	19.5610i	0.106872	−	1.66514i
$139$			20.1629i			1.71020i	0.518466	+	0.855098i	$0.326503\pi$
$139$			20.1629i			1.71020i	−0.518466	+	0.855098i	$0.673497\pi$
$140$	−11.2897	+	16.3752i	−0.954155	+	1.38396i
$141$	−34.6437	+	10.1723i	−2.91753	+	0.856664i
$142$	−6.15565	−	2.93264i	−0.516571	−	0.246102i
$143$	0.0451743	+	0.0290318i	0.00377767	+	0.00242776i
$144$	20.8897	−	4.68867i	1.74081	−	0.390723i
$145$	−1.05905	+	0.152268i	−0.0879493	+	0.0126452i
$146$	10.6969	+	0.173331i	0.885280	+	0.0143450i
$147$	3.97596	+	6.18671i	0.327931	+	0.510271i
$148$	14.0101	−	5.85735i	1.15163	−	0.481471i
$149$	11.5907	+	5.29331i	0.949549	+	0.433645i	0.829116	−	0.559077i	$-0.188844\pi$
$149$	11.5907	+	5.29331i	0.949549	+	0.433645i	0.120433	+	0.992721i	$0.461572\pi$
$150$	−21.6386	−	3.46988i	−1.76679	−	0.283314i
$151$	−7.91514	−	1.13802i	−0.644125	−	0.0926112i	−0.187492	−	0.982266i	$-0.560036\pi$
$151$	−7.91514	−	1.13802i	−0.644125	−	0.0926112i	−0.456633	+	0.889655i	$0.650945\pi$
$152$	0.185324	−	0.956367i	0.0150318	−	0.0775716i
$153$	5.62303	−	19.1503i	0.454595	−	1.54821i
$154$	0.0623025	+	0.142489i	0.00502048	+	0.0114821i
$155$	7.95065	+	9.17553i	0.638611	+	0.736997i
$156$	−0.282527	+	8.71559i	−0.0226202	+	0.697806i
$157$	6.12526	+	5.30756i	0.488849	+	0.423590i	0.864090	−	0.503337i	$-0.167895\pi$
$157$	6.12526	+	5.30756i	0.488849	+	0.423590i	−0.375241	+	0.926927i	$0.622440\pi$
$158$	−4.01326	+	2.48822i	−0.319278	+	0.197952i
$159$	6.04652	+	13.2400i	0.479520	+	1.05000i
$160$	−17.7552	−	4.04154i	−1.40367	−	0.319512i
$161$	9.15552	+	11.6492i	0.721556	+	0.918084i
$162$	4.89488	−	1.35152i	0.384578	−	0.106185i
$163$	−2.04513	+	0.933978i	−0.160187	+	0.0731548i	−0.493895	−	0.869522i	$-0.664427\pi$
$163$	−2.04513	+	0.933978i	−0.160187	+	0.0731548i	0.333708	+	0.942676i	$0.391700\pi$
$164$	−11.4365	+	12.3651i	−0.893037	+	0.965550i
$165$	−0.216845	+	0.250252i	−0.0168813	+	0.0194821i
$166$	−6.59713	−	2.05376i	−0.512037	−	0.159403i
$167$	6.40479	−	5.54978i	0.495617	−	0.429455i	−0.370847	−	0.928694i	$-0.620933\pi$
$167$	6.40479	−	5.54978i	0.495617	−	0.429455i	0.866464	+	0.499239i	$0.166387\pi$
$168$	−14.6695	+	20.5565i	−1.13177	+	1.58597i
$169$	10.2896	+	3.02129i	0.791505	+	0.232407i
$170$	−11.3230	+	12.6475i	−0.868436	+	0.970017i
$171$	0.262349	−	1.82468i	0.0200624	−	0.139537i
$172$	−1.75419	−	15.8255i	−0.133755	−	1.20668i
$173$	9.21644	−	20.1812i	0.700713	−	1.53435i	−0.138391	−	0.990378i	$-0.544193\pi$
$173$	9.21644	−	20.1812i	0.700713	−	1.53435i	0.839105	−	0.543970i	$-0.183080\pi$
$174$	−1.34762	+	0.171523i	−0.102163	+	0.0130031i
$175$	13.9357	−	8.95595i	1.05344	−	0.677006i
$176$	−0.100009	+	0.101336i	−0.00753845	+	0.00763847i
$177$	−4.79122	−	33.3237i	−0.360130	−	2.50476i
$178$	8.60170	−	12.9194i	0.644724	−	0.968348i
$179$	−1.82884	+	2.84573i	−0.136694	+	0.212700i	−0.902851	−	0.429953i	$-0.858530\pi$
$179$	−1.82884	+	2.84573i	−0.136694	+	0.212700i	0.766157	+	0.642653i	$0.222166\pi$
$180$	−33.9310	−	6.00645i	−2.52907	−	0.447694i
$181$	−2.75175	−	9.37159i	−0.204536	−	0.696585i	−0.996314	−	0.0857766i	$-0.972663\pi$
$181$	−2.75175	−	9.37159i	−0.204536	−	0.696585i	0.791779	−	0.610808i	$-0.209155\pi$
$182$	−4.23525	−	5.05082i	−0.313937	−	0.374391i
$183$	−11.0551			−0.817216
$184$	−6.79758	+	11.7385i	−0.501125	+	0.865375i
$185$	−24.4407			−1.79692
$186$	9.90481	+	11.8121i	0.726256	+	0.866108i
$187$	0.0373938	+	0.127352i	0.00273450	+	0.00931287i
$188$	24.6041	+	4.35541i	1.79444	+	0.317651i
$189$	−11.3553	+	17.6692i	−0.825976	+	1.28524i
$190$	−0.868933	+	1.30510i	−0.0630390	+	0.0946819i
$191$	0.716897	+	4.98613i	0.0518728	+	0.360784i	0.999181	+	0.0404603i	$0.0128824\pi$
$191$	0.716897	+	4.98613i	0.0518728	+	0.360784i	−0.947308	+	0.320323i	$0.896208\pi$
$192$	−22.4576	−	5.49609i	−1.62074	−	0.396646i
$193$	0.218286	−	0.140284i	0.0157126	−	0.0100979i	−0.532761	−	0.846266i	$-0.678846\pi$
$193$	0.218286	−	0.140284i	0.0157126	−	0.0100979i	0.548474	+	0.836168i	$0.315209\pi$
$194$	−13.2807	+	1.69034i	−0.953501	+	0.121360i
$195$	5.83039	−	12.7668i	0.417523	−	0.914248i
$196$	−0.560692	−	5.05832i	−0.0400494	−	0.361309i
$197$	−1.16018	+	8.06921i	−0.0826592	+	0.574907i	0.905833	+	0.423635i	$0.139246\pi$
$197$	−1.16018	+	8.06921i	−0.0826592	+	0.574907i	−0.988492	+	0.151272i	$0.951663\pi$
$198$	−0.179711	+	0.200731i	−0.0127715	+	0.0142654i
$199$	20.9070	+	6.13885i	1.48206	+	0.435172i	0.919998	−	0.391924i	$-0.128190\pi$
$199$	20.9070	+	6.13885i	1.48206	+	0.435172i	0.562061	+	0.827096i	$0.310009\pi$
$200$	12.3449	+	8.80952i	0.872916	+	0.622927i
$201$	−10.8030	+	9.36082i	−0.761982	+	0.660261i
$202$	4.74567	+	1.47738i	0.333904	+	0.103948i
$203$	0.672462	−	0.776063i	0.0471976	−	0.0544689i
$204$	−14.6350	+	15.8234i	−1.02466	+	1.10786i
$205$	24.6591	−	11.2614i	1.72226	−	0.786531i
$206$	6.34125	−	1.75088i	0.441816	−	0.121989i
$207$	−11.7689	+	22.8121i	−0.817994	+	1.58555i
$208$	2.85712	−	5.31541i	0.198106	−	0.368557i
$209$	0.00509262	+	0.0111513i	0.000352264	+	0.000771350i
$210$	34.5453	−	21.4181i	2.38386	−	1.47799i
$211$	6.22420	+	5.39330i	0.428491	+	0.371290i	0.842241	−	0.539101i	$-0.181236\pi$
$211$	6.22420	+	5.39330i	0.428491	+	0.371290i	−0.413750	+	0.910391i	$0.635781\pi$
$212$	0.326350	−	10.0675i	0.0224138	−	0.691437i
$213$	9.12494	+	10.5307i	0.625230	+	0.721554i
$214$	1.40412	+	3.21129i	0.0959837	+	0.219519i
$215$	−7.22000	+	24.5891i	−0.492400	+	1.67696i
$216$	−18.8777	−	3.65811i	−1.28447	−	0.248903i
$217$	−11.5337	−	1.65830i	−0.782960	−	0.112573i
$218$	−9.60221	−	1.53977i	−0.650343	−	0.104286i
$219$	−19.8870	−	9.08210i	−1.34384	−	0.613711i
$220$	0.211420	−	0.0883901i	0.0142539	−	0.00595926i
$221$	−3.04149	−	4.73266i	−0.204593	−	0.318353i
$222$	−31.0281	−	0.502776i	−2.08247	−	0.0337441i
$223$	12.0942	−	1.73889i	0.809890	−	0.116445i	0.275085	−	0.961420i	$-0.411294\pi$
$223$	12.0942	−	1.73889i	0.809890	−	0.116445i	0.534805	+	0.844975i	$0.320385\pi$
$224$	15.4186	−	8.22778i	1.03020	−	0.549742i
$225$	24.1432	+	15.5159i	1.60955	+	1.03439i
$226$	−10.9945	−	5.23795i	−0.731345	−	0.348423i
$227$	−12.5214	+	3.67661i	−0.831073	+	0.244025i	−0.669478	−	0.742832i	$-0.733482\pi$
$227$	−12.5214	+	3.67661i	−0.831073	+	0.244025i	−0.161595	+	0.986857i	$0.551664\pi$
$228$	−1.12998	+	1.63898i	−0.0748349	+	0.108544i
$229$		−	10.0144i		−	0.661773i	−0.943671	−	0.330887i	$-0.892652\pi$
$229$		−	10.0144i		−	0.661773i	0.943671	−	0.330887i	$-0.107348\pi$
$230$	17.3816	−	13.2110i	1.14611	−	0.871105i
$231$		−	0.317804i		−	0.0209100i
$232$	0.888105	+	0.308378i	0.0583070	+	0.0202460i
$233$	−16.2134	+	4.76067i	−1.06217	+	0.311882i	−0.765725	−	0.643168i	$-0.777620\pi$
$233$	−16.2134	+	4.76067i	−1.06217	+	0.311882i	−0.296447	+	0.955049i	$0.595802\pi$
$234$	4.91155	−	10.3094i	0.321078	−	0.673947i
$235$	−33.8319	−	21.7424i	−2.20695	−	1.41832i
$236$	−7.28466	+	22.1300i	−0.474191	+	1.44054i
$237$	9.55157	−	1.37331i	0.620441	−	0.0892060i
$238$	0.263964	−	16.2902i	0.0171102	−	1.05594i
$239$	−12.4223	−	19.3294i	−0.803529	−	1.25032i	−0.964690	−	0.263387i	$-0.915160\pi$
$239$	−12.4223	−	19.3294i	−0.803529	−	1.25032i	0.161161	−	0.986928i	$-0.448476\pi$
$240$	29.9362	+	22.1036i	1.93237	+	1.42678i
$241$	−25.9543	−	11.8530i	−1.67187	−	0.763516i	−0.999734	−	0.0230849i	$-0.992651\pi$
$241$	−25.9543	−	11.8530i	−1.67187	−	0.763516i	−0.672133	−	0.740431i	$-0.734622\pi$
$242$	−2.46280	+	15.3583i	−0.158315	+	0.987272i
$243$	9.91603	+	1.42571i	0.636114	+	0.0914594i
$244$	6.85248	+	3.40192i	0.438685	+	0.217785i
$245$	−2.30774	+	7.85943i	−0.147436	+	0.502120i
$246$	31.5370	−	13.7894i	2.01073	−	0.879180i
$247$	−0.340270	−	0.392692i	−0.0216509	−	0.0249864i
$248$	−2.50460	−	10.3697i	−0.159042	−	0.658476i
$249$	10.6711	+	9.24656i	0.676254	+	0.585977i
$250$	−0.868252	−	1.40040i	−0.0549131	−	0.0885694i
$251$	−3.24606	−	7.10788i	−0.204890	−	0.448645i	0.779093	−	0.626908i	$-0.215680\pi$
$251$	−3.24606	−	7.10788i	−0.204890	−	0.448645i	−0.983983	+	0.178262i	$0.942952\pi$
$252$	28.3863	−	16.9691i	1.78817	−	1.06895i
$253$	−0.0161767	−	0.169934i	−0.00101702	−	0.0106836i
$254$	−1.03664	−	3.75447i	−0.0650448	−	0.235577i
$255$	31.5558	−	14.4111i	1.97610	−	0.902455i
$256$	12.2290	+	10.3175i	0.764315	+	0.644843i
$257$	−4.59844	+	5.30688i	−0.286842	+	0.331034i	−0.880823	−	0.473445i	$-0.843010\pi$
$257$	−4.59844	+	5.30688i	−0.286842	+	0.331034i	0.593981	+	0.804479i	$0.297556\pi$
$258$	−9.67182	+	31.0680i	−0.602141	+	1.93421i
$259$	17.7276	−	15.3611i	1.10154	−	0.954491i
$260$	−7.54261	+	6.11932i	−0.467773	+	0.379504i
$261$	1.70697	+	0.501212i	0.105659	+	0.0310243i
$262$	6.37897	+	5.71096i	0.394094	+	0.352824i
$263$	1.07557	−	7.48075i	0.0663225	−	0.461283i	−0.929414	−	0.369039i	$-0.879687\pi$
$263$	1.07557	−	7.48075i	0.0663225	−	0.461283i	0.995736	−	0.0922440i	$-0.0294040\pi$
$264$	0.270221	−	0.107864i	0.0166310	−	0.00663860i
$265$	−6.73475	+	14.7470i	−0.413713	+	0.905904i
$266$	−0.189995	−	1.49276i	−0.0116494	−	0.0915270i
$267$	−26.6830	+	17.1481i	−1.63297	+	1.04945i
$268$	9.57675	−	2.47796i	0.584993	−	0.151365i
$269$	−2.84640	−	19.7971i	−0.173548	−	1.20705i	−0.871314	−	0.490726i	$-0.836732\pi$
$269$	−2.84640	−	19.7971i	−0.173548	−	1.20705i	0.697766	−	0.716326i	$-0.254178\pi$
$270$	25.7614	+	17.1519i	1.56779	+	1.04383i
$271$	−13.5908	+	21.1477i	−0.825580	+	1.28463i	0.130478	+	0.991451i	$0.458349\pi$
$271$	−13.5908	+	21.1477i	−0.825580	+	1.28463i	−0.956058	+	0.293177i	$0.905287\pi$
$272$	13.9407	−	5.30454i	0.845282	−	0.321635i
$273$	3.79500	+	12.9246i	0.229684	+	0.782232i
$274$	−15.0740	+	12.6400i	−0.910655	+	0.763610i
$275$	−0.190852			−0.0115088
$276$	22.3382	−	16.4141i	1.34460	−	0.988013i
$277$	15.8515			0.952423			0.476212	−	0.879331i	$-0.342010\pi$
$277$	15.8515			0.952423			0.476212	+	0.879331i	$0.342010\pi$
$278$	−21.8497	+	18.3215i	−1.31046	+	1.09885i
$279$	−5.68742	−	19.3696i	−0.340497	−	1.15963i
$280$	−28.0038	+	2.64557i	−1.67354	+	0.158103i
$281$	9.43888	−	14.6872i	0.563076	−	0.876164i	−0.436648	−	0.899632i	$-0.643835\pi$
$281$	9.43888	−	14.6872i	0.563076	−	0.876164i	0.999725	+	0.0234683i	$0.00747088\pi$
$282$	−42.5032	−	28.2986i	−2.53103	−	1.68515i
$283$	−3.67235	−	25.5418i	−0.218299	−	1.51830i	−0.744316	−	0.667827i	$-0.767224\pi$
$283$	−3.67235	−	25.5418i	−0.218299	−	1.51830i	0.526017	−	0.850474i	$-0.323685\pi$
$284$	−2.41552	−	9.33542i	−0.143335	−	0.553955i
$285$	2.69548	−	1.73228i	0.159667	−	0.102612i
$286$	0.00958834	+	0.0753339i	0.000566970	+	0.00445458i
$287$	−10.8082	+	23.6666i	−0.637986	+	1.39700i
$288$	24.0629	+	18.3768i	1.41792	+	1.08286i
$289$	−0.440442	+	3.06334i	−0.0259083	+	0.180197i
$290$	−1.12734	−	1.00928i	−0.0661996	−	0.0592671i
$291$	26.2508	+	7.70794i	1.53885	+	0.451847i
$292$	9.53216	+	11.7492i	0.557828	+	0.687572i
$293$	10.5229	−	9.11810i	0.614752	−	0.532685i	−0.290875	−	0.956761i	$-0.593946\pi$
$293$	10.5229	−	9.11810i	0.614752	−	0.532685i	0.905627	+	0.424076i	$0.139401\pi$
$294$	−3.09141	+	9.93028i	−0.180295	+	0.579146i
$295$	24.5562	−	28.3394i	1.42972	−	1.64998i
$296$	19.0780	+	9.85975i	1.10889	+	0.573086i
$297$	0.220115	−	0.100523i	0.0127724	−	0.00583294i
$298$	4.79608	+	17.3703i	0.277830	+	1.00623i
$299$	2.68712	+	6.71777i	0.155400	+	0.388499i
$300$	−15.9023	−	26.6018i	−0.918121	−	1.53586i
$301$	−10.2174	−	22.3731i	−0.588923	−	1.28956i
$302$	−5.95906	−	9.61138i	−0.342905	−	0.553073i
$303$	−7.67629	−	6.65154i	−0.440991	−	0.382121i
$304$	1.20477	−	0.668200i	0.0690984	−	0.0383239i
$305$	−8.06357	−	9.30585i	−0.461718	−	0.532851i
$306$	25.8618	−	11.3080i	1.47842	−	0.646433i
$307$	−5.86566	+	19.9766i	−0.334771	+	1.14013i	0.604402	+	0.796680i	$0.293412\pi$
$307$	−5.86566	+	19.9766i	−0.334771	+	1.14013i	−0.939173	+	0.343445i	$0.888406\pi$
$308$	−0.0977959	+	0.196990i	−0.00557244	+	0.0112246i
$309$	−13.3069	−	1.91324i	−0.757001	−	0.108840i
$310$	−2.71857	+	16.9533i	−0.154404	+	0.962885i
$311$	9.51746	+	4.34648i	0.539685	+	0.246466i	0.666558	−	0.745453i	$-0.267767\pi$
$311$	9.51746	+	4.34648i	0.539685	+	0.246466i	−0.126873	+	0.991919i	$0.540494\pi$
$312$	−9.70143	+	7.61348i	−0.549235	+	0.431028i
$313$	11.8653	+	18.4627i	0.670666	+	1.04358i	0.995215	+	0.0977075i	$0.0311510\pi$
$313$	11.8653	+	18.4627i	0.670666	+	1.04358i	−0.324549	+	0.945869i	$0.605213\pi$
$314$	−0.185705	+	11.4605i	−0.0104799	+	0.646755i
$315$	−52.6870	+	7.57524i	−2.96858	+	0.426817i
$316$	−6.34313	−	2.08800i	−0.356829	−	0.117459i
$317$	−7.13318	−	4.58422i	−0.400639	−	0.257475i	0.324770	−	0.945793i	$-0.394713\pi$
$317$	−7.13318	−	4.58422i	−0.400639	−	0.257475i	−0.725409	+	0.688318i	$0.758350\pi$
$318$	−8.85331	+	18.5832i	−0.496469	+	1.04210i
$319$	−0.0113515	+	0.00333312i	−0.000635565	+	0.000186619i
$320$	−11.7541	−	22.9130i	−0.657074	−	1.28088i
$321$		−	7.16240i		−	0.399766i
$322$	−4.30431	+	20.5068i	−0.239870	+	1.14280i
$323$		−	1.28432i		−	0.0714613i
$324$	5.91243	+	4.07627i	0.328469	+	0.226459i
$325$	7.76166	−	2.27903i	0.430540	−	0.126418i
$326$	−2.87047	−	1.36753i	−0.158980	−	0.0757405i
$327$	16.7186	+	10.7444i	0.924543	+	0.594167i
$328$	−23.7915	−	1.15735i	−1.31367	−	0.0639041i
$329$	38.2046	−	5.49299i	2.10629	−	0.302838i
$330$	−0.468229	−	0.00758711i	−0.0257751	−	0.000417657i
$331$	−8.93643	−	13.9054i	−0.491190	−	0.764307i	0.503849	−	0.863792i	$-0.331917\pi$
$331$	−8.93643	−	13.9054i	−0.491190	−	0.764307i	−0.995039	+	0.0994847i	$0.968281\pi$
$332$	−3.76908	−	9.01522i	−0.206855	−	0.494775i
$333$	36.9662	+	16.8819i	2.02573	+	0.925121i
$334$	11.8339	+	1.89764i	0.647523	+	0.103834i
$335$	−15.7593	−	2.26585i	−0.861024	−	0.123797i
$336$	−35.6060	+	2.78255i	−1.94246	+	0.151800i
$337$	4.06233	−	13.8350i	0.221289	−	0.753641i	−0.771757	−	0.635917i	$-0.780622\pi$
$337$	4.06233	−	13.8350i	0.221289	−	0.753641i	0.993046	−	0.117724i	$-0.0375599\pi$
$338$	6.07583	+	13.8957i	0.330482	+	0.755827i
$339$	16.2979	+	18.8088i	0.885182	+	1.02155i
$340$	−23.9944	−	0.777810i	−1.30128	−	0.0421826i
$341$	0.101458	+	0.0879136i	0.00549424	+	0.00476079i
$342$	2.21572	−	1.37375i	0.119812	−	0.0742836i
$343$	5.71800	+	12.5207i	0.308743	+	0.676052i
$344$	15.5554	−	16.2812i	0.838692	−	0.877823i
$345$	−43.3613	+	10.5059i	−2.33449	+	0.565621i
$346$	30.2442	−	8.35070i	1.62594	−	0.448936i
$347$	−7.08801	+	3.23699i	−0.380505	+	0.173771i	−0.596480	−	0.802628i	$-0.703434\pi$
$347$	−7.08801	+	3.23699i	−0.380505	+	0.173771i	0.215975	+	0.976399i	$0.430707\pi$
$348$	−1.41042	−	1.30450i	−0.0756067	−	0.0699287i
$349$	5.76898	−	6.65776i	0.308807	−	0.356382i	−0.580039	−	0.814589i	$-0.696963\pi$
$349$	5.76898	−	6.65776i	0.308807	−	0.356382i	0.888846	+	0.458207i	$0.151508\pi$
$350$	22.3682	+	6.96348i	1.19563	+	0.372214i
$351$	−7.75135	+	6.71658i	−0.413737	+	0.358505i
$352$	−0.200689	−	0.0162939i	−0.0106967	−	0.000868468i
$353$	−22.1233	−	6.49597i	−1.17750	−	0.345746i	−0.366292	−	0.930500i	$-0.619373\pi$
$353$	−22.1233	−	6.49597i	−1.17750	−	0.345746i	−0.811210	+	0.584754i	$0.801191\pi$
$354$	31.7577	−	35.4724i	1.68790	−	1.88534i
$355$	−2.20875	+	15.3622i	−0.117228	+	0.815342i
$356$	21.8163	−	2.41824i	1.15626	−	0.128166i
$357$	−13.8310	+	30.2858i	−0.732016	+	1.60289i
$358$	−4.74562	+	0.604012i	−0.250814	+	0.0319230i
$359$	23.1888	−	14.9026i	1.22386	−	0.786527i	0.240937	−	0.970541i	$-0.422545\pi$
$359$	23.1888	−	14.9026i	1.22386	−	0.786527i	0.982924	+	0.184014i	$0.0589090\pi$
$360$	−24.3233	−	42.2274i	−1.28195	−	2.22558i
$361$	2.68710	+	18.6892i	0.141426	+	0.983642i
$362$	7.65513	−	11.4977i	0.402345	−	0.604304i
$363$	17.1853	−	26.7408i	0.901992	−	1.40353i
$364$	1.62488	−	9.17910i	0.0851669	−	0.481116i
$365$	−6.86052	−	23.3648i	−0.359096	−	1.22297i
$366$	−10.0455	−	11.9799i	−0.525086	−	0.626200i
$367$	20.9251			1.09228			0.546141	−	0.837693i	$-0.316096\pi$
$367$	20.9251			1.09228			0.546141	+	0.837693i	$0.316096\pi$
$368$	−18.8973	+	3.30026i	−0.985090	+	0.172038i
$369$	−45.0750			−2.34651
$370$	−22.2087	−	26.4853i	−1.15457	−	1.37691i
$371$	−4.38365	−	14.9293i	−0.227588	−	0.775093i
$372$	−3.80004	+	21.4668i	−0.197023	+	1.11300i
$373$	−9.39615	+	14.6207i	−0.486514	+	0.757031i	−0.994545	−	0.104308i	$-0.966737\pi$
$373$	−9.39615	+	14.6207i	−0.486514	+	0.757031i	0.508031	+	0.861339i	$0.330374\pi$
$374$	−0.104026	+	0.156243i	−0.00537908	+	0.00807914i
$375$	0.479208	+	3.33297i	0.0247462	+	0.172114i
$376$	17.6374	+	30.6201i	0.909579	+	1.57911i
$377$	0.421848	−	0.271105i	0.0217263	−	0.0139626i
$378$	−29.4656	+	3.75032i	−1.51555	+	0.192895i
$379$	−15.7381	+	34.4616i	−0.808411	+	1.77017i	−0.194319	+	0.980938i	$0.562250\pi$
$379$	−15.7381	+	34.4616i	−0.808411	+	1.77017i	−0.614092	+	0.789235i	$0.710478\pi$
$380$	−2.20386	+	0.244287i	−0.113055	+	0.0125317i
$381$	−1.13277	+	7.87860i	−0.0580337	+	0.403633i
$382$	−4.75182	+	5.30764i	−0.243124	+	0.271562i
$383$	−33.2874	−	9.77407i	−1.70091	−	0.499431i	−0.720011	−	0.693963i	$-0.755863\pi$
$383$	−33.2874	−	9.77407i	−1.70091	−	0.499431i	−0.980896	+	0.194531i	$0.937681\pi$
$384$	−14.4508	−	29.3305i	−0.737439	−	1.49676i
$385$	0.267518	−	0.231806i	0.0136340	−	0.0118139i
$386$	0.350371	+	0.109074i	0.0178334	+	0.00555174i
$387$	27.9045	−	32.2035i	1.41847	−	1.63700i
$388$	−13.8996	−	12.8558i	−0.705646	−	0.652653i
$389$	−6.31175	+	2.88248i	−0.320019	+	0.146148i	−0.568947	−	0.822374i	$-0.692649\pi$
$389$	−6.31175	+	2.88248i	−0.320019	+	0.146148i	0.248928	+	0.968522i	$0.419922\pi$
$390$	19.1327	−	5.28272i	0.968823	−	0.267501i
$391$	−5.85404	+	16.8982i	−0.296052	+	0.854578i
$392$	4.97199	−	5.20397i	0.251124	−	0.262840i
$393$	−7.26847	−	15.9157i	−0.366646	−	0.802842i
$394$	−9.79847	+	6.07506i	−0.493640	+	0.306057i
$395$	8.12291	+	7.03854i	0.408708	+	0.354148i
$396$	−0.380822	−	0.0123448i	−0.0191370	−	0.000620351i
$397$	5.12145	+	5.91047i	0.257038	+	0.296638i	0.869572	−	0.493807i	$-0.164395\pi$
$397$	5.12145	+	5.91047i	0.257038	+	0.296638i	−0.612533	+	0.790445i	$0.709850\pi$
$398$	12.3453	+	28.2342i	0.618813	+	1.41525i
$399$	−0.866375	+	2.95060i	−0.0433730	+	0.147715i
$400$	1.67102	+	21.3826i	0.0835508	+	1.06913i
$401$	31.7183	+	4.56040i	1.58394	+	0.227735i	0.877335	−	0.479878i	$-0.159319\pi$
$401$	31.7183	+	4.56040i	1.58394	+	0.227735i	0.706600	+	0.707613i	$0.250228\pi$
$402$	−19.9603	−	3.20075i	−0.995529	−	0.159639i
$403$	−5.17593	−	2.36377i	−0.257832	−	0.117748i
$404$	2.71130	+	6.48513i	0.134892	+	0.322647i
$405$	−6.24899	−	9.72362i	−0.310515	−	0.483171i
$406$	1.45203	+	0.0235286i	0.0720633	+	0.00116770i
$407$	−0.267500	+	0.0384607i	−0.0132595	+	0.00190643i
$408$	−30.4456	−	1.48105i	−1.50728	−	0.0733227i
$409$	7.81430	+	5.02195i	0.386392	+	0.248319i	0.719387	−	0.694609i	$-0.244423\pi$
$409$	7.81430	+	5.02195i	0.386392	+	0.248319i	−0.332995	+	0.942929i	$0.608059\pi$
$410$	34.6106	+	16.4890i	1.70929	+	0.814332i
$411$	38.5731	−	11.3261i	1.90267	−	0.558675i
$412$	7.65949	+	5.28076i	0.377356	+	0.260164i
$413$			35.9891i			1.77091i
$414$	−35.4146	+	7.97538i	−1.74053	+	0.391969i
$415$			15.7271i			0.772011i
$416$	8.35627	−	1.73384i	0.409700	−	0.0850086i
$417$	55.9113	−	16.4170i	2.73799	−	0.803946i
$418$	−0.00745661	+	0.0156515i	−0.000364715	+	0.000765541i
$419$	−32.4769	−	20.8716i	−1.58660	−	1.01965i	−0.973225	−	0.229855i	$-0.926175\pi$
$419$	−32.4769	−	20.8716i	−1.58660	−	1.01965i	−0.613375	−	0.789792i	$-0.710189\pi$
$420$	54.6004	+	17.9731i	2.66423	+	0.876999i
$421$	−34.9440	+	5.02419i	−1.70307	+	0.244864i	−0.924086	−	0.382183i	$-0.875172\pi$
$421$	−34.9440	+	5.02419i	−1.70307	+	0.244864i	−0.778981	+	0.627048i	$0.784263\pi$
$422$	−0.188704	+	11.6456i	−0.00918598	+	0.566901i
$423$	36.1520	+	56.2537i	1.75777	+	2.73515i
$424$	11.2062	−	8.79441i	0.544222	−	0.427094i
$425$	18.1876	+	8.30602i	0.882230	+	0.402901i
$426$	−3.12009	+	19.4573i	−0.151169	+	0.942710i
$427$	11.6975	+	1.68185i	0.566083	+	0.0813905i
$428$	−2.20404	+	4.43960i	−0.106536	+	0.214596i
$429$	0.0437227	−	0.148906i	0.00211095	−	0.00718923i
$430$	−33.2067	+	14.5195i	−1.60137	+	0.700192i
$431$	13.1453	+	15.1704i	0.633185	+	0.730734i	0.978154	−	0.207880i	$-0.0666562\pi$
$431$	13.1453	+	15.1704i	0.633185	+	0.730734i	−0.344970	+	0.938614i	$0.612111\pi$
$432$	−13.1896	−	23.7810i	−0.634584	−	1.14416i
$433$	−19.1716	−	16.6123i	−0.921330	−	0.798337i	0.0584754	−	0.998289i	$-0.481376\pi$
$433$	−19.1716	−	16.6123i	−0.921330	−	0.798337i	−0.979806	+	0.199952i	$0.935922\pi$
$434$	−8.68338	−	14.0054i	−0.416816	−	0.672283i
$435$	1.28454	+	2.81274i	0.0615888	+	0.134861i
$436$	−7.05671	−	11.8046i	−0.337955	−	0.565339i
$437$	−0.313072	+	1.62182i	−0.0149762	+	0.0775824i
$438$	−8.22897	−	29.8034i	−0.393196	−	1.42406i
$439$	20.7654	−	9.48324i	0.991079	−	0.452610i	0.147178	−	0.989110i	$-0.452981\pi$
$439$	20.7654	−	9.48324i	0.991079	−	0.452610i	0.843901	+	0.536500i	$0.180254\pi$
$440$	0.287896	+	0.148788i	0.0137249	+	0.00709319i
$441$	8.91914	−	10.2932i	0.424721	−	0.490154i
$442$	2.36484	−	7.59638i	0.112484	−	0.361323i
$443$	−4.50488	+	3.90350i	−0.214033	+	0.185461i	−0.755279	−	0.655404i	$-0.772498\pi$
$443$	−4.50488	+	3.90350i	−0.214033	+	0.185461i	0.541245	+	0.840865i	$0.317953\pi$
$444$	−27.6497	−	34.0807i	−1.31219	−	1.61740i
$445$	−33.8973	−	9.95315i	−1.60689	−	0.471825i
$446$	12.8741	+	11.5259i	0.609606	+	0.545767i
$447$	5.24083	−	36.4508i	0.247883	−	1.72406i
$448$	22.9266	+	9.23205i	1.08318	+	0.436173i
$449$	11.6766	−	25.5682i	0.551054	−	1.20664i	−0.405234	−	0.914213i	$-0.632810\pi$
$449$	11.6766	−	25.5682i	0.551054	−	1.20664i	0.956288	−	0.292427i	$-0.0944627\pi$
$450$	5.12445	+	40.2619i	0.241569	+	1.89796i
$451$	0.252169	−	0.162059i	0.0118742	−	0.00763107i
$452$	−4.31432	−	16.6739i	−0.202929	−	0.784273i
$453$	3.28894	+	22.8751i	0.154528	+	1.07477i
$454$	−15.3620	−	10.2280i	−0.720976	−	0.480025i
$455$	−8.11148	+	12.6217i	−0.380272	+	0.591714i
$456$	−2.80288	+	0.264793i	−0.131257	+	0.0124001i
$457$	11.4987	+	39.1611i	0.537889	+	1.83188i	0.554742	+	0.832022i	$0.312817\pi$
$457$	11.4987	+	39.1611i	0.537889	+	1.83188i	−0.0168539	+	0.999858i	$0.505365\pi$
$458$	10.8522	−	9.09988i	0.507090	−	0.425209i
$459$	−25.3511			−1.18329
$460$	30.1104	+	6.83122i	1.40390	+	0.318507i
$461$	−13.4775			−0.627710			−0.313855	−	0.949471i	$-0.601621\pi$
$461$	−13.4775			−0.627710			−0.313855	+	0.949471i	$0.601621\pi$
$462$	0.344390	−	0.288781i	0.0160225	−	0.0134353i
$463$	3.12666	+	10.6484i	0.145308	+	0.494874i	0.999693	−	0.0247663i	$-0.00788418\pi$
$463$	3.12666	+	10.6484i	0.145308	+	0.494874i	−0.854385	+	0.519640i	$0.826066\pi$
$464$	0.472823	+	1.24262i	0.0219503	+	0.0576870i
$465$	18.9700	−	29.5179i	0.879712	−	1.36886i
$466$	−19.8916	−	13.2438i	−0.921460	−	0.613507i
$467$	0.809679	+	5.63144i	0.0374675	+	0.260592i	0.999942	−	0.0107805i	$-0.00343159\pi$
$467$	0.809679	+	5.63144i	0.0374675	+	0.260592i	−0.962474	+	0.271372i	$0.912523\pi$
$468$	15.6349	−	4.04548i	0.722721	−	0.187002i
$469$	12.8549	−	8.26131i	0.593582	−	0.381472i
$470$	−7.18088	−	56.4189i	−0.331229	−	2.60241i
$471$	9.73046	−	21.3067i	0.448356	−	0.981762i
$472$	−30.6007	+	12.2149i	−1.40851	+	0.562237i
$473$	−0.0403278	+	0.280486i	−0.00185427	+	0.0128968i
$474$	10.1675	+	9.10272i	0.467007	+	0.418102i
$475$	1.77194	+	0.520288i	0.0813022	+	0.0238725i
$476$	17.8928	−	14.5164i	0.820115	−	0.665360i
$477$	20.3724	−	17.6528i	0.932788	−	0.808266i
$478$	9.65863	−	31.0256i	0.441775	−	1.41908i
$479$	−15.8016	+	18.2361i	−0.721995	+	0.833227i	−0.991545	−	0.129760i	$-0.958579\pi$
$479$	−15.8016	+	18.2361i	−0.721995	+	0.833227i	0.269551	+	0.962986i	$0.413125\pi$
$480$	3.24956	+	52.5256i	0.148321	+	2.39745i
$481$	10.4195	−	4.75845i	0.475090	−	0.216967i
$482$	−10.7395	−	38.8961i	−0.489173	−	1.77167i
$483$	24.8483	−	34.8731i	1.13064	−	1.58678i
$484$	−18.8810	+	11.2869i	−0.858229	+	0.513042i
$485$	12.6590	+	27.7193i	0.574816	+	1.25867i
$486$	7.46547	+	12.0411i	0.338641	+	0.546194i
$487$	2.07401	+	1.79714i	0.0939824	+	0.0814362i	0.700585	−	0.713569i	$-0.252923\pi$
$487$	2.07401	+	1.79714i	0.0939824	+	0.0814362i	−0.606602	+	0.795005i	$0.707468\pi$
$488$	2.54017	+	10.5170i	0.114988	+	0.476081i
$489$	4.25508	+	4.91063i	0.192422	+	0.222066i
$490$	−10.6139	+	4.64087i	−0.479487	+	0.209653i
$491$	10.7149	−	36.4915i	0.483556	−	1.64684i	−0.250774	−	0.968046i	$-0.580685\pi$
$491$	10.7149	−	36.4915i	0.483556	−	1.64684i	0.734329	−	0.678793i	$-0.237497\pi$
$492$	43.5999	+	21.6452i	1.96563	+	0.975840i
$493$	1.22683	+	0.176391i	0.0552536	+	0.00794426i
$494$	0.116349	−	0.725565i	0.00523477	−	0.0326447i
$495$	0.557836	+	0.254755i	0.0250729	+	0.0114504i
$496$	8.96130	−	12.1368i	0.402374	−	0.544958i
$497$	−8.05314	−	12.5309i	−0.361232	−	0.562089i
$498$	−0.323525	+	19.9659i	−0.0144975	+	0.894694i
$499$	−3.74529	+	0.538491i	−0.167662	+	0.0241062i	−0.225635	−	0.974212i	$-0.572446\pi$
$499$	−3.74529	+	0.538491i	−0.167662	+	0.0241062i	0.0579724	+	0.998318i	$0.481536\pi$
$500$	0.728598	−	2.21340i	0.0325839	−	0.0989862i
$501$	−20.6043	−	13.2416i	−0.920533	−	0.591591i
$502$	4.75288	−	9.97637i	0.212131	−	0.445267i
$503$	−17.3591	+	5.09708i	−0.774003	+	0.227268i	−0.644801	−	0.764351i	$-0.723060\pi$
$503$	−17.3591	+	5.09708i	−0.774003	+	0.227268i	−0.129202	+	0.991618i	$0.541242\pi$
$504$	44.1826	+	15.3416i	1.96805	+	0.683369i
$505$		−	11.3133i		−	0.503436i
$506$	0.169450	−	0.171944i	0.00753298	−	0.00764386i
$507$		−	30.9927i		−	1.37644i
$508$	3.12658	−	4.53496i	0.138720	−	0.201206i
$509$	0.683452	−	0.200680i	0.0302935	−	0.00889497i	−0.266551	−	0.963821i	$-0.585884\pi$
$509$	0.683452	−	0.200680i	0.0302935	−	0.00889497i	0.296844	+	0.954926i	$0.404066\pi$
$510$	44.2906	+	21.1007i	1.96122	+	0.934353i
$511$	19.6610	+	12.6354i	0.869753	+	0.558956i
$512$	−0.0683880	+	22.6273i	−0.00302235	+	0.999995i
$513$	−2.31766	+	0.333230i	−0.102327	+	0.0147125i
$514$	−9.92931	−	0.160893i	−0.437963	−	0.00709670i
$515$	−8.09550	−	12.5968i	−0.356730	−	0.555083i
$516$	−42.4555	+	17.7498i	−1.86900	+	0.781390i
$517$	−0.404500	−	0.184729i	−0.0177899	−	0.00812437i
$518$	32.7548	+	5.25242i	1.43916	+	0.230778i
$519$	−63.4662	−	9.12507i	−2.78586	−	0.400546i
$520$	−13.4850	−	2.61312i	−0.591357	−	0.114593i
$521$	−4.41957	+	15.0517i	−0.193625	+	0.659426i	0.804251	+	0.594289i	$0.202567\pi$
$521$	−4.41957	+	15.0517i	−0.193625	+	0.659426i	−0.997876	+	0.0651366i	$0.979252\pi$
$522$	1.00794	+	2.30521i	0.0441164	+	0.100896i
$523$	−8.66514	−	10.0001i	−0.378900	−	0.437274i	0.533983	−	0.845495i	$-0.320695\pi$
$523$	−8.66514	−	10.0001i	−0.378900	−	0.437274i	−0.912883	+	0.408221i	$0.866149\pi$
$524$	−0.392302	+	12.1020i	−0.0171378	+	0.528679i
$525$	−36.1814	−	31.3514i	−1.57909	−	1.36829i
$526$	9.08390	−	5.63203i	0.396077	−	0.245568i
$527$	−5.84256	−	12.7934i	−0.254506	−	0.557290i
$528$	0.362431	+	0.194813i	0.0157728	+	0.00847814i
$529$	11.5116	−	19.9119i	0.500505	−	0.865734i
$530$	−22.1004	+	6.10212i	−0.959981	+	0.265059i
$531$	−56.7156	+	25.9012i	−2.46125	+	1.12401i
$532$	1.44499	−	1.56232i	0.0626484	−	0.0677353i
$533$	−8.32011	+	9.60192i	−0.360384	+	0.415905i
$534$	−42.8288	−	13.3331i	−1.85338	−	0.576980i
$535$	6.02910	−	5.22424i	0.260661	−	0.225864i
$536$	11.3874	+	8.12624i	0.491861	+	0.351000i
$537$	9.38023	+	2.75428i	0.404787	+	0.118856i
$538$	18.8668	−	21.0737i	0.813406	−	0.908550i
$539$	−0.0128900	+	0.0896519i	−0.000555212	+	0.00386158i
$540$	4.82199	+	43.5019i	0.207505	+	1.87202i
$541$	−8.42338	+	18.4446i	−0.362149	+	0.792996i	0.637595	+	0.770372i	$0.279929\pi$
$541$	−8.42338	+	18.4446i	−0.362149	+	0.792996i	−0.999744	+	0.0226243i	$0.992798\pi$
$542$	−35.2664	+	4.48863i	−1.51482	+	0.192803i
$543$	−23.7467	+	15.2611i	−1.01907	+	0.654915i
$544$	18.4159	+	10.2869i	0.789575	+	0.441046i
$545$	3.15021	+	21.9102i	0.134940	+	0.938531i
$546$	−10.5574	+	15.8567i	−0.451814	+	0.678605i
$547$	3.56889	−	5.55330i	0.152595	−	0.237442i	−0.756537	−	0.653951i	$-0.773110\pi$
$547$	3.56889	−	5.55330i	0.152595	−	0.237442i	0.909132	+	0.416509i	$0.136747\pi$
$548$	−27.3948	−	4.84941i	−1.17025	−	0.207157i
$549$	5.76820	+	19.6447i	0.246181	+	0.838414i
$550$	−0.173423	−	0.206818i	−0.00739477	−	0.00881875i
$551$	0.114478			0.00487694
$552$	38.0854	+	9.29182i	1.62102	+	0.395486i
$553$	−10.3156			−0.438663
$554$	14.4039	+	17.1776i	0.611961	+	0.729804i
$555$	19.9001	+	67.7735i	0.844713	+	2.87683i
$556$	−39.7085	−	7.02918i	−1.68401	−	0.298104i
$557$	−7.54329	+	11.7376i	−0.319620	+	0.497338i	−0.963471	−	0.267813i	$-0.913699\pi$
$557$	−7.54329	+	11.7376i	−0.319620	+	0.497338i	0.643851	+	0.765151i	$0.277335\pi$
$558$	15.8219	−	23.7639i	0.669796	−	1.00600i
$559$	−1.70931	−	11.8885i	−0.0722960	−	0.502830i
$560$	−28.3132	−	27.9425i	−1.19645	−	1.18078i
$561$	0.322696	−	0.207384i	0.0136243	−	0.00875578i
$562$	24.4927	−	3.11738i	1.03316	−	0.131499i
$563$	−4.99550	+	10.9386i	−0.210535	+	0.461008i	−0.985210	−	0.171352i	$-0.945186\pi$
$563$	−4.99550	+	10.9386i	−0.210535	+	0.461008i	0.774674	+	0.632360i	$0.217914\pi$
$564$	−7.95571	−	71.7730i	−0.334996	−	3.02219i
$565$	−3.94502	+	27.4382i	−0.165968	+	1.15434i
$566$	24.3415	−	27.1887i	1.02315	−	1.14283i
$567$	10.6439	+	3.12534i	0.447003	+	0.131252i
$568$	7.92146	−	11.1005i	0.332377	−	0.465765i
$569$	−16.3119	+	14.1343i	−0.683830	+	0.592542i	−0.925924	−	0.377711i	$-0.876711\pi$
$569$	−16.3119	+	14.1343i	−0.683830	+	0.592542i	0.242094	+	0.970253i	$0.422166\pi$
$570$	4.32652	+	1.34689i	0.181218	+	0.0564152i
$571$	−23.5159	+	27.1388i	−0.984111	+	1.13572i	0.00663307	+	0.999978i	$0.497889\pi$
$571$	−23.5159	+	27.1388i	−0.984111	+	1.13572i	−0.990744	+	0.135746i	$0.956657\pi$
$572$	−0.0729233	+	0.0788445i	−0.00304908	+	0.00329665i
$573$	13.2427	−	6.04774i	0.553222	−	0.252648i
$574$	−35.4676	+	9.79291i	−1.48039	+	0.408748i
$575$	−20.9425	−	14.9223i	−0.873362	−	0.622302i
$576$	1.95122	+	42.7744i	0.0813010	+	1.78227i
$577$	11.5340	+	25.2560i	0.480167	+	1.05142i	0.982417	+	0.186697i	$0.0597784\pi$
$577$	11.5340	+	25.2560i	0.480167	+	1.05142i	−0.502250	+	0.864722i	$0.667494\pi$
$578$	−3.71982	+	2.30629i	−0.154724	+	0.0959292i
$579$	−0.566738	−	0.491081i	−0.0235528	−	0.0204086i
$580$	0.0693305	−	2.13876i	0.00287879	−	0.0888071i
$581$	−9.88452	−	11.4073i	−0.410079	−	0.473256i
$582$	15.5007	+	35.4509i	0.642526	+	1.46949i
$583$	−0.0505045	+	0.172003i	−0.00209168	+	0.00712362i
$584$	−4.07049	+	21.0058i	−0.168438	+	0.869227i
$585$	−25.7284	−	3.69919i	−1.06374	−	0.152943i
$586$	19.4427	+	3.11776i	0.803172	+	0.128793i
$587$	28.8385	+	13.1701i	1.19029	+	0.543589i	0.909308	−	0.416123i	$-0.136611\pi$
$587$	28.8385	+	13.1701i	1.19029	+	0.543589i	0.280985	+	0.959712i	$0.409339\pi$
$588$	−13.5701	+	5.67337i	−0.559621	+	0.233966i
$589$	−0.702305	−	1.09281i	−0.0289380	−	0.0450284i
$590$	53.0237	+	0.859189i	2.18295	+	0.0353722i
$591$	23.3204	−	3.35296i	0.959272	−	0.137923i
$592$	6.65116	+	29.6333i	0.273361	+	1.21792i
$593$	−38.0769	−	24.4705i	−1.56363	−	1.00488i	−0.981426	−	0.191840i	$-0.938554\pi$
$593$	−38.0769	−	24.4705i	−1.56363	−	1.00488i	−0.582203	−	0.813043i	$-0.697809\pi$
$594$	0.308945	+	0.147186i	0.0126762	+	0.00603911i
$595$	−35.5820	+	10.4478i	−1.45872	+	0.428319i
$596$	−14.4653	+	20.9812i	−0.592521	+	0.859424i
$597$		−	62.9731i		−	2.57732i
$598$	−4.83803	+	9.01618i	−0.197842	+	0.368699i
$599$		−	0.227769i		−	0.00930639i	−0.999989	−	0.00465320i	$-0.998519\pi$
$599$		−	0.227769i		−	0.00930639i	0.999989	−	0.00465320i	$-0.00148116\pi$
$600$	14.3771	−	41.4050i	0.586944	−	1.69035i
$601$	−17.3126	+	5.08344i	−0.706196	+	0.207358i	−0.615059	−	0.788481i	$-0.710868\pi$
$601$	−17.3126	+	5.08344i	−0.706196	+	0.207358i	−0.0911361	+	0.995838i	$0.529050\pi$
$602$	14.9604	−	31.4020i	0.609739	−	1.27985i
$603$	22.2706	+	14.3125i	0.906931	+	0.582849i
$604$	5.00057	−	15.1912i	0.203470	−	0.618121i
$605$	35.0445	−	5.03864i	1.42476	−	0.204850i
$606$	0.232729	−	14.3625i	0.00945396	−	0.583439i
$607$	−20.9697	−	32.6294i	−0.851132	−	1.32439i	−0.944418	−	0.328748i	$-0.893373\pi$
$607$	−20.9697	−	32.6294i	−0.851132	−	1.32439i	0.0932857	−	0.995639i	$-0.470263\pi$
$608$	1.81884	+	0.698382i	0.0737639	+	0.0283231i
$609$	−2.69954	−	1.23284i	−0.109391	−	0.0499571i
$610$	2.75718	−	17.1941i	0.111635	−	0.696170i
$611$	18.6563	+	2.68237i	0.754753	+	0.108517i
$612$	35.7539	+	17.7501i	1.44527	+	0.717504i
$613$	6.99907	−	23.8366i	0.282690	−	0.962752i	−0.688657	−	0.725087i	$-0.741800\pi$
$613$	6.99907	−	23.8366i	0.282690	−	0.962752i	0.971347	−	0.237666i	$-0.0763822\pi$
$614$	−26.9777	+	11.7959i	−1.08873	+	0.476043i
$615$	−51.3056	−	59.2098i	−2.06884	−	2.38757i
$616$	−0.302334	+	0.0730231i	−0.0121814	+	0.00294218i
$617$	−3.66690	−	3.17739i	−0.147624	−	0.127917i	0.577918	−	0.816095i	$-0.303865\pi$
$617$	−3.66690	−	3.17739i	−0.147624	−	0.127917i	−0.725542	+	0.688178i	$0.758411\pi$
$618$	−10.0183	−	16.1586i	−0.402996	−	0.649993i
$619$	9.10370	+	19.9343i	0.365908	+	0.801228i	0.999617	+	0.0276562i	$0.00880438\pi$
$619$	9.10370	+	19.9343i	0.365908	+	0.801228i	−0.633709	+	0.773571i	$0.718468\pi$
$620$	−20.8419	+	12.4591i	−0.837030	+	0.500369i
$621$	32.0132	+	6.17972i	1.28464	+	0.247983i
$622$	3.93819	+	14.2632i	0.157907	+	0.571901i
$623$	30.8424	−	14.0853i	1.23568	−	0.564314i
$624$	−17.0658	−	3.59483i	−0.683180	−	0.143908i
$625$	15.1006	−	17.4270i	0.604024	−	0.697080i
$626$	−9.22557	+	29.6345i	−0.368728	+	1.18443i
$627$	0.0267757	−	0.0232013i	0.00106932	−	0.000926571i
$628$	−12.5880	+	10.2126i	−0.502316	+	0.407529i
$629$	27.1658	+	7.97660i	1.08317	+	0.318048i
$630$	−56.0843	−	50.2111i	−2.23445	−	2.00046i
$631$	2.58950	−	18.0104i	0.103086	−	0.716982i	−0.871079	−	0.491144i	$-0.836579\pi$
$631$	2.58950	−	18.0104i	0.103086	−	0.716982i	0.974165	−	0.225838i	$-0.0725120\pi$
$632$	−3.50116	−	8.77108i	−0.139269	−	0.348895i
$633$	9.88763	−	21.6509i	0.392998	−	0.860546i
$634$	−1.51403	−	11.8955i	−0.0601299	−	0.472430i
$635$	−7.45822	+	4.79311i	−0.295971	+	0.190209i
$636$	−28.1826	+	7.29218i	−1.11751	+	0.289154i
$637$	−0.546347	−	3.79993i	−0.0216471	−	0.150559i
$638$	−0.0139268	−	0.00927245i	−0.000551368	−	0.000367100i
$639$	13.9518	−	21.7094i	0.551925	−	0.858812i
$640$	14.1492	−	33.5579i	0.559294	−	1.32649i
$641$	−3.51165	−	11.9596i	−0.138702	−	0.472375i	0.860618	−	0.509251i	$-0.170078\pi$
$641$	−3.51165	−	11.9596i	−0.138702	−	0.472375i	−0.999320	+	0.0368759i	$0.988259\pi$
$642$	7.76157	−	6.50829i	0.306325	−	0.256862i
$643$	34.7765			1.37145			0.685726	−	0.727860i	$-0.259485\pi$
$643$	34.7765			1.37145			0.685726	+	0.727860i	$0.259485\pi$
$644$	−26.1335	+	13.9696i	−1.02980	+	0.550479i
$645$	74.0636			2.91625
$646$	1.39176	−	1.16703i	0.0547580	−	0.0459161i
$647$	3.60657	+	12.2828i	0.141789	+	0.482888i	0.999512	−	0.0312227i	$-0.00994010\pi$
$647$	3.60657	+	12.2828i	0.141789	+	0.482888i	−0.857724	+	0.514111i	$0.828122\pi$
$648$	0.955209	+	10.1110i	0.0375242	+	0.397199i
$649$	0.224169	−	0.348813i	0.00879938	−	0.0136921i
$650$	9.52251	+	6.34007i	0.373504	+	0.248678i
$651$	4.79256	+	33.3330i	0.187835	+	1.30642i
$652$	−1.12639	−	4.35324i	−0.0441128	−	0.170486i
$653$	−17.9373	+	11.5276i	−0.701942	+	0.451111i	−0.842313	−	0.538988i	$-0.818807\pi$
$653$	−17.9373	+	11.5276i	−0.701942	+	0.451111i	0.140371	+	0.990099i	$0.455170\pi$
$654$	3.54856	+	27.8804i	0.138760	+	1.09021i
$655$	8.09578	−	17.7273i	0.316328	−	0.692663i
$656$	−20.3646	−	26.8335i	−0.795103	−	1.04767i
$657$	−5.76229	+	40.0776i	−0.224808	+	1.56358i
$658$	40.6680	+	36.4092i	1.58541	+	1.41938i
$659$	5.15581	+	1.51388i	0.200842	+	0.0589725i	0.380606	−	0.924737i	$-0.375715\pi$
$659$	5.15581	+	1.51388i	0.200842	+	0.0589725i	−0.179764	+	0.983710i	$0.557533\pi$
$660$	−0.417246	−	0.514293i	−0.0162413	−	0.0200188i
$661$	15.0791	−	13.0661i	0.586507	−	0.508212i	−0.310296	−	0.950640i	$-0.600428\pi$
$661$	15.0791	−	13.0661i	0.586507	−	0.508212i	0.896804	+	0.442428i	$0.145883\pi$
$662$	6.94830	−	22.3195i	0.270053	−	0.867470i
$663$	−10.6471	+	12.2874i	−0.413500	+	0.477204i
$664$	6.34453	−	12.2763i	0.246216	−	0.476412i
$665$	−3.11567	+	1.42288i	−0.120820	+	0.0551768i
$666$	15.2961	+	55.3987i	0.592711	+	2.14666i
$667$	−1.50623	−	0.521803i	−0.0583214	−	0.0202043i
$668$	8.69680	+	14.5482i	0.336489	+	0.562888i
$669$	−14.6693	−	32.1212i	−0.567147	−	1.24188i
$670$	−11.8647	−	19.1366i	−0.458374	−	0.739312i
$671$	−0.102899	−	0.0891622i	−0.00397236	−	0.00344207i
$672$	−35.3696	−	36.0562i	−1.36441	−	1.39090i
$673$	−11.7294	−	13.5365i	−0.452136	−	0.521793i	0.483221	−	0.875499i	$-0.339467\pi$
$673$	−11.7294	−	13.5365i	−0.452136	−	0.521793i	−0.935357	+	0.353706i	$0.884921\pi$
$674$	18.6837	−	8.16937i	0.719670	−	0.314672i
$675$	10.2700	−	34.9763i	0.395291	−	1.34624i
$676$	−9.53721	+	19.2108i	−0.366816	+	0.738877i
$677$	−21.6422	−	3.11168i	−0.831778	−	0.119592i	−0.286746	−	0.958007i	$-0.592574\pi$
$677$	−21.6422	−	3.11168i	−0.831778	−	0.119592i	−0.545032	+	0.838415i	$0.683483\pi$
$678$	−5.57275	+	34.7524i	−0.214020	+	1.33466i
$679$	−26.6037	−	12.1495i	−1.02096	−	0.466255i
$680$	−20.9603	−	26.7085i	−0.803790	−	1.02422i
$681$	20.3903	+	31.7279i	0.781358	+	1.21582i
$682$	−0.00307598	+	0.189830i	−0.000117785	+	0.00726897i
$683$	50.9829	−	7.33023i	1.95081	−	0.280484i	0.951200	−	0.308574i	$-0.0998516\pi$
$683$	50.9829	−	7.33023i	1.95081	−	0.280484i	0.999605	+	0.0280901i	$0.00894254\pi$
$684$	3.50203	+	1.15278i	0.133904	+	0.0440778i
$685$	37.6691	+	24.2085i	1.43926	+	0.924959i
$686$	−8.37229	+	17.5736i	−0.319656	+	0.670962i
$687$	−27.7698	+	8.15396i	−1.05949	+	0.311093i
$688$	31.7780	+	2.06242i	1.21153	+	0.0786289i
$689$		−	7.59817i		−	0.289467i
$690$	−50.7861	−	37.4422i	−1.93340	−	1.42540i
$691$		−	23.2234i		−	0.883459i	−0.897148	−	0.441730i	$-0.854365\pi$
$691$		−	23.2234i		−	0.883459i	0.897148	−	0.441730i	$-0.145635\pi$
$692$	36.5314	+	25.1862i	1.38872	+	0.957437i
$693$	−0.564731	+	0.165820i	−0.0214524	+	0.00629899i
$694$	−9.94848	−	4.73960i	−0.377639	−	0.179913i
$695$	54.6010	+	35.0900i	2.07114	+	1.33104i
$696$	0.132014	−	2.71378i	0.00500397	−	0.102866i
$697$	−31.0839	+	4.46918i	−1.17739	+	0.169282i
$698$	12.4569	+	0.201849i	0.471499	+	0.00764010i
$699$	26.4025	+	41.0830i	0.998633	+	1.55390i
$700$	12.7794	+	30.5670i	0.483017	+	1.15532i
$701$	−9.20084	−	4.20188i	−0.347511	−	0.158703i	0.234010	−	0.972234i	$-0.424815\pi$
$701$	−9.20084	−	4.20188i	−0.347511	−	0.158703i	−0.581521	+	0.813531i	$0.697542\pi$
$702$	−14.3219	−	2.29660i	−0.540546	−	0.0866797i
$703$	2.58842	+	0.372158i	0.0976240	+	0.0140362i
$704$	−0.164704	−	0.232283i	−0.00620751	−	0.00875450i
$705$	−32.7447	+	111.518i	−1.23324	+	4.20002i
$706$	−13.0635	−	29.8767i	−0.491650	−	1.12443i
$707$	7.11046	+	8.20591i	0.267416	+	0.308615i
$708$	67.2973	+	2.18153i	2.52919	+	0.0819868i
$709$	5.96392	+	5.16777i	0.223980	+	0.194080i	0.759621	−	0.650366i	$-0.225385\pi$
$709$	5.96392	+	5.16777i	0.223980	+	0.194080i	−0.535641	+	0.844446i	$0.679930\pi$
$710$	−18.6544	+	11.5657i	−0.700087	+	0.434054i
$711$	−7.42405	−	16.2564i	−0.278424	−	0.609663i
$712$	22.4445	+	21.4440i	0.841142	+	0.803647i
$713$	4.25934	+	17.5796i	0.159514	+	0.658362i
$714$	−45.3873	+	12.5318i	−1.69858	+	0.468992i
$715$	0.157236	−	0.0718071i	0.00588028	−	0.00268544i
$716$	−4.96676	−	4.59376i	−0.185617	−	0.171677i
$717$	−43.4856	+	50.1850i	−1.62400	+	1.87419i
$718$	37.2204	+	11.5871i	1.38905	+	0.432428i
$719$	3.49955	−	3.03238i	0.130511	−	0.113089i	−0.587159	−	0.809471i	$-0.699754\pi$
$719$	3.49955	−	3.03238i	0.130511	−	0.113089i	0.717671	+	0.696383i	$0.245208\pi$
$720$	23.6580	−	64.7291i	0.881681	−	2.41231i
$721$	13.7891	+	4.04884i	0.513533	+	0.150787i
$722$	−17.8109	+	19.8943i	−0.662855	+	0.740389i
$723$	−11.7354	+	81.6217i	−0.436446	+	3.03555i
$724$	19.4155	−	2.15212i	0.721573	−	0.0799831i
$725$	−0.740361	+	1.62117i	−0.0274963	+	0.0602086i
$726$	44.5936	−	5.67578i	1.65502	−	0.210648i
$727$	15.3981	−	9.89574i	0.571083	−	0.367013i	−0.223004	−	0.974818i	$-0.571586\pi$
$727$	15.3981	−	9.89574i	0.571083	−	0.367013i	0.794086	+	0.607805i	$0.207950\pi$
$728$	11.4235	−	6.58001i	0.423382	−	0.243871i
$729$	−5.65340	−	39.3203i	−0.209385	−	1.45631i
$730$	19.0854	−	28.6654i	0.706382	−	1.06096i
$731$	16.0501	−	24.9744i	0.593633	−	0.923710i
$732$	3.85401	−	21.7717i	0.142448	−	0.804705i
$733$	−6.22211	−	21.1906i	−0.229819	−	0.782692i	−0.990966	−	0.134112i	$-0.957182\pi$
$733$	−6.22211	−	21.1906i	−0.229819	−	0.782692i	0.761147	−	0.648579i	$-0.224636\pi$
$734$	19.0141	+	22.6756i	0.701824	+	0.836973i
$735$	23.6730			0.873193
$736$	−20.7479	−	17.4793i	−0.764776	−	0.644296i
$737$	−0.176050			−0.00648487
$738$	−40.9585	−	48.8458i	−1.50770	−	1.79804i
$739$	−7.18128	−	24.4572i	−0.264168	−	0.899672i	−0.979594	−	0.200985i	$-0.935586\pi$
$739$	−7.18128	−	24.4572i	−0.264168	−	0.899672i	0.715427	−	0.698688i	$-0.246232\pi$
$740$	8.52050	−	48.1331i	0.313220	−	1.76941i
$741$	−0.811873	+	1.26330i	−0.0298249	+	0.0464084i
$742$	12.1949	−	18.3163i	0.447691	−	0.672412i
$743$	5.21572	+	36.2761i	0.191346	+	1.33084i	0.828450	+	0.560063i	$0.189223\pi$
$743$	5.21572	+	36.2761i	0.191346	+	1.33084i	−0.637104	+	0.770778i	$0.719868\pi$
$744$	−26.7156	+	15.3884i	−0.979442	+	0.564166i
$745$	34.5058	−	22.1756i	1.26420	−	0.812450i
$746$	−24.3818	+	3.10327i	−0.892683	+	0.113619i
$747$	10.8631	−	23.7869i	0.397461	−	0.870318i
$748$	−0.263840	+	0.0292455i	−0.00964695	+	0.00106932i
$749$	−1.08964	+	7.57863i	−0.0398147	+	0.276917i
$750$	−3.17634	+	3.54788i	−0.115984	+	0.129550i
$751$	−49.1188	−	14.4226i	−1.79237	−	0.526288i	−0.795546	−	0.605894i	$-0.792816\pi$
$751$	−49.1188	−	14.4226i	−1.79237	−	0.526288i	−0.996826	+	0.0796059i	$0.974634\pi$
$752$	−17.1549	+	46.9366i	−0.625577	+	1.71160i
$753$	−17.0670	+	14.7886i	−0.621956	+	0.538928i
$754$	0.677107	+	0.210791i	0.0246588	+	0.00767657i
$755$	−16.8567	+	19.4536i	−0.613476	+	0.707989i
$756$	−30.8387	−	28.5227i	−1.12159	−	1.03736i
$757$	−31.3442	+	14.3144i	−1.13922	+	0.520266i	−0.893496	−	0.449072i	$-0.851755\pi$
$757$	−31.3442	+	14.3144i	−1.13922	+	0.520266i	−0.245729	+	0.969339i	$0.579027\pi$
$758$	−51.6453	+	14.2597i	−1.87584	+	0.517937i
$759$	−0.458051	+	0.183221i	−0.0166262	+	0.00665050i
$760$	−2.26731	−	2.16624i	−0.0822441	−	0.0785779i
$761$	5.45157	+	11.9373i	0.197619	+	0.432726i	0.982335	−	0.187130i	$-0.0599185\pi$
$761$	5.45157	+	11.9373i	0.197619	+	0.432726i	−0.784716	+	0.619855i	$0.787191\pi$
$762$	−9.56701	+	5.93156i	−0.346576	+	0.214878i
$763$	−16.0556	−	13.9123i	−0.581253	−	0.503658i
$764$	−10.0695	−	0.326416i	−0.364302	−	0.0118093i
$765$	−42.0730	−	48.5548i	−1.52115	−	1.75550i
$766$	−19.6557	−	44.9535i	−0.710190	−	1.62424i
$767$	−4.95129	+	16.8626i	−0.178781	+	0.608871i
$768$	18.6531	−	42.3116i	0.673084	−	1.52679i
$769$	−8.77875	−	1.26219i	−0.316570	−	0.0455159i	−0.0178015	−	0.999842i	$-0.505667\pi$
$769$	−8.77875	−	1.26219i	−0.316570	−	0.0455159i	−0.298768	+	0.954326i	$0.596576\pi$
$770$	0.494285	+	0.0792614i	0.0178128	+	0.00285638i
$771$	18.4600	+	8.43040i	0.664820	+	0.303613i
$772$	0.200174	+	0.478795i	0.00720442	+	0.0172322i
$773$	−10.5244	−	16.3762i	−0.378535	−	0.589012i	0.598751	−	0.800935i	$-0.295664\pi$
$773$	−10.5244	−	16.3762i	−0.378535	−	0.589012i	−0.977286	+	0.211923i	$0.932027\pi$
$774$	60.2536	+	0.976342i	2.16577	+	0.0350939i
$775$	20.0176	−	2.87810i	0.719054	−	0.103384i
$776$	1.30099	−	26.7441i	0.0467026	−	0.960058i
$777$	−57.0302	−	36.6511i	−2.04595	−	1.31485i
$778$	−8.85895	−	4.22053i	−0.317609	−	0.151313i
$779$	−2.78302	+	0.817168i	−0.0997120	+	0.0292781i
$780$	23.1101	+	15.9330i	0.827474	+	0.570493i
$781$			0.171613i			0.00614080i
$782$	−23.6312	+	9.01120i	−0.845051	+	0.322240i
$783$		−	2.25969i		−	0.0807546i
$784$	10.1572	+	0.659211i	0.362758	+	0.0235433i
$785$	25.0328	−	7.35028i	0.893458	−	0.262343i
$786$	10.6425	−	22.3387i	0.379605	−	0.796796i
$787$	−17.3049	−	11.1212i	−0.616851	−	0.396426i	0.194569	−	0.980889i	$-0.437669\pi$
$787$	−17.3049	−	11.1212i	−0.616851	−	0.396426i	−0.811421	+	0.584462i	$0.801305\pi$
$788$	−15.4869	−	5.09791i	−0.551698	−	0.181606i
$789$	−21.6197	+	3.10845i	−0.769682	+	0.110664i
$790$	−0.246269	+	15.1982i	−0.00876187	+	0.540727i
$791$	−14.3836	−	22.3813i	−0.511422	−	0.795788i
$792$	−0.332666	−	0.423897i	−0.0118208	−	0.0150625i
$793$	5.24944	+	2.39734i	0.186413	+	0.0851321i
$794$	−1.75118	+	10.9206i	−0.0621470	+	0.387557i
$795$	46.3768	+	6.66798i	1.64482	+	0.236489i
$796$	−19.3783	+	39.0338i	−0.686847	+	1.38352i
$797$	15.0814	−	51.3625i	0.534210	−	1.81935i	−0.0380428	−	0.999276i	$-0.512112\pi$
$797$	15.0814	−	51.3625i	0.534210	−	1.81935i	0.572253	−	0.820077i	$-0.306070\pi$
$798$	−3.98469	+	1.74229i	−0.141057	+	0.0616763i
$799$	30.5081	+	35.2082i	1.07930	+	1.24558i
$800$	−21.6530	+	21.2406i	−0.765548	+	0.750970i
$801$	44.3942	+	38.4678i	1.56859	+	1.35919i
$802$	23.8797	+	38.5156i	0.843222	+	1.36003i
$803$	−0.111855	−	0.244929i	−0.00394728	−	0.00864334i
$804$	−14.6689	−	24.5385i	−0.517333	−	0.865407i
$805$	47.4795	−	4.51977i	1.67343	−	0.159301i
$806$	−2.14173	−	7.75683i	−0.0754392	−	0.273223i
$807$	−52.5794	+	24.0122i	−1.85088	+	0.845270i
$808$	−4.56396	+	8.83099i	−0.160559	+	0.310673i
$809$	12.7815	−	14.7506i	0.449372	−	0.518603i	−0.485187	−	0.874410i	$-0.661248\pi$
$809$	12.7815	−	14.7506i	0.449372	−	0.518603i	0.934559	+	0.355807i	$0.115794\pi$
$810$	4.85876	−	15.6074i	0.170719	−	0.548387i
$811$	−18.7689	+	16.2634i	−0.659067	+	0.571085i	−0.918862	−	0.394579i	$-0.870890\pi$
$811$	−18.7689	+	16.2634i	−0.659067	+	0.571085i	0.259795	+	0.965664i	$0.416345\pi$
$812$	1.29393	+	1.59488i	0.0454081	+	0.0559695i
$813$	69.7079	+	20.4681i	2.44476	+	0.717847i
$814$	−0.284749	−	0.254930i	−0.00998045	−	0.00893529i
$815$	−1.02997	+	7.16361i	−0.0360783	+	0.250930i
$816$	−26.0602	−	34.3383i	−0.912290	−	1.20208i
$817$	1.13906	−	2.49419i	0.0398506	−	0.0872607i
$818$	1.65860	+	13.0313i	0.0579916	+	0.455630i
$819$	20.9866	−	13.4873i	0.733332	−	0.471284i
$820$	13.5814	+	52.4891i	0.474283	+	1.83300i
$821$	4.14794	+	28.8495i	0.144764	+	1.00686i	0.924618	+	0.380895i	$0.124384\pi$
$821$	4.14794	+	28.8495i	0.144764	+	1.00686i	−0.779854	+	0.625961i	$0.784707\pi$
$822$	47.3240	+	31.5082i	1.65061	+	1.09898i
$823$	−7.39377	+	11.5049i	−0.257731	+	0.401036i	−0.945872	−	0.324540i	$-0.894790\pi$
$823$	−7.39377	+	11.5049i	−0.257731	+	0.401036i	0.688141	+	0.725577i	$0.258427\pi$
$824$	1.23746	+	13.0987i	0.0431091	+	0.456316i
$825$	0.155396	+	0.529229i	0.00541018	+	0.0184254i
$826$	−38.9998	+	32.7024i	−1.35698	+	1.13786i
$827$	5.74191			0.199666			0.0998328	−	0.995004i	$-0.468169\pi$
$827$	5.74191			0.199666			0.0998328	+	0.995004i	$0.468169\pi$
$828$	−40.8229	−	31.1302i	−1.41869	−	1.08185i
$829$	−10.9254			−0.379453			−0.189727	−	0.981837i	$-0.560760\pi$
$829$	−10.9254			−0.379453			−0.189727	+	0.981837i	$0.560760\pi$
$830$	−17.0427	+	14.2908i	−0.591561	+	0.496040i
$831$	−12.9066	−	43.9558i	−0.447725	−	1.52481i
$832$	9.47202	+	7.47981i	0.328383	+	0.259316i
$833$	5.13009	−	7.98258i	0.177747	−	0.276580i
$834$	68.5957	+	45.6709i	2.37527	+	1.58145i
$835$	−3.88238	−	27.0025i	−0.134355	−	0.934461i
$836$	−0.0237365	+	0.00614176i	−0.000820944	+	0.000212417i
$837$	−21.5709	+	13.8628i	−0.745600	+	0.479168i
$838$	−6.89328	−	54.1593i	−0.238125	−	1.87090i
$839$	5.25663	−	11.5104i	0.181479	−	0.397383i	−0.796927	−	0.604075i	$-0.793543\pi$
$839$	5.25663	−	11.5104i	0.181479	−	0.397383i	0.978406	+	0.206692i	$0.0662698\pi$
$840$	30.1373	+	75.4998i	1.03984	+	2.60499i
$841$	4.11141	−	28.5955i	0.141773	−	0.986051i
$842$	−37.1973	−	33.3019i	−1.28190	−	1.14766i
$843$	−48.4126	−	14.2152i	−1.66742	−	0.489598i
$844$	−12.7913	+	10.3776i	−0.440296	+	0.357212i
$845$	26.0888	−	22.6061i	0.897481	−	0.777672i
$846$	−28.1092	+	90.2927i	−0.966412	+	3.10433i
$847$	−22.2521	+	25.6803i	−0.764592	+	0.882387i
$848$	19.7129	+	4.15242i	0.676945	+	0.142595i
$849$	−67.8367	+	30.9800i	−2.32815	+	1.06323i
$850$	7.52580	+	27.2566i	0.258133	+	0.934894i
$851$	−32.3603	−	16.6949i	−1.10930	−	0.572292i
$852$	−23.9202	+	14.2993i	−0.819491	+	0.489885i
$853$	18.4378	+	40.3732i	0.631299	+	1.38235i	0.907009	+	0.421111i	$0.138360\pi$
$853$	18.4378	+	40.3732i	0.631299	+	1.38235i	−0.275710	+	0.961241i	$0.588913\pi$
$854$	8.80671	+	14.2044i	0.301359	+	0.486063i
$855$	−4.48465	−	3.88597i	−0.153372	−	0.132897i
$856$	−6.81376	+	1.64573i	−0.232889	+	0.0562500i
$857$	16.2036	+	18.6999i	0.553503	+	0.638776i	0.961696	−	0.274119i	$-0.0883864\pi$
$857$	16.2036	+	18.6999i	0.553503	+	0.638776i	−0.408193	+	0.912896i	$0.633841\pi$
$858$	0.201092	−	0.0879266i	0.00686517	−	0.00300176i
$859$	3.06616	−	10.4424i	0.104616	−	0.356290i	−0.890502	−	0.454979i	$-0.849647\pi$
$859$	3.06616	−	10.4424i	0.104616	−	0.356290i	0.995118	+	0.0986892i	$0.0314650\pi$
$860$	−45.9082	−	22.7912i	−1.56546	−	0.777172i
$861$	74.4272	+	10.7010i	2.53647	+	0.364690i
$862$	−4.49476	+	28.0299i	−0.153092	+	0.954703i
$863$	−17.6366	−	8.05438i	−0.600358	−	0.274174i	0.0919649	−	0.995762i	$-0.470685\pi$
$863$	−17.6366	−	8.05438i	−0.600358	−	0.274174i	−0.692323	+	0.721588i	$0.743413\pi$
$864$	13.7854	−	35.9022i	0.468987	−	1.22142i
$865$	−38.6110	−	60.0798i	−1.31281	−	2.04278i
$866$	0.581243	−	35.8707i	0.0197515	−	1.21893i
$867$	8.85319	−	1.27290i	0.300670	−	0.0432299i
$868$	7.28670	−	22.1362i	0.247327	−	0.751351i
$869$	0.0999803	+	0.0642535i	0.00339160	+	0.00217965i
$870$	−1.88082	+	3.94786i	−0.0637657	+	0.133845i
$871$	7.15966	−	2.10227i	0.242596	−	0.0712325i
$872$	6.37991	−	18.3736i	0.216051	−	0.622209i
$873$		−	50.6690i		−	1.71489i
$874$	−2.04198	+	1.13445i	−0.0690710	+	0.0383733i
$875$		−	3.59956i		−	0.121687i
$876$	24.8191	−	35.9989i	0.838560	−	1.21629i
$877$	23.1334	−	6.79259i	0.781160	−	0.229369i	0.133246	−	0.991083i	$-0.457460\pi$
$877$	23.1334	−	6.79259i	0.781160	−	0.229369i	0.647914	+	0.761714i	$0.275642\pi$
$878$	29.1456	+	13.8854i	0.983616	+	0.468608i
$879$	−33.8522	−	21.7555i	−1.14181	−	0.733795i
$880$	0.100369	+	0.447180i	0.00338344	+	0.0150744i
$881$	−10.0629	+	1.44683i	−0.339028	+	0.0487449i	−0.309726	−	0.950826i	$-0.600237\pi$
$881$	−10.0629	+	1.44683i	−0.339028	+	0.0487449i	−0.0293018	+	0.999571i	$0.509328\pi$
$882$	19.2589	+	0.312069i	0.648482	+	0.0105079i
$883$	19.3974	+	30.1830i	0.652775	+	1.01574i	0.997041	+	0.0768656i	$0.0244912\pi$
$883$	19.3974	+	30.1830i	0.652775	+	1.01574i	−0.344267	+	0.938872i	$0.611872\pi$
$884$	10.3807	−	4.33997i	0.349142	−	0.145969i
$885$	−98.5786	−	45.0193i	−3.31368	−	1.51331i
$886$	−8.32352	−	1.33472i	−0.279634	−	0.0448409i
$887$	17.0557	+	2.45224i	0.572676	+	0.0823383i	0.422568	−	0.906331i	$-0.361129\pi$
$887$	17.0557	+	2.45224i	0.572676	+	0.0823383i	0.150108	+	0.988670i	$0.452038\pi$
$888$	11.8072	−	60.9310i	0.396222	−	2.04471i
$889$	2.39720	−	8.16412i	0.0803996	−	0.273816i
$890$	−20.0159	−	45.7772i	−0.670933	−	1.53446i
$891$	−0.0836959	−	0.0965902i	−0.00280392	−	0.00323589i
$892$	−0.791747	+	24.4244i	−0.0265096	+	0.817789i
$893$	3.25192	+	2.81781i	0.108822	+	0.0942944i
$894$	44.2623	−	27.4426i	1.48035	−	0.917819i
$895$	4.52345	+	9.90498i	0.151202	+	0.331087i
$896$	10.8284	+	33.2334i	0.361752	+	1.11025i
$897$	16.4403	−	12.9211i	0.548926	−	0.431421i
$898$	38.3174	−	10.5798i	1.27867	−	0.353052i
$899$	1.14035	−	0.520779i	0.0380327	−	0.0173690i
$900$	−38.9735	+	42.1381i	−1.29912	+	1.40460i
$901$	12.2986	−	14.1933i	0.409726	−	0.472849i
$902$	0.404756	+	0.126005i	0.0134769	+	0.00419551i
$903$	−53.7208	+	46.5493i	−1.78772	+	1.54906i
$904$	14.1484	−	19.8264i	0.470570	−	0.659415i
$905$	−30.1671	−	8.85787i	−1.00279	−	0.294446i
$906$	−21.8002	+	24.3501i	−0.724262	+	0.808979i
$907$	0.865985	−	6.02306i	0.0287545	−	0.199992i	−0.970380	−	0.241583i	$-0.922333\pi$
$907$	0.865985	−	6.02306i	0.0287545	−	0.199992i	0.999135	+	0.0415906i	$0.0132425\pi$
$908$	−2.87545	−	25.9411i	−0.0954253	−	0.860886i
$909$	−7.81442	+	17.1112i	−0.259188	+	0.567542i
$910$	−21.0483	+	2.67898i	−0.697743	+	0.0888073i
$911$	37.1111	−	23.8499i	1.22955	−	0.790182i	0.245726	−	0.969339i	$-0.420973\pi$
$911$	37.1111	−	23.8499i	1.22955	−	0.790182i	0.983820	+	0.179157i	$0.0573371\pi$
$912$	−2.83385	−	2.79675i	−0.0938382	−	0.0926095i
$913$	0.0247486	+	0.172131i	0.000819060	+	0.00569669i
$914$	−31.9886	+	48.0454i	−1.05809	+	1.58920i
$915$	−19.2394	+	29.9371i	−0.636035	+	0.989690i
$916$	19.7223	+	3.49123i	0.651642	+	0.115353i
$917$	5.26954	+	17.9464i	0.174016	+	0.592643i
$918$	−23.0359	−	27.4719i	−0.760299	−	0.906708i
$919$	9.53477			0.314523			0.157262	−	0.987557i	$-0.449733\pi$
$919$	9.53477			0.314523			0.157262	+	0.987557i	$0.449733\pi$
$920$	19.9579	+	38.8366i	0.657991	+	1.28041i
$921$	60.1706			1.98269
$922$	−12.2467	−	14.6050i	−0.403323	−	0.480990i
$923$	−2.04929	−	6.97924i	−0.0674532	−	0.229724i
$924$	0.625877	+	0.110793i	0.0205899	+	0.00364481i
$925$	−22.0102	+	34.2486i	−0.723692	+	1.12609i
$926$	−8.69810	+	13.0642i	−0.285837	+	0.429315i
$927$	3.54332	+	24.6443i	0.116378	+	0.809425i
$928$	−0.916925	+	1.64151i	−0.0300995	+	0.0538853i
$929$	4.26906	−	2.74356i	0.140063	−	0.0900131i	−0.468733	−	0.883340i	$-0.655289\pi$
$929$	4.26906	−	2.74356i	0.140063	−	0.0900131i	0.608796	+	0.793327i	$0.291653\pi$
$930$	49.2248	−	6.26522i	1.61414	−	0.205445i
$931$	0.364078	−	0.797220i	0.0119322	−	0.0261278i
$932$	−3.72329	−	33.5899i	−0.121960	−	1.10028i
$933$	4.30338	−	29.9307i	0.140886	−	0.979887i
$934$	−5.36681	+	5.99456i	−0.175607	+	0.196148i
$935$	0.409944	+	0.120371i	0.0134066	+	0.00393654i
$936$	18.5909	+	13.2668i	0.607663	+	0.433638i
$937$	−2.72871	+	2.36444i	−0.0891431	+	0.0772429i	−0.698292	−	0.715813i	$-0.746056\pi$
$937$	−2.72871	+	2.36444i	−0.0891431	+	0.0772429i	0.609149	+	0.793056i	$0.291511\pi$
$938$	20.6333	+	6.42339i	0.673701	+	0.209731i
$939$	41.5359	−	47.9349i	1.35547	−	1.56430i
$940$	54.6136	−	59.0480i	1.78130	−	1.92593i
$941$	−43.5770	+	19.9009i	−1.42057	+	0.648752i	−0.969803	−	0.243890i	$-0.921576\pi$
$941$	−43.5770	+	19.9009i	−1.42057	+	0.648752i	−0.450766	+	0.892642i	$0.648849\pi$
$942$	31.9310	−	8.81643i	1.04037	−	0.287255i
$943$	40.3418	+	1.93351i	1.31371	+	0.0629638i
$944$	−41.0429	−	22.0612i	−1.33583	−	0.718032i
$945$	28.0862	+	61.5001i	0.913643	+	2.00060i
$946$	−0.340595	+	0.211169i	−0.0110737	+	0.00686570i
$947$	19.4905	+	16.8886i	0.633356	+	0.548806i	0.911275	−	0.411798i	$-0.135099\pi$
$947$	19.4905	+	16.8886i	0.633356	+	0.548806i	−0.277919	+	0.960605i	$0.589645\pi$
$948$	−0.625291	+	19.2894i	−0.0203085	+	0.626492i
$949$	7.47375	+	8.62517i	0.242608	+	0.279985i
$950$	1.04630	+	2.39295i	0.0339466	+	0.0776374i
$951$	−6.90396	+	23.5127i	−0.223876	+	0.762452i
$952$	31.9896	+	6.19892i	1.03679	+	0.200908i
$953$	−7.41943	−	1.06675i	−0.240339	−	0.0345555i	0.0210927	−	0.999778i	$-0.493285\pi$
$953$	−7.41943	−	1.06675i	−0.240339	−	0.0345555i	−0.261432	+	0.965222i	$0.584195\pi$
$954$	37.6414	+	6.03602i	1.21869	+	0.195423i
$955$	14.7500	+	6.73611i	0.477300	+	0.217976i
$956$	42.3976	−	17.7256i	1.37124	−	0.573286i
$957$	0.0184853	+	0.0287637i	0.000597545	+	0.000929799i
$958$	−34.1202	−	0.552878i	−1.10237	−	0.0178627i
$959$	−42.5378	+	6.11601i	−1.37362	+	0.197496i
$960$	−53.9669	+	51.2501i	−1.74177	+	1.65409i
$961$	14.1117	+	9.06902i	0.455215	+	0.292549i
$962$	14.6245	+	6.96732i	0.471513	+	0.224635i
$963$	−12.7274	+	3.73712i	−0.410136	+	0.120427i
$964$	32.3912	−	46.9818i	1.04325	−	1.51318i
$965$		−	0.835257i		−	0.0268879i
$966$	60.3694	−	4.76125i	1.94235	−	0.153191i
$967$		−	26.1514i		−	0.840972i	−0.907299	−	0.420486i	$-0.861860\pi$
$967$		−	26.1514i		−	0.840972i	0.907299	−	0.420486i	$-0.138140\pi$
$968$	−29.3879	−	10.2044i	−0.944562	−	0.327982i
$969$	−3.56138	+	1.04572i	−0.114408	+	0.0335933i
$970$	−18.5353	+	38.9059i	−0.595133	+	1.24919i
$971$	9.65741	+	6.20644i	0.309921	+	0.199174i	0.686350	−	0.727271i	$-0.259212\pi$
$971$	9.65741	+	6.20644i	0.309921	+	0.199174i	−0.376429	+	0.926445i	$0.622848\pi$
$972$	−6.26469	+	19.0314i	−0.200940	+	0.610433i
$973$	−61.6581	+	8.86510i	−1.97667	+	0.284202i
$974$	−0.0628796	+	3.88053i	−0.00201479	+	0.124340i
$975$	−12.6394	−	19.6673i	−0.404785	−	0.629858i
$976$	−9.08858	+	12.3092i	−0.290918	+	0.394007i
$977$	12.1989	+	5.57103i	0.390276	+	0.178233i	0.600882	−	0.799338i	$-0.294816\pi$
$977$	12.1989	+	5.57103i	0.390276	+	0.178233i	−0.210606	+	0.977571i	$0.567544\pi$
$978$	−1.45494	+	9.07321i	−0.0465239	+	0.290129i
$979$	−0.386664	−	0.0555940i	−0.0123578	−	0.00177679i
$980$	−14.6737	−	7.28476i	−0.468734	−	0.232703i
$981$	10.3694	−	35.3148i	0.331068	−	1.12751i
$982$	49.2806	−	21.5477i	1.57261	−	0.687615i
$983$	−28.4637	−	32.8489i	−0.907851	−	1.04772i	−0.998655	−	0.0518471i	$-0.983489\pi$
$983$	−28.4637	−	32.8489i	−0.907851	−	1.04772i	0.0908041	−	0.995869i	$-0.471056\pi$
$984$	16.1622	+	66.9157i	0.515232	+	2.13319i
$985$	19.8323	+	17.1848i	0.631909	+	0.547552i
$986$	0.923641	+	1.48974i	0.0294147	+	0.0474430i
$987$	−46.3388	−	101.468i	−1.47498	−	3.22976i
$988$	0.891986	−	0.533221i	0.0283778	−	0.0169640i
$989$	−26.3557	+	27.6250i	−0.838064	+	0.878423i
$990$	0.230825	+	0.835992i	0.00733610	+	0.0265696i
$991$	−8.38396	+	3.82883i	−0.266325	+	0.121627i	−0.544102	−	0.839019i	$-0.683130\pi$
$991$	−8.38396	+	3.82883i	−0.266325	+	0.121627i	0.277777	+	0.960646i	$0.410402\pi$
$992$	21.2950	−	1.31744i	0.676118	−	0.0418288i
$993$	−31.2830	+	36.1025i	−0.992737	+	1.14568i
$994$	6.26152	−	20.1134i	0.198603	−	0.637957i
$995$	53.0089	−	45.9325i	1.68050	−	1.45616i
$996$	−21.9302	+	17.7919i	−0.694884	+	0.563759i
$997$	−35.5705	−	10.4444i	−1.12653	−	0.330779i	−0.335186	−	0.942152i	$-0.608799\pi$
$997$	−35.5705	−	10.4444i	−1.12653	−	0.330779i	−0.791342	+	0.611373i	$0.790617\pi$
$998$	−3.98679	−	3.56929i	−0.126200	−	0.112984i
$999$	7.34603	−	51.0927i	0.232418	−	1.61650i

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	92.2.h.a.19.8	yes	100
3.2	odd	2		828.2.u.a.19.3		100
4.3	odd	2	inner	92.2.h.a.19.6	✓	100
12.11	even	2		828.2.u.a.19.5		100
23.17	odd	22	inner	92.2.h.a.63.6	yes	100
69.17	even	22		828.2.u.a.523.5		100
92.63	even	22	inner	92.2.h.a.63.8	yes	100
276.155	odd	22		828.2.u.a.523.3		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.h.a.19.6	✓	100	4.3	odd	2	inner
92.2.h.a.19.8	yes	100	1.1	even	1	trivial
92.2.h.a.63.6	yes	100	23.17	odd	22	inner
92.2.h.a.63.8	yes	100	92.63	even	22	inner
828.2.u.a.19.3		100	3.2	odd	2
828.2.u.a.19.5		100	12.11	even	2
828.2.u.a.523.3		100	276.155	odd	22
828.2.u.a.523.5		100	69.17	even	22

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	92.2.h.a.19.8

Level	$92$
Weight	$2$
Character	92.19
Analytic conductor	$0.735$
Analytic rank	$0$
Dimension	$100$
Inner twists	$4$